Lecture 22 <a href="/keyword/neutron-star/" >neutron star</a> s Black Holes Galaxies TA office hours after class today: Q. 1-2 : AB221 Q. 3-4 : MP1203A (and pickup) Q. 5-6 : MP 1416 Tutorial/Help sessions: Thurs. 6th , Thurs. 11th , Mon.15th all in Koffler KP108, 4-5pm. <a href="/keyword/neutron-star/" >neutron star</a> s Theory: Collapse of a Massive Star 1. A hypothesis worked out in the 1930s predicted that after the mass of a star s core increased beyond the Chandrasekhar limit, the star will collapse further and its electrons and protons will combine to form neutrons. 2. A <a href="/keyword/neutron-star/" >neutron star</a> is a star that has collapsed to the point at which it is supported by neutron degeneracy. Theory: Collapse of a Massive Star (cont.) 3. The diameter of a typical <a href="/keyword/neutron-star/" >neutron star</a> is only 0.2% of the diameter of a white dwarf and the <a href="/keyword/neutron-star/" >neutron star</a> is a billion times denser than a white dwarf. 4. <a href="/keyword/neutron-star/" >neutron star</a> s have masses between 1.4 and about 3.2 <a href="/keyword/solar-masses/" >solar masses</a> . The mass of a typical <a href="/keyword/neutron-star/" >neutron star</a> is 1.5 <a href="/keyword/solar-masses/" >solar masses</a> , its diameter is 20 km (width of small city), its density is 1015 g/cm3, and its temperature is 10,000,000 K. Observation: The Discovery of Pulsars 1. In 1967 Jocelyn Bell discovered an unknown source of rapidly pulsating radio waves. Subsequent discoveries of similar sources gave rise to the name pulsar. 2. A pulsar is a pulsating radio source with a regular period (between a millisecond and a few seconds) believed to be associated with a rapidly rotating <a href="/keyword/neutron-star/" >neutron star</a> . Discovery of pulsars: radio signal intensity Observation: The Discovery of Pulsars (cont.) 3. The first few pulsars discovered had pulse duration of about 0.001 second. Objects that emit pulsing signals with such duration cannot have a diameter any greater than 0.001 light-seconds, which is 300 kilometers. 4. Such a small size ruled out white dwarfs (Earth-sized objects), leaving the hypothesized <a href="/keyword/neutron-star/" >neutron star</a> as the explanation for pulsars. Illustration of light-time effect due to size of object Observation: The Crab Pulsar and Others 1. A few months after the discovery of the first pulsar, a pulsar was discovered in the Crab Nebula with a period of 0.033 second (i.e., it blinks 30 times a second). 2. The Crab pulsar emits radiation in all parts of the spectrum, from radio waves to X-rays. Its total energy output is more than 100,000 times that of the Sun. Fig. 15-15a Moderately <a href="/keyword/massive-stars/" >massive stars</a> Conclusion 1. We know that <a href="/keyword/neutron-star/" >neutron star</a> s have masses more than 1.4 <a href="/keyword/solar-masses/" >solar masses</a> but we can only estimate that the upper limit is between 2 and 4 <a href="/keyword/solar-masses/" >solar masses</a> . 2. The evolution of a moderately massive star takes it through the steps shown in Fig. 15-18 on the right. Fig. 15-18 + The Fate of Very <a href="/keyword/massive-stars/" >massive stars</a> 1. Very <a href="/keyword/massive-stars/" >massive stars</a> differ from moderately <a href="/keyword/massive-stars/" >massive stars</a> primarily in what happens to them when their core is compressed to a density greater than electron degeneracy can support. In a moderately massive star, the resulting supernova leaves a <a href="/keyword/neutron-star/" >neutron star</a> . In a very massive star, the core becomes a black hole. Black Holes 1. Neutron degeneracy cannot support a <a href="/keyword/neutron-star/" >neutron star</a> whose mass is greater than about 3 <a href="/keyword/solar-masses/" >solar masses</a> . Such a star will collapse and become a black hole. 2. The Schwarzschild radius (RS) is the radius of a sphere around a black hole (of mass M) from within which no light can escape. 3. The size of the Schwarzschild radius depends only on the mass of the star: RS = 3M (where RS is in kilometers and M in <a href="/keyword/solar-masses/" >solar masses</a> ). Black Holes (cont.) 4. A black hole is an object whose escape velocity exceeds the speed of light and therefore whose radius is less than the Schwarzschild radius. 5. An event horizon is the surface of the sphere around a black hole from which nothing can escape. Its radius is the Schwarzschild radius. Black Holes (cont.) 6. As far as we know, once a star collapses inside its event horizon, nothing can stop the star from collapsing to a single point of infinite density. This point, at the center of the black hole, is called the singularity. 