A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency $omega_a$ excites a pair of se
condary waves of frequency $omega_b+omega_c simeq omega_a$. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that $omega_b+omega_c >>omega_a$. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f_{gw} > 20 Hz and drive p-g pairs to significant energies on very short timescales (much less than the orbital decay time). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the instability and therefore cannot say precisely how it influences neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide: (i) induces significant orbital phase errors ($Delta phi$ > 1 radian) that accumulate primarily at low frequencies (f_{gw} < 50 Hz) and (ii) heats the neutron star core to T~10^{10} K. Since there are >100 unstable daughters, $Delta phi$ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from neutron star binaries at much larger orbital separations than previously thought.
We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions and nonli
near excitation of modes by the time-varying gravitational potential of the companion. This paper presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism is applicable to binaries containing stars, planets, or compact objects, we focus on solar type stars with stellar or planetary companions. Our primary results include: (1) The linear tidal solution often used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited gravity waves are unstable to parametric resonance for companion masses M > 10-100 M_Earth at orbital periods P = 1-10 days. The nearly static equilibrium tide is, however, parametrically stable except for solar binaries with P < 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes waves to grow so rapidly that they must be treated as traveling waves rather than standing waves. (3) We find a novel form of parametric instability in which a single parent wave excites a very large number of daughter waves (N = 10^3[P / 10 days]) and drives them as a single coherent unit with growth rates that are ~N times faster than the standard three wave parametric instability. (4) Independent of the parametric instability, tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.
During the early evolution of an AM CVn system, helium is accreted onto the surface of a white dwarf under conditions suitable for unstable thermonuclear ignition. The turbulent motions induced by the convective burning phase in the He envelope becom
e strong enough to influence the propagation of burning fronts and may result in the onset of a detonation. Such an outcome would yield radioactive isotopes and a faint rapidly rising thermonuclear .Ia supernova. In this paper, we present hydrodynamic explosion models and observable outcomes of these He shell detonations for a range of initial core and envelope masses. The peak UVOIR bolometric luminosities range by a factor of 10 (from 5e41 - 5e42 erg/s), and the R-band peak varies from M_R,peak = -15 to -18. The rise times in all bands are very rapid (<10 d), but the decline rate is slower in the red than the blue due to a secondary near-IR brightening. The nucleosynthesis primarily yields heavy alpha-chain elements (40Ca through 56Ni) and unburnt He. Thus, the spectra around peak light lack signs of intermediate mass elements and are dominated by CaII and TiII features, with the caveat that our radiative transfer code does not include the non-thermal effects necessary to produce He features.
According to Burrows et al.s acoustic mechanism for core-collapse supernova explosions, the primary, l=1, g-mode in the core of the proto-neutron star is excited to an energy of ~ 10^{50} ergs and damps by the emission of sound waves. Here we calcula
te the damping of the primary mode by the parametric instability, i.e., by nonlinear, 3-mode coupling between the low-order primary mode and pairs of high-order g-modes. We show that the primary mode is strongly coupled to highly resonant, neutrino damped pairs with n>10; such short wavelength interactions cannot be resolved in the simulations. We find that the parametric instability saturates the primary mode energy at ~10^{48} ergs, well below the energy needed to drive an explosion. We therefore conclude that acoustic power is unlikely to be energetically significant in core-collapse supernova explosions.
The strong degeneracy of the 12C ignition layer on an accreting neutron star results in a hydrodynamic thermonuclear runaway, in which the nuclear heating time becomes shorter than the local dynamical time. We model the resulting combustion wave duri
ng these superbursts as an upward propagating detonation. We solve the reactive fluid flow and show that the detonation propagates through the deepest layers of fuel and drives a shock wave that steepens as it travels upward into lower density material. The shock is sufficiently strong upon reaching the freshly accreted H/He layer that it triggers unstable 4He burning if the superburst occurs during the latter half of the regular Type I bursting cycle; this is likely the origin of the bright Type I precursor bursts observed at the onset of superbursts. The cooling of the outermost shock-heated layers produces a bright, ~0.1s, flash that precedes the Type I burst by a few seconds; this may be the origin of the spike seen at the burst onset in 4U 1820-30 and 4U 1636-54, the only two bursts observed with RXTE at high time resolution. The dominant products of the 12C detonation are 28Si, 32S, and 36Ar. Gupta et al. showed that a crust composed of such intermediate mass elements has a larger heat flux than one composed of iron-peak elements and helps bring the superburst ignition depth into better agreement with values inferred from observations.
