Stellar Structure Section 5: The Physics of Stellar Interiors Lecture 12 – Neutrino reactions Solar neutrinos Opacity processes: scattering, bb, bf, ff Rosseland mean opacity Physical sources: … scattering (Thomson) … bound-free and free-free absorption Continuous opacity in cool stars Approximate formulae

Neutrino reactions H-burning reactions – energy loss by neutrinos small (< 5%) Later stages of evolution – high density and temperature allow other reactions, leading to much greater energy loss (see blackboard for details):  URCA process  Photo-neutrino process  Pair neutrino process  Bremsstrahlung neutrinos  Plasma neutrinos Main-sequence stars: neutrino ‘oscillations’ – explain ‘solar neutrino problem’

Opacity Accurate calculations very complex Two major recalculations (1990s): Opacity Project (OP) (UCL) and OPAL (Lawrence Livermore National Lab, California) In outline – 4 types of process contribute to radiative opacity (see blackboard for details):  Scattering  Bound-bound transitions  Bound-free transitions  Free-free transitions Other processes (e.g. pair production) may cause absorption under very extreme conditions

Rosseland mean opacity In stellar structure equations, use the Rosseland mean opacity: (3.21) (on handout) This is a harmonic mean – so hard to add new sources of opacity Also – if opacity unknown in any frequency range, must assume it to be infinite, not zero! Ideally, need estimate of both absorption and scattering at all frequencies

Scattering Main processes:  Scattering by free electrons: important in stellar interiors  Rayleigh scattering by atoms or molecules: atmospheres only Compton scattering by free electrons – scattering with change of frequency (non-coherent or incoherent scattering) (see blackboard) Non-relativistic limit: Thomson or coherent scattering – change in frequency can be neglected Cross-section depends inversely on square of particle mass, so only electrons matter; leads (see blackboard) to opacity:  = constant = 0.02(1+X) m 2 kg -1 (5.47)

Bound-free absorption Bound-bound absorption only important in outer layers H, He ~fully ionised in interior, so main contributors are heavier atoms and ions with bound electrons Absorption is continuous above critical frequency corresponding to ionisation potential, and has simple form with frequency (see blackboard) Frequency dependence strongly modified in degenerate conditions Different critical frequency for each bound level Populations of bound levels given by Boltzmann factor Total cross-section has series of absorption ‘edges’ under envelope given by Boltzmann factor (Handout 7, top)

Free-free absorption, and continuous absorption in cool stars Free-free absorption has similar frequency dependence to bound- free absorption (except for ~0), with no critical frequency Cool stars ( K) show continuous absorption, almost independent of frequency in far-red – doesn’t seem to match Rupert Wildt (1930s): negative hydrogen ion (see blackboard) Continuous absorption dominated by bound-free H - absorption in visual, with H - free-free taking over in near infrared (Handout 7, bottom) Processes compete with neutral H absorption (Balmer, Paschen, Brackett) Enough electrons available from metals of low ionisation potential to allow H - absorption to dominate over neutral H absorption

Approximate formulae for opacity Detailed calculations of opacity: complicated, time-consuming Realistic stellar models use tables of opacity, computed at points in a grid of density and temperature; the opacity for a particular temperature and density is obtained by interpolation in tables General behaviour shown in Handout 8 (top figure) For given density,  (T) has 3 branches, ~ straight lines in log-log plot (Handout 8, bottom figure) Hence 3 approximate formulae (~ 3 mechanisms) (see blackboard) Use values in Handout to estimate mean free path of photon, and hence temperature difference between emission and absorption (see blackboard) – very small! Justifies thermodynamic equilibrium