# Spectral Evolution and Photo-ionization Analysis of Nova Cas 2020 (V1391
Cas)

G. M. Hamed Email<EMAIL_ADDRESS>Stellar Astronomy Lab, Astronomy
Department, National Research Institute of Astronomy and Geophysics, Cairo,
Egypt, 11421  Visiting Astronomer, Istanbul University, Department of
Astronomy & Space Sciences Stellar Astronomy Lab, Astronomy Department,
National Research Institute of Astronomy and Geophysics, Cairo, Egypt, 11421
H. H. Esenoglu  Istanbul University, Department of Astronomy and Space
Sciences, 34119, Beyazit, Istanbul, Türkiye  A. I. Galeev Passed away in
February 2021 Kazan Federal University, ul. Kremlevskaya 18, 420008, Kazan,
Russia; Academy of Sciences of Tatarstan, Kazan, Russia

###### Abstract

We present spectroscopic observations of Nova Cas 2020(V1391 Cas) obtained
using the Russian Turkish Telescope during different stages of its 2020
outburst. We followed the spectral evolution of the nova until it entered the
nebular phase. The expansion velocity of the ejecta reached $\sim$780
$\mathrm{km\,s^{-1}}$. The fluxes of the neutral [O I] lines at wavelengths
6300, 6364, and 5577 $\mathrm{\text{\r{A}}}$ were used to calculate the
electron temperature and the mass of neutral oxygen in the ejecta. We found
average values $\mathbf{T_{e}=4890\,K}$ ,$\mathbf{M_{OI}=2.54\times
10^{-5}}M\textsubscript{$\odot$}$ which are consistent with the values
calculated for other novae. We modeled the nova’s ejected envelope 515 days
after its discovery and found that the log elemental abundances by number
relative to Hydrogen of the envelope are He = -0.7, C = -5.5, O = -2.5, N =
-2.0 and Ne = -4.0.

Keywords: stars: novae, cataclysmic variables – stars: individual: Nova Cas
2020 (V1391 Cas) – techniques: spectroscopy

##  1 Introduction

The modern understanding of classical novae is that they are sudden outbursts
appearing on cataclysmic explosions resulting from the thermonuclear runaway
of the matter accreted on the surface of the white dwarf (Starrfield et al.,
2016; Della Valle & Izzo, 2020). Nova Cas 2020 (V1391 Cas) was discovered by
S. Korotkiy as the optical transient TCP J00114297+6611190 on 2020-07-27.9302
UT at an unfiltered magnitude of 12.9 and it was identified as a Fe II
classical nova after its discovery (Sokolovsky et al., 2020a). To follow the
spectral evolution of the nova, we took this discovery date as the start epoch
("Day 0") and provided it throughout the paper along with the observational
dates. The nova showed multiple brightness enhancements during the maximum
phase, followed by a dust formation period. Therefore, we summarized the
spectroscopic evolution of the nova in chronological order with comments by
reviewing all the literature including mostly the Astronomer’s Telegrams in
this section. The nova showed multiple secondary maxima for about three months
after the visual maximum. It is the second nova to show both CN and
$\mathrm{C_{2}}$ bands near the maximum (the first being V2676 Oph in 2012)
indicating that the envelope is Carbon rich (Fujii et al., 2021). The
discoverers reported that the object was not visible down to magnitude 13.5 on
images taken on 2020-07-06.9054 UT (Day -21) (Waagen, 2020). Pre-discovery
images of the nova provide a constraint on the outburst date between Day -1
and Day 0 (Sokolovsky et al., 2020c). Determining the maximum of the nova
outburst is crucial, as the system brightens by 6-19 magnitudes from its pre-
nova state (Warner, 2003).

The spectra used in this paper were obtained as a part of an observational
campaign to observe and study the envelopes of classical novae in different
stages of the outburst. This ongoing campaign started in mid 2020 and about 15
novae have been observed so far. This paper is the first of a series of papers
about the results of this campaign. We observed V1391 Casusing the 1.5 m
Russian Turkish Telescope (RTT150) to monitor its early spectroscopic
evolution. Here we present our observations and analysis of V1391 Cas.

###  1.1 Evolution of V1391 Cas by outburst date

Day 2
The optical spectrum was dominated by H I, Fe II, and Na I P-Cygni profiles on
the nova’s spectrum observed on 2020-07-29.025 (Day 2). The absorption of the
H$\alpha$ P-Cygni profile gave a velocity of around $-850\pm 100$ km s-1
(Sokolovsky et al., 2020a).

The nova reached its visual maximum at 10.6 mag in the V band on
2020-07-29.917 UT (Day 2) (e.g. Wenzel, 2021). After a short while, the
spectrum of V1391 Cas taken by Munari et al. (2020b) on 2020-07-29.960 UT (Day
2), showed that the spectrum changed significantly from that of (Sokolovsky et
al., 2020a). Accordingly, all P-Cyg lines were in emission, except for the
minimal photospheric absorption lines and O I (7772 Å), where absorption was
-385 km $s^{-1}$. A red continuum was dominant. All emission lines appeared
rather sharp, with an average FWHM of about 500 km $s^{-1}$. The emission in
Na I and the P-Cyg absorption in H$\alpha$ (with integrated absolute flux of
$3.543\times 10^{-12}\,erg\,cm^{-2}s^{-1}$) disappeared, and He I
$\mathbf{5876\AA}$ emerged in emission with a flux of $2.154\times
10^{-14}\,erg\,cm^{-2}\,s^{-1}$ . The large interstellar extinction was quite
evident in the significant strength of Diffuse Interstellar Bands (DIBs). The
equivalent widths (EWs in $\mathrm{\text{\r{A}}}$) of these DIBs were
calculated as follows: 5780 (0.57), 5793 (0.3), and 6613
$\mathrm{\text{\r{A}}}$ (0.37). The integrated absolute fluxes (in $10^{-12}$
erg cm2 s-1) of some representative emission lines observed in the spectrum
were given as the following: H$\alpha$ (3.54), O I 7772 (0.70), H$\beta$
(0.25), H$\gamma$ (0.06), Fe II 42 5169 (0.06), H$\delta$ (0.02), He I 5876
(0.02), Fe II 38 4583 (0.01), N II 3 5682 (0.01).

Days 3-54

Shore et al. (2020), reported that the nova monitoring, which continued for
about 12 days between 2020-07-30.7 (Day 3) and 2020-08-11.9 UT (Day 16),
showed a very significant evolution in the spectra. Accordingly, the O I 7773
$\mathrm{\text{\r{A}}}$ multiplet showed P-Cygni profiles in the first
spectrum on 2020-07-30.8 (Day 3).

According to Fujii et al. (2021), optical low-resolution spectroscopic
observations from 2020-07-31 to 2020-08-19 (Days 4-23) revealed the appearance
and disappearance of molecular absorption bands of $\mathrm{C_{2}}$ and CN in
V1391 Cas. These molecules were only present for $\sim$3 days.
$\mathrm{C_{2}}$ and probably CN formed at $\sim$5000 K in the nova envelope.
The spectral evolution and the formation conditions of the molecules are
similar to those of V2676 Oph, which is the first example of a
$\mathrm{C_{2}}$/CN-forming nova. They predicted that a late-phase grain
formation episode similar to that seen in V2676 Oph will occur in V1391 Cas.

From 2020-08-1.8 (Day 5), Fe II , 5169, and other optical Fe II transitions
showed P-Cygni profiles.

Meanwhile, Sokolovsky et al. (2020b) reported that an observation with
Swift/XRT on 2020-08-02.888 UT (Day 6) showed no X-ray source at the position
of the nova. Assuming power-law emission with the photon index of 2 and H I
column density of 8.2x1021 cm-2 this translated to the unabsorbed 0.3-10 keV
flux limit of 7x10-14 erg cm -2 s-1.

Continuing the report of Shore et al. (2020), several blueshifted low-
ionization metal absorbers, e.g. Mg II 4481, Ti II 4764, and Si II 6347, 6371
$\mathrm{\text{\r{A}}}$, were present on 2020-08-4 (Day 8) and 2020-08-6 (Day
10) and persisted but were not well resolved in subsequent spectra.

