Introduction to Black Holes and Accretion Disks Paul

Introduction to Black Holes and Accretion Disks Paul J. Wiita Georgia State University

A Few Questions 1. What is a Black Hole? 2. What is an Accretion Disk? 3. Where are they of astronomical interest?

Black Holes • A part of space-time divorced from the rest of the universe. • Not even light can escape if emitted too close to a black hole (BH); inside event horizon or Schwarzschild radius.

General Relativity and BHs • A BH is a singularity: finite amount of mass at a point, so • Density there is (nominally) INFINITE • The BH is surrounded by an event horizon or infinite redshift surface or Schwarzschild radius So a BH with Earth’s mass has RS = 1 cm! 100, 000 Msun BH has Rs = 300, 000 km or 3 x 108 km = 10 -5 parsec = 1000 light-seconds

Orbits around BHs • GR gives rise to an effective potential which yields orbits depending on the energy and angular momentum of the matter near a BH • Once beyond about 50 Rs orbits are ~ Newtonian • But, unlike Newtonian case we find an innermost stable orbit at Rms=3 Rs There is also the last possible, or marginally bound, orbit at Rmb=2 Rs • A pseudo-Newtonian potential: =GM/(r-RS) reproduces the above results • If we look for orbiting photons, instead of massive particles, there is a last stable orbit at Rph=1. 5 Rs

The Schwarzschild Metric • The space-time near a non-rotating isolated mass is described by a very simple formula, or metric.

Redshifted Emission • Photons lose energy as they climb out of the gravitational pit established by a BH. • We observe longer (redder) wavelengths (lower frequencies) compared to those emitted. • Time freezes for a distant observer watching something fall past event horizon

Gravitational Redshift • The observed frequency of a photon is lowered if the observer is at a weaker gravitational potential • The simple conservation law is |g 00|1/2 E = const. • For a non-rotating BH this becomes: N. B. : This is a coordinate singularity, NOT a real one. For Sun: z~10 -6; for WD: z~10 -4; for NS: z~0. 2

Warping of Space-Time Near BHs • In GR, matter warps space-time, so that the straightest path (geodesic) looks like a curve to us. • Analogy: weight on a tight rubber sheet depresses it, so a ball is deflected

Too much mass in too little volume! • Warping of space-time can be so severe that the region effectively pinches off and curvature becomes very strong in vicinity of BH.

Black Holes have no Hair! A BH is characterized by only: 1. Mass 2. Electric charge (astrophysically unimportant) 3. Angular momentum (spin) ergosphere

Kerr(-Newman) Black Holes • Messy metric, but key results are the presence of a static limit, inside of which one must co-rotate with the BH • The horizon moves further inward the faster the BH spins. This implies Rms and Rmb also move inward. • The amount of binding energy that is extracted from infalling matter goes up from <0. 06 to ~0. 42 m(c 2) Cosmic censorship hypothesis: < M so no naked singularities exist a

Tidal Stretching & Hawking Radiation • Large gravity differences (tides): “toothpaste tube effect” • Quantum gravity effect: Hawking temperature T=h/16 2 k. GM=6 108 K(M /M) • Hawking power: ~R 2 T 4 ~M 2/M 4 ~1/M 2 • Incredibly small if BH mass > 1017 g (rules out stars/galaxies)

It’s Hard to Find Black Holes • They don’t emit (significant) radiation • Light bending means they don’t even show up as dark spots: • Unless distance is close to RS, gravity is close to that of a regular star of the same mass

Origin of Black Holes • Collapse of very massive stars (>30 M ) can lead to BHs of ~3 -25 M (neutron stars must have masses below about 2 M ). • Lower mass (15 -30 M ) stars might still form BHs indirectly, with NS formed first, then accretion over its upper mass limit. • Collapse of densest regions of forming galaxies, either directly or through merger of stars in dense clusters can yield BHs with M > 1000 M . • Quantum fluctuations in the early universe could give primordial BHs of a wide range of masses.

Quasars • First seen as strong radio sources that looked like stars (Quasi-stellar Radio Source) • Strange emission lines: broad and at odd wavelengths • Emits optical, ultraviolet, infrared, X-rays (and sometimes radio waves) in a NON-THERMAL continuum • Variable on timescales of < 1 year at all wavelengths • Often associated with jets

Optical and Radio Images of Quasars 3 C 273 3 C 175

Strange Spectral Emission Lines

Non-thermal Continuum Radiation

Quasars are Active Galactic Nuclei • Powerhouses embedded in the center of a galaxy: outshining ALL the ~1012 stars by factors of 10 -1000! • Other AGN types include: • Seyfert galaxies (spiral galaxies with bright nuclei and strong emission lines) • Radio galaxies (weak optical cores but huge radio lobes) • BL Lacertae objects: almost no lines; very strongly variable non-thermal emission seen.

