Transcript SS_L1
1 snapshots and timescales Stellar Structure: TCD 2006: 1.1 Hertzsprung Russell diagram Stellar Structure: TCD 2006: 1.2 NGC 2266 Stellar Structure: TCD 2006: 1.3 Open cluster HR diagrams Stellar Structure: TCD 2006: 1.4 Open cluster HR diagrams MS Main Sequence TO gap GB TO Turn-off gap Hertzsprung Gap MS GB Giant Branch Stellar Structure: TCD 2006: 1.5 47 Tuc – SALT optical Stellar Structure: TCD 2006: 1.6 47 Tuc – Chandra X-ray Stellar Structure: TCD 2006: 1.7 Cen - Kitt Peak Stellar Structure: TCD 2006: 1.8 Cen - HST Stellar Structure: TCD 2006: 1.9 M5 – optical Stellar Structure: TCD 2006: 1.10 M5 Colour-Magnitude Diagram Stellar Structure: TCD 2006: 1.11 Hertzsprung Russell diagram Stellar Structure: TCD 2006: 1.12 some definitions The Sun M R L stellar mass (M / M) stellar radius (R / R) stellar luminosity (L / L) M = 1 M = 1.99 1030 kg R = 1 R = 6.96 108 m L = 1 L = 3.86 1026 W Teff effective temperature (K) = ( L / 4R2 ) 1/4 g surface gravity = GM/R2 Teff = 5780 K g = 2.74 102 m s-2 X,Y,Z mass fractions of H, He and other elements X = 0.71 Y = 0.265 Z = 0.025 t ~ 4.6 109 y t age Stellar Structure: TCD 2006: 1.13 some observational facts temperature-luminosity L ~ Teff where: ~0.4 mass-luminosity L ~ M where: ~3.8 Our theory of stellar structure must reproduce both these results Stellar Structure: TCD 2006: 1.14 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: 1.15 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 tff ~ (2/3 G)-1/2 ~ 2.2 103 (R3/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: 1.16 thermal (Kelvin) time the time required for a body to radiate its total heat energy Ekin tK ~ Ekin / L Ekin is related to Egrav by the Virial theorem Ekin = –(1/2) Egrav. But Egrav = –q GM2 / R, where q ~ unity, so that tK = q/2 GM2 / LR ~ 3 107 qM2/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: 1.17 nuclear time the fusion of four protons to create an alpha-particle releases energy Q ~ 26MeV total available nuclear energy Enuc=q M/4mp . Q q ~ unity represents fraction of the star available as nuclear fuel. ‘nuclear time’ is simply the time taken to radiate this energy tnuc = Enuc / L hydrogen-burning in main-sequence stars, tnuc ~ 1 1011 q (M/M) / (L/L) y Stellar Structure: TCD 2006: 1.18 radiative energy transport R D 1 2 N Stellar Structure: TCD 2006: 1.19 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 D2=N2 To escape, the photon must travel a distance R, which will take tdiff R2 / c ~ 5105 R y Compare the escape time for noninteracting particles (eg neutrinos): tesc = R / c = 2.3 R s R in solar units. Stellar Structure: TCD 2006: 1.20 comparative timescales Star M Sun 1 MS 5 M 5 MS 0.2 M 0.2 RG 1 WD 0.6 R 1 3 0.3 100 0.01 L Teff 1.0E+00 5760 4.5E+02 15342 2.2E-03 2280 1.5E+03 3600 1.0E-03 10243 tesc/s 2.30E+00 6.90E+00 6.90E-01 2.30E+02 2.30E-02 tff/s 2.20E+03 2.56E+04 1.62E+02 2.20E+06 1.70E+00 Stellar Structure: TCD 2006: 1.21 tdiff/y 5.00E+05 1.50E+06 1.50E+05 5.00E+07 5.00E+03 tkh/y 3.00E+07 5.52E+05 1.81E+09 1.97E+02 1.08E+12 tnuc/y 1.00E+11 1.10E+09 9.06E+12 6.55E+07 6.00E+13 1 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 Stellar Structure: TCD 2006: 1.22