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

Equations governing rocket engine Thrust are same as the accretion problem! Adding a nozzle (the hour glass shape) increases the thrust by about 60% (for adiabatic index 5/3 gas) and by a much larger factor as the index gets closer to 1. The gas speed at the Throat must be Mach 1 otherwise the Thrust will not increase! Rocket Propulsion Thrust: Equations: Eliminate rho from the two equations above to yield:

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

Binary classification

Roche Lobe Roche Potential Potential in a rotating frame:

Accretion disk (order of magnitude estimate) Theory for geometrically thin and optically thick disk 1. Disk thickness: 2. Temperature as a function of r 3. Emergent spectrum

Keith Horne, 1993, in “Accretion disks in Compact stellar systems”, Ed. J.C.Wheeler; World Scientific. During outburst Quiescence data

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

Chandrashekhar-Balbus-Hawley mechanism Analysis of a mechanical model consisting of a spring and two point mass on an orbit. Balbus & Hawley, 1998, Rev. Mod. Phys., Vol. 70, p (sections III A, B, & IV B in particular)

Schwarzschild Black-hole Metric: Effective potential: (Shapiro & Teukolsky: BH, WD & NS; chapter 12)

Effective potential for several different L The binding energy of the last stable circular orbit is: 5.72%.

Kerr Black-hole Metric in Boyer-Lindquist coordinate: |a|<M Horizon occurs where:

Ergosphere Angular speed allowed for a particle at a fixed r and theta: The quantity in the bracket must be negative. This implies That the allowed range for rotation speed is: For r<r s the particle cannot remain stationary and is forced to rotate with the black-hole. The region between r H and r s is called the Ergosphere.

Ergosphere of a Kerr black hole

Semenov et al., 2004, Science 305, 978 A simulation of a plasma-filled magnetic flux tube that accretes toward a rapidly rotating black hole. Large-scale torsional stresses are imparted to the flux tube by the plasma rotating with the spacetime geometry near the black hole in the ergosphere (the shaded region). Near the black hole, the red portion of the flux tube is of negative energy as viewed from asymptotic infinity. The inflow of this negative energy is globally equivalent to the extraction of the rotational energy of the black hole. The twisted, rotating, magnetic flux tube that is radiated in the process is a relativistic jet that transports plasma and huge reserves of electromagnetic energy at speeds close to that of light.

Semenov et al., 2004, Science 305, 978 A close-up of the dynamo region that produces the azimuthal magnetic field in the simulation of Movie S1. The dynamo is the extended region in which the azimuthal magnetic field changes sign and the flux tube changes from red to blue. Within the dynamo, Poynting flux (electromagnetic energy) is radiated outward while plasma is simultaneously torqued onto negative energy trajectories (the red portion of the flux tube) downstream.

Semenov et al., 2004, Science 305, 978 This simulation is similar to Movie S1 except that there are four accreting flux tubes, not just one. This movie shows how the quasar jets can be thought of as a bundle of twisted magnetic flux tubes. The scenario depicted in the movie is of particular interest for the relevant case in which there is a continual (not necessarily steady) accretion of vertical flux. One flux tube follows behind another as the magnetosphere is built up over time.

It can be shown that the energy (per unit mass) for the last stable circular orbit is %. Therefore, we one can extract about 42.3% energy from the accretion around a maximally rotating BH.

X-ray Bursts (type I bursts) These busts are seen once every few hours to ~ 1 day in LMXBs 70 of the ~160 LMXBs show bursting behavior). They last for s; the spectrum is thermal & the area of the emission region is consistent with n-star radius of ~10km. The energy observed is produced by thermonuclear conflagration -- nuclear burning of a thin H-He layer of accreted material on the surface of n-star. Type II bursts are produced due to accretion disk instabilities. Energy release when H-He is burned to heavier elements is about 5Mev Per proton whereas gravitational energy release per proton on the Surface of a n-star is ~200 Mev. Review: Strohmayer & Bildstein, 2003, astro-ph/ Thermally unstable H-burning occurs in a H-He layer when the accretion rate is less than 2x M o /year.

Strohmayer & Bildstein, 2003, astro-ph/

Superbursts: once in a while (perhaps one in a few years) a burst is seen with total energy release of ~10 42 erg; these last for ~ an hour and are likely produced by unstable c-burning in deeper layers.

Advection Dominated Accretion Flow (ADAF) The mass of BH at the center of our galaxy is 2.6x10 6 M o (The Eddington luminosity is 3x10 44 erg s -1 ) The observed luminosity: at the peak (sub-mm) is 3x10 -9 L Edd in the infrared band is < 3x L Edd and in quiescent x-ray < L Edd Chandra finds gas at 1kev with density ~ 30 cc in an area of size 10 arcsec surrounding the BH (Baganoff et al. 2001); the capture radius for this gas is ~ 1 arcsec. The Bondi accretion rate is ~ 3x10 20 g s -1. If the Bondi flow terminates in a thin accretion disk, the luminosity expected is ~ 3x10 40 erg s -1 (must of it in infrared and optical); this is far larger than the observed luminosity. (Narayan et al, 1998, astro-ph/ ; Narayan astro-ph/ )

Many of the nearby (low z) SMBHs have very low luminosity. This cannot be explained as a result of low gas supply alone. What might be going on in these systems is that at low accretion rate the gas does not radiate efficiently and much of the energy produced by viscous dissipation is advected into the BH (hence the name ADAF). Structure of ADAFs Two temperature plasma – p + s are much hotter than e - s. Thick disk – because c s ~ v k (v k is the Keprelian speed). v r ~ v k (v r ~  c s H/r) and   r -3/2 Positive Bernoulli parameter; so gas can flow outward

Possible detection of polarized radio emission from the Galactic center (if confirmed) suggests that the density near the center is much less than in the ADAF model (Faraday rotation will depolarize the radiation). Convection dominated accretion flow (CDAF) has a lower density (   r -1/2 ) and solve the polarization problem. In CDAF the outward convective luminosity is constant: L c ~  v c 3 r 2. The convective velocity v c ~ v k  r -1/2 Therefore,   r -1/2