The Cosmic Microwave Background and the Ionization History of the Universe

Details of how the primordial plasma recombined and how the universe later reionized are currently somewhat uncertain. This uncertainty can restrict the accuracy of cosmological parameter measurements from the Cosmic Microwave Background (CMB). More positively, future CMB data can be used to constrain the ionization history using observations. We first discuss how current uncertainties in the recombination history impact parameter constraints, and show how suitable parameterizations can be used to obtain unbiased parameter estimates from future data. Some parameters can be constrained robustly, however there is clear motivation to model recombination more accurately with quantified errors. We then discuss constraints on the ionization fraction binned in redshift during reionization. Perfect CMB polarization data could in principle distinguish different histories that have the same optical depth. We discuss how well the Planck satellite may be able to constrain the ionization history, and show the currently very weak constraints from WMAP three-year data.Comment: Changes to match MNRAS accepted versio

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

Constraints on Off-Axis X-Ray Emission from Beamed GRBs

We calculate the prompt x-ray emission as a function of viewing angle for beamed Gamma-Ray Burst (GRB) sources. Prompt x-rays are inevitable due to the less highly blueshifted photons emitted at angles greater than 1/gamma relative to the beam symmetry axis, where gamma is the expansion Lorentz factor. The observed flux depends on the combinations (gamma Delta theta) and (gamma theta_v), where (Delta theta) is the beaming angle and theta_v is the viewing angle. We use the observed source counts of gamma-ray-selected GRBs to predict the minimum detection rate of prompt x-ray bursts as a function of limiting sensitivity. We compare our predictions with the results from the Ariel V catalog of fast x-ray transients, and find that Ariel's sensitivity is not great enough to place significant constraints on gamma and (Delta theta). We estimate that a detector with fluence limit ~10^{-7} erg/cm^2 in the 2-10 keV channel will be necessary to distinguish between geometries. Because the x-ray emission is simultaneous with the GRB emission, our predicted constraints do not involve any model assumptions about the emission physics but simply follow from special-relativistic considerations.Comment: Submitted to Ap

Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of Quasars

The observed number counts of quasars may be explained either by long-lived activity within rare massive hosts, or by short-lived activity within smaller, more common hosts. It has been argued that quasar lifetimes may therefore be inferred from their clustering length, which determines the typical mass of the quasar host. Here we point out that the relationship between the mass of the black-hole and the circular velocity of its host dark-matter halo is more fundamental to the determination of the clustering length. In particular, the clustering length observed in the 2dF quasar redshift survey is consistent with the galactic halo - black-hole relation observed in local galaxies, provided that quasars shine at ~10-100% of their Eddington luminosity. The slow evolution of the clustering length with redshift inferred in the 2dF quasar survey favors a black-hole mass whose redshift-independent scaling is with halo circular velocity, rather than halo mass. These results are independent from observations of the number counts of bright quasars which may be used to determine the quasar lifetime and its dependence on redshift. We show that if quasar activity results from galaxy mergers, then the number counts of quasars imply an episodic quasar lifetime that is set by the dynamical time of the host galaxy rather than by the Salpeter time. Our results imply that as the redshift increases, the central black-holes comprise a larger fraction of their host galaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap

Gravitational Lensing of the SDSS High-Redshift Quasars

We predict the effects of gravitational lensing on the color-selected flux-limited samples of z~4.3 and z>5.8 quasars, recently published by the Sloan Digital Sky Survey (SDSS). Our main findings are: (i) The lensing probability should be 1-2 orders of magnitude higher than for conventional surveys. The expected fraction of multiply-imaged quasars is highly sensitive to redshift and the uncertain slope of the bright end of the luminosity function, beta_h. For beta_h=2.58 (3.43) we find that at z~4.3 and i*<20.0 the fraction is ~4% (13%) while at z~6 and z*<20.2 the fraction is ~7% (30%). (ii) The distribution of magnifications is heavily skewed; sources having the redshift and luminosity of the SDSS z>5.8 quasars acquire median magnifications of med(mu_obs)~1.1-1.3 and mean magnifications of ~5-50. Estimates of the quasar luminosity density at high redshift must therefore filter out gravitationally-lensed sources. (iii) The flux in the Gunn-Peterson trough of the highest redshift (z=6.28) quasar is known to be f_lambda<3 10^-19 erg/sec/cm^2/Angstrom. Should this quasar be multiply imaged, we estimate a 40% chance that light from the lens galaxy would have contaminated the same part of the quasar spectrum with a higher flux. Hence, spectroscopic studies of the epoch of reionization need to account for the possibility that a lens galaxy, which boosts the quasar flux, also contaminates the Gunn-Peterson trough. (iv) Microlensing by stars should result in ~1/3 of multiply imaged quasars in the z>5.8 catalog varying by more than 0.5 magnitudes over the next decade. The median equivalent width would be lowered by ~20% with respect to the intrinsic value due to differential magnification of the continuum and emission-line regions.Comment: 27 pages, 10 figures. Expansion on the discussion in astro-ph/0203116. Replaced with version accepted for publication in Ap

