The Phases of the Interstellar Medium

The space between stars is not empty. It holds gas and dust at a mean density of about one hydrogen atom per cubic centimetre, amounting to some ten percent of the baryonic mass of the Galactic disk, and this material is the reservoir from which new stars form and the sink into which dying stars return their processed nuclei. The interstellar medium (ISM) is not a single uniform fluid but a set of coexisting phases with temperatures spanning six orders of magnitude and densities spanning eight, held in rough pressure equilibrium and continually stirred by supernovae, stellar winds, and Galactic rotation. This lesson catalogues those phases, the thermal balance that selects them, and the three observational handles that make the neutral, dusty, and ionized components visible: the 21-cm line, the extinction law, and the physics of H II regions.

The multiphase medium

By mass the ISM is roughly 70% hydrogen, 28% helium, and 2% heavier elements, of which about half the metals are locked into solid dust grains. Its state varies enormously from place to place. It is organized into a small number of phases, each occupying a distinct region of the density–temperature plane and each maintained by a different set of heating and cooling processes.¹

• Molecular clouds. Cold ($T\sim 10$–$20\text{K}$), dense ($n\sim 10^2$–$10^6{\text{cm}}^{-3}$) regions where hydrogen is molecular (${\mathrm{H}}_2$) and self-shielded from dissociating ultraviolet light. They hold most of the ISM mass in a small fraction of its volume and are the exclusive sites of star formation.
• Cold neutral medium (CNM). Diffuse atomic hydrogen at $T\sim 50$–$100\text{K}$, $n\sim 20$–$50{\text{cm}}^{-3}$, seen in 21-cm absorption and organized into sheets and filaments.
• Warm neutral medium (WNM). Atomic hydrogen at $T\sim 6000$–$10000\text{K}$, $n\sim 0.2$–$0.5{\text{cm}}^{-3}$, the intercloud medium that fills much of the disk volume and produces broad 21-cm emission.
• Warm ionized medium (WIM). Diffuse ionized hydrogen at $T\sim 8000\text{K}$, $n\sim 0.1{\text{cm}}^{-3}$, kept ionized by ultraviolet photons leaking out of H II regions; traced by faint diffuse $\mathrm{H}\alpha$.
• Hot ionized medium (HIM). A tenuous, collisionally ionized corona at $T\sim 10^6$–$10^7\text{K}$, $n\sim 10^{-3}$–$10^{-2}{\text{cm}}^{-3}$, shock-heated by supernova blast waves and radiating in the soft X-ray and in highly ionized ultraviolet lines such as O VI.

The warm and hot phases fill most of the volume; the cold phases hold most of the mass. A useful way to read the classification is that all five phases sit at comparable thermal pressures, so that density and temperature move inversely along lines of constant $P=nkT$.

Thermal balance and the two-phase structure

Why does neutral hydrogen split into two stable phases, a cold cloud and a warm intercloud medium, rather than settling at a single temperature? The answer is a balance between heating and cooling that admits two solutions at the same pressure.

Heating of the diffuse neutral gas is dominated by the photoelectric effect on dust grains: an ultraviolet photon ejects an electron from a grain, and that electron thermalizes into the gas. Cosmic rays contribute a smaller, density-tracking term. Per unit volume the heating rate is approximately $n\Gamma$, with $\Gamma$ the heating per particle, nearly independent of density. Cooling proceeds through collisionally excited fine-structure and metastable lines, chiefly the C II$158\mu \text{m}$ line in the cold gas and O I and Lyman-$\alpha$ in the warm gas. Because cooling requires a collision, its volumetric rate scales as $n^2\Lambda (T)$, with $\Lambda (T)$ the cooling function. Thermal equilibrium sets the two equal,

Along this equilibrium locus the temperature is a decreasing function of density, and the equilibrium thermal pressure $P_{\text{eq}}=nk{T}_{\text{eq}}(n)$ is a non-monotonic, S-shaped function of $n$. Over a range of pressures the curve is triple-valued: a low-density warm solution, a high-density cold solution, and a middle branch. The middle branch has $(\partial P/\partial n{)}_{\text{eq}}<0$ and is thermally unstable — a small compression raises the cooling faster than the pressure, and the parcel runs away to the cold branch, while a small expansion runs away to the warm branch. Only the two outer branches survive, and gas at the ambient pressure divides between the cold neutral medium and the warm neutral medium. This is the Field thermal-instability criterion applied to interstellar gas.²

The hot phase is added by supernovae. A blast wave shock-heats gas to $10^6\text{K}$ and above, where the cooling time exceeds the interval between supernovae, so the hot gas persists as a pervasive, low-density component. The resulting three-phase picture — cold clouds embedded in a warm intercloud medium, all riddled with hot supernova bubbles — is the standard model of the diffuse ISM.