On 2020-08-4.9 (Day 8), blueshifted absorption was seen in the Na I D1, D2
spectral lines at -190 km s-1 with equivalent width EW = 0.1
$\mathrm{\text{\r{A}}}$. The absorption radial velocity was the same as all
other P-Cygni absorption on all Fe II lines (especially , 5169
$\mathrm{\text{\r{A}}}$).

The Si II doublet (6347, 6371 $\mathrm{\text{\r{A}}}$) showed weak emission
through 2020-08-6 (Day 10). There is a complex spectrum of weaker metal lines,
all at low velocity, and the development of this nova shows similarities to
nova DN Gem 1912 (McLaughlin, 1965). No evidence of He I 5876, 6678, and 7065
$\mathrm{\text{\r{A}}}$ was found in any spectrum.

The absorption profiles of Na I D1, D2 lines on 2020-08-6.8 (Day 10) increased
to EW = 0.5 $\mathrm{\text{\r{A}}}$ with no change in radial velocity. The
metal line absorptions displayed consistently lower radial velocity than the
Balmer lines, whose asymmetric absorptions were deepest (H$\alpha$, -250 km
s-1; H$\beta$, -210) while extending to about -620 km s-1; the emission to
absorption equivalent width ratios were 3.8 (H$\alpha$), 1.1 (H$\beta$).

On 2020-08-8.3 (Day 12), the Ca II IR transitions showed weak emission, while
O I 7773, 8446 $\mathrm{\text{\r{A}}}$ both showed P-Cyg profiles (absorption
depths of about 60% and 25%, respectively), similar to the Pa series. The 7773
$\mathrm{\text{\r{A}}}$ multiplet absorption was complex and broad, centered
at -180 km s-1, but extending to +300 km s-1 (in red), with the emission
extending to about -500 km s-1 (in blue).

From the date of first detection, 2020-07-27.23087 (Day 0), the nova showed a
series of flares (each lasting days to a week) with the brightest flare
peaking at V=10.8 on 2020-08-10.08738 (Day 14) (Sokolovsky et al., 2020c). On
2020-08-10.72 (Day 14), as reported by Shore et al. (2020), the spectrum was
dominated by the continuum and Fujii et al. (2021) identified blueshifted
absorption lines of neutral and low-ionized atomic species, such as CI, NI,
OI, SiII, and FeII.

Fujii et al. (2020) reported that the molecular absorption bands of C2 and CN
were not evident in the spectra taken on 2020-08-10.692 UT (Day 14).

Hamed et al. (2020) reported in the optical spectroscopic observations on
2020-08-10.9 (Day 14) (The flux here is in units of $\mathbf{\times
10^{-14}\,ergcm^{-2}}$ $\mathbf{s^{-1}}$ and EW in $\mathrm{\text{\r{A}}}$.)
that most of the Balmer series lines including H$\delta$ (flux=14.4, EW=2.9),
H$\gamma$ (flux=13, EW=3), and H$\beta$ (flux=11, EW=1.9) were in absorption
except for H$\alpha$ (absorption: flux=12.2, EW=0.9; emission: flux=52,
EW=3.9) which exhibited a prominent P-Cygni profile. Also, other absorption
lines were as follows: CaII H 3934 (flux=10.4, EW=3.2) and CaII K 3969
(flux=13.3, EW=4.1), HeI 4921 (flux=0.8, EW=0.1). The CaII doublet here was
strong and blue-shifted. The He I 5876, He II 4686, and N II 5682 lines were
absent in these spectra. The O I 7772 line showed a P-Cygni profile
(absorption: flux=216, EW=3.9; emission: flux=48.1, EW=0.9), and the Na I 5896
interstellar absorption line also showed a strong component.

Spectra on 2020-08-11.1 (near the light curve peak, Day 15) showed narrow P
Cygni profiles of Balmer, O I, Fe II, and Na I (Sokolovsky et al., 2020c). The
absorption troughs were at blueshifted velocities of 200-250 km s-1, while the
emission features of P Cygni profiles were relatively weak compared to
absorption. This dramatic apparent deceleration of the absorption features
(e.g. the absorption in the H$\alpha$ P-Cygni profile on Day 2 was $-850\pm
100\mathrm{kms^{-1}}$) was probably due to the photosphere receding to inner
(slower moving) regions of the expanding ejecta.

In their observations on 2020-08-11.7 (Day 15), Hamed et al. (2020) also
reported that most of the Balmer series lines including H$\delta$ (flux=1.3,
EW=0.8), H$\gamma$ (flux=6.7, EW=3.1), and H$\beta$ (flux=9, EW=2.3 ) remained
in prominent absorption except for H$\alpha$ (absorption: flux=6.8, EW=0.5;
emission: flux=42.6, EW=3.4) which exhibited the P-Cygni profile. Soon after
the EW of the absorption component of H$\alpha$ with the P-Cyg profile
increased to about 3 $\mathrm{\text{\r{A}}}$ and the EW of the emission
component was 3.5 $\mathrm{\text{\r{A}}}$. The He II 4686 and N II 5682 lines
were also absent in these spectra. The O I 7772 line showed a P-Cygni profile
(absorption: flux=31.7, EW=3.5; emission: flux=8.6, EW=0.9). The interstellar
Na I 5896 and HeI 5876 (flux=17.6, EW=3.7) absorption lines also showed a
strong component. The Ca II doublet 3934 (flux=7, EW=5.5) and 3968 (flux=6.4,
EW=4.7) were strong and blueshifted. The blue continuum of the spectra
decreased slightly from 2022-08-10.9 (Day 14) to 2020-08-11.7 (Day 15) by
about one order of magnitude.

On 2020-08-11.9 (Day 15), the flux upper limit for the He I 5876 Å emission
was <1.2x10-15 erg cm-2 s-1. Based on the velocity range of the interstellar
Na I D components ((V(LSR)=-46 to -9 km s-1) and the width of the profile (140
km s-1), the LAB survey yields a total N(H)=8.2x1021 cm-2 (Kalberla et al.,
2005). With an average velocity of -65 km s-1, H I displayed a higher velocity
than the Na I components, so this value is a possible upper limit for the
interstellar extinction in the line of sight (the profile of Na I vs H I 21 cm
also suggests that the nova is located at an intermediate distance from the
edge of the Galaxy. In some cases it would be possible to provide a range for
the distance of the nova based on the measured velocity of Na I interstellar
lines and the profile of the H I line to the direction of the nova). In light
of the still-rising optical flux and the lack of any forbidden lines
(including [O I]), the nova may be still in the optically thick stage with the
initiation of the recombination wave known from other novae in the pre-maximum
stage.

For their observations on 2020-08-12.14 (Day 16), Hamed et al. (2020) reported
that similar to their previous observations most of the Balmer series lines
remained in prominent absorption except for H$\delta$, H$\gamma$ (flux=4,
EW=6) H$\beta$ (flux=18.4, EW=11 $\mathrm{\text{\r{A}}}$), and H$\alpha$
(absorption: EW=2.2, emission: EW=4.5) which exhibited a P Cygni profile. The
He I 4921 absorption line (flux=3.1, EW=0.7) in the first spectra transformed
to emission (flux=2.2, EW=1.2) in the later spectra. Similarly, in the later
spectra, the absorption of H$\alpha$ in P-Cygni disappeared and the emission
component (flux=164, EW=22.4) was very strong. The spectra also showed a
strong emission line at a wavelength of 3451 $\mathrm{\text{\r{A}}}$ with an
EW of 6 $\mathrm{\text{\r{A}}}$. The He I 5876 line was visible. However, the
He II 4686 and N II 5682 lines were still absent. The O I 7772 line
(absorption: flux=17.9, EW=1.6; emission: flux=13.6, EW=1.2) showed a P-Cygni
profile and the Na I 5896 interstellar absorption line also showed a strong
component. The Ca II doublet 3934 (flux=1.4, EW=3.6) and 3968 in absorption
were strong and blueshifted. Here, too, the flux is in units of x10-14 erg
cm-2 s-1 and EW in $\mathrm{\text{\r{A}}}$.

