A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems

Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the published versio

On stability of discretizations of the Helmholtz equation (extended version)

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\log k)$, and, additionally, appropriate mesh refinement is used near the vertices. We also review the stability properties of two classes of numerical schemes that use piecewise solutions of the homogeneous Helmholtz equation, namely, Least Squares methods and Discontinuous Galerkin (DG) methods. The latter includes the Ultra Weak Variational Formulation

Towards absorbing outer boundaries in General Relativity

We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations on a subset of flat spacetime of the form [0,T] x B_R, where B_R is a ball of radius R, and analyze different kinds of boundary conditions on \partial B_R. Our main results are: i) We give an explicit analytic example showing that boundary conditions obtained from freezing the incoming characteristic fields to their initial values are not compatible with the constraints. ii) With the help of the exact solutions constructed, we determine the amount of artificial reflection of gravitational radiation from constraint-preserving boundary conditions which freeze the Weyl scalar Psi_0 to its initial value. For monochromatic radiation with wave number k and arbitrary angular momentum number l >= 2, the amount of reflection decays as 1/(kR)^4 for large kR. iii) For each L >= 2, we construct new local constraint-preserving boundary conditions which perfectly absorb linearized radiation with l <= L. (iv) We generalize our analysis to a weakly curved background of mass M, and compute first order corrections in M/R to the reflection coefficients for quadrupolar odd-parity radiation. For our new boundary condition with L=2, the reflection coefficient is smaller than the one for the freezing Psi_0 boundary condition by a factor of M/R for kR > 1.04. Implications of these results for numerical simulations of binary black holes on finite domains are discussed.Comment: minor revisions, 30 pages, 6 figure

The relationship between sensory sensitivity and autistic traits in the general population.

Individuals with Autism Spectrum Disorders (ASDs) tend to have sensory processing difficulties (Baranek et al. in J Child Psychol Psychiatry 47:591–601, 2006). These difficulties include over- and under-responsiveness to sensory stimuli, and problems modulating sensory input (Ben-Sasson et al. in J Autism Dev Disorders 39:1–11, 2009). As those with ASD exist at the extreme end of a continuum of autistic traits that is also evident in the general population, we investigated the link between ASD and sensory sensitivity in the general population by administering two questionnaires online to 212 adult participants. Results showed a highly significant positive correlation (r = .775, p &#60; .001) between number of autistic traits and the frequency of sensory processing problems. These data suggest a strong link between sensory processing and autistic traits in the general population, which in turn potentially implicates sensory processing problems in social interaction difficulties

Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS) V. Detection of sodium on the bloated super-Neptune WASP-166b

Planet formation processes or evolution mechanisms are surmised to be at the origin of the hot Neptune desert. Studying exoplanets currently living within or at the edge of this desert could allow disentangling the respective roles of formation and evolution. We present the HARPS transmission spectrum of the bloated super-Neptune WASP-166b, located at the outer rim of the Neptune desert. Neutral sodium is detected at the 3.4 $\sigma$ level ($0.455 \pm 0.135 \%$), with a tentative indication of line broadening, which could be caused by winds blowing sodium farther into space, a possible manifestation of the bloated character of these highly irradiated worlds. We put this detection into context with previous work claiming a non-detection of sodium in the same observations and show that the high noise in the trace of the discarded stellar sodium lines was responsible for the non-detection. We highlight the impact of this low signal-to-noise remnant on detections for exoplanets similar to WASP-166b.Comment: 7 pages, 7 figures, accepted for publication in A&

