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1 snapshots and timescales

1 snapshots and timescales. Hertzsprung - Russell diagram. NGC 2266. Open cluster HR diagrams. Open cluster HR diagrams. TO. GB. gap. MS. MS Main Sequence TO Turn-off gap Hertzsprung Gap GB Giant Branch. 47 Tuc – SALT optical. 47 Tuc – Chandra X-ray.  Cen - Kitt Peak.

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1 snapshots and timescales

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  1. 1 snapshots and timescales Stellar Structure: TCD 2006: 1.1

  2. Hertzsprung - Russell diagram Stellar Structure: TCD 2006: 1.2

  3. NGC 2266 Stellar Structure: TCD 2006: 1.3

  4. Open cluster HR diagrams Stellar Structure: TCD 2006: 1.4

  5. Open cluster HR diagrams TO GB gap MS MS Main Sequence TOTurn-off gapHertzsprung Gap GBGiant Branch Stellar Structure: TCD 2006: 1.5

  6. 47 Tuc – SALT optical Stellar Structure: TCD 2006: 1.6

  7. 47 Tuc – Chandra X-ray Stellar Structure: TCD 2006: 1.7

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

  9.  Cen - HST Stellar Structure: TCD 2006: 1.9

  10. M5 – optical Stellar Structure: TCD 2006: 1.10

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

  12. Hertzsprung - Russell diagram Stellar Structure: TCD 2006: 1.12

  13. M stellar mass (M / M) R stellar radius (R / R) L stellar luminosity (L / L) Teff effective temperature (K)= ( L / 4R2 ) 1/4 g surface gravity = GM/R2 X,Y,Z mass fractions of H, He and other elements t age The Sun M = 1 M = 1.99 1030 kg R = 1 R = 6.96 108 m L = 1 L = 3.86 1026 W Teff = 5780 K g = 2.74 102 m s-2 X = 0.71 Y = 0.265 Z = 0.025 t ~ 4.6 109 y some definitions Stellar Structure: TCD 2006: 1.13

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

  15. 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 timescales Stellar Structure: TCD 2006: 1.15

  16. 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 dynamical (free-fall) time Stellar Structure: TCD 2006: 1.16

  17. 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. thermal (Kelvin) time Stellar Structure: TCD 2006: 1.17

  18. 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 nuclear time Stellar Structure: TCD 2006: 1.18

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

  20. 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=N2 To escape, the photon must travel a distance R, which will take tdiff R2 / c ~ 5105 R y Compare the escape time for noninteracting particles (eg neutrinos): tesc = R / c = 2.3 R s R in solar units. diffusion time Stellar Structure: TCD 2006: 1.20

  21. comparative timescales Stellar Structure: TCD 2006: 1.21

  22. 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

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