there are four dimensions of parameter space:

1
EVOLUTIONARY GRID OF ACCRETING WHITE DWARF
COMPANIONS IN CATACLYSMIC VARIABLES J. BENJAMIN,
M. JENSEN, S. NADEAU, L.A. NELSON (BISHOPS U.)
EVOLUTIONARY MODELS
INTRODUCTION
METHOD OF CALCULATION
REPRESENTATIVE CASE
PARAMETER SPACE

• after 10-4 10-5 M8 of H has been accreted,
  compressional heating of the partially degenerate
  gas leads to a TNR (see Figures 1 2). Both
  cases are characterized by a rapidly growing
  temperature inversion near the base of the
  accreted material.
• the critical mass of H that needs to be accreted
  in order to produce the flash is strongly
  dependent on the value of MWD and is also
  dependent on M and the assumed core temperature
  (Tc). Note that the recurrence (i.e., flash)
  period is directly proportional to DMacc/M.
• the table below shows the critical values of
  DMacc (in units of M8) for different central
  temperatures (Tc) and two different values of the
  accretion rate. MWD has been set equal to 0.9 M8.
  

WHITE DWARF ACCRETION
TWO COMPUTATIONAL APPROACHES

• Henyey-type code (quasi-hydrostatic
  approximation)
• Fontaine, Graboske and Van Horn EOS Magni
  Mazzitelli EOS
• OPAL and Alexander low-temperature radiative
  opacities Hubbard Lampe conductive opacities
• isenthalpic, spherically symmetric accretion flow
• kinetic energy of accretion flow assumed to be
  dissipated radiatively by shocks
• Envelope Evolution
• the PDEs of stellar structure are solved using
  the Method of Lines. The properties of the core
  are dictated by the boundary conditions at the
  base of the envelope.
• zero-flux condition OR
• Tc Tboundary constant

• there are four dimensions of parameter space
• MWD
• M
• Chemical Composition (X,Z)
• Initial conditions at the onset of accretion
• thermal profile/history
• chemical profile

• White Dwarfs in interacting binary systems can
  accrete H/He-rich matter
• this leads to a number of diverse and important
  phenomena
• Classical Novae (TNR)
• Symbiotic novae
• transient phenomena
• Type Ia SNe
• quasi-steady nuclear burning (Supersoft Xray
  Sources SSXSs)
• the most comprehensively studied and observed
  systems are CVs and SSXSs
• we report on the progress that we have made in
  studying the effect of accretion for a grid of
  models covering a significant slice of parameter
  space

• Nova Cygni 1992

GRID OF MODELS

• we calculated evolutionary tracks for the
  following cases
• 0.6 M8 ? M ? 1.35 M8
• 6.5 ? log Tc (K) ? 8.0
• 10-10 M8 yr-1 ? M ? 10-6 M8 yr-1
• X0.7 Z0.02 CO cores

TEMPERATURE PROFILE
INTERACTING BINARIES
NOVA PROPERTIES

• as noted by van den Heuvel (1992), amongst
  others, the properties of the nova event are very
  dependent on MWD and M
• our models exhibit four distinct types of
  behavior
• if the mass transfer rate exceeds 10-6 M8 yr-1
  then the WD swells up and overfills its Roche
  lobe (i.e., becomes a Red Giant)
• for lower Ms (10-7 M8 yr-1) we found that the
  WDs exhibit weak pulses (i.e., quasi-steady
  nuclear burning)
• for many of these models, the thick He shell
  beneath the H shell undergoes explosive nuclear
  burning (He TNR)
• for the lowest Ms (lt 10-8 M8 yr-1 ) the WD
  experiences mild to strong H flashes (TNR)
• the transition between each of these regimes
  depends sensitively on MWD, M, and the thermal
  history of the WD
• Figure 3 shows the transition from TNRs to
  quasi-steady burning as the mass-transfer rate is
  gradually increased (for the MWD 1 M8 cases).
  Note that the cycles are composed of two distinct
  phases (i) the on phase which corresponds to
  the maximum luminosity and, (ii) the much longer
  off phase.
• Figure 4 shows the temporal evolution of the
  envelopes temperature profile through several
  nova cycles

MODEL

• CVs are close, interacting binary systems in
  which a low-mass (lt 2 M8) star transfers mass to
  its white dwarf (WD) companion via Roche-Lobe
  overflow
• the accreted gas may be channeled directly onto
  the WD (e.g., polars) or may form an accretion
  disk that experiences instabilities (e.g., dwarf
  novae DNe)

• depending on the mass and temperature of the WD
  and on the mass accretion rate (M), a
  thermonuclear runaway (TNR) can ensue causing
  most of the accreted matter to be ejected from
  the binary system (e.g., Nova Cygni Porb 1.95
  hr)
• TNRs can be periodic and recur on cycles of the
  order of days to more than 106 years. In some
  cases the mass transfer rate is sufficiently high
  that quasi-steady burning occurs on the surface
  of the WD.

