Stellar Astrophysics: Stellar Evolution Pre Main-Sequence Evolution The free-fall time scale is describing the collapse of the (spherical) cloud to a protostar 1/2 3 π t ff = 32 G ρ With the formation of the protostar, the evolution is controlled by the gravitational Kelvin-Helmholtz time-scale at which the protostar thermally adjusts 3 G M 2 t KH = >> t 10 R L ff The gravitational potential energy is slowly released The Sun contracted slowly in about 40 million years to it s mainsequence structure 1
Pre Main-Sequence Evolution Pre Main-Sequence Evolution of a Solar Mass Star Initially, the protostar contracts along the Hayashi track, a vertical line in the Hertzsprung-Russel diagram The Hayashi track is characterized by a deep convective envelope, sometimes reaching to the center of the star Deuterium fusion occurs at a low rate (not much deuterium available) With increasing core temperature, ionization increases and the convective core turns into a radiative core The luminosity begins to increase again The temperature slightly rises, since the protostar is shrinking 2
Pre Main-Sequence Evolution of a Solar Mass Star The temperature increases to a point where the luminosity becomes dominated by nuclear fusion in the core First two steps in the PP I chain and carbon-12 burning of the CNO chain The CNO reaction results in a steep temperature gradient in the core The luminosity increases eventually so much that the core expands This leads to a luminosity decrease With exhaustion of the carbon-12 supply, the protostar reaches the main sequence Pre Main-Sequence Evolution of a Brown Dwarf Star A protostar with a mass between 0.013 and 0.072 solar masses develops into a brown dwarf star Jupiter is about 0.001 solar masses Spectral class is of type L or T Deuterium burning occurs Above 0.06 solar masses also lithium burning occurs 3
Pre Main-Sequence Evolution of a Massive Star The larger the mass of a protostar, the earlier high temperatures are reached inside the core Protostars with more than 1.2 solar masses have convective cores These stars can burn carbon-12 inside the core They leave the Hayashi track earlier, increasing the temperature with less luminosity change Main-Sequence Lifetimes 4
Main-Sequence Existence While the Sun is a main-sequence star, hydrogen burning into helium occurs in the core The mass distributions X of some nuclei are given in the figure below for the present-day Sun Eventually, all the hydrogen will have been fused into helium in the core The energy generation via the PP chain stops in the core and continuous in a thick shell The isothermal helium core has to be in thermal equilibrium with the material at larger radii, which requires a pressure increase towards the center Post-Main-Sequence Existence The luminosity generated in the hydrogen burning shell eventually exceeds the one from the earlier core burning and the temperature decreases slowly (3 4) This phase ends when the mass of the isothermal core has become so great that it cannot support the material at larger radii Bahcall et al, Ap. J. 555 (2001) 5
Post-Main-Sequence Existence The maximum fraction of the star s mass that can still support the outer lying mass was derived by Schönberg and Chandrasekhar Bahcall et al, Ap. J. 555 (2001) M c 0.37 M µ env µ c 2 When the limit is reached, the core will start to collapse (4) Post-Main-Sequence Existence Stars with larger masses behave very similarly, but additionally have a convective core This leads to a fairly homogeneous composition of the core Eventually the whole star starts to contract 6
Late Stages of Stellar Evolution Development of a low mass star with 1 M after leaving the zero-age main-sequence (ZAMS) Once the core starts to contract, the gravitational energy released leads to an expansion of the envelope and the temperature to drop This is called the subgiant branch (SGB) The photospheric opacity begins to increase, resulting in the formation of a convection zone which eventually extends deep into the stars interior Late Stages of Stellar Evolution Eventually the convection zone extends to the core During this time the star is expanding on the red giant branch (RGB) The convection leads to elements created through fusion deep inside the stars interior to reach the surface (dredge-up) 7
Late Stages of Stellar Evolution The development differs from now on for stars with more or less mass than 1.8 M Stars with M < 1.8 M the helium core continuous to collapse Large energy loss through easily escaping neutrinos leads to a negative temperature gradient near the center When the core temperature reaches 10 8 K and a density of about 10 7 kg m -3, helium burning starts in the core explosively (core flash) Late Stages of Stellar Evolution The helium core burning progresses similar to the hydrogen burning A convective core develops because of the steep temperature dependence of the triple-alpha process The most blue-ward point on the horizontal branch (HB) is reached when the core molecular weight has increased to the point that the core begins to contract again Eventually the helium core is exhausted and helium shell burning begins 8