Mitigation Strategies for WFIRST Weak Lensing Systematics

Tim Eifler (JPL/Caltech)

Collaborators: Elisabeth Krause, Sergi Hildebrandt, Chris Hirata, Jason Rhodes, Charles Shapiro

What is the dominant systematic for WL ?

Wrong question! Try again…

What is the dominant systematic for WL … given a

1. Mission (instrument/survey parameters) 2. Data Vector 3. Science Case 4. Description of the Systematics

… ?

Simulated Likelihood Analyses

WFIRST • 2500 deg^2 • 60 gal/arcmin^2 • shape noise=0.26

1. Mission (Instrument/Survey Parameters

Redshift distribution • Similar parameterization as LSST (Chang et al 2013) • Choose deeper mean redshift, higher zmax

Binning Specs • 5 tomography bins • 12 l-bins (100-5000) • 180 CLs in total

2.Data Vector10 Krause et al.

0 1 2 3 4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

WFIRST

dn

/dz

z

Figure 9. LSST IA marg

c 0000 RAS, MNRAS 000, 000–000

The impact of intrinsic alignment on current and future cosmic shear surveys 5

Table 2. Fiducial cosmology, minimum and maximum of the flat prior on cosmological and intrinsic alignment parameters.

m 8 ns w0 wa b h0 As other highzother fred(shallow) fred(deep)

Fiducial 0.315 0.829 0.9603 -1.0 0.0 0.049 0.673 5.92 1.1 -0.47 0.0 0.1 0.05Min 0.1 0.6 0.85 -2.0 -2.5 0.04 0.6 0.0 -5.0 -10.0 -3.0 0.05 0.025Max 0.6 0.95 1.06 0.0 2.5 0.055 0.76 20.0 5.0 10.0 3.0 0.2 0.1

0.28 0.30 0.32 0.34 0.78 0.82 0.86 0.88 0.92 0.96 1.00 −1.4 −1.0 −0.6 −1.5 −0.5 0.5 1.5

0.7

80.8

20.8

60.8

80.9

20.9

61.0

0−

1.4

−1.0

−0.6

0.28 0.30 0.32 0.34

−1.5

−0.5

0.5

1.5

0.78 0.82 0.86 0.88 0.92 0.96 1.00 −1.4 −1.0 −0.6 −1.0 0.0 1.0 2.0

LSST HF BJ

LSST CE BJ

LSST lin BJ

LSST HF DK

Ωm σ8 ns w0 wa

wa

w0

ns

σ8

Pro

b

Figure 2. LSST IA impact

c 0000 RAS, MNRAS 000, 000–000

Shear tomography power spectra

3.Science Case

In the process of being updated using WFIRST ETC. Project with Sergi Hildebrandt, Chris Hirata, Charles Shapiro et al

cosmological parameters

halo.c

cosmo3d.cgrowth factor

D(k,z)

Plin(k,z)

distances Pnl(k,z)

Coyote U. Emulator

collapse density 𝛿c(z) peak height

𝜈 (M,z)

halo properties

Cov(l1,l2,zi,zj,zk,zl)

C(l;zi,zj)

3D- Trispectra 1-H, 2-H, HSV, lin Trispectrum

Projected Trispectra

c(M,z) b(M,z) n(M,z)

z-distr. n(z)

covariances

redshift.c

projection functions

Limber approx.

cosmo2d.c

transfer function T(k,z)

emcee.py

MCMC

log-likelihood

CosmoLike WL module - No Systematics

0.22 0.26 0.30 0.34 0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −1.5 −0.5 0.5 1.5

0.80

0.85

0.90

0.85

0.90

0.95

−1.6

−1.2

−0.8

0.22 0.26 0.30 0.34

−1.5

0.0

1.0

2.0

0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −2 −1 0 1

WFIRST no sys

1m m8 ns w0 wa

wa

w0

n sm

8Pr

ob

• 120000 MCMC steps !• ~5h walltime!• 7-dim cosmological parameter space!• Non-Gaussian covariances -> larger stats errors

cosmological parameters

halo.c

cosmo3d.cgrowth factor

D(k,z)

