  Symbiotic binaries are systems containing white dwarfs (WDs) and red giants.
Symbiotic novae are those systems in which thermonuclear eruptions occur on the
WD components. These are to be distinguished from events driven by accretion
disk instabilities analogous to dwarf novae eruptions in cataclysmic variable
outbursts. Another class of symbiotic systems are those in which the WD is
extremely luminous and it seems likely that quiescent nuclear burning is
ongoing on the accreting WD. A fundamental question is the secular evolution of
the WD. Do the repeated outbursts or quiescent burning in these accreting
systems cause the WD to gain or lose mass? If it is gaining mass, can it
eventually reach the Chandrasekhar Limit and become a supernova (a SN Ia if it
can hide the hydrogen and helium in the system)? In order to better understand
these systems, we have begun a new study of the evolution of Thermonuclear
Runaways (TNRs) in the accreted envelopes of WDs using a variety of initial WD
masses, luminosities and mass accretion rates. We use our 1-D hydro code, NOVA,
which includes the new convective algorithm of Arnett, Meakin and Young, the
Hix and Thielemann nuclear reaction solver, the Iliadis reaction rate library,
the Timmes equation of state, and the OPAL opacities. We assume a solar
composition (Lodders abundance distribution) and do not allow any mixing of
accreted material with core material. This assumption strongly influences our
results. We report here (1) that the WD grows in mass for all simulations so
that canonical `steady burning' does not occur, and (2) that only a small
fraction of the accreted matter is ejected in some (but not all) simulations.
We also find that the accreting systems, before thermonuclear runaway, are too
cool to be seen in X-ray searches for SN Ia progenitors.