7. At the singularity, time and space do not exist as separate entities. Random things can happen here but do not affect the world outside the event horizon. Properties of Black Holes 1. A black hole can be described by three numbers: mass electric charge angular momentum 2. The mass of a black hole can be measured using Kepler s third law. The electric charge of a black hole can also be measured, but is not considered in discussing black holes since they quickly become neutral through accretion. Question The Sun will: A) slowly contract from its present size and become a white dwarf B) expand, swallow the earth and eject its outer envelope C) explode as a nova D) explode as a supernova Question The Sun will: A) slowly contract from its present size and become a white dwarf B) expand, swallow the earth and eject its outer envelope C) explode as a nova D) explode as a supernova Detecting Black Holes 1. In a binary system of a black hole and a red giant (or supergiant), material will be pulled from the giant and will swirl around the black hole, causing X-rays to be released from the heated material in the disk. This is one way to detect a black hole. 2. If an X-ray source is associated with a massive star, then we can hope it is a black hole. Cygnus X-1 was the first candidate for a black hole. Very large radial velocity amplitude of companion to a black hole candidate. Radial velocity curve of the O supergiant in the system Cyg X-1, observed by Bolton &amp; Gies at DDO, Richmond Hill. First shown to be a BH candidate by Bolton at DDO in 1972. A Model of Cyg X-1: Matter is transferred from the O supergiant and forms an accretion ring, which feeds matter into the black hole. Material leaves O star here, emits lines Detecting Black Holes 3. Black hole candidates have been observed to have masses that span the entire spectrum of allowed masses, from just above the minimum 3 <a href="/keyword/solar-masses/" >solar masses</a> or so to billions of <a href="/keyword/solar-masses/" >solar masses</a> at the cores of galaxies. 4. We can distinguish between black hole candidates and <a href="/keyword/neutron-star/" >neutron star</a> s by studying the X-ray emissions that result from accretion. Our Galaxy 1. The Milky Way Galaxy is the galaxy of which the Sun is a part. From Earth, it appears as a band of light around the sky. 2. About 200 billion stars make up the Milky Way Galaxy. 3. Most stars in the Galaxy are arranged in a wheelshaped disk that circles around a bulging center. 4. The diameter of the Galaxy is about 50,000 parsecs (160,000 light-years). 5. The Sun and our solar system is about a third of the way out from the Galaxy s center (8000 pc or 26,000 lightyears). Fig. 16-2 6. Interstellar dust and gas in our Galaxy prevented the Herschels (who measured the number of stars along different directions in the 1780s) and Kapteyn (who measured the number and distance of stars along different directions in the early part of the 20th century) from getting accurate star density counts from visual observations. These inaccurate data led them to the mistaken conclusion that the Earth is near the center of the Galaxy. The Herschels' Universe (c. 1780) SUN <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> 1. A <a href="/keyword/globular-cluster/" >globular cluster</a> is a spherical group of up to hundreds of thousands of stars, found primarily in the halo of the Galaxy. Fig. 16-8 The central region of the <a href="/keyword/globular-cluster/" >globular cluster</a> M15. <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> (cont.) 2. The average separation of stars near the center of a <a href="/keyword/globular-cluster/" >globular cluster</a> is 0.5 light-year. Stars in the region of the Sun average 4 5 light-years apart. 3. Shapley (1910's) attempted to determine the Sun s location in the Galaxy using <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> . In order to determine the distance to these clusters, he used Leavitt s discovery of the Cepheid variables period-luminosity relationship and the absolute magnitude of the RR Lyrae stars. (Note: RR Lyrae stars are giants with core helium burning, unlike the supergiant Cepheids). Obtaining distances using Cepheids and RR Lyrae variables. (RR Lyrae stars all have the same absolute magnitude) + RR Lyr abs. Mag <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> (cont.) 4. Shapley showed in 1917 that <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> are distributed around the sky, centred about a point 50,000 light-years from the Sun. His discovery also showed that the Galaxy is larger than the Herschels had imagined. 