Calibrating the Planck Cluster Mass Scale with
CLASH
Mariana Penna-Lima
Centro Brasileiro de Pesquisas Fı́sicas - CBPF
in collaboration with
J. Bartlett, E. Rozo, J.-B. Melin, J. Merten, A. Evrard,
M. Postman, E. Rykoff
arXiv:1608.05356 (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
Cosmology with Galaxy Clusters
Abell 1689
Largest bounded structures
Cosmology with Galaxy Clusters
Abell 1689
Largest bounded structures
d 2N
dzd ln M
c
= Asurvey H(z)
Dc2 (z) dn(M,z)
d ln M
dn(M,z)
d ln M
M
= − ρmM(z) f (σM , z) σ1M ddσ
ln M
Cosmology with Galaxy Clusters
Abell 1689
Largest bounded structures
Top hat, Ωm = 0.3, ΩΛ = 0.7, σ8 = 0.9
100000
d 2N
dzd ln M
dN/dz
10000
c
= Asurvey H(z)
Dc2 (z) dn(M,z)
d ln M
dn(M,z)
d ln M
=
1000
M
− ρmM(z) f (σM , z) σ1M ddσ
ln M
Mariana Penna-Lima
100
0
w = −1
w = −0.8
w = −0.6
0.2 0.4 0.6 0.8
z
1
1.2 1.4
Calibrating the Planck Cluster Mass Scale with CLASH 2/12
DM Halo
⇒
Cluster
Photometric Redshift
z phot = z true + z bias ± σz0 (1 + z)
Surveys:
Dark Energy Survey (DES) – 5 filters, σz0 = 0.03, z . 1.4;
Javalambre Physics of the Accelerating Universe Astrophysical Survey
(J-PAS) – 54 narrow-band filters, σz0 = 0.003, z < 1.0;
Satélite Euclid – 7 filters, σz0 = 0.025 – 0.053, 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...
×
Z
Z
Z
~
d 2 N(λi , ziphot , θ)
true
= d ln M dλ
dz true Φ(M, z)
dz phot dλ
~
d 2 N(M, z true , θ)
P(λi |λtrue ) P(λtrue | ln M) P(ziphot |z true )
true
dz d ln M
Mariana Penna-Lima
Calibrating the Planck Cluster Mass Scale with CLASH 3/12
Scaling relation calibration
In general, we can write
ln (MO /M0 ) = ln(1 − bO ) + αO ln (Mtrue /M0 ) ,
where O is the mass proxy, such as the richness, SZ signal...
αO and bO 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
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 O1 -mass relation using a
O2 -mass relation, given that the O1 and O2 mass estimates
are independent.
Given two samples, one assumes that sample mean mass ratio
is an unbiased estimator of the mass bias between O1 and
Mtrue , i.e.,
MO1
= 1 − bO1 .
MO2 S
In this analysis, αO1 = αO2 = 1 e bO2 = 0.
Mariana Penna-Lima
Calibrating the Planck Cluster Mass Scale with CLASH 5/12
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) )
MCL [10 14 h −1 M¯ ]
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
11
10
9
8
7
6
5
4
3
2
1.4
PSZ1
Lower S/N
1.4
2
3
4
5
MPL [10 14 h −1 M¯ ]
Mariana Penna-Lima
6
7 8 9 10 11
Calibrating the Planck Cluster Mass Scale with CLASH 6/12
Planck mass scaling calibration with CLASH
Given the Planck and CLASH mass estimates, and the corresponding
MPL
= 1 − bSZ , (∆(ln ρ))2 = (∆(ln MPL ))2 + (∆(ln MCL ))2
error bars: ρ = M
CL
Inverse variance weighted mean: hρiS = 0.72 ± 0.057
Bootstrap - weighted mean: E (hρiS ) = 0.72 ± 0.059
Bootstrap - unweighted mean: E (hρiS ) = 0.76 ± 0.052
Penna-Lima et al. (2016)
1.4
1.2
MPL /MCL
1.0
0.8
0.6
0.4
0.2
0.03
Weighted mean
Bootstrap 1σ
4
5
Unweighted mean
Bootstrap 1σ
6
7
MCL [10 14 h −1 M¯ ]
8
9
10 11
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
Pseudo Number Counts
Error bars on bSZ are underestimated since we are assuming that:
αSZ = αL = 1, bL = 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:1408.013 )
Cluster Pseudo Number Counts: NcClusterPseudoCounts
Y 1 Z ∞
(i)
(i)
~
d ln MTrue n(MTrue , z i )P(MPL , MCL |MTrue , θ),
L=
N
−∞
i
~
P(MPL , MCL |MTrue , θ)
Z
=
d ln MSZ d ln ML P(MPL |MSZ )
~
×P(MCL |ML )P(ln MSZ , ln ML |MTrue , θ)
and
n(MTrue , z) = f (MTrue )
Mariana Penna-Lima
dn(MTrue , z) d 2 V
.
d ln MTrue dzdΩ
Calibrating the Planck Cluster Mass Scale with CLASH 8/12
Results
Selection function: f (MTrue ) =
1
2
h
1 + erf
ln Mtrue
√ −ln Mcut
2σcut
i
MCMC analyses using NcmFitESMCMC algorithm.
Fitting {αSZ , bSZ , σSZ , αL , bL , σL , r , Mcut , σcut , zmin , zmax }
+0.43
Flat prior on bL : 1 − bSZ = 0.71+0.45
−0.19 , 1 − bL = 0.95−0.23
Gaussian prior on bL = 0.0 ± 0.08 (Umetsu et al. (2014) ):
1 − bSZ = 0.73+0.10
−0.09
Fixing αSZ = αL = 1.0 and bL = 0.0: 1 − bSZ = 0.74 ± 0.07
Mariana Penna-Lima
Calibrating the Planck Cluster Mass Scale with CLASH 9/12
αSZ
5
0
1 − bSZ
σSZ
Mariana Penna-Lima
αL
1 − bL
L
cut
cut
Calibrating
the Planck Cluster
Mass
Scale with CLASH
10/12
σ
r
.0
.6
lnM
σ
0.6
0.4
0.2
.4
34
0.8.0
34
34
33
0.6
0.0
0.6
0.6
0.4
0.2
1.4
0.0
1.2
1.0
0.8
1.5
0.6
1.2
0.9
0.8
0.6
0.6
0.4
0.2
0
1.2
0.05
1.0
0.7
0.5
1.5
1.2
0.9
0.6
0.0
0.2
0.4
σcut
0.6
lnMcut
33 34 34 34
.6 .0 .4 .8
0.6
r
0.0
0.6
0.0
0.2
0.4
σL
0.6 0.6
0.8
1.0
1 − bL
1.2
1.4 0.6
αL
0.9
1.2
1.5 0.0
0.2
0.4
σSZ
0.6
0.8
1 − bSZ
0.5 0.7 1.0 1.2
0
5
0
5
Results: MCMC - Gaussian prior on bL = 0 ± 0.08
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
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 N200 scaling relations (7000 clusters).
Mariana Penna-Lima
Calibrating the Planck Cluster Mass Scale with CLASH
12/12