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Reminder ªMidterm Tuesday, Oct 15th ªMaterial covered: ª lectures through Oct 10 ªTextbook Ch. 1-3, 6-8 ªHW 1-3 ªBring a scientific calculator and a pencil

10/7/19 1 Lecture 12: Black Holes

ªOld ideas for black holes ªTheory of black holes ªReal-life black holes ªStellar mass ªSupermassive ªSpeculative stuff

ÓSidney Harris

10/7/19 2 I : OLD IDEAS FOR BLACK HOLES ª “What goes up must come down”… or must it?

ª Escape velocity, Vesc ª Critical velocity object must have to just escape the gravitational field of the Earth

ª V

ª V>Vesc : object never falls back to Earth ª In fact, escape velocity given in general by 2GM V = esc R when the mass of an object is M and the distance from the center is R

ª Starting from Earth’s surface, Vesc=11 km/s

10/7/19ª Starting from Sun’s surface, Vesc= 616 km/s 3 18th Century ideas

ª By making M larger and R smaller, Vesc increases ª Idea of an object with so strong that light cannot escape first suggested by Rev. John Mitchell in 1783

ª Laplace (1798) – “A luminous , of the same density as the Earth, and whose diameter should be two hundred and fifty times larger than that of the Sun, would not, in consequence of its attraction, allow any of its rays to arrive at us; it is therefore possible that the largest luminous bodies in the universe may, through this cause, be invisible.”

10/7/19 4 Quiz ªThe indirect detection of gravitational waves was done A. Detecting the precesion in the orbit of Mercury B. Detecting gravitational lensing C. Measuring changes in the length of aluminum cylinders D. Measuring the orbital decay of a double pulsar 10/7/19 5 Quiz ªThe indirect detection of gravitational waves was done A. Detecting the precesion in the orbit of Mercury B. Detecting gravitational lensing C. Measuring changes in the length of aluminum cylinders D. Measuring the orbital decay of a double pulsar 10/7/19 6 Quiz

ªThere are 2 detectors in LIGO because: A. that increases the chances that one is up during the night B. it ensures continuous operation if one breaks C. it increases the chances one is aligned with the direction of the wave D. it removes local perturbations 10/7/19 7 Quiz

ªThere are 2 detectors in LIGO because: A. that increases the chances that one is up during the night B. it ensures continuous operation if one breaks C. it increases the chances one is aligned with the direction of the wave D. it removes local perturbations 10/7/19 8 II : MODERN IDEAS ª Karl Schwarzschild (1916) ª First solution of Einstein’s equations of GR ª Describes gravitational field in (empty) space around a point mass ª Space-time interval in Schwarzschild’s solution (radial displacements only) is

22æö21GM 2 2 (DDDs) =ç÷1---2 c ( t) ( R) [ angle terms] èøcR æö2GM ç÷1- 2 èøc R ª Features of Schwarzschild’s solution: ª Yields Newton’s law of gravity, with flat space, at large R ª Space-time curvature becomes infinite at center (R=0; this is called a space-time singularity) ª Gravitational time-dilation effect becomes infinite on a spherical surface known as the horizon, where coefficient of Dt is zero ª Radius of the sphere representing the is called the , Rs

10/7/19 9 •For a body of the Sun’s mass, Schwarzschild radius 2GM R = ® 3km S c 2

• Singularity – curvature is infinite. Everything destroyed. Laws of GR break down. • Event horizon – gravitational time-dilation is infinite as observed from large distance. • Any light emitted at Rs would be infinitely redshifted - hence could not be observed from outside 10/7/19 10 More features of Schwarzschild

ª Events inside the event horizon are causally-disconnected from events outside of the event horizon (i.e. no information can be sent from inside to outside the horizon) ª Observer who enters event horizon would only feel “strange” gravitational effects if the black hole mass is small, so that Rs is comparable to observer’s size ª Once inside the event horizon, future always points toward singularity (any motion must be inward)

ª Stable, circular orbits are not possible inside 3Rs : inside this radius, orbit must either be inward or outward but not steady

ª Light ray passing BH tangentially at distance 1.5Rs would be bent around into a circle ª Thus black hole would produce “shadow” on sky 10/7/19 11 Event horizon telescope

10/7/19 12 M87, a nearby giant elliptical

10/7/19 13 Emission from relativistic jet

10/7/19 14 The relativistic electrons near the center emit in the radio

10/7/19 15 EHT image of M87

10/7/19 16 M87 accretion disk

10/7/19 17 credit ESO ªCurved space around a star…

From web site of UCSD

10/7/19 18 … and around a black hole

10/7/19 19 Rotating black holes ª (1963) ª Discovered solution to Einstein’s equations corresponding to a rotating black hole ª Kerr solution describes all black holes found in nature ª Features of the Kerr solution ª Black Hole completely characterized by its mass and spin rate (no other features [except charge]; no-hair theorem) ª Has space-time singularity and event horizon (like Schwarzschild solution) ª Also has “static surface” inside of which nothing can remain motionless with respect to distant fixed coordinates ª Space-time near rotating black hole is dragged around in the direction of rotation: “frame dragging” (aka the Lense-Thirring effect) ª Ergosphere – region where space-time dragging is so intense that its impossible to resist rotation of black hole. 10/7/19 20 Frame dragging by rotating black hole

10/7/19 21 Graphics: University of Winnipeg, Dept. Artist’s conception of rotating black hole

