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

The Global Star Formation Rate from the 1.4 GHz Luminosity Function

The decimetric luminosity of many galaxies appears to be dominated by synchrotron emission excited by supernova explosions. Simple models suggest that the luminosity is directly proportional to the rate of supernova explosions of massive stars averaged over the past 30 Myr. The proportionality may be used together with models of the evolving 1.4 GHz luminosity function to estimate the global star formation rate density in the era z < 1. The local value is estimated to be 0.026 solar masses per year per cubic megaparsec, some 50% larger than the value inferred from the Halpha luminosity density. The value at z ~ 1 is found to be 0.30 solar masses per year per cubic megaparsec. The 10-fold increase in star formation rate density is consistent with the increase inferred from mm-wave, far-infrared, ultra-violet and Halpha observations.Comment: 10 pages, 2 figures, Astrophysical Journal Letters (in press); new PS version has improved figure placemen

Thermal Emission from HII Galaxies: Discovering the Youngest Systems

We studied the radio properties of very young massive regions of star formation in HII galaxies, with the aim of detecting episodes of recent star formation in an early phase of evolution where the first supernovae start to appear. Our sample consists of 31 HII galaxies, characterized by strong Hydrogen emission lines, for which low resolution VLA 3.5cm and 6cm observations were obtained. The radio spectral energy distribution has a range of behaviours; 1) there are galaxies where the SED is characterized by a synchrotron-type slope, 2) galaxies with a thermal slope, and, 3) galaxies with possible free-free absorption at long wavelengths. The latter SEDs were found in a few galaxies and represent a signature of heavily embedded massive star clusters closely related to the early stages of massive star formation. Based on the comparison of the star formation rates determined from the recombination lines and those determined from the radio emission we find that SFR(Ha) is on average five times higher than SFR(1.4GHz). We confirm this tendency by comparing the ratio between the observed flux at 20 cm and the expected one, calculated based on the Ha star formation rates, both for the galaxies in our sample and for normal ones. This analysis shows that this ratio is a factor of 2 smaller in our galaxies than in normal ones, indicating that they fall below the FIR/radio correlation. These results suggest that the emission of these galaxies is dominated by a recent and massive star formation event in which the first supernovae (SN) just started to explode. We conclude that the systematic lack of synchrotron emission in those systems with the largest equivalent width of Hb can only be explained if those are young starbursts of less than 3.5Myr of age.Comment: Accepted for publication in Ap

The star-formation history of the universe - an infrared perspective

A simple and versatile parameterized approach to the star formation history allows a quantitative investigation of the constraints from far infrared and submillimetre counts and background intensity measurements. The models include four spectral components: infrared cirrus (emission from interstellar dust), an M82-like starburst, an Arp220-like starburst and an AGN dust torus. The 60 $\mu$m luminosity function is determined for each chosen rate of evolution using the PSCz redshift data for 15000 galaxies. The proportions of each spectral type as a function of 60 $\mu$m luminosity are chosen for consistency with IRAS and SCUBA colour-luminosity relations, and with the fraction of AGN as a function of luminosity found in 12 $\mu$m samples. The luminosity function for each component at any wavelength can then be calculated from the assumed spectral energy distributions. With assumptions about the optical seds corresponding to each component and, for the AGN component, the optical and near infrared counts can be accurately modelled. A good fit to the observed counts at 0.44, 2.2, 15, 60, 90, 175 and 850 $\mu$m can be found with pure luminosity evolution in all 3 cosmological models investigated: $\Omega_o$ = 1, $\Omega_o$ = 0.3 ($\Lambda$ = 0), and $\Omega_o$ = 0.3, $\Lambda$ = 0.7. All 3 models also give an acceptable fit to the integrated background spectrum. Selected predictions of the models, for example redshift distributions for each component at selected wavelengths and fluxes, are shown. The total mass-density of stars generated is consistent with that observed, in all 3 cosmological models.Comment: 20 pages, 25 figures. Accepted for publication in ApJ. Full details of models can be found at http://astro.ic.ac.uk/~mrr/countmodel

Critical behaviour in the nonlinear elastic response of hydrogels

In this paper we study the elastic response of synthetic hydrogels to an applied shear stress. The hydrogels studied here have previously been shown to mimic the behaviour of biopolymer networks when they are sufficiently far above the gel point. We show that near the gel point they exhibit an elastic response that is consistent with the predicted critical behaviour of networks near or below the isostatic point of marginal stability. This point separates rigid and floppy states, distinguished by the presence or absence of finite linear elastic moduli. Recent theoretical work has also focused on the response of such networks to finite or large deformations, both near and below the isostatic point. Despite this interest, experimental evidence for the existence of criticality in such networks has been lacking. Using computer simulations, we identify critical signatures in the mechanical response of sub-isostatic networks as a function of applied shear stress. We also present experimental evidence consistent with these predictions. Furthermore, our results show the existence of two distinct critical regimes, one of which arises from the nonlinear stretch response of semi-flexible polymers.

