in Today Astronomy 102: energy and black holes
Einstein's mass-energy equivalence (E = mc2). Generation of energy from black holes. The search for black holes, part 1: the discovery of active galaxy nuclei, and the evidence for the presence of black holes therein. Jet and disk around a supermassive black hole in the center of the elliptical galaxy M87, as seen by the Hubble Space Telescope (NASA/STScI).
6 March 2008 Astronomy 102, Spring 2008 1
Equivalence of mass and energy in Einstein's special theory of relativity
Mass is another form of energy. Even at rest, in the absence of electric, magnetic and gravitational fields, a body with (rest) mass m0 has energy given by E = m0c2 . Conversely, energy is another form of mass. For a body with total energy E, composed of the energies of its motion, its interactions with external forces, and its rest mass, the relativistic mass m is given by E = mc2 or m = E/c2 .
(You will need to know how to use this formula!)
6 March 2008 Astronomy 102, Spring 2008 2
Equivalence of mass and energy in Einstein's special theory of relativity (continued)
Consequences: Even particles with zero rest mass (like photons and neutrinos) can be influenced by gravity, since their energy is equivalent to mass, and mass responds to gravity (follows the curvature of spacetime). There is an enormous amount of energy stored in rest mass.
6 March 2008
Astronomy 102, Spring 2008
3
Note on energy units
Since E = mc2, the units of energy are
cm 2 gm cm2 gm = = erg 2 sec sec
Luminosity is energy per unit time, so its units are erg/sec, as we have seen. "Erg" comes from the Greek ' , which means "work" or "deed." Note also: 1 watt = 1 W = 107 erg/sec 1 joule = 107 erg 1 kWh = 1000 W1 hour = 3.61013 erg (Power-bill units).
6 March 2008 Astronomy 102, Spring 2008 4
F I H K
Equivalence of mass and energy in Einstein's special theory of relativity (continued)
Example: Liberate energy, in the form of heat or light, from 1000 kg (1 metric ton) of anthracite coal. Burn it (turns it all to CO2 and H2O): A year's supply, for a typical American family. E = 4.31017 erg = 12,000 kWh . Maximum-efficiency fusion in a star (turns it all to iron): E = 4.11024 erg = 1.11014 kWh . And, for something we can calculate in AST 102, Convert all of its rest mass (m0) to energy (m0c2): 1000 gm cm 2 More than E ==m00c 2= ?1000 kg E m c 2 = 3 10 10 1 kg s 200 times as 23 24 25 A. 9 10 erg B. 9 10 erg C. 9 10 erg productive 10 = 9 26 26 erg = 2.5 2710 17 kWh as fusion! D. 9 10 erg E. 9 10 erg
FG H
IJ F KH
I K
6 March 2008
Astronomy 102, Spring 2008
5
"Converting mass to energy" with a black hole
...by which we mean converting rest mass to heat or light. Black hole accretion: As matter falls into a black hole, it is ionized and accelerated to speeds close to that of light, and radiates light as it accelerates. The faster it goes, the higher the energy of the photons. The surface of planets or stars would stop an infalling particle before it approached the speed of light, but such speeds are possible when falling into a black hole. About 10% of the rest mass of infalling particles can be turned into energy (in the form of light) in this manner. (The other 90% is added to the mass of the black hole.)
6 March 2008 Astronomy 102, Spring 2008 6
"Converting mass to energy" with a black hole (continued)
Radio + visible light +UV + X, rays
Path of falling particle (electron or proton) Normal star size
6 March 2008
Black hole Neutron star size
7
White dwarf size
Astronomy 102, Spring 2008
"Converting mass to energy" with a black hole (continued)
Garbage (one ton) X-rays
Simultaneous solution of our energy and environmental problems? Black hole (mass of the moon) Electric power (one day's supply for Earth)
Photocells
6 March 2008
Astronomy 102, Spring 2008
8
"Converting mass to energy" with a black hole (continued)
Spinning black holes (Penrose 1969, Blandford & Znajek 1977) Since spacetime in the ergosphere rotates along with the horizon, and 0-30% of the hole's total energy is there, one can (in principle) anchor a "crank handle" there and have the black hole turn a distant motor. That's a lot of energy: for a 10 M black hole, 30% is 2 2 33 10 cm 0.3m0c = 0.3 10 2 10 gm 3 10 sec
e
F jH
I K
= 5.4 10 54 erg . The Sun will emit "only" about 2x1051 ergs in its whole life. The motor could be used to generate electricity at fairly high efficiency, until the hole stops spinning (a very long time).
