On the formation of low-mass black holes in massive binary stars

Recently (Brown \& Bethe 1994) it was suggested that most stars with main sequence mass in the range of about $18 - 30 M_{\odot}$ explode, returning matter to the Galaxy, and then go into low-mass ($\geq 1.5 M_{\odot}$) black holes. Even more massive main-sequence stars would, presumably, chiefly g o into high-mass ($\sim 10 M_{\odot}$) black holes. The Brown-Bethe estimates gave approximately $5 \times {10}^{8}$ low-mass black holes in the Galaxy. A pressing question, which we attempt to answer here, is why, with the possible exception of the compact objects in SN1987A and 4U\,1700--37, none of these have been seen. We address this question in three parts. Firstly, black holes are generally ``seen'' only in binaries, by the accretion of matter from a companion star. High mass black holes are capable of accreting more matter than low-mass black holes, so there is a selection effect favoring them. This, in itself, would not be sufficient to show why low-mass black holes have not been seen, since neutron stars (of nearly the same mass) are seen in abundance. Secondly, and this is our main point, the primary star in a binary ---the first star to evolve--- loses its hydrogen envelope by transfer of matter to the secondary and loss into space, and the resulting ``naked'' helium star evolves differently than a helium core, which is at least initially covered by the hydrogen envelope in a massive main-sequence star. We show that primary stars in binaries can end up as neutron stars even if their initial mass substantially exceeds the mass limit for neutron star formation from single stars ($\sim 18 M_{\odot}$). An example is 4U\,1223--62, in which we suggest that the initial primary mass exceeded $35 M_{\odot}$, yet X-ray pulsationsComment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

The 1.4 GHz light curve of GRB 970508

We report on Westerbork 1.4 GHz radio observations of the radio counterpart to $\gamma$-ray burst GRB~970508, between 0.80 and 138 days after this event. The 1.4 GHz light curve shows a transition from optically thick to thin emission between 39 and 54 days after the event. We derive the slope $p$ of the spectrum of injected electrons ($dN/d\gamma_{e}\propto\gamma_{e}^{-p}$) in two independent ways which yield values very close to $p=2.2$. This is in agreement with a relativistic dynamically near-adiabatic blast wave model whose emission is dominated by synchrotron radiation and in which a significant fraction of the electrons cool fast.Comment: Paper I. Accepted for publication in the Astrophysical Journal Letter

Gamma-Ray Burst and Relativistic Shells: The Surface Filling Factor

The variability observed in many complex gamma-ray bursts (GRBs) is inconsistent with causally connected variations in a single, symmetric, relativistic shell interacting with the ambient material ("external shocks"). Rather, the symmetry of the shell must be broken on an angular scale much smaller than Gamma^{-1} where Gamma is the bulk Lorentz factor for the shell. The observed variability in the external shock models arises from the number of causally connected regions that (randomly) become active. We define the "surface filling factor" to be the ratio of the area of causally connected regions that become active to the observable area of the shell. From the observed variability in 52 BATSE bursts, we estimate the surface filling factor to be typically 0.005 although some values are near unity. We find that the surface filling factor is about 0.1 Delta T/T in both the constant Gamma phase (which probably produces the GRB) and the deaccelerating phase (which probably produces the x-ray afterglows). Here, \Delta T is a typical time scale of variability and T is the time since the initial signal. We analyze the 2 hr flare seen by ASCA 36 hr after the GRB and conclude that the surface filling factor must be small (0.001) in the x-ray afterglow phase as well. Explanations for low surface filling factor can either require more or less energy (by a factor of about 1000) compared to that expected for a symmetric shell.Comment: 26 pages, 5 embedded figures, Latex, revised version as in press, ApJ, added figure to show the possible expanding shell geometries that can give low filling facto

Relativistic Winds from Compact Gamma-Ray Sources: II. Pair Loading and Radiative Acceleration in Gamma-ray Bursts

We consider the effects of rapid pair creation by an intense pulse of gamma-rays propagating ahead of a relativistic shock. Side-scattered photons colliding with the main gamma-ray beam amplify the density of scattering charges. The acceleration rate of the pair-loaded medium is calculated, and its limiting bulk Lorentz factor related to the spectrum and compactness of the photon source. One obtains, as a result, a definite prediction for the relative inertia in baryons and pairs. The deceleration of a relativistic shock in the moving medium, and the resulting synchrotron emissivity, are compared with existing calculations for a static medium. The radiative efficiency is increased dramatically by pair loading. When the initial ambient density exceeds a critical value, the scattering depth traversed by the main gamma-ray pulse rises above unity, and the pulse is broadened. These considerations place significant constraints on burst progenitors: a pre-burst mass loss rate exceeding 10^{-5} M_\odot per year is difficult to reconcile with individual pulses narrower than 10 s, unless the radiative efficiency is low. An anisotropic gamma-ray flux (on an angular scale \Gamma^{-1} or larger) drives a large velocity shear that greatly increases the energy in the seed magnetic field forward of the propagating shock.Comment: 19 pp., LaTeX (aaspp4.sty), revised 12/23/99, Ap. J. in press; summary section added and several minor improvements in presentatio

The discovery of polarization in the afterglow of GRB 990510 with the ESO Very Large Telescope

