AstroC10-F23-Midterm-2A-solutions

Astronomy C10 / L&S C70U - Fall 2023 - Professor Alex Filippenko Midte’r_(x_n\ Exam #2 — 6 November 2023 Print name: _&_!@.@Sign name; et 5 b B oaGkvident TDE b g Print your GSI's Name: —________________________ Discussion section #: oo _____ Print and sign your name on your answer form. BE SURE TO FILL IN YOUR SID # AND DISCUSSION SECTION #! 10 POINTS OFF FOR EACH, IF NOT DONE. CLOSED BOOK, CLOSED NOTES, NO CALCULATORS By completing this exam, I certify that the work is mine alone; I have not consulted anyone else, or any source of information, other than this page and my own brain. Mark all answers on your answer form. Use a pencil or pen. Completely fill in the appropriate bubble. Be sure to thoroughly erase all altered answers and stray marks! Or, a clear, big “X” can be made through unintended answers (mistakes), and then bubble in your intended response. For true/false questions: mark bubble A if the statement is true, and bubble B if false. For multiple choice questions: mark the bubble corresponding to the single best answer. All 25 questions carry equal weight. Read each question carefully before answering. There is no penalty for guessing. If you need extra room for work, use the last (blank) page. Time limit: 45 minutes — budget your time appropriately. GOOD LUCK! Possibly Useful Information d (pc) = 1/p (arcsec) d=ut density p = M/V c=3x10° km/s For a sphere, V = 37 R®, Aguface = 47R? For a circle, A= 7R?, C =27R T~ 3.14 There are about 3.2 x 107 seconds per year, and 86,400 (roughly 10°) seconds per day Degrees Kelvin = degrees Centigrade + 273; Fahrenheit = (9/5)Cent. + 32 0=~ XD 1 AU = 1.5x10% km = 8.3 light minutes 1light year (ly) ~ 63,000 AU ~ 9.5x10'? km ~ 10'® km 1pc=3826ly~3x108 cm~3x10%km 1A=108cm=10"""m=0.10m 60" (arcsec) = 1’ (arcmin), 60’ = 1° (degree), 360° = full circle = 2 radians = 24 hours ApeakT ~ 3 x 108 nm K = 3 x 107 A K M=c P=1/f £ =0T! E=hf z=(A= M)/ do=BNXo~v/cifv <02 z=y/PEd_1fralv<e F = GM M, /d? My = Myry L o M4 Rx M pt+e sn+v Rs = 2GM/c? Rohoton sphere = 3GM/c? Moy =14 Mg F=ma Myin = Pv3/27G Lihermal = 4mR%0T* (for a sphere) b= L/(4nd?) E =mc? = moc®[1 — (v?/c?)]"1/2 v = Hod, where Hy ~ 70 km/s/Mpc Q= p/perit perit = 3HE/(87G) M =v?R/G N = R.fsfpnefififoL, where R, =~ N./T (N. = # stars in galaxy, T = age of galaxy) P? = kR3 [k ~ constant ~ 47%/(GM,) if My >> Ma]; in general, P? = (4n2R%)/[G(M} + My)] For planets, v « 1/vVR tmoving = (trest)[1 = (v2/€®)]Y/? Linoving = (Lrest)[1 — (v?/c?)]V/2 1

(1) Where is the closest place you should expect to find elements formed long ago in a supernova? (a) The Orion Nebula. (b) Jupiter. (¢) The Sun. Your body. (e) Earth’s core. (2)@0r F. The Universe is currently expanding: on sufficiently large scales, the distances between galaxies and clusters of galaxies are increasing. (3) Which one of the following statements about the evolution of low-mass stars is TRUE? (a) A low-mass star will spend about half of its life on the main sequence, and about half of its life as a red giant before becoming a white dwarf. When a red giant becomes unstable, its atmosphere gets ejected as an expanding shell of ionized gas. (c) The last element the Sun will fuse before exploding as a supernova is iron. (d) Low-mass stars become brown dwarfs, and then eventually white dwarfs. (e) Mass exchange in a binary system can cause the recipient star to evolve more slowly than if it were a single star. . (4) Suppose an enemy pushes you into a black hole. Which one of the following statements is FALSE? (a) As you approach the event horizon, your enemy watching from far away would see your clock ticking progressively more slowly. As you cross the event horizon, you would witness a brilliant burst of light due to radiation emitted from inside the black hole. (c) After crossing the event horizon, all paths point toward the black hole’s central singularity, making it impossible to escape. (d) Your enemy looking from a safe distance will see you approaching the event horizon, yet never actually reaching it. (e) From your perspective, the journey toward the singularity takes a finite amount of time. (5) Which one of the following statements about galaxies is FALSE? (2) The orbital speed of stars in a spiral galaxy is linearly proportional to their distance from the center; this is described as a “flat” rotation curve. (b) The “flat” rotation curve of the Milky Way Galaxy provides evidence for dark matter, especially in the Galaxy’s halo. (c) Large clusters of galaxies would not remain gravitationally bound unless there is an additional source of gravity, not just the gravity associated with the visible galaxies. (d) If the “flat” part of the rotation curve of Galaxy Rav has three times the velocity of Galaxy Cooper, then the mass enclosed by Galaxy Rav (at a given radius) is about 9 times that of Galaxy Cooper. (e) If the orbital speed of stars in a spiral galaxy decreased substantially with increasing distance from the center, we could conclude that the mass of the galaxy is dominated by matter in the center, as in the case of the Solar System. (6) T or@ An O-type main sequence star is the most massive and therefore hottest spectral claSsification type; its high temperature allows it to fuse helium in its core while on the main sequence.

