Selection biases in empirical p(z) methods for weak lensing

To measure the mass of foreground objects with weak gravitational lensing, one needs to estimate the redshift distribution of lensed background sources. This is commonly done in an empirical fashion, i.e. with a reference sample of galaxies of known spectroscopic redshift, matched to the source population. In this work, we develop a simple decision tree framework that, under the ideal conditions of a large, purely magnitude-limited reference sample, allows an unbiased recovery of the source redshift probability density function p(z), as a function of magnitude and color. We use this framework to quantify biases in empirically estimated p(z) caused by selection effects present in realistic reference and weak lensing source catalogs, namely (1) complex selection of reference objects by the targeting strategy and success rate of existing spectroscopic surveys and (2) selection of background sources by the success of object detection and shape measurement at low signal-to-noise. For intermediate-to-high redshift clusters, and for depths and filter combinations appropriate for ongoing lensing surveys, we find that (1) spectroscopic selection can cause biases above the 10 per cent level, which can be reduced to 5 per cent by optimal lensing weighting, while (2) selection effects in the shape catalog bias mass estimates at or below the 2 per cent level. This illustrates the importance of completeness of the reference catalogs for empirical redshift estimation.Comment: matches published version in MNRA

Resampling images in Fourier domain

When simulating sky images, one often takes a galaxy image $F(x)$ defined by a set of pixelized samples and an interpolation kernel, and then wants to produce a new sampled image representing this galaxy as it would appear with a different point-spread function, a rotation, shearing, or magnification, and/or a different pixel scale. These operations are sometimes only possible, or most efficiently executed, as resamplings of the Fourier transform $\tilde F(u)$ of the image onto a $u$-space grid that differs from the one produced by a discrete Fourier transform (DFT) of the samples. In some applications it is essential that the resampled image be accurate to better than 1 part in $10^3$, so in this paper we first use standard Fourier techniques to show that Fourier-domain interpolation with a wrapped sinc function yields the exact value of $\tilde F(u)$ in terms of the input samples and kernel. This operation scales with image dimension as $N^4$ and can be prohibitively slow, so we next investigate the errors accrued from approximating the sinc function with a compact kernel. We show that these approximations produce a multiplicative error plus a pair of ghost images (in each dimension) in the simulated image. Standard Lanczos or cubic interpolators, when applied in Fourier domain, produce unacceptable artifacts. We find that errors $<1$ part in $10^3$ can be obtained by (1) 4-fold zero-padding of the original image before executing the $x\rightarrow u$ DFT, followed by (2) resampling to the desired $u$ grid using a 6-point, piecewise-quintic interpolant that we design expressly to minimize the ghosts, then (3) executing the DFT back to $x$ domain.Comment: Typographical and one algebraic correction, to appear in PASP March 201

