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PHYS 1902 (1)
Chapter 12-18

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Carleton University
PHYS 1902
Jillian Henderson

Textbook Notes Stars – Chapter 11 • Their bright surfaces send us the light that we see. Though we learn a lot about a star from studying its surface, we can never see through to a star’s interior, where the important action goes on. • A dense, opaque gas or a solid gives off a continuous spectrum—that is, light changing smoothly in intensity (brightness) from one color to the next. • Determine Temperature o a “black body” is a perfect emitter: Its spectrum depends only on its temperature, not on chemical composition or other factors o We can approximate the spectrum of the visible radiation from the outer layer of a star as a black-body curve o A different black-body curve corresponds to each temperature  As the temperature increases, the gas gives off more energy at every wavelength. Indeed, per unit of surface area, a hot black body emits much more energy per second than a cold one.  the wavelength is farther and farther toward the blue as the temperature increases o Thus, the hottest stars look blue and the coolest ones are red. Those of intermediate temperature (like the Sun) appear white, despite having spectra around yellow or green wavelengths (physiological response of our eyes) • Classifying Stars o All the spectral lines of normal stars are absorption lines which cause a star’s spectrum to  deviate from that of a black body (not by much). Helps understand a star’s composition o We can duplicate many of the contributor’s spectra on Earth o Hydrogen has easy spectra to detect, all other atoms have multiple energy levels and thus  has multiple possible spectra o The different elements can be distinguished by looking for their distinct patterns of spectral lines o Hydrogen lines are strongest at some particular temperature, and weaker at hotter temperatures (because the electrons escaped from atom) or at cooler temperatures (because electrons were in the lowest energy level) o Spectral types in order of temperature—from hottest to coolest—gave O B A F G K M  even cooler objects—ex. Brown dwarfs—have been found, and are designated L-type and T-type (not really stars though) o hydrogen lines are strongest at spectral type A, which corresponds to a surface temperature of roughly 10,000 K. o In very cool stars, those of spectral type M, the temperatures are so low (3000 K) that molecules can survive, and we see complicated sets of spectral lines o the hottest stars, of spectral type O, can reach 50,000 K. Some have shells of hot gas around them and give off emission lines, though stars generally show only absorption lines in their spectra. o Astronomers subdivide each spectral type into ten subtypes ranging from hottest (0) to coolest (9); thus, for example, we have A0 through A9 o determining its spectral type can determine its surface temperature o The Sun is a type G2 star, corresponding to a temperature of 5800 K. • Distance of Stars o Can determine distance to nearby stars with triangulation (using parallax), works to a few hundred light years o The nearest star—known as Proxima Centauri o Astrometry - Measuring the positions and motions of stars  “proper motion” - motion across the sky • Power of Stars o Luminosity – Intrinsic (how bright it would be without distance, absorption, etc.) brightness of star o Amount of energy a star gives off is denoted in joules/second o we give stars’ apparent brightnesses in “apparent magnitude.” Astronomers use a modification of the magnitude scale known as absolute magnitude  To do so, have set a specific distance to compare stars. If something is intrinsically fainter, it has a higher absolute magnitude.  Inverse-Square Law: For example, if a star’s distance is doubled, it appears four times fainter o You can determine how far away a star is by comparing how bright it looks with its intrinsic brightness o Inverse Square Law  The energy received from a star changes with the square of the distance: the energy decreases as the distance increase  Can simply express the luminosity of a star in terms of its apparent brightness and distance • Temperature-Luminosity Diagram – Plotting temperature of star (X-axis) vs. luminosity of a star (Y-axis) o Often known as “Hertzsprung–Russell diagrams” or as “H–R diagrams.” o Most stars fall in a narrow band across the temperature-luminosity diagram called the main sequence.  Normal stars in the longest-lasting phase of their lifetime are on the main sequence.  The position of a star on the main sequence turns out to be determined by its mass: Massive stars are hotter and more powerful  Position of a star does not change much while it is on the main sequence  Stars on the main sequence are called dwarfs, so the Sun is a dwarf.  