Cosmic shear

1
Cosmic shear
Current status and prospects
Henk Hoekstra Department of Physics and
Astronomy University of Victoria
2
Large scale structure
As the universe evolves, the small overdensities
caused by tiny quantum fluctuations in the early
universe grow under the influence of gravity,
whereas lower density regions expand faster than
average. The result is an intricate web of
filaments and knots (galaxy clusters, groups and
galaxies). But most of the matter is invisible
3
Large scale structure
We can simulate the formation of dark matter
structures quite well. (only gravity) Simulating
the formation of galaxies is a very complex
problem. (gastrophysics/feedback, etc.)
4
Large scale structure

• Example of the galaxy distribution based on
  semi-analytic models.
• Star formation
• SNe feedback
• Chemical enrichment
• Gas infall
• Merger history

GIF simulations, Colberg et al.
5
Large scale structure
If we change the parameters of our cosmological
model, the resulting growth of large scale
structure is modified, leading to relatively
subtle changes in the statistical clustering
properties of the matter. Therefore, measuring
the clustering properties of matter as a function
of scale and redshift can be used as a tool to
measure the cosmology! It is very different
from distance measures, such as BAO and type Ia
SNe. It is complementary, and should be seriously
taken into account for some proposed alternatives
to dark matter and dark energy.
6
How to measure it?
Always look on at the bright side
7
How to measure it?
The light distribution can tell us some things
about the dark side.
8
Can we use galaxies?
One can use the distribution of galaxies as a
proxy for the large scale mass distribution, but
this can yield biased results!
9
How to measure it?
Simple use the Force (of gravity) !
10
Gravitational lensing
As predicted in the early 20th century, rays of
light are deflected by massive objects in the
universe.
The angle of deflection is a direct measure of
mass!
11
Gravitational lensing
12
Weak gravitational lensing
Example of everyday lensing.
13
Weak gravitational lensing
Weak lensing
Strong lensing
A measurement of the ellipticity of a galaxy
provides an unbiased but noisy measurement of the
shear
14
Cosmic shear
Cosmic shear is the lensing of distant galaxies
by the overall distribution of matter in the
universe it is the most common lensing
phenomenon.
15
We can see dark matter!
Courtesy B. Jain
In the absence of noise we would be able to map
the matter distribution in the universe (even
dark clusters).
16

Why weak lensing?

• Weak lensing provides a direct measurement of
  the projected (dark) matter distribution, which
  can be used for cosmological parameter
  estimation.
• The physics is well understood General
  Relativity.
• The applications are numerous.
• statistical properties of the matter
  (cosmological parameters).
• relation between galaxies and dark matter
  (galaxy biasing).
• properties of dark matter halos (test of CDM and
  law of gravity).

17
Why cosmic shear?
Current observational constraints on the
properties of dark energy are crude at best.
Progress depends critically on how well various
cosmological probes can be understood Do we
understand what we are doing? DETF comments
The WL technique is also an emerging technique.
Its eventual accuracy will also be limited by
systematic errors that are difficult to predict.
If the systematic errors are at or below the
level asserted by the proponents, it is likely to
be the most powerful individual Stage-IV
technique and also the most powerful component in
a multi-technique program.
18
Why cosmic shear?
Although weak lensing has many interesting
applications, cosmic shear is the most demanding
and has been driving most technological
advances in the past decade.

• How do we measure this signal?
• How do we interpret this signal?

19
How to measure the signal?
The underlying assumption is that the position
angles are random in the absence of lensing. At
some level intrinsic alignments will complicate
things (can be dealt with using photometric
redshifts?).
no lensing
lensing
Averaged shape
20
How to measure the signal?

• To quantify the cosmic shear signal we use the
  ellipticity correlation functions. The results
• do not depend on survey geometry.
• provide a measure of the residual systematics.

r
no lensing
r
lensing
21
What do we need?

• The weak lensing signal is small
• We need to measure the shapes of many galaxies.
• We need to remove systematic signals at a high
  level of accuracy.

