Post on 16-Dec-2015
PulsarsBasic Properties
Supernova Explosion => Neutron Stars
2 RBS2RT
T10 2OBS
m107 8R
days26T
ms4.0T
km10R T108OBS
part of angularmomentum carried
away by shell
field lines frozeninto solar plasma
(surface field)
What is a Neutron Star ?
Pulsar Statistics => 2 basic groups
num
ber
log( T / s )
”Normal“ PulsarsT > 20 ms
T 108
S BMillisecond Pulsars1 ms < T < 20 ms
T 105
O BS
Crab: T = 33 ms Vela: T = 89 ms
Why T > 1 ms ?
virial theorem grav212
21 VEI kin
ms 5.02
5
3
5
2 2
grav2
T
R
GMVMRI
centrifugal forces would disrupt neutron star if rotating faster!
Discovery of Pulsars in Radioastronomy
PSR 1919+21T = 1.33 s
Where is the radiation coming from?
Pulsars as Magnetic Dipole Antennas
mp
mpmisaligned magnetic
rotator model
magnetic braking by emission of polarized
magnetic dipole radiation:
2212
3
40
6
I
dt
dp
cdt
dEm
333
20
6 K
Ic
pm
The Braking Index
magnetic braking predicts: 3 nK n
braking index n measurable via: 222
T
TTn
• Crab: n = 2.515 ± 0.005
• PSR 1509-58: n = 2.8 ± 0.2
• PSR 0540-69: n = 2.01 ± 0.02
not bad...but other braking mechanisms seem to be active in addition!
Magnetic Field at Surface
30
30
4 :magnitude oforder
sincos24
R
pB
eeR
pB
mS
rm
S
33
20
6 Ic
pm
s/T103 15 TTBS
Crab Pulsar: 13107.3ms33
TT T103 8SB
mp
R
re
e
SB
The Age of a Pulsar
T
T
Tn
T
n
KnKnK
nnnPn
211
1
111
1
111
01
10 8 T
10 6 T10
6 yr
1010 yr
T (s)
log 10
T·
TTP
2
1
decay of BS with τ = 107 yr
s/T103 15 TTBS
Example: Crab Pulsar
explosion observed in 1054 =>
pulsar properties today: T = 33 ms
prediction:
13107.3 T
yr 14002
T
TP
yr 948P
Not too bad !!
Rotating Pulsar = Unipolar Inductor
SindS BEB
v rotating
T
OBS
km/ 60v
T108
TO
TOE
equatorpole
ind
s1V10
s1mV10
16
12
• Eind surface forces 1012 times stronger than gravity (Crab)
• charge particles (electrons...) dragged off surface and accelerated to large energies => • pulsar wind (power source for plerions) • coherent radio emission from e+e–-cascades in
B-field at poles
T (s)
log 10
T·
Limit for Coherent Radio Emission
e+e–
dea
th li
ne
theory for coherent emission from e+e–
cascades along pole field lines =>
27 sT10 TBS
s/T103 15 TTBS
317 s10 TT
(M.A. Ruderman, P.G.Sutherland: Astrophys. J. 196 (1975) 51.)
The Pulsar Magnetosphere
magnetosphere: plasma moves along rigid field lines
2
0
2
v2
1
2
densityenergy kineticdensityenergy magnetic
B
Crab in X rays
The Pulsar Magnetosphere
rigid body approximation breaks down at
light cylinder: skm1048 3 TcRL
Magnetosphere Charge Density(P. Goldreich, W.H.Julian: Astrophys. J. 157 (1969) 839.)
|| :tionsimplifica mp
0
0
BB
E elind
ignore currents
Bel
02
density charge rotating
B
at cones neutral
Magnetosphere Charge Density
|| :tionsimplifica mp general case
Open Magnetic Field Lines
toroidal field outside light cylinder dragged by outflowing plasma
equatorial neutral current sheet for misaligned pulsar
STAR
The Origin of X and γ Radiation
vacuum gap acceleration of e± at
• polar cap ??
• outer gap ??
• other models (J.Kirk et al.) ??
differentiate by observation
• X/γ vs. radio pulse pattern
• shape of high energy cut-off
Pulse Patterns up to Egret Energies
What are Millisecond Pulsars?
T (s)
log 10
T·
mostly binary systems!
very bright X-ray sources close to
Eddington luminosity
M
McmrL
T
pgE W103.1
2 313
•
=> accretion!!
Accretion in Strong B-Fields
giant star feeds accretion disk around neutron star
accretion disk dynamics: orbits with slowly decreasing Kepler radii until plasma magnetically dominated:
71
2
12471
20
22
mM
RB
Gr S
M
Alvén radius:
rM
log ( T (L/1030W)6/7 )
log
( -T
/ T
)
·
Spin-Up Phase
angular momentum transfer from disk onto pulsar (friction at rM ):
TLMRBGIT
TS
76
73
712
724
1
620
22
2
1
end of spin-up at Ω = ΩKepler(rM):
msT10
227
6
5
3
min
SM B
GM
rT
•M = MR = 10 km L = LE
T (s)
log 10
T·
Spin-Up Limit
s/T103 15 TTBS
spin-down due to magnetic dipole radiation
limited by spin-up (Tmin):
34
15
s102 TT spin-up lim
it
fulfilled for all ms-binaries but not at all for normal pulsars (as expected)!!
Summary
• models for pulsars and X-ray binaries pretty successful
• open problem: gamma ray emission from pulsars ?
• open problem: which processes contribute to gamma ray emission from surrounding SNRs ?