Photodissociation Regions

A photodissociation region — a PDR, also read as a photon-dominated region — is the warm neutral skin of a cloud whose temperature and chemistry are dictated not by ionizing radiation but by the far-ultraviolet photons that survive it. In the band $6\,\mathrm{eV}\lesssim h\nu<13.6\,\mathrm{eV}$ a photon cannot ionize hydrogen, so it slips through the surrounding H II region — where everything above $13.6\,\mathrm{eV}$ is already consumed — and buries itself in the neutral gas beyond the ionization front. There it does three things at once: it dissociates molecules like H $_2$ and CO, it ionizes low-potential atoms (carbon, at $11.26\,\mathrm{eV}$ , becomes C $^+$ throughout), and it heats the gas by kicking photoelectrons off dust grains and PAHs. The PDR is the layer where those photons live and die. Two numbers, to first order, run the whole show: the incident FUV intensity $G_0$ in Habing units and the hydrogen density $n_\mathrm{H}$ . As dust extinction attenuates the field with depth, the gas peels into chemical shells like an onion — hydrogen turns molecular near $A_V\approx1$ – $2$ , carbon locks into CO near $A_V\approx2$ – $4$ , and the temperature falls from several hundred kelvin at the illuminated face to $\sim10\,\mathrm{K}$ inside. The FUV energy is radiated back through a handful of bright fine-structure lines, above all [C II] $158\,\mu\mathrm{m}$ , which can carry $\sim1\%$ of a galaxy's entire luminosity. Because any neutral gas touched by starlight is technically a PDR, this one construction spans the diffuse cold ISM, the glowing edge of the Orion Bar, and star-forming galaxies out to high redshift — the microphysical hinge connecting heating and cooling, thermal instability, molecular-cloud chemistry, and the CO-dark gas budget.

Key takeaways

A PDR is the warm, mostly neutral layer where far-ultraviolet photons ( $6\,\mathrm{eV}<h\nu<13.6\,\mathrm{eV}$ ) set the thermal and chemical state of gas between the H II region and the molecular cloud interior.
The FUV field is measured in Habing units $G_0$ (relative to $1.6\times10^{-3}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$ ); the structure is essentially a two-parameter family in $(G_0,\ n_\mathrm{H})$ , and the surface temperature tracks the ratio $G_0/n_\mathrm{H}$ .
Grain photoelectric emission is the dominant heating channel, with an efficiency of a few percent that collapses as the grains charge up positively in intense fields.
Cooling is by fine-structure lines: [C II] $158\,\mu\mathrm{m}$ ( $\Delta E/k=91.2\,\mathrm{K}$ ) and [O I] $63\,\mu\mathrm{m}$ ( $\Delta E/k=228\,\mathrm{K}$ ) dominate the surface, with [C I] and CO rotational lines deeper in.
Dust extinction stratifies the chemistry with depth: H $\to$ H $_2$ by self-shielding at $A_V\approx1$ – $2$ , then C $^+\to$ C $\to$ CO at $A_V\approx2$ – $4$ , leaving a molecular but CO-dark shell in between.
Key idea: a PDR is a radiatively driven stratified slab — FUV photons deposit energy through grain photoelectric heating, dust extinction sets the depth of the H/H $_2$ and C $^+$ /C/CO transitions, and the whole structure is a two-parameter family in $(G_0,\ n_\mathrm{H})$ balanced by fine-structure line cooling.

The core insight

A PDR is a radiatively driven stratified slab: FUV photons deposit energy via grain photoelectric heating, dust extinction sets the depth of the H/H $_2$ and C $^+$ /C/CO transitions, and the whole structure is a two-parameter family in $(G_0,\ n_\mathrm{H})$ balanced by fine-structure line cooling.

Where this lives today

PDR physics is the working interpretive layer between raw far-infrared spectra and physical conditions. The most vivid current arena is the Orion Bar, mapped in stratified detail by the JWST "PDRs4All" program: the telescope resolves the ionization front, PAH emission, H $_2$ vibrational lines, and the [C I] and CO layers as physically separated surfaces, exactly in the order PDR models predict. On larger scales, SOFIA's upGREAT receiver mapped [C II] $158\,\mu\mathrm{m}$ and [O I] $63\,\mu\mathrm{m}$ across star-forming regions to weigh heating and cooling budgets directly, while ALMA routinely detects [C II] in galaxies within the first billion years after the Big Bang, using the line — calibrated through PDR models — as a redshift confirmation and star-formation tracer; its "[C II] deficit" in the most luminous systems probes grain charging in extreme fields. Open problems stay sharp: the true photoelectric efficiency, the H $_2$ formation rate in intense fields, and the geometry of clumpy, non-plane-parallel PDRs all feed directly into how we read galaxy spectra.

