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X-ray transients :

4. Bondi accretion rate (spherical inflow). •. The accretion rate when the object is moving through the ISM with speed V is:. •. X-ray transients :. Rocket Propulsion. Equations governing rocket engine Thrust are same as the accretion problem!. Thrust: . Equations: .

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X-ray transients :

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

  2. Rocket Propulsion Equations governing rocket engine Thrust are same as the accretion problem! Thrust: Equations: 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! Eliminate rho from the two equations above to yield:

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

  4. Binary classification

  5. Roche Potential Potential in a rotating frame: Roche Lobe

  6. 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

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

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

  9. Chandrashekhar-Balbus-Hawley mechanism Balbus & Hawley, 1998, Rev. Mod. Phys., Vol. 70, p. 1-53 (sections III A, B, & IV B in particular) Analysis of a mechanical model consisting of a spring and two point mass on an orbit.

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

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

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

  13. 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<rs the particle cannot remain stationary and is forced to rotate with the black-hole. The region between rH and rs is called the Ergosphere.

  14. Ergosphere of a Kerr black hole

  15. 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.

  16. 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.

  17. 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.

  18. It can be shown that the energy (per unit mass) for the last stable circular orbit is 1 - 42.3%. Therefore, we one can extract about 42.3% energy from the accretion around a maximally rotating BH.

  19. X-ray Bursts (type I bursts) Review: Strohmayer & Bildstein, 2003, astro-ph/0301544 • These busts are seen once every few hours to ~ 1 day in LMXBs 70 of the ~160 LMXBs show bursting behavior). • They last for 10--100 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. • Thermally unstable H-burning occurs in a H-He layer when the accretion rate is less than 2x10-10 Mo/year. 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.

  20. Strohmayer & Bildstein, 2003, astro-ph/0301544

  21. Strohmayer & Bildstein, 2003, astro-ph/0301544

  22. Strohmayer & Bildstein, 2003, astro-ph/0301544

  23. Superbursts: once in a while (perhaps one in a few years) a burst is seen with total energy release of ~1042 erg; these last for ~ an hour and are likely produced by unstable c-burning in deeper layers.

  24. Advection Dominated Accretion Flow (ADAF) (Narayan et al, 1998, astro-ph/9803141; Narayan astro-ph/0201260) • The mass of BH at the center of our galaxy is 2.6x106 Mo (The Eddington luminosity is 3x1044 erg s-1) • The observed luminosity: at the peak (sub-mm) is 3x10-9 LEdd in the infrared band is < 3x10-10 LEdd and in quiescent x-ray < 10-11 LEdd • 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 ~ 3x1020 g s-1. If the Bondi flow terminates in a thin accretion disk, the luminosity expected is ~ 3x1040 erg s-1 (must of it in infrared and optical); this is far larger than the observed luminosity. •

  25. • 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 cs ~ vk (vk is the Keprelian speed). • vr ~ vk (vr ~  csH/r) and   r-3/2 • Positive Bernoulli parameter; so gas can flow outward

  26. • 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: Lc ~  vc3 r2 . The convective velocity vc ~ vk r-1/2 Therefore,   r-1/2

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