Nonlinear density evolution from an improved spherical collapse model

We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, $\delta$. The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of $\delta$. The key new idea is a Taylor series expansion in ($1/\delta$) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two point correlation function.Comment: 11 pages, 6 figures. Final version, contains added discussion and modified figures to match the accepted versio

Stock Option Expense, Forward-Looking Information, and Implied Volatilities of Traded Options

Prior research generally finds that firms underreport option expense by managing assumptions underlying option valuation (e.g. they shorten the expected option lives), but it fails to document management of a key assumption, the one concerning expected stock-price volatility. Using a new methodology, we address two questions: (1) To what extent do companies follow the guidance in FAS 123 and use forward looking information in addition to the readily available historical volatility in estimating expected volatility? (2) What determines the cross-sectional variation in the reliance on forward looking information? We find that firms use both historical and forward-looking information in deriving expected volatility. We also find, however, that the reliance on forward-looking information is limited to situations where this reliance results in reduced expected volatility and thus smaller option expense. We interpret this finding as managers opportunistically use the discretion in estimating expected volatility afforded by FAS 123. In support of this interpretation, we also find that managerial incentives play a key role in this opportunism

Statistical properties of Faraday rotation measure from large-scale magnetic fields in intervening disc galaxies

To constrain the large-scale magnetic field strengths in cosmologically distant galax- ies, we derive the probability distribution function of Faraday rotation measure (RM) when random lines of sight pass through a sample of disc galaxies, with axisymmetric large-scale magnetic fields. We find that the width of the RM distribution of the galaxy sample is directly related to the mean large-scale field strength of the galaxy population, provided the dispersion within the sample is lower than the mean value. In the absence of additional constraints on parameters describing the magneto-ionic medium of the intervening galaxies, and in the situation where RMs produced in the intervening galaxies have already been statistically isolated from other RM contributions along the lines of sight, our simple model of the magneto-ionic medium in disc galaxies suggests that the mean large-scale magnetic field of the population can be measured to within ~ 50% accuracy.Comment: 4 pages, Proceedings of FM8 "New Insights in Extragalactic Magnetic Fields", XXXth General Assembly of the IAU, Vienna, August 20-31, 201

The Gas Accretion Rate of Star-forming Galaxies over the last 4 Gyr

Star-forming galaxies are believed to replenish their atomic gas reservoir, which is consumed in star-formation, through accretion of gas from their circumgalactic mediums (CGMs). However, there are few observational constraints today on the gas accretion rate in external galaxies. Here, we use our recent measurement of the scaling relation between the atomic hydrogen (HI) mass $M_{HI}$ and the stellar mass $M_*$ in star-forming galaxies at $z \approx 0.35$, with the relations between the star-formation rate (SFR) and $M_*$, and the molecular gas mass $M_{Mol}$ and $M_*$, and the assumption that star-forming galaxies evolve along the main sequence, to determine the evolution of the neutral gas reservoir and the average net gas accretion rate onto the disks of star-forming galaxies over the past 4 Gyr. For galaxies with $M_* \gtrsim 10^9 M_{\odot}$ today, we find that both $M_*$ and $M_{HI}$ in the disk have increased, while $M_{Mol}$ has decreased, since $z \sim 0.35$. The average gas accretion rate onto the disk over the past 4 Gyr is similar to the average SFR over this period, implying that main-sequence galaxies have maintained a stable HI reservoir, despite the consumption of gas in star-formation. We obtain an average net gas accretion rate (over the past 4 Gyr) of $\approx 6 M_{\odot} yr^{-1}$ for galaxies with the stellar mass of the Milky Way. At low redshifts, $z \lesssim 0.4$, the reason for the decline in the cosmic SFR density thus appears to be the inefficiency in the conversion of atomic gas to molecular gas, rather than insufficient gas accretion from the CGM.Comment: Accepted for publication in The Astrophysical Journal Letter