# 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)

## CHAPTER: Energy Density Comparison

In Book Chapter on February 6, 2013 at 10:06 pm

See Draine table 1.5 The main kinds of energy present in the ISM are:

1. The CMB
2. Thermal IR from dust
3. Starlight
4. Thermal kinetic energy (3/2 nKT)
5. Turbulent kinetic energy ( $1/2 \rho \sigma_v^2$)
6. B fields ( $B^2 / 8 \pi$)
7. Cosmic rays

All of these terms have energy densities within an order of magnitude of $1 ~{\rm eV ~ cm}^{-3}$. With the exception of the CMB, this is not a coincidence. Because of the dynamic nature of the ISM, these processes are coupled together and thus exchange energy with one another.

## CHAPTER: Bruce Draine’s List of Constituents of the ISM

In Book Chapter on February 5, 2013 at 9:09 pm

(updated for 2013)

1. Gas
2. Dust
3. Cosmic Rays*
4. Photons**
5. B-Field
6. Gravitational Field
7. Dark Matter

*cosmic rays are highly relativistic, super-energetic ions and electrons

**photons include:

• The Cosmic Microwave Background (2.7 K)
• starlight from stellar photospheres (UV, optical, NIR,…)
• $h\nu$ from transitions in atoms, ions, and molecules
• “thermal emission” from dust (heated by starlight, AGN)
• free-free emission (bremsstrahlung) in plasma
• synchrotron radiation from relativistic electrons
• $\gamma$-rays from nuclear transitions

His list of “phases” from Table 1.3:

1. Coronal gas (Hot Ionized Medium, or “HIM”): $T> 10^{5.5}~{\rm K}$. Shock-heated from supernovae. Fills half the volume of the galaxy, and cools in about 1 Myr.
2. HII gas: Ionized mostly by O and early B stars. Called an “HII region” when confined by a molecular cloud, otherwise called “diffuse HII”.
3. Warm HI (Warm Neutral Medium, or “WNM”): atomic, $T \sim 10^{3.7}~{\rm K}$. $n\sim 0.6 ~{\rm cm}^{-3}$. Heated by starlight, photoelectric effect, and cosmic rays. Fills ~40% of the volume.
4. Cool HI (Cold Neutral Medium, or “CNM”). $T \sim 100~{\rm K}, n \sim 30 ~{\rm cm}^{-3}$. Fills ~1% of the volume.
5. Diffuse molecular gas. Where HI self-shields from UV radiation to allow $H_2$ formation on the surfaces of dust grains in cloud interiors. This occurs at $10~{\rm to}~50~{\rm cm}^{-3}$.
6. Dense Molecular gas. “Bound” according to Draine (though maybe not). $n >\sim 10^3 ~{\rm cm}^{-3}$. Sites of star formation.  See also Bok Globules (JC 2013).
7. Stellar Outflows. $T=50-1000 {\rm K}, n \sim 1-10^6 ~{\rm cm}^{-3}$. Winds from cool stars.

These phases are fluid and dynamic, and change on a variety of time and spatial scales. Examples include growth of an HII region, evaporation of molecular clouds, the interface between the ISM and IGM, cooling of supernova remnants, mixing, recombination, etc.

## CHAPTER: Composition of the ISM

In Book Chapter on February 5, 2013 at 9:03 pm

(updated for 2013)

• Gas: by mass, gas is 60% Hydrogen, 30% Helium. By number, gas is 88% H, 10% He, and 2% heavier elements
• Dust: The term “dust” applies roughly to any molecule too big to name. The size distribution is biased towards small (0.2 $\mu$m) particles, with an approximate distribution $N(a) \propto a^{-3.5}$. The density of dust in the galaxy is $\rho_{\rm dust} \sim .002 M_\odot ~{\rm pc}^{-3} \sim 0.1 \rho_{\rm gas}$
• Cosmic Rays: Charged, high-energy (anti)protons, nuclei, electrons, and positrons. Cosmic rays have an energy density of $0.5 ~{\rm eV ~ cm}^{-3}$. The equivalent mass density (using E = mc^2) is $9 \times 10^{-34}~{\rm g cm}^{-3}$
• Magnetic Fields: Typical field strengths in the MW are $1 \mu G \sim 0.2 ~{eV ~cm}^{-3}$. This is strong enough to confine cosmic rays.