Pulsar Ages and the Evolution of Pulsar Spin–Velocity...

Pulsar Ages and the Evolution of Pulsar Spin–Velocity Alignment

Aristeidis NoutsosMichael KramerSimon Johnston

Dominic SchnitzelerEvan Keane

NS2012b Bonn, 22 October

Ψ

v⊥S±90º

Ψ

v⊥S±90º

Ψ

v⊥S±90º

Previously on Pulsar Spin–Velocity Alignment …

0.3

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0.1

0

N

! (deg)10 20 30 40

KS probability of rejecting uniformity = 99.8%

Ψ

v⊥S±90º

…PSR 1 2 3

4

54 PSRs

S from pulsar polarisation data

v⊥ from pulsar timing / VLBI

Noutsos et al. (2012), MNRAS

uniformity

•• We used the polarisation and proper motion data of 54 pulsars to study the distribution of Ψ, the angle between S±90º and v⊥

•• We rejected that the orientations of pulsar spins and velocities are uncorrelated, with 99.8% probability

Chapter 2: Spin–Velocity Alignment with Pulsar Age

!""

"

!""

!#"""

!"#"""

!#""" !"#""" !""#"""!""#$%&'

pKS = 0.694 –0.352

+0.196

Npsr = 4

pKS = 0.879 –0.246

+0.091

Npsr = 10

pKS = 0.898 –0.212

+0.077

Npsr = 32

pKS = 0.979 –0.054

+0.016

Npsr = 12

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!""#$%&'

pKS = 0.938 –0.159

+0.049

Npsr = 14

pKS = 0.969 –0.094

+0.025

Npsr = 42

pKS = 0.991 –0.033

+0.008

Npsr = 44

pKS = 0.997 –0.013

+0.003

Npsr = 54

pKS = 0.982 –0.061

+0.015

Npsr = 46

pKS = 0.998 –0.008

+0.002

Npsr = 58

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We examined the degree of spin–velocity alignment for subsets of pulsars grouped according to characteristic age

Chapter 2: Spin–Velocity Alignment with Pulsar Age

The probability of rejecting that S–v are uncorrelated remains constant (within errors) across all pulsar characteristic ages

!"#$%&'

! ()

~ tdyn

0 100 1,000 10,000 100,000

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1

This is surprising since we expect the Galactic potential to significantly alter pulsar velocities on a dynamical timescale of

–4

–2

0

2

4

–20 –15 –10 –5 0 5

!!"!#$!%&'

(!)*+,-

"!)*+,-

!

!

"

"!

#$%

tdyn =�

GMMW

πR2MWδh

�−1/2

∼ 10 Myr

50-Myr pulsar trajectory in the Galactic potential

… and wash out any S–v correlation

But this is not what we see based on the above analysis

Pulsar Ages

The characteristic ages of pulsars are known to be unreliable*

ttrue ~ 30 kyrτc ~ 600 kyr

PSR J0538+2817

t – 20 kyr

t – 40 kyrt – 60 kyrSNR

centre

S147

Ng et al. (2007)

P = −KP 2−n ⇒ ttrue =P

(n− 1)P

�1−

�P0

P

�n−1�

* They are calculated assuming:

K ∝ (B sinα)2 = const.

P0 = 0

n = 3

(i) The pulsar was born spinning infinitely fast

(ii) The pulsar spins down by converting rotational energy to purely magnetic-dipole radiation

(iii) The pulsar maintains a constant magnetic field

Either or all of these assumptions are likely wrong for most pulsars. E.g. PSR J0538+2817 was born with

P0 ≈ 138 ms (≈ P )and is 10x younger than τc.

The distance and outward proper motion of PSR J0538+2817 from the centre of S147 imply a true age of 30–40 kyr

τc =P

2P

Pulsar Kinematic AgesAlternatively, one can estimate pulsar ages independently of a spin-down model, based on the kinematic properties of individual pulsars, assuming pulsars are born close to the Galactic plane

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1 2

3 4

5 6

-0.4-0.3-0.2-0.1

0 0.1 0.2 0.3 0.4

!"#$%&'

("#$%&'

)"#$%&'

*+

!!","-."/(0!","12"/(0

Pulsar Kinematic AgesWe integrated the equations of motion for 52 pulsars, assuming they are moving through the Galactic potential of Paczynski (1990) and using their present proper motions and locations (μl, μb, l, b, d)

zbirth

+100 pc

–100 pc

Δt = tkin

0 t0

t1

vbirth

v1

!"#$%&'()*'+,-.

Hobbs et al. (2005)

Arzoumanian et al. (2002)

we weighted the unknown vr using the distribution of vbirth

0 0.1– 0.1z (kpc)

nOB = n0 e−|z|/hOB

we weighted the unknown birth height using the distribution of OB stars (Reed 2000)

+

For each pulsar, we explored finite ranges of the unknown vr and zbirth :

vr = [–500, +500] km s–1

zbirth = [-100,+100] pc

H(vbirth)

R(zbirth)

Pulsar Kinematic Ages

The probability distribution of tkin comes from marginalising the joint probability of ℌ(vbirth) and ℜ(zbirth) over all vbirth and zbirth :

most probable kinematic age

characteristic age

p(tkin) =� ∞

0

� +100 pc

−100 pcL(vbirth, tkin)× H(vbirth)×R(zbirth)×H(τ1 − tkin)dvbirthdzbirth

τ1 = 2τc ln(P

1 ms)

(integration limit)

68% C

L

~35% of the pulsars produced more than 1 intersection with the Galactic plane and p(tkin) was complex

J0922+0638

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0.015

p (t ki

n)

J1136+1551J0837+0610

tkin / !c

0.005

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0.015

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p (t ki

n)

0.1 1 10 100tkin / !c

?

