How the inclination angle affects the electrodynamics and ...How the inclination angle affects the...
Transcript of How the inclination angle affects the electrodynamics and ...How the inclination angle affects the...
How the inclination angleaffects the electrodynamics
and statistics of radio pulsars
V.S.BeskinLebedev Physical Institute
• Pulsar MagnetosphereAxisymmetric caseOrthogonal case Inclined rotator
• Statistics of Extinct Neutron StarsEvolution of the inclination angleExtinct radio pulsarsSupersonic propeller
Pulsar Magnetosphere
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.
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.
Contopoulos, Kazanas & Fendt, ApJ, 1999
I(Ψ) Michel, 1973
3
6420
tot ~c
RΩBW
Contopoulos, Kazanas & Fendt, ApJ, 1999
I(Ψ) Arons
3
6420
tot ~c
RΩBW
Beskin, Gurevich & Istomin, JETP, 1983Beskin & Malyshkin, MNRAS, 1998
ΩΩ ≠F
const || =j
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
Orthogonal rotator, I = 0
Beskin, Gurevich & Istomin (1983)
Orthogonal rotator, I = 0
Beskin, Gurevich Mestel, Panagi & Istomin (1983) & Shibata (1999)
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.
Orthogonal rotator - energy lossBeskin, Gurevich & Istomin, JETP,1983,
Beskin & Nokhrina, Astr. Lett, 20042/1
22⎟⎠⎞
⎜⎝⎛−≈−=
cΩR
cΩB
cGJ ππρ ΩB
dS ][[1tot ∫ ××= − BJr SΩcW
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
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
Orthogonal rotator - energy lossSpitkovsky, ApJ Lett., 2006
( )θsin 141 2
3
6420
tot +≈c
RΩBW
It means that iA >>1
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.
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
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
Statistics of Extinct Neutron Stars
Energy loss for χ< π/2Magnetodipole loss
3
6420
tot 61
cRΩBIW =ΩΩ=
t
P
P0
P/Pdot
t1/2
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
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
• 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 =
Death line
Death line depends on the inclination angle
Death line
Tauris & Manchester, MNRAS, 298, 625, 1998
Gould Rankin
χ χ
P P
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)
Extinct radio pulsars (RS)
Radio pulsars Supersonic Propeller
Beskin & Eliseeva, 2005
Extinct radio pulsars
s
Extinct radio pulsars (Arons)
Radio pulsars Supersonic Propeller
Beskin & Eliseeva, 2005
Extinct radio pulsars
s
Supersonic propeller (RS)
21
cPR2πcosχ ⎟
⎠⎞
⎜⎝⎛=
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
⎟⎠⎞
⎜⎝⎛
⎟⎠⎞⎜
⎝⎛+
∫×
×+∫⋅= −⋅
⋅
−−
−
We predict for supersonic propellers
• P ~ 6−12 s• Pdot ~ 10−13
• N ~ 10−4 Νtot• Aligned or orthogonal
Radio transient sources?
ConclusionDo not remember that radio pulsarsare nonaxisymmetric objects.
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?