# Eight Years of Light from ASASSN-15oi: Towards Understanding the Late-time
Evolution of TDEs

A. Hajela DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark  K. D. Alexander  Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721-0065, USA  R. Margutti Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA  Department of Physics, University of California, Berkeley, CA 94720-7300, USA  R. Chornock Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA  M. Bietenholz  SARAO/Hartebeesthoek Radio Astronomy Observatory, PO Box 443, Krugersdorp, 1740, South Africa  C. T. Christy Department of Astronomy and Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721-0065, USA  M. Stroh Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA  G. Terreran Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA  R. Saxton  Telespazio UK for ESA, ESAC, Apartado 78, 28691 Villanueva de la Cañada, Madrid, Spain  S. Komossa  Max-Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany  J. S. Bright Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA  Astrophysics, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK  E. Ramirez-Ruiz Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA  D. L. Coppejans Department of Physics, University of Warwick, Gibbet Hill Road, CV4 7AL Coventry, United Kingdom  J. K. Leung  David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel  Y. Cendes  Department of Physics, University of Oregon, Eugene, OR 97403, USA  E. Wiston  Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA  T. Laskar Department of Physics & Astronomy, University of Utah, Salt Lake City, UT 84112, USA  Department of Astrophysics/IMAPP, Radboud University, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands  A. Horesh Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel  G. Schroeder Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA  Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3112, USA  Nayana A. J. Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA  M. H. Wieringa CSIRO Space and Astronomy, Australia Telescope National Facility, PO Box 76, 1710, Epping, NSW, Australia  N. Velez  Department of Physics, University of Oregon, Eugene, OR 97403, USA  E. Berger  Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA 02138, USA  P. K. Blanchard  Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA  T. Eftekhari  Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA  Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3112, USA  S. Gomez Space Telescope Science Institute, 3700 San Martin Dr, Baltimore, MD 21218, USA  M. Nicholl Astrophysics Research Centre, School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN, UK  H. Sears  Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA  Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3112, USA  B. A. Zauderer National Science Foundation, 2415 Eisenhower Avenue, Alexandria, Virginia 22314, USA

###### Abstract

We present the results from an extensive follow-up campaign of the Tidal
Disruption Event (TDE) ASASSN-15oi spanning $\delta t\sim 10-3000$ d, offering
an unprecedented window into the multiwavelength properties of a TDE during
its first $\approx 8$ years of evolution. ASASSN-15oi is one of the few TDEs
with strong detections at X-ray, optical/UV, _and_ radio wavelengths and
featured two delayed radio flares at $\delta t\sim 180$ d and $\delta t\sim
1400$ d. Our observations at $>1400$ d reveal an absence of thermal X-rays, a
late-time variability in the non-thermal X-ray emission, and sharp declines in
the non-thermal X-ray and radio emission at $\delta t\sim 2800$ d and $\sim
3000$ d, respectively. The UV emission shows no significant evolution at
$>400$ d and remains above the pre-TDE level. We show that a cooling envelope
model can explain the thermal emission consistently across all epochs. We also
find that a scenario involving episodic ejection of material due to stream-
stream collisions is conducive to explaining the first radio flare. Given the
peculiar spectral and temporal evolution of the late-time emission, however,
constraining the origins of the second radio flare and the non-thermal X-rays
remains challenging. Our study underscores the critical role of long-term,
multiwavelength follow-up.

Tidal Disruption Events – X-rays – ultraviolet – radio – transient

tablenum

##  1 Introduction

A star straying too close to a supermassive black hole (SMBH) of mass
$\lesssim 10^{8}\,M_{\odot}$ in the center of a galaxy is torn apart by the
strong tidal forces of the black hole. This triggers an energetic and short-
lived transient known as a TDE (Hills 1975; Rees 1988; Evans & Kochanek 1989;
Guillochon & Ramirez-Ruiz 2013). Through emitting radiation across the
electromagnetic spectrum, TDEs provide an exclusive window to study previously
dormant SMBHs, accretion physics on human-accessible timescales, initiation
and cessation of the launched outflows, and the make up of the nuclear
environment of the host galaxies (e.g., Bonnerot & Stone, 2021; Dai et al.,
2021; Gezari, 2021). Early TDE datasets typically had limited temporal and
spectral coverage, but as the quality and quantity of data have improved,
observations have uncovered a broad diversity at every wavelength of the
electromagnetic spectrum. In this context, the TDE ASASSN-15oi stands out for
its uniquely detailed dataset, with X-ray, optical, UV, and radio detections
spanning $\sim 3000$ days. We briefly review the current landscape of TDE
observations before focusing on ASASSN-15oi as a valuable test case of TDE
emission models.

The first TDE candidates were discovered as X-ray transients, and observations
over the past three decades have revealed diverse X-ray behaviors among TDEs
detected at different wavelengths. Reviews of X-ray selected TDEs can be found
in Komossa 2002; Auchettl et al. 2017; Saxton et al. 2021 and Komossa & Grupe
2023, while Guolo et al. 2023 and Yao et al. 2023 discuss X-ray properties of
optically-discovered TDEs. “Soft” X-rays, characterized by a power-law
spectrum with photon index $\Gamma_{\rm X}>3$ or a blackbody spectrum with
temperature $kT_{\rm BB}\sim 0.05$ keV, emerges from regions at a distance
$\sim r_{\rm{g}}\approx 10^{11}-10^{12}$ cm from the SMBH, where $r_{\rm{g}}$
is the gravitational radius around a $\sim 10^{6}\,M_{\odot}$ non-rotating
SMBH. This implies that soft X-rays are emitted from the material actively
accreting onto the SMBH (Dai et al., 2018). “Hard” X-rays ($\Gamma_{\rm
X}\lesssim 2$ power-law) can result either from synchrotron radiation or by
Compton up-scattering of thermal disc photons by electrons in a corona or in
an outflow. TDEs detected at X-ray energies show either, both, or neither of
these components. ASASSN-15oi is one of the few TDEs to show both a “hard” and
“soft” X-ray component (this work, also Gezari et al. 2017; Holoien et al.
2018).

The physical origin of the optical and UV emission in TDEs is less certain.
This emission arises at radii $\sim 10^{15}$ cm $>>r_{\rm g}$. One potential
scenario involves the reprocessing of disc X-rays by material at these
extended radii (Guillochon et al., 2014; Roth et al., 2016; Dai et al., 2018;
Thomsen et al., 2022). Such material could be disc winds (e.g., Miller, 2015),
or outflows launched during the circularization process (Metzger & Stone,
2016) or during stream-stream collisions (called collision induced outflows or
CIO in Lu & Bonnerot, 2020). This scenario predicts that the post-optical-peak
luminosity should trace the mass fallback rate with a characteristic
$t^{-5/3}$ decay, as indeed observed in many TDEs (e.g., Mockler et al., 2019;
Gezari, 2021). Another mechanism proposed by Piran et al. (2015) suggests that
the optical luminosity is powered directly by the stream-stream collisions,
with the gravitationally bound stellar debris stream returning to the SMBH and
self-intersecting. Recently, a third model (inspired by Loeb & Ulmer 1997) was
revived and re-analysed by Metzger (2022), where the optical emission results
from the radiative cooling of a quasi-spherical, pressure-supported envelope
formed as a result of the stellar disruption. This _cooling envelope_ model
predicts the optical/UV luminosity to decline as $t^{-3/2}$, co-incidentally
resembling the $t^{-5/3}$ decay from the re-processing scenario.

Radio emission from TDEs is primarily powered by synchrotron radiation from
outflows interacting with the surrounding medium at larger distances ($\gtrsim
10^{16}$ cm) from the SMBH (Alexander et al., 2020, and references therein).
Among TDEs that have radio detections, a few show evidence of powerful on-axis
relativistic jets. Swift J1644+57 is the canonical example of this subset
(e.g., Bloom et al., 2011; Burrows et al., 2011; Levan et al., 2011; Zauderer
et al., 2011; Berger et al., 2012; Eftekhari et al., 2018; Cendes et al.,
2021b). Another classic radio TDE, ASASSN-14li, showed evidence for only a
non-relativistic outflow instead (Alexander et al. 2016; Krolik et al. 2016,
but see also van Velzen et al. 2016). While some TDEs show radio emission
similar to ASASSN-14li’s, others remain undetected in radio observations, even
up to several hundred days post-disruption (Alexander et al., 2020).

Early radio campaigns typically ceased observations within a few months if no
emission was detected, however, recently a large fraction of TDEs ($\sim
40\%$) were found to exhibit significant radio emission $\sim$ months – years
post-discovery (Cendes et al., 2023; Anumarlapudi et al., 2024). Some examples
include iPTF16fnl (Horesh et al., 2021b), AT 2018hyz (Cendes et al., 2022;
Sfaradi et al., 2024), and IGR J12580+0134 (Perlman et al., 2022). Among this
subset, ASASSN-15oi was the first TDE to show a late-time radio brightening at
$\delta t\sim 180$ d, and about 3.5 years later, it exhibited a second
brightening 111Some TDEs with early radio emission have also shown delayed re-
brightenings: AT 2019azh re-brightened at $\sim 200$ d (Sfaradi et al., 2022),
similar to the timescale of the first radio flare in ASASSN-15oi, but unlike
ASASSN-15oi it also showed prompt radio emission starting just 21 d post-
discovery. AT 2020vwl re-brightened after $\sim 1000$ d (Goodwin et al.,
2023a), similar to the timescale of the second radio flare of ASASSN-15oi.
Radio emission modeling of AT 2020vwl in Goodwin et al. (2023b) suggests a
prompt outflow launch as well. in the VLA Sky Survey (VLASS) data, reported by
Horesh et al. (2021a). Our team independently identified this bright radio
source in VLASS data, and began a multi-wavelength follow-up campaign that
covers the time period $\delta t\approx 1471-2970$ d, which we report here.

ASASSN-15oi was optically discovered on 2015 August 14 (Brimacombe et al.
2015; we measure $\delta t$ in this paper as the time elapsed since discovery)
at a distance of $\sim 216$ Mpc (Holoien et al., 2016; Gezari et al., 2017) by
the All-Sky Automated Survey for SuperNovae (ASAS-SN; Shappee et al. 2014).
Observations of ASASSN-15oi at optical, UV, and X-ray wavelengths at $\delta
t\lesssim 600$ d were previously reported in Holoien et al. (2016); Gezari et
al. (2017); Holoien et al. (2018), and Hinkle et al. (2021). The temporal
evolution of the optical and UV luminosity at $\delta t<100$ d initially
showed an exponential decay. The optical emission subsequently faded to the
level of the host galaxy at $\gtrsim 300$ d (Holoien et al., 2016; Gezari et
al., 2017; Holoien et al., 2018) while the emission at UV wavelengths remained
above the pre-TDE host galaxy level. The X-ray emission from ASASSN-15oi, on
the other hand, was initially weaker ($\sim 10^{42}$ erg/s) compared to those
of other X-ray bright TDEs in the literature ($\sim 10^{43}$ erg/s, Guolo et
al., 2023), but it later brightened by a factor of $\sim 6$ between $\delta
t\sim 80$ and $\sim 230$ d. Previous studies identified two contributing
components to the X-ray emission: a blackbody component responsible for the
delayed brightening of the X-ray emission; and a power-law component reported
as remaining nearly constant, leading to its association with a pre-existing
Active Galactic Nucleus (AGN) (Gezari et al., 2017). We note that the archival
mid-infrared colors of ASASSN-15oi’s host galaxy, with $W1-W2\sim 0.06$, from
the Widefield Infrared Survey Explorer (_WISE_ ; Wright et al. 2010) are
inconsistent with the presence of a strong AGN activity (Assef et al., 2013,
2018), as was also reported in Holoien et al. (2018).

Our aim in this study is to investigate the emission from ASASSN-15oi using
the complete multi-wavelength dataset spanning 8 years since its discovery.
Our dataset includes previously published data ($\delta t\lesssim 600$ d),
other publicly available observations ($\delta t\gtrsim 600$ d), as well as
new observations that we acquired following the onset of the second radio
flare at $\delta t\approx 1471-2970$ d. We re-analyse the previously reported
observations in a consistent manner with the new data, and report our
inferences on the origin of the emission from ASASSN-15oi at the different
stages. The paper is organized as follows: in §2, we outline the details of
the multi-wavelength observations and our data reduction. In §3, we fit the
radio spectral energy distributions (SEDs) with different models under the
umbrella assumption that the radio observations are powered by synchrotron
emission. In §4 we divide the emission from ASASSN-15oi into thermal and non-
thermal components, discuss the possible origins of the emission at different
wavelengths, and investigate any potential inter-correlations. We provide a
summary and conclusions in §5.

##  2 Observations and Data Analysis

In this section, we present new data spanning the time period $\delta t\approx
600-3000$ d, acquired by a variety of telescopes: Swift-UVOT, Swift-XRT222For
Swift data, we provide a self-consistent flux calibration of the entire
dataset that accounts for the spectral evolution of the source. , X-ray Multi-
Mirror Mission (XMM-Newton), Karl G. Jansky Very Large Array (VLA), Very Long
Baseline Array (VLBA), Australia Telescope Compact Array (ATCA), MeerKAT
telescope and Atacama Large Millimeter/submillimeter Array (ALMA). Furthermore
to perform a systematic analysis, we homogeneously reduce all the observations
over the time period of $\delta t=8-3000$ d.

###  2.1 UV: Swift-UVOT

Figure 1: Long-term evolution of ASASSN-15oi as captured by Swift-UVOT. Filled
circles mark the total emission (i.e., TDE + host galaxy) at the location of
ASASSN-15oi. While at $\delta t\gtrsim 300\,$d the optical emission is
dominated by the host galaxy light (horizontal dotted lines as determined by
Hinkle et al. 2021), the UV emission at the location of ASASSN-15oi remains
bright and does not relax to the pre-TDE UV flux levels (horizontal dashed
line). Magnitudes have been corrected for Galactic extinction.

Swift-UVOT (Gehrels et al., 2004; Roming et al., 2005) observed ASASSN-15oi
from 2015 August 23 until 2022 October 19 ($\delta t=8-2580$ d). We analyse
all available Swift-UVOT photometric data following the prescriptions of Brown
et al. (2009), with the updated calibration files (Poole et al., 2008;
Breeveld et al., 2010). All photometry has been extracted using a 5″ radius
aperture and a 36″ region free of sources for the background. When possible,
we merged observations to achieve a minimum source detection significance of
$\approx 10\,\sigma$. Finally, we correct for Galactic extinction assuming the
Fitzpatrick (1999) reddening law and $R_{\rm{V}}=3.1$.333Hinkle et al. (2021)
adopt a Cardelli et al. (1989) reddening law. Here we adopt the Fitzpatrick
(1999) reddening law following the findings of Schlafly & Finkbeiner (2011).
For the $R_{\rm{V}}=3.1$ curves the difference in the $A_{\lambda}$ values of
Swift-UVOT filters are $\leq 0.015$ mag.  The resulting extinction corrections
are $A_{v}=0.185$ mag, $A_{b}=0.245$ mag, $A_{u}=0.294$ mag, $A_{w1}=0.377$
mag, $A_{w2}=0.551$ mag, $A_{m2}=0.547$ mag. The Swift-UVOT photometry is
presented in Table LABEL:tab:uvotphot and the long-term UV evolution of
ASASSN-15oi is shown in Figure 1. For observations at $\delta t<500\,$d we
find excellent agreement with the photometry presented in Hinkle et al.
(2021). We use the UV/optical bolometric luminosities (for epochs where
optical emission was above the host galaxy level) from Hinkle et al. (2021)
for our analysis.

In stark contrast to the X-ray and radio emission that show dramatic temporal
variability on short time scales (§2.2, §2.3, §2.4), the late-time Swift-UVOT
photometry at $\delta t>600$ d is consistent with constant flux (Figure 1). We
find no significant evidence for fading at $\delta t\approx 500-2600\,$d in
any of the Swift-UVOT filters. However, while at optical wavelengths (i.e.,
Swift-UVOT $u$, $b$, and $v$ filters) the flux is consistent with the pre-TDE
host galaxy level as determined by the updated host galaxy modeling of Hinkle
et al. (2021), at UV wavelengths (i.e., Swift-UVOT $uvw1$, $uvw2$, and $uvm2$
filters) we confirm the presence of an excess of emission that was reported by
Holoien et al. (2018) using data at earlier epochs $\delta t\approx
250-600\,$d. As of $\delta t=2600\,$d, with $m_{w1}\approx 21$ mag,
$m_{w2}\approx 22$ mag and $m_{m2}\approx 22$ mag (observed mags, AB system),
ASASSN-15oi is $\approx 0.7$ mag, $\approx 1.5$ mag and $\approx 0.9$ mag
brighter, respectively, than the best-fitting pre-TDE host galaxy model of
Hinkle et al. (2021). From a completely observational perspective that is
independent from the host galaxy light modeling, pre-TDE _Galaxy Evolution
Explorer_ (_GALEX_) observations constrain the UV emission of the host galaxy
to be $m_{NUV}>22.98$ mag (Holoien et al., 2018; Hinkle et al., 2021). For the
blackbody spectrum with $T\sim 2\times 10^{4}\,\rm{K}$ that best fits the
late-time UVOT data, the _GALEX_ NUV to Swift-UVOT $uvm2$ filter correction
term is $\delta mag\approx 0.05\,$ mag, which implies that at $\delta t\approx
2600\,$d, the UV emission is $\gtrsim 2.3$ times brighter than in the pre-TDE
era. Similarly persistent UV excesses of emission have been found in
ASASSN-14li (Brown et al., 2017), as well as in other TDEs (van Velzen et al.,
2019; Mummery et al., 2024). We note that since optical discovery, ASASSN-15oi
has radiated $\sim 1.2\times 10^{51}\,\rm{erg}$ at UV and optical wavelengths.
Finally, we note the presence of an unrelated optical/UV source at $\approx
10\arcsec$ from ASASSN-15oi (S1 hereafter), that is also bright in _Swift_
-XRT observations (see §2.2).

