Black hole primer for undergraduate students (physics/astronomy)

Lecture: black hole primer for undergraduate students and first year grad students in physics and astronomy. Prepared and taught by Prof. Rodrigo Nemmen at IAG USP.

Credit for the slides/figures belongs to Rodrigo Nemmen, unless otherwise stated.

Transcript

1. Rodrigo Nemmen IAG USP Black Holes rodrigonemmen.com @nemmen
2. Lagrangian for standard model of particle physics http://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation
3. Basic idea of general relativity: GRAVITY = SPACETIME CURVATURE
4. Basic idea of general relativity: GRAVITY = SPACETIME CURVATURE
5. A general relativity primer Einstein’s field equation Stress-energy Ricci curvature Metric Ricci scalar spacetime curvature 㱺 = constant × matter-energy Newtonian analogue Solution to field equation gives For a free particle: Geodesic equation metric Poisson equation
6. Gravity visualized: https://www.youtube.com/watch?v=MTY1Kje0yLg&list
7. Gravity visualized: https://www.youtube.com/watch?v=MTY1Kje0yLg&list
8. Gravity visualized: https://www.youtube.com/watch?v=MTY1Kje0yLg&list
9. Gravity visualized: https://www.youtube.com/watch?v=MTY1Kje0yLg&list
10. The Elegant Universe. Nova / PBS
11. The Elegant Universe. Nova / PBS
12. A concise tutorial on general relativity DOI: 10.1119/1.12853
13. What is a black hole? Remarkable prediction of general relativity Normal object Black hole surface event horizon singularity
14. Event horizon: one-way membrane, matter/ energy can fall in, but nothing gets out Black hole event horizon singularity Region inside event horizon causally cut-off from outside RS = 2GM c2 = 2.95 ✓ M M ◆ km Radius of event horizon: Schwarzschild radius
15. What is a black hole? Once inside, nothing escapes Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon
16. What is a black hole? Once inside, nothing escapes Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon
17. What is a black hole? Once inside, nothing escapes Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon
18. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
19. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes Sogro Sogra
20. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
21. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
22. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
23. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
24. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes Chuck Norris
25. Massive, compact astronomical object: gravity so strong that it traps all that fall inside the event horizon What is a black hole? Once inside, nothing escapes
26. https://xkcd.com/681/
28. VENUS MERCURY EARTH 6,379 KM To sun, far down
29. sun MERCURY
30. sun MERCURY Radii of objects not to scale 100x deeper Mercury depth gravity well To black hole, very VERY far down
31. sun VENUS MERCURY EARTH 6,379 KM To sun, far down Radii of objects not to scale 100x deeper Mercury depth gravity well To black hole, very VERY far down
32. ç depth gravity well ç Black holes have deep, relativistic gravity wells ç BLACK HOLE sun 106x deeper
33. ç depth gravity well ç Black holes have deep, relativistic gravity wells ç BLACK HOLE sun 106x deeper
34. Classical vs quantum black holes Credit: BBC Black holes from general relativity are classical objects Quantum BHs: need quantum gravity theory Quantum BHs have weird properties: Hawking radiation Information paradox Will not talk about them
35. Classical vs quantum black holes Credit: BBC Black holes from general relativity are classical objects Quantum BHs: need quantum gravity theory Quantum BHs have weird properties: Hawking radiation Information paradox Will not talk about them
36. surprise them showing places where we see BHs all around us! how can it be? how can they shine? hang-on! Luo+16 Chandra Deep Field South 81 days of exposure
37. How massive can a black hole be? BHs with M ≳ 3 Msun form naturally by gravitational collapse of massive stars No other stable equilibrium available at these masses
38. How massive can a black hole be? BHs with M ≳ 3 Msun form naturally by gravitational collapse of massive stars No other stable equilibrium available at these masses Open question: Do low-mass BHs form naturally?
39. Two populations of black holes Supermassive 106-1010 solar masses one in every galactic nucleus
40. Two populations of black holes Supermassive 106-1010 solar masses one in every galactic nucleus 5-60 solar masses ~107 per galaxy Stellar
41. Two populations of black holes Supermassive 106-1010 solar masses one in every galactic nucleus 5-60 solar masses ~107 per galaxy Stellar Open question: Do intermediate-mass BHs exist? How massive are the initial seeds of supermassive BHs?
