Non-Gaussian signatures in cosmic shear fields

1
Non-Gaussian signatures in cosmic shear fields
Masahiro Takada (Tohoku U., Japan)
Based on collaboration with Bhuvnesh Jain
(Penn) (MT Jain 04, MT Jain 07 in prep.)
Sarah Bridle (UCL) (MT Bridle 07,
astro-ph/0705.0163) Some part of my talks is
based on the discussion of WLWG
Oct 26th 07 _at_ ROE
2
Outline of this talk

• What is cosmic shear tomography?
• Non-Gaussian errors of cosmic shear fields and
  the higher-order moments
• Parameter forecast including non-Gaussian errors
• Combining WLT and cluster counts
• Summary

3
Cosmological weak lensing cosmic shear

• Arises from total matter clustering
• Not affected by galaxy bias uncertainty
• well modeled based on simulations (current
  accuracy, lt10 White Vale 04)
• A level effect needs numerous (108) galaxies
  for the precise measurements

zzs
past
zzl
observables
Large-scale structure
z0
present
4
Weak Lensing Tomography
(e.g., Hu 99, 02, Huterer 01, MT Jain 04)

• Subdivide source galaxies into several bins based
  on photo-z derived from multi-colors (e.g.,
  Massey etal07)
• ltzigt in each bin needs accuracy of 0.1
• Adds some depth information to lensing
  improve cosmological paras (including DE)

?m(z)
5
Tomographic Lensing Power Spectrum

• Tomography allows to extract redshift evolution
  of the lensing power spectrum.
• A maximum multipole used should be like
  l_maxlt3,000

6
Tomographic Lensing Power Spectrum (contd.)

• Lensing PS has a less feature shape, not like CMB
• Cant better constrain inflation parameters (n_s
  and alpha_s) than CMB
• Need to use the lensing power spectrum amplitudes
  to do cosmology the amplitude is sensitive to
  A_s, ?de0 (or ?m0), w(z).

7
Lenisng tomography (condt.)

• WLT can be a powerful probe of DE energy density
  and its redshift evolution.
• Need 3 z-bins at least, if we want to constrain
  DE model with 3 parameters (?_de,w0, wa)
• Less improvement using more than 4 z-bins, for
  the 3 parameter DE model

8
An example of survey parameters (on a behalf of
HSCWLWG)
Area 2,000 deg2 Filters B26,V26,R26,
i25.8, z24.3 Nights 150-300 nights

• PS measurement error ? (survey area)-1
• Requirements expected DE constraints should be
  comparable with or better than those from other
  DE surveys in same time scale (DES, Pan-Starrs,
  WFMOS)
• Note optimization of survey parameters are being
  investigated using the existing Suprime-Cam data
  (also Yamamoto sans talk)

9
Non-linear clustering

• Most of WL signal is from small angular scales,
  where the non-linear clustering boosts the
  lensing signals by an order of magnitude (Jain
  Seljak97).
• Large-scale structures in the non-linear stage
  are non-Gaussian by nature.
• 2pt information is not sufficient higher-order
  correlations need to be included to extract all
  the cosmological information
• Baryonic physics lgt103

Non-linear clustering
l_max3000
10
Non-Gaussianity induced by structure formation

• Linear regime O(?)ltlt1 all the Fourier modes of
  the perturbations grow at the same rate the
  growth rate D(z)
• The linear theory, based on FRW GR, gives
  robust, secure predictions
• Mildly non-linear regime O(?)1 a mode coupling
  between different Fourier modes is induced
• The perturbation theory gives the specific
  predictions for a CDM model
• Highly non-linear regime a more complicated mode
  coupling
• N-body simulation based predictions are needed
  (e.g., halo model)

• Correlations btw density perturbations of
  different scales arise as a consequence of
  non-linear structure formation, originating from
  the initial Gaussian fields
• However, the non-Gaussianity is fairly accurately
  predictable based on the CDM model

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Aspects of non-Gaussianity in cosmic shear

• Cosmic shear observables are non-Gaussian
• Including non-Gaussian errors degrades the
  cosmological constraints?
• Realize a more realistic ability to constrain
  cosmological parameters
• The dependences for survey parameters (e.g.,
  shallow survey vs. deep survey)
• Yet, adding the NG information, e.g. carried by
  the bispectrum, is useful?