The physical picture

Stand at the edge of a molecular cloud lit by a nearby O star. The star's ionizing photons ( $h\nu>13.6\,\mathrm{eV}$ ) carve out an H II region and are used up at the ionization front, where hydrogen goes neutral. But the FUV photons just below that threshold keep marching in: they cannot touch hydrogen's ground state, yet they carry ample energy to break H $_2$ and CO and eject electrons from dust. The PDR is precisely this illuminated neutral skin — warm, chemically active, stratified — that the FUV reaches before dust extinction snuffs it out, from the ionization front to the cold molecular interior a few magnitudes deeper. The internal structure is an onion peeled by depth. At the surface everything is atomic and hot (H, C $^+$ , O, several hundred kelvin), and each transition inward happens where its controlling photons run out. Hydrogen turns molecular first, self-shielding in its Lyman–Werner lines; carbon stays ionized well past that, so a layer of H $_2$ exists with no CO; only deeper does carbon lock into CO, as the temperature slides down with the vanishing heating photons. The first figure sets this geometry.

Figure

An O star lights a cloud edge: FUV photons 6-13.6 eV pass through the H II region and heat a neutral skin. Layers stratify with dust depth — H to H₂ near A_V ≈ 1 and C⁺ to C to CO near A_V ≈ 2-4 — while the temperature falls from ~500 K at the surface to ~10 K inside, for the Orion Bar with G₀ ≈ 10⁴ and n ≈ 10⁵ cm⁻³

The whole system responds to two knobs. Turn up $G_0$ and everything heats, and the chemical fronts push deeper as more dust column is needed to attenuate the stronger field. Turn up the density $n_\mathrm{H}$ and collisions grow more frequent, cooling strengthens, and the fronts move shallower. What sets the surface temperature is neither alone but the ratio $G_0/n_\mathrm{H}$ : heating scales as $G_0 n_\mathrm{H}$ while collisional cooling scales as $n_\mathrm{H}^2$ , so the balance is heating per particle over the collision rate. And the accounting closes elegantly — the FUV a galaxy pours into its PDRs is diverted a few percent into gas heating and radiated in fine-structure lines, so [C II] luminosity reads like a bolometer of the processed FUV power. The second figure makes this quantitative.

Figure

Gas temperature versus dust depth for a dense bright PDR with G₀ ≈ 10⁴ and n ≈ 10⁵ cm⁻³: T falls from ~500 K at the illuminated surface to ~10 K by A_V ≈ 5. The H to H₂ front sits at A_V ≈ 1-2 and the C⁺ to C to CO transition at A_V ≈ 2-4, so a molecular but CO-dark layer separates them

The core equations

The strength of the illuminating field is the master parameter, compressed into one dimensionless number. Because PDR microphysics responds to the broadband $6$ – $13.6\,\mathrm{eV}$ flux rather than the detailed spectral shape (the cross sections are broad), one integrates the field over that band and normalizes to the solar-neighbourhood mean.

G_0=\frac{\int_{6\,\mathrm{eV}}^{13.6\,\mathrm{eV}} 4\pi J_\nu\,\mathrm{d}\nu}{1.6\times10^{-3}\,\mathrm{erg\,cm^{-2}\,s^{-1}}} \qquad (1)

where: $G_0$ — FUV energy flux relative to the mean solar-neighbourhood value (dimensionless); $J_\nu$ — mean specific intensity of the radiation field; $1.6\times10^{-3}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$ — the Habing (1968) reference flux integrated over the FUV band. A closely related unit is the Draine field, $\chi\approx1.7\,G_0$ ; the two are interchangeable up to that factor. The gas temperature at any depth is fixed by an energy balance: in steady state the heating rate per unit volume, $n_\mathrm{H}\Gamma_\mathrm{pe}$ , equals the cooling rate $n_\mathrm{H}\Lambda$ (dominated by fine-structure lines), and their equality defines the local equilibrium temperature the second figure plotted. The heating is the engine — an FUV photon absorbed by a grain or PAH ejects a photoelectron whose surplus energy thermalizes into the gas, at a rate scaling with $G_0$ , the grain (hence gas) density $n_\mathrm{H}$ , and an efficiency $\epsilon$ carrying all the physics of grain charge and work function.

