arXiv subjects

Daniel E. Holz

Publications and source records attributed to Daniel E. Holz.

123 records · Page 7Linked to original sources

arXiv2002

Retro-MACHOs: Pi in the sky?

Shine a flashlight on a black hole, and one is greeted with the return of a series of concentric rings of light. For a point source of light, and for perfect alignment of the lens, source, and observer, the rings are of infinite brightness (in the limit of geometric optics). In this manner, distant black holes can be revealed through their reflection of light from the Sun. Such retro-MACHO events involve photons leaving the Sun, making a Pi rotation about the black hole, and then returning to be detected at the Earth. Our calculations show that, although the light return is quite small, it may nonetheless be detectable for stellar-mass black holes at the edge of our solar system. For example, all (unobscured) black holes of mass M or greater will be observable to a limiting magnitude m, at a distance given by: 0.02 pc x \sqrt[3]{10^{(m-30)/2.5} (M/10 M_sun)^2}. Discovery of a Retro-MACHO offers a way to directly image the presence of a black hole, and would be a stunning confirmation of strong-field general relativity.

astro-ph↗

arXiv2002

Corrective lenses for high redshift supernovae

Weak lensing of high-redshift Type Ia supernovae induces an external dispersion in their observed standard candle brightnesses, comparable in magnitude to the intrinsic dispersion for redshifts z>1. The same matter fluctuations responsible for the magnification of distant supernovae also generate shear in the images of background galaxies. We investigate the possibility of using lensing shear maps constructed from galaxies surrounding the supernovae as a means of correcting the lensing-induced magnification dispersion. We find that a considerable fraction of the lensing dispersion derives from sub-arcminute scales, which are not probed by shear maps smoothed on arcminute scales. We thus find that weak lensing shear maps will be of only limited value in reducing the weak lensing magnification fluctuations of supernovae.

astro-ph↗

arXiv2002

A universal probability distribution function for weak-lensing amplification

We present an approximate form for the weak lensing magnification distribution of standard candles, valid for all cosmological models, with arbitrary matter distributions, over all redshifts. Our results are based on a universal probability distribution function (UPDF), $P(η)$, for the reduced convergence, $η$. For a given cosmological model, the magnification probability distribution, $P(μ)$, at redshift $z$ is related to the UPDF by $P(μ)=P(η)/2|κ_{min}|$, where $η=1+(μ-1)/(2|κ_{min}|)$, and $κ_{min}$ (the minimum convergence) can be directly computed from the cosmological parameters ($Ω_m$ and $Ω_Λ$). We show that the UPDF can be well approximated by a three-parameter stretched Gaussian distribution, where the values of the three parameters depend only on $ξ_η$, the variance of $η$. In short, all possible weak lensing probability distributions can be well approximated by a one-parameter family. We establish this family, normalizing to the numerical ray-shooting results for a $Λ$CDM model by Wambsganss et al. (1997). Each alternative cosmological model is then described by a single function $ξ_η(z)$. We find that this method gives $P(μ)$ in excellent agreement with numerical ray-tracing and three-dimensional shear matrix calculations, and provide numerical fits for three representative models (SCDM, $Λ$CDM, and OCDM). Our results provide an easy, accurate, and efficient method to calculate the weak lensing magnification distribution of standard candles, and should be useful in the analysis of future high-redshift supernova data.

astro-ph↗

arXiv2001

Gravitational Wave Emission From Core-Collapse of Massive Stars

We derive estimates for the characteristics of gravitational radiation from stellar collapse, using recent models of the core-collapse of Chandrasekhar mass white dwarfs (accretion induced collapse), core-collapse supernovae and collapsars, and the collapse of very massive stars (~> 300 Msun). We study gravitational-wave emission mechanisms using several estimation techniques, including two-dimensional numerical computation of quadrupole wave emission, estimates of bar-mode strength, estimates of r-mode emission, and estimates of waves from black hole ringing. We also review the rate at which the relevant collapses are believed to occur, which has a major impact on their relevance as astrophysical sources. Although the latest supernova progenitor simulations produce cores rotating much slower than those used in the past, we find that bar-mode and r-mode instabilities from core-collapse supernovae remain among the leading candidate sources for LIGO-II. Accretion induced collapse (AIC) of a white dwarf could produce gravitational-wave signals similar to those from core-collapse. In the models that we examine, such collapses are not unstable to bar modes; we note that models recently examined by Liu and Lindblom, which have slightly more angular momentum, are certainly unstable to bar formation. Because AIC events are probably 1,000 times less common than core-collapse supernovae, the typical AIC event will be much further away, and thus the observed waves will be much weaker. In the most optimistic circumstances, we find it may be possible to detect gravitational waves from the collapse of 300 Msun Population III stars.

