Accretion into black holes and jet formation G.S. Bisnovatyi-Kogan IKI RAN

1. Accretion into black holes and jet formation • G.S. Bisnovatyi-Kogan • IKI RAN MEPHI school, Moscow, September 25, 2010

2. Quasars and AGN contain supermassive black holes About 10 HMXR - stellar mass black holes in the Galaxy: microquasars. Jets are observed in objects with black holes: collimated ejection from accretion disks.

3. Jet in M87: radio, 14GHz, VLA, 0.2” HST (F814W) Chandra image, 0.2”, 0.2-8 keV Adaptively smoothed Chandra image From Marshall et al. (2001)

4. 3C 273 Left: MERLIN, 1.647 GHz. Middle: HST(F622W), 6170A. Right: Chandra, 0.1 “ Marshall et al. (2000)

5. Jet in radiogalaxy IC 4296 at 20 cm with 3.2” resolution. 10” is about 2 kps. VLA, Killeen et al. (1986) Total extent is about 400 kpc

6. Microquasar GRS 1915+105 Jet ejection MERLIN 5GHz Fender (1999)

8. Sketch of the magnetic field threading an accretion disk. Shown increase of the field owing to flux freezing in the accreting disk matter At presence of large-scale magnetic field the efficiency of accretion is alvays large (0.3-0.5) of the rest mass energyflux

9. Accretion disk around BH with large scale magnetic field (non-rotating disk)

10. Turbulent electrical conductivity, analog of alpha viscosity

11. A hot corona around a black-hole accretion disk as a model for Cygnus X-1 G. S. Bisnovatyi-Kogan and S. I. Blinnikov Institute for Space Research, USSR Academy of Sciences, Moscow (Submitted April 15, 1976) Sov.Astron.Lett. 2, 191-193 (Sep.-Oct. 1976) Another mechanism for producing fast particles is analogous to the pulsar process. If magnetized matter with low angular momentum falls into the black hole (in addition to the disk accretion), a strong poloidal magnetic field will arise [19]. By analogy to pulsars [20], rotation will generate an electric field of strength E ≈ −(v/c)B in which electrons are accelerated to energies Energy ≈ R(v/c)B e ≈ 3 · 10^4 [B/(10^7 Gauss)] Mev where v/c ≈ 0.1 and R ≈ 10^7 cm is the characteristic scale. In a field B ≈ 10^7 Gauss, such electrons will generate synchrotron radiation with energies up to ≈ 10^5 keV. Just as in pulsars, it would be possible here for e+e− pairs to be formed and to participate in the synchrotron radiation.

12. Dynamo model of double radio sources Lovelace, R. V. E. Nature, vol. 262, Aug. 19, 1976, p. 649-652. Jet formation in the accretion disk around BH (sketch)

13. Relativistic magnetohydrodynamical effects of plasma accreting into a black hole Ruffini, R.; Wilson, J. R. Physical Review D, vol. 12, Nov. 15, 1975, p. 2959-2962. By an explicit analytic solution it is shown how, in the accretion of a poloidally magnetized plasma into a Kerr black hole, a torque is exerted on the infalling gas, implying the extraction of rotational energy from the black hole.The torque arises from the twisting of magnetic field lines by the frame-dragging effect. It is also shown how, under suitable conditions, a sizable charge separation can be found in the magnetosphere of accreting black holes and hence an electric charge is expected to be induced on the black hole.

14. Penrose mechanism (1969) Falling of negative energy particle into a BH from the ergosphere Magnetic Penrose mechanism:

16. 1. External magnetic field of the collapsing star is going to zero. The Magnetic Fields of Collapsing Masses and the Nature of Superstars Ginzburg, V. L. Soviet Physics Doklady, Vol. 9, p.329 (1964) 2. BH has no hair Note: The time line uses modern terminology. The term "black hole" was coined by John Wheeler (The American Scholar , Vol. 37, no 2, Spring 1968), being first used in his public lecture "Our Universe: the Known and Unknown" on 29 December, 1967. The terminology that "black holes have no hair" in respect of various uniqueness and "no hair" results, was also due to John Wheeler and was introduced in an article co-authored with Remo Ruffini (R. Ruffini and J.A. Wheeler, Physics Today24, 30 , 1971). The black hole in the paper of Blandford and Znajek has a WIG – the field is outside the horizon, but very close to it.

