Astronomy Exam 5
One minute exam: In string theory, our Universe is pictured as a
2 brane NO 3 brane 10 brane YES 3D bulk
DOPPLER SHIFTS
A blueshift is any decrease in wavelength (increase in frequency) of electromagnetic waves; the opposite effect is referred to as redshift. Increase in wavelength. In visible light, this shifts the color from the red end of the spectrum to the blue end. So, if time is stretched there's a blueshift right?
9.7 Fundamental Properties of Black Holes
According to Einstein, the fundamental properties of black holes are electrical charge (usually taken to be zero), mass, and spin (angular momentum) All other properties, radius of event horizon, Hawking temperature, come from that They have no other properties like mountains, structure, chemical composition, DNA Not even the number of protons, electrons and neutrons that fell in → profound information loss Thought experiment: one neutron star, one antineutron star Neutron star + Antineutron star → gigantic explosion However, Black hole + black hole → one large black hole Black holes transcend ordinary physics of matter/antimatter
Proving black hole question: how do the hot inner accretion regions that make gamma rays prove it has no surface (and must be a black hole)? I thought they produced xrays?
Accretion disks: outer parts of accretion disks will be cooler because low friction; hot on inside because high friction gravity; provers there's black hole ns there Can't form gamma rays on insidesurface because it's not hot enough; surface radiation will cool xrays wont become gamma rays, surface radiation will spoil it
Age and Fate of the Universe
All distances between distant galaxies are proportional to the time elapsed; distance = velocity times time Distance divided by velocity from the Doppler redshift → age of the universe about 13.8 billion years Fate of the Universe is intimately tied to the shape (we thought) In principle, we can figure out the shape and fate of our Universe by doing 3d geometry in our 3d universe in practice we often try to measure the density of the matter In which of these universes are we living?
Proving Black Holes
Astronomers search for ways to directly determine that the dark object producing X-rays is a black hole, not a neutron star How would you identify a black hole of 1 solar mass? Evidence that in some circumstances black holes, but not enutron stars, can produce very hot, rarified inner accretion regions, making gamma-rays but few X-rays This is evidence that the object has no surface Black hole candidates in the directions of Sagittarius, Ursa Majoris, Perseus, Scorpius, Ophiuchus, Vulpecula, Monoceros, Lupus, Cygnus (2) (Find and observe the constellations for sky watch Cygnus X-1 AO620-00 = Nova Mon 1975 = V616 Monocerotis- one of the first and best studied with a small mass companion, black hole about 5 solar masses V404 Cygni- somewhat evolved companion, but one of the best cases for a black hole with "dark" mass of about 12 solar masses Two candidates in the Large Magellanic Cloud: LMC X-1, LMC X-3 Total number of such systems known, about 45
Goal: To understand the nature of time-like space inside a black hole
Basic Properties of a (non-rotating) black hole singularity, empty space, time-like space
String Theory
Best current candidate for a quantum gravity "theory of everything" String theory is a quantum theory, but it also intrinsically contains curved surfaces Particles like e-, p, n are not "points" but strings, otherwise identical loops of energy that vibrate in different modes The different modes of vibrations give all the well-known particles and more Strings of energy rather than points Guitar diagram: Can't make notes with grains of sand, but with strings, you have Mozart (see image)
Goal: To understand how Stephen Hawking added some quantum theory to Einstein's theory and revolutionized our understanding of black holes
Black Hole Evaporation: Hawking Radiation- Chapter 9.6 Nature of vacuum in Quantum Theory- cannot specify the energy of anything precisely, even "zero" in a vacuum: Vacuum "boils" with creation/annihilation of particles/antiparticles Easiest to make photon = antiphoton (no mass) But also e- e+, p+ p-, neutron antineutron, neutrino anti-neutrino → affects behavior of electrons in atoms- measured to high accuracy Quantum Fuzzy Event Horizon- at the event horizon, the position of the event horizon and of particles is quantum uncertain One particle in a pair can be swallowed, the other escapes- carries off mass, energy - pure quantum effect Black holes are not just one-way affairs, with quantum effects the will lose mass and energy- Stephen Hawking's dramatic discovery
Goal: To understand the conflict between Einstein's theory of gravity and the Quantum theory Information Loss?
Black holes have only three fundamental properties: mass, spin, and electrical charge (=0 in practice) Deep issue What happens to the information about all the stuff that fell into the black hole? Quantum theory insists there must be no loss of information Maybe the information is in the Hawking radiation or maybe it is still somehow in the singularity, or stored at the event horizon Can a singularity evaporate and disappear? Don't know in absence of a theory of Quantum Gravity
New insight: (Lisa Randall 1999)
Can have large extra dimensions and gravity will still leak only a little into those extra dimensions, still weaken very nearly as 1/r2. Had assumed extra dimension was "flat" - it needn't be Leakage into higher dimensions could account for why gravity seems "weaker" than other forces Our 3D Universe could be a 3D brane in a large, extended, 4D bulk OMG WHAAAAA There could be a real, large (infinite), four-dimensional hyperspace in which our 3D Universe is embedded Plus tightly wrapped up dimensions
Gamma-Ray Bursts (Chapter 11)
Cosmic explosions, flashes of gamma-rays lasting about 30 seconds, detected by satellites Energy is expelled in narrow jets; energy comparable to that of supernovae, but all in gamma-rays, with later afterglow in X-ray, radio and optical radiation Birth of a black hole or magnetar?
