Post on 05-Jan-2016
description
Vicky Kalogera
with Bart Willems
Mike Henninger
Formation of Double Neutron Formation of Double Neutron Stars:Stars:
Kicks and TiltsKicks and Tilts
Department of Physics and Astronomy
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
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
Millisecond Pulsars
Magnetic field: ~ 109-1010 GSpin period: < 100msSpin-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
NS-NS Formation Channel
from Tauris & van den Heuvel 2003
How do Double
Neutron Stars
form ?
current properties
constrain NS #2
formation process:NS kickNS progenitor
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
NS-NS Formation Channel
animation credit:
John Rowe
PSR J0737-3039 Properties
Component A 23 ms pulsarfastest known DNS pulsar spinOrbital period 2.4 hoursclosest known DNS orbitEccentricity 0.09least eccentric of all known DNS binariesPeriastron advance 16.9° per yearfastest of all known DNS binaries
Burgay et al. 2003
PSR J0737-3039 Properties
Coalescence time 85 Myrshortest 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
PSR J0737-3039 Properties
Component B 2.8s pulsar
FIRST known DOUBLE PULSAR system!
Inclination close to 90° eclipsesunique probe into magnetospheric physics
Lyne et al. 2004
Remarkable progenitor constraints
next … Willems & VK 2004
Willems, VK, Henninger 2004
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
Orbital Evolution Backwards in Time
Orbital separation
Orbital eccentricity
A = 1.54
R⊙
e = 0.119
Gravitational Radiation: dA/dt & de/dt
The Pre-SN Orbital Separation
Evolution of A(1-e) ≤ A0 ≤ A(1+e) back
in time
The Pre-SN Orbital Separation
Evolution of A(1-e) ≤ A0 ≤ A(1+e) back
in time
The Pre-SN Orbital Separation
Evolution of A(1-e) ≤ A0 ≤ A(1+e) back
in time
The Pre-SN Orbital Separation
Evolution of A(1-e) ≤ A0 ≤ A(1+e) back
in time
The Pre-SN Orbital Separation
A(1-e) < A0
<A(1+e)
Detached vs. Semi-Detached Pre-SN Binary
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
A(1-e) < A0 <
A(1+e)
Detached: A0 > A0,crit(M0)
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 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
age dependency
The Progenitor Mass of the Last-Born NS
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
Semi-Detached Progenitors
A(1-e) < A0 <
A(1+e)
The Helium Star Progenitor Mass Revisited
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 Progenitor Mass of the Last-Born NS
A(1-e) < A0 <
A(1+e)
M0 ≥ 2.1Mo
M0 ≤ 4.7Mo
The Minimum Kick Velocity
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
A(1-e) < A0 <
A(1+e)
M0 ≥ 2.1Mo
M0 ≤ 4.7Mo
M0 ≤ M0,max(A0,Vk)
for age of 100Myr
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 1.15Ro ≤ A0 ≤ 1.72Ro and 2.1Mo ≤ M0 ≤
4.7Mo the maximum possible kick
velocity is 1660km/s
Conclusions
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
The Kick Direction
polar angle between pre-SN orbital velocity V0 and kick velocity Vk
azimuthal angle in plane to V0
Kalo
gera
(2
00
0)
0
NS1
The Kick Direction
Given a kick velocity Vk :
REAL solutions for a finite number of kick directions
Vk =
200km/s
Vk =
500km/s
The Kick Direction
Kick is generally directedopposite to the orbital motion
Regardless of
Vk and age:
115°
Isotropic Kicks
For a given kick velocity Vk :
M0 and A0 constraints translate to polar angle
constraints
Isotropic Kicks
Bayes' theorem
M1 ≤ M0 ≤
M2
A1 ≤ A0 ≤
A2
M1 ≤ M0 ≤
M2
A1 ≤ A0 ≤
A2
1 ≤ ≤
2
1 ≤ ≤
2
1 ≤ ≤
2
1 ≤ ≤
2
Vk
The Most Probable Isotropic Kick Velocity
Conclusions
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° ≤ ≤ 180°
PSR J0737-3039
Evolutionary + Kinematic History
Systemic Velocity of PSR J0737-3039
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 …
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 velocitymust trace Galactic motion back
in time to birth place
where was the system born?what is its current 3D space
velocity?
