arXiv subjects

Gary M. Bernstein

Publications and source records attributed to Gary M. Bernstein.

At least 37 records · Page 2Linked to original sources

arXiv2019

Redshift inference from the combination of galaxy colors and clustering in a hierarchical Bayesian model $-$ Application to realistic $N$-body simulations

Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broadband imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. Sánchez & Bernstein (2019) presented a hierarchical Bayesian model which estimates those from the robust combination of prior information, photometry of single galaxies and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-$z$'s to tighten the redshift posteriors, and to overcome biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $Δ\bar z \approx 0.05,$ the final biases in the posterior are $Δ\bar z \lesssim0.003.$ This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses.

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arXiv2018

Evidence for Color Dichotomy in the Primordial Neptunian Trojan Population

In the current model of early Solar System evolution, the stable members of the Jovian and Neptunian Trojan populations were captured into resonance from the leftover reservoir of planetesimals during the outward migration of the giant planets. As a result, both Jovian and Neptunian Trojans share a common origin with the primordial disk population, whose other surviving members constitute today's trans-Neptunian object (TNO) populations. The cold classical TNOs are ultra-red, while the dynamically excited "hot" population of TNOs contains a mixture of ultra-red and blue objects. In contrast, Jovian and Neptunian Trojans are observed to be blue. While the absence of ultra-red Jovian Trojans can be readily explained by the sublimation of volatile material from their surfaces due to the high flux of solar radiation at 5AU, the lack of ultra-red Neptunian Trojans presents both a puzzle and a challenge to formation models. In this work we report the discovery by the Dark Energy Survey (DES) of two new dynamically stable L4 Neptunian Trojans,2013 VX30 and 2014 UU240, both with inclinations i >30 degrees, making them the highest-inclination known stable Neptunian Trojans. We have measured the colors of these and three other dynamically stable Neptunian Trojans previously observed by DES, and find that 2013 VX30 is ultra-red, the first such Neptunian Trojan in its class. As such, 2013 VX30 may be a "missing link" between the Trojan and TNO populations. Using a simulation of the DES TNO detection efficiency, we find that there are 162 +/- 73 Trojans with Hr < 10 at the L4 Lagrange point of Neptune. Moreover, the blue-to-red Neptunian Trojan population ratio should be higher than 17:1. Based on this result, we discuss the possible origin of the ultra-red Neptunian Trojan population and its implications for the formation history of Neptunian Trojans.

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arXiv2018

Redshift inference from the combination of galaxy colors and clustering in a hierarchical Bayesian model

Powerful current and future cosmological constraints using high precision measurements of the large-scale structure of galaxies and its weak gravitational lensing effects rely on accurate characterization of the redshift distributions of the galaxy samples using only broadband imaging. We present a framework for constraining both the redshift probability distributions of galaxy populations and the redshifts of their individual members. We use a hierarchical Bayesian model (HBM) which provides full posterior distributions on those redshift probability distributions, and, for the first time, we show how to combine survey photometry of single galaxies and the information contained in the galaxy clustering against a well-characterized tracer population in a robust way. One critical approximation turns the HBM into a system amenable to efficient Gibbs sampling. We show that in the absence of photometric information, this method reduces to commonly used clustering redshift estimators. Using a simple model system, we show how the incorporation of clustering information with photo-$z$'s tightens redshift posteriors, and can overcome biases or gaps in the coverage of a spectroscopic prior. The method enables the full propagation of redshift uncertainties into cosmological analyses, and uses all the information at hand to reduce those uncertainties and associated potential biases.

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arXiv2016

An accurate and practical method for inference of weak gravitational lensing from galaxy images

We demonstrate highly accurate recovery of weak gravitational lensing shear using an implementation of the Bayesian Fourier Domain (BFD) method proposed by Bernstein & Armstrong (2014, BA14), extended to correct for selection biases. The BFD formalism is rigorously correct for Nyquist-sampled, background-limited, uncrowded image of background galaxies. BFD does not assign shapes to galaxies, instead compressing the pixel data D into a vector of moments M, such that we have an analytic expression for the probability P(M|g) of obtaining the observations with gravitational lensing distortion g along the line of sight. We implement an algorithm for conducting BFD's integrations over the population of unlensed source galaxies which measures ~10 galaxies/second/core with good scaling properties. Initial tests of this code on ~10^9 simulated lensed galaxy images recover the simulated shear to a fractional accuracy of m=0.0021+-0.0004, substantially more accurate than has been demonstrated previously for any generally applicable method. Deep sky exposures generate a sufficiently accurate approximation to the noiseless, unlensed galaxy population distribution assumed as input to BFD. Potential extensions of the method include simultaneous measurement of magnification and shear; multiple-exposure, multi-band observations; and joint inference of photometric redshifts and lensing tomography.

