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

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

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

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

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

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

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

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

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

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

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 )

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

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

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

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

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

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

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

The Death of Stars ASTR2110 Sarazin Cat s Eye Planetary Nebula

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

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

Low Mass Star (1 M ) - Cont. Inert core, must die Envelope very extended, cool. Hydrogen recombines: H + + e - H + 13.6 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

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

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

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

Planetary Nebula

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

Supernovae ASTR2110 Sarazin SN1987A - X-ray and Optical

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

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

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

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!!

Core-Collapse Supernova

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

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 10 53 ergs released in supernova!! Released from dense, NS region, only neutrinos can escape! E tot 3 x 10 53 ergs in neutrinos, main energy of core-collapse supernova!!

Energetics (Cont.) Shock and neutrinos blow off envelope of star at ~ 10,000 km/s E explsion 10 51 ergs in kinetic energy Explosion heats material to 10 9 K initially. Cools rapidly, but very bright initially L (optical, max) 10 10 L!! Would fade rapidly, but radioactivity keeps bright for months E light 10 49 ergs in light!!

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

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

Final Outcome? Explosion very complex, but... 1. 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 2. 20 M M star -> black hole

Core-Collapse Supernova

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 0.99995 c Jets blast through star, blowing it up If jets point in our direction, we see a gamma-ray burst

Collapsar Model = Supernova Due to Jets from a Black Hole