Transcript Document

Formation of Double Neutron Stars:
Kicks and Tilts
Vicky Kalogera
with
Bart Willems
Mike Henninger
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
http://imagine.gsfc.nasa.gov/docs/
science/know_l1/pulsars.html
Spin period of a few seconds
Spin-down time scale of a few 10-100Myr
Millisecond Pulsars
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
http://chandra.harvard.edu/resources/illustrations/blackholes2.html
NS-NS Formation Channel
How do Double
Neutron Stars
form ?
current properties
constrain NS #2
formation process:
NS kick
NS progenitor
from Tauris & van den Heuvel 2003
NS-NS Formation Channel
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
animation credit:
John Rowe
PSR J0737-3039 Properties
Burgay et al. 2003
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
Kalogera et al. 2004
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
Lyne et al. 2004
Component B
2.8s pulsar
FIRST known DOUBLE PULSAR system!
Inclination close to 90° eclipses
unique probe into magnetospheric physics
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 M0-A0 diagram
Orbital Evolution Backwards in Time
Gravitational Radiation: dA/dt & de/dt
Orbital separation
A = 1.54 R⊙
Orbital eccentricity
e = 0.119
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 )

age dependency
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
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
M0 ≤ 4.7Mo
(Ivanova et al. 2003)
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
and helium 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
Kalogera (2000)
0
polar angle between preSN orbital velocity V0 and
kick velocity Vk
NS1
azimuthal angle in
plane ^ to V0
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 directed
opposite to the orbital motion
Regardless of
Vk and age:
q > 115°
Isotropic Kicks
For a given kick velocity Vk :
M0 and A0 constraints translate to polar angle constraints
M1 ≤ M0 ≤ M2
A1 ≤ A0 ≤ A2
Isotropic Kicks
Bayes' theorem
Vk
q1 ≤ q ≤ q2
f1 ≤ f ≤ f2
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° ≤ q ≤ 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 velocity
must 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.
for d = 0.6 kpc
Proper motion of
100mas/yr should
be detectable in less
than 17 months
Determination of
the proper motion
will considerably
constrain W
Solid: Va
Dashed: Vd
Galactic Motion
Motion of the system backwards in time depends on
the unknown longitude of the ascending node W
(direction of Vtransverse)
AND
the unknown radial velocity Vr
2 unknown parameters
many possible trajectories
Derivation of Progenitor Constraints II
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
Kinematic Ages
1st
crossing
2nd
crossing
The system may have
crossed the disk up to 3
times in the last 100Myr
There is a wide range of W
and Vr values for which
the system is < 20Myr
old
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
Post-SN Peculiar Velocities
1st
crossing
2nd
crossing
1st crossing:
90km/s ≤ Vpec ≤ 1550km/s
2nd crossing:
120km/s ≤ Vpec ≤ 800km/s
Vpec generally increases
with increasing Vr
The Progenitor Mass of the Last-Born NS
F
I
R
S
T
C
R
O
S
S
I
N
G
The Pre-SN Orbital Separation
F
I
R
S
T
C
R
O
S
S
I
N
G
The Kick Velocity Magnitude
F
I
R
S
T
C
R
O
S
S
I
N
G
Kick Velocity Distribution
For a each value of W and Vr
M1 ≤ M0 ≤ M2
A1 ≤ A0 ≤ A2
Vk
q1 ≤ q ≤ q2
f1 ≤ f ≤ f2
Isotropic Kicks
+
Bayes' theorem
Average over all W 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 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 Tilt Distribution for Isotropic Kicks
1st crossing
2nd crossing
1st 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 Crab Pulsar Chandra X-ray image
(Lai et al. 2001, Romani 2004)
Spin-kick alignment?
http://chandra.harvard.edu/photo/2002/0052/index.html
Non-Isotropic Kicks
x = angle between pre-SN
orbital angular momentum
and kick velocity
Planar kicks: x ≈ 90°
Polar kicks: x ≈ 0° or x ≈ 180°
Progenitor Constraints for x ≤ 30°
F
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R
S
T
C
R
O
S
S
I
N
G
Progenitor Constraints for x ≤ 30°
F
I
R
S
T
C
R
O
S
S
I
N
G
Progenitor Constraints for x ≤ 30°
F
I
R
S
T
C
R
O
S
S
I
N
G
Kick Velocity Distribution for Polar Kicks
Misalignment angle x ≤ 30°
1st
crossing
1st
crossing
2nd
crossing
2nd
crossing
Spin Tilt Distribution for Polar Kicks
Misalignment angle x ≤ 30°
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: 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° and 25° ≤ x ≤ 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
ma = 1.34 mas/yr
md = -25.05 mas/yr
Spin-down age
210 Myr
Kinematic history depends on only 1 unknown
quantity: radial velocity Vr
Progenitor Constraints
Red: detached
1st crossing
Blue: mass transfer
2nd crossing
3rd crossing
Detached as well as semi-detached solutions
Red: detached
Blue: mass transfer
Kick Constraints
1st crossing
2nd crossing
3rd crossing
Kick Velocity Distribution for Isotropic Kicks
1st crossing
1st
crossing
2nd crossing
2nd
crossing
3rd crossing
3rd
crossing
Spin Tilt Distribution for Isotropic Kicks
1st crossing
1st
crossing
2nd crossing
2nd
crossing
3rd crossing
3rd
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
ma = -3.27 mas/yr
md = -1.04 mas/yr
Spin-down age
80 Myr
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
ma = -3.27 mas/yr
md = -1.04 mas/yr
Spin-down age
80 Myr
Kinematic history depends on
only 1 unknown quantity:
radial velocity Vr
Measured spin tilt
around 18° or 162°
+ ...
Progenitor Constraints
Red: detached
1st crossing
l = 18°
Blue: mass transfer
l = 162°
2nd crossing
l = 18°
l = 162°
Detached as well as semi-detached solutions
Red: detached
Blue: mass transfer
Kick Constraints
1st crossing
l = 18°
l = 162°
2nd crossing
l = 18°
l = 162°
Kick Velocity Distribution for Isotropic Kicks
1st crossing
2nd crossing
1st 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° ≤ q ≤ 180° and 25° ≤ x ≤ 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