\Gamma_\mathrm{pe}\,n_\mathrm{H}=1.3\times10^{-24}\,\epsilon\,G_0\,n_\mathrm{H}\ \ \mathrm{erg\,cm^{-3}\,s^{-1}} \qquad (2)

where: $\epsilon$ — photoelectric heating efficiency, $\sim0.01$ – $0.05$ , the fraction of absorbed FUV energy delivered to the gas as electron kinetic energy; $G_0$ — FUV field strength; $n_\mathrm{H}$ — hydrogen density. The efficiency is not constant: it falls as the charging parameter $G_0 T^{1/2}/n_e$ rises, because photoelectrons must then climb a growing positive potential. The cooling is carried by forbidden fine-structure lines, and one leads all others at the surface. Singly ionized carbon has abundance $\sim1.4\times10^{-4}$ per hydrogen and a ground term split into two levels only $91.2\,\mathrm{K}$ apart — trivially collisionally excited at PDR temperatures — so it radiates prolifically at $158\,\mu\mathrm{m}$ .

\Lambda_{[\mathrm{C\,II}]}:\ {}^2P_{3/2}\!\to{}^2P_{1/2},\quad \Delta E/k=91.2\,\mathrm{K},\quad \lambda=157.7\,\mu\mathrm{m} \qquad (3)

where: $\Delta E/k=91.2\,\mathrm{K}$ — upper-level energy in temperature units; $\lambda=157.7\,\mu\mathrm{m}$ — the transition wavelength; critical density $n_\mathrm{crit}\sim3\times10^3\,\mathrm{cm^{-3}}$ against H and $\sim60\,\mathrm{cm^{-3}}$ against electrons. In hotter, denser gas [O I] $63\,\mu\mathrm{m}$ ( $\Delta E/k=228\,\mathrm{K}$ , $n_\mathrm{crit}\sim5\times10^5\,\mathrm{cm^{-3}}$ ) takes over as the leading coolant. The chemistry is a competition between formation and destruction of each molecule. For hydrogen, formation is on grain surfaces at rate coefficient $R$ while destruction is Lyman–Werner photodissociation, attenuated both by dust ( $e^{-\tau_d}$ ) and by the molecule shielding itself.

\frac{\mathrm{d}n(\mathrm{H_2})}{\mathrm{d}t}=R\,n_\mathrm{H}\,n(\mathrm{H})-D_0\,f_\mathrm{sh}(N_{\mathrm{H_2}})\,e^{-\tau_d}\,n(\mathrm{H_2}) \qquad (4)

where: $R\sim3\times10^{-17}\,\mathrm{cm^3\,s^{-1}}$ — H $_2$ formation rate coefficient on grains; $D_0\sim5\times10^{-11}\,G_0\,\mathrm{s^{-1}}$ — unshielded photodissociation rate; $f_\mathrm{sh}(N_{\mathrm{H_2}})<1$ — self-shielding factor from line absorption; $\tau_d\approx A_V/1.086$ — dust optical depth in the FUV; $N_{\mathrm{H_2}}$ — H $_2$ column from the surface. Setting the left side to zero gives the steady-state H/H $_2$ transition. Because dust extinction is the common clock, the chemical fronts sit at characteristic depths in visual extinction — the observable signature of PDR structure.

A_V(\mathrm{H/H_2})\approx1\text{--}2,\qquad A_V(\mathrm{C^+/C/CO})\approx2\text{--}4 \qquad (5)

where: $A_V$ — visual extinction integrated from the PDR surface, a proxy for the dust (and gas) column, with $N_\mathrm{H}/A_V\approx1.9\times10^{21}\,\mathrm{cm^{-2}\,mag^{-1}}$ . The molecular hydrogen front lies strictly shallower than the CO front, which is what creates the CO-dark shell. Finally, the global energetics collapse into one ratio observers measure across whole galaxies: the fraction of reprocessed starlight emerging in the brightest cooling line.

\frac{L_{[\mathrm{C\,II}]}}{L_\mathrm{FIR}}\sim10^{-3}\text{--}10^{-2} \qquad (6)

where: $L_{[\mathrm{C\,II}]}$ — luminosity of the [C II] $158\,\mu\mathrm{m}$ line; $L_\mathrm{FIR}$ — far-infrared continuum from dust-reprocessed starlight. The ratio is a thermostat reading of PDR conditions; its decline in the most luminous systems (the "[C II] deficit") signals highly charged grains and suppressed $\epsilon$ .

