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Register a new userDistortion of the luminosity function of high-redshift galaxies by gravitational lensing
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The observed properties of high redshift galaxies depend on the underlying foreground distribution of large scale structure, which distorts their intrinsic properties via gravitational lensing. We focus on the regime where the dominant contribution originates from a single lens and examine the statistics of gravitational lensing by a population of virialized and non-virialized structures using sub-mm galaxies at z ~ 2.6 and Lyman-break galaxies at redshifts z ~ 6 - 15 as the background sources. We quantify the effect of lensing on the luminosity function of the high redshift sources, focusing on the intermediate and small magnifications, mu < 2, which affect the majority of the background galaxies, and comparing to the case of strong lensing. We show that, depending on the intrinsic properties of the background galaxies, gravitational lensing can significantly affect the observed luminosity function even when no obvious strong lenses are present. Finally, we find that in the case of the Lyman-break galaxies it is important to account for the surface brightness profiles of both the foreground and the background galaxies when computing the lensing statistics, which introduces a selection criterion for the background galaxies that can actually be observed. Not taking this criterion into account leads to an overestimation of the number densities of very bright galaxies by nearly two orders of magnitude.
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We simulate the effects of gravitational lensing on the source count of high redshift galaxies as projected to be observed by the Hubble Frontier Fields program and the James Webb Space Telescope (JWST) in the near future. Taking the mass density profile of the lensing object to be the singular isothermal sphere (SIS) or the Navarro-Frenk-White (NFW) profile, we model a lens residing at a redshift of z_L = 0.5 and explore the radial dependence of the resulting magnification bias and its variability with the velocity dispersion of the lens, the photometric sensitivity of the instrument, the redshift of the background source population, and the intrinsic maximum absolute magnitude (M_{max}) of the sources. We find that gravitational lensing enhances the number of galaxies with redshifts z >= 13 detected in the angular region theta_E/2 <= theta <= 2theta_E (where theta_E is the Einstein angle) by a factor of ~ 3 and 1.5 in the HUDF (df/d u_0 ~ 9 nJy) and medium-deep JWST surveys (df/d u_0 ~ 6 nJy). Furthermore, we find that even in cases where a negative magnification bias reduces the observed number count of background sources, the lensing effect improves the sensitivity of the count to the intrinsic faint-magnitude cut-off of the Schechter luminosity function. In a field centered on a strong lensing cluster, observations of z >= 6 and z >= 13 galaxies with JWST can be used to infer this cut-off magnitude for values as faint as M_{max} ~ -14.4 and -16.1 mag (L_{min} ~ 2.5*10^{26} and 1.2*10^{27} erg s^{-1} Hz^{-1}) respectively, within the range bracketed by existing theoretical models. Gravitational lensing may therefore offer an effective way of constraining the low-luminosity cut-off of high-redshift galaxies.
We measure the faint end slope of the galaxy luminosity function (LF) for cluster galaxies at 1<z<1.5 using Spitzer IRAC data. We investigate whether this slope, alpha, differs from that of the field LF at these redshifts, and with the cluster LF at low redshifts. The latter is of particular interest as low-luminosity galaxies are expected to undergo significant evolution. We use seven high-redshift spectroscopically confirmed galaxy clusters drawn from the IRAC Shallow Cluster Survey to measure the cluster galaxy LF down to depths of M* + 3 (3.6 microns) and M* + 2.5 (4.5 microns). The summed LF at our median cluster redshift (z=1.35) is well fit by a Schechter distribution with alpha[3.6] = -0.97 +/- 0.14 and alpha[4.5] = -0.91 +/- 0.28, consistent with a flat faint end slope and is in agreement with measurements of the field LF in similar bands at these redshifts. A comparison to alpha in low-redshift clusters finds no statistically significant evidence of evolution. Combined with past studies which show that M* is passively evolving out to z~1.3, this means that the shape of the cluster LF is largely in place by z~1.3. This suggests that the processes that govern the build up of the mass of low-mass cluster galaxies have no net effect on the faint end slope of the cluster LF at z<1.3.