The low-resolution (R$\sim$500) spectrum taken by Fujii et al. (2020) on
2020-08-12.706 UT (Day 16) also first detected the molecular absorption bands
of C2 and CN a few days after the visual brightness maximum of the nova (Fujii
et al., 2021). For typical novae ($\sim$8000K; Evans et al., 2005) the
effective temperatures of the so-called photosphere would be expected to be
too high to form a simple function of the form $\nu^{\beta}B(\nu,T)$, where B
is the Planck function at temperature T and $\beta(\simeq 1)$ is a constant
(the so-called $\beta$ index for the dust), to infrared spectra in the range
2–24 $\mu$m, and concluded that the grains eventually grew to $\sim$0.7
$\mu$m. V1391 Cas was colder than the typical novae on the date. As seen in
the novae DQ Her and V2676 Oph, the C2 and CN molecular band features that
form when the brightness is near their maximum can disappear within about one
week (Kawakita & Arai, 2017). These molecular absorption bands of C2 and CN
were also present on 2020-08-13.37 (Day 17) but not significant on
2020-08-14.79 (Day 18). They had almost vanished on 2020-08-15.69 (Day 19)
(Fujii et al., 2021). Finally, the observations of Fujii et al. (2020) on
2020-08-17.53 (Day 21) confirmed that the C2 and CN absorption lines
disappeared.

Dubovsky et al. (2021) made simultaneous photometric and spectroscopic
observations of V1391 Cas from 2020-08-14 to 22 (Day 18-26), 2020-08-28 to
09-22 (Day 32-57), and 2020-10-06 to 12-09 (Day 74-135). The evolution of
H$\alpha$’s flux, equivalent width, and FWHM values from low-resolution
spectra (R$\sim$1000) concerning the light curve in the V band of the nova
were given.

The spectra between 2020-08-14 (Day 18) and 2020-08-16 (Day 20) showed broad
emission lines with FWZI of about 2500 km s-1 while the slow velocity
absorption features of about 250 km s-1 were superimposed on top of the broad
emission (Sokolovsky et al., 2020c).

After the maximum (10.8 V-mag), the nova became fainter and fell to $\sim$13
V-mag on 2020-08-17 (Day 21) (Fujii et al., 2021).

The detection of these C2 and CN molecular absorption bands prompted Russell
et al. (2020) to search for carbon monoxide in the infrared. They found strong
emissions from both the CO fundamental and the first overtone in infrared
spectroscopic measurements of Nova V1391 Cas obtained on 2020-08-17.54 (Day
21). The atomic emission lines are dominated by C I. While other low
excitation features were also presented (H I, N I, O I, Na I, Ca II, and Fe
II), the C I multiplet at 1.0691 microns was the strongest feature in the
spectral range. Numerous other C I transitions were also available. At the
time of these measurements, there was no indication of the presence of dust in
the material ejected from the nova, but dust formation was predicted to almost
certainly occur in the next few weeks.

The spectrum obtained on 2020-08-20 (Day 24), which coincided with one of the
secondary maxima ($\sim$11.5 V-mag, Fujii et al., 2021), showed strong
absorption features with absorption troughs at a velocity of around -400 km
s-1. In some lines, these absorptions were superimposed on top of the broad
emission (FWZI $\sim$2800 km s-1) (Sokolovsky et al., 2020c).

The spectra from 2020-08-22 to 2020-08-25 (Days 26-29) showed weakening
absorption (Sokolovsky et al., 2020c).

Banerjee et al. (2020b) reported near-infrared spectroscopic measurements of
V1391 Cas on 2020-09-02.614 UT (Day 37). Accordingly, the spectrum was typical
of Fe II class novae, rich in CI lines while also displaying other usual lines
of HI, OI, NI, and NaI. HeI 1.083 microns and 2.059 microns were present but
weak. P-Cygni features were absent or very weakly seen in some of the lines
(e.g. OI 1.3164 micron). The observed FWHM and FWZI values of the Paschen beta
1.2818-micron line, which showed a double-peaked structure, were 770 and 1930
km s-1, respectively. The first overtone CO emission (Day 22) reported in
Russell et al. (2020) still persisted with the 12CO and 13CO band heads well
resolved. There was still no definitive evidence for dust between Day 22 and
Day 38. Spectra on 2020-09-04 (Day 39), coinciding with another flare peak,
showed strong absorption with absorption troughs at blueshifted velocities of
600-700 km s-1, especially in H$\beta$ and Fe II; H$\alpha$ also showed
absorption at -400 km s-1 (Sokolovsky et al., 2020c). A similar behavior was
observed in other novae with multiple maxima, where absorption lines
strengthen around the peak brightness and appear at higher velocities (e.g.
Tanaka (2011)). Such spectral evolution might be understood if the flares were
associated with multiple ejections each causing the photosphere to move
outwards (with a new bunch of fast-moving material) during the peak and then
to recede.

Woodward et al. (2020) reported infrared spectroscopic measurements of V1391
Cas on 2020-09-19.297 UT (Day 54). Accordingly, the spectra of the nova showed
that all the lines (Day 38) mentioned by Banerjee et al. (2020b) were present
and no significant evolution was seen in them. However, the first overtone CO
emission on the Day 22 (Russell et al., 2020) appeared to have either
disappeared or it could be present at a very weak level.

Days 139-141

Munari et al. (2020a) suggested that the formation of dust had already started
based on the optical spectrum of V1391 Cas taken at 2020-12-13.811 UT (Day
139). Here the brightness of the nova had dropped sharply. The spectrum had a
very red slope, and the only emission lines (non-P-Cyg absorption), all
showing a narrow profile, and together with their fluxes (x10-14 erg cm-2 s-1)
were as follows: H$\beta$ (3), FeII 4923 (1.2), FeII (1.1), FeII 5169 (1),
[OI] 6300 (6.7), [OI] 6364 (2.2), H$\alpha$ (80.7), and OI 7772 (9.5).

Follow-up observations in the near IR showed that the nova formed optically
thick dust about 141 days (2020-12-15.73) after its discovery (Banerjee et
al., 2020a). They gave the reddening as E(B-V)$\sim$1.4 mag. The (J-K) color
was in the range of 3.2-3.55, indicating that the nova generated a significant
amount of dust. They gave the dust temperature between 1200-1300 K.

The progenitor of V1391 Cas, in the GAIA DR3 catalog has a source ID of
528178486608462720 (distance=5.7 kpc and $T_{eff}$=7068 K) with RA=$00^{h}$
$11^{m}$ $42^{s}$.96 and DEC=+$66^{o}$ $11^{{}^{\prime}}$
$20^{{}^{\prime\prime}}$.80 (alerting magnitude G=11.65;
111http://gsaweb.ast.cam.ac.uk/alerts/alert/Gaia20eld).

Kolb (2020) calculated the distance of the nova to be 4.1 kpc. Here, the
maximum luminosity of V1391 Cas was taken as 10.7 mag, the absolute luminosity
as -6.5 mag, and the interstellar extinction value as A=4.2 mag. According to
the light curve ($t_{3}>100$ days), V1391 Cas was a slow nova (e.g. Wenzel,
2021). -6 to -10 mag is the range of variation for all novae (fast and slow).
Also, according to Esenoglu (1997), this value is $\leq-7.1$ mag which was
found with a new approach to the nova velocity classes (see also Dissertation:
222https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp).

##  2 Spectroscopic Observations

The observations were made using the TUG Faint Object Spectrograph and Camera
(TFOSC) mounted to the focal plane on the Russian Turkish Telescope (RTT150)
of the TUBITAK National Observatory (TUG) in Bakirlitepe, Antalya, Türkiye.
Detailed information about the specifications of the telescope and its
attached instruments can be found here
333https://tug.tubitak.gov.tr/en/teleskoplar/rtt150-telescope-0 and here
444https://tug.tubitak.gov.tr/tr/icerik/tfosc-tug-faint-object-spectrograph-
and-camera. Three grisms covering the spectral ranges
4220-6650$\mathrm{\text{\r{A}}}$ 6190-8190$\mathrm{\text{\r{A}}}$ and
3650-8740$\mathrm{\text{\r{A}}}$ with spectral resolutions
($\lambda/\bigtriangleup\lambda$) of 1331 ($\bigtriangleup\lambda=4.1$), 2189
($\bigtriangleup\lambda=3.0$), and 749 ($\bigtriangleup\lambda=12.0$, broad-
band) respectively, were used. We used an Andor iKon-L 936 BEX2-DD-9ZQ CCD
camera. The observations were made on 7 nights in 2020 and 2021. A total of 17
spectra are presented. Table 2 shows a log of the spectra used in this work.

