References: 1. Bhattacharya & van den Heuvel, Phys Reports, vol 203, 1, 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.)Kepler’s law If a compact object has mass greater than the maximum allowed for a NS (3 M o -- for causality based EoS) then the object is most likely a BH; x-ray binaries offer one of thex-ray binaries offer one of the best evidence for the existence of black-holesbest 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. Mass function: i: orbital inclination angle. P: orbital period. v 1 : observed velocity of star “1”. If you know the mass of star “1” (from optical observations) then You can determine the minimum Mass of star “2” by taking sin i=1

High-mass x-ray binary (HMXB) NS accretes from wind of its massive star companion. The wind is disrupted at R eq, 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 ~ kev; emission from polar cap. Cyclotron lines have been seen in a dozen or more systems -- E cyclo ~ 11.6 B 12 kev; the magnetic field found from this is ~ few times Gauss. Spin period -- fraction of a sec to 10 3 s; P orb ~ days. Cyclotron frequency:

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 L Eddington & NS radius. 3. Wind fed mass accretion rate in a binary system. Derive the above result in the class, and also the Bondi calculation. Many x-ray pulsars show spin-up Many x-ray pulsars show spin-up. (some have spin-down phase perhaps because of wind fluctuation leading to disk spin reversal).

X-ray transients : 4. Bondi accretion rate (spherical inflow). The accretion rate when the object is moving through the ISM with speed V is:

Low-mass x-ray binary (LMXB) Low mass star filling Roche lobe Corona Accretion disk

Mass determination in a binary system Kepler’s Law: a: semi-major axis P: orbital period i: orbital inclination angle v 1,obs : line of sight speed If we know the velocity of the 2nd star, we know a 2nd mass Function, similar to the one above, and we can determine The mass ratio (m_1/m_2); we still need the orbital inclination In order to determine the masses individually.

1. This is a low mass x-ray binary system (the companion star is low mass which Supplying gas to the compact star via Roche-lobe overflow). 2. Milli-sec pulsars have been spun-up by the accreted gas. 3. Magnetic field must be low for the NS to be spun-up to milli-sec period.

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)