Photoionization modelling of quiescence phase spectra of novae & symbiotic star

The observed spectra are presented in Fig. 1. Dates of observations are mentioned on the top right corner in each panel. The observed spectra show prominent emission features generated from the illuminated accretion disk surrounding the WD, which is also the source of the strong blue continuum. Generally, the strong, broad emission lines of hydrogen, helium, oxygen, and iron are seen in the spectra. The emission lines seen in these observed quiescence spectra are broad due to expanded disks (Anupama & Prabhu 1989; Anupama 2008). Strong optical Fe II emission lines come from an illuminated (photoionized) high density inner region of the disk. As the disk accumulates more matter, the lines weaken (Bode & Evans 2008). The spectra also show prominent absorption features in the continuum due to the cool secondaries and they reveal the properties of the secondaries.

The strong emission features observed in the spectrum of T CrB (observed on March 17, 2016) are due to H I (Balmer emissions) lines along with He I 5016, 5876, 6678 $\AA$, He II 4686 $\AA$, Fe II 5016 $\AA$ and O I 8444 $\AA$ lines. The absence of higher ionization lines can be accounted for by the absorption and softening by reradiation of all direct photons from the accretion disk. Presence of N III 4640 $\AA$ and Ca II 3933 $\AA$ along with He II 4686 $\AA$ indicate the super active phase that took place in October 2015. The strong TiO absorption features at 6180 and 7100 $\AA$ are due to the secondary.

The spectrum of GK Per was observed on January 31, 2016, about ten months after its recent dwarf nova (DN) outburst on March 2015 (Wilber et al. 2015), which lasted for 2 months. Presence of strong He I 5876, 6678 & 7065 $\AA$, and He II 4686 $\AA$ lines and Fe II features along with strong Balmer emission lines indicate towards this active phase and the bluer continuum suggests the higher temperature of the accretion disk. TiO absorption features due to the cool component are relatively weak.

The quiescence-phase spectrum of RS Oph taken on January 31, 2016, shows prominent emission lines of H (Balmer emissions) and He I 4471, 5016, 5876, 6678 & 7065 $\AA$, together with strong TiO absorption features at 5448 and 6180 $\AA$ contributed by the secondary. We observed that in comparison with the spectrum observed on April 26, 2007 (Mondal et al. 2018), Fe II lines are weaker which indicate that the accretion disk has been formed. This is in line with the fact that the mass accretion rate is high in the case of RS Oph (Yaron et al. 2005).

The spectrum of BX Mon (observed on May 13, 2016) is shown in the fourth panel of Fig. 1. The symbiotic star BX Mon was discovered by Mayall (1940) and its classification is based on the combination spectra in the optical region showing simultaneously very high excitation emission lines and low temperature absorption features (Kenyon 1986). No nova-like eruption has ever been recorded for this system. However, the eclipsing binary system shows variability with a periodicity of 1401 days and an amplitude of $\sim$ 3 magnitudes (Dumm et al. 1998). The observed spectrum is dominated by the strong TiO absorption features at 5448 and 7100 $\AA$ contributed by the cool component. Balmer emission lines are seen superimposed on the spectrum of the cool red continuum. No other strong emission lines are seen in the observed spectrum. This is possibly due to the low temperature of the disk.

For modelling of the spectra, we have considered a three component model consisting of the radiation from the central WD, photoionization emission from the accretion disk formed around the WD and the cool continuum coming from giant secondary.

To reduce the number of free parameters, we have kept the $R_{in}$ and $R_{out}$ values fixed for the objects as the number of emission lines are less in the quiescence spectra. The values of $R_{in}$ and $R_{out}$ have been calculated in the following way. Hamada & Salpeter (1961) estimated radius of a 1 $M_{\odot}$ WD as $10^{8.9}cm$. Paczynski (1977) showed that outer radius of the accretion disk can reach up to $3\times 10^{11}cm$ for a close binary system consisting of a 1 $M_{\odot}$ WD, 0.5 $M_{\odot}$ secondary and having orbital period of 3 - 10 $hr$. Combining these resutls, for simplicity of our calculations, we consider $R_{in}$ and $R_{out}$ of the accretion disk around a 1 $M_{\odot}$ WD as $10^{8.9}cm$ and $10^{11}cm$ respectively. Using these values and the relation between radius ($R_{WD}$) and mass ($M_{WD}$) of a WD, $R_{WD}\propto M_{WD}^{-1/3}$ (considering non-relativistic degeneracy), we have estimated the values of $R_{in}$ and $R_{out}$ for different systems.

Also, the semi-height of the cylindrical disk has been kept fixed as $10^{8}cm$ for the same reason. A constant mass per unit volume throughout the model shell gives the value of $\alpha$ = - 2. From the H$\alpha$/H$\beta$ line flux ratio, Hydrogen density of the disk is estimated. The rest of the elements are kept at solar abundance except for those which show strong presence of elemental lines in spectra. By matching the elemental emission lines of observed and modelled spectra, elemental abundances are determined. The spectra for giants are taken from the archival data of $1.5m$ SMARTS (Small & Moderate Aperture Research Telescope System) telescope in Cerro Tololo Inter-American Observatory (CTIO), Cerro Tololo, Chile (Riedel et al. 2007) and $4.5m$ Multiple Mirror Telescope (MMT Observatory) on Mount Hopkins, Arizona, USA (Henry et al. 1994).