Derivation ASurface temperature of a PDR from heating and cooling balance

The goal is to estimate the temperature of the illuminated face by setting grain photoelectric heating equal to [C II] fine-structure cooling, and to show along the way that the answer depends on the combination $G_0/n_\mathrm{H}$ rather than on either quantity alone — the single most useful qualitative fact about PDR thermodynamics. We write both rates per unit volume, divide, and read off the temperature through the Boltzmann factor the ratio isolates.

Step 1. Write the heating rate per unit volume from equation (2), $n_\mathrm{H}\Gamma_\mathrm{pe}=1.3\times10^{-24}\,\epsilon\,G_0\,n_\mathrm{H}$ , with $\epsilon\approx0.03$ – $0.04$ . Why: this is the FUV power the grains convert to gas heat, linear in both $G_0$ and $n_\mathrm{H}$ .

Step 2. Write the cooling rate in the low-density, subthermal limit, where each collisional excitation yields an escaping photon: $n_\mathrm{H}\Lambda_{[\mathrm{C\,II}]}\approx x_{\mathrm{C^+}}\,n_\mathrm{H}^2\,\gamma_{ul}\,(g_u/g_l)\,\Delta E\,e^{-\Delta E/kT}$ , with $x_{\mathrm{C^+}}\approx1.4\times10^{-4}$ , $\gamma_{ul}\approx8\times10^{-10}\,\mathrm{cm^3\,s^{-1}}$ , $g_u/g_l=2$ , $\Delta E/k=91.2\,\mathrm{K}$ . Why: below $n_\mathrm{crit}$ the cooling carries two powers of density — one for the C $^+$ ions, one for the colliders — and $T$ enters only through the Boltzmann factor.

Step 3. Divide heating by cooling: the density dependence reduces from $n_\mathrm{H}/n_\mathrm{H}^2$ to $1/n_\mathrm{H}$ , leaving $e^{-\Delta E/kT}\propto G_0/n_\mathrm{H}$ . Why: the surface temperature is controlled by the ratio $G_0/n_\mathrm{H}$ ; higher $G_0/n_\mathrm{H}$ demands a hotter surface to radiate the extra heat.

Step 4. Insert $G_0=1$ , $n_\mathrm{H}=100\,\mathrm{cm^{-3}}$ : heating $=5.2\times10^{-24}$ and the cooling prefactor $=2.8\times10^{-23}$ (erg cm $^{-3}$ s $^{-1}$ ), so $e^{-91.2/T}=0.19$ and $T\approx55\,\mathrm{K}$ — the cold neutral medium. A bright PDR ( $G_0\sim10^4$ , $n\sim10^4$ ) drives $T\sim500$ – $1000\,\mathrm{K}$ , warm enough for [O I] $63\,\mu\mathrm{m}$ ( $\Delta E/k=228\,\mathrm{K}$ ) to switch on. Why: recovering the CNM temperature, and the jump to $\sim10^3\,\mathrm{K}$ , checks the rate normalizations.

Go deeper · Derivation B · 1 minDepth of the H₂ dissociation front from self-shielding

Derivation BDepth of the H₂ dissociation front from self-shielding

The goal is to show that hydrogen turns molecular at a depth of only $A_V\approx1$ – $2$ , and to explain why the transition is sharp rather than gradual. The key is that H $_2$ removes its own dissociating photons: once a modest column of H $_2$ accumulates, its Lyman–Werner absorption lines saturate, the dissociation rate plummets, and the remaining molecules survive — a runaway that converts the gas over a thin shell. We balance formation against self-shielded dissociation, then convert the shielding column into extinction.

Step 1. Set the steady state from equation (4), $R\,n_\mathrm{H}\,n(\mathrm{H})=D_0\,f_\mathrm{sh}(N_{\mathrm{H_2}})\,e^{-\tau_d}\,n(\mathrm{H_2})$ , with the dissociating flux attenuated by two channels: dust $e^{-\tau_d}$ and line self-shielding $f_\mathrm{sh}$ . Why: self-shielding acts long before dust alone would suppress the field, so it is what forms the front at shallow depth.