Dark Energy Anti-gravitates: cannot be any particle, "normal" (p, n, e) or Dark Matter, that gravitates
Dark Energy force field is not accounted for by any currently known physics A major challenge to fundamental physics! Dark energy responsible for the acceleration of the expansion of the universe
New insights into information:
Derivation of the temperature of a black hole from string theory got exactly Hawking's answer But string theory is a quantum theory and exactly preserves information The implication is that Hawking was wrong that information is destroyed in a black hole and that black holes have only mass, charge and spin The information must be retained in string vibrations at the event horizon (not within the black hole) Surfaces are true repository of information, not volumes. In a hologram, the information is stored as patterns on a 2D surface. With exposure to a laser, a 3D representation of the 2D information can be restored All this led to the idea that we live in a Holographic Universe
One especially fascinating application: The Global Positioning Satellite (GPS)
Device to measure the curvature of space and the different flow of time at various levels in a gravitational field GPS depends not only on an array of satellites in orbit, but must be programmed to understand Einstein's theory of warped space and time to function properly
Review: What is hyperspace?
Dimension higher than whatever you are talking about (must specify what you're talking about) → for us, hyperspace must be 4 dimensions or higher
Goal: To understand the conflict between Einstein's theory of gravity and the Quantum theory
Einstein's theory does not incorporate any of the tenets of the quantum theory Singularity- all the mass is in a zero volume point in Einstein's theory Violates the Uncertainty Principle of Quantum Theory: cannot specify the position of anything exactly Need theory of Quantum Gravity to rectify, to understand what the "singularity" really is. Deepest issue in modern physics.
The Nature of Dark Energy
Energy of vacuum- quantum fluctuations, particle/antiparticle (recall role in Hawking radiation) predict an acceleration that is too large by a factor of 10^120. It works on Earth, but not, somehow, in deep space. "Worst prediction ever in physics" -Steven Weinberg (UT Nobel Laureate) Related phase early in Big Bang, when the Universe was a fraction of a second old. A huge "inflation" by anti-gravitating vacuum force blows the Universe so big that it is essentially flat (like the surface of the Earth appears to us, only more so!) Anti-gravitating energy went away- has come back gently in the last 5 billion years. What is it??? "Space-time diagrams" illustrate how the Big Bang led to inflation, then deceleration, and now acceleration; at each time, the space would be flat (not shown in this type of diagram)
One minute exam: It is important to understand that gamma-ray bursts emit their energy in tightly collimated beams because otherwise:
Estimates of distance will be wrong Estimates of the mass of the black hole formed will be wrong Estimates of the energy emitted will be wrong Estimates of the type of supernova in which they explode will be wrong (I think it's this because it would have to be type Ic for jet to escape from the star (since it's missing the envelope; or all of them are true?)) Hypothesis is these subclass of supernova type Ic are making black holes or magnetars and emitting htese jets of gamma
Cross-sectional view of rotating Kerr Black Hole:
Event horizons: one way membranes (first goes inward, second goes out) INWARD of OUTWARD time-like space Ergosphere: space inbetween surface of infinite redshift and outer event horizons Highly curved, rotating normal space Tap rotational energy Highly curved normal space within inner event horizon outside of singularity Ring singularity Another space through the ring (see graphic)
Chapter 12- Supernovae and the Universe
Expanding Universe- we observe all distant galaxies (so far away we cannot sense their individual gravity) moving away from us with speed proportional to distance: as if we were in the center of an explosion Our Universe is not a bomb in pre-existing empty 3-D space! Lesson from Einstein - space itself can expand carrying the (almost motionless) galaxies All distant galaxies move away from all other distant galaxies No galaxy, certainly not us, is in the center The result: speed proportional to distance
Our Expanding Universe (balloon example)
Expanding surface of a balloon as an example Expansion takes every point on the surface further from adjacent points 2D embedding diagram of a 3D expanding Universe No 2D center, no 2D edge, no 2D outside to the 2D surface There is a 3D center, a 3D edge, a 3D outside, a 3D hyperspace Property of sphere: if you fire something off in one direction it will circle around the ball and come back to the original point (parallel propogation); could be property of 3d curved space too No 2d center, 3d center inside ballon, outside in hyperspace, no 2d edge (no corners) but 3d edge kinda Same as our 3d universe, no center as there's no center to the 3d surface of ball, no edges either, no outside, 2d surface is all there is (there's outside in 3d but not 2d); what's outside my universe? We dont know but if there IS one it has to be in 4d or higher All 3D space expands- carrying essentially motionless matter (galaxies) No 3D center, no 3D edge, no 3D outside As 3D astronomers, we don't have to ask what the Universe is expanding into, but if anything it is a 4 (or more) D hyperspace, just as a 2D balloon expands into 3D hyperspace Infinite flat rubber sheet could expand without expanding into any hyperspace (2D embedding diagram example of how expansion does not necessarily mean intrusion into hyperspace)
