Terms Developed in Context
H II region
A volume of hydrogen kept ionized by Lyman-continuum photons from hot stars, with its size set by competition between photoionizations and recombinations. In this lecture, the term is not an isolated label: This concept is needed to reason about h ii regions i: photoionization equilibrium and the stromgren sphere. In photoionization equilibrium, the rate of ionizing photons absorbed within a volume must equal the rate of recombinations occurring within that same volume (each recombination "uses up" one free electron-proton pair that must be replenished by a fresh ionization to maintain a steady ionized state): Q_H = alpha_B n_e n_p V, where V is the ionized volume, n_e~n_p is the electron/proton density (assuming pure hydrogen for simplicity), and alpha_B is the case B recombination coefficient (a well-determined atomic-physics quantity, ~2.6e-13 cm^3/s at the typical Te~10^4 K of ionized nebular gas).
It is tied to the lecture’s observables or evidence in this way: A hot O or early B star emits a large flux of photons energetic enough (>13.6 eV, shortward of the Lyman limit at 91.2 nm) to photoionize neutral hydrogen; the total number of such ionizing photons emitted per second, Q_H, is a strong function of the star’s spectral type and effective temperature (calibrated by Vacca, Garmany & Shull 1996; Martins, Schaerer & Hillier 2005). A second connection is important for using the term in physical reasoning: Solving this balance for a sphere of radius R_s (volume (4/3)pi R_s^3) gives the Stromgren radius, R_s = (3 Q_H/(4 pi alpha_B n_e^2))^{1/3}: a larger ionizing luminosity Q_H produces a larger ionized region, while a denser surrounding medium (larger n_e, hence a higher recombination rate) shrinks it, both entering as cube-root dependences. The observational interpretation is constrained by Free electrons and protons in the resulting ionized gas continuously recombine (predominantly directly to excited states rather than the ground state, since ground-state recombination photons are themselves re-absorbed almost immediately -- the "on-the-spot" or case B approximation), at a rate proportional to the product of electron and proton densities and a temperature-dependent recombination coefficient, alpha_B.
Boundary and common confusion. Assuming the Stromgren radius exactly matches an H II region’s observed size. The idealized model assumes a single point-source star, spatially uniform density, and a perfectly sharp ionization front in an infinite uniform medium; real H II regions are density-bounded (limited by where the surrounding gas simply runs out, not by where ionizing photons are exhausted), non-spherical, and often ionized by multiple stars -- the model is a genuinely useful order-of-magnitude tool, not an exact prediction, and this course states that limitation explicitly. 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.
photoionization
Removal of a bound electron by absorption of a photon whose energy exceeds the ionization threshold. In this lecture, the term is not an isolated label: This concept is needed to reason about h ii regions i: photoionization equilibrium and the stromgren sphere. Solving this balance for a sphere of radius R_s (volume (4/3)pi R_s^3) gives the Stromgren radius, R_s = (3 Q_H/(4 pi alpha_B n_e^2))^{1/3}: a larger ionizing luminosity Q_H produces a larger ionized region, while a denser surrounding medium (larger n_e, hence a higher recombination rate) shrinks it, both entering as cube-root dependences.
It is tied to the lecture’s observables or evidence in this way: Free electrons and protons in the resulting ionized gas continuously recombine (predominantly directly to excited states rather than the ground state, since ground-state recombination photons are themselves re-absorbed almost immediately -- the "on-the-spot" or case B approximation), at a rate proportional to the product of electron and proton densities and a temperature-dependent recombination coefficient, alpha_B. A second connection is important for using the term in physical reasoning: Because the recombination rate scales as n_e^2 (a strong, local dependence), the ionization front separating ionized from neutral gas is predicted to be extremely thin compared to R_s itself -- the "sharp edge" that gives the Stromgren sphere its idealized name, an approximation borne out reasonably well by many observed H II regions’ sharp optical boundaries, though real regions have finite-thickness ionization fronts and often depart from perfect spherical symmetry (Lecture 12 continues with the real, non-idealized diagnostics). The observational interpretation is constrained by Bengt Stromgren (1939, ApJ 89, 526) first showed that balancing the star’s ionizing-photon output against the total recombination rate within a spherical volume predicts an extremely sharp transition from fully ionized to fully neutral gas at a well-defined radius -- confirmed observationally by the sharp optical edges seen in many real H II regions, including much of the Orion Nebula’s visible boundary.