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
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
Galactic Motion
Motion of the system backwards in time depends on the unknown longitude of the ascending
node
(direction of Vtransverse) AND
the unknown radial velocity Vr
2 unknown parameters
many possible trajectories
Derivation of Progenitor Constraints II
For each [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
Kinematic Ages
There is a wide range of and Vr 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 Vr
The system may have crossed the disk up to 3 times in the last 100Myr
1st crossing
2nd crossing
Post-SN Peculiar Velocities
1st crossing: 90km/s ≤ Vpec ≤
1550km/s
2nd crossing: 120km/s ≤ Vpec ≤
800km/s
Vpec generally
increases with increasing Vr
1st crossing
2nd crossing
The Progenitor Mass of the Last-Born NS
FIRST
CROSSING
The Pre-SN Orbital Separation
FIRST
CROSSING
The Kick Velocity Magnitude
FIRST
CROSSING
Kick Velocity Distribution
Isotropic Kicks +
Bayes' theorem
M1 ≤ M0 ≤
M2
A1 ≤ A0 ≤
A2
M1 ≤ M0 ≤
M2
A1 ≤ A0 ≤
A2
1 ≤ ≤
2
1 ≤ ≤
2
1 ≤ ≤
2
1 ≤ ≤
2
Vk
For a each value of and Vr
Average over all assuming a uniform distribution
Kick Velocity Distribution for Isotropic Kicks
1st crossing
1st crossing
2nd crossing
2nd crossing
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
Spin Tilt Distribution for Isotropic Kicks
1st crossing 1st crossing
2nd crossing 2nd crossing
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
Non-Isotropic Kicks
Planar kicks: ≈ 90°
= angle between pre-SN orbital angular momentum and kick velocity
Polar kicks: ≈ 0° or ≈ 180°
Polar kicks: ≈ 0° or ≈ 180°
Progenitor Constraints for ≤ 30°
FIRST
CROSSING
Progenitor Constraints for ≤ 30°
FIRST
CROSSING
Progenitor Constraints for ≤ 30°
FIRST
CROSSING
Kick Velocity Distribution for Polar Kicks
Misalignment angle ≤ 30°
2nd crossing
2nd crossing
1st crossing
1st crossing
Spin Tilt Distribution for Polar Kicks
2nd crossing
2nd crossing
1st crossing
1st crossing
Misalignment angle ≤ 30°
Conclusions
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° ≤ ≤ 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 Vr 500
km/s
PSR B1534+12
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 Vr
Kinematic history depends on only 1 unknown quantity: radial velocity Vr
Progenitor ConstraintsRed: detached Blue: mass
transfer
Detached as well as semi-detached solutions
2nd crossing 3rd crossing1st crossing
Kick ConstraintsR
ed
: d
eta
ched
B
lue:
mass
tr
an
sfer
1st crossing 2nd crossing 3rd crossing
Kick Velocity Distribution for Isotropic Kicks
1st crossing 1st crossing
2nd crossing
3rd crossing
2nd crossing
3rd crossing
Spin Tilt Distribution for Isotropic Kicks
1st crossing
2nd crossing
3rd crossing 3rd crossing
2nd crossing
1st crossing
PSR B1913+16
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 MyrKinematic history depends on only 1
unknown quantity: radial velocity Vr
Kinematic history depends on only 1
unknown quantity: radial velocity Vr
+ ...
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 MyrKinematic history depends on only 1
unknown quantity: radial velocity Vr
Kinematic history depends on only 1
unknown quantity: radial velocity Vr
+ ...Measured spin tilt around 18° or 162°
Measured spin tilt around 18° or 162°
Progenitor ConstraintsRed: detached Blue: mass transfer
Detached as well as semi-detached solutions
= 18° = 18° = 162° = 162°1st crossing 2nd crossing
Kick Constraints1st crossing 2nd crossing
= 18° = 18° = 162° = 162°
Red
: d
eta
ched
B
lue:
mass
tr
an
sfer
Kick Velocity Distribution for Isotropic Kicks
1st crossing 1st crossing
2nd crossing 2nd crossing
Conclusions
PSR J0737-3039
Pulsar B's helium star progenitor is most likely transferring mass to the first-born NS
NS Progenitor mass: 2Mo ≤ M0 ≤ 4.7 Mo
Kick magnitude: 60 km/s ≤ Vk ≤ 1660 km/s
most probable: 150 km/s
Kick direction: 115° ≤ ≤ 180° and 25° ≤ ≤ 155°
Tilt angles below 30°-50° are favored for Vr 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