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Hunting down systematics in moderngalaxy surveys
Mohammadjavad VakiliCenter for Cosmology and Particle Physics
New York University
Berkeley / Cosmology Seminar2017 January
Mohammadjavad Vakili/ 2017-01-24
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Outline
I Large-scale structure mocks for estimation ofgalaxy clustering covariance matrices
I Weak lensing systematicsI Point Spread FunctionI Photometric redshifts
Mohammadjavad Vakili/ 2017-01-24
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Accurate galaxy mocks for estimation ofgalaxy clustering covariance matrices
I Based on works in collaboration with:Francisco-Shu Kitaura (IAC), Yu Feng(Berkeley), Gustavo Yepes (UAM), ChengZhao (Tsinzua), Chia-Hsun Chuang (Leibniz),ChangHoon Hahn (NYU)
Mohammadjavad Vakili/ 2017-01-24
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Future of spectroscopic galaxy surveys
I Measurement of growth rate and expansionhistory with sub-percent precision
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
z
0.2
0.3
0.4
0.5
0.6
0.7
fσ
8
6DFGS
SDSS MGSSDSS LRG
BOSS LOWZBOSS CMASS
VIPERS
WiggleZ
0 0.5 1 1.5Redshift z
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Gro
wth
rate
= d
lnD
/ dl
na
DGP
f(R) k=0.02CDM
f(R) k=0.1
Right: Planck Collaboration XIII (2015), Left:DESI Collaboration (2016)
Mohammadjavad Vakili/ 2017-01-24
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Future of spectroscopic galaxy surveys
I Measurement of growth rate and expansionhistory with sub-percent precision
DESI Collaboration (2016)
Mohammadjavad Vakili/ 2017-01-24
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We need mocks for both precision andaccuracy!
I Estimation of uncertainties (covariancematrix)
I Need a large number of mocks(Nmock >> Ndata)
I Mocks need to be statistically consistent(1-point, 2-point, 3-point, ...) with the data!
I We live in the era of systematic-limitedmeasurements
I Need accurate end-to-end simulations ofgalaxy surveys to characterize sytematicuncertainties
Mohammadjavad Vakili/ 2017-01-24
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How do we efficiently generate mocks forgalaxy surveys?
I Requirements:
I Need to simulate large volumes to sample theBAO signal
I Need to accurately model nonlinear clustering(current kmax ∼ 0.25 hMpc−1)
I Need to resolve low mass halos that host faintgalaxies
I Need to accurately describe two-point andhigher-order statistics
I N -body simulations are expensive!
Mohammadjavad Vakili/ 2017-01-24
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How do we efficiently generate mocks forgalaxy surveys?
I Approximate Methods:I Approximate (DM-only) structure formation
model + Empirical sampling of galaxies/halosfrom the dark matter field
Mohammadjavad Vakili/ 2017-01-24
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State-of-the-Art: SDSS III-BOSS
I QPM (White et al. 2014)
I Low resolution N -bodyI Sample halos by matching the mass function
and large scale bias
I ALPT-PATCHY (Kitaura et al. 2016)
I perturbation theoryI Sample halos by matching the n−point
functions
Mohammadjavad Vakili/ 2017-01-24
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State-of-the-Art Approximate Methods:SDSS III-BOSS
Two-point statistics:
ξ0(s), ξ2(s)
-150
-100
-50
0
50
100
150
0 20 40 60 80 100 120
s2ξ(s)
[h−2M
pc2]
s[h−1Mpc]
0.55 < z < 0.75
QPMMD Patchy
BOSS-CMASS DR12
Mohammadjavad Vakili/ 2017-01-24
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Percentage-level accuracy galaxy mocks
I Precision large-scale structure cosmologyrequires mocks with percentage-level accuracy!
I Main challenges:I Nonlinear ScalesI RSDI Higher order Statistics
Mohammadjavad Vakili/ 2017-01-24
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Goal: Percent-level accuracy
I Main Challenges: (Quasi)Nonlinear Scales,RSD (Chuang et al. 2015):
100
200
300
400
500
600
k1.
5P
0(k
)
BigMD.SO
COLA+HOD
EZmock
HALOgen+HOD
LogNormal
PATCHY
PINOCCHIO+HOD
0.1 0.2 0.3 0.4 0.5
k [h Mpc−1 ]
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
rati
o
10
100
20
30
40
50
60708090
200
300
k1.
5P
2(k
)
BigMD.SO
COLA+HOD
EZmock
HALOgen+HOD
PATCHY
PINOCCHIO+HOD
0.1 0.2 0.3 0.4 0.5
k [h Mpc−1 ]
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
rati
o
Mohammadjavad Vakili/ 2017-01-24
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Goal: Percentage-level accuracyI Main Challenges: high-order statistics!
