Astronomy Exam 3 Study Guide PDF

CHAPTER 24: Black Holes Concept of escape speed The distance at which the escape speed from the black hole equals the speed of light is called the Schwarzschild radius. The Schwarzschild radius is also called the event horizon - the distance from the center of a black hole at wh...

CHAPTER 24: Black Holes Concept of escape speed The distance at which the escape speed from the black hole equals the speed of light is called the Schwarzschild radius. The Schwarzschild radius is also called the event horizon - the distance from the center of a black hole at which the escape velocity becomes equal to the speed of light. ○ Nothing within the event horizon can escape the black hole, including light. ○ Anything outside the event horizon is still able to escape the black hole’s gravity if it goes fast enough The escape speed from the surface of the Earth is 11.2 km/s. Need horizontal velocity to put things in orbit. Depends on the speed. Less speed = less gravity. This speed depends on the mass of the Earth and the distance of the rocket (or any other object) from the Earth’s center The larger the mass of the massive object, the higher the speed needed to escape its gravity. The larger the distance from the center of the massive object, the lower the speed needed to escape its gravity. Light can not escape the black hole past 300,000 km/s. Black Holes – masses, radii (Schwarzschild radius, event horizon): Only the most massive stars (greater than ~25 solar masses on the main sequence) form black holes. ○ The cores of these stars are greater than ~3 solar masses, too massive for neutron degeneracy pressure or any other force to support them against gravity. After a Type II supernova, the cores of these massive stars collapse to smaller and smaller sizes due to gravity. Eventually the size approaches zero and the density becomes infinitely large. This is called a singularity. Stellar black holes are between about 3 and 100 solar masses and form from a single star. Supermassive black holes are between 1 million and 1 billion solar masses. How do we detect black holes? Examples of ‘observed’ black holes – Cygnus X-1, SS 433 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. The object Cygnus X-1 is thought to be a black hole binary. The compact star is 15 MSun and the blue supergiant is 20 MSun. They orbit each other in 5.6 days. 1. Gasses from the supergiant are captured in an accretion disk around the black hole. 2. As glasses spiral toward the black hole, they are heated by friction; just outside the black hole, they are hot enough to emit x-rays.  3. Can see the effect of a black hole on matter around it General relativity – what does it describe? understanding of how gravity affects the fabric of space-time. Mass and energy "bend" spacetime, and objects move along the curved paths created by this distortion. In essence, objects are not being "pulled" by gravity; they are following the curved geometry of spacetime. Equivalence principle This principle states that the effects of gravity are indistinguishable from the effects of acceleration. For example, a person inside a sealed, accelerating spaceship cannot tell the difference between the force of gravity and the force caused by acceleration. The 5 observational tests of general relativity 1. 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. 2. We observe gravitational lenses in the Universe. ○ The “Einstein Cross” ○ The foreground galaxy is in the center. The others are 4 images of the same quasar that is, in reality, behind the galaxy and much farther away. The quasar images are also brighter than if there was no lens. ○ This gravitational lensing can displace and distort an object’s image. ○ More distant galaxies can be imaged by closer ones and show up as an Einstein ring around the nearer galaxy 3. Another prediction—the orbit of Mercury should process due to general relativistic effects near the Sun; again, the measurement agreed with the prediction ○ Prior to Einstein’s GR, it was a mystery as to why Mercury’s orbit precessed. 4. Gravitational Redshifts ○ Light escaping from near a black hole will use up energy getting out; hence its wavelength gets longer. Objects near black holes look redder than they are. 5. Gravity waves ○ Light escaping from near a black hole will use up energy getting out; hence its wavelength gets longer. Objects near black holes look redder than they are. CHAPTER 25: The Milky Way How big is it? How many stars are in it? Where is the Sun? The MW is 30 kpc or 100,000 ly across Contains 100 billion stars The sun is located in the galactic disk of the Milky Way galaxy. We are situated in a spiral arm of the disk known as the Orion Spur. The milky way is a barred spiral Distance measures: Cepheids and RR Lyrae stars – Period-Luminosity (can determine distance) relation They are extremely useful for determining distances to star clusters and galaxies in