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