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arXiv2015

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.

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arXiv2015

GalSim: The modular galaxy image simulation toolkit

GALSIM is a collaborative, open-source project aimed at providing an image simulation tool of enduring benefit to the astronomical community. It provides a software library for generating images of astronomical objects such as stars and galaxies in a variety of ways, efficiently handling image transformations and operations such as convolution and rendering at high precision. We describe the GALSIM software and its capabilities, including necessary theoretical background. We demonstrate that the performance of GALSIM meets the stringent requirements of high precision image analysis applications such as weak gravitational lensing, for current datasets and for the Stage IV dark energy surveys of the Large Synoptic Survey Telescope, ESA's Euclid mission, and NASA's WFIRST-AFTA mission. The GALSIM project repository is public and includes the full code history, all open and closed issues, installation instructions, documentation, and wiki pages (including a Frequently Asked Questions section). The GALSIM repository can be found at https://github.com/GalSim-developers/GalSim .

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arXiv2014

On-sky measurements of the transverse electric fields' effects in the Dark Energy Camera CCDs

Photo-generated charge in thick, back-illuminated, fully-depleted CCDs is transported by electric fields from the silicon substrate to the collecting well at the front gate of the CCDs. However, electric fields transverse to the surface of the CCD -with diverse origins such as doping gradients, guard rings around the imaging area of the sensor, and physical stresses on the silicon lattice- displace this charge, effectively modifying the pixel area and producing noticeable signals in astrometric and photometric measurements. We use data from the science verification period of the Dark Energy Survey (DES) to characterize these effects in the Dark Energy Camera (DECam) CCDs. The transverse fields mainly manifest as concentric rings ("tree rings") and bright stripes near the boundaries of the detectors ("edge distortions") with relative amplitudes of about 1% and 10% in the flat-field images, respectively. Their nature as pixel size variations is confirmed by comparing their photometric and astrometric signatures. Using flat-field images from DECam, we derive templates in the five DES photometric bands (grizY) for the tree rings and the edge distortions as a function of their position in each DECam detector. These templates can be directly incorporated into the derivation of photometric and astrometric solutions, helping to meet the DES photometric and astrometric requirements.

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arXiv2014

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.

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arXiv2013

Bayesian Lensing Shear Measurement

We derive an estimator of weak gravitational lensing shear from background galaxy images that avoids noise-induced biases through a rigorous Bayesian treatment of the measurement. The derived shear estimator disposes with the assignment of ellipticities to individual galaxies that is typical of previous approaches to galaxy lensing. Shear estimates from the mean of the Bayesian posterior are unbiased in the limit of large number of background galaxies, regardless of the noise level on individual galaxies. The Bayesian formalism requires a prior describing the (noiseless) distribution of the target galaxy population over some parameter space; this prior can be constructed from low-noise images of a subsample of the target population, attainable from long integrations of a fraction of the survey field. We find two ways to combine this exact treatment of noise with rigorous treatment of the effects of the instrumental point-spread function and sampling. The Bayesian model fitting (BMF) method assigns a likelihood of the pixel data to galaxy models (e.g. Sersic ellipses). The Bayesian Fourier domain (BFD) method compresses the pixel data to a small set of weighted moments calculated after PSF correction in Fourier space. A numerical test using a simplified model of a biased galaxy measurement process demonstrates that the Bayesian formalism recovers applied shears to $<1$ part in $10^3$ accuracy and provides accurate uncertainty estimates. BFD is the first shear measurement algorithm that is model-free and requires no approximations or ad hoc assumptions in correcting for the effects of PSF, noise, or sampling on the galaxy images. These algorithms are good candidates for attaining the part-per-thousand shear inference required for hemisphere-scale weak gravitational lensing surveys. (abridged)