Stars that are more luminous (intrinsically brighter), must be bigger than the main-sequence stars and are thus called giants or even supergiants  Stars that are intrinsically fainter than dwarfs (main-sequence stars) of the same color are called white dwarfs. Smaller than normal dwarfs  If a detailed analysis of the star’s spectrum reveals that it is a main-sequence star, then we know its luminosity. Comparison with its observed apparent brightness then yields its distance. This method for finding distances is known as “spectroscopic parallax.” • How Stars Move o Proper Motion of Stars  Only for the nearest stars can we easily detect any such relative motion among the stars, which is called proper motion  Proper Motion – Angular movement of stars across the sky, relative to each other  To get the velocity (km /sec) of each star in the sky, perpendicular to our line of sight, we need to also know its distance  The angular speed (proper motion) decreases with increasing distance o Radial Velocities of Stars  Radial Velocity – motion toward or away from us on a line joining us and a star • Shows up as a Doppler shift, a change of the spectrum so that what appeared at a given wavelength now appears at another wavelength o Blueshift – Color for each wavelength farther to the blue than it started out o Redshift – Color for each wavelength farther to the red than it started out • Ex. Object moving away from us, its spectrum is slightly shifted to longer wavelengths, say it’s redshifted. Opposite for blueshifted • Wavelength shift is proportional to the speed of the object. Use this to get speed of object moving away/towards • Binaries o Although the Sun is isolated, most stars are members of pairs/groups o Optical Doubles – Chance apparent associations. Two unconnected stars in the same direction in the sky o Visual Binary – Two stars revolving around each other (see them)  See better when the stars are far from each other in their orbits  Because of Kepler’s third law, these relatively large orbits correspond to long orbital periods o Spectroscopic Binaries – Spectrum shows 2 stars are present, they are distinguished by their spectra. Even if only spectrum of 1 of the stars is detected, can still tell that it is part of a spectroscopic binary if the spectral lines shift back and forth in wavelength over time (star motions/Doppler Shifts)  Closer stars orbit faster and thus have greater Doppler shifts o Eclipsing Binaries – type of binary star detectable when the light from a star periodically dims because one of the components passes in front of (eclipses) the other  Graph the “light curves” by plotting brightness over time  Only see when we are in the plane of its orbit o Astrometric Binaries – we observe a wobble in the path of a star as its proper motion takes it slowly across the sky. The wobble away from a straight line tells us that the visible star must be orbiting an invisible object, pulling the visible star from side to side • Weighing Stars o Use binary stars as primary way to measure the stellar masses, by determining how much mass the stars must have to stay in those orbits • Mass-Luminosity Relation o Mass of star is single most important characteristic. Properties and evolution depend on it o Massive main-sequence stars are far more luminous and have much shorter lives than low-mass main-sequence stars. Though massive stars start with more fuel, they consume it at a huge rate • Stars that Don’t Shine Steadily o Variable Stars – Some stars vary in brightness. Eclipsing binaries are one example of such variable stars, but other types of variable stars are actually individually changing in brightness  Long-Period Variables – A very common type of variable star changes slowly in brightness with a period of months or up to a couple of years • Such stars are giants whose outer layers actually change in size and temperature  Cepheid Variable – A star that varies between a larger, brighter state and a smaller, denser one. A strict relation exists linking the period over which the star varies with the star’s average luminosity. Supergiant stars, powerful enough that we can detect them in some of the nearby galaxies • Used as Standard Candles to measure distance to other galaxies • Compare its average luminosity with how bright it appears on average, to tell how far away the star is • Cepheid variables are rather massive stars, more massive than the Sun, at an advanced and unstable stage of their lives. They are supergiant stars, not on the main sequence. Cepheid variables are changing in size, which leads to their variations in brightness. They contract a bit, which makes them hotter, and because of a peculiarity in the structure of the star, less energy escapes. Thus the pressure rises, and they expand. They overshoot, expanding too far, and the expansion cools them. The energy easily escapes, the pressure decreases, and they respond by contracting again.  