Black Holes in AGNs

1. 20th April 2KX Black Holes in AGNs Suprit Singh Talk for the IUCAA Grad-School course ‘Extra-Galactic Astronomy II’ taught by Prof. Ishwara Chandra

2. What’s a hole anyway? • Well, it’s a ‘place’ in the spacetime where the curvature blows up… called Singularity (Classical, not to be a feature of Quantum gravity) • Can’t Specify ‘where’, as it doesn’t exist on the manifold • So we are concerned with r>0

3. Structure of Black Holes • Work of Israel, Carter, Robinson and Hawking • All but M, Q and J information is lost for bodies falling into the Black Holes • “Black Holes have No Hair” - Wheeler • Although Mathematically Complex, structurally quite Simple

4. Black Hole Types • Only 3 Special Unique solns: • Schwarzschild • Reissner – Nordstrom • Kerr

5. Rotating Black Holes • Non-zero angular momentum, J = a M • Axial symmetry • Uses Boyer-Lindquist coordinates • Take limit (a,0), we are left with Schwarzschild • Take limit (M,0), Its flativerse but not polar but Ellipsoidal ( Expected ??)

6. Event Horizon/s • Event Horizon/s are coordinate dependent artifacts where the metric for bad-coordinate system blows up but there is no spacetime singularity. • The problem can be resolved by making coordinate transformations but there are some interesting effects associated with event horizon/s as events inside the horizon have no causal connection with the outside world. They act as one way membranes. • For Δ → 0 , g11 blows up analogous to the Schwarzschild condition of r = 2M. Since Δ is quadratic in r, we have two roots here: • Hence, Kerr metric is associated with two horizons and hence shows some remarkable effects.

7. Outer and Inner Horizons • There are three possibilities: • M > a : Physical case • M = a : Unstable • M < a : Naked Singularity • The infinite redshift surfaces can be found by • The region between the Outer Horizon and Outer static limit is termed Ergosphere (Energy??)

8. The Penrose Process • A Particle (in) starts at infinity and falls into ergosphere. There it decays into two particles, (out) and (bh). Particle (bh) falls down through the Horizon, while particle (out) escapes to infinity. Energy-momentum must be preserved in the decay: p (in) = p (out) + p (bh) • The Energy of particle with rest mass m(out), which reaches out to infinity is E(out) = - K . p(out) = m(out), where K is a timelike killing vector. Thus dotting momentum conservation with K gives E(out) = E(in) - E(bh). • Now if E(bh) < 0, then we have E(out) > E (in). But there is no such thing as free lunch, the energy has to come out of something. The idea, is inside the ergosphere, the Killing vector is spacelike and so E(bh) is actually component of spatial momentum which can be negative as well and energy wil be extracted from the blackhole at the expense of its rotational energy.

9. Powering AGNs • There are namely two mechanisms to power AGNs: • Blandford-Znajek Mechanism (uses Black hole's Rotational Energy) • Accretion Disk (uses matter’s gravitational Binding energy) • The first mechanism extracts rotational energy from a rotating black hole electromagnetically. • Consider a conductor of radius rc rotating with angular velocity Ω about its symmetry axis immersed in a B-field pointing in that direction.

10. Blandford-Znajek Mechanism • The rotation produces a force on the charge carriers in the conductor located at distance ρgiven by • pointing radially away from the axis. A voltage will develop across the two stationary contacts shown, where the line integral is over any path C in the conductor connecting them. For the path shown in the figure, the only contribution to the voltage drop is from the axis to the radius rc: • where F is the Flux of magnetic flux threading the conductor. Suppose the contacts are connected by wires to an external resistance (the load). A current will flow, and power will be dissipated in the load. The rotating conductor thus acts as an electric generator. The current is

11. Blandford-Znajek Mechanism • where we have Load and Conductor resistances. Maximum power is transferred when both are equal. • Black holes have electromagnetic properties that are analogous in many ways to ordinary conductors. These follow from Maxwell's equations in black-hole spacetime. • Qualitatively: if an observer drops an electric charge into a black hole, subsequent observers can detect the charge by the long range electric field that develops outside the black hole. At very large r that field is radial and falls off like 1/r2, in accord with Coulomb's law. From the point of view of distant observers, the dropped charge never crosses the horizon but remains there, forming a surface charge distribution analogous to that of a conductor. Black holes can therefore carry electric charge.

12. Blandford-Znajek Mechanism • Suppose positive charges and negative charges fall into a black hole at a steady rate from opposite sides. The net charge of the black hole remains zero, but a net charge has been transferred from one side to the other. From the point of view of an observer outside, the black hole has conducted current. Energy is also dissipated when a black hole carries current because it is not a perfect conductor. Black holes therefore have electrical resistance. The analogies between black holes and conductors suggest that the rotational energy of a black hole could be tapped if it were immersed in a magnetic field and wired up in a way analogously. • A simple dimensional estimate for Black Hole’s resistance: The dimensions of resistance follow from Ohm's law, R = V/I. The electric potential a distance r away from a point charge q is V= q/r. The dimensions of voltage are thus [q]/L. The dimensions of current are [q]/T. Hence, the dimensions of resistance, [R] = T/L. In units where c = 1, resistance is dimensionless! Therefore, R ≈1 is a reasonable guess for the resistance of a black hole in geometrized units. This corresponds to 1/c (s/cm) in Gaussian units or about 30 ohms in SI units. This is not so very different from the approximately 376 ohm "impedance of free space" characterizing a wave guide radiating into the vacuum. A black hole is empty curved space.

13. Blandford-Znajek Mechanism • The rate at which rotational energy is extracted from a black hole of mass M and angular velocity ΩH can be roughly estimated from Power =n using this guess for the resistance and estimating the hole's size by r≈ M. The result is • which is more than sufficient to power AGN jets. But what supplies the magnetic field and what are the analogs of the wires connecting the unipolar generator to the load that are necessary to make this mechanism work? The answer is that currents in an accretion disk supply the necessary magnetic field, and the black hole makes its own wires.

14. Blandford-Znajek Mechanism • Were there no conducting connection between the accretion disk and the black hole, there would still be a voltage drop between them of order given by • This enormous voltage and the accompanying electric field would quickly accelerate any stray electron to relativistic velocities. The electron would radiate photons, which could produce electron-positron pairs . These would, in turn, accelerate, radiate, and produce more pairs. The resulting cascade would very quickly fill up the neighborhood of the black hole with a conducting plasma of electrons and positrons, electric, and magnetic fields. This is the electrically conducting link between the black hole and the outside necessary for the unipolar generation of power.

15. Accretion power : calculation • Why black holes are at the heart of most energetic phenomenon in the universe? Answer : Thermonuclear fusion vs Gravitational binding • For thermonuclear reactions, the bottom line is the transition • In forming a black hole accretion disk particles make a transition from an approximately free state a large distance away to a central bound orbit with lower energy. In the Schwarzschild case, the E per unit m, e is : • For the innermost stable circular orbit at r = 6M, this is 6%. Gravitational binding to a Schwarzschild black hole is therefore approximately six times more efficient in releasing energy than thermonuclear fusion. For rotating black holes, up to 42% of rest energy can be released in principle.

16. For Further Read • Gravity – an introduction, Jim Hartle • Black Holes - an introduction, Raine and Thomas • Active Galactic Nuclei, Blandford et all • An Invitation to Astrophysics, Paddy

17. That’s All Folks Thanks * Black hole activity suspected above