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arXiv2012

Atmospheric dispersion effects in weak lensing measurements

The wavelength dependence of atmospheric refraction causes elongation of finite-bandwidth images along the elevation vector, which produces spurious signals in weak gravitational lensing shear measurements unless this atmospheric dispersion is calibrated and removed to high precision. Because astrometric solutions and PSF characteristics are typically calibrated from stellar images, differences between the reference stars' spectra and the galaxies' spectra will leave residual errors in both the astrometric positions (dr) and in the second moment (width) of the wavelength-averaged PSF (dv) for galaxies.We estimate the level of dv that will induce spurious weak lensing signals in PSF-corrected galaxy shapes that exceed the statistical errors of the DES and the LSST cosmic-shear experiments. We also estimate the dr signals that will produce unacceptable spurious distortions after stacking of exposures taken at different airmasses and hour angles. We also calculate the errors in the griz bands, and find that dispersion systematics, uncorrected, are up to 6 and 2 times larger in g and r bands,respectively, than the requirements for the DES error budget, but can be safely ignored in i and z bands. For the LSST requirements, the factors are about 30, 10, and 3 in g, r, and i bands,respectively. We find that a simple correction linear in galaxy color is accurate enough to reduce dispersion shear systematics to insignificant levels in the r band for DES and i band for LSST,but still as much as 5 times than the requirements for LSST r-band observations. More complex corrections will likely be able to reduce the systematic cosmic-shear errors below statistical errors for LSST r band. But g-band effects remain large enough that it seems likely that induced systematics will dominate the statistical errors of both surveys, and cosmic-shear measurements should rely on the redder bands.

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arXiv2011

Lossy compression of weak lensing data

Future orbiting observatories will survey large areas of sky in order to constrain the physics of dark matter and dark energy using weak gravitational lensing and other methods. Lossy compression of the resultant data will improve the cost and feasibility of transmitting the images through the space communication network. We evaluate the consequences of the lossy compression algorithm of Bernstein et al. (2010) for the high-precision measurement of weak-lensing galaxy ellipticities. This square-root algorithm compresses each pixel independently, and the information discarded is by construction less than the Poisson error from photon shot noise. For simulated space-based images (without cosmic rays) digitized to the typical 16 bits per pixel, application of the lossy compression followed by image-wise lossless compression yields images with only 2.4 bits per pixel, a factor of 6.7 compression. We demonstrate that this compression introduces no bias in the sky background. The compression introduces a small amount of additional digitization noise to the images, and we demonstrate a corresponding small increase in ellipticity measurement noise. The ellipticity measurement method is biased by the addition of noise, so the additional digitization noise is expected to induce a multiplicative bias on the galaxies' measured ellipticities. After correcting for this known noise-induced bias, we find a residual multiplicative ellipticity bias of m ~ -4x10^{-4}. This bias is small when compared to the many other issues that precision weak lensing surveys must confront, and furthermore we expect it to be reduced further with better calibration of ellipticity measurement methods.

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arXiv2011

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.

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arXiv2011

Cosmology without cosmic variance

We examine the improvements in constraints on the linear growth factor G and its derivative f=d ln G / dln a that are available from the combination of a large-scale galaxy redshift survey with a weak gravitational lensing survey of background sources. In the linear perturbation theory limit, the bias-modulation method of McDonald & Seljak allows one to distinguish the real-space galaxy clustering from the peculiar velocity signal in each Fourier mode. The ratio of lensing signal to galaxy clustering in transverse modes yields the bias factor b of each galaxy subset (as per Pen 2004), hence calibrating the conversion from galaxy real-space density to matter density in every mode. In combination these techniques permit measure of the growth rate f in each Fourier mode. This yields a measure of the growth rate free of sample variance, i.e. the uncertainty in f can be reduced without bound by increasing the number of redshifts within a finite volume. In practice, the gain from the absence of sample variance is bounded by the limited range of bias modulation among dark-matter halos. Nonetheless, the addition of background weak lensing data to a redshift survey increases information on G and f by an amount equivalent to a 10-fold increase in the volume of a standard redshift-space distortion measurement---if the lensing signal can be measured to sub-percent accuracy. This argues that a combined lensing and redshift survey over a common low-redshift volume is a more powerful test of general relativity than an isolated redshift survey over larger volume at high redshift. An example case is that a survey of ~10^6 redshifts over half the sky in the redshift range $z=0.5\pm 0.05$ can determine the growth exponent γfor the model $f=Ω_m^γ$ to an accuracy of $\pm 0.015$, using only modes with k<0.1h/Mpc, but only if a weak lensing survey is conducted in concert. [Abridged]

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arXiv2010

Shape measurement biases from underfitting and ellipticity gradients

Precision weak gravitational lensing experiments require measurements of galaxy shapes accurate to <1 part in 1000. We investigate measurement biases, noted by Voigt and Bridle (2009) and Melchior et al. (2009), that are common to shape measurement methodologies that rely upon fitting elliptical-isophote galaxy models to observed data. The first bias arises when the true galaxy shapes do not match the models being fit. We show that this "underfitting bias" is due, at root, to these methods' attempts to use information at high spatial frequencies that has been destroyed by the convolution with the point-spread function (PSF) and/or by sampling. We propose a new shape-measurement technique that is explicitly confined to observable regions of k-space. A second bias arises for galaxies whose ellipticity varies with radius. For most shape-measurement methods, such galaxies are subject to "ellipticity gradient bias". We show how to reduce such biases by factors of 20--100 within the new shape-measurement method. The resulting shear estimator has multiplicative errors <1 part in 1000 for high-S/N images, even for highly asymmetric galaxies. Without any training or recalibration, the new method obtains Q=3000 in the GREAT08 Challenge of blind shear reconstruction on low-noise galaxies, several times better than any previous method.

