Post on 05-Jan-2016
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The effects of the complex massdistribution of clusters on weak lensing cluster surveys
Zuhui Fan Dept. of Astronomy, Peking University
Radio observations have played important roles in lensing studies
About 40% of the multiple-imaged quasars have been observed in radio band
The first lens system QSO0957+561A,B
VLBI observations show detailed correspondence between various knots of emission in the two radio images
Outline:
Introduction: Clusters as cosmological probes
Gravitational lensing effects Weak lensing selected clusters
Introduction Clusters of galaxies total mass M ~ 1014 –15 Msun
hot gas T ~ a few keV
Largest varialized objects in the universe Gravity plays dominant roles in the formation and evolution of clusters of galaxies Sensitive to cosmological models Strong sources for x-ray, SZ effects, lensing……
As a zoom lens for faint objects
Abell 2218
galaxy z ~7
z ~ 10
Statistically, the cluster number distributionversus redshift z contains much information on cosmological parameters, such as
wm ,, 8
Fan & Chiueh 2001 Fan & Chiueh 2001
Problems in cosmological applications
* theoretically: the abundance of clusters in terms of their mass * observations: the mass of a cluster is usually derived from observable quantities large uncertainties are introduced
For example
X-ray emission or SZ effects are directly associated with intracluster gas Besides gravity, gas physics affects the properties of intracluster gas considerably.
Gravitational lensing effects are directly related to the mass distribution, regardless luminous or dark components
It is expected that lensing cluster surveys can obtain mass-selected cluster samples
Gravitational lensing effects
Strong lensing effects
multiple images giant arcs
central part of galaxies or clusters
weak lensing effects Lensing effects are weak, and statistical studies are necessary.
shape distortion of background galaxies magnitude magnification of background sources
weak lensing effects
http://www.cita.utoronto.ca/~hoekstra/lensing.html
Lensing effects are related to the mass distribution along line of sights between the observer and the sources
If there exists a large cluster in a particular direction, lensing signals are expected to be peaked around the cluster
D. Wittman et al. astro-ph/0507606First Results On Shear-Selected Clusters From the Deep Len
s Survey: Optical Imaging, Spectroscopy, and X-ray Followup
8.60 of 200 Deep Lens Survey (DLS)
convergence map (Tang and Fan 2005, ApJ)
qualitatively, good correlations are seen between massive clusters and peaks in the convergence map
important questions to ask
the efficiency and completeness of lensing cluster surveys
lensing signal mass of clusters lensing-selected cluster sample truly mass-selected??
Weak lensing selected clusters
We particularly concern the quantitative correspondence between the κ value of a peak in the κ map and the mass of its associated halo
concentrate on double primary matches peak < -- > halo
angular smoothing scale θG=1 arcmin (2 arcmin) (Gaussian smoothing window function)
Simulations ( Jing 1998, 2000)
100h-1Mpc, 2563 particles force resolution: 39h-1kpc
convergence map: the Born approximation stacking mass slices
9.0,1,7.0,3.0 8 nm
Spherical NFW model
rs : characteristic scale ρs : characteristic density
given the mass of the halo M < -- > rs (through concentration parameter c=rvir/rs) ρs
one to one correspondence between M and κ at a given redshift
2)/1)(/()(
ss
s
rrrrr
scatter plot of νpeak and νnfw (ν= κ/σnoise)
correlations are seen but with large scatters
statistical distribution of c (dash-dotted line) triaxial shape of halos (dashed line)
* The uncertainty of c contributes a small portion of the dispersion
* The triaxiality contributes additional dispersions, especially at high ν for massive halos
* Still a large part of the dispersion cannot be explained by the triaxiality of halos
* Even more complex mass distribution of halos ? projection effects along the line of sights ?