Weak lensing by galaxy clusters

Der Ursprung und die Entwicklung unseres Universums zeigt sich gleichermaßen in der Raumzeit selbst wie in den Strukturen, die in ihr entstehen. Galaxienhaufen sind das Ergebnis hierarchischer Strukturbildung. Sie sind die massivsten Objekte, die sich im heutigen Universum bilden konnten. Aufgrund dieser Eigenschaft ist ihre Anzahl und Struktur hochgradig abhängig von der Zusammensetzung und Evolution des Universums. Die Messung der Anzahldichte von Galaxienhaufen beruht auf Katalogen, die nach einer beobachtbaren Größe ausgewählt werden. Die Anwendung einer Massen-Observablen-Relation (MOR) erlaubt es, die beobachtete Anzahl als Funktion der Observablen und der Rotverschiebung mit Vorhersagen zu vergleichen und so kosmologische Parameter zu bestimmen. Man kann jedoch zu Recht behaupten, dass diese Messungen noch nicht präzise im Prozentbereich sind. Hauptgrund hierfür ist das unvollständige Verständnis der MOR. Ihre Normalisierung, die Skalierung der Observablen mit Masse und Rotverschiebung und die Größe und Korrelation von intrinsischen Streuungen muss bekannt sein, um Anzahldichten korrekt interpretieren zu können. Die Massenbestimmung von Galaxienhaufen durch die differenzielle Lichtablenkung in ihrem Gravitationsfeld, i.e. durch den so genannten schwachen Gravitationslinseneffekt (weak lensing), kann erheblich hierzu beitragen. In dieser Arbeit werden neue Methoden und Ergebnisse solcher Untersuchungen vorgestellt. Zu ersteren gehören, als Teil der Datenaufbereitung, (i) die Korrektur von CCD-Bildern für nichtlineare Effekte durch die elektrischen Felder der angesammelten Ladungen (Kapitel 2) und (ii) eine Methode zur Maskierung von Artefakten in überlappenden Aufnahmen eines Himmelsbereichs durch Vergleich mit dem Median-Bild (Kapitel 3). Schließlich ist (iii) eine Methode zur Selektion von Hintergrundgalaxien, basierend auf deren Farbe und scheinbarer Magnitude, die eine neue Korrektur für die Kontamination durch Mitglieder des Galaxienhaufens einschließt, im Abschnitt 5.3.1 beschrieben. Die wissenschaftlichen Hauptergebnisse sind die folgenden. (i) Für den Hubble Frontier Field-Haufen RXC J2248.7-4431 bestimmen wir Masse und Konzentration mittels weak lensing und bestätigen die durch Röntgen- und Sunyaev-Zel'dovich-Beobachtungen (SZ) vorhergesagte große Masse. Die Untersuchung von Haufengalaxien zeigt die Abhängigkeit von Morphologie und Leuchtkraft sowie Umgebung (Kapitel 4). (ii) Unsere Massenbestimmung für 12 Galaxienhaufen ist konsistent mit Röntgenmassen, die unter Annahme hydrostatischen Gleichgewichts des heißen Gases gemacht wurden. Wir bestätigen die MOR, die für die Signifikanz der Detektion mit dem South Pole Telescope bestimmt wurde. Wir finden jedoch Diskrepanzen zur Planck-SZ MOR. Unsere Vermutung ist, dass diese mit einer flacheren Steigung der MOR oder einem größen-, rotverschiebungs- oder rauschabhängigen Problem in der Signalextraktion zusammenhängt (Kapitel 5). (iii) Schließlich zeigen wir, durch die Verbindung von Simulationen und theoretischer Modellierung, dass die Variation von Dichteprofilen bei fester Masse signifikant zur Ungenauigkeit von Massenbestimmungen von Galaxienhaufen mittels weak lensing beiträgt. Ein Modell für diese Variationen, wie das hier entwickelte, ist daher wichtig für die genaue Bestimmung der MOR, wie sie für kommende Untersuchungen nötig sein wird (Kapitel 6).The story of the origin and evolution of our Universe is told, equivalently, by space-time itself and by the structures that grow inside of it. Clusters of galaxies are the frontier of bottom-up structure formation. They are the most massive objects to have collapsed at the present epoch. By that virtue, their abundance and structural parameters are highly sensitive to the composition and evolution of the Universe. The most common probe of cluster cosmology, abundance, uses samples of clusters selected by some observable. Applying a mass-observable relation (MOR), cosmological parameters can be constrained by comparing the sample to predicted cluster abundances as a function of observable and redshift. Arguably, however, cluster probes have not yet entered the era of per cent level precision cosmology. The primary reason for this is our imperfect understanding of the MORs. The overall normalization, the slope of mass vs. observable, the redshift evolution, and the degree and correlation of intrinsic scatters of observables at fixed mass have to be constrained for interpreting abundances correctly. Mass measurement of clusters by means of the differential deflection of light from background sources in their gravitational field, i.e. weak lensing, is a powerful approach for achieving this. This thesis presents new methods for and scientific results of weak lensing measurements of clusters of galaxies. The former include, on the data reduction side, (i) the correction of CCD images for non-linear effects due to the electric fields of accumulated charges (Chapter 2) and (ii) a method for masking artifact features in sets of overlapping images of the sky by comparison to the median image (Chapter 3). Also, (iii) I develop a method for the selection of background galaxy samples based on their color and apparent magnitude that includes a new correction for contamination with cluster member galaxies (Section 5.3.1). The main scientific results are the following. (i) For the Hubble Frontier Field cluster RXC J2248.7--4431 our lensing analysis constrains mass and concentration of the cluster halo and we confirm the large mass predicted by X-ray and Sunyaev-Zel'dovich (SZ) observations. The study of cluster members shows the relation of galaxy morphology to luminosity and environment (Chapter 4). (ii) Our lensing mass measurements for 12 clusters are consistent with X-ray masses derived under the assumption of hydrostatic equilibrium of the intra-cluster gas. We confirm the MORs derived by the South Pole Telescope collaboration for the detection significance of the cluster SZ signal in their survey. We find discrepancies, however, with the Planck SZ MOR. We hypothesize that these are related either to a shallower slope of the MOR or a size, redshift or noise dependent bias in SZ signal extraction (Chapter 5). (iii) Finally, using a combination of simulations and theoretical models for the variation of cluster profiles at fixed mass, we find that the latter is a significant contribution to the uncertainty of cluster lensing mass measurements. A cosmic variance model, such as the one we develop, is necessary for MOR constraints to be accurate at the level required for future surveys (Chapter 6)

