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CATACLYSMIC VARIABLES
A Cataclysmic Variable is a binary system consisting of a white dwarf and a
normal star (companion) that has an incredibly short orbital period (1 - 12 hours).
These two stars are so close that the white dwarf literally cannibalizes its
companion (see the artist's rendition below). The mass that is lost from the
normal star generally (except for highly magnetic white dwarfs) forms an accretion
disk around the white dwarf and the hydrogen-rich matter eventually settles onto
the white dwarf’s surface. When a sufficient amount of gas has settled onto the
white dwarf’s surface, a so-called critical mass is reached and a thermonuclear
runaway ensues. This thermonuclear runaway (TNR) is basically a very-rapid phase of
nuclear burning that fuses hydrogen into helium. The explosion is usually so
violent that most of the accreted matter is expelled from the binary system in
what is referred to as a Classical Nova (CNe). An example of a recently obtained
image of a CN using the HST is shown below.
    ARTIST'S CONCEPTION
Illustration and photo are the property of the STScI and were prepared for NASA
under contract NAS5-26555.
    NOVA CYGNI 1992
FROM PRIMORDIAL BINARIES TO CVs
Cataclysmic Variables are believed to have been formed as a result of a previous
phase of mass loss in which a giant (the white dwarf’s progenitor) interacted
with the normal star (see the pictorial sequence of events on the next page).
Nature does not favor the formation of binaries with separations as small as
those of CV's. However, if the primordial binary that is originally formed
has the correct range of orbital separations and if the mass of one of the
stars is sufficiently large that it can evolve into a giant during the age of
the universe, then it is possible that a CV can form. Assuming that the giant
can swell to such a size that it engulfs the normal star, then a Common Envelope
phase ensues. During this phase, the normal star spirals in through the envelope
of the giant towards its burned out core (usually composed of a mixture of carbon
& oxygen or sometimes helium). The energetics of the phenomenon require that
the envelope of the giant be expelled (gravitationally) from the system as the
normal star spirals inwards. What remains after the process is complete is a
normal star that is in a tight (close) orbit with the core (now referred to as
either a carbon-oxygen [or helium] white dwarf). If further angular momentum losses
(due to a magnetic stellar wind or gravitational radiation) can bring
the two stars close enough, then mass transfer commences and a Classical Nova can
occur as a result of a thermonuclear explosion on the surface of the white dwarf star.
CONCLUSIONS
1) Based on our assumed BRF, we expect ~50 nova explosions per year in our galaxy
(to within a factor of 5). This rate is in concordance with previous observational
estimates that spanned the range of between 11 - 97 events/yr (Ciardullo et al. [1990],
and Liller & Mayer [1987]). Similar theoretical estimates have been obtained by
Yungelson, Livio, & Tutukov(1997).
2) The precise values of a (CE efficiency factor) and the assumed correlation
between the primordial masses of the primary and the secondary can have a significant
effect on the nova frequency distribution (see Figure 2). In particular, an
independent correlation tends to produce more systems with low-mass donors
(and concomitantly shorter orbital periods) than the q^{1/4} case. Moreover,
large values of u tend to produce many fewer TNR's at larger orbital periods
(> 5 hrs). The exact conditions under which mass transfer instabilities occur
also affect the numbers of systems that can form at large orbital periods
(> 6 hrs) thereby changing the nova frequency rate.
3) Based on our models, the frequency-averaged WD mass (MWD) undergoing
TNR's ranges from ~0.7 to 1.2 Msun. This range of values for MWD is in
agreement with the observational estimate of 0.82 +/- 0.26 Msun by Ritter and
Burkert (1986) based on a sample of 26 CV systems, and a later estimate of 0.90
Msun (Ritter et al. 1991). Systems containing He-degenerate dwarfs account for
less than 10% of the integrated nova frequency rate. For some cases, their
contribution can be as low as 1%.
4) The temperature of the accreting WD's has a significant effect on the
estimated nova frequencies for systems in the orbital period range of 1 - 2
hours (i.e., below the period gap; see Figure 2). The frequency of nova explosions
on the surfaces of hot WD's can be an order of magnitude larger compared to that
for cold WD's. The temperature effect above the period gap is considerably smaller
(~10 to 80%).
5) The ratio of the frequency of nova explosions above the period gap to that
below the gap varies from approximately unity to 12. This is in general agreement
with the observations for which the ratio is ~6.
6) The theoretical results tend to indicate that the observed frequency
distribution is best matched by having systems with cold WD's below the period
gap and having systems with hot WD's above the gap. Because systems born above
the gap evolve very quickly (< 1 Gyr) compared to systems below the gap, their
WD's are likely to be significantly hotter. The old WD's contained within the
short-period systems would have had a substantial amount of time to cool.