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