1Wilkinson Anisotropy Microwave Probe WMAP

1
Cross-Correlating the CMB with the Large Scale
Structure Niayesh Afshordi (Princeton University)
2MASS Analysis SDSS Analysis
Abstract By studying the small correlations of
the Cosmic Microwave Background with galaxy
surveys, we may learn about the dark energy, as
well as the hot gas in the universe. We describe
three such measurements (two of them, for the
first time) at redshifts 1,0.5 and 0.1 which
consistently confirm the standard model of dark
energy and show signatures of hot intra-cluster
gas below redshift of 1.
2-2 Micron All Sky Survey (2MASS) Sloan Digital
Sky Survey (SDSS) 2MASS is an all-sky near
infrared survey of point sources. The two 2MASS
telescopes in Northern and Southern hemispheres
have scanned the sky in three near infrared
frequencies around 2 microns and have identified
around 300 million stars and 1.5 million extended
sources which are mostly galaxies. The K-band
(2.17 micron) magnitude limit is 13.5 for
extended sources which places most of them around
redshift of 0.1. Due to its large area coverage
and large number of galaxies, the
cross-correlation of 2MASS with CMB may
potentially be a good indicator of both ISW and
SZ signals. SDSS is a digital survey of optical
sky, in progress, which is going to measure the
brightness of about 100 million celestial
objects. Using the photometric data, about a
million galaxies are identified and their
spectroscopic redshifts will be measured. For
the current work, we use 3400 square degrees of
the photometric data and use photometric redshift
estimates to bin them into 4 approximate redshift
bins, ranging from 0.35 to 0.57. We use the so
called Luminous Red Galaxies (LRGs) which have
been identified by their colors and trace
clusters of galaxies more strongly than ordinary
galaxies. There are about 4 million LRGs in our
sample.
1-Wilkinson Anisotropy Microwave Probe (WMAP)
Wilkinson Anisotropy Microwave Probe (WMAP) is
one of the most impressive probes of the Cosmic
Microwave Background (CMB) fluctuations , the
Roseta stone of our universe. The WMAP experiment
is based on a satellite which has now spent about
2 years in the L2 point of the Earth-sun system.
The 1 year data was released in Feb 2001, which
describes the most accurate measure of the power
spectrum of all-sky CMB fluctuations down to 0.2
degree angles. Most of these fluctuations are
primordial fluctuations when universe was 380
thousand years old and had just become
transparent. The spectrum of these fluctuations
(combined with other observational constraints)
gives impressive bounds on various cosmological
parameters and confirms the dark energy dominated
cold dark matter paradigm (see the WMAP
website). However, about 1 of these
fluctuations might be generated by the
intervening matter in the late universe. Those
are the fluctuations that we are looking at in
this work.
4-ISW at z1 Boughn Crittenden 2003 and Nolta
et al. 2003, independently, cross-correlated the
WMAP data with the NVSS radio source catalogue.
Boughn Crittenden 2003 repeated this exercise
for the HEAO-1 X-ray flux maps as well. Both
groups find a positive signal with a 2-3 sigma
significance, consistent with the ISW signal
expected from the galaxies at z1, which is the
approximate redshift of both samples. The figure
shows the cross-correlation with HEAO-1 flux map
(dots). The green curves show the
cross-correlation with a 100 random Gaussian
realizations of the sky, while the red and blue
curves show the expected cross-correlation if the
dark energy was 72 of the energy budget of the
universe. The figure corresponds to a 2.4-2.8
sigma detection.
3-Sources of Cross-Correlation between CMB and
galaxies There are many potential contaminants
of the CMB in the late universe. All the
extra-galactic contaminants are expected to trace
the large scale matter distribution in the
universe as the gravity is the main interaction
that determines the dynamics on large scales.
Because of the same reason, galaxies also trace
the large scale matter distribution. Therefore,
we expect a correlation between the galaxy and
the CMB due to its extra-galactic contaminants.
These contaminations (or secondary fluctuations)
are typically a small portion of CMB fluctuations
(less than 1 percent). The main two sources for
these fluctuations, on angles larger than 0.1
degree, are 1-Integrated Sachs-Wolfe (ISW)
effect As photons travel through the universe to
reach us, they experience the gravitational
potential of the large-scale matter distribution.
If the gravitational potential varies with time,
the photons experience a net redshift/blueshift
as it travels in and out of potential wells In
a flat universe, the large-scale variation of the
gravitational potential is a signature of the
presence of dark energy (negative pressure) in
the universe. ISW is expected to be the main
source of cross-correlation above a few degrees.
The error in ISW is dominated by cosmic variance
and so limited by the sky coverage. 2-Thermal
Sunyaev-Zeldovich (SZ) effect The inter-galactic
space inside clusters of galaxies is filled with
shock-heated plasma with temperatures of a few
keV. The CMB photons that travel through this
space may scatter off free electrons and gain
energy through inverse Compton. As a result, when
we look at the CMB photons that reach from the
direction of a cluster, we observe a deficit of
low energy and an excess of high energy photons
This is the so called thermal SZ effect which
typically dominates the cross-correlation below a
few degrees. The error in the SZ
cross-correlation signal is dominated by Poisson
noise and so limited by the number of galaxies.
6-ISW and SZ from 2MASS at z0.1
The preliminary results of our WMAP
cross-correlation with 2MASS galaxy survey
indicates a 2 and 2.5 sigma significance for
the ISW and SZ signals respectively. The ISW
signal is within 50 of the WMAP concordance
model prediction, while the SZ signal is
consistent with for the mass-temperature
relation of galaxy clusters. This is about 50
smaller than the observed normalization at low
redshift. The figure shows the cross-correlation
signal for the 3 highest frequencies of WMAP
bands (Q,V,W), while the dashed black curve is
the best fit model which was described above.

5-ISW SZ from SDSS at z0.6
This Figure shows the cross-correlation of our
deepest redshift bin (1.3 million galaxies at
z0.6) with the WMAP temperature map (Scranton et
al, 2003). The grey boxes show the
cross-correlation with the clean maps, while
the red and green curves are the best fit ISW and
SZ signals, respectively. The blue curve is the
sum of the two. We claim a 5 sigma detection of
ISW and a 4 sigma detection of SZ signals.

• References
• For an overview of the WMAP data, the full 1-year
  data release and observational/data analysis
  papers see http//lambda.gsfc.nasa.gov/product/map
  /
• 2)The 2MASS analysis Afshordi, N., Loh, Y.,
  Spergel, D.N., Strauss, M.S., in preparation
• 3)The preliminary SDSS photometric LRG analysis
  Scranton, R. et al, 2003 PRL, in preparation
• 4)Boughn, S., Crittenden, R., 2003,
  astro-ph/0305001
• 5)Nolta, M. et al, 2003 ApJ, submitted,
  astro-ph/0305097
• 6)Theoretical Study of Cross-Correlation with
  CMB Peiris, H., Spergel, D.N. 2000 ApJ, 540,
  605, and references therein.
• 7)The 2MASS data and documentation can be
  obtained from http//www.ipac.caltech.edu/2mass/
• 8)The SDSS public data and documentation can be
  obtained from http//www.sdss.org/sdss.html