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Vicky Kalogera

Department of Physics and Astronomy. Formation of Double Neutron Stars: Kicks and Tilts. Vicky Kalogera. with Bart Willems Mike Henninger. In this talk …. Pulsars and Recycling Double Neutron Star Formation The Double Pulsar PSR J0737-3039 Evolution constraints

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Vicky Kalogera

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  1. Department of Physics and Astronomy Formation of Double Neutron Stars: Kicks and Tilts Vicky Kalogera with Bart Willems Mike Henninger

  2. In this talk … • Pulsars and Recycling • Double Neutron Star Formation • The Double Pulsar PSR J0737-3039 • Evolution constraints • Kinematics constraints • Expected kicks and spin tilts • PSR B1913+16 and B1534+12

  3. Highly magnetized rapidly rotating neutron stars whose magnetic field axis is inclined with respect to their rotation axis lighthouse effect Spin period of a few seconds Spin-down time scale of a few 10-100Myr Pulsars http://imagine.gsfc.nasa.gov/docs/science/know_l1/pulsars.html

  4. Magnetic field: ~ 109-1010 G Spin period: < 100ms Spin-down time scale: ~ 100Gyr Old neutron stars which are recycled (spun-up) by mass accretion and the associated transport of angular momentum from a close binary companion Millisecond Pulsars http://chandra.harvard.edu/resources/illustrations/blackholes2.html

  5. NS-NS Formation Channel from Tauris & van den Heuvel 2003 How do Double Neutron Stars form ? current properties constrain NS #2 formation process: • NS kick • NS progenitor

  6. NS-NS Formation Channel animation credit: John Rowe

  7. Component A 23 ms pulsar fastest known DNS pulsar spin Orbital period 2.4 hours closest known DNS orbit Eccentricity 0.09 least eccentric of all known DNS binaries Periastron advance 16.9° per year fastest of all known DNS binaries PSR J0737-3039 Properties Burgay et al. 2003

  8. Coalescence time 85 Myr shortest of all known DNS binaries Drastic increase by a factor of 6-7 in estimates for gravitational wave detections by ground-based interferometers PSR J0737-3039 Properties Kalogera et al. 2004

  9. Component B 2.8s pulsar FIRST known DOUBLE PULSAR system! Inclination close to 90° eclipses unique probe into magnetospheric physics PSR J0737-3039 Properties Lyne et al. 2004 Remarkable progenitor constraints next … Willems & VK 2004 Willems, VK, Henninger 2004

  10. Post-SN orbital separation (A) and eccentricity (e) evolve due to Gravitational Radiation equations for dA/dt and de/dt need to be integrated backwards in time what is the age of PSR J0737-3039? 2) Pre- and post-SN orbital parameters are related by conservation laws of orbital energy and orbital angular momentum 3) Constraints arise from requiring physically acceptable solutions M0-A0 diagram Derivation of Progenitor Constraints

  11. Orbital Evolution Backwards in Time Gravitational Radiation: dA/dt & de/dt Orbital separation Orbital eccentricity A = 1.54 R⊙ e = 0.119

  12. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A0≤ A(1+e) back in time

  13. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A0≤ A(1+e) back in time

  14. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A0≤ A(1+e) back in time

  15. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A0≤ A(1+e) back in time

  16. A(1-e) < A0 <A(1+e) The Pre-SN Orbital Separation

  17. If left alone, a helium star of mass M0 will reach a maximum radius R0,max(M0) For a given companion mass, the size of the helium star's critical Roche lobe is determined by the orbital separation and the helium star mass RL(M0,A0) R0,max(M0) > RL(M0,A0): detached A0 > A0,crit(M0) Detached vs. Semi-Detached Pre-SN Binary

  18. A(1-e) < A0 < A(1+e) Detached: A0 > A0,crit(M0) Detached vs. Semi-Detached Pre-SN Binary

  19. The relations between the pre- and post-SN orbital parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M0≤ M0,max( A , e , A0 , Vk ) For a given age (i.e. fixed A and e), the upper limit M0,max(A0) can be determined for every admissible value of the kick velocity Vk The Progenitor Mass of the Last-Born NS  age dependency

  20. A(1-e) < A0 < A(1+e) Detached: A0 > A0,crit(M0) Mass transfer: A0≤ A0,crit(M0) M0≤ M0,max(A0,Vk) for age of 100Myr The Progenitor Mass of the Last-Born NS

  21. A(1-e) < A0 < A(1+e) Semi-Detached Progenitors

  22. Lower limit: the helium star must form a NEUTRON STAR rather than a WHITE DWARF M0≥ 2.1Mo(Habets 1986) Upper limit: the binary mass ratio cannot be too extreme if runaway mass transfer leading to a merger is to be avoided M0/MNS≤ 3.5 (Ivanova et al. 2003) M0≤ 4.7Mo The Helium Star Progenitor Mass Revisited

  23. A(1-e) < A0 < A(1+e) M0≥ 2.1Mo M0≤ 4.7Mo The Progenitor Mass of the Last-Born NS

  24. A(1-e) < A0 < A(1+e) M0≥ 2.1Mo M0≤ 4.7Mo M0≤ M0,max(A0,Vk) for age of 0Myr The Minimum Kick Velocity

  25. A(1-e) < A0 < A(1+e) M0≥ 2.1Mo M0≤ 4.7Mo M0≤ M0,max(A0,Vk) for age of 100Myr The Minimum Kick Velocity

  26. An upper limit on the magnitude of the kick velocity is set by the requirement that the binary must remain bound after the SN explosion depends on constraints on pre-SN orbital separation and helium star mass for 1.15Ro≤ A0≤ 1.72Roand 2.1Mo≤ M0≤ 4.7Mo the maximum possible kick velocity is 1660km/s The Maximum Kick Velocity