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arXiv2010

Noise and bias in square-root compression schemes

We investigate data compression schemes for proposed all-sky diffraction-limited visible/NIR sky surveys aimed at the dark energy problem. We show that lossy square-root compression to 1 bit of noise per pixel, followed by standard lossless compression algorithms, reduces the images to 2.5-4 bits per pixel, depending primarily upon the level of cosmic-ray contamination of the images. Compression to this level adds noise equivalent to <10% penalty in observing time. We derive an analytic correction to flux biases inherent to the square-root compression scheme. Numerical tests on simple galaxy models confirm that galaxy fluxes and shapes are measured with systematic biases <~10^{-4} induced by the compression scheme, well below the requirements of supernova and weak gravitational lensing dark-energy experiments. An accompanying paper (Vanderveld 2009) bounds the shape biases using realistic simulated images of the high-Galactic-latitude sky. The square-root preprocessing step has advantages over simple (linear) decimation when there are many bright objects or cosmic rays in the field, or when the background level will vary.

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arXiv2010

Improved Constraints on the Gravitational Lens Q0957+561. II. Strong Lensing

We present a detailed strong lensing analysis of an HST/ACS legacy dataset for the first gravitational lens, Q0957+561. With deep imaging we identify 24 new strongly lensed features, which we use to constrain mass models. We model the stellar component of the lens galaxy using the observed luminosity distribution, and the dark matter halo using several different density profiles. We draw on the weak lensing analysis by Nakajima et al. (2009) to constrain the mass sheet and environmental terms in the lens potential. Adopting the well-measured time delay, we find H_0 = 85 (+14/-13) km/s/Mpc (68% CL) using lensing constraints alone. The principal uncertainties in H_0 are tied to the stellar mass-to-light ratio (a variant of the radial profile degeneracy in lens models). Adding constraints from stellar population synthesis models, we obtain H_0 = 79.3 (+6.7/-8.5) km/s/Mpc (68% CL). We infer that the lens galaxy has a rising rotation curve and a dark matter distribution with an inner core. Intriguingly, we find the quasar flux ratios predicted by our models to be inconsistent with existing radio measurements, suggesting the presence of substructure in the lens.

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arXiv2009

The impact of correlated projections on weak lensing cluster counts

Large-scale structure projections are an obstacle in converting the shear signal of clusters detected in weak-lensing maps into virial masses. However, this step is not necessary for constraining cosmology with the shear-peak abundance, if we are able to predict its amplitude. We generate a large ensemble of N-body simulations spanning four cosmological models, with total volume V~1 (Gpc/h)^3 per model. Variations to the matter density parameter and amplitude of fluctuations are considered. We measure the abundance of peaks in the mass density projected in ~100 Mpc/h slabs to determine the impact of structures spatially correlated with the simulation clusters, identified by the 3D friends-of-friends algorithm. The halo model shows that the choice of the smoothing filter for the density field is important in reducing the contribution of correlated projections to individual halo masses. Such contributions are less than 2% in the case of the optimal, compensated filter used throughout this analysis. We measure the change in the mass of peaks when projected in slabs of various thicknesses. Peaks in slabs of 26 Mpc/h and 102 Mpc/h suffer an average mass change of less than 2% compared to their mass in slabs of 51 Mpc/h. We then explore the cosmology dependence of the projected-peak mass function, and find that, for a wide range of slab thicknesses (<500 Mpc/h), it scales with cosmology in exactly the same way as the 3D friends-of-friends mass function and the Sheth-Tormen formula. This extends the earlier result of Marian et al. (2009). Finally, we show that for all cosmological models considered, the low and intermediate mass bins of the peak abundance can be described using a modified Sheth-Tormen functional form to within 10%-20% accuracy.

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arXiv2009

The cosmology dependence of weak lensing cluster counts

We present the main results of a numerical study of weak lensing cluster counting. We examine the scaling with cosmology of the projected-density-peak mass function. Our main conclusion is that the projected-peak and the three-dimensional mass functions scale with cosmology in an astonishingly close way. This means that, despite being derived from a two-dimensional field, the weak lensing cluster abundance can be used to constrain cosmology in the same way as the three-dimensional mass function probed by other types of surveys.

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