We have measured stellar photometry with the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) in near ultraviolet (F275W, F336W), optical (F475W, F814W), and near infrared (F110W, F160W) bands for 117 mill
ion resolved stars in M31. As part of the Panchromatic Hubble Andromeda Treasury (PHAT) survey, we measured photometry with simultaneous point spread function fitting across all bands and at all source positions after precise astrometric image alignment (<5-10 milliarcsecond accuracy). In the outer disk, the photometry reaches a completeness-limited depth of F475W~28, while in the crowded, high surface brightness bulge, the photometry reaches F475W~25. We find that simultaneous photometry and optimized measurement parameters significantly increase the detection limit of the lowest resolution filters (WFC3/IR) providing color-magnitude diagrams that are up to 2.5 magnitudes deeper when compared with color-magnitude diagrams from WFC3/IR photometry alone. We present extensive analysis of the data quality including comparisons of luminosity functions and repeat measurements, and we use artificial star tests to quantify photometric completeness, uncertainties and biases. We find that largest sources of systematic error in the photometry are due to spatial variations in the point spread function models and charge transfer efficiency corrections. This stellar catalog is the largest ever produced for equidistant sources, and is publicly available for download by the community.
We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects
in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to $sim N^2$ for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.
The near future of astrophysics involves many large solid-angle, multi-epoch, multi-band imaging surveys. These surveys will, at their faint limits, have data on large numbers of sources that are too faint to be detected at any individual epoch. Here
we show that it is possible to measure in multi-epoch data not only the fluxes and positions, but also the parallaxes and proper motions of sources that are too faint to be detected at any individual epoch. The method involves fitting a model of a moving point source simultaneously to all imaging, taking account of the noise and point-spread function in each image. By this method it is possible to measure the proper motion of a point source with an uncertainty close to the minimum possible uncertainty given the information in the data, which is limited by the point-spread function, the distribution of observation times (epochs), and the total signal-to-noise in the combined data. We demonstrate our technique on multi-epoch Sloan Digital Sky Survey imaging of the SDSS Southern Stripe. We show that we can distinguish very red brown dwarfs by their proper motions from very high-redshift quasars more than $1.6mag$ fainter than with traditional technique on these SDSS data, and with better better fidelity than by multi-band imaging alone. We re-discover all 10 known brown dwarfs in our sample and present 9 new candidate brown dwarfs, identified on the basis of high proper motion.
