Black hole primer for undergraduate students v2 (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. This is a revised version of a previous presentation, hence the v2 tag. Gravitational waves are discussed in a separate set of slides.

To cite this presentation, please use: Nemmen 2019. DOI: https://doi.org/10.6084/m9.figshare.8050361.v1

Credit for the slides/figures belongs to Rodrigo Nemmen, unless otherwise stated.
https://rodrigonemmen.com

Transcript

1. Rodrigo Nemmen IAG USP Black Holes blackholegroup.org @nemmen
2. We entered a new golden age of black hole (astro)physics You can be part of this! blackholegroup.org
3. Index 1.Gravity: General relativity 2.What is a black hole? 3.How to “see” a BH? 4.Gravitational waves 5.Summary 6.Quiz properties of space-time in the strong-field, high-velocity regime and confirm predictions of general relativity for the nonlinear dynamics of highly disturbed black holes. II. OBSERVATION On September 14, 2015 at 09:50:45 UTC, the LIGO Hanford, WA, and Livingston, LA, observatories detected the coincident signal GW150914 shown in Fig. 1. The initial detection was made by low-latency searches for generic gravitational-wave transients [41] and was reported within three minutes of data acquisition [43]. Subsequently, matched-filter analyses that use relativistic models of com- pact binary waveforms [44] recovered GW150914 as the most significant event from each detector for the observa- tions reported here. Occurring within the 10-ms intersite FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, right column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series are filtered with a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-reject filters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain. GW150914 arrived first at L1 and 6.9þ0.5 −0.4 ms later at H1; for a visual comparison, the H1 data are also shown, shifted in time by this amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto each detector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914 [37,38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show 90% credible PRL 116, 061102 (2016) P H Y S I C A L R E V I E W L E T T E R S week ending 12 FEBRUARY 2016
4. Lagrangian for standard model of particle physics http://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation gluon (strong force) W and Z bosons (weak force) weak interactions + Higgs Higgs ghosts Faddeev-Popov ghosts S = ∫ ℒ −gd4x δS δϕ = ∂ℒ ∂ϕ − ∂μ ( ∂ℒ ∂(∂μ ϕ) ) + ⋯ = 0 action Lagrange equations
5. Basic idea of general relativity: GRAVITY = SPACETIME CURVATURE
6. A general relativity primer Einstein’s field equation Stress-energy Ricci curvature Metric Ricci scalar Rμν − 1 2 gμν R = 8πG c4 Tμν
7. A general relativity primer Einstein’s field equation Stress-energy Ricci curvature Metric Ricci scalar spacetime curvature 㱺 = constant × matter-energy Rμν − 1 2 gμν R = 8πG c4 Tμν
8. A general relativity primer Einstein’s field equation Stress-energy Ricci curvature Metric Ricci scalar 㱺 For a free particle: Geodesic equation Newtonian analogue Poisson equation spacetime curvature = constant × matter-energy Rμν − 1 2 gμν R = 8πG c4 Tμν Solution to field equation gives Line element Metric
9. Gravity visualized: https://www.youtube.com/watch?v=MTY1Kje0yLg&list
10. Gravity visualized: https://www.youtube.com/watch?v=MTY1Kje0yLg&list
11. The Elegant Universe. Nova / PBS
12. A concise tutorial on general relativity DOI: 10.1119/1.12853
13. Nova disciplina graduação 2018/2 Relatividade geral e aplicações astrofísicas AGA0319
14. What is a black hole? Remarkable prediction of general relativity Normal object Black hole surface event horizon singularity
15. 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
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. 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
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 The Rock
20. https://xkcd.com/681/
21. VENUS MERCURY EARTH 6,379 KM To sun, far down
22. sun MERCURY Radii of objects not to scale 100x deeper Mercury depth gravity well To black hole, very VERY far down
23. ç ç Black holes have deep, relativistic gravity wells ç BLACK HOLE sun 106x deeper depth gravity well
24. 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
25. 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
26. 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 quantum BHs form naturally?
27. 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?
28. 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
29. LIGO/Virgo: gravitational waves from black holes with M~20-60 Msun visible light Credit: NASA GSFC; Britannica no light!
30. Neutron stars collision → Gas + light → Probably BH w/ M~10 Msun visible light Credit: NASA GSFC; Britannica
31. 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
32. 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) How do we know they are black holes?
33. 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
34. 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
35. 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
36. Credit: unknown
37. Distribution of masses of neutron stars and stellar mass black holes Özel+12
38. Sistema Solar Sagitário A* Massa = 4×106 MSun
39. Journey to Sagittarius A*: the supermassive black hole at the center of the Milky Way
40. 10 light-days = 260 billion km black hole central black hole mass = 4✕106 solar masses Ghez, Schödel, Genzel et al.
41. How to measure black hole spin? J = aGM2 c 0  |a|  1 if t>40’: skip
42. Black hole spin generates spacetime whirlwind (non-Newtonian effect) Huge energy stored in rotating spacetime black hole Credit: Thorne
43. spinning BH https://www.youtube.com/watch?v=9MHuhcFQsBg How to reliably measure black hole spin?
