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