Optimizing weak lensing mass estimates for cluster profile uncertainty

Weak lensing measurements of cluster masses are necessary for calibrating mass-observable relations (MORs) to investigate the growth of structure and the properties of dark energy. However, the measured cluster shear signal varies at fixed mass M_200m due to inherent ellipticity of background galaxies, intervening structures along the line of sight, and variations in the cluster structure due to scatter in concentrations, asphericity and substructure. We use N-body simulated halos to derive and evaluate a weak lensing circular aperture mass measurement M_ap that minimizes the mass estimate variance <(M_ap - M_200m)^2> in the presence of all these forms of variability. Depending on halo mass and observational conditions, the resulting mass estimator improves on M_ap filters optimized for circular NFW-profile clusters in the presence of uncorrelated large scale structure (LSS) about as much as the latter improve on an estimator that only minimizes the influence of shape noise. Optimizing for uncorrelated LSS while ignoring the variation of internal cluster structure puts too much weight on the profile near the cores of halos, and under some circumstances can even be worse than not accounting for LSS at all. We briefly discuss the impact of variability in cluster structure and correlated structures on the design and performance of weak lensing surveys intended to calibrate cluster MORs.Comment: 11 pages, 5 figures; accepted by MNRA

Photometric Redshifts for Next-Generation Surveys

Photometric redshifts are essential in studies of both galaxy evolution and cosmology, as they enable analyses of objects too numerous or faint for spectroscopy. The Rubin Observatory, Euclid, and Roman Space Telescope will soon provide a new generation of imaging surveys with unprecedented area coverage, wavelength range, and depth. To take full advantage of these datasets, further progress in photometric redshift methods is needed. In this review, we focus on the greatest common challenges and prospects for improvement in applications of photo-$z$'s to the next generation of surveys: - Gains in $performance$ -- i.e., the precision of redshift estimates for individual galaxies -- could greatly enhance studies of galaxy evolution and some probes of cosmology. - Improvements in $characterization$ -- i.e., the accurate recovery of redshift $distributions$ of galaxies in the presence of uncertainty on individual redshifts -- are urgently needed for cosmological measurements with next-generation surveys. - To achieve both of these goals, improvements in the scope and treatment of the samples of spectroscopic redshifts which make high-fidelity photo-$z$'s possible will also be needed. For the full potential of the next generation of surveys to be reached, the characterization of redshift distributions will need to improve by roughly an order of magnitude compared to the current state of the art, requiring progress on a wide variety of fronts. We conclude by presenting a speculative evaluation of how photometric redshift methods and the collection of the necessary spectroscopic samples may improve by the time near-future surveys are completed.Comment: Posted with permission from the Annual Review of Astronomy and Astrophysics, Volume 60, copyright 2022 Annual Reviews, http://www.annualreviews.org

