## 2. T Pyx as a wind-driven supersoft X-ray source## 2.1. MotivationT Pyx's observational characteristics in quiescence are clearly extreme among CVs. However, as recently pointed out by Patterson et al. (1998) they are actually a good match to the properties of the supersoft x-ray sources (SSSs). Despite this empirical connection, the standard model for binary SSSs - thermal-timescale mass transfer from a companion initially more massive than the WD - cannot work for T Pyx: the shortest orbital period found in the detailed study of this phase by Deutschmann (1998) is about 6 hr, much longer than T Pyx's 1.8 hr. In fact, King et al. (2000) find that the two shortest-period systems among known binary SSSs - RX J0537.7-7034 ( hr) and SMC 13 ( hr) - are already difficult to account for within the thermal-timescale mass-transfer framework, even allowing for non-conservative evolution. We therefore propose that T Pyx is instead a member of an
(even more) exotic class of SSSs - the ## 2.2. Theoretical backgroundWe take as our starting point Eq. 7 in VK98, which gives the expected mass-loss rate from a low-mass, near-main-sequence secondary star irradiated by intense soft x-ray emission from the vicinity of the primary as In this equation, and are the mass and radius of the secondary, is the binary separation and is the luminosity of the irradiating source. The factor measures the efficiency of the irradiating spectrum in producing the wind, and measures the area of the mass-losing regions on the secondary's surface, relative to . The irradiating luminosity is most conveniently parameterized in terms of the luminosity expected for steady shell burning, , which is (Iben 1982). Defining , we therefore write the irradiating luminosity as and use the numerical factor as a measure of the efficiency with which the accreted material is actually converted into luminosity. Thus for steady shell burning, whereas for accretion onto a massive WD in the absence of any nuclear processing (). Combining Eqs. 1 and 3 yields Here, is the dimensionless
accretion rate (measured in units of the wind mass-loss rate),
, and we have used
Paczyski's (1971)
approximation for to recast
in terms of In order to determine where is the effective mass-radius index of the secondary (describing its reaction upon mass loss), and is the specific angular momentum of the escaping wind material, measured relative to the specific orbital angular momentum of the secondary. Eq. 5 gives the dimensionless RLOF mass-transfer rate in the stationary wind-driven state. It is identical to Eq. 30 of VK98, except that we have retained the explicit dependence on (VK98 set throughout). As shown by KV98, the stationary solution is stable for system parameters appropriate to T Pyx and . In deriving Eq. 5, it has been assumed that all of the material in the stellar wind from the secondary escapes. Also, the effects of mass loss from the primary have been ignored. In reality, T Pyx may undergo significant mass ejection during its nova eruptions, and the long term average may be comparable to . However, we have verified that even strong, episodic mass loss from the primary has virtually no impact on our results for T Pyx in quiescence, unless the specific angular momentum carried away by the nova ejecta is extremely high (much higher than that of the primary). In that case, the angular momentum loss associated with nova eruptions would further accelerate (and could possibly even dominate) the binary evolution. We will return to this possibility in Sect. 3. We finally consider the orbital period derivative of such a
wind-driven system. If this is entirely due to (c.f. Eq. 34 in VK98). However, the period derivative measured in real systems may differ from this, since the timescale associated with such measurements is much shorter than the timescale on which the RLOF rate can adjust itself ( yr, where is the scale height in the atmosphere of the secondary near the inner Lagrangian point). Thus observationally determined period changes could, for example, be due to fluctuations of or on timescales shorter than . ## 2.3. Application to T PyxWe are now ready to apply the wind-driven evolution scenario to
T Pyx. For definiteness in our numerical estimates, we will adopt
main-sequence-based values for the mass and radius of T Pyx's
secondary: ,
. These follow from Kepler's law, the
orbital period, Patterson's (1998) power law approximation to the the
M-dwarf mass-radius relationship of Clemens et al. (1998) and
Paczyski's (1971)
approximation for of a Roche-lobe
filling secondary star. In addition, we will use
as an estimate of the white dwarf
mass (Contini & Prialnik 1997). We therefore take the mass ratio
in T Pyx to be . We note from
