Black Holes in Universe -

From Stellar Masses to

Supramassive Objects in Galaxies

Max CamenzindCenter for Astronomy

Heidelberg (ZAH)@ Landessternwarte (2005)

Prologue: Chandrasekhar 1983• „The black holes of nature are the

most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time. And since the general theory of relativity provides only a single unique family of solutions for their descriptions, they are the simplest objects as well.“

No matter is involved in their construction [i.e. no EOS], a Black Hole is a global vacuum solution with horizon, a kind of gravitational soliton.

in Chandrasekhar (1983): „The Mathematical Theory of BHs“

Topics• The Long History of Black Hole Physics.• The Year 1963 and Kerr Black Hole

Gravitational field is not Newtonian ! • Evidence for the Existence of Black Holes

4 Classes of Astrophysical Objects. „No Hair Plane (Glatzenebene)“ (M,a).

• Accretion: New Paradigm of disk accretion onto Black Holes (Balbus & Hawley 1991).

• Magnetic Fields - The Spin Paradigm: The Ergosphere as a Source of Energy Launch Jets (Blandford & Znajek 1977) still largely not understood.

• Beyond Einstein ? Dreams and Future

The Long Way towards BHs

• 1915: Einstein postulates the field equations (together with Hilbert).

• 1916: Schwarzschild Solution Schwarzschild radius RS = 2GM/c² = 3 km M / MS

• Einstein denied the reality of Black Holes … He considered Black Holes as a mere mathematical curiosity.

• This view changed after his death detection of Quasars (> 1963) observation of Cygnus X-1 (1971)

1963 – Foundation of Black Holes

1923 - Milestone 1: George Birkhoff: Schwarzschild spacetime geometry is the unique spherically symmetric solution of the Einstein vacuum field equations

• 1939 - Robert Oppenheimer & Hartland Snyder show gravitational collapse of a pressureless homogeneous fluid sphere formation of a trapped region

• 1963 – Milestone 2: Roy Kerr solves the Einstein vacuum field equations for uncharged symmetric rotating systems

• 1963 – Milestone 3: Quasars are detected fuelled by accretion onto Black Holes

• 1965 - Ezra Newman and collaborators solve the Einstein-Maxwell equations for charged rotating systems

• 1967 - Werner Israel presents proof of a "no hair" theorem

1968 – 1977: Golden Age

• 1968 – Brandon Carter uses Hamilton-Jacobi theory to derive 1st-order equations of motion for particle moving in Kerr black holes Kerr Ray-Tracing

• 1969 - Roger Penrose discusses the Penrose process for the extraction of the spin energy from a Kerr black hole Free energy of BHs

• 1971 – Milestone 4: Identification of Cygnus X-1/HDE 226868 as a binary black hole candidate system.

• 1973 - David Robinson completes the proof of the uniqueness theorem for Kerr black holes

• 1977 – Milestone 5: Blandford-Znajek Process electromagnetic spin energy extraction from rotating black holes

• 1972 - Stephen Hawking proves that the area of a classical black hole's event horizon cannot decrease.

• 1972 - Jacob Bekenstein suggests that black holes have an entropy proportional to their surface area due to information loss effects

• 1973 - James Bardeen, Brandon Carter, and Stephen Hawking propose 4 laws of black hole mechanics in analogy with laws of thermodynamics Free energy

• 1973 - Stephen Hawking applies quantum field theory to black hole spacetimes and shows that black holes will radiate particles with a black-body spectrum which can cause black hole evaporation concept is important, but astrophysically not relevant, and still debated.

4 Laws of Black Hole Mechanics

• 1978 – Sargent et al. show evidence for a supermassive BH in the center of Messier 87 (“serious possibility”). This has been very much debated but confirmed !

