# Spectroscopic Insights into the Quiescent Stages of RS Ophiuchi (2006-2021):
Photoionization Modeling and Accretion Dynamics

Gesesew R. Habtie 1,2, Ramkrishna Das 1
1 S N Bose National Centre for Basic Sciences, Salt Lake, Kolkata 700 106,
India
2 Debre Berhan University, Debre Berhan, Ethiopia
E-mail<EMAIL_ADDRESS>0000-0001-9827-738X 0000-0002-5440-7186

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

This paper presents a comprehensive spectroscopic analysis of the nova RS
Ophiuchi during its quiescent stage, spanning a duration of approximately 13
years. The spectra exhibit prominent low-ionization emission features,
including hydrogen, helium, iron, and TiO absorption features originating from
the cool secondary component. The CLOUDY photoionization code is employed to
model these spectra, allowing us to estimate various physical parameters such
as temperature, luminosity, and hydrogen density, along with elemental
abundances and accretion rate. The central ionizing sources exhibit
temperatures in the range of $1.05-1.8~{}\times 10^{4}$ K and luminosities
between $0.1-7.9~{}\times 10^{30}$ erg s-1. Notably, He  displays an
overabundance from 2008 to 2016, returning to solar values by 2020, while Fe
appears subsolar from 2008 to 2014 but becomes overabundant from 2006 onward.
The mean accretion rate, as calculated from the model, is approximately
$1.254\times 10^{-8}M_{\odot}$ yr-1. About 47% of the critical mass was
accreted after April, 2020 ($\sim$15 months before the 2021 outburst), and
approximately 88% of the critical mass was accreted after July 20, 2018. This
non-uniform accretion rate suggests a more rapid approach towards reaching the
critical mass in the final years, possibly attributed to the heightened
gravitational pull resulting from previously accreted matter, influencing the
accretion dynamics as the system approaches the critical mass limit.

###### keywords:

accretion, accretion discs, - stars: binaries: close, stars : novae,
cataclysmic variables - line : profiles, identification, - techniques :
spectroscopic - stars : individual (Rs Oph)

††pagerange: Spectroscopic Insights into the Quiescent Stages of RS Ophiuchi
(2006-2021): Photoionization Modeling and Accretion Dynamics –A

##  1 Introduction

Nova RS Ophiuchi (RS Oph) stands out as a extensively studied symbiotic
recurrent nova (RN) that has undergone nine repeated outbursts. These notable
events occurred in the years 1898, 1907, 1933, 1945, 1958, 1967, 1985, 2006
(Schaefer, 2010), and 2021 (Pandey et al., 2022). However, the 1907 and 1945
outbursts lack full confirmation due to their alignment with the sun
(Schaefer, 2004, 2010). The recurrence of these outbursts is interspersed with
quiescent periods lasting approximately between 9 and 21 years (Schaefer,
2010). The nova system consists of a massive white dwarf
($M_{WD}=1.2-1.4M_{\odot}$) and a red giant (RG) donor of M0–2 III type with a
mass range of 0.68–0.80 M (Brandi et al., 2009; Mikołajewska & Shara, 2017;
Parthasarathy et al., 2007; Hachisu et al., 2007; Osborne et al., 2011). The
binary has an orbital period, $P_{\text{orb}}$, of 453.6 $\pm$ 0.4 days
(Brandi et al., 2009). Hjellming et al. (1986) estimated the distance to RS
Oph of d = 1.6 kpc from H i absorption line measurements.

The massive white dwarf (WD) in conjunction with its high mass-transfer rate
$\sim 2\times 10^{-7}M_{\odot}\text{yr}^{-1}$ (Walker, 1977; Booth et al.,
2016) and the gradual increment in the WD’s mass due to the accumulation of
about 10 percent of the accreted matter during each quiescent stage (Hachisu &
Kato, 2000), provides compelling evidence that RS Oph is a strong candidate
for a Type Ia supernova. This is substantiated by the fact that, over time, it
will eventually reach the Chandrasekhar limit. The net increasing rate of the
WD mass has been calculated to be $1.2\times 10^{-8}M_{\odot}\text{yr}^{-1}$
(Hachisu & Kato, 2000), further supporting the premise that RS Oph holds the
potential for evolving into a Type Ia supernova.

Despite the observational differences in orbital phase and line of sight
through the red giant wind, the 2021 outburst of RS Oph exhibited remarkable
similarity to the 2006 event (Azzollini et al., 2023). The envelope mass
accreted onto the white dwarf between the 1985 and 2006 outbursts, spanning
approximately 21 years at the optical peak, has been quantified at $4\times
10^{-6}M_{\odot}$. A considerable fraction of this mass was ejected by the
stellar wind (Kato et al., 2008). The net growth rate of the white dwarf
during this period falls within the range of $(0.5-1)\times
10^{-7}M_{\odot}yr^{-1}$. In the subsequent time frame from 2006 to 2021,
approximately 15 years, the envelope mass at the optical peak is estimated to
be $4\times 10^{-6}M_{\odot}$, accompanied by a corresponding mean accretion
rate of $4.8\times 10^{-8}M_{\odot}yr^{-1}$ (Hachisu & Kato, 2000). These
parameters serve as crucial indicators for comprehending the accretion
dynamics and evolutionary trends within the RS Oph system.

Away from the fast evolving nova eruptions, in quiescence RS Oph is powered by
accretion of material lost by the red-giant companion (RG) onto its WD (Munari
& Tabacco, 2022). RS Oph has been a popular target in searches for accretion-
induced, rapid light-variability (flickering) during its quiescence periods,
with all observing campaigns that have invariably detected its presence
(Walker, 1977; Zamanov, 2011).

During quiescence, the optical spectrum is predominantly shaped by the
presence of the giant secondary, exhibiting recombination lines of H i and He
i (Anupama & Mikołajewska, 1999). Apart from T CrB, the remaining objects in
this category display additional lines attributed to Fe II, Ca II, and OI
8446, while He II lines are notably weak or absent (Williams et al., 1994;
Anupama & Mikołajewska, 1999). Furthermore, the emission lines exhibit a
central narrow absorption, akin to the S3 class of symbiotic stars. This class
is characterized by a slow and dense wind, resulting in a profound central
reversal of the H-alpha emission line (Van Winckel et al., 1993).

During quiescence, the optical spectrum of RS Oph is dominated by the giant
secondary, featuring emission lines of H i and He i along with lines due to Fe
ii, Ca ii, and O iOI 8446Å(Anupama, 2008). The presence of weak or absent He
II lines is noted (Anupama & Mikołajewska, 1999). The emission lines exhibit a
central narrow absorption, resembling the S3 class of symbiotic stars,
indicating a slow, dense wind (Van Winckel et al., 1993).

Spectra of V3890 Sgr reveal a H $\alpha$ line structure similar to RS Oph,
with emission, broad wings, and a central absorption feature. The FWHM of the
H $\alpha$ line and its components are provided, showing moderate changes
likely linked to orbital motion. The spectra also display Balmer lines, lines
of He i, and weak He ii at 4686 A (Zemko et al., 2018).

