#  NICER Discovery of Millisecond X-ray Pulsations and an Ultracompact Orbit
in IGR J17494$-$3030

Mason Ng MIT Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Paul S. Ray
Space Science Division, U.S. Naval Research Laboratory, Washington, DC 20375,
USA  Peter Bult  Department of Astronomy, University of Maryland, College
Park, MD 20742, USA  Astrophysics Science Division, NASA Goddard Space Flight
Center, Greenbelt, MD 20771, USA  Deepto Chakrabarty MIT Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Gaurava K. Jaisawal National Space Institute,
Technical University of Denmark, Elektrovej 327-328, DK-2800 Lyngby, Denmark
Christian Malacaria NASA Marshall Space Flight Center, NSSTC, 320 Sparkman
Drive, Huntsville, AL 35805, USA  Universities Space Research Association,
NSSTC, 320 Sparkman Drive, Huntsville, AL 35805, USA  Diego Altamirano School
of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK
Zaven Arzoumanian  Astrophysics Science Division, NASA Goddard Space Flight
Center, Greenbelt, MD 20771, USA  Keith C. Gendreau  Astrophysics Science
Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Tolga
Güver Istanbul University, Science Faculty, Department of Astronomy and Space
Sciences, Beyazıt, 34119, Istanbul, Turkey  Istanbul University Observatory
Research and Application Center, Istanbul University 34119, Istanbul, Turkey
Matthew Kerr Space Science Division, U.S. Naval Research Laboratory,
Washington, DC 20375, USA  Tod E. Strohmayer Astrophysics Science Division,
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Joint Space-
Science Institute, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Zorawar Wadiasingh Astrophysics Science Division, NASA Goddard Space Flight
Center, Greenbelt, MD 20771, USA  Centre for Space Research, North-West
University, Potchefstroom Campus, Private Bag X6001, Potchefstroom 2520, South
Africa  Universities Space Research Association (USRA), Columbia, MD 21046,
USA  Michael T. Wolff Space Science Division, U.S. Naval Research Laboratory,
Washington, DC 20375, USA

(Received January 15, 2021; Revised January 29, 2021; Accepted January 31,
2021)

###### Abstract

We report the detection of 376.05 Hz (2.66 ms) coherent X-ray pulsations in
NICER observations of a transient outburst of the low-mass X-ray binary IGR
J17494$-$3030 in 2020 October/November. The system is an accreting millisecond
X-ray pulsar in a 75 minute ultracompact binary. The mass donor is most likely
a $\simeq 0.02\,M_{\odot}$ finite-entropy white dwarf composed of He or C/O.
The fractional rms pulsed amplitude is 7.4%, and the soft (1–3 keV) X-ray
pulse profile contains a significant second harmonic. The pulsed amplitude and
pulse phase lag (relative to our mean timing model) are energy-dependent, each
having a local maximum at 4 keV and 1.5 keV, respectively. We also recovered
the X-ray pulsations in archival 2012 XMM-Newton observations, allowing us to
measure a long-term pulsar spin-down rate of $\dot{\nu}=-2.1(7)\times
10^{-14}$ Hz s-1 and to infer a pulsar surface dipole magnetic field strength
of $\simeq 10^{9}$ G. We show that the mass transfer in the binary is likely
non-conservative, and we discuss various scenarios for mass loss from the
system.

stars: neutron – stars: oscillations (pulsations) – binaries: close – stars:
rotation – X-rays: binaries – X-rays: individual (IGR J17494$-$3030)

††facilities: NICER, XMM††software: astropy (Astropy Collaboration et al.,
2013), NumPy and SciPy (Oliphant, 2007), Matplotlib (Hunter, 2007), IPython
(Perez & Granger, 2007), tqdm (Da Costa-Luis et al., 2020), NICERsoft, PRESTO
(Ransom et al., 2002), PINT (Luo et al., 2020), HEASoft 6.28

##  1 Introduction

Accreting millisecond X-ray pulsars (AMXPs; see Di Salvo & Sanna, 2020, for a
recent review) are rapidly rotating, weakly magnetized ($\sim 10^{8}$ G)
neutron stars accreting from a low-mass ($\lesssim 1M_{\odot}$) companion in a
low-mass X-ray binary (LMXB). Most known AMXPs are X-ray transient systems in
which long ($\sim$years) intervals of X-ray quiescence are punctuated by brief
($\sim$weeks) outbursts of enhanced X-ray emission. These transient outbursts
are understood to arise from a thermal instability in the accretion disk
around a neutron star or black hole LMXB primary, analogous to “dwarf nova”
optical outbursts in accreting white dwarfs (see Lasota, 2001; Hameury, 2020,
and references therein).