12
Covariance matrix of PS measurement
(MT Jain 07 in prep.)

• Most of lensing signals are from non-linear
  scales the errors are non-Gaussian
• PS covariance describes correlation between the
  two spectra of multipoles l1 and l2 (Cooray Hu
  01), providing a more realistic estimate of the
  measurement errors
• The non-Gaussian errors for PS arise from the
  4-pt function of mass fluctuations in LSS

l1
l1
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Correlation coefficients of PS cov. matrix
w/o shot noise

• Diagonal Gaussian Off-diagonal NG, 4-pt
  function
• 30 bins 50ltllt3000
• If significant correlations, r_ij?1
• The NG is stronger at smaller angular scales
• The shot noise only contributes to the Gaussian
  (diagonal) terms, suppressing significance of the
  NG errors

with shot noise
14
Correlations btw Cls at different ls

• Principal component decomposition of the PS
  covariance matrix

15
Power spectrum with NG errors

• The band powers btw different ells are highly
  correlated (also see Kilbinger Schneider 05)
• NG increases the errors by up to a factor of 2
  over a range of l1000
• elllt100, gt104, the errors are close to the
  Gaussian cases

16
Signal-to-noise ratio SNR

• Data vector power spectra binned in multipole
  range, l_minltlltl_max, (and redshifts)
• In the presence of the non-Gaussian errors, the
  signal-to-noise ratio for a power spectrum
  measurement is
• For a larger area survey (f_sky ) or a deeper
  survey (n_g ), the covariance matrix gets
  smaller, so the signal-to-noise ratio gets
  increased S/N

17
Signal-to-noise ratio SNR (contd.)
Gaussian

• Multipole range 50ltlltl_max
• Non-gaussian errors degrade S/N by a factor of 2
• This means that the cosmic shear fields are
  highly non-Gaussian (Cooray Hu 01 Kilbinger
  Schneider 05)

Non-Gaussian
50ltlltl_max
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The impact on cosmo para errors

• We are working in a multi-dimensional parameter
  space (e.g. 7D)

error ellipse
?_de
w_0
w_a
n_s
.

• Volume of the ellipse VNG?2VG
• Marginalized error on each parameter ? length of
  the principal axis ?NG2(1/Np)??G (reduced by
  the dim. of para space)
• Each para is degraded by slightly different
  amounts
• Degeneracy direction is slightly changed

?_mh2
?_bh2
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An even more direct use of NG bispectrum
Bernardeau97, 02, Schneider Lombardi03,
Zaldarriaga Scoccimarro 03, MT Jain 04, 07,
Kilbinger Schneider 05
given as a function of separation l
given as a function of triangles
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A more realistic parameter forecast
MT Jain in prep. 07
WLT (3 z-bins) CMB

• Parameter errors PS, Bisp, PSBisp
• G ?(?_de)0.015, 0.014, 0.010 ? NG 0.016(7),
  0.022(57), 0.013(30)
• ?(w0) 0.18, 0.20, 0.13 ? 0.19(6), 0.29(45),
  0.15(15)
• ?(wa) 0.50, 0.57, 0.38 ? 0.52(4), 0.78(73),
  0.41(8)
• The errors from Bisp are more degraded than PS
• Need not go to 4-pt!
• In the presence of systematics, PSBisp would be
  very powerful to discriminate the cosmological
  signals (Huterer, MT 05)

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WLT Cluster Counts
MT S. Bridle astro-ph/0705.0163

• Clusters are easy to find from WL survey itself
  mass peaks (Miyazaki etal.03 see Hamana sans
  talk for the details)
• Synergy with other wavelength surveys (SZ,
  X-ray)
• Combining WL signal and other data is very useful
  to discriminate real clusters from contaminations
• Combing WL with cluster counts is useful for
  cosmology?
• Yes, would improve parameter constraints, but how
  complementary?
• Cluster counts is a powerful probe of cosmology,
  established method (e.g., Kitayama Suto 97)

Angular number counts
w0-1 ? w0-0.9
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Mass-limited cluster counts vs. lensing-selected
counts
Hamana, MT, Yoshida 04
Halo distribution
Convergence map
2 degrees

• Mass-selected sample (SZ) vs lensing-based sample

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Miyazaki, Hamana07

• Mass

Light (galaxies)
Secure candidates
X-ray
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A closer look at nearby clusters (zlt0.3)
30 clusters (Okabe, MT, Umetsu in prep.)

