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At least 1,117 records · Page 62

HOW THE DENSITY ENVIRONMENT CHANGES THE INFLUENCE OF THE DARK MATTER–BARYON STREAMING VELOCITY ON COSMOLOGICAL STRUCTURE FORMATION

We study the dynamical effect of the relative velocity between dark matter and baryonic fluids, which remained supersonic after the epoch of recombination. The impact of this supersonic motion on the formation of cosmological structures was first formulated by Tseliakhovich and Hirata, in terms of the linear theory of small-scale fluctuations coupled to large-scale, relative velocities in mean-density regions. In their formalism, they limited the large-scale density environment to be that of the global mean density. We improve on their formulation by allowing variation in the density environment as well as the relative velocities. This leads to a new type of coupling between large-scale and small-scale modes. We find that the small-scale fluctuation grows in a biased way: faster in the overdense environment and slower in the underdense environment. We also find that the net effect on the global power spectrum of the density fluctuation is to boost its overall amplitude from the prediction by Tseliakhovich and Hirata. Correspondingly, the conditional mass function of cosmological halos and the halo bias parameter are both affected in a similar way. The discrepancy between our prediction and that of Tseliakhovich and Hirata is significant, and therefore, the related cosmology and high-redshift astrophysics should be revisited. The mathematical formalism of this study can be used for generating cosmological initial conditions of small-scale perturbations in generic, overdense (underdense) background patches.

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Multi-wavelength study of the supernova remnant Kes 79 (G33.6+0.1): on its supernova properties and expansion into a molecular environment

Kes 79 (G33.6+0.1) is an aspherical thermal composite supernova remnant (SNR) observed across the electromagnetic spectrum and showing an unusual highly structured morphology, in addition to harboring a central compact object (CCO). Using the CO J = 1–0, J = 2–1, and J = 3–2 data, we provide the first direct evidence and new morphological evidence to support the physical interaction between the SNR and the molecular cloud in the local standard of rest velocity ∼105 km s{sup −1}. We revisit the 380 ks XMM-Newton observations and perform a dedicated spatially resolved X-ray spectroscopic study with careful background subtraction. The overall X-ray-emitting gas is characterized by an under-ionized (τ{sub c}∼6×10{sup 11} cm{sup −3}) cool (kT{sub c}≈0.20 keV) plasma with solar abundances, plus an under-ionized (τ{sub h}∼8×10{sup 10} cm{sup −3}) hot (kT{sub h}≈0.80 keV) plasma with elevated Ne, Mg, Si, S, and Ar abundances. The X-ray filaments, spatially correlated with the 24 μm IR filaments, are suggested to be due to the SNR shock interaction with dense gas, while the halo forms from SNR breaking out into a tenuous medium. Kes 79 appears to have a double-hemisphere morphology viewed along the symmetric axis. Projection effect can explain the multiple-shell structures and the thermal composite morphology. The high-velocity, hot (kT{sub h}∼1.4--1.6 keV) ejecta patch with high metal abundances, together with the non-uniform metal distribution across the SNR, indicate an asymmetric SN explosion of Kes 79. We refine the Sedov age to 4.4–6.7 kyr and the mean shock velocity to 730 km s{sup −1}. Our multi-wavelength study suggests a progenitor mass of ∼15–20 solar masses for the core-collapse explosion that formed Kes 79 and its CCO, PSR J1852+0040.

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PIXEL ANALYSIS OF PHOTOSPHERIC SPECTRAL DATA. I. PLASMA DYNAMICS

Recent observations of the photosphere using high spatial and temporal resolution show small dynamic features at or below the current resolving limits. A new pixel dynamics method has been developed to analyze spectral profiles and quantify changes in line displacement, width, asymmetry, and peakedness of photospheric absorption lines. The algorithm evaluates variations of line profile properties in each pixel and determines the statistics of such fluctuations averaged over all pixels in a given region. The method has been used to derive statistical characteristics of pixel fluctuations in observed quiet-Sun regions, an active region with no eruption, and an active region with an ongoing eruption. Using Stokes I images from the Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS) telescope on 2012 March 13, variations in line width and peakedness of Fe i 6301.5 Å are shown to have a distinct spatial and temporal relationship with an M7.9 X-ray flare in NOAA 11429. This relationship is observed as stationary and contiguous patches of pixels adjacent to a sunspot exhibiting intense flattening in the line profile and line-center displacement as the X-ray flare approaches peak intensity, which is not present in area scans of the non-eruptive active region. The analysis of pixel dynamics allows one to extract quantitative information on differences in plasma dynamics on sub-pixel scales in these photospheric regions. The analysis can be extended to include the Stokes parameters and study signatures of vector components of magnetic fields and coupled plasma properties.

