How the inclination angle affects the electrodynamics and statistics of radio pulsars. V.S.Beskin Lebedev Physical Institute

Transcription

1 How the inlination angle affets the eletrodynamis and statistis of radio pulsars V.S.Beskin Lebedev Physial Institute

2 Pulsar Magnetosphere Axisymmetri ase Orthogonal ase Inlined rotator Statistis of Extint Neutron Stars Evolution of the inlination angle Extint radio pulsars Supersoni propeller

3 Pulsar Magnetosphere

4 1. Axisymmetri magnetosphere Explosion in the pulsar magnetosphere siene (Contopoulos, Kazanas & Fendt, Gruzinov, Uzdensky, Mestel et al, Ogura & Kojima, Harding & Muslimov, Spitkovsky, Timokhin, Komissarov, MKinney, Arons et al, Istomin, Beskin & Nokhrina) In all the works an impliit assumption was done that the pair reation mehanism in polar region an support any urrent whih is neessary to have MHD solution up to infinity.

5 1. Axisymmetri magnetosphere Explosion in the pulsar magnetosphere siene (Contopoulos, Kazanas & Fendt, Gruzinov, Uzdensky, Mestel et al, Ogura & Kojima, Harding & Muslimov, Spitkovsky, Timokhin, Komissarov, MKinney, Arons et al, Istomin, Beskin & Nokhrina) In all the works an impliit assumption was done that the pair reation mehanism in polar region an support any urrent whih is neessary to have MHD solution up to infinity.

6 Contopoulos, Kazanas & Fendt, ApJ, 1999 I(Ψ) Mihel, 1973 W tot ~ B 0 Ω 3 4 R 6

7 Contopoulos, Kazanas & Fendt, ApJ, 1999 I(Ψ) Arons W tot ~ B 0 Ω 3 4 R 6

8 Beskin, Gurevih & Istomin, JETP, 1983 Beskin & Malyshkin, MNRAS, 1998 j =onst Ω Ω F

9 . Orthogonal rotator Exat solution for zero longitudinal eletri urrent Energy loss for loal GJ urrent Position of the light surfae PSR B Inlined split monopole

10 Orthogonal rotator, I = 0 Beskin, Gurevih & Istomin (1983)

11 Orthogonal rotator, I = 0 Beskin, Gurevih Mestel, Panagi & Istomin (1983) & Shibata (1999)

12 Orthogonal rotator, I = 0 For I = 0 the toroidal magneti field vanishes at the light ylinder. It means that for I = 0 there is NO ENERGY LOSS even for inlined rotator. All the energy loss is to be onneted with the longitudinal urrent.

13 Orthogonal rotator - energy loss ρ GJ Beskin, Gurevih & Istomin, JETP,1983, Beskin & Nokhrina, Astr. Lett, 004 ΩB = π ΩB π ΩR 1/ 1 Wtot = Ω [ r [ J B]dS S

14 Orthogonal rotator - energy loss ρ GJ Beskin, Gurevih & Istomin, JETP,1983, Beskin & Nokhrina, Astr. Lett, 004 ΩB = π ΩB π ΩR 1/ 1 Wtot = Ω [ r [ J B]dS S W tot = f 64 3 * B 0 Ω 3 4 R 6 ΩR i A i = A j / ρ GJ

15 Orthogonal rotator - energy loss Mestel, Panagi & Shibata, MNRAS,1999 j R E R B (0) GJ L L ρ ) ( ) ϕ ( 1/ tot < ΩR R Ω B W L L L R tot ) ( ) ( 4 ds ] [ 4 L R R B R E W ϕ π π = B E

16 W Orthogonal rotator - energy loss tot B Ω R It means that i A >>1 Spitkovsky, ApJ Lett., 006 ( 1 sin θ)

17 Orthogonal rotator - energy loss If i A ~ 1, then B ϕ << Β p on the light ylinder. It means that the light surfae E = B is to Loate in the very viinity of the light ylinder.

18 Inlined rotator PSR B Swith-off magnetodipole loss only W = tot 6 Swith-on urrent loss only (f * = ) W = tot The ratio W W on off B Ω R sin 3 = f * 8 P P on off B = 0 Ω 3 3 f 4 4 * R 6 χ i 0 os χ i0 os χ 1.5 sin χ

19 Inlined split monopole (Bogovalov, A&A,1999) For arbitrary inlination angle χ j = (0) ρ GJ along the axis, so that Bϕ ( RL ) E ( RL ) Hene, inline split monopole annot desribe real dipole field of radio pulsars.

20 Statistis of Extint Neutron Stars

21 Energy loss for χ< π/ Magnetodipole loss W = IΩΩ = tot 1 6 B 0 Ω 3 4 R 6 P t 1/ P 0 P/Pdot t

22 Energy loss for χ< π/ Magnetodipole loss B0 Ω W tot = IΩΩ = 6 Ω os χ = onst R sin χ P t 1/ P/osχ 0 P 0 P/Pdot t

23 Energy loss for χ< π/ Magnetodipole loss 4 B0 Ω R W tot = 3 6 Ω os χ = onst 1 6 sin χ P t 1/ P/sinχ 0 Current loss f* W tot = 8 Ω sin χ = B0 Ω onst 3 4 R 6 i 0 os P 0 χ P/Pdot t

24 Time sale of the inlination angle evolution is χ/χ the same as. τ χ = = P/ P Energy loss dereases mainly by the evolution of the inlination angle. Death line depends on the inlination angle. τ D

25 Death line Death line depends on the inlination angle

26 Death line Gould Rankin P P χ Tauris & Manhester, MNRAS, 98, 65, 1998 χ

27 New point Extint radio pulsars supersoni propeller transition line depends on the inlination angle as well. E.g., for magnetodipole energy loss P pr = P E 1 sin χ μ 30 7 v 7 P 100 s E 1 ( B ) ext (Lipunov et al, 1996)

28 Extint radio pulsars (RS) Beskin & Eliseeva, 005 s Radio pulsars Extint radio pulsars Supersoni Propeller

29 Extint radio pulsars (Arons) Beskin & Eliseeva, 005 s Radio pulsars Extint radio pulsars Supersoni Propeller

30 Supersoni propeller (RS) osχ π R = P 1

31 Supersoni propeller (Arons) N A P 5.74 ( P) = P k N P B ( 1 + B ) P 0.185P 0.8 E P y 7 14 E N B f dp 4 P y P Бескин, Елисеева, 005b

32 We predit for supersoni propellers P ~ 6 1 s Pdot ~ N ~ 10 4 Ν tot Aligned or orthogonal Radio transient soures?

33 Conlusion Do not remember that radio pulsars are nonaxisymmetri objets.

34 For disussion Can the eletri urrent be muh larger/smaller that loal GJ one? Whether the last observations of B mean the hard evidene against the free partile esape from the NS surfae. Is it possible to determine the evolution of the inlination angle?