###  2.2 X-rays: Swift-XRT

Figure 2: Long-term evolution of ASASSN-15oi as captured by Swift-XRT
(circles) and XMM-Newton (diamonds) in 0.3-10 keV. The data have been
corrected for Galactic absorption. The rise of the X-ray emission at $\delta
t\leq 350\,$d is dominated by a blackbody component (blue), while a power-law
spectral component dominates the emission at $\delta t\geq 1400\,$d. At
$>1400\,$d, the thermal X-rays become non-detectable and the non-thermal
X-rays show variability, showing a sharp decline in the latest observation at
$\delta t=2794\,$d. _Upper Panel:_ Temporal evolution of the Hardness Ratio
(HR) here defined as the ratio of the Swift-XRT counts in the 0.3–1.5 keV to
the 1.5–10. keV energy bands. The very soft emission around the time of the
light-curve peak is followed by hardening as the blackbody component subsides.

We analyse Swift-XRT data (Gehrels et al., 2004; Burrows et al., 2005) using
online tools444The Swift-XRT data products generator,
https://www.swift.ac.uk/user_objects/docs.php (Evans et al., 2009) and custom
IDL scripts following the prescriptions in Margutti et al. (2013). Swift-XRT
observed ASASSN-15oi starting on 2015 August 23 ($\delta t=8$ d). Observations
acquired under IDs 00033999 and 00095141 extend to 2020 June 21 ($\delta
t=1773$ d). They showed a progressive brightening of the source until $\delta
t\approx 350$ d, followed by rapid fading by a factor $\sim 10$ in luminosity
by $\delta t\approx 600$ d, as can be seen in Figure 2 (see also Fig. 3 from
Gezari et al. 2017 and Fig. 6 from Holoien et al. 2018). Additional XRT
observations of ASASSN-15oi acquired at $\approx 1400-1460$ d showed fainter
but persistent X-ray emission. A later-time epoch of Swift-XRT data was
acquired on 2022 March 11 ($\delta t=2401$ d) under ID 00096018. No X-ray
source is detected at the location of the transient and we infer a $3\sigma$
upper limit on the count-rate of $4.3\times 10^{-3}\rm{c\,s^{-1}}$ (exposure
time of 7.2 ks, 0.3–10 keV). Finally, ASASSN-15oi was observed with Swift-XRT
between 2022 August and October ($\delta t\approx 2540-2620$ d). We found
marginal evidence (at the level of $\approx 3.5\,\sigma$, Gaussian equivalent)
for X-ray emission at the location of ASASSN-15oi with count-rate $(1.3\pm
0.6)\times 10^{-3}\rm{c\,s^{-1}}$ (exposure time of 7.0 ks, 0.3 – 10 keV).

We extracted seven spectra (Table A.2) by grouping observations close in time.
Following Holoien et al. (2016, 2018); Gezari et al. (2017), we fitted the
spectra in the 0.3 – 10 keV energy range with an absorbed two-component model
featuring a (non-thermal) power-law and a (thermal) blackbody (BB), i.e.,
tbabs*(cflux*pow+cflux*bbody) within XSPEC v12.12.1. The Galactic neutral
hydrogen column density in the direction of the transient is
$N_{\rm{H,gal}}=5.6\times 10^{20}\,\rm{cm^{-2}}$ (Kalberla et al., 2005). We
found no evidence for intrinsic absorption and we thus assume $N_{\rm
H,int}=0\,\rm{cm^{-2}}$. The temporal evolution of the relative flux of the
thermal and non-thermal spectral components in ASASSN-15oi implies a time-
varying count-to-flux conversion factor. Following Margutti et al. (2013), we
use the results from the time-resolved spectral analysis to perform a self-
consistent flux calibration of the count-rate light-curve. Specifically, we
derive a count-to-flux conversion as a function of time since discovery by
linearly interpolating in the log space the count-to-flux conversion factors
derived from the seven spectra. For each epoch, the best-fitting blackbody
temperature ($kT_{\rm BB}$), blackbody radius $R_{\rm BB}$, power-law index
$\Gamma_{\rm X}$, unabsorbed fluxes corresponding to respective components,
and total absorbed fluxes are reported in Table A.2. The X-ray light-curve is
shown in Figure 2 and the unfolded spectra are shown in Figure 3.

###  2.3 X-rays: XMM-Newton

Figure 3: Unfolded X-ray spectra of ASASSN-15oi ranging from $\delta t\approx
76.4$ d – $1833$ d in the 0.2 – 12 (0.3 – 10) keV energy range as observed by
XMM-Newton (Swift-XRT). We plot spectra here where we have a high signal-to-
noise. Blue (pink) dashed line: blackbody (power-law) component. For all the
plots the y-axis covers the same dynamical range. At late times the blackbody
component that was responsible for the source brightening until $\delta
t\approx 350$ d becomes undetectable and the spectrum consists of an absorbed
simple power-law.

Following the prominent re-brightening of ASASSN-15oi at radio frequencies at
$\delta t\sim 1400$ d (Horesh et al. 2021a) we acquired deep X-ray
observations with XMM-Newton (Jansen et al. 2001) on 2020 October 08 ($\delta
t=1830$ d, exposure times $\approx\,23.6,23.8,\rm{and}\,12.5$ ks for MOS1,
MOS2, and pn cameras, respectively; obsID 0872390301; PI Hajela). We acquired
additional observations on 2023 April 08 ($\delta t=2794$ d, exposure times
$\approx\,21.9,21.7,\rm{and}\,17.5$ ks for MOS1, MOS2, and pn cameras,
respectively; obsID 0903330101; PI Hajela). The results from the analysis of
the earlier two XMM observations (taken at $\delta t=76.4$ and $\delta
t=234.5$ d; PI Gezari) were reported in Gezari et al. (2017) and Holoien et
al. (2018).

All XMM observations were performed with the European Photon Imaging Camera
(EPIC) detector in full-frame mode with the thin filter. We processed all the
observations using standard routines in the Scientific Analysis System
(SASversion 1.3) software package and the corresponding calibration files.
Filtering out time intervals with high background flaring activity results in
the net exposure times555We note that the slightly different net exposure
times in Gezari et al. (2017) for the first two observations likely result
from different filtering criteria. reported in Table A.2. An X-ray source is
clearly detected in three XMM observations at the position of the
radio/optical transient. However, there is no evidence of significant emission
in the last epoch at $\delta t=2794$ d. We extracted a spectrum from a
circular region of 15″ (300 pixels) radius centered at the source position,
and used a nearby 75″ source-free background region. We perform our spectral
analysis using the data from all three EPIC cameras666Gezari et al. (2017)
used only observations from EPIC-pn camera. Since pn detector has the largest
number of counts, the results will remain unaffected. (MOS1, MOS2 and pn).

We fit the data in the 0.2 - 12 keV energy range with the same two-component
model that we used for _Swift_ -XRT data: tbabs*ztbabs*(cflux*pow+cflux*bbody)
within XSPEC (v.12.12.1). We do not find evidence for significant intrinsic
absorption from a joint-fit of the the XMM epochs at $\sim 80-1400$ d
($N_{\rm{{H,int}}}<1.4\times 10^{20}\,\rm{cm^{-2}}$), therefore we proceed
with $N_{\rm{H,int}}=0$ as before. We used $N_{\rm{H,gal}}=5.6\times
10^{20}\,\rm{cm^{-2}}$ and $N_{\rm{H,int}}=0\,\rm{cm^{-2}}$, and report the
best-fitting parameters and fluxes in Table A.2, plot the light-curve in
Figure 2, and the unfolded spectra in Figure 3.

Our results for the first two epochs (at $\delta t=76.4$ d and $234.5$ d) are
broadly in agreement with those of Gezari et al. (2017) with an exception of
the power-law X-ray flux that they report as constant between epochs, but we
identify as varying. In our new observation at $\delta t=1833$ d, we find that
a blackbody component is not required and the data are well explained by a
non-thermal power-law spectrum only (Figure 3). This result is consistent with
our findings from the _Swift_ -XRT spectrum at $\delta t\approx 1400\,$d,
which was also dominated by the power-law spectral component (§2.2). Our
latest _XMM_ observation at $=2794$ d shows a sharp flux decline as the
emission becomes non-detectable.

Taken together, the _Swift_ -XRT and XMM-Newton campaigns lead to the
following observational results777Pre-TDE _ROSAT_ observations of the host
galaxy 2MASX J20390918–3045201 provide no useful constraint: Holoien et al.
(2018) report a pre-TDE X-ray flux limit of $F_{x}<1.9\times
10^{-12}\,\rm{erg\,cm^{-2}s^{-1}}$ (0.1–2.4 keV), which is larger than the
measured X-ray fluxes for ASASSN-15oi.. (i) Since optical discovery, this
transient has radiated $\sim 10^{51}\,\rm{erg}$ in X-rays. (ii) While S1
(§2.1) falls within the _XMM_ and _Swift_ -XRT PSF, we found no evidence for a
shift of the centroid of the source of X-ray emission between the second
(blackbody dominated) and the third (power-law dominated) _XMM_ epochs. We
thus exclude with confidence the possibility that the X-ray power-law is
associated with S1 and unrelated to the TDE. (iii) For $\delta t\lesssim
425\,$d the soft X-ray spectrum consists of a mixture of a thermal blackbody
component with $kT_{\rm BB}\sim 0.05\,$keV and a non-thermal power-law
component with $\Gamma_{\rm X}\sim 2$, i.e., $F_{\nu}\propto\nu^{-1}$ (Figure
3). (iv) The brightening of X-ray emission by a factor $\approx 6$ in the time
interval $\delta t\approx 10-330\,$d is due to the flux increase of the
blackbody component (Figure 2). During this time the $T_{\rm BB}$ shows no
evolution, whereas the effective $R_{\rm BB}$ increases with time from $\sim
2.3\times 10^{11}\,\rm{cm}$ to $\sim 1.3\times 10^{12}\,\rm{cm}$. Results
(iii)+(iv) confirm the findings of Holoien et al. (2016, 2018); Gezari et al.
(2017). (v) Differently from Holoien et al. (2018), we find that the blackbody
component rapidly fades between $330-425$ d and becomes undetectable by the
time of the following Swift-XRT observation at $\delta t\approx 1400\,$d. (vi)
The non-thermal power-law component in the spectra is consistently present and
dominates at $>1400$ d. The power-law flux initially decreases until around
$\approx 230$ d when the blackbody flux increases. It then brightens rapidly
until $\approx 330$ d, followed by a gradual increase until $\approx 1400$ d.
At $\gtrsim 1400$ d, significant variability is observed with a dip in the
observed flux at $\approx 1800$ d between the brighter $\approx 1400$ d and
$\approx 2580$ d observations.

###  2.4 Radio: VLA

Horesh et al. (2021a) started monitoring ASASSN-15oi with the VLA at $\delta
t=8$ d. They reported the first radio detection at $\delta t=182$ d, showing a
significant brightening of the source compared to earlier upper limits (Figure
5). The first radio brightening was followed by a second, even more dramatic
radio re-brightening at $\delta t>1400$ d. ASASSN-15oi’s second radio flare
was discovered in VLASS observations (Lacy et al., 2020). It was observed as
part of regular survey operations on 2019 July 1 ($\delta t=1417$ d),
revealing that the flux density at 3 GHz had increased by a factor of $\sim
3000$ since the 2017 observations of Horesh et al. (2021a). To further explore
the nature of this second radio flare, we obtained multi-frequency
observations with the VLA under the DDT program 20A-492 (PI: Alexander). The
data were taken when the array was in the C configuration at $\delta t=1741$
d. To monitor the spectral and temporal evolution, we obtained subsequent
broadband observations with the VLA under the programs 21A-303 (PI Hajela;
$\delta t=2129$ d) in the B configuration, and 23A-241 (PI Cendes; $\delta
t=2970$ d) in the A configuration. We observed ASASSN-15oi in a standard phase
referencing mode for 18-20 minutes at the mean frequencies of 1.5 GHz
(L-band), 3 GHz (S-band), 6 GHz (C-band), and 10 GHz (X-band). We used 3-bit
samplers for C and X bands and 8-bit samplers for L and S bands.

For the observations acquired between $\delta t=1741-2129$ d, we use the VLA
calibration pipeline packaged with CASA v.6.2.1.7, with 3C 48 = J0137+3309 as
the flux calibrator, and ICRF J210101.6$-$293327 (J2101$-$2933) as the complex
gain calibrator. For $\delta t=2970$ d, we used 3C 286 = J1331+3030 as the
flux calibrator and the new VLA calibration pipeline packaged with CASA
v.6.5.4.9. After manually inspecting the data, we further flagged antennas
with bad solutions as well as additional weak radio-frequency interference and
then re-ran the pipeline. To densely sample the SED, we divide the dataset in
every observing band further into sub-bands, and image each sub-band
individually using the CLEAN algorithm with Briggs weighting and a robust
factor of $0.5$ in CASA. Where necessary, we also use the automated self-
calibration pipeline. We note the presence of a bright source $\sim
0.3\,\arcdeg$ away in the 1.5- and 3-GHz bands, however its residual sidelobes
are below the image background rms near ASASSN-15oi. ASASSN-15oi is detected
as a very bright radio source at all frequencies. We measure the flux density
of ASASSN-15oi using the imtool package within pwkit (Williams et al., 2017)
and report the results in Table A.3. Since the flux density scale calibration
has an accuracy of 3% – 5% for our observing bands, we add a conservative 5%
systematic uncertainty in quadrature to our uncertainties. We also include
this uncertainty in the early-time observations reduced by Horesh et al.
(2021a).

###  2.5 Radio: VLBI

We observed ASASSN-15oi with the VLBA of the National Radio Astronomy
Observatory (NRAO), using all antennas except Brewster, under the program
VLBA/22A-382 (PI: Hajela). The total observing time was $5.5$ h, and the
midpoint of the observations was of 2022 February 22.75 (UT; MJD = 59632.75;
$\delta t=2384$ d). We recorded a total bandwidth of 512 MHz, centered on
$8.30$ GHz, in two polarizations, using a total bitrate of 4096 Mbps. The VLBI
data were correlated with NRAO’s VLBA processor, and the analysis carried out
with NRAO’s AIPS (Astronomical Image Processing System; Greisen 2003). The
initial flux density calibration was done through measurements of the system
temperature at each telescope, and then improved through self-calibration of
the reference source. A correction was made for the dispersive delay due to
the ionosphere using the AIPS task TECOR, although the effect at our frequency
is not large. We phase-referenced the observations of ASASSN-15oi to PMN
J2036$-$2830, using a $\sim 3.7$ min cycle, of which $\sim 2.5$ min were on
ASASSN-15oi.

We show the VLBI image of ASASSN-15oi, made using the CLEAN algorithm, in Fig.
4, The total CLEANed flux density is $1.2$ mJy, and the image background rms
is $140$ $\mu$Jy beam-1. For an ideal, unresolved source, the peak brightness
should also be $1.2$ mJy, however, the peak brightness in the image is
somewhat larger $1.5$ mJy beam-1. So, the relatively low-dynamic-range (11:1)
image allows only an approximate determination of the flux density. The
angular size of ASASSN-15oi is smaller than our FWHM resolution of $2.47\times
0.78$ mas at position angle (p.a.) $-5$°.

For marginally- or unresolved sources, such as ASASSN-15oi, the best values or
limits for the flux density and source size come from fitting models directly
to the visibility data (e.g., Bietenholz et al., 2010), rather than from
imaging. Fitting a circular Gaussian to the visibilities by least squares
(AIPS task OMFIT), we find that the best fit has a FWHM size of $0\pm 1$ mas
and a flux density of $1.4\pm 0.3$ mJy, with the caveat that the fitted size
is positively correlated with the fitted flux density. At the distance of
ASASSN-15oi, the FWHM translates to a $3\sigma$ physical source size of $\sim
9\times 10^{18}$ cm.

Figure 4: A VLBI image of ASASSN-15oi on 2022 February 22 ($\delta
t=2384\,$d), at $8.3$ GHz. The peak brightness was $1.5$ mJy beam-1, and the
image background rms brightness was $140$ $\mu$Jy beam-1. The greyscale is
labelled in mJy beam-1. The contours are drawn at $-35$, $35$, $50$
(emphasized), 70 and 90% of the peak brightness. The FWHM resolution is shown
at lower left, and was $2.47\times 0.78$ mas at p.a. $-5$°. North is up and
east to the left. Figure 5: Temporal evolution of the radio luminosity $\nu
L_{\nu}$ of ASASSN-15oi ($7-8.5$ GHz; red stars) in the context of selected
radio-bright TDEs. The filled red stars show VLA and ATCA measurements, while
the VLBA one is shown as an open red star. Other TDEs are: _Sw_ J1644+57
($15.5$ GHz compiled from Zauderer et al. 2011; Berger et al. 2012; Zauderer
et al. 2013; Eftekhari et al. 2018; Cendes et al. 2021b), AT 2022cmc ($11.5$
GHz from Andreoni et al. 2022) among the jetted-TDEs; AT 2018hyz ($5-8$ GHz
from Cendes et al. 2022), AT 2019azh ($15.5$ GHz from Sfaradi et al. 2022),
ASASSN-19bt ($5.5$ GHz from Christy et al. 2024), AT 2020vwl ($9$ GHz from
Goodwin et al. 2023b). Luminosity of all other TDEs have been adopted from
Alexander et al. (2020) in $3-9$ GHz frequency range. At $\delta t\approx
1800$ d, ASASSN-15oi is the most luminous known radio TDE among those not
reported to be associated with relativistic jets. Figure 6: Evolution of the
emission from ASASSN-15oi across the radio spectrum from the time of the first
radio detection at $\delta t=8\,$d extending to $\delta t=2970\,$d. The data
at $\delta t\geq 1741\,$d are presented here for the first time. All the flux
densities are reported in Table A.3. The single frequency VLASS and VLBA
observations are highlighted separately in the plot legend.

