Stability of a hot two-temperature accretion disc with advection

The effects of radial advection and thermal diffusion were considered in investigating the linear stability of an optically thin, two-temperature accretion disc. If the disc has only very little advection, we proved that the thermal instability exists when the disc is geometrically thin. But it dispears in a geometrically slim disc if the thermal diffusion was considered. Moreover, if the disc is advection dominated, the thermal instability does not exist. In addition, we found that the instabilities of inertial-acoustic modes exist only in a geometrically thin disc or an advection-dominated disc with low Mach number, whereas the Lightman & Eardley viscous instability always dispears in a two-temperature disc. A simple comparison also showed that an optically thin, bremsstrahlung cooling dominated disc is generally more thermally unstable than a two-temperature disc if it is not advection-dominated.Comment: 12 pages, LaTeX file, 3 figures, accepted for publication in MNRAS. Revised with a few important references added and several inaccurate references correcte

Instability of the solitary waves for the generalized Boussinesq equations

In this work, we consider the following generalized Boussinesq equation \begin{align*} \partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad (t,x)\in\mathbb R\times \mathbb R, \end{align*} with $0<p<\infty$. This equation has the traveling wave solutions $\phi_\omega(x-\omega t)$, with the frequency $\omega\in (-1,1)$ and $\phi_\omega$ satisfying \begin{align*} -\partial_{xx}{\phi}_{\omega}+(1-{\omega^2}){\phi}_{\omega}-{\phi}_{\omega}^{p+1}=0. \end{align*} Bona and Sachs (1988) proved that the traveling wave $\phi_\omega(x-\omega t)$ is orbitally stable when $0<p<4,$ $\frac p4<\omega^2<1$. Liu (1993) proved the orbital instability under the conditions $0<p<4,$ $\omega^2<\frac p4$ or $p\ge 4,$ $\omega^2<1$. In this paper, we prove the orbital instability in the degenerate case $0<p<4,\omega^2=\frac p4$ .Comment: 29 page

Possible High-Energy Neutrino and Photon Signals from Gravitational Wave Bursts due to Double Neutron Star Mergers

As the technology of gravitational-wave and neutrino detectors becomes increasingly mature, a multi-messenger era of astronomy is ushered in. Advanced gravitational wave detectors are close to making a ground-breaking discovery of gravitational wave bursts (GWBs) associated with mergers of double neutron stars (NS-NS). It is essential to study the possible electromagnetic (EM) and neutrino emission counterparts of these GWBs. Recent observations and numerical simulations suggest that at least a fraction of NS-NS mergers may leave behind a massive millisecond magnetar as the merger product. Here we show that protons accelerated in the forward shock powered by a magnetar wind pushing the ejecta launched during the merger process would interact with photons generated in the dissipating magnetar wind and emit high energy neutrinos and photons. We estimate the typical energy and fluence of the neutrinos from such a scenario. We find that $\sim$PeV neutrinos could be emitted from the shock front as long as the ejecta could be accelerated to a relativistic speed. The diffuse neutrino flux from these events, even under the most optimistic scenarios, is too low to account for the two events announced by the IceCube Collaboration, but it is only slightly lower than the diffuse flux of GRBs, making it an important candidate for the diffuse background of $\sim$PeV neutrinos. The neutron-pion decay of these events make them a moderate contributor to the sub-TeV gamma-ray diffuse background.Comment: Accepted for publication in PRD, minor revisio