Plin(k,z)

distances Pnl(k,z)

Coyote U. Emulator

collapse density 𝛿c(z) peak height

𝜈 (M,z)

halo properties

Cov(l1,l2,zi,zj,zk,zl)

C(l;zi,zj)

3D- Trispectra 1-H, 2-H, HSV, lin Trispectrum

Projected Trispectra

c(M,z) b(M,z) n(M,z)

z-distr. n(z)

covariances

photo-z model

redshift.c

projection functions

Limber approx.

cosmo2d.c

transfer function T(k,z)

nuisance.c

- shear calibration - photo-z calibration - intrinsic alignment - baryons

emcee.py

MCMC

log-likelihood

4. Description of Systematics

0.22 0.26 0.30 0.34 0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −1.5 −0.5 0.5 1.5

0.80

0.85

0.90

0.85

0.90

0.95

−1.6

−1.2

−0.8

0.22 0.26 0.30 0.34

−1.5

0.0

1.0

2.0

0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −2 −1 0 1

WFIRST no sysWFIRST bary impactWFIRST IA impact

1m m8 ns w0 wa

wa

w0

n sm

8Pr

ob

The impact of intrinsic alignment on current and future cosmic shear surveys 3

T i jkl,HSV(l1,l1, l2,l2) =

32

H20

c2 m

!4

Z h

0d

d2V

dd

!2

a()

!4

gig jgkgl

Z

dMdndM

b(M)

M

!2

|u(l1/, c(M, z())|2

Z

dM0dn

dM0b(M0)

M0

!2

|u(l2/, c(M0, z())|2

Z 1

0

kdk2

Plin (k, z())|W(ks)|2 . (8)

0.0

0.2

0.4

0.6

0.8

1.0

DES

EuclidShallow

0 1 2 3 4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

LSST

WFIRSTDeep

dn

/dz

dn

/dz

z

Figure 1. Normalized redshift distributions for the four di↵erent surveys.Top panel: DES and Euclid. Bottom panel: LSST and WFIRST.

Table 1. Survey parameters

Survey area [deg2] ngal zmax zmean zmedDES 5, 000 0.26 10 2.0 0.84 0.63LSST 18, 000 0.26 26 3.5 1.37 0.93Euclid 15, 000 0.26 20 2.5 1.37 0.93WFIRST 2, 500 0.26 55 4.0 1.37 0.93

3 SURVEYS

For our IA study we consider four di↵erent surveys: DES, Euclid,LSST and WFIRST. The corresponding redshift distributions aremodeled as

n(z) = N z↵ exp266664

zz0

!377775 . (9)

The redshift parameters ↵, , z0 and various other survey specificparameters are summarized in Table ??. For LSST we adopt theredshift distribution suggested in ? and the DES redshift distribu-tion is modeled by a modified CFHTLS redshift distribution (see ?,adjusted for the slightly lower mean redshift of DES).

4 INTRINSIC ALIGNMENT MODELS

4.1 Linear Alignment model

? parametrize the corresponding projected power spectra as

CII(`) = f 2red

Z h

0d

p2()2 PII (k, ) , (10)

CGI(`) = fred

Z h

0d

p() q()2 PI (k, ) , (11)

where the 3-dimensional IA power spectra are modelled as

PI(k, z, L) = A C1 crm

D(z)P(k, z)

1 + z1 + z0

!other LL0

!(12)

PII(k, z, L) = A2 C21

2cr2

m

D2(z)P(k, z)

1 + z1 + z0

!2other LL0

!2

.(13)

Note that C1 cr = 0.0134 according to ? and for the fit parametersA, other, we adopt the constraints from the MegaZ-LRG + SDSSLRG sample in ?, i.e. A = 5.92+0.77

0.75, other = 0.47+0.930.96, and

= 1.10+0.290.30.

