---
title: The Phases of the Interstellar Medium
draft: false
module: The Interstellar Medium
moduleNumber: 6
lessonNumber: 1
order: 601
summary: >
  The gas between the stars separates into distinct thermal phases, from cold
  molecular clouds at 10 K to a diffuse million-degree corona, held near a common
  pressure by a balance of photoelectric heating and radiative cooling. Neutral
  hydrogen is traced by the 21-cm hyperfine line, dust reddens and extinguishes
  starlight along a characteristic wavelength law, and the ultraviolet output of
  hot stars carves ionized Strömgren spheres out of the surrounding gas.
topics: [The Interstellar Medium]
sources:
  - book: Carroll & Ostlie
    ref: "Ch. 12 — The Interstellar Medium and Star Formation; §12.1 Interstellar Dust and Gas"
  - book: Maoz
    ref: "Ch. 5 — Star Formation, H II Regions, and 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.[^co-ism]

- **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 $P = n k T$.

$$
% caption: The five phases occupy distinct regions of the density-temperature
% plane, but the cold and warm neutral media share a common pressure band.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (10.6,0) node[right, black!70] {log n};
\draw[->, black] (0,0) -- (0,6.2) node[above, black!70] {log T};
% constant-pressure guide lines (P = nkT constant means log T = C - log n)
\foreach \c in {4.6,5.6}
  \draw[black, densely dotted] (0.6,\c) -- (\c,0.3);
\node[black, rotate=-40, anchor=south, font=\scriptsize] at (2.5,1.5) {constant pressure};
% phase blobs
\draw[black, thick, fill=black!6] (8.4,0.9) ellipse (1.1 and 0.55);
\node[black] at (8.4,0.9) {molecular};
\draw[acc, thick, fill=acc!10] (6.4,1.9) ellipse (0.9 and 0.5);
\node[acc] at (6.4,1.9) {CNM};
\draw[acc, thick, fill=acc!10] (3.9,4.0) ellipse (0.9 and 0.5);
\node[acc] at (3.9,4.0) {WNM};
\draw[black, thick, fill=black!6] (2.0,4.0) ellipse (0.8 and 0.5);
\node[black] at (2.2,4.0) {WIM};
\draw[black, thick, fill=black!6] (1.3,5.5) ellipse (0.9 and 0.5);
\node[black] at (1.3,5.5) {HIM};
\end{tikzpicture}
$$

## 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,

$$
n\,\Gamma = n^2\,\Lambda(T)
\qquad\Longrightarrow\qquad
\Gamma = n\,\Lambda(T).
$$

Along this equilibrium locus the temperature is a decreasing function of density, and
the equilibrium **thermal pressure** $P_{\text{eq}} = n k T_{\text{eq}}(n)$ 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.[^maoz-ism]

$$
% caption: The equilibrium pressure is S-shaped in density; the negatively sloped
% middle branch is unstable, so gas settles onto the cold or warm stable branch.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (10.4,0) node[right, black!70] {log n};
\draw[->, black] (0,0) -- (0,5.6) node[above, black!70] {log P};
% S-curve: warm branch (rising), unstable (falling), cold branch (rising)
\draw[acc, very thick] (0.6,1.2) .. controls (2.2,2.9) and (3.0,3.6) .. (3.8,3.6);
\draw[acc, very thick, densely dashed] (3.8,3.6) .. controls (4.8,3.6) and (5.4,2.2) .. (6.4,2.2);
\draw[acc, very thick] (6.4,2.2) .. controls (7.4,2.2) and (8.6,3.6) .. (9.8,5.0);
% pressure band where two phases coexist
\draw[black, densely dotted] (0,2.7) -- (9.8,2.7);
\node[black, anchor=west, font=\scriptsize] at (8.4,2.95) {ambient P};
% stable and unstable markers
\fill[black] (2.3,2.7) circle (2pt);
\node[anchor=south] at (2.3,2.85) {WNM};
\fill[black] (8.05,2.7) circle (2pt);
\node[anchor=south] at (8.05,2.9) {CNM};
\node[black, anchor=north, font=\scriptsize] at (5.1,2.55) {unstable};
\end{tikzpicture}
$$

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,

$$
\Delta E = 5.87\ \mu\text{eV},
\qquad
\lambda = \frac{hc}{\Delta E} = 21.106\ \text{cm},
\qquad
\nu = 1420.406\ \text{MHz}.
$$

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,

$$
\frac{n_1}{n_0} = \frac{g_1}{g_0}\,e^{-\Delta E / k T_{\text{spin}}}
\approx 3\,\Bigl(1 - \frac{0.068\ \text{K}}{T_{\text{spin}}}\Bigr) \approx 3,
$$

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.

$$
% caption: The hydrogen ground state splits into a hyperfine doublet; the forbidden
% spin transition between them emits the 21-cm line at 1420 MHz.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% unsplit level
\draw[black, thick] (0.4,3.6) -- (3.0,3.6);
\node[black!70, anchor=east] at (0.3,3.6) {1s};
% split levels
\draw[very thick] (5.0,4.2) -- (8.0,4.2);
\draw[very thick] (5.0,1.4) -- (8.0,1.4);
\node[anchor=west] at (8.1,4.2) {F = 1 triplet};
\node[anchor=west] at (8.1,1.4) {F = 0 singlet};
% connectors
\draw[black, densely dotted] (3.0,3.6) -- (5.0,4.2);
\draw[black, densely dotted] (3.0,3.6) -- (5.0,1.4);
% transition arrow
\draw[->, acc, very thick] (6.5,4.2) -- (6.5,1.4);
\node[acc, anchor=west] at (6.65,2.8) {emits 21 cm};
% spin cartoons
\node[black, anchor=east] at (4.9,4.2) {spins parallel};
\node[black, anchor=east] at (4.9,1.4) {spins opposed};
\end{tikzpicture}
$$