(14) Which one of the following statements about white dwarf stars is TRUE? (a) White dwarfs are located on the less luminous side of the temperature-luminosity diagram because they are currently fusing carbon and oxygen. (b) A star that begins its life on the main sequence with a mass of one solar mass will become a white dwarf of one solar mass. White dwarfs resist the inward pull of gravity with outward electron degeneracy pressure. (d) White dwarfs gradually fade as the hydrogen fuel in their core gets used up. (e) Very old white dwarfs become even smaller, fainter neutron stars. (15) Which one of the following statements about quasars is FALSE? (a) Quasars were identified to have very large redshifts yet appear much brighter than galaxies at similar redshifts, indicating that quasars are much more luminous than galaxies. (b) There are few quasars nearby to the Milky Way Galaxy because the supermassive black holes powering them have already consumed much of the gas in their environment. (c) In nearby parts of the Universe, galaxies that are found to be merging or recently merged are more likely to host a quasar than those that are not merging. (d) In order to power a quasar, energy extraction from gas accretion must be more efficient than that of chemical burning and nuclear fusion. Evidence for supermassive black holes powering quasars includes the emission of gravitational waves from the gas in the accretion disk surrounding the black hole. (16) Suppose a new Type II supernova is discovered in a nearby galaxy. Which one of the following is most likely to be TRUE? The supernova is in a spiral galaxy; spiral galaxies have many recently formed stars. (b) The supernova is in a spiral galaxy; spiral galaxies have many old stars. (c) The supernova is in an elliptical galaxy; elliptical galaxies have many recently formed stars. (d) The supernova is in an elliptical galaxy; elliptical galaxies have many old stars. (e) The supernova probably went through a previous series of nova eruptions. (17) T or To estimate the age of a star cluster using the main-sequence turn-off point, one must first know the cluster’s distance. (18) Suppose you observe a supernova in a galaxy 420 Mpc away from Earth and notice that an absorption line whose rest wavelength is 600 nm appears at 660 nm. In a uniformly expanding universe, where would you expect to find this absorption line in a galaxy 840 Mpc away? (2) 600 nm F10 Mye T 'F‘l" b) 630 —_— 2= wiw &5 aw. EC) 660 nm 1 e fwicz +he A/\‘g(hm‘)-uv) 8 gggfi Ax . £ i so L20ww ~ e 57 - amd VR Ao c 600 %120 = 20 nw | (19) T or When two black holes of mass M; and M> merge, the combined mass of the resulting black hole is equal to the sum of the original masses (M = M, + M>), because of the conservation of energy during the process of black hole merging.

Be sure you answer question #20 correctly (6 points off if incorrect)! (20) Daniel Brethauer, the Head GSI for this class (Astronomy C10 / L&S C70U, Fall 2023), () is a graduate student at UC Berkeley. b) lives on a moon orbiting Saturn. (c) is actually a punk rocker in disguise. (d) can’t possibly be human, because he’s made of lanthanide elements produced by a kilonova. (e) was brought to Earth from the Moon during the Apollo landings in the early 1970s. (21) Suppose a binary star system consists of two main-sequence stars, one O-type and one M-type. Which one of the following statements is TRUE? (a) The M-type star will be closer to the center of mass than the O-type star. (b) The M-type star will have a shorter main-sequence lifespan than the O-type star. (c) The M-type star will be more luminous than the O-type star. (d) The M-type star is more likely to eventually become a supernova than the O-type star. @ The M-type star has a smaller radius than the O-type star. (22)@01‘ F. Before settling on the main sequence, a pre-main-sequence star shines because it releases gravitational potential energy. (23) Suppose a supernova explodes in our own Milky Way Galaxy. Which one of the following statements is FALSE? (a) The supernova might have been caused by a white dwarf exploding after approaching the Chandrashekar limit from accreted mass. (b) The supernova might have been caused by a massive star’s core collapsing, rebounding, and launching an explosion. c) As a result of the explosion, elements heavier than helium were dispersed in the cosmos. The remaining compact remnant of the supernova could be an object consisting of degenerate electrons. (e) Optical light from the supernova might be difficult for us to observe because dust in the Galactic disk blocks much of it. (24) Which one of the following statements about black holes is TRUE? (a) The tidal forces of a black hole are stronger near massive black holes than low-mass ones. The escape velocity from within a black hole is greater than or equal to the speed of light. (c) Bluer photons escape black holes more easily than redder photons because bluer photons have higher energy than redder ones. (d) Black holes are in hydrostatic equilibrium, since the outward pressure from consumed photons balances their inward force of gravity. ’ (¢) If the Sun instantly turned into a black hole of the same mass, Earth’s orbit would immediately change. (25) Which one of the following statements about dark matter is FALSE? (a) Hot gas (10° K) and massive compact halo objects, such as white dwarfs, neutron stars, and brown dwarfs are considered to be “normal dark matter” because they are not easily visible yet consist of protons, neutrons, and electrons. (b) “Normal dark matter” makes up at most 5% of the contents of the Universe. (c) Gravitational lensing by clusters of galaxies provides evidence that dark matter makes up most of the total mass of the clusters. Some gravitational lenses produce background-galaxy arcs; their total mass, including dark matter, isn’t large enough to warp space-time to produce a perfect Einstein ring. (e) Much of the dark matter in the Universe is “exotic,” not consisting of normal matter. End of Examination 5