Calibrating the Planck Cluster Mass Scale with CLASH

Transcription

1 Calibrating the Planck Cluster Mass Scale with CLASH Mariana Penna-Lima Centro Brasileiro de Pesquisas Físicas - CBPF in collaboration with J. Bartlett, E. Rozo, J.-B. Melin, J. Merten, A. Evrard, M. Postman, E. Rykoff arxiv: (submitted to A&A) XIII New Physics in Space - São Paulo November 30, 2016 Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 1/12

2 Cosmology with Galaxy Clusters Abell 1689 Largest bounded structures

3 Cosmology with Galaxy Clusters Abell 1689 Largest bounded structures d 2 N dzd ln M = A survey c H(z) D2 c (z) dn(m,z) d ln M dn(m,z) d ln M = ρm(z) M f (σ M, z) 1 σ M dσ M d ln M

4 Cosmology with Galaxy Clusters Abell 1689 Largest bounded structures Top hat, Ω m = 0.3, Ω Λ = 0.7, σ 8 = d 2 N dzd ln M = A survey dn(m,z) d ln M c H(z) D2 c (z) dn(m,z) d ln M = ρm(z) M f (σ M, z) 1 σ M dσ M d ln M dn/dz 1000 w = 1 w = w = z Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 2/12

5 DM Halo Cluster Photometric Redshift z phot = z true + z bias ± σz 0 (1 + z) Surveys: Dark Energy Survey (DES) 5 filters, σz 0 = 3, z 1.4; Javalambre Physics of the Accelerating Universe Astrophysical Survey (J-PAS) 54 narrow-band filters, σz 0 = 03, z < 1.0; Satélite Euclid 7 filters, σz 0 = 25 53, z 2.0. Mass-observable Relation Cluster mass is not directly observable Major source of uncertainty Mass proxies: X-ray luminosity and ICM total thermal content, SZ signal strength, richness, weak and strong lensing... d 2 N(λ i, z phot i, θ) dz phot = dλ d ln M dλ true dz true Φ(M, z) d 2 N(M, z true, θ) dz true d ln M P(λ i λ true ) P(λ true ln M) P(z phot i z true ) Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 3/12

6 Scaling relation calibration In general, we can write ln (M O /M 0 ) = ln(1 b O ) + α O ln (M true /M 0 ), where O is the mass proxy, such as the richness, SZ signal... α O and b O are the slope and the bias, respectively, of the mass scaling relation. Calibration can be performed using cluster number counts and/or cluster clustering (correlation function), where the parameters of the mass-observable relations are fitted along with the cosmological ones. Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 4/12

7 Scaling relation calibration Simulations indicate that weak lensing (WL) mass estimates incur smaller bias than, e.g., X-ray HSE (hydrostatic equilibrium) ones. Meneghetti et al. (2010) and Becker & Kravtsov (2011) Another approach: calibration of a O 1 -mass relation using a O 2 -mass relation, given that the O 1 and O 2 mass estimates are independent. Given two samples, one assumes that sample mean mass ratio is an unbiased estimator of the mass bias between O 1 and M true, i.e., MO1 = 1 b O1. M O2 In this analysis, α O1 = α O2 = 1 e b O2 = 0. S Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 5/12

8 Planck mass scaling calibration with CLASH CLASH - Cluster Lensing And Supernova survey with Hubble 25 clusters Mass estimates from weak and strong lensing (Merten et al. (2015), Umetsu et al. (2016) ) 21 clusters in common with Planck z [0.188; 0.89] 13 clusters present in the Planck Catalog of SZ Sources (PSZ1), and 8 are detected in the Planck temperature maps M CL [10 14 h 1 M ] PSZ1 Lower S/N M PL [10 14 h 1 M ] Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 6/12

9 Planck mass scaling calibration with CLASH Given the Planck and CLASH mass estimates, and the corresponding error bars: ρ = M PL M CL = 1 b SZ, ( (ln ρ)) 2 = ( (ln M PL )) 2 + ( (ln M CL )) 2 Inverse variance weighted mean: ρ S = 0.72 ± 57 Bootstrap - weighted mean: E( ρ S ) = 0.72 ± 59 Bootstrap - unweighted mean: E( ρ S ) = 0.76 ± 52 Penna-Lima et al. (2016) MPL/MCL Weighted mean Bootstrap 1σ Unweighted mean Bootstrap 1σ MCL [10 14 h 1 M ] Weighing the Giants program (WtG) von der Linden et al. (2014) Canadian Cluster Comparison Project (CCCP) Hoekstra et al. (2015) REFLEX + BCS Simet et al. (2015) Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 7/12

10 Pseudo Number Counts Error bars on b SZ are underestimated since we are assuming that: α SZ = α L = 1, b L = 0. This approach also neglects any correlation between the lensing (L) and SZ signals, and the intrinsic scatters of the L and SZ mass distributions. We introduce a new method to calibrate the mass scaling relations when the selection function is unknown. Implemented in the Numerical Cosmology library (NumCosmo - S. Vitenti & M. Penna-Lima, ascl: ) Cluster Pseudo Number Counts: NcClusterPseudoCounts L = i 1 N P(M PL, M CL M True, θ) = d ln M True n(m True, z i )P(M (i) PL, M(i) CL M True, θ), d ln M SZ d ln M L P(M PL M SZ ) P(M CL M L )P(ln M SZ, ln M L M True, θ) and n(m True, z) = f (M True ) dn(m True, z) d ln M True d 2 V dzdω. Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 8/12

11 Results [ ( )] Selection function: f (M True ) = erf ln Mtrue ln 2σcut M cut MCMC analyses using NcmFitESMCMC algorithm. Fitting {α SZ, b SZ, σ SZ, α L, b L, σ L, r, M cut, σ cut, z min, z max } Flat prior on b L : 1 b SZ = , 1 b L = Gaussian prior on b L = ± 8 (Umetsu et al. (2014) ): 1 b SZ = Fixing α SZ = α L = 1.0 and b L = : 1 b SZ = 0.74 ± 7 Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 9/12

12 Results: MCMC - Gaussian prior on b L = 0 ± 8 r b SZ σ SZ α L b L σ L 0.2 lnm cut σ cut α SZ b SZ σ SZ α L Mariana Penna-Lima b L σ L r lnm cut σ Calibrating the Planck Cluster Mass cut Scale with CLASH 10/

13 Tension between clusters and Planck CMB Reduces the tension between CMB and clusters, 1.34σ. Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 11/12

14 Conclusions Cluster Pseudo Counts: new approach to calibrate mass scaling relations, considering the selection function and cosmology. We adopted a generic form for the CLASH selection function. Further studies should consider form well motivated from simulations, for example. Planck e Red-sequence Cluster Survey (RCS2): calibrating the SZ and N 200 scaling relations (7000 clusters). Mariana Penna-Lima Calibrating the Planck Cluster Mass Scale with CLASH 12/12