Brain World Cosmologies:
Exploring the theoretical possibility that our Universe is a 3D brane floating in a 4D bulk, with 6 wrapped-up dimensions, plus time Example: Ekypyrotic Theory (Greek, ekypyrosis = conflagration = extensive fire that destroys lots of land) Two 3D branes collide in 4D bulk hot , dense "Big Bang" but not infinite density No singularity Different gravitational waves than standard "inflation" theory- could be a test Singularity in black holes, quantum foam nested "loops" of strings? The 4D Bulk: is this where our Universe curves to when it curves, expands to when it expands, maybe... Is the Dark energy that drives the acceleration of the universe some manifestation of a "nearby" 3D Universe only a little distance away from our Universe in the 4D bulk
how they're rolled up
Figure 12.3: makes sense; 3d paper looks sd (thin); roll it up, looks like line (1d); roll tightly, looks like point (0d); so possibly higher dimensions but we can't percieve them
Simplest choices:
Finite age, re-collapsed (closed, "sphere", high density, high gravity) expand forever, v>0 (open, "Pringle", low density, low gravity) Special Case: expand forever v→ 0 as reach infinity (flat, very special density and gravity)
Cygnus X-1
First X-ray source discovered in the direction of the constellation Cygnus. Discovered in 1970's by Uhuru Satellite (Swahili for Freedom) First and still most famous stellar-mass binary black hole candidate Can't see this system with the naked eye, but can find constellation Cygnus- look for it for sky watch! see image Binary system: 30 solar mass blue supergiant (mass losing star) next to 10 solar mass star Optically Dark X-ray emitting companion (less than or equal to) 10 solar masses, >> neutron star max mass → black hole (binary system is two stars, here one star and one black hole) Could nature be tricking us? All we really know is that there is a 20solar mass "thing" emitting X-rays One possibility: 9 solar mass normal star "lost in glare" of 30 solar mass supergiant like flashlight next to searchlight. Took hard work, but by now that possibility is ruled out. (i.e. bottom picture with 1M NS and a 9M normal star is ruled out) Expect only 2 or three systems like Cygnus X-1 in our Galaxy Bright, massive, short-lied companion Maybe only one, and we found it!
Circumstantial evidence was followed by proof:
GRB 030329 was nearby, only 3 BILLION light years away! Relatively bright, an ideal target SN2003dh was discovered a week later! Spectrum of a Type Ic supernova By now many associated supernovae have been found: all are Type Ic supernovae But all Type Ic supernovae are not gamma-ray bursts
Goal: To understand what the "Dark Ages" of the Universe were, why they came to an end, and what gamma-ray bursts have to do with that.
Gamma-ray bursts are intensely bright lights Can be seen at great distance Probe cosmology, the early Universe The past is all around us, in every direction, out in space, back in time James Webb Space Telescope, 2018, first stars Gamma-ray bursts could be among the first objects seen at the end of the Dark Ages as the first stars are born and die, over 13 billion years ago.
The Current picture:
Gamma-ray bursts are result from the collapse of a massive star from which the hydrogen and most of the helium have been stripped, probably to produce a black hole (but maybe a magnetar), that emits a tightly focused, highly relativistic jet. Perhaps only in Type Ic, missing envelope, so that jet can escape from the star Every burst, twice a day somewhere in the Universe - the birth of a black hole aiming its jet at us? ~ 100 aimed elsewhere for every one aimed at us Have not yet proven that black holes are involved. Tough problem!
billards example
In this picture, ordinary forces, electromagnetism, nuclear forces correspond to "open" strings that have ends stuck on the 3D brane (stuck at each end of vector on plane?) These strings cannot "go" into the 4D bulk, we cannot "see" the 4D bulk Gravity is based on "gravitons", closed loops of strings that are not stuck on the brane. They can float off into the bulk, but in a way that gravity still weakens very nearly like a/r2
Surprising discovery:
It was long thought that supermassive black holes were somewhat incidental to galaxies Formed of matter that somehow drained into the center of the galaxy, so galaxy could have large mass or small mass black hole depending on circumstances Even stars so far from the center that they cannot possibly feel the gravity of the black hole now are moving in such a way that the larger the mass black hole, the higher the speed of the stars!
