# Dust in Space

For a typical spiral galaxy, about 1/3 of the energy radiated by stars is absorbed by interstellar dust grains and subsequently re-emitted in the infrared (Draine, page 293).  The spectrum of this infrared emission is determined by both the temperature and the composition of the absorbing/emitting dust grains.  Dust grains interact most with radiation that is about the same wavelength as the size of the grains.  For submicron sized dust, extinction is high at UV and optical wavelengths.  But, the extinction is less at infrared wavelengths.  For wavelengths longer than a few hundred microns, dust emission is typically assumed to be optically thin.  The image below of the Trapezium Cluster in the Orion Nebula shows how a dusty region can appear opaque at optical wavelengths, but glow brightly in the infrared.

In the case of optically thin emission, we can define the specific intensity as

where, $B_\nu (T_d)$ is the Planck function at a given frequency ($\nu$) and dust temperature ($T_d$) and $\tau_\nu$ is the dust optical depth.  From this, we can define the flux as

Here, $M_d$ is the total dust mass, $D$ is the distance, and $\kappa_\nu$ is the dust opacity.  This dust opacity depends on frequency and is the main source of uncertainty in this equation.  A typical parameterization is

For the ISM, the value of $\beta$ is typically about 1.7.  For circumstellar disks around young stars, however, this value can be much lower (Draine 2006).