Step 2. Insert the self-shielding law $f_\mathrm{sh}(N_{\mathrm{H_2}})\approx (N_{\mathrm{H_2}}/10^{14}\,\mathrm{cm^{-2}})^{-0.75}$ for $N_{\mathrm{H_2}}\gtrsim10^{14}\,\mathrm{cm^{-2}}$ . Why: this steep power law is the runaway — as the H $_2$ column climbs, destruction per molecule falls faster than linearly, tipping the balance decisively toward the molecular state.

Step 3. Balance is reached once $N_{\mathrm{H_2}}\sim\text{few}\times10^{20}\,\mathrm{cm^{-2}}$ (roughly half the hydrogen molecular), i.e. a total column $N_\mathrm{H}\sim(1$ – $4)\times10^{21}\,\mathrm{cm^{-2}}$ . Why: the transition is set by shielding column, not temperature or density, making it a near-universal feature of illuminated neutral gas.

Step 4. Convert with $A_V\approx N_\mathrm{H}/(1.9\times10^{21}\,\mathrm{cm^{-2}\,mag^{-1}})$ , giving $A_V\approx1$ – $2$ — deeper than the ionization front, shallower than the CO front. Why: expressing the front in $A_V$ makes it observable and locates it in the same dust-column currency that orders the whole stratification.

Go deeper · Derivation C · 1 minWhy a molecular but CO-dark layer must exist

Derivation CWhy a molecular but CO-dark layer must exist

The goal is to demonstrate that between the H/H $_2$ front and the C $^+$ /C/CO front there is necessarily a shell where the hydrogen is fully molecular but the carbon is still ionized, so that CO is absent — the origin of "CO-dark" molecular gas that biases CO-based mass estimates. The argument is about differential shielding: both photodissociate in the FUV, but H $_2$ protects itself far more effectively and wins the shielding race at shallower depth.

Step 1. H $_2$ self-shields at $A_V\approx1$ – $2$ (previous derivation) thanks to its enormous abundance and its dense forest of quickly-saturating Lyman–Werner lines. Why: abundance and line multiplicity make self-shielding efficient, and hydrogen has both in overwhelming measure, so it survives first.

Step 2. CO, by contrast, is scarcer by four orders of magnitude and shields poorly; it relies partly on H $_2$ and dust to block its dissociating lines and does not survive until $A_V\gtrsim2$ – $4$ . Why: with far fewer molecules per column, CO cannot build a saturating shielding column until much deeper, pushing its front inward relative to H $_2$ .

Step 3. The result is a shell over roughly $1\lesssim A_V\lesssim3$ where the gas is molecular (H $_2$ ) but carbon remains C $^+$ or C, with no CO — emitting in [C II] $158\,\mu\mathrm{m}$ but not CO, and holding $\sim30\%$ or more of the molecular mass in diffuse or low-metallicity gas. Why: since CO is the standard proxy for molecular mass, this dark layer means CO undercounts H $_2$ , and the correction — larger at low metallicity — must be folded into the CO X-factor.

Limiting cases

PDR behaviour sorts into a few clean regimes set by the field, the density, and the depth. The table names each corner and what it physically means.

Case	Result	Meaning
Diffuse ISM PDR	$G_0\sim1,\ n\sim10\text{--}100\,\mathrm{cm^{-3}}$	The general neutral ISM: weak field, low density, [C II] cooling dominates; this is the CNM/WNM balance.
Dense bright PDR	$G_0\sim10^4\text{--}10^6,\ n\gtrsim10^4\,\mathrm{cm^{-3}}$	A molecular-cloud face near an O star (Orion Bar): $T_\mathrm{surf}\sim500\text{--}1000\,\mathrm{K}$ , [O I] $63\,\mu\mathrm{m}$ and [C II] both strong.
High $G_0/n$ (charged grains)	$G_0/n\gtrsim10^{-2}\,\mathrm{cm^3}$	Photoelectric efficiency $\epsilon$ collapses as grains charge positively; heating saturates and the gas cannot exceed $\sim10^3\,\mathrm{K}$ .
Shielded interior	$A_V\gtrsim4$	FUV fully attenuated; heating passes to cosmic rays, $T\sim10\,\mathrm{K}$ , CO fully formed — the molecular cloud interior, no longer a PDR.