• 1992 – Microquasar GRS 1915+105 found.• 1997 – Fe line redshifts of the innermost portions of

accretion disks around rotating supermassive black holes

• 2000 - Evidence for the hypothesis that Sagittarius A* is a supermassive black hole at the centre of the Milky Way galaxy

• 2002 – The most distant Black Hole found: Cosmological Redshift z = 6.43 ! (< 1 Gyear old)

• 2005 – BHs confirmed in ~ 20 X-Ray Binary Systems !• 2005 – BHs confirmed in ~ 30 nearby galactic centers !• 2005 – BHs found in ~ 100,000 Quasars !

1978 – 2005: Observations

The Year 1963 and the Physics of Kerr Black

Hole

How to Treat Gravity of BHs ?How to Treat Gravity of BHs ?

jdxidxij

dtidxi

dtii

ds 2)( 222

/n jj

t

In GR the spacetime is a differentiable manifold. The most natural thing is to to foliate it in t=const spatial hypersurfaces t.

function lapse::

Measures the “clocks ticking rates” on two t

vectorshifti ::

tensormetricij 3:: Measures distances among points on a t

unit timelike 4-vector normal to t

Measures the “stretching” of coordinates

t

1

4

6

2 Parameters:(i) Mass M(ii)Ang. Mom. a „Charge not relevant in Astrophysics“

Event HorizonrH = M + (M² - a²)1/2

Spacetime is stationary and axisymmetric

Source: Mass

Source: Ang. Mom.

Also for NSs !

Gravity Probe-Bwill confirm theExistence ofGravitomagnetism

4 Laws of BH Mechanics

Bekenstein 1973, Bardeen et al. 1973, Hawking 1974, 1975

Extracted bymagnetic effects

Blandford-Znajek Process

Blandford & Znajek (1977)

Load atinfinity

J

„Split-Monopole“ magnetospherecoupled to rotating Horizonwith Znajek Horizon bcdrives closed current system Subject of strong criticism (Punsley)

A Modern Version of BZ Mechanism

OLC: OuterLight Surface, compactfor Black HolesA: AlfvenSurface

Plasma injection fromnear ms orbit;Plasma accretioncausal: slow ms,Alfven and fastms points

Proto-Jet

CurrentSheet

wwwww

Magnetic fieldsadvected from„Infinity“

Twisting of Magnetic Fields

• Except for induction terms, evolution of toroidal magnetic field ~ Newtonian MHD

Source: Differential plasma rotation Schwarzschild: no shear ! Extreme Kerr: biggest effect !

T ~ RB

Operates outside horizon

Black Holes 2 Energy Reservoirs• Potential energy tapped by accretion X-rays• Rotational energy tapped by magnetic fields,

similar to rotating neutron stars (Blandford & Znajek 1977) will feed energy of JETS !

LLRotRot = E = ERotRot/t/tbrake brake

~ 10~ 104646 erg/s (M erg/s (MHH/10/1099 M MSS) (t) (tHH/t/tbrakebrake))

LLRotRot = E = ERotRot/t/tbrake brake

~ 10~ 103838 erg/s (M erg/s (MHH/10 M/10 MSS) (t) (tHH/t/tbrakebrake))ttbrake brake = f (a, B,…) [BZ 1977]= f (a, B,…) [BZ 1977]

LLBZBZ = k B = k BHH² r² rHH²c (a/M)² (²c (a/M)² (FF[[HH--FF]/]/HH²) ~ M²) ~ MHH

Anatomy of Black Holes

Black Hole Ergosphere Extended Boundary

Layer

For a > 0.7, radii move inside ergosphere

Each form of matterwill be driven to corotation

within the ergosphere ! Boundary Layer near Horizon ~ rH

In Schwarzschild:No rotation near Horizon !

H = (rH)

a = 0.5

a = 1.0

Outflowsin

Quasars & Micro-

Quasars ?

„StochasticFunnel-Flow“

Krolik 2005

DiskInflow

ConicalOutflow

Field Line Twisting by Rotating Black Holes

a = 0

a = 0.9

a = 0.5

a = .998

GRMHD Simulations (Hawley et al. 2005)

Astrophysical

Black Holesin the

Universe

Black Holes as Astrophysical Objects

• [ Primordial Black Holes: M < 2 MS]

• Stellar Black Holes: 2.2 MS < M < 100 MS

• Intermediate Mass Black Holes 100 MS < M < 105 MS (?)

