# Harvard Astronomy 201b

In Uncategorized on March 28, 2013 at 7:00 am

Thermal velocity dispersions mean you have a spectral line with some width, and the width is given by thermal broadening, so that $\sigma_T=\sqrt{k_B T/\mu m_H}$ from the Equipartition Theorem. This also happens to be the sound speed!  Is it mere coincidence that thermal velocities are on order the sound speed? No!  Thermal motions are (no surprise) set by the temperature.  The sound speed is set by pressure, since sound waves are just pressure-density waves, and the pressure is also ultimately set by the temperature. So it’s not coincidence that thermal motions are sub-sonic, and supersonic motions cannot be explained by thermal broadening.