Spin–Velocity Alignment with Pulsar Age … Redux

•• We have produced a data set of 52 kinematic ages

•• This is the largest number of pulsar ages, estimated independently of a spin-down model

•• We have used the 33 most reliable estimates to examine again the degree of spin–velocity alignment as a function of pulsar age


•• We have use the 33 most reliable estimates to examine again the degree of spin–velocity alignment as a function of pulsar age

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!$)$%&%''!($)''*(+,-

pKS = 0.935 –0.153

+0.050

Npsr = 11

pKS = 0.956 –0.101

+0.033

Npsr = 30

pKS = 0.937 –0.134

+0.047

Npsr = 33

pKS = 0.791 –0.267

+0.098

Npsr = 19

pKS = 0.726 –0.324

+0.174

Npsr = 22

pKS = 0.335 –0.228

+0.242

Npsr = 3

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pKS = 0.935 –0.153

+0.050

Npsr = 11

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pKS = 0.956 –0.101

+0.033

Npsr = 30

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pKS = 0.937 –0.134

+0.047

Npsr = 33

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pKS = 0.936 –0.162

+0.050

Npsr = 4

Vela (~20 kyr)

Crab (~1 kyr)

PSR B1952+32 (~51 kyr)

PSR J0538+2817 (~30 kyr)


!!"#$%!&'(

" )*

~ tdyn

10 100 1,000 10,000 100,000

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1

Now, the probability of rejecting uniformity shows a clear downwards trend

For pulsars with tkin > tdyn , uniformity is not rejected

Our results suggest that if we use the more reliable kinematic ages instead of the characteristic ages for our sample of pulsars, then

•• Young pulsars (≲1 Myr) maintain a strong correlation (pKS ~ 95%) between their spin and velocity orientations

•• Beyond tkin~1 Myr the correlation weakens and it completely disappears for tkin ≳10 Myr

Kinematic Ages as Probes of Pulsar EvolutionThe derived kinematic ages can serve as an estimate of the pulsars true age:

n = 1 + 2τc

tkin

�1−

�P0

P

�n−1�

ttrue ≡ tkin

Hence, we can used them to test the standard assumptions of magnetic-dipole braking and infinitesimal birth periods

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P0 / P = 0

P0 / P = 0.01

P0 / P = 0.1

P0 / P = 0.5

21%29%

25%29%5%

21%18%16%

9%10%12%

P0

P0/P = 0

P0/P = 0.01

P0/P = 0.1

P0/P = 0.5

n

33 pulsars

P0,3 (ms)

p KS

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1

0 250 500 750 1000 1250

p(P 0

) [x1

0–3]

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1.0

1.5

2.5

2.0P0, 3 = 63 ms

+728–35

^

Popov & Turolla (2012)

(a)

(b)

P0 = P

�1−

�n− 1

2

�tkin

τc

� 1n−1

n=3−→ P0,3 = P

�1− tkin

τc

27 pulsars

By comparing tkin with τc , we can express the braking index as a function of P0 and vice versa

Epilogue

Epilogue•• If we take pulsar characteristic ages at face value, spin–velocity alignment does not become weaker with increasing age


! this is the opposite of what is expected for pulsars travelling through the Galactic potential



•• We have estimated 52 pulsar kinematic ages, independently of any spin-down model assumptions, by calculating the travel time between their birth places near the Galactic plane and their present locations.




! this is the largest sample of independently estimated pulsar ages





•• If we use the kinematic ages to study the evolution of spin–velocity alignment, we see a clear de-correlation between the spin and velocity orientations for ages > 10 Myr






! this the expected for the Milky Way, with the above virialisation time scale







•• Kinematic ages are potentially a powerful probe of pulsar evolution:








Using the tkin/τc ratios, we examined








Using the tkin/τc ratios, we examined‣ the distribution of braking indices for our sample, for different P0









‣ the distribution of P0, assuming magnetic-dipole braking (n = 3)










‣ the dependence of spin–velocity alignment on P0











•• The observed preference for n = 1 is an artefact of assuming P0 = 0; relaxing this assumption yields a more uniform distribution of n











•• The observed preference for n = 1 is an artefact of assuming P0 = 0; relaxing this assumption yields a more uniform distribution of n

•• The predictions of SN-kick models favouring alignment for short P0 need to be tested with more data

Coming Soon …

Path of Pulsar B0950+08

-60

-40

-20

Y (m

as)

0

20

-30 -20 -10 0X (mas)

10 20 30

1998.331

1998.874

1999.373

1999.855

ModelData

VLBA pulsar astrometry (PSR π, eΠ) Pulsar absolute polarisation data

(Effelsberg, Parkes, LOFAR, etc.)

100s more spin–velocity orientations will allow for a better statistics and hence a better understanding of the process of spin–velocity alignment

We are currently using our method for calculating pulsar kinematic ages with the 233 pulsar proper motions from Hobbs et al. (2005) as well as other measurements from the literature (MSc degree, Oliver Lux)

+

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