• Subaru is superb for WL measurement
• A detailed study of cluster physics (e.g. the
  nature of dark matter)

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Redshift distribution of cluster samples
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Cross-correlation between CC and WL
Cluster
A patch of the observed sky
Shearing effect on background galaxies

• If the two observables are drawn from the same
  survey region, the two probe the same cosmic mass
  density field in LSS
• Around each cluster, stronger shear signal is
  expected up to 10 in induced ellipticities,
  compared to a few for typical cosmic shear
• A positive cross-correlation is expected
  Clusters happen to be less/more populated in a
  given survey region than expected, the amplitudes
  of lt???gt are most likely to be smaller/greater
• Note that lt ??? gt 2pt, cluster counts (CC) 1pt
  gtno correlation for Gaussian fields

27
Cross-correlation btw CC and WL (contd.)
M/M_sgt1013

• Shown is the halo model prediction for the
  lensing power spectrum
• A correlation between the number of clusters and
  the ps amplitude at l103 is expected.

M/M_sgt1014
M/M_sgt1015
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Cross-covariance between CC WL

• Cross-covariance between PS binned in l and z and
  the cluster counts binned in z
• The cross-correlation arises from the 3-pt
  function of the cluster distribution and the two
  lensing fields of background galaxies
• The cross-covariance is from the non-Gaussianity
  of LSS
• The structure formation model gives specific
  predictions for the cross-covariance

29
SNR for CCWL

• The cross-covariance leads to degradation and
  improvement in S/N up to ?20, compared to the
  case that the two are independent

30
Parameter forecasts for CCWL
lensing-selected sample
mass-selected sample
WL
CCWL
CCWL with Cov

• Lensing-selected sample with detection threshold
  S/N10 contains clusters with gt1015Msun
• Lensing-selected sample is more complementary to
  WLT, than a mass-selected one? Needs to be more
  carefully addressed

31
HSCWLS performance (WLTCCCMB)

• Combining WLT and CC does tighten the DE
  constraints, due to their different cosmological
  dependences
• Cross-correlation between WLT and CC is
  negligible the two are considered independent
  approximately

32
Real world issues on systematic errors

• E/B mode separation as a diagnostics of
  systematics
• Non-gaussian signals in weak lensing fields
• Theoretical compelling theoretical modeling of DE
• Shape measurement accuracies vs. galaxy types,
  morphology, magnitudes
• Data reduction pipelines optimized for weak
  lensing analyses
• Exploring a possibility to self-calibrate
  systemtaics, by combining different methods
• Non-linearities in lensing reduced shear needs
  to be included?
• Intrinsic alignments
• Source clustering, source-lens coupling
• Usefulness of Flexions?
• Develop a sophisticated photo-z code
• Photo-z vs. color space?
• Requirement on spec-z sub-sample from which
  data?
• N-body simulations (initial conditions, how to
  work in multi-dimenaional parameter space for
  N-body simulations, the strategy)
• DE vs. modified gravity
• Fourier space vs. real-space explore an optimal
  method to measure power spectrum from actual
  data, with complex survey geometry
• Exploring a code of likelihood surface in a
  multi-dimensional parameter space (MCMC) how to
  combine with other probes such as CMB, 2dF/SDSS,
  .
• Can measure DE clustering or neutrino mass from
  WL or else with HSC?

33
Issues on systematics self-calibration

• If several observables (O1,O2,) are drawn from
  the same survey region e.g., WLPS, WLBisp, CC,
• Each observable contains two contributions (C
  cosmological signal and S systematics)
• Covariances (or correlation) between the
  different obs.
• If the systematics in different obs are
  uncorrelated
• The cosmological covariances are fairly
  accurately predictable
• Taking into account the covariances in the
  analysis could allow to discriminate the
  cosmological signals from the systemacs
  self-calibration
• Working in progress

34
Summary

• The non-Gaussian errors in cosmic shear fields
  arise from non-linear clustering in structure
  formation
• The CDM model provides the specific predictions,
  so the NG errors are in some sense accurately
  predictable
• Bad news the NG errors are very important to be
  included for current and, definitely, future
  surveys
• The NG degrades the S/N for the lensing power
  spectrum measurement up to a factor of 2
• Good news the NG impact on cosmo para errors are
  less significant if working in a
  multi-dimensional parameter space
• 10 for 7-D parameter space
• WLT and cluster counts, both available from the
  same imaging survey, can be used to tighten the
  cosmological constraints