44. How do we observe black holes?
48. 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?
49. m M R
50. Energy released: U = GMm R L = ˙ U = GM ˙ m R Luminosity: For black holes: η ~ 10-40% ) L = ⌘ ˙ mc2 ⌘ / M/R Radiative efficiency:
51. 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
52. Itaipu Dam − 14 GW ⌘ = mgh mc2 = 10 14 ✓ h 100 m ◆
53. ⌘ = mv2 2mc2 ⇠ 10 14 ✓ v 200 km/h ◆2
54. Nuclear fusion ⌘ = 0.008 ⇥ 0.1 ⇠ 8 ⇥ 10 4 Tsar bomba
55. 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!
56. mass supply to black hole Back-of-the-envelope estimate of accretion disk luminosity mass accretion rate mass of all water on earth ˙ m ⇠ m/t↵ = 1024 g s 1 <latexit sha1_base64="jSuvj74oFNemv/UBjFo1D8yISXY=">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</latexit> <latexit sha1_base64="jSuvj74oFNemv/UBjFo1D8yISXY=">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</latexit> <latexit sha1_base64="jSuvj74oFNemv/UBjFo1D8yISXY=">AAACKnicbZDLSgMxFIYz9VbrrerSTbAILrTOlKJuhKIblxXsBXojk2ba0GRmSM4UyjBv4iP4FG515a6IOx/EdNqFVg8EPv7/HE7O74aCa7DtqZVZWV1b38hu5ra2d3b38vsHdR1EirIaDUSgmi7RTHCf1YCDYM1QMSJdwRru6G7mN8ZMaR74jzAJWUeSgc89TgkYqZe/bPcDiGWC25pLLC+gF7eVxJ6X4Bvs2N24VDYeTsWBAZ1043Mn6eULdtFOC/8FZwEFtKhqL/9pFtFIMh+oIFq3HDuETkwUcCpYkmtHmoWEjsiAtQz6RDJ91h/zUKfYidNTE3xizD72AmWeDzhVfw7HRGo9ka7plASGetmbif95rQi8607M/TAC5tP5Ii8SGAI8yw33uWIUxMQAoYqbb2M6JIpQMOnmTB7O8vV/oV4qOnbReSgXKreLZLLoCB2jU+SgK1RB96iKaoiiJ/SCXtGb9Wy9W1PrY96asRYzh+hXWV/fdVClnQ==</latexit> <latexit sha1_base64="jSuvj74oFNemv/UBjFo1D8yISXY=">AAACKnicbZDLSgMxFIYz9VbrrerSTbAILrTOlKJuhKIblxXsBXojk2ba0GRmSM4UyjBv4iP4FG515a6IOx/EdNqFVg8EPv7/HE7O74aCa7DtqZVZWV1b38hu5ra2d3b38vsHdR1EirIaDUSgmi7RTHCf1YCDYM1QMSJdwRru6G7mN8ZMaR74jzAJWUeSgc89TgkYqZe/bPcDiGWC25pLLC+gF7eVxJ6X4Bvs2N24VDYeTsWBAZ1043Mn6eULdtFOC/8FZwEFtKhqL/9pFtFIMh+oIFq3HDuETkwUcCpYkmtHmoWEjsiAtQz6RDJ91h/zUKfYidNTE3xizD72AmWeDzhVfw7HRGo9ka7plASGetmbif95rQi8607M/TAC5tP5Ii8SGAI8yw33uWIUxMQAoYqbb2M6JIpQMOnmTB7O8vV/oV4qOnbReSgXKreLZLLoCB2jU+SgK1RB96iKaoiiJ/SCXtGb9Wy9W1PrY96asRYzh+hXWV/fdVClnQ==</latexit> m = 1M <latexit sha1_base64="UUNhnL7AdAIelSTg9fKYU6l9HDM=">AAAB/XicbZDLSsNAFIYn9VbrrerSzWARXEhJRNCNUHTjRqhgL5CGMplM2qFzCTOTQgnFp3CrK3fi1mdx4bs4TbPQ1gMDH/9/DufMHyaMauO6X05pZXVtfaO8Wdna3tndq+4ftLVMFSYtLJlU3RBpwqggLUMNI91EEcRDRjrh6Hbmd8ZEaSrFo5kkJOBoIGhMMTJW8vm1B+/7PRlJ06/W3LqbF1wGr4AaKKrZr373IolTToTBDGnte25iggwpQzEj00ov1SRBeIQGxLcoECf6LBrTROcYZPn1U3hizQjGUtknDMzV38MZ4lpPeGg7OTJDvejNxP88PzXxVZBRkaSGCDxfFKcMGglnUcCIKoINm1hAWFF7NsRDpBA2NrCKzcNb/P0ytM/rnlv3Hi5qjZsimTI4AsfgFHjgEjTAHWiCFsBAgmfwAl6dJ+fNeXc+5q0lp5g5BH/K+fwBSeWVSQ==</latexit> <latexit