### Aperture correction, Upper limit, and Standardization

```Photometry:
Aperture correction, Upper limit,
and Standardization
ASTR 3010
Lecture 11
Textbook: 10.6 & 10.7
Aperture Correction
Total enclosed counts within an aperture radius
The need for an aperture correction arises due to the difference in aperture
sizes of science targets (fainter) and of standard stars (very bright).
Why different aperture size??
Signal
Standard Stars (very bright)
signal >> noise
Signal / Noise
Noise µ N pixels
Maximum S/N : faint science target
Target Stars (faint)
signal ≈ noise
Signal
Noise µ N pixels
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)
rstd
rtgt
If standard and target are measured
at the same aperture, there is no
need for the aperture correction.
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
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* p2
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
Satm ( l,t,e,a)
Sism ( l)
Extra Galactic
Matter
Sexg ( l)
jE ( l )
1
jArrived ( l) = Satm ( l) · SISM ( l) · Sexg ( l) ·
· jE ((1+ z) l)
1+ z
mPA = mOP + Aatm + Aism + Aexg + CPZ
= mP + Aatm
Photometric Reduction
mPA = mOP + Aatm + Aism + Aexg + CPZ
= mP + Aatm
• mAP : instrumental magnitude measured inside the atmosphere
• mP : instrumental magnitude measured outside the atmosphere
Steps:
1. Preprocess images
2. Digital photometry (aperture or PSF)  mAP
3. Compute the instrumental mag outside the atmosphere  mP
4. Transform instrumental magnitudes to a standard system  mPSTD
5. Derive astrophysical and astronomical corrections
o
o
o
Corrections for absorptions: Aism, Aexg
Correction for wavelength shift: CPZ
Extract astrophysical parameters (temp, metallicity, age, distance, etc.)
Term Project Part I: Imaging Data
• Imaging data can be copied from /home/astr3010/ImagingData