4.2 Freeze-in alignment model

4.3 Jonathan Blazek alignment model

5 RESULTS

5.1 Fraction of IA contaminated galaxies

5.2 Likelihood Basics

Given a data vector D we calculate the posterior probability for apoint in the joint parameter space of cosmological parameters pco

and nuisance parameters pnu via Bayes’ theorem

P(pco,pnu|D) / Pr(pco,pnu) L(D|pco,pnu), (14)

where Pr(pco,pnu) denotes the prior probability and L(D|pco,pnu)is the likelihood. The data vector includes, for example, two-pointfunctions in the form of power spectra, which depend on both scaleand redshift. The likelihood is often assumed to be Gaussian so that

L(D|pco,pnu) = N exp1

2

h(D M)t C1 (D M)

i

| z 2(pco ,pnu)

. (15)

We abbreviate M = M(pco,pnu), i.e. the model vector M is afunction of cosmology and nuisance parameters. The normaliza-tion constant N = (2) n

2 |C| 12 in Eq. (??) can be neglected under

the assumption that the covariance is constant in parameter space.We note that assuming a constant, known covariance matrix C is

c 0000 RAS, MNRAS 000, 000–000

The impact of intrinsic alignment on current and future cosmic shear surveys 3

T i jkl,HSV(l1,l1, l2,l2) =

32

H20

c2 m

!4

Z h

0d

d2V

dd

!2

a()

!4

gig jgkgl

Z

dMdndM

b(M)

M

!2

|u(l1/, c(M, z())|2

Z

dM0dn

dM0b(M0)

M0

!2

|u(l2/, c(M0, z())|2

Z 1

0

kdk2

Plin (k, z())|W(ks)|2 . (8)

0.0

0.2

0.4

0.6

0.8

1.0

DES

EuclidShallow

0 1 2 3 4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

LSST

WFIRSTDeep

dn

/dz

dn

/dz

z

Figure 1. Normalized redshift distributions for the four di↵erent surveys.Top panel: DES and Euclid. Bottom panel: LSST and WFIRST.

Table 1. Survey parameters

Survey area [deg2] ngal zmax zmean zmedDES 5, 000 0.26 10 2.0 0.84 0.63LSST 18, 000 0.26 26 3.5 1.37 0.93Euclid 15, 000 0.26 20 2.5 1.37 0.93WFIRST 2, 500 0.26 55 4.0 1.37 0.93

3 SURVEYS

For our IA study we consider four di↵erent surveys: DES, Euclid,LSST and WFIRST. The corresponding redshift distributions aremodeled as

n(z) = N z↵ exp266664

zz0

!377775 . (9)

The redshift parameters ↵, , z0 and various other survey specificparameters are summarized in Table ??. For LSST we adopt theredshift distribution suggested in ? and the DES redshift distribu-tion is modeled by a modified CFHTLS redshift distribution (see ?,adjusted for the slightly lower mean redshift of DES).

4 INTRINSIC ALIGNMENT MODELS

4.1 Linear Alignment model

? parametrize the corresponding projected power spectra as

CII(`) = f 2red

Z h

0d

p2()2 PII (k, ) , (10)

CGI(`) = fred

Z h

0d

p() q()2 PI (k, ) , (11)

where the 3-dimensional IA power spectra are modelled as

PI(k, z, L) = A C1 crm

D(z)P(k, z)

1 + z1 + z0

!other LL0

!(12)

PII(k, z, L) = A2 C21

2cr2

m

D2(z)P(k, z)

1 + z1 + z0

!2other LL0

!2

.(13)

Note that C1 cr = 0.0134 according to ? and for the fit parametersA, other, we adopt the constraints from the MegaZ-LRG + SDSSLRG sample in ?, i.e. A = 5.92+0.77

0.75, other = 0.47+0.930.96, and

= 1.10+0.290.30.

