Introduction to Astrophysics II
Introduction to Astrophysics II ASTR 2120
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This 5 page Class Notes was uploaded by Willie Cummings on Monday September 21, 2015. The Class Notes belongs to ASTR 2120 at University of Virginia taught by Craig Sarazin in Fall. Since its upload, it has received 20 views. For similar materials see /class/209709/astr-2120-university-of-virginia in Astronomy at University of Virginia.
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Date Created: 09/21/15
Review For Test 2 The material on this test will be a comprehensive and representative sampling of material to review on the rst test to be given on Monday February 23 As such there will be seven main topics Extragalactic Distance Scale Galaxy Clustering Dark Matter Active Galaxies and Active Galactic Nuclei AGN and Cosmology There will be four multiple choice and one essay question per test Extragalactic Distance Scale 1 Parallax is not useful as a standard candle measurement out to megaparsecs because a We can see objects only out to a few kiloparsecs b Objects in the sky move too quickly for parallax measurements to be reliable c The angular deviation of celestial objects as the earth moves in its orbit would be too small to resolve d Stars are much too faint to be seen outside our own galaxy N The cosmic microwave background radiation a ls 30 K thermal emission redshifted from the era of recombination b ls isotropic to a very high level as observed by telescopes on Earth c ls an intermittent astrophysical phenomenon d ls 3 K microwave emission redshifted from the era of recombination 03 Hubble7s constant is 71 km s 1 Mpc l An object has a redshift Z 0001 It is located a 43 MPc away b 43 Mpc away 2 d 0043 Mpc away 043 Mpc away 4 The Sunyaev Zeldovich e ect affects the cosmic microwave background CMB by a b C d Redshifting light from the CMB as the universe expands Scattering and reddening light by the dust within clusters slightly redshifting CMB radiation as it passes within a cluster7s gravitational well absorption and scattering of OMB radiation by hot electrons within a cluster Standard Distance At maximum light Type la supernovae have absolute magnitudes of MB 7196 Assume a Type la supernova occurs in an extremely distant galaxy 5000 Mpc away Estimate the observed magnitude B of the supernova at maximum light ignoring the K correction e fect of redshift on the spectrum any absorption or any cosmological e ects Could this supernova be observed with the Hubble Space Telescope limited to m3 29 Galaxy Clustering 1 N 03 Hgt A collection of 1000 galaxies has an average velocity dispersion v 5000 kms The cluster is 1 Mpc in radius lts mass is a 6 X 1015 M O b 3 X 1014 M O c 6 X 1017 M 0 d 6 X 1014 M 0 Based on a velocity dispersion v 1000 kms and the fact that the mass of a proton is mp 17 X 10 24 gm and Boltzmann7s constant is 14 X 10 16 ergK the temperature within a galaxy cluster is approximately a T107K bT3gtlt109K c T108K dT3gtlt106K The following mechanism is believed to describe the formation of visible structure galaxies clusters perhaps superclusters in the universe a top down large a small formation from matter bubbles blown out by hot dark matter b Cold dark matter of unknown composition seeding small nuclei of matter growing larger as time goes on c Hot dark matter growing baryonic concentrations from small to large d An initial seed of matter collected around cosmic strings and magnetic monopoles The two point correlation function which formally describes the probability of nding another galaxy within a distance r from the rst galaxy implies that a The structure of the universe is scale free there is no large or small length scale for galaxy clustering b The size of clusters has an upper limit 7 a length scale associated with it c lmplies a universe lled with small voids and dense clusters d There is zero chance of nding two galaxies separated by a distance smaller than rmin Cluster Virialz39zatz on Consider a cluster of 1000 galaxies moving at average velocities of 1000 kms spread out over 1 Mpc The radius of each galaxy can be taken as 50 kpc How long does it take for galaxy galaxy collisions in this cluster To answer this question answer the following 1 Assume the cluster is a sphere of radius 1 Mpc What is the volume occupied by each galaxy on average N3 03 4 Each galaxy sweeps out a cylinder of radius R 50 kpc and length d vt in time t In 107 years what volume in Mpc3 is swept out The time between collisions is calculated by determining that time if during which the volume swept out by an average galaxy is the volume occupied by a given galaxy What is this time in Myr How does this compare to the age of the universe tuniverse N 1010 years Based on this crude argument could galaxy galaxy collisions equilibrate the galactic population within a cluster Dark Matter 1 4 Most of the dark matter in the universe is not baryonic because a It does not shine on its own through fusion reactions C7 There is a maximum mass that a given collection of baryonic matter can reach at a given location in space A 0 V Baryonic matter would have scattered light too easily making the universe opaque rather than transparent