6 March 2008 Astronomy 102, Spring 2008 9
"Converting mass to energy" with a black hole (continued)
Ends of shafts placed in the ergosphere of a spinning black hole. Shafts turn magnet end over Coils end.
N S
Magnet
Spinning black hole
Two long shafts
Electric power
Spinning black-hole generator
6 March 2008 Astronomy 102, Spring 2008 10
PRSs up, please.
Energy is conserved neither created nor destroyed, but changeable in form. As a rock falls into a black hole, its speed (and kinetic energy) increases and its mass (and relativistic mass-energy) increase, so something must be losing energy. What? A. It is drawing heat from the black hole's surroundings material in the surroundings is cooling down. B. Gravity is doing the work; the gravitational binding energy of the rock and the black hole must be decreasing. C. The rock gets ionized and starts radiating light, UV and Xrays, and this is an energy loss. D. The rock would start burning up: chemical energy is lost.
6 March 2008 Astronomy 102, Spring 2008 11
Mid-lecture break.
Don't forget Homework #3, which is due tomorrow evening at 5:30 PM. Please fill out the online TA evaluations, one for every TA with whom you've been working.
X-ray, visible-light, and radio images of Centaurus A, home of the nearest massive black hole.
6 March 2008 Astronomy 102, Spring 2008 12
The (retrospective) discovery of black holes: Seyfert galaxy nuclei
In 1943, Carl Seyfert, following up a suggestion by Milton Humason, noticed a class of unusual spiral galaxies, now called Seyfert galaxies. Unlike other galaxies, in short-exposure photographs they look like stars; long exposures reveal that each bright starlike object actually lies at the nucleus of a galaxy. Seyfert The starlike nucleus has lots of ionized gas, with a peculiar, broad range of ionization states and Doppler shifts indicative of very high speeds (thousands of km/s). The starlike nucleus is also bluer much than clusters of normal stars. Seyfert noted that there didn't seem to be a plausible way to explain the starlike nucleus as a collection of stars.
6 March 2008 Astronomy 102, Spring 2008 13
Seyfert galaxy NGC 4151
Long exposure, showing the central "bulge" and spiral arms (Palomar Observatory).
6 March 2008
Short exposure, showing the starlike active nucleus (NASA Hubble Space Telescope).
14
Astronomy 102, Spring 2008
The discovery of black holes: quasars
Discovered by radio astronomers: small, "starlike," bright sources of radio emission (1950s). Identified at first by visible-light astronomers as stars with extremely peculiar spectra (1950s). Maarten Schmidt (1963) was the first to realize that the spectrum of one quasar, 3C 273, was a lot like a common galaxy spectrum, but seen with a Doppler shift of about 48,000 km/sec 16% of the Maarten Schmidt in 1963 speed of light.
6 March 2008 Astronomy 102, Spring 2008 15
The discovery of black holes: quasars (continued)
High speed with respect to us: the quasars are very distant. 3C 273 is measured to be about 2 billion light years away, much further away than any galaxy known in the early 1960s. Yet they are bright: the quasars are extremely powerful. 3C 273 has an average luminosity of 1012 L , about 100 times the power output of the entire Milky Way galaxy. Observations also show that the powerful parts of quasars are very small. Radio-astronomical observations show directly that most of the brightness in 3C 273 is concentrated in a space smaller than 10 light years in diameter, a factor of about 20,000 smaller than the Milky Way galaxy.
6 March 2008 Astronomy 102, Spring 2008 16
The search for black holes: discovery of quasars (continued)
The brightness of quasars is highly, and randomly, variable. 3C 273 can change in brightness by a factor of 3 in only a month. This means that its power is actually concentrated in a region with diameter no larger than one light-month, 7.91011 km. For comparison, Pluto's orbit's diameter is about 1010 km. Major problem: how can so much power be produced in such a small space?