I BAO detection (Slepian et al. 2015)I Breaking the degeneracy betweenf , σ8 (Gill-Maŕın et al. 2014)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
B(θ
)
1e8
BigMD.SO
COLA+HOD
EZmock
HALOgen+HOD
LogNormal
PATCHY
PINOCCHIO+HOD
0.0 0.2 0.4 0.6 0.8 1.0θ12/π
0.8
0.9
1.0
1.1
1.2
rati
o
Mohammadjavad Vakili/ 2017-01-24
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PATCHY : Nonlinear Stochastic Biasing
For a given dark matter density field ρm, halos/galaxies aregenerated from a nonlinear stochastic bias model: (1)Empirical nonlinear bias
〈ρg〉(ρm) = fg θ(ρm − ρth
)︸ ︷︷ ︸threshold bias
× ραm︸︷︷︸nonlinear bias
× exp(− (ρ/ρ�)�
)︸ ︷︷ ︸exponential cutoff
(2) stochastic bias (deviation from Poissoinity):
ρg ∼ NB(〈ρg〉;β
)
Mohammadjavad Vakili/ 2017-01-24
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How can we improve Patchy?
I Limitations of PATCHY:
I Brute-force estimation of bias parametersI Limited accuracy of ALPT as a gravity solver
ALPT = LPT (on large Scales) + SC (onsmall scales)
I Solution:I Automatic estimation of bias parameters with
MCMCI Replacing the gravity solver with an
approximate N -body solver that yields abetter 1-halo term clustering
Mohammadjavad Vakili/ 2017-01-24
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New gravity solver: FastPM
I FastPM (Feng et al. 2016) : approximateparticle mesh N -body solver
I Enforces large-scale linear growth
I Scales well with resolution, time step, forceresolution, ...
Mohammadjavad Vakili/ 2017-01-24
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Strategy for generation of mocks
I Generation of a DM field with low resolutionN -body
I Constraining the patchy bias parameters byfitting P (k)
I Generation of galaxy/halo mocks
Method is currently being tested as part of theEuclid covariance project.
Mohammadjavad Vakili/ 2017-01-24
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Comparison with the BigMultiDarksimulation
Can we reproduce the population of halos (andsubhalos) in the BigMultiDark N -body Simulation(N3p = 3840
3) with a low-resolutionFastPM-PATCHY (N3p = 960
3)?
Mohammadjavad Vakili/ 2017-01-24
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Dark matter density field
1250 h−1Mpc
From left to right: BigMD, FastPM, ALPT.
Mohammadjavad Vakili/ 2017-01-24
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Dark matter density ield
625 h−1Mpc
From left to right: BigMD, FastPM, ALPT.
Mohammadjavad Vakili/ 2017-01-24
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Dark matter density field
312.5 h−1Mpc
From left to right: BigMD, FastPM, ALPT.
Mohammadjavad Vakili/ 2017-01-24
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Bias parametersδth = 1. 07+0. 02−0. 05
0.2
0.4
0.6
0.8
1.0
α
α = 0. 27+0. 03−0. 04
0.2
0.4
0.6
0.8
1.0
β
β = 0. 73+0. 09−0. 07
0.2
0.4
0.6
0.8
1.0
ρ²
ρ² = 0. 15+0. 07−0. 08
0.8
0.0
0.8
1.6
δth
0.8
0.6
0.4
0.2
0.0
²
0.2
0.4
0.6
0.8
1.0
α
0.2
0.4
0.6
0.8
1.0
β
0.2
0.4
0.6
0.8
1.0
ρ²
0.8
0.6
0.4
0.2
0.0
²
² = −0. 24+0. 18−0. 24
Mohammadjavad Vakili/ 2017-01-24
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Comparison with the BigMultiDarkSimulation
One-point PDF
100 101
100
101
102
103
104
105
106
107
Nce
lls
BigMD BDM halos
FastPM-patchy halos
ALPT-patchy halos
100 101
Nhalos
0.5
1.0
1.5
Nm
ock
cells/N
Big
MD
cells
Vakili et al. (2017)
Mohammadjavad Vakili/ 2017-01-24
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Comparison with BigMultiDark Simulation
Real Space P(k)
k [Mpc−1h]
103
104
105
P(k
)[M
pc3h−
3]
BigMD BDM halos
FastPM-patchy halos
ALPT-patchy halos
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
k [Mpc−1h]
0.90
0.95
1.00
1.05
1.10
Pm
ock(k
)/P
ref(k)
Vakili et al. (2017)
Mohammadjavad Vakili/ 2017-01-24
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Bispectrum Comparison
0.5
1.0
1.5
2.0
B(α
12)
[Mpc6h−
6]×
109
k1 =k2 =0.1 Mpc−1h
BigMD BDM halos
FastPM-patchy halos
ALPT-patchy halos
0.2 0.4 0.6 0.8 1.0
α12/π
0.8
1.0
1.2
Bm
ock(α
12)/B
Big
MD(α
12) 0.2
0.4
0.6
0.8
1.0
1.2
B(α
12)
[Mpc6h−
6]×
108
2k1 =k2 =0.3 Mpc−1h
0.2 0.4 0.6 0.8 1.0
α12/π
0.8
1.0
1.2
Bm
ock(α
12)/B
Big
MD(α
12)
Vakili et al. (2017)
Mohammadjavad Vakili/ 2017-01-24
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Anisotropic RSD (Preliminary)Work in progress!
