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 ?