Thermal emission from Isolated Neutron Stars and their surface magnetic field: going quadrupolar?

In the last few years considerable observational resources have been devoted to study the thermal emission from isolated neutron stars. Detailed XMM and Chandra observations revealed a number of features in the X-ray pulse profile, like asymmetry, energy dependence, and possible evolution of the pulse profile over a time scale of months or years. Here we show that these characteristics may be explained by a patchy surface temperature distribution, which is expected if the magnetic field has a complex structure in which higher order multipoles contribute together with the dipole. We reconsider these effects from a theoretical point of view, and discuss their implications to the observational properties of thermally emitting neutron stars.Comment: 6 pages, 1 TeX file, 6 postscript figures; macro: elsart.cls. Accepted for publication in Advances in Space Research. Manuscript Number: JASR-D-04-00405R

Pulse profiles from thermally emitting neutron stars

The problem of computing the pulse profiles from thermally emitting spots on the surface of a neutron star in general relativity is reconsidered. We show that it is possible to extend Beloborodov (2002) approach to include (multiple) spots of finite size in different positions on the star surface. Results for the pulse profiles are expressed by comparatively simple analytical formulas which involve only elementary functions.Comment: 8 pages, 6 figures, accepted for publication in Ap

An efficient algorithm for two-dimensional radiative transfer in axisymmetric circumstellar envelopes and disks

We present an algorithm for two-dimensional radiative transfer in axisymmetric, circumstellar media. The formal integration of the transfer equation is performed by a generalization of the short characteristics (SC) method to spherical coordinates. Accelerated Lambda Iteration (ALI) and Ng's algorithm are used to converge towards a solution. By taking a logarithmically spaced radial coordinate grid, the method has the natural capability of treating problems that span several decades in radius, in the most extreme case from the stellar radius up to parsec scale. Flux conservation is guaranteed in spherical coordinates by a particular choice of discrete photon directions and a special treatment of nearly-radially outward propagating radiation. The algorithm works well from zero up to very high optical depth, and can be used for a wide variety of transfer problems, including non-LTE line formation, dust continuum transfer and high temperature processes such as compton scattering. In this paper we focus on multiple scattering off dust grains and on non-LTE transfer in molecular and atomic lines. Line transfer is treated according to an ALI scheme for multi-level atoms/molecules, and includes both random and systematic velocity fields. The algorithms are implemented in a multi-purpose user-friendly radiative transfer program named RADICAL. We present two example computations: one of dust scattering in the Egg Nebula, and one of non-LTE line formation in rotational transitions of HCO$^{+}$ in a flattened protostellar collapsing cloud.Comment: 18 pages, 32 figure

Merger Remedies at the European Commission: A Multinomial Logit Analysis

This paper aims to build and empirically evaluate a discrete choice model of merger remedies as a basis for policy analysis. The database consists of 229 merger cases accepted in Phase I or Phase II of the European merger process between 1990 and 2005. We focus on the following question: Which merging firms' characteristics lead the European Commission to decide whether to require conditional acceptance? Although a lot of empirical studies have been carried out these last years, ours is distinguished by at least two original features. First, we explore determinant factors of the Commission's decisions with a neural network model differentiating cases accepted with or without remedies (either structural or behavioral). Secondly, we implement three multinomial logit models. We find that variables related to high market power lead more frequently to a remedy outcome, whatever the phase. Innovative industries such as energy, transportation and communications positively affect the probability of a behavioral remedy. Lastly, former Competition Commissioner Mario Monti's policy appears to be pro-remedy, i.e. seeking concessions from merging parties.Merger Remedies ; Antitrust ; European Commission ; Discrete Choice Models ; Self-Organizing Maps

Sequential Location under one-sided Demand Uncertainty

By entering new market, firms face uncertainty about their potential demand. We depart from the usual Hotelling duopoly model with sequential entry. Firms can locate outside the city and market conditions are common knowledge. Then we introduce one-sided demand uncertainty. It results that demand uncertainty can be seen as a diferentiation force when the first entrant faces demand uncertainty and as an agglomeration force when it is the second entrant. Finally, firm 2's imperfect information implies higher welfare losses.

