Download X-ray Binaries

References:
1. Bhattacharya & van den Heuvel, Phys Reports, vol 203, 1,1991
2. X-ray Binaries, edited by Lewin, van Paradijs, and
van den Heuvel, 1995, Cambridge university press.
Evidence for Black-Holes
•
If a compact object has mass greater than the maximum
allowed for a NS (3 Mo -- for causality based EoS) then the
object is most likely a BH; x-ray binaries offer one of the
best evidence for the existence of black-holes.
(Mass is determined using the Kepler’s law.)
• Orbits of individual stars at the center of our Galaxy
provide compelling evidence for the existence of
supermassive BHs.
• Keplerian rotation profile is the central disk of NGC 4258
(a mega-maser galaxy) as the only other case where we
are confident that there is a massive BH at the center.
High-mass x-ray binary (HMXB)
• NS accretes from wind of its massive star companion.
• The wind is disrupted at Req, where ram pressure
Equals the magnetic pressure, and is channeled onto
the magnetic pole which results in pulsed emission.
(The majority of HMXBs are x-ray pulsars.)
• Hard spectra upto ~ 10-20 kev; emission from polar cap.
• Cyclotron lines have been seen in a dozen or more
systems -- Ecyclo ~ 11.6 B12 kev; the magnetic field
found from this is ~ few times 1012 Gauss.
• Spin period -- fraction of a sec to 103s; Porb ~ 1-200 days.
HMXB continued (order of magnitude estimates)
1. Energy production efficiency onto a NS and BH.
10% for NS; 6%--42% for BHs.
2. Effective temperature for LEddington & NS radius.
3. Wind fed mass accretion rate in a binary system.
2
Ýacc   racc
M
v rel 
Ýacc
M

Ý
Mw

M ns
M * M n s

2
(v /v w ) 4
[1 (v /v w ) 2 ]3 / 2
• Many x-ray pulsars show spin-up.
(some have spin-down
phase perhaps because of wind

fluctuation leading to disk spin reversal).
4. Bondi accretion rate (spherical inflow).
Ýacc  4 
M
(GM )2
 c3

• The accretion rate when the object is moving through
the ISM with speed V is:

Ýacc  4 
M
• X-ray transients:

(GM )2
 (V 2 c 2 )3/ 2

Low-mass x-ray binary (LMXB)
Corona
Low mass star filling
Roche lobe
Accretion disk
Mass determination in a binary system
a: semi-major axis
P: orbital period
i: orbital inclination angle
v1,obs: line of sight speed
Kepler’s Law:
2  a 3/ 2
P  G 1/ 2 [m
1
v1 
v1 
2 a1
P
m 2 ]1/ 2
m1a1  m2 a2 ,
,
a  a1  a2
2 a m 2
P(m1 m 2 )
v1,obs  v1 sin i 
2 a m 2 sin i
P(m1 m 2 )
3/2
P 3 / 2 (m1 m 2 )3/ 2 v1,obs
P  (2  )1 / 2 (m
3
Pv1,obs
2 G
3/ 2 1/ 2
1/ 2
sin
i)
G
[m
m
]
2
1
2
(m 2 sin i)3
 (m
2
m
)
1
2
3/2
P 3/ 2 (m1 m 2 ) v1,obs
 (2  )1 / 2 (m
3 / 2 1/ 2
sin
i)
G
2
from Charles & Seward,
“Exploring the x-ray Universe”,
Cambridge press.
from Charles & Seward,
“Exploring the x-ray Universe”,
Cambridge press.
Correlation between spin-up rate and x-ray lumninosity
(from Charles & Seward, “Exploring the x-ray Universe”, Cambridge press)