Theoretical light curve models of the symbiotic nova CN Cha — Optical flat peak for three years

The bottom panel in Figure 1 shows, from left to right, the very fast novae V1500 Cyg 1975 and V838 Her 1991, fast nova V1668 Cyg 1978, and moderately fast nova PW Vul 1984#1. They show a sharp optical peak. The WD masses of these novae have been obtained by theoretically reproducing their light curves in the decay phase. The estimated WD mass is 1.2 $M_{\sun}$ $(X,Y,Z,Z_{\rm CO},Z_{\rm Ne})=(0.55,0.30,0.02,0.1,0.03)$ for V1500 Cyg (see Appendix of Hachisu & Kato, 2014), 1.35 $M_{\sun}$ (0.55,0.33,0.02,0.03,0.07) for V838 Her (Kato et al., 2009b), 0.98 $M_{\sun}$ $(0.45,0.18,0.02,0.35,0.0)$ for V1668 Cyg (Hachisu & Kato, 2016a), 0.83 $M_{\sun}$ $(0.55,0.23,0.02,0.2,0.0)$ for PW Vul (Hachisu & Kato, 2015).

The symbiotic nova PU Vul is a unique nova having a long-lasted optical flat-peak (see Figure 1a). A very stable flat peak lasted as long as eight years. The early spectra mimicked those of an F supergiant and no indication of strong mass ejection (Yamashita et al., 1982; Kanamitsu, 1991a). The optical spectrum was absorption-dominated until JD 2,446,000, but showed a distinct nebular feature on JD 2,447,000 (Iijima, 1989; Kanamitsu et al., 1991b). On JD 2,448,000, the optical and UV spectra showed rich emission lines which are typical in the nebular phase (Vogel & Nussbaumer, 1992; Kanamitsu et al., 1991b; Tomov et al, 1991). P Cygni line-profiles appeared in the decay phase, indicating optically thin mass-ejection from the WD photosphere (Belyakina et al., 1989; Vogel & Nussbaumer, 1992; Sion et al., 1993; Nussbaumer & Vogel, 1996).

Based on these observational aspects, Kato et al. (2012) presented a light curve model for PU Vul with the assumption of hydrostatic envelope, i.e., no optically thick winds. They calculated a theoretical light curve that fits with the observed UV 1455 Å  and optical $V$ data. They used a narrow (20Å  wide) spectral band centered at 1455 Å, which is known to be emission-line free and can be a representative of continuum flux in classical novae (Cassatella et al., 2002).

Their model shown in Figure 1 is a $0.6~{}M_{\sun}$ WD with the optically-thin mass-loss rate of $5\times 10^{-7}~{}M_{\sun}$ yr^-1 in the decay phase. The chemical composition of the envelope is assumed to be $X=0.7$, $Y=0.29$, and $Z=0.01$ because the spectra show no indication of C, O, or Ne enrichment. The blue line shows the $V$ magnitude of the photospheric emission. This model is obtained from the UV light curve fitting. The black line represent the total $V$ flux which is the summation of the photospheric emission and the emission from optically thin plasma surrounding the WD. The origin of the plasma is optically thin mass-loss in the decay phase (see Kato et al., 2012, for more detail).

The slow nova V723 Cas shows an oscillatory behavior around $M_{V}\sim-5$ in the early phase which is settled down to a smooth decline in the later phase (Figure 1b). The WD mass in V723 Cas was estimated from a model light curve analysis to be 0.5-0.55 $M_{\sun}$ with the chemical composition of $(0.55,0.23,0.02,0.2,0.0)$ (Hachisu & Kato, 2015).

Kato & Hachisu (2011) presented the light curve model assuming that the outburst of V723 Cas began as a hydrostatic envelope without winds like the PU Vul evolution, but somewhat later changed to a normal evolution with smooth light curve decline, i.e., optically thick wind phase. This model is indicated by the black line in Figure 1b.

Such a transition from hydrostatic to winds does not normally occur because a redgiant-like hydrostatic envelope has a very different structure from that of a wind mass-loss envelope. Kato & Hachisu (2011) concluded that the transition could occur only when the extended nova envelope engulfs the companion and its motion in the envelope triggered the transition. The large energy release owing to the frictional energy produces additional luminosity. We see a relaxation process in a large spike-like oscillation of the light curve.

We do not expect such a transition in CN Cha or PU Vul because they are a very wide binary and their nova envelopes/photospheres do not engulf the companion.

