Physical parameters of GRB 970508 and GRB 971214 from their afterglow synchrotron emission

We have calculated synchrotron spectra of relativistic blast waves, and find predicted characteristic frequencies that are more than an order of magnitude different from previous calculations. For the case of an adiabatically expanding blast wave, which is applicable to observed gamma-ray burst (GRB) afterglows at late times, we give expressions to infer the physical properties of the afterglow from the measured spectral features. We show that enough data exist for GRB970508 to compute unambiguously the ambient density, n=0.03/cm**3, and the blast wave energy per unit solid angle, E=3E52 erg/4pi sr. We also compute the energy density in electrons and magnetic field. We find that they are 12% and 9%, respectively, of the nucleon energy density and thus confirm for the first time that both are close to but below equipartition. For GRB971214, we discuss the break found in its spectrum by Ramaprakash et al. (1998). It can be interpreted either as the peak frequency or as the cooling frequency; both interpretations have some problems, but on balance the break is more likely to be the cooling frequency. Even when we assume this, our ignorance of the self-absorption frequency and presence or absence of beaming make it impossible to constrain the physical parameters of GRB971214 very well.Comment: very strongly revised analysis of GRB971214 and discussion, submitted to ApJ, 11 pages LaTeX, 4 figures, uses emulateapj.sty (included

The Dynamics and Light Curves of Beamed Gamma Ray Burst Afterglows

The energy requirements of gamma ray bursts have in past been poorly constrained because of three major uncertainties: The distances to bursts, the degree of burst beaming, and the efficiency of gamma ray production. The first of these has been resolved, with both indirect evidence (the distribution of bursts in flux and position) and direct evidence (redshifted absorption features in the afterglow spectrum of GRB 970508) pointing to cosmological distances. We now wish to address the second uncertainty. Afterglows allow a statistical test of beaming, described in an earlier paper. In this paper, we modify a standard fireball afterglow model to explore the effects of beaming on burst remnant dynamics and afterglow emission. If the burst ejecta are beamed into angle zeta, the burst remnant's evolution changes qualitatively once its bulk Lorentz factor Gamma < 1/zeta: Before this, Gamma declines as a power law of radius, while afterwards, it declines exponentially. This change results in a broken power law light curve whose late-time decay is faster than expected for a purely spherical geometry. These predictions disagree with afterglow observations of GRB 970508. We explored several variations on our model, but none seems able to change this result. We therefore suggest that this burst is unlikely to have been highly beamed, and that its energy requirements were near those of isotropic models. More recent afterglows may offer the first practical applications for our beamed models.Comment: 18 pages, uses emulateapj.sty, four embedded postscript figures. Submitted to The Astrophysical Journal, 199

GRB990123, The Optical Flash and The Fireball Model

We compare the ongoing observations of the remarkable burst GRB990123, the mother of all bursts, with the predictions of the afterglow theory. We show that the observations agree with the recent prediction that a reverse shock propagating into the ejecta would produce a very strong prompt optical flash. This reverse shock has also produced the 8.46GHz radio signal, observed after one day. The forward shock, which propagates into the ISM is the origin of the classical afterglow. It has produced the prompt X-ray signal as well as the late optical and IR emission. It would most likely produce a radio emission within the next few weeks. The observations suggest that the initial Lorentz factor of the ejecta was $\sim 200$. Within factors of order unity, this crude model explains all current observations of GRB990123.Comment: 14 pages including 2 figure

Identifying Gamma-Ray Burst Remnants in Nearby Galaxies

We study the spectral signatures arising from cooling and recombination of an interstellar medium whose equilibrium state has been altered over \sim 100 pc by the radiation of a Gamma-Ray Burst (GRB) and its afterglow. We identify signatures in the line diagnostics which are indicative of a photo-ionized GRB remnant which is \la 5 x 10^4 years old . We estimate that at least a few such remnants should be detectable in the Virgo cluster of galaxies. If the gamma-ray emission from GRBs is beamed to a fraction f_b of their sky, then the expected number of Virgo remnants is larger by a factor of f_b^{-1}. Virgo remnants can be resolved with arcsecond imaging, and are likely to be center-filled using narrow-band filters of high ionization lines (such as [O III] \lambda5007 or He II \lambda4686), and limb-brightened for low-ionization lines (such as [S II] \lambda6717). The non-relativistic blast wave might be visible separately, since it does not reach the outer edge of these young photo-ionized remnants. The remnants should show evidence for ionization cones if the prompt or afterglow UV emission from GRBs is beamed.Comment: 21 pages, 10 figures, submitted to Ap

