Constraints on the High-ℓ Power Spectrum of Millimeter-Wave Anisotropies from APEX-SZ

Abstract

We present measurements of the angular power spectrum of millimeter wave anisotropies with the APEX-SZ instrument. APEX-SZ has mapped 0.8 deg2 of sky at a frequency of 150 GHz with an angular resolution of 1'. These new measurements significantly improve the constraints on anisotropy power at 150 GHz over the range of angular multipoles 3000 < ℓ < 10, 000, limiting the total astronomical signal in a flat band power to be less than 105 μK2 at 95% CL. We expect both submillimeter-bright, dusty galaxies and to a lesser extent secondary cosmic microwave background anisotropies from the Sunyaev-Zel'dovich effect (SZE) to significantly contribute to the observed power. Subtracting the SZE power spectrum expected for σ8 = 0.8 and masking bright sources, the best-fit value for the remaining power is C ℓ = 1.1+0.9 –0.8 × 10–5 μK2 (1.7+1.4 –1.3 Jy2 sr–1). This agrees well with model predictions for power due to submillimeter-bright, dusty galaxies. Comparing this power to the power detected by BLAST at 600 GHz, we find the frequency dependence of the source fluxes to be if both experiments measure the same population of sources. Simultaneously fitting for the amplitude of the SZE power spectrum and a Poisson-distributed point source population, we place an upper limit on the matter fluctuation amplitude of σ8 < 1.18 at 95% confidence.

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Draft version August 15, 2009
Preprint typeset using LATEX style emulateapj v. 10/09/06
CONSTRAINTS ON THE HIGH-? POWER SPECTRUM OF MILLIMETER-WAVE ANISOTROPIES FROM
APEX-SZ
C. L. Reichardt1, O. Zahn1, P. A. R. Ade2, K. Basu3, A. N. Bender4, F. Bertoldi5, H.-M. Cho6, G. Chon3,5,12,
M. Dobbs7, D. Ferrusca1, N. W. Halverson4,13, W. L. Holzapfel1, C. Horellou8, D. Johansson8, B. R. Johnson1,
J. Kennedy7, R. Kneissl3,9,10, T. Lanting2, A. T. Lee1,11, M. Lueker1, J. Mehl14, K. M. Menten3, M. Nord3,5,
F. Pacaud5, P. L. Richards1, R. Schaaf5, D. Schwan1, H. Spieler11, A. Weiss3, B. Westbrook1
Draft version August 15, 2009
ABSTRACT
We present measurements of the angular power spectrum of millimeter wave anisotropies with the
APEX-SZ instrument. APEX-SZ has mapped 0.8 square degrees of sky at a frequency of 150GHz
with an angular resolution of 1?. These new measurements significantly improve the constraints on
anisotropy power at 150GHz over the range of angular multipoles 3000 < ? < 10,000, limiting
the total astronomical signal in a flat band power to be less than 105 µK2at 95% CL. We expect
both submillimeter-bright, dusty galaxies and to a lesser extent secondary CMB anisotropies from
the Sunyaev-Zel’dovich effect (SZE) to significantly contribute to the observed power. Subtracting
the SZE power spectrum expected for σ8= 0.8 and masking bright sources, the best fit value for the
remaining power is C?= 1.1+0.9
for power due to submillimeter-bright, dusty galaxies. Comparing this power to the power detected
by BLAST at 600 GHz, we find the frequency dependence of the source fluxes to be Sν∝ ν2.6+0.4
both experiments measure the same population of sources. Simultaneously fitting for the amplitude
of the SZE power spectrum and a Poisson distributed point source population, we place an upper
limit on the matter fluctuation amplitude of σ8< 1.18 at 95% confidence.
