Relative measurements with Synoptic surveys I.Photometry & Astrometry Eran Ofek Weizmann Institute

Talk Layout Motivation and science case Relative photometry Limiting factors Methods Linear regression Relative astrometry Effects and limiting factors Methods and results

Motivation Relative photometry Light curves Spectral energy distribution Precision driver: small variations Relative astrometry Proper motions, parallax, binarity Photometry and astrometry have much in common

Light curves Some eclipsing M-dwarfs in PTF

Asteroids rotation Poolishok et al. 2012

Asteroids rotation Poolishok et al. 2012

Photometry How? Aperture photometry e.g., phot, SExtrator PSF photometry e.g., daophot, dophot Galaxy fitting e.g., GalFit Absolute (Calibrated) Relative

Photometry Aperture photometry Summing the intensity within an aperture Complications: Subtracting the background Interpolating Optimal aperture Centering

Aperture photometry Interpolating Solution: Bickerton & Lupton 2013 Fraction of light

Aperture photometry Optimal aperture Aper Radius [pix] S/N

Aperture photometry Biases Aper Radius [pix] S/N Biases may influence photometry, mainly At the faint end (e.g., due to uncertainty in position) Fraction of light S/N

Calibrated photometry Methods Calibrate the apparatus (but atmosphere) Local standard stars Global standard stars E.g., CalibMag = InstMag + ZP + …  AM +  color +  AM color + … time…, CCD position, atmo cond,…

Calibrated photometry Photometry calibration good to 2-3% CCD 4 Ofek et al. 2012a,b

Calibrated photometry Photometry calibration good to 2-3% Using SDSS stars as standard stars to calibrate fields outside SDSS footprint (photometric nights) CCD 4 Ofek et al submitted

Relative photometry Find the ZP per image to add to magnitudes such that the scatter in the Light curves is minimized

Relative photometry The ensemble method Everett & Howell (2001) f ij – instrumental flux i-star (1..p), j-image (1..q) Solving per field  ij – instrumental flux err Normalize by the ensamble: Caveats: requires stars that appears in all images + multiple iterations

Relative photometry & LSQ Linear least squares – a reminder see a nice review in Gould (2003; arXiv/ )

Relative photometry Solution using linear least squares Linear least squares – a reminder However, sometime inversion is hard… For large sets of equations use conjugate gradient

Relative photometry Solution using linear least squares Honeycutt (1992); Padmanabhan et al. (2007); Ofek et al. (2011) m ij – instrumental mag i-star (1..p), j-image (1..q) Solving per field (overlap between fields not guaranteed)  ij – instrumental mag err

Relative photometry Using linear least squares H (“design matrix”) Observations Free parameters z

Relative photometry Simultaneous absolute calibration H is (pq)x(p+q) matrix However, rank is p+q-1 Adding calibration block

Relative photometry Additional de-trending We can add more columns to H and P. For example: Airmass x color term Positional terms Multiple CCDs (i.e, overlap) – ubercal (SDSS; PS1; LSST)

Relative photometry Relative photometry ~3-5mmag Method presented in: Ofek et al ApJ 740, 65

Relative photometry Limiting factors Poisson statistics Flat fielding Charge diffusion variations Atmospheric intensity scintilations

Relative photometry Limiting factors Credit: Malagon (BNL) Flat

Astrometry Motivation Relating objects… Is a transient associated with gal. nuc.? Searching for SN progenitors Proper motions Parallaxes Binarity

Motivation Example Astrometric amplitude of 10kK WD-WD binary at mag range

State of the art Best proper motions available: Hipparcos: ~0.25 (1 σ ) mas/yr (V<9) PS-1/MDS ~10mas/yr (1 σ ) Tonry+2012 USNO-B vs. SDSS (+): ~6 mas/yr (1 σ ) GAIA…

Large field of view What effects astrometry?

Relative astrometry Limitations However…

Large field of view Field distortion Precession/Nutation Atmospheric refraction Color dependent refraction Abberation of light Light deflection Scintillations Centeroiding

Large field of view Atmospheric refraction

Large field of view Light Deflection

Large field of view Light Deflection Differential Light difl.

Large field of view Distortions ~1”/deg Precession >3”/yr Refraction ~1-2”/deg Color Ref. ~80mas/500Å Abberation ~0.5”/deg Deflection ~0.1mas/deg Scintillations 2”/√(60 x 100)~25mas Centeroiding ? <20 mas

Stratergies for PTF PTF deep coadd vs. SDSS good for faint stars ~10 mas/yr Use PTF multiple epochs beat scintillation noise using √N Periodicity in the residuals… Binaries

Search for proper motion stars Comparing PTF deep coadd with SDSS

Search for proper motion stars Comparing PTF deep coadd with SDSS

Search for proper motion stars Comparing PTF deep coadd with SDSS

Search for proper motion stars Comparing PTF deep coadd with SDSS

Stratergies for PTF PTF deep coadd vs. SDSS good for faint stars ~10 mas/yr Use PTF multiple epochs beat scintillation noise using √N Periodicity in the residuals… Binaries

Metodology i – image, j - star X ij – (abb…) = DX i + j + X ij cos(Θ i ) – Y ij sin(Θ i ) + … a i X ij 2 + b i Y ij 2 + … (distortions per image) c X j 2 + d Y j 2 + … (distortion per set of images) e i AM ij sin(Q ij ) + f i AM ij Color j sin(Q ij ) + … g (X ij – floor(X ij )) + … (sys. Center. Errors) (proper motion) + (parallax) + … Yij – (abb…) = … Produce: ~10 7 equations with ~30,000 unknowns (single field/ccd)

Relative astrometry Ofek & Gorbikov

Preliminary results

Relative astrometry Ofek & Gorbikov

Summary Relative photometry mmag precision is possible using ground based observation Relative astrometry Sub-mas precision is possible using (non- AO) ground based observations. Both – requires excellent understanding of systematic effects. Tips: explore the residuals Relative astrometry: PTF can deliver sub-mas precision relative astrometric measurements

End Thank you!

Preliminary results

Absolute astrometry Limitations

Abs. astrometry Reference catalogs: SDSS or UCAC-3 or USNO-B1 (in SCAMP) or USNO-B1 (in Astrometry.NET) In PTF IPAC pipeline images

Abs. astrometry In PTF IPAC pipeline images

Abs. astrometry In PTF IPAC pipeline images

Search for proper motion stars Comparing PTF deep coadd with SDSS Advantage: deeper than previous surveys

Search for proper motion stars PM [“/yr] = V [km/s] / (4.74 d [pc] ) H=M+5 log 10 (V)–3.379 = m–5 log 10 (PM) Reduced Proper motion