Introduction to Black Holes and Accretion Disks

Paul J. WiitaGeorgia 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

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RS =2GM

c 2= 3km

MBH

MSun

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So a BH with Earth’s mass has RS = 1 cm!100,000,000 Msun BH has Rs = 300,000,000 km or3x108km = 10-5parsec = 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=3Rs There is also the last possible, or marginally bound, orbit at Rmb=2Rs

• 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=1.5Rs

The Schwarzschild Metric

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

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ds2 = −(1− 2GM /rc 2)dt 2 +dr2

(1− 2GM /rc 2)+ r2(dθ 2 + sin2θ dφ2)

This is in spherical coordinates; for Minkowski space we have :

ds2 = −dt 2 + dr2 + r2(dθ 2 + sin2θ dφ2)

The general form for a metric in space - time is :

ds2 = gikdxi

i,k= 0

3

∑ dx k ≡ gik dxidx k

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 |g00|1/2E = const.

• For a non-rotating BH this becomes:

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z = Δλ /λ = (λ rec − λ em ) /λ em =| g00 |−1/ 2 −1

z = (1− 2GM /rc 2)−1/ 2 −1

z ≈GM /rc 2 in the Newtonian limit, but

z→ ∞ as r→ RS

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. Mass2. 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(c2)

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rstatic (θ) ≡ M + M 2 −Q2 − a2 cos2θ

r+ ≡ M + M 2 −Q2 − a2 → M(G /c 2) as a→ M

Cosmic censorship hypothesis: a < M so no naked singularities exist

Tidal Stretching & Hawking Radiation

• Large gravity differences (tides): “toothpaste tube effect”

• Quantum gravity effect: Hawking temperature T=h/162kGM=610-8K(M/M)

• Hawking power: ~R2T4 ~M2/M4 ~1/M2

• Incredibly small if BH mass > 1017g (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

3C 273 3C 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 GalaxyCircinus 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 3C 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 dwarfsX-rays from neutron stars and stellar mass BHsMostly 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 MonitoringAller & Aller, U Michigan

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

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

Evidence for Accretion Disks in BlazarsBig blue bump in AO 0235+164

(Raiteri et al. astro-ph/0503312)

More New Evidence for Accretion Disks

• Ton 202 polarized flux with face-on Kerr disk model fitted to it (Kishimoto et al. 2004)

Optically thick: hidden Balmer edge now claimed to be seen in several quasars.

Why Quasi-Keplerian and Disk-like?

Quasi-black body fits to disk spectra

Broad K lines for NLS1s

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=1.3x1038(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 thickintermediate L/LE

cold optically thick, geometrically thin low L/LE optically thin hot flow interior to

some transition radius.

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/3RS, 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).

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tdyn (s) =104R3 / 2M8

tradial = tdynr

h

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tthermal = tdyn /α =105α 0.1−1R3 / 2M8

tvisc = tthermalr

h

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=107 r

10h

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α 0.1−1R3 / 2M8

Radial sound transmission time

For thin disks, h0.1r

M8=MBH/108M

Thermal and viscous timescales

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(~100RS) (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, ApJL)

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 80O.

Integrated flux for inclinations of (top to bottom) 1, 20, 40, 80O for a “hot” simulation using Zeus and pseudo-Newtonian potential(Armitage & Reynolds, MNRAS 2003)Significant fluctuations develop on a few rotational timescales (hours for 108M).

Spiral Shocks in Disks

• Perturbation by smaller BH can drive spiral shocks • Significant flux variations ensue on orbital timescales of the

perturber (Chakrabarti & Wiita, ApJ, 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 3C 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 = mc2

• 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 1039W

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.