RR Lyrae variables – Related to Cepheids but, have shorter periods—only several hours long—than regular Cepheids. • Clusters of Stars o Open Clusters  Groupings of dozens or a few hundred stars  Irregular shape  Found in the plane of our galaxy, specifically in or near the spiral arms  Loosely bound by gravity, gradually dissipating away as individual stars escape o Globular Clusters  Clusters of stars with spherical symmetry  Contain tens of thousands or hundreds of thousands of stars  They are more strongly bound than open clusters, although their stars do occasionally get ejected through gravitational encounters with other stars.  Above/below plane of the galaxy and form a spherical halo around the center of our Galaxy  Each is a grouping of stars that were all formed at the same time and out of the same material  10x more heavier elements found in the stars of open clusters than globular clusters • Believe globular clusters are older (formed earlier in universe) when there was a low abundance of elements heavier than hydrogen and helium • Open clusters are younger and formed after heavier elements had time to fuse in the cores of stars  Still have action going on inside of the stars even though they are old o Age of Star Clusters  Determine age of clusters by looking at their temperature- luminosity (H-R) diagrams  For the youngest open clusters, almost all the stars are on the main sequence • Stars at the upper-left part of the main sequence—which are relatively hot, luminous, and massive—live on the main sequence for much shorter times than the cooler stars, which are fainter and less massive • the length of the main sequence on the temperature- luminosity diagram of a cluster gets progressively shorter • Can tell the age of an open cluster by which stars do not appear on the main sequence o Ex. Cluster with no O and B type stars is older than a cluster that does  Because of their range of ages, all globular clusters have very similar temperature-luminosity diagrams • Thus globular clusters in our galaxy are roughly the same age Chapter 12 – How Stars Shine • Starbirth o The birth of a star begins with a nebula (a large region of gas and dust) o In a leading theory galaxies have spiral arms because a wave of compression passes by. Still another possibility is that a nearby star explodes, sending out a shock wave that compresses the gas and dust o Once the cloud gains a higher-than-average density, the gas and dust continue to collapse due to gravity o Energy is released, and the material accelerates inward. Magnetic fields may resist the infalling gas, slowing the infall o Eventually, dense cores, each with a mass comparable to that of a star, form and grow like tiny seeds within the vast cloud. o These protostars, which will collectively form a star cluster, continue to collapse, almost unopposed by internal pressure. o When a protostar becomes sufficiently dense, frequent collisions occur among its particles; hence, part of the gravitational energy released during subsequent collapse goes into heating the gas, increasing its internal pressure. o Rising pressure slows down the protostar’s collapse (Contraction) o This object is known as a pre-main-sequence star o During the contraction phase, a disk tends to form because the original nebula was rotating  slightly (protoplanetary disk) o Jets are commonly ejected in opposite directions out the poles of the rotating pre­main­sequence  star o As energy is radiated from the surface of the pre-main-sequence star, its internal pressure decreases, and it gradually contracts. This release of gravitational energy heats the interior, thereby increasing the internal temperature and pressure. o As the temperature in the interior rises, the outward force resulting from the outwardly decreasing pressure increases, and eventually it balances the inward force of gravity, a condition known as “hydrostatic equilibrium.” o “Bipolar Ejectio” – young stars send matter out in oppositely directed beams o Ejection of spinning clumps of gas help slow the star’s rate of spin o “Herbig-Haro objects” – clouds of interstellar gas heated by shock waves from jets of high-speed gas o Bow Shock wave – a shock wave like those formed by the bow of a boat plowing through the water • Where Stars Get Energy o A pre-main-sequence star will heat up until its central portions become hot enough (at least one million kelvins) for nuclear fusion to take place, at which time it reaches the main sequence of the temperature-luminosity diagram o A star’s luminosity and temperature change little while it is on the main sequence; nuclear reactions provide the stability o Such rapid, random motions in a gas are the definition of high temperature. The thermal pressure, the force from these moving particles pushing on each area of gas, is also high. The varying pressure, which decreases outward from the center, produces a force that pushes outward on any given pocket of gas. This outward force balances gravity’s inward pull on the pocket o The basic fusion process in main-sequence stars fuses four hydrogen nuclei into one helium nucleus. In the process, tremendous amounts of energy are released. o A hydrogen nucleus is but a single proton. A helium nucleus consists of two protons and two neutrons. The mass of the helium nucleus (the final product of the fusion process) is slightly less