From Small Space to Small Width in Resolution

In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of CNF formulas is always an upper bound on the width needed to refute them. Their proof is beautiful but somewhat mysterious in that it relies heavily on tools from finite model theory. We give an alternative, completely elementary proof that works by simple syntactic manipulations of resolution refutations. As a by-product, we develop a "black-box" technique for proving space lower bounds via a "static" complexity measure that works against any resolution refutation---previous techniques have been inherently adaptive. We conclude by showing that the related question for polynomial calculus (i.e., whether space is an upper bound on degree) seems unlikely to be resolvable by similar methods

Nucleosynthetic Layers in the Shocked Ejecta of Cassiopeia A

We present a three-dimensional analysis of the supernova remnant Cassiopeia A using high-resolution spectra from the Spitzer Space Telescope. We observe supernova ejecta both immediately before and during the shock-ejecta interaction. We determine that the reverse shock of the remnant is spherical to within 7%, although the center of this sphere is offset from the geometric center of the remnant by 810 km s^(–1). We determine that the velocity width of the nucleosynthetic layers is ~1000 km s^(–1) over 4000 arcsec^2 regions, although the velocity width of a layer along any individual line of sight is <250 km s^(–1). Si and O, which come from different nucleosynthetic layers in the progenitor star, are observed to be coincident in velocity space in some directions, but segregated by up to ~500 km s^(–1) in other directions. We compare these observations of the nucleosynthetic layers to predictions from supernova explosion models in an attempt to constrain such models. Finally, we observe small-scale, corrugated velocity structures that are likely caused during the supernova explosion itself, rather than hundreds of years later by dynamical instabilities at the remnant's reverse shock

Asymmetries of solar coronal extreme ultraviolet emission lines

The profiles of emission lines formed in the corona contain information on the dynamics and the heating of the hot plasma. Only recently has data with sufficiently high spectral resolution become available for investigating the details of the profiles of emission lines formed well above 10^6 K. These show enhanced emission in the line wings, which has not been understood yet. Line profiles of Fe XV formed at 2.5 MK acquired by the Extreme ultraviolet Imaging Spectrometer (EIS) onboard the Hinode solar space observatory are studied using multi Gaussian fits, with emphasis on the resulting line widths and Doppler shifts. In the major part of the active region, the spectra are best fit by a narrow line core and a broad minor component. The latter contributes some 10% to 20% to the total emission, is about a factor of 2 broader than the core, and shows strong blueshifts of up to 50 km/s. On average, the line width increases from the footpoints to the loop top for both components. A component with high upflow speeds can be found also in small restricted areas. The coronal structures consist of at least two classes that are not resolved spatially but only spectroscopically and that are associated with the line core and the minor component. Because of their huge line width and strong upflows, it is proposed that the major part of the heating and the mass supply to the corona is actually located in source regions of the minor component. The siphon flows and draining loops seen in the line core component are consistent with structures found in a 3D MHD coronal model. Despite the quite different appearance of the large active region corona and small network elements seen in transition region lines, both show similar line profile characteristics. This indicates that the same processes govern the heating and dynamics of the transition region and the corona.Comment: Astronomy & Astrophysics (accepted), 17 pages, 13 figure

Reconstructing the Properties of Dark Energy using Standard Sirens

Future space-based gravity wave experiments such as the Big Bang Observatory (BBO), with their excellent projected, one sigma angular resolution, will measure the luminosity distance to a large number of gravity wave (GW) sources to high precision, and the redshift of the single galaxies in the narrow solid angles towards the sources will provide the redshifts of the gravity wave sources. One sigma BBO beams contain the actual source only in 68 per cent cases; the beams that do not contain the source may contain a spurious single galaxy, leading to misidentification. To increase the probability of the source falling within the beam, larger beams have to be considered, decreasing the chances of finding single galaxies in the beams. Saini, Sethi and Sahni (2010) argued, largely analytically, that identifying even a small number of GW source galaxies furnishes a rough distance-redshift relation, which could be used to further resolve sources that have multiple objects in the angular beam. In this work we further develop this idea by introducing a self-calibrating iterative scheme which works in conjunction with Monte-Carlo simulations to determine the luminosity distance to GW sources with progressively greater accuracy. This iterative scheme allows one to determine the equation of state of dark energy to within an accuracy of a few percent for a gravity wave experiment possessing a beam width an order of magnitude larger than BBO (and therefore having a far poorer angular resolution). This is achieved with no prior information about the nature of dark energy from other data sets such as SN Ia, BAO, CMB etc.Comment: 12 pages, 10 figures. Expanded discussion, additional references. Main results unchanged. Matches published versio

