Chapter 6: Stellar Evolution (part 2): Stellar end-products Final evolution stages of high-mass stars Stellar end-products White dwarfs Neutron stars and black holes Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe Review Outline Final evolution stages of high-mass stars Stellar end-products White dwarfs Neutron stars and black holes Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe Review Final evolution stages of high-mass stars I What do stars in the mass range of ∼ 8 − 11M eventually evolve to is still somewhat uncertain; they may just develop degenerate O-Ne cores. I A star with mass above ∼ 11M will ignite and burn fuels heavier than carbon until an Fe core is formed which collapses and causes a supernova explosion. I For a star with mass & 15M , mass loss by the stellar wind becomes important during all evolution phases, including the MS. Kippenhahn Diagram When the degenerate core’s mass surpasses the Chandrasekhar limit (or close to it), the core contracts rapidly. No further source of nuclear energy in the iron core, the temperature rises from the contraction, but not fast enough. It collapses on a time scale of seconds! Mass-loss of high-mass stars For stars with masses & 30M , I The mass loss time scale is shorter than the MS timescale. The MS evolutionary paths of such stars converge toward that of a 30M star. I Mass-loss from Wolf-Rayet stars leads to CNO products (helium and nitrogen) exposed. I The evolutionary track in the H-R diagram becomes nearly horizontal, since the luminosity is already close to the Eddington limit. I Electrons do not become degenerate until the core consists of iron. Mass-loss of high-mass stars For stars with masses & 30M , I The mass loss time scale is shorter than the MS timescale. The MS evolutionary paths of such stars converge toward that of a 30M star. I Mass-loss from Wolf-Rayet stars leads to CNO products (helium and nitrogen) exposed. I The evolutionary track in the H-R diagram becomes nearly horizontal, since the luminosity is already close to the Eddington limit. I Electrons do not become degenerate until the core consists of iron. When the degenerate core’s mass surpasses the Chandrasekhar limit (or close to it), the core contracts rapidly. No further source of nuclear energy in the iron core, the temperature rises from the contraction, but not fast enough. It collapses on a time scale of seconds! _ I How could M and vw be measured? I In general, mass-loss rates during all evolution phases increase with stellar mass, resulting in timescales for mass loss that are less that the nuclear Kippenhahn diagram of the evolution of timescale for M & 30M . As a result, a 60 M star at Z = 0.02 with mass there is a convergence of the final loss. Cross-hatched areas indicate (pre-supernova) masses to ∼ 5 − 10M . where nuclear burning occurs, and I However, this effect is much diminished curly symbols indicate convective for metal-poor stars because the regions. See text for details. Figure mass-loss rates are generally lower at from Maeder & Meynet (1987). low metallicity. Mass loss of high-mass stars Mass loss plays an essential role in regulating the evolution of very massive stars. I WR stars are examples, following the _ 1=2 correlation: log[Mv1R ] / log[L]. I In general, mass-loss rates during all evolution phases increase with stellar mass, resulting in timescales for mass loss that are less that the nuclear Kippenhahn diagram of the evolution of timescale for M & 30M . As a result, a 60 M star at Z = 0.02 with mass there is a convergence of the final loss. Cross-hatched areas indicate (pre-supernova) masses to ∼ 5 − 10M . where nuclear burning occurs, and I However, this effect is much diminished curly symbols indicate convective for metal-poor stars because the regions. See text for details. Figure mass-loss rates are generally lower at from Maeder & Meynet (1987). low metallicity. Mass loss of high-mass stars Mass loss plays an essential role in regulating the evolution of very massive stars. I WR stars are examples, following the _ 1=2 correlation: log[Mv1R ] / log[L]. _ I How could M and vw be measured? Mass loss of high-mass stars Mass loss plays an essential role in regulating the evolution of very massive stars. I WR stars are examples, following the _ 1=2 correlation: log[Mv1R ] / log[L]. _ I How could M and vw be measured? I In general, mass-loss rates during all evolution phases increase with stellar