White Dwarfs Our goals for learning What is a white dwarf? What can happen to a white dwarf in a close binary system?
White Dwarfs are the remaining cores of dead stars like the Sun. The outer layers of the original star have been blown into a planetary nebula during the red giant phase. The carbon core (for a 1 M Sun star) is very dense. Electron degeneracy pressure balances gravity. The brightest star in the sky – Sirius – is actually a binary containing a normal star and a white dwarf. In X-ray light, the white dwarf is the brighter object! White Dwarf - Sirius B
With no internal nuclear energy source, White Dwarfs (WD) cool off, and grow dimmer with time until they become black. For a 1M Sun star the core ends up as carbon, leading to a carbon WD; for a lower mass star the core never fuses He to C and so the WD is made of helium.
WD density = 333,000 x 5.5g/cc = 1.8 tons/cc A sugar cube of WD material would weight 1.8 tons on Earth! How is this possible? M Sun = 333,000 M Earth A white dwarf is about the same size as Earth!
White dwarfs shrink when you add mass to them because their gravity gets stronger! How is this possible?
Shrinkage of White Dwarfs Quantum Mechanics says that electrons in the same place cannot be in the same “state” Adding mass to a white dwarf increases its gravity, forcing electrons into a smaller space In order to avoid being in the same state some of the electrons need to move faster Is there a limit to how much you can shrink a white dwarf ? Yes!
Einstein’s theory of relativity says that nothing can move faster than light – so that must be the limit. When electron speeds in a White Dwarf approach the speed of light, electron degeneracy pressure can no longer support the weight. Chandrasekhar found (at age 20!) that this happens when a white dwarf’s mass reaches 1.4 M Sun This is called Chandrasekhar Limit. The progenitor of a white dwarf is a star with mass < 2M Sun, so the “core” is usually <1M Sun. However, suppose there is a way to gain mass … S. Chandrasekhar Nobel Laureate; Chandra X-ray telescope named after him. The White Dwarf Mass Limit
In a binary star system, with one star more massive than the other, the more massive star is the first to become a red giant, eject its outer layers and end up as a white dwarf. Eventually, the second star (of lower initial mass) also swells up to become a red giant. What happens next? If the stars are close enough, the second star swells up to fill is ROCHE LOBE, an imaginary tear-drop shaped shell of equal gravity, and dumps matter onto the WD.
Friction in the disk makes it very hot, causing it to glow. Friction removes angular momentum from inner regions of disk, allowing matter to sink onto white dwarf. And … View from above ACCRETION DISK Hot spot in accretion disk WD
Hot hydrogen gas from the companion star accretes onto the White Dwarf, building up in a shell on its surface. Remember that the gravity of the white dwarf is huge. When the base of the shell gets hot enough, hydrogen fusion suddenly begins, leading to an explosive brightening of the White Dwarf called a NOVA.
NOVA The nova star system temporarily appears much brighter This phenomenon is regularly observed The explosion drives the accreted matter out into space The white dwarf settles down again and the build-up process starts over
Thought Question What happens to a white dwarf when it accretes enough matter to reach the 1.4 M Sun limit? A. It explodes B. It collapses into a neutron star C. It gradually begins fusing carbon in its core
Thought Question What happens to a White Dwarf in a binary system when it happens to accrete enough matter to reach the 1.4 M Sun Chandrasekhar limit? A. It explodes B. It collapses into a neutron star C. It gradually begins fusing carbon in its core This time the explosion is enormous, much more than the “nova”, we get a “supernova” explosion.
So … there are actually TWO types of Supernova! Massive star supernova: Iron core of massive (~10 M Sun ) exceeds White Dwarf mass limit and collapses into a neutron star, causing a huge explosion of outer layers of the star. White dwarf supernova: Carbon fusion suddenly begins throughout the compact White Dwarf in a binary system when accretion takes its mass above the 1.4 M Sun Chandrasekhar limit. The result is an explosion called a White Dwarf Supernova. There is no remnant. The White Dwarf is destroyed.
Nova or Supernova? Supernovae are MUCH, MUCH more luminous than novae (about 10,000 times)! Nova: H to He fusion of the accreted hydrogen layer on surface, white dwarf left intact. Supernova: complete explosion of white dwarf, nothing left behind.
Supernova Type Supernova Type Massive Star or White Dwarf in a binary system? Both types of supernova can have a peak luminosity about 10 billion times that of the Sun! Light Curves differ – i.e. the way the light fades with time (next slide) Spectra differ – exploding white dwarfs don’t have hydrogen absorption lines because they are made of either carbon or helium
One way to tell supernova types apart is with a light curve showing how luminosity changes with time. LIGHT CURVES (luminosity versus time)
What have we learned? What is a white dwarf? –A white dwarf is the inert core of a dead star –Electron degeneracy pressure balances the inward pull of gravity What can happen to a white dwarf in a close binary system? –Matter from its close binary companion can fall onto the white dwarf through an accretion disk –Accretion of matter can lead to novae and sometimes to white dwarf supernovae
Neutron Stars Our goals for learning What is a neutron star? How were neutron stars discovered? What can happen to a neutron star in a close binary system?
