Stellar Remnants White Dwarfs Neutron Stars Black Holes 1
Announcements q Homework # 5 is due today. q Homework # 6 starts today, Nov 15th. Due on Tuesday, Nov 22nd. 2
Assigned Reading Chapters: 64.4, 65.2, 67, 68. 3
White Dwarfs v End-product of evolution of stars with mass < 8 M sun v Most of the mass of a typical star is ejected outward (planetary nebula) v Remaining core (made of Helium, or Carbon+Oxygen) has a mass M<1.4 M sun (i.e., similar to the mass of our Sun) and a radius roughly like the Earth. v The density of such system is about 300,000 times greater than the average density of basaltic rocks on the Earth v Over 97% of all stars will become white dwarfs WD Sirius B Incredible density! 16 tons per cubic inch! 4
White Dwarfs are luminous enough to be routinely observed with the HST. The Universe is still too `young to contain Black Dwarfs. 5
n n n What Supports White Dwarfs? There is no fusion to counter gravitational collapse. Eventually, the electrons are forced to be close together. Electrons cannot be packed too closely (a principle from Quantum Mechanics, called the Pauli Exclusion Principle): There are only 2 different `flavors of electrons, so only 2 can occupy the same energy level. The `packed (degenerate) electrons oppose additional gravitational collapse: White dwarfs are thus supported by electron degeneracy Think of putting tennis balls in a shrinking box! 6
n n What Happens if We Add Mass to a White Dwarf? The most common White Dwarfs (made of Carbon+Oxygen) can be thought of a crystalline lattice of Carbon and Oxygen: This would be a giant diamond! Crystalline structure confirmed in 2004 by studying WD pulsations. However, as you add mass, at Mass= 1.4 M sun, gravitational pressure is too high for electrons to support it. Electrons start combining with protons, forming neutrons: a neutron star is born! The mass of 1.4 M sun, above which you cannot have a white dwarfs is called the Chandrasekhar limit (which earned the physicist Chandrasekhar a Nobel Prize in 1983) 7
Neutron stars n A neutron star --- a giant nucleus --- is formed from the collapse of a massive star (1.4 M sun < M core < 3 M sun ). n Supported by neutron degeneracy pressure (same Pauli Exclusion Principle that applies to electrons). n Only about 10 km in radius. n Neutron stars rotate A teaspoon full would contain 10 8 tons! very rapidly n (conservation of Very hot and with very strong magnetic field angular momentum 8
Neutron stars discovered as Jocelyn Bell Pulsars, thanks to their rapid rotation 9
SNR N157B in the LMC pulsar n n 16ms period The fastest young pulsar known 10
Pulsars, neutron stars light houses n Pulsar: A fast rotating, magnetized neutron star. n The jets existence is due to the rotation and to the presence of magnetic fields. n Emits both strong radiation (radio) and jets of high-energy particles. Why do they rotate fast? Conservation of Angular 11 Momentum: A.M. = M x v x R
Rotation of Neutron Stars n Angular Momentum Conservation: A.M. = MvR n M = Mass of Neutron Star; v = Rotation Speed; R = Radius A neutron star has a radius about 100,000 times smaller than that of the Sun. To compensate for the smaller radius, the rotation speed has to increase by 100,000 times. The rotation period decreases by (100,000) 2. Thus, instead of rotating in ~25 days, the Sun would rotate about 5,000 times per second! 12
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Pulsar Evolution Pulsars emit radiation (0.1%) and high energy plasma (99.9%): they loose energy The rotational energy re-supplies the energy lost from the pulsar radiation. Eventually, pulsar slows down, radio beams become weaker. Many pulsars not observable Beams do not sweep Earth, Slowed down v Too quickly due to ultra strong magnetic fields, or v Reached their final stage of `invisible neutron stars. 18
The Limit of Neutron Degeneracy (What Happens if We Add Mass to a Neutron Star?) n The upper limit on the mass of stars supported by neutron degeneracy pressure is about 3.0 M Sun (predicted by Lev Landau) n If the remaining core contains more mass, neutron degeneracy pressure is insufficient to stop the gravitational collapse. n Nothing can stop the collapse; the stellar core becomes a black hole! 19
Black holes n When the ball of neutrons collapses, it forms a singularity a small region in space with small volume and the mass of the parent material. A singularity has infinite density; nothing can escape, not even light! The most interesting aspects of a black hole are not what it s made of, but what effect is has on the space and time around 20 it.