Boundary and common confusion. Assuming the Stromgren radius exactly matches an H II region’s observed size. The idealized model assumes a single point-source star, spatially uniform density, and a perfectly sharp ionization front in an infinite uniform medium; real H II regions are density-bounded (limited by where the surrounding gas simply runs out, not by where ionizing photons are exhausted), non-spherical, and often ionized by multiple stars -- the model is a genuinely useful order-of-magnitude tool, not an exact prediction, and this course states that limitation explicitly. 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.
Lyman continuum photon
A photon with wavelength shorter than 91.2 nm and enough energy to ionize ground-state hydrogen. In this lecture, the term is not an isolated label: This concept is needed to reason about h ii regions i: photoionization equilibrium and the stromgren sphere. Because the recombination rate scales as n_e^2 (a strong, local dependence), the ionization front separating ionized from neutral gas is predicted to be extremely thin compared to R_s itself -- the "sharp edge" that gives the Stromgren sphere its idealized name, an approximation borne out reasonably well by many observed H II regions’ sharp optical boundaries, though real regions have finite-thickness ionization fronts and often depart from perfect spherical symmetry (Lecture 12 continues with the real, non-idealized diagnostics).
It is tied to the lecture’s observables or evidence in this way: Bengt Stromgren (1939, ApJ 89, 526) first showed that balancing the star’s ionizing-photon output against the total recombination rate within a spherical volume predicts an extremely sharp transition from fully ionized to fully neutral gas at a well-defined radius -- confirmed observationally by the sharp optical edges seen in many real H II regions, including much of the Orion Nebula’s visible boundary. A second connection is important for using the term in physical reasoning: In photoionization equilibrium, the rate of ionizing photons absorbed within a volume must equal the rate of recombinations occurring within that same volume (each recombination "uses up" one free electron-proton pair that must be replenished by a fresh ionization to maintain a steady ionized state): Q_H = alpha_B n_e n_p V, where V is the ionized volume, n_e~n_p is the electron/proton density (assuming pure hydrogen for simplicity), and alpha_B is the case B recombination coefficient (a well-determined atomic-physics quantity, ~2.6e-13 cm^3/s at the typical Te~10^4 K of ionized nebular gas). The observational interpretation is constrained by A hot O or early B star emits a large flux of photons energetic enough (>13.6 eV, shortward of the Lyman limit at 91.2 nm) to photoionize neutral hydrogen; the total number of such ionizing photons emitted per second, Q_H, is a strong function of the star’s spectral type and effective temperature (calibrated by Vacca, Garmany & Shull 1996; Martins, Schaerer & Hillier 2005).
Boundary and common confusion. Assuming the Stromgren radius exactly matches an H II region’s observed size. The idealized model assumes a single point-source star, spatially uniform density, and a perfectly sharp ionization front in an infinite uniform medium; real H II regions are density-bounded (limited by where the surrounding gas simply runs out, not by where ionizing photons are exhausted), non-spherical, and often ionized by multiple stars -- the model is a genuinely useful order-of-magnitude tool, not an exact prediction, and this course states that limitation explicitly. 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.
recombination
Capture of a free electron by an ion, followed by radiative cascades that can produce diagnostic emission lines. In this lecture, the term is not an isolated label: This concept is needed to reason about h ii regions i: photoionization equilibrium and the stromgren sphere. In photoionization equilibrium, the rate of ionizing photons absorbed within a volume must equal the rate of recombinations occurring within that same volume (each recombination "uses up" one free electron-proton pair that must be replenished by a fresh ionization to maintain a steady ionized state): Q_H = alpha_B n_e n_p V, where V is the ionized volume, n_e~n_p is the electron/proton density (assuming pure hydrogen for simplicity), and alpha_B is the case B recombination coefficient (a well-determined atomic-physics quantity, ~2.6e-13 cm^3/s at the typical Te~10^4 K of ionized nebular gas).
