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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.
Wind Fed Accretion
racc
bow shock
matter collects in wake
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
2GM X
Rc  2
2
VX  VW
Luminosity
2
m&w  racc 

 
m& 
4  Dorb 
L  m&c 
2
m&wc  2GM 
2
4
2

 vw 4 , if vw  v X
 Dorb 
If a neutron star binary has the following
parameters, Dorb=1012 cm, vw= 1000 km/s,
 1  R 2  c 4 
2
4
2
s




&
&


L 
mwc  4 10 (mwc )



 4  Dorb   vw  
Accreting Pulsars
High mass X-ray binary
Accretion in magnetic field
Magnetosphere boundary
Magnetopheric boundary, rM, is where the magnetic
pressure balances the ram pressure of accreted matter
pmag
B2

 pram  v 2
8
Assuming spherical accretion and a dipole field with the
dipole moment m = BSRS3, where RS and BS are the
radius of the star and the field strength at the surface.
 m& 
rM  5.110 cm  16 
 10 g/s 
8
2 / 7
 M 


 M 
1 / 7
m


 30
3 
 10 G  cm 
4/7
Accretion Torque
Angular momentum transport  m&v r
&  m&v rm
Torque on star  I
GMm&
2 &
&  2 P
Note L 
and 
rM
P
P&
6/7
Find  PL
P
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 momentum
to the neutron star when
   K (rM )
1/ 2
 r 

Peq  2
 GM 
3
M

2  R



1/ 2 
(GM )  8GMm&
12
3 / 14
BS6 / 7
For a maximum (Eddington) luminosity and typical neutron
star mass and radius, we have
Pmin
 B 
 9 
0.002s  10 G 
6/7
Emission Geometry
Accreted plasma
Shock front
Hot spot
Settling matter
Pulse Profiles
Landau Levels
Quantization of energy due to magnetic field:
Landau levels
where p|| is the momentum of the electron parallel to the field,
n is the quantum number, and Bcrit is the critical field,
Bcrit
me2c 3

 4.4 1013 G
eh
For B << Bcrit, the spacing between adjacent levels is
Ecyc  En1  En 
 B 
he
B  11.6 keV  12 
me c
 10 G 
Cyclotron Lines
X-Ray Pulsar Cen X-3
Pulses are
modulated
at orbital
period of
2.09 days
Distinguishing BH vs NS
Mass function
3
3
P
K
sin
i
M
0 0
f0 

2
(M X  M 0 )
2G
3
X
f0  M X
Compact object masses