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Maurizio Paolillo » 13.X-ray binaries

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!).

Schematic configuration of an accreting binary system (LMXB).

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:

E_lost=Gm_pM_WD/r~(6.67×10¹¹) (2×10³⁰) (1.67×10^-27)/(6.5×10⁶)~3.4×10^-14 J=240 keV per proton;
m_p ~900 MeV (0.511 MeV x 2000).

Thus GM_WD/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.

Roche lobes and Lagrangian points surrounding a binary system.

X-ray binaries: accretion modes

Transfer of mass may occur via:

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

Roche lobe overflow.

Wind capture accretion.

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.

X-ray binary lifetimes

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

τ_life~Mc²/L, where M mass of the star and L its luminosity.
The empirical relation between stellar mass and luminosity is L~M^3.5.
Combining the two: τ_life~M^-^2.5,
1M_⨀: τ_life~10¹⁰yr
10M_⨀: τ_life~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, L_eddington 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.

Galactic NS and BH masses

Estimated masses of galactic Neutron Stars and Black Hole systems.

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, T_BB 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 ⇒ kT_BB~2keV
WD: 3M_⨀, R=5000km ⇒ kT_BB~0.1keV
BH: R=2GM/c² ⇒ kT_BB~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 L_X<<10³⁸ erg/s.

LMXRBs:

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

HMXRBs:

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

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

Luminosity functions of High and Low Mass X-ray binaries (from Gilfanov 2004).

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.