Kompaneets equation for neutrinos: Application to neutrino heating in supernova explosions

We derive a `Kompaneets equation' for neutrinos, which describes how the distribution function of neutrinos interacting with matter deviates from a Fermi-Dirac distribution with zero chemical potential. To this end, we expand the collision integral in the Boltzmann equation of neutrinos up to the second order in energy transfer between matter and neutrinos. The distortion of the neutrino distribution function changes the rate at which neutrinos heat matter, as the rate is proportional to the mean square energy of neutrinos, $E_\nu^2$. For electron-type neutrinos the enhancement in $E_\nu^2$ over its thermal value is given approximately by $E_\nu^2/E_{\nu,\rm thermal}^2=1+0.086(V/0.1)^2$ where $V$ is the bulk velocity of nucleons, while for the other neutrino species the enhancement is $(1+\delta_v)^3$, where $\delta_v=mV^2/3k_BT$ is the kinetic energy of nucleons divided by the thermal energy. This enhancement has a significant implication for supernova explosions, as it would aid neutrino-driven explosions.Comment: 14 pages, 1 figure, matched to published versio

A General Relativistic study of the neutrino path and calculation of minimum photosphere for different stars

A detailed general relativistic (GR) calculation of the neutrino path for a general metric describing a rotating star is studied. We have calculated the neutrino path along a plane, with the consideration that the neutrino does not at any time leave the plane. The expression for the minimum photosphere radius (MPR) is obtained and matched with the Schwarzschild limit. The MPR is calculated for the stars with two different equations of state (EOS) each rotating with two different velocities. The results shows that the MPR for the hadronic star is much greater than the quark star and the MPR increases as the rotational velocity of the star decreases. The MPR along the polar plane is larger than that along the equatorial plane.Comment: 13 pages, 5 figures and 1 tabl

Effects of Differential Rotation on the Maximum Mass of Neutron Stars

The merger of binary neutron stars is likely to lead to differentially rotating remnants. In this paper we numerically construct models of differentially rotating neutron stars in general relativity and determine their maximum allowed mass. We model the stars adopting a polytropic equation of state and tabulate maximum allowed masses as a function of differential rotation and stiffness of the equation of state. We also provide a crude argument that yields a qualitative estimate of the effect of stiffness and differential rotation on the maximum allowed mass.Comment: 6 pages, to appear in Ap

Improved Method for Detecting Local Discontinuities in CMB data by Finite Differencing

An unexpected distribution of temperatures in the CMB could be a sign of new physics. In particular, the existence of cosmic defects could be indicated by temperature discontinuities via the Kaiser-Stebbins effect. In this paper, we show how performing finite differences on a CMB map, with the noise regularized in harmonic space, may expose such discontinuities, and we report the results of this process on the 7-year Wilkinson Microwave Anisotropy Probe data.Comment: 5 pages, 6 figures; Text has been edited, in line with the PRD articl

The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity

We study the dynamical stability against bar-mode deformation of rapidly spinning neutron stars with differential rotation. We perform fully relativistic 3D simulations of compact stars with $M/R \geq 0.1$, where $M$ is the total gravitational mass and $R$ the equatorial circumferential radius. We adopt an adiabatic equation of state with adiabatic index $\Gamma=2$. As in Newtonian theory, we find that stars above a critical value of $\beta \equiv T/W$ (where $T$ is the rotational kinetic energy and $W$ the gravitational binding energy) are dynamically unstable to bar formation. For our adopted choices of stellar compaction and rotation profile, the critical value of $\beta = \beta_{dGR}$ is $\sim 0.24-0.25$, only slightly smaller than the well-known Newtonian value $\sim 0.27$ for incompressible Maclaurin spheroids. The critical value depends only very weakly on the degree of differential rotation for the moderate range we surveyed. All unstable stars form bars on a dynamical timescale. Models with sufficiently large $\beta$ subsequently form spiral arms and eject mass, driving the remnant to a dynamically stable state. Models with moderately large $\beta \gtrsim \beta_{dGR}$ do not develop spiral arms or eject mass but adjust to form dynamically stable ellipsoidal-like configurations. If the bar-mode instability is triggered in supernovae collapse or binary neutron star mergers, it could be a strong and observable source of gravitational waves. We determine characteristic wave amplitudes and frequencies.Comment: 17 pages, accepted for publication in AP

