Finite-Size Bosonization and Self-Consistent Harmonic Approximation

The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a test we apply the method to interacting spinless fermions with modulated hopping. We calculate the finite-size corrections to the energy gap and the Drude weight and compare our results with the exact solution for special values of the model parameters

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 $B$-mode polarization power spectrum (the $BB$ spectrum) from 100 $\mathrm{deg}^2$ 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 $BB$ spectrum in five bins in multipole space, spanning the range $300 \le \ell \le 2300$, and for three spectral combinations: 95 GHz $\times$ 95 GHz, 95 GHz $\times$ 150 GHz, and 150 GHz $\times$ 150 GHz. We subtract small ($< 0.5 \sigma$ 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 $BB$ spectrum arising from the gravitational lensing of $E$-mode polarization. If we assume no other source of $BB$ power besides lensed $B$ modes, we determine a preference for lensed $B$ modes of $4.9 \sigma$. After marginalizing over tensor power and foregrounds, namely polarized emission from galactic dust and extragalactic sources, this significance is $4.3 \sigma$. Fitting for a single parameter, $A_\mathrm{lens}$, that multiplies the predicted lensed $B$-mode spectrum, and marginalizing over tensor power and foregrounds, we find $A_\mathrm{lens} = 1.08 \pm 0.26$, 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 $B$-mode power spectrum on these angular scales.Comment: 21 pages, 4 figure

ALMA Observations of SPT-Discovered, Strongly Lensed, Dusty, Star-Forming Galaxies

We present Atacama Large Millimeter/submillimeter Array (ALMA) 860 micrometer imaging of four high-redshift (z=2.8-5.7) dusty sources that were detected using the South Pole Telescope (SPT) at 1.4 mm and are not seen in existing radio to far-infrared catalogs. At 1.5 arcsec resolution, the ALMA data reveal multiple images of each submillimeter source, separated by 1-3 arcsec, consistent with strong lensing by intervening galaxies visible in near-IR imaging of these sources. We describe a gravitational lens modeling procedure that operates on the measured visibilities and incorporates self-calibration-like antenna phase corrections as part of the model optimization, which we use to interpret the source structure. Lens models indicate that SPT0346-52, located at z=5.7, is one of the most luminous and intensely star-forming sources in the universe with a lensing corrected FIR luminosity of 3.7 X 10^13 L_sun and star formation surface density of 4200 M_sun yr^-1 kpc^-2. We find magnification factors of 5 to 22, with lens Einstein radii of 1.1-2.0 arcsec and Einstein enclosed masses of 1.6-7.2x10^11 M_sun. These observations confirm the lensing origin of these objects, allow us to measure the their intrinsic sizes and luminosities, and demonstrate the important role that ALMA will play in the interpretation of lensed submillimeter sources.Comment: Accepted for publication in the Astrophysics Journa

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

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

The Redshift Evolution of the Mean Temperature, Pressure, and Entropy Profiles in 80 SPT-Selected Galaxy Clusters

(Abridged) We present the results of an X-ray analysis of 80 galaxy clusters selected in the 2500 deg^2 South Pole Telescope survey and observed with the Chandra X-ray Observatory. We divide the full sample into subsamples of ~20 clusters based on redshift and central density, performing an X-ray fit to all clusters in a subsample simultaneously, assuming self-similarity of the temperature profile. This approach allows us to constrain the shape of the temperature profile over 0<r<1.5R500, which would be impossible on a per-cluster basis, since the observations of individual clusters have, on average, 2000 X-ray counts. The results presented here represent the first constraints on the evolution of the average temperature profile from z=0 to z=1.2. We find that high-z (0.6<z<1.2) clusters are slightly (~40%) cooler both in the inner (rR500) regions than their low-z (0.3<z<0.6) counterparts. Combining the average temperature profile with measured gas density profiles from our earlier work, we infer the average pressure and entropy profiles for each subsample. Overall, our observed pressure profiles agree well with earlier lower-redshift measurements, suggesting minimal redshift evolution in the pressure profile outside of the core. We find no measurable redshift evolution in the entropy profile at rR500 in our high-z subsample. This flattening is consistent with a temperature bias due to the enhanced (~3x) rate at which group-mass (~2 keV) halos, which would go undetected at our survey depth, are accreting onto the cluster at z~1. This work demonstrates a powerful method for inferring spatially-resolved cluster properties in the case where individual cluster signal-to-noise is low, but the number of observed clusters is high.Comment: 17 pages, 13 figures, submitted to ApJ. Updated following referee repor