which they reside. Cepheids: ○ Found throughout galaxy ○ Average luminosity related to pulsation period ○ The longer a Cepheid’s period, the greater its luminosity. ○ The more luminous the Cepheid, the longer its pulsation period. RR Lyrae stars: ○ Found in globular cluster ○ Pulsation periods less than a day ○ All have about the same luminosity ○ 100 average Luminosity ○ Horizontal-branch stars Galactic structure – what are the components of the Milky Way? The disk contains gas and dust along with metal-rich stars. Metal rich = anything that has an atomic number more than helium. Metal rich forms more recently means it formed from a cloud that had the metals in it already. The halo is composed almost exclusively of old, metal-poor stars. Halo = globular clusters. older stars with less metals. No gas in halo. Formed a long time ago when the material they formed from was not enriched. Halo formed first and then disk formed later. The central bulge is a mixture of both types of stars Compare and contrast open and globular clusters The processes that formed these two types of clusters must have been very different. Globular = old, halo, metal poor Open = young, disk, metal rich Compare the Galactic Halo with the Galactic Disk Halo stars and disk stars differ in their orbits and ages. Halo stars take highly elliptical orbits around the galaxy's center, frequently far above or below the galaxy's disk, and are generally older. Disk stars orbit in nearly the same plane in the disk of the galaxy and are typically younger. Milky Way mass and rotation curve – evidence for dark matter The orbital speed of an object depends only on the amount of mass between it and the galactic center  a3/p2 As you move away from the visible galaxy, the velocity should diminish with distance, as the dashed curve shows It doesn’t; there must be much more mass outside the visible part to keep the outermost gas and stars moving with such high speeds End of visible disk Speed of outermost gas should decrease, but it doesn’t. The measured speed implies that the Milky Way’s mass is 1.5 x 1012 Msun (1.5 trillion)! This means that there is much more mass than we can ‘see’. This is observed in other galaxies as well, and is evidence for “dark matter” in the Universe. This is what we expect for the gas that’s out that far. Long String with a stone at the end. Keep it spinning. Rotation curves of other galaxies – more evidence for dark matter They remain flat as well, to distances far beyond their observable disks. They must have a substantial halo of dark matter. Rotation curves of other galaxies and the Milky Way. Can't take the spectrum of dark matter because you do not see it. Know its there because of its gravitational influence and based on what we can see. Normal matter is gravitational affected by dark matter. Gravitational lenses and cluster velocities – even more evidence for dark matter Galactic center, Sgr A*evidence for black holes. Mass of black hole – 4 million solar masses. The Milky Way’s future – collision with the Andromeda Galaxy Galactic center: ○ 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 O and B stars. ○ Adaptive optics reveal stars densely packed around the galactic center. ○ 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 X-ray source at the center Sgr A: ○ Apparently, there is an enormous black hole at the center of the galaxy, which is the source of these phenomena. It is called Sagittarius A* (Sgr A*). An accretion disk surrounding the black hole emits enormous amounts of radiation. These objects are very close to the galactic center. The orbit on the right is the best fit. It implies a central black hole mass of about 4 million solar masses, and a Schwarzschild radius of 0.1 AU Chapter 26, 27: Galaxies Classification of galaxies The Hubble Tuning Fork Diagram Spirals, Barred Spirals, Ellipticals, S0s, Irregulars – properties Spiral: ○ Hubble classified spiral galaxies according to the texture of their spiral arms and the relative size of their central bulges. Sa galaxies have smooth, broad spiral arms and the largest central bulges. Sc galaxies have narrow, well-defined arms and the smallest central bulges. ○ The components of all spiral galaxies are the same as in our own galaxy: disk, halo, bulge, and spiral arms. Kk ○ All spiral galaxies rotate fast and have a significant amount of gas. Have old and young stars Barred Spiral Galaxies: ○ As with spiral galaxies, Hubble classified barred spirals according to the texture of their spiral arms. Barred spirals are so named because the bulge has a bar going through it, and the spiral arms originate from the ends of the bar. SBa galaxies have the smoothest spiral arms and the largest central bulges. SBc galaxies have narrow, well-defined arms and the smallest central bulges. The Milky Way is a SBbc type galaxy. They also rotate fast and have a lot of gas  S0s; ○ Hubble classified elliptical galaxies according to how round