Disc Instability Outbursts in Symbiotic Star Systems
Symbiotic stars (SSs) are interacting binary systems in which a hot primary star, most likely a white dwarf, accretes matter lost by an evolved-giant star. These systems usually have long orbital periods and exhibit various kinds of outbursts, whose origin and properties are not yet completely understood. For the observed mass-transfer rates in these systems, their presumably large accretion discs are prone to thermal-viscous instabilities and are thus expected to exhibit outbursts of the type observed in dwarf nova stars.
Many disc-accreting systems such as Cataclysmic Variables (CVs) and Low mass X-ray binaries (LMXBs) exhibit outbursts that recur at regular intervals. During these outbursts, the intensity of the light curve increases by a few orders of magnitude. It is now widely accepted that the triggering mechanism for these outbursts is disc instability.
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What causes disc instability?
Under thermal equilibrium conditions, the rate at which the disc is locally heated due to viscous dissipation balances the cooling rate due to emission at that radius. For standard thin discs, the solutions of a thermal equilibrium state trace an S-shaped curve on the (Σ,Teff) plane (as shown in the figure to the right), where Σ and Teff are the surface density and effective temperature of the disc at a given radius, respectively. While the upper and lower branches of the S-curve are in a stable equilibrium, the middle branch is unstable since the rate of change of heating rate with respect to temperature is greater than the rate of change of cooling rate with respect to temperature. Therefore, any perturbations in the temperature from the middle branch lead to a “limit-cycle” behaviour where the disc oscillates between the outburst and quiescence states (i.e., the upper and lower branches).
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Although several works in the past based on the disc–instability model have successfully reproduced the outbursts in most of the CVs, and LMXBs, disc instabilities in SSs remained unexplored until recently primarily for the reason that SSs harbour large accretion discs that are challenging to evolve and second, most of the outbursts in SSs are thought to be triggered by thermonuclear burning (due to their high brightness amplitudes).
Σ−Teff S-curves computed for a 1.35 M white dwarf are plotted for various radii (r = 10^9, 10^10, 10^11 and 10^12 cm, respectively, from left to right). Solid lines represent the S-curves computed by solving the vertical structure of the disc with temperature-dependent viscosity parameter, whereas the dashed and dotted lines represent S-curves for fixed values of viscosity parameter, 0.1 and 0.01, respectively.
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Optical light-curves obtained from the disc-instability model for RS Ophiuchi parameters. Different curves are for three different mass transfer rates from the secondary companion assumed in the model: 1e-6 (dash–dotted green curve), 1e-7 (dashed blue curve) and 1e-8 (solid red curve) solar mass per year.
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RS Oph visual light-curve (data from AAVSO)
With Prof. Jean-Pierre Lasota (Institut d'Astrophysique de Paris, France) and Prof. Jean-Marie Hameury (Observatoire Astronomique de Strasbourg, France), we studied the disc instabilities in symbiotic stars, with particular emphasis on two systems: RS Ophiuchi and Z Andromeda (Bollimpalli et. al 2018). We used the 1D time-dependent numerical code developed by Hameury et al. 1998, to solve the standard disc equations in the radial dimension of a geometrically thin, optically thick disc to follow its thermal and viscous evolution.
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For the first time, we suggested that the RS Oph outbursts are recurrent ‘combination nova events’ where a series of dwarf nova outbursts can trigger the recurrent nova eruptions (caused by the thermonuclear runaway on the white dwarf surface). This might explain the puzzling observations of RS Oph light-curve such as the increase in pre-outburst luminosity and varying X-ray flux at different epochs during the quiescence. In general, the combination nova events scenario could potentially explain the short recurring timescales of the recurrent nova compared to their estimated accretion rates from observations.
For Z Andromeda, we explored the possibility that its complex light curve can be explained by the disc instability outbursts. We found for a mass-transfer rate of 1e-6 solar mass per year, the brightness amplitude of the disc instability outburst closely matches that of the 1997 outburst, but the model fails to accurately replicate the observed shape, exhibiting a longer rise-time and shorter duration. At lower mass-transfer rates, the outbursts not only deviate in shape but also appear much fainter than observed.
Our results also rule out the hypothesis of the 2000-2002 outburst of Z Andromeda being a ‘combination nova’ event. We instead suggest that the enhancement of mass transfer from the companion star could be the key, which may or may not trigger disc instability outbursts. Further studies are required to confirm this.
Visual light curves computed using the disc-instability model for Z Andromeda parameters. Here the mass transfer rate from the secondary companion is assumed to be 1e-6 solar mass per year. Different curves correspond to the irradiation of the disc by white dwarf: no irradiation (solid curve), weaker irradiation (dashed curve), strong irradiation (dotted curve).
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Z And visual light-curve (data from AAVSO)