Following a BeppoSAX alert (Piro 1999a) and the discovery of the OT at SAAO (Vreeswijk et al. 1999a), we observed GRB 990510 with the FORS instrument on ESO's VLT Unit 1 (`Antu'). The burst is unremarkable in gamma rays, but in optical is the first one to show good evidence for jet-like outflow (Stanek et al. 1999, Harrison et al. 1999). We report the detection of significant linear polarization in the afterglow: it is (1.6 +/- 0.2)% 0.86 days after trigger, and after 1.81 days is consistent with that same value, but much more uncertain. The polarization angle is constant on a time scale of hours, and may be constant over one day. We conclude that the polarization is intrinsic to the source and due to the synchrotron nature of the emission, and discuss the random and ordered field geometries that may be responsible for it.Comment: submitted to ApJ Lett., 5 pages including 2 figures, uses emulateapj.st

The hidden X-ray breaks in afterglow light curves

Gamma-Ray Burst (GRB) afterglow observations in the Swift era have a perceived lack of achromatic jet breaks compared to the BeppoSAX, or pre-Swift era. Specifically, relatively few breaks, consistent with jet breaks, are observed in the X-ray light curves of these bursts. If these breaks are truly missing, it has serious consequences for the interpretation of GRB jet collimation and energy requirements, and the use of GRBs as standard candles. Here we address the issue of X-ray breaks which are possibly 'hidden' and hence the light curves are misinterpreted as being single power-laws. We show how a number of precedents, including GRB 990510 & GRB 060206, exist for such hidden breaks and how, even with the well sampled light curves of the Swift era, these breaks may be left misidentified. We do so by synthesising X-ray light curves and finding general trends via Monte Carlo analysis. Furthermore, in light of these simulations, we discuss how to best identify achromatic breaks in afterglow light curves via multi-wavelength analysis.Comment: 4 pages, contributed talk, submitted to the proceedings of Gamma Ray Bursts 2007, Santa Fe, New Mexico, November 5-9 200

A Theory of Gamma-Ray Bursts

We present a specific scenario for the link between GRB and hypernovae, based on Blandford-Znajek extraction of black-hole spin energy. Such a mechanism requires a high angular momentum in the progenitor object. The observed association of gamma-ray bursts with type Ibc supernovae leads us to consider massive helium stars that form black holes at the end of their lives as progenitors. We combine the numerical work of MacFadyen & Woosley with analytic calculations, to show that about 1E53 erg each are available to drive the fast GRB ejecta and the supernova. The GRB ejecta are driven by the power output through the open field lines, whereas the supernova is powered by closed filed lines and jet shocks. We also present a much simplified approximate derivation of these energetics. Helium stars that leave massive black-hole remnants in special ways, namely via soft X-ray transients or very massive WNL stars. Since binaries naturally have high angular momentum, we propose a link between black-hole transients and gamma-ray bursts. Recent observations of one such transient, GRO J1655-40/Nova Scorpii 1994, explicitly support this connection: its high space velocity indicates that substantial mass was ejected in the formation of the black hole, and the overabundance of alpha-nuclei, especially sulphur, indicates that the explosion energy was extreme, as in SN 1998bw/GRB 980425. (abstract shortened)Comment: 32 pages, 8 figures, accepted for publication in New Astronom

Discrete structure of ultrathin dielectric films and their surface optical properties

The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the investigation of the near-zone optical response of dielectrics. The laws of reflection and refraction for discrete structures in the case of a regular atomic distribution are studied and the structure of evanescent harmonics induced by an external plane wave near the surface is investigated in details. It is shown by means of analytical and numerical calculations that due to the existence of the evanescent harmonics the laws of reflection and refraction at the distances from the surface less than two interatomic distances are principally different from the Fresnel laws. From the practical point of view the results of this work might be useful for the near-field optical microscopy of ultrahigh resolution.Comment: 25 pages, 16 figures, LaTeX2.09, to be published in Phys.Rev.

The Evolution of Relativistic Binary Progenitor Systems

Relativistic binary pulsars, such as B1534+12 and B1913+16 are characterized by having close orbits with a binary separation of ~ 3 R_\sun. The progenitor of such a system is a neutron star, helium star binary. The helium star, with a strong stellar wind, is able to spin up its compact companion via accretion. The neutron star's magnetic field is then lowered to observed values of about 10^{10} Gauss. As the pulsar lifetime is inversely proportional to its magnetic field, the possibility of observing such a system is, thus, enhanced by this type of evolution. We will show that a nascent (Crab-like) pulsar in such a system can, through accretion-braking torques (i.e. the "propeller effect") and wind-induced spin-up rates, reach equilibrium periods that are close to observed values. Such processes occur within the relatively short helium star lifetimes. Additionally, we find that the final outcome of such evolutionary scenarios depends strongly on initial parameters, particularly the initial binary separation and helium star mass. It is, indeed, determined that the majority of such systems end up in the pulsar "graveyard", and only a small fraction are strongly recycled. This fact might help to reconcile theoretically expected birth rates with limited observations of relativistic binary pulsars.Comment: 24 pages, 10 Postscript figures, Submitted to The Astrophysical Journa