The X-ray transient IGR J17494$-$3030 (Galactic coordinates $l=359.1^{\circ}$,
$b=-1.5^{\circ}$; hereafter called IGR J17494) was first discovered in a 2012
March outburst in the 3–80 keV hard X-ray band (IBIS and JEM-X) in an INTEGRAL
survey of the Galactic center region (Boissay et al., 2012). Soft X-ray
(0.5–10 keV) monitoring observations with Swift showed that the outburst
lasted approximately one month (Armas Padilla et al., 2013) before fading into
quiescence (Chakrabarty et al., 2013). XMM-Newton 0.5–10 keV spectroscopy
suggested that the compact primary is a neutron star (Armas Padilla et al.,
2013). A new outburst was detected with INTEGRAL in 2020 October (Ducci et
al., 2020), leading to a more precise X-ray localization with Chandra
(Chakrabarty & Jonker, 2020) and the identification of a 4.5 GHz radio
counterpart with the VLA (van den Eijnden et al., 2020).

Soft X-ray observations of the 2020 outburst with the Neutron Star Interior
Composition Explorer (NICER) revealed the presence of coherent 376 Hz
pulsations modulated by a 75 minute binary orbit, establishing the system as a
millisecond pulsar (neutron star) in an ultracompact binary (Ng et al., 2020).
In this Letter, we first outline the NICER and XMM-Newton observations and
data processing. We then present results from timing and spectral analyses of
the NICER observations, as well as from a timing analysis of the archival 2012
XMM-Newton observations. Finally, we constrain the possible nature of the
donor in the IGR J17494 system and discuss further implications of the source.

##  2 Observations and Data Processing

###  2.1 NICER

NICER is an X-ray telescope mounted on the International Space Station (ISS)
since 2017 June. NICER has 56 aligned pairs of X-ray concentrator optics and
silicon drift detectors (52 detectors are usually active on NICER). NICER is
capable of fast-timing observations in the 0.2–12.0 keV band, with timing
accuracy of time-tagged photons to better than 100 ns (Gendreau et al., 2012;
LaMarr et al., 2016; Prigozhin et al., 2016).

NICER observed IGR J17494 from 2020 October 27 to November 4111The source
became unobservable due to Sun-angle constraints around November 5. for a
total exposure time of $32.3{\rm\,ks}$ after filtering, in ObsIDs
3201850101–3201850108222During the course of the observations, several
detectors were turned off for scheduled maintenance. Detectors 01, 02, 10, 13,
34, 43, and 44 were affected. In all observations, 46–48 detectors were
active. Detectors 11, 20, 22, and 60 have been inactive since launch.. These
observations were available through the public NASA HEASARC data archive.
There were additional NICER observations, to which we did not have access,
during this interval for a proprietary guest observer investigation (PI: A.
Sanna; shown as the shaded region in the top panel of Figure 1). The events
were barycenter-corrected in the ICRS reference frame, with source coordinates
R.A. $=267.348417\arcdeg$ and Decl.$=-30.499722\arcdeg$ (equinox J2000.0)
obtained from a recent Chandra observation (Chakrabarty & Jonker, 2020), using
barycorr from FTOOLS with the JPL DE405 solar system ephemeris (Standish,
1998).

The NICER observations were processed with HEASoft version 6.28 and the NICER
Data Analysis Software (nicerdas) version 7.0 (2020-04-23_V007a). The
following criteria, which we note are relaxed compared to standard filtering
criteria as the latter were too restrictive and resulted in no events, were
imposed in the construction of the good time intervals (GTIs): no
discrimination of events when NICER (on the ISS) was inside or outside of the
South Atlantic Anomaly during the course of the observations; $\geq 20\arcdeg$
for the source-Earth limb angle ($\geq 30\arcdeg$ for the Sun-illuminated
Earth); $\geq$ 38 operational Focal Plane Modules (FPMs); undershoot (dark
current) count-rate range of 0–400 per FPM (underonly_range); overshoot
(saturation from charged particles) count-rate range of 0–2 per FPM
(overonly_range and overonly_expr); pointing offset is $<0.015\arcdeg$ from
the nominal source position.

We analyzed spectral data using XSPEC v12.11.1 (Arnaud, 1996). NICER data were
selected in the range 1–10 keV, to avoid contamination from optical loading
and significant interstellar absorption at lower energy. The spectra were
rebinned to have at least 25 counts per bin. Background spectra were extracted
using nibackgen3C50 version 6 from the official NICER
tools333https://heasarc.gsfc.nasa.gov/docs/nicer/tools/nicer_bkg_est_tools.html..
Standard response files made available by the NICER team were used to perform
spectral
analysis444https://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/data/nicer/xti/index.html..

