The distribution of microlensed light curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.Comment: 12 pages, including 9 figures. Submitted to M.N.R.A.S. Revised version includes a short section on the applicability of the metho

Smooth Boundaries to Cosmological HII Regions from Galaxy Clustering

The HII regions around quasars and galaxies at redshifts beyond the epoch of reionisation will provide prime targets for upcoming 21cm campaigns using a new generation of low-frequency radio observatories. Here we show that the boundaries of these HII regions will not be sharp. Rather, the clustering of sources near massive galaxies results in a neutral fraction that rises gradually towards large radii from an interior value near zero. A neutral fraction corresponding to the global background value is typically reached at a distance of 2-5 times the radius of the HII region around the central massive galaxy.Comment: 5 Pages, 3 figures. Submitted to MNRA

The stellar mass function and star formation rate-stellar mass relation of galaxies at z ~ 4 - 7

We investigate the evolution of the star formation rate-stellar mass relation (SFR-M*) and Galaxy Stellar Mass Function (GSMF) of z ~ 4-7 galaxies, using cosmological simulations run with the smoothed particle hydrodynamics code P-GADGET3(XXL). We explore the effects of different feedback prescriptions (supernova driven galactic winds and AGN feedback), initial stellar mass functions and metal cooling. We show that our fiducial model, with strong energy-driven winds and early AGN feedback, is able to reproduce the observed stellar mass function obtained from Lyman-break selected samples of star forming galaxies at redshift 6 < z < 7. At z ~ 4, observed estimates of the GSMF vary according to how the sample was selected. Our simulations are more consistent with recent results from K-selected samples, which provide a better proxy of stellar masses and are more complete at the high mass end of the distribution. We find that in some cases simulated and observed SFR-M* relations are in tension, and this can lead to numerical predictions for the GSMF in excess of the GSMF observed. By combining the simulated SFR(M*) relationship with the observed star formation rate function at a given redshift, we argue that this disagreement may be the result of the uncertainty in the SFR-M* (Luv-M*) conversion. Our simulations predict a population of faint galaxies not seen by current observations.Comment: 23 Pages, 13 figures, modified to match accepted version to MNRA

Luminosity Functions of Lyman Alpha Emitting Galaxies and Cosmic Reionization of Hydrogen

Recent observations imply that the observed number counts of Lya Emitters (LAEs) evolved significantly between z=5.7 and z=6.5. It has been suggested that this was due to a rapid evolution in the ionisation state, and hence transmission of the IGM which caused Lya flux from z=6.5 galaxies to be more strongly suppressed. In this paper we consider the joint evolution of the Lya and UV luminosity functions (LFs) and show that the IGM transmission evolved between z=6.5 and z=5.7 by a factor 1.1 <R < 1.8 (95% CL). This result is insensitive to the underlying model of the Lya LF (as well as cosmic variance). Using a model for IGM transmission, we find that the evolution of the mean IGM density through cosmic expansion alone may result in a value for the ratio of transmissions as high as R=1.3. Thus, the existing LFs do not provide evidence for overlap. Furthermore, the constraint R<1.8 suggests that the Universe at z=6.5 was more than half ionised by volume, i.e. x_i,V>0.5.Comment: MNRAS in press. Constraints from rest-frame UV LF added. Discussion added on cosmic variance. Lower limit on x_i,V lowered to 0.5 (from 0.8

Improved Constraints on The Neutral Intergalactic Hydrogen Surrounding Quasars at Redshifts z>6

We analyze the evolution of HII regions around the seven known SDSS quasars at z>6. The comparison between observed and model radii of the HII regions generated by these quasars individually, suggests that the surrounding intergalactic hydrogen is significantly neutral. When all constraints are combined, the existing quasar sample implies a volume averaged neutral fraction that is larger than 10% at z>6. This limited sample permits a preliminary analysis of the correlations between the quasar parameters, the sizes of their HII regions, and the associated constraints on the neutral hydrogen fraction. We find no evidence in these correlations to contradict the interpretation that the red side of the Gunn-Peterson trough corresponds to the boundary between an HII region and a partially neutral IGM.Comment: 9 pages, 4 figures. Submitted to Ap

The Imprint of Cosmic Reionization on Galaxy Clustering

We consider the effect of reionization on the clustering properties of galaxy samples at intermediate redshifts (z~0.3-5.5). Current models for the reionization of intergalactic hydrogen predict that overdense regions will be reionized early, thus delaying the build up of stellar mass in the progenitors of massive lower-redshift galaxies. As a result, the stellar populations observed in intermediate redshift galaxies are somewhat younger and hence brighter in overdense regions of the Universe. Galaxy surveys would therefore be sensitive to galaxies with a somewhat lower dark matter mass in overdense regions. The corresponding increase in the observed number density of galaxies can be parameterized as a galaxy bias due to reionization. We model this process using merger trees combined with a stellar synthesis code. Our model demonstrates that reionization has a significant effect on the clustering properties of galaxy samples that are selected based on their star-formation properties. The bias correction in Lyman-break galaxies (including those in proposed baryonic oscillation surveys at z<1) is at the level of 10-20% for a halo mass of 10^12 solar masses, leading to corrections factors of 1.5-2 in the halo mass inferred from measurements of clustering length. The reionization of helium could also lead to a sharp increase in the amplitude of the galaxy correlation function at z~3. We find that the reionization bias is approximately independent of scale and halo mass. However since the traditional galaxy bias is mass dependent, the reionization bias becomes relatively more important for lower mass systems. The correction to the bias due to reionization is very small in surveys of luminous red galaxies at z<1.Comment: 17 pages, 6 figures. Submitted to MNRA