Principles of Stellar Evolution

Lecture 1 given at the "Look & Listen" Astrophysics School, Playa del Carmen (Mexico), 2014. Topics: Basic principles of stellar evolution. Massive Stars.

Transcript

1. Principles of Stellar Evolution Matteo Cantiello Kavli Institute for Theoretical Physics (University of California Santa Barbara)
2. Useful Resources:  Stellar Structure and Evolution (Kippenhahn & Weigert)  Introduction: Stellar Structure and Evolution (D. Prialnik) Mexico 2014 Matteo Cantiello Look&Listen
3. Useful (Free) Resources:  Notes from Stellar Evolution Class (O. Pols) http://www.astro.ru.nl/~onnop/education/stev_utrecht_notes/  Notes from Nucleosynthesis Class (N. Langer) http://www.astro.uni-bonn.de/~nlanger/siu_web/nucscript/Nucleo.pdf Mexico 2014 Matteo Cantiello Look&Listen
4. Computational Resources: Mexico 2014 Matteo Cantiello Look&Listen  MESA Stellar Evolution Code: mesa.sourceforge.net  MESA Instrument Papers (Paxton et al. 2011, 2013) Bill Paxton, father of MESA MESA is a state-of-the-art, modular, open source suite for stellar evolution
5. Hydrostatic Equilibrium Mexico 2014 Matteo Cantiello Look&Listen Mass Conservation Hydrostatic Equlibrium
6. Hydrostatic Equilibrium Mexico 2014 Matteo Cantiello Look&Listen Hydrostatic Equlibrium H.E. + Perfect Gas ...
7. Virial Theorem Mexico 2014 Matteo Cantiello Look&Listen A relation between the gravitational potential energy and the internal energy of a star in H.E. (perfect gas). It says that a more tightly bound star must have a higher internal energy, i.e. it must be hotter. A star that contracts quasi-statically must get hotter
8. Dynamical Timescale Mexico 2014 Matteo Cantiello Look&Listen The timescale on which a star reacts to a perturbation of hydrostatic equilibrium.
9. Dynamical Timescale Mexico 2014 Matteo Cantiello Look&Listen The timescale on which a star reacts to a perturbation of hydrostatic equilibrium. If H.E. can not be restored one expect to witness a catastrophic event on a short timescale!
10. L = ˙ Eint Thermal Timescale Mexico 2014 Matteo Cantiello Look&Listen How fast a star reacts to a perturbation of thermal equilibrium? It’s also the timescale of contraction of a star where the nuclear energy generation suddenly disappeared
11. Thermal Timescale Mexico 2014 Matteo Cantiello Look&Listen How fast a star reacts to a perturbation of thermal equilibrium? It’s also the timescale of contraction of a star where the nuclear energy generation suddenly disappeared
12. Nuclear Timescale Mexico 2014 Matteo Cantiello Look&Listen A star can remain in thermal equilibrium for as long as its nuclear fuel supply lasts. The energy source of nuclear fusion is the direct conversion of a small fraction φ of the rest mass of the reacting nuclei into energy Main sequence
13. M-L, R-L relationships Mexico 2014 Matteo Cantiello Look&Listen From Double-Lined Eclipsing Binaries (see O.Pols Lectures)
14. Timescales Mexico 2014 Matteo Cantiello Look&Listen Main Sequence tnuc tKH tdyn 1 MSun 10 MSun 100 MSun 1010 yr 107 yr 0.02 d ~107 yr 104 yr 0.1 d ~106 yr 103 yr 0.5 d
15. Timescales Mexico 2014 Matteo Cantiello Look&Listen During the main sequence Main Sequence tnuc tKH tdyn 1 MSun 10 MSun 100 MSun 1010 yr 107 yr 0.02 d ~107 yr 104 yr 0.1 d ~106 yr 103 yr 0.5 d