Table 1: Observation log of RTT150 TFOSC spectra. DATE | TIME | JD | Days | Exposure | Standard |  $\lambda$ Range | R | Airmass
---|---|---|---|---|---|---|---|---
| (UT) | (2459000+) | (after Discovery)* | (s) | Star |  ($\mathrm{\text{\r{A}}}$) | (Grism) |
2020-08-10 | 21:19:19.60 | 072.38842 | 13.96 (Day 14) | 1200 | BD+28D4211 | 3650-8740 | 749 (15) | 1.34
| 22:29:39.50 | 072.43726 | 14.01 (Day 14) | 600 |  | 4200-6650 | 1331 (7) | 1.23
| 23:07:26.20 | 072.4635 | 14.03 (Day 14) | 600 |  | 6190-8190 | 2189 (8) | 1.19
2020-08-11 | 19:16:31.00 | 073.30314 | 14.87 (Day 14) | 600 | BD+28D4211 | 3650-8740 | 749 (15) | 1.70
| 21:57:17.70 | 073.41479 | 14.98 (Day 14) | 600 |  | 4200-6650 | 1331 (7) | 1.27
| 22:28:05.00 | 073.43617 | 15.01 (Day 15) | 900 |  | 6190-8190 | 2189 (8) | 1.23
2020-08-12 | 01:43:37.10 | 074.57196 | 16.14 (Day 16) | 600 | GD 248 | 3650-8740 | 749 (15) | 1.16
| 01:55:47.20 | 074.58041 | 16.15 (Day 16) | 600 |  | 6190-8190 | 2189 (8) | 1.17
| 02:07:47.30 | 074.58874 | 16.16 (Day 16) | 600 |  | 4200-6650 | 1331 (7) | 1.18
2020-09-08 | 02:21:05.66 | 101.59798 | 43.17 (Day 43) | 900 | B0+25d4655 | 4200-6650 | 1331 (7) | 1.35
| 02:37:36.36 | 101.60945 | 43.18 (Day 43) | 900 |  | 6190-8190 | 2189 (8) | 1.37
2020-11-15 | 00:46:13.80 | 169.5321 | 111.10 (Day 111) | 600 | G191B2B | 4200-6650 | 1331 (7) | 1.91
| 00:58:56.30 | 169.5321 | 111.11 (Day 111) | 900 |  | 6190-8190 | 2189 (8) | 1.98
2020-12-17 | 18:58:19.10 | 201.2905 | 142.86 (Day 143) | 1200 | G191B2B | 4200-6650 | 1331 (7) | 1.25
| 19:54:19.80 | 201.2905 | 142.90 (Day 143) | 1800 |  | 6190-8190 | 2189 (8) | 1.34
2021-12-24 | 17:22:08.40 | 573.2237 | 514.79 (Day 515) | 3600 | G191B2B | 4200-6650 | 1331 (7) | 1.18
| 18:26:16.80 | 573.2683 | 514.84 (Day 515) | 3600 |  | 6190-8190 | 2189 (8) | 1.24
* Day 0 is JD 2459058.43 |  |  |  |  |  |  |  |

Our first three nights of spectroscopic and photometric observations coincide
with the visual maximum and the rapid magnitude decrease following it while
our last spectroscopic observations are obtained after the nova’s magnitude
has risen after long dip due to dust formation (see Figs. 1 & 2). The
photometric data with the blue circles in Figures 1 and 2 were taken from the
AAVSO database 555(https://www.aavso.org). In addition, the 9 data points of 3
$V$ and 6 $B$-bands indicated by the red circles were taken by the RTT150
telescope with 10s exposure close to the maximum light. Therefore it would be
interesting to see the spectral behavior of the nova at these epochs. The same
Andor iKon-L CCD camera was used for the photometric observations with a field
of view of $11.1^{{}^{\prime}}$ x $11.1^{{}^{\prime}}$. For convenience, the
times of the spectroscopic observations are labeled in Figures 1 and 2 over
the AAVSO light curves.

Figure 1: V1391 Cas $V$-band observations (blue circles) from the AAVSO
database. Only the 3 photometric data (red circles) belong to the RTT150. The
times of the spectroscopic observations are labeled over the light curve with
brown-filled squares and vertical dash-dotted lines. There are shown the
phases of 17 spectra taken over nearly 500 days on the light curve.
Accordingly, Days 14, 15, and 16 were closest to the maximum light, while Day
43 was in the post-outburst multiple maxima. Day 111 is in the decline just
after the multiple maxima, and Day 143 is in the decline before the
transitional (nebular) phase. Finally, Day 515 corresponded to the afterglow
minimum caused by dust from the transitional phase. The larger plot shows the
light curve from the discovery until the dust formation epoch while the
smaller plot shows the entire light curve. Figure 2: Same as Figure 1 but for
the $B$-band. Only the 6 photometric data (red circles) belong to the RTT150.
Here, there are shown the phases of 17 spectra taken over nearly 500 days on
the light curve. Accordingly, Days 14, 15, and 16 were closest to maximum
light, while Days 43 and 111 were in the post-outburst multiple maxima. Day
143 is in the decline after multiple maxima. It seems data missing in the
AAVSO light curve from Day 143 to Day 515 due to dust in the transitional
phase.

The spectra taken using the three grisms are plotted in Figs. 3, 4, and 5. The
common aspects of the spectra given in the figures are as follows: 1) The
spectra are indicated with different colors. 2) Some spectral lines are also
marked. 3) The days of the spectra taken after the outburst are shown on the V
and B-bands light curves with dash-dotted lines (see Figures 1 and 2).

Figure 3: V1391 Cas observations in the blue part 4220-6650
$\mathrm{\text{\r{A}}}$ with 1331 resolution (grism 7). In this region and at
this resolution, the evolution of the spectra (trend of the continuum, change
of spectral lines) is seen for about 500 days after the discovery of the nova
(from Day 14 to Day 515). Figure 4: V1391 Cas observations in the red part
6190-8190 $\mathrm{\text{\r{A}}}$ with 2189 resolution (grism 8). In this
region and at this resolution, the evolution of the spectra (trend of the
continuum, change of spectral lines) is seen for about 500 days after the
discovery of the nova (from Day 14 to Day 515). Figure 5: V1391 Cas
observations in the blue-red part 3650-8740 $\mathrm{\text{\r{A}}}$ with 749
resolution (broad-band grism 15). In this region and at this resolution, the
evolution of the spectra (trend of the continuum, change of spectral lines) is
seen for about 3 days after the discovery of the nova (from Day 14 to Day 16).

The basic data reduction was made using the Image Reduction and Analysis
Facility (IRAF) version 2.16 Tody (1993) and the task splot was used for
measuring the spectral lines. The multiple peaked lines were deblended using
the deblending method of splot where gaussian profiles were fitted for each
peak. Many frames were heavily affected by cosmic rays so the LACosmic routine
of van Dokkum (2001) was used for cosmic ray removal making use of its Astro-
SCRAPPY version (McCully et al., 2018). Spectrophotometric standard stars from
Oke (1990) were used for the flux calibration. These stars are listed in the
sixth column of Table 2. The standard method for flux calibration in IRAF was
used. All the spectra were corrected for interstellar extinction adopting a
value of $E(B-V)=1.39$ calculated by Munari et al. (2020b) adopting an $R_{V}$
value of 3.1. This value is consistent with the extinction values obtained
from the interstellar dust maps of Schlegel et al. (1998) and Schlafly &
Finkbeiner (2011). This value is also consistent with the value calculated for
the extinction of supernovae by Foight et al. (2016). The dust_extinction tool
included in Astropy (Astropy Collaboration et al., 2013, 2018) using the
interstellar extinction curves of Fitzpatrick et al. (2019) was used to
correct for interstellar extinction. The methods described by Lenz & Ayres
(1992) were used to calculate the errors in the line fluxes and velocities,
while Cayrel (1988) method was used to calculate the uncertainty in equivalent
widths determinations. The Astropy affiliated package photutils was used for
calculating the magnitude in the photometric observations (Bradley et al.,
2020). For the 2021 observations, we used the Astropy affiliated package
ccdproc (Craig et al., 2017) for image reduction and a special python routine
developed by TUG staff (Khamitov et al., 2020) was used for spectrum
extraction and wavelength calibration.

