# Harvard Astronomy 201b

## CHAPTER: Relevant Velocities in the ISM

In Book Chapter on February 28, 2013 at 3:06 am

(updated for 2013)

Note: it’s handy to remember that 1 km/s ~ 1 pc / Myr.

• Galactic rotation: 18 km/s/kpc (e.g. 180 km/s at 10 kpc)
• Isothermal sound speed: $c_s =\sqrt{\frac{kT}{\mu}}$
• For H, this speed is 0.3, 1, and 3 km/s at 10 K, 100 K, and 1000 K, respectively.
• Alfvén speed: The speed at which magnetic fluctuations propagate. $v_A = B / \sqrt{4 \pi \rho}$ Alfvén waves are transverse waves along the direction of the magnetic field.
• Note that $v_A = {\rm const}$ if $B \propto \rho^{1/2}$, which is observed to be true over a large portion of the ISM.
• Interstellar B-fields can be measured using the Zeeman effect. Observed values range from $5~\mu {\rm G}$ in the diffuse ISM to $1 mG$ in dense clouds. For specific conditions:
• $B = 1~\mu{\rm G}, n = 1 ~{\rm cm}^{-3} \Rightarrow v_A = 2~{\rm km~s}^{-1}$
• $B = 30~\mu {\rm G}, n = 10^4~{\rm cm}^{-3} \Rightarrow v_A = 0.4~{\rm km~s}^{-1}$
• $B = 1~{\rm mG}, n = 10^7 {\rm cm}^{-3} \Rightarrow v_A = 0.5~{\rm km~s}^{-1}$
• Compare to the isothermal sound speed, which is 0.3 km/s in dense gas at 20 K.
• $c_s \approx v_A$ in dense gas
• $c_s < v_A$ in diffuse gas
• Observed velocity dispersion in molecular gas is typically about 1 km/s, and is thus supersonic. This is a signature of the presence of turbulence. (see the summary of Larson’s seminal 1981 paper)