169 research outputs found
On theories of random variables
We study theories of spaces of random variables: first, we consider random
variables with values in the interval , then with values in an arbitrary
metric structure, generalising Keisler's randomisation of classical structures.
We prove preservation and non-preservation results for model theoretic
properties under this construction: i) The randomisation of a stable structure
is stable. ii) The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type
Hypernatural Numbers as Ultrafilters
In this paper we present a use of nonstandard methods in the theory of
ultrafilters and in related applications to combinatorics of numbers
Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data
We present measurements of the -mode polarization angular auto-power
spectrum () and temperature--mode cross-power spectrum () of the
cosmic microwave background (CMB) using 150 GHz data from three seasons of
SPTpol observations. We report the power spectra over the spherical harmonic
multipole range , and detect nine acoustic peaks in the
spectrum with high signal-to-noise ratio. These measurements are the most
sensitive to date of the and power spectra at and , respectively. The observations cover 500 deg, a fivefold increase
in area compared to previous SPTpol analyses, which increases our sensitivity
to the photon diffusion damping tail of the CMB power spectra enabling tighter
constraints on \LCDM model extensions. After masking all sources with
unpolarized flux mJy we place a 95% confidence upper limit on residual
polarized point-source power of at , suggesting that the damping tail
dominates foregrounds to at least with modest source masking. We
find that the SPTpol dataset is in mild tension with the model
(), and different data splits prefer parameter values that differ
at the level. When fitting SPTpol data at we
find cosmological parameter constraints consistent with those for
temperature. Including SPTpol data at results in a preference for
a higher value of the expansion rate (H_0 = 71.3 \pm
2.1\,\mbox{km}\,s^{-1}\mbox{Mpc}^{-1} ) and a lower value for present-day
density fluctuations ().Comment: Updated to match version accepted to ApJ. 34 pages, 17 figures, 6
table
Performance and on-sky optical characterization of the SPTpol instrument
In January 2012, the 10m South Pole Telescope (SPT) was equipped with a
polarization-sensitive camera, SPTpol, in order to measure the polarization
anisotropy of the cosmic microwave background (CMB). Measurements of the
polarization of the CMB at small angular scales (~several arcminutes) can
detect the gravitational lensing of the CMB by large scale structure and
constrain the sum of the neutrino masses. At large angular scales (~few
degrees) CMB measurements can constrain the energy scale of Inflation. SPTpol
is a two-color mm-wave camera that consists of 180 polarimeters at 90 GHz and
588 polarimeters at 150 GHz, with each polarimeter consisting of a dual
transition edge sensor (TES) bolometers. The full complement of 150 GHz
detectors consists of 7 arrays of 84 ortho-mode transducers (OMTs) that are
stripline coupled to two TES detectors per OMT, developed by the TRUCE
collaboration and fabricated at NIST. Each 90 GHz pixel consists of two
antenna-coupled absorbers coupled to two TES detectors, developed with Argonne
National Labs. The 1536 total detectors are read out with digital
frequency-domain multiplexing (DfMUX). The SPTpol deployment represents the
first on-sky tests of both of these detector technologies, and is one of the
first deployed instruments using DfMUX readout technology. We present the
details of the design, commissioning, deployment, on-sky optical
characterization and detector performance of the complete SPTpol focal plane.Comment: 15 pages, 6 figures. Conference: SPIE Astronomical Telescopes and
Instrumentation 201
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
A Measurement of the Cosmic Microwave Background Gravitational Lensing Potential from 100 Square Degrees of SPTpol Data
We present a measurement of the cosmic microwave background (CMB)
gravitational lensing potential using data from the first two seasons of
observations with SPTpol, the polarization-sensitive receiver currently
installed on the South Pole Telescope (SPT). The observations used in this work
cover 100 deg of sky with arcminute resolution at 150 GHz. Using a
quadratic estimator, we make maps of the CMB lensing potential from
combinations of CMB temperature and polarization maps. We combine these lensing
potential maps to form a minimum-variance (MV) map. The lensing potential is
measured with a signal-to-noise ratio of greater than one for angular
multipoles between . This is the highest signal-to-noise mass map
made from the CMB to date and will be powerful in cross-correlation with other
tracers of large-scale structure. We calculate the power spectrum of the
lensing potential for each estimator, and we report the value of the MV power
spectrum between as our primary result. We constrain the ratio
of the spectrum to a fiducial CDM model to be . Restricting ourselves to
polarized data only, we find . This measurement rejects the hypothesis of no lensing at
using polarization data alone, and at using both
temperature and polarization data.Comment: 16 pages, 8 figure
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
South Pole Telescope Software Systems: Control, Monitoring, and Data Acquisition
We present the software system used to control and operate the South Pole
Telescope. The South Pole Telescope is a 10-meter millimeter-wavelength
telescope designed to measure anisotropies in the cosmic microwave background
(CMB) at arcminute angular resolution. In the austral summer of 2011/12, the
SPT was equipped with a new polarization-sensitive camera, which consists of
1536 transition-edge sensor bolometers. The bolometers are read out using 36
independent digital frequency multiplexing (\dfmux) readout boards, each with
its own embedded processors. These autonomous boards control and read out data
from the focal plane with on-board software and firmware. An overall control
software system running on a separate control computer controls the \dfmux
boards, the cryostat and all other aspects of telescope operation. This control
software collects and monitors data in real-time, and stores the data to disk
for transfer to the United States for analysis
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
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