1. Merger Simulations (examining the onset and outcome of various instabilities) Joel E. Tohline Louisiana State University Collaborators: J. Frank, P. Motl, W. Even, D. Marcello, G. Clayton, C. Fryer, S. Diehl

2. Part I: Broad Context 9/03/2009LSU: Physics & Astronomy Colloquium

3. Double White Dwarfs (DWDs) 9/03/2009LSU: Physics & Astronomy Colloquium

4. Binary System Parameters (circular orbit; point-mass system) 9/03/2009LSU: Physics & Astronomy Colloquium

5. Binary System Parameters (circular orbit; point-mass system) Sufficient to specify: M, q, P orb 9/03/2009LSU: Physics & Astronomy Colloquium

6. Binary System Parameters (circular orbit; WD mass-radius relationship) R1R1 R2R2 a M2M2 M1M1 9/03/2009LSU: Physics & Astronomy Colloquium

7. Binary System Parameters (circular orbit; WD mass-radius relationship) R1R1 R2R2 a M2M2 M1M1 9/03/2009LSU: Physics & Astronomy Colloquium

8. Binary System Parameters (mass-transfer system) R1R1 R2R2 a M2M2 M1M1 donor 9/03/2009LSU: Physics & Astronomy Colloquium

9. Binary System Parameters (circular orbit; point-mass system) Sufficient to specify: M, q, P orb 9/03/2009LSU: Physics & Astronomy Colloquium

10. (slide stolen from this past Friday’s talk by Nelemans) 9/29/2009Lorentz Center: Stellar Mergers

11. (slide stolen from this past Friday’s talk by Nelemans) 9/29/2009Lorentz Center: Stellar Mergers

12. Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers

13. Gravitational-Wave Detectors 9/03/2009LSU: Physics & Astronomy Colloquium

14. Hanford Observatory Livingston Observatory Laser Interferometer Gravitational-wave Observatory (LIGO) 9/03/2009LSU: Physics & Astronomy Colloquium

15. Laser Interferometer Gravitational-wave Observatory (LIGO)

16. Gravitational-Wave Signal characterized by amplitude “h” and frequency “f” 9/03/2009LSU: Physics & Astronomy Colloquium

17. Gravitational-Wave Signal characterized by amplitude “h” and frequency “f” From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium

18. Classic “chirp” Signal due to point-mass binary inspiral From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium

19. Classic “chirp” Signal due to point-mass binary inspiral From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium

20. Classic “chirp” Signal due to point-mass binary inspiral From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium During inspiral: h ~ f 2/3

21. High-Frequency Sources of Gravitational Radiation Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

22. Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

23. Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

24. Radiation from Hulse-Taylor Pulsar Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

25. Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

26. Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

27. Low-Frequency Sources of Gravitational Radiation Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

28. Laser-Interferometer Space Antenna (LISA) 9/03/2009LSU: Physics & Astronomy Colloquium

29. High-Frequency Sources of Gravitational Radiation Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

30. DWD Orbit Evolutions in LISA’s Strain-Frequency Domain 9/03/2009LSU: Physics & Astronomy Colloquium [Kopparapu & Tohline (2007)]

31. DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium “detached” inspiral “mass-transferring” out-spiral

32. DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium

33. DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium “detached” inspiral “mass-transferring” out-spiral

34. DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium

35. DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium

36. Part II: This Work 9/03/2009LSU: Physics & Astronomy Colloquium

37. General Context of this Work Onset and nonlinear development of mass-transfer in Double White Dwarf (DWD) binaries – Initiated by Roche Lobe Overflow (RLOF) – Followed through  40 orbits. Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion 9/29/2009Lorentz Center: Stellar Mergers

38. General Context of this Work Onset and nonlinear development of mass-transfer in Double White Dwarf (DWD) binaries – Initiated by Roche Lobe Overflow (RLOF) – Followed through  40 orbits. Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion 9/29/2009Lorentz Center: Stellar Mergers

39. General Context of this Work Onset and nonlinear development of mass-transfer in Double White Dwarf (DWD) binaries – Initiated by Roche Lobe Overflow (RLOF) – Followed through  40 orbits. Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion 9/29/2009Lorentz Center: Stellar Mergers

40. General Context of this Work Onset and nonlinear development of mass-transfer in Double White Dwarf (DWD) binaries – Initiated by Roche Lobe Overflow (RLOF) – Followed through  40 orbits. Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion 9/29/2009Lorentz Center: Stellar Mergers