The nova was very faint on Day 143 and only a few emission lines were visible.
This is consistent with the dust formation reported by Banerjee et al.
(2020a). On Day 162, the nova was detectable using direct imaging but it was
too faint to produce a good spectrum using RTT150. We were able to observe the
nova again on Day 515 when the dust had dissipated. It should be noted that
there is no information in the literature on nova evolution for days 143 and
515 in Section 1.1.

We made use of the NIST database of Kramida et al. (2020) to determine the
rest wavelengths of spectral lines. The spectral evolution of some prominent
lines shows that the H$\alpha$ line started with a clear P-Cygni profile with
the absorption feature at about -200 $\mathrm{km\,s^{-1}}$ on Day 14 (see
Table 3, Day 14). The observations taken in the following days showed that the
line got weaker in both absorption and emission (see Table 3, Day 15 and 16,
and also Figure 9). These spectra showed also that the line was weak but blue-
shifted (see Figure 7(a)). In the observations taken on Day 43, the absorption
component almost disappeared and the line was completely in emission. By Day
111 the line reached its maximum flux in our observations and it showed a
double-peaked profile with the red peak having the higher flux. On Day 143
spectra, the line showed multiple peaks while the blue peak had the highest
flux (see Figs. 7(a) and 9, Tables 3 and 5). The H$\beta$ line showed an
absorption feature in Day 14 observations. Then the emission component grew
stronger and the absorption component got blue-shifted in the Day 15
observations. By the time of our observations on Day 43, the line transformed
completely to emission. It reached its maximum flux in Day 111 spectra and for
Day 143 spectrum, it was undetected. It reappeared in emission in Day 515
observations (see Table 5 and Figs. 7(b), and 9). The evolution of the O I
7772 $\mathrm{\text{\r{A}}}$ line showed very similar behavior to the
evolution of the H$\alpha$ line where the line shows a P-Cygni profile with
the absorption component blue-shifted at a velocity of about -130
$\mathrm{km\,s^{-1}}$. In a similar behavior to that of H$\alpha$, the line
got weaker in both absorption and emission in Day 15 observations. In Day 16
spectra the line was blue-shifted while remaining weak. In Day 43 spectra, the
absorption component nearly disappeared and the line was in emission (see
Figs. 7(c), 8, and 9). This similarity was also noted in the behavior of both
H$\alpha$ and O I 7772 lines in the spectra of the classical nova V659 Sct
(Jack et al., 2020). However, the flux of the emission line of H$\alpha$ was
much stronger in the spectrum taken on Day 43.

Table 3: The evolution of the equivalent widths of the absorption component of some lines. The three dots (…) indicate that the line was undetected. Element | Day 14 | Day 15 | Day16 | Day 43
---|---|---|---|---
H$\alpha$ | $2.2\pm 0.9$ | $3.1\pm 0.3$ |  |
H$\beta$ | $2.1\pm 0.2$ | $1\pm 1$ |  |
O I 7772 | $3.7\pm 0.8$ | $3.6\pm 0.7$ | $2.9\pm 0.5$ | $0.6\pm 0.3$
Fe II 4924 | $0.5\pm 0.2$ | $2.0\pm 0.3$ | $1.0\pm 0.2$ |
5169 | $1.1\pm 0.2$ | $1.2\pm 0.7$ |  |
5232 | $0.3\pm 0.2$ |  |  |
6456 | $1.1\pm 0.2$ | $1.1\pm 0.2$ |  |
Table 4: The evolution of the integrated flux of the emission component of some lines (in $\mathrm{10^{-11}\,erg\,cm^{-1}\,s^{-1}}$) . Element | Day 14 | Day 15 | Day16 | Day 43 | Day 111 | Day 143 | Day 515
---|---|---|---|---|---|---|---
H $\alpha$ | $4.4\pm 0.5$ | $0.60\pm 0.09$ | $1.24\pm 0.06$ | $107\pm 2$ |  $8.0\pm 0.3$* |  $0.16\pm 0.03$** | $0.60\pm 0.03$
|  |  |  |  | $141\pm 2$ | $0.72\pm 0.02$ |
|  |  |  |  |  | $0.218\pm 0.006$ |
H $\beta$ | $0.14\pm 0.02$ | $0.15\pm 0.02$ | $2.1\pm 0.3$ | $10\pm 1$ |  $4.5\pm 0.3$ ** |  | $0.48\pm 0.06$
|  |  | $0.62\pm 0.01$ |  | $19.7\pm 0.3$ |  |
|  |  |  |  | $17.5\pm 0.3$ |  |
H$\gamma$ |  |  | $0.9\pm 0.1$ | $2.5\pm 0.3$ | $14.5\pm 0.6$ |  | $0.23\pm 0.07$
|  |  |  | $0.97\pm 0.03$ |  |  |
|  |  |  | $1.29\pm 0.04$ |  |  |
O I 7772 | $0.71\pm 0.08$ | $0.100\pm 0.009$ | $0.089\pm 0.0007$ | $6.2\pm 0.1$ |  $18.40\pm 0.02$ * |  |
|  |  | $0.081\pm 0.0001$ |  | $9.6\pm 0.1$ |  |
Fe II 4924 |  |  | $0.5\pm 0.1$ | $3.3\pm 0.2$ | $9.1\pm 0.2$ |  |
| $0.32\pm 0.02$ |  | $0.67\pm 0.06$ | $2.8\pm 0.2$ | $5.5\pm 0.1$ |  |
5169 | $0.56\pm 0.03$ | $0.45\pm 0.03$ | $1.6\pm 0.1$ | $2.6\pm 0.2$ | $3.1\pm 0.1$ |  |
6456 | $0.34\pm 0.03$ | $0.036\pm 0.0003$ |  |  $0.38\pm 0.01$* | $3.27\pm 0.01$ |  |
|  |  |  | $0.47\pm 0.01$ |  |  |
5235 | $0.80\pm 0.01$ | $0.105\pm 0.003$ | $0.94\pm 0.04$ | $0.423\pm 0.007$ |  |  |
5276 |  |  |  |  | $1.26\pm 0.02$ |  |
[N II] 5755 |  |  |  |  |  |  | $0.41\pm 0.03$
[O III] 4363 |  |  |  |  |  |  | $0.8\pm 0.1$
4959 |  |  |  |  |  |  | $3.1\pm 0.3$
5007 |  |  |  |  |  |  | $9\pm 1$
[O I] 5577 |  |  |  |  $1.7\pm 0.1$ * | $1.8\pm 0.2$ | $0.10\pm 0.02$ |
6300 |  |  |  |  $2.3\pm 0.1$ * |  $4.9\pm 0.3$ * | $0.5\pm 0.1$ | $0.068\pm 0.004$
|  |  |  | $2.53\pm 0.08$ | $4.8\pm 0.3$ |  |
6364 |  |  |  |  $0.78\pm 0.03$ * |  $1.84\pm 0.08$ * | $0.15\pm 0.03$ | $0.036\pm 0.004$
|  |  |  | $0.80\pm 0.03$ | $1.58\pm 0.06$ |  |
[O II] 7320 |  |  |  |  |  |  | $0.123\pm 0.007$
∗ Double Peaked |  |  |  |  |  |  |
∗∗ Multiple Peaked |  |  |  |  |  |  |

On Day 16 low-resolution spectra, CN and $\mathbf{C_{2}}$ bands are clearly
visible. This was also noted by Fujii et al. (2021) for this nova.

