# Mixing of hot shocked plasma with cold gas in Nova YZ Ret 2020

Sharon Mitrani  Department of Physics, Technion, Haifa 32000, Israel  Ehud
Behar  Department of Physics, Technion, Haifa 32000, Israel  MIT Kavli
Institute for Astrophysics and Space Research, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  Jeremy J. Drake  Lockheed Martin, 3251
Hanover Street, Palo Alto, CA 94304  Marina Orio  Department of Astronomy,
University of Wisconsin, 475 N. Charter Str., Madison, WI 53706, USA  INAF-
Padova, vicolo Osservatorio 5, I-35122 Padova, Italy  Kim Page  School of
Physics and Astronomy, The University of Leicester, University Road, Leicester
LE1 7RH, UK  Valentina Canton  INAF-Padova, vicolo Osservatorio 5, I-35122
Padova, Italy  Jan-Uwe Ness  European Space Agency (ESA), European Space
Astronomy Centre (ESAC), Camino Bajo del Castillo s/n, E-28692 Villanueva de
la Cañada, Madrid, Spain  Kirill Sokolovsky  Department of Astronomy,
University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL
61801, USA  Sternberg Astronomical Institute, Moscow State University,
Universitetskii pr. 13, 119992 Moscow, Russia

###### Abstract

The origin of bright X-ray emission lines that appear late in a nova eruption
remains largely a puzzle. We present two high-resolution X-ray grating spectra
of the classical nova YZ Ret, observed 77 and 115 days post-eruption, using
XMM-Newton and Chandra, respectively. Both spectra feature resolved emission
lines blueshifted by $v=-1500$ km s-1 and broadened by $\sigma_{v}=500$ km
s-1. The two spectra are well described by a collisionally ionized plasma of
$kT\sim 70$ eV that dimmed by a factor of $\sim 40$ between the two exposures.
The spectra also show narrow radiative recombination continua (RRCs) of C+4,
C+5, and N+5, indicating the interaction of the hot ionized plasma with cold
electrons of $kT\sim 2$ eV. The high-$n$ Rydberg series of C+4 is anomalously
bright, allowing us to measure the electron density through continuum
lowering, which is in agreement with the He-like N+5 density diagnostic of
$n_{e}=(1.7\pm 0.4)\times 10^{11}$ cm-3. The high population of these high-$n$
levels constitutes the best evidence to date of charge exchange (CX) with
neutral H in an astrophysical ionized plasma. The remarkable fact that the
velocity and plasma temperature are the same after 38 days, despite the high
density and decreasing flux is evidence for ongoing heating. We suggest the
heating is due to a reverse shock in the nova ejecta, which forms a thin X-ray
shell. The narrow RRCs and CX are attributed to direct mixing with cold gas,
which overtakes the hot plasma either from the shock front, or through the
contact discontinuity.

##  1 Introduction

Classical and recurrent novae are interacting binary systems hosting a white
dwarf (WD). Their eruptions are attributed to a thermonuclear runaway (TNR) in
the atmosphere of the WD, which has been accreting material from its binary
companion. Models predict that TNR is followed by a radiation driven wind,
which depletes the accreted envelope (Starrfield et al., 2012; Wolf et al.,
2013), or by a wind originating in the common envelope, most likely because of
double Roche-lobe filling (see Shen & Quataert, 2022).

Novae eruptions are luminous at all wavelengths, from $\gamma$-rays to radio.
X-rays specifically provide an important window to understand their physics.
Early in the nova eruption, the X-rays are attributed to powerful shocks in
the outflow. Line-resolved X-ray grating spectra have been successfully
described by collisional ionization steady-state models (see the discussions
in Orio, 2012; Drake et al., 2016; Peretz et al., 2016; Orio et al., 2020;
Chomiuk et al., 2021). However, transient states occur early in the eruption
(Orio et al., 2023; Islam & Mukai, 2023). Nova shocks are powerful enough that
they can produce $\gamma$-ray emission (Franckowiak et al., 2018), of either
leptonic (e.g., inverse Compton off of accelerated electrons) or hadronic
origin (proton interactions producing neutral pions that emit $\gamma$-rays as
they decay).

After a few days to almost a year, most novae transition to the supersoft
phase, where the X-ray luminosity can exceed 1038 erg s-1 (Eddington level for
$\simeq$ 1 M⊙), with all the flux emitted below 0.8 keV (see review by Orio,
2012). This happens because the WD atmosphere contracts at constant bolometric
luminosity, so that the effective temperature keeps on increasing and the peak
wavelength of the emission moves from the optical range, to the UV and extreme
UV, and eventually to the soft X-rays within weeks. The source continues to be
powered by shell burning. The central source appears as a thermal continuum
X-ray supersoft source (SSS), with a peak temperature up to $10^{6}$ K, for a
time lasting from days to a few years (Yaron et al., 2005). The more massive
the WD, the shorter is the SSS phase (Yaron et al., 2005; Starrfield et al.,
2012; Wolf et al., 2013).

The 2020 nova YZ Ret discussed in this paper appeared to follow the trend of
brightening and softening, as expected in the emergence of the SSS, however
the X-ray luminosity remained much below the level of other novae (e.g. Orio
et al., 2022). When the high resolution X-ray observations were triggered,
quite surprisingly only an emission line spectrum was observed, with no sign
of the WD continuum (SSS) (Sokolovsky et al., 2022). The SSS could be obscured
by an accretion disk, indicating a high inclination system (Ness et al.,
2013). In this paper, we analyze and discuss the puzzling X-ray spectra of the
nova, at X-ray maximum flux and during the decay phase.

###  1.1 Nova outburst of YZ Ret

Nova YZ Ret nova erupted in a known binary with a WD. For a summary of
previous observations, see Sokolovsky et al. (2022). It was discovered in
outburst at 5th magnitude on 2020 July 15, and the optical maximum was later
discovered to have occurred on 2020 July 11 at 3.7 mag (Kaufman et al., 2020).
Hence, YZ Ret became visible with the naked eye and the second-brightest nova
in a decade. Optical spectroscopic follow-up confirmed it to be a nova (Aydi
et al., 2020). Kaufman et al. (2020) described the spectrum after the onset of
the eruption as that of a Fe II-type nova (according to the classification
scheme of Williams, 1992), but Carr et al. (2020) reported a He/N-type on
later days. There is now a common understanding that these are successive
phases in the spectral evolution of novae (Aydi et al., 2023). From an
overabundance of oxygen and prominent UV emission lines in the UV, Izzo et al.
(2020) concluded that the nova erupted on an ONe WD. However, we find no
oxygen in the X-ray spectrum.

An X-ray flash detected from YZ Ret immediately after the outburst was
ascribed to the fireball phase, namely an early SSS phase of a few hours, when
the nova is still undergoing the TNR (König et al., 2022). YZ Ret was detected
in $\gamma$-rays (0.1-1 GeV) with Fermi-LAT, and in hard X-rays (3-79 keV)
with NuSTAR, during its first two weeks. Sokolovsky et al. (2022) fitted the
X-ray broad band spectra with unusual abundances from their model, namely a
collisionally-ionized plasma either deficient in iron or overabundant in
oxygen and nitrogen. They also showed the XMM-Newton high resolution grating
spectrum, which is the focus of the present paper, but did not analyze it.

YZ Ret was classified as a VY Scl system (Sokolovsky et al., 2022, and
references therein). VY Scl binaries were defined by Honeycutt & Kafka (2004)
as cataclysmic variables undergoing fading of the optical light by 1.5 to 7
mag over less than 150 days, and these states recur over timescales from weeks
to years. In the more common high state, VY Scl binaries have large optical
and UV luminosity. This is interpreted as evidence that most of the time mass
transfer onto the WD occurs at a rate $\dot{m}>10^{-10}$ M⊙ yr-1, necessary to
sustain an accretion disc in a stable hot state in which dwarf novae outbursts
are suppressed. The low states have been attributed to a sudden drop of
$\dot{m}$ from the secondary, or even to a total cessation of mass transfer
(King & Cannizzo, 1998; Hessman, 2000), perhaps due to spots on the surface of
the secondary covering the L1 point (Livio & Pringle, 1994) or non-equilibrium
of the irradiated atmosphere of the donor (Wu et al., 1995). Monitoring the
X-ray emission of a few of these peculiar binaries, Zemko et al. (2014) ruled
out non-explosive thermonuclear burning.