Subject headings: cosmic microwave background — cosmology:observations — cosmology: cosmologi-
cal parameters — infrared: galaxies
−0.8×10−5µK2(1.7+1.4
−1.3Jy2sr−1). This agrees well with model predictions
−0.2if
1. INTRODUCTION
Primary anisotropy in the cosmic microwave back-
ground (CMB) radiation is produced by inhomogeneities
in the hot baryon-photon plasma at the epoch of re-
combination. The amplitude of these anisotropies as a
function of angular scale has been used to infer precise
constraints on the parameters of the standard ΛCDM
model (Dunkley et al. 2009; Komatsu et al. 2009). On
angular scales below several arcminutes, the primary
anisotropy is damped by photon diffusion and the ob-
served power is expected to be dominated by sources of
1Department of Physics, University of California, Berkeley, CA,
94720
2School of Physics and Astronomy, Cardiff University, CF24
3YB Wales, UK
3Max Planck Institute for Radioastronomy, 53121 Bonn, Ger-
many
4Center for Astrophysics and Space Astronomy, Department
of Astrophysical and Planetary Sciences, University of Colorado,
Boulder, CO 80309
5Argelander Institute for Astronomy, Bonn University, Bonn,
Germany
6National Institute of Standards and Technology, Boulder, CO,
80305
7Department of Physics, McGill University, Montr´ eal, Canada,
H3A 2T8
8Onsala Space Observatory, Chalmers University of Technology,
SE-439 92 Onsala, Sweden
9Joint ALMA Office, Av El Golf 40, Piso 18, Santiago, Chile
10ESO, Alonso de Cordova 3107, Vitacura, Santiago, Chile
11Lawrence Berkeley National Laboratory, Berkeley, CA, 94720
12Max Planck Institute for Extraterrestrial Physics, 85748
Garching, Germany
13Department of Physics, University of Colorado, Boulder, CO
80309
14University of Chicago, 5640 South Ellis Avenue, Chicago, IL
60637
foreground emission and the interaction of the CMB with
intervening structure. In particular, the inverse Comp-
ton scattering of CMB photons off hot plasma bound to
clusters of galaxies (Sunyaev & Zel’dovich 1972) gives
rise to a spectral distortion of the CMB known as the
Sunyaev-Zel’dovich effect (SZE). At frequencies less than
∼ 220GHz, the SZE produces a decrement in the CMB
intensity in the direction of a galaxy cluster. Galaxy clus-
ters produce (secondary) anisotropy power on arcminute
scales corresponding to their angular size. The observed
SZE power depends sensitively on the abundance of clus-
ters and the history of structure formation. In particular,
the amplitude of the SZE power scales as σ7
is the rms fluctuation of matter on scales of 8h−1Mpc,
and serves as an independent probe of the amplitude of
density perturbations (Komatsu & Seljak 2002).
Evidence for small scale power beyond that expected
from the primary CMB has been reported by the Berke-
ley Illinois Maryland Association (BIMA) and Cos-
mic Background Imager (CBI) interferometers operat-
ing at 30GHz. These measurements find a level of SZE
anisotropy power consistent with a value of σ8somewhat
greater than those preferred by other contemporary mea-
surements, which favor σ8∼ 0.8 (Vikhlinin et al. 2009;
Komatsu et al. 2009). BIMA observations at 30GHz
covering a total of 0.1deg2of sky produced a nearly 2σ
detection of excess power in a flat band centered at a
multipole ? = 5237 (Dawson et al. 2006). Due to the
non-Gaussian distribution of the SZE on the sky and the
low significance of the detection, this resulted in only
weak constraints on the matter power spectrum normal-
ization, σ8= 1.03+0.20
with the CBI experiment at 30GHz over a larger field
8, where σ8
−0.29at 68% confidence. Observations
arXiv:0904.3939v2 [astro-ph.CO] 15 Aug 2009

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were used to produce a > 3σ detection of excess power
on angular scales ? ∈ [1800,4000] (Sievers et al. 2009).
Interpreting this power as being due to the SZE, they
find σ8= 1.015 ± 0.06 at 68% confidence. However, re-
cent observations with the SZA experiment operating at
30GHz and covering a total of 2deg2of sky, have de-
termined an upper limit on the excess power in broad
band centered at multipole ? = 4066 which is signifi-
cantly lower than the band powers reported by CBI and
appears to be consistent with more conventional values
of σ8∼ 0.8 (Sharp et al. 2009). The SZA team interprets
the higher power measured by CBI as potentially being
due to an unsubtracted population of radio sources.
At 150GHz, we expect the SZE and emission from
distant dusty galaxies to contribute significantly to the
power on angular scales corresponding to ? > 2500. The
ACBAR experiment reported a ∼ 1σ excess power at
? > 2000, that if interpreted as the SZE, would be con-
sistent with the higher value for σ8 preferred by CBI
(Reichardt et al. 2009). However, the ACBAR results
are in excellent agreement with a more standard value
σ8 ∼ 0.8 when one considers the expected foreground
emission from IR point sources. The QUaD collabora-
tion has recently released a 150GHz power spectrum for
? > 2000 (QUaD collaboration: R. B. Friedman et al.
2009). The QUaD bandpowers appear (numerical values
have not yet been released) to be systematically lower
than those produced by ACBAR with no evidence for
contributions from secondary anisotropy or foreground
emission. Bolocam has recently published new results
for anisotropy power at 150GHz on angular scales above
? = 3000 (Sayers et al. 2009). They report upper limits
on the power of 1080µK2at 95% confidence in a wide
bin centered at ? = 5700 and determine that σ8< 1.57
at 90% confidence. New high resolution and sensitiv-
ity bolometer arrays operating at millimeter wavelengths
such as those currently deployed on the APEX, SPT, and
ACT telescopes have the capacity to drastically improve
constraints on the SZE and point source contributions to
the high-? power spectrum.
