H II region
Definition: A volume of hydrogen kept ionized by Lyman-continuum photons from hot stars, with its size set by competition between photoionizations and recombinations.
Why it matters here: 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).
Relationship: 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).
Limitation or 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.
photoionization
Definition: Removal of a bound electron by absorption of a photon whose energy exceeds the ionization threshold.
Why it matters here: 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.
Relationship: 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.
Limitation or 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.
Lyman continuum photon
Definition: A photon with wavelength shorter than 91.2 nm and enough energy to ionize ground-state hydrogen.
Why it matters here: 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).
Relationship: 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.
Limitation or 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.
recombination
Definition: Capture of a free electron by an ion, followed by radiative cascades that can produce diagnostic emission lines.
Why it matters here: 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).
Relationship: 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).
Limitation or 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.
case B recombination coefficient
Definition: An effective recombination rate coefficient that excludes direct captures to the ground state because their ionizing photons are assumed to be reabsorbed locally.
Why it matters here: 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.
Relationship: 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.
Limitation or 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.
Stromgren sphere
Definition: The idealized ionized volume whose integrated recombination rate balances the source’s ionizing-photon production rate.
Why it matters here: 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).
Relationship: 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.
Limitation or 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.
ionization-bounded region
Definition: An H II region containing enough gas to absorb nearly all incident ionizing photons before they escape.
Why it matters here: 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).
Relationship: 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).
Limitation or 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.