Isolate the complexity of the mass distribution from the projection effects
generate κ map including only those matched halos
with other particles removed
-- > κsingle or νsingle
comparison
Comparison
dominant part of the dispersion is associated with the complex mass distribution of halos themselves
σtri σsingle σpeak
νnfw=4.5 0.56 1.11 1.29νnfw=5 0.66 1.23 1.39νnfw=6 0.88 1.37 1.53
substructures
triangles: substructures
substructures contribute to the lower-end dispersion
hidden substructures along line of sights
contribute to high-end dispersion as well
results (θG=1 arcmin)
* lensing signals from clusters are far more complex than the spherical NFW model can describe * triaxial mass distribution must be taken into accou
nt * large substructures have important effects * projection effects play minor roles
νnfw=4.5 νnfw=5 νnfw=6
0.25 0.18 0.152/12
single
singlepeak
θG=2 arcmin
comparison
* Projection effects are much more significant than that of θG=1 arcmin
σtri σsingle σpeak
νnfw=4.5 0.44 0.77 1.49νnfw=5 0.49 0.98 1.39νnfw=6 0.61 1.02 1.80
An example
conclusions
* θG=1 arcmin : the lensing signals are dominantly determined by the properties of clusters themselves no simple κ – M correspondence κ-selected not M-selected triaxiality, substructures …
* θG=2 arcmin: projection effects are stronger not preferred in lensing surveys
* the box size of the simulations are relatively small * full ray tracing: evaluate the line-of-sight projection effects more accurately
* the effects of noise: intrinsic non-spherical shape of galaxies
Discussion redshift information:
precise values are not needed applicable to large surveys, such as Planck multi-frequency observations
depending on the cluster-finding algorithm, the final SZE signals are constructed through the weighted average of signals from
different
frequency channels
relativistic effects can be weaker than that
for the v=353 GHz
the flux limit for completeness can be
as high as 200 mJy
Multi-parameter determination
e.g., Ωm, σ8, w
Searching for clusters with weak lensing surveys
Inhomogeneous matter distribution distorts
background source galaxies, and generates correlated distortion signals
Gravitational lensing effect is directly associated with weighted surface mass
distribution κ
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δ: density fluctuation field a: cosmological scale factor ω: comoving radial distance fk: comoving angular diameter distance p(ω): distribution function of source galaxies H0: Hubble constant Ω0: cosmological mass density parameter
Clusters of galaxies are expected to be associated with peaks in κ-map. This is the basic idea of lensing cluster surveys
* Is there a one-to-one correspondence between a peak and a halo? * selection function: mass selected? * completeness and efficiency
halodark
arcmin1oversmoothed
map
al.etHamanaT.
Visually: good correlation theoretically expected κ value from a cluster “observed” κ value ?
mis-matches physical reasons? projection effects
Theoretical modeling:
spherical mass distribution NFW profile one to one correspondence between κ and M mass selected
With simulation data from Dr. Jing et al. analyze the dispersion between the theoretical expected lensing signals with “observed” ones
gGnoise
noise
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possible reasons for the dispersion: projection effect nonspherical mass distribution of dark halos high resolution numerical studies of Jing et al. triaxial dark matter halos
orientation
ecb cee ,,
Conclusion statistical uncertainty of the concentration
parameter - account for small part of the dispersion nonsphericity and statistical uncertainty in the axial ratios account for large part of the dispersion especially for the high tail part
Theoretical modeling mass selected
better modeling:
P: probability function
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M
halo
halothsGth
dM
zMdndM
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zMdnzMHdM
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dM
zMdnzMPdM
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dVdzN halo
thsGth
* find P(νth, M, z) * theoretical calculations on the number distribution versus simulations * different cosmological models * understand the projection effect void structures multiple halos * add in noise
On going research and future plans SZ effects clusters detected through gravitational lensing effects dark energy properties: w, dw/dt
LISA: prediction of GW sources from cosmological point of view new window for cosmological studies
Cosmological merging SMBH-galaxy evolution of model -- history - correlations --- binary MBH
# of LISA sources redshift distribution
distribution: orientation of the triaxial halos
ecb cee ,,