Whats The Effect Of Nova Eruption On the Donor Star In A Cataclysmic Variable? (Planetary Science)

Cataclysmic variable stars are binary stars that consist of two components; a white dwarf primary, and a mass transferring secondary. The stars are so close to each other that the gravity of the white dwarf distorts the secondary, and the white dwarf accretes matter from the companion. Therefore, the secondary is often referred to as the donor star. The infalling matter, which is usually rich in hydrogen, forms in most cases an accretion disk around the white dwarf.

Schematic of a non-magnetic cataclysmic variable. A white dwarf (on the right) accretes matter through an accretion disk, fed by a Roche-lobe-filling main-sequence donor star (on the left). Matter from the donor star travels in a stream from the Lagrange point L1 and meets the accretion disk at a hot spot. The white dwarf has a mass of 0.8 M, its companion is a main sequence star of 0.5 M and their centres are separated by 1.64 R. © Philip D. Hall

As hydrogen accumulates on the white dwarf’s surface, the density and temperature at the base of the accreted layer rise. At some point, a critical mass is reached, and the accumulated layer explodes in a thermonuclear runaway— a nova. The binary system survives the explosion, mass accumulates once again on top of the white dwarf, and the nova recurs on a time-scale that depends on the accretion rate and on the white dwarf’s mass.

During and immediately after a nova eruption, the white dwarf’s luminosity is close to the Eddington limit. The companion is irradiated and heated to a surface temperature that is an order of magnitude hotter than its pre-eruption (main sequence) effective temperature. In 1988, Kovetz and colleagues studied the response of the companion to such irradiation and calculated the heat penetration into its atmosphere. They showed that as the heated layers expand, the donor overflows its Roche lobe more than in quiescence, and the mass transfer rate increases by orders of magnitude. Recently, Hillman and colleagues demonstrated that this irradiation-driven enhanced mass transfer may dominate the long term evolution of CVs over multiple nova cycles.

Now, Ginzburg and Quataert revisited the heating of the donor star by the hot white dwarf during and after a nova eruption using a combination of analytical arguments and experiments with the mesa stellar evolution code. They calculated the enhanced mass transfer rate following a nova and improve upon Kovetz et al. and Hillman et al. by refining their power-law scaling for how this rate depends on the irradiation temperature and on the donor’s mass. More importantly, they revise upwards the normalization of the mass transfer rate.

They first showed that a nova eruption irradiates and heats the donor star in a cataclysmic variable to high temperatures Tirr, causing its outer layers to expand and overflow the Roche lobe. They then, calculated the donor’s heating and expansion both analytically and numerically and found that irradiation drives enhanced mass transfer from the donor at a rate,

which reaches m• ∼ 10¯6 M yr¯1 at the peak of the eruption — about a thousand times faster than during quiescence. As the nova subsides and the white dwarf cools down, m• drops to lower values.

Finally, they discussed the decline of the mass transfer rate back to quiescence as the white dwarf cools down after a nova. They found that under certain circumstances, the decline halts and the mass transfer persists at a self-sustaining rate of m• ∼ 10¯7 M yr¯1 for up to ∼ 10³ yr after the eruption. At this rate, irradiation by the white dwarf’s accretion luminosity is sufficient to drive the mass transfer on its own.

Figure 1. The self-sustaining (bootstrapping) irradiation temperature Tirr ∝ m•^1/4 as a function of ΔrL ≡ rL – r(0), the difference between the donor’s Roche lobe rL and its non-irradiated radius r(0) © Ginzburg and Quataert

This ‘bootstrapping’ state may explain the high quiescent accretion rates (∼ m• ∼ 10¯7 M yr¯1) recently observed for the recurrent novae T Pyxidis (T Pyx) and IM Normae (IM Nor). If the self-sustaining rate is sufficiently high, the white dwarf can burn accreted hydrogen stably, potentially explaining long-lived supersoft X-ray sources with short orbital periods like RX J0537.7–7034 and 1E 0035.4–7230 as well.

Finally, they concluded that whether or not a system reaches the self-sustaining state is sensitive to the donor’s chromosphere structure, as well as to the orbital period change during nova eruptions.

Reference: Sivan Ginzburg, Eliot Quataert, “Novae heat their food: mass transfer by irradiation”, ArXiv, pp. 1-8, 2021. https://arxiv.org/abs/2104.11250

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