Cosmology and Cluster Astrophysics
with Weak Gravitational Lensing andthe Sunyaev-Zel’dovich Eﬀect
第31回理論懇シンポジウム
2018/12/20 京都大学基礎物理学研究所

大里 健
東京大学物理学専攻
Based on
KO, Flender, Nagai, Shirasaki, and Yoshida; MNRAS, 475, 532 (2018)
KO, Miyatake, Nagai, Shirasaki, Yoshida, and HSC WL WG; in prep.

Cosmology and Cluster Astrophysics
with Weak Gravitational Lensing andthe Sunyaev-Zel’dovich Eﬀect
第31回理論懇シンポジウム
2018/12/20 京都大学基礎物理学研究所

大里 健
東京大学物理学専攻
Based on
KO, Flender, Nagai, Shirasaki, and Yoshida; MNRAS, 475, 532 (2018)
KO, Miyatake, Nagai, Shirasaki, Yoshida, and HSC WL WG; in prep.

Weak Gravitational Lensing
The large-scale structures induce weak gravitational lensing effect.
We can probe into the matter distribution in an unbiased way.
The images of galaxies are distorted
due to the foreground gravitational field,
and the distortion can be detectedby statistically analyzing many images.

Convergence field:

2H
30
κ(θ) =Ωm2( c )× dχ f(χs, χ)δ(DA(χ)θ, χ)∫lensing kernel density

Oguri+ (2018)

2D mass map from HSC

The Sunyaev-Zel’dovich Eﬀect
Galaxy clusters

all-sky Compton-y map
by Planck

Flux variation
w.r.t. black body

Planck col. (2016)

218 GHzΔT
ex + 1hν=y x x−4 , x =( e −1)
TkT

σTkB
PdlCompton-y y =emec 2 ∫Frequency

Sunyaev and Zel’dovich (1972, 1980)

Cosmology with WL and tSZ
We can place stringent constraints on cosmological parameterswith auto-power spectra of convergence (WL) and Compton-y (tSZ).
tSZ auto-power spectrum analysis

σ8HSC

Planck
HSC+Planck
HSCHikage+ (2018)

Neutrino mass [eV]ΩmMatter density

hAmplitude of fluctuation

HSC cosmic shear analysis

wσ8ΩmhBolliet+ (2018)

Auto 2pt Correlations
WL
1

Power spectrum / 2pt correlation

2CosmologytSZ
12Cosmology

Power spectrum / 2pt correlation

Auto 2pt Correlations
WL
1

Power spectrum / 2pt correlation

2Cosmology

tSZ
1

Joint Analysis?

2Cosmology

Power spectrum / 2pt correlation

Cross 2pt Correlations
WL
12tSZ
12

Cross-correlations!

Why Cross-Correlation?
•A naive advantage over auto-correlation is addition of independent
information useful for breaking parameter degeneracy.

Why Cross-Correlation?
•A naive advantage over auto-correlation is addition of independent
information useful for breaking parameter degeneracy.
✦Especially in the case of cross-correlation between
high S/N and low S/N observables, the cross-correlation becomes
more powerful!

X = WL, galaxies, CMB temp. Y = tSZ, CMB pol., GW source2(S/N)XY≫
1(S/N)2YY

Cross-correlation outperforms
auto-correlation!

Why Cross-Correlation?
•A naive advantage over auto-correlation is addition of independent
information useful for breaking parameter degeneracy.
✦Especially in the case of cross-correlation between
high S/N and low S/N observables, the cross-correlation becomes
more powerful!

X = WL, galaxies, CMB temp. Y = tSZ, CMB pol., GW source2(S/N)XY≫
1(S/N)2YY

Cross-correlation outperforms
auto-correlation!

If the observable Y contains unique information (e.g., cluster
astrophysics), cross-correlation should be the first way to go!

