A Strömgren Sphere refers to the spherical region of ionized hydrogen (H II region) surrounding a hot, massive star emitting high-energy ultraviolet (UV) radiation. Named after the Danish astronomer Bengt Strömgren, who first calculated the equilibrium conditions of such regions in 1939, this concept is crucial in the study of ionized interstellar media (ISM), star formation, and galactic dynamics.
The Strömgren Sphere represents the balance between two competing processes: the ionizing UV photons from the central star and the recombination of free electrons with protons (neutral hydrogen atoms). Understanding the Strömgren Sphere involves calculating the radius at which the rate of photoionization equals the rate of recombination, marking the boundary between ionized hydrogen and neutral hydrogen in the interstellar medium.
The UV photons emitted by a massive O-type or B-type star can ionize hydrogen atoms within the surrounding ISM. Each ionized hydrogen atom emits an electron and a proton, which may eventually recombine. The ionization equilibrium is established when the rate of ionizing photons matches the recombination rate. Mathematically, this balance defines the radius of the Strömgren Sphere, RS, and can be derived from the following condition:
ne np αB = S / (4π RS3 / 3),
where:
ne = number density of free electronsnp = number density of protons (assumed equal to the electron density in pure hydrogen regions)αB = recombination coefficient for hydrogen, considering recombinations to all excited states (case B recombination)S = ionizing photon luminosity (number of ionizing photons emitted per second by the star)In equilibrium, this equation is solved for RS, the Strömgren radius, which determines the size of the ionized region. For typical O-type stars with high ionizing fluxes, the Strömgren radius can range from a few parsecs to tens of parsecs, depending on the density of the surrounding medium.
To derive the Strömgren radius, we begin with the ionization balance equation, expressing the total number of ionizing photons equal to the number of recombinations within the sphere. For simplicity, in a fully ionized hydrogen region, we assume that ne ≈ np ≈ nH (where nH is the hydrogen number density), and integrating over the volume of the sphere gives:
S = (4π / 3) RS3 nH2 αB.
Solving for RS, we get the Strömgren radius as:
RS = (3 S / (4π nH2 αB))1/3.
This radius represents the region around a star where hydrogen remains ionized. Beyond this boundary, the radiation is insufficient to ionize the hydrogen atoms faster than they can recombine, and the gas becomes neutral.
Several factors affect the structure and evolution of the Strömgren Sphere:
αB value for "case B" recombination, which excludes recombinations to the ground state (since such photons are immediately re-absorbed).In a steady state, the radius RS remains constant, but in realistic astrophysical scenarios, the star's UV output may change, and the surrounding gas may be dynamically evolving, affecting the structure and size of the ionized region.
The Strömgren Sphere model is widely applicable in different astrophysical environments:
Strömgren Spheres are typically observed as emission nebulae in regions of recent star formation. The Hα line (656.3 nm), emitted by hydrogen recombining in the ionized region, is one of the key observational signatures of these regions. Radio observations at wavelengths corresponding to free-free emission also provide insights into the size and density structure of these ionized regions.
Modern observations with instruments such as the Hubble Space Telescope (HST) and radio telescopes have allowed for detailed studies of Strömgren Spheres in nearby star-forming regions, helping to refine theoretical models.
The Strömgren Sphere is a fundamental concept in astrophysics, describing the ionized regions around young, massive stars. Understanding the balance of ionization and recombination, as well as the factors influencing the sphere's size and evolution, is critical for studying stellar feedback, H II regions, and the ionization of the interstellar medium. Both theoretical calculations and observational data continue to enhance our knowledge of these vital regions in the life cycle of stars and galaxies.