This paper presents new measurements of small scale
anisotropy power made with the APEX-SZ bolometer
array on the Atacama Pathfinder Experiment (APEX)
telescope from its high elevation site in the Atacama
Desert. This work significantly improves the constraints
on excess power above that expected from primary CMB
anisotropy at ? > 3000 at a frequency of 150GHz. In
Section 2, we describe the APEX-SZ instrument and the
observations used to produce the results presented in this
paper. The beam and calibration of the instrument are
described in Section 3. The algorithms used in the pro-
duction of the temperature maps and the power spectrum
are described in Section 4. In Section 5, we present the
power spectrum results and address sources of foreground
emission. Our conclusions are summarized in Section 6.
2. INSTRUMENT AND OBSERVATIONS
APEX-SZ is an array of 330 transition-edge supercon-
ducting (TES) bolometers operating at 150 GHz (Schwan
et al. 2003; Dobbs et al. 2006; Schwan et al. 2009). The
bolometers are cooled to 280mK via a three stage He
sorption fridge and mechanical pulse tube cooler and in-
strumented with a frequency-domain multiplexed read-
out system. The array observes from the 12m APEX
telescope on the Atacama plateau in Chile (G¨ usten et al.
2006) and has approximately 1?FWHM beams with a 22?
field-of-view (FOV). The extremely dry and stable atmo-
spheric conditions make the Atacama one of the best sites
for millimeter-wave astronomy.
The band powers reported in this work are derived
from a single, 0.8 deg2field observed by APEX-SZ for 10
nights in August and September of 2007. This field is a
subset of the XMM-LSS field (Pierre et al. 2004) and is
centered on a moderately massive, X-ray detected clus-
ter, XLSSU J022145.2-034614, with an X-ray tempera-
ture of 5 keV (Willis et al. 2005; Pacaud et al. 2007). A
joint analysis of the X-ray and SZ data will be under-
taken in a separate paper. A circular scan strategy was
used instead of a raster scan to improve the observing
efficiency. The scan strategy concentrates the integra-
tion time at the center of the map causing the time per
pixel to increase steadily from the edges of the map to
the center. The total integration time is 2.9k detector-
hours. The map center reached a depth of 12 µK per 1?
pixel. More details on the instrument and scan strategy
can be found in Halverson et al. (2009) (hereafter H08)
and Schwan et al. (2009).
3. BEAM AND CALIBRATION
The average beam of the APEX-SZ bolometers is mea-
sured with daily observations of Mars. At 8??diameter,
Mars is nearly a point source for the 1?APEX-SZ beam,
and it is sufficiently bright to map the beam near side-
lobes to below -25 dB. The measured beam agrees well
with the ZEMAX15simulated beam profiles when opti-
cal cross-talk is taken into account. The near sidelobes
increase the real beam solid angle by 32% compared to
the best fit Gaussian beam. We divide the measurement
uncertainty on the beam into two parts. The main lobe is
well-fit by a Gaussian, and we estimate the measurement
uncertainty on the FWHM to be 2.5%. Due to the large
angular scale of the sidelobe structure, a mis-estimation
of beam sidelobe will effectively cause a mis-calibration
of the band powers. We include the uncertainty in the
total beam area in the calibration error.
The observations of Mars are used to establish the
absolute calibration of the APEX-SZ instrument. The
temperature of Mars for our observation frequency and
dates is taken from the Rudy model (Rudy et al. 1987;
Muhleman & Berge 1991), that has been updated and
maintained by Bryan Butler16. The Rudy model is com-
pared with measurements of the brightness temperature
of Mars made with the WMAP satellite at 93GHz dur-
ing five periods across several years (Hill et al. 2009).
The WMAP measurements of Mars have uncertainty of
< 1% and we adjust the normalization of the Rudy
Model down by 5.2% to bring it into agreement with
the WMAP measurements. Combining the ∼ 1% un-
certainty in the WMAP Mars measurements, the 1.0%
scatter in the 93GHz WMAP to Rudy Model compar-
ison, and 0.9% for the uncertainty in the extrapolation
from 93GHz, where the Rudy Model is calibrated, to our
observing frequency, we find the total uncertainty in the
Mars brightness temperature to be 1.7%.
The calibration of each detector is set by comparing the
15http://www.zemax.com
16http://www.aoc.nrao.edu/∼bbutler/work/mars/model/

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peak amplitude in a map of Mars to the expected am-
plitude given the temperature and size of Mars and the
size of the detector’s beam. A correction factor for the
atmospheric opacity is applied which is always less than
3%. The overall calibration uncertainty is estimated to
be 5.5% in temperature, with the dominant errors due to
a 4% uncertainty in the beam area, a 3% uncertainty to
account for temporal variations between the model pre-
diction and the temperature measured by APEX-SZ, the
1.7% uncertainty in the temperature of Mars, and a 1.4%
uncertainty in the conversion of brightness temperature
to CMB temperature for the measured APEX-SZ band.