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21 cm Signal Recovery via Robust Principal Component Analysis

The redshifted 21 cm signal from neutral hydrogen (H i) is potentially a very powerful probe for cosmology, but a difficulty in its observation is that it is much weaker than foreground radiation from the Milky Way as well as extragalactic radio sources. The foreground radiation at different frequencies, however, is coherent along one line of sight, and various methods of foreground subtraction based on this property have been proposed. In this paper, we present a new method based on robust principal component analysis (RPCA) to subtract the foreground and extract the 21 cm signal, which explicitly uses both the low-rank property of the frequency covariance matrix (i.e., frequency coherence) of the foreground and the sparsity of the frequency covariance matrix of the 21 cm signal. The low-rank property of the foreground’s frequency covariance has been exploited in many previous works on foreground subtraction, but to our knowledge the sparsity of the frequency covariance of the 21 cm signal is first explored here. By exploiting both properties in the RPCA method, the frequency covariance matrix of the foreground and the 21 cm signal can be separated accurately. We then use the generalized internal linear combination method to recover the 21 cm signal from the data. Our method is applicable both to a small patch of sky with the flat-sky approximation and to a large area of sky where the sphericity has to be considered. It is also easy to extend to deal with more complex conditions such as a sky map with defects.

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On the formation of molecular clumps in QSO outflows

We study the origin of the cold molecular clumps in quasar outflows, recently detected in CO and HCN emission. We first describe the physical properties of such radiation-driven outflows and show that a transition from a momentum- to an energy-driven flow must occur at a radial distance of R≈0.25 kpc. During this transition, the shell of swept-up material fragments due to Rayleigh–Taylor instabilities, but these clumps contain little mass and are likely to be rapidly ablated by the hot gas in which they are immersed. We then explore an alternative scenario in which clumps form from thermal instabilities at R≳1 kpc, possibly containing enough dust to catalyze molecule formation. We investigate this process with 3D two-fluid (gas+dust) numerical simulations of a kpc{sup 3} patch of the outflow, including atomic and dust cooling, thermal conduction, dust sputtering, and photoionization from the QSO radiation field. In all cases, dust grains are rapidly destroyed in ≈10{sup 4} years; and while some cold clumps form at later times, they are present only as transient features, which disappear as cooling becomes more widespread. In fact, we only find a stable two-phase medium with dense clumps if we artificially enhance the QSO radiation field by a factor of 100. This result, together with the complete destruction of dust grains, renders the interpretation of molecular outflows a very challenging problem.

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ON THE NON-KOLMOGOROV NATURE OF FLARE-PRODUCTIVE SOLAR ACTIVE REGIONS

A magnetic power spectral analysis is performed on 53 solar active regions, observed from 2011 August to 2012 July. Magnetic field data obtained from the Helioseismic and Magnetic Imager, inverted as Active Region Patches, are used to study the evolution of the magnetic power index as each region rotates across the solar disk. Active regions are classified based on the numbers and sizes of solar flares they produce in order to study the relationship between flare productivity and the magnetic power index. The choice of window size and inertial range plays a key role in determining the correct magnetic power index. The overall distribution of magnetic power indices has a range of 1.0–2.5. Flare-quiet regions peak at a value of 1.6. However, flare-productive regions peak at a value of 2.2. Overall, the histogram of the distribution of power indices of flare-productive active regions is well separated from flare-quiet active regions. Only 12% of flare-quiet regions exhibit an index greater than 2, whereas 90% of flare-productive regions exhibit an index greater than 2. Flare-quiet regions exhibit a high temporal variance (i.e., the index fluctuates between high and low values), whereas flare-productive regions maintain an index greater than 2 for several days. This shows the importance of including the temporal evolution of active regions in flare prediction studies, and highlights the potential of a 2–3 day prediction window for space weather applications.

