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