The observations included in this article were triggered after Swift XRT
monitoring showed the emergence of a soft and luminous object, with the aim of
studying the WD emission in the SSS phase. It was soon realized from XMM-
Newton (Sokolovsky et al., 2022) and NICER spectra (Orio et al., 2022) that
the X-rays from YZ Ret cannot be attributed to the WD. Detecting such soft
X-ray flux from Galactic novae is not often possible due to Galactic column
densities of $N_{\rm H}>10^{21}$ cm-2. However, YZ Ret is at a Galactic
latitude of $-46^{\circ}$, with a low column density of only $N_{\rm
H}=1.2\times 10^{20}$ cm-2 (Kalberla et al., 2005). The distance to the nova
is fairly well determined with GAIA, as $2.5\pm 0.3$ kpc (Bailer-Jones et al.,
2021), which allowed to estimate its X-ray luminosity at a few $10^{35}$ erg
s-1. Indeed, this is an order of magnitude smaller than even the least
luminous SSS-WD (generally, few 1036 erg s-1 to few 1038 erg s-1, Starrfield
et al., 2012).

The two high resolution observations presented here confirm X-ray line
emission with no photospheric SSS whatsoever. The SSS, thought to be the
smoking gun of nuclear burning, has not been observed also in a few other
novae and non-outbursting WD-SSS. Ness et al. (2013) explained the missing SSS
with a non-disrupted (or quickly rebuilt) accretion disk in systems with high
inclination. Notwithstanding, and as we show in the following sections, the
spectra of YZ Ret are like no other, providing unprecedented insights into the
atomic processes of shocked novae outflows. We describe the observations in
Sec. 2, the spectral diagnostic methods in Sec. 3, and their rich application
to the spectra in Sec. 4. In Sec. 5 we report global fits to the spectra. We
discuss all of the results in Sec. 6 and list our conclusions in Sec. 7.

##  2 Observations

YZ Ret was monitored in outburst with the Swift X-ray Telescope (XRT, Burrows
et al., 2005) over 155 days with a cadence that ranged from every 2 days to
weekly monitoring. Two X-ray gratings observations of YZ Ret were triggered 77
and 115 days after the eruption; the first observation with the XMM-Newton
Reflection Grating Spectrometers (RGS, den Herder et al., 2001), and the
second one with the Chandra Low Energy Transmission Grating (LETG, Brinkman et
al., 2000).

###  2.1 Swift XRT lightcurve

Fig. 1 shows the XRT lightcurve featuring a rapid increase in count rate and a
rapid decrease in hardness after day 50. At about day 90 the count rate
started decreasing monotonically until day 160 when monitoring stopped. The
RGS observation at day 77 caught the nova close to its highest state, while
the LETG observation was carried out when the XRT count rate was more than an
order of magnitude lower. Both grating spectra show a rich emission-line
spectrum with no obvious continuum.

Figure 1: Swift XRT count rate (top panel) and hardness ratio (lower panel)
measured in the first 155 days of the nova outburst. The vertical dashed lines
indicate the observations of XMM-Newton (day 77) and Chandra (day 115). The
observations obtained between days 27 and 42 were affected by high background
emission below 0.5 keV. In these cases, the spectrum was fitted over 1-10 keV,
and the model extrapolated down to 0.3 keV to estimate the count rate over the
full 0.3-10 keV band. These data points are marked with x.

###  2.2 XMM-Newton/RGS spectrum

Nova YZ Ret was observed with XMM-Newton 77 days after the initial eruption,
between 2020-09-23 13:36 and 2020-09-23 21:22 UT (ObsID 0871010101; PI: K.
Sokolovsky) for a total exposure time of 28 ks. The Swift XRT count rate
during that week was around 2 cts s-1, already close to its maximum. We use
both RGS1 and RGS2 first-order spectra in the wavelength range of 5–37 Å,
corresponding to the 0.33–2.5 keV energy range. We extracted the spectra with
the XMM-SAS (XMM Science Analysis System) version 19.1111https://xmm-
tools.cosmos.esa.int/external/xmm_user_support/documentation/sas_usg/USG.pdf
rgsproc task. Periods of high background were rejected. As explained in detail
in Sokolovsky et al. (2022), we corrected the RGS spectra for pile up. Fig. 2
shows the spectra observed with RGS1 and RGS2.

###  2.3 Chandra/LETG spectrum

YZ Ret was observed with the Chandra LETG on 2020-10-31 for 31 ks. At the time
of the YZ Ret eruption, the High Resolution Camera (HRC) aboard Chandra was
not available in its HRC-S configuration, which is usually used with LETG (up
to 175 Å). Instead, we used the HRC-I configuration to obtain a spectrum
between 1.2 and 71 Å. The data were extracted with the Chandra CIAO data
analysis package version 4.14.1 and the first-order grating redistribution
matrix files and ancillary response files, using the CIAO task chandra repro,
with version 4.8.5 of the calibration package CALDB. We summed the positive-
and negative- first order spectra with the combine grating spectra CIAO task,
to increase the signal-to-noise ratio (S/N). We did not correct for the higher
spectral orders, which have a negligible contribution. YZ Ret is by far
fainter during this epoch than during the XMM-Newton observation. Fig. 3 shows
the LETG spectrum.

Figure 2: Fluxed spectrum of nova YZ Ret, observed in 2020-09-23 by XMM-
Newton/RGS 77 days after the eruption. Black and red data are, respectively,
RGS 1 and 2. Spectral lines of N+5, C+4, and C+5 are identified. The most
prominent spectral feature is the narrow RRC of C+4 at 31.5 Å, along with the
C+4 He series converging to it. The much fainter narrow C+5 RRC is just barely
observed around 25.2 Å, along with the C+5 Lyman series. The N+5 RRC at 22.3Å
and its He series are also detected, and are shown more clearly in panel (a)
of Fig.11.  Figure 3: Spectrum of YZ Ret observed on 2020-10-31 for 31 ks with
Chandra and the LETG+HRC-I instrumental setup. For clarity, given the low
count rates, the spectrum is presented in photons (not flux), and with the
fitted model (Sec. 5) to guide the eye. with residuals plotted in lower panel.

##  3 Diagnostic methods for high resolution spectra

In order to properly model the rich line resolved spectra, we employ a
collisional-radiative (CR) model. Assuming the ions are collisionally-ionized,
excited by electrons, and in steady-state, the model computes level
populations, and predicts the emission spectral line intensities (in units of
ph s-1cm-3) associated with each transition between bound levels $j$ and $i$
($j>i$) at the source

$I_{ji}=n_{j}A_{ji}$ (1)

where $n_{j}$ (cm-3) is the number density of ions in level $j$ and $A_{ji}$
(s${}^{-1})$ is the Einstein coefficient for spontaneous radiative decay. The
level populations generally depend on electron density $n_{e}$ and temperature
$T_{e}$. At sufficiently high density, electron impact transitions between
excited levels can change the relative populations ($n_{j}$ in Eq. 1), hence
the density sensitivity and diagnostics. The populations of all levels of a
given ion are obtained by solving rate equations that include all of the
processes that populate and depopulate each level (Mitrani & Behar, 2023).
Here, we add ionization and recombination processes. The atomic structure and
coefficients were computed using the relativistic Hebrew University Lawrence
Livermore Atomic Code (HULLAC, Bar-Shalom et al., 2001).