LoCuSS: First Results from Strong-lensing Analysis of 20 Massive Galaxy Clusters at z~0.2

We present a statistical analysis of a sample of 20 strong lensing clusters drawn from the Local Cluster Substructure Survey (LoCuSS), based on high resolution Hubble Space Telescope imaging of the cluster cores and follow-up spectroscopic observations using the Keck-I telescope. We use detailed parameterized models of the mass distribution in the cluster cores, to measure the total cluster mass and fraction of that mass associated with substructures within R<250kpc.These measurements are compared with the distribution of baryons in the cores, as traced by the old stellar populations and the X-ray emitting intracluster medium. Our main results include: (i) the distribution of Einstein radii is log-normal, with a peak and 1sigma width of =1.16+/-0.28; (ii) we detect an X-ray/lensing mass discrepancy of =1.3 at 3 sigma significance -- clusters with larger substructure fractions displaying greater mass discrepancies, and thus greater departures from hydrostatic equilibrium; (iii) cluster substructure fraction is also correlated with the slope of the gas density profile on small scales, implying a connection between cluster-cluster mergers and gas cooling. Overall our results are consistent with the view that cluster-cluster mergers play a prominent role in shaping the properties of cluster cores, in particular causing departures from hydrostatic equilibrium, and possibly disturbing cool cores. Our results do not support recent claims that large Einstein radius clusters present a challenge to the CDM paradigm.Comment: 28 pages, 14 figures, accepted for publication in MNRAS, replaced with accepted versio

Multiabsorber Transition-Edge Sensors for X-Ray Astronomy

We are developing arrays of position-sensitive microcalorimeters for future x-ray astronomy applications. These position-sensitive devices commonly referred to as hydras consist of multiple x-ray absorbers, each with a different thermal coupling to a single-transition-edge sensor microcalorimeter. Their development is motivated by a desire to achieve very large pixel arrays with some modest compromise in performance. We report on the design, optimization, and first results from devices with small pitch pixels (&lt;75 m) being developed for a high-angular and energy resolution imaging spectrometer for Lynx. The Lynx x-ray space telescope is a flagship mission concept under study for the National Academy of Science 2020 decadal survey. Broadband full-width-half-maximum (FWHM) resolution measurements on a 9-pixel hydra have demonstrated E(FWHM) = 2.23 0.14 eV at Al-K, E(FWHM) = 2.44 0.29 eV at Mn-K, and E(FWHM) = 3.39 0.23 eV at Cu-K. Position discrimination is demonstrated to energies below &lt;1 keV and the device performance is well-described by a finite-element model. Results from a prototype 20-pixel hydra with absorbers on a 50-m pitch have shown E(FWHM) = 3.38 0.20 eV at Cr-K1. We are now optimizing designs specifically for Lynx and extending the number of absorbers up to 25/hydra. Numerical simulation suggests optimized designs could achieve 3 eV while being compatible with the bandwidth requirements of the state-of-the art multiplexed readout schemes, thus making a 100,000 pixel microcalorimeter instrument a realistic goal