Only recently we have been able to overcome both
obstacles, although we still need various
improvements to deal with the next generation of
surveys
22
Build a big camera

• 1 square degree field of view
• 350 megapixels

Megacam
23
Put it on a good telescope
Such as the CFHT or VST, LSST, SNAP, etc
24
and take a lot of data!
CFHTLS RCS2 KIDS
Thats when the fun starts
25
Dealing with systematics

• The induced lensing signal is small and
  observational distortions are typically larger
  than the lensing signal.
• The observed shapes of galaxies need to be
  corrected for
• PSF anisotropy
• Circularisation by seeing
• Camera shear

Various correction techniques have been developed
and tested extensively. In particular the Kaiser
et al. (1995) approach is widely used. This
method works fine for current data sets, but we
need improved methods for upcoming large surveys
shapelets?
26
Dealing with systematics the PSF
The first step in the correction for the PSF is
to identify a suitable sample of stars
27
Dealing with systematics the PSF
The shape parameters from the stars allow us to
quantify the PSF anisotropy variation and the
effect of seeing
Old Megacam PSF anisotropy pattern
28
Dealing with systematics the PSF
Weak lensing is rather unique in the sense that
we can study systematics very well. Several
diagnostic tools can be used. However, knowing
systematics are present doesnt mean we know how
to deal with them But we can readily simulate
weak lensing surveys. The Shear TEsting Programme
(STEP) is aiming to improve our techniques this
way.
29
Dealing with systematics tests
The lensing signal should be curl-free. We can
project the correlation functions into one that
measures the divergence and one that measures
the curl E-B mode decomposition. We can also
look for correlations between the corrected
galaxy shapes and the PSF anisotropy.
E-mode (curl-free)
B-mode (curl)
30
Dealing with systematics tests
It is relatively easy to create simulated data to
test the measurement techniques. The Shear
TEsting Programme is an international
collaboration to provide a means to benchmark the
various methods. So far two papers have been
published (Heymans et al., 2006 and Massey et
al., 2007). These results provide a snapshot of
the current accuracy that can be reached (1-2).
31
Dealing with systematics tests
Correction for PSF anisotropy
Correction for PSF size
Heymans et al. (2006)
32
Dealing with systematics improvements

• There are two concerns with PSF correction
• Correct PSF model?
• Correct correction?

Jarvis Jain (2004) have shown how to get a
(near?) perfect PSF model. Much work is
devoted to improve the correction itself
(shapelets, lensreg, etc.)
Once we have solved these problems
33
What does the signal mean?
The statistical properties of the (dark) matter
distribution depend on the cosmology. The power
spectrum (the variance as a function of scale)
contains a wealth of information.
34
What does the signal mean?
The cosmic shear signal is mainly a measurement
of the variance in the density fluctuations.
Same lensing signal
To first order lensing measures a combination of
the amount of matter Wm and the normalisation of
the power spectrum s8.
35
What does the signal mean?
We want to know the convergence (or projected
mass) power spectrum
But we can measure
Shear correlation function at separation Q
Aperture mass (Map) variance at scale Q
36
What does the signal mean?
The lensing signal depends on the (non-linear)
matter power spectrum this gives extra
sensitivity to the parameter estimation and can
break degeneracies We need improved estimates
for the power spectrum in the non-linear regime
(now use Peacock Dodds and Smith et al. (2003)
recipes). The lensing signal depends on the
redshift distribution of the (faint) source
galaxies this allows us to measure how structure
grows in the universe We need better estimates
for the source redshift distribution, e.g. from
photometric redshift surveys.
37
What have we done so far?
Since the first detections reported in spring
2000, many cosmic shear measurements have been
published.
Status in 2001
Courtesy Y. Mellier
38
some old surveys

• Red-sequence Cluster Survey (RCS)
• Data taken with CFHT and CTIO.
• 53 square degrees analysed.
• Measured gt 2x106 galaxy shapes down to R24.
• VIRMOS-DESCART
• Data taken with CFHT
• 11 square degrees analysed
• Measured gt 8x105 galaxy shapes down to IAB24.5
• CTIO survey
• Data taken with CTIO
• 80 square degrees down to R23

39
CTIO survey
Jarvis et al. (2006)
40
CFHT Legacy Survey
The Canada-France-Hawaii Telescope Legacy
Survey is a five year project, with three major
components

• Very Wide Survey solar system
• 600 square degrees
• around ecliptic (strip)
• Wide Survey weak lensing
• 170 square degrees (3 fields)
• 5 filters (u,g,r,i,z)
• ilt24.5
• Deep Survey type Ia supernovae
• 4 square degrees (4 fields)
• repeated observations in 5 filters
• expect 1000 supernovae!

