Transcript n ics

The Braking Indices
of
Radio Pulsars
Wu Fei
Dep. Astronomy, Peking University
2003.10.21
Introduction
&
 For rotation-powered pulsars, energy loss rate E& I 
&, 
&
&can be
where  is the angular velocity of rotation. , 
obtained observationally.
&
&/ 
&2 (   K n ) parameter describing pulsars’ spin n  
down, employed to test pulsar emission models as well.
 The observed braking indices
B0531+21
B1509-58
B0540-69
B0833-45
J1119-6127
2.510.01
2.837 0.001
2.2 0.1
1.4 0.2
2.91 0.05
 Dipole radiation
& E&
E
d

  3
Ed  22 /(3c3 ) 4  6.2 1027 B122 R66 4ergs/s
n  3???
Some efforts
 Force-free precession of a distorted neutron star (Macy
1974)
 Existence of a companion star (Deminanski 1979)
 Neutrino and photon radiation from superfluid neutron
vortexes (Peng & Huang 1982)
 Multipole field or field evolution (Blandford & Romani 1988)
 Non-standard vacuum dipole model (Melatos 1997)
 Accretion torque (Menou 2001)
 Propeller torque applied by the debris disk (Alpar 2002)
Assumption
 Consider the pulsar braking torques due to magnetodipole
radiation and unipolar generator.
 Energy loss rate of aligned rotators: E&u  2 rp2c where
rp  R R / c ,   GJ
 Assumption: E& E&d  E&u  2 2 /(3c3 )4 , where
  sin 2   5.4 109 R63 B121 cos 2 2  ,
 model-dependent parameters: B12 , 
 Energy conservation:
& 2 23 / 3c3 I

Application
 Xu & Qiao (2001) ApJ: 561,L85
 ICS-induced SCLF model does not work solely on Vela
(PSR B0833-45) and PSR B0540-69.
 For Vela pulsar, obtained   90o calls for improved pulsar
emission models.
Pulsar’s emission models

Goldreich-Julian charge density
E  ( r )  B / c  0
GJ 




 E
 B 
1


1

2
2
2
2
4
2 c  1   r sin  / c 
Ruderman-Sutherland vacuum gap
(VG) model
Near threshold vacuum gap (NTVG)
model
Space charge-limited flow (SCLF)
model
Outer gap (OG) model
Inducement

Imperfect points of RS75 model:
1.
2.
The binding energy problem of ions on the neutron star
surface
Only half of the neutron stars are applicable

Two scenarios:
1.
2.
Bare strange stars (Xu et al. 1999)
Neutron stars with multipolar surface magnetic fields (Gil
& Mitra 2001)
NTVG model
 Stronger field
Larger ion cohesive energy
 Near Threshold Vacuum Gap model (Gil & Mitra, 2001)
 Neutron stars with multipolar surface magnetic fields:
Bs  0.1Bq ; 4.4 1012 G, field curvature radius  neutron star
radius: 0.01  6  1.0
 Different estimates of cohesive energy of surface iron ions
 Abrahams & Shapiro 1991 (AS91)  ; 0.9 B120.73keV
 Jones 1986 (J86)  ; 0.18B120.7 keV
n(P): CR-NTVG model
NTVG
nCR
(  0o )  1.24
n(P): ICS-NTVG model
NTVG
nICS
(  0o )  1.12
Comparison
Model
VG
(CR)
VG
(ICS)
NTVG
(CR)
NTVG
(ICS)
SCLF
(CR)
SCLF
(ICS)
OG
n(=0)
0.86
1.14
1.24
1.12
1.25
2.38
-0.71
n(=90)
3.00
n (obverved)
1.4<n<2.9
Possible picture: VG+OG
 It is quite possible that both inner and outer gaps
coexist in a magnetosphere (Usov 2000; Xu &
Qiao 2001) in order to close the global electric
current.
 But the interaction between two gaps and the pair
plasma properties are very uncertain.
 Employ typical parameters: k  6  R6  B12  1
(except B12=10 in NTVG models)
 Neglect the possible interaction between gaps.
n(P): CR-VG+OG model
n(P): ICS-VG+OG model
 ICS-VG + OG model prefer to work in the pulsar magnetosphere, since
other models provides very small n, while observed braking indices
range from 1.4 to 2.9
n(P): CR-NTVG+OG model
n(P): ICS-NTVG+OG model
n(P): CR-SCLF+OG model
n(P): ICS-SCLF+OG model
Conclusion & discussion

NTVG
NTVG
nCR
(  0o )  1.24, nICS
(  0o )  1.12
both smaller than 1.4, so
NTVG model passes the test proposed by Xu & Qiao 2001
 “ICS-VG + Outer” gaps prefer to work in the pulsar
magnetosphere, since other models implies very small n,
while observed indices range from 1.4 to 2.9
 Little difference between CR-induced and ICS-induced for
NTVG model, form which the energy loss rate is relatively
small compared with the outer gap