Are different universes in Schwarzschild and Kerr solutions to non-rotating and rotating black holes real? In Real Universe:
Light (at least!) falls into the black hole Photons are Doppler blue shifted, accelerated to higher energy → the energy/mass warps the space and changes the mathematical, hence the physical solution Theory of relativety aspect gravity well warps space and slows down time ; light going out of the gravity well is red shifted (surface of infinite red shift is from light going out not in); if you're bserving light from within the black hole is blue shifted (light entering black hole is blue shifted, can't see it; words described in context of observer far away looking at it) So probably not in this case, but stay tuned
Extend the argument to higher dimensions than 3.
Light and electricity might be stuck in 3D, but gravity probes all space, whether its dimension. Gravity is a creature of space and time. An "area" is one dimension less than the total volume corresponding to a given dimension of space. If gravity extends to a fourth dimension, where "volumes" scale like r^4 and "surfaces" scale like r^3, then gravity would be diluted in 4D by 1/"area"; a/r3 in 4D Obviously wrong! Even Newton knew that gravity weakens as the inverse of distance squared, not as distance cubed! Implication (it was long thought): IF there is a fourth (or higher) dimension it must be "wrapped up" so gravity has nowhere to go
One minute exam: How can we discover a stellar mass black hole that has no accretion disk around it?
Look for x-rays (no, need accretion disk) Look for gamma-rays (no, need accretion disk) Look for jets (YES?) Look for gravitational lensing (think we need accretion disk for that); We can;t or gravitational lensing CORRECT; bends light from other things from gravity; we dont see why but we see brighter star from light curving around star focusing the light
The story so far: (just second day, early)
Look up at the sky and wonder about the stars Betelgeuse is a red supergiant about to collapse Collapse can lead to supernova explosions and the production of neutron stars, but also of black holes. Black holes are predicted by Einstein to have a singularity, infinite density, infinite tidal forces, the end of space and time We need a new all-embracing Quantum Gravity to know what the "singularity" really is
Rotating Kerr Black Hole:
Mass and spin, but no electrical charge Assume all mass is in the singularity, no mass anywhere else (assumption necessary to solve equations) Find singularity is a ring (not a point) 0 thickness, infinity density, still infinite tidal forces Infinite universes! (implicitly spread through hyperspace)
Interstellar
McConaughey in the Tesseract (a 4D "cube") inside the supermassive black hole, Gargantua, ranging in time as well as 3D/4D perspectives. He taps out the "solution to quantum gravity". All this was based on these string theory, 4D hyperspace bulk, ideas
Galaxies "know" how big a black hole to make
Mechanism uncertain: Does the galaxy control the black hole or the black hole somehow control the galaxy? Most popular current idea: energy from the accretion of matter into disk around black hole feeds back to the surrounding galaxy, blowing excess galaxy gas away when galaxies are young and growing
Supermassive black holes
Million to a billion solar masses In the middle of our galaxy and in the middle of many, many others
Dark Matter
Most gravitating matter in the Universe is mysterious Dark Matter Not composed of p, n, e- the stuff of stars, galaxies, planets, and people Dark matter was never composed of that stuff (or would upset observed mix of hydrogen and helium from the Big Bang), so also not black holes once made from ordinary star stuff Some yet undiscovered particles that only interact by gravity and by the weak nuclear force, no electrical force, no strong nuclear force: 5 x more total density and mass than "normal" stuff stars, gas, etc. Computer simulations show that from the tiniest wrinkles of quantum uncertainty in the Big Bang, the Dark Matter agglomerates to form all the Large Scale Structure, galaxies, clusters of galaxies in the Universe Ordinary matter, protons, electrons, settles to center of Dark Matter lumps to form galaxies and clusters of galaxies. Our familiar Universe of stars and galaxies would not exist without the Dark Matter. Density of Dark Matter is not enough to close the Universe. → Universe is "open"? (3D Pringle) No p, e, n; dark matter builds up and become gravitational wells, p, e, n fall into these wells and accumulate to form stars (v important)
Is this real, or just mathematical fantasy?
