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

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

Application of the Contouring Method to Extended Microlensed Sources

The method devised by Lewis et al. (1993) for calculating the light curve of a microlensed point source is expanded to two dimensions to enable the calculation of light curves of extended sources. This method is significantly faster than the ray shooting method that has been used in the past. The increased efficiency is used to obtain much higher resolution light curves over increased timescales. We investigate the signatures arising from different source geometries in a realistic microlensing model. We show that a large fraction of high magnification events (HMEs) in image A of Q2237+0305 involve only one caustic, and could therefore yield information on the structure of the quasar continuum through the recognition of a characteristic event shape. In addition, the cataloguing of HMEs into morphological type will, in theory, enable the direction of the transverse motion, as well as the source size to be obtained from long term monitoring.Comment: 10 pages including 4 figures. Accepted for publication in M.N.R.A.

The relation between star formation rate and stellar mass of galaxies at z ∼\sim 1-4

The relation between the Star Formation Rate (SFR) and stellar mass (${\rm M}_{\star}$) of galaxies represents a fundamental constraint on galaxy formation and has been studied extensively both in observations and cosmological simulations. However, the observed amplitude has not been successfully reproduced in simulations, indicating either that the halo accretion history and baryonic physics are poorly modeled or that observations contain biases. We examine the evolution of the SFR$-{\rm M}_{\star}$ relation of $z\sim1-4$ galaxies and display the inconsistency between observed relations that are obtained using different techniques. We employ cosmological hydrodynamic simulations and compare these with a range of observed SFR$-{\rm M}_{\star}$ relations. We find that numerical results are consistent with observations that use Spectral Energy Distribution (SED) techniques to estimate star formation rates and dust corrections. On the contrary, simulations are not able to reproduce results that were obtained by combining only UV and IR luminosities. These imply SFRs at a fixed stellar mass that are larger almost by a factor of 5 than those of SED measurements for $z \sim1.5-4$. Furthermore, we find remarkable agreement between the numerical results from various authors who have employed different cosmological codes and run simulations with different resolutions. This is interesting for two reasons. A) simulations can produce realistic populations of galaxies within representative cosmological volumes even at relatively modest resolutions. B) It is likely that current numerical codes that rely on similar subgrid multiphase Inter-Stellar Medium (ISM) models and are tuned to reproduce statistical properties of galaxies, produce similar results for the SFR$-{\rm M}_{\star}$ relation by construction, regardless of resolution, box size and, to some extent, the adopted feedback prescriptions.Comment: 16 pages, 6 figures, 3 tables, accepted for publication in PAS

Constraining the Quasar Contribution to the Reionisation of Cosmic Hydrogen

Absorption spectra of high redshift quasars suggest that the reionisation of cosmic hydrogen was complete near z~6. The dominant sources of ionising photons responsible for this reionisation are generally thought to be stars and quasars. In this paper we make a quantitative estimate of the relative contributions made by these sources. Our approach is to compute the evolution of the post overlap ionising background radiation by combining semi-analytic descriptions of reionisation in a clumpy medium with a model for the quasar luminosity function. Our overall model has two free parameters, the star formation efficiency and the minimum quasar luminosity. By adjusting these parameters, we constrain the relative contributions made by stars and quasars through comparison with reported observations (Fan et al. 2005). We find that the relative quasar contribution (at z=5.7) to the ionising background was between 1.4% and 14.5%. The range of uncertainty is dominated by the unknown minimum quasar luminosity.Comment: 8 pages, 2 figures. Accepted for publication in MNRA

Intensity mapping cross-correlations II: HI halo models including shot noise

HI intensity mapping data traces the large-scale structure matter distribution using the integrated emission of neutral hydrogen gas (HI). The cross-correlation of the intensity maps with optical galaxy surveys can mitigate foreground and systematic effects, but has been shown to significantly depend on galaxy evolution parameters of the HI and the optical sample. Previously, we have shown that the shot noise of the cross-correlation scales with the HI content of the optical samples, such that the shot noise estimation infers the average HI masses of these samples. In this article, we present an adaptive framework for the cross-correlation of HI intensity maps with galaxy samples using our implementation of the halo model formalism (Murray et al 2018, in prep) which utilises the halo occupation distribution of galaxies to predict their power spectra. We compare two HI population models, tracing the spatial halo and the galaxy distribution respectively, and present their auto- and cross-power spectra with an associated galaxy sample. We find that the choice of the HI model and the distribution of the HI within the galaxy sample have minor significance for the shape of the auto- and cross-correlations, but highly impact the measured shot noise amplitude of the estimators, a finding we confirm with simulations. We demonstrate parameter estimation of the HI halo occupation models and advocate this framework for the interpretation of future experimental data, with the prospect of determining the HI masses of optical galaxy samples via the cross-correlation shot noise.Comment: 15 pages, 8 figures, 3 tables. Comments welcom

