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
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