astro-ph↗

arXiv2001

Seeing double: strong gravitational lensing of high-redshift supernovae

With the advent of large, deep surveys, the observation of a strongly gravitationally lensed supernova becomes increasingly likely. High-redshift surveys continue apace, with a handful of type Ia supernovae observed to date at redshifts of one or greater. In addition, a satellite (the Supernova/Acceleration Probe [SNAP]) has been proposed dedicated to observing thousands of supernovae per year out to a redshift of 1.7. Although it is exceedingly unlikely that we will see a multiply-imaged supernova from ongoing surveys, we find that SNAP would observe at least eight such events per year. Since having a standard candle is inessential to most lensing studies, SNAP's large sample of type II supernovae contributes to this rate. Each case of strong lensing allows for a precise determination of time delays, image separations, and relative image magnifications, and the SNAP strong-lensing database will offer measures of $Ω_m$, $Ω_Λ$, and $H_0$, independent of SNAP's primary goal of establishing the distance-redshift relation. These systems also constrain models for the matter density profiles of galaxies and clusters. Furthermore, lensed type Ia supernovae afford the opportunity to break the mass-sheet degeneracy found in many lensing measurements.

astro-ph↗

arXiv2001

Hydrostatic Expansion and Spin Changes During Type I X-Ray Bursts

We present calculations of the spin-down of a neutron star atmosphere due to hydrostatic expansion during a Type I X-ray burst. We show that (i) Cumming and Bildsten overestimated the spin-down of rigidly-rotating atmospheres by a factor of two, and (ii) general relativity has a small (5-10%) effect on the angular momentum conservation law. We rescale our results to different neutron star masses, rotation rates and equations of state, and present some detailed rotational profiles. Comparing with recent observations of large frequency shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if the atmosphere rotates rigidly is a factor of two to three less than the observed values. If differential rotation is allowed to persist, we find that the upper layers of the atmosphere spin down by an amount comparable to the observed values; however, there is no compelling reason to expect the observed spin frequency to be that of only the outermost layers. We conclude that hydrostatic expansion and angular momentum conservation alone cannot account for the largest frequency shifts observed during Type I bursts.

astro-ph↗

arXiv2001

Collisional Dark Matter and Scalar Phantoms

As has been previously proposed, a minimal modification of the standard $SU(3)\times SU(2)\times U(1)$ theory provides a viable dark matter candidate. Such a particle, a scalar gauge singlet, is naturally self-interacting---making it of particular interest given recent developments in astrophysics. We review this dark matter candidate, with reference to the parameter ranges currently under discussion.

hep-ph↗

arXiv2001

Constant Crunch Coordinates for Black Hole Simulations

We reinvestigate the utility of time-independent constant mean curvature foliations for the numerical simulation of a single spherically-symmetric black hole. Each spacelike hypersurface of such a foliation is endowed with the same constant value of the trace of the extrinsic curvature tensor, $K$. Of the three families of $K$-constant surfaces possible (classified according to their asymptotic behaviors), we single out a sub-family of singularity-avoiding surfaces that may be particularly useful, and provide an analytic expression for the closest approach such surfaces make to the singularity. We then utilize a non-zero shift to yield families of $K$-constant surfaces which (1) avoid the black hole singularity, and thus the need to excise the singularity, (2) are asymptotically null, aiding in gravity wave extraction, (3) cover the physically relevant part of the spacetime, (4) are well behaved (regular) across the horizon, and (5) are static under evolution, and therefore have no ``grid stretching/sucking'' pathologies. Preliminary numerical runs demonstrate that we can stably evolve a single spherically-symmetric static black hole using this foliation. We wish to emphasize that this coordinatization produces $K$-constant surfaces for a single black hole spacetime that are regular, static and stable throughout their evolution.

gr-qc↗

arXiv1999

Limits on the Density of Compact Objects from High Redshift Supernovae

Due to the effects of gravitational lensing, the magnification distribution of high redshift supenovae can be a powerful discriminator between smooth dark matter and dark matter consisting of compact objects. We use high resolution N-body simulations in combination with the results of simulations with compact objects to determine the magnification distribution for a Universe with an arbitrary fraction of the dark matter in compact objects. Using these distributions we determine the number of type Ia SNe required to measure the fraction of matter in compact objects. It is possible to determine a 20% fraction of matter in compact objects with 100-400 well measured SNe at $z \sim 1$, assuming the background cosmological model is well determined.

astro-ph↗

arXiv1998

Apparent horizons in simplicial Brill wave initial data

We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.

gr-qc↗

arXiv1998

Gravitational Lensing Limits on the Average Redshift of Gamma-Ray Bursts

The lack of bright host galaxies in several recently examined gamma-ray burst (GRB) error boxes suggests that the redshifts of cosmological GRBs may be significantly higher than previously believed. On the other hand, the non-detection of multiple images in the BATSE 4B catalog implies an upper limit on the average redshift of GRBs. Here, we calculate an upper limit to , independent of the physical model for GRBs, using a new statistical lensing method that removes distance ambiguities, and thus permits accurate computation of the lensing rate at high z. The upper limit on depends directly on the cosmological parameters Omega and Lambda. If there are no multiple images among the brightest 80% of the first 1802 bursts in the BATSE 4B catalog, then, at the 95% confidence level, is less than 2.2, 2.8, 4.3, or 5.3 for (Omega,Lambda) values of (0.3, 0.7), (0.5, 0.5), (0.5, 0.0), or (1.0, 0.0), respectively. The 68% upper limit to the average redshift is comparable to or less than the median redshift of GRBs in scenarios in which the GRB rate is proportional to the rate of star formation, for any cosmology. The uncertainty in the lensing rate --- arising from uncertainties in the cosmological parameters and in the number density and average velocity dispersion of galaxies --- will be reduced significantly in the next few years by a new generation of experiments and surveys. Moreover, the continued increase in the number of GRBs observed by BATSE will greatly constrain their redshift distribution.