Variability of GRB Afterglows Due to Interstellar Turbulence

Gamma-Ray Burst (GRB) afterglows are commonly interpreted as synchrotron emission from a relativistic blast wave produced by a point explosion in an ambient medium, plausibly the interstellar medium of galaxies. We calculate the amplitude of flux fluctuations in the lightcurve of afterglows due to inhomogeneities in the surrounding medium. Such inhomogeneities are an inevitable consequence of interstellar turbulence, but could also be generated by variability and anisotropy in a precursor wind from the GRB progenitor. Detection of their properties could provide important clues about the environments of GRB sources. We apply our calculations to GRB990510, where an rms scatter of 2% was observed for the optical flux fluctuations on the 0.1--2 hour timescale during the first day of the afterglow, consistent with it being entirely due to photometric noise (Stanek et al. 1999). The resulting upper limits on the density fluctuations on scales of 20-200 AU around the source of GRB990510, are lower than the inferred fluctuation amplitude on similar scales in the Galactic interstellar medium. Hourly monitoring of future optical afterglows might therefore reveal fractional flux fluctuations at the level of a few percent.Comment: 18 pages, submitted to Ap

The Redshift of GRB 970508

GRB 970508 is the second gamma-ray burst (GRB) for which an optical afterglow has been detected. It is the first GRB for which a distance scale has been determined: absorption and emission features in spectra of the optical afterglow place GRB 970508 at a redshift of z >= 0.835 (Metzger et al. 1997a, 1997b). The lack of a Lyman-alpha forest in these spectra further constrains this redshift to be less than approximately 2.3. I show that the spectrum of the optical afterglow of GRB 970508, once corrected for Galactic absorption, is inconsistent with the relativistic blast-wave model unless a second, redshifted source of extinction is introduced. This second source of extinction may be the yet unobserved host galaxy. I determine its redshift to be z = 1.09^{+0.14}_{-0.41}, which is consistent with the observed redshift of z = 0.835. Redshifts greater than z = 1.40 are ruled out at the 3 sigma confidence level.Comment: Accepted to The Astrophysical Journal (Letters), 10 pages, LaTe

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

Identifying the Environment and Redshift of GRB Afterglows from the Time-Dependence of Their Absorption Spectra

The discovery of Gamma-Ray Burst (GRB) afterglows revealed a new class of variable sources at optical and radio wavelengths. At present, the environment and precise redshift of the detected afterglows are still unknown. We show that if a GRB source resides in a compact (<100pc) gas-rich environment, the afterglow spectrum will show time-dependent absorption features due to the gradual ionization of the surrounding medium by the afterglow radiation. Detection of this time-dependence can be used to constrain the size and density of the surrounding gaseous system. For example, the MgII absorption line detected in GRB970508 should have weakened considerably during the first month if the absorption occurred in a gas cloud of size <100pc around the source. The time-dependent HI or metal absorption features provide a precise determination of the GRB redshift.Comment: 13 pages, 4 figures, submitted to ApJ

BATSE Observations of Gamma-Ray Burst Tails

I discuss in this paper the phenomenon of post-burst emission in BATSE gamma-ray bursts at energies traditionally associated with prompt emission. By summing the background-subtracted signals from hundreds of bursts, I find that tails out to hundreds of seconds after the trigger may be a common feature of long events (duration greater than 2s), and perhaps of the shorter bursts at a lower and shorter-lived level. The tail component appears independent of both the duration (within the long GRB sample) and brightness of the prompt burst emission, and may be softer. Some individual bursts have visible tails at gamma-ray energies and the spectrum in at least a few cases is different from that of the prompt emission.Comment: 33 Pages from LaTex including 7 figures, with aastex. To appear in Astrophysical Journa