###  3.1 Narrow Radiative Recombination Continua (RRCs)

####  3.1.1 $T_{e}$ Diagnostics

The free-bound transition of a plasma electron recombining with an ion emits a
photon with an energy that equals the kinetic energy of the electron plus the
ionization energy $\rm E_{ion}$ (of the recombined species). The emitted
photons delineate the energy distribution of the electrons in the plasma,
e.g., a Maxwell-Boltzmann (MB) distribution. Since the emitted photons have a
sharp minimum energy of $\rm E_{ion}$, the radiative recombination continuum
(RRC) features a sharp edge at this energy, and usually a MB distribution
thereafter:

$f(E)=\begin{cases}0,&E<\rm{E}_{ion}\\\
(C/kT_{e})e^{-\frac{(E-\rm{E}_{ion})}{kT_{e}}},&E\geq\rm{E}_{ion}\end{cases}$
(2)

where $C$ is a flux normalization factor.

In hot plasmas ($T_{e}>10^{5}$ K), the RRC is significantly broadened by the
temperature, and is hard to discriminate from other continuua, primarily
bremsstrahlung. When the plasma is colder ($T_{e}<10^{5}$ K), narrow RRCs can
be discerned in the spectrum, and their width provides exquisite $T_{e}$
diagnostics. Narrow RRCs are routinely observed in photoionized plasmas
(Liedahl & Paerels, 1996; Kinkhabwala et al., 2002), where the electrons
remain cold despite the high-energy ionizing photons and the high ionization
degree of the plasma. However, narrow RRCs were also observed in a few hot,
shocked X-ray sources, where no photo-ionizing continuum was observed nor
expected (Schild et al., 2004; Nordon et al., 2009; Yamaguchi et al., 2009).
In nova V4743 Sgr, a bright C+4 RRC was observed during the obscuration of the
SSS (Ness et al., 2003, Fig. 4 therein), but not identified.

####  3.1.2 High-$n$ Rydberg Series

When the RRC is sufficiently bright and narrow, and the resolution of the
spectrometer sufficiently high, one can hope to resolve the Rydberg series of
high-$n$ (principal quantum number) emission lines converging onto the RRC. We
are aware of one such observation to date (Nordon et al., 2009), and the
second one is the present RGS spectrum of YZ Ret. If observed, this line
series enables an interesting density diagnostic. The branching ratio for
radiative decay from high-$n$ levels, e.g., to the ground level (i.e., the
observed X-ray line) is suppressed by collisional ionization, for which the
rates increase with $n$. Thus, at some $n_{\rm max}$ value, ionization
dominates over line emission and the series is truncated. This effect of
continuum lowering is known since the early days of quantum mechanics (Dewey &
Robertson, 1928; Inglis & Teller, 1939). Since collisional ionization rates
($S^{CI}$) increase with $n_{e}$ and radiative decays ($A$) do not, the
observed $n_{\rm max}$, or equivalently the effective widening of the RRC
edge, is a sensitive diagnostic of $n_{e}$:

$\frac{A_{n_{\rm max}+1,1}}{S^{CI}_{n_{\rm max}+1}}<n_{e}<\frac{A_{n_{\rm
max},1}}{S^{CI}_{n_{\rm max}}}$ (3)

High-$n$ levels are broadened by the Stark effect, which depends strongly on
the plasma (ion) density. This makes the high order lines blend with the RRC
above some $n_{\rm max}$ that depends on ion density, assumed to be $\sim
n_{e}$. Inglis & Teller (1939) give the following expression for the
dependence of density on $n_{max}$ in the Stark effect:

$n_{e}=0.027n_{max}^{-7.5}a_{0}^{-3}$ (4)

where $a_{0}=0.529\times 10^{-8}$ cm is the Bohr radius.

###  3.2 He-like lines

The most common density diagnostic X-ray lines are those of the so-called He-
like triplets, whose relative intensities depend on the density and
temperature of the plasma (Gabriel & Jordan, 1969). The three transitions from
the 1s2s, 1s2p3/2, and 1s2p1/2 $J=1$ levels to the ground level
1s${}^{2}\,(J=0)$ are referred to, respectively, as the forbidden ($f$),
intercombination ($i$), and resonance ($r$) lines. The 1s2s $(J=1)$ level is a
meta-stable level with a relatively long life time. Hence, the line ratio

$R(n_{e})=\frac{f}{i}$ (5)

is sensitive to $n_{e}$ in a defined range where collisional de-excitation
rates are comparable to the (low) decay rate $A_{ji}$ from that level. These
density ranges in He-like ions increase with the atomic number, as $A_{ji}$
increases with the nuclear charge (Gabriel & Jordan, 1969). Using the CR model
we compute the expected ratios as a function of $n_{e}$, and infer the density
by comparing with the measured ratio.

###  3.3 Emission Measure

The emitted flux from an optically thin uniform plasma is proportional to the
emission measure $EM=\int n_{e}n_{H}dV\approx n_{e}n_{H}V$ where $n_{H}$
(cm-3) is the hydrogen density, and $V$ (cm3) is the volume of the emitting
plasma. An $EM$ can be obtained directly from discrete features, in this case
the RRC photon luminosity $L_{RR}=n_{q}n_{e}\alpha^{RR}V$, where $\alpha^{RR}$
is the RR rate coefficient, and $n_{q}$ is the number density of the
recombining ion $q$. Since $n_{q}=f_{q}A_{Z}n_{H}$, the photon flux can be
written as:

$F^{RRC}=\frac{1}{4\pi d^{2}}f_{q}A_{Z}\alpha^{RR}EM$ (6)

where $f_{q}$ is the ion fraction, $A_{Z}$ is the elemental abundance, and $d$
is the distance to the source. In a hot collisionally-ionized plasma, where
all photons are emitted following electron-ion collisions, the photon flux $F$
is exactly proportional to the $EM$. Thus, by measuring the flux, one obtains
the $EM$. In the Xspec (Arnaud, 1996) model we use in Sec. 5 (bvapec, Smith et
al., 2001), $F$ is parameterized by:

$F=\frac{10^{-14}}{4\pi d^{2}}EM$ (7)

Once $d$ is known, and the density is measured, the $EM$ reveals the emitting
volume $V$.

##  4 Analysis of XMM-Newton RGS spectrum

The RGS spectrum allows us to derive the temperatures, densities, and EM of
the X-ray source at day 77. The Lyman, and He series of C+5 and C+4, as well
as that of N+5, are clearly identified, all blueshifted from their laboratory
wavelengths. The predominant feature in the spectrum is the narrow RRC of C+4
around 31.5 Å, which is broadened and asymmetric due to the electron
temperature on the short-wavelength side, and the high-$n$ lines on its long-
wavelength side. Similar but much fainter features are the narrow C+5 and N+5
RRCs observed around 25.2Å and 22.3Å, respectively. The He-like triplet of N+5
is observed around 29Å, and the He-like triplet of C+4 is at 40Å outside the
RGS band.

###  4.1 C+4, C+5 and N+5 RRCs

A zoom into the C+4 RRC region between 30-33.5 Å is shown in Fig. 4, with the
bright RRC blueshifted by $\sim 1500$ km s-1 and peaking at 31.45 Å. We
modeled this region with an RRC (Eq. 2) and a series of gaussians representing
the Rydberg series. The RRC model provides a temperature measurement of
$kT_{e,C^{+4}}$=$(1.96\pm 0.04)$ eV. The series of unresolved C+4 lines are
fixed to the theoretical wavelengths of the $np$ to $1s$ transitions, and
their Gaussian width to that of the global fit $\sigma_{v}=520$ km s-1 (Sec.
5). Line intensities for $n\geq 10$ are scaled as $n^{-3}$, to follow the
hydrogenic scaling of the Einstein coefficients. This is a good approximation
for high-$n$ levels, which are populated according to the Boltzmann
distribution, and their close proximity implies comparable populations. The
best fit to the spectrum is obtained when the highest level transition is
$n_{\rm max}=35$. In Fig. 5 (left panel), we plot the Cstat ($C$) fitting
parameter as a function of $n_{\rm max}$, which demonstrates that $\Delta
C_{\rm stat}=1$ corresponds to $n_{\rm max}=35^{+10}_{-5}$. Performing the
same fit with $\chi^{2}$ yields $n_{max}=34^{+8}_{-5}$ with 90% confidence.