the outset that even this rather low value for We begin by noting that, for a low-mass secondary undergoing adiabatic mass loss, we may take (VK98). Next, we consider two extreme estimates for the angular momentum loss parameter . To obtain a lower limit, we note that the stellar wind material will carry away at least the specific angular momentum of the secondary, in which case (this is the case considered by VK98). On the other hand, the stellar wind material may extract angular momentum from the binary system by frictional processes. An upper limit to the amount of specific angular momentum that is likely to be extracted this way is given by the specific angular momentum of particles escaping through the outer Lagrangian points, which is (Sawada et al. 1984; Flannery & Ulrich 1977; Nariai 1975). Here is the angular velocity of the binary system, and, in our notation, the corresponding angular momentum loss parameter is . These estimates, together with , yield () and (). Substituting these values back into Eq. 4, along with , we obtain for T Pyx if it has settled into a stationary, wind-driven state. The corresponding luminosity is given by Eq. 3 as Thus wind-driving can indeed account for T Pyx's extreme accretion rate and luminosity, provided that the various efficiency factors in Eqs. 7 and 8 are not too far from unity. VK98 have argued that in SSSs, since soft x-rays are absorbed well above the photosphere and should therefore be quite efficient at driving the wind. The factor is just the area of the mass-losing regions on the secondary divided by , so that mass loss from the entire front hemisphere would correspond to . We may therefore also expect , even if the secondary is partially shielded by an optically thick accretion disk. However, the most interesting parameter in this context is . As noted in Sect. 2.2, energy release by accretion yields . The upper limit in this inequality corresponds to a Carbon-core WD of maximum mass (1.4 ) and minimum radius (; Hamada-Salpeter 1961). For a 1.2 WD on the same mass-radius relation, we have . Thus gravitational energy release alone can only meet the system's luminosity requirements if the WD is even more massive than we have assumed and . The alternative is that nuclear processing continues in T Pyx even in quiescence. This would imply that nuclear burning in T Pyx occurs both quasi-steadily (in quiescence) and explosively (during outbursts), with the former taking place at a rate slightly below the accretion rate. From an empirical point of view, this does not seem unreasonable: as noted by Patterson et al. (1998), some SSSs in the LMC and M31 are recurrent (see Kahabka 1995), and the galactic novae GQ Mus and V1974 remained luminous soft x-ray sources for several years after their nova eruptions (Shanley et al. 1995; Krautter et al. 1996). Symbiotic stars (SySs) provide another interesting point of comparison. Several classical SySs, such as Z And, exhibit erupting behaviour even though though their quiescent luminosities () suggest nuclear processing as the dominant power source (Mürset, Nussbaumer, Schmid & Vogel 1991). In addition, the luminosities of symbiotic novae (a distinct class from the classical SySs) remain high for decades after their outbursts (Mürset & Nussbaumer 1994). From a theoretical point of view, the situation is somewhat more difficult. The problem is that the rate at which steady nuclear processing can proceed is not, in principle, a tunable parameter. Based on 1-dimensional models, explosive and steady processing are generally expected to be mutually exclusive regimes, whose dividing line is a function of accretion rate and white dwarf mass (Iben 1982). Thus steady burning is not expected to occur for accretion rates less than . The accretion rates predicted by our wind-driven model are below this line (albeit by only a factor of 2.5 for and ).On the other hand, nuclear processing on real WDs is unlikely to be well-described by spherically symmetric models. For example, thermonuclear runaways (TNRs) triggered by localized temperature or pressure fluctuations may not always spread and evolve into global TNRs (Shara 1982; Shankar & Arnett 1994). Quasi-steady quiescent burning in T Pyx could therefore conceivably be the collective outcome of many successive localized TNRs. The individual mini-eruptions would not necessarily be obvious observationally, provided they are sufficiently small and frequent. These localised TNRs could process non-degenerate material more slowly than it accretes, leading to the build-up of a more and more massive non-degenerate envelope and, eventually, to a global TNR. The preceding is a highly speculative scenario, and we do not mean
to endorse it too strongly. We have outlined it mainly to provide a
specific illustration of the general idea that (quasi-)steady and
explosive nuclear processing might take place in the same object. This
general idea is not new. It was first suggested by Webbink et al.
(1986) and again by Patterson et al. (1998), both times without any
specific model in mind. The main achievement of the wind-driving
mechanism is that, given a high radiative efficiency, T Pyx's
high mass accretion rate and luminosity can be accounted for
self-consistently. We do, of course, acknowledge that the requirement
implies a fair amount of
fine-tuning, regardless of whether one invokes an extremely massive WD
or quiescent nuclear burning. But some theoretical fine-tuning seems
reasonable for a system like T Pyx, whose short orbital period,
high luminosity and ability to produce nova eruptions are a unique
combination among CVs and SSSs. This is not to say that the
wind-driven evolutionary channel must be narrow: most other
wind-driven systems may be characterized by somewhat higher accretion
rates than T Pyx and may therefore be We finally turn to the orbital period derivative. On substituting
the values for Patterson et al. (1998) derived yr from the periodic dip in T Pyx's optical light curve, but more recent timings suggest a slower rate of change. In any case, as noted in the discussion following Eq. 6, the observed may not be a valid estimate of the stationary (long-term average) value. © European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |