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Measuring the Growth Factor
via Gravitational Lensing
James Taylor
University of Waterloo
Origins of Dark Energy Origins Institute, May 14-17 2007
Observational Paths to Dark Energy
• line-of-sight distances, e.g. DL(a) from SNe
• physical scales, e.g. the sound horizon from
Baryon Acoustic Oscillations
• volumes, e.g. from cluster number counts?
} geometry
• the growth of potential fluctuations (ISW)
• the growth of linear fluctuations (cosmic shear)
• the abundance of non-linear fluctuations
(cluster number counts)
} growth of
structure
• the differential growth of non-linear structure
Both ultimately measure H(a) or i(a),
but with very different redshift weighting.
Origins of Dark Energy Origins Institute, May 14-17 2007
Probes of Structure Formation
Initial perturbations are small, grow linearly to amplitude D(a):
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Growth Factor: TIFF (LZW) decomp resso r
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Horellou & Berge 2005
(normalized to 1 at the a = 1), where
D is the amplitude of the growing mode.
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For other e.o.s., varies with a:
Origins of Dark Energy Origins Institute, May 14-17 2007
Probes of structure growth using gravitational lensing:
1) Cosmic shear from weak lensing
linear and non-linear fluctuations on a range of scales
(complicated inversion problems)
2) Cluster detection and characterization from weak and strong lensing
abundance of high peaks in the density field
(degenerate in 8 and growth)
3) Differential growth of non-linear structure
(interesting, but may be hard to calibrate?)
Origins of Dark Energy Origins Institute, May 14-17 2007
Cosmic Shear, etc. overdense underdense B-mode
(systematic)
Mass overdensity produces tangential distortion of
light rays from background objects; underdensity
produces radial distortion.
Effect always small, so need to average over 100s of objects (i.e. galaxies)
limit to scales probed, intrinsic shape noise.
* Can look at resulting signal statistically: shear correlation measuring correlation of
overdense/underdense regions as a function of angular scale.
* Can also make smoothed maps of resulting shear or convergence.
Redshift dependence of effect is very slow, producing a very broad kernel in redshift
space:
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Origins of Dark Energy Origins Institute, May 14-17 2007
3D Lensing Tomography zs = 0.8 zs = 1.0
sensitivity
1/c
Single source plane produces one weighted
measurement of mass along the l.o.s.
In principle, differences between planes can produce
a 3D mass map or more indirect 3D shear statistics
Some problems from extent of redshift kernel,
inaccuracies in photo-zs
Origins of Dark Energy Origins Institute, May 14-17 2007
The COSMOS Survey P.I. Nick Scoville
Origins of Dark Energy Origins Institute, May 14-17 2007
The COSMOS Survey
2 square degree ACS mosaic
current lensing results from
1.64 square degrees
2-3 million galaxies down to
F814WAB = 26.6
15-band photometry,
photo-zs with dz ~ 0.03(1+z)
to z = 1.4 and IF814W = 24
follow-up in X-ray, radio, IR, UV
Origins of Dark Energy Origins Institute, May 14-17 2007
WL Convergence Maps
Massey, Rhodes, Leauthaud
Capak, Koekemoer, Scoville, Refregier
cut catalogue down to
40 galaxies/arcmin2 to remove bad zs
correct for PSF variations, CTE
Get lensing maps, low-resolution
3D maps, various measures of power
in 2D and restricted 3D
results compare well with baryonic
distributions (e.g. galaxy distribution)
Origins of Dark Energy Origins Institute, May 14-17 2007
Systematics
instrumental systematics a major and unanticipated headache
(PSF variations, CTE)
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Origins of Dark Energy Origins Institute, May 14-17 2007
The Final Result
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TIFF (LZW) decomp ressor
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E-modes (left) versus B-modes (right)
Origins of Dark Energy Origins Institute, May 14-17 2007
Seeing the Growth of Structure Directly
actually quite complicated to show the
growth of structure going forward in time
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Origins of Dark Energy Origins Institute, May 14-17 2007
Measuring the Growth of Structure
Calculate the shear correlation function divided by the integrated lensing
sensitivity to a given slice, and rescale to a fixed physical scale, assuming
the signal is coming from the redshift of peak sensitivity.
Get (rather noisy) measure of the growth of structure:
Massey et al. 2007b
Origins of Dark Energy Origins Institute, May 14-17 2007
3D Mass Distribution
Final result: first 3D map of the mass (or potential) distribution in a large
volume. Note this is only 1.6 square degrees on the sky.
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Massey et al. 2007a
Origins of Dark Energy Origins Institute, May 14-17 2007
Shear vs. photo-z around peaks, along promising lines
of sight
Origins of Dark Energy Origins Institute, May 14-17 2007
Shear vs. photo-z around peaks, along promising lines
of sight
N.B. angular-
diameter
Taylor et al. distance-z
in prep. relation
Origins of Dark Energy Origins Institute, May 14-17 2007
Summary 2D
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Can get constraints on the amplitude of fluctuations:
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Need a larger volume to get constraints on the equation of state
(current estimate: w = -1 ± 1 with this volume)
Working from space does not automatically make systematics vanish.
Physically, projection effects and photo-z errors a major issue.
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Origins of Dark Energy Origins Institute, May 14-17 2007
Second Method: Cluster Number Counts
Count the number of high peaks in the universe
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In principle a very sensitive measure TIFF (Un compressed) decompressor
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In practice, mass calibrations a problem
Also constrained to do this at fairly low redshift
(esp. for x-ray) and fairly large mass
Weller & Battye 2003
N.B. Press-Schechter:
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How to break sigma-growth factor degeneracy?
Origins of Dark Energy Origins Institute, May 14-17 2007
Third Method: Differential Growth
Dark matter halos achieve a different degree of relaxation depending
on their growth rate (mass accretion rate versus crossing time?)
The change between the mixed and unmixed regions corresponds to a
change in the slope of the density profile: r-1 to r-3
This is measured as halo concentration: c rs/rvir; rs where slope is r-2
Thus the concentration of the density profile contains information
about prior growth
Other structural features (substructure, elongation, spin?)
track this one parameter
Origins of Dark Energy Origins Institute, May 14-17 2007
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Andrei Kravtsov
Some reassuring simplifications in the non-linear regime:
e.g. a single-parameter density profile
Navarro et al. 2004
Similarly, a single-parameter mass-accretion history?
cf. van den Bosch, Wechsler et al., Mo et al.
Origins of Dark Energy Origins Institute, May 14-17 2007
So how do haloes grow?
Extended Press-Schechter (e.g. Lacey & Cole 1993)
mass accretion history = random walk in / (where c/D)
high
increasing barrier height QuickTime™ and a
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: height of barrier low
perturbation has to
cross to collapse big small
(M) : variance
on mass scale M
decreasing scale
Origins of Dark Energy Origins Institute, May 14-17 2007
What does concentration measure?
Mass accretion histories
correspond to linear
trajectories in - space
Transformation to M - a
introduces curvature
concentration depends on QuickTime™ and a
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epoch where transition from
fast to slow accretion starts
Depends mainly on dlnD/dlna
Origins of Dark Energy Origins Institute, May 14-17 2007
What does concentration measure?
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Concentration set in transition
from fast to slow accretion
curvature in log(M/M0) vs. log(a)
mainly due to curvature in D(a)
So in effect we can measure
fast
dlnD/dln(a) with some weighting.
cNFW ~ 4 (ao/ac)
Origins of Dark Energy Origins Institute, May 14-17 2007
Concentration versus mass accretion history
Wechsler et al. 2002: ac/ao vs concentration Zhao et al. 2003a: better fitting function
Origins of Dark Energy Origins Institute, May 14-17 2007
Can we measure concentration?