Collisional and dynamic evolution of dust from the asteroid belt

The size and spatial distribution of collisional debris from main belt asteroids is modeled over a 10 million year period. The model dust and meteoroid particles spiral toward the Sun under the action of Poynting-Robertson drag and grind down as they collide with a static background of field particles

Weak lensing by galaxy clusters

Der Ursprung und die Entwicklung unseres Universums zeigt sich gleichermaßen in der Raumzeit selbst wie in den Strukturen, die in ihr entstehen. Galaxienhaufen sind das Ergebnis hierarchischer Strukturbildung. Sie sind die massivsten Objekte, die sich im heutigen Universum bilden konnten. Aufgrund dieser Eigenschaft ist ihre Anzahl und Struktur hochgradig abhängig von der Zusammensetzung und Evolution des Universums. Die Messung der Anzahldichte von Galaxienhaufen beruht auf Katalogen, die nach einer beobachtbaren Größe ausgewählt werden. Die Anwendung einer Massen-Observablen-Relation (MOR) erlaubt es, die beobachtete Anzahl als Funktion der Observablen und der Rotverschiebung mit Vorhersagen zu vergleichen und so kosmologische Parameter zu bestimmen. Man kann jedoch zu Recht behaupten, dass diese Messungen noch nicht präzise im Prozentbereich sind. Hauptgrund hierfür ist das unvollständige Verständnis der MOR. Ihre Normalisierung, die Skalierung der Observablen mit Masse und Rotverschiebung und die Größe und Korrelation von intrinsischen Streuungen muss bekannt sein, um Anzahldichten korrekt interpretieren zu können. Die Massenbestimmung von Galaxienhaufen durch die differenzielle Lichtablenkung in ihrem Gravitationsfeld, i.e. durch den so genannten schwachen Gravitationslinseneffekt (weak lensing), kann erheblich hierzu beitragen. In dieser Arbeit werden neue Methoden und Ergebnisse solcher Untersuchungen vorgestellt. Zu ersteren gehören, als Teil der Datenaufbereitung, (i) die Korrektur von CCD-Bildern für nichtlineare Effekte durch die elektrischen Felder der angesammelten Ladungen (Kapitel 2) und (ii) eine Methode zur Maskierung von Artefakten in überlappenden Aufnahmen eines Himmelsbereichs durch Vergleich mit dem Median-Bild (Kapitel 3). Schließlich ist (iii) eine Methode zur Selektion von Hintergrundgalaxien, basierend auf deren Farbe und scheinbarer Magnitude, die eine neue Korrektur für die Kontamination durch Mitglieder des Galaxienhaufens einschließt, im Abschnitt 5.3.1 beschrieben. Die wissenschaftlichen Hauptergebnisse sind die folgenden. (i) Für den Hubble Frontier Field-Haufen RXC J2248.7-4431 bestimmen wir Masse und Konzentration mittels weak lensing und bestätigen die durch Röntgen- und Sunyaev-Zel'dovich-Beobachtungen (SZ) vorhergesagte große Masse. Die Untersuchung von Haufengalaxien zeigt die Abhängigkeit von Morphologie und Leuchtkraft sowie Umgebung (Kapitel 4). (ii) Unsere Massenbestimmung für 12 Galaxienhaufen ist konsistent mit Röntgenmassen, die unter Annahme hydrostatischen Gleichgewichts des heißen Gases gemacht wurden. Wir bestätigen die MOR, die für die Signifikanz der Detektion mit dem South Pole Telescope bestimmt wurde. Wir finden jedoch Diskrepanzen zur Planck-SZ MOR. Unsere Vermutung ist, dass diese mit einer flacheren Steigung der MOR oder einem größen-, rotverschiebungs- oder rauschabhängigen Problem in der Signalextraktion zusammenhängt (Kapitel 5). (iii) Schließlich zeigen wir, durch die Verbindung von Simulationen und theoretischer Modellierung, dass die Variation von Dichteprofilen bei fester Masse signifikant