relative measurements with synoptic surveys i.photometry & astrometry eran ofek weizmann...
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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
al. 2
012
Asteroids rotationPoolis
hok
et
al. 2
012
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
Ofe
k et
al. 2
012
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
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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
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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
Ligh
t D
efle
ctio
n
Large field of viewLight Deflection
Diff
eren
tial L
ight
difl
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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