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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

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Neutron star evolution: the main parameters P, dot P, B, ………. χ 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 Our aim is to compare the standard assumptions made in NSs studies with theoretical models and to analyse the obtained results.

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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

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Magneto-dipole losses P 0 /cos t 1/2 P0P0 P t

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Death line for mag-d. losses log P Usually any possible dependence of the death line on the inclination angle is ignored.

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Lifetime as an active pulsar This value significantly differs from the one without accounting for the evolution of the inclination angle.

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Braking index All known n br are smaller than 3 Name n P J1842-02582.650.326 B9531+212.510.033 B1509-582.840.151 J1119-61272.910.408 B0540-692.140.050 B0833-451.40.089 (Livingstone et al. astro-ph/0601530) There are many attempts to solve this problem (discs, internal structure, etc.)

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Age estimates for mag-d. 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.

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Longitudinal current losses

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t P P0P0 t 14/13 P/sin

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Tracks on P-Pdot diagram B=const, χ=const B=const, χ≠const Evolution with changing χ on the P-Pdot diagram is somehow similar to the evolution with decaying B.

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Death line for current losses 1 P sin χ (Beskin, Gurevich, Istomin 1993)

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Orthogonal rotators See detailed explanation in (Beskin, Nokhrina 2004) P sin χ

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Beskin, Gurevich & Istomin, JETP,1983, Beskin & Nokhrina, Astr. Lett, 2004 Orthogonal rotators: details

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Age estim. for current losses Pulsars usually faster become orthogonal rotators than cross the deathline.

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Period distributions 37 active PSRs with τ ch > τ kin 1523 active PSRs from the ATNF

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Inclination angle distribution 107 active PSRs (Rankin 1990) 43 active PSRs (Beskin et al. 1993)

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Initial periods The initial periods are close to the observed.

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Different neutron stars HB-PSRs SGRs AXPs The Mag. Seven RRATs

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Age estimates 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.

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Age estimates and χmax χmax corresponds to the moment when a NS leaves the stage of active PSRs. With χmax we have lower age estimates.

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Evolutionary tracks Arons (free) RS (hindered) Beskin, Eliseeva 2005

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Track reconstruction 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.

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Track reconstruction Time of evolution as an active PSR Time of evolution as an extinct PSR

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XDINS RX J0720.4-3125 P obs =8.39 sec B=10 14 G Χ obs = 50 o P obs =8.39 sec B=10 13.5 G Χ obs = 50 o P obs =8.39 sec B=10 13 G Χ obs = 50 o Τ ind = 1 Myr

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AXP 1E 2259+586 P obs =6.98 sec B=6 10 13 G Χ obs = 70 o B=6 10 13 G Χ obs = 85 o B=6 10 13 G Χ obs = 80 o B=10 14 G Χ obs = 85 o Τ ind = 0.01 Myr

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XDINS RX J0720.4-3125 P obs =8.39 sec B=10 13 G Χ obs = 5 o Τ ind = 1 Myr P obs =8.39 sec B=10 14 G Χ obs = 5 o

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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 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).

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Discussion: particle escape 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.

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Discussion: AXPs and SGRs AXPs and SGRs should be born with long periods, if any of the two models 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 wide range of χ.

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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 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

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Summary 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

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