###  2.6 Radio: ATCA

We acquired observations of ASASSN-15oi (Project code: C3325; PI: Alexander)
on 2022 September 30 ($\delta t=2596$ d) with ATCA. The observations were
conducted in the 6D configuration, consisting of all six 22 m diameter
antennae (Wilson et al., 2011). The observing bands were centered at
frequencies 2.1, 5.5, and 9 GHz, with a total bandwidth of 2 GHz in each of
the bands. For calibration purposes, PKS 1934$-$638 served as the primary
calibrator for all observing bands, whereas PKS 1921$-$293 (J2024$-$3253) was
observed in $\sim$2.5 minute scans enclosing each scan of ASASSN-15oi, and was
used as the secondary calibrator to calibrate the time-varying complex gains
in the 2.1 GHz (5.5 and 9 GHz) observing band(s).

We carry out the data reduction following the standard calibration procedures
in Miriad (Sault et al., 1995), with some additional manual flagging. We also
split the data into sub-bands, followed by imaging using inverted
visibilities, and deconvolving the images using the multi-frequency synthesis
CLEAN algorithm (Högbom, 1974; Clark, 1980; Sault & Wieringa, 1994), and
calculated the flux density by fitting a point source model to the target in
the image plane. We add 10% systematic uncertainty in quadrature to our
measurements (Tingay et al., 2003).

###  2.7 Radio: MeerKAT

We obtained observations with the MeerKAT radio telescope in 580 – 1015 MHz
(UHF) and 0.8 – 2 GHz (L) bands on 2022 December 9 (SCI-20220822-YC-01, PI:
Cendes; $\delta t=2674$ d) and 2023 January 5 (DDD-20220414-YC-01, PI: Cendes;
$\delta t=2701$ d). We used ICRF J193925.0$-$634245 as the flux density
calibrator and QSO PKS J2052$-$3640 as the phase and gain calibrator. We use
the calibrated images obtained from the SARAO Science Data Processor pipeline
(SDP)888https://skaafrica.atlassian.net/wiki/spaces/ESDKB/pages/338723406/. We
measured the flux density of ASASSN-15oi using the imtool package within pwkit
(Williams et al., 2017). Since these observations are close in time to the
ATCA observations (§2.6) with a mean observation epoch $\approx 2660$ d, we
model them together in §3.

###  2.8 Radio: ALMA

Finally, we obtained mm-wavelength observations of ASASSN-15oi with ALMA under
program 2019.1.01166.T (PI: Alexander). A single epoch of observations at
Bands 3 and 6 (mean frequencies 97.5 GHz and 232 GHz respectively) was
obtained on 2022 September 29 ($\delta t\approx 2128$ d). The data were
reduced and imaged using the standard NRAO ALMA pipeline in CASA. We add a
$3\%$ and $6\%$ systematic uncertainty in quadrature to our Band 3 and Band 6
measurements, respectively.

All the radio flux densities are recorded in Table A.3. The radio light curve
and SEDs are shown in Figures 5 and 6, respectively. In Figure 5, we note that
the VLBA measurement of $1.4\pm 0.3$ mJy, at $8.30$ GHz is lower by $5\sim
6\sigma$ than the flux densities of $4.7\pm 0.2$ and $4.2\pm 0.4$ mJy measured
with the VLA and ATCA at comparable times and frequencies (§2.4 and 2.6,
respectively; see Table A.3). This discrepancy could indicate true radio
variability at timescales of $\sim 300$ d at later stages of ASASSN-15oi’s
evolution, however a low signal-to-noise ratio of the VLBI image (as mentioned
in §2.5) and a relatively low source declination ($\sim-30{\arcdeg}$) for
VLBA999https://science.nrao.edu/facilities/vlba/docs/manuals/oss/vlba-
declination-limits may impact this flux density measurement. In addition,
since the radio emission measured by other telescopes in the nearby epochs
show a simple trend of $t^{-2}$, the case of variability less likely. We
therefore, do not include the VLBA measurement in our analysis. To alleviate
such issues in the future, we encourage simultaneous observations with the
VLBA and other radio telescopes, e.g., VLA, to get full spectral information.
We finally also note the discrepancy between the MeerKAT and ATCA data in the
$2660$ d SED at $\sim 2$GHz in Figure 6. However, these are marginally
consistent within $3\sigma$, and the difference could be due to inter-
calibration issues between the two telescopes. In the next section we model
the radio SEDs and for this particular frequency and epoch, we proceed with
assuming $3\sigma$ uncertainties on the MeerKAT measurement, instead of the
usual $1\sigma$ for all others.

##  3 Radio Data Modeling

###  3.1 Fitting of Individual SEDs

We show the radio SEDs of ASASSN-15oi in Figure 6. Spectral evolution is
evident, with some SEDs described by a single power-law
($F_{\nu}\propto\nu^{\alpha}$), and others requiring up to three power-law
segments. To fit the SEDs containing _one_ break we use the following
parametric model:

$F_{\nu}=F_{b_{1}}\Big{[}\Big{(}\dfrac{\nu}{\nu_{b_{1}}}\Big{)}^{\alpha_{i}/s_{1}}+\Big{(}\dfrac{\nu}{\nu_{b_{1}}}\Big{)}^{\alpha_{j}/s_{1}}\Big{]}^{s_{1}}$
(1)

and to accommodate _two_ breaks, we modify the above model as follows:

$\begin{split}\rm{Equation\,\ref{eq:BPL}}\times\left[1+\Big{(}\frac{\nu}{\nu_{b_{2}}}\Big{)}^{(\alpha_{k}-\alpha_{j})/s_{2}}\right]^{s_{2}},\end{split}$
(2)

where $\nu_{b_{1,2}}$ are the two break frequencies, $s_{1,2}$ define the
sharpness of the two breaks (larger $|s|$ represents a smoother break), and
$\alpha_{i,j,k}$ are the power-law indices corresponding to the three spectral
segments. The optically thick emission manifests as a spectrum with positive
slope ($\alpha>0$) that we label $\alpha_{\rm thick}$. The optically thin
emission has a negative slope ($\alpha<0$) and is labelled with $\alpha_{\rm
thin}$. If both of these segments are present, their asymptotic intersection
is the peak of the SED and is represented by $F_{\rm pk}=F_{\rm b_{1}}$ and
$\nu_{\rm{pk}}=\nu_{\rm b_{1}}$. If there is an additional break frequency
$\nu_{q}$ on the optically thin section of the SED, the power-law index of the
steeper segment at higher frequencies is referred to as $\alpha_{q}$.

We perform a Markov Chain Monte Carlo (MCMC) fit (using the emcee python
package; Foreman-Mackey et al. 2013) to the individual radio SEDs. For SEDs
featuring both $\alpha_{\rm thin}$ and $\alpha_{q}$ spectral segments, we
introduce an additional constraint to our fitting procedure i.e.
$\alpha_{q}-\alpha_{\rm thin}=-0.5$101010This assumption is valid for the
physical models used in §3.2 and §3.3.. We provide the details of the fits and
our assumptions in Appendix B in §B.1 and §B.2. Due to the complex spectral
shapes of the SEDs, we fit them with different models and calculate the Akaike
Information Criterion (AIC) and the Bayesian Information Criterion (BIC)
values for comparison. The details of our model selection are given in §B.3
and Table B.1.

We briefly summarize our results for each SED fit here. For the first radio
flare SEDs $\\#1,2,3$ (see Table 1), we perform a fit with both Equation 1 (as
was also done by Horesh et al. 2021a) and Equation 2. Based on the AIC and BIC
values in Table B.1, both fits to these SEDs are statistically equivalent.
However, as the fits with Equation 1 have already been presented in Horesh et
al. (2021a), here we proceed with the best-fitting parameters from Equation 2.
We individually fit for $\alpha_{\rm thick,thin}$, $F_{\rm pk}$, $\nu_{\rm
pk}$ and $\nu_{q}$ in SEDs $\\#2$ and $3$, resulting in $\alpha_{\rm
thick}\sim+1$. We follow a similar process for SED $\\#1$ but fix $\alpha_{\rm
thick}=1$ as there are too few measurements below $\nu_{\rm pk}$ to allow an
independent constraint. The optically thick segments of the SED is similarly
not sampled in SEDs $\\#4$ and $5$. These epochs show a statistically strong
preference for Equation 1 fit with the spectral break $\nu_{\rm
b_{1}}=\nu_{q}$. SEDs $\\#6,7$ are best fitted with a simple power-law.

For the second radio flare (§B.2) SEDs, we fix $\alpha_{\rm thick}=5/2$ as is
typically done for TDEs. Equation 2 is the statistically preferred model for
SEDs $\\#8,10,11$, while Equation 1 is preferred for SED $\\#9$. A peak can
only be constrained for SEDs $\\#1,2,3$, and $9$. For every other SED
($\\#4,5,6,7,8,10,11$) where a peak cannot be constrained, we assume a lower-
limit on $F_{\rm pk}$ and an upper-limit on $\nu_{\rm pk}$ as the maximum
observed flux density and its corresponding frequency, respectively. We report
the best-fitting parameters for all SEDs in Table 1, present the fits in
Figure 7, and show the evolution of the SED peaks and $\nu_{q}$ in Figure 8.

Table 1: Results of the MCMC fitting of the individual radio SEDs with $>2$
data points. We fit different models to the SEDs and only report the
parameters of the preferred model based on the AIC and BIC values reported in
Table B.1 (see §3 for details). For all SEDs except $\delta t=2129$, we assume
$s=-0.3$, and $s_{2}=-0.003$; we instead use $s=-1$ to accommodate the broader
peak of the $\delta t=2129$ SED. Where $\nu_{q}$ is identified, we use
$\alpha_{q}=\alpha_{\rm thin}-0.5$. The central values reported here are the
median of the posterior distribution, and the errors denote the 68% credible
interval.

SED | Epoch | $\alpha_{\rm thick}$ | $\alpha_{\rm thin}$ | $F_{\rm pk}$ | $\nu_{\rm pk}$ | $\nu_{q}$
---|---|---|---|---|---|---
$\\#$ | (d) |  |  | (mJy) | (GHz) | (GHz)
SEDs associated with the First Radio Flare
1 | 182 | $1$ | $-0.7^{+0.2}_{-0.2}$ | $1.7^{+0.1}_{-0.1}$ | $7.1^{+0.9}_{-0.8}$ | $18^{+8}_{-6}$
2 | 190 | $0.8^{+0.1}_{-0.1}$ | $-1.0^{+0.1}_{-0.2}$ | $1.5^{+0.1}_{-0.1}$ | $9.7^{+0.9}_{-0.8}$ | $17^{+9}_{-3}$
3 | 197 | $1.0^{+0.1}_{-0.1}$ | $-0.9^{+0.1}_{-0.1}$ | $1.4^{+0.1}_{-0.1}$ | $8.4^{+0.6}_{-0.5}$ | $20^{+3}_{-2}$
4 | 233[a,b] | – | $-0.4_{-0.1}^{+0.3}$ | $>1.0$ | $<3$ | $11_{-6}^{+2}$
5 | 283[a,b] | – | $-0.5_{-0.1}^{+0.2}$ | $>1.0$ | $<3$ | $9_{-4}^{+2}$
6 | 369[b] | – | $-0.2^{+0.1}_{-0.1}$ | $>0.7$ | $<3$ | –[c]
7 | 576[b] | – | $-0.5^{+0.2}_{-0.2}$ | $>0.3$ | $<3$ | –[c]
SEDs associated with the Second Radio Flare[d]
8 | 1741[b] | $5/2$ | $-0.15_{-0.09}^{+0.07}$ | $<10.8$ | $<1.8$ | $6.8_{-1.2}^{+2.6}$
9 | 2129 | $5/2$ | $-0.64_{-0.03}^{+0.03}$ | $19_{-1}^{+1}$ | $0.9_{-0.1}^{+0.1}$ | –[c]
10 | 2660[b] | $5/2$ | $-0.54^{+0.04}_{-0.04}$ | $<9.8$ | $<0.8$ | $16^{+5}_{-4}$
11 | 2970[b] | $5/2$ | $-0.32_{-0.06}^{+0.08}$ | $<4.1$ | $<1.2$ | $4.9^{+0.9}_{-1.1}$

Note. — ${\rm{\displaystyle[{a}]}}$ These SEDs show no low frequency turnover,
but show a steepening at high frequencies. We therefore fit them with Equation
(1), where the two spectral indices are given by $\alpha_{\rm thin}$ and
$\alpha_{\rm q}=\alpha_{\rm thin}-0.5$.

${\rm{\displaystyle[{b}]}}$ In these SEDs, we use the maximum observed
$F_{\nu}$, and the corresponding frequency as the limits on $F_{\rm{pk}}$ and
$\nu_{\rm pk}$.

${\rm{\displaystyle[{c}]}}$ $\nu_{q}$ is not observed in these SEDs.

${\rm{\displaystyle[{d}]}}$ For these SEDs, the optically thick part of the
spectrum cannot be constrained. We fix $\alpha_{\rm thick}=5/2$.

Figure 7: Radio SEDs of ASASSN-15oi and the best-fitting models: SED
$\\#1,2,3,8,10,11$ are fitted with Equation 2, while SED $\\#4,5,9$ with
Equation 1. SED $\\#6,7$ are fitted with a simple power-law. The solid grey
curves are a selection of 50 models randomly sampled from the posterior
distribution. Where applicable, dotted lines show the asymptotic power-laws
with the best-fitting spectral indices (the medians of the posterior
distributions), and the empty squares are the intersection of the $\alpha_{\rm
thick}$ and $\alpha_{\rm thin}$ segments in the respective SEDs. For clarity,
we have also zoomed-in on the frequencies around $\nu_{q}$ in some SEDs.
Figure 8: The evolution of the radio SED peak flux density $F_{\rm pk}$ and
the break frequencies $\nu_{\rm pk}$ and $\nu_{q}$ with time. Table 2:
Physical parameters inferred from the equipartition modeling of the radio
data, detailed in §3, assuming $\epsilon_{\rm e}=\epsilon_{\rm B}=0.1$. Here,
$p$ is derived from $\alpha_{\rm{thin}}$ resulting from the MCMC fitting of
the observed SEDs. $\alpha_{\rm{thin}}$, $F_{\rm pk}$, and $\nu_{\rm pk}$
values reported in Table 1 are used to derive the physical parameters
according to the model described by Chevalier (1998). The derivations of the
physical parameters in Equations (D1) – (D4) is dependent on $p>2$. For SEDs
with $p<2$, we use Equations (E3) – (E5). The values in the table are
sensitive to $F_{\rm pk}$, and $\nu_{\rm pk}$, and therefore to how smoothly
the power-laws are joined in the broken power-law model (i.e., to the value of
$|s|$).

SED | $\delta t$ | $p$ | $B_{\rm eq}$ | $U_{\rm eq}$ | $R_{eq}$ | $n_{\rm e,eq}$ |  $v_{\rm eq}$[a]
---|---|---|---|---|---|---|---
$\\#$ | (d) |  | (G) | ($\times 10^{49}$ erg) | ($\times 10^{16}$ cm) | ($\times 10^{3}$ cm-3) | ($\times$speed of light)
Modeling of SEDs associated with the First Radio Flare.
1 | 182 | $2.3^{+0.3}_{-0.3}$ | $0.41^{+0.08}_{-0.06}$ | $0.9^{+0.5}_{-0.2}$ | $4.0^{+0.3}_{-0.3}$ | $9^{+4}_{-2}$ | $0.084^{+0.007}_{-0.006}$
2 | 190 | $3.0^{+0.5}_{-0.3}$ | $0.74^{+0.34}_{-0.18}$ | $1.9^{+3.5}_{-0.9}$ | $3.5^{+0.4}_{-0.3}$ | $38^{+30}_{-16}$ | $0.070^{+0.006}_{-0.007}$
3 | 197 | $2.7^{+0.2}_{-0.2}$ | $0.55^{+0.09}_{-0.08}$ | $1.0^{+0.5}_{-0.3}$ | $3.4^{+0.2}_{-0.2}$ | $24^{+9}_{-6}$ | $0.066^{+0.003}_{-0.003}$
4 | 233 | $\sim 1.8$ |  $<$ 0.16 | $>0.45$ |  $>$ 6.0 |  $<$ 0.9 | $>0.1$
5 | 283 | $\sim 1.9$ | $<0.16$ | $>0.54$ | $>6.3$ | $<1.2$ | $>0.1$
6 | 369 | $\sim 1.4$ |  $<$ 0.18 |  $>$ 0.25 |  $>$ 4.4 |  $<$ 5.4 |  $>$0.04
7 | 576 | $\sim 1.9$ |  $<$ 0.18 |  $>$ 0.13 |  $>$ 3.6 |  $<$ 20 |  $>$0.02
Modeling of SEDs associated with the Second Radio Flare
8 | 1741 | $\sim 1.3$ | $<0.08$ | $>9$ | $>26$ | $<0.72$ | $>0.06$
9 | 2129 | $2.2^{+0.1}_{-0.1}$ | $0.04^{+0.01}_{-0.01}$ | $93^{+9}_{-6}$ | $90^{+8}_{-5}$ | $0.02^{+0.01}_{-0.01}$ | $0.16^{+0.01}_{-0.01}$
10 | 2660 | $2.1^{+0.1}_{-0.1}$ | $<0.04$ | $>52$ | $>75$ | $<0.04$ | $>0.10$
11 | 2970 | $\sim 1.6$ | $<0.06$ | $>6$ | $>27$ | $<0.89$ | $>0.03$

Note. — ${\rm{\displaystyle[{a}]}}$ The velocity is measured with respect to
days since the optical discovery. We note that velocities of the outflow at
one epoch relative to the other epoch can be calculated as $\Delta R/\Delta
t$.