More details on the beam estimation and calibration can
be found in H08.
4. ANALYSIS
4.1. Map-Making
The filtering and map-making process used in this
analysis follows the approach detailed in H08 for anal-
ysis of the Bullet cluster. We briefly outline the major
steps here, while highlighting any differences in the fil-
tering between this work and the Bullet cluster analy-
sis. The timestream processing is designed to remove
scan-synchronous noise, atmospheric fluctuations, and
1/f noise.The scan pattern includes boresight eleva-
tion changes which modulate the air mass along the
line of sight. This signal is removed by fitting for a
cosecant(el) term. 1/f noise in the system is filtered from
the timestream by a 0.3 Hz 8-pole Butterworth high-pass
filter (HPF). The typical length scale of atmospheric fluc-
tuations is much larger than the FOV, so fluctuations
are highly correlated across the APEX-SZ array. This
correlated term is removed by fitting for a low order spa-
tial polynomial across the focal plane at each time sam-
ple. We remove a 2ndorder spatial mode in this work.
The cumulative effect of the filtering is to completely
remove structures corresponding to angular multipoles
below ? ? 1400.
weighted according to the filtered timestream RMS and
binned into 20??map pixels.
After filtering, the timestreams are
4.2. Power Spectrum Estimation
The band powers, qB, are reported in CMB tempera-
ture units of µK2and parametrize the power spectrum
according to
?(? + 1)
2π
C?≡ D?=
?
B
qBχB?
(1)
where χB? are top hat functions; χB? = 1 for ? ∈ B
and 0 for ? ?∈ B. We use a pseudo-C?power spectrum
estimator (Hivon et al. 2002). In this formalism, the map
spectrum (also called the pseudo-C?or˜C?) depends on
the true spectrum (C?) as:
˜C?= M???T??B2
˜C? is calculated using the flat-sky approximation, in
which the spherical harmonic transform of the sky re-
duces to a Fourier transform of the map. This is an ex-
cellent approximation for a sub-degree sized map. The
experimental beam function is described by B?, and the
mode-coupling due to finite sky coverage is denoted by
M???. T? represents the transfer function of the map-
making process which would ideally be equal to one. In
??C??.
(2)
practice, the HPF applied to the APEX-SZ timestreams
eliminates power on scales ? < 1400 so T?= 0 on these
scales and remains below one at all ?.
MASTER algorithm (Hivon et al. 2002), we measure the
transfer function using a set of Monte-Carlo sky realiza-
tions that have been passed through the full pipeline,
from the timestreams to the maps. These simulated sky
maps include a lensed WMAP5+ACBAR best fit CMB
model (Hill et al. 2009; Reichardt et al. 2009), realiza-
tions of the SZE signal (Shaw et al. 2009), and real-
izations of the point source populations (Negrello et al.
2007; Granato et al. 2004; de Zotti et al. 2005). This
set of signal-only simulations is also used to estimate the
cosmic variance contribution to the band power uncer-
tainties.
The mode-coupling matrix M??? is calculated analyti-
cally for the two sky masks used to estimate the APEX-
SZ band powers. These masks describe the weighting
applied to each pixel in the map before calculating the
Fourier transform and are analogous to windowing data
in a 1D Fourier transform. We begin by applying an
inverse-noise weighting to each pixel, based on the diag-
onal elements of the pixel-pixel noise covariance matrix.
This effectively de-weights the noisy edges of the map,
and is near-optimal in the low signal-to-noise per pixel
regime. We modify this simple mask to exclude pixels
near detected clusters or point sources. There are two
X-ray detected clusters in the field; XLSSU J022145.2-
034614 and XLSSU J022157.4-034001. The field was cen-
tered on the first and more massive of these clusters,
which would introduce a bias into the determination of
the SZE amplitude. The central cluster is masked to a di-
ameter of 6?in the first mask, hereafter the Cluster mask.
The second cluster is fainter, and was detected only in a
joint analysis of X-ray and optical data (Andreon et al.
2005). We tested the effects of masking the second cluster
as well and did not see a significant change in the band
powers. The second mask removes the 27 point sources
detected in the APEX-SZ map in addition to the cen-
tral cluster. These sources are found by using SExtrac-
tor (Bertin & Arnouts 1996) to select sets of neighboring
pixels above 3σ in an optimally filtered map. This corre-
sponds approximately to a detection threshold of 2 mJy.
We discuss these sources further in §5.1. This mask will
be referred to as the Cluster + Sources mask. We tested
the effect of masking all NVSS or bright Spitzer sources
within the field, and observed no significant change in
power.
