self-calibration David W. Hogg (NYU) (MPIA) (Flatiron) 

What is self-calibration? Traditional calibration: Compare sources to (bright) standard stars taken as part of a calibration project. Or arcs and lamps. Self-calibration: Use the fact that the same source is observed by different parts of the detector, or in different modes. Enforce consistency to calibrate. 

Why employ self-calibration? Self-calibration uses the science data themselves to perform the calibration. Mitigate issues of cross-comparing observations at very different SNRs or exposure times. Reduce calibration overheads (though not to zero). It is more informative: Most of your photons are science photons! Simplify operations. 

Precise photometric surveys are all self-calibrated. SDSS Classic™ pioneered this in the optical (more in a moment). CMB surveys (NASA WMAP and ESA Planck, for instance, but all of them) have always been self-calibrated (you absolutely must self-calibrate if you want to do part-in-a-million intensity mapping!). NASA Kepler’s PDC detrending and my group’s CPM method are both forms of self-calibration. They were critical for exoplanet discovery. 

How did we calibrate the SDSS Classic™ imaging? Every star has 5 (true) magnitudes. Every night has 5 (true) extinctions (airmas terms). Every CCD column (why column?) has a photometric zeropoint. Many stars are observed on different nights in different CCDs or different CCD columns. Solve a very large set of linear equations (convex optimization FTW). 

Padmanabhan et al, arXiv:astro-ph/0703454 

Padmanabhan et al, arXiv:astro-ph/0703454 

There’s always a null space to any self-calibration. In the SDSS, there are five overall photometric zeropoints you can’t learn by self-calibration alone. We used certain F stars as absolute references. 

How are Kepler light curves self-calibrated? There are 105-ish stars with simultaneously measured light curves. These stars are not associated with one another. Any sense in which you can predict one star’s variability using other stars must be a spacecraft effect, not an intrinsic variability. Note the causal language (Wang et al, arXiv:1508.01853). 

Redundancy is critical. The key thing is to observe the same thing in different ways, and fit for all the dependencies that must be calibration-related. Diversify your data in the directions in which you most distrust your calibration (could be airmass, PSF, exposure time, detector orientation, season, etc.) 

Holmes, Hogg, & Rix, arXiv:1203.6255 

Could we self-calibrate the spectrographs? In spectrophotometric properties? Yes! In wavelength solution? For BOSS, Yes! For APOGEE, No! In EPRV spectrographs? Hell Yes! (work in progress by Lily Zhao, Yale). 

Could we self-calibrate element abundances? Stellar element abundances can depend strongly on position in the Galaxy, and on kinematics. They should not depend strongly on surface gravity (with exceptions). They should not depend on fiber number, airmass, or extinction. Can we use these principles to self-calibrate? (Hogg et al, SDSS Project 202) 

Image credit: Anna-Christina Eilers (MIT) 

Image credit: Anna Christina Eilers (MIT) 

Image credit: Anna Christina Eilers (MIT) 

Summary Self-calibration is more precise than traditional calibration. It reduces overheads and simplifies operations, but it introduces important survey design considerations. There are prospects for further improvements to SDSS-IV and SDSS-V data.