Robert Mochkovitch

The cooling of co white dwarfs: influence of the internal chemical distribution

White dwarfs are the remnants of stars of low and intermediate masses on the main sequence. Since they have exhausted all of their nuclear fuel, their evolution is just a gravothermal process. The release of energy only depends on the detailed internal structure and chemical composition and on the properties of the envelope equation of state and opacity; its consequences on the cooling curve (i.e., the luminosity vs. time relationship) depend on the luminosity at which this energy is released. The internal chemical profile depends on the rate of the 12C(α, γ)16O reaction as well as on the treatment of convection. High reaction rates produce white dwarfs with oxygen-rich cores surrounded by carbon-rich mantles. This reduces the available gravothermal energy and decreases the lifetime of white dwarfs. In this paper we compute detailed evolutionary models providing chemical profiles for white dwarfs having progenitors in the mass range from 1.0 to 7 M☉, and we examine the influence of such profiles in the cooling process. The influence of the process of separation of carbon and oxygen during crystallization is decreased as a consequence of the initial stratification, but it is still important and cannot be neglected. As an example, the best fit to the luminosity functions of Liebert et al. and Oswalt et al. gives an age of the disk of 9.3 and 11.0 Gyr, respectively, when this effect is taken into account, and only 8.3 and 10.0 Gyr when it is neglected.

The expected thermal precursors of gamma‐ray bursts in the internal shock model

The prompt emission of gamma-ray bursts probably comes from a highly relativistic wind which converts part of its kinetic energy into radiation via the formation of shocks within the wind itself. Such ‘internal shocks’ can occur if the wind is generated with a highly non-uniform distribution of the Lorentz factor. We estimate the expected photospheric emission of such a relativistic wind when it becomes transparent. We compare this thermal emission (temporal profile + spectrum) with the non-thermal emission produced by the internal shocks. In most cases, we predict a rather bright thermal emission that should already have been detected. This favours acceleration mechanisms for the wind where the initial energy input is under magnetic rather than thermal form. Such scenarios can produce thermal X-ray precursors comparable to those observed by Ginga and WATCH/GRANAT.

The redshift distribution of Swift gamma-ray bursts: evidence for evolution

We predict the redshift distribution of long gamma-ray bursts (GRBs) with Monte Carlo simulations. Our improved analysis constrains free parameters with three kinds of observation: (i) the log N - log P diagram of Burst and Transient Source Experiment (BATSE) bursts; (ii) the peak energy distribution of bright BATSE bursts and (iii) the High Energy Transient Explorer (HETE2) fraction of X-ray rich GRBs and X-ray flashes. The statistical analysis of the Monte Carlo simulation results allows us to carefully study the impact of the uncertainties in the GRB intrinsic properties on the redshift distribution. The comparison with Swift data then leads to the following conclusions. The Amati relation should be intrinsic, if observationally confirmed by Swift. The progenitor and/or the GRB properties have to evolve to reproduce the high mean redshift of Swift bursts. Our results favour an evolution of the efficiency of GRB production by massive stars, that would be nearly six to seven times higher at z ∼ 7 than at z ∼ 2. We finally predict around 10 GRBs detected by Swift at redshift z > 6 for a 3-yr mission. These may be sufficient to open a new observational window over the high redshift Universe.

Can the early X-ray afterglow of gamma-ray bursts be explained by a contribution from the reverse shock

We propose to explain the recent observations of GRB early X-ray afterglows with SWIFT by the dissipation of energy in the reverse shock which crosses the ejecta as it is decelerated by the burst environment. We compute the evolution of the dissipated power and discuss the possibility that a fraction of it can be radiated in the X-ray range. We show that this reverse shock contribution behaves in a way very similar to the observed X-ray afterglows if the following two conditions are satisfied: (i) the Lorentz factor of the material which is ejected during the late stages of source activity decreases to small values < 10 and (ii) a large part of the shock dissipated energy is transferred to a small fraction (� ∼ 10 2 ) of the electron population. We also discuss how our results may help to solve some puzzling problems raised by multiwavelength early afterglow observations such as the presence of chromatic breaks.

The Fate of Merging White Dwarfs

We present a smoothed particle hydrodynamics simulation of the coalescence of two carbon-oxygen white dwarfs, and we discuss the subsequent evolution of the resulting object. We consider in particular the case of three hot and massive white dwarfs, PG 0136+251, PG 1658+441, and GD 50, not located in any cluster or association, which have been suggested to result from a coalescence process (Bergeron et al.). We show that the merged object must lose about 90% of its original angular momentum to become sufficiently compact and reach the observed surface gravities log g ≈ 9. Since the three candidates are DA white dwarfs, we examine the efficiency of the accretion process from the interstellar medium to build the observed hydrogen envelope. Finally, the fact that the three merger candidates are located within 80 pc (two within 40 pc) imposes severe constraints on the evolution process. We connect this statistical problem to the evolutionary timescale of the merged object. We show that in order to explain the observed three white dwarfs, the coalescence scenario implies a large timescale.

The Physics of Crystallizing White Dwarfs

White dwarfs can be used as Galactic chronometers and, therefore, provide important information about Galactic evolution if good theoretical models of their cooling are available. Consequently, it is natural to wonder if all the sources or sinks of energy are correctly taken into account. One energy source is partial differentiation of the chemical components of the white dwarf upon crystallization. In this paper we use a new formalism to show that if there is a redistribution of the elements inside the star, there is a net release of energy that must be radiated away and that slows down the cooling rate of the white dwarf.

