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On the Effect of Explosive Thermonuclear Burning on the Accreted Envelopes of White Dwarfs in Cataclysmic Variables

The detection of heavy elements at suprasolar abundances in the atmospheres of some accreting white dwarfs in cataclysmic variables, coupled with the high temperatures needed to produce these elements requires explosive thermonuclear burning. The central temperatures of any formerly more massive secondary stars in CVs undergoing hydrostatic CNO burning are far too low to produce these elements. Evidence is presented that at least some cataclysmic variables contain donor secondaries that have been contaminated by repeated novae ejecta and are transferring this material back to the white dwarf. This scenario does not exclude the channel in which formerly more massive donor stars underwent CNO processing in ystems that underwent thermal timescale mass transfer. Implications for the progenitors of CVs are discussed.


Introduction
Approximately 20% of the cataclysmic variables (CVs) reveal large abundance ratios of nitrogen to carbon, most commonly from the ratio of intensities of N v (1238, 1242) to C iv (1548, 1550) resonance doublet emission lines in the far ultraviolet (Gänsicke et al. 2003). The N v emission is typically very strong and the C iv emission is very weak or absent. This enhancement of nitrogen and depletion of carbon is the hallmark of CNO processing during Hydrogen burning via the CNO bi-cycle. The emission lines almost certainly arise from the accretion disk (or boundary layer) that forms when the Roche-lobe filling donor secondary transfers gas to the white dwarf primary star. The N/C abundance anomaly has also been seen in magnetic CVs such as AE Aqr (Mouchet et al. 2003), BY Cam (Mouchet et al. 2003), V1309 Ori (Szkody & Silber 1996) and MN Hya (Schmidt & Stockman 2001), A less common manifestation of the N/C abundance anomaly is seen in a few cases where detected N and C absorption lines form in the exposed white dwarf photosphere itself.
The two best examples are the white dwarfs in VW Hyi (Sion et al. 1995(Sion et al. , 1997(Sion et al. , 2001 and U Gem (Sion et al. 1998). Does the N/C abundance anomaly arise from a formerly more massive secondary star (capable of CNO burning) having been peeled away by mass transfer down to its CNO-processed core, due to mass transfer? Or does the N/C anomaly originate in the white dwarf itself due to unstable CNO burning associated with nova explosions or possibly by dredgeup and mixing in consequence of a dwarf nova outburst?
The question of which star, the white dwarf or the donor main sequence star, is responsible for the N/C anomaly is critical. If the N/C anomaly originated in the donor, then the donor had to be more massive than its present value to sustain CNO burning. This could be the case if the CVs with the N/C anomaly are the descendants of the supersoft X-ray binaries, when the formerly more massive donor in the system underwent thermal timescale mass transfer at a high rate, thus driving steady thermonuclear burning on the white dwarf at the accretion supply rate. In this Letter, I present evidence that, for at least a fraction of the CVs that reveal the N/C anomaly, the origin of the CNO processed abundances lies with the white dwarf which subsequently contaminated the secondary donor star with the ejecta of many past repeated nova explosions.

Chemical Abundances
For the vast majority of the CVs that exhibit the N/C anomaly, the highly non-solar abundances of N and C are inferred qualitatively from emission line intensity ratios and no other atomic species are used. There have been no reported abundances of N and C determined ab initio from fitting emission line profiles, to date. However, a handful of dwarf novae, all but one below the CV period gap with orbital periods below 2 hours, were observed during dwarf nova quiescence when the accretion rate is very low and the white dwarf completely dominates the far ultraviolet band. These systems are BW Scl, SW UMa, BC UMa and VW Hyi while U Gem is the only system above the period gap. The chemical abundances of their accreted metals have been derived largely from high quality HST and FUSE spectra by fitting the observed metal lines with rotationally broadened theoretical line profiles, using TLUSTY and SYNSPEC (Hubeny 1988;Hubeny & Lanz 1995). In three SU UMa-type CVs, BW Scl, SW UMa and BC UMa, the detected photospheric features reveal aluminum abundances of 3.0±0.8, 1.7±0.5, and 2.0±0.5, respectively (Gänsicke et al. 2005).
The dwarf nova VW Hydri's white dwarf is also detected during dwarf nova quiescence and is modestly hotter than the white dwarfs in the three systems above, and has a slightly longer orbital period. A plethora of photospheric absorption features due to metals have been detected in the VW Hyi white dwarf. The derived abundances (relative to solar values) from profile fitting are Al 3, Si 0.3, C 0.3, O 3, N 3.0, Al 2.0, P 20, and Mn 50 (Sion et al. 1995). Large suprasolar phosphorus abundances result from thermonuclear runaways on ONeMg white dwarfs (Starrfield et al. 2006;Jose et al. 2006).
The exposed white dwarf in the dwarf nova U Gem also exhibits a rich array of absorption features due to metals in both IUE and FUSE spectra (Sion et al. 1995). From HST and FUSE spectra, the U Gem white dwarf has the largest photospheric N/C ratio of any CV white dwarf (Sion et al. 1997;Long et al. 2006).