The measured band powers will be the sum of the sig-
nal and noise band powers,
D?= DS
and we must subtract the expected noise contribution
to recover the underlying signal spectrum. The noise
contribution to the APEX-SZ band powers is estimated
from the average power in a set of 2200 jack-knife maps
between two randomly selected half sets of the ∼1100
complete observations of the field. These difference maps
effectively remove sky signal, while preserving correlated
noise in the timestreams on time scales shorter than
the few minute length of a scan with randomized phase.
Noise on longer time scales has been removed by the 0.3
Hz HPF. The expectation value of the noise band pow-
ers, ?DN
Following the
?+ DN
?
(3)
??, is taken to be the mean band powers measured

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4
across the set of 2200 jack-knives. The approach is sim-
ilar to that used in the analysis of the Bolocam power
spectrum (Sayers et al. 2009). We apply the same pro-
cedure to signal-only simulated maps and confirm that
any residual signal power due to the small pointing, fil-
tering and weighting differences between observations is
negligible.
5. BAND POWERS AND σ8
The power spectrum presented in Figure 1 is the prod-
uct of applying the analysis in Section 4 to APEX-SZ
observations of the XMM-LSS field. The band powers
for angular multipoles from 3000 to 10,000 are tabulated
in Table 1. The band powers can be compared to a theo-
retical model using the window functions. The numerical
values for the band powers and window functions can be
downloaded from the APEX-SZ website17.
The APEX-SZ band powers show a tendency to in-
crease on smaller angular scales, suggestive of the ?2
shape that a Poisson distribution of point sources will
have in a plot of ?(? + 1)C?/2π. The contribution of
the primary CMB will be small at these small angu-
lar scales, and we subtract the estimated contribution
for the best fit WMAP5+ACBAR lensed ΛCDM power
spectrum before fitting for the amplitude of a constant
C?. The beam and calibration uncertainty is incorpo-
rated by averaging the likelihood function over a set
of 200 Monte Carlo realizations. The best fit power is
C?= 1.0+0.9
source and SZE contributions. Results for both masks
are tabulated in the first row of Table 2.
pected SZE power spectrum for σ8= 0.8 is subtracted
in addition to the primary anisotropies, the average C?
drops slightly to 0.9+0.9
source amplitude for σ8= 0.8, 92% of the astronomical
power in the map is produced by point sources rather
than the SZE. These results are obtained after masking
the bright, central cluster. Leaving the central cluster
unmasked increases the fit power by ∼1.0 ×10−5µK2.
We also report the results after masking the sources in-
ternally detected in the map at > 3σ in the second row of
Table 2. These results are consistent with and improved
over the previous ACBAR constraints from ? < 3000
of C? = 2.7+1.1
should be compared with caution as the two experiments
have different flux cuts for source masking, and the ex-
cess power will depend on the flux to which sources have
been masked.
We also investigate the effects of allowing the ampli-
tude of the SZE power spectrum to float freely. The SZE
power spectrum template is based on the simulations in
Shaw et al. (2009). The simulations are for a WMAP5
cosmology with σ8 = 0.77. The amplitude of the SZE
power spectrum is expected to scale approximately as
σ7
In practice, the APEX-SZ data set lacks the sensitivity to
make a detection of SZE power; however, the results can
be used to place an upper limit on σ8. The upper limits
on σ8and the point source amplitudes for the joint fit are
reported in Table 2. We assume a flat prior on σ8. The
exact amplitude of the SZE spectrum is only poorly un-
derstood, leading to a 10% systematic uncertainty on σ8
−0.6× 10−5µK2, which includes both the point
If the ex-
−0.6×10−5µK2. At the best-fit point
−2.6× 10−5µK2. However, these numbers
8, so the derived SZE amplitude can be related to σ8.
17http://bolo.berkeley.edu/apexsz/index.html
(Komatsu & Seljak 2002). This systematic uncertainty
is not included in the reported upper limits.
The non-Gaussian distribution of the SZE is very im-
portant on small patches of sky (Cooray 2001; Zhang
et al. 2006). We incorporate the non-Gaussian statistics
into our analysis by returning to the set of simulated
SZ skys (Shaw et al. 2009). We extract 7500 indepen-
dent realizations of the APEX-SZ map and calculate the
power in each realization under the two masks. The maps
have been convolved by the experimental beam and do
not include noise. This process maps out the full, non-
Gaussian cosmic variance of the expected SZE power for
σ8= 0.77. We scale this to other cosmologies by assum-
ing that the probability of measuring a power X will scale
with σ8as
?σ8
Bayes’ theorem with a flat prior in σ8 is applied to
find a posterior probability density, P(σ8|X). We de-
termine the probability of a given SZE power from the
data by marginalizing over a point source component as
described in the last paragraph. Finally, the likelihood
function of σ8given the APEX-SZ data d is calculated
by
P(σ8|d) =
and integrated to find the 95% CL upper limit on σ8. The
limit rises to σ8 < 1.18, substantially weaker than the
limit of σ8< 0.94 derived under Gaussian assumptions
(see the third row of Table 2, labeled “Unconstrained
σ8”). The marginalized likelihood function for both σ8
and CPS
?