41
CFHT Legacy Survey
42
CFHTLS first results
20 square degree used in Hoekstra et al. (2006)
43
CFHTLS first results
44
CFHTLS first results
Hoekstra et al. (2006)
45
CFHTLS first results
WideDeep (cheap tomography)
Wide only
46
Comparison of results
Benjamin et al. (2007) compared and carefully
combined the results for 4 surveys. The total
area is about 100 square degrees.
47
Comparison of results
48
Comparison of results
We think the observed lensing signal is fairly
accurate. But how about the interpretation. Do we
know? Were getting there! The early results
were based on the HDF photometric redshift
distribution. The redshift distribution obtained
by Ilbert et al. (2006) based on CFHTLS Deep data
suggests a higher mean redshift!
49
CFHTLS-Deep redshifts
Knowledge of the source redshifts is currently
the dominant limiting factor for cosmic shear
surveys. Redshift information will allow for a
proper interpretation of the signal, improve
accuracy on w and help with intrinsic
alignments. A lot of work is needed to improve
the current situation!
50
Comparison of results
Benjamin et al. (2007)
51
Comparison of results
The new analysis also includes a proper
accounting for non-linear covariance (Semboloni
et al. 2006)
52
Does the signal make sense?
YES!

• Consistency of different measurements
• Vanishing B-modes
• Redshift dependence (!?)
• Shape of the signal
• all support the cosmological origin of the
  observed weak lensing signal.

53
CFHTLS the next step

• Since the publication of the first results
  several things have happened
• Image quality has improved
• More data have been taken (140 sq. deg in i)
• 30 sq. deg. of u,g,r,i,z

• Reduced systematics
• Can probe larger scales
• Improve estimates of cosmological parameters
  using photo-zs

54
CFHTLS the next step
Improvements in image quality
August 2005 L3 flip Spacer tilt
55
CFHTLS the next step
Improvements in PSF anisotropy
before
after
56
CFHTLS the next step
We have recently analysed 50 sq. deg of i data
57
CFHTLS the next step
Fu et al. (in prep)

• Line ?80.85 ?m0.27 ?0.73 h0.71
  ltzsgt0.85 ?e 0.36 ngal15 gal/arcmin2
• Errors Poissoncosmic variance included

58
CFHTLS the next step

• Some other cosmic shear projects
• Tomography using the current set of ugriz data.
• Measurement of higher order statistics

Van Waerbeke et al. (in prep)
59
Details, details, details
The devil is in the details. The accuracy of
first cosmic shear surveys is mostly limited by
statistical noise (small areas). For the next
generation many subtle effect need to be taken
into account. We are discovering these as we go
along
60
Details non-linear power spectrum

• Large numerical simulationsraytracing
• Good initial conditions
• Effects of baryons?

61
Details non-linear covariance
Semboloni et al. (2006) showed that on small
scales the non-linearity of structures results in
a much higher covariance than naively estimated
from Gaussian approximations.
62
Details non-linear covariance
It changes the accuracy on small scales
63
Details intrinsic alignments
Dealing with intrinsic alignments will benefit
greatly from photometric redshift data. This will
eliminate the classical alignments. However,
Hirata et al. and Heymans et al. have pointed out
more subtle effects, namely the alignment between
shear (LSS) and intrinstic alignments. CFHTLS
and other surveys will allow us to measure the
amplitude of the intrinsic alignments.
64
Details complex survey area
Virmos F14
Survey areas are complicated. This can result in
E-B mode mixing. Do we need new statistical
tools? (Kilbinger et al. 2006)
65
What to do next?
The study of dark energy is an important
application of cosmic shear. The CFHTLS will
provide the first constraints from a ground based
survey. But a useful measurement of the dark
energy parameters requires much better
precision. The several hundred million dollar
question is Can we reach the 1 precision from
the ground or should we go to space?
66
Advantages of space

• much smaller PSF
• optical NIR bands
• higher source density
• higher source redshift
• better photo-zs
• large reduction in systematics

SuperNova Acceleration Probe
67
Conclusions
The measurement of the cosmic shear signal using
CFHTLS data is progressing well, and a dramatic
improvement in the accuracy of cosmological
parameters is expected in the coming years.
BUT
68
There is some(?) work left
We need to improve our knowledge of

• Source redshift distribution
• photometric redshift from the survey data
• deep (photometric) redshift surveys
• Non-linear power spectrum
• large numerical simulations
• good initial conditions
• Intrinsic alignments of galaxies
• can be dealt with using photometric redshifts
• Observational systematic effects
• Improved correction schemes
• Detailed simulations