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

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. Pulsars 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 http://imagine.gsfc.nasa.gov/docs/ science/know_l1/pulsars.html

4. Millisecond Pulsars Magnetic field: ~ 10 9 -10 10 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 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. PSR J0737-3039 Properties 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 Burgay et al. 2003

8. PSR J0737-3039 Properties 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 Kalogera et al. 2004

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

10. Derivation of Progenitor Constraints 1)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 M 0 -A 0 diagram

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

12. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A 0 ≤ A(1+e) back in time

13. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A 0 ≤ A(1+e) back in time

14. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A 0 ≤ A(1+e) back in time

15. The Pre-SN Orbital Separation Evolution of A(1-e) ≤ A 0 ≤ A(1+e) back in time

16. The Pre-SN Orbital Separation A(1-e) < A 0 <A(1+e)

17. Detached vs. Semi-Detached Pre-SN Binary If left alone, a helium star of mass M 0 will reach a maximum radius R 0,max (M 0 ) 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 R L (M 0,A 0 ) R 0,max (M 0 ) > R L (M 0,A 0 ): detached A 0 > A 0,crit (M 0 )

18. Detached vs. Semi-Detached Pre-SN Binary A(1-e) < A 0 < A(1+e) Detached: A 0 > A 0,crit (M 0 )

19. The Progenitor Mass of the Last-Born NS The relations between the pre- and post-SN orbital parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M 0 ≤ M 0,max ( A, e, A 0, V k ) For a given age (i.e. fixed A and e), the upper limit M 0,max (A 0 ) can be determined for every admissible value of the kick velocity V k  age dependency

20. The Progenitor Mass of the Last-Born NS A(1-e) < A 0 < A(1+e) Detached: A 0 > A 0,crit (M 0 ) Mass transfer: A 0 ≤ A 0,crit (M 0 ) M 0 ≤ M 0,max (A 0,V k ) for age of 100Myr

21. Semi-Detached Progenitors A(1-e) < A 0 < A(1+e)

22. The Helium Star Progenitor Mass Revisited Lower limit: the helium star must form a NEUTRON STAR rather than a WHITE DWARF M 0 ≥ 2.1M o (Habets 1986) Upper limit: the binary mass ratio cannot be too extreme if runaway mass transfer leading to a merger is to be avoided M 0 /M NS ≤ 3.5 (Ivanova et al. 2003) M 0 ≤ 4.7M o

23. The Progenitor Mass of the Last-Born NS A(1-e) < A 0 < A(1+e) M 0 ≥ 2.1M o M 0 ≤ 4.7M o

24. The Minimum Kick Velocity A(1-e) < A 0 < A(1+e) M 0 ≥ 2.1M o M 0 ≤ 4.7M o M 0 ≤ M 0,max (A 0,V k ) for age of 0Myr

25. The Minimum Kick Velocity A(1-e) < A 0 < A(1+e) M 0 ≥ 2.1M o M 0 ≤ 4.7M o M 0 ≤ M 0,max (A 0,V k ) for age of 100Myr

26. The Maximum Kick Velocity 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 andhelium star mass for 1.15R o ≤ A 0 ≤ 1.72R o and 2.1M o ≤ M 0 ≤ 4.7M o the maximum possible kick velocity is 1660km/s

27. Conclusions PSR J0737-3039 Pulsar B's helium star progenitor is most likely transferring mass to the first-born NS NS progenitor mass: 2 M o ≤ M 0 ≤ 4.7 M o Kick magnitude: 60 km/s ≤ V k ≤ 1660 km/s

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

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

30. The Kick Direction Kick is generally directed opposite to the orbital motion Regardless of V k and age:  115°

31. Isotropic Kicks For a given kick velocity V k : M 0 and A 0 constraints translate to polar angle constraints Isotropic Kicks Bayes' theorem M 1 ≤ M 0 ≤ M 2 A 1 ≤ A 0 ≤ A 2 M 1 ≤ M 0 ≤ M 2 A 1 ≤ A 0 ≤ A 2  1 ≤  ≤  2  1 ≤  ≤  2  1 ≤  ≤  2  1 ≤  ≤  2 VkVk

32. The Most Probable Isotropic Kick Velocity

33. Conclusions PSR J0737-3039 Pulsar B's helium star progenitor is most likely transferring mass to the first-born NS NS progenitor mass: 2 M o ≤ M 0 ≤ 4.7 M o Kick magnitude: 60 km/s ≤ V k ≤ 1660 km/s most probable: 150 km/s Kick direction: 115° ≤  ≤ 180°

34. PSR J0737-3039 Evolutionary + Kinematic History

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

36. Beyond the Evolutionary Constraints 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?

37. Birth Sites of Double Neutron Stars 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

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

39. Galactic Motion Motion of the system backwards in time depends on the unknown longitude of the ascending node  (direction of V transverse ) AND the unknown radial velocity V r 2 unknown parameters many possible trajectories

40. Derivation of Progenitor Constraints II For each  [0, 360] and V r [-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