We present a Bayesian framework to account for the magnification bias from both strong and weak gravitational lensing in estimates of high-redshift galaxy luminosity functions. We illustrate our method by estimating the $zsim8$ UV luminosity function using a sample of 97 Y-band dropouts (Lyman break galaxies) found in the Brightest of Reionizing Galaxies (BoRG) survey and from the literature. We find the luminosity function is well described by a Schechter function with characteristic magnitude of $M^star = -19.85^{+0.30}_{-0.35}$, faint-end slope of $alpha = -1.72^{+0.30}_{-0.29}$, and number density of $log_{10} Psi^star [textrm{Mpc}^{-3}] = -3.00^{+0.23}_{-0.31}$. These parameters are consistent within the uncertainties with those inferred from the same sample without accounting for the magnification bias, demonstrating that the effect is small for current surveys at $zsim8$, and cannot account for the apparent overdensity of bright galaxies compared to a Schechter function found recently by Bowler et al. (2014a,b) and Finkelstein et al. (2014). We estimate that the probability of finding a strongly lensed $zsim8$ source in our sample is in the range $sim 3-15 %$ depending on limiting magnitude. We identify one strongly-lensed candidate and three cases of intermediate lensing in BoRG (estimated magnification $mu>1.4$) in addition to the previously known candidate group-scale strong lens. Using a range of theoretical luminosity functions we conclude that magnification bias will dominate wide field surveys -- such as those planned for the Euclid and WFIRST missions -- especially at $z>10$. Magnification bias will need to be accounted for in order to derive accurate estimates of high-redshift luminosity functions in these surveys and to distinguish between galaxy formation models.
We investigate the gravitational lensing properties of lines of sight containing multiple cluster-scale halos, motivated by their ability to lens very high-redshift (z ~ 10) sources into detectability. We control for the total mass along the line of sight, isolating the effects of distributing the mass among multiple halos and of varying the physical properties of the halos. Our results show that multiple-halo lines of sight can increase the magnified source-plane region compared to the single cluster lenses typically targeted for lensing studies, and thus are generally better fields for detecting very high-redshift sources. The configurations that result in optimal lensing cross sections benefit from interactions between the lens potentials of the halos when they overlap somewhat on the sky, creating regions of high magnification in the source plane not present when the halos are considered individually. The effect of these interactions on the lensing cross section can even be comparable to changing the total mass of the lens from 10^15 M_sun to 3x10^15 M_sun. The gain in lensing cross section increases as the mass is split into more halos, provided that the lens potentials are projected close enough to interact with each other. A nonzero projected halo angular separation, equal halo mass ratio, and high projected halo concentration are the best mass configurations, whereas projected halo ellipticity, halo triaxiality, and the relative orientations of the halos are less important. Such high mass, multiple-halo lines of sight exist in the SDSS.
By cross-correlating large samples of galaxy clusters with publicly available radio source catalogs, we construct the volume-averaged radio luminosity function (RLF) in clusters of galaxies, and investigate its dependence on cluster redshift and mass. In addition, we determine the correlation between the cluster mass and the radio luminosity of the brightest source within 50 kpc from the cluster center. We use two cluster samples: the optically selected maxBCG cluster catalog and a composite sample of X-ray selected clusters. The radio data come from the VLA NVSS and FIRST surveys. We use scaling relations to estimate cluster masses and radii to get robust estimates of cluster volumes. We determine the projected radial distribution of sources, for which we find no dependence on luminosity or cluster mass. Background and foreground sources are statistically accounted for, and we account for confusion of radio sources by adaptively degrading the resolution of the radio source surveys. We determine the redshift evolution of the RLF under the assumption that its overall shape does not change with redshift. Our results are consistent with a pure luminosity evolution of the RLF in the range 0.1 < z < 0.3 from the optical cluster sample. The X-ray sample extends to higher redshift and yields results also consistent with a pure luminosity evolution. We find no direct evidence of a dependence of the RLF on cluster mass from the present data, although the data are consistent with the most luminous sources only being found in high-mass systems.
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