5. In the 1920s, Oort and Lindblad studied the motions of great number of stars near the Sun and found that there is a pattern in these velocities. They concluded that the center of the Galaxy is thousands of light-years away in the direction of Sagittarius. <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> (cont.) 6. In 1930, the interstellar dust was discovered, resolving the conflict between the discoveries of Shapley, Oort, and Lindblad and the star counts of Herschel and Kapteyn. The dust absorbed light in the disk, and we had not been able to see far enough in the disk to detect that we are far from the Galactic Centre. Shapley's distribution of <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> ==&gt; this model The Herschels' model of the Galaxy Nuclear Bulge Components of the Galaxy 1. The Galaxy contains four components: the disk (which contains the Sun), the nuclear bulge, the halo, and the galactic corona (outer halo). Fig. 16-11 2. The disk is the large, flat part of the Galaxy that rotates in a plane around the nucleus. The disk contains stars and most of the gas and dust in the Galaxy It is about 1,000 parsecs thick. 3. Almost all O-type stars lie within about 100 parsecs of the galactic plane. The disk appears bluish because of the presence of the hot O and B main sequence stars. 4. The nuclear bulge is the central region of the Galaxy. It is about 2000 parsecs in diameter. It contains both young and old stars and appears reddish because of the presence of many red giants and supergiants. 5. The Galactic halo is the outermost part of the Galaxy. It is fairly spherical in shape and lies beyond the spiral component. The outer halo is sometimes called the Galactic corona and may contain large amounts of unseen matter. 6. Milky Way properties: Radius of disk = 80,000 light-years Radius of nuclear bulge = 3000 light-years Total radius of halo = 200,000 light-years Sun s distance from center = 26,000 light-years Sun s orbital period = 250,000,000 years Thickness of disk = 3000 light-years Number of stars = 200 to 400 billion Galactic Motions 1. If we assume that the average velocity of all <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> , relative to the Galactic center, is zero, then we can use the Doppler effect to measure the velocities of the <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> relative to the Sun and attribute the average motion that is observed to the motion of the Sun. 2. The Sun is traveling in a nearly circular path around the Galactic center at a speed of about 220 km/s. 3. With the radius of the Sun s orbit equal to 8,000 parsecs, the Sun takes about 230 million years to complete one revolution around the center of the Galaxy. Motions of the <a href="/keyword/globular-clusters/" ><a href="/keyword/globular-cluster/" >globular cluster</a> s</a> Galactic Motions (cont.) 4. The galactic rotation curve is a graph of the orbital speed of objects in the galactic disk as a function of their distance from the center. 5. A galactic rotation curve for our Galaxy indicates that large amounts of unseen mass orbit the center far beyond the Sun s orbit. If all mass were what we could see, tis would be the rotation curve. The observed rotation curve: a lot of unseen mass at large radii. Fig. 16-13 The Mass of the Galaxy 1. Oort and Lindblad discovered in 1927 that the Galaxy in the Sun s neighborhood undergoes differential rotation. This allows the use of Kepler s third law (as we studied earlier) to find the mass of the Galaxy inside the Sun s orbit. 2. The mass of the inner Galaxy is estimated at 100 billion <a href="/keyword/solar-masses/" >solar masses</a> . Recent analysis of the rotation patterns in the outer parts of the Galaxy indicates that the total mass of the Galaxy is about 1012 <a href="/keyword/solar-masses/" >solar masses</a> (10 times more mass than calculated for the inner Galaxy). The Mystery of the Spiral Nebulae Leading into the 1920's, a great debate developed regarding the nature of spiral nebulae , such as the great nebula M31 in Andromeda. The Great Debate: April 1920, Shapley argued for nearby objects, Curtis for distant island universes Were such objects in our own (newly mapped) Milky Way, or were they much more distant Island Universes separate from and resembling our Milky Way Galaxy? Van Maanen made some erroneous observations suggesting that the proper motions due to their rotation could be seen, suggesting they were nearby. The issue was resolved by Hubble (1923) when he found Cepheids in M31 and thus obtained a distance &gt;&gt; our Galaxy. The Hubble Classification 1. In 1924, Hubble found Cepheid variables in three spiral nebulae, showing they were actually <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> . The evidence galaxies existed outside the Milky Way expanded our appreciation of the size of the universe. 