or flattened they look. ○ A galaxy that appears round is labeled E0, and the flattest appearing elliptical galaxies are designated E7. ○ They show little or no rotation and have no gas. ○ The stars have randomly oriented orbits around the center of the galaxy. ○ Their reddish colors are due to the predominance of old red stars. ○ No gas, no rotation, no star formation. Do not rotate or spin like a disk but have random rotation around the center. Mostly red. Look red because they are old stars. Irregulars: ○ Irregular galaxies tend to be small and forming new stars rapidly; they have a wide variety of disorganized shapes. The Small and Large Magellanic Clouds are the largest close neighbors to our own Milky Way ○ Irregular galaxies show no rotation and have significant amounts of gas. Tend to be small and forming new stars rapidly. Have a lot of gas, dust, star formation. They are small and have no significant rotation so you can not give them shape. They have a wide variety of shapes. Active Galaxies and Quasars - properties: Active Galaxies ○ The radiation from these galaxies is called non-stellar radiation because most of their light does not come from stars. ○ Active galactic nuclei (AGN) are unusual because their luminosity is dominated by activity in and around the galactic center. ○ Radio galaxies emit very strongly in the radio portion of the spectrum. They may have enormous lobes, invisible to optical telescopes, perpendicular to the plane of the galaxy. ○ Two galaxies that collide spin around a massive black hole. Creates jets ○ Active galaxies have some or all of the following properties: high luminosity non-stellar energy emission variable energy output, indicating a small nucleus jets and other signs of explosive activity broad emission lines, indicating rapid rotation Quasars:  ○ Quasars – “quasi-stellar radio sources” are star-like in appearance but have very unusual spectral lines. They used to be called radio stars prior to 1963 ○ It was realized that quasar spectra were normal, but enormously redshifted. Here is the recent HST image of 3C 273 on the left and its 1963 discovery spectrum on the right. This quasar has a jet ○ The bright source is the quasar – they live in the centers of galaxies that often show evidence for mergers. Quasars are the most energetic of active galaxies. ○ a supermassive black hole in the center of a distant galaxy, where matter forms a rapidly rotating accretion disk as it falls in towards the black hole, emitting tremendous amounts of energy Chapter 28: The Large Scale Structure of the Universe Distance measures – Cepheids: Cepheid variables allow measurement of galaxy distances to about 25 Mpc away. Cepheids are called “standard candles”. These are objects whose known intrinsic characteristics can be used to determine distances. Here’s an example: M101 This star varies by a factor of two in brightness every 7 weeks. Recall that the period –luminosity relation of Cepheids gives the galaxy’s distance. This star varies by a factor of two in brightness every 7 weeks. Recall that the period –luminosity relation of Cepheids gives the galaxy’s distance. Type Ia Supernovae: Supernovae are extremely bright, outshining the entire galaxy of stars in which they reside. easily detected, but very rare, occurring only about once every 50 years in our galaxy. very uniform in brightness at maximum light. They can be used as a STANDARD CANDLE. Since we know their intrinsic brightness, we can determine their distance as long as we can see them! Inverse square law at work again! Distance ladder: With these additions, the cosmic distance ladder can be extended to about  1 Gpc (gigaparsec – a billion parsecs – 10 9 pc) ‘Spectroscopic Parallax’ is a distance determination using the Main Sequence spectral type of a star. Its luminosity can be read off the HR diagram and its distance can be determined. We will not discuss the Tully-Fisher method Redshift and Hubble’s Law: Universal recession: all galaxies (with nearby exceptions * ) seem to be moving away from us. The redshift of their motion is correlated with their distance. * M31 and the Virgo cluster are blue shifted Calcium absorption is red shifted. If you can see a shift, you can measure how fast it is moving. Red shifted = moving away from us. Redshift z = v/c ○ Change in wavelength = doppler shift Measure speed of objects This plot shows the relation between distance and recession velocity for the five galaxies in the figure on slide 8. The larger the distance, the larger the velocity of the galaxy. This is Hubble’s Law ○ 𝐻0 ≈ 70 km/s/Mpc Father away a galaxy is from us, the faster it is moving If velocity is small, then the distance is small. Velocity is portion to distance. High redshift = farther away. Low redshift galaxies are close to us. Local Group (Milky Way, Andromeda + satellites):: This is the Local Group of galaxies, about 54 galaxies within about 1 Mpc of the Milky Way. There