Why Cross-Correlation?
•A naive advantage over auto-correlation is addition of independent
information useful for breaking parameter degeneracy.
✦Especially in the case of cross-correlation between
high S/N and low S/N observables, the cross-correlation becomes
more powerful!
Contents of this talk

X = WL, galaxies, CMB temp. Y = tSZ, CMB pol., GW source
Part I: Cosmological analysis of the measurement of2tSZ-WL
cross-correlations
with RCSLenS and Planck(S/N)XY
Cross-correlation outperforms≫1
auto-correlation!
2(S/N)Part II:Measurementsof the tSZ-WL cross-correlations
YYwith HSC and Planck
If the observable Y contains unique information (e.g., clusterastrophysics), cross-correlation should be the first way to go!

Strategy✦Example: RCSLenS x Planck measurement of WL-tSZ cross-correlations.

2PCF

Error (covariance)
Covariance matrix can be
estimated from mock simulations
or directly from observation.

SignalPredictions depend on model andcosmology, and fast calculation
is essential.

separation [arcmin]

Hojjati+ (2017)

Analytical Prediction of Signal
Theoretical prediction of cross spectra is based on halo model.
All matter and gas is associated with halos.

yκyκ(1h)yκ(2h)
Cℓ = Cℓ+ Cℓ2dV
dnyκ(1h)Cℓ= dzdMyℓ(M, z)κℓ(M, z)∫ dzdΩ ∫dM2dVyκ(2h)Cℓ= dzPm(k = ℓ/DA, z)∫ dzdΩ
dndn× dM1dM2b(M1, z)yℓ(M1, z)b(M2, z)κℓ(M2, z)
∫dM1
dM2

Correlation function can be obtained via Hankel transform.

ℓdℓ yκ
ξ (θ) =Cℓ J0(ℓθ)∫ 2πyκ

Analytical Prediction of Signal
Theoretical prediction of cross spectra is based on halo model.
All matter and gas is associated with halos.

yκyκ(1h)yκ(2h)
Cℓ = Cℓ+ Cℓwell calibrated withN-body simulations

2dV
dnyκ(1h)Cℓ= dzdMyℓ(M, z)κℓ(M, z)∫ dzdΩ ∫dM
2dVyκ(2h)
Cℓ= dzPm(k = ℓ/DA, z)∫ dzdΩ
dndn× dM1dM2b(M1, z)yℓ(M1, z)b(M2, z)κℓ(M2, z)
∫dM1
dM2

Correlation function can be obtained via Hankel transform.

ℓdℓ yκ
ξ (θ) =Cℓ J0(ℓθ)∫ 2πyκ

Analytical Prediction of Signal
Theoretical prediction of cross spectra is based on halo model.
All matter and gas is associated with halos.

yκyκ(1h)yκ(2h)
Cℓ = Cℓ+ Cℓ2well calibrated with
N-body simulations

d Vdnyκ(1h)Cℓ= dz
dMyℓ(M, z)κℓ(M, z)∫ dzdΩ ∫dMConvergence
Projection ofNFW profile

2dVyκ(2h)Cℓ= dzPm(k = ℓ/DA, z)∫ dzdΩ
dndn
× dM1dM2b(M1, z)yℓ(M1, z)b(M2, z)κℓ(M2, z)∫dM1dM2Correlation function can be obtained via Hankel transform.

ℓdℓ yκ
ξ (θ) =Cℓ J0(ℓθ)∫ 2πyκ

Analytical Prediction of Signal
Theoretical prediction of cross spectra is based on halo model.
All matter and gas is associated with halos.

yκyκ(1h)yκ(2h)
Cℓ = Cℓ+ Cℓ2well calibrated withN-body simulations

d Vdnyκ(1h)Cℓ= dzdMyℓ(M, z)κℓ(M, z)∫ dzdΩ ∫dMConvergence
Projection ofNFW profile2dVCompton-yyκ(2h)Cℓ= dzPm(k = ℓ/DA, z)
Projection of∫ dzdΩpressure profile
dndn× dM1dM2b(M1, z)yℓ(M1, z)b(M2, z)κℓ(M2, z)
∫dM1
dM2

Correlation function can be obtained via Hankel transform.