In this study, we have collected spectroscopic data of RS Oph from February
2008 until April 2020. We describe our dataset in Sect. 2; in Sect. 3, we
discuss spectral characteristics observed during quiescence; in Sect. 4, we
describe the modeling strategy and technique using the cloudy photoionization
tool; in Sect. 5, we provide the results from the model, and finally, a brief
discussion of our results and conclusions are given in Sect. 6 and 7,
respectively.

##  2 Data Set

For the present study we used a spectroscopic data available in Astronomical
Ring for Access to Spectroscopy Database (ARAS Database111 https://aras-
database.github.io/database/novae.html; Teyssier (2019)), Stony Brook/SMARTS
Atlas of (mostly) Southern Novae
(222http://www.astro.sunysb.edu/fwalter/SMARTS/NovaAtlas/rsoph/rsoph.html(Walter
et al., 2012), and Astrosurf Recurrent
Nova333http://astrosurf.com/buil/us/rsoph/rsoph.htm. Out of the eight spectra
selected for analysis, six were obtained from the ARAS database, one from
Stony Brook, and one from Astrosurf. The ARAS Symbiotics Project is composed
of a cluster of compact telescopes, with diameters spanning from 20 cm to 60
cm. These telescopes are outfitted with spectrographs featuring resolutions
ranging from R $\sim$ 500 to 15,000. The instruments cover a wavelength
spectrum from 3600 Å to approximately 9000 Å and are specifically designed for
monitoring eruptive variable stars. The Stony Brook/SMARTS Atlas database
contains both spectroscopy and photometry obtained since 2003. This data
facilitate systematic studies of the nova phenomenon and correlative studies
with other comprehensive data sets (Walter et al., 2012).

In addition to the eight spectra, we also utilized a spectrum of an M2III type
star, predicted to be the companion star of the WD of Rs Oph (Pickles, 1998;
Anupama & Mikołajewska, 1999; Mondal et al., 2020), obtained from the European
Southern Observatory (ESO)
website444https://www.eso.org/sci/facilities/paranal/decommissioned/isaac/tools/lib.html.
This spectrum was used to incorporate the absorption components of a spectrum
originating from the secondary star.

The spectra were obtained by various observers at different observatories,
including Cerro Tololo Inter-American Observator (CTIO) in Chile, Castanet-
Tolosan Observatoty (CTO) in France, West Challow Observatory (WCO) in
England, Santa Maria de Montmagastrell Observatory (SMMO) in Spain, Mill Ridge
Observatory (MRO), Vihorlat National Telescope (VNT) at the Astronomical
Observatory at Kolonica Saddle in Slovakia, Labastide St Sernin (LSS) in
France, Three Hills Observatory (THO) in the UK, and Desert Celestial
Observatory (DCO) in the USA. The instrumentation and observation details for
each observatory and the log of observations are presented in Table 1.

Table 1: Log of optical spectral observation of Rs Oph, during its quiescent
stages between the 2006 and 2021 outbursts.

MJD | Date 2021 (UT) | NDi(days) | Observer | Observatory | Spectrograph | Camera | Rii | Coverage (Å) | TTEiii(s)
---|---|---|---|---|---|---|---|---|---
54518 | 22 Feb. 2008 | 740 | SB1 | CTIOa | venerable RC | 1K CCD | - | 2720-9558 | 300
55423 | 15 Aug. 2010 | 1645 | BUI2 | CTOb | LISA | QSI583 | 620 | 3829-7317 | 4200
56104 | 26 Jun. 2012 | 2326 | BUI2 | CTOb | LISA | Atik314L+ | 1000 | 3829-7317 | 2113
56862 | 24 Jul. 2014 | 3085 | DBO3 | WCOc | LISA | SXVR-H694 | 870 | 3800-7591 | 4441
57620 | 20 Aug. 2016 | 3843 | JGF4 | SMMOd | LHIRES | ATIK 460EX | 1101 | 3917-7475 | 4019
58319 | 20 Jul. 2018 | 4542 | LES5 | MROe | echelle | ASI1600mm | 12000 | 4031-7950 | 8590
58945 | 06 Apr. 2020 | 5168 | LES5 | MROe | echelle | ASI1600mm | 14000 | 4031-7955 | 7397
59281 | 08 Mar. 2021 | 5504 | PAD6 | VNTf | LISA | Atik 460ex | 824 | 4000-7500 | 1822

Note: (i)Number of days counted from $t_{0}$ (2021 June 12.959 UT, MJD
59378.459), iiResolution; iiiTotal Time of Exposure; (1)Stony Brook using
(a)Cerro Tololo Inter-American Observator (CTIO); (2)Christian Buil using
(b)Castanet-Tolosan Observatoty; (3)David Boyd using (c)West Challow
Observatory, 4Joan Guarro Flo using (d)Santa Maria de Montmagastrell
Observatory; (5)Tim Lester using (e)Mill Ridge Observatory, (6)Pavol A.
Dubovsky using (f)Vihorlat National Telescope.

##  3 General descriptions of the spectra

We selected eight spectra covering the wavelength range of $\sim$ 3900 to
$\sim$ 7500 Å and a resolution range of $\sim$ 620 to 14,000 for spectral
analysis and modeling purposes, encompassing the time duration between the two
consecutive outbursts (2006 & 2021). While modeling, we incorporated a
spectrum of an M2III type obtained from the European Southern Observatory
(ESO)
website555https://www.eso.org/sci/facilities/paranal/decommissioned/isaac/tools/lib.html.
Both the modeled and observed spectra are normalized to the line flux of H
$\beta$, and the observed spectra are de-reddened by E(B-V)=0.73 (Snijders,
1987; Pandey et al., 2022).

The spectra of RS Oph observed during its quiescent period between the 2006
and 2021 outbursts are depicted in the two panels of Fig. 1. The respective
observation dates are indicated at the top-left corner of each panel. For this
study, we selected eight spectra with nearly two-year intervals, except for
the last one, which has only a one-year difference. The spectra span from
February 22, 2008, to August 2021, covering approximately 5504 days of the
quiescent stage. These spectra exhibit prominent emission features originating
from the illuminated accretion disc surrounding the white dwarf (WD).

Figure 1:  Dereddened spectra of Rs Oph, illustrating the spectroscopic
evolution from days +0.99 to +14.91 in the upper panel and from days +17.97 to
+25.84 in the lower panel. For the sake of clarity, the spectra are offset by
the amount indicated on the left side of the figure. The ordinate scale is
logarithmic to emphasise the visibility of weaker features relative to the
emission feature of H $\alpha$. ’atm’ stands for atmospheric absorption seen
at around 6876 Å, which appeared in all spectra at decreasing strengths.

The observed spectra display strong and broad emission lines attributed to
hydrogen, helium, and iron, but the broadness of the lines noticed decreasing
with time. The strong emission features noticed in the spectrum observed on
2008 February 22 are a result of recombination lines such as Balmer lines
(from H $\alpha$ to H 8) and He I (4922, 5016, 5876 6678, and 7065 Å) lines.
However, the presence of some Fe ii lines is also expected, either
independently or blended, such as Fe ii (4233, 4491, 4584, 4924, 5018 Å). The
absence of higher ionization lines can be accounted for by the absorption and
softening caused by the reradiation of all direct photons from the accretion
disc.