41. General Context of this Work Onset and nonlinear development of mass-transfer in Double White Dwarf (DWD) binaries – Initiated by Roche Lobe Overflow (RLOF) – Followed through  40 orbits. The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH 9/29/2009Lorentz Center: Stellar Mergers

42. General Context of this Work Onset and nonlinear development of mass-transfer in Double White Dwarf (DWD) binaries – Initiated by Roche Lobe Overflow (RLOF) – Followed through  40 orbits. The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH 9/29/2009Lorentz Center: Stellar Mergers

43. 0; Pure Hydro 0 ; 9/29/2009Lorentz Center: Stellar Mergers

44. General Context of this Work Equation of state: While we have used a zero- temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (  = 5/3 adiabatic) flows – a reasonably good approximation for low-mass white dwarfs – broadly appealing because polytropes are scale-free Effects of photon radiation ignored (until very recently) Keeping the “micro-physics” simple … – makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation – Makes it easier to ascertain what is physics and what is purely numerical 9/29/2009Lorentz Center: Stellar Mergers

45. General Context of this Work Equation of state: While we have used a zero- temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (  = 5/3 adiabatic) flows – a reasonably good approximation for low-mass white dwarfs – broadly appealing because polytropes are scale-free Effects of photon radiation ignored (until very recently) Keeping the “micro-physics” simple … – makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation – Makes it easier to ascertain what is physics and what is purely numerical 9/29/2009Lorentz Center: Stellar Mergers

46. General Context of this Work Equation of state: While we have used a zero- temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (  = 5/3 adiabatic) flows – a reasonably good approximation for low-mass white dwarfs – broadly appealing because polytropes are scale-free Effects of photon radiation ignored (until very recently) Keeping the “micro-physics” simple … – makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation – Makes it easier to ascertain what is physics and what is purely numerical 9/29/2009Lorentz Center: Stellar Mergers

47. General Context of this Work Equation of state: While we have used a zero- temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (  = 5/3 adiabatic) flows – a reasonably good approximation for low-mass white dwarfs – broadly appealing because polytropes are scale-free Effects of photon radiation ignored (until very recently) Keeping the “micro-physics” simple … – makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation – Makes it easier to ascertain what is physics and what is purely numerical 9/29/2009Lorentz Center: Stellar Mergers

48. General Context of this Work Equation of state: While we have used a zero- temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (  = 5/3 adiabatic) flows – a reasonably good approximation for low-mass white dwarfs – broadly appealing because polytropes are scale-free Effects of photon radiation ignored (until very recently) Keeping the “micro-physics” simple … – makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation – Makes it easier to ascertain what is physics and what is purely numerical 9/29/2009Lorentz Center: Stellar Mergers

49. General Context of this Work Equation of state: While we have used a zero- temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (  = 5/3 adiabatic) flows – a reasonably good approximation for low-mass white dwarfs – broadly appealing because polytropes are scale-free Effects of photon radiation ignored (until very recently) Keeping the “micro-physics” simple … – makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation – Makes it easier to ascertain what is physics and what is purely numerical 9/29/2009Lorentz Center: Stellar Mergers

50. Some Theoretical Considerations “Darwin Instability” – Has been mentioned several different times over the course of this workshop as relevant to mergers (e.g., DWDs and WUMa systems) – Point along a (synchronously rotating) binary inspiral sequence at which J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability  loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

51. Some Theoretical Considerations “Darwin Instability” – Has been mentioned several different times over the course of this workshop as relevant to mergers (e.g., DWDs and W UMa systems) – Point along a (synchronously rotating) binary inspiral sequence at which J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability  loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

52. Some Theoretical Considerations “Darwin Instability” – Has been mentioned several different times over the course of this workshop as relevant to mergers (e.g., DWDs and W UMa systems) – Point along a (synchronously rotating) binary inspiral sequence at which J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability  loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

53. Some Theoretical Considerations “Darwin Instability” – Has been mentioned several different times over the course of this workshop as relevant to mergers (e.g., DWDs and W UMa systems) – Point along a (synchronously rotating) binary inspiral sequence at which J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability  loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

54. Equal-mass DWD Sequences 9/29/2009Lorentz Center: Stellar Mergers New & Tohline 1997

55. Equal-mass DWD Sequences 9/29/2009Lorentz Center: Stellar Mergers New & Tohline 1997 Minimum J

56. Equal-mass DWD Sequences 9/29/2009Lorentz Center: Stellar Mergers New & Tohline 1997 Contact

57. Unequal-mass (q = ½) DWD Sequence 9/29/2009Lorentz Center: Stellar Mergers Evan & Tohline 2009

58. Unequal-mass (q = ½) DWD Sequence 9/29/2009Lorentz Center: Stellar Mergers Evan & Tohline 2009 Contact

59. Some Theoretical Considerations “Darwin Instability” (cont.) – Not relevant to the onset of mass-transfer in DWD binaries because the less massive star fills its Roche Lobe before the binary reaches J min along its inspiral sequence. 9/29/2009Lorentz Center: Stellar Mergers

