Minimum-Width Double-Strip and Parallelogram Annulus

In this paper, we study the problem of computing a minimum-width double-strip or parallelogram annulus that encloses a given set of n points in the plane. A double-strip is a closed region in the plane whose boundary consists of four parallel lines and a parallelogram annulus is a closed region between two edge-parallel parallelograms. We present several first algorithms for these problems. Among them are O(n^2) and O(n^3 log n)-time algorithms that compute a minimum-width double-strip and parallelogram annulus, respectively, when their orientations can be freely chosen

Optimal Consensus set for nD Fixed Width Annulus Fitting

International audienceThis paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. We present an algorithm, that provides the optimal solution(s) within a time complexity O(N n+1 log N) for dimension n, N being the number of points. Our algorithm guarantees optimal solution(s) and has lower complexity than previous known methods

Model-independent X-ray mass determinations

A new method is introduced for making X-ray mass determinations of spherical clusters of galaxies. Treating the distribution of gravitating matter as piecewise constant and the cluster atmosphere as piecewise isothermal, X-ray spectra of a hydrostatic atmosphere are determined up to a single overall normalizing factor. In contrast to more conventional approaches, this method relies on the minimum of assumptions, apart from the conditions of hydrostatic equilibrium and spherical symmetry. The method has been implemented as an XSPEC mixing model called CLMASS, which was used to determine masses for a sample of nine relaxed X-ray clusters. Compared to conventional mass determinations, CLMASS provides weak constraints on values of M_500, reflecting the quality of current X-ray data for cluster regions beyond r_500. At smaller radii, where there are high quality X-ray spectra inside and outside the radius of interest to constrain the mass, CLMASS gives confidence ranges for M_2500 that are only moderately less restrictive than those from more familiar mass determination methods. The CLMASS model provides some advantages over other methods and should prove useful for mass determinations in regions where there are high quality X-ray data.Comment: 12 pages, 8 figures, accepted for publication in Ap

Estimating the bispectrum of the Very Small Array data

We estimate the bispectrum of the Very Small Array data from the compact and extended configuration observations released in December 2002, and compare our results to those obtained from Gaussian simulations. There is a slight excess of large bispectrum values for two individual fields, but this does not appear when the fields are combined. Given our expected level of residual point sources, we do not expect these to be the source of the discrepancy. Using the compact configuration data, we put an upper limit of 5400 on the value of f_NL, the non-linear coupling parameter, at 95 per cent confidence. We test our bispectrum estimator using non-Gaussian simulations with a known bispectrum, and recover the input values.Comment: 17 pages, 16 figures, replaced with version accepted by MNRAS. Primordial bispectrum recalculated and figure 11 change

Modeling Self-Subtraction in Angular Differential Imaging: Application to the HD 32297 Debris Disk

We present a new technique for forward-modeling self-subtraction of spatially extended emission in observations processed with angular differential imaging (ADI) algorithms. High-contrast direct imaging of circumstellar disks is limited by quasi-static speckle noise and ADI is commonly used to suppress those speckles. However, the application of ADI can result in self-subtraction of the disk signal due to the disk's finite spatial extent. This signal attenuation varies with radial separation and biases measurements of the disk's surface brightness, thereby compromising inferences regarding the physical processes responsible for the dust distribution. To compensate for this attenuation, we forward-model the disk structure and compute the form of the self-subtraction function at each separation. As a proof of concept, we apply our method to 1.6 and 2.2 micron Keck AO NIRC2 scattered-light observations of the HD 32297 debris disk reduced using a variant of the "locally optimized combination of images" (LOCI) algorithm. We are able to recover disk surface brightness that was otherwise lost to self-subtraction and produce simplified models of the brightness distribution as it appears with and without self-subtraction. From the latter models, we extract radial profiles for the disk's brightness, width, midplane position, and color that are unbiased by self-subtraction. Our analysis of these measurements indicates a break in the brightness profile power law at r~110 AU and a disk width that increases with separation from the star. We also verify disk curvature that displaces the midplane by up to 30 AU towards the northwest relative to a straight fiducial midplane.Comment: Accepted for publication in ApJ, 20 pages, 10 figures, 1 tabl

Galaxy Cluster Pressure Profiles as Determined by Sunyaev Zel'dovich Effect Observations with MUSTANG and Bolocam I: Joint Analysis Technique

We present a technique to constrain galaxy cluster pressure profiles by jointly fitting Sunyaev-Zel'dovich effect (SZE) data obtained with MUSTANG and Bolocam for the clusters Abell 1835 and MACS0647. Bolocam and MUSTANG probe different angular scales and are thus highly complementary. We find that the addition of the high resolution MUSTANG data can improve constraints on pressure profile parameters relative to those derived solely from Bolocam. In Abell 1835 and MACS0647, we find gNFW inner slopes of $\gamma = 0.36_{-0.21}^{+0.33}$ and $\gamma = 0.38_{-0.25}^{+0.20}$, respectively when $\alpha$ and $\beta$ are constrained to 0.86 and 4.67 respectively. The fitted SZE pressure profiles are in good agreement with X-ray derived pressure profiles.Comment: 12 pages, 12 figures. Submitted to Ap