1. The Critical Neutrino Luminosity and its Observational Signatures Ondřej Pejcha with Todd Thompson, Christopher Kochanek, Basudeb Dasgupta Department of Astronomy, Ohio State University, USA (now Hubble Fellow at Princeton University)

2. Critical neutrino luminosity Neutrino mechanism: heating due to neutrinos from the PNS, the shock is revived when L > L crit (Burrows & Goshy 1993) Why does L crit exist? What are its implications for thermodynamic properties of the flow? Burrows & Goshy (1993)

3. Isothermal supernova Version of Bondi accretion - Ṁ fixed, vary c T (Pejcha & Thompson 2012)

4. Isothermal supernova

16. antesonic condition

17. Antesonic condition 0.193 ± 0.009 for a wide range of Ṁ, M, r, microphysics Pejcha & Thompson (2012) More realistic calculation (EOS, neutrino heating & cooling, Y e, dL/dr) – proved equivalence to isothermal supernova Investigated in time- dependent calculations (Couch 2012; Murphy & Meakin 2011; Dolence et al. 2012; Müller et al. 2012; Takiwaki et al. 2012; Ott et al. 2013 and others)

18. Properties of L crit Sensitivity of the neutrino mechanism to physical effects Rotation, convection and equation of state (Yamasaki & Yamada 2005, 2006; Couch 2013; Suwa et al. 2013) Different heating & cooling functions, accretion luminosity (Pejcha & Thompson 2012) Collective neutrino oscillations (Pejcha, Dasgupta & Thompson 2012) Parameters of the problem with more realistic calculation Ṁ, M, r  (Pejcha & Thompson 2012) Systematics of Ṁ (t), M(t), r (t) – which stars explode? What are the explosion and remnant properties? (Pejcha & Thompson, in preparation)

19. Synthetic supernovae Evolution of Ṁ (t), M(t), r (t), L core (t) for each progenitor Determine L crit (t) as a sequence of steady-state models Introduced parameterized artificial explosions Determine remnant masses, explosion energy (gain region mass), explosion time & neutrino luminosity Compare with observations Pejcha & Thompson (in preparation)

20. Progenitor dependence of neutrino mechanism Pejcha & Thompson (in preparation)

22. Constraints from observations Neutron star masses immediately comparable to observations – Pejcha, Thompson & Kochanek (2012)

23. Double neutron stars probe supernova mechanism Bayesian comparison of supernova explosion models –Double neutron stars → birth masses –Piston-driven explosion models of Zhang, Woosley & Heger (2008) – piston at S/N A = 4 k B and iron core –No SN progenitors subject to binary evolution –Progenitors independent/correlated with uniform/twin P(q) –Fallback/no fallback Pejcha, Thompson & Kochanek (2012)

24. Example: best model no fallback NS mass = iron core mass

25. Double neutron stars probe supernova mechanism Explosion initiated at iron core No fallback Implications for nucleosynthesis, explosion energies etc.

26. Conclusions Understanding of core-collapse supernova mechanism important for nucleosynthesis, explosion dynamics, remnant properties and their connection – observationally testable! Revival of steady-state accretion shock by neutrinos – L crit Isothermal supernova explains L crit and gives antesonic condition – diagnostic of explosion (Pejcha & Thompson 2012) Physical effects quantified through L crit (Pejcha & Thompson 2012; Pejcha, Dasgupta & Thompson 2012) L crit convolved with progenitor structure gives testable predictions Double neutron stars constrain the explosion mechanism (Pejcha, Thompson & Kochanek 2012)

27. Backup slides

28. Which stars explode? Smartt (2009)

29. Mass cut separating remnant and ejecta low NS masshigh NS mass Iron core

30. Stalled accretion shock Janka (2001) L

31. Example: bad model with fallback

32. Critical neutrino luminosity 1D steady-state calculation between PNS surface and shock (Burrows & Goshy 1993, Yamasaki & Yamada 2005, 2007) Reason for existence of L crit unknown Relation of L crit to quantities measurable in simulations unknown

33. What are the properties of the explosions? ? ? Smartt (2009), Janka (2012)

34. What are the properties of the remnants and the nucleosynthetic yields?

35. What are the properties of neutron stars and black holes? Özel et al. (2012)

36. What is the mechanism of core-collapse supernova explosion? Parameterized 3D simulation of Nordhaus et al. (2010)

37. Collective neutrino oscillations Three neutrino flavors emanating from PNS Little absorption of x in the important region Possibility of self-induced flavor conversion and enhanced heating rate Suppressed by matter effects (interaction with e + /e - ) Pejcha, Dasgupta & Thompson (2012)

38. Dynamical effects Yamasaki & Yamada (2007): overstable modes below L crit 1D time-dependent calculation (Fernandez 2012) – explosions before L crit Yamasaki & Yamada (2005): stable for L ≤ L crit

40. Antesonic condition Couch (2012) – evaluated at maximal shock radii, antesonic ratio normalized to expected value antesonic condition useful diagnostic of proximity to explosion Murphy & Meakin (2011), Dolence et al. (2012), Müller et al. (2012), Takiwaki et al. (2012)

41. Critical sound speed For fixed parameters, there is critical c T above which accretion with shock impossible, because boundary condition cannot be satisfied Coordinates of the critical point calculated analytically – antesonic condition

42. A more realistic calculation 1D steady-state accretion shock problem –Optically-thin heating & cooling –Equation of state: relativistic electrons and positrons with chemical potential and nonrelativistic free protons and neutrons –Boundary value problem for a system of 1 st order nonlinear differential equations with one boundary free (shock radius is eigenvalue) Boundary conditions –Two shock jump conditions – Ṁ fixed everywhere –Y e = 26/56 at shock –L = L core at the neutrinosphere

44. Many simulations fail to revive the shock wave Core collapse Buras et al. (2006)

45. Multi-dimensional effects

46. Accretion luminosity Up to ~25% reduction of L crit

47. Multi-dimensional effects 1D, 2D and 3D from Nordhaus et al. (2010) Murphy & Burrows (2008), Nordhaus et al. (2010), Hanke et al. (2011), Couch (2012)

48. Time dependence and explosions Time dependence – Fernández (2012) Systematics with Ṁ (t), M(t), r (t) – which stars explode? What are the explosion and remnant properties? L crit – systematic way for making observable predictions of the neutrino mechanism How are progenitors different? Pejcha & Thompson (in preparation)

49. Progenitor dependence of neutrino mechanism Woosley, Heger & Weaver (2002) progenitors

50. Progenitor dependence of neutrino mechanism Janka (2001) L

51. Progenitor dependence of neutrino mechanism Woosley, Heger & Weaver (2002) progenitors with GR1D (O’Connor & Ott 2010)

52. Synthetic supernovae

53. Observed properties f = 0.3f = 0.4

54. Boundary conditions

59. Different physics

61. wave heating from Metzger et al. (2007)

62. Time dependence and explosions Linear stability analysis (radial, non-radial) builds on steady-state solutions Isothermal (and adiabatic) supernova Gradual increase of complexity (realistic equation of state, progressively more complex radiation transport) Possibility of yet undiscovered instability as a result of accretion luminosity Systematics with Ṁ, M, r – which stars explode?

63. Multi-dimensional effects convection (Burrows et al. 1995), Standing Accretion Shock Instability (SASI) and/or advective-acoustic instability (Blondin et al. 2003, Foglizzo 2002), acoustic mechanism (Burrows et al. 2006) Burrows et al. (2006)

64. Multi-dimensional effects