ℓdℓ yκ
ξ (θ) =Cℓ J0(ℓθ)∫ 2πyκ

Analytical Prediction of Signal
Theoretical prediction of cross spectra is based on halo model.
All matter and gas is associated with halos.

yκyκ(1h)yκ(2h)
Cℓ = Cℓ+ Cℓ2

well calibrated with
N-body simulations

d Vdnyκ(1h)Cℓ= dzdMyℓ(M, z)κℓ(M, z)∫ dzdΩ ∫dMConvergence
Projection of
NFW profile

2dV
Compton-yyκ(2h)Cℓ= dzPm(k = ℓ/DA, z)
Projection of∫ dzdΩ
pressure profile
dndn× dM1AnalyticaldM2b(Mz)b(M2, z)κℓ(M2, z)modeling1, z)yℓ(M1, of∫dM1
dM2
pressure profile is critical!

Correlation function can be obtained via Hankel transform.

ℓdℓ yκ
ξ (θ) =Cℓ J0(ℓθ)∫ 2πyκ

Models of ICM Profiles
Generalized NFW (GNFW) profile

Earlier works include Kaiser (1986); Makino+ (1998); Suto+ (1998);
Komatsu & Seljak (2001, 2002); Ostriker+ (2005); Bode+ (2009)

Planck col. (2013)

P0Pe(r) = γ
x (1 + x α)(β−γ)/αPressure

Parametrized in the similar way to NFW profile.
Parameters are fitted against X-ray orSZ observations.

x = r/R500c, P0 ∝ (M500c)

23

Analytical model (Shaw+, 2010; Flender+, 2016)

dPtotdΦ(r)= − ρg(r), Ptot ∝ ρg1.2
drdr

To determine the normalization,Radius
Flender+ (2016)

Gas mass

The gas density/pressure profiles are determined fromfluid equations. Feedback processes are incorporated
by introducing free parameters.

Work by expansion

Eg,f = Eg,i + ϵDM | EDM | + ϵf M*c 2 + ΔEp
Dynamical friction SNe/AGN feedback

Total massNon-thermal Pressure
NOTE: From X-ray and SZ, only thermal pressure component canbe observed, but simulations suggest that turbulent motion
can also balance the self-gravity of galaxy clusters.
This another source of pressure is called as non-thermal pressure.

Non-thermal Pressure
NOTE: From X-ray and SZ, only thermal pressure component canbe observed, but simulations suggest that turbulent motion
can also balance the self-gravity of galaxy clusters.
This another source of pressure is called as non-thermal pressure.
BUT it is hard to measure the non-thermal pressure
since it requires high-res. spectroscopy.
We incorporate this effect in a phenomenological manner.
Hydrostatic bias
for GNFW profile

Non-thermal pressure profile
for analytic profile

1.8

Pnthr
β(r) = α(1 + z)
Ptot
( R500c )MHSE=1−bMtrue
Studies on mass calibration with WL
suggest b ~ 0.1—0.4. Medezinski+ (2018);

Miyatake, …, KO, … (2018)

Based on hydro. simulations.
Lau+ (2009);
Nelson+ (2014)

All-Sky Mock Simulations✦For more reliable estimation of covariance, we make advantage of
all-sky N-body simulations. We can incorporate various effects, e.g.,survey geometry, noise, and beam convolution.
All-sky convergence map

Shirasaki+ (2015); Takahashi,…,KO,… (2017)

All-sky Compton-y map

KO+ (in prep.)Compton-y Auto-Spectra
Planck (data) + mock (covariance)
GNFW profile

SPTACT

Analytic profile

Multipole

KO, Flender, Nagai, Shirasaki, and Yoshida (2018)

Cross-Correlation Functions
RCSLenS x Planck (data) + mock (covariance)
GNFW profile
Analytic profile

KO, Flender, Nagai, Shirasaki, and Yoshida (2018)

Constraints on Non-Thermal Pressure
Non-thermal pressure profile
Amplitude of matter fluctuation

for analytic profile<yy> only

0.8

Pnthr
β(r) = α0(1 + z)
Ptot
( R500c )<yy>+<yκ><yκ> only

Amplitude of non-thermal pressure

KO, Flender, Nagai, Shirasaki, and Yoshida (2018)