Bond angle distribution in amorphous germania and silica

The distribution of Ge-O-Ge and Si-O-Si bond angles alpha in amorphous germania and silica is re-determined on the basis of diffraction experiments. The bond angle alpha joining adjacent tetrahedra is the central parameter of any continuous random network description (CRN) of these glasses. New high energy photon diffraction experiments on amorphous germania (at photon energies of 97 and 149 keV) are presented, covering the momentum transfer 0.6-33.5 AA^{-1}. In photon diffraction experiments on GeO2 the contribution of the OO pairs is very small. To obtain a similar information for amorphous SiO2, high energy photon diffraction experiments have been combined with neutron diffraction data on amorphous silica in order to eliminate the OO- partial structure factor. With this technique it is shown that the Si-O-Si angle distribution is fairly narrow (sigma=7.5 degree) and in fact comparable in width to the Ge-O-Ge angle distribution (sigma=8.3 degree), a result which differs from current opinion. The narrower distribution found in this study are in much better agreement to the determinations based on 29Si-MAS-NMR. Among the various models relating the chemical shift to the bond angle, best agreement is found with those models based on the secant model. Sharp components in the bond angle distribution can be excluded within the reached real space resolution of 0.09 AA.Comment: 12 pages LATEX, 13 Postscript figures, experimental data includes as LATEX comment

Contamination and exclusion in the sigma Orionis young group

We present radial velocities for 38 low-mass candidate members of the sigma Orionis young group. We have measured their radial velocities by cross-correlation of high resolution (R~6000) AF2/WYFFOS spectra of the gravity sensitive NaI doublet at 8183, 8195Angstroms. The total sample contained 117 objects of which 54 have sufficient signal-to-noise to detect NaI at an equivalent width of 3Angstroms, however we only detect NaI in 38 of these. This implies that very low-mass members of this young group display weaker NaI absorption than similarly aged objects in the Upper Scorpius OB association. We develop a technique to assess membership using radial velocities with a range of uncertainties that does not bias the selection when large uncertainties are present. The resulting membership probabilities are used to assess the issue of exclusion in photometric selections, and we find that very few members are likely to be excluded by such techniques. We also assess the level of contamination in the expected pre-main sequence region of colour-magnitude space brighter than I = 17. We find that contamination by non-members in the expected PMS region of the colour-magnitude diagram is small. We conclude that although radial velocity alone is insufficient to confirm membership, high signal-to-noise observations of the NaI doublet provide the opportunity to use the strength of NaI absorption in concert with radial velocities to asses membership down to the lowest masses, where Lithium absorption no longer distinguishes youth.Comment: 11 pages, MNRAS accepted. Online data available from: http://www.astro.ex.ac.uk/people/timn/Catalogues/service.htm

Background derivation and image flattening: getimages

Modern high-resolution images obtained with space observatories display extremely strong intensity variations across images on all spatial scales. Source extraction in such images with methods based on global thresholding may bring unacceptably large numbers of spurious sources in bright areas while failing to detect sources in low-background or low-noise areas. It would be highly beneficial to subtract background and equalize the levels of small-scale fluctuations in the images before extracting sources or filaments. This paper describes getimages, a new method of background derivation and image flattening. It is based on median filtering with sliding windows that correspond to a range of spatial scales from the observational beam size up to a maximum structure width $X_{\lambda}$. The latter is a single free parameter of getimages that can be evaluated manually from the observed image $\mathcal{I}_{\lambda}$. The median filtering algorithm provides a background image $\tilde{\mathcal{B}}_{\lambda}$ for structures of all widths below $X_{\lambda}$. The same median filtering procedure applied to an image of standard deviations $\mathcal{D}_{\lambda}$ derived from a background-subtracted image $\tilde{\mathcal{S}}_{\lambda}$ results in a flattening image $\tilde{\mathcal{F}}_{\lambda}$. Finally, a flattened detection image $\mathcal{I}_{{\lambda}\mathrm{D}}{\,=\,}\tilde{\mathcal{S}}_{\lambda}{/}\tilde{\mathcal{F}}_{\lambda}$ is computed, whose standard deviations are uniform outside sources and filaments. Detecting sources in such greatly simplified images results in much cleaner extractions that are more complete and reliable. As a bonus, getimages reduces various observational and map-making artifacts and equalizes noise levels between independent tiles of mosaicked images.Comment: 14 pages, 11 figures (main text + 3 appendices), accepted by Astronomy & Astrophysics; fixed Metadata abstract (typesetting