are plotted in Figure 2, while the 2d likelihood
surface for both parameters is shown in Figure 3. The
upper limit is sensitive to the prior chosen since APEX-
SZ does not make a detection of SZE power. A flat prior
on power, σ7
the flat prior on σ8, and raises the upper limit from 1.18
to σ8 < 1.50 at 95% CL. This is entirely due to the
weighting by the prior as the prior probability for σ8= 2
is 240 times the probability of σ8= 0.8.
Finally, we combine the four APEX-SZ band powers
into a single band to facilitate the comparison to other
data sets. The resulting upper limit is ∼ 100µK2af-
ter including the APEX-SZ calibration and beam uncer-
tainty as shown in the last row of Table 2, “Flat Ex-
cess”. We have assumed that D?is constant across the
four bands and subtracted the contribution due to the
primary CMB anisotropies. However, this upper limit
does not include a non-Gaussian contribution to cosmic
variance.
P(X|σ8) =
0.77
?7
P(
?0.77
σ8
?7
X |σ8= 0.77).
(4)
?
dXP(σ8|X)P(X|d) (5)
8, strongly prefers higher values of σ8than
5.1. Radio and IR source contributions
Submillimeter bright galaxies and radio sources
are expected to dominate the primary temperature
anisotropies for ? ? 2500 at 150 GHz. The exact contri-
bution from point sources, especially radio sources, will
depend on our ability to detect and mask the brightest
sources. The exact 3σ detection threshold in the APEX-
SZ map depends on the map position due to the uneven
coverage, but is approximately 2 mJy on average. As
discussed below, the predicted band powers are fairly in-
sensitive to the precise cut level unless it shifts by an

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5
BIMA
SZA
Bolocam
Fig. 1.— Band powers derived from the APEX-SZ map plotted over a model (thick black line) including the primary CMB anisotropies,
a SZE model for σ8 = 0.8 (short dashed purple line) , and the predicted point source contribution for a 2 mJy cut threshold (long
dashed purple line) . This model is not a fit to the APEX-SZ band powers. We also plot for comparison the theory spectrum (thin
black line) if we increase σ8 to APEX-SZ’s 95% CL upper limit of 1.18. The APEX-SZ band powers for the Cluster mask are plotted
with blue squares, while the Cluster+Sources mask results are shown as black circles. The Cluster mask band powers have been shifted
by ∆? = 200 to the right for clarity. BIMA (turquoise diamond and upper limit - Dawson et al. (2006)), SZA (green circle - Sharp
et al. (2009)), and Bolocam (red upper limit - Sayers et al. (2009)) have previously released band-powers centered at ? > 3000. The
upper limits are shown at 95% CL. BIMA and SZA operate at 30 GHz where there will be four times as much SZE power as at 150 GHz
and we expect the foregrounds to be dominated by radio sources rather than dusty galaxies. The plotted theory spectra are for 150 GHz
only.
TABLE 1
Band powers
Cluster masked
q (µK2)
-74
26
-58
546
Cluster + Sources masked
q (µK2)
-66
9
14
558
? range
3000-4000
4000-6000
6000-8000
8000-10000
?eff
3532
4957
6968
8844
σ (µK2)
94
73
132
280
σ (µK2)
98
77
138
296
Note. — Band multipole range and weighted value ?eff, band powers q, and uncertainty σ from the analysis of the XMM-LSS
field with two masks. The first two columns (Cluster masked) show the results when the central X-ray detected cluster in the
field is masked to 6?diameter. The second set of columns (Cluster + Sources masked) masks twenty-seven > 3σ sources detected
in the map to 1.5?diameter as well as the cluster. More details on the masks can be found in §4.2.
order of magnitude. We assume both populations are
drawn from a Poisson distribution.
The number counts of dusty, submillimeter bright
galaxies are modeled in Negrello et al. (2007) based
on surveys at higher frequencies. Deep, high-resolution
maps of the 150 GHz sky are expected to be confusion-
limited by these sources. The anisotropies are the result
of variations in the number of very faint sources with
fluxes around 0.5 mJy. A 1 mJy point source will pro-
duce an increment of 20 µK in the APEX-SZ map. The
APEX-SZ map of the XMM-LSS field is too shallow to
pick out these sub-mJy sources, and we see no evidence of
reaching the confusion-limit in the current observations.
