* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lect16-3-28-and-30-1..
Auriga (constellation) wikipedia , lookup
Formation and evolution of the Solar System wikipedia , lookup
History of Solar System formation and evolution hypotheses wikipedia , lookup
Corona Australis wikipedia , lookup
Gamma-ray burst wikipedia , lookup
Spitzer Space Telescope wikipedia , lookup
Cassiopeia (constellation) wikipedia , lookup
Theoretical astronomy wikipedia , lookup
Star of Bethlehem wikipedia , lookup
Nebular hypothesis wikipedia , lookup
Observational astronomy wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
Dyson sphere wikipedia , lookup
First observation of gravitational waves wikipedia , lookup
Perseus (constellation) wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
Cygnus (constellation) wikipedia , lookup
Stellar kinematics wikipedia , lookup
History of supernova observation wikipedia , lookup
H II region wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Crab Nebula wikipedia , lookup
Corvus (constellation) wikipedia , lookup
Timeline of astronomy wikipedia , lookup
4/1/2011 The fusion of large nuclei to form elements heavier than carbon requires extremely high temperatures to overcome the large electromagnetic repulsion of these nuclei. Stars 3 This happens only in high-mass stars, where the crushing weight of the outer layers of these stars makes these conditions possible. Notes compiled by In these stars, nuclear fusion proceeds to its theoretical end point, after which the core of the star collapses catastrophically, setting p explosion. p off a supernova Paul Woodward Department of Astronomy University of Minnesota While on the main sequence, a high-mass star establishes a higher temperature in its hydrogen burning core than is found at the center of a star like the Sun. At this higher temperature, hydrogen nuclei (protons) have enough energy to slam into carbon, nitrogen, and oxygen nuclei as well as into other protons. The C, N, and O nuclei, even though they make up only about 2% of the core, act as catalysts for hydrogen fusion into helium. That is, the concentrations of C, N, and O are left unchanged by the fusion reactions, but they permit hydrogen to fuse into helium through a chain of reactions, called the CNO cycle, that makes the helium production rate far higher than would be possible through the proton-proton chain alone. p of the CNO cycle y are shown on the next slide. The 6 steps Just as for the proton-proton chain, 4 protons are replaced, ultimately, by one helium nucleus. Thus the energy produced by one trip through this reaction chain is the same as that produced by the proton-proton chain; however, the rate at which this energy is produced is greater. The rate of nuclear energy generation in a high-mass star is so great that the flux of photons carrying that heat outward through the star is enormous. A star of more than 2 solar masses goes through the same stages that we have described for stars like the Sun, but of course much more rapidly. Although photons are massless, they do carry momentum, which they can impart to the stellar matter through which they move, bouncing many times back and forth from its electrons, ions, and atoms. However, helium burning begins in these massive stars gradually, not by means of a helium flash. The core temperatures for these stars are so high that degeneracy pressure plays no role up to this point. photons to the ggas ggenerates a This momentum transfer from the p phenomenon we call radiation pressure. y a few hundred thousand yyears,, or even less,, helium After only becomes exhausted in the core of a high-mass star. Since normal gas pressure is created by the collisions of atoms with other atoms, transferring momentum, it is natural to consider this same sort of process, but now involving atoms and photons, as generating a pressure. Fusion then proceeds in a helium-burning shell around the inert carbon core, and a hydrogen-burning shell is located still further out. In very high mass stars, radiation pressure can be more important than normal gas pressure in supporting the outer layers. Intermediate mass stars, between 2 and 8 solar masses, are prevented by degeneracy pressure from fusing iron. These stars blow away their outer layers and end up as white dwarfs. 1 4/1/2011 For a high mass star, with more than 8 solar masses, degeneracy pressure never halts the collapse of its carbon core. The core temperature reaches the 600 million K needed to fuse carbon into heavier elements. Carbon burning may last only as long as a few hundred years. As each stage of core burning ceases, the core collapses still further, becomes still denser and hotter, and a still heavier element begins to be produced. produced The final stages of nuclear fusion in the core of such a star are complex. Helium captures are some of the simpler reactions that occur (see next slide), but ultimately even heavy nuclei can fuse with other heavy nuclei. Some of the fusion reactions produce free neutrons, which may fuse with heavy nuclei to make many of the elements we find on Earth. Ultimately, the core of a high mass star begins to resemble an onion, with an whole sequence of shells burning various elements. In the final days of such a star, iron is produced in a siliconburning core. Each time the star’s core collapses further, the surrounding shell burning intensifies, and the star’s outer layers inflate further. Each time the core ignites again, the outer layers may contract a bit. However, the changes in overall luminosity are not as great for such a star as they are for a star like the Sun in moving from the main sequence through its subsequent giant phases. In the H-R diagram, a high mass star thus tends to move in a zigzag fashion across the upper part of the diagram, toward the realm of the red supergiants. Fig. 16.17 Life tracks on the H-R diagram from main-sequence star to red supergiant for selected high mass stars. (from models by A. Maeder and G. Meynet.) Betelgeuse, Orion’s upper left shoulder star, is the best known red supergiant. Its radius is 800 times that of the sun, or about 4 times the distance from the Sun to the earth. 