Emission line diagnostics of the progenitors of type Ia supernova

In this dissertation, we consider the origin of thermonuclear
supernovae, known by their observational classification as type Ia
(hereafter SNe Ia). In particular, we develop an entirely new means
to test the ``single-degenerate'' hypothesis, in which the
progenitors of these tremendous explosions are suggested to be hot
and luminous accreting white dwarfs. We then strongly constrain the
role of any such ``hot-mode'' SN Ia progenitor channel using both a
population-based argument and an individual case study, before
concluding with some more general considerations of nebulae ionized
by accreting white dwarfs. Type Ia supernovae have now been the
subject of intensive study for decades, particularly in light of
their role as standard(-izable) candles in measuring cosmological
distances. However, there remains no consensus model for the
evolutionary channel(s) by which they originate. In the so-called
``double-degenerate'' scenario, a binary pair of white dwarfs shed
angular momentum through gravitational-wave radiation, until they
inspiral and merge, triggering an explosion. Alternatively, in the
classic picture of the single-degenerate scenario, a white dwarf
accretes hydrogen-rich material from some main sequence or red
giant companion, and grows through nuclear burning of this material
at its surface until reaching sufficient mass to trigger an
explosion. This suggests that single-degenerate progenitors should
be extremely luminous sources in the EUV and soft X-ray bands
during the accretion phase (lasting $\sim 10^{5}$--$10^{6}$ years).
For this reason, such objects are generally associated with
observed ``supersoft X-ray sources'' (SSSs). Previous efforts to
detect or constrain the role of any such channel have focused on
detecting these objects directly in the soft X-ray band (photon
energies in the range 0.3 -- 0.7 keV), either on an individual
basis or as the combined emission of a diffuse population. Such an
approach has yielded important constraints, but only if white
dwarfs accrete principally at very high temperatures (T $\sim$
$5\times 10^{5}$K). However, observed SSSs are understood to lie in
a broad range of temperatures, with a possible range of at least $2
\times 10^{5}$--$10^{6}$K, and some theoretical models suggest even
lower temperatures are possible. This necessitates the development
of an alternative, complimentary test which can constrain the
luminosity of accreting white dwarfs across a wider range of
photospheric temperatures. In this work, we demonstrate that if the
single-degenerate model is correct, then accreting, nuclear-burning
white dwarfs should provide the dominant source of ionizing
radiation in passively-evolving galaxies, roughly 40\% of which are
known to host extended low-ionization emission-line regions
(so-called ``retired'' galaxies, i.e. emission-line galaxies
without either a central AGN or significant ongoing star
formation). Therefore, one can search for the presence of any
high-temperature single-degenerate progenitor population in these
galaxies by looking for emission lines characteristic of ionization
by very high-temperature ($10^{5}$ K -- $10^{6}$ K) sources. In
particular, we find that recombination lines of He II, and
forbidden lines of [N I] and [O I], provide the most sensitive
diagnostics in retired galaxies to assess the role of accreting
white dwarfs as SN Ia progenitors in any ``{\bf hot}-mode'' (T
$\gtrsim 1.2\times 10^{5}$K) accretion regime. Following this, we
limit the contribution of any high-temperature single-degenerate
channel to the SN Ia rate at relatively early delay-times (1 Gyr
$\leq$ t $\leq$ 4 Gyr) to $