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

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

Identifiability of Causal Graphs using Functional Models

This work addresses the following question: Under what assumptions on the data generating process can one infer the causal graph from the joint distribution? The approach taken by conditional independence-based causal discovery methods is based on two assumptions: the Markov condition and faithfulness. It has been shown that under these assumptions the causal graph can be identified up to Markov equivalence (some arrows remain undirected) using methods like the PC algorithm. In this work we propose an alternative by defining Identifiable Functional Model Classes (IFMOCs). As our main theorem we prove that if the data generating process belongs to an IFMOC, one can identify the complete causal graph. To the best of our knowledge this is the first identifiability result of this kind that is not limited to linear functional relationships. We discuss how the IFMOC assumption and the Markov and faithfulness assumptions relate to each other and explain why we believe that the IFMOC assumption can be tested more easily on given data. We further provide a practical algorithm that recovers the causal graph from finitely many data; experiments on simulated data support the theoretical findings

Microwave polarization in the direction of galaxy clusters induced by the CMB quadrupole anisotropy

Electron scattering induces a polarization in the cosmic microwave background (CMB) signal measured in the direction of a galaxy cluster due to the presence of a quadrupole component in the CMB temperature distribution. Measuring the polarization towards distant clusters provides the unique opportunity to observe the evolution of the CMB quadrupole at moderate redshifts, z~0.5-3. We demonstrate that for the local cluster population the polarization degree will depend on the cluster celestial position. There are two extended regions in the sky, which are opposite to each other, where the polarization is maximal, 0.1(tau/0.02) microK in the Rayleigh-Jeans part of the CMB spectrum (tau being the Thomson optical depth across the cluster) exceeding the contribution from the cluster transverse peculiar motion if v_t<1300 km/s. One can hope to detect this small signal by measuring a large number of clusters, thereby effectively removing the systematic contribution from other polarization components produced in clusters. These polarization effects, which are of the order of (v_t/c)^2 tau, (v_t/c) tau^2 and (kT_e/m_ec^2) tau^2, as well as the polarization due to the CMB quadrupole, were previously calculated by Sunyaev and Zel'dovich for the Rayleigh-Jeans region. We fully confirm their earlier results and present exact frequency dependencies for all these effects. The polarization is considerably higher in the Wien region of the CMB spectrum.Comment: 8 pages, 5 figures, submitted to MNRA

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

The Lorentz Force and the Radiation Pressure of Light

In order to make plausible the idea that light exerts a pressure on matter, some introductory physics texts consider the force exerted by an electromagnetic wave on an electron. The argument as presented is both mathematically incorrect and has several serious conceptual difficulties without obvious resolution at the classical, yet alone introductory, level. We discuss these difficulties and propose an alternate demonstration.Comment: More or less as in AJ

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

Three-dimensional simulations of type Ia supernovae

We present the results of three-dimensional hydrodynamical simulations of the subsonic thermonuclear burning phase in type Ia supernovae. The burning front model contains no adjustable parameters so that variations of the explosion outcome can be linked directly to changes in the initial conditions. In particular, we investigate the influence of the initial flame geometry on the explosion energy and find that it appears to be weaker than in 2D. Most importantly, our models predict global properties such as the produced nickel masses and ejecta velocities within their observed ranges without any fine tuning.Comment: 7 pages, 5 figures, accepted by A&