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Measurements of Solar Differential Rotation and Meridional Circulation from Tracking of Photospheric Magnetic Features

Long-lived rotational and meridional flows are important ingredients of the solar cycle. Magnetic field images have typically been used to measure these flows on the solar surface by cross-correlating thin longitudinal strips or square patches across sufficiently long time gaps. Here, I use 1 month of SDO/HMI line-of-sight magnetic field observations, combined with the Southwest Automatic Magnetic Identification Suite magnetic feature-tracking code to measure the motion of individual features in these magnetograms. By controlling for perturbations due to short-lived flows and due to false motions from feature interactions, I effectively isolate the long-lived flows traced by the magnetic features. This allows me to produce high-resolution (2° bins) differential rotation measurements with well-characterized variances and covariances of the fit parameters. I find a sidereal rotational profile of (14.296 ± 0.006) + (−1.847 ± 0.056)sin{sup 2} b + (−2.615 ± 0.093) sin{sup 4} b, with units of deg day{sup −1}, and a large covariance σ {sub BC} {sup 2} = −4.87 × 10{sup −3}(deg day{sup −1}){sup 2}. I also produce measurements of the much weaker meridional flow that are broadly consistent with previous results. These measurements exhibit a peak flow of 16.7 ± 0.6 m s{sup −1} at latitude b = 45° but are insufficiently characterized at higher latitudes to ascertain whether the chosen functional form 2cos bsin b is appropriate. This work demonstrates that measuring the motions of individual features in photospheric magnetograms can produce high-precision results in relatively short time spans, and suggests that high-resolution non-longitudinally averaged photospheric velocity residual measurements could be produced to compare with coronal results and to provide other diagnostics of the solar dynamo.

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Various Local Heating Events in the Earliest Phase of Flux Emergence

Emerging flux regions (EFRs) are known to exhibit various sporadic local heating events in the lower atmosphere. To investigate the characteristics of these events, especially to link the photospheric magnetic fields and atmospheric dynamics, we analyze Hinode, Interface Region Imaging Spectrograph (IRIS), and Solar Dynamics Observatory data of a new EFR in NOAA AR 12401. Out of 151 bright points (BPs) identified in Hinode/SOT Ca images, 29 are overlapped by an SOT/SP scan. Seven BPs in the EFR center possess mixed-polarity magnetic backgrounds in the photosphere. Their IRIS UV spectra (e.g., Si iv 1402.8 Å) are strongly enhanced and red- or blueshifted, with tails reaching ±150 km s{sup −1}, which is highly suggestive of bi-directional jets; each brightening lasts for 10–15 minutes, leaving flare-like light curves. Most of this group show bald patches, the U-shaped photospheric magnetic loops. Another 10 BPs are found in unipolar regions at the EFR edges. They are generally weaker in UV intensities and exhibit systematic redshifts with Doppler speeds up to 40 km s{sup −1}, which could exceed the local sound speed in the transition region. Both types of BPs show signs of strong temperature increase in the low chromosphere. These observational results support the physical picture that heating events in the EFR center are due to magnetic reconnection within cancelling undular fields like Ellerman bombs, while the peripheral heating events are due to shocks or strong compressions caused by fast downflows along the overlying arch filament system.

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Velocity Anisotropy in Self-gravitating Molecular Clouds. I. Simulation

The complex interplay between turbulence, magnetic fields, and self-gravity leads to the formation of molecular clouds out of the diffuse interstellar medium (ISM). One avenue of studying this interplay is by analyzing statistical features derived from observations, where the interpretation of these features is greatly facilitated by comparisons with numerical simulations. Here we focus on the statistical anisotropy present in synthetic maps of velocity centroid data, which we derive from three-dimensional magnetohydrodynamic simulations of a turbulent, magnetized, self-gravitating patch of ISM. We study how the orientation and magnitude of the velocity anisotropy correlate with the magnetic field and with the structures generated by gravitational collapse. Motivated by recent observational constraints, our simulations focus on the supersonic (sonic Mach number M≈2--17) but sub- to trans-alfvénic (alfvénic Mach number M{sub A}≈0.2--1.2) turbulence regime, and we consider clouds that are barely to mildly magnetically supercritical (mass-to-flux ratio equal to once or twice the critical value). Additionally we explore the impact of the turbulence driving mechanism (solenoidal or compressive) on the velocity anisotropy. While we confirm previous findings that the velocity anisotropy generally aligns well with the plane-of-sky magnetic field, our inclusion of the effects of self-gravity reveals that in regions of higher column density, the velocity anisotropy may be destroyed or even reoriented to align with the gravitationally formed structures. We provide evidence that this effect is not necessarily due to the increase of M{sub A} inside the high-density regions.