These three components (black-body radiation of the WD, model generated emission line spectra and absorption spectra of giants) are then added up in various ratios to get the final best-fit model spectra using the $\chi^{2}$ minimization technique. Both the observed and model generated spectra are normalized with respect to H$\beta$ line. Observed (black solid) and modelled spectra (red dashed) are shown in Fig. 2. The relative fluxes of the best-fit model predicted lines, observed lines and corresponding $\chi^{2}$ values are presented in Table LABEL:chisq-table-2; and the best-fit model parameters are presented in Table LABEL:Quiescence-Parameters. From the best-fit model spectra, contribution of the components are also determined. In the following subsections, details of the parameters for individual nova are discussed.

T Coronae Borealis (T CrB): For T CrB, we have considered a high mass hot WD (1.37 $M_{\odot}$, $T=10^{4.1}K$) surrounded by a cylindrical accretion disk ($R_{in}=10^{8.85}cm$, $R_{out}=10^{10.95}cm$) of thick H-rich material ($n_{H}=10^{11.2}cm^{-3}$). Presence of higher ionization lines (e.g. N III, He II, Ca II) indicate the presence of some hot centres in the accretion disk. Thus, for the modelling, we considered two shells with different temperatures ($T=10^{5}K$, $L=10^{32}erg/s$ for higher ionization lines and $T=10^{4.1}K$, $L=10^{34}erg/s$ for lower ionization lines) and added them to match the emission features. The absorption features seen in the observed spectrum are due the secondary. Previously, Kleinmann & Hall (1986) suggested a spectral type of M2-M5 III and Mürset & Schmid (1999) suggested a spectral type of M4.5 III for the secondary of T CrB. Anupama & Mikolajewska (1999) determined a spectral type of M3 - 4 III. We added the spectrum of M4 type giant with the modelled spectrum and found that it fits well with the absorption features. As the properties of M4 type giant ($T\sim 3500K$, $L\sim 7L_{\odot}$) does not contribute any emission lines in the spectra, all the emission features for the T CrB spectrum are generated from the accretion disk. So only the model spectrum generated from the disk added with the black-body radiation from the WD was sufficient to produce the emission lines. By fitting the emission lines of different elements with varying abundances, we estimate the elemental abundances using $\chi^{2}$ values. Elemental abundances of He, Fe and O are estimated using the prominent emission features. The strong Fe II 5016 $\AA$ line is blended with He I. But as He abundance is estimated from other strong He I lines, we consider the blended Fe II line to estimate the Fe II abundance.

GK Persei (GK Per): We considered a 0.87 $M_{\odot}$ WD for modelling GK Per spectra and calculated $R_{in}$ and $R_{out}$ as $10^{8.92}cm$ and $10^{11.02}cm$. To generate higher ionization lines (e.g. He II), we had to adopt a higher effective temperature for the source. The best-fit model reveals $T=10^{4.5}K$, $L=10^{34.5}erg/s$ and $n_{H}=10^{11.5}cm^{-3}$. The high temperature and luminosity indicate towards the active phase of the dwarf nova outburst in March 2015. From the He I and He II lines, abundance of helium is estimated as 0.8 with respect to solar abundances, which is subsolar. Abundances of other elements could not be estimated due to the absence of prominent lines. Absence of Fe II features can be accounted for a thick disk as the Fe II lines are softened by the optically thick, cooler outer region of the disk. Earlier, Gallagher & Oinas (1974) determined the type of secondary as K2 V - IV and Morales-Reuda et al. (2002) found the donor star type as K1 IV. In this case, we observed that the spectrum of K5 V giant fits well with the absorption features seen in the observed spectrum. So, a spectrum of K5 V giant was added with the CLOUDY modelled spectrum to get the final spectrum.

RS Ophiuchi (RS Oph): RS Oph system is composed of a massive WD ($\sim$ 1.37 $M_{\odot}$) primary accompanied by a red giant secondary. The radii of accretion disk are calculated as $R_{in}=10^{8.85}cm$ and $R_{out}=10^{10.95}cm$. From the best-fit model, we find that the hot and luminous WD ($T=10^{4.2}K$ and $L=10^{32.0}erg/s$) is surrounded by a dense accretion disk of H-rich material ($n_{H}=10^{11.1}cm^{-3}$). A spectral type of M2 III fits the TiO absorption features of the secondary well. These two spectra are added with the black-body radiation continuum from the WD ($T=10^{4.2}K$) to get the final model generated spectrum. Helium abundance is estimated as 0.3 with respect to solar abundances, which is also subsolar. Only one prominent Fe II line is present but that too is blended, so, abundance of Fe cannot be estimated accurately. Since there were no prominent lines of other elements, the abundances of other elements could not be estimated. In previous work, Mondal et al. (2018) used CLOUDY code to model the quiescence phase spectrum of RS Oph taken on April 26, 2007 and estimated the physical parameters of the system and also estimated spectral class of the secondary as M2 III type which matches with previous results by Worters et al. (2007) and Anupama & Mikolajewska (1999).

