Photometry Atmosphere & Standardization ASTR 3010 Lecture 13 Textbook 10.6 & 10.7

Extinction by Atmosphere Observing the incoming radiation at depth H in the atmosphere. Observing the incoming radiation at depth H in the atmosphere. Measured spectrum φ A (λ) where optical depth τ where optical depth τ and X is air mass. 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 m λ for any other stars! X 0123 slope = k

Sources of extinction 1.Rayleigh scattering 2.Absorption by Ozone 3.Scattering by Aerosols 4.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 stationary 2.k is isotropic when these two conditions are met, the night is called “photometric” X 0123 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 m λ 3.From the Bouguer line of your measurements 4.Variable extinction / multi-night data o measure two standard stars at a given time at different airmass o repeat the pair observation several times per night 5.Use all data X 0123

Heterochromatic extinction Apparent magnitudes versus airmass  different slopes for different colors Apparent magnitudes versus airmass  different slopes for different colors Forbes Effect = spectrum of a star changes with airmass

2 nd order extinction coefficients Taylor Expand k P (or parameterize k P ) Taylor Expand k P (or parameterize k P ) For example, (B-V) color can be used to indicate the spectral shape. 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 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 λ 1 and λ 2 where standard wavelengths are λ S1 and λ S2. instrumental (outside the atmosphere) magnitudes measured with two filters at λ 1 and λ 2 where standard wavelengths are λ S1 and λ S2.From we get Then, color term color coefficient efficiency term zero-point constant

Transformation to a standard system In practice, you measure m λ1 and (color index) 12 or m λ1 and m λ2 In practice, you measure m λ1 and (color index) 12 or m λ1 and m λ2 then plot X = Color Index 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 Four stars in this field are photometric standards. Their measured magnitudes are given below. (B-V)Vb(1)b(2)v(1)v(2) Airmass Star A Star B Star C Star D

Example (Homework) 1.Calculate extinction coefficients for the instrumental system for B and V bands. 2.Compute the standard transformation coefficients α V and α B-V (or α B ) 3.Calculate standard magnitudes of Obj1 (i.e., V and B-V) whose instrumental magnitudes are v=9.850 and b= taken at airmass=1.50 (B-V)Vb(1)b(2)v(1)v(2) Airmass Star A Star B Star C Star D

Example (Homework) 1.Calculate extinction coefficients for the instrumental system for B and V bands. (B-V)Vb(1)b(2)v(1)v(2) Airmass Star A Star B Star C Star D unknown Plot b(2)-b(1)/(X 2 -X 1 ) and measure the slope for k 1 (B-V)

Example (Homework) 2.Compute the standard transformation coefficients α V and α B-V (or α B ) (B-V)Vb(1)b(2)v(1)v(2) Airmass Star A Star B Star C Star D Plot as a function of color index (e.g., B-V)  Slope = α 12  y-intercept= α 1

Example (Homework) 3.Calculate standard magnitudes of Obj1 (i.e., V and B-V) whose instrumental magnitudes are v=9.850 and b= 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