photoelectric heating
Definition: Gas heating caused when ultraviolet photons eject energetic electrons from dust grains or large molecules and those electrons transfer energy to the gas.
Why it matters here: This concept is needed to reason about heating, cooling, and thermal instability. At thermal equilibrium, the total heating rate per unit volume Gamma(n) equals the total cooling rate Lambda(n,T)n^2 (cooling from two-body collisional processes scales as n^2); solving Gamma=Lambda n^2 for the equilibrium T at each assumed pressure traces out a curve in P-T (or, equivalently, T-n) space.
Relationship: It is tied to the lecture’s observables or evidence in this way: Ultraviolet starlight photons ejecting photoelectrons from interstellar dust grains is the dominant heating mechanism in the diffuse neutral ISM (Bakes & Tielens 1994; Wolfire et al. 1995, 2003), with a heating rate per particle that depends only weakly on gas temperature.
Limitation or common confusion: Treating "thermal equilibrium" as synonymous with "thermally stable." A gas parcel can satisfy Gamma=Lambda n^2 exactly (be in instantaneous thermal equilibrium) while still being thermally unstable in the Field (1965) sense if it sits on the wrong branch of the curve; equilibrium is a necessary but not sufficient condition for a long-lived, physically realized phase.
radiative cooling
Definition: Loss of gas thermal energy through photons emitted after collisional excitation, recombination, or other microscopic processes.
Why it matters here: This concept is needed to reason about heating, cooling, and thermal instability. Because the fine-structure/Lyman-alpha cooling rate rises very steeply with T while photoelectric heating is comparatively flat, this equilibrium curve is S-shaped: two stable branches (a cold, dense one and a warm, tenuous one) at nearly the same pressure, joined by a middle branch on which pressure decreases as temperature increases at fixed density -- the Field (1965) instability condition.
Relationship: It is tied to the lecture’s observables or evidence in this way: The dominant coolants are collisionally excited fine-structure lines -- principally singly ionized carbon’s [C II] 158 micron line in the CNM/WNM, and Lyman-alpha (121.6 nm) in warmer, more ionized gas -- whose emissivities depend strongly (often close to exponentially, via the Boltzmann excitation factor) on temperature.
Limitation or common confusion: Treating "thermal equilibrium" as synonymous with "thermally stable." A gas parcel can satisfy Gamma=Lambda n^2 exactly (be in instantaneous thermal equilibrium) while still being thermally unstable in the Field (1965) sense if it sits on the wrong branch of the curve; equilibrium is a necessary but not sufficient condition for a long-lived, physically realized phase.
fine-structure line
Definition: A spectral line between closely spaced sublevels produced by spin-orbit coupling, often an efficient coolant because modest-temperature collisions can excite it.
Why it matters here: This concept is needed to reason about heating, cooling, and thermal instability. A gas parcel perturbed onto the unstable middle branch cannot return to it: any small increase in T there causes cooling to fall faster than heating, so the parcel runs away to still higher T (toward the WNM branch) rather than restoring itself; the reverse runs away to lower T (toward the CNM branch). This is exactly the physical mechanism that sorts the diffuse ISM into two discrete, stable phases rather than a continuum.
Relationship: It is tied to the lecture’s observables or evidence in this way: Field (1965, ApJ 142, 531) showed analytically that an isobaric (constant-pressure) gas parcel is thermally unstable wherever the net cooling rate decreases with increasing temperature at fixed pressure -- exactly the condition realized on the steep, negative-slope middle branch of the heating/cooling curve between the CNM and WNM equilibrium points.
Limitation or common confusion: Treating "thermal equilibrium" as synonymous with "thermally stable." A gas parcel can satisfy Gamma=Lambda n^2 exactly (be in instantaneous thermal equilibrium) while still being thermally unstable in the Field (1965) sense if it sits on the wrong branch of the curve; equilibrium is a necessary but not sufficient condition for a long-lived, physically realized phase.
thermal equilibrium curve
Definition: The locus of density, temperature, and pressure states for which volumetric heating equals volumetric cooling.
