Photometry:Aperture correction, Upper limit,

and Standardization

ASTR 3010

Lecture 11

Textbook: 10.6 & 10.7

Aperture Correction

The need for an aperture correction arises due to the difference in aperture sizes of science targets (fainter) and of standard stars (very bright).

Total enclosed counts within an aperture radius

Why different aperture size??

Signal

Signal / NoiseStandard Stars (very bright)signal >> noise

Maximum S/N : faint science target

Signal

Signal / Noise

Target Stars (faint)signal ≈ noise

Aperture Photometry

For optimal photometry, it is better to use a smaller aperture for the science targets and a larger aperture for the standard stars.

PSF shape remains the same b/w target and standard star measurements.

Aperture Correction Factor (r)= E(r)/E(∞), where E is an encircled energy.

Aperture correction• aperture correction

Inst. Flux of the Standard Star =Flux(rstd)*ap_correction(rstd)

Inst. Flux of the Target Star =Flux(rtgt)*ap_correction(rtgt)

If standard and target are measured at the same aperture, there is no need for the aperture correction.

rstd

rtgt

True Flux of Target Star = Flux of Std. Star * (Inst. Flux of tgt / Inst. Flux of std.)

Upper limit of an undetected source• In a digital image of your target, the object was not detected. The standard

deviation of the image pixel values is p=3.56.

What is the upper limit (3) for the brightness of your object?

0. The object was not detected because of the Poissonian noise from the sky

1. Expected sky flux = p2

2. For the source aperture of N pixels, expected total signal from the sky = N* p

2

3. Uncertainty of this value = sqrt(N* p2 )=sqrt(N)*p

4. 3 sigma upper limit = 3*sqrt(N)*p

What we measure (φarr) vs what we want to measure (φE).

ISM Extra Galactic

Matter

Photometric Reduction

• mAP : instrumental magnitude measured inside the atmosphere

• mP : instrumental magnitude measured outside the atmosphereSteps:1. Preprocess images2. Digital photometry (aperture or PSF) mA

P 3. Compute the instrumental mag outside the atmosphere mP 4. Transform instrumental magnitudes to a standard system mP

STD

5. Derive astrophysical and astronomical correctionso Corrections for absorptions: Aism, Aexg

o Correction for wavelength shift: CPZ

o Extract astrophysical parameters (temp, metallicity, age, distance, etc.)

Term Project Part I: Imaging Data• Imaging data can be copied from /home/astr3010/ImagingData

at your home directory..cp ../ImagingData/* .

• Start the pre-processing of these CCD data.

• Check “TermProject_photometry.pptx from the “lecture notes” page

In summary…

Important Concepts• Aperture correction• Upper limit calculation

Important Terms• Aperture Correction

Chapter/sections covered in this lecture : Not in the textbook