Be born slow or die fast

Spin evolution of neutron stars with alignment and counteralignment

S. Eliseeva, S. Popov, V. Beskin

astro-ph/0611320

Neutron star evolution: the main parameters

P, dot P, B, ………. χ

χ

The latter one is often ignored.

We revisit magneto-rotationalevolution of NSs taking intoaccount the evolution of theinclination angle using twomodels of spin-down:• magneto-dipole• longitudinal current losses

Our aim is to compare the standard assumptions made inNSs studies with theoreticalmodels and to analyse the obtained results.

Evolution of the angle χ

We study magneto-rotational evolution of neutron stars taking into account evolution of the angle between spin and magnetic axis.

It is important that in both models, magneto-dipole and current losses,there are invariants:

Magneto-dipole losses Current losses

Magneto-dipole losses

P0/cos

t1/2

P0

P

t

Death line for mag-d. losses

log P

log P•

•••

••

•

•

••

••

•

Usually any possible dependenceof the death line on the inclinationangle is ignored.

Lifetime as an active pulsar

This value significantly differs from the one without accounting for theevolution of the inclination angle.

Braking index

All known nbr are smaller than 3

Name n P

J1842-0258 2.65 0.326

B9531+21 2.51 0.033

B1509-58 2.84 0.151

J1119-6127 2.91 0.408

B0540-69 2.14 0.050

B0833-45 1.4 0.089

(Livingstone et al. astro-ph/0601530)

There are many attempts to solve this problem (discs, internal structure, etc.)

Age estimates for mag-d.

Pulsars faster becomealigned rotators thancross the death line.

For small initial periodsno significant spin-downis possible, unless the initial angle was very closeto 90 degrees.

Highly magnetized NSsreach the stage of aligned rotators very quickly.

Longitudinal current losses

Longitudinal current losses

cosi4 03

6420

2*

tot c

RBfW

t

P

P0

t14/13

P/sin

Tracks on P-Pdot diagram

B=const, χ=const

B=const, χ≠const

Evolution with changing χ on the P-Pdot diagram issomehow similar to theevolution with decaying B.

Death line for current losses

1

P

sin χ

(Beskin, Gurevich, Istomin 1993)

Orthogonal rotators

See detailed explanation in (Beskin, Nokhrina 2004)

P

sin χ

2/1

22

c

R

ccGJ BB

A3

6420

3*

tot i64

c

R

c

RBfW

dS ][[1tot BJr ScW

cj GJ||A /i Beskin, Gurevich & Istomin, JETP,1983, Beskin & Nokhrina, Astr. Lett, 2004

Orthogonal rotators: details

Age estim. for current losses

Pulsars usually faster become orthogonal rotators than cross the deathline.

Period distributions

37 active PSRs with τch > τkin 1523 active PSRs from the ATNF

Inclination angle distribution

107 active PSRs (Rankin 1990)

43 active PSRs (Beskin et al. 1993)

Initial periods

The initial periods areclose to the observed.

Different neutron stars

HB-PSRs

SGRs

AXPs

The Mag. Seven

RRATs

Age estimates

Accounting for the evolution of the inclination angle has a strong impactonto age estimates of NSs of different types.We give estimates of ages of neutron stars of different types fortwo models of energy losses: magneto-dipole and longitudinal currents.

Age estimates and χmaxχmax corresponds to the moment when aNS leaves the stage of active PSRs.

With χmax we havelower age estimates.

Evolutionary tracks

Arons(free)

RS(hindered)

Beskin, Eliseeva 2005

Track reconstruction

We follow the procedure which we call “inverse track reconstruction”.Knowing the present-day period, angle χ, and the magnetic fieldwe reconstruct the track backwards in time.The procedures is done only for the current losses model.

Track reconstruction

Time of evolution as an active PSR

Time of evolution as an extinct PSR

XDINS RX J0720.4-3125

Pobs=8.39 sec

B=1014 G

Χobs = 50o

Pobs=8.39 sec

B=1013.5 G

Χobs = 50o

Pobs=8.39 sec

B=1013 G

Χobs = 50o

Τ ind = 1 Myr

AXP 1E 2259+586

Pobs=6.98 sec

B=6 1013 G

Χobs = 70o

B=6 1013 G

Χobs = 85o

B=6 1013 G

Χobs = 80o

B=1014 G

Χobs = 85o

Τ ind = 0.01 Myr

XDINS RX J0720.4-3125

Pobs=8.39 sec

B=1013 G

Χobs = 5o

Τ ind = 1 Myr

Pobs=8.39 sec

B=1014 G

Χobs = 5o

Discussion: role of invariants

In both models we discussed quick evolution of NSs towards low losses is due to the existence of invariants.

Of course, the invariants exist only under specific ideal assumptions.

Even without changes in the electro-magnetic “sector” of models,there is a possibility that some non-EM mechanism (like thosediscussed by Macy 1974 or debris discs) are important.

Other possibilities can be related to debris discs (Menou et al. 2001)and vortex line migration (Ruderman).

Discussion: particle escape

In the case of current losses information about distribution of χ behindthe death line can help to choose between free and hindered particle escape.

For free escape all NSs should have sin χ close to 1.However, it is necessary to be sure that significant evolution of theinclination angle took place.

Discussion: AXPs and SGRs

AXPs and SGRs should be born with long periods, if any of the twomodels of energy losses is directly applicable.

Highly magnetized NSs are ideal to test models and to learn something about initial parameters:• Their magneto-rotational evolution is very rapid• There are estimates of their inclination angles (from X-ray light curves, for example)• There are independent age estimates

Observations show that highly magnetized NSs cover a widerange of χ.

Discussion: population synthesis

The usual assumption is that sin χ = 1 = const Somehow, this can be applied also to the case of slowly varying χ, unless it is close to 0 (or 90 in the current losses model).

At the moment there is no theoretical reason to expect slowly varying χ. As we demonstrated,in both models χ varies on the same time scale as P.On the other hand, observational data do not requirestrong evolution of χ during PSR life.

So, assumptions of popsynthesis models are incontradiction with models of spin-down.

Even if both models of energy losses are not correct, the evolution of the inclination angle is a skeleton in a cupboard of popsynthesis models

Summary

We demonstrate that direct application of both – magneto-dipole andcurrent losses – models of radio pulsars leads to absurd results, unlesssome specific assumptions are made:

• initial periods are close to the observed ones or• initial inclination angles are within 1 degree from maximum losses

Both options can be seriously criticized, and detailed population synthesiswhich takes into account the evolution of the inclination angle is necessary.

So, we conclude, that direct application of both models is inappropriate.However, the standard assumption is also not absolutely reliable.

We do not understand well enough how pulsars spin down