17. Uniform field B_0 at infinity is growing during spherical accretion

18. A COSMIC BATTERY RECONSIDERED G. S. Bisnovatyi-Kogan, R. V. E. Lovelace and V. A. Belinski The Astrophysical Journal, 580:380–388, 2002 Fields near horizon observed by the distant observer x_0~1 is the Lagrangian coordinate near the horizon, D is determined by the unperturbed field at large distance. Radial component of B is growing logarithmivcally, and cannot be so large at the horizon.

19. Sketch of picture of a disk accretion on to a black hole at sub-critical luminosity. I – radiation dominated region, electron scattering. II – gas-dominated region, electron scattering. III- gas-dominated region, Krammers opacity.

20. Magnetic diffusivityis of the order of kinematic viscosity in the turbulent disk, D>>1

22. Large scale magnetic field is amplified during the disk accretion, due to currents in the radiative outer layers, with very high electrical conductivity Bisnovatyi-Kogan, Lovelace, 2007, ApJL, 667: L167–L169, 2007 October 1

23. Inthis situation we may expect a nonuniform distribution of the angular velocityover the disk thickness: The main body of the turbulent disk is rotates withthe velocity close to the Keplerian one, and outer optically thin layers rotatesubstantially slower by ~30%. Turbulence in the outer layers is produced by shear instability B(min) ~ 10^8/sqrt(M_solar) for Schwarzschild BH Magnetic field may be ~10 times larger for rapid Kerr BH

24. ADVECTION/DIFFUSION OF LARGE-SCALE B FIELD IN ACCRETION DISKS R.V. E. Lovelace, D.M. Rothstein, & G.S. Bisnovatyi-Kogan ApJ, 701:885–890, 2009 August 20 Here, we calculate the vertical (z) profiles of the stationary accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity due to the MRI and the fact that the turbulence vanishes at the surface of the disk.

25. Equations: stationary axisymmetric accretion flows, and the weak large-scale magnetic field, taking into account the turbulent viscosity and diffusivity , , Boundary condition on the disk surface:

26. Solution (examples) Free parameters: Magnetic Prandtl number =\nu_t/\eta~1, and \nu-kinematic viscosity, \eta-conductivity (turbulent) \eta=\sigma_t

27. G.S. Bisnovatyi-Kogan, R.V. E. Lovelace (in preparation) • Boundary condition on the disk surface: u_r=0 • 2. Only one free parameter: Magnetic Prandtl number =\nu_t/\eta~1 • In a stationary disk vertical magnetic field has a unique value

28. The value of \beta is the boundary one, at which inflow is along the whole disk thickness

29. Jet in M 87: Radio: 6 cm (up), Optical: V-band (middle), Chandra: X-ray 0.1-10 keV (down)Wilson , Yang (2001) Jet in M 87: Radio: 6 cm (up), Optical: V-band (middle), Chandra: X-ray 0.1-10 keV (down)Wilson , Yang (2001)

30. W.A.Hiltner ApJ, 1959

31. Magnetic collimation is connected with torsionaloscillations of a cylinder with elongated magnetic field. We consider a cylinder with a periodically distributed initial rotation around the cylinder axis. The stabilizingazimuthal magnetic field is created by torsional oscillations. Approximate simplified model is developed. Ordinary differential equation is derived, and solved numerically,what gives a possibility to estimate quantitatively the range of parameterswhere jets may be stabilized by torsional oscillations. Bisnovatyi-Kogan, MNRAS 376, 457 (2007)

33. Axially symmetric MHD equations in comoving coordinate system, jet velocity is suggested to be constant Euler equations