The strong TiO absorption features at 5448 and 6180 Å are caused by the
secondary. The Fe ii emission lines are a product of illumination from a high-
density inner region of the disc undergoing photoionization. The quiescence
phase of Rs Oph starts from $\sim$ 250 d, as a clear signatures of resumption
of accreting matter and TiO  molecules detected at various wavelengths such as
4762, 5448, 5598, 5629 and 6159 Å (Worters et al., 2007, 2008; Mondal et al.,
2018).

The emission line profiles of the strongest four Balmer lines are depicted in
the two panels of Fig. 2. The left column comprises the profiles of the H
$\alpha$ and H $\beta$ lines, while the right column encompasses the profiles
of the H $\gamma$ and H $\delta$ lines. The figure encompasses eight days’
worth of profiles for each line. Of these, the profiles from 2018 and 2020,
acquired through a high-resolution telescope, distinctly exhibit a central
double-peaked component feature. This feature, previously observed in prior
outbursts (Brandi et al., 2009; Zamanov, 2011; Worters & Rushton, 2014), is
notably conspicuous. The presence of a central, robust absorption feature in H
$\alpha$ is mirrored in H $\beta$, suggesting a common origin for both lines.

Figure 2:  Plot of H $\alpha$, H $\beta$, H $\gamma$, and H $\delta$ emission
line profiles of RS Oph during the quiescence phase happened between the 2006
and 2021 eruption. The dates presented in the left column also correspond to
the respective right column in the same row. Similarly, the line labels
presented at the top of each column also correspond to all rows below. The
legends on the top panels of each column apply to all the panels below, and
the dates provided on the right side of the second column serve as labels for
the corresponding rows in the left column.

These profiles reveal an H $\alpha$ line structure akin to that observed
during the quiescent stage of a preceding nova outburst (Brandi et al., 2009;
Zamanov, 2011). The full width at half maximum (FWHM) of the H $\alpha$ line
ranges from approximately 300 to 750 km/s, indicating increased strength
compared to the quiescent stage of the nova in 1985. Specifically, the broad
component of H $\alpha$ exhibits a FWHM of 747 km/s.

The H $\alpha$ line displays subtle positional shifts toward either the blue
or red side, attributed to the orbital motion of the system. A similar
phenomenon was observed in nova V3890 Sgr (Zemko et al., 2018). Comparable
shifts in central position are noted in other Balmer lines (H $\beta$, H
$\gamma$, and H $\delta$), albeit to a lesser extent in most cases.

The evolution of quiescence spectra of Rs Oph from day 740 to 5504, counted
from 2006 Feb. 12.83 UT (which is considered as the outburst date ($t=0$)) is
described here in Fig. 2 . The spectra cover the region from 4000 to 8000 Å.
The prominent emission lines are marked in the figure. Strong emission
patterns from the illuminated accretion disk that surrounds the WD, which is
also the source of the strong blue continuum, are seen in the spectra. In
general in all the quiescence phase, there was the appearance of strong and
broad emission lines of hydrogen, helium and iron lines. The emission lines
seen in these observed quiescence phase spectra are broad because of expanded
discs (Anupama & Prabhu, 1989). Intense optical Fe II emission lines originate
from a well-illuminated (photoionized) inner region of the disk with high
density. As the disk accrues additional matter, these lines diminish, as noted
by Bode & Evans (2008). The spectra also exhibit distinct absorption
characteristics within the continuum, indicating the presence of cool
secondaries and providing insights into the properties of these secondary
components. Due to the cold secondaries, the spectra also exhibit noticeable
continuous absorption features and expose the secondaries’ characteristics.

The spectrum captured on the day 740 (2008 Feb. 22.9 UT), shows prominent
emission lines of H  (Balmer lines), He i ($\lambda$4922, $\lambda$5016,
$\lambda$5876, $\lambda$6678, and $\lambda$7065 )Å, and O i $\lambda$ 8444Å
together with significant secondary-contributed TiO  absorption features at
5448 and 6180 Å.

The most noticeable characteristic observed in the emission lines of the
spectra considered in this study is a decrease in the width of Balmer lines
over time (see Fig. 2). Among the spectra presented in Fig. 1, the maximum
FWHM values for H $\alpha$ and H $\beta$ are 1055.9 km s-1and 1034.89 km s-1,
respectively. Both of these values are obtained from the spectra observed on
February 21, 2008. On the contrary the minimum FWHM is found to be 203.87 km
s-1.

##  4 Photoionization Model Analysis

We used the 2023 released version of the cloudy code
(C23)666https://trac.nublado.org/; Chatzikos et al. (2023) to model the
spectra of nova RS Oph during its quiescent phase following the 2006 outburst.
cloudy has been effectively applied to study novae including during the
quiescent stage of a nova (Das & Mondal, 2015; Mondal et al., 2018; Pavana et
al., 2019; Mondal et al., 2020). cloudy simulates the physical conditions of
non-equilibrium gas clouds exposed to an external radiation field by using
detailed microphysics. It predicts the emission-line spectrum based on
assumptions about the gas’s physical conditions (ionisation, density,
temperature, and chemical composition). The photoionization code cloudy  uses
a set of input parameters to compute the ionization, thermal and chemical
state of a non-equilibrium gas cloud, illuminated by a central source, and it
predicts the resulting spectra. The input parameters include the temperature
(T) in Kelvins and luminosity (L) in erg s-1 of the central ionising source,
hydrogen number density ($n$) in cm-3, filling factor, covering factor,
elemental abundances, and inner and outer radii (cm) of the surrounding
ejecta. To generate synthetic model spectra, we incorporated all of these
input parameters in our model along with the abundances of only those elements
whose emission lines are observed in the spectra, while other elements are
kept at their solar values from (Grevesse et al., 2010). In cloudy hydrogen
density and filling factor varies radial as
$n(r)=n(r_{o})(r/r_{o})^{\alpha}~{}\text{cm}^{-3}$ and
$f(r)=f(r_{o})(r/r_{o})^{\beta}$, respectively, where $\alpha$ and $\beta$ are
the exponents of the power laws, and $r_{0}$ is the inner radius. The density
of the shell is controlled by a hydrogen density parameter with a power-law
density profile and an exponent of -2 because it provides a steady mass per
unit volume throughout the model disk ($\dot{\textrm{M}}=$ const). The ratio
of the filled to vacuum volumes in the ejecta are set to 0.1, which is the
value used in other recent Cloudy studies (Das & Mondal, 2015; Mondal et al.,
2018, 2020).

The goodness of our model fit is estimated from the $\chi^{2}$ and
$\chi_{red}^{2}$ of the model; using
$\chi^{2}=\sum_{i=1}^{n}\frac{(M_{i}-O_{i})^{2}}{\sigma^{2}}$, and
$\chi_{red}^{2}=\frac{\chi^{2}}{\nu}$ respectively, where $O_{i}$ and $M_{i}$
are the ratios of observed and modelled line fluxes to the H $\beta$ line
flux, respectively, $\sigma_{i}$ is the error in the observed flux ratio,
$\nu$ is the degrees of freedom given by $n-n_{p}$, n is the number of
observed lines, and $n_{p}$ is the number of free parameters.An ideal model
has a $\chi^{2}\approx\nu$ (Schwarz et al., 2001). Thus, the $\chi^{2}_{red}$
value of a model has to be low (typically in the range of 1-2) in order to be
considered acceptable and well fitted. Normally, $\sigma$ ranges from 10 to 30
percent, depending on how strong it is relative to the continuum and whether
it can blend with other lines in the spectrum (Helton et al., 2010).

