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How the inclination angleaffects the electrodynamics
and statistics of radio pulsars
V.S.BeskinLebedev Physical Institute
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• Pulsar MagnetosphereAxisymmetric caseOrthogonal case Inclined rotator
• Statistics of Extinct Neutron StarsEvolution of the inclination angleExtinct radio pulsarsSupersonic propeller
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Pulsar Magnetosphere
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1. Axisymmetric magnetosphere• Explosion in the pulsar magnetosphere science
(Contopoulos, Kazanas & Fendt, Gruzinov, Uzdensky, Mestel et al, Ogura & Kojima, Harding & Muslimov, Spitkovsky, Timokhin, Komissarov, McKinney, Arons et al, Istomin, Beskin & Nokhrina)
• In all the works an implicit assumption was done that the pair creation mechanism in polar region can support any current which is necessary to have MHD solution up to infinity.
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1. Axisymmetric magnetosphere• Explosion in the pulsar magnetosphere science
(Contopoulos, Kazanas & Fendt, Gruzinov, Uzdensky, Mestel et al, Ogura & Kojima, Harding & Muslimov, Spitkovsky, Timokhin, Komissarov, McKinney, Arons et al, Istomin, Beskin & Nokhrina)
• In all the works an implicit assumption was done that the pair creation mechanism in polar region can support any current which is necessary to have MHD solution up to infinity.
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Contopoulos, Kazanas & Fendt, ApJ, 1999
I(Ψ) Michel, 1973
3
6420
tot ~c
RΩBW
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Contopoulos, Kazanas & Fendt, ApJ, 1999
I(Ψ) Arons
3
6420
tot ~c
RΩBW
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Beskin, Gurevich & Istomin, JETP, 1983Beskin & Malyshkin, MNRAS, 1998
ΩΩ ≠F
const || =j
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2. Orthogonal rotator
• Exact solution for zero longitudinal electric current
• Energy loss for local GJ current• Position of the light surface• PSR B1931+24• Inclined split monopole
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Orthogonal rotator, I = 0
Beskin, Gurevich & Istomin (1983)
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Orthogonal rotator, I = 0
Beskin, Gurevich Mestel, Panagi & Istomin (1983) & Shibata (1999)
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Orthogonal rotator, I = 0
• For I = 0 the toroidal magnetic field vanishes at the light cylinder.
• It means that for I = 0 there is NO ENERGY LOSS even for inclined rotator.
• All the energy loss is to be connected with the longitudinal current.
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Orthogonal rotator - energy lossBeskin, Gurevich & Istomin, JETP,1983,
Beskin & Nokhrina, Astr. Lett, 20042/1
22⎟⎠⎞
⎜⎝⎛−≈−=
cΩR
cΩB
cGJ ππρ ΩB
dS ][[1tot ∫ ××= − BJr SΩcW
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Orthogonal rotator - energy lossBeskin, Gurevich & Istomin, JETP,1983,
Beskin & Nokhrina, Astr. Lett, 20042/1
22⎟⎠⎞
⎜⎝⎛−≈−=
cΩR
cΩB
cGJ ππρ ΩB
cj GJ||A ρ/i =
A3
6420
3*
tot i64
⎟⎠⎞
⎜⎝⎛=
cΩR
cRΩBfW
dS ][[1tot ∫ ××= − BJr SΩcW
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Orthogonal rotator - energy lossMestel, Panagi & Shibata, MNRAS,1999
cj
RERB (0)GJ
||LL ρ)()( ≈ϕ
1/2
3
6420
tot ⎟⎠⎞
⎜⎝⎛<
cΩR
cRΩBW
2LLL
Rtot )()(
4dS ][
4L
RRBREccW ϕππ≈×= ∫ BE
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Orthogonal rotator - energy lossSpitkovsky, ApJ Lett., 2006
( )θsin 141 2
3
6420
tot +≈c
RΩBW
It means that iA >>1
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Orthogonal rotator - energy loss
• If iA ~ 1, then Bϕ << Βp on the light cylinder.• It means that the lightsurface |E| = |B| is to Locate in the very vicinity of the light cylinder.
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Inclined rotator – PSR B1931+24• Switch-off – magnetodipole loss only
• Switch-on – current loss only (f* = 1.592 –1.96)
• The ratio
χsin61 2
3
6420
tot cRΩBW =
χcosi8 03
6420
2*
tot cRΩBfW =
5.1χsinχcosi
43
20
2*
off
on
off
on ≈==f
PP
WW
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Inclined split monopole (Bogovalov, A&A,1999)
For arbitrary inclinationangle χ
along the axis, so that
Hence, incline split monopolecannot describe real dipolefield of radio pulsars.
cj (0)GJ|| ρ =
)()( LL RERB ≈ϕ
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Statistics of Extinct Neutron Stars
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Energy loss for χ< π/2Magnetodipole loss
3
6420
tot 61
cRΩBIW =ΩΩ=
t
P
P0
P/Pdot
t1/2
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Energy loss for χ< π/2Magnetodipole loss
χsin61 2
3
6420
tot cRΩBIW =ΩΩ=
const χcos =Ω
t
P
P0
P/Pdot
t1/2
P/cosχ0
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Energy loss for χ< π/2Magnetodipole loss
Current loss
χcosi8 03
6420
2*
tot cRΩBfW =
χsin61 2
3
6420
tot cRΩBW =
const χcos =Ω
const χsin =Ω
t
P
P0
P/Pdot
t1/2
P/sinχ0
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• Time scale of the inclination angle evolution _______is the same as .
• Energy loss decreases mainly by the evolution of the inclination angle.
• Death line depends on the inclination angle.
χχ/τχ = PP/τD =
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Death line
Death line depends on the inclination angle
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Death line
Tauris & Manchester, MNRAS, 298, 625, 1998
Gould Rankin
χ χ
P P
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New point• Extinct radio pulsars – supersonic propeller
transition line depends on the inclination angle as well.
• E.g., for magnetodipole energy loss
χsin 21
Epr PP =
( )sP
Bvcμ 1002
1
6ext
21
72
17
21
30E
−
≈(Lipunov et al, 1996)
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Extinct radio pulsars (RS)
Radio pulsars Supersonic Propeller
Beskin & Eliseeva, 2005
Extinct radio pulsars
s
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Extinct radio pulsars (Arons)
Radio pulsars Supersonic Propeller
Beskin & Eliseeva, 2005
Extinct radio pulsars
s
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Supersonic propeller (RS)
21
cPR2πcosχ ⎟
⎠⎞
⎜⎝⎛=
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Supersonic propeller (Arons)
Бескин, Елисеева, 2005b
( ) ( )
0.93.1
1.7
12
P
0.185P 1427
3.7
12
PA69
P105
2.74
12
2
fNE
5
3
Py0.1B1
dPP
y
B1BPNkP101.2PN
0.8E
25-2
674
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞⎜
⎝⎛+
∫×
×+∫⋅= −⋅
⋅
−−
−
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We predict for supersonic propellers
• P ~ 6−12 s• Pdot ~ 10−13
• N ~ 10−4 Νtot• Aligned or orthogonal
Radio transient sources?
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ConclusionDo not remember that radio pulsarsare nonaxisymmetric objects.
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For discussion• Can the electric current be much
larger/smaller that local GJ one?• Whether the last observations of B1931+24
mean the hard evidence against the free particle escape from the NS surface.
• Is it possible to determine the evolution of the inclination angle?