2 4/1/2011 The sequence of episodes of production in the core of ever heavier elements ceases with the production of iron. The nuclear particles are more tightly bound in iron than in any other nucleus (and therefore iron has the least mass per nucleon of any nucleus). It is therefore impossible to generate any additional energy by fusing more nuclear particles with iron nuclei. In fact, to do this requires that energy be injected, not produced. One might then wonder where all those heavier elements, like lead and uranium that occur naturally on Earth, come from. We will get to that presently. Once iron accumulates in the core of a high mass star, its end is near. Iron piles up in the core until its degeneracy pressure can no longer support it against gravity. The iron core of a high mass star is first supported against gravity by degeneracy pressure, an expression of the inability of electrons in the core to be squeezed into too small a space. However, as the iron continues to pile up in the core, and the core shrinks further, it becomes possible for electrons to combine with protons to form neutrons, releasing neutrinos in the process. Once this starts, it proceeds apace. In a fraction of a second, an iron core with a mass about equal to that of our Sun and a size larger than that of the Earth can collapse to form a ball of neutrons just a few kilometers across! This is like the fusion reaction to end all fusion reactions, the final core is essentially a giant nucleus! This neutron core is supported against gravity by the degeneracy pressure of the neutrons (like electrons, two of them can’t be in the same place at the same time either). The gravitational collapse of the core releases an astronomical amount of energy. The supernova explosion momentarily floods the material surrounding the core with neutrons. The energy released can be more than 100 times the energy the Sun will radiate over its entire 10-billion-year lifetime. Elements heavier than iron can be made in neutron capture reactions which absorb rather than produce energy. This energy, much of it in the form of neutrinos produced from the combination of electrons and protons, drives a shock front into the outer layers of the star. As far as we know, this is the source of elements like lead which, although rare, nevertheless can be found on earth in quantities sufficient to provide bullets for a world war or two. These layers Th l are then h heated h d andd accelerated l d outward, d making ki this hi gas radiate light with a brilliance comparable to 10 billion suns for a short period (days) and causing the gas ultimately to mix with the surrounding interstellar medium. If indeed we are correct that elements heavier than helium are generated in stars, returned to the interstellar gas through stellar winds, planetary nebula ejection, and through supernova explosions, then on the average older stars should have smaller proportions of these elements. This is indeed the case. The oldest stars, in globular clusters, typically have only 0.1% of their mass in such heavy elements, while recently formed stars have between 2% and 3% of their masses in these elements. This gas, which may later become incorporated in new stars, contains the heavy elements created in the massive star as well as heavy elements created during the star’s final moments, when free neutrons are abundant and react with other nuclei. 3 4/1/2011 We also think that heavy element fusion in stars involves the capture of helium nuclei, which have two protons and two neutrons. Thus we predict that there should be a greater relative abundance of heavier elements with even numbers of protons. This is indeed the case, as is shown on the next slide. The Crab Nebula, shown on the next slide, is the remnant of a recent supernova, a star that exploded in 1054. We know this date precisely, because it was recorded by the Chinese. At the center of the Crab nebula there is a pulsar, a rapidly rotating neutron star. This confirms our theoretical ideas that such objects j should remain after a supernova explosion. Other supernovae in our galaxy during the last 1000 years occurred in 1006, 1572, and 1604. We observe many such explosions in other galaxies. The Crab Nebula, in Taurus, M1, or NGC 1952, Hubble Space Telescope WFPC2. Exploded 1054. The Crab Nebula, in Taurus, M1, or NGC 1952, central pulsar seen in X-rays and optical light. 4 4/1/2011 The Crab Nebula, in Taurus, M1, or NGC 1952, central pulsar seen in X-rays (2008) The supernova observed by Tycho Brahe in 1572, known as Tycho’s supernova, left behind an expanding remnant called Cas A. A sequence of detailed radio observations of this remnant have been carried out that allow us to make a very short movie showing its expansion. Tycho Brahe’s Supernova Optical and radio observations of Tycho’s Supernova Remnant, VR53A. VLA Radio Image of the Cas A Supernova Remnant Chandra satellite X-ray image of Cas A 5 4/1/2011 The galaxy is actually littered with bubbles in the interstellar medium which have been formed by supernovae. Supernova HD 56925 (from Astronomy, Jan., 1992, p. 49) A particularly beautiful old supernova remnant is the Cygnus Loop, which covers a huge region of the sky. The Cygnus Loop, NGC 6960-92, in red light with 48-inch Schmidt Another old supernova remnant, which also has a pulsar in it, is the Vela supernova remnant. The Vela Supernova Remnant -- Royal Observatory, Edinburgh 6 4/1/2011 If we want to see supernovae in our lifetimes, we must look in other galaxies. Supernovae can rival entire galaxies in brightness, so you might think they would be easy to spot. Here’s