Transcript Default

Using the Sunyaev-Zel'dovich
Array in Detailed Studies of
Galaxy Clusters
3rd Biennial Leopoldina Conference
Dark Energy
9th October 2008
Tony Mroczkowski (Columbia / UPenn)
with
the Sunyaev-Zel'dovich Array (SZA) Collaboration
and
Daisuke Nagai (Yale)
The SZA Collaboration
Chicago: John Carlstrom (P.I.), Tom Culverhouse, Chris
Greer, Ryan Hennessy, Dan Marrone, Erik Leitch, Mike
Loh, Clem Pryke, Megan Roscioli, Matthew Sharp
Columbia: Amber Miller, Tony Mroczkowski, Stephen
Muchovej
Caltech (OVRO): David Hawkins, James Lamb, David
Woody
NASA/MSFC: Marshall Joy
U. Alabama: Esra Bulbul, Max Bonamente, Nicole Hasler
Overview
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Why we study galaxy clusters
The tools we choose for studying cluster gas —
SZ+X-ray observations
The Sunyaev-Zel'dovich Array
An improved SZ model to fit current SZ
observations.
Upcoming results to expect from the SZA
Why study galaxy clusters?
Provide independent, complementary tests of cosmology.
Large, statistically-complete samples (>100) can be used to
measure the growth of structure.
Smaller samples (~50) can be used to probe the expansion of
the universe (e.g. recent gas fraction studies, such as the Xray only studies in Allen et al. 2007 and Vikhlinin et al.
2008).
Small samples can also be used to determine the Hubble
constant as a function of redshift by combining X-ray+SZ
data (e.g. Bonamente et al. 2004), independent of CMB and
SNe results.
To maximize the utility of clusters, we must relate their
observable properties of clusters to their total masses.
Tools to Probe the Intracluster Medium (ICM)
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The ICM (cluster gas) is optically thin, so we can simply
perform the line of sight integral of the plasma's emission.
X-ray surface brightness SX is strongly dependent on electron
density, ne(r).
The X-ray emissivity, ee is weakly dependent on temperature
(as above).
A complementary tool:
The Sunyaev-Zel'dovich (SZ) Effect
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image from L. Van Speybroeck.
The SZ effect is due to inverse
Compton scattering of CMB
photons by electrons in the ICM.
~1% of CMB photons are scattered
to higher energies, leaving an
intensity decrement at our
observing frequencies, 30 and 90
GHz.
The thermal SZ effect is a measure
of electron pressure integrated
along the line of sight (as shown in
next slide).
Utility of SZ Cluster Studies
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The SZ effect can be measured from the ground, by relatively
inexpensive radio telescopes.
SZ intensity is redshift independent.
The SZ effect provides a measurable quantity, Yint,which is the
integral of line of sight Compton y within some radius on the sky.
Yint scales robustly with cluster total mass (e.g. Motl et al. 2005,
Nagai 2006, Reid & Spergel 2006). This is exactly what we want
when performing cosmology with a large sample of clusters.
A radio interferometer measures the Fourier transform of Compton
y, which scales as Yint within each Fourier mode probed by a pair of
antennae. This makes interferometers ideal instruments for
constraining Yint.
The Sunyaev-Zel'dovich Array (SZA)
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We built an 8-element interferometer in the Owens Valley, a desert
in eastern California (USA).
The SZA's compact configuration allows it to probe short u,vspacings, corresponding to ~1-6' on the sky (where u and v are the
Fourier conjugates of spatial coordinates x and y).
Each antenna has a 26-36 GHz (“30 GHz”) and an 85-115 GHz
(“90 GHz”) wideband receiver, selected by the tertiary mirror.
Wide correlator (8-GHz) bandwidth allows fast detection of
clusters in targeted observations.
The interferometric imaging capabilities of the SZA make it a good
complement to current SZ survey experiments, such as the South
Pole Telescope (SPT), the Atacama Cosmology Telescope (ACT),
and the Atacama Pathfinder EXperiment (APEX).
SZA configuration
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6 antennae form the
15 baselines of the
compact inner array,
probing large
arcminute scales
2 antennae form 13
more long baselines,
used to constrain the
fluxes of unresolved
radio sources in the
cluster field (i.e.
“point sources”).
SZA 30+90 GHz combined u,v-space coverage
Some photos of the SZA
Results to expect soon from the SZA
Collaboration:
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The SZA has performed a cluster survey at 30 GHz,
covering ~ 5.5 deg2. Look for results in S. Muchovej et al.
in 1-2 months.
The SZA has also performed a 1-5 arcminute-scale CMB
angular power spectrum measurement (l ~ 4000,
competitive with BIMA and CBI). Look for M. Sharp et
al. later this year.
Each of these measurements will place new and
independent constraints on s8.
The SZA continues to perform detailed cluster studies, the
goals of which I will describe.
Modeling the SZE signal
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With interferometric SZ data in hand, we fit models to it in order to
extract meaningful, physical parameters. These models fill in
information on the scales we do not probe.
Since the SZ signal is directly proportional to electron pressure, we
chose to model the cluster pressure profile.
Most previous SZ+X-ray studies have relied on the isothermal -model.
