Black Holes ASTR 2110 Sarazin. Calculation of Curved Spacetime near Merging Black Holes

Transcription

1 Black Holes ASTR 2110 Sarazin Calculation of Curved Spacetime near Merging Black Holes

2 Test #2 Monday, November 13, 11-11:50 am Ruffner G006 (classroom) Bring pencils, paper, calculator You may not consult the text, your notes, or any other materials or any person You may bring a 3x5 card with equations ~2/3 Quantitative Problems (like homework problems) ~1/3 Qualitative Questions Multiple Choice, Short Answer, Fill In the Blank questions No essay questions

3 Black Holes ASTR 2110 Sarazin Calculation of Curved Spacetime near Merging Black Holes

4 Black Holes Gravity crushes star to a point = singularity Surrounded by ``surface from which nothing can escape = event horizon

5 Schwarzschild Metric for Karl Schwarzschild (1916): Black Hole Spherical coordinates. Non-rotating black hole " ( ds) 2 = $ c 1 2GM # c 2 r " ( ds) 2 = c 1 R S $ # r dt % ' & R S 2GM c 2 = 3 km % dt' & 2 2 " $ $ $ # " M $ # M " $ $ $ # % ' & dr 1 R S r dr 1 2GM c 2 r 2 % ' ' ' & 2 % ' ' ' & ( r dθ ) 2 ( r sinθ dφ) 2 ( r dθ ) 2 ( r sinθ dφ) 2

6 Black Hole Physics Nothing Escapes Event Horizon Radius and Time Reverse 2 Roles!! " ( ds) 2 = c 1 R S # r dt % & 2 " $ Radius always goes down, time can go $ ' $ dr ' ( r dθ ) 2 r sinθ dφ backwards r < R S R S r >1 $ # 1 R S r 1 R S r % ' ' & imaginary, (dt) 2 term negative (normally positive) (dr) 2 term positive (normally negative) r t radius and time reverse roles!! " $ # 1 R S r ( ) 2 % ' & 2 < 0

7 Infall into Black Hole infalling person outside observer infall slows, v è 0, redshift, fades away, hovers forever just above horizon

8 Black Hole Physics Orbits near Black Hole In general, complex. Consider circular orbits Newton: any radius possible GR: No stable circular orbits r 3 R S

9 Black Hole Physics Black Holes Have No Hair No matter what they swallow, only retain: Mass M, Charge Q, Spin Angular Momentum J Interstellar matter, very high electrical conductivity è shorts out charge Astrophysical Black Holes: Mass M, Spin Angular Momentum J

10 Spinning Black Holes Kerr Metric (Boyer-Linquist Coordinates) " ( ds) 2 = 1 R r % S $ ' c dt # ρ 2 & ( ) 2 ρ 2 ( ) 2 Δ dr2 ρ dθ " r 2 +α 2 + R Srα 2 % $ sin 2 θ ' sinθ dφ # ρ 2 & R S = 2GM c 2 Schwarzschild radius ( ) 2 + 2R Srα sin 2 θ ρ 2 cdt dφ α J Mc (units of length) ρ 2 r 2 +α 2 cos 2 θ (units of length) Δ r 2 R S r +α 2 (units of length 2 )

11 Kerr Metric Spinning Black Holes Exterior Solution Event Horizon Oblate spheroid ergosphere Can escape, but must rotate with black hole side view top view

12 Kerr Metric Spinning Black Holes Interior Solution Ring singularity Inner Horizon!? But interior solution is unstable

13 Kerr Metric Worm holes?? Spinning Black Holes Unstable è closes as soon as anything enters it! black hole white hole Closed wormhole

14 Energy from Black Holes Penrose Mechanism Rotating BH Throw something out backwards E out E in + Δmc 2!! May not be important in nature (too complicated), but

15 Solution to Mankind s Problems Biggest problems: Get rid of garbage, pollution Make energy Build city around rotating BH

16 Energy from Black Holes Natural Method Drop matter into BH carelessly Bump into, rub against other matter Friction è KE è heat è light Virial Thm. mass m mass m Heat (1/2) PE (1/2) GMm/R S (1/2) GMm / (2GM/c 2 ) E out = Heat mc 2 /4!!! Accretion by BHs is biggest important energy source in Universe

17 Black Hole Physics Black Hole Surface Areas When BHs merge, mass can increase or decrease Total surface area of BH horizons always increases in GR 2 nd Law of BH Dynamics Entropy always increases S = c3 k 4 G A T = c 3 8πkGM Entropy Temperature

18 The Death of Stars ASTR2110 Sarazin Cat s Eye Planetary Nebula

19 Low Mass Star (1 M ) Left as AGB (red supergiant) with C/O core, giant H envelope H envelope, ~ few AU C/O core, ~ 10 9 cm, degenerate & inert