In order to measure $n_{e}$ from $n_{\rm max}$, we need to scale $A$ and
$S^{CI}$ with $n$ (see Eq. 3). We extrapolated the HULLAC values for $n\geq
10$ according to $A_{n\rightarrow 1}\propto n^{-3}$,
$S^{CI}_{n\rightarrow\infty}\propto n^{2}\log(n)$ (Lotz, 1968), which implies
(c.f., Eq. 3):

$n_{e}\simeq\frac{A_{n_{\rm max}\rightarrow 1}}{S^{CI}_{n_{\rm
max}\rightarrow\infty}}\propto\frac{n_{\rm max}^{-5}}{\log(n_{\rm max})}$ (8)

The inferred $n_{e}$ from $n_{\rm max}=35^{+10}_{-5}$ is
$n_{e,RRC}=(2.4^{+3.0}_{-1.8})\times 10^{11}$ cm-3. Such high densities occur
either in the dense blobs of ejecta, or in the accretion disk. Similarly high
density has been found in Chandra X-ray grating spectroscopy of nova V959 Mon
(Peretz et al., 2016).

Figure 4: The 2020 RGS spectrum of YZ Ret in the range 30-33.5 Å highlighting
the C+4 RRC region. Black and red data are RGS 1, and 2, respectively. The
solid line is a model fitting the RRC, and the $n$ to 1 Rydberg series up to
$n_{\rm max}$ as gaussians. The RRC exponential width on its blue side
indicates $kT_{e,C^{+4}}=1.96\pm 0.04$ eV. The best-fit $n_{\rm max}$ is 35
(see Fig. 5).

Figure 5:  Values of $C_{\rm stat}$ obtained from fitting the Rydberg series
up to $n_{\rm max}$, the maximal $n\rightarrow 1$ transition included in the
model for C+4 (left) and C+5 (right). The minimal $C_{\rm stat}$ value (red
dot) and uncertainty region of $\Delta C_{\rm stat}=1$ (black dots) yield
$n_{\rm max}=35^{+10}_{-5}$ for C+4, and $n_{\rm max}=38(>27)$ for C+5, which
from Eq. 3 indicates an electron density of
$n_{e,RRC}=(2.4^{+3.0}_{-1.8})\times 10^{11}$ cm-3 (for C+4) and
$n_{e,RRC}=(1.6(<9.6))\times 10^{11}$ cm-3 (for C+5) at 90% confidence.

The same diagnostics were applied to the C+5 RRC, which is observed at 25.2Å.
The short-wavelength exponential profile yields a temperature measurement of
$kT_{e,C^{+5}}=1.9\pm 0.2$ eV, consistent with the C+4 temperature. The long-
wavelength side of the C+5 RRC was fitted with a high-$n$ levels series of
Gaussians as the C+4 RRC yielding $n_{\rm max}=38$. Fig. 5 (right panel) shows
that $n_{\rm max}$ can only be constrained from below $n_{\rm max}>27$. Using
Eq. 8 we infer a density of $n_{e,RRC}<9.6\times 10^{11}$ cm-3 (upper limit),
with a best fit of $n_{e,RRC}=1.6\times 10^{11}$ cm-3.

The same procedure was applied to the N+5 RRC, which only provides an upper
limit of $kT_{e,N^{+5}}<1.5$ eV. The low flux of the N+5 RRC does not allow
fitting of the high-$n$ series and thus, no density diagnostic.

Interestingly, if we plug in the best constrained $n_{\rm max}=35$ from C+4
into the Stark-broadening density diagnostic (Eq. 4), we obtain
$n_{e,Stark}=4.8\times 10^{11}$ cm-3, which is within the uncertainties of the
collisional continuum lowering estimate of Eq. 8. In summary, the RRCs of YZ
Ret at day 77 indicate the presence of $kT_{e}\approx 2$ eV electrons with an
electron density in the range of $1-5\times 10^{11}$ cm-3.

###  4.2 Charge Exchange

How exactly the high-$n$ levels get so highly populated in YZ Ret and their
lines so intense is an intriguing question. In fact, to the best of our
knowledge, such a spectrum of C+4 has never been observed, including not in
the laboratory. The high intensity of high-$n$ lines is a smoking gun of
charge exchange (CX). However, due to energy conservation, CX is highly
selective in its population of excited levels. C+5 exchanging charge with a
neutral H atom, both in the ground state, results primarily in C+4 ions in the
$n=4$ levels, with $n=3,5$ levels being appreciably less populated (Nolte et
al., 2012). High collision velocities could result in somewhat higher levels,
but equal fluxes of $n=4-7$ lines and beyond as observed in Fig. 4 can not be
explained by a high velocity alone. Conversely, CX with excited H atoms (or of
excited C+5 in the initial state) requires much less energy to pull out the
bound electron, and thus can end in higher-$n$ levels of C+4 (e.g., Janev &
Winter, 1985). Since excited levels are close to each other, CX with H in
(multiple) excited levels will populate a broader distribution of C+4 high-$n$
levels, as observed here.

We therefore suggest CX in YZ Ret is occurring with excited H. At the measured
electron density in the ionized gas of $n_{e}\approx 10^{11}$ cm-3, $n=2$
levels would be populated to 0.2% of the ground level. We have no measure of
the neutral gas density, which could be denser than the ionized one. We
conclude that the high-$n$ lines of C+4 in the RGS spectrum of YZ Ret feature
the first unambiguous, and most conspicuous evidence for CX in an
astrophysical plasma (at least aside from the solar wind). Moreover, CX is
completely in line with the observation of highly charged ions mixing with
cold gas, as evident also by the RRCs.

###  4.3 He-like N+5 lines

In this section, we perform a direct measurement of the N+5 He-like line
intensities, in order to infer the density of the plasma by using Eq.5. Fig.6
shows the three observed spectral lines of He-like N+5, fitted with three
Gaussians. The measured wavelength and flux of each line is presented in
Table. 1, and the measured $f/i$ ratio is $R(n_{e})_{\rm{N}^{+5}}=1.1\pm 0.2$
(Eq. 5). The average blueshift of the three lines is $v=-1620\pm 80$ km/s,
which is slightly higher than the global fit value in Sec. 5. The discrepancy
can be due to an asymmetry of the $r$ line, and 1s$2l2l^{\prime}$ satellite
lines that blend with the N+5 lines, mostly the $i$ line, similar to the
$2l2l^{\prime}$ satellites of C+5 at 33.85Å (Sec.4.4).

We solve the rate equations (Sec. 3) to obtain the theoretical ratio at
$kT_{e}$=2 eV (the cold recombining plasma component described in Sec. 4.1)
and at 70 eV (the hot plasma component described in Sec. 5) to cover the
expected temperature range. The computed $f/i$ ratio as a function of $n_{e}$
is presented in Fig. 7. The measured value of $R(n_{e})_{\rm{N}^{+5}}=1.1\pm
0.2$ indicates $n_{e}=(1.7\pm 0.4)\times 10^{11}$ cm-3, and $n_{e}=(5.8\pm
0.7)\times 10^{10}$ cm-3 for 2 eV and 70 eV, respectively. If satellite lines
indeed blend with the $i$ line, $R(n_{e})$ is likely higher and the density is
slightly lower (Fig. 7). The density for 2 eV is consistent with the value we
obtained from $n_{\rm max}$ at the RRC $n_{e,RRC}=(2.4^{+3.0}_{-1.8})\times
10^{11}$ cm-3, and a factor 3 higher than the 70 eV value. The above
measurement does not include photo-excitation (PE) because there is no
observed continuum in the YZ Ret spectra.

