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Stellar Remnants White Dwarfs, Neutron Stars and Black Holes Warm Up-12/11/12 1. 2. 3. 4. When a white dwarf forms, is the former star always at the end of its life cycle? What can happen to it? Does degeneracy still exist in stellar remnants? What is the Chandrasekhar number and what does it mean? What is the exclusion principle? Warm Up 1. 2. 3. 4. 5. What is the exclusion principle? How does a low-mass star become a high-mass stellar remnant? What is gravitational red-shift? What happens to a white dwarf as mass is added to it? If you pack electrons too closely, they remain in what state? Warm Up 1. 2. 3. 4. 5. 6. What is a nova and how do they occur? What is a Roche Lobe? What is a LaGrange Point? What is a mass transfer stream? What is an accretion disk? What is a neutron star? Warm Up 1. 2. 3. 4. 5. 6. 7. What was the mission objective for Apollo 13? Where was Apollo supposed to land? Who was the mission commander? Who was the mission pilot? What mishap occurred on board that threatened the mission? What additional problems (2) did the crew encounter? What were the solutions to those problems? Warm Up 1. 2. 3. 4. 5. 6. 7. What is electron degeneracy and which stellar remnant is it associated with? What is neutron degeneracy and which stellar remnant is it associated with? What two forces provide equilibrium to white dwarfs? What two forces provide equilibrium to neutron stars? Why can nothing escape from inside the event horizon of a black hole? What happens to white dwarfs that exceed the Chandrasekhar limit? Contrast Type I supernovae with Type II supernovae. Word Wall Elements Example/Characteristic Example/Characteristic Example/Characteristic Definition WORD WORD Used correctly in a sentence Simile Simile Simile Vocabulary for Word Wall Elements Type I Supernova Type II Supernova Roche Lobe/LaGrange Point White Dwarf/Nova Neutron Star/Pulsar Black Hole/Schwarzschild Radius/Event Horizon Event Horizon/Escape Velocity White Dwarfs and Light As light loses energy its wavelengths begin to increase and they are stretched toward the red end of the spectrum. This phenomenon is called gravitational redshift. The amount of shift depends on the star’s mass. Warm Up 1. 2. 3. What is a gravitational red shift? When a star reaches the end of its evolutionary cycle, is it necessarily the end of its life? Is light a particle or a wave? Why? Stellar Remnants All stars must eventually die. Space is littered with their bodies. Because they have exhausted their fuel, they no longer shine. The environment in which they were created made them quite exotic. Stellar forces have crushed white dwarfs to the point that a piece the size of an ice cube would weigh around 16 tons. Stellar Remnants Neutron stars have been crushed to the point that their electrons and protons have been merged. In the most massive stars, the stars have collapsed so completely that their immense gravity warps space to the extent that no light escapes from them. Dead Doesn’t Mean Inconspicuous While these remnants are dead as far as stellar evolution is concerned, many still effect those things around them. Some steal matter from there companions until they explode while some collapse even more until they reach an explosive end. White Dwarfs White dwarfs, the remnants of small mass stars, have a diameter about the size of the Earth. While they do not shine, they do radiate heat. The average surface temperature of a white dwarf is about 10,000 K. White Dwarfs The composition of the star is mainly carbon and oxygen with a thin surface layer of hydrogen and helium. There is far too little gas to ever combust, however. White dwarfs simply continue to cool and reach a core temperature of around 20,000 K. White Dwarfs It would take longer than the Universe has existed for one to cool to the extent it would no longer be detected. These remnants are called black dwarfs. The Structure of a White Dwarf There density and lack of fuel make white dwarfs different from ordinary stars, although they are at hydrostatic equilibrium. External pressure is supplied by an interaction between its electrons that limit how many can occupy a given volume. This gives the remnant a peculiar property, added mass will make the white dwarf shrink. The Structure of a White Dwarf Even more crucial, the mass of the remnant must be below critical level or they will collapse more. Also, because they are so dense ( 1 ton/cm3) the star’s atoms are packed very tightly, this compresses the orbits of the electrons circling their nuclei. The electrons are packed so tightly that many of them cannot relax from an excited state into a ground state. The Structure of a White Dwarf This leads to degeneracy pressure (as you know). The physical law called the exclusion principle limits the number of electrons that can be squeezed into a volume. When a gas is squeezed to this extent it heats up but does not create a corresponding increase in the star’s pressure. Degeneracy Pressure and the Chandrasekhar Limit Added mass makes the dwarf shrink despite degeneracy. The additional gravitational forces created by this additional mass squeezes the star even more. The remnant creates enough degeneracy pressure to overcome these additional forces until its mass reaches the