Lecture Notes Astronomy 3/24 - 3/26
Lecture Notes Astronomy 3/24 - 3/26 ASTRON 0089
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324 Chapter 12 Part II Neutron Stars After a Type 1 carbon detonation supernova little or nothing remains of the original white dwarf After a Type 11 core collapse supernova part of the core may survive it is very dense as dense or denser than an atomic nucleus and is called a neutron star because it s made entirely of neutrons In the most massive stars black holes form The existence of neutron stars was theorized in 1933 but weren t discovered until 1967 Neutron stars are 13 times as massive as the Sun but are so dense that they re extremely small Incredible Densities 1 cubic cm of neutron star material size of grape has a mass of about 500 billion kg or 500 million tons as much as 10000 battleships The force of gravity at the surface of a white dwarf is about 300000 times that on Earth The force of gravity at the surface of a neutron star is about 1 trillion times that on Earth A neutron star is like a single gigantic atomic nucleus a unique form a matter that s poorly understood Other Properties of Neutron Stars Rotation as the parent star collapses the neutron core spins more and more rapidly 0 Typical periods are fractions of a second 0 If you shrank the Sun down to a neutronstar size it would rotate once every 10 seconds Magnetic field as the star collapses the neutron star s magnetic field becomes more and more concentrated and hence enormously strong 0 Like on Earth a neutron star s magnetic pole may not match up exactly with its rotation axis 0 The powerful magnetic field can accelerate particles and produce radiation with observable consequences Pulsars The first pulsar was discovered by Jocelyn Bell in 1967 it was an object emitting extraordinarily regular pulses of radio waves After some initial confusion it was realized that this was a neutron star spinning very rapidly nothing else would be small enough to emit bright pulses with such high frequency A 001 second pulse must come from something smaller than 001 sec x c 3000 km in diameter or it would be smeared out What causes the pulses The lighthouse effect strong jets of light are emitted at the north and south magnetic poles of a neutron star we see a pulse when the beam points at us Evolution of a pulsar Pulsars radiated their energy away quite rapidly the radiation weakens and stops in a few tens of millions of years making the neutron star virtually undetectable Pulsars won t be visible on Earth if their jets aren t pointing our way About 1500 pulsars are known but our galaxy should contain many more neutron stars some are just too old to be seen or their jets point in wrong direction for us to ever see them Pulsars are sometimes found in supernova remnants there is a pulsar at the center of the Crab Nebula Pulsars are also observed to pulse in the gammaray spectrum and at radio and visible wavelengths matter is accelerated to high energies by a pulsar s magnetic eld The Crab Nebula is close enough we can observe it in detail we can see ripples extending outward from the Crab pulsar at half the speed of light NeutronStar Binaries Bursts of Xrays have been observed from many objects in our galaxy Xray Bursts Xray bursts are thought to originate on neutron stars that have binary partners the process is similar to a nova occasional fusion areups However the gravitational field is much stronger around a neutron star so much more energy is released r radius is tiny in a neutron star compared to a white dwarf so the gravitational force is much bigger Gammaray Bursts Gammaray bursts have also been observed first spotted by satellites looking for violations of treaties banning aboveground nuclear tests that emit gamma rays For many years their existence was kept secret from astronomers At first gammaray bursts were thought to be higherenergy versions of Xray bursts However Xray bursts tend to lie in the plane of our galaxy gammaray bursts are spread uniformly over the sky This suggests they re far away from us in other galaxies Models for GammaRay Bursts Long GammaRay Bursts o A redgiant star collapses onto its core becoming so dense that it expels its outer layers in a supernova explosion o Hypernova star explodes at the end of its life 0 A black hole forms and exploded material forms an accretion disk gamma rays are released in a jet Short GammaRay Bursts less than 2 seconds 2 neutron stars merging 0 Stars in a compact binary system begin to spiral inward eventually colliding o The resulting torus has at its center a powerful black hole Black Holes The mass of a neutron star can t exceed about 3 solar masses if the core remnant is more massive than that nothing will stop its collapse and it will become smaller and smaller and denser and denser Eventually the gravitational force is so intense that even light can t escape the remnant has become a black hole The formation of a black hole 1 2 A supergiant star has relatively weak gravity so emitted photons travel in essentially straight lines As the star collapses into a neutron star the surface gravity