Title: Sample variance in weak lensing: How many simulations are required?

Abstract

Constraining cosmology using weak gravitational lensing consists of comparing a measured feature vector of dimension N_b with its simulated counterpart. An accurate estimate of the N_b × N_b feature covariance matrix C is essential to obtain accurate parameter confidence intervals. When C is measured from a set of simulations, an important question is how large this set should be. To answer this question, we construct different ensembles of N_r realizations of the shear field, using a common randomization procedure that recycles the outputs from a smaller number N_s ≤ N_r of independent ray-tracing N-body simulations. We study parameter confidence intervals as a function of (N_s, N_r) in the range 1 ≤ N_s ≤ 200 and 1 ≤ N_r ≲ 105. Previous work [S. Dodelson and M. D. Schneider, Phys. Rev. D 88, 063537 (2013)] has shown that Gaussian noise in the feature vectors (from which the covariance is estimated) lead, at quadratic order, to an O(1/N_r) degradation of the parameter confidence intervals. Using a variety of lensing features measured in our simulations, including shear-shear power spectra and peak counts, we show that cubic and quartic covariance fluctuations lead to additional O(1/N²_r) error degradation that is not negligible when N_r ismore » only a factor of few larger than N_b. We study the large N_r limit, and find that a single, 240 Mpc/h sized 512³-particle N-body simulation (N_s = 1) can be repeatedly recycled to produce as many as N_r = few × 10⁴ shear maps whose power spectra and high-significance peak counts can be treated as statistically independent. Lastly, a small number of simulations (N_s = 1 or 2) is sufficient to forecast parameter confidence intervals at percent accuracy.« less

Authors:

Petri, Andrea ^[1]; May, Morgan ^[2]; Haiman, Zoltan ^[3]

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+ Show Author Affiliations

1. Columbia Univ., New York, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
2. Brookhaven National Lab. (BNL), Upton, NY (United States)
3. Columbia Univ., New York, NY (United States)

Publication Date:

Thu Mar 24 00:00:00 EDT 2016

Research Org.:

Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1245392

Alternate Identifier(s):

OSTI ID: 1243154

Report Number(s):

BNL-111951-2016-JA
Journal ID: ISSN 2470-0010; PRVDAQ; KA2301020

Grant/Contract Number:  

SC00112704; AC02-98CH10886; SC0012704; ACI-1053575

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review D

Additional Journal Information:

Journal Volume: 93; Journal Issue: 6; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

79 ASTRONOMY AND ASTROPHYSICS