an example. Apparently somebody was watching back in 1941. The Vela pulsar -- Chandra X-ray observatory The pulsar is moving through the SN remnant in the direction of arrow Supernova in NGC 4725, a type Sb/SBb galaxy in Coma Bernices. Two views, May 10, 1940 and January 2, 1941. Supernova in NGC 4096 1961 (Lick Observatory) Supernova in NGC 4303 during and before outburst (1964) The Hubble Space Telescope images on the next slide pinpoint three distant supernovae, which exploded and died billions of years ago. Scientists are using these faraway light sources to estimate if the universe was expanding at a faster rate long ago and is now slowing down. Images of SN 1997cj are in the left hand column; SN 1997ce, in the middle; and SN 1997ck, on the right. All images were taken by y the Hubble telescope’s p Wide Field and Planetary y Camera 2. The top row of images are wider views of the supernovae. The supernovae were discovered in April 1997 in a ground-based survey at the Canada-France-Hawaii Telescope on Mauna Kea, Hawaii. 7 4/1/2011 Once the supernovae were discovered, the Hubble telescope was used to distinguish the supernovae from the light of their host galaxies. A series of Hubble telescope images were taken in May and June 1997 as the supernovae faded. Six Hubble telescope observations spanning five weeks were taken for each supernova. This time series enabled scientists to measure the brightness and create a light curve. Scientists then used the light curve to make an accurate estimate of the distances to the s perno ae Scientists combined the estimated distance with supernovae. ith the measured velocity of the supernova’s host galaxy to determine the expansion rate of the universe in the past (5 to 7 billion years ago) and compare it with the current rate. These supernovae belong to a class called Type Ia, which are considered reliable distance indicators. Looking at great distances also means looking back in time because of the finite velocity of light. SN 1997ck exploded when the universe was half its present age. It is one of the most distant supernovae ever discovered (at a redshift of 0.97), erupting 7.7 billion years ago. The two other supernovae exploded about 5 billion years ago. SN 1997ce has a redshift of 0.44; SN 1997cj, 0.50. SN 1997ck is in the constellation Hercules; Herc les; SN 1997ce is in Lynx, L n just north of Gemini; and SN 1997cj is in Ursa Major, near the Hubble Deep Field. Credits: Peter Garnavich, Harvard-Smithsonian Center for Astrophysics, the High-z Supernova Search Team, and NASA The most spectacular supernova of recent years was the one in 1987 that happened in a close companion galaxy of our own, the Large Magellanic Cloud. This supernova explosion rejuvenated the careers of an entire generation of aging supernova buffs. Amazingly, the outburst was actually detected on earth by two neutrino detectors, corroborating our view that the supernova shock is driven dri en by b an astounding asto nding fl flux of these eextremely tremel weakly eakl interacting particles. Supernova 1987A and the Tarantula Nebula Supernova 1987A progenitor star -- Anglo-Astral. Tel. Board 8 4/1/2011 Hubble Space Telescope mosaic of SN1987A and its surroundings Supernova 1987A light curve -- European Southern Observatory The ring structures around this supernova look very much like the structures observed in some planetary nebulae, like the Hourglass Nebula, for example. Perhaps the star that exploded had already lost much of its outer layers in strong stellar winds before it blew up. The precursor star was blue, not red, and this suggests mass loss before the explosion. One possibility, suggested by Chris Burrows, is that the two rings might be “painted” by a high-energy beam of radiation or particles, like a spinning light-show laser beam tracing circles on a screen. The source of the radiation might be a previously unknown stellar remnant that is a binary companion to the star that exploded in 1987. Images taken by Hubble show a dim object in the position of the suspected source of the celestial light show. The striking Hubble picture actually shows three rings. The smaller “center” ring of the trio was seen previously. The larger pair of outer rings were also seen in ground-based images, but their interpretation was not possible until the higher resolution Hubble observations. Though all of the rings probably are inclined to our view (so that they appear to intersect), they probably are in three different planes. The small bright p g ringg lies in a plane p containingg the supernova; the two rings lie in front and behind it. To create the beams illuminating the outer rings, the remnant would need to be a compact object such as a black hole or neutron star with a nearby companion. Material falling from the companion onto the compact object would be heated and blasted back into space along two narrow jets, along with a beam of radiation. 9 4/1/2011 As the compact object spins it might wobble or precess about its axis, like a child’s top winding down. The twin beam would then trace out great circles like jets of water from a spinning lawn sprinkler. If the rings are caused by a jet, however, the beams are extremely narrow (collimated to within one degree). The jet model explains why the rings appear to be mirror imaged, and why they appear to be symmetrical about a point offset from the center of the explosion. Burrows got the idea for the beam explanation when he noticed that where a ring appears brighter, an equally bright region appears on opposite ring. By connecting lines between the similar clumps on opposite rings Burrows found a common center. However, it is offset from the heart of the supernova ejecta. When Burrows did a detailed inspection of the HST image, he found a dim object which may be the source of the beam at the predicted location. The object is about 1/3 light-year from the center of