##  5 Model Results

In this study, we modeled a total of seven spectra, offering broader spectral
coverage ($\sim$ 3900 to $\sim$ 7500 Å ) and featuring a greater number of
emission lines ($\sim$ 12 to 18 lines). These spectra span approximately
twelve years (2008-2020), representing the duration when the nova was in the
quiescent stage. The seven epochs were chosen with the aim of sampling the
entire duration at roughly regular intervals for the sake of completeness,
considering the availability of ideal spectra as well. The chosen seven epochs
are Epoch 1 (2008-Feb-22), 2 (2010-Aug-15), 3 (2012-Jun-26), 4 (2014-Jul-24),
5 (2016-Aug-20), 6 (2018-Jul-20), and 7 (2020-Apr-2020); corresponding to days
740, 1645, 2326, 3085, 3843, 4542, and 5168, respectively. Among these seven
epochs, the first five were modeled with one component, whereas the remaining
two used two components of density and temperature.

To model the quiescent phase spectra of RS Oph, we developed a three-part
model, consisting of the white dwarf (WD), the accretion disk formed on the
WD’s surface, and the secondary star that feeds material to the accretion
disk. The absorption features seen in the observed spectrum are a result of
the secondary star. Various research results have showed the secondary of nova
Rs Oph could be M0/M2III type (Scott et al., 1994; Anupama & Mikołajewska,
1999; Mondal et al., 2020). Therefore in this study we added the spectrum of
the M2III-type giant to the modelled spectrum and found that it fits well with
the absorption features. Only the model spectrum generated from the disk added
with the black-body radiation from the WD was sufficient to produce the
emission lines.

Initially, during the early years of the quiescent phase (from 2008-2016), we
employed a one-component density profile across the radial distance of the
accretion disk. However, as the nova approached the 2021 outburst (e.g in 2018
and 2020), the accretion disk expanded significantly, leading to the emergence
of diverse spectral lines. To account for this, we divided the accretion disk
into two components (see Fig. 3) with distinct density and temperature
profiles and we added them to match the emission features by multiplying with
the corresponding covering factors. We considered a small changes in
temperature we assumed the luminosity won’t vary much as a result we didn’t
change the luminosity. The inner region, characterized by higher density and
temperature, was responsible for the generation of various iron lines observed
in the spectrum, while the helium lines primarily originated from the same
region. The Balmer lines, on the other hand, were produced by both components
(Habtie et al., 2024; Pandey et al., 2022).

Figure 3: Schematic diagram of a nova system at the quiescence stage. The
accretion disk is assumed to be cylindrical in shape and has two components of
density and temperature. The symbols $R_{0}$, $R_{1}$, and $R_{2}$ represent
the radius of the white dwarf (inner radius of the inner disk component), the
outer radius of the inner disk component (the inner radius of the outer disk
component), and the outer radius of the outer disk component, respectively.

To minimize the number of free parameters, the density power, filling factor,
and inner and outer radii are held constant during the iterative process of
fitting the observations. The hydrogen density, underlying luminosity, and
effective blackbody temperature are allowed to vary. In addition, only the
abundances of elements with observed lines are allowed to vary. All others are
either set fully off or fixed at their solar values.

The inner and outermost radii of the accretion disc are calculated to be
$R_{\text{in}}=10^{8.85}$ cm and $R_{\text{out}}=10^{13}$ cm. These radii are
determined in the following ways:

  1. 1.

To estimate the inner radius, we applied a rule by (Paczynski, 1977), which
states that for a mass of $1M_{\odot}$, the inner radius is $10^{8.9}$ cm. By
incorporating these values into the known relationship of radius and masses of
the white dwarf (i.e., $M_{\text{WD}}^{(1/3)}R_{\text{WD}}$ = constant) (Gehrz
et al., 1998), and applying it for the case of RS Oph, we found the inner
radius of the accretion disk to be approximately $10^{8.85}$ cm.

  2. 2.

To estimate the maximum possible radius of the accretion disk, we used the
relation $R_{\text{A.disk}}(\text{max})/a=0.60/(1+q)$, where $a$ and $q$
represent the separation and ratio between the primary and secondary stars,
respectively (Paczynski, 1977; Lasota et al., 2008; Sun et al., 2023). For the
case of the secondary star being an M2III type star, whose mass ranges from
0.68 to $0.8M_{\odot}$ (Mikołajewska & Shara, 2017), we took the average of
the lowest and highest possible masses of the secondary, which is
$0.74M_{\odot}$, for better accuracy. Using Kepler’s third law and
substituting the mentioned values along with the orbital period of 453.6 days
(Brandi et al., 2009), we obtained the separation ($a$) to be $2.217\times
10^{11}$ m. We also obtained the value ratio ($q$) to be $q=0.54$. Finally,
the maximum accretion disk radius of RS Oph was calculated to be $8.637\times
10^{12}$ cm. However, for the sake of simplicity, we used $10^{13}$ cm for our
modeling.

As our model comprises about seven epochs, the outer radii of individual
epochs, excluding the last epoch, were decided according to the fitting level
of the synthetic spectrum with the observed one. While not solely relying on
the fitting, we assumed that the accretion disk size grew linearly with time.
With this assumption in mind, we used the best-fitting level to determine the
exact values of radii.

From the best-fitting model, we have obtained values for various physical and
chemical parameters of the RS Oph system during its quiescent phase. These
parameters include the temperature and luminosity of the source, hydrogen
number density, dimensions, and composition of the accretion disk formed on
the surface of the white dwarf (see Table 2). In Fig. 4, we present the best-
fitting synthetic spectra overlaid on the observed spectra of RS Oph on seven
distinct days, covering a roughly estimated range of two years. Both the
modeled and observed spectra are normalized to the line flux of H $\beta$, and
the observed spectra are dereddened by E(B-V)=0.73 (Snijders, 1987; Pandey et
al., 2022).

Figure 4:  Observed spectra during the quiescence phase of novae RS Oph (grey
dashed line) alongside model-generated spectra (red solid line). Dates of
observation for each epoch are indicated on the right side of each panel.
Spectra have been normalized with respect to the H $\beta$ line. Prominent
emission lines are highlighted in the figure. For more details, please refer
to Section 5.

We computed a set of synthetic spectra by simultaneously varying all the
aforementioned input parameters in smaller increments across a broad sample
space. The temperature ranged from $10^{3.5}$ to $10^{6}$ K, luminosity varied
between $10^{37}$ and $10^{38}$ erg s-1, and ejecta density spanned $10^{6.5}$
to $10^{13}\text{cm}^{-3}$, concurrently with the elemental abundances.
Multiple test models were iterated across all epochs before arriving at the
final model. Initial visual examinations were conducted, and models that did
not align with the observed spectrum were discarded. To assess the fit
quality, we calculated the $\chi^{2}$ and $\chi^{2}_{\text{red}}$ values of
the model, as discussed in section 4. A comparison of the relative fluxes for
the best-fitting model-predicted lines and the observed lines during the early
phase is presented in Table 3, along with the corresponding $\chi^{2}$. For
the calculation of $\chi^{2}$ values, we selected emission lines that appear
in both observational and modeled spectra. To determine the line fluxes in
individual emission lines, interactive flux measurements were performed by
fitting Gaussians using the splot task of the onedspec package in IRAF. To
mitigate inaccuracies related to flux calibration among various epochs, flux
ratios of observed and modeled emission lines relative to H $\beta$ were
calculated.