than the sum of the masses of the four hydrogen nuclei (protons) that went into it. A small amount of the mass “disappears” in the process. The mass difference does not really disappear, but rather is converted into energy. This energy is known as the “binding energy” of the nucleus o All the main-sequence stars are approximately 90 per cent hydrogen (a lot of fuel) • Atoms and Nuclei o An atom consists of a small nucleus surrounded by electrons. Most of the mass of the atom is in the nucleus, which takes up a very small volume in the center of the atom. The effective size of the atom, the chemical interactions of atoms to form molecules, and the nature of spectra are all determined by the electrons. o Each element is defined by the number of protons in its nucleus  Can have different number of neutrons, known as isotopes o Radioactive – Unstable isotope, after a time, will spontaneously change into another isotope or element o During certain types of radioactive decay, as well as when a free proton and electron combine to form a neutron, a particle called a neutrino (neutral particle) is given off  Interacts with hardly anything, gives conditions of inside of Sun • Stars Shining Brightly o For nuclear fusion to begin, atomic nuclei must get close enough to each other so that the force that holds nuclei together, the “strong nuclear force”, can play its part. o At the high temperatures (millions of kelvins) typical of a stellar interior, some nuclei occasionally have enough energy to overcome electrical repulsion. They come sufficiently close to each other that they essentially collide, and the strong nuclear force takes over. o Once nuclear fusion begins, enough energy is generated to maintain the pressure and prevent further contraction. The pressure provides a force that pushes outward strongly enough to balance gravity’s inward pull o The fusion process is self-regulating. The star finds a balance between thermal pressure pushing out and gravity pushing in and thus achieves stability on the main sequence (at a constant temperature and luminosity). o The greater a star’s mass, the hotter its core becomes before it generates enough pressure to counteract gravity. The hotter core gives off more energy, so the star becomes brighter, explaining why main-sequence stars of large mass have high luminosity. o Massive stars use their nuclear fuel at a much higher rate than less massive stars, and thus have a shorter life since they use their fuel faster • Why Stars Shine o Proton-Proton Chain – This sequence uses six hydrogen nuclei (protons), and winds up with one helium nucleus plus two protons. The net transformation is four hydrogen nuclei into one helium nucleus.  The original six protons contained more mass than do the final single helium nucleus plus two protons. The small fraction of mass that disappears is converted into an amount of energy o For stellar interiors significantly hotter than that of the Sun, the carbon-nitrogen- oxygen (CNO) cycle dominates. This cycle begins with the fusion of a hydrogen nucleus (proton) with a carbon nucleus  As in the proton-proton chain, four hydrogen nuclei have been converted into one helium nucleus and an amount of energy has been released o Later in their lives, when they are no longer on the main sequence, stars can have even higher interior temperatures. They then fuse helium nuclei to make carbon nuclei (triple-alpha process: 3 helium go into making 1 carbon) o Nucleosynthesis – A series of other processes that can build still heavier elements inside very massive stars. • Brown Dwarfs o When a pre-main-sequence star has at least 7.5 per cent of the Sun’s mass, nuclear reactions begin and continue, and it becomes a normal star o A star with less than 7.5 per cent of the Sun’s mass, the central temperature does not become hot enough for nuclear reactions using ordinary hydrogen (protons) to be sustained o These objects called brown dwarfs shine dimly, shrinking and dimming as they age. they all shrink to the same radius, about that of the planet Jupiter o If you detect lithium in the spectrum of a dim star, it is probably a brown dwarf rather than a cool, ordinary dwarf star • Solar Neutrino Experiment o Neutrinos interact so weakly with matter, when they’re born in Sun they zip out into space at almost the speed of light and reach Earth in 8 minutes o Neutrinos should be produced in large quantities in the proton-proton chain along with positrons (anti-electron) o Only 1/3 of the neutrinos detected than expected. Believe neutrinos change after they are released (change/oscillate to three different types of neutrinos) o Sudbury Neutrino Observatory (SNO) has confirmed that most neutrinos change type between the Sun and Earth, accounting for original deficit • The End State of Stars o The mass of an isolated, single star determines its fate Death of Stars – Chapter 13 • The more massive a star is, the shorter it stays on the main sequence • Death of Sun (and other “lightweight” stars up to 10 solar masses) o As fusion exhausts the