Chadrasakher Limit, about 1.4 solar masses. Degeneracy Pressure and the Chandrasekhar Limit Physicists believe that when the Chadrasekher Limit is reached that the white dwarf may attain densities necessary to develop high mass star formations such as neutron stars and black holes. White Dwarfs and Light As light escapes from a body it has to work against that body’s gravity, like a ball rolling up hill. Light, however, cannot slow down, but it can lose energy. Light’s energy determines its frequency. White Dwarfs in Binary Systems Isolated dwarfs cool off and eventually disappear, but in a binary systems this is not necessarily true. Some dwarfs capture gas from their neighboring companion. The gas is rich in hydrogen. This gas builds until it reaches the point of ignition. White Dwarfs in Binary Systems But, as we have seen, nuclear burning in a degenerate gas can get explosive. This detonating gas is expelled into space where it forms an expanding sphere of hot gas. When this phenomenon was first witnessed by ancient astronomers it was called “nova stella”, for new star. We use the shortened form today, nova. Mass Transfer in Binary Systems Both the dwarf and the companion are surrounded by a region in which all material is gravitationally attached to that body. This region is known as a Roche Lobe. It is a teardrop-shaped boundary, that should the star expand beyond it, the material outside it will fall into the other star. Mass Transfer in Binary Systems The actual matter is passed through a mass transfer stream. Where this stream passes from the meeting Roche Lobes is called the LaGrange Point. The LaGrange Point is a point of gravitational neutrality where the influence of each star counteracts the gravitational force of its companion. To pass the LaGrange point is to put yourself under the gravitational influence of one member of the binary pair. Binary Pair Diagram The Type I Supernova The nova process can repeat itself over and over again given that the dwarf does not accumulate too much material. If enough gas gathers to push the dwarf over the Chandrasekhar Limit, the star will collapse unto a Type I supernova. This rapid collapse will eventually cause the remnant to reignite and blow itself apart. The Type I Supernova The Type I supernova leaves behind no remnant, but completely destroys itself. The iron that is in your blood was probably made this way. Neutron Stars In the 1930’s, astrophysicists Walter Baade (like the thing that washes your butt) and Fritz Zwicky (great American name) proposed the Type II (or high mass stellar collapse) supernova. Almost as an afterthought, they further proposed that the core remnant of such an explosion would result in a neutron stars. Neutron Stars While the neutron star looked good on paper, no one actually started looking for one for some time because astronomers believed them to be too small to observe. Theoretically, neutron stars would be tiny even compared to the small white dwarf. Neutron Stars According to Baade and Zwicky’s calculations the neutron stars should have a radius of about 10 kilometers and a mass of several times that of the Sun. They also predicted that neutron stars have a maximum possible mass (like the white dwarf does) of 2 to 3 solar masses. Pulsars and the Discovery of the Neutron Star Due to a lack pf observational evidence, the scientists’ ideas lay dormant for 3 decades until 1967. In that year British scientists observed fluctuating radio signals from strange, distant galaxies. A graduate student, Jocelyn Bell, noticed an odd radio signal with a very precise repetitive cycle (1.33 seconds). The signal was dubbed “LGM-1” for little green men 1. Pulsars Over the next few weeks, the group found several more pulsating radio sources that they began to call “pulsars”. They knew that the pulsating rates were likely related to the densities of the objects, so they realized that the sources were extremely dense. Calculated densities made it very unlikely that the sources were white dwarfs. Warm Up 1. 2. 3. What is a pulsar? Why do they rotate so rapidly? What do we actually hear coming from a pulsar? Pulsars In searching for an explanation, astronomers began to take a new look at Fritz and Zwicky’s 30 year old ideas about neutron stars. It was Italian astronomer Franco Pacini that linked the super dense neutron star idea with the rapidly pulsating radio signals by proposing that the stars didn’t actually pulse, but rather rotate rapidly. Some rotate as fast as 30 times per second. Pulsars So, how can a stellar core spin so rapidly? The answer is simple. It is the conservation of angular momentum. Like an ice skater bringing in her arm to spin more rapidly, when a star collapses its radius is slashed. Conservation of Angular Momentum The law of conservation of angular momentum states that: L = MVR where L is angular momentum M is mass of the object V is rotational velocity of an object And R is the object’s radius. Conservation of Angular Momentum Angular momentum must be conserved, therefore according to L = MVR, if radius decreases then velocity must increase to keep L constant. Emissions from Neutron Stars Like big motors, by varying their magnetic fields, neutron stars create an electric field. This electric field strips charged particles off the surface of the