PHOTOMETRIC ANALYSIS   (PA)

The PA module constructs a photometric time series, i.e., a light curve from the pixels defined to contain the optimal aperture, and associated background pixels. The data are in the form of integrated (total) photoelectrons collected during either a 1-minute or 30-minute observation. For each observation, a timestamp is associated, defined as the modified Julian date at the midpoint of the observation. Each data point in the time series is the direct sum of the photoelectron counts within a pre-defined target aperture. Bright star apertures may contain scores of pixels, while the faintest sources may have a single-pixel aperture. Source apertures are constructed to maximize the signal-to-noise ratio of the light curves and take into account the varying pixel response function across the focal plane. Details about the source apertures are provided here, and by Bryson etal.

The primary functions of PA are: (a) Derive the integrated flux for up to 165,000 sources observed on 30 minute timescales (long cadence data) and up to 512 sources observed on one minute timescales (short cadence data), from the calibrated pixels in each target’s aperture. (b) Determine the photocenters of each source in detector and astronomical coordinates. (c) Compute barycentric corrected timestamps for each target. This software component consists of a few dozen procedures, coded in Matlab.

The tasks performed by PA are:

1. Barycentric time correction
   Photometry is collected on a mobile platform, not connected to Earth, moving in a Earth-trailing heliocentric orbit. Timestamps associated with each observation must be adjusted to a common system for comparison to related and ancillary observations taken on Earth or other spacecraft. Additionally, precision timing is essential for interpretation of transit photometry, therefore the Project continues to work to improve the accuracy of derived timestamps. These values are computed using the onboard clock and a detailed ephemeris of the spacecraft trajectory. A further correction is applied such that the mid-cadence timestamp references the time of signal capture at the solar system barycenter. The barycentric corrections produced in PA also compensates for the small timing offsets produced by readout of the array.
    

2. "Argabrightening" event detection
   During the initial quarters of science operation, an occasional diffuse illumination of portions of the focal plane lasting a few minutes was detected. The origin of these brightenings is not currently known. The software searches for these events, and flags the affected pixels. Event detection occurs first in the PA module flow, to ensure that this brightening is not confused with much more localized excess photoelectrons produced by cosmic rays. Pixels affected by argabrightening are "gapped" in the light curve, i.e., set to -Inf. Listings of the specfic affected cadences are presented in the relevant data release notes for each quarter; users should examine the release note associated with your data and note possibly corrupted observations.
    

3. Cosmic ray cleaning
   Kepler is affected by the solar and Galactic high energy particle flux, with an expected rate of ~3 per day per pixel (Jenkins etal 2010). CRs impact at all angles of incidence; each event contributes charge to ~4 adjacent pixels. In PA, CRs are identified and subtracted in both background and source pixels, using a robust outlier identification algorithm. Since CRs are more easily detected in photometrically quiet sources, miitigation is more effective for those sources. The user is cautioned that CRs may not be adequately removed from bright pixels, but the overall effect on light curve precision will be minimal. The same method and parameters are used for both long and short cadence observations. PA also logs detected CRs, and derived CR metrics for impact rate and mean depositd energy. CR maps for pixels of interest will eventually be available through MAST.
    

4. Background removal
   A background signal is subtracted from each pixel (before summing) in the optimal aperture. Since each source aperture does NOT include extra pixels to evaluate the local background, Kepler collects a distinct set of background pixels on each channel for this purpose. A grid of background apertures are defined on each channel, roughly symmetric across the focal plane. Each aperture generally contains four pixels, ~8x8'' square. About 4400 usuable pixels within 1125 apertures lie in each channel, selected to avoid nearby stars and potentially saturated columns. The integrated diffuse background at each target pixel location is derived by fitting a 2-D polynomial to the calibrated background pixels for each cadence, then interpolating the fit for the specific pixels in the target aperture.
   No background pixels are collected at 1-minute intervals. For this data, the long cadence background polynomials are temporally interpolated to the midpoints of the short cadence intervals. Short cadence data users should be aware that changes in the background which occur on timescales less than 30 minutes are not captured by the current operations mode.
   Additional information about backgrounds can be found here and in the data release notes.
    