to radiation d From nucleogenetic arguments the ratio of light isotopes implies that only a small fraction of the universe7s mass is baryonic The following is known to be a true statement about dark matter 9 It interacts with normal matter only through gravitational attraction AA C7 It is dominated by fast light but abundant neutrinos Black holes are believed to be a dominant source of dark matter mass A 0 d A It is dominated by WlMPS weakly interacting massive particles The two dominant components to the energy density of the universe are a dark matter 2 positive intrinsic energy density of the vacuum b c d positive intrinsic energy density of the vacuum 2 dark matter negative intrinsic energy density of the vacuum 2 dark matter VVVV photons 2 dark matter For the given Hubble constant the mass density of the universe due to dark matter is approximately 10 24 gm cm 3 Assume this matter density is dominated by quantum black holes with mass of 1020 gm These black holes are separated by approximately a 1 pc b 10 pc c 1 Mpc d 002 pc Active Galaxies and Active Galactic Nuclei AGN 1 The broad line emission in some Seyfert galaxies comes from the inner regions of the central engine Some of the evidence for this is that a Scattering by the dense plasma in the central region is large enough to broaden narrow emission lines b Emission lines from near the central engine are due to atomic transitions that are naturally broad c They are due to the higher temperature alone d They are due to the fast rotational velocities close to the central black hole N The radio emission from the lobes and jets of radio galaxies is due to the a frictional interaction of the jet plasma with the surrounding medium b Synchrotron emission due to electrons gyrating in a magnetic eld c Scattering of electrons in the plasma with the cosmic microwave background radiation d Synchrotron emission due to protons gyrating in a magnetic eld 03 The e iciency of radiated luminosity falling into a black hole is most comparable to a The e iciency of ssion reactions b The e iciency of fusion reactions c The e iciency of matter to energy conversion d The e iciency of high explosive chemical reactions such as TNT Hgt A black hole of 107 solar masses powers a quasar and it accretes matter at a rate of 10 6 MO yr l lts luminosity is a 3 X 1040 erg s l b 3 X 1035 erg s l c 3 X 1044 erg s l d 3 X 1033 erg s l Maximum Accretion Rate Onto a Black Hole Here we will use the Eddington limit to determine the maximum mass accretion rate M onto a black hole of mass M 1 An electron has cross section to absorb photons of lt7 7 X 10 25 cm Using the radiative ux F which has units of luminosityarea c the speed of light and a the cross sectional area for the absorption of photons calculate out the force acting on an electron due to radiation 2 This radiation force is balanced out by the gravitational force Take electron to be at the Schwarzchild radius of this black hole Derive an equation for the radiative ux that will balance out the gravitational force The mass of the electron is me 3 Derive an expression for the ux F from the mass accretion rate and the mass of the black hole M Assume the radiation is purely isotropic hint the ux F L 47139R2 schwarzchild 4 Equate the above and get a relation for the maximum accretion rate M for a black hole of mass M 4 Cosmology 1 The era of recombination occurred at a time when the energy density of the universe a Was dominated by dark matter Was dominated by dark energy c Was dominated by baryonic matter d Was dominated by radiation N CDA yperbolic geometry of spacetime7 in the absence of dark energy a b C d An observational horizon that decreases in absolute size beyond a certain time ls characterized by the fact that parallel lines always converge The volume enclosed within a sphere of radius R is larger than 7TR3 The volume enclosed within a sphere of radius R is smaller than 7TR3 03 The simplest models of the quintessence is one in which a It has negative energy density and arbitrary positive or negative pressure b It is characterized by pressure P 7 A02 c It can result in the ripping of spacetime at some moment in the future asymptotic runaway expansion d It can have either positive or negative energy density Hgt One of many interesting conclusions of the WMAP survey of the cosmic microwave background was that a The size of the observational horizon is consistent with what we know from previous7 independent observations b The atness of spacetime was con rmed to a high degree of accuracy c Fluctuations in the background are due to overdensities in the opaque plasma7 due to the interactions of baryonic with hot dark matter d The map shows strong evidence for anomalous artifacts cosmic strings and other topological defects in spacetime that in ationary expansion should have diluted The Expansion of the Open Universe Consider an open universe consisting of normal matter and radiation7 such that 90 lt 1 The evolution of this universe is characterized by the following equations7 where R is the scale factor of the universe R 1 at the current epoch and t is the time from the Big Bang R 1970 1220 cosh6 71 2 H t 0 sinh i 6 0 179032
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