Figure 2 shows the optical data for CN Cha, $V$ (red dots) and $g$ (magenta dots) taken from ASAS-SN (Shappee et al., 2014; Jayasinghe et al., 2019), and $V$ (cyan blue dots) from AAVSO. We see that the flat phase variation in CN Cha is much smaller than that in V723 Cas, or in other similar novae, like HR Del, V5558 Sgr, in which optical/$V$ magnitudes change by 2-3 mag (Figure 6 in Kato & Hachisu, 2011).

Lancaster et al.’s spectrum taken on JD 2458554.672 (downward arrow labeled “Sp” in Figure 1a) shows many narrow emission lines including P Cygni profiles, suggesting optically-thin wind mass loss. Although we do not find UV flux data in the decay phase of CN Cha, its resemblance to PU Vul suggests that the $V$ band flux is dominated by that of optically thin plasma outside the WD photosphere. Our model in Figure 2 is calculated from the photospheric blackbody emission, which does not include the $V$ flux from optically-thin nebular emission. Thus, we may take the observed data as the upper limit for our model $V$ light curve.

In slow novae, the envelope is almost in hydrostatic balance until it reaches optical maximum. In the phases of flat optical peak and after that, the energy generation rate of nuclear burning is balanced with the energy loss from the photosphere, i.e., $L_{\rm nuc}=L_{\rm ph}$. First, we integrated the hydrostatic equation with the diffusion equation from the photosphere to the base of envelope. We use the OPAL opacity (Iglesias & Rogers, 1993). The model parameters are the WD mass, WD radius (radius at the base of envelope), and chemical composition of envelope. Then, we make a sequence of envelope solutions in the order of decreasing mass. This sequence is a good approximation of nova evolution when no optically thick winds occur. The time interval $\Delta t$ between two successive solutions is obtained from $\Delta t=\Delta M_{\rm env}/(\dot{M}_{\rm nuc}+\dot{M}_{\rm wind})$, where $\Delta M_{\rm env}$ is the difference between the envelope masses of the two successive solutions, and $\dot{M}_{\rm wind}$ and $\dot{M}_{\rm nuc}$ are the wind mass-loss rate of optically thin winds and hydrogen nuclear burning rate, respectively. Here, $\dot{M}_{\rm nuc}$ is calculated from the envelope structure and chemical composition of envelope, but we assume the value of $\dot{M}_{\rm wind}$ as mentioned below. This method has been used to follow the supersoft X-ray phase of novae after the optically thick wind stops (Kato & Hachisu, 1994; Sala & Hernanz, 2005) or to follow PU Vul evolution in which the optically thick winds does not occur throughout the outburst (Kato et al., 2011, 2012). In the flat-peak phase, we have no wind mass loss, $\dot{M}_{\rm wind}=0$. In the later decay phase of $T_{\rm ph}>10,000$ K, we assume optically thin mass-loss ($\dot{M}_{\rm wind}\sim$ several $\times 10^{-7}~{}M_{\odot}$ yr^-1) after Kato et al. (2011, 2012) in PU Vul.

In the rising phase, we assume that the envelope is in hydrostatic balance, but the energy generation rate is slightly larger than the thermal equilibrium, i.e., $L_{\rm nuc}>L_{\rm ph}$, by a few to several percent. We obtained envelope solutions to be consistent with the observational data. This part is plotted with a dotted line in Figure 2(top).

The ignition mass is approximately obtained as the mass at $t=0$ when the photospheric temperature goes down to $\log T$ (K)=4.9, as shown in the middle panel of Figure 2. The envelope mass decreases only by a few percent from $t=0$ to $t=600$ day.

We assume Population II composition for the accreted matter, i.e., $Z=0.004$ with/without additional CO enhancement $Z_{\rm CO}$. For comparison, we calculated model D ($Z=0.01$) as listed in Table 1.

The absolute $V$ magnitudes, $M_{V}$, for the standard Johnson $V$ bandpass are calculated from the photospheric temperature, $T_{\rm ph}$, and luminosity, $L_{\rm ph}$. The UVW2 band flux is calculated from the blackbody emission between 1120 and 2640 Å.

Table 1 lists our models. It shows, from left to right, the WD mass $M_{\rm WD}$, chemical composition of the envelope $X$, $Y$, $Z$, $Z_{\rm CO}$, WD radius, ignition mass $M_{\rm ig}$, distance modulus in the $V$ band $(m-M)_{V}$, and assumed optically-thin wind mass-loss rates $\dot{M}_{\rm wind}$.