10/7/19 22 III : Real-life black holes

ª So much for theory – what about reality ª Thought to be two (maybe three?) classes of black hole in nature ª “Stellar mass black holes” – left over from the collapse/implosion of a massive star (about 10 solar masses) ª “Supermassive black holes” – giants that currently sit at the centers of galaxies (range from millions to billions of solar masses) ª “Intermediate-mass black holes” – suggested by recent observations (hundreds to thousand of solar masses) 10/7/19 23 Stellar mass black holes

ª End of massive star’s life… ª In core, fusion converts hydrogen to heavier elements (eventually, core converted to iron Fe). ª Core collapses under its own weight ª Huge energy release: Rest of star ejected – Type II Supernova ª Either a black hole or remains

10/7/19 24 Quiz

ªThe ergosphere is A. the region from which light cannot escape B. the region from which the gravity of the black hole cannot be resisted C. the region where the rotation of the black hole cannot be resisted D. the Schwarschild radius 10/7/19 25 Quiz

ªThe ergosphere is A. the region from which light cannot escape B. the region from which the gravity of the black hole cannot be resisted C. the region where the rotation of the black hole cannot be resisted D. the Schwarschild radius 10/7/19 26 Quiz

ªWhere do stellar mass black-holes come from? A. End stage of a low-mass star B. End stage of a white dwarf C. End stage of a high-mass star D. The imagination of SF authors

10/7/19 27 Quiz

ªWhere do stellar mass black-holes come from? A. End stage of a low-mass star B. End stage of a white dwarf C. End stage of a high-mass star D. The imagination of SF authors

10/7/19 28 Black holes in binary systems ª If black hole is formed in binary star system, ª Tidal forces can rip matter of the other star ª Matter goes into orbit around black hole – forms an accretion disk ª As matter flows in towards the black hole, it gives up huge amount of energy ªanalogy to hydroelectric power derived when water falls over a dam ª Energy is first converted to heat, raising gas temperature in accretion disk to millions of degrees ª Hot accretion disk radiates away energy, emitted as X-rays ª These systems are called X-ray binaries

10/7/19 29 “X-ray” binary

Outer layers of a nearby star are pulled off by 10/7/19 tides, crash into accretion disk around BH 30 Accretion disk from numerical simulation

ª Turbulence develops and causes gas to accrete (flow inward) onto the black hole

10/7/19 31 J. Hawley, U. Virginia Supermassive black holes (SMBHs) ªFound in the centers of galaxies

10/7/19 32 Center of the Milky Way: Sgr A* ª The center of our own Galaxy ª Can directly observe orbiting an unseen object ª Need a black hole with mass of 3.7 million solar masses to explain stellar orbits ª Best case yet of a black hole.

10/7/19 33 M87

ª Another example – the SMBH in the galaxy M87 ª Can see a gas disk orbiting galaxy’s center ª Measure velocities using the Doppler effect (red and blue shift of light from gas) ª Need a 3 billion solar mass SMBH to explain gas disk velocities

10/7/19 34 Active Galactic Nuclei

ª M87 shows signs of “central activity” ª The Jet ª Jet of material squirted from vicinity of SMBH ª Lorentz factor of >6 ª Powerful (probably as powerful as galaxy itself) ª What powers the jet? ª Accretion power ª Extraction of spin-energy of the black hole

10/7/19 35 Artist’s conception of M87 system

MUSE: Supermassive Black Hole 10/7/19 (“Black Holes and Revelations” 2009) 36 ª M87 is example of an “active galactic nucleus” ª Material flows (accretes) into black hole ª Energy released by accretion of matter powers energetic phenomena ªEmission from radio to gamma-rays ªJets ª Supermassive black hole equivalent to the X-ray binaries systems ª Particularly powerful active galactic nuclei are sometimes called Quasars

10/7/19 37 1966 Cover, discovery of QSOs

10/7/19 38 Water masers and dynamics in NGC 4258

Masers reveal a tiny warped disk around a massive black hole

Miyoshi et al 1995; Greenhill et al 1996; Herrnstein et al. 1998

10/7/19 39 The powerful radio-galaxy Cygnus-A

Radio image with the Very Large Array in New Mexico 10/7/19 40 Another example… the “Seyfert galaxy” MCG-6-30-15

10/7/19 41 Model for MCG-6-30-15 inferred on basis of X-ray data from XMM- Newton observatory: magnetic fields transfer energy of spin from black hole to accretion disk!

10/7/19 42 What can come out of black hole?

…more than you might think! ª Magnetic fields threading ergosphere can attach to and drag surrounding matter, reducing the black hole’s spin and energy ª “”: black hole slowly evaporates due to effects ª Particle/antiparticle pair is created near BH ª One particle falls into horizon; the other escapes ª Energy to create particles comes from gravity outside

horizon 3 æ M ö t =1010 yrs ´ç ÷ evap è 1012 kg ø ª Solar-mass black hole would take 1065 years to evaporate! ª Mini-black holes that could evaporate are not known to exist now, but possibly existed in early Universe

10/7/19 43 White holes and Worm holes

ª GR does not know about entropy: there is a symmetric solution for a BH known as a White-hole ª What if we can connect a BH and a WH to form a worm home? ª Shown by Rosen & Einstein for a Swartzschild BH, but it isn’t stable and it cannot avoid the singularity ª Solution developed by K. Thorne, but requires exotic matter. Other solutions exist…

10/7/19 44 Alcubierre drives

ª Since we are on the topic, here is another “faster than light” trick ª Metric mathematically developed by Miguel Alcubierre, also needs “exotic matter”/”negative energy”

10/7/19 45