It is tied to the lecture’s observables or evidence in this way: A hot O or early B star emits a large flux of photons energetic enough (>13.6 eV, shortward of the Lyman limit at 91.2 nm) to photoionize neutral hydrogen; the total number of such ionizing photons emitted per second, Q_H, is a strong function of the star’s spectral type and effective temperature (calibrated by Vacca, Garmany & Shull 1996; Martins, Schaerer & Hillier 2005). A second connection is important for using the term in physical reasoning: Solving this balance for a sphere of radius R_s (volume (4/3)pi R_s^3) gives the Stromgren radius, R_s = (3 Q_H/(4 pi alpha_B n_e^2))^{1/3}: a larger ionizing luminosity Q_H produces a larger ionized region, while a denser surrounding medium (larger n_e, hence a higher recombination rate) shrinks it, both entering as cube-root dependences. The observational interpretation is constrained by Free electrons and protons in the resulting ionized gas continuously recombine (predominantly directly to excited states rather than the ground state, since ground-state recombination photons are themselves re-absorbed almost immediately -- the "on-the-spot" or case B approximation), at a rate proportional to the product of electron and proton densities and a temperature-dependent recombination coefficient, alpha_B.
Boundary and common confusion. Assuming the Stromgren radius exactly matches an H II region’s observed size. The idealized model assumes a single point-source star, spatially uniform density, and a perfectly sharp ionization front in an infinite uniform medium; real H II regions are density-bounded (limited by where the surrounding gas simply runs out, not by where ionizing photons are exhausted), non-spherical, and often ionized by multiple stars -- the model is a genuinely useful order-of-magnitude tool, not an exact prediction, and this course states that limitation explicitly. 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.
case B recombination coefficient
An effective recombination rate coefficient that excludes direct captures to the ground state because their ionizing photons are assumed to be reabsorbed locally. In this lecture, the term is not an isolated label: This concept is needed to reason about h ii regions i: photoionization equilibrium and the stromgren sphere. Solving this balance for a sphere of radius R_s (volume (4/3)pi R_s^3) gives the Stromgren radius, R_s = (3 Q_H/(4 pi alpha_B n_e^2))^{1/3}: a larger ionizing luminosity Q_H produces a larger ionized region, while a denser surrounding medium (larger n_e, hence a higher recombination rate) shrinks it, both entering as cube-root dependences.
It is tied to the lecture’s observables or evidence in this way: Free electrons and protons in the resulting ionized gas continuously recombine (predominantly directly to excited states rather than the ground state, since ground-state recombination photons are themselves re-absorbed almost immediately -- the "on-the-spot" or case B approximation), at a rate proportional to the product of electron and proton densities and a temperature-dependent recombination coefficient, alpha_B. A second connection is important for using the term in physical reasoning: Because the recombination rate scales as n_e^2 (a strong, local dependence), the ionization front separating ionized from neutral gas is predicted to be extremely thin compared to R_s itself -- the "sharp edge" that gives the Stromgren sphere its idealized name, an approximation borne out reasonably well by many observed H II regions’ sharp optical boundaries, though real regions have finite-thickness ionization fronts and often depart from perfect spherical symmetry (Lecture 12 continues with the real, non-idealized diagnostics). The observational interpretation is constrained by Bengt Stromgren (1939, ApJ 89, 526) first showed that balancing the star’s ionizing-photon output against the total recombination rate within a spherical volume predicts an extremely sharp transition from fully ionized to fully neutral gas at a well-defined radius -- confirmed observationally by the sharp optical edges seen in many real H II regions, including much of the Orion Nebula’s visible boundary.
Boundary and common confusion. Assuming the Stromgren radius exactly matches an H II region’s observed size. The idealized model assumes a single point-source star, spatially uniform density, and a perfectly sharp ionization front in an infinite uniform medium; real H II regions are density-bounded (limited by where the surrounding gas simply runs out, not by where ionizing photons are exhausted), non-spherical, and often ionized by multiple stars -- the model is a genuinely useful order-of-magnitude tool, not an exact prediction, and this course states that limitation explicitly. 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.
Stromgren sphere
The idealized ionized volume whose integrated recombination rate balances the source’s ionizing-photon production rate. In this lecture, the term is not an isolated label: This concept is needed to reason about h ii regions i: photoionization equilibrium and the stromgren sphere. Because the recombination rate scales as n_e^2 (a strong, local dependence), the ionization front separating ionized from neutral gas is predicted to be extremely thin compared to R_s itself -- the "sharp edge" that gives the Stromgren sphere its idealized name, an approximation borne out reasonably well by many observed H II regions’ sharp optical boundaries, though real regions have finite-thickness ionization fronts and often depart from perfect spherical symmetry (Lecture 12 continues with the real, non-idealized diagnostics).