are three spirals in this group—the Milky Way, Andromeda (M31), and M33. These and their satellites—about 54 galaxies in all—form the Local Group. Such a group of galaxies, held together by its own gravity, is called a galaxy Cluster. Dust in the plane of the Galactic disk obscures any additional dwarf galaxies that may be behind it. (You can learn more about the Local Group in the video linked on slide 2.) Virgo cluster, Local Supercluster, Coma cluster, superclusters: Virgo ○ The nearest rich galaxy cluster. It is much larger than the Local Group, containing more than 2000 galaxies. The Virgo Cluster spans over 10 degrees in the sky! Its diameter is about 3 Mpc Local Supercluster  ○ Clusters of galaxies are themselves grouped together in huge associations called superclusters. ○ A typical supercluster contains dozens of individual clusters spread over a region of space up to 150 million ly across (~50 Mpc). ○ Clusters of galaxies cluster to form superclusters. ○ The Local Supercluster spans about 50 Mpc and contains several tens of thousands of galaxies. Coma cluster ○ 100 Mpc away. Galaxies arranged in filamentary structures and voids The Hubble Deep Field an 11-day HST exposure of a narrow pencil beam of sky. There are 10,000 galaxies in this image. This small pinpoint of the Universe reveals the evolution of galaxies, like an ice core. We see evidence for the assembly of galaxies in deep images of the Universe like the Hubble Deep Field The Hubble Deep Field, along with other deep Hubble images, provides a snapshot through time, which can be used to search for distant elliptical galaxies, or primeval galaxies that might later evolve into elliptical galaxies. The farther away the object, the younger it appears in Hubble's gaze. The Deep Field was like a core sample of space, showing galaxies at different and earlier stages of development the deeper they appeared in the image Assembly of galaxies and galaxy formation – dark matter halos Just as stars form around gravitational instabilities in molecular clouds, galaxies formed around gravitational instabilities in the universe. Dwarf galaxies formed first, with larger galaxies, clusters, superclusters, and filaments forming later in a process called hierarchical clustering. For this to have happened, the universe must not have been entirely uniform, but must have had denser regions, which were amplified over time by gravity. The density variations in the early Universe (from normal matter) are not great enough for larger structures to form. Dark matter (not made up of neutrons and protons) must provide the clumpiness in the universe for structures to form around. Forming a Galaxy Dark matter collapses first to form clumps. Dark matter can only collapse so far because it cannot lose the energy that keeps it from collapsing more. Dark matter halos are therefore larger than galaxies. The gravitational pull of dark matter clumps pulls in normal matter, which can radiate more energy and collapse further. Normal matter loses energy through radiation and collapses to the center of the clump, forming stars and galaxies. Dwarf galaxies merge to form larger galaxies Simulations reproduce observed structure Simulations Reproduce Structure: Simulations with only certain combinations of mass, CMB variations, types of dark matter, dark matter halos, and values for the dark energy produce structures like we observe in the Sloan Digital Sky Survey (SDSS). The fact that simulations match the data so well gives us some confidence in our models. Chapter 29: Cosmology and the Universe The Cosmological Principle: Universe is homogeneous and isotropic Cosmological principle: the physical laws and the properties of the universe are the same everywhere (homogeneous) and in all directions (isotropic) The cosmological principle is true only on large scales Same in all directions: isotropic Same as observer 1: homogeneous The expanding Universe –what the Hubble Law means The farther away a galaxy is, the faster it is moving away from us Measuring the redshift of a galaxy gives its recession velocity, which in turn through Hubble’s Law, gives its distance. REDSHIFT is now a proxy for DISTANCE. “High redshift” means “very far away”. The 4 main pieces of evidence for the Big Bang theory: Cosmological Redshifts of Galaxies Cosmic Microwave Background radiation Formation of large scale structure in the Universe Abundances of hydrogen and helium Our Universe – has no center and no edge Cosmological redshift A light wave traveling through an expanding universe “stretches,” that is, its wavelength increases. A redshift caused by the expansion of the universe is properly called a “cosmological redshift.” Doppler shifts are caused by an object’s motion through space, whereas a cosmological redshift is caused by the expansion of space. The redshift tells us how much the universe has expanded since a galaxy’s light was emitted. The scale factor (R U) is