# Maurizio Paolillo » 13.X-ray binaries

### Contents

• Low-mass X-ray binaries.
• High-mass X-ray binaries.
• Accretion disk structure.
• Spectral signatures.
• Ultraluminous X-ray binaries (ULX)

### X-ray binaries

Binary stars are a common configuration in the Universe.

Binary systems where one of the members is a compact stellar remnant (white dwarf, neutron star or Black Hole) can become strong sources of X-ray radiation, when matter lost from one member is accreted on the compact companion.

X-ray binaries are commonly divided into Low and High mass X-ray binaries (LMXB or HMXB) depending on the mass of the donor star (N.B. not of the compact object!).

### Efficiency of accretion processes

Accretion onto a compact object is one of the most efficient energy production processes.
Consider for instance accretion onto a White Dwarf:

• Elost=GmpMWD/r~(6.67×1011) (2×1030) (1.67×10-27)/(6.5×106)~3.4×10-14 J=240 keV per proton;
• mp ~900 MeV (0.511 MeV x 2000).

Thus GMWD/rc2=0.02% of rest mass is released in accretion.
Consider that the average efficiency of fusion processes is ~ 0.7%.

Exercise: calculate the efficiency for a Neutron Star (1.4M, R=10km ) or a Black Hole (R=2GM/c2 ) X-ray binary.

### Binary star orbits

The path of a particle orbiting a binary system is influenced by the gravitational potential of the system.

• Roche lobes: the equipotential surfaces. The volume around a star in a binary system in which, if you were to release a particle, it would fall back onto the surface of that star.
• L1: inner Lagrangian point where the gravity from the two stars is equal. Mass is transferred from one star to the other through L1.

### X-ray binaries: accretion modes

Transfer of mass may occur via:

1. Roche-lobe overflow through L1. An accretion disk is formed.
2. Capture of the stellar wind of the primary. An accretion disk may form.

### HMXB vs LMXB

HMXRBs:

• primary massive star (>2M);
• short-lived (~107yr);
• measure instantaneous star-formation rate.

LMXRBs:

• primary low-mass star (~1M);
• long lived (~109yr);
• measure star-formation integrated over the lifetime of the galaxy, i.e. total stellar mass.

Evolution timescale is approximately the time it takes for the star to radiate the energy produced by H→He thermonuclear reactions:

τlife~Mc2/L, where M mass of the star and L its luminosity.
The empirical relation between stellar mass and luminosity is L~M3.5.
Combining the two: τlife~M-2.5,
1M: τlife~1010yr
10M: τlife~107yr

Thus:
LMXBs are associated with older stellar populations than HMXBs.

### Eddington luminosity and mass limit

In the assumption of spherical accretion it is possible to derive limits on the mass and luminosity of the accreting object considering that radiation pressure cannot exceed gravitational pull. This limit is commonly referred to as “Eddington limit”.
The radiation force on a free electron (the gas can be assumed completely ionized) is: $F_l=\frac{L\sigma_T}{4\pi r^2 c}$

Where $\sigma_T$ is the Thomson cross section described in a previous lecture, while the gravitational force: $F_g=\frac{GMm}{r^2}$

At equilibrium the two will balance each other yielding: $L_{Edd}=\frac{4\pi cGMm}{\sigma_T}$

The upper limit in luminosity, Leddington scales with mass of accreting source: $L_{Edd}=1.3\times 10^{38}M/M_\odot$ erg/s

The inverse argument yields a lower mass limit for a given luminosity.

### Galactic Black Hole binaries Black hole X-ray binaries in our Galaxy. The figure shows the companion star and the accretion disc (including its inclination) drawn to scale. For a comparison, the Sun - Mercury distance is shown.

### X-ray binaries: disk temperatures

To understand the radiation emitted by an accretion disk we can assume that the disk emits as a Black Body.
We define a Black-body temperature, TBB as the typical temperature of the source if it radiated as black body: $L=2\pi r^2 \sigma T_{BB}^4$ $T_{BB}=\left (\frac{L}{2\pi r^2 \sigma}\right )^{1/4}$

For typical values of compact accreting sources (white dwarfs, neutron stars and black holes) black body radiation peaks at the X-ray regime.
Assuming the Eddinghton limit: $kT_{BB}=6.7\times [(M/M_\odot) (R/km)^{-2}]^{1/4}$

Using typical values for accreting sources:
NS: 1.4M, R=10km ⇒ kTBB~2keV
WD: 3M, R=5000km ⇒ kTBB~0.1keV
BH: R=2GM/c2kTBB~1keV(M/M)-1/4
Actually the disk radiates as a multi-temperature BB, with the highest temperatures reached at the inner edges (see lectures on AGNs for a detailed treatement).

### X-ray binary spectra

Complex X-ray spectra:

• Power-law component with Γ=1-2 (hot corona + Compton scattering)
• Black-body component at soft energies (<1keV; accretion disk)

The spectral analysis is complicated by variability, change of the relative normalization of the different componente (the so called high/low states), the presence of different levels of photoelectric absorption etc… X-ray spectrum of an accreting binary system, with a cold accretion disk component and a hot power-law component due to, i.e. comptonization in a hot corona.

### X-ray binaries: luminosity distribution

X-ray binaries typically have LX<<1038 erg/s.

LMXRBs:

• Flat distribution at faint-end.
• Max luminosities ~1038-1039 erg/s.

HMXRBs:

• Power-law distribution.
• Max LX~ 1040 erg/s, i.e. brighter than the Milky Way!!!

For LX>1039 erg/s we enter the ULX regime, since the Eddington argument implies very large masses of the accreting object.

### Ultra-Luminous X-ray Sources

Based on the Eddington limit argument, X-ray binaries with luminosities in excess of ~1039 erg/s are believed to host intermediate mass black holes with masses M~100M. Their existence and origin are however still matter of debate.

Alternative explanations include:

• Non-spherical accretion, thus allowing violation of the Eddington limit;
• Collimated emission, i.e. in a funnel, so that the total luminosity is lower than in the case of spherical symmetry, allowing smaller masses for the accreting object. An X-ray binary system with collimated emission along the jet. These configurations can appear as ULXs even if of low mass.

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