Astrophysics II. Ugeseddel nr. 2.
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1 Jørgen Christensen-Dalsgaard 5 eptember 013. The lectures in Q1 take place Mondays 10:15 1 and Thursdays 14:15-16:00. The Exercises will be on Wednesdays 14:15-17:00. Brandon Tingley will instruct the exercises. Lectures and exercise classes are in room The primary website for the course is Preliminary schedule for the first 5 weeks of the course: Monday 6/8: Introduction (LN, Chapter 1). Thursday 9/8: Equation of state (LN, Chapter 3). tart of hydrostatic equilibrium (LN, Chapter 4) Monday /9: Continue hydrostatic equilibrium (LN, Chapter 4). Energy transport by radiation (LN, Chapter 5) Thursday 5/9: Opacity, etc. (LN, ections ). Convection (LN, Chapter 6). Monday 9/9: Estimates of stellar luminosity (LN, Chapter 7). tart energy generation (LN, Chapter 8) Thursday 1/9: More on energy generation (LN, Chapter 8). Monday 16/9: tar formation (LN, Chapter 10). Main sequence stars (LN, Chapter 11). Thursday 19/9: Post-main-sequence evolution (LN, Chapter 1). Monday 3/9: upernovae (LN, Chapter 14). Nucleosynthesis (LN, Chapter 15). Final stages (LN, Chapter 16). Thursday 6/9: Likely spill-over. The exercises on Wednesday 11 eptember 013 cover the following four exercises: Exercise no. 7 The thermal timescale for the un is 30 million years and reflects the time it takes for energy to diffuse from the core to the surface of the un. In relation to this it is of interest to discuss the energy transport speed at different depths in the un. This is the purpose of the present exercise. Astro_II-7.1: The thermal timescale (Kelvin-Helmholtz timescale) is: ide 1
2 t KH GM L U L tot how that one can express the time it takes the energy to diffuse through a sphere of thickness dr at a distance r from the centre of the star. u( is the internal energy density and L( is the total Luminosity: dt 4 r u( dr L( Use the connection between u and P to determine the the energy velocity dr/dt as a function of r, P( and L( and show that for the un this velocity is (in cgs-units): v Energy dyn cm s L / L r P Astro_II-7.: Use the table below to calculate the energy velocity in different parts of the un (from tabel page 147 in Lecture Notes). r/ L/L log(p cm²/dyn) Astro_II-7.3: Estimate based on this - the total time it takes energy to diffuse from the core to the surface and compare to the 30 million years found by use of the thermal time scale. Astro_II-7.4: The convection zone in the un is extending from r/=0.711 to the surface. How long will it take for the energy to move through the convection zone? ide
3 Exercise no. 8 We will in this exercise discuss the core of a solar-like star. The two figures show temperature and pressure in the un as a function of r/. (values from Table 11. in Lecture Notes on tellar tructure and Evolution). The curves show analytic fits to the two profiles. In the centre we find: T ( T P( C P C e e r 8r where T C and P C are the central temperature and pressure. is the stellar radius and r is the distance from the centre. Astro_II-8.1: Determine the value for d lnt d ln P P T dt dr dp dr 1 near the centre of the star, and check whether energy is transported by convection or radiation near the centre. We assume that the equation for the ideal gas can be used to describe the properties of the matter in the interior of this star. ide 3
4 Astro_II-8.: how that the density can be described as (if we assume that µ is constant ( r e 7r ) C Exercise no. 9 The mean free path for a photon is given by (5.13): 1 n 1 Astro_II-9.1: Estimate the mean free path at different distances from the solar centre using the values from table 11.: r/ log(ρ cm³/g) κ g/cm² Exercise no. 10 We assume that tar no. 1: in two different stars can be approximated as: ide 4
5 ( r ) tar no. : ( r ) where r is the distance from the centre and is the stellar radius. We assume that the gas is described by the ideal gas equation. Astro_II-10.1: Plot as a function of r/ and show for the two stars where energy is transported by convection and by radiation. Astro_II-10.: Calculate the positions of the convection zones in the two stars. ide 5
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A first look at the Sun M= 2 10 30 Kg R=7 10 8 m N p =M/m p =10 57 L=4 10 26 W Observables about global properties: -Mass, Luminosity, Radius, - Metal content of the photosphere - Age A first look at the