2. Hubble divided galaxies into three basic types: spiral, elliptical, and irregular. Each major classification contains subdivisions. 3. An elliptical galaxy is one of a class of galaxies that have smooth spheroidal shapes. An irregular galaxy is a galaxy of irregular shape that cannot be classified as spiral or elliptical. Fig. 17-1 <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> Fig. 17-2c 1. Hubble divided <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> into two groups: ordinary spirals and barred spirals. 2. Ordinary spirals are designated with an S; barred spirals are designated with an SB. 3. A barred <a href="/keyword/spiral-galaxy/" >spiral galaxy</a> is a <a href="/keyword/spiral-galaxy/" >spiral galaxy</a> in which the spiral arms come from the ends of a bar through the nucleus rather than from the nucleus itself. <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> (cont.) 4. Each type of <a href="/keyword/spiral-galaxy/" >spiral galaxy</a> is then further subdivided into categories a, b, c, depending on how tightly the spiral arms are wound around the nucleus. Galaxies with the most tightly wound arms are type a; they also have the most prominent nuclear bulges. 5. Up to 2/3 of all spirals contain bars. The bar system provides an efficient mechanism for fueling star birth at the center of an SB galaxy. <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> (cont.) 6. Galaxies that seem to have the nuclear bulge and disk of a spiral, but no arms, are called S0. 7. Type c spirals contain more gas and dust than type a, resulting in a larger proportion of their mass being involved in star formation. 8. Most <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> are from 50,000 to 2,000,000 million light-years across and contain from 109 to 1012 stars. 1. Elliptical galaxies are ellipsoids; they are classified from round (E0) to very elongated (E7). 2. Most of the galaxies in existence are ellipticals, but most of these are smaller than <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> . 3. A few giant elliptical galaxies have 2 1013 stars and are thus larger than any <a href="/keyword/spiral-galaxy/" >spiral galaxy</a> . Elliptical Galaxies Centaurus A. Marina Rejkuba (ESO-Garching) et al., ISAAC, VLT ANTU telescope, ESO Paranal Obs Irregular Galaxies 1. Fewer than 20% of all galaxies fall in the category of irregulars, and they are all small, normally having fewer than 25% of the number of stars in the Milky Way. 2. Collisions between galaxies are not unusual because on average galaxies are separated by distances only about 20 times their diameter. On the other hand, stars in a galaxy rarely collide since they are separated by distances that are millions of time their diameter. Irregular Galaxies (cont.) 3. Because of their great distances, galaxies exhibit no proper motion. Evidence of past collisions has to come from present appearance. 4. Computer simulations show that colliding galaxies actually pass through one another with few collisions between individual stars. However, the large dust and gas clouds in the galaxies make them more likely targets, resulting in increased star formation rates. Fig. 17-6a Fig. 17-6c Irregular Galaxies (cont.) 5. Bursts of star formation may also occur as a result of tidal interactions among neighboring galaxies. 6. Galactic cannibalism often occurs as a result of collisions. Hubble s Tuning Fork Diagram 1. Hubble s tuning fork diagram relates the various types of galaxies. In his plan, S0 galaxies form the connecting link, because they have characteristics of both elliptical and <a href="/keyword/spiral-galaxies/" >spiral galaxies</a> . 2. Astronomers once also thought the diagram represented an evolutionary sequence, but this interpretation has been discarded as old stars have been found in all three types. Hubble s Tuning Fork Diagram Fig. 17-7 Readings for Lecture 23 COSMOLOGY! Sections 17-2, 17-4 Sections 18-1, 18-2, 18-3, 18-4, 18-5, 18-6, 18-7