Terms Developed in Context
photoelectric heating
Gas heating caused when ultraviolet photons eject energetic electrons from dust grains or large molecules and those electrons transfer energy to the gas. In this lecture, the term is not an isolated label: 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.
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. A second connection is important for using the term in physical reasoning: 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. The observational interpretation is constrained by 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.
Boundary and 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. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.
radiative cooling
Loss of gas thermal energy through photons emitted after collisional excitation, recombination, or other microscopic processes. In this lecture, the term is not an isolated label: 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.
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. A second connection is important for using the term in physical reasoning: 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. The observational interpretation is constrained by 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.
Boundary and 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. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.
fine-structure line
A spectral line between closely spaced sublevels produced by spin-orbit coupling, often an efficient coolant because modest-temperature collisions can excite it. In this lecture, the term is not an isolated label: 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.
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. A second connection is important for using the term in physical reasoning: 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. The observational interpretation is constrained by 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.
Boundary and 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. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.
thermal equilibrium curve
The locus of density, temperature, and pressure states for which volumetric heating equals volumetric cooling. In this lecture, the term is not an isolated label: 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.
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. A second connection is important for using the term in physical reasoning: 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. The observational interpretation is constrained by 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.
Boundary and 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. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.
thermal instability
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. In this lecture, the term is not an isolated label: 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.
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. A second connection is important for using the term in physical reasoning: 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. The observational interpretation is constrained by 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.
Boundary and 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. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.
isobaric perturbation
A small change followed at approximately constant pressure, so density and temperature vary inversely while thermal stability is tested. In this lecture, the term is not an isolated label: 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.
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. A second connection is important for using the term in physical reasoning: 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. The observational interpretation is constrained by 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.
Boundary and 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. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.