arXiv subjects
Publications and source records attributed to Abraham Loeb.
We examine the gravitational lensing effect of a foreground galaxy cluster on the number count statistics of background X-ray sources. The lensing produces a deficit in the number of resolved sources in a ring close to the critical radius of the cluster. This deficit could be detected at the $\sim 3σ$ level with the AXAF-ACIS camera.
We investigate the formation of molecular hydrogen (H_2) in a primordial H+He gas cloud irradiated by a power-law UV flux. We find that at high densities (>1 cm^{-3}) and low temperatures (<10^4 K), the background radiation enhances the formation of H_2 and results in molecular cooling dominating over photoionization heating. This process could accelerate the collapse and fragmentation of dense objects at high redshifts.
I calculate the contribution of Bremsstrahlung emission from Lyman-alpha absorption clouds to the brightness of the microwave sky. The calculation is based only on the assumption that the clouds below the Lyman-limit are in photoionization equilibrium with a UV background radiation, and avoids any uncertainty about the clumpiness of the gas. I predict a minimum fluctuation amplitude in the Rayleigh-Jeans regime of DeltaT/T = 10^{-5.5+-0.4}*J_21*(L/5cm)^2, which varies over characteristic angular scales of 1-100'', where L is the observed wavelength and J_21 is a weighted redshift average of the UV background intensity at the Lyman-limit in units of 10^{-21} erg cm^{-2} s^{-1} Hz^{-1} sr^{-1}. Detection of this signal can be used to map the intergalactic hydrogen distribution and to calibrate the UV background at high redshifts. Existing VLA observations constrain J_21<10^{1.3+-0.4}, unless some of the extended flat-spectrum sources which were detected are Lyman-alpha absorption systems.
We investigate the early formation of bound objects with masses comparable to the cosmological Jeans mass (10^5 solar masses). We follow the growth of isolated spherically symmetric density peaks starting from the linear perturbative regime. The initial parameters correspond to density peaks of various widths and heights in a Cold Dark Matter cosmology. We use a one-dimensional spherical Lagrangian hydrodynamics code to follow the dynamical, thermal, and non-equilibrium chemical evolution of the gas. The system includes a collisionless dark matter component and a baryonic component composed of the nine species H, H^-, H^+, He, He^+, He^{++}, H_2, H_2^+, and e^-. All relevant chemical reactions between these species and their cooling mechanisms are included in the calculations. We find that radiative cooling by H_2 affects the collapse dynamics of the gas only after it has already virialized and become part of the bound object. Therefore, radiative cooling is unlikely to have triggered the initial collapse of perturbations at redshifts z>10. Nevertheless, objects with baryonic masses well below the linear-theory Jeans mass (<10^3 solar masses) collapse due to shell crossing by the dark matter. Such objects could be the progenitors of a primordial population of high-mass stars in the intergalactic medium.
We use Monte Carlo realizations of halo formation histories and a spherical accretion model to calculate the expected scatter in the velocity dispersions of galactic halos of a given mass due to differences in their formation times. Assuming that the rotational velocity of a spiral galaxy is determined by the velocity dispersion of its halo and that its luminosity is related to its total baryonic mass, this scatter translates to a minimum intrinsic scatter in the Tully-Fisher relation. For popular cosmological models we find that the scatter due to variations in formation histories is by itself greater than allowed by observations. Unless halos of spiral galaxies formed at high redshift (z>1) and did not later accrete any significant amount of mass, the Tully-Fisher relation is not likely to be the direct result of cosmological initial conditions but rather a consequence of a subsequent feedback process.
Damped Lyman-alpha absorbers are believed to be associated with galactic disks. We show that gravitational lensing can therefore affect the statistics of these systems. First, the magnification bias due to lensing raises faint QSOs above a given magnitude threshold and thereby enhances the probability for observing damped absorption systems. Second, the bending of light rays from the source effectively limits the minimum impact parameter of the line-of-sight relative to the center of the absorber, thus providing an upper cut-off to the observed neutral hydrogen (HI) column density. The combination of these effects yields a pronounced peak in the observed abundance of absorbers with high column densities (>2*10^{21} cm^{-2}) and low redshifts (z<1). The inferred value of the cosmological density parameter of neutral hydrogen, Omega_{HI}, increases with increasing redshift and luminosity of the sources even if the true HI density remains constant. This trend resembles the observed evolution of Omega_{HI}(z). Damped Lyman-alpha absorbers with column densities >10^{21} cm^{-2} and redshifts 0.5<z<1 are reliable flags for lensed QSOs with a close pair of images separated by 0.3 arcsec. Detection of these gravitational lensing signatures with the Hubble Space Telescope can be used to constrain the depth of the absorber potential-wells and the cosmological constant.