The 21-centimetre line of atomic hydrogen

Atomic hydrogen, the dominant constituent of the neutral phases, has no optical or ultraviolet emission line accessible at $100\text{K}$: the first electronic excitation, Lyman-$\alpha$, lies at $10.2\text{eV}$, far beyond thermal reach. What makes the neutral ISM observable is a transition within the $1s$ ground state itself. The proton and electron each carry a magnetic moment, and their coupling splits the ground state into a hyperfine doublet: a higher triplet with the spins parallel (total spin quantum number $F=1$) and a lower singlet with the spins antiparallel ($F=0$). The splitting is minute,

The transition is magnetic-dipole and strongly forbidden; the spontaneous decay coefficient is $A_{10}=2.85\times 10^{-15}{\text{s}}^{-1}$, corresponding to a radiative lifetime of about $11\text{Myr}$ for an isolated atom. No individual atom would ever be seen to decay on a human timescale, but the ISM contains so many that the line is bright. Collisions couple the level populations to the kinetic temperature; because $\Delta E/k=0.068\text{K}$ is far below any ISM temperature, the populations follow the statistical-weight ratio $g_1/g_0=3$ almost exactly,

where the spin temperature $T_{\text{spin}}$ parametrizes the doublet population. Three-quarters of the atoms sit in the upper state at any moment. Because the emission is optically thin in most directions, the integrated line intensity is directly proportional to the column density of neutral hydrogen, making 21-cm surveys the primary map of the atomic ISM and, through the Doppler shift of the line, of Galactic rotation.

Interstellar dust: extinction and reddening

About one percent of the ISM mass is solid dust: grains of silicate and carbonaceous material with sizes from a few nanometres to about a micron, condensed in the cool outflows of evolved stars and grown in molecular clouds. Dust removes starlight from the line of sight by absorption and scattering, an effect called extinction. A star of intrinsic magnitude $M$ at distance $d$ is observed at

where the extinction $A_{\lambda }>0$ dims the star by grains along the path. Extinction is strongly wavelength dependent, rising toward the blue and ultraviolet because grains scatter short wavelengths more efficiently (the cross-section peaks when the wavelength is comparable to the grain size). Blue light is therefore removed preferentially, and starlight that survives the passage is reddened. The difference in extinction between two bands is the color excess,

the amount by which dust has reddened the observed color past the intrinsic color $(B-V{)}_0$. The ratio of total to selective extinction,

for the diffuse ISM, holds to within a narrow spread and rises toward larger grains in dense clouds. The full run of $A_{\lambda }$ against wavelength is the extinction curve: it climbs from the infrared through the optical, shows a broad bump at $2175\text{A˚}$ attributed to small carbonaceous grains, and rises steeply into the far ultraviolet where the smallest grains dominate.³

Because the reddening $E(B-V)$ grows in proportion to the dust column, it doubles as a measurement of the dust — and, through the gas-to-dust ratio, of the total hydrogen column along the line of sight. A reddened star traces a fixed slope in a color–color diagram, the reddening vector, whose length measures the dust column and whose known direction allows the intrinsic stellar color to be recovered.

H II regions and ionization fronts

Where a hot O or B star is embedded in gas, its ultraviolet output ionizes the surrounding hydrogen. Only photons above the Lyman limit, $h\nu >13.6\text{eV}$ ($\lambda <912\text{A˚}$), can ionize hydrogen from the ground state, and an O star emits a copious rate $N_{\text{uv}}$ of them. The ionized region is an H II region (the spectroscopic notation: H I is neutral, H II is singly ionized hydrogen). Inside it, ionizations and recombinations balance in equilibrium. Ignoring the thin surface layer, every ionizing photon is absorbed within the region, so the total ionization rate $N_{\text{uv}}$ equals the total recombination rate integrated over the volume,

where $n_e\approx n_p\approx n$ for pure hydrogen and ${\alpha }_B$ is the case-B recombination coefficient (summed over captures to excited states, since direct recombination to the ground state emits a new ionizing photon). Solving for the radius of the ionized sphere gives the Strömgren radius,

The ionized gas recombines and cascades, producing the recombination lines that make H II regions the glowing red nebulae of the disk — $\mathrm{H}\alpha$ at $656.3\text{nm}$ dominates the visible spectrum — together with collisionally excited forbidden lines such as O III at $500.7\text{nm}$. The sharp edge of the Strömgren sphere and the recombination spectrum together let an H II region be used to count the ionizing output, and hence the mass, of its exciting star.

Cosmic rays and magnetic fields

Two further constituents share the energy budget of the ISM without contributing much mass. Cosmic rays are relativistic protons and nuclei accelerated in supernova shocks; they pervade the disk with an energy density near $1\text{eV}{\text{cm}}^{-3}$ and ionize the interiors of molecular clouds that ultraviolet light cannot penetrate, setting the ionization fraction that couples the gas to the magnetic field. The interstellar magnetic field threads the whole medium at a strength of a few microgauss, revealed by the polarization of starlight (elongated grains align with the field) and by Faraday rotation. Its energy density is also close to $1\text{eV}{\text{cm}}^{-3}$. The thermal gas pressure, the turbulent kinetic energy, the magnetic field, and the cosmic rays all carry comparable energy densities, a rough equipartition that keeps the disk in vertical hydrostatic balance and makes the magnetic field a significant player in the support of clouds against collapse — the subject of the next lesson.

The 21-cm line, the extinction law, and the H II region between them expose the neutral, dusty, and ionized ISM. The coldest, densest phase — the molecular clouds — holds the gas dense enough for gravity to overcome pressure and begin the collapse that forms stars.