Relative measurements withSynoptic 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 curvesSome eclipsing M-dwarfs in PTF

Asteroids rotationPoolis

hok

et

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Asteroids rotationPoolis

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Photometry

How? Aperture photometry e.g., phot, SExtrator PSF photometry e.g., daophot, dophot Galaxy fitting e.g., GalFit

Absolute (Calibrated)Relative

PhotometryAperture photometry

Summing the intensity within an apertureComplications: Subtracting the background Interpolating Optimal aperture Centering

Aperture photometryInterpolating

Solution:Bickerton & Lupton 2013

Fraction of light

Aperture photometryOptimal aperture

Aper Radius [pix]

S/N

Aperture photometryBiases

Aper Radius [pix]

S/N

Biases may influence photometry, mainlyAt the faint end (e.g., due to uncertainty in position)

Fra

ctio

n of

ligh

t

S/N S/N

Calibrated photometryMethods

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

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a,b

Calibrated photometry

Photometry calibration good to 2-3%

Using SDSS starsas standard stars tocalibrate fields outsideSDSS footprint(photometric nights)

CCD 4

Ofek et al. 2011 submitted

Relative photometry

Find the ZP per image to add to magnitudes such that the scatter in theLight curves is minimized

Relative photometryThe ensemble method

Everett & Howell (2001)

fij – 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 & LSQLinear least squares – a reminder see a nice review in Gould (2003; arXiv/0310577)

)()(1

22 HPmHPm ijT

ij ij

Relative photometrySolution using linear least squares

Linear least squares – a reminder

However, sometime inversion is hard…

For large sets of equations use conjugate gradient

Relative photometrySolution using linear least squares

Honeycutt (1992); Padmanabhan et al. (2007); Ofek et al. (2011)

mij – instrumental mag

i-star (1..p), j-image (1..q)

Solving per field (overlap between fields not guaranteed)

ij – instrumental mag err

ijij zmm

Relative photometryUsing linear least squares

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m

m

m

m

m

m

P

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i

j

m

z

P

H (“design matrix”)

Observations

Free p

ara

mete

rs

ijij zmm z <m>

Relative photometrySimultaneous absolute calibration

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P H is (pq)x(p+q) matrixHowever, rank is p+q-1

jM

M1

100

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000 Adding calibration block

Relative photometryAdditional 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)

obsbm

Relative photometry

Relative photometry ~3-5mmag

Method presented in: Ofek et al. 2011 ApJ 740, 65

Relative photometryLimiting factors

Poisson statistics

Flat fielding

Charge diffusion variations

Atmospheric intensity scintilations

Relative photometryLimiting factors

Credit: Malagon (BNL)Flat

AstrometryMotivation

Relating objects… Is a transient associated with gal. nuc.? Searching for SN progenitors

Proper motions

Parallaxes

Binarity

Motivation ExampleAstrometric amplitude of 10kK WD-WD

binary at 14-18 mag range

State of the art

Best proper motions available: Hipparcos: ~0.25 (1σ) mas/yr (V<9)

PS-1/MDS ~10mas/yr (1σ) Tonry+2012

USNO-B vs. SDSS (+): ~6 mas/yr (1σ)

GAIA…

Large field of viewWhat effects astrometry?

Relative astrometryLimitations

However…

Large field of viewField distortion

Precession/Nutation

Atmospheric refraction

Color dependent refraction

Abberation of light

Light deflection

Scintillations

Centeroiding

Large field of viewAtmospheric refraction

Large field of viewLight Deflection

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Large field of viewLight Deflection

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Large field of viewDistortions ~1”/deg Precession >3”/yrRefraction ~1-2”/degColor Ref. ~80mas/500ÅAbberation ~0.5”/degDeflection ~0.1mas/degScintillations 2”/√(60 x 100)~25masCenteroiding ? <20 mas

Stratergies for PTFPTF 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 starsComparing PTF deep coadd with SDSS

Search for proper motion starsComparing PTF deep coadd with SDSS

Search for proper motion starsComparing PTF deep coadd with SDSS

Search for proper motion starsComparing PTF deep coadd with SDSS

Stratergies for PTFPTF 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

Metodologyi – image, j - star

Xij – (abb…) = DX

i + <X>

j + X

ij cos(Θ

i) – Y

ij sin(Θ

i) + …

a

i X

ij2 + b

i Y

ij2 + … (distortions per image)

c Xj2 + d Y

j2 + … (distortion per set of images)

ei 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: ~107 equations with ~30,000 unknowns (single field/ccd)

Relative astrometryOfek & Gorbikov

Preliminary results

Preliminary results

Relative astrometryOfek & Gorbikov

SummaryRelative photometry0.5-1 mmag precision is possible usingground based observation Relative astrometrySub-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

EndThank you!

Preliminary results

Preliminary results

Absolute astrometryLimitations

Abs. astrometry

Reference catalogs:

SDSS or UCAC-3 or USNO-B1 (in SCAMP)orUSNO-B1 (in Astrometry.NET)

In PTF IPAC pipeline images

Abs. astrometryIn PTF IPAC pipeline images

Abs. astrometryIn PTF IPAC pipeline images

Search for proper motion starsComparing PTF deep coadd with SDSS

Advantage: deeper than previous surveys

Search for proper motion starsPM[“/yr] = V[km/s] / (4.74 d[pc])

H=M+5 log10(V)–3.379 = m–5 log10(PM)ReducedProper motion