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L 3: Collapse phase – theoretical models

L 3: Collapse phase – theoretical models. Background image: courtesy ESO - B68 with VLT ANTU and FORS 1. L 3: Collapse phase – theoretical models. The Formation of Stars Chapters: 9, 10, 12. Background image: courtesy ESO - B68 with VLT ANTU and FORS 1.

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L 3: Collapse phase – theoretical models

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  1. L 3: Collapse phase – theoretical models Background image: courtesy ESO - B68 with VLT ANTU and FORS 1 L 3 - Stellar Evolution I: November-December, 2006

  2. L 3: Collapse phase – theoretical models The Formation of Stars Chapters: 9, 10, 12 Background image: courtesy ESO - B68 with VLT ANTU and FORS 1 L 3 - Stellar Evolution I: November-December, 2006

  3. L 3: Collapse phase – theoretical models Barnard 68 considered a pre-collapse/collapse candidate Background image: courtesy ESO - B68 with VLT ANTU and FORS 1 L 3 - Stellar Evolution I: November-December, 2006

  4. L 3: Collapse phase – theoretical models If you discuss methods and techniques of collapse calculations: consider sensitivity to gridding, boundary conditions; access to a standard code? (run it) Background image: courtesy ESO - B68 with VLT ANTU and FORS 1 L 3 - Stellar Evolution I: November-December, 2006

  5. Time scales: low mass star formation L 3 - Stellar Evolution I: November-December, 2006

  6. Generic types of theories of collapse analytical semi-analytical numerical L 3 - Stellar Evolution I: November-December, 2006

  7. Jeans (1927) MNRAS 87, 720 On Liquid Stars Joel Tholine (1982) Hydrodynamic Collapse Fundamental Cosmic Physics Vol. 8, pp. 1-82 L 3 - Stellar Evolution I: November-December, 2006

  8. Early Work Basic Insights L 3 - Stellar Evolution I: November-December, 2006

  9. density x10 x 2 time L 3 - Stellar Evolution I: November-December, 2006

  10. Self-similarity solutions Isothermal spherical collapse Penston 1969, MNRAS 144, 425 Larson 1969, MNRAS 145, 271 Shu 1977, ApJ 214, 488 Hunter 1977, ApJ 218, 834 L 3 - Stellar Evolution I: November-December, 2006

  11. Mass Definition Continuity Equation Momentum equation eos L 3 - Stellar Evolution I: November-December, 2006

  12. Similarity Variable L 3 - Stellar Evolution I: November-December, 2006

  13. L 3 - Stellar Evolution I: November-December, 2006

  14. Palla & Stahler call this Eq the isothermal Lane-Emden equation LE derived for polytropes ( P = k r n ), e.g.fully convective stars: n=3/2 (=1+1/m) L 3 - Stellar Evolution I: November-December, 2006

  15. density velocity LP = Larson, Penston H = Hunter EW = Expansion Wave (Shu) L 3 - Stellar Evolution I: November-December, 2006

  16. density velocity LP = Larson, Penston H = Hunter EW = Expansion Wave (Shu) supersonic L 3 - Stellar Evolution I: November-December, 2006

  17. centrally condensed Bonnor 1956 MNRAS 116, 351 flat distribution Shu 1977 extreme case L 3 - Stellar Evolution I: November-December, 2006

  18. Inside-out collapse (Shu 1977) Mass accretion rate a constant of the cloud Mass accretion time scale L 3 - Stellar Evolution I: November-December, 2006

  19. Foster & Chevalier 1993 Numerical simulations of non-singular isothermal spheres Like Hunter 1977: 1 solution has Shu’s EW as 1 limit models resemble LP with infall v ~ - 3 cs (homologous inflow) Why Shu 1977 commonly used ? (in particular, dM/dt = constant) L 3 - Stellar Evolution I: November-December, 2006

  20. Foster & Chevalier 1993, ApJ 416, 311 r -3/2 r -2 Initial & boundary conditions density (t = 0 at core formation; t ~ 2 tff) L 3 - Stellar Evolution I: November-December, 2006

  21. Foster & Chevalier Cloud boundary xmax = 6.541 compressional luminosity: pre-core formation L 3 - Stellar Evolution I: November-December, 2006