###  5.1 Temperature, Luminosity and Density

From the first epoch (2008) to the fifth (2016), we applied a one-component
model. The temperature and luminosity of the source increased from
$1.047\times 10^{4}$ K and $1\times 10^{29}$ erg s-1to $1.202\times 10^{4}$ K
and $1\times 10^{30}$ erg s-1, respectively. Similarly, the density and outer
radius increased from $3.16\times 10^{7}$ $cm^{-3}$ and $3.20\times 10^{9}$ cm
to $6.309\times 10^{8}$ $cm^{-3}$ and $1.584\times 10^{11}$ cm, respectively.
For the sixth and seventh epochs, a two-component model was employed, where
the hydrogen number density and temperature varied. We opted not to vary the
luminosity, as we observed that the fitting process was somewhat insensitive
to small variations in luminosity. Similar to the patterns observed in the
previous epochs, the temperature, luminosity, and density continued to
increase in these cases as well (see the values in columns 7-10 of Table 2).

###  5.2 Elemental composition

In all of the epochs we modeled and analyzed, we have detected the presence of
He i and Fe ii, in addition to the ubiquitous Balmer lines typical of such
novae. Our modeling revealed a significant decrease in the abundance of helium
throughout the quiescent stage of the nova RS Oph. For example, the He /He
$\odot$ ratio was reported as 2.4 in the first epoch but decreased to the
solar value for epochs 6 and 7. In the initial three epochs (2008, 2010, and
2012), Fe  exhibited subsolar abundances in the accretion disk. However, from
the fourth epoch (2014) onward, it showed a considerable increase, appearing
overabundant. The Fe /Fe $\odot$ ratio in the first and last epochs was
obtained as 0.5 and 2.5, respectively. This indicates a significant
enhancement in iron abundance as the nova approaches the upcoming outburst,
possibly due to the secondary star continuously providing a substantial amount
of cold iron through the inner Lagrange point (see rows 7 and 8 of Table 2,
counting from bottom to top). The possible reason for this enhanced abundance
of iron over the solar value could be because the companion star had evolved
beyond the main-sequence level (Bode & Evans, 2008)

The helium abundance across all epochs was determined by fitting the prominent
He i lines (4026, 4471, 4922, 5016, 5048, 5876, 7065 Å). Most likely, the
majority of these lines originated from the inner portion of the accretion
disk, which is denser than the outer portion. During modeling, we clearly
observed that a higher density needed to be set to achieve a better fit over
these lines. Moreover, the two-component model for the last two epochs clearly
illustrated this by showing that most of the mentioned helium lines originated
from the inner disk component. This is consistent with Zemko et al. (2018),
for the case 2011 and 2012. Some helium lines are blended with other lines,
such as He i 4922 and 5016, making it difficult to conclusively determine the
absolute generating regions of helium in the accretion disk. This observation
of helium generated from higher density regions is also common in other nova
systems (e.g., V1674 Her (Habtie et al., 2024; Pandey et al., 2022)).

The iron abundance for each epoch was determined by fitting specific lines
from Fe ii (4233, 4415, 4491, 4584, 4629, 4924, 5018, 5169, 5232, 5276, 5361,
and 5538 Å). These lines predominantly originated from lower-density regions
of the disk, with some contributions observed from higher-density areas. This
observation is consistent with Banerjee et al. (2009), who pointed out that
the Fe II emission, which seems to be favored by high-density conditions,
originates from a region associated with the contact discontinuity. Fe ii
signifies a low ionization stage, suggesting its origin in a zone
characterized by low kinetic temperature (a similar reasoning applies to the
presence of neutral o i lines, indicating their coexistence with Fe ii).

###  5.3 Accretion mass & rate

The ejected mass within the model disk could be calculated using the following
equation, (Schwarz et al., 2001):

$M_{\text{disc}}=n(r_{0})f(r_{0})\int_{R_{\text{in}}}^{R_{\text{out}}}\left(\frac{r}{r_{0}}\right)^{\alpha+\beta}2\pi
rdr\int_{0}^{h}dz,$ (1)

where $n(r_{0})$ represents the hydrogen density ($\text{cm}^{-3}$) and
$f(r_{0})$ stands for the filling factor at the inner radius of the shell
($r_{0}$). The exponents $\alpha$ and $\beta$ correspond to the power laws.
The values for density, filling factor, $\alpha$, and $\beta$ are directly
adopted from the best-fitting cloudy model parameters (refer to Table 2). The
estimation of the total ejected shell mass involved multiplying the mass in
both density components (clump and diffuse) with their corresponding covering
factors and subsequently adding them together. Consequently, the ejected
hydrogen shell masses for epochs 1, 2, 3, 4, 5, 6, and 7 are estimated to be:
$8.94\times 10^{-16}M_{\odot}$, $5.39\times 10^{-15}M_{\odot}$, $2.52\times
10^{-14}M_{\odot}$, $4.033\times 10^{-14}M_{\odot}$, $8.019\times
10^{-14}M_{\odot}$, $3.646\times 10^{-8}M_{\odot}$, and $1.63\times
10^{-7}M_{\odot}$ , respectively. Fig. 5 illustrates the growth of the
accretion disk over time in terms of both mass and radius.

According to Worters et al. (2007); Mondal et al. (2018), the presence of an
accretion disk was detected in April 2007. Therefore, we assumed that the mass
estimated from the first epoch in our model represents the amount accreted
from that day. As a result, we considered our quiescent phase modeling of RS
Oph spectra to cover a period of 13 years. Utilizing the accreted masses
estimated from the best-fit parameters of our photoionization model, we
calculated a mean accretion rate of approximately $1.254\times
10^{-8}M_{\odot}$ $\text{yr}^{-1}$. Remarkably, this value is in excellent
agreement with the previous estimates independently made by Hachisu & Kato
(2000) and Nelson et al. (2011), both of which were approximately $1.2\times
10^{-8}M_{\odot}$ $\text{yr}^{-1}$.

The critical accretion disk mass necessary for initiating thermonuclear
runaway (TNR) can be estimated by considering the critical pressure in the
inner layers of the disk ($10^{15}$ $Ncm^{-2}$) (Truran & Livio, 1986), as
expressed by the formula:

$M_{\text{acc}}\approx\dfrac{4\pi
R_{\text{WD}}^{4}}{GM_{\text{WD}}}P_{\text{crit}}$ (2)

where $G=6.67\times 10^{-11}$ $Nm^{2}kg^{-2}$, and $R_{\text{WD}}$ and
$M_{\text{WD}}$ represent the radius and mass of the white dwarf (WD).
Additionally, we determine the WD radius using the Nauenberg (1972) mass-
radius approximation given in Yaron et al. (2005):

$R_{\text{WD}}\approx 1.12\times
10^{-2}\left[\left(\dfrac{M_{\text{WD}}}{M_{ch}}\right)^{-2/3}-\left(\dfrac{M_{\text{WD}}}{M_{ch}}\right)^{2/3}\right]^{1/2}R_{\odot},$
(3)

We obtained WD radii ($R_{\text{WD}}$) of approximately $1.72$ and
$1.159\times 10^{8}$ cm, respectively. The critical mass required to be
accreted onto the WD was then computed using equation 2, resulting in values
of $3.066\times 10^{-7}M_{\odot}$ and $6.27\times 10^{-8}M_{\odot}$,
respectively.