• Supermassive Black Holes: 105 MS < M < 1010 MS reside in center of galaxies at all redshifts, 0 < z < 10 (?).

High-Mass XBCygnus X-1

Black Holes areformed in stellarCollapse >100.000 BHs in the Galaxy

1971 monitoredby UHURU

Cyg X-1 – Activity Cycles (VLA / RXTE)

When high in X-rays minimum in radio and vice versa Jet launch

Radio

X-Rays

HX

Low-MassX-Ray

Binaries

DIFFERENT BINARY SYSTEMS• type of the donor star type of accretion (wind or Roche lobe overflow)

• very different scales:

Every X-ray binary is a

possible microquasar!

J.A. Orosz

Stellar Mass Spectrum Clear Separation NSs vs BHs

NS

BHs

X-Ray Emission:VARIABILITY on all Time Scales

• Variations = changes in the state of the source

• lightcurves: GX 339-4 / GRS 1915+105

Variations on very different time scales !

“easy” observations for human time scale

X (2-10 keV)

Radio (2,25 GHz)

Rau et al (2003)

GX339-4 lightcurve

1996 2003GRS 1915+105

accretion / ejection coupling

• cycles of 30 minutes in GRS 1915+105 : ejections after an X-ray dip refilling of the internal part of the disc ? transient ejections during changes of states

same phenomenum in the quasar 3C 120 ? far slower !

Mirabel et al (1998)

Marscher et al (2002)

GRS 1915+105

Microquasar

SUPERLUMINAL EJECTIONS

• Move on the sky plane ~103 times faster• Jets are two-sided (allow to solve equations max. distance)

same Lorentz factor as in Quasars : ~ 5-10

Mirabel & Rodriguez (1994)

VLA at 3.5 cm

VLBI at 22 GHz ~ 1.3 cm

~ arcsec. scale ~ milliarcsec.

scale

QUASARS MICROQUASARS

Mirabel et al. 1992

Quasar 3C 223 Microquasar 1E1740.7-2942

radio (VLA) observations at 6 cm

VLA at 1477MHz ~ 20 cm

Black Holes in E-GalaxiesDrive Jets

Cygnus A (VLA)3C 219 (VLA)

Non-thermalRadio Plasma

--------- 100 kpc ------------

A. Müller (LSW) 2004

Black Hole Mass ~ Bulge Mass

for Inactive Galaxies30 NearbyGalaxies:

MH ~ 0.14% MB

MagorrianRelation

(N. Häring& H.-W. Rix:ApJL 2004)

Mass vs Luminosity of Quasars

LE = 2 x 1031 Watt x (M/MS) ~ 5 x 104 LS

maximumluminosityminimum mass for BHs

Black Hole „Two-Hair Plane“

RL Quasars,Radio Galaxies

BH sinGalacticCentersand QSOs

BH

s at High

R

edsh

ifts

Microq

uasars, S

tellar BH

s, M* >

30 In

termed

iate Mass

BH

s ???P

opu

lation III B

Hs

Neu

tron

Stars

Spin a of a Black Hole can bedetermined from Photon Propagation

Equations of geodesics integrable Carter Integrals

Imageof aRing

Line Emission from BH

Accretion

Schwarzschild Extreme Kerr

ExtremeRedshift

High-Redshift Quasars(SDSS)Form

inPrimordi

al Clusters

Very massive BHs

form very early !

