197 research outputs found
Log-concavity and lower bounds for arithmetic circuits
One question that we investigate in this paper is, how can we build
log-concave polynomials using sparse polynomials as building blocks? More
precisely, let be a
polynomial satisfying the log-concavity condition a\_i^2 \textgreater{} \tau
a\_{i-1}a\_{i+1} for every where \tau
\textgreater{} 0. Whenever can be written under the form where the polynomials have at most
monomials, it is clear that . Assuming that the
have only non-negative coefficients, we improve this degree bound to if \tau \textgreater{} 1,
and to if .
This investigation has a complexity-theoretic motivation: we show that a
suitable strengthening of the above results would imply a separation of the
algebraic complexity classes VP and VNP. As they currently stand, these results
are strong enough to provide a new example of a family of polynomials in VNP
which cannot be computed by monotone arithmetic circuits of polynomial size
A Comparison of Cosmological Parameters Determined from CMB Temperature Power Spectra from the South Pole Telescope and the Planck Satellite
The Planck cosmic microwave background (CMB) temperature data are best fit
with a LCDM model that is in mild tension with constraints from other
cosmological probes. The South Pole Telescope (SPT) 2540 SPT-SZ
survey offers measurements on sub-degree angular scales (multipoles ) with sufficient precision to use as an independent check of
the Planck data. Here we build on the recent joint analysis of the SPT-SZ and
Planck data in \citet{hou17} by comparing LCDM parameter estimates using the
temperature power spectrum from both data sets in the SPT-SZ survey region. We
also restrict the multipole range used in parameter fitting to focus on modes
measured well by both SPT and Planck, thereby greatly reducing sample variance
as a driver of parameter differences and creating a stringent test for
systematic errors. We find no evidence of systematic errors from such tests.
When we expand the maximum multipole of SPT data used, we see low-significance
shifts in the angular scale of the sound horizon and the physical baryon and
cold dark matter densities, with a resulting trend to higher Hubble constant.
When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky
data but keep the multipole range restricted, we find differences in the
parameters and . We perform further checks, investigating
instrumental effects and modeling assumptions, and we find no evidence that the
effects investigated are responsible for any of the parameter shifts. Taken
together, these tests reveal no evidence for systematic errors in SPT or Planck
data in the overlapping sky coverage and multipole range and, at most, weak
evidence for a breakdown of LCDM or systematic errors influencing either the
Planck data outside the SPT-SZ survey area or the SPT data at .Comment: 14 pages, 7 figures. Updated 1 figure and expanded on the reasoning
for fixing the affect of lensing on the power spectrum instead of varying
Alen
Consistency of cosmic microwave background temperature measurements in three frequency bands in the 2500-square-degree SPT-SZ survey
We present an internal consistency test of South Pole Telescope (SPT)
measurements of the cosmic microwave background (CMB) temperature anisotropy
using three-band data from the SPT-SZ survey. These measurements are made from
observations of ~2500 deg^2 of sky in three frequency bands centered at 95,
150, and 220 GHz. We combine the information from these three bands into six
semi-independent estimates of the CMB power spectrum (three single-frequency
power spectra and three cross-frequency spectra) over the multipole range 650 <
l < 3000. We subtract an estimate of foreground power from each power spectrum
and evaluate the consistency among the resulting CMB-only spectra. We determine
that the six foreground-cleaned power spectra are consistent with the null
hypothesis, in which the six cleaned spectra contain only CMB power and noise.