The properties of axisymmetric accretion flows of cold adiabatic gas with zero total energy in the vicinity of a Newtonian point mass are characterized by a single dimensionless parameter, the thickness of incoming flow. In the limit of thin accretion flows with vanishing thickness, we show that the governing equations become self-similar, involving no free parameters. We study numerically thin accretion flows with finite thickness as well as those with vanishing thickness. Mass elements of the incoming flow enter the computational regime as thin rings. In the case with finite thickness, after a transient period of initial adjustment, an almost steady-state accretion shock with a small oscillation amplitude forms, confirming the previous work by Molteni, Lanzafame, \& Chakrabarti (1994). The gas in the region of vorticity between the funnel wall and the accretion shock follows closed streamlines, forming a torus. This torus, in turn, behaves as an effective barrier to the incoming flow and supports the accretion shock which reflects the incoming gas away from the equatorial plane. The postshock flow, which is further accelerated by the pressure gradient behind the shock, goes through a second shock which then reflects the flow away from the symmetry axis to form a conical outgoing wind. As the thickness of the inflowing layer decreases (or if the ratio of the half thickness to the distance to the funnel wall along the equatorial plan is smaller than $\sim0.1$), the flow becomes unstable. In the case with vanishing thickness, the accretion shock formed to stop the incoming flow behind the funnel wall oscillates quasi-periodically with an amplitude comparable to the thickness. The structure between the funnel wall and the accretion shock is destroyed as the shock moves inwards toward the central mass and re-generated
The standard light curve of a microlensing event provides only two constraints on the six unknown parameters of the lens. We show that narrow-band photometry during a microlensing event of a giant star can in addition determine the angular radius of the Einstein ring and the proper motion of the lens. This possibility results from the fact that the extended atmospheres of giants emit the cores of resonant lines primarily from a narrow ring (limb brightening). The radius of the emission ring can be determined to a precision of 20% by detailed spectroscopic observations of the source after the lensing event has ended. A considerable fraction of the clump giant stars in the bulge have a ring radius >10^{12} cm, within the range of Einstein radii for sub-solar mass lenses. The extended thin ring also provides a sensitive probe of possible planetary companions as it sweeps across the lens plane. The ring signature can be detected photometrically, using a narrow-band filter centered on the CaII K line at 3933 A.
We discuss several constraints on the properties of gamma-ray bursts (GRB) at cosmological distances. First we use the requirement that burst sources must be optically thin to pair production by photon-photon collisions in order to produce the observed nonthermal spectra. We derive probability distributions for the minimum Lorentz expansion factor, the radiation energy, the maximum baryonic mass, and the maximum surrounding gas density in the events, based on 254 events from the second BATSE catalog. Secondly, the time variabilities of the bursts in the BATSE catalog are used to place an upper bound on the curvature radius of the emitting surface in the events. This is based on the requirement that the emitting region seen by the observer must be sufficiently small to produce the observed variability without violating causality. Finally, we discuss the association of cosmological GRB with galaxies. We consider eight bright and well-localized bursts detected by the Pioneer Venus Orbiter, whose positional error boxes contain no bright galaxies. Using the local luminosity function of galaxies, we calculate the probability for not seeing the GRB host galaxy. This probability tends to increase as the width of the GRB luminosity function increases. However, the allowed width of the GRB luminosity function is restricted by the number-count statistics of the bursts.
