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Be born slow or die fast

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Be born slow or die fast

Spin evolution of neutron stars with alignment and counteralignment

S. Eliseeva, S. Popov, V. Beskin

astro-ph/0611320

P, dot P, B, ………. χ

- The latter one is often ignored.
- We revisit magneto-rotational
- evolution of NSs taking into
- account the evolution of the
- inclination angle using two
- models of spin-down:
- magneto-dipole
- longitudinal current losses

χ

Our aim is tocompare the

standard assumptions made in

NSs studies with theoretical

models and to analyse the

obtained results.

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

- We demonstrate that direct application of both – magneto-dipole and
- current losses – models of radio pulsars leads to absurd results, unless
- some 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 synthesis
- which 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

Pulsars faster become

aligned rotators than

cross the death line.

For small initial periods

no significant spin-down

is possible, unless the

initial angle was very close

to 90 degrees.

Highly magnetized NSs

reach the stage of

aligned rotators very quickly.

B=const, χ=const

Evolution with changing χ

on the P-Pdot diagram is

somehow similar to the

evolution with decaying B.

B=const,

χ≠const

Pulsars usually faster become orthogonal rotators than cross the deathline.

Accounting for the evolution of the inclination angle has a strong impact

onto age estimates of NSs of different types.

We give estimates of ages of neutron stars of different types for

two models of energy losses: magneto-dipole and longitudinal currents.

We follow the procedure which we call “inverse track reconstruction”.

Knowing the present-day period, angle χ, and the magnetic field

we reconstruct the track backwards in time.

The procedures is done only for the current losses model.

Time of evolution as an active PSR

Time of evolution as an extinct PSR

Pobs=8.39 sec

B=1013.5 G

Χobs = 50o

Τ ind = 1 Myr

Pobs=8.39 sec

B=1014 G

Χobs = 50o

Pobs=8.39 sec

B=1013 G

Χobs = 50o

Pobs=6.98 sec

B=6 1013 G

Χobs = 80o

B=6 1013 G

Χobs = 70o

Τ ind = 0.01 Myr

B=1014 G

Χobs = 85o

B=6 1013 G

Χobs = 85o

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 those

discussed 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).

In the case of current losses information about distribution of χ behind

the 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 the

inclination angle took place.

- 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 wide

range of χ.

AXPs and SGRs should be born with long periods, if any of the two

models of energy losses is directly applicable.

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 modelsχ varies on the same time scale as P.

On the other hand, observational data do not require

strong evolution of χ during PSR life.

So, assumptions of popsynthesis models are in

contradiction 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