Must be able to test: Physicists are straining to devise such tests. Does gravity behave a little differently than 1/r2, for instance like 1/r^2.001, that would be hint of higher dimensions? Curved space near event horizons of black holes might be different than standard Einstein gravity- can that be measured with X-rays, or, now, with gravitational waves? Interactions in particle accelerators could be different if some energy disappears into the 4D bulk (as closed string gravitons). The Large Hadron Collider (LHC) at CERN, near Geneva, is operating. Strong expectation that evidence for new physics, confirming or denying string theory ideas, will be seen. Not yet, the physics community is holding its collective breath... The Large Hadron Collider (LHC) at CERN in Switzerland may see the first hints of extra dimensions
Gamma-Ray Bursts unite stars and cosmology
Mystery since late 60's - satellites to monitor space nuclear test ban treaty, avoid confusion between astronomical effects, and bombs Flare of gamma rays lasts ~ 30 seconds Never repeat - for 30 years, no optical counterpart, Can't focus gamma-rays. Do not know which of millions of stars to look at. Did not know the distance: guesses ranged from within the Solar system to cosmologically distant
inverse squre relates to dimensions
Old argument: there could not be a large fourth spatial dimension Behavior of light, electrical force and gravity in 3D The luminosity or lines of force flow out through larger area at larger distance. The strength (brightness or lines of force per unit area) is thus diluted by 1/area → 1/r2 in 3D Area is one dimension less than volume The "2" in the inverse square law is exactly "1" less than the total number of large dimensions, "3"
One minute exam: The best candidate for a binary star system with a black hole is:
One with a 30 solar mass ordinary star companion NO possibly only Cygnus X-1 One with a ½ solar mass ordinary star companion YES, because there are 45ish already mostly proved; and since the star companions are so small, we know they're not hiding another star One with two black holes in orbit Cygnus X-1
Circumstantial arguments for presence of black hole in a binary system:
Only neutron stars and black holes have the high gravity necessary for intense X-rays Use Kepler's laws to measure the total mass of the system, astronomy to determine the mass of the mass-losing star, subtract to get mass of "unseen" companion emitting X-rays Maximum mass of neutron star is ~2 solar masses Intense X-ray source in binary star system with mass exceeding 2 solar masses is, by a process of elimination, a candidate black hole There are about 20 binary star black hole candidates in our Galaxy and in the Large Magellanic Cloud (near enough to detect the X-rays) that have masses measured to be greater than 3 solar masses, and hence too massive to be a neutron star There are another 25 binary star black hole candidates with similar X-ray properties, but no measured mass
Hawking Radiation
Particles surrouding event horizon some are eaten up by black hole some are spit out Loss of energy is not arbitrary, it may come out in a very precise form... According to Hawking, Black holes radiate Hawking radiation as if they had a precise temperature that depends (inversely) on the mass Black holes are not totally black Given enough time, black holes with evaporate! If the black hole as the mass of a star, the time to evaporate will be much longer than the age of the Universe, so unimportant in practical terms If the black hole has the mass of a mountain or asteroid, it can evaporate in the age of the Universe (13.8 billion years) As mass decreases, T increases With energy loss → less mass → hotter → more radiation. Runaway process. Small mass black holes can disappear within the age of the Universe, ending in a final explosion of gamma-ray radiation. Theories that mini-black holes might be created in the Big Bang (but no hint in any observation) Don't quite understand Hawking radiation/temperature: Hawking's basic theory is it's emitted as heat higher mass coorelates with lower temerpature (and vice versa); hawkings theory trying to tie together einstein's singlularity with quantum mechanics generally
Einstein's theory predicts singularities at the beginning of the Big Bang and in the centers of black holes where matter is crushed to a point with infinite density, time and space come to a halt. Quantum theory says the position of nothing, not even a singularity, can be specified exactly (the Uncertainty Principle applied to singularities)
Quantum theory is designed to work in flat, or gently curving space. It does not make sense when the curvature of space is tighter than the "wavelength", the uncertainty in position, of a particle. Each great theory of 20th century physics contradicts the other! We need an embracing theory of quantum gravity that will reduce to ordinary gravity and ordinary quantum theory where they work well (away from singularities and with non-severe curvature- same thing!), but will also tell us what a "singularity" really is Can use current theories to "predict" the conditions for which the theoretical collision occurs, where the theory of quantum gravity is most crucially needed, effectively the scale of length where quantum uncertainty and space-time curvature are equal. Planck length: about 10e-33 cm, vastly smaller than any particle, but still not zero Planck density: about 10e93 g/cm3, huge, but not infinite Planck time: about 10e-43 s, short, but not zero! Cannot predict earlier times in the Big Bang On the Planck scale, not just that the position of things would be uncertain in space, but that space and time themselves could be quantum uncertain, "up" "down" "before" "after" difficult if not impossible to define Spacetime becomes a "quantum foam" (a poetic concept without a mathematical/physical framework)
Supermassive Black Holes
Quasars: active galactic nuclei; extremely bright mass of energy and light Long suspected in quasars: huge power from small volume, billion solar mass black hole could do it More recently, proof that many ordinary galaxies also have a supermassive black hole in their centers (dead quasar) Again, do not yet see a "dark spot" but use kepler's Laws, motion of many stars, gas orbital period separation 3.7 million solar mass black hole in our galaxy (UCLA link) Center of Milky Way Galaxy in direction of constellation Sagittarius- (find Sagittarius for sky watch) Up to 10 billion solar mass black holes in quasars (may be 17 billion) Jet from billion solar mass black hole in center of M87, large elliptical galaxy in the Virgo cluster (find Virgo!)