16. A hot gas radiates energy Mexico 2014 Matteo Cantiello Look&Listen How energy escapes from the stellar interiors?
17. A hot gas radiates energy Mexico 2014 Matteo Cantiello Look&Listen How energy escapes from the stellar interiors? F = KrT 1) Heat Diffusion
18. A hot gas radiates energy Mexico 2014 Matteo Cantiello Look&Listen How energy escapes from the stellar interiors? Heat diffusion proceeds through the random thermal motion of particles across gradients in temperature F = KrT 1) Heat Diffusion
19. A hot gas radiates energy Mexico 2014 Matteo Cantiello Look&Listen How energy escapes from the stellar interiors? Heat diffusion proceeds through the random thermal motion of particles across gradients in temperature Particles can be either photons (radiative diffusion) or gas particles (conduction) F = KrT 1) Heat Diffusion
20. LTE Mexico 2014 Matteo Cantiello Look&Listen Local Thermodynamic Equilibrium is achieved when sufficient interactions take place between the material particles (‘collisions’) and between the photons and mass particles (scattering and absorptions). In LTE the radiation field becomes isotropic and the photon energy distribution is described by the Planck function. The statistical distributions of both mass particles and photons are then characterized by a single temperature T. Stellar interiors are in LTE. The mean free path for a photon in the solar interior is about 1cm << R
21. F = KrT K = 1 3 vlC v = c l = 1/⇢ C = dU dT = 4aT3 Radiative Diffusion Mexico 2014 Matteo Cantiello Look&Listen Valid for all particles in LTE (Local Kinetic Temperature = Planck Temperature of radiation field) (Photons)
22. Radiative Diffusion Mexico 2014 Matteo Cantiello Look&Listen
23. Energy Transport in Stars Mexico 2014 Matteo Cantiello Look&Listen How energy escapes from the stellar interiors? 2) Convection
24. Energy Transport in Stars Mexico 2014 Matteo Cantiello Look&Listen How energy escapes from the stellar interiors? 2) Convection Radiative diffusion can transport energy outwards, however the higher the luminosity, the higher the temperature gradient required. It turns out there is a limit for such a gradient above which an instability in the stellar plasma sets is. This instability is called Convection
25. ⇢2, P2 ⇢⇤ > ⇢2 ⇢⇤ < ⇢2 Convection Mexico 2014 Matteo Cantiello Look&Listen Rise and Adiabatic Expansion ⇢1, P1 Stable: Unstable: ⇢⇤ ⇢1, P1 P⇤ = P2
26. Radiative Temperature Gradient Mexico 2014 Matteo Cantiello Look&Listen H.E. Radiative Transport
27. ⇢2, P2 rrad  rad Convection Mexico 2014 Matteo Cantiello Look&Listen Rise and Adiabatic Expansion ⇢1, P1 Stability for ⇢⇤ P1 = P2 ⇢1, P1 Schwarzschild Stability Criterion ⇢⇤ > ⇢2
28. rrad < rad rrad < rad + rµ Schwarzschild vs Ledoux Mexico 2014 Matteo Cantiello Look&Listen Schwarzschild Criterion In the presence of a compositional gradient: Ledoux Criterion In stellar evolution calculations convective regions are established using one of the above criteria. Then the transport of energy (and the convective velocities) is solved using the mixing length theory (MLT, e.g. Prandtl, Böhm-Vitense) )
29. l = ↵HP HP = dr dP P l Mixing Length Theory Mexico 2014 Matteo Cantiello Look&Listen A blob starts somewhere with DT > 0 and loses identity after a typical mixing length distance. It dissolves into its surroundings and deposits its energy there. Where MLT works surprisingly well in regions where convection is efficiently transporting the flux (adiabatic convection). It basically allows to calculate stellar evolution.