Seyfert Galaxy Circinus galaxy, about 13 million light-years away, is a nearby AGN; the very intense optical core is comparable in brightness to all the stars put together.

AGN Variability (Seyfert 3 C 84)

Rapid Variations Mean Small Sizes • Characteristic change of power on time t implies a size, R ~ ct (c = speed of light) • Typical time for quasar brightness change ~ 1 year means typical size of ~1 light-year • This is comparable to the outermost edge of the solar system (comets in Oort cloud) • So quasar energy comes from a very small (by galactic standards) volume!

Powerful Radio Galaxy: Cygnus A

Nearby Radio Galaxy: Centaurus A

Typical Quasars Don’t Look Too Bright

But they are Very Powerful Because Very Far Away (big cosmological redshift) • Hubble’s Law: • Velocity proportional to distance • Huge redshifts imply most quasars billions of light-years away so LUMINOUS

Accretion Disks • Form when gas spirals down into a massive object. Seen in: • Stars (and planetary systems) being born • Binary stellar systems with compact component: white dwarf--CVs, neutron star (XRBs) or black hole (HMXRBs) • Possibly involved in Gamma-Ray Bursts • Active Galactic Nuclei

In an Accretion Disk • • Mass moves inward Angular momentum is carried outward Friction (viscosity) in the gas heats it up Usually most of this heat is radiated from the disk surface giving: Ultraviolet radiation from white dwarfs X-rays from neutron stars and stellar mass BHs Mostly visible and UV from AGN BHs • Most logical way to launch jets

Blazar Characteristics • • • Rapid variability at all wavelengths Radio-loud AGN Optical polarization synchrotron domination BL Lacs show extremely weak emission lines Double humped SEDs: RBL vs XBL? Core dominated quasars clubbed w/ BL Lacs to form the blazar class • Population statistics indicate that BL Lacs are FR I RGs viewed close to jet direction (Padovani & Urry 1992)

Long-term Radio Monitoring Aller & Aller, U Michigan

Microvariability & Intraday Variability too! Romero, Cellone & Combi; Quirrenbach et al (2000)

Blazar SED: 3 C 279 (Moderski et al. 2003)

Evidence for Accretion Disks in Blazars Big blue bump in AO 0235+164 (Raiteri et al. astro-ph/0503312)

More New Evidence for Accretion Disks Optically thick: hidden Balmer edge now claimed to be seen in several quasars. • Ton 202 polarized flux with face-on Kerr disk model fitted to it (Kishimoto et al. 2004)

Why Quasi-Keplerian and Disk-like? Quasi-black body fits to disk spectra Broad K lines for NLS 1 s Variable Double peaked lines [here H lines: Strateva et al, AJ (2003)] Jets probably require disks as launching pads

Eddington Luminosity • Both radiation pressure and gravity are inverse square forces, so there is a simple upper limit to the power that can emerge (from a spherical geometry) • LE=1. 3 x 1038(M/M ) erg/s • This assumes just the minimal opacity, from electron scattering, but is reasonable for both very hot stars and the inner parts of accretion disks. • As the amount of mass fed into a BH approaches that needed to generate LE, we expect the disk to thicken and drive off winds.

Accretion Flow Geometries • Quasi-accepted picture: L/LE determines disk thickness and extent toward BH: very high L/LE geometrically & optically thick intermediate L/LE cold optically thick, geometrically thin low L/LE optically thin hot flow interior to some transition

Viscosity Mechanisms • Standard molecular and radiative viscosites are almost certainly far too small to drive significant accretion • The fundamental picture (Shakura & Sunyaev 1973) involves either turbulent viscosity or magnetic stresses: Tr = p • In reality, will be function of time and place • Magneto Rotational Instabilities (Balbus & Hawley 1991) are now believed to provide adequate viscosity even from very weak seed magnetic fields

Key Timescales for Accretion • With R = r/3 RS, a quasi-Keplerian flow, h the thickness and the viscosity parameter, the fastest expected direct variations are on dynamical times of hours for SMBHs (e. g. Czerny 2004). M 8=MBH/108 M Radial sound transmission time Thermal and viscous timescales For thin disks, h 0. 1 r

Longest Timescale? • Governed by rate at which outer disk is fed • Probably the rate at which gas is injected into the core of a galaxy (bars within bars to drive inward? ) • Dominated by galactic mergers (probably major) and timescales > 107 years; can exceed 108 yr Does harassment (mere passage) work? • Does the AGN self-regulate, with its energy injection halting the inflow of gas? • Most likely depends on whether quasi-isotropic winds & star-burst supernovae OR narrow jets carry off most kinetic energy from AGN.