We check whether the gas may be photo-ionized and PE processes could
dramatically change our density measurement. The unobserved ionizing source we
hypothesize is a continuum black body with a temperature of $kT_{bb}$=50 eV
and a luminosity of $L=10^{38}$ erg s-1, high but typical for a SSS. In photo-
ionization steady state, the PE flux and $n_{e}$ are related through the
ionization parameter $\xi=L/(n_{e}r^{2})$, where $r$ is the distance from the
ionizing source to the emitting plasma. N+5 typically forms at $\xi=10$ erg
s-1cm (Kallman et al., 2009). Adding PE processes slightly reduces the density
by 20%; at $kT_{e}=2$ eV, $n_{e}=(1.4\pm 0.4)\times 10^{11}$ cm-3. $\xi=10$
erg s-1cm then implies $r=(7.6\pm 0.9)\times 10^{12}$ cm. The outflow moving
at 1500 km s-1 will reach a much larger distance at its observed age of 77
days. In addition, the second observation by Chandra shows the outflow at a
similar ionization degree, which would be different if it moved away and was
photo-ionized by the same SSS flux (see discussion in Sec. 6).

Figure 6: The $r,i,f$ lines of N+5 observed in the YZ Ret RGS spectrum. The
measured $f/i$ ratio is $1.1\pm 0.2$.  Table 1: Measurements of the three He-
like N+5 $n=2\rightarrow 1,J=1\rightarrow 0$ transitions. The average
blueshift velocity is $v=-1620\pm 80$ km/s.

Line | Transition |  $\lambda_{meas.}$[Å] |  $\lambda_{rest}^{(a)}$[Å] |  $\Delta\lambda$[Å] | Velocity [km/s] | Flux [10-3 ph s-1 cm-2]
---|---|---|---|---|---|---
$r$ | $1s2p_{1/2}\rightarrow 1s^{2}$ | $28.63\pm 0.01$ | $28.787\pm 0.001$ | $-0.15\pm 0.01$ | $-1640\pm 100$ | $(5.5\pm 0.2)$
$i$ | $1s2p_{3/2}\rightarrow 1s^{2}$ | $28.91\pm 0.02$ | $29.081\pm 0.001$ | $-0.17\pm 0.02$ | $-1760\pm 210$ | $(1.4\pm 0.2)$
$f$ | $1s2s\rightarrow 1s^{2}$ | $29.39\pm 0.01$ | $29.534\pm 0.001$ | $-0.14\pm 0.01$ | $-1460\pm 100$ | $(1.6\pm 0.2)$

Note. —

(a) Cann & Thakkar (1992); Drake (1969, 1971), taken from the NIST atomic
database

Figure 7: Computed $f/i$ ratio as a function of $n_{e}$ for $kT_{e}=2$ eV
(blue) and 70 eV (green). The blue dashed line is the measured $f/i$ ratio in
the spectrum. Shaded areas indicate uncertainties. The measured ratio
indicates a density of $n_{e}=(1.7\pm 0.4)\times 10^{11}$ cm-3, for 2 eV,
fully consistent with $n_{e,RRC}=(2.4^{+3.0}_{-1.8})\times 10^{11}$ cm-3
(Sec.4.1), which is represented by the red shaded area.

###  4.4 Dielectronic recombination satellites

Prominent dielectronic recombination (DR) satellite lines of C+4 between
33.8-34.4 Å, and of C+3 between 35-35.8 Å are observed in the RGS spectrum of
YZ Ret (Fig.8, panel (e) of Fig. 11). These lines exist in the hot collisional
component (bvapec), but are by far weaker than the observed intensities. The
same DR satellites are seen in laboratory plasma, such as laser-produced
plasma (Seely et al., 1981), where the electron density exceeds $n_{e}\simeq
10^{20}$ cm-3. In that case, one observes 1s-2p transitions produced by the
2p$2l^{\prime}$ and 2p$3l^{\prime}$ doubly excited levels decaying to
1s$n^{\prime}l^{\prime}$, at wavelengths above and below 34 Å, respectively
(c.f. Fig.3 in Seely et al., 1981). In contrast, in the present YZ Ret
spectrum, $n_{e}$ is much lower, and the $2l3l^{\prime}$ lines are much
brighter than the dim $2l2l^{\prime}$ lines (Fig. 8). These DR satellites are
all about 300 eV above the 1s continuum (see energy diagram in Fig. 9, left
panel). Therefore, as the temperature approaches $kT\simeq 100$ eV, which is
sufficient for dielectronic capture, they should all be populated, and appear
in the spectrum. The weakness of the 2l$2l^{\prime}$ DR resonances above 34 Å
in the YZ Ret spectrum compared to the bright 2l$3l^{\prime}$ ones just below
34 Å beg for an explanation.

Figure 8: Dielectronic recombination satellite lines of C+4 and C+3 observed
in the RGS 1 and 2 (black, red) spectrum, much above the plasma model
prediction (solid line). The data were rebinned for clarity. The C+3 satellite
lines (right panel) may be blended with Ca+10 or Ar+8 lines.

The peculiar satellites intensity ratios can be explained by a different
mechanism than DR, which is selective PE photo-pumping from the 1s$2l$ levels
to the $2l3l^{\prime}$ levels, by the intense C+4 RRC flux in the narrow band
of 392-420 eV (29.5-31.6 Å, Fig. 11, panel (d)). This selective photo-pumping
to $2l3l^{\prime}$ explains why the lower $2l2l^{\prime}$ levels are not
populated (Fig. 9, left panel). For this mechanism to operate, the 1s$2l$
levels need to be sufficiently populated, namely $n_{e}$ needs to be
sufficiently high. At a density of $n_{e}\simeq 10^{11}$ cm-3, the 1s2s (J=1)
excited level is populated to 0.2% of the ground level by CE processes, to be
subsequently photo-excited to the $2l3l^{\prime}$ doubly excited levels. The
density dependence of the population of this level provides another
diagnostic, pointing yet again to $n_{e}\simeq 10^{11}$ cm-3, see right panel
of Fig. 9. The diagnostic was done with the line ratio of
33.87Å(satellite)/33.97(C${}^{+4}\beta$), but it’s not exclusive to the
C${}^{+4}\beta$ line. The ratio of the satellite line to C+5 Ly$\alpha$ can
also be used as a density diagnostic, because the density affects the
population of the 1s2l (for C+4) and 2l (for C+5) in a similar way. The
correct line ratios are obtained in our model for a density of $n_{e}=(1.0\pm
0.4)\times 10^{11}$ cm-3, in agreement with the density measurements in
Sections 4.1, 4.3.

The resulting synthetic spectrum of the $kT=70$ eV CR model is shown in Fig.
10. The model includes the DR of C+5 via the doubly excited $2l2l^{\prime}$
and $2l3l^{\prime}$ configuration complexes, with an addition of photo-
exciting flux, with the spectrum of the cold C+4 RRC between 392-420 eV. The
spectrum in Fig. 10 was computed at $n_{e}=10^{11}$ cm-3, and matches the
intensities of the satellite lines observed in YZ Ret.

The presence of a strong satellite line at 33.87 Å, along with the absence of
strong matching satellite lines at 33.5 Å and 33.67 Å (rest frame) thus shows
an interaction between the hot (70 eV) and cold (2 eV) components of the
plasma. The RRC photon flux that is required for PE by the CR model in order
to produce the correct intensities of the satellite lines is $F_{\rm
RRC}=10^{28}$ ph s-1 cm-2. From the distance to YZ Ret of $d=7.8\times
10^{21}$ cm away (Bailer-Jones et al., 2021), we know the RRC luminosity
$L_{\rm RRC}$. If this was a point source, the distance $r$ from it at which
$F_{\rm RRC}=L_{\rm RRC}/(4\pi r^{2}$) is $r=10^{7}$ cm. This small distance
is consistent with the physical picture of a thin shock-heated layer that is
discussed in Sec. 6.2, where the ions mix with the cold electrons.

