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

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

3. 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

4. Light curves Some eclipsing M-dwarfs in PTF

5. Asteroids rotation Poolishok et al. 2012

6. Asteroids rotation Poolishok et al. 2012

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

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

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

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

11. 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

12. 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,…

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

14. 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. 2011 submitted

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

16. 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

17. Relative photometry & LSQ Linear least squares – a reminder see a nice review in Gould (2003; arXiv/0310577)

18. 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

19. 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

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

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

22. 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)

23. Relative photometry Relative photometry ~3-5mmag Method presented in: Ofek et al. 2011 ApJ 740, 65

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

25. Relative photometry Limiting factors Credit: Malagon (BNL) Flat

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

27. Motivation Example Astrometric amplitude of 10kK WD-WD binary at 14-18 mag range

28. 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…

29. Large field of view What effects astrometry?

30. Relative astrometry Limitations However…

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

32. Large field of view Atmospheric refraction

33. Large field of view Light Deflection

34. Large field of view Light Deflection Differential Light difl.

35. 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

36. 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

37. Search for proper motion stars Comparing PTF deep coadd with SDSS

38. Search for proper motion stars Comparing PTF deep coadd with SDSS

39. Search for proper motion stars Comparing PTF deep coadd with SDSS

40. Search for proper motion stars Comparing PTF deep coadd with SDSS

41. 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

42. 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)

43. Relative astrometry Ofek & Gorbikov

44. Preliminary results

46. Relative astrometry Ofek & Gorbikov

47. Summary Relative photometry 0.5-1 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

48. End Thank you!

49. Preliminary results

51. Absolute astrometry Limitations

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

53. Abs. astrometry In PTF IPAC pipeline images

54. Abs. astrometry In PTF IPAC pipeline images

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

56. 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