the supernova explosion. From previous HST observations and images at lower resolution taken at ground-based observatories, astronomers had expected to see an hourglass-shaped bubble being blown into space by the supernova’s progenitor star. The rings are probably on the surface of the hourglass shape. The hourglass was formed by a wind of slow-moving gas that was ejected by the star when it was a red supergiant, and a much faster wind of gas that followed during the subsequent blue supergiant stage. The hourglass was produced by the fact that the stellar wind from the red giant was denser in the equatorial plane of the star. When the star reached the blue supergiant stage, the faster winds tended to break out at the poles of the star. Energetic radiation from the supernova explosion illuminated the dense gaseous material in the equatorial “waist” of the hourglass, causing it to glow -- thus explaining the central bright ring. The two outer rings might be painted on the surface of the hourglass by a very different process, by the beams from the stellar remnant. In any case, the expanding ejecta are just now beginning to strike the ring of material surrounding the star. The first knot in the ring around the star began to light up in 1997. Now the rest of the ring is beginning to light up. It could shine extremely brightly for as much as a decade. 10 4/1/2011 A recent HST photo, showing the ring beginning to shine brightly. Bright areas on this image mark the regions of difference between recent and older photos of SN1987A The study of stellar evolution, and of supernova explosions in particular, is almost totally dependent upon computer simulation. One of the supernova explosion simulations, performed by a computer code built from one that I wrote, made the cover of Physics Today a few years ago. That same computer code was used to try to understand how heavy elements processed only onl in the deep stellar interior could co ld have ha e gotten to the surface and been observed so soon after the explosion. That simulation made the cover of Science magazine, and it helped us to understand how the very heavy elements get into the interstellar medium efficiently enough to end up in stars like our own, and of course in planets like our own even more importantly. Convective instabilities in an axisymmetric simulation of the collapsed iron core of a 15-solarmass star just 70 msec before supernova explosion. Neutinos from electron capture in the core heat the surrounding matter to produce vigorous convection that triggers the explosion. Colors indicate surviving electron population per nucleon (from about 0.1, green, to about 0.5, red) d) and d arrows show h velocities. l iti An A accretion shock, briefly stalled, at the red-purple boundary liberates protons from heavy nuclei. (Adam Burrows, John Hayes, and Bruce Fryxell, University of Arizona) 11 4/1/2011 This computation of the same fluid instability that mixes the layers of processed gas in a supernova explosion was performed with our code to match a lab experiment. Stars 4 Notes compiled by Paul Woodward Department of Astronomy University of Minnesota We will begin by briefly reviewing the life histories of low-mass and high-mass stars that we have been discussing. The low-mass stars burn hydrogen in their cores on the main sequence, burn hydrogen in shells around inert helium cores as subgiants and red giants, burn helium in their cores and hydrogen in shells as helium-burning stars on the “horizontal branch” in the H-R diagram, burn helium and hydrogen in shells around inert carbon cores as red giants again, and finally shed their outer l layers as planetary l t nebulae, b l exposing i their th i carbon b cores, supported by electron degeneracy pressure, as white dwarfs. A white dwarf is extremely dense. Two dice made from white dwarf material would weigh 5 tons, about as much as 3 cars (see next slide). A solar mass is packed into the volume of the earth. The more massive a white dwarf is, the smaller it is, up to a limit, the Chandrasekhar limit of 1.4 solar masses, after which a white dwarf must collapse to form a neutron star. The size of the white dwarf Sirius B compared to the Earth and Sun 12 4/1/2011 We now review the life history of a massive star. It is roughly the same, except much faster, up to the generation of an inert carbon core. However, in a massive star, the carbon core is much hotter, so that it is not supported by electron degeneracy pressure but by the pressure that comes from heat energy. The carbon core ultimately reaches the 600 million degrees K needed for fusion of carbon, and the star keeps burning, developing a whole series of nuclear burning shells around an iron core. The final catastrophe for a massive star comes when the electrons in its iron core, unable to support the star by their degeneracy pressure, are forced to combine with the protons to form neutrons (and neutrinos). Neutron stars can pack a solar mass into a sphere only 10 km across! They are like gigantic nuclei held together not by the strong nuclear force, but by gravity. A paper clip made from neutron star material would outweigh Mt. Everest! The escape velocity from a neutron star’s surface is about half the speed of light, and photons which do emerge do so with a gravitational redshift that increases their wavelengths by about 15%. The core collapses suddenly to form a neutron star, or possibly a black hole, releasing vast energy in the form of neutrinos. When the iron core of a massive star collapses to form a neutron star, its angular momentum remains unchanged, while its size is dramatically reduced. Even if it was hardly rotating at all as an iron core, by the time it ends up as a neutron star, it is bound to be spinning rapidly. During its collapse, the magnetic field in the core is carried along with the material, forcing the magnetic field lines very closely g and