Groups and clusters of galaxies hosting a quasar can be found through the detection of Lyman-alpha absorption lines beyond the quasar redshift. The effect occurs whenever the distortion to the redshift distribution of Lyman-alpha clouds induced by the cluster potential extends beyond the proximity effect of the quasar. Based on CDM cosmological models for the evolution of structure, we predict the probability for finding lines beyond the quasar redshift ($z_{abs}>z_Q$) under the assumption that the physical properties of Lyman-alpha clouds are not affected by flows on large scales (1 Mpc and more) in the quasi-linear regime. If quasars randomly sample the underlying galaxy distribution, the expected number of lines with $z_{abs}>z_Q$ per quasar can be as high as 0.25[(dN/dz)/350] at $z=2$, where $dN/dz$ is the number of Lyman-alpha lines per unit redshift far from the quasar. The probability is enhanced if quasars typically reside in small groups of galaxies. A statistical excess of Lyman-alpha lines is expected near very dim quasars or around metal absorption systems. Due to clustering, the standard approach to the proximity effect overestimates the ionizing background flux at high redshifts by up to a factor of 3. This result weakens the discrepancy between the deduced background flux and the contribution from known populations of quasars.
Quasars are the earliest objects known to exist. We examine their origin in the context of popular models for structure formation in the universe. We show that seeds for quasar black holes could have originated from the initial cosmological collapse of overdense regions with unusually small rotation. Most of these seeds have a mass of order 10^6 solar masses, just above the cosmological Jeans mass. For Cold Dark Matter cosmologies, we find of order one seed black hole per bright galaxy. After the galaxy forms, the seeds inside its bulge sink to the center by dynamical friction. We also describe a few empirical methods to study the properties of quasars and their environments. These include: probing quasar hosts through [C II] emission, finding quasar lifetimes from the ``proximity effect'' along two lines of sight, and measuring the amplitude of clustering at high redshifts through the detection of Lyman-alpha clouds beyond the quasar redshift.
We show that seeds for quasar black holes could have originated from the initial cosmological collapse of overdense regions with unusually small rotation. The gas in these rare regions collapses into a compact disk that shrinks on a short viscous time scale. Using an analytical model, we calculate the low-spin tail of the probability distribution of angular momenta for objects that collapse out of a Gaussian random field of initial density perturbations. The population of low-spin systems is significant for any viable power spectrum of primordial density perturbations. Most objects form just above the cosmological Jeans mass (\sim 10^5 M_sun) at high redshifts z>10. In the standard cold dark matter cosmology, the comoving density of 10^{6-7} M_sun objects with viscous evolution times shorter than 10^{6-7} years is about 10^{-3} (h/0.5)^3 Mpc^{-3}, comparable to the local density of bright galaxies. The seed black holes tend to reside within larger mass systems that collapse later and supply the gas needed for the bright quasar activity.
The central mass distribution of clusters of galaxies can be inferred from gravitationally lensed arcs with known redshifts. For the Abell cluster 2218, this method yields a core mass which is larger by a factor of $2.5 \pm 0.5$ than the value deduced from X-ray observations, under the assumptions that the gas is supported by thermal pressure and that the cluster is spherical. We show that a non-thermal pressure support is the most plausible explanation for this discrepancy. Such a pressure can be naturally provided by strong turbulence and equipartition magnetic fields ($\sim 50μ$G) that are tangled on small spatial scales (<10 kpc). The turbulent and magnetic pressures do not affect the measured Sunyaev-Zel'dovich effect for this cluster. Intracluster magnetic fields with a comparable magnitude ($\sim 10^{1-2} μ$G) have already been detected by Faraday rotation in other clusters. If generic, a small-scale equipartition magnetic field should affect the structure of cooling flows and must be included in X-ray determinations of cluster masses.
We present an analytical model for the non-spherical collapse of overdense regions out of a Gaussian random field of initial cosmological perturbations. The collapsing region is treated as an ellipsoid of constant density, acted upon by the quadrupole tidal shear from the surrounding matter. The dynamics of the ellipsoid is set by the ellipsoid self-gravity and the external quadrupole shear. Both forces are linear in the coordinates and therefore maintain homogeneity of the ellipsoid at all times. The amplitude of the external shear is evolved into the non-linear regime in thin spherical shells that are allowed to move only radially according to the mass interior to them. We describe how the initial conditions can be drawn in the appropriate correlated way from a random field of initial density perturbations. By considering many random realizations of the initial conditions, we calculate the distribution of shapes and angular momenta acquired by objects through the coupling of their quadrupole moment to the tidal shear. The average value of the spin parameter, 0.04, is found to be only weakly dependent on the system mass, the mean cosmological density, or the initial power spectrum of perturbations, in agreement with N-body simulations. For the cold dark matter power spectrum, most objects evolve from a quasi-spherical initial state to a pancake or filament and then to complete virialization. Low-spin objects tend to be more spherical. The evolution history of shapes is primarily induced by the external shear and not by the initial triaxiality of the objects. The statistical distribution of the triaxial shapes of collapsing regions can be used to test cosmological models against galaxy surveys on large scales.
