### A Interstellar Extinction and Reddening

Interstellar space is not empty but is permeated by the Interstellar Medium (ISM). The ISM affects starlight which passes through it and the effects of the ISM on the observed magnitudes and colours of stars must be allowed for if their intrinsic properties are to be recovered. However, correction for interstellar effects is usually considered part of the astrophysical analysis of observations rather than part of their data reduction. Hence it is only mentioned here briefly in an appendix.

The main components of the ISM are gas and dust. Interstellar gas will tend to absorb (and re-radiate in a different wave-band) and dust will scatter the stellar radiation. These effective losses are known collectively as extinction. Unfortunately, generally extinction is not uniform across the whole spectrum. The observed magnitude (${m}_{obs}\left(\lambda \right)$) at some wavelength, $\lambda$, of a star will be the sum of its intrinsic magnitude (${m}_{int}\left(\lambda \right)$) and some extinction factor ($A\left(\lambda ,position\right)$) known as the total absorption16 which is dependent on both the wavelength of observation and the position of the star (which determines how much ISM is traversed by the observed light). Now $A$ can be written as the product of an absorption coefficient, ${\kappa }_{a}\left(\lambda \right)$, which is a function only of wavelength and a factor which is dependent only on the quantity of the ISM along the line of sight. We can define a function:

 $\zeta \left(\lambda \right)=\frac{{\kappa }_{a}\left(\lambda \right)}{{\kappa }_{a}\left(\lambda =5500\right)}$ (20)

This equation is the interstellar absorption law and is normalized at 5500Å  (that is, in the centre of the ‘visible’). Shorter wavelength light is affected more than longer wavelengths, so it is often also referred to as the reddening curve. Now we can write an extinction correction:

 $A\left(\lambda ,position\right)=\zeta \left(\lambda \right){A}_{1}\left(position\right),$ (21)

were ${A}_{1}\left(position\right)$ is a function only of the location of the observed star. So finally we have:

 ${m}_{obs}={m}_{int}\left(\lambda \right)+\zeta \left(\lambda \right){A}_{1}\left(position\right).$ (22)

Simple models[40] have been derived to model the distribution of the absorbing medium in the Galaxy, and maps[5960] showing the amount of absorption as a function of Galactic longitude and latitude ($l$, $b$) and distance are available. The reddening curve $\zeta \left(\lambda \right)$ when plotted against $\left(1/\lambda \right)$ is pretty linear across the UBVRI bands[64]. It is therefore relatively easy to correct any observed magnitude for the effects of interstellar extinction.

There is little interstellar extinction at infrared wavelengths. Hence objects which are heavily obscured at optical wavelengths, because they are deeply embedded in dense interstellar clouds, can often be observed at infrared wavelengths.

16Total absorption in, say, the $V$-band would usually be written as ${A}_{V}$ and known as the visual extinction.