A neutron “star” is the ball of neutrons left behind by a massive-star supernova. Degeneracy pressure of neutrons supports a neutron star against gravity. Chandra X-ray image (23 lyr across) of neutron star and supernova remnant. What is a neutron star?
The crushing force of gravity is enormous. Electron degeneracy pressure goes away because electrons are forced to combine with protons, making neutrons and neutrinos. Neutrons collapse to the center, forming a very compact neutron star. Insert TCP 5e Figure 17.16 In the ultra-dense core of a massive star Remember that the atom is mostly empty space; nuclei are now touching each other!
A teaspoon of neutron material would weigh billions of tons on Earth! A neutron star is about the same size as a small city (10 km) but contains much more mass than the Sun.
Discovery of Neutron Stars Using a radio telescope in 1967, Jocelyn Bell (then a graduate student at Cambridge, England) noticed very regular pulses of radio emission coming from a single part of the sky. The object was called a pulsar. How were neutron stars discovered?
Pulsar at center of Crab Nebula supernova remnant pulses 30 times per second. We now know that this is a spinning neutron star.
A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis.
The radiation beams sweep through space, like lighthouse beams, as the neutron star rotates. The beam of intense radiation looks like a pulse as it sweeps across the Earth. The electromagnetic radiation is generated by electrons spiraling in a strong magnetic field.
Why Pulsars must be Neutron Stars Circumference of NS = 2π (radius) ~ 60 km Spin Rate of Fast Pulsars ~ 1000 cycles per second Surface Rotation Velocity ~ 60,000 km/s ~ 20% speed of light ~ escape velocity from NS This is an enormous velocity for a rotation. Anything else would be torn to pieces!
Why do neutron stars spin so fast? Pulsars spin fast because the core’s rotation speeds up as it collapses from normal size to a neutron star; remember the ice-skater. Conservation of angular momentum The change in radius is huge from the original stellar core size down to the tiny neutron star size, and therefore the spin-up is enormous. Example: Sun’s rotation rate is ~2km/s and radius is 700,000 km. Scale radius down to 10 km scale up rotation to 140,000 km/s (~0.5 c). Note: Lighthouse beaming effect means that we miss lots of spinning neutron stars because the beam is not pointed in our direction!
Matter falling toward a neutron star forms an accretion disk, just as in a white-dwarf binary. Accreting matter adds angular momentum to neutron star, increasing its spin rate. What happens to a neutron star in a close binary system? Matter accreting onto a neutron star can eventually become hot enough for helium fusion. The sudden onset of fusion produces a burst of X-rays.
What have we learned? What is a neutron star? –A ball of neutrons left over from a massive star supernova and supported by neutron degeneracy pressure How were neutron stars discovered? –Beams of radiation from a rotating neutron star sweep through space like lighthouse beams, making them appear to pulse –Observations of these pulses were the first evidence for neutron stars
What have we learned? What can happen to a neutron star in a close binary system? –The accretion disk around a neutron star gets hot enough to produce X-rays, making the system an “X-ray binary” –Sudden fusion events periodically occur on the surface of an accreting neutron star, producing “X-ray bursts”. These have been observed.
The Neutron Star Limit Quantum mechanics says that neutrons in the same place cannot be in the same state, but … Neutron degeneracy pressure can no longer support a neutron star against gravity if the neutron mass exceeds about 3 M Sun (This is the equivalent of the Chandrasekhar Limit for electron degeneracy pressure) Beyond the neutron star limit, no known force can resist the crush of gravity. As far as we know, gravity crushes all the matter into a single point known as a singularity.
Black Holes: Gravity’s Ultimate Victory Our goals for learning What is a black hole? What would it be like to visit a black hole? Do black holes really exist?
What is a black hole? A black hole is an object whose gravity is so powerful that not even light can escape it. The incredible density of matter required to do this warps spacetime, creating what is effectively a bottomless pit from which there is no escape.