###  2.2 XMM-Newton

XMM-Newton performed a $43{\rm\,ks}$ observation of IGR J17494 on 2012 March
31 (ObsID 0694040201). The EPIC-PN camera was operated in timing mode,
yielding a time resolution of 29.56 $\mu$s, which is sufficient to allow us to
search for the presence of coherent pulsations. We processed these data using
SAS version 18.0 and the latest version of the calibration
files555https://www.cosmos.esa.int/web/xmm-newton/current-calibration-files.
Applying standard screening criteria, we retained only those events with
photon energies in the 0.4–10 keV range, with $\textsc{pattern}\leq 4$ and
screening $\textsc{flag}=0$. Source events were extracted from rawx columns
$[34:42]$, while background events were extracted from rawx $[51:59]$.
Constructing a $32$-s resolution light curve of the source and background
data, we find that the source count-rate gradually decreased over the span of
the observation, dropping from 2 ct s-1 to 1 ct s-1. Additionally, we filtered
out an episode of background flaring that occurred between $15750{\rm\,s}$ and
$21500{\rm\,s}$ after the start of the observation. Finally, we applied
barycentric corrections to the cleaned event data, again using the JPL DE405
solar system ephemeris and the source coordinates quoted previously.

##  3 Results

###  3.1 NICER

The NICER 1–7 keV light curve for the 2020 outburst is shown in the top panel
of Figure 1. The source gradually faded until MJD 59155.4, after which it
decayed more rapidly. The X-ray spectrum prior to the proprietary data gap was
fairly constant and well-fit with a two-component absorbed power-law and
blackbody model (tbabs(powerlaw+bbodyrad) in XSPEC), with absorption column
density $n_{\rm H}=2.07(6)\times 10^{22}{\rm\,cm^{-2}}$, photon index
$\Gamma=1.90(6)$, blackbody temperature $kT=0.58(3)$ keV, and blackbody radius
$R_{\rm bb}=2.9(5)\,d_{10}$ km, where $d_{10}$ is the source distance in units
of 10 kpc. The uncertainties are reported at the 90% confidence level. The
reduced $\chi^{2}$ ($\chi_{\nu}^{2}$) of the fit was $1.14$ for 849 degrees of
freedom. The spectrum softened during the late decay phase of the outburst,
where the same two-component model fit yielded $\Gamma=4.3_{-0.6}^{+0.9}$ and
$n_{\rm H}$ is assumed to be unchanged throughout the observations. The peak
absorbed 1–10 keV flux we observed was $1.01\times
10^{-10}{\rm\,erg\,s^{-1}\,cm^{-2}}$ on MJD $59149.4$, corresponding to an
unabsorbed flux of $1.43\times 10^{-10}{\rm\,erg\,s^{-1}\,cm^{-2}}$. The
lowest absorbed flux we measured was $1.21\times
10^{-12}{\rm\,erg\,s^{-1}\,cm^{-2}}$ on MJD $59157.5$, corresponding to an
unabsorbed flux of $3.23\times 10^{-12}{\rm\,erg\,s^{-1}\,cm^{-2}}$. This is
roughly a factor of 3 fainter than the minimum flux detected by XMM-Newton at
the end of the 2012 outburst (Armas Padilla et al., 2013). A more detailed
X-ray spectral analysis will be reported elsewhere.

We first detected X-ray pulsations with a data analysis pipeline that employs
multiple techniques666https://github.com/masonng-astro/nicerpy_xrayanalysis,
particularly with Lv3_incoming.py and scripts therein for X-ray pulsation
searches, including averaged power spectral stacking with Bartlett’s method
(Bartlett, 1948) and acceleration searches with PRESTO (Ransom et al., 2002).
The initial detection was made through PRESTO, an open-source pulsar timing
software package777https://github.com/scottransom/presto designed for
efficient searches for binary millisecond pulsars. We ran a Fourier-domain
acceleration search scheme with the accelsearch task over the range 1–1000 Hz,
and posited that the Doppler motion would cause the possible signal to drift
over a maximum of 100 bins in Fourier frequency space. This yielded a strong
$\simeq 376.05{\rm\,Hz}$ pulsation candidate (trial-adjusted significance of
$3.5\sigma$) in the 2–12 keV range.

Figure 1: Top: NICER 1–7 keV light curve for IGR J17494. The shaded band
denotes a gap where proprietary NICER data was unavailable to us. Middle:
Pulse arrival time delay as a function of orbital phase relative to the
ascending node. The crosses are our measurements, and the solid curve is our
best-fit model. The squares are the fit residuals, plotted on a 30$\times$
magnified scale. Bottom: Pulse profiles in the 1–3 keV (solid red) and 3–7 keV
(dashed blue) bands. The 1–3 keV profile contains a significant second
harmonic.

After initial identification of the candidate in the 2–12 keV range, we
optimized the pulse significance by adjusting the energy range to maximize the
$Z_{1}^{2}$ statistic, where

$Z_{1}^{2}=\frac{2}{N}\left[\left(\sum_{j=1}^{N}\cos 2\pi\nu
t_{j}\right)^{2}+\left(\sum_{j=1}^{N}\sin 2\pi\nu t_{j}\right)^{2}\right],$
(1)

where $t_{j}$ are the $N$ photon arrival times (Buccheri et al., 1983). We
found that an optimal energy range of 1.01–7.11 keV yielded
$Z_{1}^{2}=1915.41$. Our subsequent timing analyses were carried out over 1–7
keV.

