The Milky Way - 2 ASTR 2110 Sarazin. Center of the Milky Way

Transcription

1 The Milky Way - 2 ASTR 2110 Sarazin Center of the Milky Way

2 Final Exam Tuesday, December 12, 9:00 am noon Ruffner G006 (classroom) You may not consult the text, your notes, or any other materials or any person You may bring a three 3x5 cards with equations Bring pencils, paper, calculator ~2/3 Quantitative Problems (like homework problems) ~1/3 Qualitative Questions Multiple Choice (scantron), Short Answer, Fill In the Blank No essay questions

3 Final Exam (Cont.) Equation/Formula Card: You may bring three 3x5 inch index cards with equations and formulae written on both sides. DO NOT LIST pc, AU, M, L, R DO NOT INCLUDE ANY QUALITATIVE MATERIAL (text, graphs, definitions, etc.) Obviously, you can reuse the cards from Tests 1 & 2, and make the third card for material since Test 2

4 Final Exam (Cont.) Material: Final exam will cover the entire semester Chapters : Preface, 1-3, 5-7, 13-19, 23.3 Coordinate, Orbits Milky Way Extra emphasis on material not on first two tests Compact Binaries, Interstellar Medium, Milky Way Chapters 16, 17.1, 18 (pp ), 19 Homeworks Know pc, AU, M solar, L solar, R solar

5 Homework #11 Not due until Monday, December 4 Any late homeworks must also be turned in by Monday, December 4, by 5 pm in my office mail box

6 Final Exam (Cont.) Review Session: Monday, December 11 12:30-2:30 pm Ruffner G006 (classroom) Mainly material since test 2?

7 The Milky Way - 2 ASTR 2110 Sarazin Center of the Milky Way

8 Motions in the Milky Way vertical motions out of disk rotation within disk Jan Oort ( )

9 Rotation of Disk of Milky Way Oort 1920 s v(r), Ω(r) v(r) / r = 2π / P orb Supported by gravity a cent = v2 r GM(r) r 2 v(r) = GM(r) r Ω(r) = GM(r) r 3 r GC

10 Rotation of Disk of Milky Way Assume circular orbits Actual orbits more complex Epicycles radially and vertically

11 Rotation of Disk of Milky Way Assume circular orbits Actual orbits more complex Epicycles radially and vertically Average lots of stars = circular orbit LSR = Local Standard of Rest = average motion of stars near the Sun Complication: see motions relative to us R 0 = distance of Sun to GC 8 kpc Ω 0 = angular velocity of LSR

12 Relative Motions v( l) = Ωr cosα Do relative radial velocity first v LSR ( l) = Ω 0 R 0 cos(90 l) = Ω 0 R 0 sinl v r = v( l) v LSR ( l) = Ωr cosα Ω 0 R 0 sinl Sine Law sinl r = sin(90 +α) R 0 = cosα R 0 R 0 90 o l α! l! Ω 0 90 o - l! d r 90 o + α! Ω α cosα = R 0 r sinl v r = R 0 (Ω Ω 0 )sinl v t = R 0 (Ω Ω 0 )cosl dω çsimilarly GC

13 Nearby stars Nearby Stars In optical, extinction means can only see nearby stars d << R 0 Define: A R 0 2 $ & % B A Ω 0 dω dr v r Ad sin(2l) ' ) ( R 0 *, +, -, v t = d[acos(2l)+ B] Oort's Constants

14 Nearby Stars v r Ad sin(2l) v t = d[acos(2l)+ B] Double sine? subtract LSR velocity

15 Nearby Stars

16 Oort s Constant R 0 = 8 kpc A = 14.4 km/s/kpc B = 12.0 km/s/kpc Ω 0 = A B = 26.4 km/s/kpc v 0 = Ω 0 R 0 = 210 km/s

17 Constant Rotation Velocity? Try simple model: v(r) = v 0 = constant Ω(r) = v(r) / r = v 0 / r " $ # dω dr % ' & A R 0 2 = v 0 = v 0 R 0 r 2 R 0 R = Ω R 0 " $ # dω dr % ' = + 1 & R 0 2 Ω 0 B A Ω 0 = 1 2 Ω 0 B = A A = 14.4 km/s/kpc B = 12.0 km/s/kpc A è v(r) constant in MW

18 21 cm Observations of Rotation Radio not affected by extinction, see through MW 21 cm è accurate wavelength for Doppler shift Large distance è proper motion small è v r only v r = R 0 (Ω Ω 0 )sinl R 0 l! d Ω r min GC

19 21 cm Observations of Rotation v r = R 0 (Ω Ω 0 )sinl Ω GM(r) / r 3 = 4πG ρ / 3 ρ decreases with r (Ω Ω 0 ) largest when r smallest R 0 l! d Ω tangent point r min v r max = R 0 sinl [Ω(r min ) Ω 0 ] r min r min = R 0 sinl GC