  27. PSR J0737-3039 Pulsar B's helium star progenitor is most likely transferring mass to the first-born NS NS progenitor mass: 2 Mo ≤ M0 ≤ 4.7 Mo Kick magnitude: 60 km/s ≤ Vk≤ 1660 km/s Conclusions

  28. polar angle between pre-SN orbital velocity V0 and kick velocity Vk The Kick Direction 0 Kalogera (2000) NS1 azimuthal angle in plane ^ to V0

  29. Given a kick velocity Vk : REAL solutions for a finite number of kick directions The Kick Direction Vk = 200km/s Vk = 500km/s

  30. The Kick Direction Kick is generally directed opposite to the orbital motion Regardless of Vk and age: q > 115°

  31. For a given kick velocity Vk : M0 and A0 constraints translate to polar angle constraints Isotropic Kicks Bayes' theorem Isotropic Kicks Vk M1≤ M0≤ M2 A1≤ A0≤ A2 q1≤q≤q2 f1≤ f≤f2

  32. The Most Probable Isotropic Kick Velocity

  33. PSR J0737-3039 Pulsar B's helium star progenitor is most likely transferring mass to the first-born NS NS progenitor mass: 2 Mo ≤ M0 ≤ 4.7 Mo Kick magnitude: 60 km/s ≤ Vk≤ 1660 km/s most probable: 150 km/s Kick direction: 115°≤q≤ 180° Conclusions

  34. PSR J0737-3039 Evolutionary + Kinematic History

  35. Ransom et al. 2004 : PSR J0737-3039: Vtransverse≈ 140 km/s from scintillation observations But... unknown orientation in the plane of the sky! and unknown radial velocity … Systemic Velocity of PSR J0737-3039

  36. So far all constraints from stellar and binary evolution However... the DNS center-of-mass may receive a significant kick: mass loss + supernova kick but... current velocity ≠ post-SN velocity must trace Galactic motion back in time to birth place where was the system born? what is its current 3D space velocity? Beyond the Evolutionary Constraints

  37. DNS binaries form from massive primordial binaries vertical scale height of 50-70 pc Center-of-mass kick imparted at first SN: ~ a few 10 km/s (Brandt & Podsiadlowski 95, Wex et al. 00, Pfahl et al. 02) the system is probably still close to the Galactic plane when the second NS is formed We assume that the DNS was born in the Galactic disk Birth Sites of Double Neutron Stars

  38. Proper Motion Velocity components in R.A. and Decl. Proper motion of 100mas/yr should be detectable in less than 17 months for d = 0.6 kpc Determination of the proper motion will considerably constrain W Solid: Va Dashed: Vd

  39. Motion of the system backwards in time depends on Galactic Motion the unknown longitude of the ascending node W (direction of Vtransverse) AND the unknown radial velocity Vr 2 unknown parameters many possible trajectories

  40. For each W [0 , 360] and Vr [-1500 , 1500] km/s Trace the motion back in time to a maximum age of 100Myr Each crossing of the trajectory with the Galactic plane is considered a possible birth site The times of the plane crossings yield kinematic age estimates Post-SN peculiar velocity at birth = total systemic velocity - local Galactic rotational velocity Combine with stellar and binary evolution constraints Derivation of Progenitor Constraints II

  41. Kinematic Ages The system may have crossed the disk up to 3 times in the last 100Myr 1st crossing There is a wide range of W and Vr values for which the system is < 20Myr old 2nd crossing For ages > 20Myr disk crossings only occur for tight ranges of W and Vr If the system crossed the Galactic plane twice it is at least 20Myr old

  42. Post-SN Peculiar Velocities 1st crossing 1st crossing: 90km/s ≤ Vpec≤ 1550km/s 2nd crossing 2nd crossing: 120km/s ≤ Vpec≤ 800km/s Vpec generally increases with increasing Vr

  43. The Progenitor Mass of the Last-Born NS F I R S T C R O S S I N G

  44. The Pre-SN Orbital Separation F I R S T C R O S S I N G

  45. The Kick Velocity Magnitude F I R S T C R O S S I N G

  46. Isotropic Kicks + Bayes' theorem Kick Velocity Distribution For a each value of W and Vr Vk M1≤ M0≤ M2 A1≤ A0≤ A2 q1≤q≤q2 f1≤ f≤f2 Average over all W assuming a uniform distribution

  47. Kick Velocity Distribution for Isotropic Kicks 1st crossing 1st crossing 2nd crossing 2nd crossing

  48. Mass transfer spinning up pulsar A: expected to align pulsar A's spin axis with the pre-SN orbital angular momentum axis Kick: the post-SN orbit is inclined w/r to the pre-SN orbit Pulsar A's spin axis misaligned w/r to post-SN orbital angular momentum axis The misalignment angle l depends only on q not on f Distribution functions for the misalignment angle are derived in a similar way as the kick velocity distributions Spin-Orbit Misalignment

  49. Spin Tilt Distribution for Isotropic Kicks 1st crossing 1st crossing 2nd crossing 2nd crossing

  50. Recent observations of the Crab and Vela pulsars suggest a possible alignment between the projected proper motion and spin axis (Lai et al. 2001, Romani 2004) Spin-kick alignment? Non-Isotropic Kicks Crab Pulsar Chandra X-ray image http://chandra.harvard.edu/photo/2002/0052/index.html

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