Constraints on Non-Thermal Pressure
Non-thermal pressure profile
Amplitude of matter fluctuation

for analytic profile<yy> only

0.8

Pnthr
β(r) = α0(1 + z)
Ptot
( R500c )<yy>+<yκ>!
nsioneT<yκ> only

Amplitude of non-thermal pressure

KO, Flender, Nagai, Shirasaki, and Yoshida (2018)

Constraints on Non-Thermal Pressure
Non-thermal pressure profile
Amplitude of matter fluctuation

for analytic profile<yy> only

0.8

Pnthr
β(r) = α0(1 + z)
Ptot
( R500c )<yy>+<yκ>!
nsioneTIssues on this analysis of RCSLenS x Planck results:
The pressure profiles are calibrated against
low-z and cluster-size halos, and it leads tolarge uncertainty
high-z or group-size halos.
<yκ>foronly➡We need deeper measurements like HSC-Planck!
Amplitude of non-thermal pressure

KO, Flender, Nagai, Shirasaki, and Yoshida (2018)

Subaru Hyper Suprime-Cam@Mauna Kea

HSC-SSP WL Survey✦HSC S16A
Wide and deep WL survey which covers 136.9 deg2
−2n=24.6
arcminwith mean i-band seeing ~ 0’’.58 and eﬀ

c.f., for RCSLenSneﬀ = 5.8 arcmin−2

Convergence
KO, Miyatake, Nagai, Shirasaki, Yoshida+ (in prep.)Measurements of Cross-Correlations
Null tests passed

GNFWyHSC x PlanckarinimelPr

6 HSC patches

KO, Miyatake, Nagai, Shirasaki, Yoshida+ (in prep.)Constraints on Cosmological Parametersωb

In this analysis, GNFW profile is used.

ωcWith the prior from Planck CMB measurements,
we can place tight constraints on cosmologicalparameters along with hydrostatic mass bias!

nshAs

Hydrostatic bias

bfor GNFW profile

MHSE=1−bMtrue

KO, Miyatake, Nagai, Shirasaki, Yoshida+ (in prep.)Fraction of mass supported by thermal pressure

Constraints on Mass Bias
CS82-ACT
HSC-Planck

No non-thermal pressure
LoCuSS
CCCP

HSC-ACT

PSZ2LenS

Planck tSZ auto-power spectrum(Bolliet+, 2018)

CLASH

WtG

High non-thermal pressure= Mass supported by thermal pressure

KO, Miyatake, Nagai, Shirasaki, Yoshida+ (in prep.)Fraction of mass supported by thermal pressure

Constraints on Mass Bias
CS82-ACT

No non-thermal pressure

HSC-Planck

LoCuSS
CCCP

HSC-ACT

CLASH

PSZ2LenS

WtGThis work
Planck tSZ auto-power spectrum(Bolliet+, 2018)

High non-thermal pressure= Mass supported by thermal pressure

KO, Miyatake, Nagai, Shirasaki, Yoshida+ (in prep.)Fraction of mass supported by thermal pressure

Constraints on Mass Bias
CS82-ACT

No non-thermal pressure

HSC-PlanckLoCuSS

Our results show higher b than CCCP
WL mass calibration measurements,
CLASH
HSC-ACT
PSZ2LenS
WtG
and imply the possible redshift evolution of massbias!

This work
Planck tSZ auto-power spectrum(Bolliet+, 2018)

High non-thermal pressure= Mass supported by thermal pressure

KO, Miyatake, Nagai, Shirasaki, Yoshida+ (in prep.)Summary•Weak lensing and the thermal Sunyaev-Zel’dovich effectare promising probes into the large-scale structure
and thermodynamical properties of intra-cluster medium.
•Cross-correlation provides additional information
with high S/N significance compared with auto-correlations.
•Halo model calculation and N-body simulations areused to predict the signal and estimate the covariance matrix.
This study presents the first attempt to estimate
covariance matrix from realistic mock simulations.
•HSC is the unique WL survey which can probe into
the large-scale structures and galaxy clusters at high redshifts,
and the redshift evolution of them by tomography.