###  3.2 Equipartition Physical Parameters from a Quasi-spherical Outflow
Model

Using the inferred SED peak and $\alpha_{\rm thin}$, we can now estimate the
physical parameters of the outflow responsible for the radio emission. To that
end we adopt a synchrotron self-absorption (SSA) model given by Chevalier
(1998), as commonly used in the TDE literature (e.g., Alexander et al., 2020,
and references therein). This model assumes that the synchrotron radiation is
powered by the relativistic electrons accelerated by a shock interacting with
the ambient medium, resulting in a broadband SED. Below the SED peak
($\nu<\nu_{\rm pk}$), the synchrotron radiation is self-absorbed resulting in
$F_{\nu}\propto\nu^{5/2}$. At $\nu>\nu_{\rm pk}$, the spectrum becomes
optically-thin and follows $F_{\nu}\propto\nu^{-(p-1)/2}$, where $p$ is the
power-law index of the population of accelerated electrons. In the context of
our model parameters in §3.1, the spectral indices become $\alpha_{\rm
thick}=5/2$ and $\alpha_{\rm thin}=-(p-1)/2$. The indices $p$ derived from the
best-fitting $\alpha_{\rm thin}$ for each SED are reported in Table 2.
Clearly, the abrupt changes in $p$ between epochs are unphysical for a single
population of radiating electrons, suggesting the presence of multiple
synchrotron sources instead. This interpretation will be corroborated further
as we proceed with our analysis.

For SEDs $\\#1,2,$ and $3$, we have $\alpha_{\rm thick}\sim 1\neq 5/2$. A
shallow optically thick slope can possibly be explained by a clumpy medium
(e.g., Weiler et al., 2002; Björnsson & Keshavarzi, 2017), a possibility also
explored by Horesh et al. (2021a). These inhomogeneities result in a
superposition of several SSA spectra with different peaks. In this case, the
physical parameters derived from the Chevalier (1998) analysis are
representative of the population of electrons that dominate the peak of the
SED.

We adopt a volume filling factor of $f=0.5$ in the equations presented in
DeMarchi et al. (2022) to constrain the post-shock magnetic field $B$, the
radius of the emitting region $R$, the internal energy $U$, the electron
number density of the ambient medium $n_{e}$, and the average velocity of the
shock as $v=R/\delta t$. The equations in DeMarchi et al. (2022) generalize
those originally presented in Chevalier (1998) for an arbitrary value of $p$
(see also Chevalier & Fransson 2017). The expressions for $B,R,U$ and $n_{e}$
are presented in Appendix D. Equations (D1 – D4) are derived assuming
$\gamma_{\rm{max}}\to\infty$, where $\gamma_{\rm max}$ is the maximum Lorentz
factor attained by the electrons accelerated by the shock. In this case, for
the energy density in the electrons to be finite, $p>2$ is required.
Conversely, a $p<2$ requires finite $\gamma_{\rm{max}}$. We derive equations
for this regime in Appendix E. We note that multi-dimensional particle-in-cell
simulations suggest $\gamma_{\rm max}\lesssim 10^{8}$ (Sironi et al., 2013).
$B$, $R$ and $U$ are all proportional to $\gamma_{\rm max}$. Here, we assume
$\gamma_{\rm max}=10^{3}$ (with these electrons emitting synchrotron radiation
at $\sim 3$ THz for a non-relativistic shock). All the parameters are in
c.g.s. units.

As this model has many free parameters, a unique solution is generally only
possible if multiple spectral breaks of the synchrotron spectra can be
measured directly from the data. In the absence of other constraints, the
system is assumed to be in equipartition, i.e., the fraction of internal
energy in the relativistic electrons $(\epsilon_{\rm e}$) is equal to the
fraction of internal energy of the post-shock magnetic field ($\epsilon_{\rm
B}$). We note that there is no observational support for such a choice, but
this is a standard assumption in the field. This enables us to estimate the
physical parameters even if only $F_{\rm pk}$, $\nu_{\rm pk}$ and $p$ can be
measured directly. Here we assume $\epsilon_{\rm e}=\epsilon_{\rm B}=0.1$, as
is typically assumed in the TDE literature, to estimate the physical
parameters of the synchrotron-emitting region. Where the peak was not
constrained, the limits on $F_{\rm pk}$ and $\nu_{\rm pk}$ translate into
limits on the inferred physical quantities. We denote parameters ($X$) that
were calculated assuming equipartition conditions as $X_{eq}$.

The resulting values are reported in Table 2, and the evolution of these
parameters are visualized in Figure 9. We note the dramatic increase in the
inferred energy between the two flares from $U_{\rm eq}\sim 10^{49}$ erg at
$\delta t=182$ d to $U_{\rm eq}\sim 10^{51}$ erg at $\delta t=2129$ d. This
implies that a different, more powerful source is needed to explain the second
radio flare. We explore a scenario of a relativistic jet as a source of
emission for the second radio flare in §3.3. In the next section we briefly
discuss the inferences that can be drawn if we assume that $\nu_{q}$ is the
synchrotron cooling break.

####  3.2.1 Synchrotron Cooling Break

Table 3: We measure $B_{\rm c}$ from Equation (3) using the constrained $\nu_{q}$, then solve for $\epsilon_{\rm B,c}$ from Equation D1 or E3, assuming $\epsilon_{\rm e,c}\geq 10^{-4}$ as long as the resulting $\epsilon_{\rm B,c}<1$. SED |  $\delta t$ |  $B_{\rm c}$ |  $\epsilon_{\rm B,c}$
---|---|---|---
$\\#$ |  (d) |  (G) |
1 |  182 |  $0.72$ |  $\approx\epsilon_{\rm{e},c}$
2 |  190 |  $0.73$ |  $\approx\epsilon_{\rm{e},c}$
3 |  197 |  $0.66$ |  $\approx\epsilon_{\rm{e},c}$
4 |  233 |  $0.72$ |  $\geq 0.052$
5 |  283 |  $0.68$ |  $\geq 0.045$
8 |  1741 |  $0.23$ |  $\geq 0.005$
10 |  2660 |  $0.12$ |  $\geq 0.018$
11 |  2970 |  $0.17$ |  $\geq 0.009$

We can relax the assumption of equipartition, i.e. partially break the
degeneracy between $\epsilon_{e}$ and $\epsilon_{B}$, if we can measure
another characteristic of the synchrotron spectrum, such as the synchrotron
cooling break $\nu_{\rm cool}$. This enables a more accurate estimate of the
outflow parameters. For ASASSN-15oi, the break $\nu_{{q}}$ constrained in §3.1
for some SEDs may be interpreted as $\nu_{\rm cool}$.

For a non-relativistic shock, $\nu_{\rm{cool}}$ is calculated as:

$\nu_{\rm{cool}}=\frac{18\pi
m_{\rm{e}}cq_{\rm{e}}}{\sigma_{T}^{2}{B_{c}}^{3}(t_{\rm{dyn}})^{2}}$ (3)

where $m_{\rm{e}}$ and $q_{\rm{e}}$ are the mass and the charge of the
electron, $c$ is the speed of light, $\sigma_{T}$ is the Thomson cross-
section, $B_{c}$ is the magnetic field, and $t_{\rm{dyn}}$ is the dynamical
time. Note that we represent the physical parameters here as $X_{c}$ to
differentiate these estimates from the equipartition ones above.

SEDs $\\#1,2$ and $3$ have two break frequencies (see §3.1). To test whether
the second break frequency could be the synchrotron cooling frequency, we
assume $t_{\rm dyn}=\delta t$ and $B_{c}=B_{\rm eq}$ in Equation 3, and find
that $\nu_{\rm cool}\approx\nu_{q}$ within $1\sigma$ for SEDs $\\#2$ and $3$
and within $3\sigma$ for SED $\\#1$. This supports our findings that there are
two break frequencies as well as the initial equipartition assumption.
However, we note that the uncertainties on the best-fitting $\nu_{q}$ are
large so we cannot conclusively claim that these are the cooling breaks.

We fitted for $\nu_{q}$ in SEDs $\\#4,5,8,10,11$ in §3.1. For each of these
SEDs, if we assume, $t_{\rm dyn}=\delta t$ and $\nu_{\rm cool}=\nu_{q}$, the
measured $B_{c}$ from Equation 3 (in Table 3) is different from $B_{\rm eq}$
in Table 2. Using $B_{c}$, we can solve for
$\epsilon_{\rm{B},c}/\epsilon_{\rm{e},c}$ using either Equation D1 or E3. With
our initial assumption of $\epsilon_{\rm e,c}=0.1$, we obtain
$\epsilon_{\rm{B},c}>1$. This is clearly unphysical. Smaller values of
$\epsilon_{\rm{e},c}$ (specifically $10^{-4}\leq\epsilon_{\rm{e},c}<0.1$)
would yield acceptable $\epsilon_{\rm{B},c}$ values. Here, we adopt
$\epsilon_{\rm{e},c}\geq 10^{-4}$, where this lower-bound is set by the
simulations in e.g., Park et al. (2015) for non-relativistic collisionless
shocks. The upper-bound on $\epsilon_{\rm e,c}$ is set by the condition
$\epsilon_{\rm B,c}<1$. Both $B_{c}$ and the allowed range of
$\epsilon_{\rm{B},c}$ are reported in Table 3. As can be seen from Table 3,
our choices yield extreme ratios of the microphysical shock parameters
$\epsilon_{\rm{B},c}/\epsilon_{\rm{e},c}\lesssim 500$.

There is a third possibility that the breaks constrained here are not
synchrotron cooling breaks. Indeed, the shallow $\alpha_{\rm thin}$ found in
most of these SEDs hints at a contribution from multiple synchrotron shocks.
Several SSA spectra with different $p$ values can superimpose to create a
shallow ($p<2$) optically thin segment, e.g. as also seen in some AGNs
(Kellermann & Pauliny-Toth, 1969). This may indeed be true as we see
$\alpha_{q}$ in SEDs $\\#4,5,8,10,11$ resembles the $\alpha_{\rm thin}$
expected from a standard SSA spectrum, i.e. only a single synchrotron
component dominates at higher frequencies. Finally, the steep jumps,
particularly in the inferred density $n_{\rm e,eq}$ between $\delta t\approx
197$ d and $233$ d also suggest an inhomogeneous medium. Thus, a likely
unified scenario where the SED properties and the abrupt jumps in the physical
parameters of the system can be explained is that of ‘multiple outflows
launched in an inhomogeneous medium’. We discuss this scenario further in
§4.2.

Figure 9: Physical parameters from the modeling of the radio data assuming
equipartition. The dramatic jumps in the magnetic field and density estimate
from the SEDs within the first radio flare suggest an inhomogeneous medium, or
multiple synchrotron sources. A significant jump in the energy inferred for
the first and second radio flare hints at two distinct sources of emission for
the two flares.

###  3.3 Physical Parameters From An Off-Axis Relativistic Jet

Here, we examine if an off-axis relativistic jet could power the second radio
flare at $\delta t\gtrsim 1400$ d. This scenario is commonly invoked for
explaining the delayed radio emission in TDEs (see e.g., Perlman et al. 2022;
Cendes et al. 2022; Matsumoto & Piran 2023; Sfaradi et al. 2024; Christy et
al. 2024). Matsumoto & Piran (2023) provide a generalized treatment of jets
viewed at arbitrary angles in the context of TDEs. Compared to the Chevalier
(1998) model, in a jetted relativistic regime three additional variables come
into play: the jet Lorentz factor, $\Gamma$, the jet opening angle
$\theta_{\rm{jet}}$, and the viewing angle, $\theta_{\mathrm{obs}}$, i.e., the
angle between the jet axis and the observer’s line of sight. The jet energy
per solid angle is assumed to be constant for $\theta<\theta_{\rm{jet}}$ and 0
at larger angles (a so-called “top-hat" jet). The equations derived in
Matsumoto & Piran (2023) are applicable for a system in equipartition and we
follow Christy et al. (2024) to incorporate the corrections outlined in §3 and
§4.2.2 of Barniol Duran et al. (2013) for a more general system. Proceeding as
in §3.2.1 and assuming our measured high-frequency break ($\nu_{q}$) as the
relativistic synchrotron cooling break ($\nu_{\rm cool,jet}$), allows us to
relax the assumption of equipartition. This results in $\epsilon_{\rm
B,jet}<1$ for $\epsilon_{\rm{e,jet}}=0.1$, reported in Table 4, in contrast to
the non-relativistic uncollimated blastwave scenario.

Here, we consider a dynamically spreading jet whose opening angle $\theta_{\rm
jet}=1/\Gamma$ grows as the jet decelerates. This is equivalent to considering
only the energy within an angle of $1/\Gamma$ from our line of sight. As
material at larger angles has a negligible contribution to the observed
emission due to relativistic beaming, this provides the minimum energy
necessary to explain our observations at each epoch. In contrast, a narrow jet
with constant opening angle $\theta_{\rm jet}\sim 10^{\circ}$ (typical of AGN
jets), which is more physically likely, would require higher Lorentz factors
and correspondingly larger emission radii to produce the same observed
emission.

As Matsumoto & Piran (2023)’s analysis only applies for $p>2$, we perform this
analysis only on the $\delta t=2129$ and $2660$ d SEDs. For the $\theta_{\rm
jet}\geq 1/\Gamma$ case, we calculate the radius that minimizes the total
energy under a $p=2.1$ power law distribution of electrons (resulting from the
best-fitting $\alpha_{\rm thin}$ in §3.1). We assume equipartition, with
$\epsilon_{\rm e,jet}=\epsilon_{\rm B,jet}=0.1$ for the $2129$ d SED and break
the degeneracy in the $2660$ d SED using the constrained $\nu_{\rm cool,jet}$.
We carry out MCMC analysis as before, and all the best-fitting values are
reported in Table 4 for two illustrative scenarios: a promptly-launched jet
with $t_{\rm dyn}=\delta t$ (top rows) and a delayed jet launched with $t_{\rm
dyn}=\delta t-1471$ d (bottom rows). Here the delayed jet’s launch date is
chosen to be the time of the first detection of the second flare; the true
launch date is presumed to be between these two extremes. Times measured since
these jet launch dates are represented as $\delta t_{\rm jet}$. For each
launch date, we also consider two possible observer viewing angles:
$\theta_{obs}=30^{\circ}$ and $\theta_{obs}=90^{\circ}$.

Now we discuss the fitting results and the associated caveats. For the most
off-axis case ($\theta_{\rm obs}\approx 90{\arcdeg}$) at the latest possible
jet launch time, the jet models require $\Gamma\gtrsim 3$. This is an
unusually large Lorentz factor for an outflow $\sim 4$ years after its launch,
given the high-density nuclear environments in which TDEs occur. The required
jet energy is also high in most cases ($U_{\rm jet}\gtrsim 10^{52}$ erg, Table
4), but is similar to the energies previously inferred for radio-luminous TDEs
with powerful on-axis relativistic jets (e.g., Berger et al., 2012; Zauderer
et al., 2013; Brown et al., 2015; Cenko et al., 2012). Note that the lowest
energy is inferred for the $\delta t_{\rm jet}=658$ d SED with $\theta_{\rm
obs}=90\arcdeg$ but this is the equipartition energy; if the system is not in
equipartition the true energy will be even higher. With the equipartition
$R_{\rm jet}$ and $\Gamma$ for this epoch, the emitting region has a
transverse size of $R_{\rm jet}/\Gamma\sim 6\times 10^{17}$ cm. In comparison,
our VLBA observation at $=2384$ d in §2.5 gives a $3\sigma$ upper limit to the
physical source size of $<9\times 10^{18}$ cm, which is not constraining. The
less off-axis cases all require even higher jet Lorentz factors, which we
consider to be physically unlikely. Furthermore, if the emission was powered
by an off-axis jet, $\Gamma_{\rm jet}$ is expected to decrease with time.
However, in Table 4, we do not see such a trend. A single-component top-hat
jet is thus unlikely to explain the second radio flare of ASASSN-15oi.

Table 4: Physical Parameters derived from the off-axis jet model of §3.3. The
constraint on the SED peak translates into limits on physical parameters. We
break the degeneracy using the constrained $\nu_{q}=\nu_{\rm cool,jet}$ to
solve for $\epsilon_{\rm B,jet}$, and assuming $\epsilon_{\rm e,jet}=0.1$. The
last column gives the transverse size of the emitting region. As can be seen,
the VLBA $3\sigma$ upper-limit on the source size of $<9\times 10^{18}$ cm is
non-constraining in all the cases.

SED | $\delta t_{\rm jet}$ | $\theta_{\rm obs}$ | $\epsilon_{\rm B,jet}$ |  | $B_{\rm jet}$ | $U_{\rm jet}$ | $R_{\rm jet}$ | $n_{\rm e,jet}$ | $\Gamma_{\rm jet}$ | $R_{\rm{jet}}/\Gamma$
---|---|---|---|---|---|---|---|---|---|---
$\\#$ | (d) | (°) |  |  | (G) | ($\times 10^{52}$ erg) | ($\times 10^{18}$ cm) | (cm-3) |  | ($\times 10^{17}$ cm)
Times measured as days since discovery |
9 | $2129^{*}$ | $30$ | $0.1$ |  | $0.22^{+0.02}_{-0.02}$ | $33.7^{+3.7}_{-3.4}$ | $49.5^{+0.1}_{-0.1}$ | $0.15^{+0.06}_{-0.04}$ | $59^{+4}_{-5}$ | $\sim 8.4$
10 | $2660$ | $30$ | $0.003$ |  | $<0.04$ | $>51$ | $>37.1$ | $>0.3$ | $>41$ | $\sim 9.0$
9 | $2129^{*}$ | $90$ | $0.1$ |  | $0.25^{+0.03}_{-0.03}$ | $6.0^{+0.5}_{-0.6}$ | $6.58^{+0.02}_{-0.02}$ | $0.9^{+0.2}_{-0.2}$ | $8^{+1}_{-1}$ | $\sim 8.6$
10 | $2660$ | $90$ | $0.015$ |  | $<0.07$ | $>5.2$ | $>6.24$ | $>0.8$ | $>6$ | $\sim 1.0$
Times measured as days elapsed since T${}_{0}=1471$ d[a] |
9 | $658^{*}$ | $30$ | $0.1$ |  | $0.14^{+0.01}_{-0.01}$ | $2.0^{+0.2}_{-0.2}$ | $15.23^{+0.03}_{-0.03}$ | $0.13^{+0.04}_{-0.03}$ | $25^{+2}_{-2}$ | $\sim 6.0$
10 | $1189$ | $30$ | $0.051$ |  | $<0.07$ | $>4.7$ | $>24.9$ | $>0.1$ | $>26$ | $\sim 9.6$
9 | $658^{*}$ | $90$ | $0.1$ |  | $0.15^{+0.02}_{-0.02}$ | $0.32^{+0.03}_{-0.04}$ | $1.94^{+0.02}_{-0.02}$ | $0.7^{+0.2}_{-0.2}$ | $3.2^{+0.2}_{-0.3}$ | $\sim 6.1$
10 | $1189$ | $90$ | $0.293$ |  | $<0.14$ | $>1$ | $>4.1$ | $>0.1$ | $>4$ | $\sim 1.0$

Note. — ∗ These values are equipartition values, and any deviation from
equipartition will result in an increase in the energy and density estimate.

