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
Poolishok et al. 2012
Asteroids rotation
Poolishok et al. 2012
Asteroids rotation
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
S/N
Optimal aperture
Aper Radius [pix]
Aperture photometry
S/N
Fraction of light
Biases
S/N
S/N
Biases may influence photometry, mainly
At the faint end (e.g., due to uncertainty in
position)
Aper Radius [pix]
Calibrated photometry
Methods
Calibrate the apparatus (but atmosphere)
Local standard stars
Global standard stars
E.g.,
CalibMag = InstMag + ZP + …
aAM + b color + c AM color + …
time…, CCD position, atmo cond,…
Calibrated photometry
Photometry calibration good to 2-3%
Ofek et al. 2012a,b
CCD 4
Calibrated photometry
Ofek et al. 2011 submitted
Photometry calibration good to 2-3%
Using SDSS stars
as standard stars to
calibrate fields outside
SDSS footprint
(photometric nights)
CCD 4
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)
Solving per field
i-star (1..p),
j-image (1..q)
fij – instrumental flux
sij – 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/0310577)
1 

T
2
c  (mij  HP) s ij (mij  HP)
2
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)
Solving per field (overlap between fields not guaranteed)
i-star (1..p),
j-image (1..q)
mij – instrumental mag
sij – instrumental mag err
mij  m j  zi
Relative photometry m  m  z
ij
j
i
Using linear least squares
z
<m>
0
0
1 0 0  0 0
1
 
 

m11
  m12
P

m13
  

0 1 0  1 0
0

m21
0 1 0  0 1
0 1 0  0 0
0
1


m22
m23
   
  



zj



P  mi

?
?
?
H (“design matrix”)
Observations
Free parameters
1 0 0  1 0
1 0 0  0 1
Relative photometry
Simultaneous absolute calibration
1 0 0  1 0
1 0 0  0 1
0
0
1 0 0  0 0
1
 
 

m11
  m12
P

m13
  

0 1 0  1 0
0

m21
0 1 0  0 1
0 1 0  0 0
0
1


m22
m23
   
  
H is (pq)x(p+q) matrix
However, rank is p+q-1


0
0
0

0
0
0

0
0
0

 1 0 0 
 0 1 0 
 0 0 1 

  
M1

Mj

Adding calibration block
Relative photometry
Additional de-trending
We can add more columns to H and P.
For example:
obs

m
b
Airmass x color term
Positional terms
Multiple CCDs (i.e, overlap) –
ubercal (SDSS; PS1; LSST)
Relative photometry
Method presented in: Ofek et al. 2011 ApJ 740, 65
Relative photometry ~3-5mmag
Relative photometry
Limiting factors
Poisson statistics
Flat fielding
Charge diffusion variations
Atmospheric intensity scintilations
Relative photometry
Limiting factors
Flat
Credit: Malagon (BNL)
Astrometry
Motivation
Relating objects…
Is a transient associated with gal. nuc.?
Searching for SN progenitors
Proper motions
Parallaxes
Binarity
Motivation Example
1
1
3
10
30
100
1
3
10
30
300
100
100
1
1000
10
300
Astrometric amplitude of 10kK WD-WD
binary at 14-18 mag range
0.3
3
10
30
100
300
0
Period [yr]
10
1000
0 .3
0.1
0.1
10
−1
0.1
1
0.3
10
−2
10
0
10
1
10
2
Distance [pc]
10
3
10
4
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 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
Light Deflection
Large field of view
Differential Light difl.
Light Deflection
Large field of view
Distortions
~1”/deg
Precession
>3”/yr
Refraction
~1-2”/deg
Color Ref.
Abberation
Deflection
Scintillations
Centeroiding
~80mas/500Å
~0.5”/deg
~0.1mas/deg
2”/√(60 x 100)~25mas
?
<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
Xij – (abb…) = DXi + <X>j + Xij cos(Θi) – Yij sin(
i) + …
ai Xij2 + bi Yij2 + … (distortions per image)
c Xj2 + d Yj2 + … (distortion per set of images)
ei AMij sin(Qij) + fi AMij Colorj sin(Qij) + …
g (Xij – floor(Xij)) + …
(sys. Center. Errors)
(proper motion) + (parallax) + …
Yij – (abb…) = …
Produce: ~107 equations with ~30,000 unknowns (single field/ccd)
Relative astrometry
Ofek & Gorbikov
Preliminary results
Preliminary results
Relative astrometry
Ofek & Gorbikov
Summary
Relative photometry
0.5-1 mmag precision is possible using
ground based observation
Relative astrometry
Sub-mas precision is possible using (nonAO) ground based observations.
Both – requires excellent understanding of
systematic effects.
Tips: explore the residuals
End
Thank you!
Preliminary results
Preliminary results
Absolute astrometry
Limitations
Abs. astrometry
In PTF IPAC pipeline images
Reference catalogs:
SDSS or UCAC-3 or USNO-B1 (in SCAMP)
or
USNO-B1 (in Astrometry.NET)
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])
Reduced
Proper motion
H=M+5 log10(V)–3.379 = m–5 log10(PM)