30. Occurrence of Convection Mexico 2014 Matteo Cantiello Look&Listen  A large value of k (opacity). E.g. Cool, opaque envelopes  A large value of l/m. That is regions with large energy flux  Small value of the adiabatic gradient. E.g. due to partial ioniziation
31. ✏pp / T4 ✏CNO / T18 ✏3↵ / ⇢2T40 Energy Generation Mexico 2014 Matteo Cantiello Look&Listen log T log  

ε CNO Cycle Triple  

α PP Chain Sun
32. Occurrence of Convection Mexico 2014 Matteo Cantiello Look&Listen Low Mass stars Massive stars Radiative core Convective envelope Convective core Radiative envelope e.g 1M Sun e.g 20 M Sun l/m ⇡ ✏nuc
33. Occurrence of Convection Mexico 2014 Matteo Cantiello Look&Listen Low Mass stars Massive stars Radiative core Convective envelope Convective core Radiative envelope e.g 1M Sun e.g 20 M Sun l/m ⇡ ✏nuc
34. 5 Equations of Stellar Evolution Mexico 2014 Matteo Cantiello Look&Listen Continuity Eq. Hydrostatic Equilibrium Energy Generation + Eq. of State Energy Transport
35. Stellar Evolution “The life of any star is a continual struggle between its gravitational force, trying to collapse it, and the pressure gradient supporting it. Stars are gravitationally confined thermonuclear reactors. As long as they remain non-degenerate, overheating leads to expansion and cooling, while cooling leads to contraction and heating. Therefore stars are generally stable. Since the pressure in an ideal gas depends on temperature, stars must remain hot to balance gravity. Being hot, they must also radiate. The energy lost through the stellar luminosity is provided by either gravitational contraction or nuclear reactions. The latter change the composition, implying a star has to evolve. This is the reason for "Stellar Evolution". Mexico 2014 Matteo Cantiello Look&Listen Stan Woosley’s lectures
36. Massive Stars I Matteo Cantiello Kavli Institute for Theoretical Physics (University of California Santa Barbara)
37. Massive Stars
38. Massive Stars
39. Massive Stars Mexico 2014 Matteo Cantiello Look&Listen  Energy / Momentum in ISM  Stellar Winds, SNe  Nucleosynthesis  Remnants: NS and BHs  Magnetars, Pulsars, Long GRBs... Importance of magnetic fields and final angular momentum budget
40. Because of the general tendency of the interior temperature of main sequence stars to increase with mass, stars of over two solar mass are chiefly powered by the CNO cycle(s) rather than the pp cycle(s). This, plus the increasing fraction of pressure due to radiation, makes their cores convective. Massive Stars Mexico 2014 Matteo Cantiello Look&Listen Massive stars Convective core Radiative envelope e.g 20 M Sun l/m ⇡ ✏nuc Stan Woosley’s lectures
41. Because of the general tendency of the interior temperature of main sequence stars to increase with mass, stars of over two solar mass are chiefly powered by the CNO cycle(s) rather than the pp cycle(s). This, plus the increasing fraction of pressure due to radiation, makes their cores convective. Massive Stars Mexico 2014 Matteo Cantiello Look&Listen Massive stars Convective core Radiative envelope e.g 20 M Sun l/m ⇡ ✏nuc Stan Woosley’s lectures
42. Massive Stars Mexico 2014 Matteo Cantiello Look&Listen Photons can be treated as quantum-mechanical particles that carry momentum and therefore exert pressure when they interact with matter.
