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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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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

    • 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

Pulsars

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


Millisecond pulsars

Magnetic field: ~ 10 magnetic field axis is inclined with respect to their rotation axis 9-1010 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


NS-NS Formation Channel magnetic field axis is inclined with respect to their rotation axis

from Tauris & van den Heuvel 2003

How do Double

Neutron Stars

form ?

current properties

constrain NS #2

formation process:

  • NS kick

  • NS progenitor


NS-NS Formation Channel magnetic field axis is inclined with respect to their rotation axis

animation credit:

John Rowe


Psr j0737 3039 properties

Component A 23 ms pulsar magnetic field axis is inclined with respect to their rotation axis

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


Psr j0737 3039 properties1

Coalescence time 85 Myr magnetic field axis is inclined with respect to their rotation axis

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


Psr j0737 3039 properties2

Component B 2.8s pulsar magnetic field axis is inclined with respect to their rotation axis

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


Derivation of progenitor constraints

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


Orbital evolution backwards in time
Orbital Evolution Backwards in Time due to

Gravitational Radiation: dA/dt & de/dt

Orbital separation

Orbital eccentricity

A = 1.54 R⊙

e = 0.119


The pre sn orbital separation
The Pre-SN Orbital Separation due to

Evolution of A(1-e) ≤ A0≤ A(1+e) back in time


The pre sn orbital separation1
The Pre-SN Orbital Separation due to

Evolution of A(1-e) ≤ A0≤ A(1+e) back in time


The pre sn orbital separation2
The Pre-SN Orbital Separation due to

Evolution of A(1-e) ≤ A0≤ A(1+e) back in time


The pre sn orbital separation3
The Pre-SN Orbital Separation due to

Evolution of A(1-e) ≤ A0≤ A(1+e) back in time


A 1 e a 0 a 1 e

A(1-e) < A due to 0 <A(1+e)

The Pre-SN Orbital Separation


Detached vs semi detached pre sn binary

If left alone, a helium star of mass M due to 0 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 a 0 a 1 e detached a 0 a 0 crit m 0

A(1-e) < A due to 0 < A(1+e)

Detached: A0 > A0,crit(M0)

Detached vs. Semi-Detached Pre-SN Binary


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

The Progenitor Mass of the Last-Born NS

age dependency


The progenitor mass of the last born ns1

A(1-e) < A parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M0 < 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


A 1 e a 0 a 1 e1

A(1-e) < A parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M0 < A(1+e)

Semi-Detached Progenitors


The helium star progenitor mass revisited

Lower limit: parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M 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


A 1 e a 0 a 1 e m 0 2 1m o m 0 4 7m o

A(1-e) < A parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M0 < A(1+e)

M0≥ 2.1Mo

M0≤ 4.7Mo

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 m 0 m 0 max a 0 v k for age of 0myr

A(1-e) < A parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M0 < 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 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

A(1-e) < A parameters (conservation laws of orbital energy and orbital angular momentum) have REAL solutions only if M0 < A(1+e)

M0≥ 2.1Mo

M0≤ 4.7Mo

M0≤ M0,max(A0,Vk) for age of 100Myr

The Minimum Kick Velocity


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≤ 1.72Roand 2.1Mo≤ M0≤ 4.7Mo the maximum possible kick velocity is 1660km/s

The Maximum Kick Velocity


Conclusions

PSR J0737-3039 by the requirement that the binary must remain bound after the SN explosion

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


Polar angle between pre sn orbital velocity v 0 and kick velocity v k

polar angle between pre-SN orbital velocity V by the requirement that the binary must remain bound after the SN explosion0 and kick velocity Vk

The Kick Direction

0

Kalogera (2000)

NS1

azimuthal angle in plane ^ to V0


Given a kick velocity v k real solutions for a finite number of kick directions

Given a kick velocity V by the requirement that the binary must remain bound after the SN explosionk :

REAL solutions for a finite number of kick directions

The Kick Direction

Vk = 200km/s

Vk = 500km/s


The kick direction
The Kick Direction by the requirement that the binary must remain bound after the SN explosion

Kick is generally directed

opposite to the orbital motion

Regardless of

Vk and age:

q > 115°


For a given kick velocity V by the requirement that the binary must remain bound after the SN explosionk :

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


The most probable isotropic kick velocity
The Most Probable Isotropic Kick Velocity by the requirement that the binary must remain bound after the SN explosion


Conclusions1

PSR J0737-3039 by the requirement that the binary must remain bound after the SN explosion

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


Psr j0737 3039 evolutionary kinematic history

PSR J0737-3039 by the requirement that the binary must remain bound after the SN explosion

Evolutionary + Kinematic History


Systemic velocity of psr j0737 3039

Ransom et al. 2004 : by the requirement that the binary must remain bound after the SN explosion

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


Beyond the evolutionary constraints

So far all constraints from stellar and binary evolution by the requirement that the binary must remain bound after the SN explosion

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


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

Birth Sites of Double Neutron Stars


Proper motion
Proper Motion binaries vertical scale height of 50-70 pc

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


Motion of the system backwards in time depends on

Motion of the system backwards in time depends on binaries vertical scale height of 50-70 pc

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


Derivation of progenitor constraints ii

For each binaries vertical scale height of 50-70 pc 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