The Halo White Dwarf Population

Halo white dwarfs can provide important information about the properties and evolution of the Galactic halo. In this paper we compute, assuming a standard initial mass function (IMF) and updated models of white dwarf cooling, the expected luminosity function, both in luminosity and in visual magnitude, for different star formation rates. We show that a deep enough survey (limiting magnitude 20) could provide important information about the halo age and the duration of the formation stage. We also show that the number of white dwarfs produced using the recently proposed biased IMFs cannot represent a large fraction of the halo dark matter if they are constrained by the presently observed luminosity function. Furthermore, we show that a robust determination of the bright portion of the luminosity function can provide strong constraints on the allowable IMF shapes.

Prompt thermal emission in gamma-ray bursts

Context. Gamma-ray burst (GRB) spectra globally appear non-thermal, but recent observations of a few bursts with Fermi GBM have confirmed previous indications from BATSE of the presence of an underlying thermal component. Photospheric emission is indeed expected when the relativistic outflow emerging from the central engine becomes transparent to its own radiation, with a quasi- blackbody spectrum in absence of additional sub-photospheric dissipation. However, its intensity strongly depends on the acceleration mechanism - thermal or magnetic - of the flow. Aims. We aim to compute the thermal and non-thermal emissions (light curves and spectra) produced by an outflow with a variable Lorentz factor, where the power u Eiso injected at the origin is partially thermal (fractionth ≤ 1) and partially magnetic (fraction 1− � th). The thermal emission is produced at the photosphere, and the non-thermal emission in the optically thin regime. Apart from the value ofth, we want to test how the other model parameters affect the observed ratio of the thermal to non-thermal emission. Methods. We followed the adiabatic cooling of the flow from the origin to the photosphere and computed the emitted radiation, which is a sum of modified black bodies at different temperatures (as the temperature strongly depends on the Lorentz factor of each shell at transparency). If the non-thermal emission comes from internal shocks, it is obtained from a multi-shell model where a fraction of the energy dissipated in shell collision is transferred to electrons and radiated via the synchrotron mechanism. If, conversely, the non-thermal emission originates in magnetic reconnection, the lack of any detailed theory for this process forced us to use a very simple parametrisation to estimate the emitted spectrum. Results. If the non-thermal emission is made by internal shocks, we self-consistently obtained the light curves and spectra of the thermal and non-thermal components for any distribution of the Lorentz factor in the flow. If the non-thermal emission results from magnetic reconnection we were unable to produce a light curve and could only compare the respective non-thermal and thermal spectra. In the different considered cases, we varied the model parameters to see when the thermal component in the light curve and/or spectrum is likely to show up or, on the contrary, to be hidden. We finally compared our results to the proposed evidence for the presence of a thermal component in GRB spectra. Focussing on GRB 090902B and GRB 10072B, we showed how these observations can be used to constrain the nature and acceleration mechanism of GRB outflows.

UHECR acceleration at GRB internal shocks

We study the acceleration of cosmic-ray protons and nuclei at GRB internal shocks. Physical quantities (magnetic fields, baryon and photon densities, shock velocity) and their time evolution, relevant to cosmic-ray acceleration and energy losses, are estimated using the internal shock modeling implemented by Daigne & Mochkovitch (1998). Within this framework, we consider di erent hypotheses about the way the energy dissipated at internal shocks is shared between accelerated cosmic-rays, electrons and the magnetic field. We model cosmicray acceleration at mildly relativistic shocks, using numerical tools inspired by the work of Niemiec & Ostrowski (2004), including all the significant energy loss processes that might limit cosmic-ray acceleration at GRB internal shocks. We calculate cosmic-ray and neutrino release from single GRBs, for various prompt emission luminosities, assuming that nuclei heavier than protons are present in the relativistic wind at the beginning of the internal shock phase. We find that protons can only reach maximum energies of the order 10 19:5 eV in the most favorable cases, while intermediate and heavy nuclei are able to reach higher values of the order of 10 20 eV and above. The spectra of particles escaping from the acceleration site are found to be very hard for the di erent nuclear species. In addition a significant and much softer neutron component is present in the cases of intermediate and high luminosity GRBs due to the photodisintegration of accelerated nuclei during the early stages of the shock propagation. As a result, the combined spectrum of protons and neutrons from single GRBs is found to be much softer than those of the other nuclear species. We calculate the di use UHECR flux expected on Earth by convoluting the cosmic-ray output from single GRBs of various luminosities by the GRB luminosity function derived by Wanderman & Piran (2010). We show that only the models assuming that (i) the prompt emission represent only a very small fraction of the energy dissipated at internal shocks (especially for low and intermediate luminosity bursts), and that (ii) most of this dissipated energy is communicated to accelerated cosmic-rays, are able to reproduce the magnitude of the UHECR flux observed on Earth. For these models, the observed shape of the UHECR spectrum can be well reproduced above the ankle and the evolution of the composition is compatible with the trend suggested by Auger data. We discuss the implications of the softer proton component (consequence of the neutron emission in the sources) for the phenomenology of the transition from Galactic to extragalactic cosmic-ray, in the light of the recent composition analyses from the KASCADE-Grande experiment. Finally, we find that the associated secondary particle di use fluxes do not upset any current observational limit or measurement. Di use neutrino flux from GRB sources of the order of those we calculated should however be detected with the lifetime of neutrino observatories such as IceCube or KM3Net.

The final stages of evolution of cold, mass-accreting white dwarfs

The evolution of solid C + O white dwarf models upon mass accretion is calculated up to the point of either explosive thermonuclear ignition or gravitational collapse. It is shown that both explosions and quiet collapses to a neutron star are possible for each of two different phase diagrams for high-density C + O mixtures. The ranges of initial masses and temperatures and of accretion rates leading to the different outcomes are determined. Problems concerning the chemical composition of the accreted matter and the effects of tidal dissipation are discussed. 68 references.