Stars VThe Bizarre Stellar Graveyard

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Attendance Quiz

Are you here today?

(a) yes

(b) no

(c) c! I told you not to stick your finger in that black hole!

Here!

Exam Grades

• Average for Midterm #2 = 68%• To help those of you who may have struggled on the midterms,

I have instituted the following exam grading policy: • The lower of your two midterms scores can be replaced by your final

exam, if your final score is higher than either midterm• Thus, if you get a final exam score higher than either midterm, the exam

portion of your grade (which is 60% of your total grade) will be 40% final exam, 20% higher midterm

• If you get a final exam score lower than both midterms, your exam grade will be 20% final exam, 20% each of the two midterms

• Remember, there is no curve in this class, so everyone wins with this policy!

Today’s Topics

• The Bizarre Stellar Graveyard• White dwarfs• Neutron stars

• Pulsars• Supernova/Neutron Star connection

• Black holes• General relativity• What is a black hole?• Bizarre things happen if you fall into a black hole!• Evidence for black holes

• Gamma ray bursts

The Bizarre Stellar Graveyard

• White dwarfs• Neutron stars• Black holes• General relativity

Not  a  photograph!

White Dwarfs and Electron Degeneracy Pressure• Low and intermediate mass stars (M < 8 M�) end their lives as white dwarfs,

small (R ~ Rearth), dense (> 1,000 kg/cc) balls of He, C, and/or O held up by electron degeneracy pressure

• This pressure results from a physics principle known as the Pauli Exclusion Principle, which states that no two particles with certain properties, known as fermions (e.g., electrons) can occupy the same quantum state simultaneously

• This same principle explains why electrons fill the orbital energy states in atoms the way they do, in turn explaining the chemical properties of the elements

White Dwarfs and Electron Degeneracy Pressure• In a very dense, hot electron gas, such as occurs in a white dwarf, the Pauli

Exclusion Principle, together with the Heisenberg Uncertainty Principle, means that as gravity tries to compress the electrons together, they respond by moving faster, independent of temperature, providing a pressure that counteracts gravity

• An analogy can be made to a number of people in a room who so much dislike sitting next to each other that they will get up and move if someone sits next to them

• If the number of seats is restricted, and the number of people increased (the equivalent of compression of the electrons), the people will start getting up and moving around the room faster

The Chandrasehkar Limit• As the mass of the white dwarf increases, the

pressure of gravity increases, the white dwarf shrinks, the electrons move faster, and the degeneracy pressure increases to compensate

• Thus, more massive white dwarfs are actually smaller than less massive white dwarfs

• As the mass of the WD approaches 1.4 M�, the electrons’ speeds approach the speed of light, and the nature of the pressure changes

• This fundamental limit on the speed of the electrons limits the pressure the electrons can provide, and eventually gravity wins

• If M > 1.4 M�, the degeneracy pressure cannot balance gravity and the core contracts further

• This limit was determined in 1930 by the Indian astrophysicist Subramanyan Chandrasekhar, and hence is named after him

Neutron Stars• If the core mass exceeds 1.4 M�, it will collapse

until neutron degeneracy pressure halts the contraction due to gravity

• When the pressure in the core becomes so high, the protons and electrons are squeezed together to form neutrons and a neutrino is also released

• These neutrinos carry away 100 times as much energy as the prodigious energy we see in a supernova and play a critical role in powering the supernova explosion

• Neutrons are also fermions, and follow the Pauli Exclusion Principle

• However, since they are so much more massive than electrons, they musts be much more compressed for degeneracy pressure to come into play

• Thus neutron stars are about 100,000,000 times more dense than white dwarfs, similar to the density of a neutron

• A mass >1.4 M� is crushed into a space the size of a city (10-20 km)

Crab  Nebula  -­ exploded  in  1054

Pulsars• How do we know neutron stars exist?• In 1967, a 24-y.o. graduate student

named Jocelyn Bell discovered surprisingly regular radio signals from space

• The period of this particular pulsar is 0.71451866398 seconds (very regular!)