A fit of the data to this model results in a chi-squared value of 236.3 for 235
degrees of freedom, and the probability to exceed this chi-squared value is
46%.Comment: 21 pages, 4 figures, current version matches version published in
JCA
Sunyaev-Zel'dovich Cluster Profiles Measured with the South Pole Telescope
We present Sunyaev-Zel'dovich measurements of 15 massive X-ray selected
galaxy clusters obtained with the South Pole Telescope. The Sunyaev-Zel'dovich
(SZ) cluster signals are measured at 150 GHz, and concurrent 220 GHz data are
used to reduce astrophysical contamination. Radial profiles are computed using
a technique that takes into account the effects of the beams and filtering. In
several clusters, significant SZ decrements are detected out to a substantial
fraction of the virial radius. The profiles are fit to the beta model and to a
generalized NFW pressure profile, and are scaled and stacked to probe their
average behavior. We find model parameters that are consistent with previous
studies: beta=0.86 and r_core/r_500 = 0.20 for the beta model, and (alpha,
beta, gamma, c_500)=(1.0,5.5,0.5,1.0) for the generalized NFW model. Both
models fit the SPT data comparably well, and both are consistent with the
average SZ profile out to the virial radius. The integrated Compton-y parameter
Y_SZ is computed for each cluster using both model-dependent and
model-independent techniques, and the results are compared to X-ray estimates
of cluster parameters. We find that Y_SZ scales with Y_X and gas mass with low
scatter. Since these observables have been found to scale with total mass, our
results point to a tight mass-observable relation for the SPT cluster survey.Comment: 21 pages, 24 figures, updated to published versio
A Comparison of Maps and Power Spectra Determined from South Pole Telescope and Planck Data
We study the consistency of 150 GHz data from the South Pole Telescope (SPT)
and 143 GHz data from the Planck satellite over the patch of sky covered by the
SPT-SZ survey. We first visually compare the maps and find that the residuals
appear consistent with noise after accounting for differences in angular
resolution and filtering. We then calculate (1) the cross-spectrum between two
independent halves of SPT data, (2) the cross-spectrum between two independent
halves of Planck data, and (3) the cross-spectrum between SPT and Planck data.
We find the three cross-spectra are well-fit (PTE = 0.30) by the null
hypothesis in which both experiments have measured the same sky map up to a
single free calibration parameter---i.e., we find no evidence for systematic
errors in either data set. As a by-product, we improve the precision of the SPT
calibration by nearly an order of magnitude, from 2.6% to 0.3% in power.
Finally, we compare all three cross-spectra to the full-sky Planck power
spectrum and find marginal evidence for differences between the power spectra
from the SPT-SZ footprint and the full sky. We model these differences as a
power law in spherical harmonic multipole number. The best-fit value of this
tilt is consistent among the three cross-spectra in the SPT-SZ footprint,
implying that the source of this tilt is a sample variance fluctuation in the
SPT-SZ region relative to the full sky. The consistency of cosmological
parameters derived from these datasets is discussed in a companion paper.Comment: 15 pages, 9 figures. Published in The Astrophysical Journal. Current
arxiv version matches published versio
A CMB lensing mass map and its correlation with the cosmic infrared background
We use a temperature map of the cosmic microwave background (CMB) obtained
using the South Pole Telescope at 150 GHz to construct a map of the
gravitational convergence to z ~ 1100, revealing the fluctuations in the
projected mass density. This map shows individual features that are significant
at the ~ 4 sigma level, providing the first image of CMB lensing convergence.
We cross-correlate this map with Herschel/SPIRE maps covering 90 square degrees
at wavelengths of 500, 350, and 250 microns. We show that these
submillimeter-wavelength (submm) maps are strongly correlated with the lensing
convergence map, with detection significances in each of the three submm bands
ranging from 6.7 to 8.8 sigma. We fit the measurement of the cross power
spectrum assuming a simple constant bias model and infer bias factors of
b=1.3-1.8, with a statistical uncertainty of 15%, depending on the assumed
model for the redshift distribution of the dusty galaxies that are contributing
to the Herschel/SPIRE maps.Comment: 5 pages, 3 figures, to be submitted to ApJ
South Pole Telescope Detections of the Previously Unconfirmed Planck Early SZ Clusters in the Southern Hemisphere
We present South Pole Telescope (SPT) observations of the five galaxy cluster
candidates in the southern hemisphere which were reported as unconfirmed in the
Planck Early Sunyaev-Zel'dovich (ESZ) sample. One cluster candidate, PLCKESZ
G255.62-46.16, is located in the 2500-square-degree SPT SZ survey region and
was reported previously as SPT-CL J0411-4819. For the remaining four
candidates, which are located outside of the SPT SZ survey region, we performed
short, dedicated SPT observations. Each of these four candidates was strongly
detected in maps made from these observations, with signal-to-noise ratios
ranging from 6.3 to 13.8. We have observed these four candidates on the