Hot CNO Burning and the Abundances of Elements in the Mass Range A > 20
It is well known that Hydrostatic hydrogen burning via the CNO bi-cycle powers upper main sequence stars with masses M > 1.3M ⊙ and the reactions are highly temperaturesensitive. It is equally clear that hot CNO burning depletes the abundance of carbon while increasing the abundance of nitrogen. Hence, the CNO burning of a previously more massive CV secondary star could give the large N/C abundance ratios that one observes in ∼20% of the CV population. However, even in main sequence stars as massive as 5 to 10M ⊙ , the core temperatures do not exceed ∼ 5 × 10 7 K.
The suprasolar chemical abundances of nuclides with A>20 that have been detected in the photospheres of the accreting white dwarfs in several dwarf novae (e.g. Al, P, Mn) present a serious problem for any previously more massive CV secondary. First of all, there is no leakage of A>20 elements linking the CNO reactions to A>20 species. Hence, any nuclide with A>20, during hydrogen burning, is not matter that is converted from CNO material. Thus hydrostatic burning beyond the CNO mass range must begin from pre-existing A>20 nuclides. For example, the suprasolar abundance of 27 Al must be formed in proton capture reactions starting with seed 24 Mg (Iliadis 2007) and so on. At temperatures below 5 × 10 7 K, it is not possible for 27 Al to be produced from pre-existing 24 Mg. The Coulomb barrier is simply far too high for such proton capture reactions. Indeed, to build up the 27 Al by depleting 24 Mg by proton capture reactions, the temperature of a main sequence star would have to be ∼ 7.5 × 10 7 K, which corresponds to a 25M ⊙ star to explain the observed Mg-Al anti-correlation observed in globular cluster stars (Prantzos et al. 2007).

Summary of Conclusions
The production of A>20 nuclides during hydrogen burning requires temperatures between 100 million and 400 million degrees K to affect the needed transmission through the Coulomb barriers of these heavier nuclei. The only thermonuclear environment that reaches these temperatures is during explosive hydrogen burning, e.g. a classical nova thermonuclear runaway. Hence, the detection of such nuclei as P and Al at suprasolar abundance in the surface layers of accreting white dwarfs in dwarf novae implies their origin within the white dwarf. In the absence of mixing of the accreted material with the nucleosynthetic products in the transition region at the base of the accreted envelope where thermonuclear burning occurs, the matter flowing over from the secondary star to the white dwarf would cover its surface layers. Hence, for some fraction of the CVs exhibiting the N/C anomaly, the donor secondary star's large N/C abundance ratio arose from repeated nova-contamination. This conclusion is supported by the following considerations.
(1) During the hydrostatic hydrogen burning of a 2 to 3 M ⊙ main sequence star, the central temperature, while on the main sequence, reaches approximately 2.2 × 10 7 K generating nuclear energy via the CNO reactions which convert hydrogen into helium. Thus, since the most likely mass range for a formerly more massive CV secondary is 2 to 3 M ⊙ , the core temperatures of such stars are far too small to allow the formation of nuclei in the mass range A≥20. Thus, the detection of odd-numbered nuclides like Al, P and Mn implies that the white dwarf, not the secondary, is responsible for these nuclides. Since these heavy nuclei were accreted, the implication is that the secondary star, at least in the dwarf novae that are cited above, was contaminated by repeated nova ejecta and is transferring this nova-polluted material back to the white dwarf via Roche lobe overflow.
(2) IR spectroscopy of VW Hyi's secondary star appears to have solar abundance (Hamilton et al. 2011) but the accreting white dwarf in the system, detected during quiescence, has a large N/C ratio in its surface layers (Sion et al. 1995(Sion et al. , 1997(Sion et al. , 2001. If the IR spectroscopic result of Hamilton et al. (2011) is confirmed, then this result suggests that the large N/C ratio originated in the white dwarf, the same origin as the nuclides in the mass range A>20.
(3) The FUSE spectra of U Gem's white dwarf photosphere reveals absorption features of P v during quiescence, weeks after a dwarf nova outburst would have dredged it up. Phosphorus is a nuclide that should be produced in high abundance at the very high temperatures of classical nova explosions and is seen in the surface layers of the white dwarfs in both VW Hyi and U Gem. In the atmosphere of U Gem's white dwarf, with a quiescent surface temperature of ∼ 30, 000K, the diffusion timescale for a phosphorus ion is shorter than 3 days (Paquette et al. 1986). Hence, the photospheric P v had to be accreted from the secondary. Thus, this implies that the donor star was contaminated by material that underwent explosive CNO burning of elements beyond A>20. The secondary star in U Gem has a large N/C ratio (Hamilton et al. 2011). While it cannot be excluded that the large N/C ratio originated in its formerly more massive secondary star, this would mean that the detected nuclide 31 P originated in the white dwarf but that the large N/C ratio originated separately in the secondary star. An appeal to Occam's razor would suggest this to be less likely since two separate thermonuclear processes would be involved instead of only one.
(4) To date, no pre-CV white dwarf or pre-CV secondary star has yet been found to have surface abundances indicative of prior CNO processing. Yet it is the pre-CVs which are thought to be the immediate progenitors of the cataclysmic variables.
Finally, while this work supports the idea that nova-contamination of the secondaries has taken place in the dwarf novae cited in this Letter, this channel for the production of A > 20 stable nuclides and a large N/C ratio may be represent only a small subset of the CVs that show large N/C abundance ratios. The dominant channel may still be the thermal timescale mass transfer systems accreting at high rates from a formerly more massive secondary. Nevertheless, further investigations of how much material lands on the donor star in consequence of repeated nova explosions are clearly warranted.