thus amplifying p y g the field strength g mightily. g y together Right after the neutron star is formed, we can expect its magnetic field to be as much as a trillion times that of the Earth. As the neutron star rotates, and its magnetic fields are whipped around by that rotation, somehow beams of radiation are driven out along the directions of the magnetic poles. When the magnetic poles do not coincide with the rotation axis, these beams of radiation sweep around like a lighthouse beam. 13 4/1/2011 Fig. 17.9b This artwork likens a pulsar (top) to a lighthouse (bottom). If a pulsar’s radiation beams, channeled by its magnetic field, are not aligned with its rotation axis, these beams will sweep through space. We see a pulse of radiation each time such a beam sweeps by us, hence the name “pulsar.” Fig. 17.9a Fig. 17.8 These time-lapse photos of the pulsar in the Crab Nebula, which lies to the upper left of the unrelated star at the center, show how the pulsar flashes on and off about abo t 30 times a second. (Jocelyn Bell was at the controls when the pulses first appeared) (the controls, and the instrument, were conceived by her thesis advisor, Anthony Hewish, who was awarded the Nobel Prize) The Crab Nebula, shown on the next slide, is the remnant of a recent supernova, a star that exploded in 1054. We know this date precisely, because it was recorded by the Chinese. At the center of the Crab nebula there is a pulsar, a rapidly rotating neutron star (rotating 30 times per second). This confirms our theoretical ideas that such objects should remain after a supernova explosion. explosion The Crab Nebula, in Taurus, M1, or NGC 1952, Hubble Space Telescope WFPC2. Exploded 1054. Other supernovae in our galaxy during the last 1000 years occurred in 1006, 1572, and 1604. We observe many such explosions in other galaxies. 14 4/1/2011 The Crab Nebula The colorful photo on the left in the next slide shows a groundbased image of the entire Crab Nebula. The nebula, which is 10 light-years across, is located 7,000 light-years away in the constellation Taurus. The green, yellow and red filaments concentrated toward the edges of the nebula are remnants of the star that were ejected into space by the explosion. At the center of the Crab Nebula lies the Crab Pulsar -- the collapsed core of the exploded star. The Crab Pulsar is a rapidly rotating neutron star – an object only about six miles across, but containing more mass than our Sun. As it rotates at a rate of 30 times per second the Crab Pulsar's powerful magnetic field sweeps around, accelerating particles, and whipping them out into the nebula at speeds close to that of light. The blue glow in the inner part of the nebula -- light emitted by energetic electrons as they spiral through the Crab’s magnetic field -- is powered by the Crab Pulsar. The picture on the right shows a Hubble Space Telescope image of the inner parts of the Crab. The pulsar itself is visible as the left of the pair of stars near the center of the frame. Surrounding the pulsar is a complex of sharp knots and wisp-like features. This image is one of a sequence of Hubble images taken over the course of several months. months This sequence shows that the inner part of the Crab Nebula is far more dynamic than previously understood. The Crab literally “changes it stripes” every few days as these wisps stream away from the pulsar at half the speed of light. The Hubble Space Telescope photo was taken Nov. 5, 1995 by the Wide Field and Planetary Camera 2 at a wavelength of around 550 nanometers, in the middle of the visible part of the electromagnetic spectrum. Credit: Jeff Hester and Paul Scowen (Arizona State University), and NASA The three pictures shown on the next slide are taken from a series of Hubble Space Telescope images. They show dramatic changes in the appearance of the central regions of the Crab Nebula. These include wisp-like structures that move outward away from the pulsar at half the speed of light, as well as a mysterious “halo” which remains stationary, but grows brighter then fainter over time. Also seen are the effects of two polar jets that move out along the rotation axis of the pulsar. The most dynamic feature seen -- a small knot that “dances dances around around” so much that astronomers have been calling it a “sprite” -- is actually a shock front (where fast-moving material runs into slower-moving material) in one of these polar jets. The telescope captured the images with the Wide Field and Planetary Camera 2 using a filter that passes light of wavelength around 550 nanometers, near the middle of the visible part of the spectrum. The Crab Nebula is located 7,000 light-years away in the constellation Taurus. Credit: Jeff Hester and Paul Scowen (Arizona State University), and NASA 15 4/1/2011 As the neutron star at the center of the Crab Nebula spins on its axis 30 times a second, its twin searchlight beams sweep past the Earth, causing the neutron star to blink on and off. Because of this flickering, the neutron star is also called a “pulsar.” In addition to the pulses, the neutron star’s rapid rotation and intense magnetic field act as an immense slingshot, accelerating subatomic particles to close to the speed of light and flinging them off into space. In a dramatic series of images assembled over several months of observation, Hubble shows what happens as this magnetic pulsar “wind” runs into the body of the Crab Nebula. The glowing, eerie shifting patterns of light in the center of the Crab are created by electrons and positrons (anti-matter electrons) as they spiral around magnetic field lines and radiate away energy. This lights up the interior volume of the nebula, which is more than 10 light-years across. The Hubble team finds that material doesn’t move away from the pulsar in all directions, but instead is concentrated into two polar “jets” and a wind moving out from the star’s equator. The most dynamical feature in the inner part of the Crab is the point where one of the polar jets runs into the surrounding material forming a shock front. The shape and position of this feature shifts about so rapidly that astronomers describe it as a “dancing g sprite,” p , or “a cat on a hot plate.” p The equatorial wind appears as a series of wisp-like features that steepen, brighten, then fade as they move away from the pulsar to well out into the main body of the nebula. The Crab Nebula, in Taurus, M1, or NGC 1952, central pulsar seen in X-rays and optical light. The Crab Nebula, in Taurus, M1, or NGC 1952, central pulsar seen in X-rays (2008) A pulsar has also been found in the center of the Vela supernova remnant. Once we knew that pulsars existed, it proved easy to search for them, and lots of them were found. 