Magnification Bias Corrections to Galaxy-Lensing Cross-Correlations

Galaxy-galaxy or galaxy-quasar lensing can provide important information on the mass distribution in the Universe. It consists of correlating the lensing signal (either shear or magnification) of a background galaxy/quasar sample with the number density of a foreground galaxy sample. However, the foreground galaxy density is inevitably altered by the magnification bias due to the mass between the foreground and the observer, leading to a correction to the observed galaxy-lensing signal. The aim of this paper is to quantify this correction. The single most important determining factor is the foreground redshift z: the correction is small if the foreground galaxies are at low redshifts but can become non-negligible for sufficiently high redshifts. For instance, we find that for the multipole l=1000, the correction is above 1%*(5s-2)/b for z<0.37, and above 5%*(5s-2)/b for z<0.67, where s is the number count slope of the foreground sample, and b its galaxy bias. These considerations are particularly important for geometrical measures, such as the Jain and Taylor ratio or its generalization by Zhang et al. Assuming (5s-2)/b=1, we find that the foreground redshift should be limited to z<0.45 in order to avoid biasing the inferred dark energy equation of state w by more than 5%, and that even for a low foreground redshift (< 0.45), the background samples must be well separated from the foreground to avoid incurring a bias of similar magnitude. Lastly, we briefly comment on the possibility of obtaining these geometrical measures without using galaxy shapes, using instead magnification bias itself.Comment: 10 pages, 7 figures; v2: minor revisions, as accepted for publication in Physical Review

Anisotropic Magnification Distortion of the 3D Galaxy Correlation: II. Fourier and Redshift Space

In paper I of this series we discuss how magnification bias distorts the 3D correlation function by enhancing the observed correlation in the line-of-sight (LOS) orientation, especially on large scales. This lensing anisotropy is distinctive, making it possible to separately measure the galaxy-galaxy, galaxy-magnification {\it and} magnification-magnification correlations. Here we extend the discussion to the power spectrum and also to redshift space. In real space, pairs oriented close to the LOS direction are not protected against nonlinearity even if the pair separation is large; this is because nonlinear fluctuations can enter through gravitational lensing at a small transverse separation (or i.e. impact parameter). The situation in Fourier space is different: by focusing on a small wavenumber $k$, as is usually done, linearity is guaranteed because both the LOS and transverse wavenumbers must be small. This is why magnification distortion of the galaxy correlation appears less severe in Fourier space. Nonetheless, the effect is non-negligible, especially for the transverse Fourier modes, and should be taken into account in interpreting precision measurements of the galaxy power spectrum, for instance those that focus on the baryon oscillations. The lensing induced anisotropy of the power spectrum has a shape that is distinct from the more well known redshift space anisotropies due to peculiar motions and the Alcock-Paczynski effect. The lensing anisotropy is highly localized in Fourier space while redshift space distortions are more spread out. This means that one could separate the magnification bias component in real observations, implying that potentially it is possible to perform a gravitational lensing measurement without measuring galaxy shapes.Comment: 14 pages, minor revisions, as accepted for publication in Physical Review

Lensing Corrections to Features in the Angular Two-Point Correlation Function and Power Spectrum