The top panel in Figure 2 shows the light curve fitting of model A with the observation. The model light curve shows a flat optical peak, which is the most expanded phase of photosphere, and its photospheric temperature is as low as $T_{\rm ph}<10,000$ K, as shown in the middle panel. We fit our theoretical curve with the observation to obtain the distance modulus in the $V$ band, i.e., $(m-M)_{V}=m_{V}$(obs) $-M_{V}$(model)=13.2.

The envelope mass gradually decreases because of hydrogen burning at a rate of $\dot{M}_{\rm nuc}\sim 1.7\times 10^{-7}~{}M_{\sun}$ yr^-1. In the decay phase of $T_{\rm ph}>10,000$ K, we assume the optically-thin wind mass-loss as done in the PU Vul model by Kato et al. (2011) and Kato et al. (2012). For simplicity, we assume a constant mass loss rate ($\dot{M}_{\rm wind})$. The $V$ magnitude decays as $T_{\rm ph}$ increases with time, while the photospheric luminosity $L_{\rm ph}$ is almost constant. If we assume a larger mass-loss rate, the $V$ magnitude decays faster because the envelope mass decreases more quickly.

From the resemblance of the light curve to PU Vul and the presence of emission lines that indicate the optically thin mass-loss, we regard that the $g$ light curve is strongly contaminated with nebular emission as often observed in the nebular phase of novae (e.g., Kato et al. (2012) for PU Vul, Hachisu & Kato (2006) for V1668 Cyg). In other words, the photospheric (continuum) component would be much fainter than $g$ light curve.

We plot three light curves with different wind mass-loss rates in the top panel of Figure 2. The mass loss starts at the point denoted by the open small circle in the middle panel. The model with $\dot{M}_{\rm wind}=1\times 10^{-7}~{}M_{\odot}$ yr^-1 is too slow and rejected.

Figure 3 shows the light curve fittings of model B, model C, and model D. We obtain the distance modulus in the $V$ band from the flat-peak phase, and the lower limit of mass-loss rates from the decay phase.

It is difficult to further constrain the mass loss rate in CN Cha. The bottom panel in Figure 2 shows the UV light curves of the three different mass-loss models. If we have UV observations in the decay phase, we can determine the mass-loss rate by comparing them with the model light curves.

In PU Vul, UV 1455 Å  band light curve is obtained with IUE that represents temperature evolution in the decay phase. Kato et al. (2011) and Kato et al. (2012) determined the optically-thin wind mass-loss rate to be $\dot{M}_{\rm wind}=(2-5)\times 10^{-7}~{}M_{\sun}$ yr^-1 for a $\sim 0.6~{}M_{\sun}$ WD.

The mass loss rate obtained in PU Vul may be a representative of mass loss rates in the extended nova envelope for the particular case of no optically thick winds. We plot the model of $\dot{M}_{\rm wind}=5\times 10^{-7}~{}M_{\sun}$ yr^-1 by the thick solid black line in Figures 2 and 3. We thus exclude model C.

For a less massive WD ($M_{\rm WD}\lesssim 0.55~{}M_{\sun}$), the envelope mass is larger while the nuclear burning rate $\dot{M}_{\rm nuc}$ is smaller. Thus, the evolution timescale is much more longer than those in models B and C. To reproduce a reasonable light curve for CN Cha, we need to take a much more larger $\dot{M}_{\rm wind}$. Thus, less massive WDs than those in models B and C are unlikely.

Figure 4 shows the distance modulus in the $V$ band, $(m-M)_{V}$, calculated from light curve fitting. The photospheric luminosity at the flat-peak is brighter for more massive WDs, so that the $(m-M)_{V}$ becomes larger with the increasing $M_{\rm WD}$. The horizontal solid/dotted blue lines indicate $(m-M)_{V}=12.9\pm 0.3$, calculated from a Gaia eDR3 distance, $d=3.05^{+0.19}_{-0.17}$ kpc (Bailer-Jones et al., 2021), and scattering in ASAS-SN $V$ data. From this plot, we may exclude $M_{\rm WD}\lesssim 0.5~{}M_{\sun}$ and $M_{\rm WD}>0.6~{}M_{\sun}$. Thus, models A and B are reasonable for CN Cha.

For models A, B, and C, we adopt a WD (radius) in a thermal balance with a relatively large mass-accretion rate of several $\times 10^{-8}~{}M_{\sun}$ yr^-1 (Kato et al., 2020). For model D, we take a smaller WD radius for a colder WD for comparison, and increase the heavy element enrichment to $Z=0.01$. The resultant distance modulus $(m-M)_{V}$ increases by 0.15 mag, because model D is brighter than model C mainly because of a smaller WD radius. Note that model D is for a Population I star and disfavored as a model of CN Cha.