Common trapThe ionization front and the dissociation front are not the same surface

It is tempting to picture a single edge where the gas turns neutral and molecular at once. It has two distinct edges. The ionization front, set by the exhaustion of $h\nu>13.6\,\mathrm{eV}$ photons, is where hydrogen goes neutral; the H/H $_2$ dissociation front lies deeper, at $A_V\approx1$ – $2$ , set by the $\sim11$ – $13.6\,\mathrm{eV}$ Lyman–Werner photons that survive past it. The whole PDR is the neutral atomic layer between them and the CO front beyond. A second, related trap is to treat the photoelectric efficiency $\epsilon$ as constant: it is not. As the field charges grains and PAHs, each photoelectron climbs a larger positive potential, so $\epsilon$ falls from a few percent toward $<1\%$ in intense fields. That is exactly why the surface temperature is governed by $G_0/n$ and not $G_0$ alone, and why the hottest PDRs still cap near $\sim10^3\,\mathrm{K}$ .

Worked examples

1 · The surface temperature of a diffuse PDR (fully worked)

Take the local ISM: $G_0=1$ , $n_\mathrm{H}=100\,\mathrm{cm^{-3}}$ , photoelectric efficiency $\epsilon=0.04$ , and cool through [C II] $158\,\mu\mathrm{m}$ with $x_{\mathrm{C^+}}=1.4\times10^{-4}$ , $\gamma_{ul}=8\times10^{-10}\,\mathrm{cm^3\,s^{-1}}$ , $g_u/g_l=2$ , $\Delta E/k=91.2\,\mathrm{K}$ . Find the equilibrium temperature.

Step 1. Heating rate per volume from equation (2): $\Gamma_\mathrm{pe}n_\mathrm{H}=1.3\times10^{-24}\times0.04\times1\times100=\mathbf{5.2\times10^{-24}\ erg\,cm^{-3}\,s^{-1}}$ . This is the FUV power the grains hand to the gas.

Step 2. Cooling prefactor per volume, the temperature-independent part of $x_{\mathrm{C^+}}n_\mathrm{H}^2\gamma_{ul}(g_u/g_l)\Delta E$ : with $\Delta E=k\times91.2\,\mathrm{K}=1.26\times10^{-14}\,\mathrm{erg}$ , evaluate $1.4\times10^{-4}\times(100)^2\times8\times10^{-10}\times2\times1.26\times10^{-14}=\mathbf{2.8\times10^{-23}\ erg\,cm^{-3}\,s^{-1}}$ ; the cooling is this times $e^{-91.2/T}$ .

Step 3. Balance heating and cooling: $e^{-91.2/T}=5.2\times10^{-24}/2.8\times10^{-23}=0.186$ , so $T=91.2/1.68=\mathbf{54\ K}$ .

Step 4. Interpret. A few tens of kelvin is exactly the cold neutral medium (CNM), observed at $\sim40$ – $100\,\mathrm{K}$ . The estimate is schematic — the exact value depends on $\epsilon$ , the rate coefficient, and coolants like [O I] and Ly $\alpha$ — but the physics is right: a weak field on moderately dense gas settles to CNM temperatures, while $G_0=10^4$ , $n=10^4$ drives $T$ toward $\sim500$ – $1000\,\mathrm{K}$ where [O I] $63\,\mu\mathrm{m}$ dominates. Result: $T\approx55\,\mathrm{K}$ , set by $G_0/n_\mathrm{H}$ , recovering the CNM.

2 · Depth of the dissociation front, and the [C II] bolometer

Part A: at the H/H $_2$ front the total hydrogen column is $N_\mathrm{H}\approx2\times10^{21}\,\mathrm{cm^{-2}}$ ; convert to $A_V$ . Part B: a galaxy has $L_\mathrm{FIR}=10^{11}\,L_\odot$ ; estimate its [C II] luminosity.

Step 1. With $N_\mathrm{H}/A_V=1.9\times10^{21}\,\mathrm{cm^{-2}\,mag^{-1}}$ , $A_V=2\times10^{21}/1.9\times10^{21}=\mathbf{1.05\ mag}$ . The molecular front sits near $A_V\approx1$ , deeper than the ionization front and shallower than the CO front at $A_V\approx2$ – $4$ — the standard stratification.

Step 2. For the bolometer, apply equation (6) with a mid-range $L_{[\mathrm{C\,II}]}/L_\mathrm{FIR}\approx3\times10^{-3}$ : $L_{[\mathrm{C\,II}]}\approx3\times10^{-3}\times10^{11}=\mathbf{3\times10^{8}\ L_\odot}$ . A single far-infrared line carrying $10^{8}$ – $10^{9}\,L_\odot$ is why [C II] is detectable in normal galaxies to high redshift with ALMA.