Comerford & Natarajan 2007:
X-ray and Lensing concentrations for O(100) clusters
Origins of Dark Energy Origins Institute, May 14-17 2007
N.B. other age indicators: Halo Substructure
The “radial period” (period for subsequent pericentric
passages)
is the fundamental timescale for subhalo evolution
substructure
tracks tH
Radius/Rvi
r
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Energy/Vc2
Taylor & Babul 2004
Origins of Dark Energy Origins Institute, May 14-17 2007
Substructure reflects balance between accretion and disruption
Taylor & Babul 2005a
Origins of Dark Energy Origins Institute, May 14-17 2007
Overall effect of age on the substructure mass function:
Taylor & Babul 2005a
Origins of Dark Energy Origins Institute, May 14-17 2007
Global Substructure vs. Age Relation
Overall correlation between age and substructure fraction:
number of massive satellites strongly correlated with recent merger history
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Zentner et al. 2005
Origins of Dark Energy Origins Institute, May 14-17 2007
Three Lensing Surveys:
* COSMOS (Scoville PI, Ellis, Massey, Rhodes, Leauthaud, Finoguenov)
2 deg2 ACS weak lensing, plus X-ray & other supporting observations
~150 extended X-ray peaks, ~ 20 in lensing map, z = 0.15 –0.85, M 5e13
.
* Suprime22 (Miyazaki/Ellis, Green, Hamana, Massey)
22 deg2 Subaru weak lensing, some x-ray, Keck/Subaru redshifts ~80
objects from lensing (with masses to ~50%), z = 0.15–0.8, , M 1e14
* LoCuSS (Smith PI)
~all sky, nearby massive cluster survey z = 0.15–0.25, Lx limited, ACS
snapshot lensing, some ground-based NIR, XMM & archival Chandra x-ray,
objects typically 5e14, current sample of 30 clusters, final sample of ~100
Origins of Dark Energy Origins Institute, May 14-17 2007
LoCuSS: Sample
Original Idea:
• Target = 100 clusters
• Brightest X-ray clusters
over a narrow z range
suited to f.o.v. of WFPC/ACS Pilot (XBACs): JPK+ GO:8249
• 21 archival HST clusters LoCuSS (BCS+eBCS+REFLEX):
GPS+ GO:10881
• 143 SNAPSHOT targets
– ~50% observed by
mid-2008
Current Status:
– More or less complete
data on 43 clusters
– Many are strong lensing
systems
Origins of Dark Energy Origins Institute, May 14-17 2007
Why the diversity of cluster morphologies?
What is happening physically?
(Smith et al. 2005)
Origins of Dark Energy Origins Institute, May 14-17 2007
Disturbed Versus Undisturbed Smith et al., 2005, MNRAS, 359, 417
Undisturbed Disturbed Disturbed
uni-modal (3/10) multi-modal (4/10) uni-modal (3/10)
Mass
X-ray
Ndm 1 2 1
fsub 0.03±0.01 0.23±0.01 0.04±0.01
Ttot/Tann 0.8±0.1 1.0±0.1 1.0±0.2
Δr (kpc) <4 40±8 88±4
Origins of Dark Energy Origins Institute, May 14-17 2007
Structural segregation in the
M-T relation?
• Mass measurement wrong for
non-SL clusters?
Structural
segregation • Core-related phenomena?
[~40%]
– Pederson et al., 0603260
• Cluster-cluster mergers?
Possible – Ricker & Sarazin 2001,
Systematics?
[~10-20%] Randall et al. 2003
• What else?
Smith et al., 2005, MNRAS, 359, 417
Origins of Dark Energy Origins Institute, May 14-17 2007
Compare main central component to the substructure:
A wide range of substructure fractions age difference?
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(Smith et al. 2005)
Overall, seems likely that substructure and possibly X-ray
scaling offsets provide another way of quantifying age
obsevationally.
Origins of Dark Energy Origins Institute, May 14-17 2007
Summary
The measuring the growth factor provides a complimentary estimate of the
equation of state, with different redshift weighting.
At least three methods exist; the third relies on the statistics of halo growth
and the effect of mass accretion rates on halo profiles, substructure
and other properties (spin? X-ray scaling offsets? AGN activity?).
Whether this third method can be calibrated to a useful degree is not clear;
then again similar problems exist with cluster mass measurements.
Origins of Dark Energy Origins Institute, May 14-17 2007
Recent Suprime22 Results
(Green et al. 2006) 8
6
3
worse seeing
better seeing
Log(volume)
Origins of Dark Energy Origins Institute, May 14-17 2007
COSMOS Xray-lensing comparison
(Finoguenov et al. 2006, Taylor et al in prep.)
8 6 3
Log(volume)
Origins of Dark Energy Origins Institute, May 14-17 2007
