Close binaries with accreting white dwarf appear as CVs (or related objects) as long as hydrogen burning is not ignited in the accreted matter. They appear as novae when the gas is electron-degenerate at ignition leading to a thermonuclear runaway and they become CBSS when the gas is still nondegenerate at ignition and stable burning ensues. The outcome depends on the thermal history of the white dwarf, i.e., on the present core temperature and the time scale of previous accretion. Compression raises the temperature and pressure at the base of the envelope until the ignition takes place at Tlgn-1.5 x 107Kand Pign = 1018 - 1020 dyne cm-2 . For the long-term mean accretion rates typical of CVs driven by gravitational radiation and magnetic braking (Figs. 12.8 and 12.9), ignition cannot be avoided. Only if the rate drops continually below a few times 10-13 M0 yr-1, does cooling win over compressional heating and a cold degenerate configuration results .
Degeneracy is measured by the parameter y with ey ^ p/t5/2 and the condition y — 0 or T;rit — 3 x 107 (P /1019 dyne cm 2)2/5 K delineates the beginning of strong degeneracy. Stable burning can commence if the base temperature at ignition significantly exceeds Tcrit, a strong nova explosion ensues if it falls significantly below Tcrit. The transition is smooth in the sense that moderate degeneracy causes weak shell flashes with little or no mass ejection.
The mass of the accreted envelope above a level with hydrostatic pressure Pign,19 in units of 1019dynecm-2 is Macc ~ 3 x 10-5Pign,19(M/M0)-5 M0, where the mass-radius relation of white dwarfs has been approximated as R « M-1. The envelope mass at ignition decreases steeply with increasing M, and so does the recurrence time scale Trec — Macc/M of the shell flashes. Example, for a 1.25M0 white
NS _ aOOOyrs
_ JiN SOyrs
NS _ aOOOyrs
_ JiN SOyrs
Fig. 12.9 Characteristics of hydrogen burning on accreting white dwarfs as a function of the white dwarf mass and the accretion rate. Curves denote the Eddington luminosity for a hydrogen mass fraction X = 0.70 (dotted), the band of steady hydrogen burning  (solid), and the nova dud line , below which strong nova explosions occur (dashed). Also indicated are the types of outburst  and models of continuously burning very hot white dwarfs  (filled circles)
dwarf accreting at M = 10-7M0, Pign,19 — 0.2  and the recurrence time becomes as short as Trec — 20 yrs.
Figure 12.9 summarizes the results on the outcome of nuclear burning on accreting white dwarfs. The continuous-burning zone is limited toward large M by the core-mass luminosity relation Lcrit — 4.6 x 104(M/M0 - 0.26) L0 , which can be converted to a maximum accretion rate Mcrit = Lcrit/eX = 6.6 x 10-7(M/M0 -0.26) M0yr-1, by division by the energy yield for hydrogen burning e — 6 x 1018 erg s-1 and the assumed hydrogen mass fraction of the accreted matter taken to be X — 0.70 (upper solid curve). This limit is close to the Eddington luminosity and accretion rate4 (dotted curve). Above Mcrit, a giant envelope was thought to form , quenching the short-wavelength emission from the burning zone. The existence of a quasi-static atmosphere seems to be impossible, however, given the large opacity for matter with near-solar metalicity and instead a radiation-driven wind develops . This argument is based on the OPAL opacities , which were revised significantly upward from the older Los Alamos values. Toward smaller Ml, the width of the continuous burning zone is about a factor of 2.5 in accretion rate , below which weak flashes of intermittent burning occur. Such objects do not eject
4 The dotted curve in Fig. 12.9 represents the electron-scattering Eddington luminosity divided by eX. Without burning, the Eddington accretion rate rises to the conventional value Medd = Ledd R/GM.
mass and can appear either as CBSS (QR And = RX J0019.8+2156 [4,22] may be such a case) or as symbiotic or recurrent nonejecting novae and temporary supersoft X-ray sources. Shell flashes eject less mass than accreted, possibly down to the nova dud line  (dashed curve). Included in Fig. 12.9 is the outcome of nova model calculations giving the type of nova and the rounded recurrence times [68,101]. The abbreviations refer to symbiotic and recurrent novae (SymN and RN), which mostly eject no matter, and to classical novae of the different speed classes, very slow novae (NVS), slow (NS), medium slow (NM), fast (NF), and very fast novae (NVF). The dividing line between SymN/RN and classical nova events approximately agrees with Livio's earlier estimate of the nova dud line . The Prialnik and Kovetz calculations [68,101] were performed for white dwarfs with core temperatures up to 5 x 107 K. If the accreting white dwarf is still hotter, hydrogen ignition will occur further away from the degeneracy line and stable burning can proceed at lower accretion rates. Starrfield  has published models for hot 1.35M0 white dwarfs, which burn hydrogen steadily as far down as 1.6 x 10—8M0 yr—1 (solid dots). At an M still lower by a decade (open circle), the star experienced a strong helium shell flash, which leads to mass loss or disruption of the star before it reaches the carbon deflagration mass of 1.38M0. In summary, there seems to be a wider range of conditions for quasi-steady hydrogen burning than indicated by the narrow band in Fig. 12.9 labeled "steady burning" and the problem of fine-tuning the accretion rate is probably less severe than thought previously. The results are promising with respect to the possibility to drive white dwarfs with M > 0.9M0 toward the Chandrasekhar mass into a deflagration SN Ia event [26,82].5
CVs accreting at roughly M < 10—9 M0 yr—1 expel more mass in a classical nova outbursts than they accrete in the quiescent intervals [68,101]. As a result, the white dwarf cannot secularly gain mass by accretion. Furthermore, it retains little or no hydrogen after the outburst and the phase of supersoft X-ray emission of the postnova may be short or even missing .
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