20 Low Mass Star - Death G Asymptotic Giant Branch = Supergiant (I) Red supergiant Inert carbon/oxygen core E F D MS A B C H

21 Low Mass Star (1 M ) - Cont. Inert core, must die Envelope very extended, cool. Hydrogen recombines: H + + e - H ev Gravitational binding energy per atom = G M m H / R 10 ev (M / M )(R/AU) -1 H shell ejected, (1/2) m H v 2 ~ few ev, v ~ 20 km/s Planetary Nebula

22 Low Mass Star - Death G F D E MS A B C H

23 Planetary Nebula & White Dwarf Degenerate core revealed, becomes a white dwarf C/O for Sun other composition for other masses Core initially very hot, T eff ~ 100,000 K, lots of UV, ionizes planetary nebula Fast wind from WD sweeps envelope into shell

24 Low Mass Star - Death G F D E MS A B C H

25 Planetary Nebula & White Dwarf Degenerate core revealed, becomes a white dwarf C/O for Sun other composition for other masses Core initially very hot, T eff ~ 100,000 K, lots of UV, ionizes planetary nebula Fast wind from WD sweeps envelope into shell

26 Planetary Nebula

27 Planetary Nebula

28 Planetary Nebula

29 Planetary Nebula

30 Planetary Nebula

31 Planetary Nebula

32 Planetary Nebula

33 Planetary Nebula

34 Planetary Nebula

35 Planetary Nebula & White Dwarf Degenerate core revealed, becomes a white dwarf C/O for Sun other composition for other masses Core initially very hot, T eff ~ 100,000 K, lots of UV, ionizes planetary nebula Fast wind from WD sweeps envelope into shell WD cools, fades away

36 Low Mass Star - Death G F D E MS A B C H

37 Supernovae ASTR2110 Sarazin SN1987A - X-ray and Optical

38 High Mass Star (>8 M ) Left as red supergiant with Fe core and many burning shells

39 High Mass Star - Death A) Inert Fe core, many burning shells B) Either Red Supergiant or blue WR star

40 Fe Core Fe core, no fuel left, inert core, supported by electron degeneracy pressure Fe core ~ Fe white dwarf (outer envelope extended, weight not so large) M core 1.4 M Chandrasekhar mass implodes! Heat, Fe nuclei p, n p + + e - n + ν e, lots of neutrinos

41 Neutron Core Core is now mainly neutrons Core collapses until R ~ 10 km, neutrons become degenerate, degeneracy pressure Neutron core bounces, hits infalling gas at v ~ c/3 Shock from bounce plus neutrinos blow out envelope of star Core-Collapse Supernova!!

42 Core-Collapse Supernova

43 Core-Collapse Supernova

44 Core-Collapse Supernova Core becomes a neutron star (at least initially) Very, very dense

45 Energetics Virial Theorem: E NS = (1/2) PE During infall, ΔE = ΔPE PE So, E binding = (1/2) PE (1/2) G M 2 /R G(1.4 M ) 2 / (10 km) is released E tot 3 x ergs released in supernova!! Released from dense, NS region, only neutrinos can escape! E tot 3 x ergs in neutrinos, main energy of core-collapse supernova!!

46 Energetics (Cont.) Shock and neutrinos blow off envelope of star at ~ 10,000 km/s E explsion ergs in kinetic energy Explosion heats material to 10 9 K initially. Cools rapidly, but very bright initially L (optical, max) L!! Would fade rapidly, but radioactivity keeps bright for months E light ergs in light!!

47 Energetics (Cont.) Amazing result: most of energy comes out in neutrinos

48 Heavy Elements If explosion is efficient, most of materials outside of iron core are ejected. Also, fusion during explosion makes more heavy elements Supernova make and/or disperse most of the heavy elements in the Universe!! But, iron core -> neutron star, core-collapse SN don t disperse much iron

49 Final Outcome? Explosion very complex, but If nearly all outer layers are ejected: neutron star, M 1.4 M 2. If enough of outer layers remain or fall back so that M 3 M è Black Hole Uncertain theoretical problem, but if initial mass of star is 1. 8 M M star 20 M -> neutron star M M star -> black hole

50 Core-Collapse Supernova

51 Alternative: Collapsar Model = Supernova Due to Jets from a Black Hole Core of massive star (50 M 8 ) collapses, forms black hole Rotating material from star falls onto BH Black holes shoots out jets of gas at c Jets blast through star, blowing it up If jets point in our direction, we see a gamma-ray burst

52 Collapsar Model = Supernova Due to Jets from a Black Hole