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

Very Massive Stars in High-Redshift Galaxies

A significant fraction of Lyman Alpha (Lya) emitting galaxies (LAEs) at z> 5.7 have rest-frame equivalent widths (EW) greater than ~100 Angstrom. However only a small fraction of the Lya flux produced by a galaxy is transmitted through the IGM, which implies intrinsic Lya EWs that are in excess of the maximum allowed for a population-II stellar population having a Salpeter mass function. In this paper we study characteristics of the sources powering Lya emission in high redshift galaxies. We propose a simple model for Lya emitters in which galaxies undergo a burst of very massive star formation that results in a large intrinsic EW, followed by a phase of population-II star formation with a lower EW. We confront this model with a range of high redshift observations and find that the model is able to simultaneously describe the following eight properties of the high redshift galaxy population with plausible values for parameters like the efficiency and duration of star formation: i-iv) the UV and Lya luminosity functions of LAEs at z=5.7 and 6.5, v-vi) the mean and variance of the EW distribution of Lya selected galaxies at z=5.7, vii) the EW distribution of i-drop galaxies at z~6, and viii) the observed correlation of stellar age with EW. Our modeling suggests that the observed anomalously large intrinsic equivalent widths require a burst of very massive star formation lasting no more than a few to ten percent of the galaxies star forming lifetime. This very massive star formation may indicate the presence of population-III star formation in a few per cent of i-drop galaxies, and in about half of the Lya selected galaxies.Comment: 11 pages, 7 figures, MNRAS in press, comments by referee included, references added+update

Fluctuations in 21cm Emission After Reionization

The fluctuations in the emission of redshifted 21cm photons from neutral inter-galactic hydrogen will provide an unprecedented probe of the reionization era. Conventional wisdom assumes that this 21cm signal disappears as soon as reionization is complete, when little atomic hydrogen is left through most of the volume of the inter-galactic medium (IGM). However observations of damped Ly-alpha absorbers indicate that the fraction of hydrogen in its neutral form is significant by mass at all redshifts. Here we use a physically-motivated model to show that residual neutral gas, confined to dense regions in the IGM with a high recombination rate, will generate a significant post-reionization 21cm signal. We show that the power-spectrum of fluctuations in this signal will be detectable by the first generation of low-frequency observatories at a signal-to-noise that is comparable to that achievable in observations of the reionization era. The statistics of 21cm fluctuations will therefore probe not only the pre-reionization IGM, but rather the entire process of HII region overlap, as well as the appearance of the diffuse ionized IGM.Comment: 10 pages, 5 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