It is well known that magnification bias, the modulation of galaxy or quasar source counts by gravitational lensing, can change the observed angular correlation function. We investigate magnification-induced changes to the shape of the observed correlation function w(\theta) and the angular power spectrum C_{\ell}, paying special attention to the matter-radiation equality peak and the baryon wiggles. Lensing mixes the correlation function of the source galaxies with the matter correlation at the lower redshifts of the lenses. Since the lenses probe structure nearer to the observer, the angular scale dependence of the lensing terms is different from that of the sources, thus the observed correlation function is distorted. We quantify how the lensing corrections depend on the width of the selection function, the galaxy bias b, and the number count slope s. The correction increases with redshift and larger corrections are present for sources with steep number count slopes and/or broad redshift distributions. The most drastic changes to C_{\ell} occur for measurements at z >~1.5 and \ell <~ 100. For the source distributions we consider, magnification bias can shift the matter-radiation equality scale by 1-6% at z ~ 1.5 and by z ~ 3.5 the shift can be as large as 30%. The baryon bump in \theta^2w(\theta) is shifted by <~ 1% and the width is typically increased by ~10%. Shifts of >~ 0.5% and broadening of >~ 20% occur only for very broad selection functions and/or galaxies with (5s-2)/b>~2. However, near the baryon bump the magnification correction is not constant but a gently varying function which depends on the source population. Depending on how the w(\theta) data is fitted, this correction may need to be accounted for when using the baryon acoustic scale for precision cosmology.Comment: v2: 8 pages, 5 figures, text and figures condensed, references adde

Gravitational Lensing as Signal and Noise in Lyman-alpha Forest Measurements

In Lyman-alpha forest measurements it is generally assumed that quasars are mere background light sources which are uncorrelated with the forest. Gravitational lensing of the quasars violates this assumption. This effect leads to a measurement bias, but more interestingly it provides a valuable signal. The lensing signal can be extracted by correlating quasar magnitudes with the flux power spectrum and with the flux decrement. These correlations will be challenging to measure but their detection provides a direct measure of how features in the Lyman-alpha forest trace the underlying mass density field. Observing them will test the fundamental hypothesis that fluctuations in the forest are predominantly driven by fluctuations in mass, rather than in the ionizing background, helium reionization or winds. We discuss ways to disentangle the lensing signal from other sources of such correlations, including dust, continuum and background residuals. The lensing-induced measurement bias arises from sample selection: one preferentially collects spectra of magnified quasars which are behind overdense regions. This measurement bias is ~0.1-1% for the flux power spectrum, optical depth and the flux probability distribution. Since the effect is systematic, quantities such as the amplitude of the flux power spectrum averaged across scales should be interpreted with care.Comment: 22 pages, 8 figures; v2: references added, discussion expanded, matches PRD accepted versio

Acceleration and Classical Electromagnetic Radiation

Classical radiation from an accelerated charge is reviewed along with the reciprocal topic of accelerated observers detecting radiation from a static charge. This review commemerates Bahram Mashhoon's 60th birthday.Comment: To appear in Gen. Rel. Gra

Large-Scale QSO-Galaxy Correlations and Weak Lensing

Several recent studies show that bright, intermediate and high redshift optically and radio selected QSOs are positively correlated with nearby galaxies on a range of angular scales up to a degree. Obscuration by unevenly distributed Galactic dust can be ruled out as the cause, leaving weak statistical lensing as the physical process responsible. However the amplitude of correlations on < 1 degree scales is at least a factor of a few larger than lensing model predictions. A possible way to reconcile the observations and theory is to revise the weak lensing formalism. We extend the standard lensing formulation to include the next higher order term (second order) in the geodesic equation of motion for photons. We derive relevant equations applicable in the weak lensing regime, and discuss qualitative properties of the updated formulation. We then perform numerical integrations of the revised equation and study the effect of the extra term using two different types of cosmic mass density fluctuations. We find that nearby large-scale coherent structures increase the amplitude of the predicted lensing-induced correlations between QSOs and foreground galaxies by ~ 10% (not a factor of several required by observations), while the redshift of the optimal, i.e. `most correlated' structures is moved closer to the observer compared to what is predicted using the standard lensing equation.Comment: extended Section 2; 20 pages, including 4 figures, accepted to Ap