The acceleration searches indicated that the pulsation frequency is modulated
by a binary orbit. We used the acceleration data to estimate an initial timing
model with a provisional circular orbit. We then used this initial model to
construct $35$ pulse times of arrival (TOAs) with the photon_toa.py tool in
the NICERsoft888https://github.com/paulray/NICERsoft data analysis package,
using a Gaussian pulse template and ensuring an integration time of 500 s for
each TOA (with minimum exposure time of 200 s). We then used these TOAs to
compute corrections to our initial orbit model using weighted least-squares
fitting with the PINT pulsar data analysis package (Luo et al., 2020). Our
best-fit orbit ephemeris is shown in Table 1, and the orbital decay curve is
shown in the middle panel of Figure 1. Using our best-fit timing model,
pulsations were detected throughout the entire outburst. At the end of the
observations, we were able to detect the pulsations in observations from MJD
59154–59157 (November 1–4) by combining all the data. The mean unabsorbed flux
over this 4-day interval was $8.5\times 10^{-12}$ erg s-1 cm-2 (1–10 keV). We
did not have sufficient sensitivity to detect the pulsations in individual
pointings from these dates. The time-averaged fractional root-mean-squared
(rms) pulsed amplitude was 7.4% (1–7 keV). Examining the lower and higher
energies separately, we found amplitudes of 7.2% in the 1–3 keV band and 8.7%
in the 3–7 keV band. The soft and hard X-ray pulse profiles are shown in the
bottom panel of Figure 1. The 1–3 keV profile shows the presence of a second
harmonic; this component is not significantly detected in the 3–7 keV profile.
To further examine the energy dependence of the pulse waveform, we adaptively
binned the timing data in energy. We required the energy bins to contain a
multiple of 5 pulse-invariant (PI) energy channels (0.05 keV), such that each
bin contained at least 5000 counts. For each of these energy bins, we then
folded the data using our best-fit timing solution and measured the
background-corrected fractional rms pulsed amplitude and the pulse phase
offset relative to the model. The resulting energy dependencies are shown in
Figure 2. The pulsed amplitude has a local maximum of 11% at 4 keV, while the
pulse phase lag has a local maximum of $+0.05$ cycles (130 $\mu$s) at around
1.5 keV.

Figure 2: Top: Fractional rms pulsed amplitude as a function of energy, as
measured by NICER. Bottom: Pulse phase lag as a function of energy, as
measured by NICER. The lag is measured relative to the best-fit timing model
in Table 1.

###  3.2 XMM-Newton

The uncertainty in our $P_{\rm orb}$ value does not allow us to coherently
extrapolate our timing model back to the 2012 outburst. Thus, we searched for
pulsations in the XMM-Newton data by constructing a grid of trial
$T_{\mathrm{asc}}$ values around the local epoch that spanned one orbital
period. The grid resolution was set to 50 s, which is equivalent to $4\arcdeg$
in orbital longitude. For each trial ephemeris, we then demodulated the event
data and computed the $Z_{1}^{2}$ statistic (see Eq. 1). We evaluated this
statistic for pulse frequencies in a $\pm 3{\rm\,mHz}$ window around the spin
frequency measured with NICER, adopting a frequency resolution of $1/T$, with
$T$ the duration of the XMM-Newton observation. The best candidate solution
produced by this search had $Z_{1}^{2}=89$, which converts to a trial-adjusted
pulse detection significance of $8\sigma$.

Adopting the best $T_{\mathrm{asc}}$ and pulse frequency from the grid search
as a provisional model, we performed a phase-coherent pulse analysis. We
divided the light curve into $\approx 3$ ks segments, and measured the pulse
phase in each segment separately. The phase residuals were fit using a
circular orbital model and constant spin frequency, where we kept the orbital
period and projected semimajor axis fixed at their NICER values. The best-fit
values were $\nu_{2012}=376.0501759(19)$ Hz and $T_{\rm asc,2012}=$ MJD
$56017.33680(5)$. Comparing to our NICER measurement, we find
$\Delta\nu\equiv\nu_{2020}-\nu_{2012}=-5.7\pm 1.9$ mHz. This indicates long-
term spin-down of the pulsar between outbursts, at a rate
$\dot{\nu}=-2.1(7)\times 10^{-14}$ Hz s-1. Owing to the uncertainty in exact
orbital cycle count between the 2012 and 2020 epochs, we are unable to use
these $T_{\rm asc}$ measurements to further refine the orbital period.

The XMM-Newton data also showed an energy-dependent trend in pulse phase lag
similar to that observed in the NICER data. We were unable to measure an
energy-dependence in the pulsed amplitude with XMM-Newton, but the results
from the two data sets were consistent within the measurement uncertainties.