Chapter 10: Finding Black Holes for Real
Reading: 10.1-.4, 10.9 We know that massive stars evolve to form iron cores that absorb energy and collapse. A compact object must be left behind. Some explode and leave rotating, magnetic pulsars Some explode and leave highly magnetic magnetars Some explode and leave black holes or completely collapse to leave black holes We don't know which massive stars do which! Tendency to think that more massive stars are more prone to making black holes, but the rotation of the star, the presence of a binary companion, and other factors may influence the outcome We do know that black holes exist, so some stars make them.
Non-rotating Schwarzschild Black Hole:
Same diagram as above: event horizon is also surface of infinite red-shift Mass, rotate or not rotate, electrically charged or uncharged (three properties of black holes) Mass, but no spin, no electrical charge (theoretical black hole, doesn't exist in practice) - Assume all mass is in singularity, no mass anywhere else (assumption needed to solve equations) Find two Universes, each of infinite space, connected at one instant by the singularity Cannot pass from one to the other if travel at less than at speed of light Embedding diagram:
Stellar mass black holes:
Several to ~10 solar masses In binary systems in our Galaxy or nearby galaxies
To be mathematically self-consistent:
Space in which strings vibrate has 10 space dimensions + time First notions: 3 big space dimensions + time Other 7 spatial dimensions "wrapped up" on "string length scale", not known precisely, somewhat larger than the Planck scale, but very tiny so we cannot easily "see"
Mathematics of string theory is complex: Only approximation solutions so far, but:
String theory "contains" Einstein's Theory mathematically on large enough spatial scales that strings "loops" are tiny, just as Einstein's theory "contains" Newton's mathematical theory of gravity on length scales where gravity is weak. Can solve string theory near the event horizon (much larger than string scale) to determine the temperature of a black hole, get exactly Hawking's answer- deep connection between string theory and black holes Cannot yet solve for "singularity", but prospect to do so. Singularity would not be zero size and infinite density, but some behavior on the string length scale, not quantum foam but some "stringy" nature Information fallen into black holes could be retained in string vibrations (or radiated away in "stringy" Hawking radiation)
Small mass companions
Surprisingly, most binary black hole candidates have small mass main sequence companions, typically ~½ solar mass Observe ~45 such systems and guess there may be ~1000 in the Galaxy For systems with small mass companions cannot hide a 3rd star in the system → excellent black hole candidates Evidence still circumstantial but virtual proof of black hole Not sure how these binary systems form Would have expected massive stars that can make black holes in core collapse to have massive companions, like Cygnus X-1 Need to have black hole very close to small mass companion, current separation smaller than size of the star that made the black hole Possibilities: Black hole progenitor swallows small mass companion while a red giant? Companion forms from left-overs of collapse that formed the black hole?
Embedding diagram?
Taking a given space and reducing it down a dimension to step outside and look at it (stand out in hyperspace and look at it)
Einstein's theory says that for a Universe that is the same, on average, everywhere, there are only three basic shapes it can have
The 3D analog of a spherical surface- CLOSED UNIVERSE The 3D analog of a "saddle" or "Pringle shape"- OPEN UNIVERSE- no parallel propagation The 3D analog of a flat plane- FLAT UNIVERSE; parallel propagation The 2d embedding diagrams of these 3d universes are, respectively, a sphere, an infinite saddle or pringle, and an infinitely flat plane (image is helpful from slide) A closed universe is finite in space and time, the other two are infinite in space and time, but all must have started 13.8 billion years ago in the Big Bang ONLY one of these is true, these are three possibilities Figure 11.2: A patch of the space in a universe expands, drawing all galaxies away from all others, independent of the overall shape of the curvature of the universe:
One Minute Exam: Einstein says that more distant galaxies move away from us more rapidly b/c
The Earth is the center of the universe (buuuuull) The universe blew up in the Big Bang like a bomb blowing up in three-dimensional space (no, that implies that there is a special place in the universe that's special, and that's just not true) Our 3D universe expands into 4D hyperspace (maybe, but nothing to do with Einstein) Space expands, carrying all galaxies far away from each other (intrinsic property of space) (CORRECT)
Now a whole new way! The LIGOrevolution
The LIGOrevolution Laser Interferometer Gravitational-Wave Observatory) Gravitational waves from two inspiralling, merging black holes a billion light year's away One in Livingston, LA and one in Hanford, WA Effect of gravitational waves on a ring of particles: ^Get closer and closer, like basketballs on a trampoline, cause ripples in space → distortion of space Merging and ringdown of two black holes and their gravitational lens distortion of the star field behind them: Inspiral and merging of two black holes and the corresponding behavior in an embedding diagram to show how the surrounding space itself is warped. Sound track of "chirp" is across the bottom:
One Minute Exam 3: Dark Energy is responsible for:
The acceleration of the Universe YES The dark space between stars and galaxies The clumping of matter to form stars and galaxies The Dark Ages after the initial Big Bang
One Minute Exam 2: Dark Matter is responsible for:
The acceleration of the Universe: No The dark space between stars and galaxies: The clumping of matter to form stars and galaxies YES The Dark Ages after the initial Big Bang
The Multiverse:
The idea that there could be many 3D universes separated in 4D hyperspace
Correlation between black hole mass and galaxy bulge mass:
The implication is that the mass of the galaxy (at least the inner portions, the budge) is always close to 800 times the mass of the black hole This means that the formation of the black hole is somehow intimately connected with the formation and structure of the whole galaxy
Bubble Universes:
The individual universes created from the parameters of the String Landscape that populate the Multiverse One idea: when a black hole forms a "singularity" in one universe, a new universe is born "elsewhere" in hyperspace
Holographic Universe:
The notion that the real information content is imprinted in quantum bits on the surface, the event horizon, of the observable universe What we regard as the physics (and chemistry and biology) in our 3 dimensions, is fundamentally set and controlled by information and physics on the 2D surface around us (the Big Bang is in every direction) Closely related to the understanding that the information of what fell into a black hole is retained in string vibrations at the event horizon surface of a black hole We are just 3D hologram projections from the 2D surface around us.
