Differential Photometry With Variable Reference Stars

5th COROT week 1

Differential Photometry With Differential Photometry With Variable Reference StarsVariable Reference Stars

Christopher Broeg, AIU Jena / MPE Garching, Germany

Matilde Fernández, Instituto de Astrofisica de Andalusia, CSIC, Spain

Ralph Neuhäuser, AIU Jena, Germany

5th COROT week 2C. Broeg

OutlineOutline

MotivationDifferential photometry revisitedUsing weighted CSGetting a Good Value for Examples & ComparisonSummary

5th COROT week 3C. Broeg

MotivationMotivation

Often no standard stars in the FOVMain sequence stars are not constant in

brightness down to arbitrary accuracy levelsIt is always better to check for constant

brightness than to assume it

5th COROT week 4C. Broeg

Differential Photometry RevisitedDifferential Photometry Revisited

Extinction by a constant factor can be cancelled by subtraction of a constant comparison star (CS) due to the logarithmic scale

This works as well for an arbitrarily averaged CS

5th COROT week 5C. Broeg

Using Weighted CSUsing Weighted CS

What is the best choice for the weights?Any choice of weights is fine

choose weights so such the error of the artificial CS gets minimized

choose weights

This gives the lowest error for CS while still compensating for extinction

21

i

iCS

w

5th COROT week 6C. Broeg

Getting a Good Value for Getting a Good Value for

A robust estimator s of can be determined directly from the measurements, without relying on the instrumental errors

How?– Compare each CS with remaining CS– Calculate of the time series of CS brightnesses– This is used for weights of new calculation– Repeat until convergence

C. Broeg 75th COROT week

Iterative Algorithm: Sequence of operationsIterative Algorithm: Sequence of operationsStart

calculate newmagnitudes

output results

, ,read data: ,i io CS o CSm

calculate differ-ential magnitudes:

i

j

i i

w

CS i

w

CS CS CS j i

m m m

m m m

new weights 21

i

iCS

w

( )i i

j

i i

CS CS

w

CS CS CS j i

stddev m

m m m

new oldm m

calculate initialweights:

2i

2 2 2

1w

( )i i nI

err

err Factor

, ,CS i CS ierr

User input:

nI

CS,i ,

change and

so that

err

If for some CS this is not

possible, remove them.

CS i

Factor

Differential Photometry

5th COROT week 8C. Broeg

ExampleExampless: Output: Output

5th COROT week 9C. Broeg

Comparison With Ordinary Method (1) - LightcurveComparison With Ordinary Method (1) - Lightcurve

New method

Weights ~ m-3

No weights

5th COROT week 10C. Broeg

Comparison With Ordinary Method (2) – Phased LcComparison With Ordinary Method (2) – Phased Lc

New method

Weights ~ m-3

No weights

Please notice the different scales!!!

5th COROT week 11C. Broeg

Comp. cont. – only best 6 CS for comparisonComp. cont. – only best 6 CS for comparison

New method

Weights ~ m-7

Weights ~ m-3

6 brightest CS only

Again, please notice the different scales!!!

5th COROT week 12C. Broeg

SummarySummary

Algorithm automatically gets best S/N possible for the CS

Variable CS are detected and quantifiedWell defined error bars are calculatedThe method is clearly superior to

unweighted mean even when using the same CS (bad CS already rejected)

5th COROT week 13C. Broeg

AddendumAddendum

A paper presenting this method will be published in Astronomical Notes.If you are interested and want further information please contact:Christopher Broeg, Schillergässchen 2-3, 07745 Jena, Germanybroeg@astro.uni-jena.de

Thank you for your time!