a measure of how much the universe has expanded Motion of space = cosmological redshift The Cosmic Microwave Background; its temperature now As the universe expands from a hot, dense point, the temperature of spacetime decreases. That temperature today is about 3º K. What is the CMB? Era of recombination? The radiation from this temperature is all around us, and is called the cosmic microwave background. They concluded that, if the Big Bang occurred, this radiation should be permeating the universe and should be detectable with a microwave antenna. Instead, it was the cosmic microwave background radiation - very strong evidence that the Big Bang really happened. The cosmic background radiation consists of photons from when the universe was about 400,000 years old. This is called the Era of Recombination: Before recombination: ○ Temperatures were so high that electrons and protons could not combine to form hydrogen atoms. ○ The universe could not combine to form hydrogen atoms ○ The universe is opaque: Photons underwent frequent collisions with electrons ○ Matter and radiation were at the same temperature After recombination: ○ Temperatures become low enough for hydrogen atoms to form  ○ The universe becomes transparent: Collins between photons and atoms become infrequent ○ Matter and radiation were no longer the same temperature Origin of structure in the Universe (galaxies formation, distribution) The magnitude of these temperature variations is tiny – about 1 part in 100,000. These variations in temperature indicate that the density of the early universe was slightly different from place to place - the seeds of structure were indeed present when the microwave background was released This is a temperature variation map of the sky taken with the Planck satellite at 0.07 o resolution. Galaxies form in the denser, red, regions. Voids form from in less dense, blue, regions Gravity starts making the slightly over-dense regions a little more dense … Those 1 part in 100,000 deviations from perfect uniformity allow gravity to form galaxies in the large, lacey, filamentary structures that we see today. Abundance of hydrogen, helium, deuterium Everywhere in the universe, about 25% of the mass of ordinary matter (not dark matter) is helium. No object has a helium fraction lower than 25%. The helium must have been present in the clouds that preceded the formation of stars and galaxies. The universe must have once been hot enough to fuse hydrogen into helium, just like what happens in the Sun. The Big Bang Theory predicts a He fraction of 25%. The Universe cooled too quickly for heavier elements to form Fate of the universe – Cosmology and GRT The universe is expanding now. Future expansion could be faster or slower. Expansion could halt and reverse. Fate depends on how much matter there is in the universe. Gravity from ordinary and dark matter slows the expansion. The Universe may or may not be able to 'escape' from its own gravity Critical density of the Universe Critical density is the density needed to almost slow the universe to a stop, but not reverse it. We call the maximum density the Universe could have without eventually re-collapsing the critical density. Matter is 30% of critical density How Type 1a supernovae are used to show presence of dark energy Expansion is speeding up today in the universe. Distance and velocity. What does dark energy do? Dark energy - some force that is pushing galaxies faster apart today. Causing the Universe to accelerate now. The repulsive effect of this dark energy increases as the Universe expands. As more space is created, more dark energy and its repulsive effect is entering the Universe, causing space to expand faster. And the force of gravity, that counters the expansion, weekends. The Universe will therefore expand forever. H0 is the current rate of expansion. The rate was smaller in the past and is going to get larger in the future. Summary of what we know about the Universe – age and content The Universe is ~13.7 billion years old. The CMB is from ~400,000 years after the Big Bang. First stars ignited ~400 million years after the Big Bang. Content of the Universe today: ○ ~5% Atoms, ~27% Dark Matter, ~68% Dark Energy. ○ (Atoms are all the stars, galaxies, dust, people....i.e., normal matter) Expansion rate today (Hubble constant): H 0 ~ 70 km/sec/Mpc For the theory that fits our data, the Universe will expand forever. (The nature of dark energy is still a mystery. If it changes with time, or if other unknown things happen in the universe, this conclusion could change.) Dark Matter vs Dark Energy: Dark matter makes up most of the mass of galaxies and galaxy clusters, and is responsible for the way galaxies are organized on grand scales. Dark energy, meanwhile, is the name we give the mysterious influence driving the accelerated expansion of the universe. Now, combining these equations, we can solve for the distance: d = c x z / H0