Table 1:  IGR J17494$-$3030 timing parameters from the 2020 outburst  Parameter | Value
---|---
Right ascension, $\alpha$ (J2000) | $267.348417\arcdeg$
Declination, $\delta$ (J2000) | $-30.499722\arcdeg$
Position epoch (TT) | MJD $59156.34$
Spin frequency, $\nu_{0}$ (Hz) | $376.05017022(4)$
Spin frequency derivative (during outburst), $|\dot{\nu}|$ (Hz/s) | $<1.8\times 10^{-12}$
Spin epoch, $t_{0}$ (TDB) | MJD $59149.0$
Binary period, $P_{\rm orb}$ (s) | $4496.67(3)$
Projected semimajor axis, $a_{x}\sin i$ (lt-ms) | $15.186(12)$
Epoch of ascending node passage, $T_{\rm asc}$ (TDB) | MJD $59149.069012(15)$
Eccentricity, $e$ | $<0.006\ (2\sigma)$
Spin frequency derivative (long-term), $\dot{\nu}$ (Hz/s) | $-2.1(7)\times 10^{-14}$

##  4 Discussion

The discovery of coherent millisecond X-ray pulsations from IGR J17494$-$3030
definitively identifies the source as an accreting neutron star. We can use
the long-term spin-down of the pulsar between its 2012 and 2020 X-ray
outbursts to estimate the pulsar’s magnetic field strength. Assuming that the
spin-down is due to magnetic dipole radiation, we can calculate the pulsar’s
magnetic dipole moment (Spitkovsky, 2006)

$\displaystyle\mu$ $\displaystyle=5.2\times
10^{26}\left(1+\sin^{2}\alpha\right)^{-1/2}$
$\displaystyle\times\left(\frac{I}{10^{45}\text{ g
cm}^{2}}\right)^{1/2}\text{G cm}^{3},$ (2)

where $\alpha$ is the angle between the magnetic and spin axes, and $I$ is the
neutron star moment of inertia. The corresponding surface dipole field
strength of $\simeq 10^{9}$ G is on the high end of the distribution inferred
for other AMXPs (Mukherjee et al., 2015).

We found that the fractional rms pulsed amplitude and the pulse phase of IGR
J17494 vary as a function of photon energy. Both the amplitude and the phase
lag reach a local maximum at a (different) characteristic energy of 4 and 1.5
keV, respectively. Energy-dependent variations of the pulse waveform are
ubiquitous among AMXPs, although the location of these local maxima varies
greatly from source to source (Gierliński et al., 2002; Gierliński & Poutanen,
2005; Falanga et al., 2005; Patruno et al., 2009; Falanga et al., 2012). The
behavior can be understood through a two-component emission model, with
thermal emission originating from the stellar surface and scattered Compton
emission originating from some height above the surface (Gierliński et al.,
2002; Wilkinson et al., 2011). Accounting for the difference in geometry and
emission patterns, such a model can self-consistently explain the energy
dependence of both the phase lags and the pulsed amplitudes (Poutanen &
Gierliński, 2003).

Our measurement of a 75 min binary orbit allows us to constrain the nature of
the mass donor in this system. The vast majority of Roche-lobe–filling LMXBs
and cataclysmic variables contain hydrogen-rich donor stars, and they all have
binary periods $P_{\rm orb}\gtrsim 80$ min (Paczynski & Sienkiewicz, 1981;
Rappaport et al., 1982). The so-called ultracompact binaries ($P_{\rm
orb}\lesssim 80$ min) have H-depleted donors (Nelson et al., 1986; Pylyser &
Savonije, 1988, 1989; Nelemans et al., 2010). IGR J17494 has the longest known
period for an ultracompact LMXB and lies near the period boundary, making it a
particularly interesting case. We also note the recent discovery of the
rotation-powered millisecond gamma-ray pulsar PSR J1653$-$0158 in a 75 min
(non-accreting) binary (Nieder et al., 2020). This is the shortest orbital
period known for a rotation-powered binary pulsar, and this “black widow”
system is believed to have evolved from an ultracompact LMXB after mass
transfer ended.