Figure 1 Thermal profile of a 0.7 M8 CO WD
undergoing accretion at 1x10-8 M8 yr-1. Each
curve corresponds to an evolutionary time (Dt)
measured relative to the first model in the
sequence. Log T(K) is plotted against the log of
the mass fraction (as measured from the surface).
Figure 2 Thermal profile of a 0.7 M8 CO WD
undergoing accretion at 1x10-8 M8 yr-1. Each
curve corresponds to an evolutionary time (Dt)
measured relative to the first model in the
sequence. Log T(K) is plotted against the log of
the mass fraction (as measured from the surface).
WD OBSERVATIONS

• one important question concerns the evolution of
  the gravo-thermal properties of the WD on both
  short- and long-term timescales as it evolves in
  CV/SSXS systems
• for example, Nelson et al. (2003) show that the
  orbital period distribution of galactic novae can
  be reconciled with the observed one if it is
  assumed that the internal temperature of the WDs
  decreases with decreasing Porb
• Gansicke (1997) using spectroscopic data from IUE
  and HST concludes that the temperatures of the
  seven magnetic CVs in his sample decrease with
  decreasing Porb. This conclusion is in perfect
  agreement with our understanding of the secular
  evolution of CVs.
• ideally we need to observe the DNe subclass in a
  state of prolonged quiescence while M is small
  (and the accretion luminosity is unimportant)
• multiwavelength analyses of the boundary layers
  in WDs could be used to infer the interior
  temperatures of WDs
• this type of observational program is currently
  being undertaken (Howell et al. 1999 Szkody et
  al. 2002)

LUMINOSITY EVOLUTION
INTERIOR TEMPERATURE EVOLUTION
SUMMARY

• as has been shown by several researchers (e.g.,
  Paczynski and Zytkow 1978 Iben 1982 Sion and
  Starrfield 1985, 1994 Prialnik and Kovetz 1995),
  the behavior and properties of the nova events
  can depend sensitively on the mass of the WD and
  the accretion rate
• we have also systematically explored the effects
  of assuming different initial gravo-thermal
  profiles and find that they too can be important
  factors

FUTURE WORK
PREPRINT REQUESTS LNELSON_at_UBISHOPS.CA

• although we have explored a significant slice of
  parameter space, we need to examine the evolution
  for a much wider range of initial conditions
  (e.g., thermal histories)
• we plan to investigate the dependence of TNRs on
  chemical composition (i.e., varying the H
  abundance and metallicity)
• we will extend the grid by coupling the evolution
  of the WDs self-consistently with the evolution
  of the parent CV systems (this implies the
  inclusion of time-dependent mass-accretion rates)
• finally we plan to carry out population syntheses
  to determine whether steady-burning sources
  (e.g., SSXSs) can be the true progenitors of Type
  Ia SNe

Figure 3 Temporal evolution of the luminosity
for several representative cases. Mass transfer
rate of 1x10-9 M8 yr-1 (i) Black curve MWD
0.95 M8 (ii) Red curve MWD 1.0 M8 (iii)
Blue curve MWD 1.1 M8. Setting MWD 1.0 M8,
and increasing M yields the following (iv) Green
curve M 6x10-8 M8 yr-1 (v) Pink curve M
5x10-7 M8 yr-1. The inset shows the evolution of
case (iv) on an appropriately short time scale.
Note the transition from strong TNRs to mild
recurrent flashes. Higher Ms lead to quasi-steady
nuclear burning (pink curve).
Figure 4 Temporal evolution of the internal
temperature of several shells of a 1 M8 white
dwarf accreting mass at 1x10-8 M8 yr-1. The
evolution is followed over several flashes. The
log of the mass fractions (as measured from the
surface) are -7 (black curve), -6.5, -6, -5.5,
-5, and -4.5 (cyan curve), respectively. Note the
temperature inversion near the flash event.
This research was supported in part by the
Natural Sciences and Engineering Research Council
(NSERC) of Canada.