hydrogen in the center of a star (after about 10 billion years on the main sequence, for the Sun), its core’s internal pressure diminishes because temperatures are not yet sufficiently high to fuse helium into heavier elements o Gravity pulls the core in, heating it up again. Hydrogen begins to “burn” more vigorously in the now hotter shell around the core  Once again nuclear fusion o The new energy causes the outer layers of the star to swell and become very large o The solar surface will be relatively cool for a star, only about 3000 K, so it will appear reddish. Such a star is called a red giant  Appear in top right of H-R Diagram  Red giants are so luminous that we can see them at quite a distance o The contracting core eventually becomes so hot that helium will start fusing into carbon (via the triple-alpha process) and oxygen nuclei, but this stage will last only a brief time  The star becomes slightly cooler and fainter. o We end up with a star whose core is carbon and oxygen, and is surrounded by shells of helium and hydrogen that are undergoing fusion. o Not being hot enough to fuse carbon nuclei, the core once again contracts and heats up, generating energy and causing the surrounding shells of helium and hydrogen to fuse even faster than before  Makes the outer layers expand again, and the star becomes an even larger red giant. o Planetary Nebula – Visible glowing shell of ejected gas  As the star grows still larger during the second red-giant phase, the loosely bound outer layers can continue to drift outward until they leave the star  “Central star of a planetary nebula” is the remains of the star, its exposed hot core. On its way to becoming a white dwarf o Through a series of winds and planetary-nebula ejections, all stars that are initially up to 10 times the Sun’s mass manage to lose most of their mass. The remaining stellar core is less than 1.4 times the Sun’s mass. o When this contracting core reaches about the size of the Earth, “electron degeneracy pressure” succeeds in counterbalancing gravity so that the contraction stops  It comes from the resistance of electrons to being packed too closely together; they become “degenerate” (indistinguishable) o The result is a type of star called a white dwarf  Density way up, not enough mass to be neutron star o A white dwarf ’s mass cannot exceed 1.4 times the Sun’s mass; it would become unstable and either collapse or explode o White dwarfs are very faint and therefore hard to detect. o White-dwarf stars have all the energy they will ever have. Slowly burn energy until they eventually become so cool and dim that they can no longer be seen o Main-sequence stage is longest of star’s active life, white dwarf is longest of entire life o Sun’s Evolution and H-R Diagram  Initially the Sun will become a red giant, growing much more luminous (moving up in the diagram) and a bit cooler (moving slightly to the right), as its helium core contracts while surrounded by a hydrogen-burning shell (billions of years). When the core becomes sufficiently hot to ignite helium, producing carbon (triple-alpha process) and oxygen nuclei, the Sun will briefly (100 million years) become a bit less luminous and hotter (wiggle in H-R diagram). It will subsequently become an even larger red giant, growing even more luminous (moving up in the diagram) and slightly cooler (moving a bit to the right) as the carbon-oxygen core contracts while surrounded by helium-burning and hydrogen-burning shells. The Sun will then lose its outer envelope of gases through winds and gentle ejections, producing planetary nebulae and revealing a hotter surface (since those layers used to be in the hot interior). The luminosity, however, will stay roughly the same, as the burning shells of hydrogen and helium generate the energy. Thus, the Sun will quickly move to the left in the temperature-luminosity diagram. As the supply of hydrogen and helium dwindles, the Sun will contract, but at the same time its temperature will decrease; thus, it will move steeply down toward the lower right of the diagram. When the contracting Sun reaches roughly the size of the Earth, pressure from electron degeneracy will dominate completely, thwarting further contraction. However, the Sun will continue to cool, so its luminosity will continue to drop, though not as rapidly as when it was contracting. Thus, the Sun will move less steeply toward the lower right of the diagram. This stage will last tens of billions of years, eventually producing a very dim white dwarf. o Binary Star Evolution  Most stars are in binary systems, and the stars can exchange matter.  