remnant and hurls them at nearly the speed of light out into space. Emissions from Neutron Stars As these particles ride the neutron star’s electric field away from the star they produce radiation, much like a radio transmitter does. This radiation, called non-thermal radiation is funneled through the poles and emitted in the shape of a tight cone. The Pulsar As these dense bodies rotate at astounding speeds, they radiate outward from their magnetic poles. The magnetic and rotational poles do not coincide and the radiation beams obliquely to the axis of rotation. Like a giant lighthouse, only if the Earth lies in the path of the radiation, is it seen. The Pulsar Emitting this tremendous radiation field does have its drawbacks, however. Like dragging an anchor, the field slowly decreases the rotational rate on the pulsar. Eventually, the neutron star/pulsar will cease to rotate and it will then become “invisible” to us. 1. 2. 3. 4. 5. 6. 7. 8. 9. What did Fritz and Zwicky propose? What is the estimated mass of a neutron star? What was the name of the first pulsar, discovered by Jocelyn Bell? Why do pulsars spin so quickly? What does the law of conservation of angular momentum state? If a star collapses and its radius is reduced, what happens to its rotational velocity? The energy released from a neutron star is in the form of what? What happens to pulsars over time? Why? Are pulsars frequently detected in binary pairs? Neutron Stars in Binary Systems Because neutron stars come from supernovae, they rarely exist in binary pairs. The explosive forces that create neutron stars often destroy or dislodge their companion. Black Holes When stars that are more massive than 10 solar masses reach the end of their lives, they can compress their cores with so much pressure that they rift the fabric of space-time. To understand black holes you have to understand escape velocity! Escape Velocity Escape velocity is the speed an object must attain to prevent being drawn back into another body’s gravity. The shuttle has to go about 7 miles per second to escape Earth’s gravity. Escape Velocity Mathematically, escape velocity is defined as : V = (2GM/R)1/2 where: V = Escape velocity G = Gravitational constant (6.8 10-11 m/s) M= Mass (kg) R = Radius of object (m) Practical Application For example, which has the higher escape velocity, our Sun or a white dwarf with one solar mass? The white dwarf, because its radius is 100 times less has an escape velocity (1001/2) or 10 times greater than our Sun. That's about 6,000 km/sec. See? Practical Application What about a neutron star whose radius is 105 times smaller than the Sun? Its escape velocity jumps to 180,000 m/s or about half the speed of light. Further compact a neutron star till its radius is four times smaller still and its escape velocity exceeds the speed of light and a black hole is created. Early Supporters The idea of an object whose escape velocity exceeded the speed of light was proposed in 1780’s by English cleric, John Mitchell. Slightly more than a decade later, French mathematician Pierre Simon Laplace entertained the same idea. Go Figure Following their logic and using an improved escape velocity, you can calculate radii needed to become a black hole. The formula: R = 2GM/c2 where: G = Gravitational constant (6.8 x 10-11 m/s) M= Mass (kg) c = speed of light Go Figure How small would you have to shrink our Sun for it to become a black hole? You would have to shrink it to about 3 kilometers across or 1.9 miles. Why Space is Like a Water Bed Imagine taking a baseball and placing it in the middle of water bed. The ball makes a small depression in the mattress. You roll a marble past the depression and the marble it trapped in the curvature of the mattress and comes to rest beside the baseball. Why Space is Like a Water Bed Now, imagine placing a bowling ball in the center of the bed. The depression is ever deeper, the curvature more exaggerated. The marble now rolls in father and hits the bottom harder. The Formation of Black Holes We infer from this analogy that strength of attraction between bodies depends on the amount the surface into which it is embedded is curved. Gravity works like this according to general relativity. The Formation of Black Holes Now replace the bowling ball with the a safe and it will tear through the fabric of the mattress. So too, a black hole is a tear in the fabric of space time. The Formation of Black Holes A German astrophysicist Karl Schwarzschild pioneered the calculations describing the structure of black holes. The distance across a black hole is called the Schwarzschild radius in his honor. Black Holes If you look at general relativity to find out the size of black holes you get the same answer we got before: R = 2GM/c2 . The Curvature of Space General relativity (Einstein) predicted these curves in space and they have been proven to exist experimentally. The effect of this curvature can be measured when looking at radio or light waves and it exactly coincides with predictions. Black Holes Where this exaggerated curvature prevents even light from escaping is call the event horizon and it coincides with the point where escape velocity is greater than the speed of light. This marks the point where nothing can escape from the black holes gravitational attraction.