KERR BLACK HOLES Karl Mannheim Universitt Wrzburg MAGIC Physics - - PowerPoint PPT Presentation

KERR BLACK HOLES

Karl Mannheim – Universität Würzburg MAGIC Physics Meeting DESY Zeuthen – 19.06.2015

OVERVIEW

• Vacuum solutions of Einstein‘s equations
• Accreting Black Holes
• Blandford-Znajek mechanism
• Measurements of the Black Hole spin
• Plasma injection and particle acceleration

Kerr metric (1963) in Boyer-Lindquist coordinates

for a black hole rotating in the f - direction Angular momentum per unit mass (Kerr parameter) For a  0 the Schwarzschild metric (1915) is recovered.

Frame-dragging: mixed coordinate terms due to

• ff-diagonal terms in

metric tensor gmu

= 0 (event horizons)

Vacuum solutions of Einstein‘s equations

= 0 (singularity)

Inner (Cauchy) and outer horizons solving D=0 Scharzschild horizon r+ = 2 GM = rS (a  0) Maximally rotating Kerr horizon r+ = GM = rS /2 (a  GM) Maximally spinning Black Holes are just half the size of Scharzschild Black Holes (and non-charged)

Vacuum solutions of Einstein‘s equations (often a* = a/GM is used)

The solution of S=0 describes the singularity where the curvature goes to infinity: For a = 0 (Schwarzschild), we get the point r = 0. For|a|>0 (Kerr), we get r = 0 only for q=p/2 but for q = 0 we get r=a defining a ring-like singularity. Entering from the poles, a freely falling observer does not meet the singularity but falls into another Universe through a wormhole …

Vacuum solutions of Einstein‘s equations

„Waterfall“ model (Hamilton & Lisle 2004) Vacuum solutions of Einstein‘s equations

Vacuum solutions of Einstein‘s equations

Vacuum solutions of Einstein‘s equations

The ergosphere is the region defined by where even light (propagating in the f-direction) stands still as it is forced to corotate with

• spacetime. Matter moves even slower than light

with negative energy trajectories. The ergospheric minimum radius r0 = r+ = GM (for a=amax=GM) occurs at the poles (q=p/2), and the maximum radius r0 = rS = 2GM is achieved at the equator (q=0).

Vacuum solutions of Einstein‘s equations

Penrose-process

Vacuum solutions of Einstein‘s equations

The outgoing particle gains energy at the expense of the rotational energy of the Black Hole. Caveat: need decay process where speed

• f product particles

differs by >c/2.

Accreting Black Holes

l-4/3 Accretion disk Eddington luminosity LE = 4pGNMmpc/sT = 1011 L8 (M/106M8) Growth time tE = Mc2/LE = 4 x 108 yrs

Francis et al. 1991

Accreting Black Holes

Quasar: Black Hole with high accretion rate

Mc Kinney et al. (2012)

Blandford-Znajek mechanism

• Poynting flux expelled from ergosphere L ~ B2 R2 a2
• Thermal pair production of virialized plasma
• Pair production optical depth tgg = 200 L/LE
• Plasma injection (Levinson 2015, Krakow)  Force-free relativistic jet

Johnson et al. (1997) NGC4151 Blandford-Znajek mechanism

• S. Koide et al. (Science 2002, vol. 295, p. 1688)

Blandford-Znajek Mechanismus

Blandford-Znajek Mechanismus

Hercules A Credit: NASA VLA/HST-WFC3

Radiojets emerging from accreting black holes

Pjet ~ Laccretion

Rawlings & Saunders, Nature (1991) Blandford-Znajek mechanism

Measurements of spin

• Temperature of inner edge
• f accretion disk (innermost

stable circular orbit)

• Relativistically broadened

Fe Ka lines

• Quasi-period oscillations
• Stellar/Supermassive BHs

Measuring spin in high-accretion Black Holes

Credit: Narayan

Measurements of spin

• Test BZ-mechanism
• Fit SED with parameters

scaled according to VLBI core shifts

• Get Kerr paramter a*
• Phd-thesis T. Steinbring

Measuring spin in low-accretion Black Holes

Measurements of spin

R ~ 11 m (M87)

Dolemann et al., Science, 2012

R ~ 0.2 m (IC 310)

Aleksic et al., Science, 2014

These methods are model- dependent and probe physics at a distance from the Black Hole. What about direct methods in sources with low accretion rate?

• Imaging (EHT)
• High-energy variability

(MAGIC!)

Levinson & Rieger (2011)

Aleksic et al., Science (2014)

Low accretion rate

• tgg = 200 L/LE < 1
• Vacuum gaps
• E parallel B
• Particle acceleration
• Potential drop 1020 eV
• Pair production at very

high energies

• Gamma-ray emission
• K. Hirotani, priv. com.

Multi-TeV gamma rays

Hot ion supported torus with 109 K electrons

Plasma-injection and particle acceleration

SUMMARY

• Astrophysical BHs form by accretion and have spin
• Observational manifestations of spin:
• Disk properties (ISCO)
• Relativistic jets due to Poynting flux driven out by the

BZ-mechanism and spinning down the Black Hole

• Pulsar-like acceleration mechanisms close to

ergosphere ( K. Hirotoni)

Backup slides

Neronov et al. (2012): Using the exact solution due to R. Wald for a poloidal magnetic field parallel to the angular momentum

• f the black hole,

protons are suggested as the seed particles

Plasma-injection and particle acceleration

KM 1995

ICECUBE „Physics Breakthrough 2013“

Plasma-injection and particle acceleration

ln ~ 100 g10 kpc

„Neutron bomb“ could explain UHE cosmic rays after b- decay (avoiding adiabatic losses)

Chandra/Apex Plasma-injection and particle acceleration

• K. Murase et al. (2013)

pp Plasma-injection and particle acceleration

Big Bird

• 2 PeV event of Dec 4th 2012

(Aartsen et al. 2014)

• RA = 208.4◦, Dec = −55.8◦

(J2000)

• Mean positional uncertainty:

15.9 deg ⇒ 17 coincident gamma blazars (2LAC)

Kadler et al., Krakow Conf. (2015) Plasma-injection and particle acceleration

PKS B1424-418: Spectrum

Theoretical prediction: 2.2 PeV neutrino events in IceCube

Plasma-injection and particle acceleration

Time of gamma-ray outburst matches the neutrino arrival time

PKS B1424-418

Plasma-injection and particle acceleration

PROBABILITY FOR CHANCE COINCIDENCE?

Most extreme

blazar outburst (southern sky)

Most energetic neutrino

(southern sky)

~5%

Plasma-injection and particle acceleration Kadler et al., Krakow Conf. (2015)

~1/G

v ~ 1 v = 0 Dt ~ rg = m Dt ~ r‘ / G

since r‘ = G rg  Dt ~ m

Variability signature of black hole origin

Central machine

Lukas Cranach d.Ä. (1526)

• K. Hirotani (priv. comm.)

Aleksic et al., Sci 346, 6213 (2014)