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Forced Photometry refers to photometric measurements conducted at a prespecified location. 

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Traditionally, projects which use multiple exposures to increase the depth and sensitivity of the observations have generated something equivalent to the stack images produced by the IPP pipeline. In theory, the photometry of the stack images produces the ‘best’ photometry catalog, with best sensitivity and the best data quality at all magnitudes (c.f, CFHT Legacy survey, COSMOS, etc). In practice, the stack images have some significant limitations due to the difficulty of modelling the PSF variations. This difficulty is particularly severe for the PS1 3π survey stacks due to the combination of the substantial mask fraction of the individual exposures, the large instrinsic image quality variations within a single exposure, and the wide range of image quality conditions under which data were obtained and used to generate the 3π PV3 stacks.

For any specific stack, the point spread function at a particular location is the result of the combination of the point spread functions for those individual exposures which went into the stack at that point. Because of the high mask fraction, the exposures which contributed to pixels at one location may be somewhat different just a few tens of pixels away. Because of the intrinsic variations in the PSF across an exposure and because of the variations from exposure to exposure, the distribution of point spread functions of the images used at one position may be quite different from those at a nearby location. In the end, the stack images have a effective point spread function which is not just variable, but changing significantly on small scales in a highly textured fashion.

Any measurement which relies on a good knowledge of the PSF at the location of an object either needs to determine the PSF variations present in the stack, or the measurement will be somewhat degraded. The highly textured PSF variations make this a very challenging problem: not would such a PSF model require an unusually fine-grained PSF model, there would likely not be enough PSF stars in an given stack to determine the model at the resolution required. The IPP photometry analysis code uses a PSF model with 2D variations using a grid of at most 6 × 6 samples per skycell, a number reasonably well-matched to the density of stars at most moderate Galactic latitudes. This scale is far too large to track the fine-grained changes apparent in the stack images. Thus PSF photometry as well as convolved Galaxy models in the stack are degraded by the PSF variations. Aperture-like measurements are in general not as affected by the PSF variations, as long as the aperture in question is large compared to the FWHM of the PSF.

The PV3 3π analysis solves this problem by using the sources detected in the Stack images and performing forced photometry on the individual warp images used to generate the stack. This analysis is performed on all warps for a single filter as a single job, though this is more of a bookkeeping aid as it is not necessary for the analysis of the different warps to know about the results of the other warps.

In the forced warp photometry, the positions of sources are loaded from the stack out- puts. PSF stars are pre-identified and a PSF model generated for each warp based on those stars, using the same stars for all warps to the extent possible (PSF stars which are excessively masked on a particular image are not used to model the PSF). The PSF model is fitted to all of the known source positions in the warp images. Aperture magnitudes, Kron magnitudes, and moments are also measured at this stage for each warp. Note that the flux measurement for a faint, but significant, source from the stack image may be at a low significance (< 5σ) in any individual warp image; the flux may even be negative for specific warps. When combined together, these low-significance measurements will result in a signficant measurement as the signal-to-noise increases by √N.

Tables with forced photometry on Stack Images (DR1)

FILL!

Tables with forced photometry on Warp Images (DR2)

  • ForcedWarpMeasurement: Contains single epoch forced photometry of individual measurements of objects detected in the stacked images. The identifiers connecting the measurement back to the original image and to the object association are provided. PSF, aperture, and Kron (1980) photometry are included, along with sky and detector coordinate positions. References: Kron, R. G. 1980, ApJS, 43, 305.
  • ForcedWarpExtended: Contains the single epoch forced photometry fluxes within the SDSS R5 (r = 3.00 arcsec), R6 (r = 4.63 arcsec), and R7 (r = 7.43 arcsec) apertures (Stoughton 2002) for objects detected in the stacked images. References: Stoughton, C., Lupton, R. H., Bernardi, M., et al. 2002, AJ, 123, 485.
  • ForcedWarpLensing: Contains the Kaiser et al. (1995) lensing parameters measured from the forced photometry of objects detected in stacked images on the individual single epoch data. References: Kaiser, N., Squires, G., and Broadhurst, T. 1995, ApJ, 449, 460.
  • ForcedGalaxyShape: Contains the extended source galaxy shape parameters. All filters are matched into a single row. The positions, magnitudes, fluxes, and Sersic indices are inherited from their parent measurement in the StackModelFit tables, and are reproduced here for convenience. The major and minor axes and orientation are recalculated on a warp-by-warp basis from the best fit given these inherited properties. References: Sersic, J. L. 1963, Boletin de la Asociacion Argentina de Astronomia La Plata Argentina, 6, 41.
  • ForcedWarpMasked: Contains an entry for objects detected in the stacked images which were in the footprint of a single epoch exposure, but for which there are no unmasked pixels at that epoch.

Tables with mean forced photometry from Warp Images (DR1)

  • ForcedMeanObject: Contains the mean of single-epoch photometric information for sources detected in the stacked data, calculated as described in Magnier et al. (2013). The mean is calculated for detections associated into objects within a one arcsecond correlation radius. PSF, Kron (1980), and SDSS aperture R5 (r = 3.00 arcsec), R6 (r = 4.63 arcsec), and R7 (r = 7.43 arcsec) apertures (Stoughton 2002) magnitudes and statistics are listed for all filters. References: Kaiser, N., Squires, G., and Broadhurst, T. 1995, ApJ, 449, 460; Kron, R. G. 1980, ApJS, 43, 305; Magnier, E. A., Schlafly, E., Finkbeiner, D., et al. 2013, ApJS, 205, 20; Stoughton, C., Lupton, R. H., Bernardi, M., et al. 2002, AJ, 123, 485.
  • ForcedMeanLensing: Contains the mean Kaiser et al. (1995) lensing parameters measured from the forced photometry of objects detected in stacked images on the individual single epoch data. References: Kaiser, N., Squires, G., and Broadhurst, T. 1995, ApJ, 449, 460.

The specific contents of each Table can be obtained from the linked pages.

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