astro-ph↗

arXiv1998

Lensing and high-z supernova surveys

Gravitational lensing causes the distribution of observed brightnesses of standard candles at a given redshift to be highly non-gaussian. The distribution is strongly, and asymmetrically, peaked at a value less than the expected value in a homogeneous Robertson-Walker universe. Therefore, given any small sample of observations in an inhomogeneous universe, the most likely observed luminosity is at flux values less than the Robertson-Walker value. This paper explores the impact of this systematic error due to lensing upon surveys predicated on measuring standard candle brightnesses. We re-analyze recent results from the high-z supernova team (Riess et al. 1998), both when most of the matter in the universe is in the form of compact objects (represented by the empty-beam expression, corresponding to the maximal case of lensing), and when the matter is continuously distributed in galaxies. We find that the best-fit model remains unchanged (at Omega_m=0, Omega_Lambda=0.45), but the confidence contours change size and shape, becoming larger (and thus allowing a broader range of parameter space) and dropping towards higher values of matter density, Omega_m (or correspondingly, lower values of the cosmological constant, Omega_Lambda). These effects are slight when the matter is continuously distributed. However, the effects become considerably more important if most of the matter is in compact objects. For example, neglecting lensing, the Omega_m=0.5, Omega_Lambda=0.5 model is more than 2 sigma away from the best fit. In the empty-beam analysis, this cosmology is at 1 sigma.

astro-ph↗

arXiv1998

A New Method for Determining Cumulative Gravitational Lensing Effects in Inhomogeneous Universes

We present a new approach to calculating the statistical distributions for magnification, shear, and rotation of images of cosmological sources due to gravitational lensing. In this approach one specifies an underlying Robertson-Walker cosmological model together with relevant information on the clumping of matter on scales much smaller than the Hubble radius. The geodesic deviation equation is then integrated backwards in time until the desired redshift is reached, using a Monte Carlo procedure wherein each photon beam in effect ``creates its own universe'' as it propagates. The approach is somewhat similar to that used in ``Swiss cheese'' models, but the ``cheese'' has been completely eliminated, the matter distribution in the ``voids'' need not be spherically symmetric, and the total mass in each void need equal the corresponding Robertson-Walker mass only on average. We show that when the matter in the universe consists of point masses, the statistical distributions of the lensing images are essentially independent of both the mass spectrum and clustering properties of the point masses, provided that the clustering is spherical. We apply our results (i) to argue that the positive correlation recently found between quasar luminosity and the number of absorption line systems is not likely to be due to lensing, and (ii) to determine the amount of ``noise'' and possible bias produced by lensing in measurements of $q_0$ using distant supernovae.

astro-ph↗

arXiv1995

Photon Statistics Limits for Earth-Based Parallax Measurements of MACHO Events

We analyze the limitations imposed by photon counting statistics on extracting useful information about MACHOs from Earth-based parallax observations of microlensing events. We find that if one or more large (say $2.5\,\rm m$) telescopes are dedicated to observing a MACHO event for several nights near maximum amplification, then it is possible, in principle, to measure the velocity of the MACHO well enough to distinguish between disk and halo populations for events with $ω{A_m}\!^2 \gta 1\,\rm day^{-1}$, where $ω^{-1}$ denotes the timescale of the event and $A_m$ denotes its maximum amplification. Thus, if it turns out to be possible to reduce all other sources of error to below that of photon statistics, it may be feasible to do useful Earth-based parallax observations for high amplification events.

astro-ph↗

arXiv1994

Spin Dynamics of the LAGEOS Satellite in Support of a Measurement of the Earth's Gravitomagnetism

LAGEOS is an accurately-tracked, dense spherical satellite covered with 426 retroreflectors. The tracking accuracy is such as to yield a medium term (years to decades) inertial reference frame determined via relatively inexpensive observations. This frame is used as an adjunct to the more difficult and data intensive VLBI absolute frame measurements. There is a substantial secular precession of the satellite's line of nodes consistent with the classical, Newtonian precession due to the non-sphericity of the earth. Ciufolini has suggested the launch of an identical satellite (LAGEOS-3) into an orbit supplementary to that of LAGEOS-1: LAGEOS-3 would then experience an equal and opposite classical precession to that of LAGEOS-1. Besides providing a more accurate real-time measurement of the earth's length of day and polar wobble, this paired-satellite experiment would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite, and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. Consequently, we undertake here a theoretical effort to model the spin ndynamics of LAGEOS. In this paper we present our preliminary results.

gr-qc↗