16 4/1/2011 Close Binary Stars Notes compiled by Paul Woodward Department of Astronomy University of Minnesota The Vela Supernova Remnant -- Royal Observatory, Edinburgh A large fraction of stars are located in binary systems. Binary stars are born at the same time and evolve separately according to the principles of stellar evolution theory laid out earlier. However, when the more massive of the two stars evolves off the main sequence toward its giant star phase, very interesting things can happen if the two stars are orbiting each other at a sufficiently small separation. separation We will discuss here only the case of close binary stars. During the main sequence stage of both stars’ lives, tidal forces alter the shapes of the stars, so that when the stars are closest to each other they become elongated, with the elongation directions along the line joining their centers. This is because each star attracts the near side of the other more than it does the far side. The periodic elongation of the two stars upon closest approach results in friction within each star, even though the stars are made of gases. These frictional forces are minimized when the two stars orbit each other in circular orbits and rotate synchronously, so that they each always present the same face to each other. The action of the frictional forces therefore leads ultimately to such a state. (This process is familiar from our study of the moons of Jupiter. It also is at work in locking the Earth’s Moon’s rotation rate to its orbital period, so that we always see the same face of the Moon.) The following slide shows a Roche diagram. The lines on the diagram are equipotential surfaces. The diagram is drawn in the equatorial plane of two orbiting stars in a binary system, and the diagram is drawn in a frame of reference rotating with the stars’ orbital motion. That is, in the diagram, the centers of the two stars remain fixed at the two points labeled M1 and M2 . The lines drawn in the diagram are actually the intersections of equipotential surfaces with the equatorial plane of the two stars. Along each equipotential line, there is no effective gravitational force felt in the direction of the line; instead, the effective gravity (the gravity with the centrifugal force of the orbital motion taken into account) pulls only in the direction perpendicular to the line. (from Shu, The Physical Universe) This means that no effective gravitational potential energy is liberated or gained by moving along an equipotential line. 17 4/1/2011 Thus, an object, like a star, made of gas free to move around must have its surface lie along an equipotential line. If this were not so, some of the gas on the surface could move in such a way as to fill an area of vacuum and at the same time liberate gravitational potential energy. The lines in the Roche diagram have their weird shapes partly because the two stars are orbiting about each other. Centrifugal g from this rotation are included in the diagram’s g forces arising equipotential lines. In this rotating frame of reference, the net forces on a particle which is located on an equipotential line are in the direction perpendicular to the line. We call these net forces on a particle the effective gravity at that particle’s location. The point labeled L1 on the Roche diagram is the point at which the effective gravity vanishes. That is, a particle at this Lagrangian point feels no net attraction to either star. (from Shu, The Physical Universe) The surfaces of constant pressure in stars that are motionless in the orbit frame of reference must coincide with the equipotential surfaces (the effective gravity has no component along the equipotential) The surfaces of constant density in stars that are motionless in the orbit frame of reference must coincide with the equipotential surfaces, because these are surfaces of constant pressure. (from Shu, The Physical Universe) The equipotential surfaces in the Roche diagram must be surfaces of constant pressure. If this were not so, then pressure differences along these surfaces, unopposed by the effective gravity, would set up motions in the stars’ gas that would tend to eliminate the pressure differences. Thus if the stars have been orbiting each other for a long time, we can be sure that the pressures have equalized on the equipotential surfaces. If the gas density were to vary along the equipotential surfaces, then the greater weight of gas above one point on the surface would cause the pressure there to be greater than at another point. Again, these pressures would equalize by means of gas motions driven by the pressure differences. The result is that the equipotential surfaces are also surfaces of equal pressure, density, and temperature. (from Shu, The Physical Universe) The surfaces of the two stars orbiting each other, which are of course surfaces where the density passes through some relatively small value, must therefore be equipotential surfaces. The Roche diagram therefore indicates that if the radii of the stars are both small compared to their mutual separation, then the surfaces of the stars are roughly spherical. However, if the stellar radii are large, then the stars’ shapes can be g y distorted by y their mutual ggravitational attraction. highly One limiting case is when both stars are so large that they are just touching. Then each star is said to fill its Roche lobe, and the two stars look like the 3-D representation of the Roche lobes in the second slide. This analysis leads to a standard classification of binary stars, which is given on the third slide. 