zur Ungenauigkeit von Massenbestimmungen von Galaxienhaufen mittels weak lensing beiträgt. Ein Modell für diese Variationen, wie das hier entwickelte, ist daher wichtig für die genaue Bestimmung der MOR, wie sie für kommende Untersuchungen nötig sein wird (Kapitel 6).The story of the origin and evolution of our Universe is told, equivalently, by space-time itself and by the structures that grow inside of it. Clusters of galaxies are the frontier of bottom-up structure formation. They are the most massive objects to have collapsed at the present epoch. By that virtue, their abundance and structural parameters are highly sensitive to the composition and evolution of the Universe. The most common probe of cluster cosmology, abundance, uses samples of clusters selected by some observable. Applying a mass-observable relation (MOR), cosmological parameters can be constrained by comparing the sample to predicted cluster abundances as a function of observable and redshift. Arguably, however, cluster probes have not yet entered the era of per cent level precision cosmology. The primary reason for this is our imperfect understanding of the MORs. The overall normalization, the slope of mass vs. observable, the redshift evolution, and the degree and correlation of intrinsic scatters of observables at fixed mass have to be constrained for interpreting abundances correctly. Mass measurement of clusters by means of the differential deflection of light from background sources in their gravitational field, i.e. weak lensing, is a powerful approach for achieving this. This thesis presents new methods for and scientific results of weak lensing measurements of clusters of galaxies. The former include, on the data reduction side, (i) the correction of CCD images for non-linear effects due to the electric fields of accumulated charges (Chapter 2) and (ii) a method for masking artifact features in sets of overlapping images of the sky by comparison to the median image (Chapter 3). Also, (iii) I develop a method for the selection of background galaxy samples based on their color and apparent magnitude that includes a new correction for contamination with cluster member galaxies (Section 5.3.1). The main scientific results are the following. (i) For the Hubble Frontier Field cluster RXC J2248.7--4431 our lensing analysis constrains mass and concentration of the cluster halo and we confirm the large mass predicted by X-ray and Sunyaev-Zel'dovich (SZ) observations. The study of cluster members shows the relation of galaxy morphology to luminosity and environment (Chapter 4). (ii) Our lensing mass measurements for 12 clusters are consistent with X-ray masses derived under the assumption of hydrostatic equilibrium of the intra-cluster gas. We confirm the MORs derived by the South Pole Telescope collaboration for the detection significance of the cluster SZ signal in their survey. We find discrepancies, however, with the Planck SZ MOR. We hypothesize that these are related either to a shallower slope of the MOR or a size, redshift or noise dependent bias in SZ signal extraction (Chapter 5). (iii) Finally, using a combination of simulations and theoretical models for the variation of cluster profiles at fixed mass, we find that the latter is a significant contribution to the uncertainty of cluster lensing mass measurements. A cosmic variance model, such as the one we develop, is necessary for MOR constraints to be accurate at the level required for future surveys (Chapter 6)