BX Monocerotis (BX Mon): Symbiotic star BX Mon shows similar observational behaviour as the quiescence phase nova. For the modelling of the spectrum of BX Mon, we have considered a similar approach of three component model consisting of WD, accretion disk and the giant and added the spectra to match with the observed one. We have considered mass of the primary as 0.55 $M_{\odot}$ and obtained $R_{in}=10^{8.98}cm$ and $R_{out}=10^{11.09}cm$ for accretion disk. From the best-fit model, we got the hot WD ($T=10^{4.1}K$, $L=10^{31.5}erg/s$) is surrounded by thick H-rich ($n_{H}=10^{11.4}cm^{-3}$) cylindrical accretion disk. Elemental abundance cannot be estimated as the prominent emission lines of other elements except Balmer lines are absent. Previously Mürset & Schmid (1999) determined a spectral type of the secondary as M4 - 5.5 III. We added a spectrum of M4.5 III type with the modelled spectrum and found it matches well with the absorption features seen in the observed spectrum. Thus, it confirms that the secondary type for BX Mon is M4.5 III.

V3890 Sagittarii (V3890 Sgr): We used the published optical spectroscopic data of V3890 Sgr observed at VBO on March 21, 1998 (Anupama & Mikelojewska, 1999). The spectrum shows prominent Balmer emission lines along with strong Fe II lines, indicating the accretion disk is not fully formed. Absence of higher ionization lines marks the quiescence phase of the system. The absorption features are due to the giant secondary. Using the previously calculated value of the mass of WD primary as 1.35 $M_{\odot}$, we find $R_{in}=10^{8.86}cm$ and $R_{out}=10^{10.96}cm$ for accretion disk. From the best-fit CLOUDY model, we concluded that the system consists of an ionizing source of low temperature ($T=10^{4.05}K$) and luminosity ($10^{29.3}ergs/s$) surrounded by a cylindrical accretion disk of H-rich material ($n_{H}=10^{11.2}cm^{-3}$). Using the prominent He I (5016, 5876, 6678 $\&$ 7065 $\AA$) and Fe II (5016, 5159 $\&$ 5317 $\AA$) lines, elemental abundances of helium and iron are estimated as 1.5 and 10 respectively with respect to solar abundances. Also, a spectral type M5 III added to the model generated spectrum to match the absorption features and we found that the spectrum fits well. Anupama & Mikelojewska (1999) determined the type of the secondary as M5 III. Harrison et al. (1993) also indicated a spectral type M5 III based on the infrared photometric data during 1990 outburst. Our result matches with the previous results. In general, we use IRAF software to measure the flux of emission lines, but in case of the observed spectrum of V3890 Sgr, H$\alpha$ line is truncated. So, we have used line fluxes measured by Anupama & Mikelojewska (1999). Probably due to the difference in method for the measurement and presence of fewer emission lines, we obtained a higher $\chi^{2}_{red}$ value.

V745 Scorpii (V745 Sco): To study the quiescence phase spectrum of V745 Sco, we have modelled the published optical spectroscopic data taken on March 20, 1998 (Anupama & Mikelojewska, 1999) using CLOUDY photoionization code. The spectrum shows prominent Balmer emission lines although the blue region is not well resolved. Prominent Fe II and He I lines can also be easily identified. The strong TiO absorption features are due to the secondary companion. The radii for accretion disk have been calculated as $R_{in}=10^{8.86}cm$ and $R_{out}=10^{10.96}cm$ for a WD mass of 1.35 $M_{\odot}$. The best-fit model results a hot central source with relatively lower temperature ($T=10^{4.02}K$) and luminosity ($L=10^{29.1}ergs/s$), is surrounded by thick H-rich ($n_{H}$ = $10^{11.1}cm^{-3}$) cylindrical accretion disk. From the prominent He I 5016, 5876, 6678 & 7065 $\AA$ lines and Fe II 5016 & 5169 $\AA$ lines, elemental abundances of helium and iron are estimated as 1.1 and 10 respectively with respect to solar abundances. Williams et al. (1991) suggested the red giant companion of V745 Sco as M6 - 8 III type, Duerbeck (1989) classified it as M6 III and Harrison et al. (1993), based on the infrared spectra inferred a spectral type of M4 III. Based on the TiO and VO indices of the optical spectra, Anupama & Mikelojewska (1999) suggested a spectral type of M4 - 5 III, while the Na I index indicated towards a M6 III type. From our study, we have observed that the spectrum of a M5.5 III type giant fits the absorption features well. So, a spectrum of M5.5 III type giant is added to get the final spectrum.