The dusty galaxy contribution to the APEX-SZ band
powers is predicted by the model presented in Negrello
et al. (2007) to be C?= 1.1 ×10−5µK2(1.7 Jy2sr−1)
in the absence of clustering, which is in good agreement
with the measured point source power in Table 2. The
predicted power from dusty galaxies is nearly indepen-
dent of the flux cut level above 1 mJy. Dusty galaxies
are expected to account for most of the power in the
APEX-SZ maps.
The BLAST collaboration recently released measure-
ments of the power spectrum of the cosmic far-infrared
background at frequencies of 600 GHz to 1.2 THz (Viero
et al. 2009).BLAST measured a Poisson contribu-
tion from star-forming galaxies with an amplitude of
2.63±0.1×103Jy2sr−1at 600 GHz. A clustering term
is detected as well on angular scales larger than those
probed by APEX-SZ. Expressing the frequency depen-
dence of the source fluxes as S(ν) ∝ να, we can derive
an effective spectral index, α, by comparing the power

Page 6

6
TABLE 2
Point source power and σ8 constraints
Cluster masked Cluster + Sources masked
Zero SZE power:
CPS
?
(10−5µK2)
Fixed σ8 = 0.8 :
CPS
?
(10−5µK2)
Unconstrained σ8:
CPS
?
(10−5µK2)
σ8 (G) (95% CL)
σ8 (NG) (95% CL)
Flat excess:
(with ?center = 4966)
D? (µK2)
95% CL
1.0+0.9
−0.6
1.2+1.0
−0.8
0.9+0.9
−0.6
1.1+0.9
−0.8
0.9+0.9
−0.6
0.94
1.18
1.1+0.9
−0.8
0.94
1.18
33+37
−24
97
36+39
−26
105
Note. — The constraint on point source power CPS
set are tabulated for different assumptions about the SZE power and masks. The expected primary CMB anisotropy power
has been subtracted from the measured band powers. We show the upper limit on σ8 with (NG) and without (G) accounting
for the non-Gaussian distribution of the SZE. Accounting for the non-Gaussianity in the expected SZE sky weakens the upper
limit considerably. The first column (Cluster masked) shows the results when the massive, X-ray detected cluster in the field is
masked to 6?diameter. The second column (Cluster + Sources masked) excludes the > 3σ sources detected in the map as well
as the cluster. More details on the masks can be found in §4.2. The measured point source power is in excellent agreement with
the predicted amplitude of 1.1×10−5µK2(1.7 Jy2sr−1) for the sum of the radio and dusty galaxy models in all cases. We also
show the results under the assumption that the power at high-? above the primary CMB anisotropies can be modeled as a flat
band-power. The 95% CL upper limit on a flat excess of <105 µK2includes the beam and calibration uncertainties but does
not include non-Gaussian contributions to cosmic variance.
?
, and the 95% CL upper limit on σ8 derived from the APEX-SZ data
measured by BLAST at 600 GHz to the point source
power likelihood function of the APEX-SZ maps at 150
GHz. This index will depend on the the spectra of the
individual galaxies and their redshift distribution. We
find that a spectral index of α = 2.64+0.4
BLAST power to match the best-fit C?= 1.1+0.9
µK2(1.7+1.4
ferred spectral index agrees well with previous estimates
for sub-mm bright galaxies. Knox et al. (2004) examined
nearby galaxy data and found Sν∝ ν2.6±0.3. In an alter-
native approach, Greve et al. (2004) compared the flux of
sources in overlapping regions observed by MAMBO (1.2
mm) and SCUBA (850 µm) and found the fluxes scaled
as Sν∝ ν2.65. The point source power in the APEX-SZ
data set at 150 GHz is consistent with being entirely due
to a population of dusty submm-bright galaxies such as
those observed by BLAST.
We also consider radio sources as a potential fore-
ground in the APEX-SZ maps. Granato et al. (2004) and
de Zotti et al. (2005) have modeled the number counts of
several classes of radio sources at tens of GHz. We derive
Cradio
?
from their modeled number counts at 150 GHz.
The radio source power is dependent on the brightest
objects and is expected to scale approximately linearly
with the source cut threshold. At the 2 mJy source cut
threshold of APEX-SZ, Cradio
?
dusty galaxy contribution.
We find 27 point sources above 3 σ (∼2 mJy) in the
APEX-SZ maps using the approach outlined in §4.2.
Eight of these sources are within 1?of a NVSS source
and are likely radio sources. We expect four false de-
tections based on Gaussian statistics and the number of
beam-sized pixels in the APEX-SZ map. The remaining
sources are tentatively identified as dusty galaxies. We
−0.2scales the
−0.8×10−5
−1.3Jy2sr−1) of the APEX-SZ data. This in-
should be ? 5% of the
can compare the observed number counts in the APEX-
SZ maps with other experiments at 150 GHz, however
most previous experiments were targeting larger angular
scales and are relatively insensitive to dim point sources.