Chapter 14: Quantum Gravity- The final Frontier
The remainder of the class will be spent exploring various aspects of the most fundamental issue of modern physics: reconciling Einstein's thoery of gravity as curved space with the quantum theory of how things behave at a fundamental microscopic level The problem: each of these great theories of 20th century physics contradict one another at a fundamental level
Add up all the normal matter (not much, about 4% of the amount it would take to close the universe, just the lowest amount to be flat and not open), Dark Matter (about 23%) and the mass equivalent of the Dark Energy (E=mc2, about 73%) and find that the Universe has just the very special density to be flat
The universe is flat (in 3D) on average Still have individual stars, neutron stars, black holes, galaxies, that curve the space around them causing the small scale, local effects of gravity Just as a table top is composed of atoms and molecules on small scales, but is flat for all practical purposes when we sit down to eat The best current guess is that or real 3D uNiverse is essentially 3D flat - but accelerating!
One minute exam 2: What is the relation between the mass of a supermassive black hole and the galaxy in which it resides?
There is none, the black hole can be big or small, depending on how it grew and for how long NO The larger the mass of the galactic buldge, the smaller the mass of the black hole NO The larger the mass of the galactic bulge, the larger the mass of the black hole YES The larger the mass of the whole galaxy, the larger the mass of the black hole
Black Holes for Real
There may be 1-100 million black holes in the Galaxy made by collapsing stars over the history of the Galaxy That means that the nearest black hole may be only a few tens of light years away. How do we find them? Black holes made from stars are really black! (Negligible Hawking radiation) Those alone in space are not impossible to find, but very tough. They will gravitationally lens stars behind them. Event horizon of 10 solar mass black hole has a radius of 30 km ~ 20 miles, somewhat bigger than the size of Austin, easily fit between Georgetown and San Marcos Very black None yet identified Look for binary systems, where mass accretion occurs Will not see the black hole, do not yet have the technology to "see"a black spot, but that is getting closer with the Event Horizon array of radio telescopes Can detect the halo of X-rays from orbiting matter, the accretion disk, near the event horizon that will reveal the presence and nature of the black hole Look in accreting binary systems
The equations of string theory predict not only 1D strings, but "surfaces"
These "surfaces" can be of any dimension less than the total of the space containing them, 10 These surfaces can also wiggle and vibrate In analogy to membranes, they are called branes of dimension p, or p-brains. A point is a zero-brane, a line a one-brane, ect. The hyperspace "Volume" in which a brane is immersed is known as the bulk Some strings are loops with their ends attached to branes Branes are their own thing only dimensions within strings of string theory, then our dimensions are separate so that makes sense Other strings are closed loops that can float off away from the brane, into the bulk This led to a revolution in our perspective on the Universe
Two images
Two images: different vibrations lead to different shapes with same fundamental loop of strings (two overalls verses sun like image); just example, many different ways to vibrate
One Minute Exam: The type of supernova used to discover the acceleration of the Universe was:
Type Ia (yes) Type Ib Type Ic Type II
Goal: To understand how Type Ia supernovae taught us a new lesson about the universe and what that lesson was
Type Ia have consistent brightness, like a bright flashlight to measure age of universe, measure brightness allows you to measure distance; → can measure acceleration (use distance with redshift, shows it's accelerating) We thought we were trying to determine the density of the Universe to determine how strongly it was decelerated by gravity and hence whether it were open, closed, or flat. Nature threw us a curveball SN were the key! Use Type I1 supernovae (brightest ~ uniform behavior) Carefully map distances (dimmer appearance means further away), velocities (Doppler red shifts) in all directions More subtle techniques than making parallel lines or drawing triangles, but still amounts to "doing 3D geometry" Type 1A supernovae are generally the brightest and can be seen at cosmological distances They were used as cosmological probes... (see image) to discover the acceleration of the Universe... (see image) Ie: used supernovae to prove universe is accelerating not decelerating The supernovae were found to be a little too dim at given expansion velocity (red shift) → further away than expected for a "normal" gravitating Universe How do you get further away at a given current velocity? → Universe has been accelerating!! (and it is somewhat older than a coasting Universe would have been) Ball throwing analogy: throw ball up, gravity brings ball back down, that's what they were looking for, that deceleration, that would suggest a closed universe. But they instead found signs of acceleration
The problems get ever deeper
With quantum entanglement, you can't clearly differentiate the observer who watches the volunteer turn black at the event horizon and the volunteer who rapidly plunges in and dies. With Hawking radiation the volunteer may hit a blazing "firewall" and die that way Large masses have low temperatures, so negligible hawking radiation; so feeble we can't measure it Hawking recently suggested that maybe event horizons are not permanent Total confusion in physics as to the correct way to think about all this Thinking about black holes remains on the intellectual frontiers A proper theory of quantum gravity may reconcile these issues Book by Leonard Susskind - Black Hole Wars: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics, will discuss later. You may be a hologram...