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Global Crustal Dynamics of Magnetars in Relation to Their Bright X-Ray Outbursts

This paper considers the yielding response of a neutron star crust to smooth, unbalanced Maxwell stresses imposed at the core–crust boundary, and the coupling of the dynamic crust to the external magnetic field. Stress buildup and yielding in a magnetar crust are global phenomena: an elastic distortion radiating from one plastically deforming zone is shown to dramatically increase the creep rate in distant zones. Runaway creep to dynamical rates is shown to be possible, being enhanced by in situ heating and suppressed by thermal conduction and shearing of an embedded magnetic field. A global and time-dependent model of elastic, plastic, magnetic, and thermal evolution is developed. Fault-like structures develop naturally, and a range of outburst timescales is observed. Transient events with time profiles similar to giant magnetar flares (millisecond rise, ∼0.1 s duration, and decaying power-law tails) result from runaway creep that starts in localized sub-kilometer-sized patches and spreads across the crust. A one-dimensional model of stress relaxation in the vertically stratified crust shows that a modest increase in applied stress allows embedded magnetic shear to escape the star over ∼3–10 ms, dissipating greater energy if the exterior field is already sheared. Several such zones coupled to each other naturally yield a burst of duration ∼0.1 s, as is observed over a wide range of burst energies. The collective interaction of many plastic zones forces an overstability of global elastic modes of the crust, consistent with quasi-periodic oscillation (QPO) activity extending over ∼100 s. Giant flares probably involve sudden meltdown in localized zones, with high-frequency (≫100 Hz) QPOs corresponding to standing Alfvén waves within these zones.

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Magnetic Flux Emergence and Decay Rates for Preceder and Follower Sunspots Observed with HMI

We quantify the emergence and decay rates of preceder (p) and follower (f) sunspots within 10 active regions from 2010 to 2014 using Space-weather Helioseismic Magnetic Imager Active Region Patch data. The sunspots are small to mid-sized regions and contain a signed flux within a single polarity sunspot of (1.1--6.5)×10{sup 21} Mx. The net unsigned flux within the regions, including plage, ranges from (5.1--20)×10{sup 21} Mx. Rates are calculated with and without intensity contours to differentiate between sunspot formation and flux emergence. Signed flux emergence rates, calculated with intensity contours, for the p (f) spots average 6.8(4.9)×10{sup 19} Mx hr{sup −1}, while decay rates are −1.9(−3.4)×10{sup 19} Mx hr{sup −1}. The mean, signed flux emergence rate of the regions, including plage, is 7.1×10{sup 19} Mx hr{sup −1}, for a mean peak flux of 5.9×10{sup 21} Mx. Using a synthesis of these results and others reported previously, there is a clear trend for larger flux regions to emerge faster than smaller ones. Observed emergence rates (dϕ/dt, Mx hr{sup −1}) scale with total signed peak flux, ϕ-tilde {sub max}, as a power law with an exponent of 0.36, i.e., dϕ/dt=A ϕ-tilde {sub max}{sup 0.36}. The observed rates may assist in constraining the boundary and initial conditions in simulations which already demonstrate increased rates for flux tubes with higher buoyancy and twist, or in the presence of a strong upflow. Overall, the observed emergence rates are smaller than those in simulations, which may indicate a slower rise of the flux in the interior than what is captured in simulations.