Surrounding each star is a region known as the Roche lobe, in which its gravity dominates over that of the other star. The Roche lobes of the two stars join at a point between them, forming a “figure-8” shape  Consider two main-sequence stars. As the more massive star evolves to the red giant phase, it fills its Roche lobe, and gas can flow from this “donor” star toward the lower-mass companion. The recipient star can gain considerable mass, and it subsequently evolves faster than it would have as a single star. Note that the flowing matter forms an accretion disk around the recipient star because of the rotation of the system  If one star is already a white dwarf and the companion (donor) fills its Roche lobe, a nova (an old star that brightens by a factor of a hundred to a million) can result  The brightening of a nova can occur in at least two ways: • First, as gas from the donor accumulates in the accretion disk, the disk becomes unstable and suddenly dumps material onto the white dwarf. The gravitational energy is converted to emitted light • Matter can accumulate on the white dwarf ’s surface and suddenly undergo nuclear fusion, when it gets hot and dense enough. This mechanism can brighten the system far more than the release of gravitational energy  A nova is caused by the accretion of hydrogen on to the surface of the star, which ignites and starts nuclear fusion (Wikipedia) • Supernovae o Stars with mass like the Sun often let of a planetary nebulae and end as a white dwarf, but some along with massive stars end in a supernovae o Core-Collapse Supernovae  Stars over 8x the mass of the Sun use up the hydrogen in their core much quicker. For these massive stars, the outer layers expand as the helium core contracts. The star has become so large that we call it a red supergiant.  Eventually, the core temperature reaches 100 million degrees, and the triple-alpha process begins. Some of the carbon nuclei then fuse with a helium nucleus (alpha particle) to form oxygen. The carbon-oxygen core of a supergiant contracts, heats up, and begins fusing into still heavier elements. The ashes of one set of nuclear reactions become the fuel for the next set. Each stage of fusion gives off energy.  Finally, even iron builds up. When iron fuses into heavier elements, it takes up energy instead of giving it off. No new energy is released to make enough pressure to hold up the star against the force of gravity pulling in; thus, the iron doesn’t fuse.  The mass of the iron core increases as nuclear fusion of lighter elements takes place, and its temperature increases. Eventually the temperature becomes so high that the iron begins to break down (disintegrate) into smaller units like helium nuclei. This breakdown soaks up energy and reduces the pressure. The core can no longer counterbalance gravity, and it collapses. The core’s density becomes so high that electrons are squeezed into the nuclei. They react with the protons there to produce neutrons and neutrinos  The collapsing core of neutrons overshoots its equilibrium size and rebounds outward, like someone jumping on a trampoline. The rebounding core collides with the inward-falling surrounding layers and propels them outward, greatly assisted by the plentiful neutrinos  The star explodes, achieving luminosity rivaling the brightness of a billion normal stars. It has become a supernova  The core remains as a compact sphere of neutrons called a neutron star. There is even some evidence that occasionally, the neutron star further collapses to form a black hole.  Such supernovae, known as Type II, mark the violent death of heavyweight stars • Unlike Type I, they have hydrogen lines in their spectra • Type Ib and Ic are variations of heavyweight star explosions lacking H from losing outer atmosphere through wind or companion star  Because of the collapse of the iron core, they’re also a core-collapse supernova. o White Dwarf Supernovae (Type 1a)  Come from carbon-oxygen white dwarfs in closely spaced (tight bound) binary systems  Gas can be transferred from the companion to the white dwarf, via an accretion disk. However, the white dwarf avoids surface explosions (novae), so the white dwarf ’s mass can grow.  If the companion adds too much matter to the white dwarf, causing the white dwarf to reach the Chandrasekhar limit (max mass of white dwarf) of 1.4 solar masses, it becomes unstable and undergoes a runaway chain of nuclear-fusion reactions. Heavy elements are synthesized from carbon and oxygen.  This energy makes the white dwarf literally explode, leaving no compact remnant (unlike the case in a core-collapse supernova, which produces a neutron star or a black hole). o Observing Supernovae  Whereas novae are small eruptions involving only a tiny fraction of a star’s mass, supernovae involve entire stars. A supernova may appear about as bright as the entire galaxy it is in.  A relatively nearby supernova might appear as bright as the full moon, and be visible night and day.  Supernova Remnants – Regions of gas in our Galaxy, the gas spread out by the explosion of a supernova o Supernovae and Us  The heavy elements that are formed and thrown out by both core- collapse supernovae and white-dwarf supernovae are necessary for life as we know it. • Only known source of most heavy elements • Spread out into space and are then incorporated when new planets/stars form o When the core of a massive star collapses, creating a neutron star and a supernova, theorists tell us that many neutrinos are produced o Our basic ideas of how Type II supernovae occur were validated: A neutron star had indeed been created, at least temporarily. o Cosmic Rays  Cosmic Rays – High energy particles received from space. Are the nuclei of atoms moving at tremendous speeds.  