However, we know clusters are not isothermal over a broad radial
extent.
We have recently demonstrated the utility of a new electron pressure
profile in fitting SZ observations (see http://arxiv.org/abs/0809.5077).
This profile, proposed by Nagai et al. 2007, is motivated by fits to the
pressure profiles using detailed X-ray studies (from Vikhlinin et al.
2006) and high-resolution cluster simulations (Kravtsov et al. 2005).
The Nagai '07 (N07) Profile
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This is a generalization of the NFW profile, a 2-parameter profile used
to fit DM halos of simulated clusters.
g describes the inner slope, a describes intermediate slopes, and b
describes the outer slope of the cluster pressure profile.
N07 found rs ~ r500/C500 for concentration factors 1.3-1.8.
We first used the fixed slopes (,,)=(1.3, 4.3, 0.7) from the
original N07 paper. We also tested (,,)=(0.9, 5.0, 0.4), the slopes
in a new erratum to N07, and found no significant change.
P0 and rs are the parameters we vary. This provides an extra degree of
freedom over the isothermal b-model used in many previous SZ studies.
Combining the N07 Pressure Profile
for the SZ fit with X-ray imaging
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Assuming a popular LCDM cosmology (M=0.3, =0.7,
h=0.7), we tested the joint-fit of SZ+X-ray imaging
observations without using X-ray spectroscopic information.
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X-ray imaging is used here to determine density.
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The pressure fit is driven by SZ data.
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Temperature is derived from the simultaneously-fit density and
pressure.
We use a Markov chain Monte Carlo (MCMC) process to fit the
SZ+X-ray data. This jointly maximizes the likelihood of the fit
to both types of data, as well as exploring the probability
density distribution of the model fits.
The X-ray density profile
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30-GHz SZA observations are sensitive to clusters on large scales.
Typical (10-20 ks) X-ray observations of intermediate and high
redshift clusters lack the ability to constrain detailed core structure.
We are interested in the bulk properties of clusters (e.g. at
overdensities D=2500 and D=500, within which the average density
is D times the critical density of the universe).
We chose the density profile used by Vikhlinin et al. 2006, but
stripped the components used in fitting the cluster cores.
We call this the “Simplified Vikhlinin Model,” or SVM:
Testing the N07+SVM profiles
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We chose 3 clusters, well-studied in the X-ray, on which to test
these profiles: Abell 1835 (z=0.25), Abell 1914 (z=0.17), and
CL J1226.9+3332 (z=0.89).
All 3 clusters have exceptional Chandra X-ray data.
We compared our results to independent, detailed X-ray
analyses, performed by Ben Maughan, who fit the clusters using
the Vikhlinin et al. '06 temperature and density profiles.
The independent X-ray spectroscopic analysis of the highredshift cluster CL1226 additionally used XMM-Newton data,
yielding much tighter constraints than typically available for
clusters at high redshift.
SZA cluster observations
Contours are 2-s. Integration times were 18.5 and 11.5 hours, respectively.
Figure from Mroczkowski et al. 2008 (http://arxiv.org/abs/0809.5077)
Derived Total Masses
Figure from Mroczkowski et al. 2008 (http://arxiv.org/abs/0809.5077)
Conclusions
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The new pressure profile fits well.
When combined with X-ray, it provides an independent measure
cluster radial temperature profiles. Since the intensity of the SZ
effect is redshift-independent, and high-significance X-ray
spectra are difficult/expensive to obtain, this method could
prove a valuable, complementary tool.
Accurate modeling of cluster properties will reduce systematic
biases in cosmological tests employing clusters.
By include spectroscopic X-ray information, we can now use
this model to constrain fgas(z) and H(z).
Ongoing projects utilizing these new models
to fit targeted observations of clusters:
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The N07 profile is being used to determine SZ cluster scaling
relations (e.g. SZ flux versus Mtot from X-ray and gravitational
lensing). Look for Marrone et al. in early 2009.
Detailed joint SZ+X-ray fitting of targeted observations of clusters
will lead to better determinations of the Hubble constant and the
hot gas fraction (without assuming we know angular diameter
distance to the cluster). Look for Hasler et al. in 2009.
Constrain Helium sedimentation in the cores of clusters (ala
Markevitch 2007, Peng & Nagai 2008). Look for Bulbul et al. in
2009.
end
Why should pressure follow a profile
like the dark matter halo?
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Aside from clusters that have undergone recent mergers,
they are usually close to hydrostatic equilibrium – the force
of pressure equals the force of gravity.
Dark matter dominates the gravitational potential, and
resides in self-similar halos.
Inhomogeneities in pressure propagate at the speed of
sound, so they do not last long.
The integral of pressure is thermal energy. Thermal energy
closely tracks the potential energy of the cluster (to the
extent that HSE is dominated by thermal pressure).
Modeling the SZE+X-ray data
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Fit the X-ray image in image space
Fit the interferometric data in
Fourier space
The profiles we vary are the N07
pressure and SVM density profiles.
Te(r) is derived from the fit Pe(r)
and ne(r), and is used to model the
X-ray surface brightness.
Compare these to independent Xray-only analysis, as well as joint
fits of an isothermal -model