60. Some Theoretical Considerations Mass-Transfer Instability – Once the less massive WD (donor) fills its Roche Lobe and begins to transfer mass to its more massive companion (accretor)… Donor’s radius expands:  don =  lnR don /  lnM don Roche geometry readjusts:  RL =  lnR RL /  lnM don – Parameter, D = ½(  don –  RL ), governs stability … Stable against further mass-transfer if D > 0 Dynamically unstable if D < 0 9/29/2009Lorentz Center: Stellar Mergers

61. Some Theoretical Considerations Mass-Transfer Instability – Once the less massive WD (donor) fills its Roche Lobe and begins to transfer mass to its more massive companion (accretor)… Donor’s radius expands:  don =  lnR don /  lnM don Roche geometry readjusts:  RL =  lnR RL /  lnM don – Parameter, D = ½(  don –  RL ), governs stability … Stable against further mass-transfer if D > 0 Dynamically unstable if D < 0 9/29/2009Lorentz Center: Stellar Mergers

62. Some Theoretical Considerations Mass-Transfer Instability – Once the less massive WD (donor) fills its Roche Lobe and begins to transfer mass to its more massive companion (accretor)… Donor’s radius expands:  don =  lnR don /  lnM don Roche geometry readjusts:  RL =  lnR RL /  lnM don – Parameter, D = ½(  don –  RL ), governs stability … Stable against further mass-transfer if D > 0 Dynamically unstable if D < 0 9/29/2009Lorentz Center: Stellar Mergers

63. Some Theoretical Considerations Mass-Transfer Instability (cont.) – For n = 3/2 polytropic EOS and assumption of conservative mass transfer (CMT)  don =   RL = 2q – 5/3 – Parameter, D = ½(  don –  RL ) = (2/3 – q), System stable if q < q crit = 2/3 Dynamically unstable if q > q crit 2/3 9/29/2009Lorentz Center: Stellar Mergers

64. Some Theoretical Considerations Mass-Transfer Instability (cont.) – For n = 3/2 polytropic EOS and assumption of conservative mass transfer (CMT)  don =   RL = 2q – 5/3 – Parameter, D = ½(  don –  RL ) = (2/3 – q), System stable if q < q crit = 2/3 Dynamically unstable if q > q crit 2/3 9/29/2009Lorentz Center: Stellar Mergers

65. Some Theoretical Considerations Mass-Transfer Instability (cont.) – For much more complete discussion, including important considerations of non-CMT Paczyński (1967) King & Kolb (1995) Marsh, Nelemans & Steeghs (2004) Gokhale, Peng & Frank (2007) Belczynski et al. (2008) -- StarTracks 9/29/2009Lorentz Center: Stellar Mergers

66. Key Questions [that we may be able to answer with numerical simulations] 1.At onset, is mass-transfer stable or unstable? 2.If unstable, what is the hydrodynamic outcome of instability? 3.Do results depend on choice of numerical algorithm? 4.How does outcome depend on the system’s ability to cool (via photon radiation)? 5.What about super-Eddington accretion? 9/29/2009Lorentz Center: Stellar Mergers

67. 1. Is mass-transfer stable or unstable? We’ll discuss this question in the context of an “M tot - q 0 ” parameter-space diagram that contains a hypothetical population of newborn double white dwarf binaries … 9/29/2009Lorentz Center: Stellar Mergers

68. 1. Is mass-transfer stable or unstable? We’ll discuss this question in the context of an “M tot - q 0 ” parameter-space diagram that contains a hypothetical population of newborn double white dwarf binaries … 9/29/2009Lorentz Center: Stellar Mergers

69. Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers

70. Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers

71. Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers ** NOT ** precursors for Type Ia SNe

72. 1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit  2/3 – But maybe, q crit  1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

73. 1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit  2/3 – But maybe, q crit  1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

74. 1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit  2/3 – But maybe, q crit  1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

75. 1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit  2/3 – But maybe, q crit  1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

76. 1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit  2/3 – But maybe, q crit  1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

77. If q crit = 2/3 … 9/29/2009Lorentz Center: Stellar Mergers Stable mass-transfer q crit

78. 1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit  2/3 – But maybe, q crit  1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