##  4 Discussion

Figure 10: Bottom Panel: Multi-band light-curve evolution of ASASSN-15oi from
the time of discovery until $\sim 3000$ d. The thermal emission is represented
by squares, and the non-thermal emission in circles. We plot the bolometric
UVO emission in green. The UVO bolometric luminosity was calculated only for
the epochs where enough spectral coverage was present across the UV and
optical bands. At $\sim 3000$ d post-disruption, the UVOT-m2 band luminosity
($\nu L_{\nu}$ at $\approx 1.5\times 10^{15}\,$Hz; small empty green circles)
converges to a constant value, in contrast with continuing variability in the
non-thermal X-rays. We show a dotted line with the trend $\propto t^{-3/2}$
predicted by the cooling envelope model for the optical luminosity. The
thermal bolometric X-ray luminosity is presented with light purple squares.
The non-thermal power-law (PL) component of the X-rays in the energy range
0.3–10 keV is plotted with dark purple circles. The non-thermal radio ($\nu
L_{\nu}$ at $\nu\sim 7.5$ GHz) is plotted in orange, where the VLBA
observation is presented with an empty circle. _Top Panel:_ We plot the ratio
of the total observed thermal bolometric luminosities $L_{X,BB}+L_{UVO}$ to
$L_{\rm{Edd}}$ at $\lesssim 300$ d. We note that it remains constant between
$\delta t\approx 80-230$ d, with the rise in thermal X-ray emission
compensating for the decline in the UVO emission.

Figure 10 shows the contemporaneous evolution of the emission associated with
ASASSN-15oi at all wavelengths. Here is a brief overview of how the luminosity
changes over time at each wavelength:

  1. 1.

The UV/optical (UVO) bolometric luminosity ($L_{\rm UVO,bol}$) remains stable
for the first $\sim 50$ d (with the luminosity consistent within $1\sigma$)
and subsequently shows a steep decline. It plateaus starting at $\delta
t\approx 200$ d for $\sim 100$ d before the optical luminosity fades to the
host galaxy level. In contrast, the UV luminosity continues to plateau out to
$\sim 3000$ d as an excess of emission compared to the host galaxy.

  2. 2.

The X-ray luminosity has two components characterized by a blackbody and a
power-law spectrum, respectively. The X-ray blackbody flux shows little to no
variation for the first $\sim 80$ d. Over the following $\sim 150$ d, it
brightens significantly by a factor of $\sim 6$, accompanied by an increase in
$R_{\rm BB}$ but not $T_{\rm BB}$. Similar to the UVO emission, the X-ray
blackbody flux shows little variation from $\delta t\sim 200-300$ d. The
blackbody X-rays then fade to non-detectable levels at $\delta t>1400$ d.

  3. 3.

The top panel of Figure 10 shows the total observed thermal bolometric
luminosity, $L_{\rm bol}=L_{\rm{UVO,bol}}+L_{\rm{X,BB,bol}}$, where
$L_{\rm{UVO,bol}}$ is adopted from Hinkle et al. (2021) and
$L_{\rm{X,BB,bol}}$ is calculated using the best-fitting $R_{\rm BB}$ and
$T_{\rm BB}$ in Table A.2. As can be seen, the thermal bolometric luminosity
remains constant during the period $\delta t\sim 80-230$ d before abruptly
declining. As noted in the above points, the UVO and thermal X-ray
luminosities show simultaneous opposite trends between $\sim 80-230$ d, and
add up to a constant $L_{\rm bol}$, suggesting that the UVO and thermal X-ray
emission are related.

  4. 4.

The non-thermal X-ray flux remains stable (with luminosity consistent within
$1\sigma$) up to $\delta t\approx 230$ d (this timescale coincides with the
blackbody X-ray peak), thereafter increasing as $\propto t^{4}$. The
luminosity shows a further plateau starting from $\delta t\approx 330$ d to
$\delta t\approx 1440$ d. At $\delta t>1440$ d, there is significant
variability with fluctuations as $\sim t^{\pm 9}$, observed at timescales of
$\sim 1$ year. In our last observation, the luminosity fades below detectable
levels, exhibiting a $\propto t^{-24}$ decline following the $\delta t\approx
2580$ d detection.

  5. 5.

In the radio, ASASSN-15oi exhibits two distinct flares, with the first radio
detection at $\delta t=182$ d. It rises from the earlier non-detections as
$F_{\nu}\propto t^{4.5}$ and subsequently declines as $\sim t^{-1}$.

  6. 6.

The second radio flare was first detected at $\delta t\approx 1471$ d (with a
rise of $\sim t^{4}$ from the last observation of the first flare) and
subsequently fades as $\propto t^{-1.5}$ from $\delta t\gtrsim 1741-2660$ d.
Between the $2660$ d and $2970$ d observations, the light curve declines
steeply as $t^{-7}$.

Observations at UVO wavelengths and of the blackbody component of the X-ray
radiation can be best described as thermal emission with maximum temperatures
of $\approx 5\times 10^{4}$ K, and $\approx 6\times 10^{5}$ K, respectively.
The associated radius of the thermal X-ray emission is $\sim(2-13)\times
10^{11}\,\rm{cm}$, which is comparable to the inner regions ($\lesssim
4r_{\rm{g}}$) of an accretion disc around a $M_{\rm BH}=2.5\times
10^{6}\,M_{\odot}$ non-rotating SMBH111111We provide other host galaxy mass
estimates of ASASSN-15oi that have been reported in the literature in Appendix
F, and note that using these other estimates has no major impact on our
conclusions.. This $M_{\rm BH}$ was reported by (Gezari et al. 2017); and we
adopt this value for our subsequent analysis. The UVO emission originates from
a region extending out to $\sim 10^{15}\,\rm{cm}>>r_{\rm g}$. Conversely, both
the emission detected at radio wavelengths, and the contribution of the power-
law component to the observed X-rays, can be characterized as non-thermal.
Below we discuss the possible physical origin of each emission component.

###  4.1 Thermal Emission from ASASSN-15oi as explained by the “cooling
envelope” model

In a previous investigation of ASASSN-15oi (Gezari et al., 2017) that extended
to $\delta t\sim 600$ d, it was suggested that the prompt UVO emission
originated in shocks resulting from stream-stream collisions during the
process of circularization, but owing to inefficiencies in this process, the
formation of the accretion disc was postponed causing a delayed rise in
thermal X-rays (at $\delta t\sim 100$ days). Motivated by points $\\#$1, 2,
and 3 in the above list, we explore an alternate scenario of a cooling
envelope model proposed by Metzger (2022), where the UVO and thermal X-rays
can be explained in a unified scenario. It is similar to the assumptions made
by Gezari et al. (2017) in that the accretion is delayed. However, the
difference is that in the cooling envelope model, the debris circularizes
promptly and efficiently (e.g., as seen in recent simulations, Steinberg &
Stone 2024), and forms a quasi-spherical pressure-supported envelope. The
envelope undergoes Kelvin-Helmholtz contraction and cools radiatively
resulting in a fading UV and optical luminosity, as observed. As the envelope
is contracting, material is gradually accreted onto the SMBH causing the
delayed rise in the X-rays. This scenario is more appealing for explaining the
decline in the UV/optical bolometric luminosity together with the rise in
thermal X-ray emission and the subsequent UV/optical/X-ray luminosity
plateaus.

In the cooling envelope model, the debris stream promptly circularizes on the
fallback timescale of the most tightly bound debris according to

$t_{\rm{fb}}\simeq 41\,\rm{d}\left(\frac{\emph{k}}{0.8}\right)^{-3/2}\,M_{\rm
BH,6}^{1/2}\,m_{*}^{1/5}$ (4)

where $k$ is the constant related to stellar structure and rotation prior to
disruption, and is taken as $k=0.8$ for a $\gamma=5/3$ polytropic star (as
assumed in Metzger 2022); $M_{\rm BH,6}$ is the mass of the SMBH in units of
$10^{6}M_{\odot}$ and $M_{*}=m_{*}M_{\odot}$ is the mass of the disrupted
star. Assuming that the disruption occurs at the time of the optical
discovery, when a star with mass $m_{*}=1\,M_{\odot}$ is disrupted on a path
with a penetration factor $\beta=1$ (with $k\simeq 0.8$), a pressure-supported
quasi-spherical envelope is formed at $t_{\rm fb}\approx 60$ d 121212If the
timescale of envelope formation, and hence $t_{\rm{fb}}$, is the same as the
time at which the UVO luminosity starts decaying at $t=45$ d, the disrupted
star will have m${}_{*}\approx 0.2\,\rm{M_{\odot}}$. On the other hand, if we
assume $m_{*}=1\,\rm{M_{\odot}}$, we get M${}_{\rm{BH}}\approx 1.2\times
10^{6}\,\rm{M_{\odot}}$, lower than most of the mass estimates in the
literature, but consistent with the studies by Wevers et al. (2019, 2020);
Mummery et al. (2024). None of these mass estimates will significantly change
our results. (plotted in grey dotted line in Figure 10).

The cooling envelope model predicts an initial photospheric radius of
$R_{\rm{ph}}\approx 6\times 10^{14}\,\rm{cm}$ (eq. 17 in Metzger 2022),
similar to the observed $R_{\rm ph}\sim 2\times 10^{14}$ cm of the optical
emission from Hinkle et al. (2021) at $t=t_{\rm{fb}}$. The initial optical
luminosity of $2.5\times 10^{43}\,\rm{erg/s}$ at $\nu=6.8\times 10^{14}\,$Hz
predicted by this model (given by their eq. 32 for mass estimates used here)
is in good agreement with the observed optical luminosity of $\sim 1.5\times
10^{43}\,\rm{erg/s}$ at $t=t_{\rm{fb}}$. As the envelope contracts, the
optical luminosity decreases while the accretion rate increases, leading to a
delayed rise in the X-rays. We see both the decrease in optical luminosity and
rise in X-ray luminosity over a period of $\sim 150$ days.131313We note that
the declining opacity of the envelope and/or a widening of the accretion
funnel may further contribute to the increased X-ray luminosity.

If there is sufficient energy feedback from accretion, the envelope remains
“puffed up”, i.e., depending on how efficiently accretion energy goes into the
envelope vs. being radiated, it can result in a flat light curve at all
frequencies. We calculate the start time of this phase using the envelope-
radius evolution eq. 27 in Metzger 2022 (also plotted in grey dotted line in
Figure 10). The observed R${}_{\rm{ph}}\approx 8\times 10^{13}$ cm during this
phase matches the model’s prediction (given by their eq. 37). Another robust
prediction of the cooling envelope model is for the total radiated luminosity
to remain constant at the Eddington luminosity ($L_{\rm Edd}$) while the
envelope is contracting. In ASASSN-15oi the total thermal bolometric
luminosity ($L_{\rm bol}$) indeed remains constant (from $t_{\rm fb}$ until
the accretion peak at $230$ d; top panel in Figure 10), although at sub-
Eddington levels with $L_{\rm bol}\sim(0.2-0.3)L_{\rm{Edd}}$ which are
consistent with other TDEs (e.g., Wevers et al., 2017). This can be reconciled
with the expectations if either most of the radiation is emitted at
unobservable EUV wavelengths, and/or if the uncertainty in $M_{\rm BH}$ leads
to an error in the calculation of $L_{\rm Edd}$.

With this set-up, the cooling envelope model predicts that the envelope would
be completely accreted by $\delta t\sim 350$ d (their eq. 38; plotted in grey
dotted line in Figure 10). However, more realistically, the envelope might
settle into an unobscured disc post X-ray peak, which can be modeled as a
viscously spreading disc (e.g., Cannizzo et al., 1990; Shen & Matzner, 2014;
Mummery, 2021). The resulting decrease in the inner disc temperature would
account for the exponential decline in thermal X-rays observed after $\sim
350$ d. As the disc spreads outwards to larger radii, the emitting area
increases while it cools, resulting in an almost constant emission that
dominates the UV wavelengths (as these wavelengths lie near the Rayleigh-Jeans
part of the disc spectrum). This is indeed the case in ASASSN-15oi, even at
very late-times ($\delta t\approx 2900$ d). Previous studies by van Velzen et
al. (2019), Mummery & Balbus (2020); Mummery et al. (2024), and Guolo et al.
(2023), have also demonstrated that the late-time UV flattening observed in
many other TDEs (e.g., ASASSN-14li, iPTF16fnl) is disc dominated and can be
explained by longer ($\sim\mathcal{O}(10^{3})$ d) viscous timescales at these
larger radii.

Finally, while the predictions of the cooling envelope model and the
subsequent evolution to a bare accretion disc matches well with most of the
thermal emission, certain other features observed in ASASSN-15oi remain
unexplained. Particularly, the constant $L_{\rm UVO,bol}$ at $\delta t\lesssim
t_{\rm fb}=60$ d is not explained by the current analytical model. One can
speculate that this flattening results from the complex processes taking place
prior to/during the envelope formation, perhaps even due to stream-stream
collisions as proposed by Gezari et al. (2017). Regarding the X-ray emission,
the low S/N in the individual _Swift_ -XRT observations during this period
limits our understanding of the X-ray emission behavior at early-times. We
also currently lack an explanation for the observed temporal evolution of the
temperature and radius of the thermal X-ray emitting region. A gradual rise in
the accretion rate is expected to result in an increase in the temperature and
a decrease in the radius. Here instead, the X-ray blackbody temperature
exhibits little variation (marginally constant or else gradually decreasing
with time as $T_{\rm BB}\propto t^{-0.2}$) and the best-fitting blackbody
radius ($R_{\rm BB}$) seems to increase ($\sim 1.3\times 10^{12}$ cm) near the
epochs of the peak accretion before returning to the pre-peak levels ($\sim
0.3\times 10^{12}$ cm). This would be a problem if we were looking at a bare
accretion disc at early times, however, as the geometry of the cooling
envelope model is complex, we can expect an unconventional evolution of the
thermal X-ray parameters depending on our observing angle.

###  4.2 Non-thermal Emission from ASASSN-15oi

Figure 11: ASASSN-15oi in the context of other TDEs in the literature. The
first radio flare of ASASSN-15oi shows energetics ($U_{\rm eq}$ from §3.2)
similar to other non-relativistic TDEs, while the second flare is the most
energetic of the subset. For the purpose of comparison, we re-calculate the
energetics of other TDEs using the same Chevalier (1998) formulation that we
used for ASASSN-15oi along with assuming equipartition. The two estimates for
AT 2018hyz and AT 2019dsg are due to two different inferences of the outflow
launch time. We also include some jetted TDEs that make-up a very small
fraction of all TDEs. Other references: ASASSN-14li (Alexander et al. 2016);
AT 2018hyz Cendes et al. (2022); CNSS J0019+00 (Anderson et al., 2020); AT
2019dsg (Cendes et al., 2021a); AT 2020opy (Goodwin et al., 2022); AT 2020vwl
(Goodwin et al., 2023b).

Unlike the thermal emission, the spectral and temporal evolution of the non-
thermal emission (see points #4, #5 and #6 in the overview list of §4) is
extremely complex. In this section, we briefly speculate on different physical
processes/origins and additionally investigate whether the radio and non-
thermal X-rays are physically related.

####  4.2.1 Possible Origin of the First Radio Flare

Figure 12: Broad-band radio-to-X-ray SEDs of ASASSN-15oi associated with the
radio flares at $\delta t\approx 233$ d (top, also coinciding with the peak of
the X-rays) and $\delta t\approx 2660$ d, (bottom). Grey shaded areas are the
$3\sigma$ ranges of the best-fitting spectra extrapolated from the radio
observations to the X-rays. We also plot the median $\alpha_{\rm thin}$ and
$\alpha_{q}$ segments as dotted lines. The open circles are UVOT-M2
observations. The plotted X-ray observations are the power-law component. At
$233$ d, the X-rays are consistent within $3\sigma$ of the extrapolation.
However, the X-rays at $2580$ d (closer in epoch to the radio observations)
are clearly in excess. The X-ray upper-limit at $\approx 2794$ d, the next
closest epoch to the radio, is also shown.

The first radio flare was analysed in detail by Horesh et al. (2021a). Our
results are broadly consistent with their study. A particular feature of the
system parameters determined here is the significant jump in the density
estimates between the SEDs at $\delta t\approx 197$ d and $233$ d, similar to
the inferences by Horesh et al. (2021a). Horesh et al. (2021a) suggested that
the outflow responsible for the first radio flare was not likely to be
launched at the time of disruption but was delayed as a consequence of an
accretion state transition. Zhuang et al. (2024) proposed that the first radio
flare is powered by the interaction of an outflow with three different clouds
present around the SMBH at $\sim$ parsec scales. Their model explains the
observed temporal evolution, although a close examination of their fig. 13
reveals discrepancies with the observed SEDs. Here, we discuss our
interpretation of the power source of the first radio flare.