We place empirical constraints on the physical properties of $γ-$ray burst events at cosmological distances. In particular we derive probability distributions for the radiation energy $E_γ$, the minimum Lorentz factor $γ_{\rm min}$, the maximum baryonic mass $M_{\rm max}$ and the upper bound on the surrounding gas density $n_{\rm max}$ in the events, based on 169 bursts from the first BATSE catalog. Using peak flux as a distance indicator we probe bursts where the constraints are stronger than average. The resulting variance and skewness of the cosmological probability distributions are calculated in addition to their mean values: $\langle E_γ\rangle=4\times 10^{51} h^{-2} {\rm erg}$, $\langle γ_{\rm min}\rangle= 5\times 10^2$, $\langle M_{\rm max}\rangle=10^{-5}ξ^{-1} M_\odot$, and $\langle (γ/γ_{\rm min})^{-5} n_{\rm max}\rangle\lsim 10^{2} ξ^{-1}{\rm cm^{-3}}$, where $ξ$ is the fraction of the total energy which is converted to $γ-$rays. The distribution of burst energies ends at about $10^{53} {\rm erg}$, close to the binding energy of a neutron star.
It is well known that the standard transport equations violate causality when gradients are large or when temporal variations are rapid. We derive a modified set of transport equations that satisfy causality. These equations are obtained from the underlying Boltzmann equation. We use a simple model for particle collisions which enables us to derive moment equations non-perturbatively, i.e. without making the usual assumption that the distribution function deviates only slightly from its equilibrium value. We apply the model to two problems: particle diffusion and viscous transport. In both cases we show that signals propagate at a finite speed and therefore that the formalism obeys causality. When the velocity gradient is large on the scale of a mean free path, the viscous shear stress is suppressed relative to the prediction of the standard diffusion approximation. The shear stress reaches a maximum at a finite value of the shear amplitude and then decreases as the velocity gradient increases. In the case of a steady Keplerian accretion disk with hydrodynamic turbulent viscosity, the stress-limit translates to an upper bound on the Shakura-Sunyaev $α$-parameter, namely $α<0.07$. The limit on $α$ is much stronger in narrow boundary layers where the velocity shear is larger than Keplerian.
The observed spatial distribution of $γ-$ray bursts indicates that they probably originate at cosmological distances. At this distance scale their variability timescale and flux above MeV imply an initial optical-depth to pair production $> 10^{10}$. This appears to be in conflict with their highly non-thermal spectra. We show that this difficulty can be removed if axion bursts from supernovae are converted to $γ-$rays over cosmological distances. Nonthermal bursts with the relevant flux, duration, variability and spectra are obtained just for the range of axion masses of $10^{-5}-10^{-4}{\rm eV}$ that accounts for the cold dark matter in the universe. The observed rate of $γ-$ray bursts implies that axions should be converted efficiently to photons in only one out of $\sim 10^{4}$ supernovae.
We study the diffusion of helium and other heavy elements in the solar interior by solving exactly the set of flow equations developed by Burgers for a multi-component fluid, including the residual heat-flow terms. No approximation is made concerning the relative concentrations and no restriction is placed on the number of elements considered. We give improved diffusion velocities for hydrogen, helium, oxygen and iron, in the analytic form derived previously by Bahcall and Loeb. These expressions for the diffusion velocities are simple to program in stellar evolution codes and are expected to be accurate to $\sim 15\%$. Our complete treatment of element diffusion can be directly incorporated in a standard stellar evolution code by means of an exportable subroutine, but, for convenience, we also give simple analytical fits to our numerical results.