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Kiloparsec-scale Simulations of Star Formation in Disk Galaxies. IV. Regulation of Galactic Star Formation Rates by Stellar Feedback

Star formation from the interstellar medium of galactic disks is a basic process controlling the evolution of galaxies. Understanding the star formation rate (SFR) in a local patch of a disk with a given gas mass is thus an important challenge for theoretical models. Here we simulate a kiloparsec region of a disk, following the evolution of self-gravitating molecular clouds down to subparsec scales, as they form stars that then inject feedback energy by dissociating and ionizing UV photons and supernova explosions. We assess the relative importance of each feedback mechanism. We find that H{sub 2}-dissociating feedback results in the largest absolute reduction in star formation compared to the run with no feedback. Subsequently adding photoionization feedback produces a more modest reduction. Our fiducial models that combine all three feedback mechanisms yield, without fine-tuning, SFRs that are in excellent agreement with observations, with H{sub 2}-dissociating photons playing a crucial role. Models that only include supernova feedback—a common method in galaxy evolution simulations—settle to similar SFRs, but with very different temperatures and chemical states of the gas, and with very different spatial distributions of young stars.

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Predicting Solar Flares Using SDO /HMI Vector Magnetic Data Products and the Random Forest Algorithm

Adverse space-weather effects can often be traced to solar flares, the prediction of which has drawn significant research interests. The Helioseismic and Magnetic Imager (HMI) produces full-disk vector magnetograms with continuous high cadence, while flare prediction efforts utilizing this unprecedented data source are still limited. Here we report results of flare prediction using physical parameters provided by the Space-weather HMI Active Region Patches (SHARP) and related data products. We survey X-ray flares that occurred from 2010 May to 2016 December and categorize their source regions into four classes (B, C, M, and X) according to the maximum GOES magnitude of flares they generated. We then retrieve SHARP-related parameters for each selected region at the beginning of its flare date to build a database. Finally, we train a machine-learning algorithm, called random forest (RF), to predict the occurrence of a certain class of flares in a given active region within 24 hr, evaluate the classifier performance using the 10-fold cross-validation scheme, and characterize the results using standard performance metrics. Compared to previous works, our experiments indicate that using the HMI parameters and RF is a valid method for flare forecasting with fairly reasonable prediction performance. To our knowledge, this is the first time that RF has been used to make multiclass predictions of solar flares. We also find that the total unsigned quantities of vertical current, current helicity, and flux near the polarity inversion line are among the most important parameters for classifying flaring regions into different classes.

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Solar Active Region Coronal Jets. II. Triggering and Evolution of Violent Jets

We study a series of X-ray-bright, rapidly evolving active region coronal jets outside the leading sunspot of AR 12259, using Hinode/X-ray telescope, Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI), and Interface Region Imaging Spectrograph (IRIS) data. The detailed evolution of such rapidly evolving “violent” jets remained a mystery after our previous investigation of active region jets. The jets we investigate here erupt from three localized subregions, each containing a rapidly evolving (positive) minority-polarity magnetic-flux patch bathed in a (majority) negative-polarity magnetic-flux background. At least several of the jets begin with eruptions of what appear to be thin (thickness ≲2{sup ′′}) miniature-filament (minifilament) “strands” from a magnetic neutral line where magnetic flux cancelation is ongoing, consistent with the magnetic configuration presented for coronal-hole jets in Sterling et al. (2016). Some jets strands are difficult/impossible to detect, perhaps due to, e.g., their thinness, obscuration by surrounding bright or dark features, or the absence of erupting cool-material minifilaments in those jets. Tracing in detail the flux evolution in one of the subregions, we find bursts of strong jetting occurring only during times of strong flux cancelation. Averaged over seven jetting episodes, the cancelation rate was ∼1.5×10{sup 19} Mx hr{sup −1}. An average flux of ∼5×10{sup 18} Mx canceled prior to each episode, arguably building up ∼10{sup 28}–10{sup 29} erg of free magnetic energy per jet. From these and previous observations, we infer that flux cancelation is the fundamental process responsible for the pre-eruption build up and triggering of at least many jets in active regions, quiet regions, and coronal holes.