43. Evolution in the Rho-T Plane Mexico 2014 Matteo Cantiello Look&Listen 2 4 6 8 10 log ρ c (g cm−3) 8.5 9.0 9.5 10.0 log T c (K) Γ 1 < 4/3 He C Ne O Si Evolution to core−collapse M/M 100: Z=0.02 / crit = 0.2 M/M 120: Z=0.001 = 0.2 Ω Ω Ω/Ω crit ≤ ≥ 1000M 500M 250M 150M 120M 100M 90M 80M 70M 60M 50M 40M 30M Paxton et al. (2013)
44. Burning Phases Mexico 2014 Matteo Cantiello Look&Listen Woosley at al. 2002 15MSun
45. Burning Phases Mexico 2014 Matteo Cantiello Look&Listen Quatert & Shiode at al. 2002
46. Late Burning Phases Mexico 2014 Matteo Cantiello Look&Listen Woosley at al. 2002 TC,9 ~ 0.7 TNe,9 ~ 1.45 TO,9 ~ 1.9 TSi,9 ~ 3.4
47. Timescales Mexico 2014 Matteo Cantiello Look&Listen Red Super Giant burning He tnuc tKH tdyn 20 MSun ~105 yr ~ yr 0.5 yr GMmEnv 2RL
48. Timescales Mexico 2014 Matteo Cantiello Look&Listen Red Super Giant after C-burning tnuc tKH tdyn 20 MSun <1 yr ~ yr 0.5 yr GMmEnv 2RL
49. ⌧nuc ⌧KH ⌧KH = GMmEnv 2RL Frozen-in Envelopes Mexico 2014 Matteo Cantiello Look&Listen Energy Generation occurs in the core on a timescale Envelope can react to changes in the energy generation rate only on a thermal timescale ⌧nuc < ⌧KH When the envelope can be considered “frozen” in the stellar structure
50. ⌧nuc ⌧KH ⌧KH = GMmEnv 2RL Frozen-in Envelopes Mexico 2014 Matteo Cantiello Look&Listen Energy Generation occurs in the core on a timescale Envelope can react to changes in the energy generation rate only on a thermal timescale After the end of C-burning the star has only a few years to live. So anything happening in the core can not influence the surface appearance of stars just before they go SN
51. ⌧nuc ⌧KH ⌧KH = GMmEnv 2RL Frozen-in Envelopes Mexico 2014 Matteo Cantiello Look&Listen Energy Generation occurs in the core on a timescale Envelope can react to changes in the energy generation rate only on a thermal timescale This simple argument, plus the expected absence of energy generation in the stellar envelope led to the belief that stars should just see the SN explosion and not much shortly before
52. ⌧nuc ⌧KH Frozen-in Envelopes Mexico 2014 Matteo Cantiello Look&Listen Energy Generation occurs in the core on a timescale Envelope can react to changes in the energy generation rate only on a thermal timescale
53. Adiabatic exponent: measures the response of the pressure to adiabatic compression or adiabatic expansion, i.e. to a change in the density. ad = 4 3 4 3  ad  5 3 Adiabatic Exponent Mexico 2014 Matteo Cantiello Look&Listen ad = 5 3 For extremely relativistic particles For non-relativistic particles For a mixture of gas and radiation
54. Adiabatic exponent: measures the response of the pressure to adiabatic compression or adiabatic expansion, i.e. to a change in the density. ad > 4 3 Dynamical Stability Mexico 2014 Matteo Cantiello Look&Listen Dynamical Stability Requires A global dynamical instability is obtained when < 0
55. Adiabatic exponent: measures the response of the pressure to adiabatic compression or adiabatic expansion, i.e. to a change in the density. Dynamical Stability Mexico 2014 Matteo Cantiello Look&Listen Since Massive stars are radiation dominated they are prone to become dynamically unstable Pair-production at very high T is also lowering the adiabatic exponent and leads to a disruption of the star (PISN)
56. Final Fate of Massive Stars Mexico 2014 Matteo Cantiello Look&Listen
57. Core compactness Mexico 2014 Matteo Cantiello Look&Listen Calculated at M=2.5MSun O’Connor & Ott 2011 Explosion for BH formation for
58. Core compactness Mexico 2014 Matteo Cantiello Look&Listen O’Connor & Ott 2011
59. Woosley et al. 2002
60. HRD Mexico 2014 Matteo Cantiello Look&Listen Smith (2010)