PhotometryAtmosphere & Standardization
ASTR 3010
Lecture 13
Textbook 10.6 & 10.7
Extinction by Atmosphere• Observing the incoming radiation at depth H in
the atmosphere. Measured spectrum φA(λ)
where optical depth τ
and X is air mass.
Different notations
Bouguer’s Law
Take multiple measurements of non-varying object at several different airmasses!
one can get a mean extinction coeff from the slope
with known airmass, one can recover mλ for any other stars! X
0 1 2 3
slope = k
Sources of extinction
1. Rayleigh scattering2. Absorption by Ozone
3. Scattering by Aerosols4. Molecular-band absorption
stable over long time
variable due to a weather system
Photometric Condition
To be able to use Bouguer’s Law, we need two conditions
1. k is stationary2. k is isotropic
when these two conditionsare met, the night is called“photometric”
X0 1 2 3
slope = k
Example of non-stationary extinction during the obs.
Measuring monochromatic extinction
1. Assume use observatory’s value
2. Use a reference observe a star with known mλ
3. From the Bouguer line of your measurements
4. Variable extinction / multi-night datao measure two standard stars at a given time at different airmass
o repeat the pair observation several times per night
5. Use all data
X0 1 2 3
Heterochromatic extinction• Apparent magnitudes versus airmass different slopes for different colors
Forbes Effect
= spectrum of a star changes with airmass
2nd order extinction coefficients
• Taylor Expand kP (or parameterize kP)
• For example, (B-V) color can be used to indicate the spectral shape.
• This color-dependent term is not changing rapidly and takes many data to measure one can use observatory’s value
Transformation to a standard system• instrumental (outside the atmosphere) magnitudes measured with two
filters at λ1 and λ2 where standard wavelengths are λS1 and λS2.
From
we get
Then,
color termcolor coefficient
efficiency termzero-point constant
Transformation to a standard system
• In practice, you measure mλ1 and (color index)12 or mλ1 and mλ2
then plot
X = Color Index-1 0 +1 +2
Example (Homework)An observer used B and V filters to obtain four exposures of the same field at different air masses: two B exposures at air masses 1.05 and 2.13, and two V exposures at airmasses 1.10 and 2.48. Four stars in this field are
photometric standards. Their measured magnitudes are given below.
(B-V) V b(1) b(2) v(1) v(2)
Airmass 1.05 2.13 1.10 2.48
Star A -0.07 12.01 9.853 10.687 8.778 9.427
Star B 0.36 12.44 10.693 11.479 9.160 9.739
Star C 0.69 12.19 10.759 11.462 8.873 9.425
Star D 1.15 12.89 11.898 12.547 9.522 10.001
Example (Homework)
1. Calculate extinction coefficients for the instrumental system for B and V bands.
2. Compute the standard transformation coefficients αV and αB-V (or αB)3. Calculate standard magnitudes of Obj1 (i.e., V and B-V) whose
instrumental magnitudes are v=9.850 and b=10.899 taken at airmass=1.50
(B-V) V b(1) b(2) v(1) v(2)
Airmass 1.05 2.13 1.10 2.48
Star A -0.07 12.01 9.853 10.687 8.778 9.427
Star B 0.36 12.44 10.693 11.479 9.160 9.739
Star C 0.69 12.19 10.759 11.462 8.873 9.425
Star D 1.15 12.89 11.898 12.547 9.522 10.001
Example (Homework)
1. Calculate extinction coefficients for the instrumental system for B and V bands.
(B-V) V b(1) b(2) v(1) v(2)
Airmass 1.05 2.13 1.10 2.48
Star A -0.07 12.01 9.853 10.687 8.778 9.427
Star B 0.36 12.44 10.693 11.479 9.160 9.739
Star C 0.69 12.19 10.759 11.462 8.873 9.425
Star D 1.15 12.89 11.898 12.547 9.522 10.001
unknown unknown
Plot b(2)-b(1)/(X2-X1) and measure the slope for k1(B-V)
Example (Homework)
2. Compute the standard transformation coefficients αV and αB-V (or αB)
(B-V) V b(1) b(2) v(1) v(2)
Airmass 1.05 2.13 1.10 2.48
Star A -0.07 12.01 9.853 10.687 8.778 9.427
Star B 0.36 12.44 10.693 11.479 9.160 9.739
Star C 0.69 12.19 10.759 11.462 8.873 9.425
Star D 1.15 12.89 11.898 12.547 9.522 10.001
Plot as a function of color index (e.g., B-V)
Slope = α12 y-intercept = α1
Example (Homework)3. Calculate standard magnitudes of Obj1 (i.e., V and B-V) whose
instrumental magnitudes are v=9.850 and b=10.899 taken at airmass=1.50
In summary…
Important Concepts• Bouguer’s Law• Photometric condition• Standard Transformation
Important Terms• Extinction coefficient• Forbes effect
Chapter/sections covered in this lecture : 10.6 & 10.7