Discovery of diffuse radio emission at the center of the most X-ray-luminous cluster RX J1347.5-1145

We report on new VLA radio observations of the distant cluster RX J1347.5-1145, which is the most luminous in X-rays. We aim at investigating the possible presence of diffuse and extended radio emission in this very peculiar system which shows both a massive cooling flow and merging signatures. New low resolution (~18 arcsec) VLA radio observations of this cluster are combined with higher resolution (~2 arcsec) data available in the VLA archive. We discover the presence of a diffuse and extended (~500 kpc) radio source centered on the cluster, unrelated to the radio emission of the central AGN. The properties of the radio source, in particular a) its occurrence at the center of a massive cooling flow cluster, b) its total size comparable to that of the cooling region, c) its agreement with the observational trend between radio luminosity and cooling flow power, indicate that RX J1347.5-1145 hosts a radio mini-halo. We suggest that the radio emission of this mini-halo, which is the most distant object of its class discovered up to now, is due to electron re-acceleration triggered by the central cooling flow. However, we also note that the morphology of the diffuse radio emission shows an elongation coincident with the position of a hot subclump detected in X-rays, thus suggesting that additional energy for the electron re-acceleration might be provided by the submerger event.Comment: 5 pages, 6 figures, accepted for publication in A&A Letter

Relativistic stars in differential rotation: bounds on the dragging rate and on the rotational energy

For general relativistic equilibrium stellar models (stationary axisymmetric asymptotically flat and convection-free) with differential rotation, it is shown that for a wide class of rotation laws the distribution of angular velocity of the fluid has a sign, say "positive", and then both the dragging rate and the angular momentum density are positive. In addition, the "mean value" (with respect to an intrinsic density) of the dragging rate is shown to be less than the mean value of the fluid angular velocity (in full general, without having to restrict the rotation law, nor the uniformity in sign of the fluid angular velocity); this inequality yields the positivity and an upper bound of the total rotational energy.Comment: 23 pages, no figures, LaTeX. Submitted to J. Math. Phy

Cosmological Lower Bound on Dark Matter Masses from the Soft Gamma-ray Background

Motivated by a recent detection of 511 keV photons from the center of our Galaxy, we calculate the spectrum of the soft gamma-ray background of the redshifted 511 keV photons from cosmological halos. Annihilation of dark matter particles into electron-positron pairs makes a substantial contribution to the gamma-ray background. Mass of such dark matter particles must be <~ 100 MeV so that resulting electron-positron pairs are on-relativistic. On the other hand, we show that in order for the annihilation not to exceed the observed background, the dark matter mass needs to be >~ 20 MeV. We include the contribution from the active galactic nuclei and supernovae. The halo substructures may increase the lower bound to >~ 60 MeV.Comment: 5 pages, 5 figures; accepted for publication in PRD, Rapid Communicatio

Detecting relic gravitational waves in the CMB: A statistical bias

Analyzing the imprint of relic gravitational waves (RGWs) on the cosmic microwave background (CMB) power spectra provides a way to determine the signal of RGWs. In this Letter, we discuss a statistical bias, which could exist in the data analysis and has the tendency to overlook the RGWs. We also explain why this bias exists, and how to avoid it.Comment: 4 pages, 1 figur

On the Maximum Mass of Differentially Rotating Neutron Stars

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations which are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.Comment: 4 pages, 2 figures, uses emulateapj.sty; to appear in ApJ Letter