Thought Question What happens to the escape velocity from an object if you shrink it? A. It increases B. It decreases C. It stays the same Hint:
Thought Question What happens to the escape velocity from an object if you shrink it? A. It increases B. It decreases C. It stays the same Hint: g = GM/R 2 Shrinking means smaller R larger g
Calculating the Escape Velocity from an object of mass M Initial Kinetic Energy Final Gravitational Potential Energy = = m (escape velocity) 2 m G x (Mass) 2 (Radius) Suppose the escape velocity = speed of light (c)? The radius is … R S = 2GM/c 2 Once an object of mass M shrinks below R s light cannot escape it. Schwarzschild Radius
“Surface” of a Black Hole The “surface” of a black hole is the radius at which the escape velocity equals the speed of light. This spherical surface is known as the event horizon. There is no actual surface at this location; it is a boundary in space. The radius of the event horizon is known as the Schwarzschild radius. Example: Light would not be able to escape Earth’s surface if you could shrink Earth’s mass into a volume of radius < 1 cm
The Event Horizon of a 3 M Sun black hole is also about as big as a small city. For a 1 M Sun black hole, R S = 3 km. Comparing Neutron Stars and Black Holes Massive star supernovae, with a core >3M Sun, can make a black hole instead of a neutron star. 10km versus 9km
No Escape Nothing can escape from within the event horizon because nothing can go faster than light. No escape means there is no more contact with something that falls in. Whatever falls in can increase the black hole’s mass, change the spin or charge of the black hole, but otherwise loses its identity. The region of spacetime within event horizon is effectively cut-off from the rest of the universe.
Singularity Beyond the neutron star limit, no known force can resist the crush of gravity. We are not aware of some other kind of “degeneracy” pressure that can halt the collapse As far as we know, gravity crushes all the matter into a single point known as a singularity. Whether this happens or not may never be known as nothing can escape from within the event horizon
Thought Question How does the radius of the event horizon change when you add mass to a black hole? A. Increases B. Decreases C. Stays the same
Thought Question How does the radius of the event horizon change when you add mass to a black hole? A. Increases B. Decreases C. Stays the same R = GM/c 2, so adding mass makes the black hole’s event horizon grow even bigger.
If the Sun shrank to a Black Hole of equal mass, its gravity would be different only near the Event Horizon, i.e. 3 km from center. (The current radius of the Sun is ~700,000 km!) There would be no change in the Earth’s orbit. Black holes don’t suck! They just pull due to gravity. Contours of gravity are the same at large distances Analogy: The rubber sheet is stretched immensely by the mass concentrated into a small point. In fact, the sheet ruptures.
Grid markers show that space is being stretched near the hole. Because the speed of light is constant, light waves take extra time to climb out of a deep hole in spacetime. This means photon frequency must decrease, leading to a gravitational redshift in the wavelength of the light.
The stretching of spacetime near the Event Horizon also means that time passes more slowly the closer you are to the BH. Clocks tick slower. If you are approaching the BH directly then you are not aware of this change. Time seems to flow normally. You cross the Event Horizon and are lost forever. From afar however, it seems to take you forever to reach the Black Hole.
Thought Question Is it easy or hard to fall into a black hole? A. Easy B. Hard Hint: A black hole with the same mass as the Sun wouldn’t be much bigger than a college campus
Tidal forces (i.e. the change in gravity with distance) near the Event Horizon of a 3 M Sun Black Hole would be lethal to humans. The force is trillions of times that which raises the tides on the Earth. Tidal forces would actually be much gentler near a supermassive black hole because its radius is much bigger.
Black Hole Verification Need to measure mass —Use orbital properties of companion —Measure velocity and distance of orbiting gas It’s a black hole if it’s not a star and its mass exceeds the neutron star limit (~3 M Sun )
Some X-ray binaries contain compact objects of mass exceeding 3 M Sun which are very likely to be black holes. Remember, a normal high-mass star is very luminous.
One famous X-ray binary with a likely black hole is in the constellation Cygnus; Cygnus X-1.
What have we learned? What is a black hole? –A black hole is a massive object whose radius is so small that the escape velocity exceeds the speed of light What would it be like to visit a black hole? –You can orbit a black hole like any other object of the same mass—black holes don’t suck! –Near the event horizon time slows down and tidal forces are very strong Do black holes really exist? –Some X-ray binaries contain compact objects too massive to be neutron stars—they are almost certainly black holes
The Origin of Gamma Ray Bursts Our goals for learning Where do gamma-ray bursts come from? What causes gamma-ray bursts?
Gamma-Ray Bursts These are very, brief bursts of gamma rays coming from deep space They were first detected in the 1960s during the cold war by satellites designed to detect nuclear testing by the Soviet Union Gamma rays are already “high energy”. To receive a high rate of these photons from galaxies far beyond the Milky Way VERY powerful explosion.
Observations in the 1990s showed that many gamma- ray bursts were coming from very distant galaxies To reach us, these energy bursts must be among the most powerful explosions in the universe—are we witnessing the formation of a black hole?
Supernovae and Gamma-Ray Bursts Observations show that at least some gamma-ray bursts are produced by “hyper” supernova explosions in distant galaxies Some others may come from collisions between neutron stars in a binary system with TWO neutron stars This is a current area of astrophysical research today
What have we learned? Where do gamma-ray bursts come from? –Most gamma-ray bursts come from distant galaxies –They must be among the most powerful explosions in the universe, probably signifying the formation of black holes What causes gamma-ray bursts? –At least some gamma-ray bursts come from supernova explosions