arXiv subjects

C. Mason

Publications and source records attributed to C. Mason.

22 records · Page 2Linked to original sources

arXiv2014

Through the looking GLASS: HST spectroscopy of faint galaxies lensed by the Frontier Fields cluster MACS0717.5+3745

The Grism Lens-Amplified Survey from Space (GLASS) is a Hubble Space Telescope (HST) Large Program, which will obtain 140 orbits of grism spectroscopy of the core and infall regions of 10 galaxy clusters, selected to be among the very best cosmic telescopes. Extensive HST imaging is available from many sources including the CLASH and Frontier Fields programs. We introduce the survey by analyzing spectra of faint multiply-imaged galaxies and $z\gtrsim6$ galaxy candidates obtained from the first seven orbits out of fourteen targeting the core of the Frontier Fields cluster MACS0717.5+3745. Using the G102 and G141 grisms to cover the wavelength range 0.8-1.7$μ$m, we confirm 4 strongly lensed systems by detecting emission lines in each of the images. For the 9 $z\gtrsim6$ galaxy candidates clear from contamination, we do not detect any emission lines down to a seven-orbit 1$σ$ noise level of $\sim$5$\times$10$^{-18}$erg s$^{-1}$cm$^{-2}$. Taking lensing magnification into account, our flux sensitivity reaches $\sim$0.2-5$\times$10$^{-18}$erg s$^{-1}$cm$^{-2}$. These limits over an uninterrupted wavelength range rule out the possibility that the high-$z$ galaxy candidates are instead strong line emitters at lower redshift. These results show that by means of careful modeling of the background - and with the assistance of lensing magnification - interesting flux limits can be reached for large numbers of objects, avoiding pre-selection and the wavelength restrictions inherent to ground-based multi-slit spectroscopy. These observations confirm the power of slitless HST spectroscopy even in fields as crowded as a cluster core.

astro-ph.GA↗

arXiv2001

Log--Sobolev Inequalities and Regions with Exterior Exponential Cusps

We begin by studying semigroup estimates that are more singular than those implied by a Sobolev embedding theorem but which are equivalent to certain logarithmic Sobolev inequalities. We then give a method for showing such log--Sobolev inequalities hold for Euclidean regions that satisfy a certain Hardy-type inequality. Our main application is to show that domains with exterior exponential cusps, and hence no Sobolev embedding theorem, satisfy such heat kernel bounds provided the cusp is not too sharp. Finally we consider a rotationally invariant domain with an exponentially sharp cusp and show that ultracontractivity does break down after a certain point.

math.SP↗

arXiv2001

Perturbation of Domain: Singular Riemannian Manifolds

We study a class of Riemannian manifolds which are equipped with a singular metric. In particular we study a domain perturbation problem for the Dirichlet eigenvalues which depends on the best constant in the Hardy Inequality. However, we show that for these manifolds the constant is such that existing theorems cannot be applied and then prove better estimates that overcome this. Finally we set up an example that can be used to show that our results are optimal. The methods for doing this final step are contained in another paper in a more general ode setting.

math.SP↗

arXiv2001

Perturbation of Domain: Ordinary Differential Equations

We work with the Friedrichs extension of a one dimensional Schrodinger whose potential has a certain type of regular singularity near one end point. We study the effect on the eigenvalues of shrinking the region slightly near the end point. In particular we calculate the rate at which the eigenvalues of the smaller region converge to the eigenvalues of the larger region as the region expands. A result of this type was needed by that author in another paper concerned with a domain perturbation problem on Riemannian manifolds. The problem here, however, is stated purely in terms of ordinary differential equations.

math.SP↗