CMB Polarization B-mode Delensing with SPTpol and Herschel

We present a demonstration of delensing the observed cosmic microwave background (CMB) B-mode polarization anisotropy. This process of reducing the gravitational-lensing generated B-mode component will become increasingly important for improving searches for the B modes produced by primordial gravitational waves. In this work, we delens B-mode maps constructed from multi-frequency SPTpol observations of a 90 deg$^2$ patch of sky by subtracting a B-mode template constructed from two inputs: SPTpol E-mode maps and a lensing potential map estimated from the $\textit{Herschel}$ $500\,\mu m$ map of the CIB. We find that our delensing procedure reduces the measured B-mode power spectrum by 28% in the multipole range $300 < \ell < 2300$; this is shown to be consistent with expectations from theory and simulations and to be robust against systematics. The null hypothesis of no delensing is rejected at $6.9 \sigma$. Furthermore, we build and use a suite of realistic simulations to study the general properties of the delensing process and find that the delensing efficiency achieved in this work is limited primarily by the noise in the lensing potential map. We demonstrate the importance of including realistic experimental non-idealities in the delensing forecasts used to inform instrument and survey-strategy planning of upcoming lower-noise experiments, such as CMB-S4.Comment: 17 pages, 10 figures. Comments are welcome

The Growth of Cool Cores and Evolution of Cooling Properties in a Sample of 83 Galaxy Clusters at 0.3 < z < 1.2 Selected from the SPT-SZ Survey

We present first results on the cooling properties derived from Chandra X-ray observations of 83 high-redshift (0.3 < z < 1.2) massive galaxy clusters selected by their Sunyaev-Zel'dovich signature in the South Pole Telescope data. We measure each cluster's central cooling time, central entropy, and mass deposition rate, and compare to local cluster samples. We find no significant evolution from z~0 to z~1 in the distribution of these properties, suggesting that cooling in cluster cores is stable over long periods of time. We also find that the average cool core entropy profile in the inner ~100 kpc has not changed dramatically since z ~ 1, implying that feedback must be providing nearly constant energy injection to maintain the observed "entropy floor" at ~10 keV cm^2. While the cooling properties appear roughly constant over long periods of time, we observe strong evolution in the gas density profile, with the normalized central density (rho_0/rho_crit) increasing by an order of magnitude from z ~ 1 to z ~ 0. When using metrics defined by the inner surface brightness profile of clusters, we find an apparent lack of classical, cuspy, cool-core clusters at z > 0.75, consistent with earlier reports for clusters at z > 0.5 using similar definitions. Our measurements indicate that cool cores have been steadily growing over the 8 Gyr spanned by our sample, consistent with a constant, ~150 Msun/yr cooling flow that is unable to cool below entropies of 10 keV cm^2 and, instead, accumulates in the cluster center. We estimate that cool cores began to assemble in these massive systems at z ~ 1, which represents the first constraints on the onset of cooling in galaxy cluster cores. We investigate several potential biases which could conspire to mimic this cool core evolution and are unable to find a bias that has a similar redshift dependence and a substantial amplitude.Comment: 17 pages with 15 figures, plus appendix. Published in Ap

Twitter-based analysis of the dynamics of collective attention to political parties

Large-scale data from social media have a significant potential to describe complex phenomena in real world and to anticipate collective behaviors such as information spreading and social trends. One specific case of study is represented by the collective attention to the action of political parties. Not surprisingly, researchers and stakeholders tried to correlate parties' presence on social media with their performances in elections. Despite the many efforts, results are still inconclusive since this kind of data is often very noisy and significant signals could be covered by (largely unknown) statistical fluctuations. In this paper we consider the number of tweets (tweet volume) of a party as a proxy of collective attention to the party, identify the dynamics of the volume, and show that this quantity has some information on the elections outcome. We find that the distribution of the tweet volume for each party follows a log-normal distribution with a positive autocorrelation of the volume over short terms, which indicates the volume has large fluctuations of the log-normal distribution yet with a short-term tendency. Furthermore, by measuring the ratio of two consecutive daily tweet volumes, we find that the evolution of the daily volume of a party can be described by means of a geometric Brownian motion (i.e., the logarithm of the volume moves randomly with a trend). Finally, we determine the optimal period of averaging tweet volume for reducing fluctuations and extracting short-term tendencies. We conclude that the tweet volume is a good indicator of parties' success in the elections when considered over an optimal time window. Our study identifies the statistical nature of collective attention to political issues and sheds light on how to model the dynamics of collective attention in social media.Comment: 16 pages, 7 figures, 3 tables. Published in PLoS ON