Figure 9: Left: Energy diagram of the C+5 & C+4 levels that are included in
the CR model. Ions are excited by CE (red arrow), and further by PE (green
arrow) selectively to the $2l3l^{\prime}$ configuration complex, by C+4 RRC
photons of 392-420 eV (29.5-31.6 Å). The ions decay to 1s$3l$ levels, which
produce the 33.87Å satellite line (blue arrow) that is shown in Fig. 10 and in
the observed YZ Ret spectrum (Fig. 8). Right: Intensity ratio of the 33.87Å
satellite line and C+4 He$\beta$ at 33.97Å, as a function of $n_{e}$. Since
the population of the 1s$2l$ levels depends on $n_{e}$, the line ratio
provides a density diagnostic of $n_{e}=(1.0\pm 0.4)\times 10^{11}$ cm-3,
consistent with the other density measurements (Sections 4.1, 4.3). Figure 10:
Synthetic spectrum produced by C+5 & C+4 CR model with $kT=70$ eV, and
$n_{e}=10^{11}$ cm-3, including DR via the doubly excited $2l2l^{\prime}$ and
$2l3l^{\prime}$ configuration complexes, with an addition of PE. The colored
lines are the individual transitions while the red line is their sum, which
shows line ratios that match the observed spectrum of YZ Ret. The spectrum is
blueshifted by $v=-1500$ km s-1

###  4.5 Volume and mass of the emitting plasma

In this section, we use the best-fitted fluxes of the (mixed) cold (RRCs) and
hot (Sec. 5) plasmas listed in Table 2, to infer their volume from the density
measurement (Eqs. 6, 7). In all the calculations, we use a distance to YZ Ret
of $d=(7.8\pm 0.7)\times 10^{21}$ cm (Bailer-Jones et al., 2021), a solar
carbon abundance of $A_{C}=4\times 10^{-4}$ (Wilms et al., 2000), and the
density value we obtained in Sec. 4.3, $n_{e}=(1.7\pm 0.4)\times 10^{11}$
cm-3.

For the cold plasma, we use the radiative recombination rate coefficients at 2
eV, $\alpha^{RR}_{C^{+5}}=2.33\times 10^{-12}$ cm-3 s-1 and
$\alpha^{RR}_{C^{+6}}=3.15\times 10^{-12}$ cm-3 s-1 (computed by HULLAC) in
Eq. 6 to obtain $f_{C^{+5}}V=(8\pm 4)\times 10^{35}$ cm3 and
$f_{C^{+6}}V=(1.2\pm 0.6)\times 10^{34}$ cm3. If we assume the C+4 and C+5
RRCs are emitted from the same volume, then we can infer the ion fraction
ratio $f_{C^{+6}}/f_{C^{+5}}=(1.5\pm 0.9)\%$, meaning the carbon in the plasma
is dominated by the C+5 ion ($f_{C^{+5}}\simeq 1$), which is consistent with
the ionization balance of a hot plasma at a temperature of $kT_{e}\simeq 70$
eV. Finally, we obtain a volume of $V_{\rm cold}=(8\pm 4)\times 10^{35}$ cm3.

The volume of the hot plasma (bvapec model) is obtained from Eq. 7, by
assuming the standard $n_{e}/n_{H}=1.2$ density ratio for a fully ionized,
solar abundance plasma. If the hydrogen abundance is different than solar, one
needs to introduce a correction factor (Leahy et al., 2023). We obtain
$V_{\rm{hot}}=(6\pm 3)\times 10^{35}$ cm3, which is consistent with $V_{\rm
cold}$, again lending to the notion that the hot and cold plasmas are mixed.
Given the volume and density, we can estimate the mass in the X-ray source as
$M=\mu m_{p}n_{e}V$, where $\mu m_{p}=1.3m_{p}$ is the mean atomic mass in the
plasma, $m_{p}$ being the proton mass. This estimate yields
$M=10^{-10}M_{\odot}$, which is fitting for such a low luminosity source. In
Sec. 6 we show that the mass outflow rate is normal, but that the short
cooling times leave only a small mass of hot gas at any given time.

##  5 Global fitting

###  5.1 XMM-Newton/RGS

We zoom into the XMM-Newton RGS spectrum (Fig. 2) with five panels in Fig. 11.
The best-fitted model (solid line in the figure) is a low-density,
collisionally-ionized plasma model with varying abundances. The C abundance is
set the unity. This is complemented by the RRCs and high-$n$ line series of
Sec. 4.1. In Xspec (Arnaud, 1996), the bvapec component (Smith et al., 2001)
represents an outflowing ($v=-1504\pm 12$ km s-1) collisionally ionized plasma
at $kT_{e}=73\pm 1$ eV, with lines kinematically broadened by
$\sigma_{v}=520\pm 4$ km/s. Three redge components represent the colder $\sim
2$ eV RRCs of C+4, C+5, and N+5. The series of agauss Gaussian lines represent
the high-$n$ lines converging to the C+4 and C+5 RRCs (Sec.4.1). The model
also includes a Galactic absorption tbabs component with $N_{H}=1.24\times
10^{20}$ cm-2 (Kalberla et al., 2005).

The hot plasma model (red dotted line in Fig. 12) tightly constrains the
outflow velocity and plasma temperature, yields the abundances of N, Ca, and
provides an upper limit for the O abundance (see Table 3). However, it cannot
produce the RRCs, the high-order line series (black dotted lines in Fig. 12),
or the DR satellite lines. More specifically, the observed intensities of the
Lyman and Helium line series of C+5 and C+4 are by far stronger in the
spectrum than their hot-plasma values, starting already from $n=4$ ($\gamma$)
and up to much higher and unresolved $n$ values. These series can be seen in
panels (b) and (d) of Fig.11, where the hot plasma model has been appreciably
enhanced with a series of Gaussians as in Sec. 4.1. The DR satellites of C+4
and C+3 are observed, respectively, between 33.8-34.4 Å and between 35-35.8 Å
(panel (e) of Fig.11), and are also not nearly as strong in the model. These
lines are calculated separately in Sec. 4.4 (Fig. 8). Finally, the relative
intensities of the He$\alpha$ N+5 lines observed between 28.6-29.4 Å (panel
(c) of Fig.11) and of He$\beta$ at 24.76 Å (panel (b) of Fig.11) are
inconsistent with the model intensities, due to its low density approximation
(Sec.4.3).

###  5.2 Chandra/LETG

YZ Ret was observed with the Chandra LETG (Fig.13), 38 days after the RGS
observation. The LETG extends the RGS waveband (up to 37Å) to 71Å, but the
source at this stage was much fainter. We fitted the LETG spectrum with a
similar model to that of the RGS. As in the RGS spectrum, the prominent
features in the LETG spectrum are the C+4 RRC and the thermal line emission.
The C+5 RRC and high-$n$ lines are present, but too faint to be fitted.

The bvapec component represents an outflowing ($v=-1468\pm 90$ km s-1)
collisionally-ionized plasma at $kT_{e}=65\pm 5$ eV. The kinematic broadening
can not be constrained and fixed to the RGS best-fit value $\sigma_{v}=520$
km/s. The RRC of C+4 indicates a cold temperature of $kT_{e}<2.1$ eV. The
softer spectrum of LETG allows us to constrain the abundances of Mg, Si, S,
Ar, and Fe that were not available with the RGS. The measured parameters from
RGS and LETG fitted spectra are compared in Tables 2, 3.

Figure 11:  The full spectrum of YZ Ret observed by XMM-Newton RGS 1 (black)
and RGS 2 (red) in the range of 20-37Å. The spectrum shows emission lines of
several ions such as C+4, C+5, N+5, N+6, and Ca+10. The solid line represents
the fitted model of a velocity broadened collisionally ionized plasma (bvapec)
with 3 colder RRC components for C+4, C+5 and N+5 (redge), along with a series
of gaussians to correct the amplitudes of the C+4 and C+5 high-$n$ transitions
(agauss). Note that the y-axis scale of the different panels is not the same.
Figure 12: Theoretical model for the RGS spectral range of 28-35.5 Å. The hot
component (bvapec) is plotted in (dotted) red. The RRC and the Rydberg series,
which arise from the mixing with the cold medium, are plotted in (dotted)
black, and the total in (solid) blue.