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Successive Two-sided Loop Jets Caused by Magnetic Reconnection between Two Adjacent Filamentary Threads

We present observational analysis of two successive two-sided loop jets observed by the ground-based New Vacuum Solar Telescope and the space-borne Solar Dynamics Observatory . The two successive two-sided loop jets manifested similar evolution processes and both were associated with the interaction of two small-scale adjacent filamentary threads, magnetic emerging, and cancellation processes at the jet’s source region. High temporal and high spatial resolution observations reveal that the two adjacent ends of the two filamentary threads are rooted in opposite magnetic polarities within the source region. The two threads approached each other, and then an obvious brightening patch is observed at the interaction position. Subsequently, a pair of hot plasma ejections are observed heading in opposite directions along the paths of the two filamentary threads at a typical speed for two-sided loop jets of the order 150 km s{sup −1}. Close to the end of the second jet, we report the formation of a bright hot loop structure at the source region, which suggests the formation of new loops during the interaction. Based on the observational results, we propose that the observed two-sided loop jets are caused by magnetic reconnection between the two adjacent filamentary threads, largely different from the previous scenario that a two-sided loop jet is generated by magnetic reconnection between an emerging bipole and the overlying horizontal magnetic fields.

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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 \textit{Planck} satellite over the 2540 $\text{deg}^2$ patch of sky covered by the SPT-SZ survey. We first visually compare the maps and find that the map residuals appear consistent with noise after we account for differences in angular resolution and filtering. To make a more quantitative comparison, we calculate (1) the cross-spectrum between two independent halves of SPT 150 GHz data, (2) the cross-spectrum between two independent halves of \textit{Planck} 143 GHz data, and (3) the cross-spectrum between SPT 150 GHz and \textit{Planck} 143 GHz 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 parameter characterizing the relative calibration between the two. As a by-product of this analysis, we improve the calibration of SPT data by nearly an order of magnitude, from 2.6\% to 0.3\% in power; the best-fit power calibration factor relative to the most recent published SPT calibration is $1.0174 \pm 0.0033$. Finally, we compare all three cross-spectra to the full-sky \textit{Planck} $143 \times 143$ power spectrum and find a hint ($\sim$1.5$\sigma$) for differences in the power spectrum of the SPT-SZ footprint and the full-sky power spectrum, which we model and fit as a power law in the spectrum. The best-fit value of this tilt is consistent between the three cross-spectra in the SPT-SZ footprint, implying that the source of this tilt---assuming it is real---is a sample variance fluctuation in the SPT-SZ region relative to the full sky. Despite the precision of our tests, we find no evidence for systematic errors in either data set. The consistency of cosmological parameters derived from these datasets is discussed in a companion paper.

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Radius-to-frequency Mapping and FRB Frequency Drifts

We build a model of radius-to-frequency mapping in magnetospheres of neutron stars and apply it to frequency drifts observed in fast radio bursts (FRBs). We assume that an emission patch propagates along the dipolar magnetic field lines, producing coherent emission with frequency, direction, and polarization defined by the local magnetic field. The observed temporal evolution of the frequency depends on the relativistic effects of time contraction and the curvature of the magnetic field lines. The model generically produces linear scaling of the drift rate, $\dot{\omega}$ ∝-${\omega}$, matching both numerically and parametrically the rates observed in FBRs; a more complicated behavior of $\dot{\omega}$ is also possible. Fast rotating magnetospheres produce higher drifts rates for similar viewing parameters than the slowly rotating ones. In the case of repeaters, the same source may show variable drift patterns depending on the observing phase. We expect rotational of polarization position angle through a burst, though by smaller amount than in radio pulsars. All of these findings compare favorably with properties of FBRs, strengthening their possible loci in the magnetospheres of neutron stars.

Magnetars↗

Measurement of the Cosmic Microwave Background Polarization Lensing Power Spectrum from Two Years of POLARBEAR Data

Here, we present a measurement of the gravitational lensing deflection power spectrum reconstructed with two seasons of cosmic microwave background polarization data from the Polarbear experiment. Observations were taken at 150 GHz from 2012 to 2014 and surveyed three patches of sky totaling 30 square degrees. We test the consistency of the lensing spectrum with a cold dark matter cosmology and reject the no-lensing hypothesis at a confidence of 10.9σ, including statistical and systematic uncertainties. We observe a value of A L = 1.33 ± 0.32 (statistical) ±0.02 (systematic) ±0.07 (foreground) using all polarization lensing estimators, which corresponds to a 24% accurate measurement of the lensing amplitude. Compared to the analysis of the first-year data, we have improved the breadth of both the suite of null tests and the error terms included in the estimation of systematic contamination.

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