Universitat de - Departament d'Astronomia i Meteorologia ...

2 Chapter 1. Introduction and background
Several scenarios have been proposed to explain the X-ray emission of X-ray bina-
ries, depending on the nature of the compact object, its magnetic field in the case
of neutron stars and on the geometry of the accretion flow. In any case, the ac-
creted matter is accelerated to relativistic speeds, transforming its potential energy
provided by the intense gravitational field of the compact object into kinetic energy.
Assuming that this kinetic energy is finally radiated, we can compute the accretion
luminosity as:
Laccr 1
2 ˙
MaccrV 2 =
GMX ˙
Maccr
RX
, (1.1)
where ˙
Maccr is the accretion rate, V is the free fall speed defined as V = 2GMX/RX,
G is the gravitational constant and MX and RX are the mass and radius of the com-
pact object, respectively. On the other hand, there is a maximum theoretical value
for the accretion rate, when the radiation pressure balances gravity, called the Ed-
dington limit and expressed as:
˙
MEdd = 4πmpcRX
σT
, (1.2)
where mp is the proton mass, c is the speed of light and σT is the Thomson cross
section. The corresponding luminosity can be expressed as:
LEdd = 4πGMXmpc
σT
. (1.3)
In an X-ray binary, the accreted matter carries angular momentum, and on its
way to the compact object it usually forms an accretion disk around it. The matter
in the disk looses angular momentum due to viscous dissipation, which produces a
heating of the disk, and falls towards the compact object in a spiral trajectory. The
black body temperature of the last stable orbit in the case of a BH accreting at the
Eddington limit is given by:
T
2 × 10
K
7
−1/4 MX
M⊙
. (1.4)
For a compact object of a few solar masses the obtained temperature is ∼ 10 7 K.
At this temperature the energy will be mainly radiated in the X-ray domain of the
electromagnetic spectrum.
Using Eq. 1.1 we can see that for an accreting BH, taking as final radius the
Schwarzschild radius defined as RS = 2GMX/c 2 , the emitted accretion luminosity
is:
Laccr 1
2 ˙
Maccrc 2 . (1.5)