QUaD (QUaD collaboration: R. B. Friedman et al. 2009)
and ACBAR (Reichardt et al. 2009) both report ∼0.1
radio sources per square degree with a flux detection
threshold of many tens of mJy. The deepest previously
published map at 150 GHz is from Bolocam (Sayers et al.
2009) which reports no sources above 10 mJy in a 1 deg2
patch. As dN(>S)/dS is expected to fall steeply above 1
mJy for dusty galaxies, the scarcity of detected sources
in these maps is not particularly surprising. The BLAST
source catalogue (Dye et al. 2009) of 351 sources detected
at 250, 350 or 500 µm allows a more interesting cross-
comparison. The BLAST catalogue has 294 sources per
square degree in the deep coverage region and 15 sources
per square degree in the shallow coverage region. At 500
µm, the detection threshold of the BLAST catalogue is
30 mJy and 100 mJy respectively. For the best-fit effec-
tive spectral index of α = 2.64 derived earlier, this corre-
sponds to a source detection threshold at 150 GHz of 0.8
and 2.6 mJy respectively. These two detection thresholds
bracket the average APEX-SZ 3σ detection threshold
of 2 mJy, and the observed APEX-SZ non-radio source
number density of 19 sources/deg2falls between these
two source densities as we would expect.
number counts in the APEX-SZ maps appear consistent
with the numbers expected for dusty galaxies.
The source
6. CONCLUSIONS
Observations with the APEX-SZ instrument have been
used to constrain the power in excess of the primary
CMB temperature anisotropies at 150GHz. This power
is expected to be dominated by emission from sub-mm

Page 7

7
Fig. 2.— [s
¯ashed and upper x-axis] Marginalized likelihood function for Cps
bright, dusty galaxies and the APEX-SZ band powers
are consistent with this hypothesis. We find excellent
agreement between the point source power in the APEX-
SZ maps and model predictions based on observations at
other frequencies. We estimate that the flux of these sub-
mm bright galaxies scales with frequency as Sν∼ ν2.64
by comparing the power measured by BLAST at 600
GHz to the best-fit point source power in the APEX-
SZ maps at 150 GHz. Determining the contribution of
these foreground sources not only constrains models for
the population of dusty galaxies, but is important for
planning current and future observations of secondary
CMB anisotropies at these wavelengths.
We also place upper limits on σ8from fits to the am-
plitude of the SZE power spectrum while marginalizing
over a Poisson point source contribution. We assume a
template for the SZE power spectrum derived from sim-
ulations by Shaw et al. (2009) with the amplitude of the
SZE power spectrum scaling as σ7
limit of σ8 < 1.18 at 95% confidence.
similar to the constraints from the CBI and BIMA inter-
ferometers operating at 30GHz. The limits from SZA,
QUaD, or ACBAR would likely be slightly lower, but
they did not express their results in terms of upper lim-
its on σ8. At these frequencies and angular scales, the
previous best limit comes from Sayers et al. (2009), who
used observations with the Bolocam instrument to con-
strain σ8< 1.57 at 90% confidence.
A third of the APEX-SZ instrument was recently up-
¯olid and lower x-axis] Marginalized likelihood function for σ8 for a flat prior on σ8 after accounting for non-Gaussianity.
?. These curves are for the Cluster+Sources mask.
graded to more sensitive detectors with improved optical
efficiencies. In the next year, the remainder of the focal
plane will be upgraded resulting in significant improve-
ments to the instrument’s mapping speed. The instru-
ment will continue observing in the next several years
with a focus on developing a catalog of clusters with
SZE, X-ray and optical observations across the South-
ern hemisphere.
[d
8. We find an upper
This result is
7. ACKNOWLEDGMENTS
We thank the staff at the APEX telescope site, led by
David Rabanus and previously by Lars-˚ Ake Nyman, for
their dedicated and exceptional support. We also thank
LBNL engineers John Joseph and Chinh Vu for their
work on the readout electronics. APEX-SZ is funded
by the National Science Foundation under Grant No.
AST-0138348. Work at LBNL is supported by the Di-
rector, Office of Science, Office of High Energy and Nu-
clear Physics, of the U.S. Department of Energy under
Contract No. DE-AC02-05CH11231. Work at McGill is
supported by the Natural Sciences and Engineering Re-
search Council of Canada and the Canadian Institute for
Advanced Research. This research used resources of the
National Energy Research Scientific Computing Center,
which is supported by the Office of Science of the U.S.
Department of Energy under Contract No. DE-AC02-
05CH11231. Nils Halverson acknowledges support from
an Alfred P. Sloan Research Fellowship.
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