We promptly dismissed the result derived from a mass of 1.377$M_{\odot}$ as it
proves incompatible with our model. This outcome implies that the critical
accreted mass is lower than the mass estimated by our model approximately 15
months before the outburst, a scenario deemed implausible. Consequently, we
exclusively selected the mass of 1.35$M_{\odot}$ for subsequent analysis.

In the context of the temporal span extending from the initial reported onset
of accretion in April 2007 (Worters et al., 2007; Mondal et al., 2018) to the
subsequent outburst in August 2021, spanning approximately 14 years, we
calculated the mean accretion rate for white dwarf masses of 1.35$M_{\odot}$
to be $2.19\times 10^{-8}M_{\odot}\text{yr}^{-1}$. This calculated value
exhibited reasonable alignment with the accretion rate determined through our
model, which was $1.254\times 10^{-8}M_{\odot}$ $\text{yr}^{-1}$.

Upon scrutinizing the acquired results, a noteworthy observation emerges: the
accretion rate derived from our model exhibits closer proximity to the
accretion rate associated with a WD mass of $1.35M_{\odot}$. This proximity
serves as an indicative insight, suggesting that the true mass of the white
dwarf (WD) in the system Rs Oph may approximate $\sim 1.35M_{\odot}$ but be
less than $1.377M_{\odot}$ as it provides us with an invalid output.

Figure 5: Temporal Evolution of Accretion Disk Mass and Radius: This plot
showcases the dynamic interplay between accretion disk mass and radius over
time, providing a comprehensive view of the system’s evolution.

##  6 Discussion

The paper explores the optical spectral evolution of Rs Oph during its
quiescent phase, spanning from nearly the onset of the quiescent phase
following the 2006 outburst to the 2021 outburst. Despite Rs Oph being well-
studied, the quiescent stage of the nova remains largely unexplored. The
observed quiescent phase spectra considered in this study bear a strong
resemblance to some of the spectra observed at the same phase following the
1985 outburst. For instance, the $1987^{th}$ spectrum provided by Anupama &
Prabhu (1989) shows a striking similarity to that of the $2008^{th}$ spectrum
of the 2006 outburst. However, the spectrum collected in 1988 exhibits a
considerable mismatch with any of the spectra considered in this study.
Notably, in the 1988 spectrum, H $\beta$ appears with a line strength
comparable to other non-Balmer lines, a situation that doesn’t occur in any of
the spectra considered in this study. This phase, potentially resembling
previous outbursts, exhibits many variations in the physical conditions at
different epochs, providing valuable insights into the system. The study
benefits from comprehensive coverage, enabling the investigation of distinct
ionization lines and the evolution of line profiles, shedding light on the
nuanced characteristics of Rs Oph during its quiescent stage.

Using photoionization cloudy modeling, we estimated various parameters of the
accretion disk formed on the surface of the white dwarf, with all values
provided in Table 2. In the initial couple of years, starting from 2008, we
observed a relatively cool and less luminous system, possibly indicating that
it had fully entered the quiescent phase with minimal matter accretion at that
moment. Over time, both the temperature and luminosity increased. Similarly,
due to the limited amount of matter accreted during that period, the hydrogen
number density appeared low initially but evolved rapidly. The dimensions of
the accretion disk also increased monotonically in the radial component of a
cylindrical geometry.

According to our model, during the initial four years from 2008, the abundance
of iron was significantly lower than the solar value. This discrepancy could
be attributed to the limited quantity of accreted matter, resulting in an
insufficient amount of iron reaching the disk. The model predicts that the
iron abundance surpasses the solar value from 2014 onward, increasing rapidly.
This trend aligns with the notion that iron originates from the secondary
star.

From the best-fit parameters obtained through our photoionization model, we
determined the mass of the accretion disk at seven different epochs during the
quiescent stage from 2008 to 2020. In the first epoch, as anticipated, the
white dwarf (WD) accreted a relatively small mass of $8.94\times
10^{-16}M_{\odot}$. This observation aligns with expectations, considering
that the nova had transitioned to the quiescent phase in April 2007 (Mondal et
al., 2018), less than a year before the first epoch. The accretion mass showed
a gradual increase during Epochs 2, 3, 4, and 5, measuring $5.39\times
10^{-15}M_{\odot}$, $2.52\times 10^{-14}M_{\odot}$, $4.033\times
10^{-14}M_{\odot}$, and $8.019\times 10^{-14}M_{\odot}$, respectively. In
these epochs, the accretion mass exhibited a relatively slower growth rate.
However, during Epochs 6 and 7, the accretion disk’s mass increased more
rapidly, reaching $3.646\times 10^{-8}M_{\odot}$ and $1.63\times
10^{-7}M_{\odot}$, respectively. The observed acceleration of accretion rate
can be attributed to the overall increase in the mass of the system (white
dwarf and accretion disk) caused by the accumulation of matter on the white
dwarf’s surface. This results in a more efficient extraction of material from
the secondary star’s surface, utilizing the enhanced gravitational pull.

Employing Equation 2, we computed the critical mass of the accretion disk
essential for initiating thermonuclear runaway (TNR) for a specific white
dwarf (WD) mass (1.35$M_{\odot}$) to be $2.32\times 10^{-7}M_{\odot}$.
According to our model, by Epoch 7 (2020), the accreted mass on the WD had
reached approximately $1.63\times 10^{-7}M_{\odot}$, resulting in a deficit of
$1.436\times 10^{-7}M_{\odot}$ to reach the critical mass limit. We observed
that only 53% of the critical mass had been accreted by February 22, 2020,
with the remaining substantial mass (approximately 47%) accreted onto the
white dwarf in the subsequent 15 months.

If we commence the analysis from 2018, where the model estimated the accreted
mass up to July 20, 2018, as $3.646\times 10^{-8}M_{\odot}$, the deficit to
reach the critical mass is approximately $2.7\times 10^{-7}M_{\odot}$;
representing about 88% of the critical mass required to initiate the TNR
processes.

This observation highlights that the accretion rate in the final years is
significantly higher than in the preceding years, attributed to the increased
gravitational attraction resulting from the mass already deposited onto the
WD.

Table 2: Best Fit cloudy Model Parameters for Quiescent Stages of RS Oph: 2006
to 2021 Outburst.