42. X-ray binaries, M~5-20Msun, 107 objects per galaxy visible light Credit: NASA GSFC; Britannica
43. X-ray binaries, M~5-20Msun, 107 objects per galaxy visible light Credit: NASA GSFC; Britannica
44. XRBs show dramatic state transitions, whose origin is unknown X-ray binaries, M~5-20Msun, 107 objects per galaxy visible light Credit: NASA GSFC; Britannica
45. M81 NGC 1097 M87 One supermassive BH in every galactic nuclei, M~106-1010Msun visible light Credit: NASA, HST, CXC
46. M81 NGC 1097 M87 One supermassive BH in every galactic nuclei, M~106-1010Msun Do dwarf galaxies host supermassive BHs? visible light Credit: NASA, HST, CXC
47. Criteria used to identify astrophysical BHs Must be compact: radius < few Rs Must be massive: M > several Msun, too massive to be a neutron star (Mns,crit ≤ Msun) These are strong reasons for BH candidates It is possible to empirically prove the existence of event horizons Prove that BHs have event horizons (soon: Event Horizon Telescope, LIGO) How do we know they are black holes?
48. Black holes are the most perfect macroscopic objects in the universe A black hole has no-hair (no-hair theorem) Made only of spacetime warpage Mass M Spin: angular momentum J Charge Q J = a GM2/c 0  |a|  1 RS = 2GM c2
49. Fg = Fc ) GMm r2 = mv2 r Measuring mass in astronomy Test particle in circular orbit M m v Best mass estimates are dynamical ) M = v2r G Alternatively, Kepler’s third law P2 r3 = 4⇡2 G(M + m) ) M ⇡ 4⇡2r3 GP2
50. Fg = Fc ) GMm r2 = mv2 r Measuring mass in astronomy Test particle in circular orbit M m v Fc=Fg Best mass estimates are dynamical ) M = v2r G Alternatively, Kepler’s third law P2 r3 = 4⇡2 G(M + m) ) M ⇡ 4⇡2r3 GP2
51. Exercise Suppose a star is measured in a circular orbit with P=15 years and r=1000 au. Compute M. M m Kepler’s third law ) M ⇡ 4⇡2r3 GP2 r 1 au = 1.5E11 m G = 6.67E-11 N m2/kg2 Msun = 2E30 kg
52. Credit: unknown
53. Credit: unknown
54. Distribution of masses of neutron stars and stellar mass black holes Özel+12
57. Sistema Solar Sagitário A* Massa = 4×106 MSun
58. Journey to Sagittarius A*: the supermassive black hole at the center of the Milky Way
59. Journey to Sagittarius A*: the supermassive black hole at the center of the Milky Way
60. 10 light-days = 260 billion km black hole Ghez, Schödel, Genzel et al.
61. central black hole mass = 4✕106 solar masses Ghez, Schödel, Genzel et al.
62. How to measure black hole spin? J = aGM2 c 0  |a|  1
63. Black hole spin generates spacetime whirlwind (non-Newtonian effect) Huge energy stored in rotating spacetime black hole Credit: Thorne
64. spinning BH https://www.youtube.com/watch?v=9MHuhcFQsBg
65. spinning BH https://www.youtube.com/watch?v=9MHuhcFQsBg
66. spinning BH https://www.youtube.com/watch?v=9MHuhcFQsBg How to reliably measure black hole spin?
67. How do we observe black holes?
72. Credit: ESO Black holes surrounded by accretion disks, release enormous amounts of light How efficient is the release of light?
73. Credit: ESO Black holes surrounded by accretion disks, release enormous amounts of light How efficient is the release of light?
74. Credit: ESO Black holes surrounded by accretion disks, release enormous amounts of light Credit: NatGeo v → c near the horizon How efficient is the release of light?