Figure 13: The full spectrum of YZ Ret observed with Chandra and the
HRC-I+LETG instrumental setup. The spectrum is presented with the fitted
model, the residuals (lower panels) and the identified lines. The cold
temperature C+4 RRC is still visible at 31.5 Å. In panel (b), where the
effective area around the carbon edge of the detector is particularly low, the
data are rebinned for visual clarity. Table 2: Best-fit spectral parameters
obtained from XMM-Newton RGS and Chandra LETG.

Observation | Component | Temperature [eV] | Velocity [km/s] |  $\sigma_{\nu}$ [km/s] | Flux [$10^{-3}$ ph s-1 cm-2] | Volume [$10^{35}$ cm3]
---|---|---|---|---|---|---
XMM-Newton RGS | bvapec | $73\pm 1$ | $-1504\pm 12$ | $520\pm 4$ | $(184\pm 2)^{\,(a)}$ | $(6\pm 3)$
| $C^{+4}RRC$ | $1.96\pm 0.04$ | ” | ” | $(24.2\pm 0.4)$ | $(8\pm 4)$
| $C^{+5}RRC$ | $1.9\pm 0.2$ | ” | ” | $(0.5\pm 0.05)$ | -
| $N^{+5}RRC$ | $<1.5$ | ” | ” | $(0.05\pm 0.02)$ | -
Chandra LETG | bvapec | $65\pm 5$ | $-1468\pm 90$ | ” | $(4.4\pm 0.5)^{\,(a)}$ | $(50\pm 20)$
| $C^{+4}RRC$ | $<2.1$ | ” | ” | $(0.9\pm 0.3)$ | -

Note. — ($a$) Measured in the range of 0.3-0.7 keV

Table 3: Elemental abundances of the hot gas relative to solar (Wilms et al.,
2000) as measured by the bvapec model. Unlisted elements are not observed and
were taken at solar values.

Element |  XMM-Newton RGS |  | Chandra LETG |
---|---|---|---|---
C | 1.00 |  | 1.00 |
N | $0.81\pm 0.03$ |  | $0.7\pm 0.4$ |
O | $<5\times 10^{-4}$ |  | $<0.2$ |
Mg | -(a) |  | $1.5\pm 0.6$ |
Si | -(a) |  | $1.1\pm 0.4$ |
S | -(a) |  | $1.7\pm 0.4$ |
Ar | -(a) |  | $1.5\pm 0.4$ |
Ca | $1.2\pm 0.1$ |  | $<6.6$ |
Fe | - |  | $4.0\pm 3.3$ |

Note. — ($a$) Set to the values obtained by the Chandra fitted spectrum.

##  6 Discussion

The key diagnostic is the high density $n_{e}=10^{11}$ cm-3, which implies
extremely short time scales. For a C+5 recombination rate coefficient of
$\alpha^{RR}\sim 3\times 10^{-13}$ cm3 s-1, the recombination (and ionization)
time is $\sim 30$ s. For a solar abundance plasma at $kT=70$ eV, the cooling
function is $\Lambda\simeq 10^{-22}$ erg cm3s-1 (Sutherland & Dopita, 1993),
and thus the radiative cooling time is $\tau=kT/n_{e}\Lambda\simeq 10$ s. The
fact that the X-ray source persists on much longer time scales implies
continuous heating, which can be attributed to a reverse shock in the nova
ejecta. Only the most recently shocked gas remains hot, resulting in a thin
X-ray emitting shell, consistent with the theory of Hachisu & Kato (2023). The
reverse shock velocity can remain constant for a long time as it moves through
the ejecta (Hachisu & Kato, 2023), as also expected in supernova remnants
(Micelotta et al., 2016, Fig. 4 therein).

If we ascribe a width $\delta r\approx v\tau\approx 10^{9}$ cm to the shell
during the RGS epoch, the thin shell geometry implies $V=\Omega r^{2}\delta
r$, where $\Omega$ is the opening angle of the flow in sr. For $V_{\rm
hot}=6\times 10^{35}$ cm3; $\Omega r^{2}=6\times 10^{26}$ cm2. From here, the
mass outflow rate in the shell is $\dot{M}=\Omega r^{2}nv\mu m_{p}$. Plugging
in all the above estimated parameters, we obtain $\dot{M}=3\times
10^{-4}\,M_{\odot}$ yr-1. Since in this approximation, $\delta
r\propto\tau\propto 1/n_{e}$, as the outflow expands and the density
decreases, $\delta r$ increases. In Section 4.4, we estimated the length scale
of mixing between the hot and cold gas to be even smaller than $10^{9}$ cm.

###  6.1 Shock heating and cooling

Direct evidence for the shocked plasma comes from the line widths. The
measured $\sigma_{v}=500$ km s-1 corresponds to a post-shock C ion
($M_{C}=12m_{p}$) temperature of $kT=12m_{p}\sigma_{v}^{2}=30$ keV. The reason
we do not observe such high electron temperatures and fully charged ions is a
combination of the long electron-ion interaction times, and the efficient
electron cooling. At $10^{11}$ cm-3, electrons would need $\sim 200$ s to
reach the ion temperature (Fig. 4.5 in Vink, 2020), while their cooling times
are tens of seconds.

Assuming 30 keV is the shock temperature $kT_{s}$, the relative velocity
$v_{s}$ between the shock and the unshocked ejecta (neglecting radiation
losses) is given by $kT_{s}=(3/16)m_{p}v_{s}^{2}$, or $v_{s}=4000$ km s-1. The
reverse shock is often much slower in the observed frame (Micelotta et al.,
2016). Thus, $v_{s}$ is approximately the velocity of the unshocked ejecta. As
expected, it is higher than 1500 km s-1, the velocity of the plasma after it
is shocked. The high velocity of $4000$ km s-1 suggests the ejecta escaped
from close to the photosphere of the WD, yet is shocked further out.

###  6.2 Comparing the two epochs, evidence for a standing shock?

What can we learn from comparing the RGS (day 77) and LETG (day 115) spectra?
Both are fitted well with a 70 eV plasma model (bvapec). The lines in both are
blueshifted by $\sim-1500$ km s-1, and broadened by $\sigma_{v}\sim 500$ km
s-1. Both spectra feature narrow ($\sim 2$ eV) RRCs representing a cold plasma
component. However, the X-ray flux on day 115 is about 40 times lower (c.f.
Fig. 1), which is approximately true separately for both the hot and
recombining components. Table. 2 summarizes the important fitted parameters.

If the X-ray source is moving out at 1500 km s-1 over these 38 days, it
traveled a distance of $5\times 10^{14}$ cm. Since the X-rays started to rise
$\approx 20$ days earlier, by day 77 it could have already reached $\sim
2.5\times 10^{14}$ cm. Interestingly, Nova Delphini 2013 was also observed
with gratings late (days 87 and 114 there), featuring blueshifted C and N
lines, but in absorption with the SSS as a back-lighter (Milla & Paerels,
2023). The fast velocities at these late times led those authors as well to
explain the absorption by a thin shell ejected early, but now $10^{15}$ cm
away from the center. The X-ray source in YZ Ret seems to be in a similar
situation, only the SSS is obscured.

Returning to the conical outflow geometry, and using a distance at the RGS
epoch of $r=2.5\times 10^{14}$ cm, and $V_{\rm hot}=\Omega r^{2}\delta r=(6\pm
3)\times 10^{35}$ cm3, we get $\Omega\delta r=(8\pm 3)\times 10^{5}$ cm. If
$\delta r\approx 10^{9}$ cm, it implies a minuscule $\Omega$ of $8\times
10^{-4}$ sr, namely small and dense blobs of ejecta. If on the other hand
$\delta r\approx 10^{7}$ cm (Sec. 4.4), then $\Omega\sim 8\times 10^{-2}$ sr,
or a few degrees. At the LETG epoch, the gas expanded by a factor of 3 to
$r=7.5\times 10^{14}$ cm. Assuming $\Omega\delta r$ remained the same, given
similar cooling times, the corresponding volume on day 115 increased by a
factor of 9, $V_{\rm hot}\propto r^{2}=(5\pm 2)\times 10^{36}$ cm3. The day
115 LETG X-ray flux is a factor $\sim 40$ lower than on day 77. Thus, from Eq.
7, $n_{e}$ decreased by only a factor of 2, and so did the cooling time,
justifying an approximately constant $\delta r$.

