V652HER AND MERGED BINARY WHITE DWARF MODELS

As already indicated, V652Her is an important EHe star because its relatively short pulsation period and large amplitude pulsations allow its overall dimensions to be determined with high precision. The pulsation properties have been determined from visual and ultraviolet spectrophotometry and from spectroscopy by Landolt (1975), Hill et al. (1981), Lynas-Gray et al (1984) and Jeffery & Hill (1986). The simple saw-tooth shape of the radial-velocity curve implies that the pulsation can be divided quite simply into a short impulse phase lasting

cycles, followed by a near free-fall phase for the remainder of the cycle. Combining these data, Lynas-Gray et al. (1984) obtained a direct measurement of the radius $R=2.0\pm0.2$ $\rm R_{\odot}$ and mass $M_{\rm D}=0.7^{+0.4}_{-0.3}$ $\rm M_{\odot}$ . A refinement of the measurement of

led Jeffery et al. (1999) to obtain $M_{\rm D}=0.69\pm0.15\mbox{\,$\rm M_{\odot}$}$ , with $T=24\,450\pm500\,$ K, $\log g=3.68\pm0.05$ (cgs) and $L\sim10^3$ $\rm L_{\odot}$ . In contrast to most EHes, V652Her is nitrogen rich and carbon and oxygen poor, implying that its surface is predominantly CNO-processed. The period change discovered and refined by Kilkenny & Lynas-Gray (1982,1984) and Kilkenny et al. (1996) translates into a contraction rate $\dot{R}/R \sim 2.10^{-4} \,$ yr $^{-1}$ , together with nonlinear terms $\ddot{R}$ and $\dddot{R}$ .

With a lower luminosity and a purely CNO-processed surface, the evolutionary status of V652Her has long been regarded as possibly quite different to most EHes. Jeffery (1984) constructed a set of highly artificial ``helium horizontal branch models'' in which a 0.5 $\rm M_{\odot}$ helium-burning core was surrounded by an envelope with a very low hydrogen abundance. Because of the low hydrogen-abundance, the luminosity of the H-burning shell at the core-envelope interface was very high and the star evolved rapidly towards the helium main-sequence. Whilst able to match $M, L, T, \dot{R}$ and surface composition, these models could only suggest a possible structure for V652Her, rather than explain its origin.

Other highly artificial models in the horizontal-branch family have been constructed, notably by Sweigart (1997), but fail to provide either a hydrogen-poor surface or a self-consistent explanation of their origin. Similarly, no ``final-flash'' models have been computed which match the observed properties of V652Her.

Saio & Nomoto (1998) made the first successful models for the merger of two carbon-oxygen white dwarfs, and prompted Saio & Jeffery (2000) to attempt models for the merger of two helium white dwarfs. Following orbital decay, the less massive white dwarf in a double-degenerate suffers total tidal disruption on a dynamical timescale; the debris forms a thick disk around the surviving white dwarf. The latter then accretes matter from the disk until the envelope is sufficiently massive that nuclear reactions, in this case $3\alpha$ burning, are initiated at the core-envelope interface. At this point, the star expands to become a cool helium giant. Heating of the core surface by the nuclear-burning shell, or flame, lifts the local electron-degeneracy so that the flame migrates inwards. Because the flame migration proceeds stepwise, the surface evolution follows a series of loops of increasing

and decreasing

, until the flame reaches the core centre, whereupon the star assumes the structure of a helium main-sequence star or hot subdwarf. A schematic of the evolution is shown in Fig. 2.

The evolution sequence for a 0.476 $\rm M_{\odot}$ helium white dwarf accreting 0.233 $\rm M_{\odot}$ helium-rich debris passes exactly through the observed locus for V752Her. To within the numerical uncertainty of the calculations, this model also has the correct pulsation properties, $\Pi$ and $\dot{\Pi}$ . As yet, the higher order terms $\ddot{R}$ and $\dddot{R}$ (Kilkenny et al. 1996) cannot be reproduced.

**Figure 3:** The ultraviolet and radial velocity behaviour of HD168476=PVTel (from Jeffery et al. 2000). From top to bottom, the four panels show the variation of *T $_{\rm eff}$* , $\theta$ , $F_{\rm IUE}$ and . Superimposed on each is a sine curve; the period for all four fits is indicated in the top panel, the phase and amplitude were obtained from an independent least-squares fit to each set of data (solid curves). The dashed curve represents the product of the fits $\theta^2$ *T $_{\rm eff}$* scaled to the same mean value as $F_{\rm IUE}$ .
$\begin{figure} \epsfxsize =85mm \epsfbox{fig_hd168476.ps}\end{figure}$

**Table 1:** Mass estimates (in $\rm M_{\odot}$ ) for PVTel variables from (i) spectroscopy $M_{\rm S}$ using the $M_{\rm c}-L_{\rm s}$ relation from Jeffery (1988), (ii) pulsation periods $M_{\rm P}$ (Saio & Jeffery 1988) and (iii) direct measurement $M_{\rm D}$ (Jeffery et al. 2000).
Star	$M_{\rm S}$	$M_{\rm P}$	$M_{\rm D}$
HD168476=PVTel	0.95	0.85	0.82
BD+1 $^\circ$ 4381=FQAqr	1.09	0.93	0.03
LSIV-1 $^\circ$ 2=V2244Oph	0.66	0.94	0.76