Cosmic Quasar Population

H0 = 70 km/s/Mpc

k = 0.0

m = 0.3

= 0.7

QSO densitiesaugmented byfactor 3due to obscuration M. Camenzind 2005

Cosmic History & Black Holes

recombination

Cosmic Dark Age: no light no star, no quasar; IGM: HI

First light: the first galaxies and quasars in the universeEpoch of reionization: radiation from the first object lit up and ionize

IGM : HI HII reionization completed, the universe is transpartent and the dark ages ended

today

Credit: G. Fishman et al., BATSE, CGRO, NASA

BATSE GRB Final Sky Map: Astronomy Picture of the Day 2000 June 28

Gamma-Ray Burst Durations

Two Populations: Short – 0.03-3s Long – 3-1000sPossible third Population 1-10s

A Slow Explosion of massive star Formation of rotating BH with JETS long duration burst

Credit: Y. Grosdidier (U. Montreal) et al., WFPC2, HST, NASA

“Astronomy Picture of the Day: 2003 March 25”

On the Origin of Gold: Astronomy Picture of the Day: 2005 May 15

Merging of 2 neutron stars short bursts formation of a BH

New Paradigm for ADs:Disks are not viscous –Disks are turbulent -Turbulence driven by weak magnetic fields - Radiative MHD key vehicle[Balbus & Hawley 1991,98]

New Insight:Accretion is Turbulent

- not Viscous

New Paradigm:BHs in Different Accretion

States• BHs grow by accretion processes.• MHD turbulence drives angular

momentum transport in acretion disks (Balbus & Hawley magnetorotational instability, MRI). Disks are turbulent, not viscous !

• The well-known thin disk accretion model (Shakura & Sunyaev) only applies for high accretion rates, typically more than a few percent Eddington.

Truncated accretion at lower rates.

Two different accretion states depending on the accretion rate for given mass

Brinkmann& CamenzindLSW 2004

Esin et al. 1995A. Müller (LSW 2004)

Accretion Statesof Cyg X-1

High State (HS)[truncation radiusnear rms]Low State (LS)[truncation radiusmoves away]TransitionsEnergy emittedin Comptonizedphotons

What tell us X-rays?

MCG-6-30-15HST/WFPC-2

XMM-Newton 0.5-10keV light curve(Fabian et al. 2002)

Rapid X-ray variability of AGN strongly suggests X-rays come from innermost regions of accretion disk

GRMHD Accretion from a Torusas Initial Condition

Non-Radiative Accretion Flows

De Villiers, Hawley &Krolik 2003- 2005(3D non-conservativeGRMHD in BL);Gammie et al.2003, 2004(2D conservativeGRMHD in BL coordinates) Initial condition

(exact mech. equilibrium+ weak magnetic fields)

Initial State „Final State“

Meridional Planethrough a BHColour: Density

Torus+ weakmagnetic fields

TurbulentThick Disk Keplerian

Gammie et al. 2004

OutflowsFunnel

MagneticFields(originallyconfinedto torus)evolvetowardsa completelyturbulentstate.

Angularmomentum istransportedoutwards, someaccreted tospin up BH.

Fender 2004; Belloni 2005

When Plasma is included Ergospheric Jets ?

Beyond Einstein – The Observer‘s Dreams

2012 2020 2030Today

XMM

Planck

XEUS

NASA Homepage

XEUS - ESA

Beyond Einstein –

Heavy Numerical

Computations

Robust parallel GRMHD Codes

Beyond Einstein: Is there really a

Singularity in the Black Hole ?

Vacuum energy ispresent everywherein the Universe( Dark Energy)

Change theInterior of aBlack Hole

Regular state !

Mazur & Mottola 2001, 2004

Conclusions - Visions• Mass spectrum is continuous from stellar to 10

billion solar masses. Gap from 100 – 105 MS ?• But Kerr parameter a is not yet measurable !• GRMHD (> 2000) Plasma dynamics near BHs can

be successfully treated within Godunov schemes Use Kerr coordinates, bc within horizon ! MRI accretion theory is now tractable !

• Strong B-field limit (which is unphysical !): GR Magnetodynamics confirms BZ mechanism of energy extraction out of the ergosphere Jets are ergospheric plasma flows ?

• Weak field limit of GRMHD (relevant for MRI) is in unsatisfactory state, most results based on non-conservative methods Turbulent accretion to rotating BHs essentially unsolved, but now tractable with modern methods.

Also include radiation effects, which is important for high accretion rates at high z.