From our measured orbital parameters, the binary mass function of IGR J17494
is

$\displaystyle f_{m}$ $\displaystyle\equiv\frac{(M_{d}\sin i)^{3}}{(M_{\rm
ns}+M_{d})^{2}}=\frac{4\pi^{2}(a_{x}\sin i)^{3}}{GP_{\rm orb}^{2}}$
$\displaystyle\approx 1.39\times 10^{-6}\ M_{\odot},$ (3)

where $M_{\rm ns}$ is the neutron star mass, $M_{d}$ is the donor mass,
$a_{x}\sin i$ is the projected semimajor axis, and the binary inclination $i$
is defined as the angle between the line of sight and the orbital angular
momentum vector. For a given value of $M_{\rm ns}$, we can use Equation 4 to
calculate $M_{d}$ as a function of $i$ (see top panel of Figure 3). Assuming
$M_{\rm ns}=1.4\ (2.0)\,M_{\odot}$, the minimum donor mass (for an edge-on
binary with $i=90^{\circ}$) is 0.014 (0.018) $M_{\odot}$. For a random
ensemble of binaries, the probability distribution of $\cos i$ is uniformly
distributed and $\Pr(i<i_{0})=1-\cos i_{0}$. Thus, the donor mass is likely to
be very low, with a 90% confidence upper limit of $M_{d}<0.033\
(0.041)\,M_{\odot}$ for $M_{\rm ns}=1.4\ (2.0)\,M_{\odot}$.

Assuming a Roche-lobe–filling donor, we can calculate the donor radius $R_{d}$
as a function of $M_{d}$ (Eggleton, 1983); this is shown in the bottom panel
of Figure 3 for $M_{\rm ns}=1.4\,M_{\odot}$. For comparison, the figure also
shows the mass-radius relations for different types of low-mass stars: cold
white dwarfs (WDs; Zapolsky & Salpeter, 1969; Rappaport & Joss, 1984; Nelemans
et al., 2001); hot (finite-entropy) WDs composed of either He, C, or O (Deloye
& Bildsten, 2003); and low-mass H-rich stars, including brown dwarfs (Chabrier
et al., 2000). We see that cold WD models are inconsistent with our measured
mass-radius constraint, indicating that thermal bloating is likely important.
Moderately hot He WDs with central temperature $T_{c}=2.5\times 10^{6}$ K or
C/O WDs with $T_{c}=5\times 10^{6}$ K are consistent with our constraint at
high binary inclination. Hotter WDs and moderately old (cool) brown dwarfs are
also consistent, but the required inclinations have low a priori probability.
Finally, H-rich dwarfs above the mass-burning limit are also possible, but
only for extremely low (improbable) inclinations. We conclude that the donor
is likely to be a $\simeq 0.02\,M_{\odot}$ finite-entropy He or C/O white
dwarf.

Figure 3: Top: Donor star mass $M_{d}$ as a function of binary inclination
$i$, assuming $M_{\rm ns}=1.4\,M_{\odot}$. The a priori probability
distribution is uniform in $\cos i$, so low masses are likeliest. Bottom:
Mass-radius constraints for the donor star. The thick solid black curve is the
mass-radius constraint for a Roche-lobe–filling donor from our orbital
measurements. The dashed black line shows cold WD models. The blue and red
lines show representative “warm” and hot WD models, respectively, with He
(dotted), C (dashed), and O (dash-dotted) compositions. These models take
$T_{c}=2.5$ and 7.9 MK for He and $T_{c}=5$ and 10 MK for C/O. The solid cyan
curves show brown dwarf models for ages 0.1, 0.5, 1.0, 5.0, and 10.0 Gyr (from
top to bottom). The likeliest donor is a warm $\simeq 0.02M_{\odot}$ He or C/O
WD.

The angular momentum evolution of the binary is described by (Verbunt, 1993;
Verbunt & van den Heuvel, 1995)

$-\frac{\dot{J}}{J}=-\frac{\dot{M}_{d}}{M_{d}}\,f_{\rm ML},$ (4)

where $\dot{J}$ is the rate of change of the orbital angular momentum $J$ due
to effects other than mass loss from the system, $\dot{M}_{d}$ ($<0$) is the
rate of change of the donor mass, and the dimensionless factor $f_{\rm ML}$ is
given by

$f_{\rm ML}=\frac{5}{6}+\frac{n}{2}-\beta
q-\frac{(1-\beta)(q+3\alpha)}{3(1+q)},$ (5)

where $q=M_{d}/M_{\rm ns}\ll 1$ is the binary mass ratio, $\beta$ is the
fraction of $\dot{M}_{d}$ that accretes onto the neutron star ($\beta=1$ for
conservative mass transfer),

$n=\frac{d(\ln R_{d})}{d(\ln M_{d})}$ (6)

denotes how the donor radius $R_{d}$ changes with mass loss, and $\alpha$ is
the specific angular momentum of any (non-conservative) mass lost from the
system in units of the donor star’s specific angular momentum. Thus, $\alpha$
parameterizes the site of any mass ejection from the system, where
$\alpha\simeq 1$ for mass loss close to the donor and $\alpha\simeq q^{2}$ for
mass loss close to the pulsar. Mass transfer in ultracompact binaries is
primarily driven by angular momentum loss due to gravitational radiation from
the binary orbit (see Rappaport et al., 1982, and references therein); for a
circular orbit, this loss is given by (Landau & Lifshitz, 1989; Peters, 1964)

