Diffusion time approximation for the radiative zone using a 3D random walk:
t ≈ R² / (λ c) with steps N ≈ (R/λ)². Change mean free path λ and effective thickness R.
1.0e-2 m
5.00e+8 m
Steps N ≈ (R/λ)²
2.50e+21
Total path ≈ N·λ (m)
2.50e+19 m
Diffusion time t ≈ R²/(λ c)
8.34e+10 s
t in years
2642,5 yr
Reference: c = 2.9979×10⁸ m/s. Radiative-zone thickness in the Sun ≈ (0.71−0.25)R☉ ≈ 0.46 R☉ ≈ 3.2×10⁸ m.
Timeline (illustrative)
Radiative diffusion (this calculator) Convection to photosphere (days–weeks) Vacuum flight 1 AU (8 min 20 s)
Bar lengths are qualitative; the numeric times are shown above.
How photons “appear” at the surface
Birth (γ in MeV): pp-chain reactions in the core produce gamma-rays and neutrinos.
Thermalization: Compton/Thomson scattering, bound–bound, bound–free, free–free exchange energy with plasma; energies cascade to keV→eV.
Random walk: countless scatterings; direction and energy are re-sampled at each step.
Convection: increased opacity triggers buoyant transport in the outer ~30% radius.
Photosphere: last scatter near optical depth ~1; photons stream freely to space.
Important: the photon you detect is not the same γ born in the core; the energy has been handed off many times before a new photon last-scatters outward.
Layer diagram
Neutrinos leave almost instantly; photons reflect the star’s thermodynamic history.