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

(Mass is determined using the Kepler’s law.)

If a compact object has mass greater than the maximumallowed for a NS (3 Mo -- for causality based EoS) then theobject is most likely a BH; x-ray binaries offer one of the best evidence for the existence of black-holes.

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.

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High-mass x-ray binary (HMXB)

NS accretes from wind of its massive star companion.

The wind is disrupted at Req, where ram pressureEquals the magnetic pressure, and is channeled ontothe 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 moresystems -- Ecyclo ~ 11.6 B12 kev; the magnetic fieldfound from this is ~ few times 1012 Gauss.Spin period -- fraction of a sec to 103s; Porb ~ 1-200 days.

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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.

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˙ M acc = π racc2 vrel ρ

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˙ M acc˙ M w

= M nsM * +M ns( )

2 (v /vw )4

[1+ (v /vw )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).

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X-ray transients:•

4. Bondi accretion rate (spherical inflow).

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˙ M acc ≈ 4πρ∞(GM )2

c∞3

The accretion rate when the object is moving through the ISM with speed V is:

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˙ M acc ≈ 4πρ∞(GM )2

(V 2 +c∞2 )3/ 2

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Low-mass x-ray binary (LMXB)

Low mass star filling Roche lobe

Corona

Accretion disk

Mass determination in a binary system

Kepler’s Law:

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P = 2π a 3/2

G1/ 2 [m1 +m2 ]1/ 2

v1 = 2πa1P , m1a1 = m2a2, a = a1 + a2

v1 = 2πa m2

P(m1 +m2 )

v1,obs = v1 sini = 2πa m2 sin iP(m1 +m2 )

P =P 3/2 (m1 +m2 )3/ 2 v1,obs

3/ 2

(2π )1/ 2 (m2 sin i)3/ 2 G1/ 2 [m1 +m2 ]1/2 =P 3/ 2 (m1 +m2 ) v1,obs

3/ 2

(2π )1/ 2 (m2 sin i)3/ 2 G1/ 2

Pv1,obs3

2πG = (m2 sin i)3

(m1 +m2 )2

a: semi-major axisP: orbital periodi: orbital inclination anglev1,obs: line of sight speed

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)