benmontet
commented
6 years ago I like this idea a lot. Your description matches my experience perfectly---even on few-day timescales, the PSF changes enough to affect your photometric estimates at the level of Kepler precision.
There's another axis which matters as well, which is wavelength! Red stars have different PSFs than blue stars to the point where it's not useful to declare a single PSF at a given location and time.
Nevertheless, this is an important problem to understand. I think the benefits for OG Kepler are limited, since aperture photometry does work extremely well nearly always there, but I'm becoming increasingly convinced this is the right approach for TESS. The stellar density is high enough (in units of stars per pixel, or stars per PSF size, I suppose) to where aperture photometry is going to fail pretty often. Just look at the FFIs! We need alternative methods there. I'd argue that TESS is going to be a lot like certain K2 clusters in terms of stellar density, and that's where I think PSF modeling will be useful for Kepler/K2.
I think the right approach is more or less the following (and am working on this currently with an eye towards TESS, and will be continuing at the Preparing for TESS meeting happening soon. We welcome collaborations!)
- Build a PSF at a given pixel. Assume (for a minute) nearby stars share this PSF exactly.
- Build a flexible but very slowly varying perturbation onto this PSF as a function of time to account for time-variability
- Build an additional perturbation for each nearby star that is maybe not a function of time to account for positional variability. Force it to be small, because it is.
- Build a flat field, possibly by using a functional form (side note @gully: what form did you use when you played with this?) or inferring it underneath the pixel shifts over the campaign. The latter might be running us out of free parameters.
In a world where TESS isn't happening, I don't think the benefit for doing this for Kepler is there (maybe for the K2 clusters) but I feel that this is (perhaps one of multiple) right approaches for TESS!
Description
The Kepler Point Spread Function (PSF), like any real-world optical instrument, depends on its location in the focal plane, both x, y, and radial distance z. The conspicuous variations in the PSF shape can be seen in a Full Frame Image possessing an even stretch. In some places the PSF appears undersampled, and in other regions it appears oversampled and distorted. The PSF also varies in time, as the space craft heats up and cools down cyclicly with different delivered solar insolation on its various surfaces, perhaps causing minuscule albeit non-negligible shifts in the focus of the telescope as the telescope slightly lengthens or the index of refraction of the corrector plate changes. Although the physical origin of the variations may not be known, the effect is clear.
Mapping the delivered PSF in space (pixel x,y, and channel number) and time (cadence) would provide an easy to use input for PSF photometry.
Benefits
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