Quasars
active galactic nuclei; extremely bright mass of energy and light
Dark Ages:
after the universe cooled off a million years after the Big Bang, before the stars and galaxies first formed half a billion years later
Event Horizon Telescope
array of radio telescopes plans to examine the massive black hole in the center of the Milky Way Image: Perez and Wagoner, Stanford: computer simulation of radiation from inner black hole accretion disk
Goal: To understand what a gamma-ray burst "afterglow" is and why it's so important Revolution in 1997
first detection of "afterglow" - optical, radio, X-ray, fading light Position localized- could bring full armament of modern astronomy to bear on the fading radiation → found bursts were in distant galaxies- all at huge, cosmological distances, billions of light years away → very bright to shine that far If gamma-ray bursts shine equally in all directions, the energy released in gamma rays would be 1000-10,000X SN (supernova) or 10-100 X core collapse neutrinos Comparable to total annihilation of entire star into pure energy (**** ton of energy) Goal: To understand the energy in gamma-ray bursts and why it is important that the energy is "beamed" BUT light bulb versus laser pointer or flashlight (example in class?) Bursts do not radiate in all directions! They are strongly focused into jets! Bursts are focused into only about 1/100 of the total area of the sky Typical gamma-ray burst energy ~ ⅓ supernova kinetic energy But send matter at 99.997% of the speed of light Supernova energy into a mass equivalent to Jupiter, not mass of the Sun, as for supernovae They explode ~100 times more often than observed (could observe about 2 per day if looked in all directions, all the time) because most have the jet aimed away from us Find all gamma-ray bursts in regions of massive young stars (spiral arms of spiral galaxies, irregular star-forming galaxies like the LMC) Something to do with death of massive stars Explode once every 10e4-e5 years in a given galaxy versus about once per 10e2 years for ordinary supernovae, so relatively rare Most popular guess is that gamma-ray bursts represent the birth of a black hole in the collapse of a massive star. Alternative suggestion- might be a highly magnetized neutron star or magnetar (Chapter 8) Early circumstantial evidence for several bursts associated with supernovae: Are gamma-ray bursts produced in some form of core-collapse supernova?
Concept Check: What is the "inverse r-squared law?"
gravity, electromagnetic force, light (intensity of light) drops of at rate of inverse of distance squared
Figure: embedding diagram kind of thing;
schematic illustrations of how tiny "wrapped up" extra dimensions could be associated with our 3D space- something like an embedding diagram of the higher dimensional space, so our 3D space is reduced to 2D and the higher dimensional wrapped spaces are reduced to 3D: At each point in the 2D space (not just at the intersections of grid lines), there is little 1D loop of one wrapped up extra dimension: At each point in the 2D space (not just at the intersections of grid lines), there is a little 2D "sphere" of two wrapped-up extra dimensions: Representation of a Calabi-Yau space, with 6 wrapped-up extra dimensions. Calibi-Yau space gives string vibrations the properties of known particles.: At each point in the 2D space (not just at the intersections of grid lines), there is a little 6D Calibi-Yau space of six-wrapped up extra dimensions:
Hubble deep field- every speck a galaxy
what's goin on Pointed at black area (can't see anything) Dim specks are almost from when the galaxy was formed (really far back in time)
Intermediate mass black holes:
~1000-10,000 solar masses In binary systems or stellar clusters in our Galaxy or nearby galaxies
Other arguments, especially careful to study of the small irregularities of the temperature of the cosmic background radiation left over from the Big Bang, confirm the evidence from supernovae
→ Accelerating Universe - confirmed by all tests applied so far. → Universe is filled with an even more mysterious Dark Energy The dark energy seems to be some sort of force field (like a magnetic field only different), that permeates the vacuum, empty space, and that pushes, anti-gravitates! (like two magnetic same poles, don't like each other) As space expands there is just more vacuum filled with this force field, so the effect is not diluted by the expansion