becomes stronger and photons follow curved paths Continued collapse intensifies the surface gravity and so photons follow paths more sharply curved When the star shrinks past the critical size it becomes a black hole photons follow paths that curve back into the black hole so no light escapes When the star becomes a black hole not even photons emitted directly upward from the surface can escape they undergo an infinite gravitational redshift and disappear Schwarzschild radius the radius at which the escape speed from the black hole equals the speed of light 0 The Earth s Schwarzschild radius is about a centimeter the Sun s is about 3 km 0 Once the black hole has collapsed the Schwarzschild radius is also called the event horizon nothing within the event horizon can escape the black hole 0 The Schwarzschild radius or size of black hole is R 2GMcA2 o G gravitational constant c speed of light M mass of black hole Matter encountering a black hole will experience enormous tidal forces that will both heat it enough to radiate and tear it apart The human body can t withstand stress greater than 1020 g pull of gravity on Earth The breaking point would occur around 3000 km from a 10 solar mass black hole We can orbit a black hole a safe distance away but can t get too close Space Travel Near Black Holes The gravitational effects of a black hole are unnoticeable outside of a few Schwarzschild radii at this distance black holes don t suck in material any more than an extended mass would The orbit of an object near a black hole is basically the same as its orbit near a star of the same mass More on the Formation of a Black Hole 1 2 3 A black hole sharply curves the spacetime around it Far from the black hole spacetime is nearly flat close to the black hole the curvature forms a well that is in nitely deep Objects that venture too close to the black hold can t escape from the well Neither light nor anything else is able to escape the gravitational attraction of the crushed core In a sense a hole is punched in the fabric of the universe and the dying star seems to disappear into this cavity None of the star s mass is lost when it collapses to form a black hole and a black hole s gravitational in uence can still be felt by other objects How do you observe a black hole The Effects of Black Holes In binary systems the mass from one star may be captured by the black hole This material spirals into the black hole with so much speed that it emits X ray light Gases from the supergiant are captured into an accretion disk around the black hole As gases spiral toward the black hole they are heated by friction just outside the black hole they re hot enough to emit Xrays The Environment of an Accreting Black Hole If a black hole is rotating it can generate strong electric and magnetic elds in its immediate vicinity These fields draw material from the accretion disk around the black hole and accelerate it into oppositely directed jets along the black hole s rotation aXis Xrays from the hot disk excite iron atoms in the torus making them glow Fastmoving jets of subatomic particles are formed and ejected by electric and magnetic fields General Relativity and Gravity Matter tends to warp spacetime and in doing so redef1nes straight lines the path a light beam would take A black hole occurs when the indentation caused by the mass of the hole becomes inf1nitely deep 326 Tests of General Relativity Deflection of starlight by the sun s gravity was measured during the solar eclipse of 1919 the results agreed with the predictions of general relativity Another prediction the orbit of Mercury should precess due to general relativistic effects near the Sun again the measurement agreed with the prediction Gravity Waves Just as we detect electromagnetic waves when charges accelerate in a radio antenna or on a star general relativity predicts that accelerating masses should radiate gravity waves Orbiting objects should lose energy by emitting gravitational radiation the amount of energy is tiny and these waves haven t yet been observed directly However a neutronstar binary system has been observed the orbits of the star are slowing at just the rate predicted if gravity waves are carrying off the lost energy Laser Interferometric Gravitywave Observatory designed to detect gravitational waves no waves have been detected yet acts as a gravity wave telescope LISA laser interferometer space antenna Three antennae orbiting the Sun forming an equilateral triangle 5 million km apart it will be sensitive to waves from superrnassive black holes near centers of galaxies Chapter 13 Our Parent Galaxy The Milky Way From Earth we see few stars when looking out of our galaxy and many stars when looking in the Milky Way is what our galaxy looks like in the night sky The Milky Way is 30 kpc or 100000 ly across and contains 100 billion stars We determine our location in the Galaxy by observing globular clusters which form a spherical halo centered on the center of the Galaxy Measuring Distances in the Milky Way Cataclysmic variables variable stars novae supernovae Xray busts and related phenomena Intrinsic variables