0.0 0.1 0.2 0.3 0.4 0.5
k hMpc−1
0.85
0.90
0.95
1.00
1.05
1.10
1.15
Pm
ock(k,µ
)/P
ref(k,µ
)
µ=0.1
µ=0.3
µ=0.5
µ=0.7
µ=0.9
Mohammadjavad Vakili/ 2017-01-24
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Summary
I We have presented a new version of thePATCHY code with MCMC estimation of biasparameters and FastPM gravity solver.
I By testing our method with the halos in theBigMultiDark simulation, we recover P (k) at∼ 2% level to high k modes (k ∼ 0.4 hMpc−1),and the bispectrum at a ∼ 15− 20% level!
I Redshift space clustering results are not idealyet! But a different approach for treatment ofRSD is currently being developed.
Mohammadjavad Vakili/ 2017-01-24
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Tackling PSF and photometric redshiftsystematics in imaging surveys
I Based on works in collaboration with:David Hogg (NYU, CCA), Alex Malz (NYU)
Mohammadjavad Vakili/ 2017-01-24
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LSST and the next generation of imagingsurveys
0.26 0.30 0.34 0.38N = 280001 Bandwidth = 0.001184
Den
sity
0.80 0.85 0.90N = 280001 Bandwidth = 0.002538
Den
sity
0.60 0.64 0.68 0.72N = 280001 Bandwidth = 0.001319
Den
sity
−1.5 −1.0 −0.5N = 280001 Bandwidth = 0.0208
Den
sity
−1.5 −0.5 0.5 1.5N = 280001 Bandwidth = 0.1012
Den
sity
0.80
0.85
0.90
1
1
1
1
1
1
1
1
0.60
0.64
0.68
0.72
1
1
1
1
1
1
−1.
5−
1.0
−0.
5
1
1
1
1
0.26 0.30 0.34 0.38
−1.
5−
0.5
0.5
1.5
0.80 0.85 0.900.60 0.64 0.68 0.72 −1.5 −1.0 −0.5 −3 −2 −1 0 1 2 3N = 280001 Bandwidth = 0.1012
Den
sity
clusteringcosmic shearclusterN3x2pt3x2pt+clusterN+clusterWL
Ωm σ8 h w0 wa
wa
w0
hσ 8
Pro
b
Kraus & Eifler 2016
Mohammadjavad Vakili/ 2017-01-24
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LSST and the next generation of imagingsurveys
Jain et al. 2015Mohammadjavad Vakili/ 2017-01-24
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Weak lensing measurements
I Weak lensing measurements are the basis ofmany powerful probes:
I Cosmic ShearI Galaxy Cluster CosmologyI Cross-correlation with CMB and galaxies
Hildebrandt et al. 2016Mohammadjavad Vakili/ 2017-01-24
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Weak lensing measurements
I Weak lensing measurements are the basis ofmany powerful probes:
I Cosmic ShearI Galaxy Cluster CosmologyI Cross-correlation with CMB and galaxies
Mantz et al. 2014Mohammadjavad Vakili/ 2017-01-24
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Weak lensing is limited by systematics
I The problem of inferring the cosmic shearsignals from observations is far from idealized.Cosmic shear signal is dominated by:
I the PSFI shape noiseI Intrinsic alignmentsI and many more: Blending, noise bias, ...