Parameters | Values
---|---
Epoch 1 | Epoch 2 | Epoch 3 | Epoch 4 | Epoch5 | Epoch6 | Epoch7
|  |  |  |  |  | diskin | diskout | diskin | diskout
Black Body Temperature ($\times 10^{4}$K) | 1.047 | 1.072 | 1.096 | 1.148 | 1.202 | 1.698 | 1.096 | 1.778 | 1.122
Luminosity ($\times 10^{30}$ erg s-1) | 0.100 | 0.158 | 0.316 | 0.501 | 1.000 | 3.981 | 3.981 | 7.943 | 7.943
Hydrogen density ($\times 10^{10}\text{cm}^{-3}$) | 0.316 | 1.000 | 3.162 | 3.981 | 6.309 | 10.00 | 1.000 | 31.62 | 3.162
$\alpha$ | -2.000 | -2.000 | -2.000 | -2.000 | -2.000 | -2.000 | -2.000 | -2.000 | -2.000
Inner radius ($\times 10^{9}\text{cm}$)a | 0.708 | 0.708 | 0.708 | 0.708 | 0.708 | 0.708 | 31.62 | 0.708 | 31.622
Outer radius ($\times 10^{11}\text{cm}$)a | 0.032 | 0.126 | 0.50 | 1.584 | 6.309 | 0.316 | 10.00 | 0.316 | 100.0
Filling Factora | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100
$\beta$a | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000
Covering factor (AD:BB:SE) | 45.5:15.5:39.0 | 62.5:15.5:22.0 | 63.0:17.5:19.5 | 59.0:10.0:33.0 | 65.0:16.0:17.0 | 42.0:3.0:8.0 | 44.0:3.0:8.0 | 43.0:2.0:3.0 | 49.0:3.0:3.0
He /He ☉b | 2.400 | 1.800 | 2.100 | 2.100 | 2.100 | 1.100 | 1.100 | 1.000 | 1.000
Fe /Fe ☉b | 0.500 | 0.500 | 0.800 | 1.900 | 2.100 | 2.400 | 2.400 | 2.500 | 2.500
Ejected matter mass ($\times 10^{-5}~{}M_{\sun}$) | - | - | - | - | - | - | -
Number of lines | 22.0 | 17.0 | 20.0 | 18.0 | 19.0 | 19 | 19
Number of free parameters | 6.000 | 6.000 | 6.000 | 6.000 | 6.000 | 6.000 | 6.000
Degrees of freedom | 16.00 | 11.00 | 14.00 | 12.00 | 13.00 | 13 | 13
$\chi_{\text{tot}}^{2}$ | 28.314 | 16.203 | 27.834 | 16.652 | 17.8561 | 13.263 | 14.471
$\chi_{\text{red}}^{2}$ | 1.771 | 1.473 | 1.988 | 1.388 | 1.374 | 1.020 | 1.113

Note: a stands for the quantity is not considered as a free parameter.
b Abundances are given in logarithmic scale, relative to the solar value. Due
to an unprecedented mismatch between the model and observed spectra, we have
excluded the presence of certain elements in our
model spectra, including Carbon, Oxygen, Nitrogen, and Neon.

Table 3: Observed and best-fit cloudy model line flux values for quiescent phase epochs of Rs Oph. Line |  | Epoch 1 (2008Feb22) | Epoch 2 (2010Aug15) | Epoch 3 (2012Jun26) | Epoch 4 (2014Jul24) | Epoch 5 (2016Aug20) | Epoch 6 (2018Jul20) | Epoch (2020Apr06)
---|---|---|---|---|---|---|---|---
ID |  $\lambda$ (Å) | mod. | Obs. | $\chi^{2}$ | mod. | Obs. | $\chi^{2}$ | mod. | Obs. | $\chi^{2}$ | mod. | Obs. | $\chi^{2}$ | mod. | Obs. | $\chi^{2}$ | mod. | Obs. | $\chi^{2}$ | mod. | Obs. | $\chi^{2}$
H 8 | 3770 | 0.332 | 0.271 | 0.365 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -
H $\eta$ | 3835 | 0.149 | 0.185 | 0.132 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -
H $\zeta$ | 3889 | 0.165 | 0.125 | 0.164 | 0.417 | 0.331 | 2.945 | 0.324 | 0.287 | 0.095 | 0.330 | 0.172 | 1.482 | - | - | - | - | - | - | - | - | -
H $\epsilon$ | 3970 | 0.086 | 0.188 | 1.051 | 0.288 | 0.248 | 0.655 | 0.296 | 0.441 | 1.447 | 0.167 | 0.336 | 1.688 | 0.162 | 0.066 | 0.416 | - | - | - | - | - | -
He i | 4026 | - | - | - | - | - | - | 0.257 | 0.376 | 0.971 | 0.229 | 0.111 | 0.827 | 0.110 | 0.134 | 0.026 | - | - | - | - | - | -
H $\delta$ | 4101 | 0.404 | 0.355 | 0.244 | 0.530 | 0.424 | 4.571 | 0.372 | 0.277 | 0.633 | 0.368 | 0.210 | 1.477 | 0.356 | 0.470 | 0.577 | 0.227 | 0.202 | 0.081 | 0.209 | 0.232 | 0.102
Fe ii | 4233 | 0.099 | 0.088 | 0.013 | 0.196 | 0.220 | 0.222 | 0.259 | 0.242 | 0.020 | 0.083 | 0.087 | 0.001 | 0.097 | 0.116 | 0.016 | 0.068 | 0.073 | 0.003 | 0.056 | 0.095 | 0.307
H $\gamma$ | 4340 | 0.832 | 0.743 | 0.792 | 0.666 | 0.688 | 0.197 | 0.658 | 0.869 | 3.076 | 0.631 | 0.661 | 0.054 | 0.615 | 0.533 | 0.295 | 0.456 | 0.284 | 3.652 | 0.431 | 0.204 | 10.51
Fe ii | 4415 | 0.286 | 0.109 | 3.130 | - | - | - | 0.391 | 0.412 | 0.030 | 0.260 | 0.303 | 0.106 | 0.120 | 0.082 | 0.066 | 0.118 | 0.041 | 0.742 | 0.059 | 0.030 | 0.171
He i | 4471 | - | - | - | - | - | - | - | - | - | - | - | - | 0.238 | 0.107 | 0.761 | 0.149 | 0.037 | 1.534 | 0.094 | 0.068 | 0.138
Fe ii | 4491 | 0.542 | 0.237 | 9.288 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | -
Fe ii | 4584 | 0.406 | 0.318 | 0.788 | 0.378 | 0.351 | 0.277 | 0.324 | 0.511 | 2.143 | - | - | - | 0.091 | 0.162 | 0.229 | 0.105 | 0.107 | 0.00037 | 0.055 | 0.059 | 0.003
Fe ii | 4629 | 0.652 | 0.527 | 1.561 | - | - | - | 0.468 | 0.765 | 6.143 | - | - | - | 0.115 | 0.249 | 0.795 | 0.153 | 0.026 | 1.984 | 0.055 | 0.071 | 0.052
H $\beta$ | 4861 | 1.000 | 1.000 | 0.000 | 1.000 | 1.000 | 0.000 | 1.000 | 1.000 | 0.000 | 1.000 | 1.000 | 0.000 | 1.000 | 1.000 | 0.000 | 1.000 | 1.000 | 0.000 | 1.000 | 1.000 | 0.000
He i | 4922 | 0.395 | 0.591 | 3.850 | 0.281 | 0.336 | 1.229 | 0.327 | 0.459 | 1.206 | 0.392 | 0.458 | 0.257 | 0.178 | 0.283 | 0.492 | - | - | - | - | - | -
Fe ii | 4924 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 0.277 | 0.111 | 3.385 | 0.091 | 0.099 | 0.016
He i | 5016 | 0.326 | 0.515 | 3.587 | 0.289 | 0.205 | 2.845 | 0.335 | 0.547 | 3.129 | 0.374 | 0.651 | 4.528 | 0.163 | 0.311 | 0.979 | - | - | - | - | - | -
Fe ii | 5018 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 0.155 | 0.125 | 0.10754 | 0.121 | 0.124 | 0.003
He i | 5048 | 0.441 | 0.349 | 0.835 | - | - | - | - | - | - | - | - | - | 0.105 | 0.272 | 1.243 | - | - | - | - | - | -
Fe ii | 5169 | 0.246 | 0.290 | 0.196 | 0.313 | 0.391 | 2.451 | 0.237 | 0.075 | 1.822 | 0.400 | 0.505 | 0.654 | 0.165 | 0.214 | 0.107 | 0.197 | 0.169 | 0.111 | 0.139 | 0.082 | 0.657
Fe ii | 5232 | 0.337 | 0.356 | 0.035 | 0.289 | 0.227 | 1.516 | 0.201 | 0.355 | 1.647 | 0.315 | 0.463 | 1.302 | 0.121 | 0.116 | 0.001 | 0.142 | 0.111 | 0.115 | 0.036 | 0.061 | 0.117
Fe ii | 5276 | 0.428 | 0.585 | 2.453 | 0.384 | 0.418 | 0.473 | 0.265 | 0.383 | 0.966 | 0.357 | 0.291 | 0.259 | 0.130 | 0.308 | 1.392 | 0.155 | 0.082 | 0.648 | 0.076 | 0.068 | 0.012
Fe ii | 5361 | 0.463 | 0.785 | 10.346 | 0.404 | 0.268 | 7.391 | 0.271 | 0.468 | 2.696 | 0.474 | 0.616 | 1.195 | - | - | - | 0.134 | 0.072 | 0.473 | 0.067 | 0.061 | 0.009
Fe ii | 5538 | - | - | - | - | - | - | - | - | - | - | - | - | 0.207 | 0.228 | 0.021 | 0.086 | 0.063 | 0.066 | 0.031 | 0.043 | 0.028
He i | 5876 | 0.541 | 0.565 | 0.056 | 0.551 | 0.558 | 0.021 | 0.471 | 0.391 | 0.435 | 0.617 | 0.456 | 1.523 | 0.477 | 0.454 | 0.024 | 0.286 | 0.233 | 0.347 | 0.243 | 0.138 | 2.242
H $\alpha$ | 6563 | - | - | - | 3.499 | 3.376 | 6.087 | - | - | - | - | - | - | 3.368 | 3.839 | 9.871 | - | - | - | - | - | -
He i | 6678 | 0.727 | 0.730 | 0.001 | 0.365 | 0.348 | 0.114 | 0.162 | 0.252 | 0.573 | 0.373 | 0.458 | 0.430 | 0.172 | 0.151 | 0.022 | 0.104 | 0.105 | 0.000 | 0.073 | 0.064 | 0.01502
He i | 7065 | 0.545 | 0.682 | 1.883 | 0.2815 | 0.325 | 0.764 | 0.157 | 0.264 | 0.802 | 0.331 | 0.452 | 0.869 | 0.127 | 0.236 | 0.523 | 0.111 | 0.097 | 0.027 | 0.049 | 0.070 | 0.094

