Stellar Structure: TCD 2006: snapshots and timescales

Stellar Structure: TCD 2006: 1.2 Hertzsprung - Russell diagram

Stellar Structure: TCD 2006: 1.3 NGC 2266

Stellar Structure: TCD 2006: 1.4 Open cluster HR diagrams

Stellar Structure: TCD 2006: 1.5 Open cluster HR diagrams TO MS gap GBMS Main Sequence TO Turn-off gap Hertzsprung Gap GB Giant Branch

Stellar Structure: TCD 2006: Tuc – SALT optical

Stellar Structure: TCD 2006: Tuc – Chandra X-ray

Stellar Structure: TCD 2006: 1.8  Cen - Kitt Peak

Stellar Structure: TCD 2006: 1.9  Cen - HST

Stellar Structure: TCD 2006: 1.10 M5 – optical

Stellar Structure: TCD 2006: 1.11 M5 Colour-Magnitude Diagram

Stellar Structure: TCD 2006: 1.12 Hertzsprung - Russell diagram

Stellar Structure: TCD 2006: 1.13 some definitions Mstellar mass (M / M  ) Rstellar radius (R / R  ) Lstellar luminosity (L / L  ) T eff effective temperature (K) = ( L / 4  R 2 ) 1/4 g surface gravity = GM/R 2 X,Y,Zmass fractions of H, He and other elements tage The Sun M = 1 M  = kg R = 1 R  = m L = 1 L  = W T eff = 5780 K g = m s -2 X = 0.71 Y = Z = t ~ y

Stellar Structure: TCD 2006: 1.14 some observational facts temperature-luminosity L ~ T eff  where:  ~0.4 mass-luminosity L ~ M  where:  ~3.8 Our theory of stellar structure must reproduce both these results

Stellar Structure: TCD 2006: 1.15 stellar timescales Stars such as the Sun clearly do not change their properties rapidly. So how fast can they change ? Dynamically – free-fall Thermally – radiative cooling Chemically – nucleosynthesis Radiatively – diffusion

Stellar Structure: TCD 2006: 1.16 dynamical (free-fall) time the time required for a body to fall through a distance of the order R under the influence of a (constant) gravitational acceleration equal to the surface gravity of a star of mass M t ff ~ (2/3  G  ) -1/2 ~ (R 3 /M) 1/2 s where R and M are in solar units. also: the characteristic time for a significant departure from hydrostatic equilibrium to alter the state of a star appreciably, the time taken for a body orbiting at the surface of the star to make one complete revolution, the time for a sound wave to propagate through the star Rearranging, we obtain the period mean density relation:  ~ (G ) -1/2 ~.04 / ( / ) -1/2

Stellar Structure: TCD 2006: 1.17 thermal (Kelvin) time the time required for a body to radiate its total heat energy E kin t K ~ E kin / L E kin is related to E grav by the Virial theorem E kin = –(1/2) E grav. But E grav = –q GM 2 / R, where q ~ unity, so that t K = q/2 GM 2 / LR ~ qM 2 /LR y where M, L and R are in solar units. The “Kelvin time” is the relaxation time for departure of a star from thermal equilibrium. Also the time required for a star to contract from infinite dispersion to its present radius at constant L.

Stellar Structure: TCD 2006: 1.18 nuclear time the fusion of four protons to create an alpha-particle releases energy Q ~ 26MeV total available nuclear energy E nuc =q M/4m p. Q q ~ unity represents fraction of the star available as nuclear fuel. ‘nuclear time’ is simply the time taken to radiate this energy t nuc = E nuc / L hydrogen-burning in main-sequence stars, t nuc ~ q (M/M  ) / (L/L  ) y

Stellar Structure: TCD 2006: 1.19 radiative energy transport R D 1 2 N

Stellar Structure: TCD 2006: 1.20 diffusion time Energy liberated as photons interacts by a series of scattering collisions, mainly with electrons. Scattering is isotropic, so energy transport is most correctly described by the diffusion equation. If the photon-path is a random-walk of N steps, each of length, the total distance travelled is d=N, but the nett distance travelled is D 2 =N 2 To escape, the photon must travel a distance R, which will take t diff  R 2 / c ~ 5  10 5 R y Compare the escape time for noninteracting particles (eg neutrinos): t esc = R / c = 2.3 R s R in solar units.

Stellar Structure: TCD 2006: 1.21 comparative timescales

Stellar Structure: TCD 2006: snapshots and timescales -- review The Hertzsprung-Russell diagram Clusters: Open, Globular Features: Main Sequence, Turnoff, Giant Branch Empirical Relations: Mass-Luminosity, Mass-Radius Timescales: Dynamical, Thermal, Nuclear