Strömgren Sphere: HII Region Growth

Ionizing Star

UV photon rate Q 1.0×10⁴⁹ s⁻¹

Gas density n 100 cm⁻³

Simulation speed 1.0×

Ionization Front

Strömgren radius R_s

— pc

Current front R(t)

— pc

Recombination time

— yr

Elapsed time

0 yr

Ionized volume fraction

0.0%

How it works

A hot O/B star floods the surrounding neutral hydrogen with ultraviolet photons above 13.6 eV, each of which can ionize one atom. Free electrons and protons constantly recombine, releasing a fresh ionizing photon (case-B recombination). Equilibrium — the Strömgren sphere — is reached when the total photoionization rate inside a radius R exactly balances the total recombination rate:

Q = (4/3)π R_s³ n² α_B

R_s = ( 3Q / (4π n² α_B) )^(1/3)

where Q is the star's ionizing photon output (s⁻¹), n is the hydrogen number density (cm⁻³) and α_B ≈ 2.6×10⁻¹³ cm³ s⁻¹ is the case-B recombination coefficient at ~10⁴ K. The front does not jump straight to R_s — it grows from ignition following the classic time-dependent solution (Strömgren 1939 / Spitzer):

R(t) = R_s · ( 1 − e^(−t/t_rec) )^(1/3)
t_rec = 1 / (n α_B)      (recombination time)

UV photon rate Q — sets the star's ionizing luminosity; a bright O star emits ~10⁵⁰ photons/s, a late B star ~10⁴⁷.
Gas density n — denser gas recombines faster, so it both shrinks R_s and shortens t_rec (front reaches equilibrium sooner but at a smaller radius).
Simulation speed — plays through the exponential approach to equilibrium; real HII regions take anywhere from ~10² to ~10⁵ years to light up.
Pink particles are photoionized (H⁺, glowing in Hα); brown particles are still neutral, unionized hydrogen (H I) — exactly what real emission nebulae like the Orion Nebula show at their ionization boundary.

Ionized (H⁺, Hα glow) Neutral (H I) Ionizing star

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