Polarization of kilonova emission from a black hole-neutron star merger

A multi-messenger, black hole (BH) - neutron star (NS) merger event still remains to be detected. The tidal (dynamical) ejecta from such an event, thought to produce a kinonova, is concentrated in the equatorial plane and occupies only part of the whole azimuthal angle. In addition, recent simulations suggest that the outflow or wind from the post-merger remnant disk, presumably anisotropic, can be a major ejecta component responsible for a kilonova. For any ejecta whose photosphere shape deviates from the spherical symmetry, the electron scattering at the photosphere causes a net polarization in the kilonova light. Recent observational and theoretical polarization studies have been focused to the NS-NS merger kilonova AT2017gfo. We extend those work to the case of a BH-NS merger kilonova. We show that the degree of polarization at the first $\sim 1$ hr can be up to $\sim$ 3\% if a small amount ($10^{-4} M_{\odot}$) of free neutrons have survived in the fastest component of the dynamical ejecta, whose beta-decay causes a precursor in the kilonova light. The polarization degree can be $\sim$ 0.6\% if free neutrons survived in the fastest component of the disk wind. Future polarization detection of a kilonova will constrain the morphology and composition of the dominant ejecta component, therefore help to identify the nature of the merger.Comment: 10 pages, 5 figures. Accepted for publication in Ap

The Laplacian Eigenvalues and Invariants of Graphs

In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues.Comment: 10 pages,Filomat, 201

Transport Coefficients from Extremal Gauss-Bonnet Black Holes

We calculate the shear viscosity of strongly coupled field theories dual to Gauss-Bonnet gravity at zero temperature with nonzero chemical potential. We find that the ratio of the shear viscosity over the entropy density is $1/4\pi$, which is in accordance with the zero temperature limit of the ratio at nonzero temperatures. We also calculate the DC conductivity for this system at zero temperature and find that the real part of the DC conductivity vanishes up to a delta function, which is similar to the result in Einstein gravity. We show that at zero temperature, we can still have the conclusion that the shear viscosity is fully determined by the effective coupling of transverse gravitons in a kind of theories that the effective action of transverse gravitons can be written into a form of minimally coupled scalars with a deformed effective coupling.Comment: 23 pages, no figure; v2, refs added; v3, more refs added; v4, version to appear in JHE