The energy and the velocity of the outflow that powers the initial radio flare
are similar to other non-relativistic TDEs (as seen in Figure 11). However,
the timescale at which the first radio emission appears in ASASSN-15oi and the
steep rise ($F\propto t^{4}$) from the prior non-detections are unusual
compared to non-relativistic TDEs with “prompt” emission (e.g., AT 2019dsg in
Figure 5). Among commonly invoked scenarios that can also explain the somewhat
higher kinetic energy in this case (e.g., compared to the energy in
ASASSN-14li as inferred by Krolik et al. 2016), we disfavor the scenario
whereby the radio emission is powered by the interaction of a super-Eddington
accretion-driven wind outflow with the ambient medium (Alexander et al., 2016;
Cendes et al., 2021a). This would require large accretion rates that are not
inferred in ASASSN-15oi until _after_ the appearance of the first radio flare.

Instead, we find the case of a stream-stream Collision Induced Outflow (CIO)
proposed by Lu & Bonnerot (2020) more likely. Episodic mass ejections during
the envelope formation (at timescales $\lesssim t_{\rm fb}\sim 60$ d) are
expected due to the repeated orbits of the self-colliding streams around the
SMBH. This process creates a clumpy medium with fast moving material driving
multiple shocks of varying energies (and possibly different microphysical
paramaters). For a significant amount ($>20\%$) of initially unbound tidal
debris moving at $0.01-0.1\,c$, CIO is expected to dissipate $10^{49}-10^{52}$
erg kinetic energy over a diverse set of timescales. It is subsequently
possible in this scenario that an outflow could decelerate over $\sim 100$ d
and power the first radio flare. The radio SEDs and derived velocity and
energy from the first flare ( see §3.2) are consistent with this scenario
involving multiple outflows in an inhomogeneous medium. Detailed modeling for
this scenario is left for future work.

####  4.2.2 Possible Origin of the Second Radio Flare

As seen in Figure 11, the outflow that powers the second radio flare carries
substantially more energy than the first flare, suggesting distinct physical
origins. In the recent study by Sato et al. (2024), these authors modeled the
two flares (with observations at $\delta t<1500$ d) with a structured jet
model consisting of a wide jet (responsible for the first flare) and a narrow
jet (responsible for the second flare) with different shock microphysics,
essentially the same scenario as the two distinct outflows that we propose
here. Their conclusions are based solely on the temporal evolution. Their
narrow jet (with $\theta_{\rm jet}\sim 6\arcdeg$ and $\theta_{\rm obs}\sim
70\arcdeg$) component that is responsible for the second radio flare carries
kinetic energy ($E_{\rm{k}}\sim 10^{52}$ erg) similar to other TDEs in the
literature. It is unclear, however, if their model can explain the observed
spectral evolution.

Here, we propose that the second radio flare is powered by an outflow
different from that of the first radio flare, and was likely launched when the
accretion rate peaked (at $\gtrsim 200$ d) in the context of the cooling
envelope model discussed in §4.1. The outflow(s) may manifest as a
relativistic jet or a quasi-spherical mildly-relativistic wind interacting
with the ambient medium. However, the details of the outflow powering the
second radio flare are not well captured by simplified models like those
presented in §3, invoking the need for a more intricate system, perhaps
similar to the one proposed for the first radio flare in the previous section,
but with a more powerful source that is launched significantly later after the
disruption.

####  4.2.3 Possible Origin of the Non-thermal X-rays

If the radio emission is indeed powered by synchrotron emission, it may extend
to X-ray energies as well. We verify here if the non-thermal X-rays and first
radio flare share the same synchrotron spectrum. As can be seen in the top
panel of Figure 12, the non-thermal X-rays fall within the $3\sigma$ region of
the extrapolated models141414As discussed in §3.2.1, the break in the radio
SED is likely not $\nu_{\rm cool}$. The real synchrotron cooling break can
possibly lie between radio and X-rays and cause an even steeper spectral
segment which when extrapolated to X-ray wavelengths might make the observed
X-rays appear in excess. at $\sim 233$ d (the only epoch when both X-rays and
radio were observed simultaneously). However, X-ray emission existed prior to
the first radio flare making them causally unrelated, unless the radio
emission was absorbed at frequencies at least as high as $22$ GHz for the
first $180$ d. An extremely large $n_{\rm e}\sim 10^{7}\,\rm{cm^{-3}}$ is
required if the source was synchrotron self-absorbed and its SSA spectrum were
to peak at $\sim 22$ GHz with $F_{\nu}\sim 0.06$ mJy at $\lesssim 180$ d,
which is unlikely. The higher densities found at $\sim 180$ d in §3.2 could
also potentially result in free-free absorption of the radio emission (Weiler
et al., 2002). The free-free absorption optical depth is given by $\tau_{\rm
FFA}\propto T^{-1.35}\nu^{-2.1}n_{e}^{2}l$ (Mezger & Henderson 1967), where
$T$ is the temperature of the absorbing gas and $l$ is the optical path along
the line of sight. With the estimated $n_{e}$ for $\delta t=182$ d SED in
Table 2, we find $\tau_{\rm FFA}<1$ at $\sim 22$ GHz. Therefore, if there was
emission present at this frequency, it is unlikely to be affected by either
synchrotron self-absorption or free-free absorption. Finally, the evolution of
power-law X-rays and the radio emission is distinct, as can be seen in Figure
10, challenging this interpretation further.

Furthermore, there is no strong evidence that the second radio flare and the
late-time non-thermal X-ray emission share the same synchrotron spectrum
because: (1) as seen in the lower panel of Figure 12, the $\delta t=2580$ d
X-rays (closest to the epoch of the $\delta t\approx 2660$ d radio SED) are in
excess of the extrapolation of the best-fitting radio model beyond $3\sigma$.
Therefore, the X-rays likely require a different mechanism. (2) In the latest
observations, the steep decline in the X-ray emission at $=2790$ d precedes
the steep decline in the radio emission at $=2970$ d, also making them
temporally inconsistent.

A common source for non-thermal X-rays in TDEs, independent of synchrotron
emission that powers radiation at radio wavelengths, is the inverse Compton
scattering of the lower-energy disc photons by an electron corona. Such
coronae were identified in AT 2019ehb (Yao et al., 2022), in AT 2018fyk
(Wevers et al., 2021) and a few others (Guolo et al., 2023), and can
form/become strong during soft-to-hard state transitions (e.g., Done et al.,
2007), similar to X-ray binary systems (XRBs). The phenomenology of
ASASSN-15oi does hint at state transitions of hard $\rightarrow$ soft
$\rightarrow$ hard (top panel in Figure 2), and a direct comparison to the
above studies suggest the presence of a corona at least at $\delta t\gtrsim
300$ d, after the soft-to-hard transition. A hard-to-soft transition was
observed in AT 2019azh in Sfaradi et al. (2022), followed by a late-time radio
flare at $\sim 200$ d, similar to timescales of the first radio flare of
ASASSN-15oi. Here, the first radio flare occurs during the hard-to-soft
transition, more alike XRBs, as also invoked by Horesh et al. (2021a).

Assuming that the early- and late-time non-thermal X-rays share the same
physical origin, we find several temporal features that can also support the
corona (or a near-disc) origin. First, the power-law component declining when
the blackbody component (originating near the inner disc regions) showed an
increase at $\sim 230$ d hints that the non-thermal X-rays are affected by the
accretion process in the inner disc region. Second, the non-thermal X-rays
showing significant variability at $>1400$ d may hint at changes in the disc
(and/or corona). We note that the outer disc is likely stable, as the late-
time UV emission originating in the outer regions (as discussed in §4.1)
continues to plateau. And finally, the lag between the steep decline in the
non-thermal X-rays and the steep decline in the radio at $\sim 3000$ d can
possibly be explained as a delay caused by the propagation of information from
the inner regions of the disc to the radio-emitting components at larger
distances from the SMBH (De Colle et al., 2012).

We briefly speculate on one possible scenario where all these characteristics
can be accounted for. We base our arguments on the premise that physical
processes governing accretion are universal around BHs of different masses,
and therefore, we draw inspiration from the phenomenon observed in AGN and XRB
systems. The scenario is that of a hybrid disc, with the inner disc
transitioning from a disc/corona system (possibly representative of the system
at $\lesssim 1400$ d) to an Advection-Dominated Accretion Flow (ADAF; e.g.,
Narayan & Yi 1994; Czerny et al. 2000). The outer disc is likely a
geometrically thin, optically thick stable standard disc. This transition in
the inner regions can be triggered by a decrease in the mass-accretion rate
beyond a critical value, as often seen in XRBs in their low-hard state (e.g.,
Esin et al., 1997; van der Klis, 2004). In XRBs/AGNs, such a transition
typically occurs at $\lesssim 10^{-2}\dot{M}_{\rm Edd}$, where ${\dot{M}}_{\rm
Edd}$ is the Eddington mass accretion rate, which for our SMBH mass would
translate to $\sim 10^{42}$ erg/s, as observed. Furthermore, at the interface
between the inner ADAF and the outer regions, there may exist a narrow
unstable zone where radiation pressure instabilities can induce the observed
X-ray variability. The instabilities are driven on viscous timescales which
can be shortened depending on the size of this unstable zone, and can range
over timescales of $\sim$ months - years (e.g., Sniegowska et al., 2020),
aligning with our observed non-thermal X-ray variability. As an example, a
recent study by Veronese et al. (2024) attributed the long-term X-ray
variability (at timescales of $\sim 10$ years) in Mrk 1018, a changing-look
AGN, to a similar accretion flow transition in the inner disc.

There are other physical processes such as wind-torus interaction proposed by
Mou et al. (2021) and Mou & Wang (2021) that can produce variability in the
non-thermal emission at late-times on $\sim$ months - years timescales. (Such
torii are usually present at $\sim 0.1$ pc around AGNs.) In this case, the
model-predicted luminosity $\gtrsim 10^{41}$ erg/s matches the observed power-
law X-ray luminosity. However, first, there are no infrared observations of
ASASSN-15oi that could have confirmed a presence of a torus. Furthermore, the
archival mid-infrared WISE colors of the host galaxy also do not support the
presence of a strong AGN around which such torii are usually present. And
second, if this were the case, that would imply that the early- and late-time
non-thermal X-rays are powered by different sources. We also want to emphasize
that other TDEs have also shown late-time X-ray variability, albeit on shorter
timescales ($\lesssim$ days in e.g., in AT 2018fyk,Wevers et al. 2021). Due to
our sparse temporal coverage, our observations are not sensitive to
variability on $\sim$day timescales, if it existed. Finally, we stress that
our discussion here is only speculative, and we leave a more in-depth
quantitative analysis, including testing for variability of the late-time non-
thermal X-rays at shorter timescales to future work.

##  5 Summary and Conclusions

In this study we have presented one of the most extensive datasets for a TDE,
namely ASASSN-15oi, and our analysis thereof. ASASSN-15oi was observed across
the electromagnetic spectrum using an array of telescopes including the VLA,
VLBA, MeerKAT, ATCA, ALMA, Swift-UVOT, Swift-XRT, and XMM-Newton. We re-
reduced and re-analysed the previously reported UV and X-ray observations here
to provide a homogeneous dataset. We also present new observations obtained
through our coordinated multi-wavelength campaigns, particularly following the
occurrence of the second radio flare, at $\delta t>1400$ d until $\sim 8$
years. We note that ASASSN-15oi was the first TDE observed to have multiple
radio flares and highlights the importance of long-term monitoring of TDEs. We
study the emission at different wavelengths individually, but also investigate
any physical connection between them within the framework of existing models.
We summarize our findings below.

We divide the observed emission of ASASSN-15oi into thermal and non-thermal
emission. We treat the emission dominating the optical and UV wavelengths and
the blackbody component of the X-rays as thermal. We establish (in §4.1) that
the _cooling envelope_ model proposed by Metzger (2022) explains the evolution
of the thermal emission in ASASSN-15oi extremely well. In this model, the
radiative cooling of a quasi-spherical envelope formed after the stellar
disruption drives the optical/UV emission, different from the interpretations
of typical TDEs, where the optical/UV emission is either produced in stream-
stream collisions, or via reprocessing of the X-rays by the surrounding
material. This model naturally explains the delayed rise of the thermal X-rays
as more and more material gets accreted onto the SMBH. The envelope then
transforms into a bare accretion disc that spreads outwards on long viscous
timescales, explaining the eventual decline in the thermal X-rays in the inner
regions and the late-time persisting UV plateau emitting from the outer disc.

Unlike the thermal emission, qualitatively explaining the non-thermal
emission, i.e. the power-law component of the X-rays and the radio emission,
is more challenging. In §4.2, we posit the first ($\delta t\lesssim 600$ days)
and second ($\delta t\gtrsim 1400$ days) radio flares to have distinct
origins. A simplified approach of either a spherical blastwave, or an
ultrarelativistic off-axis jet interacting with the ambient medium alone
cannot explain the observed spectral and temporal radio evolution without
requiring unphysical conditions. Therefore, to account for the spectral
variations and the sharp jumps in the physical parameters of the system (as
derived in §3.2) within the first radio flare, we invoke a more complex system
with ‘multiple shocks driven in a clumpy medium’ such as that produced by
stream-stream collision induced outflows (discussed in §4.2) during the
envelope formation. The second radio flare is possibly produced by a similarly
complex, but more powerful outflow launched as a result of the accretion rate
reaching its peak in the context of the cooling envelope model. Finally, the
non-thermal X-rays and the radio emission do not arise from same synchrotron
spectra. In §4.2.3, we briefly discuss the near-disc origin of the non-thermal
X-rays. We emphasize that this is purely speculative, and future monitoring of
ASASSN-15oi and developing more sophisticated models will be crucial to
confirm the origin of its late-time emission.

In conclusion, the multiwavelength observations of ASASSN-15oi reveal a
complex picture of TDEs and their long-term evolution. The detailed dataset
allows us to probe the different emission mechanisms at various frequencies
and phases in the “life” of a TDE. This study emphasizes the importance of
late-time observations across the electromagnetic spectrum to better
understand TDEs. As a final example, the late-time monitoring may help address
the "missing energy" problem in TDEs (as detailed in Lu & Kumar 2018) where
the observed radiated energy in most TDEs is $\approx 10^{51}$ erg (e.g.,
Mockler & Ramirez-Ruiz, 2021) falling short of the expected $10^{52}-10^{53}$
erg. Since its discovery, ASASSN-15oi has radiated $2\times 10^{51}$ erg in
X-rays, UV and optical, with the first radio flare contributing an additional
a few $\times 10^{49}$ erg of kinetic energy. We further find that the second
radio flare carries an energy $\gtrsim 10^{51}$ erg (in §3.2), potentially
more if a jet is involved. This suggests that kinetic energy of the outflows
is a substantial fraction of the overall energy budget and that multiple
delayed radio flares could be more common in TDEs (as indeed found in Cendes
et al. 2023) harboring the energy deficit. Thus, long-term monitoring of TDEs
is crucial, not only to understand their complexities, but also to uncover
hidden or delayed emission sources that may resolve the missing energy
problem. Exploring the late-time phase in TDEs has only been a recent
occurrence, and ASASSN-15oi has clearly demonstrated its importance, but also
a need for more complex and nuanced models to incorporate the diverse and
evolving nature of TDEs.

## Acknowledgments

The authors thank Clement Bonnerot, Damiano Caprioli, Brian Metzger, and
Juergen Ott from the NRAO helpdesk for helpful discussions. We acknowledge the
use of public data from the Swift data archive. XMM-Newton is an ESA science
mission with instruments and contributions directly funded by ESA Member
States and NASA. The National Radio Astronomy Observatory is a facility of the
National Science Foundation operated under cooperative agreement by Associated
Universities, Inc. The MeerKAT telescope is operated by the South African
Radio Astronomy Observatory, which is a facility of the National Research
Foundation, an agency of the Department of Science and Innovation. The
Australia Telescope Compact Array is part of the Australia Telescope National
Facility which is funded by the Australian Government for operation as a
National Facility managed by CSIRO. This paper makes use of the following ALMA
data: ADS/JAO.ALMA#2019.1.01166.T. ALMA is a partnership of ESO (representing
its member states), NSF (USA) and NINS (Japan), together with NRC (Canada),
NSTC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ.

A. Hajela was supported by a Future Investigators in NASA Earth and Space
Science and Technology (FINESST) award #80NSSC19K1422 during the initial
stages of this project. A. Hajela also acknowledges support from the Carlsberg
Foundation Fellowship Programme by Carlsbergfondet. K. D. Alexander and C. T.
Christy acknowledge support provided by the National Science Foundation
through award SOSPA9-007 from the NRAO and award AST-2307668. R. Margutti
acknowledges support by the National Science Foundation under award No.
AST-2221789 and AST-2224255. The TReX team at UC Berkeley is partially funded
by the Heising-Simons Foundation under grant 2021-3248 (PI: Margutti). M.
Bietenholz is grateful for computing and office support from York University,
Canada. A. Horesh is grateful for the support by the the United States-Israel
Binational Science Foundation (BSF grant 2020203) and by the Sir Zelman Cowen
Universities Fund. This research was supported by the ISRAEL SCIENCE
FOUNDATION (grant No. 1679/23).

