## More Photometry

Please refer to the Basic Photometry page for more fundamental information.

The photons you detect have been transmitted through the interstellar medium and, unless you observe from space, through the Earth's atmosphere. Both affect the fluxes.

## Atmospheric Extinction

This figure shows the extinction as a function of wavelength for targets at 1, 2, and 3 airmasses, at Kitt Peak, under normal conditions.

These curves depend on conditions: even clear photometric skies can have differing levels of humidity or other aerosols, or of dust (from volcanoes), which affect the overall shape of these curves.

The extinction solution is unique to a particular observatory, since it depends in part on the altitude (1 air mass at CTIO [7,000 ft] is more air than 1 air mass at Mauna Kea [13,700 ft]).

Your photometric solution will account for the atmospheric extinction.

## Interstellar Extinction

Interstellar extinction is characterized by Aλ, the extinction in magnitudes as a function of wavelength λ. Aλ depends both on the distance to your object (it is larger for more distant objects on the same line of sight), and on the direction to your object (the interstellar medium is not uniform).

The shape of the interstellar extinction curve is characterized by the quantity RV, the ratio of total to selective extinction.

RV = AV/EB-V

EB-V, the extinction, is (B-V)obs - (B-V)0, where the subscripts refer to the observed and intrinsic colors of the target.

In the standard diffuse ISM, R = 3.1

source: http://nedwww.ipac.caltech.edu/level5/Fitzpatrick/Figures/figure1.gif

In general, the extinction law is Aλ/EB-V = X + RV, where X, a function of wavelength, is a tabulated (or analytical) function.

Aλ/AV = X/RV + 1

This figure, from Mathis, 1990, ARAA, 28, 37, shows the extinction law for three stars with different values of RV. RV is larger in denser regions. Large RV indicates larger than normal gray extinction, and presumably larger grains. The 2175A bump is ubiquitous. The strength of the 2175A bump is proportional to RV-1, suggesting that small grains are more effective in causing this feature.

You can formulate the extinction in terms of the Hydrogen column density nH. The transmission

T = e-σnH

σnH = -ln(10-0.4 AV)

For EB-V = 1 and RV = 3.1, AV = 3.1, and nH = 5.8 x 1021 cm-2.

In the X-rays, absorption is provided by bound-free absorption. H bound-free absorption at 912 Angstroms makes the ISM opaque. Bound-free absorption is proportional to ν3. The absorption cross section per H atom is plotted above. The transmission for EB-V=1 is plotted below.

## Color-Color and Color-Magnitude Diagrams

Color-color diagrams are useful because colors are distance-independent.

Color-color diagrams can be used to separate dwarfs from giants.

An infrared color-color diagram for stars in the belt of Orion.

An infrared color-magnitude diagram for stars in the belt of Orion. Reddening moves stars off to the right

An optical color-color diagram for stars in the belt of Orion.

An optical color-magnitude diagram for stars in the belt of Orion. Reddening moves stars to the lower right

## Other Effects

• Airglow

• Telluric Absorption

### References

Savage and Mathis 1979, ARAA 17, 73
Cruddace et al. 1974, ApJ, 187, 497
Seaton 1979, MNRAS, 187, 73p
Clayton, Cardelli, and Mathis 1979, ApJ, 345, 245
Mathis 1990, ARAA 28, 37