18 4/1/2011 (from Shu, The Physical Universe) (from Shu, The Physical Universe) (from Shu, The Physical Universe) (from Shu, The Physical Universe) (from Shu, The Physical Universe) (from Shu, The Physical Universe) 19 4/1/2011 (from Shu, The Physical Universe) (from Shu, The Physical Universe) The semidetached binary star Algol, in the constellation Perseus, consists of a 3.7 solar mass star on the main sequence and a 0.8 solar mass star that is a subgiant. One would expect the more massive star in the pair to have evolved more rapidly, leaving the main sequence first. One must therefore conclude that the 0.8 solar mass subgiant has transferred much of its originally far larger mass to its main sequence companion companion. The main sequence star is now far more massive, and its evolution rate will therefore be accelerated. Before its companion leaves its giant phase, it is possible that the main sequence companion will grow into a giant, presumably transferring mass back to create a common envelope star system. First stage in the evolution of an Algol-type binary system. 20 4/1/2011 Second stage in the evolution of an Algol-type binary system. Third stage in the evolution of an Algol-type binary system. Stage 1 Stage 2 Fig. 16.24 Artist’s conception of the development of the Algol close binary system. Stage 3 The Algol system is a semidetached binary in which the star with the smaller radius is a main sequence star. Algol is already fairly interesting, but things can get even more exotic if the smaller, companion star is a white dwarf. Because a white dwarf is so compact, the stream of gas from a giant star companion that fills its Roche lobe will liberate a large amount of gravitational potential energy in falling all the way down toward the surface of the white dwarf. Because the infalling gas will have some orbital angular momentum, and because this angular momentum will be preserved, the stream of gas will miss the tiny white dwarf, whipping around it in an elliptical orbit (see illustration on second slide). Since the gas stream will remain in the equatorial plane, it must strike itself after missing the white dwarf surface, leading to the formation of an accretion disk. 21 4/1/2011 (from Shu, The Physical Universe) Second stage in the formation of an accretion disk. The stream of matter dissipates much of its kinetic energy, but its angular momentum remains. First stage in the formation of an accretion disk. The stream of matter misses the companion and strikes itself. (from Shu, The Physical Universe) A close, low-mass binary star, which in this case is also a cataclysmic variable star system. 22 4/1/2011 Fig. 17.3 A red giant star with a white dwarf companion There is not as yet an adequate understanding of why gas in an accretion disk tends to slowly spiral into the center, ultimately falling onto the surface of the central object. In order to spiral in, angular momentum must be removed from the gas, generally through some process or processes that transport it outward through the disk. These processes are not well understood, but we can (and many astronomers do) think about these processes as frictional di i i dissipation. Kepler’s laws demand that the inner parts of the disk orbit much more rapidly about the central object than the outer parts. Frictional or viscous forces try to make the disk rotate as a solid body, which requires that the central regions lose and the outer regions gain angular momentum. A constant stream of gas therefore lands on the central white dwarf from the inner part of the accretion disk. Fig. 17.4 A mechanism for nova outbursts Fig. 17.4 A mechanism for nova outbursts The hydrogen-rich gas from the giant star companion of the white dwarf therefore ultimately lands on the surface of the white dwarf. As more and more hydrogen-rich gas piles up on the white dwarf, it ultimately becomes dense and hot enough for the hydrogen to fuse into helium. The hydrogen shell burning causes the white dwarf to suddenly flare up up, for a few weeks weeks, as a nova. nova Such a nova outburst can be as luminous as 100,000 Suns. Heat and pressure from this explosive hydrogen burning at the surface of the white dwarf forces material near the surface out into space, where it can be visible as a nova remnant. 23 4/1/2011 Nova Herculis (1934), showing large change in brightness between March 10 and May 6 of 1935. The nova remnant, after the initial outburst dies down, may be most luminous in the infrared. The expanding shell of gas cools as it expands, but still radiates strongly in the infrared. A typical nova light curve With each nova outburst, the white dwarf in a binary system can gradually grow more massive. (However, the most recent research on this subject challenges this idea.) Ultimately, it reaches a mass, near Chandrasekhar’s famous white dwarf mass limit of about 1.4 solar masses, where it can no longer support itself against gravity by means of electron degeneracy pressure. At this critical point, it begins to collapse, growing hotter as it liberates gravitational potential energy. Because the white dwarf is degenerate, once the temperature required to ignite carbon fusion is reached, this fusion begins explosively. As the fusion reactions liberate nuclear energy in the form of heat, the thermal pressure is insufficient to expand the material and reduce the nuclear reaction rate. Electron degeneracy pressure still dominates. Consequently, the nuclear fusion rate shoots up almost instantly, and there is an explosion. The white dwarf explodes as a white dwarf supernova. 