Mass Calibration and Cosmological Analysis of the SPT-SZ Galaxy Cluster Sample Using Velocity Dispersion σv\sigma_v and X-ray YXY_\textrm{X} 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 ($\sigma_v$) and 16 X-ray Yx measurements of sample clusters, we simultaneously calibrate the mass-observable relation and constrain cosmological parameters. The calibrations using $\sigma_v$ and Yx are consistent at the $0.6\sigma$ level, with the $\sigma_v$ calibration preferring ~16% higher masses. We use the full cluster dataset to measure $\sigma_8(\Omega_ m/0.27)^{0.3}=0.809\pm0.036$. 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 $\sum m_\nu=0.06$ eV, we find the datasets to be consistent at the 1.0$\sigma$ level for WMAP9 and 1.5$\sigma$ for Planck+WP. Allowing for larger $\sum m_\nu$ further reconciles the results. When we combine the cluster and Planck+WP datasets with BAO and SNIa, the preferred cluster masses are $1.9\sigma$ higher than the Yx calibration and $0.8\sigma$ higher than the $\sigma_v$ 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 $\Omega_ m=0.299\pm0.009$ and $\sigma_8=0.829\pm0.011$. Within a $\nu$CDM model we find $\sum m_\nu = 0.148\pm0.081$ eV. We present a consistency test of the cosmic growth rate. Allowing both the growth index $\gamma$ and the dark energy equation of state parameter $w$ to vary, we find $\gamma=0.73\pm0.28$ and $w=-1.007\pm0.065$, demonstrating that the expansion and the growth histories are consistent with a LCDM model ($\gamma=0.55; \,w=-1$).Comment: Accepted by ApJ (v2 is accepted version); 17 pages, 6 figure

Analysis of Sunyaev-Zel'dovich Effect Mass-Observable Relations using South Pole Telescope Observations of an X-ray Selected Sample of Low Mass Galaxy Clusters and Groups

(Abridged) We use 95, 150, and 220GHz observations from the SPT to examine the SZE signatures of a sample of 46 X-ray selected groups and clusters drawn from ~6 deg^2 of the XMM-BCS. These systems extend to redshift z=1.02, have characteristic masses ~3x lower than clusters detected directly in the SPT data and probe the SZE signal to the lowest X-ray luminosities (>10^42 erg s^-1) yet. We develop an analysis tool that combines the SZE information for the full ensemble of X-ray-selected clusters. Using X-ray luminosity as a mass proxy, we extract selection-bias corrected constraints on the SZE significance- and Y_500-mass relations. The SZE significance- mass relation is in good agreement with an extrapolation of the relation obtained from high mass clusters. However, the fit to the Y_500-mass relation at low masses, while in good agreement with the extrapolation from high mass SPT clusters, is in tension at 2.8 sigma with the constraints from the Planck sample. We examine the tension with the Planck relation, discussing sample differences and biases that could contribute. We also present an analysis of the radio galaxy point source population in this ensemble of X-ray selected systems. We find 18 of our systems have 843 MHz SUMSS sources within 2 arcmin of the X-ray centre, and three of these are also detected at significance >4 by SPT. Of these three, two are associated with the group brightest cluster galaxies, and the third is likely an unassociated quasar candidate. We examine the impact of these point sources on our SZE scaling relation analyses and find no evidence of biases. We also examine the impact of dusty galaxies using constraints from the 220 GHz data. The stacked sample provides 2.8$\sigma$ significant evidence of dusty galaxy flux, which would correspond to an average underestimate of the SPT Y_500 signal that is (17+-9) per cent in this sample of low mass systems.Comment: 15 pages, 7 figure

Two TPX2-Dependent Switches Control the Activity of Aurora A

Aurora A is an important oncogenic kinase for mitotic spindle assembly and a potentially attractive target for human cancers. Its activation could be regulated by ATP cycle and its activator TPX2. To understand the activation mechanism of Aurora A, a series of 20 ns molecular dynamics (MD) simulations were performed on both the wild-type kinase and its mutants. Analyzing the three dynamic trajectories (Aurora A-ATP, Aurora A-ADP, and Aurora A-ADP-TPX2) at the residue level, for the first time we find two TPX2-dependent switches, i.e., switch-1 (Lys-143) and switch-2 (Arg-180), which are tightly associated with Aurora A activation. In the absence of TPX2, Lys-143 exhibits a “closed” state, and becomes hydrogen-bonded to ADP. Once TPX2 binding occurs, switch-1 is forced to “open” the binding site, thus pulling ADP away from Aurora A. Without facilitation of TPX2, switch-2 exits in an “open” conformation which accompanies the outward-flipping movement of P·Thr288 (in an inactive conformation), leading to the crucial phosphothreonine exposed and accessible for deactivation. However, with the binding of TPX2, switch-2 is forced to undergo a “closed” movement, thus capturing P·Thr288 into a buried position and locking its active conformation. Analysis of two Aurora A (K143A and R180A) mutants for the two switches further verifies their functionality and reliability in controlling Aurora activity. Our systems therefore suggest two switches determining Aurora A activation, which are important for the development of aurora kinase inhibitors

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