• Nothing so regular had ever been found in astronomy, and one original thought was that these were signals from aliens (LGM)

• When pulsars were found at the center of two supernova remnants, this confirmed that they were natural phenomena

Crab Nebula• The Crab Nebula is the remnant of a

supernova that exploded in 1054• Seen by the Chinese, Japanese,

Persians, Native Americans?• At the center of the supernova

remnant is a star (see arrow) that had been studied for years

• Looking closer, it was found to be flickering ~30x/second

• This was the pulsar left over from the SN explosion

• It has a period ofP = 0.033326323455 sec

Pulsars

• The radio waves are coming from electrons spiraling around the magnetic field of the neutron star, which is spinning very fast

• The magnetic field funnels the radio waves into a beam, which makes the spinning neutron star like a lighthouse, where we “see” the radio waves as they sweep past the Earth

Kamiokande  detector,  JapanZinc  mine/1000-­m  underground16-­m  high  x  15.6-­m  diameter3000  tons  water/1000  PMTs

Pulsars, Neutron Stars, and Supernovae• Over 1500 pulsars have been found, with

more being discovered all the time• Here is the “sound” of the pulsar at the

center of the Vela supernova remnant, with a period of 0.09 sec, meaning it spins 11 times per second!

• A few pulsars spin close to a thousand times per second

• These so-called “millisecond pulsars” have periods of about 1 msec (1/1000th of a sec)

• This pulsar has a period of 0.001557 sec which means it spins 640 times/sec (~E)

• Why do they spin so fast?• Like the ice-skater (and molecular clouds),

they spin faster as they collapse (Demo)• Other evidence for the connection between

supernova, neutron stars, and pulsars came when 11 neutrinos were detected coming from nearby SN 1987A

Supernovae and Black Holes• Supernovae can also lead to black holes• If the core mass exceeds ~ 3 M�, then

neutron degeneracy pressure cannot resist gravity (the exact mass of a star with a 3 M� core is not known, but is estimated to be about 25 M�)

• In this case, gravity ultimately wins, and nothing can stop the collapse of the star until it reaches infinite density in a point

• This state is called a black hole, because the pull of gravity is so strong that even light cannot escape

• How is this possible?• When gravity becomes this strong,

Newton’s theory of gravity no longer works

Not  a  photograph!

General Relativity• Since light particles (photons) have no

mass, how can they feel gravity?• Just as Einstein overturned Newton’s

laws of mechanics with special relativity, he also overturned Newton’s Law of Gravity with general relativity

• Problems with Newton’s Law of Gravity1. Observational - the perihelion of Mercury

precesses in a way that Newton cannot fully explain

2. Theoretical - action at a distance, i.e., how does gravity work across space?

Equivalence Principle• Einstein’s solution - the equivalence principle: there is no way

to tell the difference between being in a gravitational field and accelerating in space, away from all masses

• Consider a ball thrown horizontally in each frame (whiteboard)• Now consider the same problem with a light beam• The equivalence principle suggests that light will bend near a

massive body

Curved Spacetime - What is it?• Newton’s version of gravity has a mysterious “force” acting across

space• In Einstein’s version, mass distorts spacetime itself - the larger the

mass, the greater the distortion• Since this distortion (shown here as the bending of a 2-D sheet into

the 3rd dimension) happens in the 4th spatial dimension, we can’t see it, but it is real - how do we know?

Curved Spacetime - What is it?• In “empty” space (no mass), objects travel in straight lines• When a mass is present (like the Sun), then nearby spacetime is distorted or

curved, so that other masses (like the earth or a comet) will follow a curved path (e.g., an orbit)

• Since space itself is bent, anything (including light) will follow a curved path if it passes near a massive object

• This was confirmed in 1919, during an eclipse; a star’s position was shown to have moved due to its light passing near the Sun

• Here is an actual photograph of a star taken during the 1919 eclipse - the red dot shows where the star “should” have been

Einstein’s  Cross

Other Evidence of Curved Spacetime• If light from a very distant object (e.g., a distant galaxy) passes a

relatively nearer and massive object (e.g., a galaxy cluster), then the light of the farther object can be bent so that multiple images will appear - (Interactive Figure 22.9)

• This is known as gravitational lensing

What is a Black Hole?• The curvature of spacetime doesn’t only depend on the mass of the object but

also on its density• As a star’s core collapses and becomes more dense, the space around it is bent

more and more• In a massive star, the core collapses utterly, until it bends spacetime so much

that nothing can escape, not even light• The place where nothing can escape is called the event horizon, since events

inside this point cannot be seen in the outside world• This is considered the edge of the black hole

Some Strange Effects• To an outside observer, time appears to

slow down as you approach a black hole• Thus, if you tried to send signals to

someone on Earth telling them about your journey into a black hole, the signals would come out slower and slower, and the signals you sent right at the edge would never get out

• Someone “watching” you would never actually see you “fall in”

• Instead you would appear to fall slower and slower but never quite make it in

• In addition, since the light would be shifted to longer and longer wavelengths, you would also fade away (in visible light)

Not  a  photograph!