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

Self-Regulated Growth of Supermassive Black Holes in Galaxies as the Origin of the Optical and X-ray Luminosity Functions of Quasars

We postulate that supermassive black-holes grow in the centers of galaxies until they unbind the galactic gas that feeds them. We show that the corresponding self-regulation condition yields a correlation between black-hole mass (Mbh) and galaxy velocity dispersion (sigma) as inferred in the local universe, and recovers the observed optical and X-ray luminosity functions of quasars at redshifts up to z~6 based on the hierarchical evolution of galaxy halos in a Lambda-CDM cosmology. With only one free parameter and a simple algorithm, our model yields the observed evolution in the number density of optically bright or X-ray faint quasars between 2<z<6 across 3 orders of magnitude in bolometric luminosity and 3 orders of magnitude in comoving density per logarithm of luminosity. The self-regulation condition identifies the dynamical time of galactic disks during the epoch of peak quasar activity (z~2.5) as the origin of the inferred characteristic quasar lifetime of ~10 million years. Since the lifetime becomes comparable to the Salpeter e-folding time at this epoch, the model also implies that the Mbh-sigma relation is a product of feedback regulated accretion during the peak of quasar activity. The mass-density in black-holes accreted by that time is consistent with the local black-hole mass density of ~(0.8-6.3) times 10^5 solar masses per cubic Mpc, which we have computed by combining the Mbh-sigma relation with the measured velocity dispersion function of SDSS galaxies (Sheth et al.~2003). Applying a similar self-regulation principle to supernova-driven winds from starbursts, we find that the ratio between the black hole mass and the stellar mass of galactic spheroids increases with redshift as (1+z)^1.5 although the Mbh-sigma relation is redshift-independent.Comment: 10 pages, 5 figures, submitted to Ap

Effect of Gravitational Lensing on Measurements of the Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect of a cluster of galaxies is usually measured after background radio sources are removed from the cluster field. Gravitational lensing by the cluster potential leads to a systematic deficit in the residual intensity of unresolved sources behind the cluster core relative to a control field far from the cluster center. As a result, the measured decrement in the Rayleigh-Jeans temperature of the cosmic microwave background is overestimated. We calculate the associated systematic bias which is inevitably introduced into measurements of the Hubble constant using the SZ effect. For the cluster A2218, we find that observations at 15 GHz with a beam radius of 0'.4 and a source removal threshold of 100 microJy underestimate the Hubble constant by 6-10%. If the profile of the gas pressure declines more steeply with radius than that of the dark matter density, then the ratio of lensing to SZ decrements increases towards the outer part of the cluster.Comment: 11 pages, 3 figures, submitted to ApJ

Probing the Mass Fraction of MACHOs in Extragalactic Halos

Current microlensing searches calibrate the mass fraction of the Milky Way halo which is in the form of Massive Compact Halo Objects (MACHOs). We show that surveys like the Sloan Digital Sky Survey (SDSS) can probe the same quantity in halos of distant galaxies. Microlensing of background quasars by MACHOs in intervening galaxies would distort the equivalent width distribution of the quasar emission lines by an amplitude that depends on the projected quasar-galaxy separation. For a statistical sample of detectable at the >2sigma level out to a quasar-galaxy impact parameter of several tens of kpc, as long as extragalactic halos are made of MACHOs. Detection of this signal would test whether the MACHO fraction inferred for the Milky-Way halo is typical of other galaxies.Comment: 12 pages, 2 figures, submitted to ApJ Letter

Descending from on high: Lyman series cascades and spin-kinetic temperature coupling in the 21 cm line

We examine the effect of Lyman continuum photons on the 21 cm background in the high-redshift universe. The brightness temperature of this transition is determined by the spin temperature T_s, which describes the relative populations of the singlet and triplet hyperfine states. Once the first luminous sources appear, T_s is set by the Wouthuysen-Field effect, in which Lyman-series photons mix the hyperfine levels. Here we consider coupling through n>2 Lyman photons. We first show that coupling (and heating) from scattering of Lyman-n photons is negligible, because they rapidly cascade to lower-energy photons. These cascades can result in either a Lyman-alpha photon -- which will then affect T_s according to the usual Wouthuysen-Field mechanism -- or photons from the 2s -> 1s continuum, which escape without scattering. We show that a proper treatment of the cascades delays the onset of strong Wouthuysen-Field coupling and affects the power spectrum of brightness fluctuations when the overall coupling is still relatively weak (i.e., around the time of the first stars). Cascades damp fluctuations on small scales because only ~ 1/3 of Lyn photons cascade through Lyman-alpha, but they do not affect the large-scale power because that arises from those photons that redshift directly into the Lyman-alpha transition. We also comment on the utility of Lyman-n transitions in providing "standard rulers" with which to study the high-redshift universe.Comment: Accepted by MNRAS. 10 pages, 8 figures. Minor revisions + corrected normalisation of figure