20 21 cm Observations of Rotation v r max = R 0 sinl [Ω(r min ) Ω 0 ] r min = R 0 sinl Measure v r max vs. l Ω(r min ) R 0 l! d Ω v(r min ) = Ω(r min ) r min, different l r min v(r) = rotation curve of MW r min GC

21 Rotation Curve of Milky Way v(r) constant 210 km/s

22 Mapping the Milky Way Once rotation curve v(r) known: l and v r è location in galaxy Inner MW, 2 locations!

23 The Milky Way Center: The Nearest Supermassive Blackhole

24 In Sagittarius, in southern sky Can t observe in optical due to dust, A V ~ 30 mag!! Observe in radio, IR, hard X-rays, gamma-rays Radio: Center of Milky Way Bright radio source, Sgr A, one of first radio sources found beyond Solar System

25 Center of Milky Way - Radio

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29 Center of Milky Way - Radio Bright radio source, Sgr A, one of first radio sources found beyond Solar System Lots going on, molecular clouds, supernova remnants, massive stars, diffuse synchrotron emission Zoom in: Sgr A -> Sgr A West -> Sgr A* Sgr A* very compact, highly variable Recently VLBA: Sgr A* < 0.3 AU in size Active Galactic Nucleus (AGN) = accreting supermassive blackhole (SMBH) But, very faint, typically L(radio, Sgr A*) ~ L, L(bol) <~ 10 3 L

30 Center of Milky Way IR

31 Center of Milky Way - IR Large star cluster, n(stars) ~ 10 7 stars/pc 3 globular clusters Lots of stellar interactions, even collisions Stars orbit point in space = Sgr A*

32 IR Movie of Star Orbits and BH

33 Star Orbits Near Sgr A*

34 Stars orbit point in space = Sgr A* Kepler s Third Law: Mass = 3.7 x 10 6 M Mass must lie within: <30 AU from orbits Central SMBH <0.3 AU from radio size of Sgr A* R Sch (3.7 x 10 6 M ) = 0.07 AU Only a BH could have this much mass in such a small region Center of Milky Way = Sgr A* = supermassive black hole with 3.7 x 10 6 M

35 Stellar Populations in the Milky Way ASTR 2110 Sarazin

36 Connection between Age of Objects Location (disk or halo, spiral arms in disk?) Motion, Orbits Stellar Populations Rotate together in disk, circular orbits, like Sun, nearby stars move slowly relative to Sun Random, non-circular, halo orbits Amount of heavy elements (C, N, O, Fe, )

37 Stellar Populations Age Location Distribution Velocity * Heavy Elements Pop I young disk patchy low high Pop II old halo smooth high low * relative to LSR

38 Connection between Age of Objects Location (disk or halo, spiral arms in disk?) Motion, Orbits Stellar Populations Rotate together in disk, circular orbits, like Sun, nearby stars move slowly relative to Sun Random, non-circular, halo orbits Amount of heavy elements (C, N, O, Fe, )

39 Stellar Pop. - Ages 5000 Myr Pop. I Pop. II

40 Stellar Populations Age Location Distribution Velocity * Heavy Elements Pop I young disk patchy low high Pop II old halo smooth high low * relative to LSR

41 Connection between Age of Objects Location (disk or halo, spiral arms in disk?) Motion, Orbits Stellar Populations Rotate together in disk, circular orbits, like Sun, nearby stars move slowly relative to Sun Random, non-circular, halo orbits Amount of heavy elements (C, N, O, Fe, )

42 Stellar Pop. - Locations Pop. I Pop. II

43 Stellar Pop. - Locations Oldest objects in halo, like globular clusters

44 Stellar Pop. - Locations Youngest objects in spiral arms (OB stars, HII regions)

45 Stellar Populations Age Location Distribution Velocity * Heavy Elements Pop I young disk patchy low high Pop II old halo smooth high low * relative to LSR

46 Connection between Age of Objects Location (disk or halo, spiral arms in disk?) Motion, Orbits Stellar Populations Pop. I: Rotate together in disk, circular orbits, like Sun, nearby stars move slowly relative to Sun Pop. II: Random, non-circular, halo orbits Amount of heavy elements (C, N, O, Fe, )

47 Stellar Pop. - Orbits Pop. I Pop. II

48 Stellar Pop. - Orbits Pop. I: Disk orbits

49 Stellar Pop. - Orbits Extreme Pop. II: Halo orbits

50 Stellar Pop. - Orbits Pop. I Pop. II

51 Stellar Populations Age Location Distribution Velocity * Heavy Elements Pop I young disk patchy low high Pop II old halo smooth high low * relative to LSR

52 Stellar Populations