  22. Tscharnuter 1d models of 1 Mo collapse: 1st core formation 0.01 Mo Foster & Chevalier Cloud boundary xmax = 6.541 compressional luminosity: pre-core formation L 3 - Stellar Evolution I: November-December, 2006

  23. Inside-out collapse (Shu 1977) Why Shu 1977 commonly used ? ...computational convenience ...small number of parameters L 3 - Stellar Evolution I: November-December, 2006

  24. Gravitational collapse: Example inside-out (Shu 1977, ApJ 214, 488) ~ r p ~ r a p = -1.5 a = -0.5 p = -2 a= 0 not from Shu model Rinf = cstinf adapted from Hartstein & Liseau 1998, AA 332, 703 L 3 - Stellar Evolution I: November-December, 2006

  25. predicted spectral line profiles of ground state ortho- and para-water (H2O) for inside-out collapse [B 335] infall region unresolved at 557 GHz adapted from Hartstein & Liseau 1998, AA 332, 703 Herschel HIFI Sn/TA ~ 500 Jy/K and o/p = 3 assumed L 3 - Stellar Evolution I: November-December, 2006

  26. Magnetised isothermal clouds Magnetic fields neglected in hydrodynamics of isothermal spheres: not important ?... Book Chapters 9 + 10 Examples: Krasnopolsky & Königl 2002 Self-similar collapse of rotating magnetic molecular cloud cores, ApJ 580, 987 Allen, Shu & Li 2003 Collapse of singular isothermal toroids, I. Nonrotating ApJ 599, 351 II. Rotation & magnetic braking ApJ 599, 363 L 3 - Stellar Evolution I: November-December, 2006

  27. Allen et al: Development of pseudodisk Constant mass accretion rate L 3 - Stellar Evolution I: November-December, 2006

  28. Anything missing ? L 3 - Stellar Evolution I: November-December, 2006

  29. Isothermal eos No heating and cooling processes included Spherical, nonrotating, nonmagnetic, 1 Mo definition continuity momentum energy ! rad transfer ! Winkler & Newman 1980, ApJ 236, 201; ApJ 238, 311 L 3 - Stellar Evolution I: November-December, 2006

  30. Stahler, Shu & Taam 1980, ApJ 241, 637; ApJ 242, 226 protostellar evolution during main accretion phase Pre-main-sequence evolution begins after collapse or main accretion phase L 3 - Stellar Evolution I: November-December, 2006

  31. Stahler (and Palla & Stahler ch. 11.2): stellar birthline Deuterium burning acts as a thermostat 2H(p, g)3He Reaction rates (Harris et al. 1983, ARAA 21, 165) -> temperature sensitivity Assignment: anyone? Deuterium Burning Protostellar Pulsations L 3 - Stellar Evolution I: November-December, 2006

  32. Protostar evolution of a single star Fragmentation during collapse ? L 3 - Stellar Evolution I: November-December, 2006

  33. Analytically, Tohline (1982): fragmentation of isothermal or adiabatic spheres • Isothermal collapse (G = 1): • Perturbation analysis of pressure-free sphere -> fragmentation during collapse • No preferred wavelength -> perturbations of all sizes grow at the same rate Real clouds not pressure-free and adiabatic case more relevant... L 3 - Stellar Evolution I: November-December, 2006

  34. 2.Adiabatic collapse: L 3 - Stellar Evolution I: November-December, 2006

  35. Numerically, Reid et al. 2002, ApJ 570, 231 See movie in L7 numerical simulations Rapid collapse Sheets: Burkert & Hartmann 2004 ApJ 616, 288 General discussion: Hennebelle et al. 2004, MNRAS 348, 687 L 3 - Stellar Evolution I: November-December, 2006

  36. L 3: conclusions • analytical collapse solutions differ in results • one such solution has remained `successful´: • inside-out versus outside-in collapse • similarity technique applied also to magnetised • and rotating clouds • numerical simulations indicate otherwise, but • dM/dt = constant still preferred (?) • L 3: open questions • how realistic are the assumptions made (resulting • in e.g. supersonic/subsonic flow) ? • what is the `correct eos´ ? • how important is geometry ? Initial & boundary • conditions ? L 3 - Stellar Evolution I: November-December, 2006

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