No Pulsar Kicks from Deformed Neutrinospheres

In a supernova core, magnetic fields cause a directional variation of the neutrino refractive index so that resonant flavor oscillations would lead to a deformation of the "neutrinosphere" for, say, tau neutrinos. The associated anisotropic neutrino emission was proposed as a possible origin of the observed pulsar proper motions. We argue that this effect was vastly overestimated because the variation of the temperature over the deformed neutrinosphere is not an adequate measure for the anisotropy of neutrino emission. The neutrino flux is generated inside the neutron star core and is transported through the atmosphere at a constant luminosity, forcing the temperature gradient in the atmosphere to adjust to the inflow of energy from below. Therefore, no emission anisotropy is caused by a deformation of the neutrinosphere to lowest order. An estimate of the higher-order corrections must take into account the modified atmospheric temperature profile in response to the deformation of the neutrinosphere and the corresponding feedback on the core. We go through this exercise in the framework of a simplified model which can be solved analytically.Comment: Final version with minor corrections, to be published in PRD. Includes a "Note Added" in response to astro-ph/981114

Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments

We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless (CT) approach that has improved stability properties in evolving weak and strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the range of resolutions used in our 3D simulations.Comment: 17 pages, 15 figures. Small changes in the text, and a change in the list of authors. One new reference adde

Mass estimation in the outer regions of galaxy clusters

We present a technique for estimating the mass in the outskirts of galaxy clusters where the usual assumption of dynamical equilibrium is not valid. The method assumes that clusters form through hierarchical clustering and requires only galaxy redshifts and positions on the sky. We apply the method to dissipationless cosmological N-body simulations where galaxies form and evolve according to semi-analytic modelling. The method recovers the actual cluster mass profile within a factor of two to several megaparsecs from the cluster centre. This error originates from projection effects, sparse sampling, and contamination by foreground and background galaxies. In the absence of velocity biases, this method can provide an estimate of the mass-to-light ratio on scales ~1-10 Mpc/h where this quantity is still poorly known.Comment: 14 pages, 7 figures, MN LaTeX style, MNRAS, in pres

On the Microlensing Optical Depth of the Galactic Bar

The microlensing probability (optical depth $\tau$) toward the Galactic center carries information about the mass distribution of the Galactic bulge/bar, so can be used to constrain the very uncertain shape parameters of the bar. We find $tau$ depends on the bar mass, radial profile, angle, axis scale lengths and boxyness by a few simple analytical formulae, which shows: (1) $\tau$ is proportional to the mass of the bar, $M$. (2) $\tau$ falls along the minor axis with a strong gradient. (3) An oblate bulge can have more optical depth than a triaxial bar if the bar angle $\alpha>45$ degress. (4) $\tau$ is the largest if the angle $\alpha$ and the axis ratio $y_0/x_0$ conspires so that $y_0/x_0=\tan \alpha$. (5) At a fixed field on the minor axis but away from the center, boxy bars with a flat density profile tend to give a larger optical depth than ellipsoidal bars with a steep profile. (6) Main sequence sources should have a significantly lower (20-50\% lower) optical depth than red clump giants if main sequence stars are not observed as deep as the bright clump giants. An application to four COBE-constrained models (Dwek et al. 1994) shows most models produce optical depth $2\sigma$ lower than MACHO and OGLE observed values even with both a massive bar $2.8\times 10^{10} M_\odot$ and a full disk. The high $\tau$ argues for a massive ($> 2\times 10^{10}M_\odot$) boxy bar with $y_0/x0\approx \tan\alpha$ and $\alpha<20$ deg and with a flat radial profile up to corotation.Comment: 28 pages including 6 postscript figures in uuencoded compressed tar file. Submitted to MNRA

Welfare spending and ethnic heterogeneity: Evidence from a massive immigration wave

The aim of this paper is to examine the relationship between ethnic heterogeneity and redistribution, by using the recent and massive arrival of immigrants in Spain. Specifically, we focus on the effect of changes in immigrant density, recorded between 1998 and 2006, on contemporaneous changes in municipal welfare spending. We instrument for immigrant density using established settlement patterns per country of origin so as to assign predicted flows of immigrants to municipalities. We find that welfare spending increased less in those municipalities that recorded the largest increases in immigrant density. We also provide evidence of a positive relationship between immigrant density and the vote share accruing to right-wing parties. Hence, our results are consistent with theories that predict a negative relationship between ethnic heterogeneity and redistribution.welfare spending, ethnic heterogeneity, redistribution, immigration

Dynamics of Primordial Black Hole Formation

We present a numerical investigation of the gravitational collapse of horizon-size density fluctuations to primordial black holes (PBHs) during the radiation-dominated phase of the Early Universe. The collapse dynamics of three different families of initial perturbation shapes, imposed at the time of horizon crossing, is computed. The perturbation threshold for black hole formation, needed for estimations of the cosmological PBH mass function, is found to be $\delta_{\rm c} \approx 0.7$ rather than the generally employed $\delta_{\rm c} \approx 1/3$, if $\delta$ is defined as \Delta M/\mh, the relative excess mass within the initial horizon volume. In order to study the accretion onto the newly formed black holes, we use a numerical scheme that allows us to follow the evolution for long times after formation of the event horizon. In general, small black holes (compared to the horizon mass at the onset of the collapse) give rise to a fluid bounce that effectively shuts off accretion onto the black hole, while large ones do not. In both cases, the growth of the black hole mass owing to accretion is insignificant. Furthermore, the scaling of black hole mass with distance from the formation threshold, known to occur in near-critical gravitational collapse, is demonstrated to apply to primordial black hole formation.Comment: 10 pages, 8 figures, revtex style, submitted to PR