If an object is incredibly dense and compact, we find that it can trap light in 2GM v esc = R G = Gravitational Const.; M = Mass; R = Radius If V esc =c, the Sun would need to be only 3 km in radius 21
The gravity near Black Holes is so strong to bend space, time, and light! The position of a black hole is called a `singularity ; it is a `hole in space! Around this hole, space is bent, like placing a cannon ball in the center of a bed. 22
The Size of a Black Hole n The extent of a black hole is called its event horizon. Nothing escapes the event horizon! n The radius of the event horizon is the Schwarzschild radius given by: R s = 2GM/c 2 23
Some Examples of Black Hole Sizes n A 3M Sun black hole would have a Schwarzschild radius of ~10km. It would fit in Amherst. n A 3 billion M Sun black hole would have a radius of 60 AU just twice the radius of our solar system. n Some primordial black holes may have been created with a mass equal to that of Mount Everest. They would have a radius of just 1.5x10-15 m smaller than a hydrogen atom! 24
Some Odd Properties of Space Around a Black Hole n Light emitted near the surface (event horizon) of a black hole is redshifted as it leaves the intense gravitational field. n For someone far away, time seems to runs more slowly near the surface of a black hole. An astronaut falling into a black hole would seem to take forever to fall in. 25
Gravitational Redshifts A photon will give up energy while climbing away from a mass. It is trading its own energy for gravitational potential energy. 26
Survey Question If your buddy were falling into a black hole, what kind of telescope would you need in order to see him/her wave goodbye as they crossed the event horizon? 1) A large radio telescope. 2) A large infrared telescope. 3) A large visible light telescope? 4) A large X-ray telescope? 27
Time runs more slowly in the presence of a gravitational field. Strobe light 1s No gravitational field. 28
Time runs more slowly in the presence of a gravitational field. Observer is far away from the gravitational field Strobe light (according to the clock) 1s Big gravitational field for the clock. (same concept as the increased frequency of light as it escapes the gravitational field) 29
Black Holes Don t Suck! n Many people are under the impression that the gravity of black holes is so strong that they suck in everything around them. n Imagine what would happen if the Sun were to instantly turn into a black hole. What would happen to the Earth? 30
Black Holes Don t Suck! F g = GM M n The masses of the Sun and Earth don t change (M 1 and M 2 ) n The Earth is the same distance from the Sun as it was before (d = 1 AU) n Therefore, the force on the Earth would remain exactly the same! d 1 2 2 31
Black Holes Don t Suck! n So why are black holes so infamous? The reason is that the mass is so compact that you can get within a few kilometers of a full solar mass of material. Today, if you stood on the surface of the Sun, much of the material is hundreds of thousands of kilometers away. With a black hole, the mass is so concentrated that you can get very close to the full mass. n Gravity strength is extreme near a B.H. And so is the tidal field 32
The tidal forces near a moderate sized black hole are lethal! An astronaut (or any other object) would be shredded. 33
How Do We `See A Black Hole? n Short answer we don t. n But we can see: either the lensing effect (bending of light due to the extreme gravitational fields) or the radiation from the material falling into a black hole. 34
Lensing (Light Bending) from a Black Hole!
Gravitational lensing (a prediction of Einstein s General Relativity) 36
Cygnus X-1 is one of the brightest X- ray sources in the sky HD 226868 Cygnus X-1 The blue supergiant is so large, that its outer atmosphere can be drawn into the black hole. As the material spirals into the black hole, it heats up to millions of degrees and emits X-ray radiation. 37
How do we `see Black Holes n When matter falls into a B.H. it gets very, very hot. It emits X-ray. n Candidate B.H. s are powerful X-ray emitters, especially if they show very rapid variability (=small size) n They can also emit jets (similar to pulsars) Black Hole Jet in the center of the galaxy M87 (HST picture) 38
Survey Question Your doomed friend remembers that s/he has a rocket that s/he can use to temporarily stop her/his descent into the black hole. With visions of heroism in your head, you tie a rope to your waist and jump out of your spaceship to go and rescue her/him. How does time appear (to you) to progress for you and your friend as you approach her/ him? 1) Your own time seems to run normally and your friend s time seems to run faster and faster as you approach him. 2) Your own time seems to run slower and slower as you fall and your friend s time seems to continue to run at the same slow rate. 39
Survey Question Your doomed friend remembers that s/he has a rocket that s/he can use to temporarily stop her/his descent into the black hole. With visions of heroism in your head, you tie a rope to your waist and jump out of your spaceship to go and rescue her/him. How does time appear (to you) to progress for you and your friend as you approach her/ him? 1) Your own time seems to run normally and your friend s time seems to run faster and faster as you approach him. 2) Your own time seems to run slower and slower as you fall and your friend s time seems to continue to run at the same slow rate. 40