Determining the HI content of galaxies via intensity mapping cross-correlations

We propose an innovative method for measuring the neutral hydrogen (HI) content of an optically-selected spectroscopic sample of galaxies through cross-correlation with HI intensity mapping measurements. We show that the HI-galaxy cross-power spectrum contains an additive shot noise term which scales with the average HI brightness temperature of the optically-selected galaxies, allowing constraints to be placed on the average HI mass per galaxy. This approach can estimate the HI content of populations too faint to directly observe through their 21cm emission over a wide range of redshifts. This cross-correlation, as a function of optical luminosity or colour, can be used to derive HI-scaling relations. We demonstrate that this signal will be detectable by cross-correlating upcoming Australian SKA Pathfinder (ASKAP) observations with existing optically-selected samples. We also use semi-analytic simulations to verify that the HI mass can be successfully recovered by our technique in the range M_HI > 10^8 M_solar, in a manner independent of the underlying power spectrum shape. We conclude that this method is a powerful tool to study galaxy evolution, which only requires a single intensity mapping dataset to infer complementary HI gas information from existing optical and infra-red observations.Comment: 8 pages, 4 figures, submitted to MNRA

A small source in Q2237+0305 ?

Microlensing in Q2237+0305 between 1985 and 1995 (eg. Irwin et al. 1989; Corrigan et al. 1991; Ostensen et al. 1996) has been interpreted in two different ways; as microlensing by stellar mass objects of a continuum source having dimensions significantly smaller than the microlens Einstein radius (ER) (eg. Wambsganss, Paczynski & Schneider 1990; Rauch & Blandford 1991), and as microlensing by very low mass objects of a source as large as 5 ER (Refsdal & Stabell 1993; Haugan 1996). In this paper we present evidence in favour of a small source. Limits on the source size (in units of ER) are obtained from the combination of limits on the number of microlens Einstein radii crossed by the source during the monitoring period with two separate light-curve features. Firstly, recently published monitoring data (Wozniak et al. 2000; OGLE web page) show large variations (~0.8-1.5 magnitudes) between image brightnesses over a period of 700 days or ~15% of the monitoring period. Secondly, the 1988 peak in the image A light-curve had a duration that is a small fraction (<0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large-rapid variation limits the source size to be <0.2 ER (95% confidence). The width of the light-curve peak provides a stronger constraint of <0.02 ER (99% confidence). The Einstein radius (projected into the source plane) of the average microlens mass (m) in Q2237+0305 is ER ~ 10^{17}\sqrt{m} cm. The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.Comment: 8 pages, 3 figures, accepted for publication in M.N.R.A.

Interpretation of the OGLE Q2237+0305 microlensing light-curve

The four bright images of the gravitationally lensed quasar Q2237+0305 are being monitored from the ground (eg. OGLE collaboration, Apache Point Observatory) in the hope of observing a high magnification event (HME). Over the past three seasons (1997-1999) the OGLE collaboration has produced microlensing light-curves with unprecedented coverage. These demonstrate smooth, independent (therefore microlensing) variability between the images (Wozniak et al. 2000a,b; OGLE web page). We have retrospectively compared probability functions for high-magnification event parameters with several observed light-curve features. We conclude that the 1999 image C peak was due to the source having passed outside of a cusp rather than to a caustic crossing. In addition, we find that the image C light-curve shows evidence for a caustic crossing between the 1997 and 1998 observing seasons involving the appearance of new critical images. Our models predict that the next image C event is most likely to arrive 500 days following the 1999 peak, but with a large uncertainty (100-2000 days). Finally, given the image A light-curve derivative at the end of the 1999 observing season, our modelling suggests that a caustic crossing will occur between the 1999 and 2000 observing seasons, implying a minimum for the image A light-curve ~1-1.5 magnitudes fainter than the November 1999 level.Comment: 11 pages, 15 figures. Accepted for publication in M.N.R.A.

Redshifted 21cm Observations of High Redshift Quasar Proximity Zones

The introduction of low-frequency radio arrays is expected to revolutionize the study of the reionization epoch. Observation of the contrast in redshifted 21cm emission between a large HII region and the surrounding neutral inter-galactic medium (IGM) will be the simplest and most easily interpreted signature. However the highest redshift quasars known are thought to reside in an ionized IGM. Using a semi-analytic model we describe the redshifted 21cm signal from the IGM surrounding quasars discovered using the i-drop out technique (i.e. quasars at z~6). We argue that while quasars at z<6.5 seem to reside in the post overlap IGM, they will still provide valuable probes of the late stages of the overlap era because the light-travel time across a quasar proximity zone should be comparable to the duration of overlap. For redshifted 21cm observations within a 32MHz bandpass, we find that the subtraction of a spectrally smooth foreground will not remove spectral features due to the proximity zone. These features could be used to measure the neutral hydrogen content of the IGM during the late stages of reionization. The density of quasars at z~6 is now well constrained. We use the measured quasar luminosity function to estimate the prospects for discovery of high redshift quasars in fields that will be observed by the Murchison Widefield Array.Comment: 14 pages, 9 figures. Accepted for publication in MNRA