##  Appendix A Broadband Observations of ASASSN-15oi

Table A.1: Swift-UVOT Photometry. All the magnitudes and the corresponding errors are reported in the AB magnitude system, and are corrected for galactic extinction.  Epoch (MJD) |  $\delta t$ (d) | Filter | Magnitude | Error |  | Epoch (MJD) |  $\delta t$ (d) | Filter | Magnitude | Error
---|---|---|---|---|---|---|---|---|---|---
57259.41 | 11.41 | v | 15.974 | 0.051 |  | 57336.40 | 88.4 | uvw1 | 19.039 | 0.099
57264.42 | 16.42 | v | 16.298 | 0.056 |  | 57339.43 | 91.43 | uvw1 | 18.991 | 0.101
57270.71 | 22.71 | v | 16.664 | 0.057 |  | 57342.10 | 94.10 | uvw1 | 19.059 | 0.124
57276.13 | 28.13 | v | 16.781 | 0.070 |  | 57345.79 | 97.79 | uvw1 | 19.261 | 0.150
57280.72 | 32.72 | v | 16.831 | 0.071 |  | 57348.41 | 100.41 | uvw1 | 19.319 | 0.113
57288.50 | 40.5 | v | 16.793 | 0.073 |  | 57468.80 | 220.80 | uvw1 | 20.265 | 0.197
57300.57 | 52.57 | v | 16.953 | 0.054 |  | 57484.95 | 236.95 | uvw1 | 20.532 | 0.153
57318.89 | 70.89 | v | 17.061 | 0.059 |  | 57508.58 | 260.58 | uvw1 | 20.416 | 0.103
57340.96 | 92.96 | v | 17.066 | 0.061 |  | 57527.29 | 279.29 | uvw1 | 20.450 | 0.113
57501.11 | 253.11 | v | 17.016 | 0.064 |  | 57572.84 | 324.84 | uvw1 | 20.596 | 0.127
57572.85 | 324.85 | v | 17.135 | 0.064 |  | 57602.41 | 354.41 | uvw1 | 20.714 | 0.148
57602.42 | 354.42 | v | 17.195 | 0.074 |  | 58674.29 | 1426.29 | uvw1 | 20.633 | 0.090
58674.29 | 1426.29 | v | 17.139 | 0.041 |  | 59020.30 | 1772.30 | uvw1 | 20.684 | 0.203
59649.93 | 2401.93 | v | 17.234 | 0.088 |  | 59649.93 | 2401.93 | uvw1 | 20.698 | 0.200
59784.74 | 2536.74 | v | 17.109 | 0.105 |  | 59828.39 | 2580.39 | uvw1 | 21.003 | 0.235
57259.40 | 11.40 | b | 15.995 | 0.039 |  | 57259.41 | 11.41 | uvm2 | 15.590 | 0.041
57259.42 | 16.42 | b | 16.374 | 0.042 |  | 57259.43 | 16.43 | uvm2 | 16.017 | 0.042
57268.75 | 20.75 | b | 16.542 | 0.043 |  | 57268.79 | 20.79 | uvm2 | 16.366 | 0.052
57272.57 | 24.57 | b | 16.808 | 0.047 |  | 57272.58 | 24.58 | uvm2 | 16.516 | 0.044
57276.12 | 28.12 | b | 16.919 | 0.049 |  | 57276.13 | 28.13 | uvm2 | 16.750 | 0.046
57280.71 | 32.71 | b | 17.046 | 0.051 |  | 57280.72 | 32.72 | uvm2 | 16.951 | 0.047
57285.64 | 37.64 | b | 17.147 | 0.065 |  | 57285.64 | 37.64 | uvm2 | 17.174 | 0.045
57291.48 | 43.48 | b | 17.241 | 0.067 |  | 57291.59 | 43.59 | uvm2 | 17.340 | 0.054
57294.61 | 46.61 | b | 17.358 | 0.074 |  | 57294.62 | 46.62 | uvm2 | 17.545 | 0.047
57300.26 | 52.26 | b | 17.355 | 0.071 |  | 57300.27 | 52.27 | uvm2 | 17.793 | 0.048
57303.66 | 55.66 | b | 17.406 | 0.081 |  | 57303.66 | 55.66 | uvm2 | 17.945 | 0.053
57306.52 | 58.52 | b | 17.345 | 0.075 |  | 57306.52 | 58.52 | uvm2 | 18.014 | 0.052
57309.48 | 61.48 | b | 17.462 | 0.080 |  | 57309.48 | 61.48 | uvm2 | 18.122 | 0.054
57312.20 | 64.20 | b | 17.349 | 0.086 |  | 57312.20 | 64.20 | uvm2 | 18.203 | 0.056
57318.77 | 70.77 | b | 17.573 | 0.085 |  | 57318.87 | 70.87 | uvm2 | 18.537 | 0.176
57324.08 | 76.08 | b | 17.630 | 0.123 |  | 57324.09 | 76.09 | uvm2 | 18.653 | 0.071
57328.14 | 80.14 | b | 17.644 | 0.093 |  | 57328.17 | 80.17 | uvm2 | 18.730 | 0.066
57333.48 | 85.48 | b | 17.634 | 0.100 |  | 57333.52 | 85.52 | uvm2 | 18.984 | 0.077
57336.40 | 88.40 | b | 17.649 | 0.116 |  | 57336.41 | 88.41 | uvm2 | 19.000 | 0.072
57340.73 | 92.73 | b | 17.687 | 0.089 |  | 57339.44 | 91.44 | uvm2 | 19.091 | 0.077
57347.12 | 99.12 | b | 17.817 | 0.098 |  | 57343.93 | 95.93 | uvm2 | 19.031 | 0.085
57501.10 | 253.10 | b | 17.914 | 0.065 |  | 57348.42 | 100.42 | uvm2 | 19.084 | 0.077
57572.84 | 324.84 | b | 17.907 | 0.061 |  | 57468.80 | 220.80 | uvm2 | 20.788 | 0.175
57602.41 | 354.41 | b | 17.861 | 0.064 |  | 57476.65 | 228.65 | uvm2 | 20.874 | 0.178
58674.29 | 1426.29 | b | 17.931 | 0.041 |  | 57497.32 | 249.32 | uvm2 | 21.166 | 0.180
59649.93 | 2401.93 | b | 17.890 | 0.077 |  | 57514.00 | 266 | uvm2 | 21.197 | 0.153
59784.74 | 2536.74 | b | 17.803 | 0.095 |  | 57531.25 | 283.25 | uvm2 | 21.153 | 0.234
57259.40 | 11.40 | u | 15.972 | 0.037 |  | 57572.85 | 324.85 | uvm2 | 21.767 | 0.185
57259.41 | 16.41 | u | 16.434 | 0.040 |  | 57602.42 | 354.42 | uvm2 | 21.251 | 0.154
57268.75 | 20.75 | u | 16.728 | 0.041 |  | 58674.29 | 1426.29 | uvm2 | 21.423 | 0.126
57272.57 | 24.57 | u | 16.964 | 0.044 |  | 59016.54 | 1768.54 | uvm2 | 21.373 | 0.290
57276.12 | 28.12 | u | 17.199 | 0.047 |  | 59649.93 | 2401.93 | uvm2 | 21.368 | 0.247
57280.71 | 32.71 | u | 17.460 | 0.050 |  | 59828.39 | 2580.39 | uvm2 | 21.488 | 0.313
57285.64 | 37.64 | u | 17.572 | 0.062 |  | 57257.83 | 9.83 | uvw2 | 15.957 | 0.039
57291.48 | 43.48 | u | 17.697 | 0.065 |  | 57259.40 | 11.40 | uvw2 | 15.986 | 0.039
57294.61 | 46.61 | u | 17.933 | 0.075 |  | 57259.42 | 16.42 | uvw2 | 16.300 | 0.040
57300.26 | 52.26 | u | 18.080 | 0.078 |  | 57268.75 | 20.75 | uvw2 | 16.455 | 0.043
57303.65 | 55.65 | u | 18.048 | 0.084 |  | 57272.57 | 24.57 | uvw2 | 16.656 | 0.041
57306.52 | 58.52 | u | 18.165 | 0.085 |  | 57276.12 | 28.12 | uvw2 | 16.842 | 0.041
57309.48 | 61.48 | u | 18.283 | 0.090 |  | 57280.72 | 32.72 | uvw2 | 17.044 | 0.042
57312.20 | 64.20 | u | 18.331 | 0.109 |  | 57285.64 | 37.64 | uvw2 | 17.157 | 0.044
57318.77 | 70.77 | u | 18.338 | 0.093 |  | 57291.49 | 43.49 | uvw2 | 17.312 | 0.046
57326.21 | 78.21 | u | 18.413 | 0.084 |  | 57294.62 | 46.62 | uvw2 | 17.331 | 0.045
57335.04 | 87.04 | u | 18.452 | 0.086 |  | 57300.27 | 52.27 | uvw2 | 17.550 | 0.046
57340.73 | 92.73 | u | 18.731 | 0.113 |  | 57303.66 | 55.66 | uvw2 | 17.577 | 0.048
57347.11 | 99.11 | u | 18.787 | 0.119 |  | 57306.52 | 58.52 | uvw2 | 17.756 | 0.049
57460.27 | 212.27 | u | 19.321 | 0.063 |  | 57309.48 | 61.48 | uvw2 | 17.815 | 0.049
57501.10 | 253.10 | u | 19.327 | 0.104 |  | 57312.20 | 64.20 | uvw2 | 17.933 | 0.052
57572.84 | 324.84 | u | 19.264 | 0.093 |  | 57318.77 | 70.77 | uvw2 | 18.168 | 0.053
57602.41 | 354.41 | u | 19.247 | 0.100 |  | 57324.08 | 76.08 | uvw2 | 18.254 | 0.064
58674.29 | 1426.29 | u | 19.264 | 0.057 |  | 57328.14 | 80.14 | uvw2 | 18.342 | 0.058
59649.93 | 2401.93 | u | 19.246 | 0.119 |  | 57333.48 | 85.48 | uvw2 | 18.548 | 0.066
59784.73 | 2536.73 | u | 19.074 | 0.142 |  | 57336.41 | 88.41 | uvw2 | 18.545 | 0.062
57259.40 | 11.40 | uvw1 | 15.770 | 0.040 |  | 57339.43 | 91.43 | uvw2 | 18.606 | 0.066
57259.41 | 16.41 | uvw1 | 16.153 | 0.041 |  | 57342.10 | 94.10 | uvw2 | 18.603 | 0.077
57268.75 | 20.75 | uvw1 | 16.459 | 0.042 |  | 57345.79 | 97.79 | uvw2 | 18.652 | 0.083
57272.57 | 24.57 | uvw1 | 16.678 | 0.044 |  | 57348.41 | 100.41 | uvw2 | 18.782 | 0.066
57276.12 | 28.12 | uvw1 | 16.985 | 0.046 |  | 57468.80 | 220.80 | uvw2 | 20.830 | 0.191
57280.71 | 32.71 | uvw1 | 17.207 | 0.047 |  | 57476.65 | 228.65 | uvw2 | 20.702 | 0.165
57285.64 | 37.64 | uvw1 | 17.419 | 0.050 |  | 57493.43 | 245.43 | uvw2 | 20.916 | 0.207
57291.48 | 43.48 | uvw1 | 17.667 | 0.053 |  | 57501.27 | 253.27 | uvw2 | 21.062 | 0.175
57294.61 | 46.61 | uvw1 | 17.782 | 0.056 |  | 57506.29 | 258.29 | uvw2 | 21.073 | 0.199
57297.05 | 49.05 | uvw1 | 18.047 | 0.078 |  | 57515.12 | 267.12 | uvw2 | 21.112 | 0.243
57300.26 | 52.26 | uvw1 | 18.059 | 0.059 |  | 57521.44 | 273.44 | uvw2 | 21.178 | 0.215
57303.65 | 55.65 | uvw1 | 18.239 | 0.069 |  | 57530.88 | 282.88 | uvw2 | 21.300 | 0.218
57306.52 | 58.52 | uvw1 | 18.313 | 0.067 |  | 57585.00 | 337 | uvw2 | 21.259 | 0.105
57309.47 | 61.47 | uvw1 | 18.337 | 0.066 |  | 57839.52 | 591.52 | uvw2 | 21.406 | 0.137
57312.20 | 64.20 | uvw1 | 18.496 | 0.076 |  | 58674.29 | 1426.29 | uvw2 | 21.521 | 0.102
57318.77 | 70.77 | uvw1 | 18.590 | 0.072 |  | 59016.54 | 1768.54 | uvw2 | 21.468 | 0.246
57324.08 | 76.08 | uvw1 | 18.861 | 0.104 |  | 59649.93 | 2401.93 | uvw2 | 21.464 | 0.197
57328.14 | 80.14 | uvw1 | 18.967 | 0.088 |  | 59828.39 | 2580.39 | uvw2 | 21.289 | 0.215
57333.48 | 85.48 | uvw1 | 18.992 | 0.093 |  |  |  |  |  |
Table A.2: Best-fitting results from the time-resolved X-ray spectral analysis
of ASASSN-15oi using _Swift_ -XRT (upper part) and XMM-Newton (lower part).
The data require two components of emission using a spectral model of the form
tbabs*(cflux*pow+cflux*bbody) within XSPEC. We adopted $N_{\rm
H,gal}=5.59\times 10^{20}\,\rm{cm^{-2}}$, $N_{\rm H,int}=0\,\rm{cm^{-2}}$,
redshift, $z=0.0484$. XMM-Newton (_Swift_ -XRT) observations are fitted in
0.2–12 keV (0.3–10 keV) energy range. Fluxes are reported in the 0.3–10 keV
energy range, uncertainties are reported at 68% confidence ($1\,\sigma$)
level, and upper limits are reported at $3\,\sigma$ confidence level.
$\Gamma_{X}$ is the power-law photon index, and $kT_{\rm BB}$ is the observed
blackbody temperature in keV units. For XMM-Newton we report the EPIC-pn
exposure times after removal of the time intervals affected by high
background.

$\delta t^{a}$ | Exposure | PL | BB | Total | Source
---|---|---|---|---|---
|  | $\Gamma_{X}$ | Unabsorbed Flux | kTBB | Unabsorbed Flux | RBB | Absorbed Flux |
(d) | (ks) |  | ($\times 10^{-14}$ erg/cm2/s) | ($\times 10^{-2}$ keV) | ($\times 10^{-13}$ erg/cm2/s) | ($\times 10^{12}$ cm) | ($\times 10^{-14}$ erg/cm2/s) |
Swift-XRT
$58.6$ | $61.7$ | $1.7^{+0.5}_{-0.5}$ | $2.4^{+0.7}_{-0.7}$ | $4.5^{+0.5}_{-0.6}$ | $1.3^{+0.2}_{-0.2}$ | $0.4^{+0.4}_{-0.1}$ | $7^{+1}_{-1}$ | This Work
$252.1$ | $31$ | $2.0$ | $<3.6$ | $4.9^{+0.3}_{-0.3}$ | $6.5^{+0.7}_{-0.6}$ | $0.6^{+0.2}_{-0.1}$ | $29^{+1}_{-6}$ | This Work
$329.0$ | $11.7$ |  }2*[$2.0$] | $4.1^{+2.1}_{-1.7}$ |  }2*[$5.2^{+0.4}_{-0.4}$] | $8.9^{+1.2}_{-1.0}$ | $0.6^{+0.2}_{-0.2}$ | $44^{+5}_{-5}$ | This Work
$425.1$ | $6.1$ |  | $5.3^{+3.1}_{-2.4}$ |  | $2.9^{+0.9}_{-0.7}$ | $0.3^{+0.1}_{-0.1}$ | $18^{+5}_{-3}$ | This Work
$1444.9$ | $25.3$ | $2.3^{+0.3}_{-0.3}$ | $8.5^{+1.4}_{-1.5}$ | $5.2$ | $<0.6$ | – | – | This Work
$2401$ | 7.2 | $2$ | $<17$ | – | – | – | – | This Work
$2580$ | 7.0 | $2$ | $5.3^{+2.5}_{-2.5}$ | – | – | – | – | This Work
XMM-Newtonb
$76.4$ | $10.3$ | $2.5^{+0.8}_{-0.8}$ | –c | $4.7^{+0.2}_{-0.2}$ | $1.6$ | $0.4$ | $7$ | Gezari et al. (2017)
$76.4$ | 12.4 | $1.7^{+1.0}_{-0.8}$ | $2.3^{+0.8}_{-0.8}$ | $6.2^{+6}_{-6}$ | $1.2^{+0.5}_{-0.5}$ | $0.5^{+0.6}_{-0.6}$ | – | Holoien et al. (2018)
$76.4$ | $9.7$ | $1.5^{+0.5}_{-0.4}$ | $1.9^{+0.6}_{-0.6}$ | $5.1^{+0.3}_{-0.3}$ | $1.3^{+0.1}_{-0.1}$ | $0.2^{+0.1}_{-0.1}$ | $8^{+1}_{-1}$ | This Work
$234.5$ | $12.0$ | $3.3^{+1.3}_{-1.3}$ | – | $4.2^{+0.1}_{-0.1}$ | $18$ | $2.1$ | $37$ | Gezari et al. (2017)
$234.5$ | $14.0$ | $4.8^{+2.6}_{-1.2}$ | $1.5^{+0.8}_{-0.8}$ | $5.3^{+2}_{-2}$ | $3.2^{+0.9}_{-1.0}$ | $1.1^{+0.8}_{-0.8}$ | – | Holoien et al. (2018)
$234.5$ | $10.9$ | $3.1^{+1.2}_{-0.9}$ | $0.9^{+0.7}_{-0.5}$ | $4.2^{+0.1}_{-0.1}$ | $8.9^{+0.2}_{-0.2}$ | $1.3^{+0.1}_{-0.1}$ | $38^{+1}_{-1}$ | This Work
$1833$ | $12.5$ | $2.0^{+0.3}_{-0.3}$ | $1.0^{+0.4}_{-0.2}$ | $5.2$ | $<4.2\times 10^{-2}$ | – | – | This Work
$2794$ | $19.7$ | $2$ | $<0.8$ | – | – | – | – | This Work

Note. — a For _Swift_ -XRT we list the mean time of arrival of photons. From
top to bottom, the interval of times of extraction of the spectra are
$9.8-100.5$ d, $212.2-285.5$ d, $285.5-346.4$ d, $346.4-585.7$ d,
$1394.9-1774.2$ d, $2401$ d and $2540-2620$ d.

b For XMM, we provide the numbers reported in the earlier works of Gezari et
al. (2017), and Holoien et al. (2018) for the purpose of comparison.

c The columns with no values (–) were not reported in the previously published
works. The empty columns in the last XMM and XRT observations where we report
the values from this work are because of the unconstrained nature of the BB
component at these epochs.

