skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

Abstract

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment’s beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.

Authors:
 [1];  [1];  [2];  [1];  [3];  [4];  [5];  [6];  [1]
  1. Univ. of Melbourne, Parkville VIC (Australia). School of Physics
  2. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy
  3. Argonne National Lab. (ANL), Argonne, IL (United States). High Energy Physics Div.; Univ. of Chicago, IL (United States). Kavli Inst. for Cosmological Physics (KICP)
  4. Univ. of Chicago, IL (United States). Kavli Inst. for Cosmological Physics (KICP); Univ. of Chicago, IL (United States). Dept. of Astronomy and Astrophysics
  5. Univ. of Illinois, Urbana, IL (United States). Dept. of Astronomy, Dept. of Physics
  6. Univ. of Chicago, IL (United States). Dept. of Astronomy and Astrophysics
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF); Australian Research Council
OSTI Identifier:
1393569
Grant/Contract Number:
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Cosmology and Astroparticle Physics
Additional Journal Information:
Journal Volume: 2017; Journal Issue: 08; Journal ID: ISSN 1475-7516
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; CMBR polarization; Galaxy clusters; Weak gravitational lensing

Citation Formats

Raghunathan, Srinivasan, Patil, Sanjaykumar, Baxter, Eric J., Bianchini, Federico, Bleem, Lindsey E., Crawford, Thomas M., Holder, Gilbert P., Manzotti, Alessandro, and Reichardt, Christian L. Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/08/030.
Raghunathan, Srinivasan, Patil, Sanjaykumar, Baxter, Eric J., Bianchini, Federico, Bleem, Lindsey E., Crawford, Thomas M., Holder, Gilbert P., Manzotti, Alessandro, & Reichardt, Christian L. Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments. United States. doi:10.1088/1475-7516/2017/08/030.
Raghunathan, Srinivasan, Patil, Sanjaykumar, Baxter, Eric J., Bianchini, Federico, Bleem, Lindsey E., Crawford, Thomas M., Holder, Gilbert P., Manzotti, Alessandro, and Reichardt, Christian L. 2017. "Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments". United States. doi:10.1088/1475-7516/2017/08/030.
@article{osti_1393569,
title = {Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments},
author = {Raghunathan, Srinivasan and Patil, Sanjaykumar and Baxter, Eric J. and Bianchini, Federico and Bleem, Lindsey E. and Crawford, Thomas M. and Holder, Gilbert P. and Manzotti, Alessandro and Reichardt, Christian L.},
abstractNote = {We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment’s beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.},
doi = {10.1088/1475-7516/2017/08/030},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 08,
volume = 2017,
place = {United States},
year = 2017,
month = 8
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on August 25, 2018
Publisher's Version of Record

Save / Share:
  • The work presented in this paper evaluates the statistical characteristics of regional bias and expected error in reconstructions of real PET data of human brain fluorodeoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task that the authors have investigated is that of quantifying radioisotope uptake in regions-of-interest (ROI's). They first describe a robust methodology for the use of the MLE method with clinical data which contains only one adjustable parameter: the kernel sizemore » for a Gaussian filtering operation that determines final resolution and expected regional error. Simulation results are used to establish the fundamental characteristics of the reconstructions obtained by out methodology, corresponding to the case in which the transition matrix is perfectly known. Then, data from 72 independent human brain FDG scans from four patients are used to show that the results obtained from real data are consistent with the simulation, although the quality of the data and of the transition matrix have an effect on the final outcome.« less
  • In this study, we determine the concentration–mass relation of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble survey in theories of gravity that directly modify the lensing potential. We model the clusters as Navarro–Frenk–White haloes and fit their lensing signal, in the Cubic Galileon and Nonlocal gravity models, to the lensing convergence profiles of the clusters. We discuss a number of important issues that need to be taken into account, associated with the use of non-parametric and parametric lensing methods, as well as assumptions about the background cosmology. Our results show that the concentrationmore » and mass estimates in the modified gravity models are, within the error bars, the same as in Λ cold dark matter. This result demonstrates that, for the Nonlocal model, the modifications to gravity are too weak at the cluster redshifts, and for the Galileon model, the screening mechanism is very efficient inside the cluster radius. However, at distances ~ [2–20] Mpc/h from the cluster centre, we find that the surrounding force profiles are enhanced by ~ 20–40% in the Cubic Galileon model. This has an impact on dynamical mass estimates, which means that tests of gravity based on comparisons between lensing and dynamical masses can also be applied to the Cubic Galileon model.« less
  • Weak lensing provides an important route toward collecting samples of clusters of galaxies selected by mass. Subtle systematic errors in image reduction can compromise the power of this technique. We use the B-mode signal to quantify this systematic error and to test methods for reducing this error. We show that two procedures are efficient in suppressing systematic error in the B-mode: (1) refinement of the mosaic CCD warping procedure to conform to absolute celestial coordinates and (2) truncation of the smoothing procedure on a scale of 10'. Application of these procedures reduces the systematic error to 20% of its originalmore » amplitude. We provide an analytic expression for the distribution of the highest peaks in noise maps that can be used to estimate the fraction of false peaks in the weak-lensing κ-signal-to-noise ratio (S/N) maps as a function of the detection threshold. Based on this analysis, we select a threshold S/N = 4.56 for identifying an uncontaminated set of weak-lensing peaks in two test fields covering a total area of ∼3 deg{sup 2}. Taken together these fields contain seven peaks above the threshold. Among these, six are probable systems of galaxies and one is a superposition. We confirm the reliability of these peaks with dense redshift surveys, X-ray, and imaging observations. The systematic error reduction procedures we apply are general and can be applied to future large-area weak-lensing surveys. Our high-peak analysis suggests that with an S/N threshold of 4.5, there should be only 2.7 spurious weak-lensing peaks even in an area of 1000 deg{sup 2}, where we expect ∼2000 peaks based on our Subaru fields.« less
  • In order to study properties of the Maximum Likelihood Estimator (MLE) algorithm for image reconstruction in Positron Emission Tomographyy (PET), the algorithm is applied to data obtained by the ECAT-III tomograph from a brain phantom. The procedure for subtracting accidental coincidences from the data stream generated by this physical phantom is such that he resultant data are not Poisson distributed. This makes the present investigation different from other investigations based on computer-simulated phantoms. It is shown that the MLE algorithm is robust enough to yield comparatively good images, especially when the phantom is in the periphery of the field ofmore » view, even though the underlying assumption of the algorithm is violated. Two transition matrices are utilized. The first uses geometric considerations only. The second is derived by a Monte Carlo simulation which takes into account Compton scattering in the detectors, positron range, etc. in the detectors. It is demonstrated that the images obtained from the Monte Carlo matrix are superior in some specific ways. A stopping rule derived earlier and allowing the user to stop the iterative process before the images begin to deteriorate is tested. Since the rule is based on the Poisson assumption, it does not work well with the presently available data, although it is successful wit computer-simulated Poisson data.« less
  • Cited by 4