Step 3. Sanity check: the $A_V\approx1$ front matches the atomic surface layer resolved in PDRs like the Orion Bar, and the $\sim0.3\%$ [C II] fraction is typical of star-forming galaxies (dipping to $\sim10^{-3}$ in the most luminous systems — the [C II] deficit). Results: dissociation front at $A_V\approx1$ ; $L_{[\mathrm{C\,II}]}\approx3\times10^{8}\,L_\odot$ .

Physics of the portrait

The modern PDR is a theorist's construction: a stack of coupled chemical and thermal balances, solved self-consistently as a function of depth, that turns two input numbers into a full prediction of line ratios. No single person owns it, but one theorist did more than anyone to assemble it into the quantitative tool astronomers now reach for by reflex.

Origins · 1 minDavid Hollenbach and how this was discovered

David Hollenbach

foundational theorist of photodissociation regions · interstellar medium and star-formation astrophysics

David Hollenbach built much of the physics that turns a lit cloud edge into a calculable object. Trained at Cornell under Edwin Salpeter, his 1971 paper with Werner and Salpeter worked out how molecular hydrogen forms on grains and is destroyed by ultraviolet light in neutral regions — the seed of all that followed. The field crystallized in 1985, when Hollenbach and Alexander Tielens published a comprehensive model of dense neutral gas under intense far-ultraviolet radiation, coupling photoelectric heating, fine-structure and molecular cooling, and a depth-dependent chemistry into one self-consistent slab applied to the Orion Bar — the work that named and defined the photodissociation region. Their 1997 Annual Review article, "Photodissociation Regions in the Interstellar Medium of Galaxies," became the field's standard reference, extending the framework to the neutral ISM of whole galaxies and establishing [C II] $158\,\mu\mathrm{m}$ as its signature diagnostic. With Mark Wolfire and Christopher McKee he pushed the same physics into the thermal balance of the diffuse ISM and, in 2010, quantified the CO-dark molecular gas hiding in the C $^+$ /C layer. The through-line of his career is one conviction: that the observable structure of neutral gas — its temperature, chemistry, and brightest lines — is written in the competition between far-ultraviolet heating and radiative cooling.

History

1968

— Habing fixes the mean interstellar FUV flux at 1.6×10⁻³ erg cm⁻² s⁻¹

1971

— Hollenbach, Werner and Salpeter model H₂ formation and photodissociation on grains

1985

— Tielens and Hollenbach publish the foundational photodissociation-region model

1997

— Hollenbach and Tielens review PDRs in Annual Review of Astronomy and Astrophysics

2022

— JWST resolves the layered PDR structure of the Orion Bar

Going further

Texts. Tielens, The Physics and Chemistry of the Interstellar Medium (2005), ch. 9 · Draine, Physics of the Interstellar and Intergalactic Medium (2011), ch. 30–31 · Carroll & Ostlie, An Introduction to Modern Astrophysics, 2nd ed., ch. 12. Foundational papers. Tielens & Hollenbach 1985, ApJ 291, 722 · Hollenbach & Tielens 1997, ARA&A 35, 179 · Wolfire, Hollenbach & McKee 2010, ApJ 716, 1191 (CO-dark gas) · Draine & Bertoldi 1996, ApJ 468, 269 (self-shielding). The key numerical values used throughout are: Habing flux $1.6\times10^{-3}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$ ; [C II] line at $\lambda=157.7\,\mu\mathrm{m}$ with $\Delta E/k=91.2\,\mathrm{K}$ ; [O I] line at $\lambda=63.2\,\mu\mathrm{m}$ with $\Delta E/k=228\,\mathrm{K}$ ; carbon ionization potential $11.26\,\mathrm{eV}$ ; and the dust-to-gas ratio $N_\mathrm{H}/A_V\approx1.9\times10^{21}\,\mathrm{cm^{-2}\,mag^{-1}}$ (Bohlin et al. 1978). The photoelectric heating normalization is from Bakes & Tielens 1994; the H $_2$ formation rate and self-shielding scaling from Draine & Bertoldi 1996; the $G_0/n$ scaling and $A_V$ front depths from Tielens & Hollenbach 1985 and Hollenbach & Tielens 1997.