6 March 2008
Astronomy 102, Spring 2008
17
Why does rapidly-variable brightness mean small size?
If a quasar's brightness varies a lot in a month, why does that mean that the power comes from a region no bigger than a light month?
A. If it were any bigger, the energy input that "throws the switch" would have to travel faster than light. B. Relativistic length contraction: it just looks smaller, to a distant observer. C. Gravitational time dilation: the slow arrival over a month of the brighter signal must mean the region near the horizon of a black hole is involved.
6 March 2008 Astronomy 102, Spring 2008 18
How are quasars powered?
Requirements: need to make 1012 L in a sphere with circumference 2.51012 km (0.26 ly) or smaller. Here are a few ways one can produce that large a luminosity in that small a space. 107 stars of maximum brightness, 105 L . Problem: such stars only live 106 years or so. We see so many quasars in the sky that they must represent a phenomenon longer lived than that. 1012 solar-type stars: each with L = 1 L , M = 1 M . Problems: stars would typically be only about 6x1012 cm apart, less than half the distance between Earth and Sun. They would collide frequently.
6 March 2008 Astronomy 102, Spring 2008 19
How are quasars powered (continued)?
they would weigh 1012 M . The Schwarzschild circumference for that mass is
F 6.67 10-8 cm3 I e1012 2 10 33 gmj 4 G J gm sec 2 K H 4GM CS = = 2 cm I 2 c F 3 1010 H sec K F light year I = 2.0 light years , 18 = 1.9 10 cm H 9.46 1017 cmK
larger than that of the space in which they're confined. Thus if you assembled that collection of stars in that small a space, you would have made a black hole, not a cluster of stars.
6 March 2008
Astronomy 102, Spring 2008
20
How are quasars powered? (continued)
Accretion of mass onto a black hole. Luminosity = energy/time. (1012 L = 3.81045 erg/sec) Energy = luminosity time. But Energy (radiated) = total energy efficiency = mc2 efficiency, so Mass = luminosity time / (efficiency c2) For a time of 1 year (3.16107 sec), and an efficiency of 10%, we get Mass = (3.81045 erg/sec)(3.16107 sec)/(0.1)(31010 cm/sec)2 = 1.31033 gm = 0.7 M . The black hole would have to swallow 0.7 M per year, a very small amount on a galactic scale. No problem.
6 March 2008 Astronomy 102, Spring 2008 21
Other evidence for black holes in quasars: apparent faster-than-light motion
The innermost parts of the radio jet in 3C 273 consists mainly of small "knots" with separation that changes with time, as shown in these radio images taken over the course of three years (Pearson et al. 1981, Nature 290, 366). The brightest (leftmost) one corresponds to the object at the center of the quasar. One tick mark on the map border corresponds to 20.2 light years at the distance of 3C 273. Thus the rightmost knot looks to have moved about 21 light years in only three years. It moves at seven times the speed of light? (?!!)
6 March 2008 Astronomy 102, Spring 2008 22
Positions of knot when two pictures were taken, one year apart.
Faster-than-light motion in quasar jets: an optical illusion (as we'll discuss three lectures hence)
Speed of knot (close to the speed of light)
B
Light paths:
Small angle: the A knot's motion is Not drawn to scale! mostly along the line of sight. Light path B is shorter than path A. If the knot's speed is close to the speed of light, B is almost a light-year shorter than A. This "head start" makes the light arrive sooner than expected, giving the appearance that the knot is moving faster than light. (Nothing actually needs to move that fast for the knot to appear to move that fast.)
6 March 2008 Astronomy 102, Spring 2008 23
Other evidence for black holes in quasars: apparent faster-than-light motion (continued)
Thus apparent speeds in excess of the speed of light can be obtained. The apparent speeds only turn out to be much in excess of the speed of light if the actual speed of the radioemitting knots is pretty close to the speed of light. Ejection speeds in astrophysics tend to be close to the escape speed of the object that did the ejecting. What has escape speeds near the speed of light? Neutron stars (but they can't produce the quasar's luminosity) Black holes - like the one that can produce the quasar's luminosity!
6 March 2008 Astronomy 102, Spring 2008 24