75. m M R
77. Energy released: U = GMm R
78. Energy released: U = GMm R L = ˙ U = GM ˙ m R Luminosity:
79. Energy released: U = GMm R L = ˙ U = GM ˙ m R Luminosity: ) L = ⌘ ˙ mc2
80. Energy released: U = GMm R L = ˙ U = GM ˙ m R Luminosity: ) L = ⌘ ˙ mc2 ⌘ / M/R Radiative efficiency:
81. Energy released: U = GMm R L = ˙ U = GM ˙ m R Luminosity: For black holes: η ~ 10-40% ) L = ⌘ ˙ mc2 ⌘ / M/R Radiative efficiency:
82. Sugar (sucrose) C12 H22 O11 1g ! 4 kcal= 16.2 kJ = 1e23 eV ⌘ = E mc2 = 1.6 ⇥ 1011erg 9 ⇥ 1020erg = 2 ⇥ 10 10 R. Nemmen
83. Sugar (sucrose) C12 H22 O11 1g ! 4 kcal= 16.2 kJ = 1e23 eV ⌘ = E mc2 = 1.6 ⇥ 1011erg 9 ⇥ 1020erg = 2 ⇥ 10 10 R. Nemmen
84. Itaipu Dam − 14 GW ⌘ = mgh mc2 = 10 14 ✓ h 100 m ◆
85. Itaipu Dam − 14 GW ⌘ = mgh mc2 = 10 14 ✓ h 100 m ◆
86. ⌘ = mv2 2mc2 ⇠ 10 14 ✓ v 200 km/h ◆2
87. ⌘ = mv2 2mc2 ⇠ 10 14 ✓ v 200 km/h ◆2
88. Nuclear fusion ⌘ = 0.008 ⇥ 0.1 ⇠ 8 ⇥ 10 4 Tsar bomba
89. Nuclear fusion ⌘ = 0.008 ⇥ 0.1 ⇠ 8 ⇥ 10 4 Tsar bomba
90. Credit: ESO Radiative efficiency: Black holes surrounded by accretion disks, release enormous amounts of light ⌘ rad = Erad out Egas in = 10 40% 100x more efficient than nuclear fusion! Most efficient radiators in the universe Radiate across all eletromagnetic spectrum!
91. Credit: ESO Radiative efficiency: Black holes surrounded by accretion disks, release enormous amounts of light ⌘ rad = Erad out Egas in = 10 40% 100x more efficient than nuclear fusion! Most efficient radiators in the universe Radiate across all eletromagnetic spectrum!
92. Hercules A Black holes also produce relativistic jets of particles Size of the galaxy
93. Hercules A Black holes also produce relativistic jets of particles 3C 31 ~1 Mpc ~100 kpc
94. Hercules A Black holes also produce relativistic jets of particles 3C 31 ~1 Mpc ~100 kpc M87
95. Gamma-ray bursts 3C 31 4 I.F. Mirabel Fig. 1.2 The British journal Nature announced on July 16, 1992 the discovery of a microquasar in the Galactic center region [22]. The image shows the synchrotron emission at a radio wavelength of 6 cm produced by relativistic particles jets ejected from some tens of kilometers to light years Black hole binaries (microquasars) ~1 pc 1E1740.7-2942 ~1 Mpc ~100 kpc Active galactic nuclei ~10-4 pc? Tidal disruption events
96. How are relativistic jets produced by black holes? Conjecture: from spinning black holes Growing evidence that this is correct Theory/simulations Observations (?)
97. https://www.youtube.com/watch?v=9MHuhcFQsBg Penrose process: Spinning black hole has free energy that can be extracted Rotational energy of spacetime (frame dragging) Thought experiment by Penrose that demonstrates the principle, probably not important in astrophysics But magnetized accretion disks is promising Penrose 1969 Ruffini & Wilson 1975; Blandford & Znajek 1977
98. https://www.youtube.com/watch?v=9MHuhcFQsBg Penrose process: Spinning black hole has free energy that can be extracted Rotational energy of spacetime (frame dragging) Thought experiment by Penrose that demonstrates the principle, probably not important in astrophysics But magnetized accretion disks is promising Penrose 1969 Ruffini & Wilson 1975; Blandford & Znajek 1977
99. Toy model for jet production from black hole: rotation + accretion + B Semenov+04, Science possibilities remain to be better explored in future simula- tions of accretion flows. Interestingly enough, s is similar to the dispersion of s values obtained in the hydrodynamic RIAF simulations of Yuan, Wu & Bu (2012); Bu et al. (2013) for a range of initial conditions. Range of black hole spins and/or magnetic flux threading the horizon – If powerful jets are produced via the BZ mecha- nism then the two fundamental parameters that regulate the jet power are the black hole spin a and the magnetic flux h threading the horizon, besides the mass (Blandford & Znajek 1977; Semenov, Dyadechkin & Punsly 2004): Pjet / ⇠ ✓ a h M ◆2 ; (9) i.e., a and h are degenerate to some extent (cf. Jet power Blandford & Znajek 77; Komissarov+; Nemmen+07; Tchekhovskoy+ spin magnetic flux Blandford-Znajek mechanism: magnetic flux tube spinning black hole ergosphere ⇠ a2 ˙ Mc2 ⊵