Prerequisites. Phases of the Interstellar Medium · Interstellar Gas Heating and Cooling Processes · Interstellar Dust Grains · Interstellar Extinction and Reddening. Leads to. Molecular Clouds and Giant Molecular Clouds · CO as a Molecular Gas Tracer and the X-Factor · Thermal Instability and the Two-Phase Medium · The 21 cm Line of Neutral Hydrogen.

:::faq[Why does the gas cool through forbidden lines like [C II]?] The brackets flag a forbidden transition — a magnetic-dipole or electric-quadrupole decay far slower than an allowed line. In a laboratory that slowness would not matter, because collisions would de-excite the atom before it radiated. But interstellar gas is so rarefied that an excited C $^+$ ion, once collisionally bumped to its fine-structure level, usually emits its $158\,\mu\mathrm{m}$ photon first, carrying energy out. Because C $^+$ is abundant and its upper level lies only $91.2\,\mathrm{K}$ above ground, these forbidden emissions — invisible in dense terrestrial gas — are the dominant coolant of the PDR.

Ask the tutor: Ask me to walk you through why the surface temperature depends on $G_0/n$ and not $G_0$ alone, or to trace a photon from the star through each chemical front to the CO-dark shell.

What is the difference between a PDR and an H II region?

They are neighbouring layers around the same star but governed by different photons. An H II region is fully ionized gas maintained by photons above $13.6\,\mathrm{eV}$ ; it ends at the ionization front where those photons run out. A PDR is the neutral gas just beyond, ruled by the softer FUV photons ( $6$ – $13.6\,\mathrm{eV}$ ) that could not ionize hydrogen and passed straight through. In the H II region hydrogen is H $^+$ at $\sim10^4\,\mathrm{K}$ ; in the PDR it is neutral, carbon is C $^+$ , and the temperature falls from hundreds of kelvin to $\sim10\,\mathrm{K}$ inside — where the star's non-ionizing luminosity is finally absorbed.

Why is the field measured in Habing units G₀ instead of physical flux?

Because PDR processes respond to the total far-ultraviolet energy in the $6$ – $13.6\,\mathrm{eV}$ band, not the spectral detail — the cross sections for photodissociation and photoelectric emission are broad, so integrating over the band captures the relevant physics in one number. Normalizing to the solar-neighbourhood mean, $1.6\times10^{-3}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$ , gives the dimensionless $G_0$ , which makes results portable: a $G_0=10^4$ PDR behaves like any other of the same density. The related Draine field uses a slightly different reference, $\chi\approx1.7\,G_0$ .

How does photoelectric heating actually work?

A far-ultraviolet photon strikes a dust grain or a large PAH and ejects an electron, much like the photoelectric effect on a metal surface. That photoelectron carries kinetic energy equal to the photon energy minus the work function minus whatever electrostatic barrier the grain's charge presents; when it collides with the gas, that surplus thermalizes as heat. It is efficient at low field strength — a few percent of the absorbed FUV energy becomes heat — but falls as the field charges the grains positively, since each new photoelectron must climb a larger potential hill. Dust, not the gas atoms, is the intermediary that couples starlight to the temperature of neutral gas.

What exactly is the CO-dark molecular gas, and why does it matter?

It is molecular hydrogen with no accompanying CO. Because H $_2$ self-shields at $A_V\approx1$ – $2$ while CO does not survive until $A_V\approx2$ – $4$ , a shell exists where the hydrogen is fully molecular but the carbon is still C $^+$ or neutral C, so no CO forms. Astronomers usually trace molecular gas with CO — H $_2$ itself is nearly invisible in cold interiors — so this shell is real molecular mass that CO surveys miss, showing up as [C II] $158\,\mu\mathrm{m}$ with no matching CO line. In diffuse or low-metallicity gas it can hold $30\%$ or more of the molecular mass, so correcting for it is essential when using CO to weigh galaxies and calibrate the CO-to-H $_2$ factor.

Is the whole interstellar medium technically a PDR?

In a real sense, yes — any neutral gas exposed to starlight has its surface chemistry and temperature set by the ambient far-ultraviolet field, which is the definition of a PDR. The diffuse ISM at $G_0\sim1$ and low density is, in effect, a very low-intensity PDR, and the cold and warm neutral media emerge from exactly the heating–cooling balance described here. What people usually mean by "a PDR," though, is the bright, dense, sharply stratified case near a hot star like the Orion Bar. The point is that the same $(G_0,\ n)$ physics describes both the faint pervasive medium and the spectacular nebular edge — they differ only in where they sit on the $G_0/n$ axis.