Dithering Strategies and Point-Source Photometry

The accuracy in the photometry of a point source depends on the point-spread function (PSF), detector pixelization, and observing strategy. The PSF and pixel response describe the spatial blurring of the source, the pixel scale describes the spatial sampling of a single exposure, and the observing strategy determines the set of dithered exposures with pointing offsets from which the source flux is inferred. In a wide-field imaging survey, sources of interest are randomly distributed within the field of view and hence are centered randomly within a pixel. A given hardware configuration and observing strategy therefore have a distribution of photometric uncertainty for sources of fixed flux that fall in the field. In this article we explore the ensemble behavior of photometric and position accuracies for different PSFs, pixel scales, and dithering patterns. We find that the average uncertainty in the flux determination depends slightly on dither strategy, whereas the position determination can be strongly dependent on the dithering. For cases with pixels much larger than the PSF, the uncertainty distributions can be non-Gaussian, with rms values that are particularly sensitive to the dither strategy. We also find that for these configurations with large pixels, pointings dithered by a fractional pixel amount do not always give minimal average uncertainties; this is in contrast to image reconstruction for which fractional dithers are optimal. When fractional pixel dithering is favored, a pointing accuracy of better than $\sim 0.15$ pixel width is required to maintain half the advantage over random dithers

Generating and Analyzing Constrained Dark Energy Equations of State and Systematics Functions

Some functions entering cosmological analysis, such as the dark energy equation of state or systematic uncertainties, are unknown functions of redshift. To include them without assuming a particular form we derive an efficient method for generating realizations of all possible functions subject to certain bounds or physical conditions, e.g. w\in[-1,+1] as for quintessence. The method is optimal in the sense that it is both pure and complete in filling the allowed space of principal components. The technique is applied to propagation of systematic uncertainties in supernova population drift and dust corrections and calibration through to cosmology parameter estimation and bias in the magnitude-redshift Hubble diagram. We identify specific ranges of redshift and wavelength bands where the greatest improvements in supernova systematics due to population evolution and dust correction can be achieved.Comment: 12 pages, 11 figures; v2 minor revisions, higher resolution figures, matches PRD versio

Measuring the 3D shape of X-ray clusters

Observations and numerical simulations of galaxy clusters strongly indicate that the hot intracluster x-ray emitting gas is not spherically symmetric. In many earlier studies spherical symmetry has been assumed partly because of limited data quality, however new deep observations and instrumental designs will make it possible to go beyond that assumption. Measuring the temperature and density profiles are of interest when observing the x-ray gas, however the spatial shape of the gas itself also carries very useful information. For example, it is believed that the x-ray gas shape in the inner parts of galaxy clusters is greatly affected by feedback mechanisms, cooling and rotation, and measuring this shape can therefore indirectly provide information on these mechanisms. In this paper we present a novel method to measure the three-dimensional shape of the intracluster x-ray emitting gas. We can measure the shape from the x-ray observations only, i.e. the method does not require combination with independent measurements of e.g. the cluster mass or density profile. This is possible when one uses the full spectral information contained in the observed spectra. We demonstrate the method by measuring radial dependent shapes along the line of sight for CHANDRA mock data. We find that at least 10^6 photons are required to get a 5-{\sigma} detection of shape for an x-ray gas having realistic features such as a cool core and a double powerlaw for the density profile. We illustrate how Bayes' theorem is used to find the best fitting model of the x-ray gas, an analysis that is very important in a real observational scenario where the true spatial shape is unknown. Not including a shape in the fit may propagate to a mass bias if the x-ray is used to estimate the total cluster mass. We discuss this mass bias for a class of spacial shapes.Comment: 29 pages, 16 figure