mass, resulting in timescales for mass loss that are less that the nuclear Kippenhahn diagram of the evolution of timescale for M & 30M . As a result, a 60 M star at Z = 0.02 with mass there is a convergence of the final loss. Cross-hatched areas indicate (pre-supernova) masses to ∼ 5 − 10M . where nuclear burning occurs, and I However, this effect is much diminished curly symbols indicate convective for metal-poor stars because the regions. See text for details. Figure mass-loss rates are generally lower at from Maeder & Meynet (1987). low metallicity. Outline Final evolution stages of high-mass stars Stellar end-products White dwarfs Neutron stars and black holes Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe Review Stellar end-products It is primarily the mass of a star that decides the outcome at the end of the stellar evolution. The radii of WDs are not too different from the −2 Earth’s (about 10 R ). Thus, the average density is near 106 g cm−3. White dwarfs WDs are the stellar end-products of relatively low-mass stars. Observations show two peaks in the mass distribution of WDs: I (Isolated) stars normally undergo the AGB phase, accounting for most of the WDs observed with their mass peaking at 0:67 ± 0:21 M (Zorotovic et al. 2011). I A helium white dwarf can theoretically be made by mass transfer in a binary. But, many He white dwarfs apparently single, puzzlingly. I But, mean white dwarf mass in CVs is high (∼ 0:83 ± 0:24 M ; Zorotovic et al. 2011), which cannot be explained by selection effects. We still don’t understand how CVs evolve. They may contribute to the single-degenerate progenitors of type Ia SNe. White dwarfs WDs are the stellar end-products of relatively low-mass stars. Observations show two peaks in the mass distribution of WDs: I (Isolated) stars normally undergo the AGB phase, accounting for most of the WDs observed with their mass peaking at 0:67 ± 0:21 M (Zorotovic et al. 2011). I A helium white dwarf can theoretically be made by mass transfer in a binary. But, many He white dwarfs apparently single, puzzlingly. I But, mean white dwarf mass in CVs is high (∼ 0:83 ± 0:24 M ; Zorotovic et al. 2011), which cannot be explained by selection effects. We still don’t understand how CVs evolve. They may contribute to the single-degenerate progenitors of type Ia SNe. The radii of WDs are not too different from the −2 Earth’s (about 10 R ). Thus, the average density is near 106 g cm−3. WD structure and cooling The structure of a WD approximately consists of two parts: I an isothermal degenerate electron core. Why is this a reasonable assumption? I a thermal radiative envelope with negligible mass and energy source. The internal energy source is primarily the thermal energy stored by the ions (as the heat capacity of the electrons is negligible). Neglecting the mass and energy in the envelope, the total thermal energy is 3MkTc UI = ; (1) 2µI mA where Tc is the temperature of the core. The luminosity can be expressed as dU L = − I (2) dt and is determined by Tc and the WD mass M. This expression is to be found. In the radiative envelope, dT 3 κρ L = − ; dr 4ac T 3 4πr 2 Replacing dr with the hydrostatic equation, using the Kramers’ opacity, and integrate the equation from the surface, where P = T = 0, inward, we have M 1=2 P / T 17=4: L Reversing back to the density, M 1=2 ρ / T 13=4; L which holds down to Rc, where the ideal electron pressure and the degenerate electron pressure are the same: ρ 5=3 kT = K (ρ/µe) µemA where K is just a constant. We further assume that there is no sudden jump in both density and temperature across the radius. Eliminating ρ between the above two equations, obtain L=L −3 7 7=2 ≈ 9 × 10 (Tc=10 K ) M=M Placing the above in Eq. 2 and then integrating it, we get 5=2 5=2 τcool / (1=Tc − 1=Tc;0 ) For Tc Tc;0, we have 5=7 6 M=M τcool = 2:5 × 10 yr L=L For example, about 2 × 109 yrs would be required for the luminosity of −4 a 1M WD to drop to 10 L . Afterward, the cooling can be accelerated by crystallization. The WD quickly becomes invisible. Neutron stars and black holes What end-product a massive star produces probably depends on many factors (e.g., rotation, magnetic field, etc.). But its initial mass and metallicity may play a major role: Neutron stars are the stellar remnants of massive stars, with initial mass mostly in the range of ∼ 10 − 25M . The alternative stellar end-products of such massive stars are black holes.