24 4/1/2011 We have already discussed neutron stars and pulsars as the remnants of the supernova explosions of massive stars. Particularly interesting things can happen when neutron stars are located in binary systems. Just like white dwarfs, neutron stars can cause the formation of accretion disks around themselves when mass is transferred from a giant companion star that tries to expand past the limits of its Roche lobe. lobe However, when hydrogen-rich gas falls onto the surface of a neutron star, immensely more gravitational potential energy is released than when the same amount of gas falls onto a white dwarf. The accretion disks around neutron stars are therefore hotter and more luminous than those around white dwarfs, and they emit huge quantities of X-rays (a very energetic form of light). Fig. 17.11 Matter accreting onto a neutron star adds angular momentum, increasing the neutron star’s rate of spin. As the material from the accretion disk falls onto the neutron star, it imparts what remains of its angular momentum to the neutron star. The result is that the neutron star spins faster and faster as it accretes more and more material. The neutron star can end up spinning hundreds of times per second, and thus earn the name millisecond pulsar. The X-ray emission from an X-ray binary, as a binary system with an accreting neutron star is called, can come in powerful bursts. These bursts come from episodes of helium fusion at the base of the thin, meter-thick layer of hydrogen-rich material on the surface of the neutron star. Each burst lasts only a few seconds. X-ray binaries are concentrated in the disk of the Galaxy, just like the stars, gas, and dust of the Galaxy. A neutron star accreting mass steadily in a binary system could ultimately become a black hole. A supernova explosion of a massive star could also leave a black hole behind, rather than a neutron star. In either of these ways, a binary system could end up with a black hole in it. The classic candidate for such a system is the X-ray binary Cygnus X-1. This system contains an extremely bright star with an estimated mass of 18 solar masses. Doppler shifts of its spectral lines indicate that this star orbits an unseen companion with a mass of about 10 solar masses. Even with the various uncertainties in these mass estimates, the companion seems well above the neutron star mass limit of about 3 solar masses. Fig. 17.15b An artist’s concept of the Cygnus X-1 system. The X-rays come from the high temperature gas in the accretion disk surrounding the black hole. 25 4/1/2011 The upper limit to the possible mass of a neutron star is not precisely known, but we believe that it is less than 3 solar masses. The possible states of matter above nuclear density are fundamentally unknown to us. Above this mass limit, we believe that neutron degeneracy pressure can no longer support the object against its own gravity. Nevertheless, regardless of what form matter might take within a collapsing neutron star, we believe that nothing could halt the collapse. The increasing heat of the material, due to the release of gravitational potential energy, actually acts as an additional source of gravitational force, through Einstein’s mass-energy relationship. Remember that the electrons in a white dwarf at the white dwarf mass limit become so energetic that they can combine with the protons to form neutrons, a far denser state of matter, leading to the collapse of the white dwarf against gravity. Just so, presumably, the neutrons of a neutron star near the neutron star mass limit become so energetic that they can combine with each other to produce more massive baryons (the family of particles to which neutrons and protons belong), which take up less space. The neutron star would then collapse further under its gravity. This time, however, we believe that the collapse would take the neutron star literally “out of sight” to form a black hole. We believe that collapse into a black hole is therefore inevitable. The form that the matter of the former neutron star takes once it disappears from our view is in a sense irrelevant, since we could perform no experiments to verify theoretical ideas on this subject. The results of such experiments would need to be communicated to us from within the black hole, but not even light can escape the gravitational force there. We can think of a black hole as mass that is so concentrated that gravity is so strong near it that even light is deflected so greatly that it orbits the mass concentration rather like the way the planets orbit the Sun. A black hole has what we call an event horizon, beyond which events are unobservable to us. Inside the event horizon, gravity is so strong that the escape velocity exceeds the speed of light. Even light cannot escape from within the event horizon. Light loses energy upon working its way out from a strong gravitational field. This energy loss takes the form of a redshift, and we call it the gravitational redshift. Fig. 17.12 (a) A 2-D representation of “flat” space-time. The circumference of each circle is 2π times its radius. radius (b) A 2-D representation of the “curved” space-time around a black hole. The black hole’s mass distorts space-time, making the radial distance between two circles larger than it would be in a “flat” space-time. Light emitted directly outward from the location of the event horizon is infinitely redshifted, that is, it reaches locations far from the black hole redshifted to infinite wavelength (zero energy), and is thus invisible. We will discuss all this more in a later lecture. 3 Solar mass black hole with photon sphere, event horizon, Schwarzschild radius, incoming light 26