It is tied to the lecture’s observables or evidence in this way: Bengt Stromgren (1939, ApJ 89, 526) first showed that balancing the star’s ionizing-photon output against the total recombination rate within a spherical volume predicts an extremely sharp transition from fully ionized to fully neutral gas at a well-defined radius -- confirmed observationally by the sharp optical edges seen in many real H II regions, including much of the Orion Nebula’s visible boundary. A second connection is important for using the term in physical reasoning: In photoionization equilibrium, the rate of ionizing photons absorbed within a volume must equal the rate of recombinations occurring within that same volume (each recombination "uses up" one free electron-proton pair that must be replenished by a fresh ionization to maintain a steady ionized state): Q_H = alpha_B n_e n_p V, where V is the ionized volume, n_e~n_p is the electron/proton density (assuming pure hydrogen for simplicity), and alpha_B is the case B recombination coefficient (a well-determined atomic-physics quantity, ~2.6e-13 cm^3/s at the typical Te~10^4 K of ionized nebular gas). The observational interpretation is constrained by A hot O or early B star emits a large flux of photons energetic enough (>13.6 eV, shortward of the Lyman limit at 91.2 nm) to photoionize neutral hydrogen; the total number of such ionizing photons emitted per second, Q_H, is a strong function of the star’s spectral type and effective temperature (calibrated by Vacca, Garmany & Shull 1996; Martins, Schaerer & Hillier 2005).
Boundary and common confusion. Assuming the Stromgren radius exactly matches an H II region’s observed size. The idealized model assumes a single point-source star, spatially uniform density, and a perfectly sharp ionization front in an infinite uniform medium; real H II regions are density-bounded (limited by where the surrounding gas simply runs out, not by where ionizing photons are exhausted), non-spherical, and often ionized by multiple stars -- the model is a genuinely useful order-of-magnitude tool, not an exact prediction, and this course states that limitation explicitly. 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.
ionization-bounded region
An H II region containing enough gas to absorb nearly all incident ionizing photons before they escape. In this lecture, the term is not an isolated label: This concept is needed to reason about h ii regions i: photoionization equilibrium and the stromgren sphere. In photoionization equilibrium, the rate of ionizing photons absorbed within a volume must equal the rate of recombinations occurring within that same volume (each recombination "uses up" one free electron-proton pair that must be replenished by a fresh ionization to maintain a steady ionized state): Q_H = alpha_B n_e n_p V, where V is the ionized volume, n_e~n_p is the electron/proton density (assuming pure hydrogen for simplicity), and alpha_B is the case B recombination coefficient (a well-determined atomic-physics quantity, ~2.6e-13 cm^3/s at the typical Te~10^4 K of ionized nebular gas).
It is tied to the lecture’s observables or evidence in this way: A hot O or early B star emits a large flux of photons energetic enough (>13.6 eV, shortward of the Lyman limit at 91.2 nm) to photoionize neutral hydrogen; the total number of such ionizing photons emitted per second, Q_H, is a strong function of the star’s spectral type and effective temperature (calibrated by Vacca, Garmany & Shull 1996; Martins, Schaerer & Hillier 2005). A second connection is important for using the term in physical reasoning: Solving this balance for a sphere of radius R_s (volume (4/3)pi R_s^3) gives the Stromgren radius, R_s = (3 Q_H/(4 pi alpha_B n_e^2))^{1/3}: a larger ionizing luminosity Q_H produces a larger ionized region, while a denser surrounding medium (larger n_e, hence a higher recombination rate) shrinks it, both entering as cube-root dependences. The observational interpretation is constrained by Free electrons and protons in the resulting ionized gas continuously recombine (predominantly directly to excited states rather than the ground state, since ground-state recombination photons are themselves re-absorbed almost immediately -- the "on-the-spot" or case B approximation), at a rate proportional to the product of electron and proton densities and a temperature-dependent recombination coefficient, alpha_B.
Boundary and common confusion. Assuming the Stromgren radius exactly matches an H II region’s observed size. The idealized model assumes a single point-source star, spatially uniform density, and a perfectly sharp ionization front in an infinite uniform medium; real H II regions are density-bounded (limited by where the surrounding gas simply runs out, not by where ionizing photons are exhausted), non-spherical, and often ionized by multiple stars -- the model is a genuinely useful order-of-magnitude tool, not an exact prediction, and this course states that limitation explicitly. 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.