$-\left(\frac{\dot{J}}{J}\right)_{\rm
GW}=\frac{32\,G^{3}}{5\,c^{5}}\frac{M_{\rm ns}M_{d}(M_{\rm
ns}+M_{d})}{a^{4}},$ (7)

where $a$ is the binary separation. Inserting this into the left-hand side of
Equation 4, we can then calculate the gravitational-wave–driven mass transfer
rate from the donor into the accretion disk as

$\dot{M}_{\rm
GW}=-\dot{M}_{d}=\frac{32G^{3}}{5c^{5}}\left(\frac{4\pi^{2}}{G}\right)^{4/3}\frac{M_{\rm
ns}^{8/3}\,q^{2}}{(1+q)^{1/3}\,P_{\rm orb}^{8/3}\,f_{\rm ML}}$ $\approx
2.6\times 10^{-12}\left(\frac{M_{\rm ns}}{1.4M_{\odot}}\right)^{2/3}$
$\times\left(\frac{M_{d}}{0.014M_{\odot}}\right)^{2}\left(\frac{f_{\rm
ML}}{0.66}\right)^{-1}M_{\odot}\mbox{\rm\, yr${}^{-1}$}.$ (8)

Our scaling value of $f_{\rm ML}=0.66$ corresponds to $n=-1/3$ (typical for
degenerate donors) and $\beta=1$.

Although accretion onto the neutron star is mediated by episodic outbursts,
mass continuity requires that the long-term average accretion luminosity
reflect $\dot{M}_{\rm GW}$ if the mass transfer is conservative. Our
observations are not ideal for examining this, since we did not observe the
early (brightest) part of the 2020 outburst with NICER. However, the
unabsorbed 0.5–10 keV X-ray fluence in the 2012 outburst was $1.1\times
10^{-4}$ erg cm-2 (Armas Padilla et al., 2013). Assuming that the 2012
outburst was typical, that the long-term average accretion rate is dominated
by the outbursts, and that there were no intervening outbursts between 2012
and 2020, the outburst separation of $\approx 3100$ days yields a long-term
average X-ray flux of $F_{x,{\rm avg}}=3.9\times 10^{-13}$ erg s-1 cm-2
(0.5–10 keV). We can then write the accretion luminosity as

$\frac{GM_{\rm ns}\beta\dot{M}_{\rm GW}}{R_{\rm
ns}}=\left(\frac{\Delta\Omega}{4\pi}\right)4\pi d^{2}f_{\rm bol}\,F_{x,{\rm
avg}},$ (9)

where $R_{\rm ns}$ is the neutron star radius, $d$ is the distance to the
source, $f_{\rm bol}$ is the bolometric correction (accounting for accretion
luminosity outside the 0.5–10 keV bandpass), and $\Delta\Omega$ is the solid
angle into which the accretion luminosity is emitted. Based on the INTEGRAL
hard X-ray observations in 2012 (Boissay et al., 2012), we estimate $f_{\rm
bol}\approx 1.7$. Assuming $R_{\rm ns}=10$ km and taking $\beta=1$ and
$\Delta\Omega=4\pi$, we obtain an implausibly large distance of 20 kpc.
Although it is not impossible that the source lies on the far side of the
Galaxy, a location near the Galactic center is far more likely given the line
of sight. There are several reasons that our distance estimate might be
significantly inflated. Obtaining a more plausible distance of 8 kpc would
require

$\displaystyle\frac{1}{\beta}\left(\frac{\Delta\Omega}{4\pi}\right)\left(\frac{f_{\rm
bol}}{1.7}\right)\left(\frac{f_{\rm ML}}{0.66}\right)$
$\displaystyle\times\left(\frac{M_{\rm
ns}}{1.4\,M_{\odot}}\right)^{-5/3}\left(\frac{M_{d}}{0.014\,M_{\odot}}\right)^{-2}$
$\displaystyle\times\left(\frac{F_{x,{\rm avg}}}{3.9\times 10^{-13}\mbox{\rm\
erg~{}s${}^{-1}$~{}cm${}^{-2}$}}\right)$ $\displaystyle\approx$ $\displaystyle
6.$ (10)

Some combination of these factors may be different than what we assumed above.
However, a heavier neutron star ($M_{\rm ns}>1.4\,M_{\odot}$), a heavier mass
donor (equivalent to a lower binary inclination), or significant beaming
($\Delta\Omega<4\pi$) would further inflate the distance estimate. Also, our
estimate of $f_{\rm bol}$ is fairly robust, given the broad X-ray coverage of
the INTEGRAL data. It is possible that we have underestimated $F_{x,{\rm
avg}}$. This could happen if we missed accretion outbursts that occurred
between 2012 and 2020, or if the quiescent (non-outburst) flux is as high as
$\sim 10^{-12}$ erg s-1 cm-2. The former possibility can be explored through a
careful analysis of archival X-ray monitoring data, while the latter
possibility could be checked through sensitive X-ray observations of the
source in quiescence.

