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Dr Matt Burleigh The Sun and the Stars Slide 2 Dr Matt Burleigh The Sun and the Stars The Hertzsprung-Russell Diagram (E. Hertzsprung and H.N. Russell) Plot of surface temperature versus luminosity, or colour (e.g. B-V) versus absolute magnitude M, and various other combinations Hot Cool dim bright What are the physical mechanisms responsible for the L,T sequence? Slide 3 Dr Matt Burleigh The Sun and the Stars The Harvard Classification scheme is an excitation-ionization scheme The physical properties of stellar atmospheres are determined by : i) Temperature, T ii) Pressure, P iii) chemical composition, Slide 4 Dr Matt Burleigh r = R r Centre (r = 0) (r) P + dPPdr Hydrostatic Equilibrium A star is in hydrostatic equilibrium no net force acting on gas (i.e. gravity balanced by pressure) Slide 5 Dr Matt Burleigh The Sun and the Stars In hydrostatic equilibrium no net force acting on gas (i.e. gravity balanced by pressure) Consider a slab of gas area A, thickness r Force due to gravity F g, is given by This must be balanced by the upward pressure (remember P=F/A), that is rearrange, as r 0, then where g is the surface gravity, (ie. gravitational acceleration at r=R) If we express the pressure, P in terms of the optical depth, , then Gas pressure depends on opacity , and surface gravity g Slide 6 Dr Matt Burleigh E.g. Suns central pressure What is the pressure at the centre of the Sun? First calculate average density: M =1.989x10 30 kg, R =6.96x10 8 m (avg) = 3M /4 R 3 =1410 kgm -3 Then calculate pressure using Hydrostatic Equilibrium: Integrate from P c to P R and from R=R 0 =0 to R= R , If surface pressure = 0, then P c ~ G M (ave) / R = 2.7x10 14 Nm -2 Slide 7 Dr Matt Burleigh The Sun and the Stars We assume that particle densities are high enough that the gas is in thermodynamic equilibrium (i.e. all processes and their inverses occur at the same rate). The gas obeys the ideal gas law, Where the particle number density n is related to the mass density , and chemical composition (the mean molecular weight), by For pure hydrogen, =1 ionised hydrogen, =1/2 (for ionized H there are roughly equal nos. of e- and p+, and m e Dr Matt Burleigh CNO cycle Stellar Thermonuclear Reactions The Carbon cycle (CNO cycle) also converts H to He but requires a C nucleus as a catalyst Requires temperatures >1.6x10 7 K Occurs in Sun but minor compared to PPI More important fusion process for stellar masses >1.1M sun Since requires a C nucleus, only occurs in Pop I stars Second and fifth steps occur because 13 N and 15 O are unstable isotopes with half lives of only a few minutes Slide 14 Dr Matt Burleigh CNO Cycle Slide 15 Dr Matt Burleigh Stellar Thermonuclear Reactions At very high temperatures, ~10 8 K, other processes fuse Helium (alpha particles) into heavier elements Triple alpha process: The triple alpha process is first stage of helium burning in an evolved star that has left the main sequence In most massive stars, then burn C, Ne, O and Mg up to Fe