Why it matters here: This concept is needed to reason about heating, cooling, and thermal instability. At thermal equilibrium, the total heating rate per unit volume Gamma(n) equals the total cooling rate Lambda(n,T)n^2 (cooling from two-body collisional processes scales as n^2); solving Gamma=Lambda n^2 for the equilibrium T at each assumed pressure traces out a curve in P-T (or, equivalently, T-n) space.
Relationship: It is tied to the lecture’s observables or evidence in this way: Ultraviolet starlight photons ejecting photoelectrons from interstellar dust grains is the dominant heating mechanism in the diffuse neutral ISM (Bakes & Tielens 1994; Wolfire et al. 1995, 2003), with a heating rate per particle that depends only weakly on gas temperature.
Limitation or common confusion: Treating "thermal equilibrium" as synonymous with "thermally stable." A gas parcel can satisfy Gamma=Lambda n^2 exactly (be in instantaneous thermal equilibrium) while still being thermally unstable in the Field (1965) sense if it sits on the wrong branch of the curve; equilibrium is a necessary but not sufficient condition for a long-lived, physically realized phase.
thermal instability
Definition: Runaway departure from an equilibrium state when a small thermal perturbation changes heating and cooling in a way that amplifies rather than erases the perturbation.
Why it matters here: This concept is needed to reason about heating, cooling, and thermal instability. Because the fine-structure/Lyman-alpha cooling rate rises very steeply with T while photoelectric heating is comparatively flat, this equilibrium curve is S-shaped: two stable branches (a cold, dense one and a warm, tenuous one) at nearly the same pressure, joined by a middle branch on which pressure decreases as temperature increases at fixed density -- the Field (1965) instability condition.
Relationship: It is tied to the lecture’s observables or evidence in this way: The dominant coolants are collisionally excited fine-structure lines -- principally singly ionized carbon’s [C II] 158 micron line in the CNM/WNM, and Lyman-alpha (121.6 nm) in warmer, more ionized gas -- whose emissivities depend strongly (often close to exponentially, via the Boltzmann excitation factor) on temperature.
Limitation or common confusion: Treating "thermal equilibrium" as synonymous with "thermally stable." A gas parcel can satisfy Gamma=Lambda n^2 exactly (be in instantaneous thermal equilibrium) while still being thermally unstable in the Field (1965) sense if it sits on the wrong branch of the curve; equilibrium is a necessary but not sufficient condition for a long-lived, physically realized phase.
isobaric perturbation
Definition: A small change followed at approximately constant pressure, so density and temperature vary inversely while thermal stability is tested.
Why it matters here: This concept is needed to reason about heating, cooling, and thermal instability. A gas parcel perturbed onto the unstable middle branch cannot return to it: any small increase in T there causes cooling to fall faster than heating, so the parcel runs away to still higher T (toward the WNM branch) rather than restoring itself; the reverse runs away to lower T (toward the CNM branch). This is exactly the physical mechanism that sorts the diffuse ISM into two discrete, stable phases rather than a continuum.
Relationship: It is tied to the lecture’s observables or evidence in this way: Field (1965, ApJ 142, 531) showed analytically that an isobaric (constant-pressure) gas parcel is thermally unstable wherever the net cooling rate decreases with increasing temperature at fixed pressure -- exactly the condition realized on the steep, negative-slope middle branch of the heating/cooling curve between the CNM and WNM equilibrium points.
Limitation or common confusion: Treating "thermal equilibrium" as synonymous with "thermally stable." A gas parcel can satisfy Gamma=Lambda n^2 exactly (be in instantaneous thermal equilibrium) while still being thermally unstable in the Field (1965) sense if it sits on the wrong branch of the curve; equilibrium is a necessary but not sufficient condition for a long-lived, physically realized phase.