DISK INSTABILITIES • many of them. How many are important, especially for blazars? • Radiation pressure instability • Magneto-rotational instabilities • Flares from Coronae • Internal oscillatory modes (diskoseismology) • Avalanches or Self-Organized Criticality • Spiral shocks induced by companions or interlopers

Radiation Pressure Instability Long known that -disks are unstable if radiation pressure dominated (Shakura & Sunyaev 1976) • AGN models should be Prad dominated over a wide range of accretion rates and radii • Computed variations are on tvisc(~100 RS) (Janiuk et al. 2000; Teresi et al 2004) • May have been seen in the microquasar GRS 1915+105 (over 100’s of sec). • Scaled to AGN masses: significant outbursts, but over years to decades from X-rays through IR.

SPH simulation of Shakura-Sunyaev instability (Teresi, Molteni & Toscano, MNRAS 2004)

MRI Induced Variations • Magneto-Rotational Instabilities (e. g. Balbus & Hawley 1991) are commonly agreed to be present • Probably produce effective disk ~ 0. 01 -0. 10 Total (solid), magnetic stress (dashed) and fluid (dotted) viscosities at a disk center (Armitage 1998, Ap. JL) Also produce changes in dissipation and accretion rate Some disk clumping, but not destruction (profile changes? )

Turbulence in a Magnetized Disk Distant observer views of inner disk @ inclination angle = 55 and 80 O. Integrated flux for inclinations of (top to bottom) 1, 20, 40, 80 O for a “hot” simulation using Zeus and pseudo-Newtonian potential (Armitage & Reynolds, MNRAS 2003) Significant fluctuations develop on a few rotational timescales (hours for 108 M ).

Spiral Shocks in Disks • Perturbation by smaller BH can drive spiral shocks • Significant flux variations ensue on orbital timescales of the perturber (Chakrabarti & Wiita, Ap. J, 1993) Perturbers w/ 0. 1 and 0. 001 MBH

Spiral Shocks and Line Variations • This type of shock provides the best fits to changes in double hump line profiles seen in about 10% of AGN (Chakrabarti & Wiita 1994) Model vs. data for 3 C 390. 3 H broad lines in 1976 & 1980. Expected variations.

Flares and Coronae • Plenty of debate over the relative contribution of disk coronal flares to X-ray (predominantly) and other band (secondarily) emission and variability. • Clearly an important piece of the Seyfert variability but probably usually a small piece of blazar emission. • Total energy releasable from low density coronal flares is probably too small unless ”avalanche” or self-organized criticality process is triggered, perhaps propagating inward within a disk (Mineshige et al. 1994; Yang et al. 2000); easily produces PSD. • But flares can provide low level X-ray variations visible when other activity is minimal; maybe a bit of optical variability too.

Cyg X-1: Radio Image & X-ray light curve Combining observations at many wavelengths, we conclude:

Cygnus X-1 is a Black Hole Binary

Accretion Disks are Efficient • E = mc 2 • Complete conversion of mass to energy is only possible in matter-antimatter annihilation • But normal accretion disks can convert > 5. 7% and up to 32% of mass to energy. The first comes from Schwarzschild, the second from fastest Kerr w/ photon feedback (a = 0. 9982). • This is far better than chemical reactions (~ 0. 0001 %) or even nuclear fusion (~0. 7 %) • Full conversion of 1 M /year = 5. 7 1039 W

Accretion Disks Can Launch Jets Numerical simulations of jet launching and propagation. (PLATON; Stone)

Fitting Things Together: Quasars (and Blazars) Require: • • Tremendous powers: 1039 Watts > 1012 L Small volumes because of rapid variations Jet production (frequently) THEREFORE, the standard model now involves BHs + Accretion Disks • Accretion disks are very compact, with most energy coming out within 20 RS or ~5 light-hours for 108 M BH

Evidence for Supermassive Black Holes NGC 4261: at core of radio emitting jets is a clear disk ~300 light-yrs across and knot of emission near BH

Direct Evidence for Rotating Disk Masers formed in warped disk in NGC 4258 (and a few other Seyfert galaxies)

Supermassive BH at Core of Milky Way Radio core of Sgr A* is unresolved at 43 GHz, very close to RS for a 2. 6 million solar mass BH “weighed” by orbits of stars measured over a decade in the infrared.

Active Galactic Nucleus Model

Orientation Based Unification Picture

CONCLUSIONS • Black holes are the natural endpoint of massive star evolution and they have been detected in our galaxy and nearby ones. • Quasars are distant, extremely powerful cores of galaxies. • Accretion disks are efficient and ubiquitous: they are important for stellar and galactic astronomy: can be intimately related to galaxy growth and even large scale structure. • Accretion disks around supermassive BHs (106 to 1010 M ) are the source of the tremendous powers emitted by quasars and other active galactic nuclei.