photometry atmosphere & standardization astr 3010 lecture 13 textbook 10.6 & 10.7
TRANSCRIPT
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