Galaxy-Quasar correlations between APM galaxies and Hamburg-ESO QSOs

We detect angular galaxy-QSO cross-correlations between the APM Galaxy Catalogue and a preliminary release (consisting of roughly half of the anticipated final catalogue) of the Hamburg-ESO Catalogue of Bright QSOs as a function of source QSO redshift using multiple cross-correlation estimators. Each of the estimators yield very similar results, implying that the APM catalogue and the Hamburg-ESO survey are both fair samples of the respective true galaxy and QSO populations. Though the signal matches the expectations of gravitational lensing qualitatively, the strength of the measured cross-correlation signal is significantly greater than the CDM models of lensing by large scale structure would suggest. This same disagreement between models and observation has been found in several earlier studies. We estimate our confidence in the correlation detections versus redshift by generating 1000 random realizations of the Hamburg-ESO QSO survey: We detect physical associations between galaxies and low-redshift QSOs at 99% confidence and detect lensing associations at roughly 95% confidence for QSOs with redshifts between 0.6 and 1. Control cross-correlations between Galactic stars and QSOs show no signal. Finally, the overdensities (underdensities) of galaxies near QSO positions relative to those lying roughly 135 - 150 arcmin away are uncorrelated with differences in Galactic extinction between the two regions, implying that Galactic dust is not significantly affecting the QSO sample.Comment: 35 pages total, including 9 figures. Accepted by the Astrophysical Journa

High redshift AGNs from the 1Jy catalogue and the magnification bias

We have found a statistically significant (99.1 \%) excess of red ($O-E>2$) galaxies with photographic magnitudes $E<19.5$, $O< 21$ taken from the APM Sky Catalogue around $z \sim 1$ radiosources from the 1Jy catalogue. The amplitude, scale and dependence on galaxy colours of the observed overdensity are consistent with its being a result of the magnification bias caused by the weak gravitational lensing of large scale structures at redshift $z \approx 0.2-0.4$ and are hardly explained by other causes, as obscuration by dust.Comment: uuencoded file containing 3 ps files: the main text, a table and a figure. To appear in ApJ Letter

Size Bias in Galaxy Surveys

Only certain galaxies are included in surveys: those bright and large enough to be detectable as extended sources. Because gravitational lensing can make galaxies appear both brighter and larger, the presence of foreground inhomogeneities can scatter galaxies across not only magnitude cuts but also size cuts, changing the statistical properties of the resulting catalog. Here we explore this size bias, and how it combines with magnification bias to affect galaxy statistics. We demonstrate that photometric galaxy samples from current and upcoming surveys can be even more affected by size bias than by magnification bias.Comment: 4 pages; 3 figures. Accepted for publication in Phys. Rev. Let.; v2: incorporating referee's comments; v3: updated acknowledgment

Phylogenetic Analysis of the MS4A and TMEM176 Gene Families

The MS4A gene family in humans includes CD20 (MS4A1), FcRbeta (MS4A2), Htm4 (MS4A3), and at least 13 other syntenic genes encoding membrane proteins, most having characteristic tetraspanning topology. Expression of MS4A genes is variable in tissues throughout the body; however, several are limited to cells in the hematopoietic system where they have known roles in immune cell functions. Genes in the small TMEM176 group share significant sequence similarity with MS4A genes and there is evidence of immune function of at least one of the encoded proteins. In this study, we examined the evolutionary history of the MS4A/TMEM176 families as well as tissue expression of the phylogenetically earliest members, in order to investigate their possible origins in immune cells.Orthologs of human MS4A genes were found only in mammals; however, MS4A gene homologs were found in most jawed vertebrates. TMEM176 genes were found only in mammals and bony fish. Several unusual MS4A genes having 2 or more tandem MS4A sequences were identified in the chicken (Gallus gallus) and early mammals (opossum, Monodelphis domestica and platypus, Ornithorhyncus anatinus). A large number of highly conserved MS4A and TMEM176 genes was found in zebrafish (Danio rerio). The most primitive organism identified to have MS4A genes was spiny dogfish (Squalus acanthus). Tissue expression of MS4A genes in S. acanthias and D. rerio showed no evidence of expression restricted to the hematopoietic system.Our findings suggest that MS4A genes first appeared in cartilaginous fish with expression outside of the immune system, and have since diversified in many species into their modern forms with expression and function in both immune and nonimmune cells