79. If q crit = 1/5 … 9/29/2009Lorentz Center: Stellar Mergers Stable mass-transfer q crit

80. 1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit  2/3 – But maybe, q crit  1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

81. q 0 = 0.5 (stable mass-transfer) 9/29/2009Lorentz Center: Stellar Mergers

82. 2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

83. 2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

84. 2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

85. 2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

86. 2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

87. q 0 = 0.7 (tidal disruption of donor) 9/29/2009Lorentz Center: Stellar Mergers

88. What is hydrodynamic outcome of instability? 9/29/2009Lorentz Center: Stellar Mergers Credit: W. Even

89. What is hydrodynamic outcome of instability? 9/29/2009Lorentz Center: Stellar Mergers Credit: W. Even

90. What is hydrodynamic outcome of instability? 9/29/2009Lorentz Center: Stellar Mergers Credit: W. Even 00

91. 2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

92. If q crit = 2/3 and q merge = 0.9 … 9/29/2009Lorentz Center: Stellar Mergers Stable mass-transfer Tidal disruption of donor Donor plunges into accretor q crit q merge

93. 3. Do Results Depend on Choice of Numerical Algorithm? We are in the middle of a collaborative project in which an extensive set of binary simulations is being carried out to compare results from two very different numerical algorithms: – Our grid-based, finite-volume hydrocode [P. Motl, W. Even, J.E. Tohline] – A smoothed-particle hydrocode (SPH) used by Fryer’s group at LANL [S. Diehl, C. Fryer] Preliminary report: Amazingly good agreement for unstable (i.e., merger or tidal disruption) evolutions if … – Simulations start from identical “quiet” starts; – The number of SPH particles is comparable to number of grid cells. 9/29/2009Lorentz Center: Stellar Mergers

94. 3. Do Results Depend on Choice of Numerical Algorithm? We are in the middle of a collaborative project in which an extensive set of binary simulations is being carried out to compare results from two very different numerical algorithms: – Our grid-based, finite-volume hydrocode [P. Motl, W. Even, J.E. Tohline] – A smoothed-particle hydrocode (SPH) used by Fryer’s group at LANL [S. Diehl, C. Fryer] Preliminary report: Amazingly good agreement for unstable (i.e., merger or tidal disruption) evolutions if … – Simulations start from identical “quiet” starts; – The number of SPH particles is comparable to number of grid cells. 9/29/2009Lorentz Center: Stellar Mergers

95. 3. Do Results Depend on Choice of Numerical Algorithm? We are in the middle of a collaborative project in which an extensive set of binary simulations is being carried out to compare results from two very different numerical algorithms: – Our grid-based, finite-volume hydrocode [P. Motl, W. Even, J.E. Tohline] – A smoothed-particle hydrocode (SPH) used by Fryer’s group at LANL [S. Diehl, C. Fryer] Preliminary report: Amazingly good agreement for unstable (i.e., merger or tidal disruption) evolutions if … – Simulations start from identical “quiet” starts; – The number of SPH particles is comparable to number of grid cells. 9/29/2009Lorentz Center: Stellar Mergers

96. Do Results Depend on Choice of Numerical Algorithm? 9/29/2009Lorentz Center: Stellar Mergers LSU grid code LANL SPH code 10 6 particles10 5 particles

97. 4. How Does Outcome Depend on System’s Ability to Cool? In our collaboration with the LANL group, we are also examining two extremes: – Using an “ideal-gas” equation of state, the accreted layers trap all of the heat that is generated through the accretion shock (no cooling) – Using a “polytropic” equation of state, the accreted layers are allowed to cool back down to the specific entropy of the donor material Preliminary report: Unstable (i.e., merger or tidal disruption) evolutions change only in relatively subtle ways when the “ideal-gas” EOS is used in place of the “polytropic” EOS. (On this point, as well, there is good agreement between the SPH and grid- code simulations.) 9/29/2009Lorentz Center: Stellar Mergers

98. 4. How Does Outcome Depend on System’s Ability to Cool? In our collaboration with the LANL group, we are also examining two extremes: – Using an “ideal-gas” equation of state, the accreted layers trap all of the heat that is generated through the accretion shock (no cooling) – Using a “polytropic” equation of state, the accreted layers are allowed to cool back down to the specific entropy of the donor material Preliminary report: Unstable (i.e., merger or tidal disruption) evolutions change only in relatively subtle ways when the “ideal-gas” EOS is used in place of the “polytropic” EOS. (On this point, as well, there is good agreement between the SPH and grid- code simulations.) 9/29/2009Lorentz Center: Stellar Mergers

