Accretion in Binaries II
• Classes of X-ray binaries– Low-mass (BH and NS)– High-mass (BH and NS)– X-ray pulsars (NS)– Be/X-ray binaries (NS)
• Distinguishing NS versus BH binaries
X-Ray Binaries
• Low mass: companion star mass less than one solar mass
• High mass: companion star mass greater than one solar mass.
bow shockmatter collects in wake
racc
Wind Fed Accretion
Wind Fed Accretion
Matter in wind will accrete if its speed is less than the escape speed from the compact object at the radius of closest approach
Vw = wind velocity
Vx = velocity of compact object
Rc = capture radius
22
2
WX
Xc VV
GMR
Luminosity
Xwworb
w
orb
accw
vvifvD
GMcmcmL
D
rmm
,2
4
4
4
222
2
If a neutron star binary has the followingparameters, Dorb=1012 cm, vw= 1000 km/s,
)(1044
1 242
42
cmcmv
c
D
RL ww
worb
s
Accreting Pulsars
High mass X-ray binary
Accretion in magnetic field
Magnetosphere boundary
Assuming spherical accretion and a dipole field with the dipole moment = BSRS
3, where RS and BS are the radius of the star and the field strength at the surface.
Magnetopheric boundary, rM, is where the magnetic pressure balances the ram pressure of accreted matter
22
8vp
Bp rammag
7/4
330
7/17/2
168
cmG10g/s10 cm101.5
M
MmrM
Accretion Torque
7/6
2
Find
2 and Note
staron Torque
transportmomentumAngular
PLP
P
PPr
mGML
rvmI
rvm
M
m
Accretion Torque
Pulse Period Variations
What happens if the spin rate of the pulsar is faster than Keplerian rotation rate at the magnetospheric boundary?
Corotation radius lies outside magnetopheric boundary
Equilibrium Period
The accreted matter ceases to transfer angular momentumto the neutron star when
For a maximum (Eddington) luminosity and typical neutron star mass and radius, we have
7/6
9min
G10002.0
B
s
P
7/6
14/312
2/1
2/13
8)(
22
)(
SM
eq
MK
BmGM
R
GMGM
rP
r
Emission Geometry
Accreted plasma
Shock front
Settling matterHot spot
Pulse Profiles
Landau Levels
Quantization of energy due to magnetic field:
Landau levels
where is the momentum of the electron parallel to the field,n is the quantum number, and Bcrit is the critical field,
||p
Ghe
cmB ecrit
1332
104.4
For B << Bcrit, the spacing between adjacent levels is
G
BkeVB
cm
ehEEE
enncyc 121 10
6.11
Cyclotron Lines
X-Ray Pulsar Cen X-3
Pulses are modulated at orbital period of 2.09 days
Distinguishing BH vs NS
G
KP
MM
iMfX
X
2)(
sin 300
20
33
0
XMf 0Mass function
Compact object masses