Absence of reflection as a function of the coupling constant

We consider solutions of the one-dimensional equation $-u'' +(Q+ \lambda V) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $\lambda \in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_{\lambda} \}_{\lambda \in \mathbb{R}}$ which satisfy $u_{\lambda}(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(\lambda) := W[u_0, u_{\lambda}]$, the Wronskian of $u_0$ and $u_{\lambda}$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + \lambda V u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$.Comment: To appear in Journal of Mathematical Physic

Faint Radio Sources and Star Formation History

Faint extragalactic radio sources provide important information about the global history of star formation. Sensitive radio observations of the Hubble Deep Field and other fields have found that sub-mJy radio sources are predominantly associated with star formation activity rather than AGN. Radio observations of star forming galaxies have the advantage of being independent of extinction by dust. We use the FIR-radio correlation to compare the radio and FIR backgrounds, and make several conclusions about the star forming galaxies producing the FIR background. We then use the redshift distribution of faint radio sources to determine the evolution of the radio luminosity function, and thus estimate the star formation density as a function of redshift.Comment: 12 pages, 9 figures, latex using texas.sty, to appear in the CD-ROM Proceedings of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.: J. Paul, T. Montmerle, and E. Aubourg (CEA Saclay). No changes to paper, just updated publication info in this commen

High Redshift Supernovae in the Hubble Deep Field

Two supernovae detected in the Hubble Deep Field using the original December 1995 epoch and data from a shorter (63000 s in F814W) December 1997 visit with HST are discussed. The supernovae (SNe) are both associated with distinct galaxies at redshifts of 0.95 (spectroscopic) from Cohen etal. (1996) and 1.32 (photometric) from the work of Fernandez-Soto, Lanzetta, and Yahil (1998). These redshifts are near, in the case of 0.95, and well beyond for 1.32 the greatest distance reported previously for SNe. We show that our observations are sensitive to SNe to z < 1.8 in either epoch for an event near peak brightness. Detailed simulations are discussed that quantify the level at which false events from our search phase would start to to arise, and the completeness of our search as a function of both SN brightness and host galaxy redshift. The number of Type Ia and Type II SNe expected as a function of redshift in the two HDF epochs are discussed in relation to several published predictions and our own detailed calculations. A mean detection frequency of one SN per epoch for the small HDF area is consistent with expectations from current theory.Comment: 62 pages, 17 figures, ApJ 1999 in pres

On the nature of the ISO-selected sources in the ELAIS S2 region

We have studied the optical, near-IR and radio properties of a complete sample of 43 sources detected at 15-micron in one of the deeper ELAIS repeatedly observed region. The extragalactic objects in this sample have 15-micron flux densities in the range 0.4-10 mJy, where the source counts start diverging from no evolution models. About 90% of the sources (39 out of 43) have optical counterparts brighter than I=21 mag. Eight of these 39 sources have been identified with stars on the basis of imaging data, while for another 22 sources we have obtained optical spectroscopy, reaching a high identification percentage (30/43, ~70%). All but one of the 28 sources with flux density > 0.7 mJy are identified. Most of the extragalactic objects are normal spiral or starburst galaxies at moderate redshift (z_med~0.2); four objects are Active Galactic Nuclei. We have used the 15-micron, H_alpha and 1.4-GHz luminosities as indicators of star-formation rate and we have compared the results obtained in these three bands. While 1.4-GHz and 15-micron estimates are in good agreement, showing that our galaxies are forming stars at a median rate of ~40 Mo/yr, the raw H_alpha-based estimates are a factor ~5-10 lower and need a mean correction of ~2 mag to be brought on the same scale as the other two indicators. A correction of ~2 mag is consistent with what suggested by the Balmer decrements H_alpha/H_beta and by the optical colours. Moreover, it is intermediate between the correction found locally for normal spirals and the correction needed for high-luminosity 15-micron objects, suggesting that the average extinction suffered by galaxies increases with infrared luminosity.Comment: 19 pages, 11 figures (3 in JPEG format), MNRAS, accepte