34. Maxwell equations Poisson equation Energy equation, Equation of state

35. Profiling in axially symmetric MHD equations R(t; z) is the radius of the cylinder, f=0.

36. Substituting into the original system of the equations, we obtain for the profiling functionsthe following equations (1) (2) The last 3 relations(4)-(6)determine conservation of mass, and magnetic flux equivalent to freezing condition (3) (4) (5) (6) In our subsequent consideration the arbitrary functions will be taken as constants:

37. Equilibrium configuration and linear oscillations ~exp i(kz -it) Dispersion equation:

38. 1. Nonrotating, nonmagnetized cylinder. This equation describes the only possible mode, remaining after fixing v_z= 0,and uniform density over the radius. It corresponds to homologous mode ofperturbation, where only radius and density (pressure) are oscillating. Thefrequency becomes zero at = 1 (isotherm). This degeneration is connected with the property of self-gravitating cylinder, which equilibrium is neutral (takes place at any radius) for the isothermal equation of state. This degeneration is equivalent to the well-known case at = 4/3 for a spherical star. While we are not interested in study of homologousoscillations, we'll take = 1 in all father consideration, with dispersion equation

39. 2. Rotating non-magnetized cylinder, Here the solution ofdispersion equation describes the trivial mode with zero frequency, connectedwith pure rotational perturbations, and radial oscillations due to an action ofthe centrifugal force

40. 3. Non-rotating magnetized cylinder, The first type of wave corresponds to perturbation only of the radial velocity. This solutioncorresponds to the Alfven wave along the axis, where only radius is perturbed,and no rotation appears. The second type of wave describes perturbations ofangular velocity at constant radius. Thiswave corresponds to a pure torsional alfven wave along the cylinder axis.

41. Farther simplification: reducing the problemto system of ordinary differential equations While in the relativistic jet the self-gravitating force is expected to be muchless than the magnetic and pressure forces, we neglect gravity in the subsequentconsideration. Without gravity the equilibrium static state of the cylinder doesnot exist. We need to solve numerically the system of nonlinear equations to check the possibility of the existence of a cylinder, whichradius remains to be finite due to torsional oscillations (dynamic confinement). We'll try instead to reduce the system to ordinary equations,making additional simplifications.

42. In the cylinder which confinement is reached due tostanding magneto-torsional oscillations, there are points along z-axis where rotational velocity always remains zero. Let us take = 0 in the plane z = 0.If the period of torsional oscillations along z axis is equal to z_0, then = 0 atz= z_0/2, and z=-z_0/2. Let us write the equations in the plane z = 0, where =0 All value in this plane we denote by (~).

43. Initial conditions for this system are

44. If the cylinder is symmetric relative to the plane z = 0,

45. Finally, we have the following approximate system of equations, describing the non-linear torsional oscillations of the cylinder (1) (2) (3) The combination of last two equations gives: With account of it the first and third equations give the equation

46. Introduce non-dimensional variables in which differential equations have a form Here the simplest initial conditions are chosen. Therefore, the problem is reduced to a system (49) with two non-dimensionalparameter: y (taken=1 in calculations), and

47. In non-dimensional variables differential equations have a form (\tau – time; y- radius; z- radial velocity} Solutions for these initial conditions are obtained at different D When y(0) is different from 1, there is a larger variety of solutions: regular and chaotic (in preparation) Frequency of oscillations \omega is taken from linear approximation (Alfven). Angular amplitude \Omega is a free parameter.

48. Three possibilities 1. The oscillation amplitude is low, so the cylinder suffers unlimited expansion (no confinement) 2. The oscillation amplitude is too high, so the pinch action of the toroidal fieeld destroys the cylinder, and leads to formation of separated blobs. 3. The oscillation amplitude is moderate, so the cylinder survives for anunlimited time, and its parameters (radius, density, magnetic field etc.) changeperiodically, or quasi-periodically in time.

49. Numerical solution 1. At D = 1.5 and 2 there is no confinement, and radius grows to infinityafter several low-amplitude oscillations