99. 4. How Does Outcome Depend on System’s Ability to Cool? In our collaboration with the LANL group, we are also examining two extremes: – Using an “ideal-gas” equation of state, the accreted layers trap all of the heat that is generated through the accretion shock (no cooling) – Using a “polytropic” equation of state, the accreted layers are allowed to cool back down to the specific entropy of the donor material Preliminary report: Unstable (i.e., merger or tidal disruption) evolutions change only in relatively subtle ways when the “ideal-gas” EOS is used in place of the “polytropic” EOS. (On this point, as well, there is good agreement between the SPH and grid- code simulations.) 9/29/2009Lorentz Center: Stellar Mergers

100. 4. How Does Outcome Depend on System’s Ability to Cool? 9/29/2009Lorentz Center: Stellar Mergers

101. 5. What About Super-Eddington Accretion? Up to now, our simulations have not included forcing due to a radiative flux. Hence, we have not been in a position to examine how the dynamics is altered when the accretion flow resulting from unstable mass-transfer becomes “super- Eddington”. – Does mass (and angular momentum) get ejected from the system? – Does a significant “common envelope” form as a result? We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la Hayes et al. (2006). 9/29/2009Lorentz Center: Stellar Mergers

102. 5. What About Super-Eddington Accretion? Up to now, our simulations have not included forcing due to a radiative flux. Hence, we have not been in a position to examine how the dynamics is altered when the accretion flow resulting from unstable mass-transfer becomes “super- Eddington”. – Does mass (and angular momentum) get ejected from the system? – Does a significant “common envelope” form as a result? We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la Hayes et al. (2006). 9/29/2009Lorentz Center: Stellar Mergers

103. 5. What About Super-Eddington Accretion? Up to now, our simulations have not included forcing due to a radiative flux. Hence, we have not been in a position to examine how the dynamics is altered when the accretion flow resulting from unstable mass-transfer becomes “super- Eddington”. – Does mass (and angular momentum) get ejected from the system? – Does a significant “common envelope” form as a result? We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la ZEUS-MP (Hayes et al. 2006). 9/29/2009Lorentz Center: Stellar Mergers

104. 0; Pure Hydro 0 ; 9/29/2009Lorentz Center: Stellar Mergers

105. 9/29/2009Lorentz Center: Stellar Mergers

106. 5. What About Super-Eddington Accretion? For an opacity of the form … we can write … so we can define, where, Then, f Edd > 1 means super-Eddington accretion. 9/29/2009Lorentz Center: Stellar Mergers

107. 5. What About Super-Eddington Accretion? 9/29/2009 If we actually set … then, f Edd climbs above unity (i.e., the flow becomes super- Eddington) when climbs above 10 -12. This is not good because, with present numerical techniques, we cannot resolve mass-transfer rates ( ) substantially smaller than 10 -4. Solution: Artificially lower K 1 by a factor of 10 10. Then, f Edd will climb above unity when climbs above 10 -2. Lorentz Center: Stellar Mergers

108. 5. What About Super-Eddington Accretion? 9/29/2009 If we actually set … then, f Edd climbs above unity (i.e., the flow becomes super- Eddington) when climbs above 10 -12. This is not good because, with present numerical techniques, we cannot resolve mass-transfer rates ( ) substantially smaller than 10 -4. Solution: Artificially lower K 1 by a factor of 10 10. Then, f Edd will climb above unity when climbs above 10 -2. Lorentz Center: Stellar Mergers

109. 5. What About Super-Eddington Accretion? 9/29/2009 If we actually set … then, f Edd climbs above unity (i.e., the flow becomes super- Eddington) when climbs above 10 -12. This is not good because, with present numerical techniques, we cannot resolve mass-transfer rates ( ) substantially smaller than 10 -4. Solution: Artificially lower K 1 by a factor of 10 10. Then, f Edd will climb above unity when climbs above 10 -2. Lorentz Center: Stellar Mergers

110. Very Preliminary Results from this new Radiation-Hydro code 9/29/2009Lorentz Center: Stellar Mergers

111. Very Preliminary Results from this new Radiation-Hydro code (movies not attached) 9/29/2009Lorentz Center: Stellar Mergers Credit: D. Marcello & P. Motl

112. Summary Hopefully, answers to the set of questions we are probing with hydrodynamic simulations … – Will advance our fundamental understanding of a variety of issues related stellar mergers; – Will help determine what branching ratios are appropriate to use at key points along the decision trees of stellar-population synthesis codes 9/29/2009Lorentz Center: Stellar Mergers

113. Thanks! 9/29/2009Lorentz Center: Stellar Mergers