Don’t Visit a Black Hole!• As you approach a black hole,

you will feel enormous tidal forces, because your feet will be accelerating much more than your head (if you go in feet first)

• For example, if your feet were 100 m from a 3 M� black hole, you would feel a force on your feet of 1.58 x 1018 N but a force on your head of 1.51 x 1018 N, for a whopping difference of 7 x 1016 N!

• That is more than enough to tear you apart!

Evidence for Black Holes• Although light cannot escape a black hole, matter falling into a black hole will be

accelerated and will emit large amounts of high-energy radiation (usually X-rays and gamma rays)

• Thus, a binary where one member is a black hole can be a strong X-ray source (such as Cygnus X-1)

• Also, there is evidence from the orbits of stars near the center of the Milky Way that there is a massive (many million M�) black hole right at the center

• There is evidence that most if not all galaxies have such black holes at their center

Evidence for Black Holes

Black  hole  here!

Gamma Ray Bursts• In the 1960s, the US military launched secret satellites to search for gamma

rays from Soviet nuclear bomb tests• The bursts they detected were, in fact, coming from space• These bursts have energies that last from 0.01 to 1000 seconds and have

rise times as short as 0.0001 sec, implying that the size scale on which their source is operating is very small

Gamma Ray Bursts• The source of these bursts was a mystery, in part because their distance was

unknown• One way to solve that problem would be to study their distribution

– If their distribution followed the ecliptic, then they were in our solar system– If their distribution followed the galactic plane, then they were in our galaxy– If their distribution was isotropic, then they were extragalactic

• However, early gamma ray telescopes did not have good angular resolution

Explorer  11  satellite

Gamma Ray Bursts• With the launching of the Compton Gamma Ray Observatory (CGRO) in 1991,

gamma-ray astronomy came into the modern era• The CGRO used 8 detectors to allow it to determine the direction of a gamma-ray

source of about 1 degree (compared to a few arcseconds for most optical telescopes)• The CGRO detected about 1 gamma-ray burst per day, on average• After a few years, it was clear that the distribution was isotropic

Gamma Ray Bursts

Gamma Ray Bursts• The isotropic distribution meant that GRBs were either coming from a small region

of the Milky Way near the Sun or they were extragalactic• The definite identification of GRBs with an extragalactic source came in 1997 from

another gamma-ray/X-ray satellite, BeppoSAX• After it detected the gamma-ray burst GRB 970228, its X-ray detectors localized

the source well enough for optical telescopes to identify the galaxy from which the burst had come

• The energies implied are enormous, comparable to Type II supernovae• However, the required energy might be less if these events are beamed, like pulsars

What are Gamma Ray Bursts?• Some GRBs, those that last more than 2 seconds, are known as “long-soft” GRBs,

and have been visually identified with known supernovae• These probably occur when the most massive stars collapse into black holes• Shorter GRBs, those that last less than 2 seconds, are known as “short-hard” GRBs,

must come from very small region of space• These events are believed to be caused by the merger of two neutron stars or a

neutron star and a black hole in a binary

Image  Credit:  SXS,  the  Simulating   eXtreme Spacetimes (SXS)  project  (http://www.black-­holes.org)

LIGO Hanford

33 33

Michelson Interferometer• Light splits and takes two

paths – by measuring the path difference, gravity waves can be detected

• Sensitivity depends chiefly on length of arms and laser power

• Arms are 4 kilometers(!) long, and the light bounces back and forth ~60 times, making the effective length almost 250 km

• Capable of detecting motions of 1/10,000th the diameter of a proton!

X

Y

Laser

Photodiode

Simulation of 2 Black Holes Colliding

Simulation:  Simulating  eXtreme  Spacetimes  (SXS)  Project

Gravitational waves detected!!!• Detected September 14, 2015• Detected at two sites 7 ms apart (indicating travel at speed of light)• Two black holes of 36 and 29 solar masses merged to form a 62 solar mass

black hole: 3 solar masses were radiated away as gravitational wave energy• Event took place 1.3 billion light years away (hence 1.3 billion years ago)