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Register a new userCorrecting the z~8 Galaxy Luminosity Function for Gravitational Lensing Magnification Bias
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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.
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Magnification changes the observed number counts of galaxies on the sky. This biases the observed tangential shear profiles around galaxies, the so-called galaxy-galaxy lensing (GGL) signal, and the related excess mass profile. Correspondingly, inference of physical quantities, such as the mean mass profile of halos around galaxies, are affected by magnification effects. We use simulated shear and galaxy data of the Millennium Simulation to quantify the effect on shear and mass estimates from magnified lens and source number counts. The former are due to the large-scale matter distribution in the foreground of the lenses, the latter are caused by magnification of the source population by the matter associated with the lenses. The GGL signal is calculated from the simulations by an efficient fast-Fourier transform that can also be applied to real data. The numerical treatment is complemented by a leading-order analytical description of the magnification effects, which is shown to fit the numerical shear data well. We find the magnification effect is strongest for steep galaxy luminosity functions and high redshifts. For a lens redshift of $z_mathrm{d}=0.83$, a limiting magnitude of $22,mathrm{mag}$ in the $r$-band and a source redshift of $z_mathrm{s}=0.99$, we find that a magnification correction changes the shear profile up to $45%$ and the mass is biased by up to $55 %$. For medium-redshift galaxies the relative change in shear and mass is typically a few percent. As expected, the sign of the bias depends on the local slope of the lens luminosity function $alpha_mathrm{d}$, where the mass is biased low for $alpha_mathrm{d}<1$ and biased high for $alpha_mathrm{d}>1$. Whereas the magnification effect of sources is rarely than more $1%$, the statistical power of future weak lensing surveys warrants correction for this effect.
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.
A SST survey in the NOAO Deep-Wide Field in Bootes provides a complete, 8-micron-selected sample of galaxies to a limiting (Vega) magnitude of 13.5. In the 6.88 deg$^2$ field sampled, 79% of the 4867 galaxies have spectroscopic redshifts, allowing an accurate determination of the local (z<0.3) galaxy luminosity function. Stellar and dust emission can be separated on the basis of observed galaxy colors. Dust emission (mostly PAH) accounts for 80% of the 8 micron luminosity, stellar photospheres account for 19%, and AGN emission accounts for roughly 1 %. A sub-sample of the 8 micron-selected galaxies have blue, early-type colors, but even most of these have significant PAH emission. The luminosity functions for the total 8 micron luminosity and for the dust emission alone are both well fit by Schechter functions. For the 8 micron luminosity function, the characteristic luminosity is u L_{ u}^*(8.0 micron) = 1.8 times 10^{10}$ Lsun while for the dust emission alone it is 1.6 x 10^{10}$ Lsun ull. The average 8 micron luminosity density at z<0.3 is 3.1 x 10^7 Lsun Mpc^{-3}, and the average luminosity density from dust alone is 2.5 x 10^7 Lsun Mpc^{-3}. This luminos ity arises predominantly from galaxies with 8 micron luminosities ($ u L_{ u}$) between $2times 10^9$ and $2 x 10^{10}$ Lsun, i.e., normal galaxies, not LIRGs or ULIRGs.
The significant increase in precision that will be achieved by Stage IV cosmic shear surveys means that several currently used theoretical approximations may cease to be valid. An additional layer of complexity arises from the fact that many of these approximations are interdependent; the procedure to correct for one involves making another. Two such approximations that must be relaxed for upcoming experiments are the reduced shear approximation and the effect of neglecting magnification bias. Accomplishing this involves the calculation of the convergence bispectrum; typically subject to the Limber approximation. In this work, we compute the post-Limber convergence bispectrum, and the post-Limber reduced shear and magnification bias corrections to the angular power spectrum for a Euclid-like survey. We find that the Limber approximation significantly overestimates the bispectrum when any side of the bispectrum triangle, $ell_i<60$. However, the resulting changes in the reduced shear and magnification bias corrections are well below the sample variance for $ellleq5000$. We also compute a worst-case scenario for the additional biases on $w_0w_a$CDM cosmological parameters that result from the difference between the post-Limber and Limber approximated forms of the corrections. These further demonstrate that the reduced shear and magnification bias corrections can safely be treated under the Limber approximation for upcoming surveys.
Gravitational lensing magnification modifies the observed spatial distribution of galaxies and can severely bias cosmological probes of large-scale structure if not accurately modelled. Standard approaches to modelling this magnification bias may not be applicable in practice as many galaxy samples have complex, often implicit, selection functions. We propose and test a procedure to quantify the magnification bias induced in clustering and galaxy-galaxy lensing (GGL) signals in galaxy samples subject to a selection function beyond a simple flux limit. The method employs realistic mock data to calibrate an effective luminosity function slope, $alpha_{rm{obs}}$, from observed galaxy counts, which can then be used with the standard formalism. We demonstrate this method for two galaxy samples derived from the Baryon Oscillation Spectroscopic Survey (BOSS) in the redshift ranges $0.2 < z leq 0.5$ and $0.5 < z leq 0.75$, complemented by mock data built from the MICE2 simulation. We obtain $alpha_{rm{obs}} = 1.93 pm 0.05$ and $alpha_{rm{obs}} = 2.62 pm 0.28$ for the two BOSS samples. For BOSS-like lenses, we forecast a contribution of the magnification bias to the GGL signal between the multipole moments, $ell$, of 100 and 4600 with a cumulative signal-to-noise ratio between 0.1 and 1.1 for sources from the Kilo-Degree Survey (KiDS), between 0.4 and 2.0 for sources from the Hyper Suprime-Cam survey (HSC), and between 0.3 and 2.8 for ESA Euclid-like source samples. These contributions are significant enough to require explicit modelling in future analyses of these and similar surveys. Our code is publicly available within the textsc{MagBEt} module (url{https://github.com/mwiet/MAGBET}).
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