other stars whose luminosity varies in a regular way but much more subtly 0 RR Lyrae stars and Cepheids 2 types of intrinsic variables that are useful for determining distances to clusters and galaxies in which they reside Cepheid Variables Henrietta Leavitt discovered the periodluminosity relation for Cepheid variables The longer a Cepheid s period the greater its luminosity The periodluminosity law can be used to determine distances Knowing the star s periodicity you can nd out how far away the star must be to give the observed brightness inverse square law of radiation Found throughout the Galaxy Pulsation periods of l 50 days Average luminosity related to pulsation period The more luminous the Cepheid the longer its pulsation period RR Lyrae Variables Horizontalbranch stars that all have roughly the same average luminosity of about 100 L Found in globular clusters these clusters aren t all in the plane of the galaxy so they aren t obscured by dust and can be measured Pulsation periods less than a day All have about the same luminosity By using the periodluminosity relationship for these stars we can determine the distances to globular clusters The variability of Cepheid and RR Lyrae stars comes from a dynamic balance between gravity and pressure they have large oscillations around stability They get bigger and smaller as they try to adjust themselves to gravity and radiation pressure Galactic Structure Disk contains gas and dust along with metalrich Population 1 stars Halo composed almost exclusively of old metalpoor Population 11 stars Central bulge mixture of Population I and Population 11 stars Stellar orbits in the disk move in a plane and in the same direction orbits in the halo and bulge are much more random they all orbit the center of the Galaxy The Formation of the Milky Way The formation of the galaxy is believed to be similar to the formation of the solar system but on a much larger scale Globular clusters formed rst during the initial collapse of the Milky Way and remained in random orbits around the center The Mass of the Milky Way Galaxy The orbital speed of an object depends only on the amount of mass between it and the galactic center Total mass solar masses orbit size AUquot3 orbit period yearsquot2 The sun is 8 kpc from the center and takes 225 million years to orbit the Galaxy this gives the MWG a mass of at least 90 billion solar masses As in a binary star system if the size and period of the orbit are known the mass can be calculated As you move away from the visible galaxy the velocity should diminish with distance 0 It doesn t there must be much more mass outside the visible part to reproduce the observed curve This means that there s much more mass than we can see this was observed in other galaxies as well and is evidence for dark matter in the Universe The measured speed implies that the Milky Way s mass is 600 billion The Galaxy and its Dark Matter Halo The dark matter in our Galaxy forms a spherical halo whose center is at the center of the visible Galaxy The extent of the dark matter halo is unknown but its diameter is at least 100 kpc The total mass of the dark matter halo is at least 10 times the combined mass of all the stars dust gas and planets in the Milky Way What could this dark matter be It s dark at all wavelengths not just the visible Stellarmass black holes Not enough of them could ve been created Brown faint whitered dwarfs Currently the best starlike option but not enough could ve been formed Weird subatomic particles Could be although no direct evidence so far Dark Matter Speculations MACHOS Massive Compact Halo Objects 0 Brown dwarfs white dwarfs black holes 0 Can only account for about half of the dark matter halo 0 Searched for via gravitational lensing WIMPS Weakly Interacting Massive Particles 0 Theoretical and notyetdetected More evidence for dark matter Galaxies in clusters are moving faster than can be explained by the observable mass At the speed they re moving they should ve escaped the gravitational pull of the cluster And much more mass than we can see is responsible for bending the light from background objects A galaxy must be surrounded by an invisible halo of dark matter 85 of matter in the Universe is dark The nature of dark matter remains one of the biggest unsolved problems in modern astrophysics Infrared and Radio Observations of the Galactic Nucleus In an infrared image the reddish band is dust in the plane of the Galaxy and the fainter bluish blobs are interstellar clouds heated by young 0 and B stars Adaptive optics reveal stars densely packed around the galactic center The galactic center appears to have A stellar density a million times higher than near the Sun A ring of molecular gas 400 pc across Strong magnetic fields A rotating ring or disk of matter a few parsecs across A strong Xray source at the center Apparently there is an enormous black hole at the center of the galaxy which is the source of these phenomena it s called Sagittarius A An accretion disk surrounding the black hole emits enormous amounts of radiation
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