The He I 4921 $\mathrm{\text{\r{A}}}$ was one of the prominent lines observed
in our spectra. It was not observable in Day 14 spectra. It started to show a
P-Cygni profile on Day 15. By Day 43 the absorption component disappeared and
the line was completely in emission (similar to the behavior of the profiles
of H$\alpha$ and H$\beta$ lines). It reached the maximum flux in Day 111
observations and by Day 143 it was not observable (see Fig. 7(e)).

Numerous Fe II lines are seen in the spectra. The most prominent of these
lines are the 42 multiplet lines at the wavelengths 4924
$\mathrm{\text{\r{A}}}$, $\mathrm{\text{\r{A}}}$, and 5169
$\mathrm{\text{\r{A}}}$. These three lines showed P-Cygni profiles for the
first two nights (Days 14 and 15). Then they showed only emission components
reaching maximum fluxes on Day 111. Similar behavior was shown by the 5235
$\mathrm{\text{\r{A}}}$, 5276 $\mathrm{\text{\r{A}}}$, and 5317
$\mathrm{\text{\r{A}}}$ Fe II lines. The fluxes are presented in Tables 3 and
5. The 6456 $\mathrm{\text{\r{A}}}$ Fe II line was seen in absorption on Day
14-15 low-resolution spectra and it transitioned to P-Cygni profile for Day 15
low-resolution spectrum. The evolution of the Fe II $\mathrm{\text{\r{A}}}$
line is presented as a sample of Fe II lines in Fig. 7(d). Fig. 10 shows the
evolution of the flux of some prominent emission lines.

On Day 515 observations, some higher ionization lines such as [O III] 4363
$\mathrm{\text{\r{A}}}$, [O III] 4959 $\mathrm{\text{\r{A}}}$, [O III] 5007
$\mathrm{\text{\r{A}}}$, [O II] 7320 $\mathrm{\text{\r{A}}}$ and [N II] 5577
$\mathrm{\text{\r{A}}}$ appeared in the spectra (see Table 5 for the fluxes of
these lines).

The expansion velocity of the envelope was calculated from the FWHM of the
emission component of the H$\alpha$ line (corrected for instrumental
resolution) using the same method used by Munari et al. (2010). The expansion
velocity has risen from $\sim$ 80 $\mathrm{km\,s^{-1}}$ on Day 13 to $\sim$
780 $\mathrm{km\,s^{-1}}$ on Day 143. It has decreased again to $\sim$ 360
$\mathrm{km\,s^{-1}}$ on Day 515. A plot of the evolution of the expansion
velocity is shown in Fig. 6.

Figure 6: The expansion velocity of V1391 Cas using the H$\alpha$ FWHM.

(a) H$\alpha$.

(b) H$\beta$.

(c) O I 7772 $\mathrm{\text{\r{A}}}$.

(d) Fe II 5018 $\mathrm{\text{\r{A}}}$.

(e) He I 4921 $\mathrm{\text{\r{A}}}$.

Figure 7: Spectral evolution of some prominent features. Figure 8: Evolution
of the equivalent width of absorption component of O I
7772$\mathrm{\text{\r{A}}}$ line.  Figure 9: Evolution of the equivalent width
of emission components of some prominent lines.  Figure 10: Evolution of the
flux of emission components of some prominent lines.

In the spectrum of Day 43, the forbidden lines [O I] 5577
$\mathrm{\text{\r{A}}}$ along with the [O I] $\lambda\lambda$ 6300
$\mathrm{\text{\r{A}}}$, 6364 $\mathrm{\text{\r{A}}}$ doublet started to show
in the spectra. These lines were observable until Day 143. The Integrated
fluxes are included in Table 5.

Table 6: Evolution of the equivalent width of [O I] forbidden lines. Table 7: * Day | Element | EW ($\mathrm{\text{\r{A}}}$)
---|---|---
43 | [O I] 5577 | $20.6\pm 0.6$
111 |  | $14.5\pm 0.7$
143 |  | $86\pm 1$
43* | [O I] 6300 | $31.0\pm 0.2$
43 |  | $32.3\pm 0.1$
111* |  | $40.14\pm 0.3$
111 |  | $38.1\pm 0.3$
143 |  | $293\pm 1$
515 |  | $97.6\pm 0.6$
43* | [O I] 6364 | $8.9\pm 0.2$
43 |  | $8.9\pm 0.1$
111* |  | $12.3\pm 0.2$
111 |  | $10.2\pm 0.2$
143 |  | $53\pm 1$
515 |  | $51\pm 1$
* double-peaked. ∗ Double Peaked |  |

##  3 The Mass of The Ejected Envelope

###  3.1 The mass of neutral oxygen in the ejecta

Using the method described by Williams (1994), the ratio of the fluxes of the
6300 $\mathrm{\text{\r{A}}}$ to 6364 $\mathrm{\text{\r{A}}}$ [O I] lines
(${F_{\lambda 6300}}/{F_{\lambda 6364}}$, see Table 8) was found to be almost
3$\colon$1 throughout the first three observations where this doublet was
observable. This is identical to the theoretical value calculated from the
ratio of the transition probabilities of this doublet (Williams, 1994). This
result is in contrast to most of the novae which show values less than 3
(Williams, 1994). See Table 6 for the equivalent widths of the [O I] lines.

The ratio of the fluxes of this [O I] doublet (${F_{\lambda 6300}}/{F_{\lambda
6364}}$) was used to calculate the optical depth of the ejecta at $\lambda
6300$ using the equation

$\frac{F_{\lambda 6300}}{F_{\lambda 6364}}=\frac{1-e^{-\tau}}{1-e^{-\tau/3}}$
(1)

The calculated optical depth along with the ratio of the fluxes of the nebular
line $\lambda 6300$ and the auroral $\lambda 5577$ line (equation 1) was used
to calculate the electron temperature $T_{e}$ in the region where the [O I]
lines are formed, where

$T_{e}=\frac{11200}{log[43\tau\mathbin{/}(1-e^{-\tau})\times F_{\lambda
6300}\mathbin{/}F_{\lambda 5577}]}$ (2)

The electron temperature ($T_{e}$) with the flux of the auroral $\lambda 5577$
line (${F_{\lambda 5577}}$) was used to obtain the mass of neutral oxygen in
the ejecta using the equation

$M_{OI}=152d^{2}\,e^{\frac{22850}{T_{e}}}\frac{\tau}{1-e^{-\tau}}\times
F_{\lambda 6300}$ (3)

where d is the distance in kiloparsecs and the flux (${F_{\lambda 6300}}$) is
corrected for interstellar reddening (see Williams, 1994 for equations).

Selvelli & Gilmozzi (2019) concluded that the average absolute magnitude for
classical novae 15 days after the maximum to be

$M_{V,15}=-5.71\pm 0.40$ (4)

the $V$ magnitude of V1391 Cas 15 days after the maximum was 12.16 which
yields a distance of $\sim$5.2 kpc. Using this value we obtain the neutral
oxygen masses tabulated in Table 8.

All the values of $F_{\lambda 6300}/F_{\lambda 6364}$ are almost equal to 3
therefore we adopt a value of 2.84 for the calculations of $\tau_{\lambda
6300}$, $T_{e}$ and $M_{OI}$. Our calculations (see Table 8) give an average
electron temperature $\mathbf{T_{e}=4890\,K}$ and an average neutral oxygen
mass $\mathbf{M_{OI}=2.54\times 10^{-5}}M\textsubscript{$\odot$}$. The values
we obtained for $M_{OI}$ are comparable to the values reported for other novae
by Williams (1994).