##  7 Conclusions

In conclusion, our investigation of RS Oph during the quiescent phase between
the 2006 and 2021 outbursts employed photoionization-based modeling and
spectroscopic analysis to elucidate the accretion disk formation process,
encompassing its composition, mass, and dimensions. The key findings are
summarized as follows:

  1. 1.

The spectra during the quiescent phase reveal distinctive low-ionization
emission features, including hydrogen, helium, iron, and TiO absorption
features originating from the cool secondary component.

  2. 2.

Utilizing the CLOUDY photoionization code, we determined that the central
ionizing sources exhibit temperatures in the range of $1.05-1.8~{}\times
10^{4}$ K and luminosities between $0.1-7.9~{}\times 10^{30}$ erg s-1.

  3. 3.

The abundance of He  displayed temporal variations, showing an overabundance
from 2008 to 2016, returning to solar values by 2020. Meanwhile, Fe  appeared
subsolar from 2008 to 2014 but became overabundant from 2006 onward.

  4. 4.

The critical mass of the white dwarf (WD) has been calculated for WD masses of
$1.35M_{\odot}$ and $1.377M_{\odot}$, resulting in values of $3.066\times
10^{-7}M_{\odot}$ and $6.27\times 10^{-8}M_{\odot}$, respectively. The latter
result was excluded from consideration as it is already less than the accreted
mass determined at our last epoch (February 22, 2020). This exclusion supports
the conclusion that the mass of the WD likely falls within the range of
$1.350M_{\odot}\leq M_{WD}<1.377M_{\odot}$.

  5. 5.

The mean accretion rate, as calculated from the model, is approximately
$1.254\times 10^{-8}M_{\odot}$ yr-1. However, it is important to note that
this value does not imply uniform accretion dynamics over time. About 47% of
the critical mass was accreted in the last 15 months, and approximately 88% of
the critical mass was accreted after July 20, 2018. This non-uniform accretion
rate suggests a more rapid approach towards reaching the critical mass in the
final years. This phenomenon could be attributed to the heightened
gravitational pull resulting from previously accreted matter, influencing the
accretion dynamics as the system approaches the critical mass limit.

## Acknowledgments

We thank the S. N. Bose National Centre for Basic Sciences and the World
Academy of Science (TWAS) for their funding support. We are grateful to F.
Teyssier for coordinating the ARAS Eruptive Stars Section. Equally, we
appreciate the ARAS observers for generously sharing their observations with
the public. Special acknowledgments go to David Boyd, Pavol A. Dubovsky,
Christian Buil, Joan Guarro Flo, Tim Lester, and Stony Brook for their
valuable spectroscopic observations. We also thank Dr. Anindita Mondal for her
discussions and email guidance on utilizing cloudy modeling scripts for
quiescent stages. GRH acknowledges the supports from Debre Berhan university,
Debre Berhan, Ethiopia.

## Data Availability

The paper utilizes spectroscopic data obtained from three sources: the
Astronomical Ring for Access to Spectroscopy Database (ARAS Database777
https://aras-database.github.io/database/novae.html; Teyssier (2019)), Stony
Brook/SMARTS Atlas of (mostly) Southern Novae
(888http://www.astro.sunysb.edu/fwalter/SMARTS/NovaAtlas/rsoph/rsoph.html(Walter
et al., 2012)), European Southern Observatory (ESO)
999https://www.eso.org/sci/facilities/paranal/decommissioned/isaac/tools/lib.html
(Pickles, 1998), and Astrosurf Recurrent
Nova101010http://astrosurf.com/buil/us/rsoph/rsoph.htm. These spectroscopic
data were employed to analyse the spectral evolution of the system and for
modeling purposes presented in Fig. 1 and 4.

## References

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##  Appendix A Some extra material

If you want to present additional material which would interrupt the flow of
the main paper, it can be placed in an Appendix which appears after the list
of references.