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GRBs from Compact Binary Mergers

GRBs from Compact Binary Mergers. Lecture 6: Binary Merger BHAD models – C.Fryer (UA/LANL). Accretion Disk Solution From Popham et al. 1999. In the optically-thin limit, the relativistic Solution of a Black Hole Accretion Disk Model can be Solved! But not all disks

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GRBs from Compact Binary Mergers

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  1. GRBs from Compact Binary Mergers Lecture 6: Binary Merger BHAD models – C.Fryer (UA/LANL)

  2. Accretion Disk Solution From Popham et al. 1999 In the optically-thin limit, the relativistic Solution of a Black Hole Accretion Disk Model can be Solved! But not all disks Are optically thin.

  3. Models With Modified Potentials Seem to Get the Same Rough Result, At least At large Radii! MacFadyen & Woosley

  4. Two Jet Drivers: Neutrinos & e+,e- pair plasma Neutrino Annihilation Scattering Absorption Densities above 1010-1011 g cm-3 Temperatures above a few MeV Disk Cools via Neutrino Emission

  5. Two Engine Drives – Neutrinos & Magnetic Fields • Source of Magnetic Field – Dynamo in accretion disk. • Source of Jet Energy - I) Accretion Disk II) Black Hole Spin

  6. Can Solve The neutrino Engine, and It places Severe Constraints On the Progenitor. For Magnetic Fields, Anything Goes!

  7. Compact Binary Mergers • Binary Terminology • NS/NS mergers – formation scenarios and simulations • BH/NS mergers • BH/WD mergers • Rates and Distribution – comparison to observations

  8. Black Hole Accretion Disk System: Binaries • Neutron Star – Neutron Star Mergers (Hulse-Taylor Pulsar System) • Black Hole – Neutron Star Mergers • Black Hole – White Dwarf Mergers

  9. Binary Evolution is Important for nearly All GRB progenitors! For merging binaries, It is essential that The binaries be Close. • Massive Star – Star that, if not affected by binary mass transfer would undergo core-collapse (MSN~ 8-10 solar masses) Definition of Terms: Fryer, Woosley & Hartmann 1999

  10. Definition of Terms: • Roche-Lobe Overflow: When a star expands (in the giant or supergiant branch) in a binary, the outer layers of the star may feel greater gravitational attraction to the companion star, causing this material to “overflow” onto that companion. • Common Envelope Evolution (CE): If this overflow proceeds faster than the companion star can accrete material, the expanding star envelops the companion, leading to two stellar cores within a single common envelope. Primary or Secondary or

  11. Definition of Terms: • Black Hole Mass (MBH) – transition mass for black hole formation. • He core – helium core of massive star: helium core masses will also have transitions for neutron star and black hole formation. • Mp,Ms – masses of primary (most massive) and secondary (least massive) stars in a binary. Fryer, Woosley & Hartmann 1999

  12. NS-NS binaries • (also known as Double • Neutron Star Binaries) • 3 primary mechanisms • exist: • I) Primary collapses to a NS. • Common envelope evolution • tightens binary so that a close • NS-NS binary is formed after • the collapse of the secondary.

  13. NS-NS binaries • (also known as Double • Neutron Star Binaries) • 3 primary mechanisms exist: • I) Primary collapses to a NS. • Common envelope evolution • tightens binary so that a close • NS-NS binary is formed after • the collapse of the secondary. • II) Both stars evolve off the • main sequence at roughly • the same time. Hydrogen • and Helium CE phases • tighten binary.

  14. NS-NS binaries • (also known as Double • Neutron Star Binaries) • 3 primary mechanisms exist: • I) Primary collapses to a NS. • Common envelope evolution • tightens binary so that a close • NS-NS binary is formed after • the collapse of the secondary. • II) Both stars evolve off the • main sequence at roughly • the same time. Hydrogen • and Helium CE phases • tighten binary. • III) No common envelope phase. • Well placed NS kick creates • a tight binary.

  15. For most equations of state, NS-NS mergers produce A black hole surrounded by An accretion disk. Equatorial view of disk Conditions – density, Temperature, electron Fraction and entropy Ruffert & Janka 1999

  16. Disk Structure for NS-NS Mergers Densities exceed 1011 g cm-3, Temperatures exceed a few MeV, Disk masses range from 0.03-0.25 solar masses Ruffert & Janka 1999

  17. NS-NS Mergers – Neutrino Emission These dense, hot disks emit copious neutrinos ~1053 erg/s

  18. Neutrino Annihilation Strongest Along the Orbital Axis Energy Deposition can exceed a few times 1049 erg

  19. NS-NS Merger: Neutrino-Driven Mechanism

  20. NS-NS Mergers Disk profiles leave a vacuum along the orbital axis. This opening funnels the explosion. Although it will not produce few degree jets without the aid of magnetic fields, it does produced beamed explosions. Ruffert et al. 1997

  21. BH-NS binaries • 3 primary mechanisms exist: • I) Primary collapses to a BH. • Common envelope evolution • tightens binary so that a close • BH-NS binary is formed after • the collapse of the secondary. • Similar to Scenario I for NS-NS • binary formation.

  22. BH-NS binaries • 3 primary mechanisms exist: • I) Primary collapses to a BH. • Common envelope evolution • tightens binary so that a close • BH-NS binary is formed after • the collapse of the secondary. • Similar to Scenario I for NS-NS • binary formation. • II) Primary collapses to a NS. But • in common envelope phase, it • accretes too much material • and collapses to form BH.