The continuous shock over 38 days in Sec. 6.2 suggests a large distance from
the center, and poses a challenge with its extremely small opening angle
$\Omega$. However, a reverse shock does not need to expand so fast, or at all.
In a standing shock, the ejecta flows from the center at several 1000 km s-1,
collides with the shock front, and exits the shock region at 1500 km s-1 (see
Sec. 6.1 for the velocity and temperature estimates), while the shock location
remains constant in the observer’s frame of reference. Since the cooling time
is short, we observe fresh (recently) shocked ejecta at each time. The fact
that the temperature and velocity broadening are similar after 38 days,
attests to the constant relative velocities of the ejecta and the shock over
this long time scale. In this scenario, the X-ray flux variability in Fig. 1
can be ascribed to the varying mass outflow rate of the nova. A factor of 40
fainter X-rays with LETG compared to the RGS, thus indicates a similar factor
reduction in the density, from 1011 cm-3 to a few 109 cm-3. For a standing
shock unfortunately, we have no distance diagnostics. In the thin shell
geometry, a location closer to the center implies a larger opening angle,
since the measured volume is $V\propto\Omega r^{2}$. If, say, $\Omega\sim 1$
sr, with $\delta r\sim 10^{9}$ cm, it would imply a distance of $r={\rm
few}\times 10^{13}$ cm, and higher for smaller $\delta r$.

###  6.3 The Cool Plasma Component

The outflow velocity and the volume estimates of the cold plasma (2 eV from
the RRCs) are almost identical to that of the hot plasma, which suggests the
two components are physically connected. This is not the first time narrow
RRCs are observed in shocked X-ray sources. Schild et al. (2004) found C+4 and
C+5 RRCs in the RGS spectrum of the colliding wind binary $\gamma^{2}$ Vel,
which indicate a temperature of 40kK (few eV) in a hot (keV) plasma. Nordon et
al. (2009) analyzed the C+5 RRC in the LETG spectrum of the planetary nebula
BD$+30^{\circ}3639$, and found a temperature of $kT_{e}=1.7\pm 1.3$ eV in a
hot 160-260 eV plasma. These RRCs were unambiguously detected in high-
resolution grating spectra. Fe+24 and Fe+25 RRCs were detected with the Suzaku
CCDs in supernova remnants (Ozawa et al., 2009; Yamaguchi et al., 2009) at
much higher temperatures of $kT\simeq 1$ keV. All of these findings combined
suggest that narrow RRCs are a common feature of shocked plasmas.

The physical origin of these RRCs and the source of cold electrons are
debated. While adiabatic cooling and ionization freezing has been proposed
(Schild et al., 2004; Yamaguchi et al., 2009), we suspect there is genuine
mixing of cold electrons with the highly-charged ions. Mixing with cold gas
can occur either at the reverse-shock front between shocked and unshocked
wind, or at the contact discontinuity, at the interface between shocked ejecta
and the dense, much cooler, shocked ISM gas. Computing the penetration depth
of 2 eV electrons into the hot gas region, by taking the Larmor radius in a
$1\mu G$ magnetic field, one gets $R_{L}\simeq 5\times 10^{6}$ cm, which is
comparable to the hot thin shell size estimated in Sec. 4.4. Neutral atoms
from the cold phase of course penetrate the hot gas smoothly, with no magnetic
obstacle. These neutrals are discussed in Sec. 4.2. Another possible scenario
is runaway radiative cooling. The cooling function of astrophysical plasmas
peaks sharply at $\Lambda\approx 10^{21}$ erg cm3s-1 between $4.2\,{\rm
K}<\log T<5.7$ K (e.g., Sutherland & Dopita, 1993). This implies that gas
cooling below $\sim 50$ eV would rapidly cool down to 1-2 eV. At the density
of $10^{11}$ cm-3 this cooling time is $\tau<1$ s. This could explain why we
observe narrow RRCs, namely no gas whatsoever at temperatures above 2 eV.

The X-ray source in YZ Ret is exceptional in its high density, small volume,
and prominent RRCs. We suspect that under these conditions, the highly charged
ions are completely immersed in the dense cold gas, the source of which could
be one of the above. Another source of cold material could be an accretion
disk. Ness et al. (2013) suggested that X-ray emission line spectra observed
with no SSS after nova eruptions originate in high-inclination systems, where
the SSS is obscured by optically thick material, formed in a disk around it.
This disk can explain the lack of an observed SSS in YZ Ret, and provide a
cold dense medium that the shocked gas runs into to produce the observed
narrow RRCs and the CX. However, since the RRCs and high-$n$ lines are
blueshifted, the wind would need to carry cool disk material with it without
slowing down. The geometry and inclination of the system would need to be fine
tuned to completely hide the WD, but allow us to still observe the approaching
wind interacting with the edge of the disk.

##  7 Conclusions

We observed nova YZ Ret 2020 77 and 115 days after the eruption with XMM-
Newton and Chandra gratings, respectively. The X-ray flux decreased by a
factor of $\sim 40$ between epochs. Both X-ray spectra are characterized by
emission lines with no sign of thermal emission from the SSS. In the following
we summarize our conclusions from the analysis of the two spectra:

  1. 1.

Three totally different density diagnostics, namely using $f/i=1.1\pm 0.1$ in
He-like N (Sec. 4.3), $n_{\rm max}=35^{+10}_{-5}$ in the 1s$nl$ Rydberg series
of He-like C (Sec. 4.1), and 1s$n^{\prime}l^{\prime}$ satellite line ratios of
He-like C (Sec. 4.4), all point to $n_{e}\simeq 10^{11}$ cm-3.

  2. 2.

This key density diagnostic indicates radiative cooling and recombination
times of the order of tens of seconds, which must imply ongoing heating,
ascribed to a thin shock-heated layer of $10^{7}-10^{9}$ cm in the nova ejecta
(Sections 4.4, 6).

  3. 3.

The emission lines originate in collisionally ionized plasma of $kT_{e}\simeq
70$ eV that was heated by the shock (Sec. 5), but may not have had time to
reach its maximal temperature or ionization degree due to the rapid radiative
cooling. The $\sigma_{v}=500$ km s-1 broadened lines suggest the ions may
still be hot at $kT\sim 30$ keV.

  4. 4.

The narrow RRCs in the spectrum indicate the presence of cold 2 eV electrons,
recombining with the hot, highly-charged C and N ions (Sec. 4.1). These cold
electrons could have crossed into the shocked region via the contact
discontinuity, or the shock front (Sec. 6.3).

  5. 5.

The DR satellite line observed at 33.87Å (rest frame) indicates a close
interaction between the hot (70 eV) and cold (2 eV) components via photo-
pumping. The high photon flux that is needed to produce the observed satellite
line ratios implies the two are mixed (Sec. 4.4).

  6. 6.

The high-$n$ Rydberg series of C+4 suggests highly charged ions are undergoing
CX with neutral atoms, furthering the evidence for mixing of shocked and cold
gas in the nova.

The consistently high outflow velocity of $-1500$ km s-1 over 38 days would
imply a source size of $\sim 10^{15}$ cm (Sections 4.5, 6.1), but an outflow
with a disturbingly minuscule opening angle, consistent maybe with small dense
blobs and a low volume filling factor. Conversely, invoking a standing reverse
shock could imply a shorter distance, and thus alleviate the small opening
angle problem.

S.M. and E.B. were supported in part by a Center of Excellence of the Israel
Science Foundation (grant No. 1937/19). M.O. was supported by a Chandra-
Smithsonian award for the Chandra/LETG observation. This paper employs a list
of Chandra datasets, obtained by the Chandra X-ray Observatory, contained in
the Chandra Data Collection (CDC) 233 https://doi.org/10.25574/cdc.233
(catalog doi:10.25574/cdc.233)

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