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

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

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

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

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

46. Kick Velocity Distribution Isotropic Kicks + Bayes' theorem M 1 ≤ M 0 ≤ M 2 A 1 ≤ A 0 ≤ A 2 M 1 ≤ M 0 ≤ M 2 A 1 ≤ A 0 ≤ A 2  1 ≤  ≤  2  1 ≤  ≤  2  1 ≤  ≤  2  1 ≤  ≤  2 VkVk For a each value of  and V r Average over all  assuming a uniform distribution

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

48. Spin-Orbit Misalignment 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 depends only on  not on  Distribution functions for the misalignment angle are derived in a similar way as the kick velocity distributions

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

50. Non-Isotropic Kicks 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? http://chandra.harvard.edu/photo/2002/0052/index.html Crab Pulsar Chandra X-ray image

51. Non-Isotropic Kicks Planar kicks:  ≈ 90°  = angle between pre-SN orbital angular momentum and kick velocity Polar kicks:  ≈ 0° or  ≈ 180°

52. Progenitor Constraints for  ≤ 30° F I R S T C R O S I N G

53. Progenitor Constraints for  ≤ 30° F I R S T C R O S I N G

54. Progenitor Constraints for  ≤ 30° F I R S T C R O S I N G

55. Kick Velocity Distribution for Polar Kicks Misalignment angle  ≤ 30° 2 nd crossing 1 st crossing

56. Spin Tilt Distribution for Polar Kicks 2 nd crossing 1 st crossing Misalignment angle  ≤ 30°

57. Conclusions PSR J0737-3039 Pulsar B's helium star progenitor is most likely transferring mass to the first-born NS NS progenitor mass: 2 M o ≤ M 0 ≤ 4.7 M o Kick magnitude: 60 km/s ≤ V k ≤ 1660 km/s most probable: 150 km/s Kick direction: 115° ≤  ≤ 180° and 25° ≤  ≤ 155° Kicks are directed opposite to orbital motion and cannot be too closely aligned with the pre-SN orbital angular momentum Tilt angles below 30°-50° are favored for V r < 500 km/s

58. PSR B1534+12

59. PSR B1534+12 Properties Wolszczan 1991; Stairs et al. 2002; Konacki et al. 2003; Arzoumanian et al. 1999 Spin period 37.90 ms Orbital period 10.1 hours Eccentricity 0.274 Periastron advance 1.76° per year Proper motion   = 1.34 mas/yr   = -25.05 mas/yr Spin-down age 210 Myr Kinematic history depends on only 1 unknown quantity: radial velocity V r

60. Progenitor Constraints Red: detached Blue: mass transfer Detached as well as semi-detached solutions 2 nd crossing 3 rd crossing 1 st crossing

61. Kick Constraints Red: detached Blue: mass transfer 1 st crossing2 nd crossing3 rd crossing

62. Kick Velocity Distribution for Isotropic Kicks 1 st crossing 2 nd crossing 3 rd crossing 2 nd crossing 3 rd crossing

63. Spin Tilt Distribution for Isotropic Kicks 1 st crossing 2 nd crossing 3 rd crossing 2 nd crossing 1 st crossing

64. PSR B1913+16

65. PSR B1913+16 Properties Hulse & Taylor 1975; Taylor et al. 1976, 1979; Taylor & Weisberg 1982, 1989; Damour & Taylor 1991; Arzoumanian et al. 1999 Spin period 59.03 ms Orbital period 7.75 hours Eccentricity 0.617 Periastron advance 4.23° per year Proper motion   = -3.27 mas/yr   = -1.04 mas/yr Spin-down age 80 Myr Kinematic history depends on only 1 unknown quantity: radial velocity V r +...

66. PSR B1913+16 Properties Hulse & Taylor 1975; Taylor et al. 1976, 1979; Taylor & Weisberg 1982, 1989; Damour & Taylor 1991; Arzoumanian et al. 1999 Spin period 59.03 ms Orbital period 7.75 hours Eccentricity 0.617 Periastron advance 4.23° per year Proper motion   = -3.27 mas/yr   = -1.04 mas/yr Spin-down age 80 Myr Kinematic history depends on only 1 unknown quantity: radial velocity V r +... Measured spin tilt around 18° or 162°

67. Progenitor Constraints Red: detached Blue: mass transfer Detached as well as semi-detached solutions = 18° = 162° 1 st crossing2 nd crossing

68. Kick Constraints 1 st crossing2 nd crossing = 18° = 162° Red: detached Blue: mass transfer

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

70. Conclusions PSR J0737-3039 Pulsar B's helium star progenitor is most likely transferring mass to the first-born NS NS Progenitor mass: 2M o ≤ M 0 ≤ 4.7 M o Kick magnitude: 60 km/s ≤ V k ≤ 1660 km/s most probable: 150 km/s Kick direction: 115° ≤  ≤ 180° and 25° ≤  ≤ 155° Tilt angles below 30°-50° are favored for V r < 500 km/s PSR J0737-3039, PSR B1534+12 and PSR 1913+16 Kicks are directed opposite to orbital motion and cannot be too closely aligned with the pre-SN orbital angular momentum