## 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

$$
m = M + 5\log_{10}\!\Bigl(\frac{d}{10\ \text{pc}}\Bigr) + A_\lambda,
$$

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**,

$$
E(B-V) = A_B - A_V = (B-V)_{\text{obs}} - (B-V)_0,
$$

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

$$
R_V \equiv \frac{A_V}{E(B-V)} \approx 3.1
$$

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 $2175\ \text{Å}$
attributed to small carbonaceous grains, and rises steeply into the far ultraviolet
where the smallest grains dominate.[^co-dust]

$$
% caption: Extinction rises from the infrared into the ultraviolet, with a broad
% carbonaceous bump at 2175 angstroms and a steep far-ultraviolet climb.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (10.4,0) node[right, black!70] {inverse wavelength};
\draw[->, black] (0,0) -- (0,5.2) node[above, black!70] {extinction};
% main extinction curve rising to the left(IR) - right(UV); bump partway
\draw[acc, very thick] (0.5,0.6) .. controls (2.4,1.4) and (3.4,1.9) .. (4.6,2.3)
  .. controls (5.3,2.55) and (5.6,3.4) .. (6.1,3.4)
  .. controls (6.6,3.4) and (6.7,2.7) .. (7.2,2.7)
  .. controls (8.0,2.9) and (8.8,4.4) .. (9.8,5.0);
\node[acc, anchor=south] at (6.1,3.5) {2175 bump};
% band ticks
\foreach \x/\lab in {1.2/IR, 3.6/optical, 6.1/UV, 9.2/far UV}
  \node[black, anchor=north, font=\scriptsize] at (\x,-0.05) {\lab};
\end{tikzpicture}
$$

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.

$$
% caption: Dust shifts a star along a fixed reddening vector in the color-color
% plane; its length gives the dust column, its direction recovers the true color.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (7.0,0) node[right, black!70] {B minus V};
\draw[->, black] (0,0) -- (0,5.0) node[above, black!70] {U minus B};
% intrinsic point
\fill[black] (1.4,3.4) circle (2.4pt);
\node[anchor=south east] at (1.35,3.5) {intrinsic};
% reddening vector
\draw[->, acc, very thick] (1.4,3.4) -- (4.6,1.4);
\fill[black] (4.6,1.4) circle (2.4pt);
\node[black, anchor=west] at (4.7,1.4) {observed};
\node[acc, anchor=south west, font=\scriptsize] at (2.8,2.6) {reddening vector};
\end{tikzpicture}
$$

## 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, $h\nu > 13.6\ \text{eV}$
($\lambda < 912\ \text{Å}$), 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,

$$
N_{\text{uv}} = \frac{4}{3}\pi R_S^3\, n_e n_p\, \alpha_B
\approx \frac{4}{3}\pi R_S^3\, n^2\, \alpha_B,
$$

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**,

$$
R_S = \left( \frac{3\,N_{\text{uv}}}{4\pi\, n^2\, \alpha_B} \right)^{1/3}.
$$

> **Worked example.** An O6 star emits $N_{\text{uv}} = 10^{49}\ \text{s}^{-1}$
> ionizing photons into gas of density $n = 10\ \text{cm}^{-3}$, with
> $\alpha_B = 2.6 \times 10^{-13}\ \text{cm}^3\,\text{s}^{-1}$ at $10^4\ \text{K}$.
> Then
> $$
> R_S = \left( \frac{3 \times 10^{49}}{4\pi \times 10^2 \times 2.6\times10^{-13}} \right)^{1/3}
> \text{cm} \approx 4.5 \times 10^{19}\ \text{cm} \approx 15\ \text{pc}.
> $$
> The transition from fully ionized to fully neutral gas, the **ionization front**,
> is thin: its width is the mean free path of an ionizing photon,
> $\ell \sim 1/(n\sigma) \sim 0.005\ \text{pc}$ for a photoionization cross-section
> $\sigma \sim 6\times10^{-18}\ \text{cm}^2$, three thousand times smaller than $R_S$.

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.

$$
% caption: An O star ionizes a Strömgren sphere out to the radius where ionizations
% balance recombinations, bounded by a thin ionization front against neutral gas.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% neutral surroundings
\fill[black] (-0.2,-0.2) rectangle (10.6,5.4);
\node[black, anchor=north west] at (0.1,5.3) {neutral H I};
% ionized sphere
\fill[acc!12] (5.2,2.6) circle (2.7);
\draw[acc, very thick] (5.2,2.6) circle (2.7);
\node[acc] at (5.2,4.0) {ionized H II};
% central star
\fill[black] (5.2,2.6) circle (3.5pt);
\node[black, anchor=north] at (5.2,2.4) {O star};
% Stromgren radius marker
\draw[->, black] (5.2,2.6) -- (7.9,2.6);
\node[black!70, anchor=south] at (6.6,2.65) {Stromgren radius};
% ionization front label
\draw[->, black] (8.9,1.2) -- (7.1,1.9);
\node[black!70, anchor=north west] at (8.6,1.2) {ionization front};
\end{tikzpicture}
$$

## 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](/astrophysics-cosmology/ism-and-star-formation/molecular-clouds-and-gravitational-collapse).

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.

[^co-ism]: Carroll & Ostlie, §12.1 — Interstellar Dust and Gas: the composition, phases, and physical conditions of the interstellar medium.
[^maoz-ism]: Maoz, §5.1–5.2 — the multiphase interstellar medium, thermal balance, and the heating and cooling processes that set the neutral phases.
[^co-dust]: Carroll & Ostlie, §12.1 — interstellar extinction, reddening, the color excess, the ratio of total to selective extinction, and the extinction curve.