The factor $f_{\rm ML}$ may be somewhat larger than we assumed. Although we
calculated it using the usual value of $n=-1/3$ for degenerate donors, Deloye
& Bildsten (2003) showed that the WD donors in ultracompact binaries can have
$n$ values in the range of $-0.1$ to $-0.2$ due to the importance of Coulomb
interactions for extremely low donor masses. However, this is unlikely to
increase $f_{\rm ML}$ by more than a factor of $\simeq 1.2$.

Non-conservative mass transfer ($\beta<1$) is a more promising avenue. The
radio detection of IGR J17494 (van den Eijnden et al., 2020) points to the
likelihood of a collimated jet ejection during the outburst. Moreover, a
similar distance conundrum was invoked to infer non-conservative mass transfer
in the ultracompact LMXB pulsar XTE J0929$-$314 (Marino et al., 2017) as well
as several other AMXPs (Marino et al., 2019). Also, there was evidence found
for an outflow in the ultracompact LMXB pulsar IGR J17062$-$6143 (Degenaar et
al., 2017; van den Eijnden et al., 2018), possibly arising from a magnetic
propeller-driven wind from the inner accretion disk (Illarionov & Sunyaev,
1975).

During the long periods of X-ray (accretion) quiescence, mass loss from the
binary could arise from several different mechanisms. These are motivated by
the study of rotation-powered radio millisecond pulsars in detached (non-
accreting) binaries: the so-called “black widow” ($M_{c}\lesssim
0.05M_{\odot}$) and “redback” ($M_{c}\gtrsim 0.1M_{\odot}$) systems, where
$M_{c}$ is the companion mass (see, e.g., Romani et al., 2016, and references
therein). One possibility is black-widow–like ablation of the companion,
driven by rotation-powered gamma-ray emission from the pulsar (Ginzburg &
Quataert, 2020). Such ablation could also be driven by particle heating via
the rotation-powered pulsar wind (see Harding & Gaisser, 1990, and references
therein). Hard X-rays and gamma-rays from the intrabinary shock observed in
many black widow systems could significantly affect the mass loss rate
(Wadiasingh et al., 2018). Another possibility is that the pulsar wind could
drive an outflow from the inner Lagrange ($L_{1}$) point by overcoming the ram
pressure of accreting material (Burderi et al., 2001; Di Salvo et al., 2008).

As an example, we consider the case of gamma-ray ablation. If we assume the
gamma-ray luminosity is $\simeq 10\%$ of the spin-down luminosity ($\simeq
3\times 10^{35}$ erg s-1 based on our long-term $\dot{\nu}$ measurement) as
typically seen in black widow systems (Abdo et al., 2013), this would imply a
companion mass loss rate of $\sim 10^{-11}M_{\odot}/{\rm yr}$ (Ginzburg &
Quataert, 2020). For a source distance of 8 kpc and assuming that
gravitational wave losses dominate in Equation 4, this implies $\beta\approx
0.04$ and $\alpha\approx 0.4$, suggesting that the mass ejection occurs
somewhere between the pulsar and the $L_{1}$ point ($\alpha\approx 0.8$).
However, Ginzburg & Quataert (2020) argue that magnetic braking of the donor
(through magnetic coupling to the ablated wind) likely dominates gravitational
radiation as an angular momentum sink in black widow systems. If so, then that
could both decrease $\beta$ and increase $\alpha$ even further in our case.

All of the X-ray–quiescent mechanisms mentioned above rely on the system
entering a rotation-powered radio pulsar state during X-ray quiescence. We
note that a growing class of so-called transitional millisecond pulsars
(tMSPs) has been identified that switch between LMXB and radio pulsar states
(see Papitto & de Martino, 2020, for a review). The known tMSPs would be
classified as redback systems in their radio pulsar state. If IGR J17494 is a
tMSP, then its low companion mass would make it a black widow system in its
rotation-powered state. We note that the X-ray properties of IGR J17494
correspond to those of the so-called very faint X-ray transients (VFXTs;
Wijnands et al., 2006), whose low outburst luminosities and long-term
accretion rates are difficult to understand. Our observations support the
suggestion that some VFXTs may also be tMSPs (Heinke et al., 2015). The
distinction between VFXTs and ordinary LMXBs may somehow relate to the level
of non-conservative mass transfer.

M.N. and this work were supported by NASA under grant 80NSSC19K1287 as well as
through the NICER mission and the Astrophysics Explorers Program. NICER work
at NRL is also supported by NASA. D.A. acknowledges support from the Royal
Society. This research has made use of data and/or software provided by the
High Energy Astrophysics Science Archive Research Center (HEASARC), which is a
service of the Astrophysics Science Division at NASA/GSFC and the High Energy
Astrophysics Division of the Smithsonian Astrophysical Observatory.

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