Mohammadjavad Vakili/ 2017-01-24
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Impact of the PSF (CFHTLenS)
Heyman et al. 2011
Mohammadjavad Vakili/ 2017-01-24
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Impact of the PSF (DES)
100 101 102
θ (arcmin)
10−7
10−6
10−5
ξ +∆e(θ)
Jarvis et al. 2016
Mohammadjavad Vakili/ 2017-01-24
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A closer look at the atmospheric PSFVariation of LSST atmospheric PSF ellipticitiesacross the FoV Simulations run by LSST PhotonSimulator (Peterson 2011)
Mohammadjavad Vakili/ 2017-01-24
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A closer look at the atmospheric PSFIn practice, we can only empirically estimate thePSF at the positions of stars and predict its valueelsewhere
Mohammadjavad Vakili/ 2017-01-24
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LSST Atmospheric turbulenceHow can we optimally interpolate the PSF?
Vakili et al. in preparation: Gaussian Processinterpolation method beats a more traditionalpolynomial interpolation. Atmosphere still causesconfusion in sub-arcminute scales!
Mohammadjavad Vakili/ 2017-01-24
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Weak lensing is limited by systematics : theimpact of Photo-z’s
I Accurate redshift probabilities are needed fortomographic two-point function calculations,determination of redshift distributions,inference of cluster masses.
1
0
1
2
3
4
5
n(z
)
0.1
-
Common photo-z estimation methods
I Template fitting
I Machine Learning
I Cross-correlation with spectroscopic sample
0.0 0.5 1.0 1.5 2.0z
0.5
1.0
1.5
2.0
2.5
3.0
P(z
)
Galaxy's true redshiftRandom forestPhysical model
Mohammadjavad Vakili/ 2017-01-24
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Combining different datasets : WFIRST andLSST
I Accuracy and precision of P (z) for individualgalaxies can be enhanced by combining thedata from overlapping surveys:
Mohammadjavad Vakili/ 2017-01-24
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LSST filters
Mohammadjavad Vakili/ 2017-01-24
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WFIRST filters
Mohammadjavad Vakili/ 2017-01-24
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LSST and WFIRST
P (z|F̂, {SEDk}) =∫ ∏
k
dtkP (z, tk|F̂, {SEDk})
F̂ = {F̂LSST, F̂WFIRST}Template library {SEDk} from Brown et al. (2014)used in LSST DC1.
Mohammadjavad Vakili/ 2017-01-24
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P (z|F̂) with single exposure LSST andWFIRST?
Mohammadjavad Vakili/ 2017-01-24
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P (z|F̂) with single exposure LSST andWFIRST?
WFIRST photo-z is limited by distinguishinggalaxy SED’s at WFIRST wavelengths
Mohammadjavad Vakili/ 2017-01-24
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P (z|F̂) with single exposure LSST andWFIRST?
Mohammadjavad Vakili/ 2017-01-24
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P (z|F̂) with single exposure LSST andWFIRST?
WFIRST photo-z is limited by distinguishinggalaxy SED’s at WFIRST wavelengths
Mohammadjavad Vakili/ 2017-01-24
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n(z) with single exposure LSST andWFIRST?
How well can we recover the redshift distributions?p(N|{dk}) ∝p(N ) exp[−
∫N (z)dz]×∏k ∫ p(zk|dk)p(zk) dzk
n(z) = dNdz
Mohammadjavad Vakili/ 2017-01-24
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n(z) with single exposure LSST andWFIRST?
How well can we recover the redshift distributions?
0.3 0.6 0.9 1.2 1.5 1.8redshift
0.00
0.05
0.10
0.15
0.20
0.25
0.30
n(z
)
WFIRST
LSST
LSST + WFIRST
True n(z)
Mohammadjavad Vakili/ 2017-01-24
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n(z) with single exposure LSST andWFIRST?
How well can we recover the redshift distributions?
0.3 0.6 0.9 1.2 1.5 1.8redshift
0.5
1.0
1.5
n(z
)/n
tru
e(z)
WFIRST
LSST
LSST + WFIRST
Mohammadjavad Vakili/ 2017-01-24
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How do we optimally combine differentdatasets
I Treat different datasets independently
I Simultaneously constrain photometry andshapes with both datasets:
P (F̂, e|dpixel)
wheredpixel
is the pixel-level data from all band-passes
Mohammadjavad Vakili/ 2017-01-24
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How do we optimally combine differentdatasets
I Real World scenario:
Mohammadjavad Vakili/ 2017-01-24
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Joint vs Independent modeling of bandpasses
I Joint modeling of all band-passes at the pixellevel could mitigate the biases in fluxestimates and hence the redshifts
Mohammadjavad Vakili/ 2017-01-24
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Summary
I The impact of PSF residual systamtics can becontrolled if we use a more flexible GaussianProcess model for PSF interpolation.
I We have presented results showing thataccuracy and precision of photometricredshift probabilities can be enhanced bycombining datasets.
I Joint modeling of all bandpasses at the pixellevel leads to more robust photometricredshift estimation.
Mohammadjavad Vakili/ 2017-01-24