5. Aperture Photometry
   Each source is defined by a target aperture mask and the optimal photometric aperture. The optimal aperture contains a subset of the total pixels in the mask. Ideally the number of extra pixels recorded should be small, to maximize the number of observed sources, however a contrasting constraint is the desire to capture all pixels which might be useful. Users may wish to perform custom photometry, by altering the mix of included pixels, but have no recourse if the needed pixels were not obtained in the first place.

   Example of a aperture mask. The grey pixels define the total assigned aperture; the white pixels define the optimal photometric aperture.

   The flux is the unweighted sum of pixels in the optimal aperture after background removal, termed Simple Aperture Photometry, (SAP). This aperture is defined as the pixel set with the largest derived signal-to-noise ratio, taking into account the Poisson noise for the source and background, read noise, and quantization noise. Note that the optimal aperture does not necessarily capture the total flux from a source, but is designed to minimize noise for maximum transit detection sensitivity. Users with other science applications should keep this issue in mind. Users should also note that not all of the flux in the optimal aperture is due to the primary target. The PSF wings from surrounding sources will affect photometry in the optimal aperture. The crowding metric is defined as the fraction of flux in the optimal aperture produced by the target. This metric is computed for each target list each quarter. The excess flux due to crowding within the optimal aperture is removed when the light curves are corrected in the next processing step, PDC.

   Since the spacecraft rolls 90 degrees each quarter, any given source will lie on a different CCD after each roll. Apertures are re-defined for each quarter, to account for the different pixel response functions of the CCDs on which the source may fall.

   In the currently exported FITS light curve files, the output of PA is labeled "raw" flux to distinguish it from light curves which have been corrected for systematic effects in the subsequent PDC software module. At present, there is no flagging of individual bad pixels in the aperture photometry, nor does PA exclude known bad pixels by "gapping" observations. Compromised data is marked on a per channel and cadence basis, e.g., the Argabrightening events described above. Individual bad pixels will affect one or more cadence observations of individual targets; users are cautioned to inspect the target pixels if they suspect corrupted data is producing an odd light curve.
    

6. Source centroids
   Target motions occur for a number of known and unplanned reasons. The photocenter of each source is referred to as the source centroid. Both to quantify source motion amplitudes, and to identify and potentially correct systematic motions, flux-weighted centroids are calculated for all defined sources for each cadence. These data are also important for transit analysis and false postive rejection.
   The dominant source of long-term source motion, differential velocity abberation (DVA), is produced by the spacecraft motion during each quarter. Each source traces a small elliptical arc across the detectors over the period of Kepler's orbit. Unplanned source motions may occur due to random pointing jitter, pointing drift, and focus changes induced by thermal transients. During the course of each quarterly observing cycle, a set of (~325) reference pixels data are downlinked twice per week, to monitor the health of the spacecraft. If a serious amount of drift is seen in the centroids of these pixels, a commanded attitude adjustments may be initiated, producing a quasi-discontinuous change in the centroid locations.
   The derived centroids are tabulated in the light curve file exported to MAST, and provide a centroid motion time series for each source. These data can be used by GOs to ascertain the effect of positional stability on their light curves.

   

   An example of a motion centroid time series. Motion of the nominal "center" of channel 1 (also termed mod.out 2.1) is displayed for Q0. The large systematic drift is due to differential velocity abberation. Since this channel is located at the edge of the FOV, it also exhibits greater sensitivity to focus jitter and drift. The total amplitude of the centroid motion is on order 0.1 pixels, equivalent to 0.4 arcseconds.

7. Astrometric solution
   PA performs a standard function of astronomical data pipelines: assignment of celestial coordinates to detector pixels. On order 200 optimal sources are selected on each channel: bright, unsaturated, minimally-crowded, main sequences stars. A 2-D polynomial fit is constructed from the source row and column centroids for each channel and cadence. Right ascension and declination for each pixel are interpolated by mapping the polynomial fit to detector locations (row, column) for a given output channel. The astrometric solution is derived for each cadence independently.
    

8. Computation of metrics
   The PA module computes a variety of measures describing photometer performance, both as a health assessment and to support systematic error mitigation in following processing steps.
    

   The output of this module is a photometric time series: flux per unit time interval continuously observed for about 90 days, excluding about 1 day each month for the data downlink, and any safe modes or other anomaly. These light curves are then passed to the Pre-Search Data Conditioning (PDC), for correction of systematic errors. br>