  23. BH-NS binaries • 3 primary mechanisms exist: • I) Primary collapses to a BH. • Common envelope evolution • tightens binary so that a close • BH-NS binary is formed after • the collapse of the secondary. • Similar to Scenario I for NS-NS • binary formation. • II) Primary collapses to a NS. But • in common envelope phase, it • accretes too much material • and collapses to form BH. • III) No common envelope phase. • Well placed NS kick creates • a tight binary.

  24. Why the Oscillatory Orbital Behavior Inward Motion: Gravitational Wave emission tightens orbit Outward Motion: Orbital Angular Momentum conservation means that as the lower-mass neutron star accretes onto the black hole, the orbit will expand. But orbital angular momentum is not entirely conserved. NS Expansion: NSs expand as they lose mass

  25. Transport of Angular Momentum DJorb = - a1DM(1-b) v r - a2DM b v r r=a (r is orbital separation) v2/a = G (MBH+MNS)/a2 Eq. 1) vr=[G(MNS+MBH)a]0.5 =jsystem Specific angular momentum of system a1 = jejected/jsystem = specific angular momentum of material ejected divided by specific angular momentum of system a2 = jspin+disk/jsystem = specific angular momentum of material which goes into spinning up the black hole or into an accretion disk divided by specific angular momentum of system

  26. DM = Mass lost by neutron star b = fraction of mass lost by the neutron star which is accreted onto the black hole. (1-b) mass ejected by system Eq. 1 dMNS= -DM dJ/dMNS =a1 (1-b) [Ga(MNS+MBH)]0.5 + a2b [Ga(MNS+MBH)]0.5 But we also know the total orbital angular momentum: Jorb = [Ga/(MNS+MBH)]0.5 MNSMBH From which we can calculate the derivative: dJorb/dMNS = d/dMNS G0.5a0.5/(MNS+MBH)0.5 MNSMBH

  27. dJorb/dMNS = d/dMNS G0.5a0.5/(MNS+MBH)0.5 MNSMBH = da/dMNS [Ga/(MNS+MBH)]0.5/2a MNS MBH +d(MNS+MBH)/dMNS[Ga/(MNS+MBH)]0.5/[-2(MNS+MBH)]MNSMBH +dMNS/dMNS[Ga/(MNS+MBH)]0.5MBH +dMBH/dMNS[Ga/(MNS+MBH)]0.5MNS Eq. 2 Comparing Eq. 1 to Eq. 2 and solving for da, we get: da/a = [2a1(1-b)+2a2b] (MNS+MBH)/(MNSMBH)dMNS + d(MNS+MBH)/(MNS+MBH) – 2dMNS/MNS – 2dMBH/MBH Simplify First Term (MNS+MBH)/(MNSMBH)dMNS =dMNS/MBH+dMNS/MNS =-1/b dMBH/MBH +dMNS/MNS dMBH=-bdMNS da/a = [2a1(1-b)+2a2b] [-1/b dMBH/MBH+dMNS/MNS] + d(MNS+MBH)/(MNS+MBH) – 2dMNS/MNS – 2dMBH/MBH

  28. da/a = [2a1(1-b)+2a2b] [-1/b dMBH/MBH+dMNS/MNS] + d(MNS+MBH)(MNS+MBH) – 2dMNS/MNS – 2dMBH/MBH Integrate lna = [2a1(1-b)+2a2b]/-b lnMBH + [2a1(1-b)+2a2b] lnMNS+ ln(MNS+MBH) – 2lnMNS – 2lnMBH a/a0 = (MNS+MBH)/(M0NS+M0BH) (MNS/M0NS) C1 (MBH/M0BH)C2 where C1 = 2a1(1-b)+2a2b-2 C2 = -2a1(1-b)/b-2a2-2

  29. Energy Deposition From Neutrino Annihilation

  30. NS/BH – Neutrino Driven Mechanism

  31. BH-WD binaries • 3 primary mechanisms exist: • I) Primary collapses to a BH. • Secondary becomes a WD. • Magnetic braking tightens • binary until it merges.

  32. BH-WD binaries • 3 primary mechanisms exist: • I) Primary collapses to a BH. • Secondary becomes a WD. • Magnetic braking tightens • binary until it merges. • II) Primary collapses to a NS or • BH. Common envelope phase • causes the NS to become a • BH and tightens binary.

  33. BH-WD binaries • 3 primary mechanisms exist: • I) Primary collapses to a BH. • Secondary becomes a WD. • Magnetic braking tightens • binary until it merges. • II) Primary collapses to a NS or • BH. Common envelope phase • causes the NS to become a • BH and tightens binary. • III) No common envelope phase. • Well placed NS kick creates • a tight binary.

  34. White Dwarf’s orbit also Expands due to angular Momentum conservation. The white dwarf also Expands as it loses Mass. But the WD is disrupted At much larger radii Than the NS (hence, The disk has much More angular momentum and accretes at lower Rates) Fryer et al. 1999

  35. Mass Transfer Rates More than An order of Magnitude Lower Than NS/BH mergers

  36. WD/BH Mergers - Summary

  37. Formation Rates Dependence On Kick Velocities

  38. Comparing To Observations

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