Some from Sun, others from other sources  Can’t determine their origin because the magnetic field bends them  “primary cosmic rays” collide with atmosphere, then “secondary cosmic rays” are generated due to collisions with air molecules • Pulsars o Neutron Stars  The collapsed core in a core-collapse supernova is a very compact object, generally a neutron star consisting mainly of neutrons  Neutron stars have measured masses of about 1.4 Suns (some up to 2 or 3), 1.4 solar masses is the limit for white dwarfs  Neutron stars are only about 20 or 30 km across  At such high densities, the neutrons resist being further compressed; they become “degenerate” • A pressure (“neutron-degeneracy pressure”) is created, which counterbalances the inward force of gravity  When an object contracts, its magnetic field is compressed. As the magnetic-field lines come together, the field gets stronger. A neutron star is so much smaller than the Sun that its magnetic field should be about a trillion times stronger. o Discovery of Pulsars  In 1967 Jocelyn Bell discovered a wavered radio signal, and the position of the source remained fixed.  The signal, when spread out, was a set of regularly spaced pulses and was briefly called LGM, for “Little Green Men” (thought to be extraterrestrial)  Multiple sources found and named Pulsars because they gave out pulses of radio waves o What Are Pulsars  Most are concentrated in the relatively flat plane of our galaxy  A white dwarf is too large to rotate fast enough to cause pulsations as rapid as those that occur in a pulsar; it would be torn apart.  The only remaining possibility is the rotation of a neutron star  The lighthouse model for pulsars – Just as a lighthouse seems to flash light every time its beam points toward you, a pulsar is a rotating neutron star.  The magnetic field of a neutron star is extremely high. This can lead to a powerful beam of radio waves. If the magnetic axis is tilted with respect to the axis of rotation, the beam from stars oriented in certain ways will flash by us at regular intervals (Wouldn’t see if beams were oriented in other directions) o The Crab, Pulsars and Supernovae  Discovered pulsar in the Crab Nebula, pulsing 30 times per second  Although every pulsar is a neutron star, not every neutron star is a pulsar • Neutron star may not have a beam of radiation if it’s rotating too slowly o Slowing pulsars and fast pulsars  “Millisecond Pulsar” – Rotate EXTREMELY fast, with period of a few milliseconds  Pulsars slow down equal to the amount of energy they’re giving off. The faster the pulsar is rotating, the faster it’s slowing down  Very fast rotating pulsars in a binary system have a more gradual slowdown rate because of their interactions with their companion  Many millisecond pulsars are found in globular clusters, and stripping material from companion and spinning up an accretion disk o Binary Pulses and Gravitational Waves  “Binary Pulsar” – Another neutron star in close orbit with the pulsar is rapidly pulling it to and fro, shortening and lengthening the interval between the pulses that reached us on Earth • One of the neutron stars is not a pulsar • has an elliptical orbit that can be traced out by studying small differences in the time of arrival of the pulses. • The pulses come a little less often when the pulsar is moving away from us in its orbit, and a little more often when the pulsar is moving toward us. • General relativity explains that much like Mercury’s orbit, the much stronger gravity in the binary-pulsar system, more pronouncedly changes its orbit every year  Gravitational Waves – wiggles in the curvature of space–time caused by fluctuations of the positions of masses. Should travel through space  Believe binary-pulsar systems orbits moving close together means they’re giving of gravitational waves  Double Pulsars – Pulses detected from both pulsars orbiting each other. • The closer together, the more gravitational energy given of (Same for binary-pulsar system)  To try to detect gravitational waves, the Laser Interferometer Gravitational-wave Observatory (LIGO) uses complicated lasers, optics, and electronics to see whether a 100-m length is distorted as a gravitational wave goes by o A Pulsar with a Planet  First detected extrasolar planet was from observing a pulsar  The arrival time of the pulsar’s radio pulses varied slightly, indicating that something is orbiting the pulsar and pulling it slightly back and forth  Concluded that the variations in the pulse-arrival time are caused by three planets in orbit around the pulsar  Astronomers think that neutron stars are formed in supernova explosions, so any original planets almost certainly didn’t survive the explosion. 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