Kinematic ages
Kinematic Ages binaries vertical scale height of 50-70 pc

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


Post sn peculiar velocities
Post-SN Peculiar Velocities binaries vertical scale height of 50-70 pc

1st crossing

1st crossing:

90km/s ≤ Vpec≤ 1550km/s

2nd crossing

2nd crossing:

120km/s ≤ Vpec≤ 800km/s

Vpec generally increases with increasing Vr


The progenitor mass of the last born ns2
The Progenitor Mass of the Last-Born NS binaries vertical scale height of 50-70 pc

F

I

R

S

T

C

R

O

S

S

I

N

G


The pre sn orbital separation4
The Pre-SN Orbital Separation binaries vertical scale height of 50-70 pc

F

I

R

S

T

C

R

O

S

S

I

N

G


The kick velocity magnitude
The Kick Velocity Magnitude binaries vertical scale height of 50-70 pc

F

I

R

S

T

C

R

O

S

S

I

N

G


Isotropic kicks bayes theorem

Isotropic Kicks binaries vertical scale height of 50-70 pc

+

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


Kick velocity distribution for isotropic kicks
Kick Velocity Distribution for Isotropic Kicks binaries vertical scale height of 50-70 pc

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-Orbit Misalignment


Spin tilt distribution for isotropic kicks
Spin Tilt Distribution for Isotropic Kicks A's spin axis with the pre-SN orbital angular momentum axis

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?

Non-Isotropic Kicks

Crab Pulsar Chandra X-ray image

http://chandra.harvard.edu/photo/2002/0052/index.html


Non isotropic kicks1
Non-Isotropic Kicks possible alignment between the projected proper motion and spin axis

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
Progenitor Constraints for possible alignment between the projected proper motion and spin axisx≤ 30°

F

I

R

S

T

C

R

O

S

S

I

N

G


Progenitor constraints for x 301
Progenitor Constraints for possible alignment between the projected proper motion and spin axisx≤ 30°

F

I

R

S

T

C

R

O

S

S

I

N

G


Progenitor constraints for x 302
Progenitor Constraints for possible alignment between the projected proper motion and spin axisx≤ 30°

F

I

R

S

T

C

R

O

S

S

I

N

G


Kick velocity distribution for polar kicks
Kick Velocity Distribution for Polar Kicks possible alignment between the projected proper motion and spin axis

Misalignment angle x≤ 30°

1st crossing

1st crossing

2nd crossing

2nd crossing


Spin tilt distribution for polar kicks
Spin Tilt Distribution for Polar Kicks possible alignment between the projected proper motion and spin axis

Misalignment angle x≤ 30°

1st crossing

1st crossing

2nd crossing

2nd crossing


Conclusions2

PSR J0737-3039 possible alignment between the projected proper motion and spin axis

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

Conclusions


Psr b1534 12

PSR B1534+12 possible alignment between the projected proper motion and spin axis


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

PSR B1534+12 Properties

Kinematic history depends on only 1 unknown quantity: radial velocity Vr


Progenitor constraints
Progenitor Constraints Arzoumanian et al. 1999

Red: detached Blue: mass transfer

3rd crossing

1st crossing

2nd crossing

Detached as well as semi-detached solutions


Kick constraints
Kick Constraints Arzoumanian et al. 1999

1st crossing

2nd crossing

3rd crossing

Red: detached Blue: mass transfer


Kick velocity distribution for isotropic kicks1
Kick Velocity Distribution for Isotropic Kicks Arzoumanian et al. 1999

1st crossing

1st crossing

2nd crossing

2nd crossing

3rd crossing

3rd crossing


Spin tilt distribution for isotropic kicks1
Spin Tilt Distribution for Isotropic Kicks Arzoumanian et al. 1999

1st crossing

1st crossing

2nd crossing

2nd crossing

3rd crossing

3rd crossing


Psr b1913 16

PSR B1913+16 Arzoumanian et al. 1999


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

PSR B1913+16 Properties

Kinematic history depends on only 1 unknown quantity: radial velocity Vr

+ ...


Psr b1913 16 properties1

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

PSR B1913+16 Properties

Kinematic history depends on only 1 unknown quantity: radial velocity Vr

+ ...

Measured spin tilt around 18° or 162°


Progenitor constraints1
Progenitor Constraints Weisberg 1982, 1989; Damour & Taylor 1991; Arzoumanian et al. 1999

Red: detached Blue: mass transfer

1st crossing

2nd crossing

l = 162°

l = 18°

l = 162°

l = 18°

Detached as well as semi-detached solutions


Kick constraints1
Kick Constraints Weisberg 1982, 1989; Damour & Taylor 1991; Arzoumanian et al. 1999

1st crossing

2nd crossing

l = 18°

l = 162°

l = 18°

l = 162°

Red: detached Blue: mass transfer


Kick velocity distribution for isotropic kicks2
Kick Velocity Distribution for Isotropic Kicks Weisberg 1982, 1989; Damour & Taylor 1991; Arzoumanian et al. 1999

1st crossing

1st crossing

2nd crossing

2nd crossing


Conclusions3

PSR J0737-3039 Weisberg 1982, 1989; Damour & Taylor 1991; Arzoumanian et al. 1999

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

Conclusions


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