100. Toy model for jet production from black hole: rotation + accretion + B Semenov+04, Science possibilities remain to be better explored in future simula- tions of accretion flows. Interestingly enough, s is similar to the dispersion of s values obtained in the hydrodynamic RIAF simulations of Yuan, Wu & Bu (2012); Bu et al. (2013) for a range of initial conditions. Range of black hole spins and/or magnetic flux threading the horizon – If powerful jets are produced via the BZ mecha- nism then the two fundamental parameters that regulate the jet power are the black hole spin a and the magnetic flux h threading the horizon, besides the mass (Blandford & Znajek 1977; Semenov, Dyadechkin & Punsly 2004): Pjet / ⇠ ✓ a h M ◆2 ; (9) i.e., a and h are degenerate to some extent (cf. Jet power Blandford & Znajek 77; Komissarov+; Nemmen+07; Tchekhovskoy+ spin magnetic flux Blandford-Znajek mechanism: ⇠ a2 ˙ Mc2 ⊵
101. Kudos to Alice Harding (NASA GSFC) https://www.youtube.com/watch?v=R173dLIktsw How to make a black hole jet at home: Homopolar generator
102. Kudos to Alice Harding (NASA GSFC) https://www.youtube.com/watch?v=R173dLIktsw How to make a black hole jet at home: Homopolar generator
103. Gustavo Soares PhD Artur Vemado undergrad (IC) Henrique Gubolin Msc Fabio Cafardo PhD Raniere Menezes PhD Ivan Almeida Msc http://rodrigonemmen.com/group/ Rodrigo Nemmen Apply to join my group Roberta Pereira undergrad (IC)
104. “Weather forecast for black holes” Virtual laboratory of numerical relativistic astrophysics Gravity: general relativity Gas (plasma) Electromagnetic fields
105. Required physics: Fluid dynamics + electrodynamics Plus: equation of state D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ Fluid dynamics conservation equations Mass Momentum Energy D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ r · Frad r · q D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ r · Frad r · q D⇢ Dt + ⇢r · v = 0 ⇢ Dv Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ Maxwell equations
106. Equations of general relativistic magnetohydrodynamics Plus: equation of state ideal MHD condition Kerr metric Conservation of Particle number Energy-momentum r⌫(⇢u⌫) = 0 r⌫Tµ⌫ = 0 r⌫ ⇤ Fµ⌫ = 0 r⌫Fµ⌫ = Jµ Maxwell equations r⌫ ⇤ Fµ⌫ = 0 r⌫Fµ⌫ = Jµ Fµ⌫u⌫ = 0 ds 2 = ↵ 2 dt 2 + ij( dx i + p = ( 1)⇢✏ ;l s the stress energy tensor. In a coordinate basis, ffiffiffiffiffiffiffi Àg p Tt  Á ¼ À@i ffiffiffiffiffiffiffi Àg p Ti  À Á þ ffiffiffiffiffiffiffi Àg p T  À ; ð4Þ notes a spatial index and À  is the connection. rgy momentum equations have been written with dex down for a reason. Symmetries of the metric conserved currents. In the Kerr metric, for exam- xisymmetry and stationary nature of the metric o conserved angular momentum and energy cur- eneral, for metrics with an ignorable coordinate rce terms on the right-hand side of the evolution or Tt l vanish. These source terms do not vanish quation is written with both indices up. ss energy tensor for a system containing only a id and an electromagnetic field is the sum of a Tl fluid ¼ ð þ u þ pÞulu þ pgl ð5Þ The rest of M and are not n MHD. Maxwell’s by taking the Here FÃ l ¼ 1 2 tensor (MTW which can be The comp blul ¼ 0. Fol where i denotes a spatial index and À  is the The energy momentum equations have bee the free index down for a reason. Symmetrie give rise to conserved currents. In the Kerr me ple, the axisymmetry and stationary nature give rise to conserved angular momentum a rents. In general, for metrics with an ignora xl the source terms on the right-hand side o equation for Tt l vanish. These source terms when the equation is written with both indices The stress energy tensor for a system con perfect fluid and an electromagnetic field is fluid part, Tl fluid ¼ ð þ u þ pÞulu þ pgl (here u  internal energy and p  press electromagnetic part, Tl EM ¼ Fl F À 1 4 glF F :