Characterization and correction of charge-induced pixel shifts in DECam

Interaction of charges in CCDs with the already accumulated charge distribution causes both a flux dependence of the point-spread function (an increase of observed size with flux, also known as the brighter/fatter effect) and pixel-to-pixel correlations of the Poissonian noise in flat fields. We describe these effects in the Dark Energy Camera (DECam) with charge dependent shifts of effective pixel borders, i.e. the Antilogus et al. (2014) model, which we fit to measurements of flat-field Poissonian noise correlations. The latter fall off approximately as a power-law r^-2.5 with pixel separation r, are isotropic except for an asymmetry in the direct neighbors along rows and columns, are stable in time, and are weakly dependent on wavelength. They show variations from chip to chip at the 20% level that correlate with the silicon resistivity. The charge shifts predicted by the model cause biased shape measurements, primarily due to their effect on bright stars, at levels exceeding weak lensing science requirements. We measure the flux dependence of star images and show that the effect can be mitigated by applying the reverse charge shifts at the pixel level during image processing. Differences in stellar size, however, remain significant due to residuals at larger distance from the centroid.Comment: typo and formatting fixes, matches version published in JINS

Environment-based selection effects of Planck clusters

We investigate whether the large scale structure environment of galaxy clusters imprints a selection bias on Sunyaev Zel'dovich (SZ) catalogs. Such a selection effect might be caused by line of sight (LoS) structures that add to the SZ signal or contain point sources that disturb the signal extraction in the SZ survey. We use the Planck PSZ1 union catalog (Planck Collab- oration et al. 2013a) in the SDSS region as our sample of SZ selected clusters. We calculate the angular two-point correlation function (2pcf) for physically correlated, foreground and background structure in the RedMaPPer SDSS DR8 catalog with respect to each cluster. We compare our results with an optically selected comparison cluster sample and with theoretical predictions. In contrast to the hypothesis of no environment-based selection, we find a mean 2pcf for background structures of -0.049 on scales of $\lesssim 40'$, significantly non-zero at $\sim 4 \sigma$, which means that Planck clusters are more likely to be detected in regions of low background density. We hypothesize this effect arises either from background estimation in the SZ survey or from radio sources in the background. We estimate the defect in SZ signal caused by this effect to be negligibly small, of the order of $\sim 10^{-4}$ of the signal of a typical Planck detection. Analogously, there are no implications on X-ray mass measurements. However, the environ- mental dependence has important consequences for weak lensing follow up of Planck galaxy clusters: we predict that projection effects account for half of the mass contained within a 15' radius of Planck galaxy clusters. We did not detect a background underdensity of CMASS LRGs, which also leaves a spatially varying redshift dependence of the Planck SZ selection function as a possible cause for our findings.Comment: 14 pages, 9 figure

MC2^2: Subaru and Hubble Space Telescope Weak-Lensing Analysis of the Double Radio Relic Galaxy Cluster PLCK G287.0+32.9

The second most significant detection of the Planck Sunyaev Zel'dovich survey, PLCK~G287.0+32.9 ($z=0.385$) boasts two similarly bright radio relics and a radio halo. One radio relic is located $\sim 400$ kpc northwest of the X-ray peak and the other $\sim 2.8$ Mpc to the southeast. This large difference suggests that a complex merging scenario is required. A key missing puzzle for the merging scenario reconstruction is the underlying dark matter distribution in high resolution. We present a joint Subaru Telescope and {\it Hubble Space Telescope} weak-lensing analysis of the cluster. Our analysis shows that the mass distribution features four significant substructures. Of the substructures, a primary cluster of mass $M_{200\text{c}}=1.59^{+0.25}_{-0.22}\times 10^{15} \ h^{-1}_{70} \ \text{M}_{\odot}$dominates the weak-lensing signal. This cluster is likely to be undergoing a merger with one (or more) subcluster whose mass is approximately a factor of 10 lower. One candidate is the subcluster of mass$M_{200\text{c}}=1.16^{+0.15}_{-0.13}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$located$\sim 400$kpc to the southeast. The location of this subcluster suggests that its interaction with the primary cluster could be the source of the NW radio relic. Another subcluster is detected$\sim 2$Mpc to the SE of the X-ray peak with mass$M_{200\text{c}}=1.68^{+0.22}_{-0.20}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$. This SE subcluster is in the vicinity of the SE radio relic and may have created the SE radio relic during a past merger with the primary cluster. The fourth subcluster,$M_{200\text{c}}=1.87^{+0.24}_{-0.22}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$, is northwest of the X-ray peak and beyond the NW radio relic.Comment: 19 pages, 14 figures; Accepted to Ap