Table 8: The mass of neutral oxygen in the ejecta. Day | $\frac{F_{\lambda 6300}}{F_{\lambda 6364}}$ | $\tau_{\lambda 6300}$ | $\frac{F_{\lambda 6300}}{F_{\lambda 5577}}$ |  $T_{e}$(K) | $M_{OI}(M\textsubscript{$\odot$}\times 10^{-5})$
---|---|---|---|---|---
43 | $3.05\pm 0.08$ | 0.172 | $2.84\pm 0.08$ | 5276 | $1.62$
111 | $2.8\pm 0.1$ | 0.172 | $5.4\pm 0.3$ | 4665 | $5.72$
143 | $3.3\pm 0.8$ | 0.172 | $5\pm 1$ | 4829 | $0.28$

###  3.2 Determination of the electron density

We used the [O III] lines to determine the $\mathrm{n_{e}}$ using the ratio of

$\frac{F_{\lambda 4363}}{F_{\lambda 4959}+F_{\lambda 5007}}$ (5)

The ratio yielded a value of $0.066\pm 0.009$ from the spectra taken on Day
515. We used PyNeb (Luridiana et al., 2015) nebular analysis code assuming
several temperatures and densities and then plotting the ratio of the line
emissivities (equation 5) as a function of the electron density ($n_{e}$)
computed for different electron temperatures to get Figure 11. Our ratio
yielded initial estimates for the electron densities and electron temperatures
which were used to make initial estimates for the abundances of oxygen and
nitrogen abundances using PyNeb. These values are listed in Table 10.

Table 9: Initial PyNeb Values. $T_{e}$ (K) |  $log(n_{e})$ ($\mathrm{cm^{-3}}$) | Oa | Na
---|---|---|---
8000 | 6.943 | -3.915 | -4.568
10000 | 6.509 | -4.695 | -5.245
12000 | 6.252 | -5.166 | -5.653
14000 | 6.069 | -5.487 | -5.934
16000 | 5.925 | -5.723 | -6.143
18000 | 5.810 | -5.903 | -6.304
a Log abundance by number relative to Hydrogen. Figure 11: $[OIII]F_{\lambda
4363}/(F_{\lambda 4959}+F_{\lambda 5007})$ vs Electron Density for different
Temperature Densities generated by PyNeb. Our observed line ratio (the
horizontal line) is used to determine the electron density of the ejecta.

###  3.3 Photoionization Analysis

Figure 12: Best Fitting Cloudy Model.

We used the photoionization code Cloudy version C17.02 (Ferland et al., 2017)
to model the envelope of the nova based on the values we obtained from the
nebular analysis of the spectrum on Day 515 (Table 10) as initial values
(hereinafter referred to as "input"). Starting from these values, we assumed
values of log($n_{H}$) to be equal to the electron densities in Table 10. We
ran thousands of models assuming we have a blackbody ionizing source (The
underlying WD) with temperatures ranging from 80000 to 200000 K (input 1). We
assumed the inner radius of the envelope to be 15.19 (input 2) as an initial
estimate based on the average expansion speed determined from the width of the
H$\alpha$ line (input 3 as 780 $\mathrm{km\,s^{-1}}$). We varied the filling
factor from 0.05 to 0.8 (input 4). The log of the luminosity of the white
dwarf was varied from 35.5 to 36.5 $\mathrm{erg\,s^{-1}}$ (input 5). The
parameters of the best-fitting model are tabulated in Table 11. The synthetic
spectrum of this model is plotted in Fig 12. The chi-squared goodness of fit
test of this model concerning the observed spectrum yielded $16\%$. Table 13
compares the observed emission lines with the lines calculated by the model.

Table 11: Cloudy Best Fit Parameters. Parameter | Value
---|---
log $n_{H}$ ($\mathrm{cm^{-3}}$) | 5.81
$T_{BB}$ (K) | $2\times 10^{5}$
log luminosity ($\mathrm{erg\,s^{-1}}$) | 36.5
Filling Factor | 0.05
log ($R_{in}$ ) (cm) | 16.0
He a | -0.7
C | -5.5
O | -2.5
N | -2.0
Ne | -4.00
a Log abundance by number relative to Hydrogen. Table 12: Best Fit Cloudy Emission Lines. Line ID |  $\lambda$ (Å) | Modelled | Observed | $\chi^{2}$
---|---|---|---|---
H$\gamma$ | 4340 | 0.471 | 0.479 | 0.0001
H$\alpha$ | 6562 | 2.79 | 1.25 | 0.85
H$\beta$ | 4861 | 1.0 | 1.0 | 0.0
[N II] | 5755 | 0.74 | 0.85 | 0.017
[O III] | 4363 | 0.49 | 1.67 | 2.88
[O III] | 4959 | 5.74 | 6.46 | 0.09
[O III] | 5007 | 17.13 | 18.75 | 0.15
[O I] | 6300 | 0.07 | 0.14 | 0.06
[O I] | 6364 | 0.023 | 0.075 | 0.11
[O II] | 7320 | 0.077 | 0.256 | 0.415
Total $\chi^{2}$ |  |  |  | 4.58

###  3.4 Total Mass of the Ejecta

We follow the method used by Ederoclite et al. (2006) to calculate the total
mass of hydrogen in the ejecta using the equation:

$M_{H}=4\pi n_{e}m_{H}\epsilon\delta R^{2}$ (6)

where $n_{e}$ is the electron density, $m_{H}$ is the mass of the hydrogen
atom, $\epsilon$ is the filling factor calculated from the flux of the
$H_{\alpha}$ line from the equation,

$\epsilon=\frac{F_{H}}{g\,n_{e}^{2}\,V}$ (7)

where $F_{H}$ is the flux of $H_{\alpha}$ or $H_{\beta}$ line and $g$ is the
volume emissivity of the used line, V is the volume of the envelope given by

$V=4\pi\times R\times\delta$ (8)

we get the radius of the envelope at day 515 by using the average expansion
velocity $v_{{exp}_{av}}\sim 350km/s$.

$\delta$ is the thickness of the envelope calculated from the equation:

$\delta=R\frac{v_{th}}{v_{exp}}$ (9)

where $v_{th}$ is the thermal velocity given by,

$v_{thermal}=\sqrt{\frac{3kT_{e}}{m_{p}}}$ (10)

where k is the Boltzmann constant, $T_{e}$ is the electron velocity and
$m_{p}$ is the proton mass Ederoclite et al., 2006; Tarasova, 2019, and
references,therein. We used the values of $T_{e}=18000\,K$ and
$log(n_{e})=5.81$ since these values yielded the best-fit cloudy model. We
used PyNeb to calculate the emissivities of $H_{\alpha}$ and $H_{\beta}$ lines
for the mentioned temperature and densities. we list the calculated physical
parameters in Table 14.

parameter | value
---|---
$v_{th}$ | $21\,km\,s^{-1}$
R | $1\,\times 10^{16}\,cm$
$\delta$ | $6.05\,\times 10^{14}$
V | $7.6\,\times 10^{47}\mathbf{cm^{3}}$
$g_{\alpha}$ | $2.0\,\times 10^{-25}$
$g_{\beta}$ | $7.25\,\times 10^{-26}$
$\epsilon_{{H}_{\alpha}}$ | 0.02
$\epsilon_{{H}_{\beta}}$ | 0.05
$M_{H}(H_{\alpha})$ |  $1.05\,\times 10^{-5}$ $M\textsubscript{$\odot$}$
$M_{H}(H_{\beta})$ |  $2.3\,\times 10^{-5}$ $M\textsubscript{$\odot$}$
$M_{tot}(H_{\alpha})$ |  $2.1\,\times 10^{-5}$ $M\textsubscript{$\odot$}$
$M_{tot}(H_{\beta})$ |  $4.6\,\times 10^{-5}$ $M\textsubscript{$\odot$}$
Table 14: Physical parameters of the nova envelope on day 515

Our calculated values for the mass of hydrogen range between $1.05\,\times
10^{-5}$ $M\textsubscript{$\odot$}$ and $2.3\,\times 10^{-5}$
$M\textsubscript{$\odot$}$. Our abundance analysis suggests that hydrogen
comprises about 0.5 of the mass of the envelope which yields a total mass of
the ejected envelope ($M_{tot}$) ranging between $2.1\,\times 10^{-5}$
$M\textsubscript{$\odot$}$ and $4.6\,\times 10^{-5}$
$M\textsubscript{$\odot$}$ where

$M_{tot}=\frac{M_{H}}{X}$ (11)

where $X$ is the hydrogen mass fraction. Our values are consistent with the
masses of most of the novae (see Tarasova, 2019; Della Valle & Izzo, 2020).