107. 256 x 256 x 64 r θ 3D computational mesh 4×106 resolution elements Need to evolve to t>15000 M (4 yrs for a 109 BH) Global, general relativistic MHD (GRMHD) simulations of gas around spinning BHs HARM code + MPI + 3D = HARMPI Gammie+03; Tchekhovskoy
108. McKinney et al. 2013, Science Black hole weather forecast
109. McKinney et al. 2013, Science Black hole weather forecast
110. Moscibrodzka
111. Moscibrodzka
112. Moscibrodzka Jet-disk connection? Predictive model for full radiation spectrum Predictive model for dynamical evolution
113. We are starting to treat the radiation from these systems y x Units of GM/c2 phd, Gustavo soares Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
114. We are starting to treat the radiation from these systems y x Units of GM/c2 phd, Gustavo soares Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
115. y x Units of GM/c2 phd, Gustavo soares Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
116. y x Units of GM/c2 phd, Gustavo soares Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
117. y x Units of GM/c2 Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
118. Chan+15a,b ApJ radio 10 GHz 1.3mm IR 2.1μm X-rays Future: Radiative transfer and GPU- accelerated ray tracing in BH spacetimes ptg
119. Chan+15a,b ApJ radio 10 GHz 1.3mm IR 2.1μm X-rays Future: Radiative transfer and GPU- accelerated ray tracing in BH spacetimes ptg
120. Remarkable connection between central black holes and host galaxies: the M-σ relation MBH = 2 ⇥ 108M ✓ 200 km s 1 ◆5.6 Woo+13; McConnell & Ma 13; Heckman & Best ARA&A 14 1010 109 108 107 106 60 80 100 200 300 400 Elliptical/classical bulge Pseudobulge AGN Quiescent 9.0 6 7 8 9 10 M BH /M Velocity dispersion/km s–1 log 10 (M BH /M ) M a b Figure 9 nualreviews.org sonal use only. mass central black hole host galaxy propriety: σbulge (km/s) Fundamental link between BH growth and galaxy evolution
121. Why are black holes and host galaxies connected? SMBH
122. Why are black holes and host galaxies connected? SMBH Grapefruit
123. Why are black holes and host galaxies connected? SMBH Grapefruit
124. Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) galaxy time
125. Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) <10-4 pc galaxy time SMBH
126. Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) time BH accretion
127. Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) time outflows
128. Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) time
131. How do supermassive black holes affect their host galaxies? What is their cosmological evolution?
132. 10 Mpc Fabian 12 ARAA; Tombesi+15 Nature; Cheung+16 Nature; Vogelsberger+14 Nature Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) “BH explosions” in the simulation
133. 10 Mpc Fabian 12 ARAA; Tombesi+15 Nature; Cheung+16 Nature; Vogelsberger+14 Nature Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) “BH explosions” in the simulation
134. PI: S. Doeleman (MIT/Haystack) idéia original: H. Falcke (Radboud) Attaining the impossible: first image of an event horizon just around the corner Credit: Science Magazine
135. PI: S. Doeleman (MIT/Haystack) idéia original: H. Falcke (Radboud) Attaining the impossible: first image of an event horizon just around the corner Credit: Science Magazine
136. Gravitational waves: ask me after the lecture
137. Summary: Black holes Black holes: collapsed objects from which nothing can escape (once inside) Astrophysical labs of general relativity, fluid dynamics and electrodynamics that can’t be found on Earth Brightest systems in the universe Important for galaxy formation/evolution Open questions in the field Very soon: first image of event horizon LIGO is opening new observational windows If you are interested in doing research in these topics, please talk to me
138. Github Twitter Web E-mail Bitbucket Facebook Blog figshare rodrigo.nemmen@iag.usp.br http://rodrigonemmen.com @nemmen rsnemmen http://facebook.com/rodrigonemmen nemmen http://astropython.blogspot.com http://bit.ly/2fax2cT