Merger Remedies at the European Commission: A Multinomial Logit Analysis

This paper aims to build and empirically evaluate a discrete choice model of merger remedies as a basis for policy analysis. The database consists of 229 merger cases accepted in Phase I or Phase II of the European merger process between 1990 and 2005. We focus on the following question: Which merging firms’ characteristics lead the European Commission to decide whether to require conditional acceptance? Although a lot of empirical studies have been carried out these last years, ours is distinguished by at least two original features. First, we explore determinanting factors of the Commission’s decisions with a neural network model differentiating cases accepted with or without remedies (either structural or behavioral). Secondly, we implement three multinomial logit models. We find that variables related to high market power lead more frequently to a remedy outcome, whatever the phase. Innovative industries such as energy, transportation and communications positively affect the probability of a behavioral remedy. Lastly, former Competition Commissioner Mario Monti’s policy appears to be pro-remedy, i.e. seeking concessions from merging parties.

On the Mathematical Character of the Relativistic Transfer Moment Equations

General--relativistic, frequency--dependent radiative transfer in spherical, differentially--moving media is considered. In particular we investigate the character of the differential operator defined by the first two moment equations in the stationary case. We prove that the moment equations form a hyperbolic system when the logarithmic velocity gradient is positive, provided that a reasonable condition on the Eddington factors is met. The operator, however, may become elliptic in accretion flows and, in general, when gravity is taken into account. Finally we show that, in an optically thick medium, one of the characteristics becomes infinite when the flow velocity equals $\pm c/\sqrt 3$. Both high--speed, stationary inflows and outflows may therefore contain regions which are ``causally'' disconnected.Comment: 16 pages, PlainTex, accepted for publication in MNRA

Bare quark stars or naked neutron stars? The case of RX J1856.5-3754

In a cool neutron star (T less than or similar to 10(6) K) endowed with a rather highmagnetic field (B greater than or similar to 10(13) G), a phase transition may occur in the outermost layers. As a consequence, the neutron star becomes "bare,'' i.e., no gaseous atmosphere sits on the top of the crust. The surface of a cooling, bare neutron star does not necessarily emit a blackbody spectrum because the emissivity is strongly suppressed at energies below the electron plasma frequency, omega(p). Since omega(p) approximate to 1 keV under the conditions typical of the dense electron gas in the condensate, the emission from a T similar to 100 eV bare neutron star will be substantially depressed with respect to that of a perfect Planckian radiator atmost energies. Here we present a detailed analysis of the emission properties of a bare neutron star. In particular, we derive the surface emissivity for an Fe composition in a range of magnetic fields and temperatures representative of cooling isolated neutron stars, like RX J1856.5 - 3754. We find that the emitted spectrum is strongly dependent on the electron conductivity in the solid surface layers. In the cold electron gas approximation ( no electron-lattice interactions), the spectrum turns out to be a featureless depressed blackbody in the 0.1 - 2 keV band with a steeper low-energy distribution. When damping effects due to collisions between electrons and the ion lattice ( mainly due to electron-phonon interactions) are accounted for, the spectrum is more depressed at low energies and spectral features may be present, depending on the magnetic field strength. Details of the emitted spectrum are found, however, to be strongly dependent on the assumed treatment of the transition from the external vacuum to the metallic surface. The implications of our results for RX J1856.5 - 3754 and other isolated neutron stars are discussed

Magnetars: the physics behind observations

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst--active X-ray pulsars, the Anomalous X-ray Pulsars (AXPs) and the Soft Gamma Repeaters (SGRs); the latter emitted also three "giant flares," extremely powerful events during which luminosities can reach up to 10^47 erg/s for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or "outbursting," and "low-field" magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent X-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.Comment: 81 pages, 24 figures, This is an author-created, un-copyedited version of an article submitted to Reports on Progress in Physic