Table A.3: Radio Observations of the TDE ASASSN-15oi. The VLA observations at $\delta t\lesssim 600$ d were reported in Horesh et al. (2021a), however we include the contribution for systematic uncertainties here that accounts for the inaccuracies in the flux density calibration. A 5%, 10%, 3%, and 6% systematic uncertainty is added in quadrature to the uncertainties of all the flux densities measured by the VLA, ATCA, and ALMA Band 3 and ALMA Band 6, respectively. For MeerKAT, the reported uncertainties are a combination of 5% systematic, image background rms, and the standard deviation over three methods ((i) peak brightness (interpolated between pixels); (ii) fit beam-shaped Gaussian + zero-level; and (iii) total over a 10 pixel region, corrected for the fitted zero level from previous fit) of extracting the flux density — all added in quadrature. The upper limits are reported as 3 $\times$ the image background rms values.  Date | Observatory | Project | $\nu$ | Fν | Source
---|---|---|---|---|---
|  |  | (GHz) | (mJy) |
$\delta t=8$ d
2015-Aug-22 | VLA | 16A-422 | 6.1 |  $<$0.03 | Horesh et al. (2021a)
|  | (PI: Horesh) | 7.1 |  $<$0.03 |
|  |  | 22 |  $<$0.06 |
$\delta t=23$ d
2015-Sep-06 | VLA | 16A-422 | 6.1 |  $<$0.04 | Horesh et al. (2021a)
|  | (PI: Horesh) | 7.1 |  $<$0.04 |
|  |  | 22 |  $<$0.07 |
$\delta t=90$ d
2015-Nov-12 | VLA | 16A-422 | 6.1 |  $<$0.06 |
|  | (PI: Horesh) | 7.1 |  $<$0.06 |
|  |  | 22 |  $<$0.03 |
$\delta t=182$ d
2016-Feb-12 | VLA | 16A-422 | 4.8 | 1.11 $\pm$ 0.06 | Horesh et al. (2021a)
|  | (PI: Horesh) | 7.4 | 1.32 $\pm$ 0.07 |
|  |  | 19 | 0.83 $\pm$ 0.05 |
|  |  | 21 | 0.81 $\pm$ 0.04 |
|  |  | 23 | 0.64 $\pm$ 0.04 |
|  |  | 25 | 0.59 $\pm$ 0.04 |
$\delta t=190$ d
2016-Feb-20 | VLA | 16A-422 | 3 | 0.55 $\pm$ 0.03 | Horesh et al. (2021a)
|  | (PI: Horesh) | 4.8 | 0.89 $\pm$ 0.05 |
|  |  | 7.4 | 1.12 $\pm$ 0.06 |
|  |  | 9 | 1.20 $\pm$ 0.06 |
|  |  | 11 | 1.07 $\pm$ 0.06 |
|  |  | 13 | 1.10 $\pm$ 0.06 |
|  |  | 15 | 0.93 $\pm$ 0.05 |
|  |  | 17 | 0.78 $\pm$ 0.04 |
|  |  | 19 | 0.72 $\pm$ 0.04 |
|  |  | 21 | 0.57 $\pm$ 0.03 |
|  |  | 23 | 0.49 $\pm$ 0.03 |
|  |  | 25 | 0.45 $\pm$ 0.03 |
$\delta t=197$ d
2016-Feb-27 | VLA | 16A-422 | 3 | 0.50 $\pm$ 0.03 | Horesh et al. (2021a)
|  | (PI: Horesh) | 4.5 | 0.69 $\pm$ 0.04 |
|  |  | 5.5 | 0.88 $\pm$ 0.04 |
|  |  | 6.5 | 1.04 $\pm$ 0.05 |
|  |  | 7.5 | 1.12 $\pm$ 0.06 |
|  |  | 9 | 1.07 $\pm$ 0.06 |
|  |  | 11 | 1.03 $\pm$ 0.05 |
|  |  | 13 | 0.93 $\pm$ 0.05 |
|  |  | 15 | 0.79 $\pm$ 0.04 |
|  |  | 17 | 0.70 $\pm$ 0.04 |
|  |  | 19 | 0.72 $\pm$ 0.04 |
|  |  | 21 | 0.69 $\pm$ 0.04 |
|  |  | 23 | 0.53 $\pm$ 0.03 |
|  |  | 25 | 0.43 $\pm$ 0.03 |
$\delta t=233$ d
2016-Apr-03 | VLA | 16A-422 | 3 | 1.01 $\pm$ 0.06 | Horesh et al. (2021a)
|  | (PI: Horesh) | 4.5 | 0.95 $\pm$ 0.05 |
|  |  | 5.5 | 0.82 $\pm$ 0.04 |
|  |  | 6.5 | 0.76 $\pm$ 0.04 |
|  |  | 7.5 | 0.72 $\pm$ 0.04 |
|  |  | 8.5 | 0.69 $\pm$ 0.04 |
|  |  | 9.5 | 0.64 $\pm$ 0.03 |
|  |  | 10.5 | 0.64 $\pm$ 0.03 |
|  |  | 11.5 | 0.59 $\pm$ 0.03 |
|  |  | 12.5 | 0.58 $\pm$ 0.03 |
|  |  | 13.5 | 0.51 $\pm$ 0.03 |
|  |  | 14.5 | 0.45 $\pm$ 0.03 |
$\delta t=283$ d
2016-May-23 | VLA | 16A-422 | 3 | 1.03 $\pm$ 0.06 | Horesh et al. (2021a)
|  | (PI: Horesh) | 5 | 0.85 $\pm$ 0.04 |
|  |  | 7 | 0.67 $\pm$ 0.04 |
|  |  | 9 | 0.58 $\pm$ 0.03 |
|  |  | 11 | 0.52 $\pm$ 0.03 |
|  |  | 13 | 0.43 $\pm$ 0.02 |
|  |  | 15 | 0.36 $\pm$ 0.02 |
|  |  | 17 | 0.32 $\pm$ 0.02 |
$\delta t=369$ d
2016-Aug-17 | VLA | 16A-422 | 3 | 0.69 $\pm$ 0.04 | Horesh et al. (2021a)
|  | (PI: Horesh) | 5 | 0.62 $\pm$ 0.04 |
|  |  | 7 | 0.57 $\pm$ 0.03 |
|  |  | 9 | 0.55 $\pm$ 0.03 |
$\delta t=576$ d
2017-March-12 | VLA | 16A-422 | 3 | 0.31 $\pm$ 0.07 | Horesh et al. (2021a)
|  | (PI: Horesh) | 5 | 0.23 $\pm$ 0.03 |
|  |  | 7 | 0.21 $\pm$ 0.02 |
|  |  | 9 | 0.20 $\pm$ 0.02 |
$\delta t=1417$ d
2019-Jul-01 | VLA | VLASS | 3 | 9.5 $\pm$ 0.5 |
$\delta t=1741$ d
2020-May-20 | VLA | 20A-492 | 1.3 | 9.8 $\pm$ 0.5 | This Work
|  | (PI: Alexander) | 1.8 | 10.8 $\pm$ 0.6 |
|  |  | 2.5 | 10.1 $\pm$ 0.5 |
|  |  | 3.5 | 9.6 $\pm$ 0.5 |
|  |  | 5 | 9.3 $\pm$ 0.5 |
|  |  | 7 | 8.4 $\pm$ 0.4 |
|  |  | 9 | 7.3 $\pm$ 0.3 |
|  |  | 11 | 6.3 $\pm$ 0.4 |
$\delta t=2129$ d
2021-Jun-08 | VLA | 21A-303 | 1.2 | 11.3 $\pm$ 0.6 | This Work
|  | (PI: Hajela) | 1.6 | 11.2 $\pm$ 0.6 |
|  |  | 1.9 | 10.8 $\pm$ 0.6 |
|  |  | 2.3 | 9.9 $\pm$ 0.6 |
|  |  | 2.8 | 9.2 $\pm$ 0.5 |
|  |  | 3.2 | 8.6 $\pm$ 0.4 |
|  |  | 3.8 | 7.9 $\pm$ 0.4 |
|  |  | 4.5 | 7.1 $\pm$ 0.4 |
|  |  | 5.5 | 6.2 $\pm$ 0.3 |
|  |  | 6.5 | 5.4 $\pm$ 0.3 |
|  |  | 8.5 | 4.7 $\pm$ 0.2 |
|  |  | 9.5 | 4.4 $\pm$ 0.2 |
|  |  | 10.5 | 4.1 $\pm$ 0.2 |
|  |  | 11.5 | 3.8 $\pm$ 0.2 |
$\delta t=2384$ d
2022-Feb-22 | VLBI | BH238 | 8.3 | 1.4 $\pm$ 0.3 | This Work
|  | (PI: Hajela) |  |  |
$\delta t=2660$ d
2023-Jan-05 | MeerKAT | DDD-20220414-YC-01 | 0.8 | 9.8 $\pm$ 0.5 | This Work
2022-Dec-09 | MeerKAT | SCI-20220822-YC-01 | 1.3 | 6.4 $\pm$ 0.3 |
|  | (PI: Cendes) |  |  |
2022-Sep-30 | ATCA | C3325 | 1.3 | 9.7 $\pm$ 1.3 |
|  | (PI: Alexander) | 1.8 | 8.5 $\pm$ 0.9 |
|  |  | 2.4 | 7.4 $\pm$ 0.8 |
|  |  | 2.9 | 6.7 $\pm$ 0.7 |
|  |  | 4.7 | 4.9 $\pm$ 0.5 |
|  |  | 5.2 | 4.8 $\pm$ 0.5 |
|  |  | 5.8 | 4.4 $\pm$ 0.4 |
|  |  | 6.3 | 4.2 $\pm$ 0.4 |
|  |  | 8.2 | 3.6 $\pm$ 0.4 |
|  |  | 8.7 | 3.5 $\pm$ 0.3 |
|  |  | 9.3 | 3.4 $\pm$ 0.3 |
|  |  | 9.9 | 3.2 $\pm$ 0.4 |
2022-Sep-29 | ALMA | 2019.1.01166.T | 97.5 | 0.38 $\pm$ 0.02 |
|  | (PI: Alexander) | 233 | 0.16 $\pm$ 0.02 |
$\delta t=2970$ d
2023-Oct-01 | VLA | 23A-241 | 1.2 | 4.1 $\pm$ 0.2 | This Work
|  | (PI: Cendes) | 1.5 | 3.7 $\pm$ 0.2 |
|  |  | 1.9 | 3.5 $\pm$ 0.2 |
|  |  | 2.3 | 3.5 $\pm$ 0.2 |
|  |  | 2.9 | 3.1 $\pm$ 0.2 |
|  |  | 3.6 | 3.1 $\pm$ 0.2 |
|  |  | 4.5 | 2.6 $\pm$ 0.1 |
|  |  | 5.5 | 2.4 $\pm$ 0.1 |
|  |  | 6.5 | 2.1 $\pm$ 0.1 |
|  |  | 7.5 | 1.9 $\pm$ 0.1 |
|  |  | 8.5 | 1.7 $\pm$ 0.1 |
|  |  | 9.5 | 1.5 $\pm$ 0.1 |
|  |  | 10.5 | 1.4 $\pm$ 0.1 |
|  |  | 11.5 | 1.4 $\pm$ 0.1 |

##  Appendix B Radio Spectral Fitting and the Model Selection Criteria

In sections §B.1 and §B.2, we explain the fitting process in details, along
with our underlying assumptions. In §B.3, we give details on our model
selection criteria.

###  B.1 Fit of SEDs associated with the first radio flare

We first fit the $\delta t=182$ d, $190$ d, and $197$ d SEDs with Equation
(2), assuming values of $s_{1}=-0.3$ and a sharper $s_{2}=-0.003$. We set
$\alpha_{\rm{thick,\,thin}}$ as free parameters for the $190$ and $197$ d
SEDs, resulting in $\alpha_{\rm thick}\sim+1$. We fix $\alpha_{\rm thick}$ at
+1 for the 182 d SED, at which there are too few measurements below $\nu_{\rm
pk}$ to allow an independent constraint. A second break is weakly constrained
in all three SEDs as $\nu_{q}\sim 18-20$ GHz (an example of the corner plot
with posterior distributions of the fit parameters for $\delta t=190$ d is
shown in Figure C.1). Due to large uncertainties on $\nu_{q}$ (in particular
up to $\sim 40$% for the $182$ d SED), we also compute a fit without a
$\nu_{q}$ break (i.e., Equation 1) for each SED, which was the model used by
Horesh et al. (2021a). Comparing the two models, we find that $\Delta$AIC$<2$
and $\Delta$BIC$<2$, indicating no strong preference for either model (Table
B.1).

The SEDs at $\delta t=233$ d and $283$ d do not show a strong evidence of a
low-frequency turnover (i.e., no $\alpha>0$ segment is present), but do
exhibit a slight steepening at higher frequencies. We fit these SEDs with
Equation 1 (with $\nu_{b_{1}}=\nu_{q}$, $\alpha_{i}=\alpha_{\rm thin}$ and
$\alpha_{j}=\alpha_{q}$), and $\nu_{q}$ is constrained to $\sim 10$ GHz in
both SEDs. We also attempted a simple power-law fit of the form
$F\propto\nu^{\alpha_{\rm thin}}$. Based on the AIC and BIC values (given in
Table B.1) for the two models, the model with _one_ break is marginally
preferred over a simple power-law for $\delta t=233$ d SED (with
$\Delta\rm{AIC}=2.5$ and $\Delta\rm{BIC}=2.1$) and is strongly preferred for
$\delta t=283$ d (with $\Delta\rm{AIC}=6.2$ and $\Delta\rm{BIC}=6.1$). At
$\delta t=369$ d and $\delta t=576$ d, the SEDs show no low frequency
turnovers or high frequency steepening, and are therefore fitted with a simple
power-law of the form $F\propto\nu^{\alpha_{\rm thin}}$.

###  B.2 Fit of SEDs associated with the second radio flare

We treat the SEDs taken during the second flare (i.e., at $\delta t\gtrsim
1400$ d) independently of the earlier ones where we let $\alpha_{\rm thick}$
vary freely. Here, instead we try fitting the SEDs with both Equation 2 (with
$\alpha_{\rm thick,thin}$ spectral segments) and 1 with $\alpha_{\rm
thick}=5/2$ (as expected for standard self-absorbed synchrotron spectra in the
context of TDEs; e.g., Alexander et al. 2020). Similar to the previous SEDs,
we adopt $s_{1}=-0.03$ and $s_{2}=-0.003$ (unless otherwise mentioned); and
the AIC and BIC values are reported in Table B.1.

For the SEDs at $\delta t=1741$ d, $2660$ d and $2970$ d, we find that the
model with two breaks is a better fit. Here $\nu_{q}$ is constrained to $\sim
7$ GHz, $\sim 19$ GHz and $\sim 5$ GHz, respectively. In these SEDs, the
peak’s location largely mirrors the priors, and in particular, the lower bound
on the peak frequency remains unconstrained, resulting in only limits on the
SED peak. In contrast, the SED at $\delta t=2129$ d prefers the model with
only one break and the peak is robustly constrained. However this SED exhibits
a smoother turnover compared to others, requiring $|s_{1}|>0.03$. We thus
assume $s_{1}=-1$ here and report the results accordingly.

###  B.3 Model Selection Criteria

We use the Akaike Information Criterion (AIC) and the Bayesian Information
Criterion (BIC) in §3.1 as a means for model selection. These statistical
measures compare how well the models fit the observed data, with both criteria
penalizing the models that have more parameters. BIC imposes a stricter
penalty, making it more conservative. The aim is to achieve an optimal balance
between goodness of fit and the complexity of the model.

The AIC is given by:

$\text{AIC}=2k-2\ln(L),$ (B1)

and the BIC is given by:

$\text{BIC}=k\ln(n)-2\ln(L)$ (B2)

where $k$ is the number of free parameters used in our MCMC fitting, $L$ is
the maximum likelihood of the model and $n$ is the number of observations.

As mentioned in §3.1, we use one or more models to fit for some SEDs. The
models are as follows: (i) models with 0 breaks are represented by
$F\propto\nu^{\alpha_{\rm thin}}$, (ii) models with 1 break are given by
Equation 1, and (iii) models with 2 breaks are given by Equation 2. We give
the corresponding AIC and BIC in Table B.1. Values of $\Delta AIC>2$ and
$\Delta BIC>2$ show a statistically stronger preference for the model with the
_lower_ AIC and BIC values.

Table B.1: The values of AIC and BIC for the different models at various
epochs are reported here. The three models compared are: (i) a model with 0
breaks of the form $F\propto\nu^{-\alpha_{\rm thin}}$, (ii) a model with 1
break of the form of Equation 1, and (iii) a model with 2 breaks represented
by Equation 2.

$\delta t^{a}$ | 0 Break | 1 Break | 2 Breaks
---|---|---|---
(d) | AIC | BIC | AIC | BIC | AIC | BIC
182 | – | – | 17.0 | 16.4 | 15.9 | 15.1
190 | – | – | 23.3 | 25.2 | 22.5 | 24.9
197 | – | – | 32.8 | 35.4 | 30.8 | 33.9
233a | 17.4 | 18.4 | 14.9 | 16.3 | 16.8 | 18.7
283a | 18.2 | 18.3 | 12.0 | 12.2 | 14.6 | 14.9
1741 | 40 | 40.2 | 34.7 | 35.0 | 13.2 | 13.5
2129 | – | – | 10.3 | 12.4 | 13.4 | 15.5
2660 | – | – | 53.2 | 55.5 | 16.3 | 11.0
2970 | – | – | 25.6 | 27.5 | 16.1 | 18.7

Note. — $[a]$ In these SEDs, the ‘1 Break’ model given by Equation 1 has
$\nu_{b_{1}}=\nu_{q}$, $\alpha_{i}=\alpha_{\rm thin}$ and
$\alpha_{j}=\alpha_{q}$.

##  Appendix C Posterior distribution of fit parameters of the radio SED at
$\delta t\approx$190 d