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
Vacuum solutions of Einstein‘s equations Kerr metric (1963) in Boyer-Lindquist coordinates for a black hole rotating in the f - direction Angular momentum per unit mass (Kerr parameter) Frame-dragging: mixed = 0 (singularity) coordinate terms due to off-diagonal terms in = 0 (event horizons) metric tensor g mu For a 0 the Schwarzschild metric (1915) is recovered.
Vacuum solutions of Einstein‘s equations Inner (Cauchy) and outer horizons solving D =0 Scharzschild horizon r + = 2 GM = r S (a 0) (often a* = a/GM is used) Maximally rotating Kerr horizon r + = GM = r S /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 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 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 r 0 = r + = GM (for a=a max =GM) occurs at the poles ( q=p/2 ), and the maximum radius r 0 = r S = 2GM is achieved at the equator ( q= 0 ).
Vacuum solutions of Einstein‘s equations
Vacuum solutions of Einstein‘s equations Penrose-process The outgoing particle gains energy at the expense of the rotational energy of the Black Hole. Caveat: need decay process where speed of product particles differs by >c/2.
Accreting Black Holes
Accreting Black Holes Francis et al. 1991 Quasar: l -4/3 Black Hole with high accretion rate Accretion disk Eddington luminosity L E = 4 p G N Mm p c/ s T = 10 11 L 8 (M/10 6 M 8 ) Growth time t E = Mc 2 /L E = 4 x 10 8 yrs
Blandford-Znajek mechanism Blandford-Znajek mechanism • Poynting flux expelled from ergosphere L ~ B 2 R 2 a 2 • Thermal pair production of virialized plasma • Pair production optical depth t gg = 200 L/L E • Plasma injection (Levinson 2015, Krakow) Force-free relativistic jet NGC4151 Johnson et al. (1997) Mc Kinney et al. (2012)
Blandford-Znajek Mechanismus Blandford-Znajek S. Koide et al. (Science 2002, vol. 295, p. 1688) Mechanismus
Blandford-Znajek mechanism Radiojets emerging from accreting black holes Hercules A Credit: NASA VLA/HST-WFC3 P jet ~ L accretion Rawlings & Saunders, Nature (1991)
Measurements of spin Measuring spin in high-accretion Black Holes Temperature of inner edge • of accretion disk (innermost stable circular orbit) Relativistically broadened • Fe K a lines Quasi-period oscillations • Stellar/Supermassive BHs • Credit: Narayan
Measurements of spin Measuring spin in low-accretion Black Holes Test BZ-mechanism • Fit SED with parameters • scaled according to VLBI core shifts Get Kerr paramter a* • Phd-thesis T. Steinbring •
Measurements of spin These methods are model- R ~ 11 m (M87) dependent and probe physics at Dolemann et al., Science, 2012 a distance from the Black Hole. What about direct methods in sources with low accretion rate? R ~ 0.2 m (IC 310) • Imaging (EHT) Aleksic et al., Science, 2014 • High-energy variability (MAGIC!)
Plasma-injection and particle acceleration Hot ion supported Levinson & Rieger (2011) Low accretion rate torus with 10 9 K electrons t gg = 200 L/L E < 1 • Vacuum gaps • K. Hirotani, priv. com. E parallel B • Particle acceleration • Potential drop 10 20 eV • Pair production at very • high energies Gamma-ray emission • Multi-TeV gamma rays Aleksic et al., Science (2014)
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
Plasma-injection and particle acceleration Neronov et al. (2012): Using the exact solution due to R. Wald for a poloidal magnetic field parallel to the angular momentum of the black hole, protons are suggested as the seed particles
Plasma-injection and particle acceleration ICECUBE „ Physics Breakthrough 2013“ KM 1995
Plasma-injection and particle acceleration „ N eutron bomb“ could explain UHE cosmic rays after b - decay (avoiding adiabatic losses) l n ~ 100 g 10 kpc Chandra/Apex
Plasma-injection and particle acceleration K. Murase et al. (2013) pp
Plasma-injection and particle acceleration Big Bird Kadler et al., Krakow Conf. (2015) • 2 PeV event of Dec 4 th 2012 (Aartsen et al. 2014) • RA = 208.4 ◦ , Dec = −55.8 ◦ (J2000) • Mean positional uncertainty: 15.9 deg ⇒ 17 coincident gamma blazars (2LAC)
Plasma-injection and particle acceleration PKS B1424-418: Spectrum Theoretical prediction: 2.2 PeV neutrino events in IceCube
Plasma-injection and particle acceleration PKS B1424-418 Time of gamma-ray outburst matches the neutrino arrival time
Plasma-injection and particle acceleration PROBABILITY FOR CHANCE COINCIDENCE? ~5% Most extreme blazar outburst Most energetic neutrino (southern sky) (southern sky) Kadler et al., Krakow Conf. (2015)
Central machine Variability signature of black hole origin ~1/G v ~ 1 v = 0 D t ~ r g = m D t ~ r‘ / G since r‘ = G r g D t ~ m
Lukas Cranach d.Ä. (1526)
K. Hirotani (priv. comm.)
Aleksic et al., Sci 346 , 6213 (2014)
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