4.2 Freeze-in alignment model

4.3 Jonathan Blazek alignment model

5 RESULTS

5.1 Fraction of IA contaminated galaxies

5.2 Likelihood Basics

Given a data vector D we calculate the posterior probability for apoint in the joint parameter space of cosmological parameters pco

and nuisance parameters pnu via Bayes’ theorem

P(pco,pnu|D) / Pr(pco,pnu) L(D|pco,pnu), (14)

where Pr(pco,pnu) denotes the prior probability and L(D|pco,pnu)is the likelihood. The data vector includes, for example, two-pointfunctions in the form of power spectra, which depend on both scaleand redshift. The likelihood is often assumed to be Gaussian so that

L(D|pco,pnu) = N exp1

2

h(D M)t C1 (D M)

i

| z 2(pco ,pnu)

. (15)

We abbreviate M = M(pco,pnu), i.e. the model vector M is afunction of cosmology and nuisance parameters. The normaliza-tion constant N = (2) n

2 |C| 12 in Eq. (??) can be neglected under

the assumption that the covariance is constant in parameter space.We note that assuming a constant, known covariance matrix C is

c 0000 RAS, MNRAS 000, 000–000

• IA input: NLA BJ’11 Mega-z model!• fred computed from extrapolated LF from GAMA, DEEP2!• Baryons input: AGN from OWLS simulations

0.22 0.26 0.30 0.34 0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −1.5 −0.5 0.5 1.5

0.80

0.85

0.90

0.85

0.90

0.95

−1.6

−1.2

−0.8

0.22 0.26 0.30 0.34

−1.5

0.0

1.0

2.0

0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −2 −1 0 1

WFIRST no sysWFIRST bary sysWFIRST IA sysWFIRST obs sys

1m m8 ns w0 wa

wa

w0

n sm

8Pr

ob

• IA input: NLA BJ’11 Coyote Universe power spectrum!• IA marg: NLA BJ’11 Halofit power spectrum, 9 nuisance (+7 cosmo) params!• Baryons input: AGN from OWLS simulations!• Baryons marg: 3-4 PCs informed by 11 baryonic scenarios excluding AGN

• Observational systematics:!• Multiplicative shear calibration (5 params, Gaussian

prior sigma=0.005)!• Gaussian photo-z errors (sigma=0.05) with

Gaussian priors on bias=0.005 and sigma=0.006

Systematics Mitigation Plan

Reduce the number of nuisance parameters

account for correlations

Strong priors on these nuisance parameters

Observations/Mocks/Theory feedback loop

Targeted estimators for systematics - ext. data/other probes

PCA Marginalization (TE, Krause, et al 2014)

• Test Impact of all sorts of sys (instrument/survey strategy)

• Test scale+redshift dependence • Test degeneracy with cosmology

Accurate parameterizations for systematics

Simulated Analyses

Ultimate solution to WL systematics: Multi-probe analysis with consistent, forward modeling of all systematics

0.22 0.26 0.30 0.34 0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −1.5 −0.5 0.5 1.5

0.80

0.85

0.90

0.85

0.90

0.95

−1.6

−1.2

−0.8

0.22 0.26 0.30 0.34

−1.5

0.0

1.0

2.0

0.80 0.85 0.90 0.85 0.90 0.95 −1.6 −1.2 −0.8 −2 −1 0 1

WFIRST no sysWFIRST IA CE HFWFIRST IA lin HFWFIRST IA DK HF

1m m8 ns w0 wa

wa

w0

n sm

8Pr

ob

• Different IA input models, all analyzed with NLA BJ’11

CosmoLike Core Routines

parameters.c

basics.c recompute.c cosmo3D.c redshift.c

halo.cHOD.c

cosmo2D_cl.c

cosmo2D_wl.c

cosmo2D_ggl.c

cosmo2D_mag.c

baryons.c

IA.c

CMB.cCMBxLSS.c

cluster.c SN.c

compression.c

EBfunctions.c

covariances_3D.c covariances_wl.c

covariances_ggl.c covariances_cl.c

covariances_x.c covariances_mag.c

CosmoLike Core Routines

parameters.c

basics.c recompute.c cosmo3D.c redshift.c

halo.cHOD.c

cosmo2D_cl.c

cosmo2D_wl.c

cosmo2D_ggl.c

cosmo2D_mag.c

baryons.c

IA.c

CMB.cCMBxLSS.c

cluster.c SN.c

compression.c

EBfunctions.c

covariances_3D.c covariances_wl.c

covariances_ggl.c covariances_cl.c

covariances_x.c covariances_mag.c