Magellan-Baade telescope and used these data to estimate cluster redshifts from
the red sequence. Resulting redshifts range from 0.24 to 0.46. We report
measurements of Y_0.75', the integrated Comptonization within a 0.75' radius,
for all five candidates. We also report X-ray luminosities calculated from
ROSAT All-Sky Survey catalog counts, as well as optical and improved SZ
coordinates for each candidate. The combination of SPT SZ measurements, optical
red-sequence measurements, and X-ray luminosity estimates demonstrates that
these five Planck ESZ cluster candidates do indeed correspond to real galaxy
clusters with redshifts and observable properties consistent with the rest of
the ESZ sample.Comment: 7 emulateapj pages, 4 figures, 1 table. Revised to match published
versio
Measurements of Sub-degree B-mode Polarization in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data
We present a measurement of the -mode polarization power spectrum (the
spectrum) from 100 of sky observed with SPTpol, a
polarization-sensitive receiver currently installed on the South Pole
Telescope. The observations used in this work were taken during 2012 and early
2013 and include data in spectral bands centered at 95 and 150 GHz. We report
the spectrum in five bins in multipole space, spanning the range , and for three spectral combinations: 95 GHz 95 GHz, 95
GHz 150 GHz, and 150 GHz 150 GHz. We subtract small ( in units of statistical uncertainty) biases from these spectra and
account for the uncertainty in those biases. The resulting power spectra are
inconsistent with zero power but consistent with predictions for the
spectrum arising from the gravitational lensing of -mode polarization. If we
assume no other source of power besides lensed modes, we determine a
preference for lensed modes of . After marginalizing over
tensor power and foregrounds, namely polarized emission from galactic dust and
extragalactic sources, this significance is . Fitting for a single
parameter, , that multiplies the predicted lensed -mode
spectrum, and marginalizing over tensor power and foregrounds, we find
, indicating that our measured spectra are
consistent with the signal expected from gravitational lensing. The data
presented here provide the best measurement to date of the -mode power
spectrum on these angular scales.Comment: 21 pages, 4 figure
Detection of B-mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope
Gravitational lensing of the cosmic microwave background generates a curl
pattern in the observed polarization. This "B-mode" signal provides a measure
of the projected mass distribution over the entire observable Universe and also
acts as a contaminant for the measurement of primordial gravity-wave signals.
In this Letter we present the first detection of gravitational lensing B modes,
using first-season data from the polarization-sensitive receiver on the South
Pole Telescope (SPTpol). We construct a template for the lensing B-mode signal
by combining E-mode polarization measured by SPTpol with estimates of the
lensing potential from a Herschel-SPIRE map of the cosmic infrared background.
We compare this template to the B modes measured directly by SPTpol, finding a
non-zero correlation at 7.7 sigma significance. The correlation has an
amplitude and scale-dependence consistent with theoretical expectations, is
robust with respect to analysis choices, and constitutes the first measurement
of a powerful cosmological observable.Comment: Two additional null tests, matches version published in PR
Mass Calibration and Cosmological Analysis of the SPT-SZ Galaxy Cluster Sample Using Velocity Dispersion and X-ray Measurements
We present a velocity dispersion-based mass calibration of the South Pole
Telescope Sunyaev-Zel'dovich effect survey (SPT-SZ) galaxy cluster sample.
Using a homogeneously selected sample of 100 cluster candidates from 720 deg2
of the survey along with 63 velocity dispersion () and 16 X-ray Yx
measurements of sample clusters, we simultaneously calibrate the
mass-observable relation and constrain cosmological parameters. The
calibrations using and Yx are consistent at the level,
with the calibration preferring ~16% higher masses. We use the full
cluster dataset to measure . The
SPT cluster abundance is lower than preferred by either the WMAP9 or
Planck+WMAP9 polarization (WP) data, but assuming the sum of the neutrino
masses is eV, we find the datasets to be consistent at the
1.0 level for WMAP9 and 1.5 for Planck+WP. Allowing for larger
further reconciles the results. When we combine the cluster and
Planck+WP datasets with BAO and SNIa, the preferred cluster masses are
higher than the Yx calibration and higher than the
calibration. Given the scale of these shifts (~44% and ~23% in mass,
respectively), we execute a goodness of fit test; it reveals no tension,
indicating that the best-fit model provides an adequate description of the
data. Using the multi-probe dataset, we measure and
. Within a CDM model we find eV. We present a consistency test of the cosmic growth rate.
Allowing both the growth index and the dark energy equation of state
parameter to vary, we find and ,
demonstrating that the expansion and the growth histories are consistent with a
LCDM model ().Comment: Accepted by ApJ (v2 is accepted version); 17 pages, 6 figure
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