Unified gravity and Rossby mode analysis in accreting white dwarf stars

Dwarf novae are a subset of cataclysmic variables that accrete
material intermittently in short-duration outbursts with sometimes long
quiescent intervals in between. During the quiescent state, the white dwarf
(WD) photosphere may be observable. Some of these systems show periodic
variability consistent with a non-radial oscillations. Asteroseismology has
become a unique tool for the measurement of internal structure of the WDs,
such as their masses, radii, temperatures and rotation profiles. A few stable
periodicities have been observed for these systems, but the lack of complete
and accurate theoretical models has hindered the real diagnosis of the
observed pulsations. Though the associated pulsations in accreting WDs are
thought to be g-modes, some work in the literature suggests that these
pulsations could be Rossby modes (r-modes). Here, to elucidate this, we
present a first simultaneous analysis of g- and r-mode pulsations in accreting
WDs including a full computation of visibility accounting for the distribution of
variation over the WD surface. We show that, up to the second lowest degree
(l=2), neither g nor r-modes have a clear advantage in visibility. Although, a
few retrograde r-mode orders exhibit a larger visibility, the low-order g modes
possess higher frequency in the star's frame making them more likely to be
driven within the convective driving scenario commonly applied to isolated
WDs. Therefore, we favor a g-mode origin for the observed periods in accreting
WDs. We also explore how the normal mode frequencies vary with changes in
properties of the WD such as mass, core temperature and accreted layer
thickness. We propose a potential new method to identify the mode orders
based on time variation of frequencies during the months of cooling after the
accretion event.