Post on 16-Nov-2018
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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