##  4 Discussion and Summary

The spectrum of the nova evolved from being optically thick dominated by
absorption lines to optically thin spectra in less than 30 days. In such an
early phase, the outer parts of the ejecta became exposed to emission from
hotter regions enhancing the ionization which is shown in the increasing flux
of the emission components of the lines and the disappearance of the
absorption components. The agreement between the observed flux ratio of the [O
I] $\lambda\lambda$ 6300 $\mathrm{\text{\r{A}}}$, 6364 $\mathrm{\text{\r{A}}}$
doublet (${F_{\lambda 6300}}/{F_{\lambda 6364}}$), and the theoretical value
could be attributed to that the ejected envelope of V1391 Cas is optically
thin and it is devoid of the dense globules responsible for the [O I] optical
thickness in other novae. The absorption components of the Hydrogen lines
disappeared by Day 43. The emission lines got stronger and the spectra evolved
towards the nebular phase. The absence of forbidden lines of high ionization
species in Day 43 spectra suggests that the nova was in the pre-nebular phase.
The nova transitioned to the nebular phase before Day 111 since we see the
strongest emission lines where the ejecta is optically thin and exposed to
radiation from the hot white dwarf. Our last observation on Day 515, shows
multiple [O III] lines along with the [N II] 5577 $\mathrm{\text{\r{A}}}$
which shows that the nova is in the late nebular stage.

Aydi et al. (2020) showed that classical novae can have multiple distinct
outflows of mass ejection near the optical peak. Two of these outflows can be
seen as a slow component and a fast component of P-Cygni profiles in lines
near the optical peak. During the first three nights of observations (near the
optical peak), our spectra showed two of these outflows in the absorption
component of the P-Cygni profiles of some lines mainly H$\alpha$ and O I 7772
$\mathrm{\text{\r{A}}}$. These components consist of firstly a slow component
with speeds of $\sim$ -200 $\mathrm{km\,s^{-1}}$ and -190
$\mathrm{km\,s^{-1}}$ for the H$\alpha$ line in Day 14 and 15 observations
(Figs. 13(a) and 13(b)) then the fast component of mass ejection appeared at a
speed of $\sim$ -350 $\mathrm{km\,s^{-1}}$ (Fig. 13(c)). For the O I 7772
$\mathrm{\text{\r{A}}}$ line, slow component had speeds of $\sim$ -150
$\mathrm{km\,s^{-1}}$ and -90 $\mathrm{km\,s^{-1}}$ for Day 14 and 15
observations (Figs. 13(d) and 13(e)). For the third night, the speed of the
absorption component was at a moderate speed of $\sim$ -150
$\mathrm{km\,s^{-1}}$ (Fig. 13(f) ).

(a) H$\alpha$.

(b) Same as Fig. 13(a) for the following night.

(c) Same as Fig. 13(a) for the third night. However here the green line
represents the fast mass ejection component.

(d) O I 7772 $\mathrm{\text{\r{A}}}$.

(e) Same as Fig. 13(d) for the following night.

(f) Same as Fig. 13(d) for the third night.

Figure 13: The P-Cygni profile of two prominent lines. The red dash-dotted
line represents the rest velocity. The green line represents the slow velocity
component.

The increase in the expansion velocity, measured by the H$\alpha$ line, with
time during the pre-nebular and nebular phases, is a result of the outer
ejecta being exposed to radiation from the central source.

The formation of the optically thick dust obscured the nova and it is now very
faint in the optical region of electromagnetic radiation.

Our calculated value for the neutral oxygen mass ($\mathbf{M_{OI}=2.54\times
10^{-5}M\textsubscript{$\odot$}}$) are slightly higher than the values
obtained for other novae [e.g. $M_{OI}=2.52\times
10^{-5}M\textsubscript{$\odot$}$ Williams (1994) and $M_{OI}=5.15\times
10^{-5}M\textsubscript{$\odot$}$ Munari et al. (2010)].

Novae show jitters in their light curve as they decline in brightness until
they experience a sudden drop in brightness associated with dust formation in
the ejecta when the gas cools down to a temperature of about 1400 K. This dust
blocks the light from the underlying photosphere (note our attempted
observations on day 162). As the shell expands, the dust dilutes geometrically
and the photosphere is visible again at a brightness slightly lower than
before the dip. This recovery occurred about a year after the outburst and we
obtained spectroscopic observations of the nova on Day 515. In these
observations, we can see that the ionization is enhanced further leading to
strong emission of lines with high excitation energies (e.g. [O III] lines
along with the [N II] 5577 $\mathrm{\text{\r{A}}}$).

The Galactic coordinates of the nova are l=$118^{o}.93153$, b=$+03^{o}.62587$
(666https://simbad.cds.unistra.fr). If we assume the distance from DR3 is 5.7
kpc, we can calculate the height of the nova from the center plane of our
Galaxy as z=360 pc. Fast novae located at z<100 pc are associated with the
disk, while slow novae up to z$\leq 1000$ pc are associated with the galactic
bulge (Della Valle et al., 1992). Nova Cas 2020 is a type of nova that has a
slow light curve decay ($t_{3}=120$ days, Schaefer, 2022), and it belongs to
the group of bulge novae.

We will be able to measure the size of the nova shell by using the expansion
velocity of $\sim 780\pm 20\mathrm{km\,s^{-1}}$ together with the expansion
parallax method by observing with narrow bands of H$\alpha$ and [O III] in the
years following the explosion when the radius of the ejecta is large enough to
be measured from ground-based instruments such the RTT150-TFOSC in Antalya or
DAG 4-meters telescope in Erzurum, and we will be able to obtain the more
precise distance of the nova and its absolute brightness at the outburst.

We were able to model the spectra of Day 515 using Cloudy and we found that
the ejected envelope developed into a diffuse cloud with log Hydrogen density
of 5.81 $\mathrm{cm^{-3}}$ and elemental abundances (log by number relative to
Hydrogen) of He = -0.7, C = -5.5, O = -2.5, N -2.0, Ne = -4.00.

We summarized the results of the spectral evolution and photoionization
analysis of V1391 Cas in the following.

  * •

We have determined that the ejection’s expansion velocity is approximately 780
$\mathrm{km\,s^{-1}}$.

  * •

We measured the electron temperature ($T_{e}$) to be 4966 K and determined
that the average mass of neutral oxygen in the ejecta was $2.54\times
10^{-5}M\textsubscript{$\odot$}$.

  * •

We modeled the envelope ejected by the nova 515 days after its discovery and
calculated the elemental abundances relative to hydrogen.

  * •

The total mass of the ejected envelope of the nova 515 days after its
discovery was $\sim 3.3\times 10^{-5}M\textsubscript{$\odot$}$.

## Aknowledgments

We thank TUBITAK for partial support in using RTT150 (Russian-Turkish 1.5-m
telescope in Antalya) with project numbers 1628 and 949. GMH also thanks
Turkey Scholarships Postdoctoral Research Fellowship for the financial
support. GMH acknowledges travel support from Science, Technology & Innovation
Funding Authority (STDF) under grant number 45779 during the final stages of
this work. The work of AIG was carried out at the expense of a grant allocated
by the KFU (project 0671-2020-0052 of the state task 075-00216-20-05). This
study was supported by the following project of Istanbul University Scientific
Research Projects Unit (BAP): FBA-2020-36956. We acknowledge Kottamia Center
of Scientific Excellence for Astronomy and Space Science, STDF project No.
5217 for providing computational facilities used in part of this work. We
acknowledge with thanks the variable star observations from the AAVSO
International Database contributed by observers worldwide and used in this
research. We also acknowledge the British Astronomical Association, Variable
Star Section and Svensk Amator Astronomisk Forening, variabelsektionen
(Sweden) for the photometric data used in this paper. We would like to thank
Professor Şölen Balman for proof reading the manuscript and for her important
remarks. We are grateful to the anonymous referees for the helpful suggestions
and comments which improved the quality of the manuscript. GMH gratefully
thanks Istanbul University, Department of Astronomy and Space Sciences for
hospitalities.

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