sha1_base64="UUNhnL7AdAIelSTg9fKYU6l9HDM=">AAAB/XicbZDLSsNAFIYn9VbrrerSzWARXEhJRNCNUHTjRqhgL5CGMplM2qFzCTOTQgnFp3CrK3fi1mdx4bs4TbPQ1gMDH/9/DufMHyaMauO6X05pZXVtfaO8Wdna3tndq+4ftLVMFSYtLJlU3RBpwqggLUMNI91EEcRDRjrh6Hbmd8ZEaSrFo5kkJOBoIGhMMTJW8vm1B+/7PRlJ06/W3LqbF1wGr4AaKKrZr373IolTToTBDGnte25iggwpQzEj00ov1SRBeIQGxLcoECf6LBrTROcYZPn1U3hizQjGUtknDMzV38MZ4lpPeGg7OTJDvejNxP88PzXxVZBRkaSGCDxfFKcMGglnUcCIKoINm1hAWFF7NsRDpBA2NrCKzcNb/P0ytM/rnlv3Hi5qjZsimTI4AsfgFHjgEjTAHWiCFsBAgmfwAl6dJ+fNeXc+5q0lp5g5BH/K+fwBSeWVSQ==</latexit> <latexit sha1_base64="UUNhnL7AdAIelSTg9fKYU6l9HDM=">AAAB/XicbZDLSsNAFIYn9VbrrerSzWARXEhJRNCNUHTjRqhgL5CGMplM2qFzCTOTQgnFp3CrK3fi1mdx4bs4TbPQ1gMDH/9/DufMHyaMauO6X05pZXVtfaO8Wdna3tndq+4ftLVMFSYtLJlU3RBpwqggLUMNI91EEcRDRjrh6Hbmd8ZEaSrFo5kkJOBoIGhMMTJW8vm1B+/7PRlJ06/W3LqbF1wGr4AaKKrZr373IolTToTBDGnte25iggwpQzEj00ov1SRBeIQGxLcoECf6LBrTROcYZPn1U3hizQjGUtknDMzV38MZ4lpPeGg7OTJDvejNxP88PzXxVZBRkaSGCDxfFKcMGglnUcCIKoINm1hAWFF7NsRDpBA2NrCKzcNb/P0ytM/rnlv3Hi5qjZsimTI4AsfgFHjgEjTAHWiCFsBAgmfwAl6dJ+fNeXc+5q0lp5g5BH/K+fwBSeWVSQ==</latexit> <latexit sha1_base64="UUNhnL7AdAIelSTg9fKYU6l9HDM=">AAAB/XicbZDLSsNAFIYn9VbrrerSzWARXEhJRNCNUHTjRqhgL5CGMplM2qFzCTOTQgnFp3CrK3fi1mdx4bs4TbPQ1gMDH/9/DufMHyaMauO6X05pZXVtfaO8Wdna3tndq+4ftLVMFSYtLJlU3RBpwqggLUMNI91EEcRDRjrh6Hbmd8ZEaSrFo5kkJOBoIGhMMTJW8vm1B+/7PRlJ06/W3LqbF1wGr4AaKKrZr373IolTToTBDGnte25iggwpQzEj00ov1SRBeIQGxLcoECf6LBrTROcYZPn1U3hizQjGUtknDMzV38MZ4lpPeGg7OTJDvejNxP88PzXxVZBRkaSGCDxfFKcMGglnUcCIKoINm1hAWFF7NsRDpBA2NrCKzcNb/P0ytM/rnlv3Hi5qjZsimTI4AsfgFHjgEjTAHWiCFsBAgmfwAl6dJ+fNeXc+5q0lp5g5BH/K+fwBSeWVSQ==</latexit> luminosity L ⇠ 0.1 ˙ mc2 ⇠ 1044 erg s 1 <latexit sha1_base64="CPLrxAY7pm8Mi7vXZH0LnnNhTsY=">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</latexit> <latexit sha1_base64="CPLrxAY7pm8Mi7vXZH0LnnNhTsY=">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</latexit> <latexit sha1_base64="CPLrxAY7pm8Mi7vXZH0LnnNhTsY=">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</latexit> <latexit sha1_base64="CPLrxAY7pm8Mi7vXZH0LnnNhTsY=">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</latexit> M = 108M <latexit sha1_base64="Qx6B5oAZkTr4aexN7DRjylTUHuU=">AAACAHicbZC7SgNBFIbPxluMt6ilzWAQLCTsimAaIWhjE4hgLpBswuzsJBkyu7PMzAbCksansNXKTmx9EwvfxclmC038YeDj/Odw5vxexJnStv1l5dbWNza38tuFnd29/YPi4VFTiVgS2iCCC9n2sKKchbShmea0HUmKA4/Tlje+m/utCZWKifBRTyPqBngYsgEjWJtSr3bj2L0KqvW7whe6XyzZZTsVWgUngxJkqveL311fkDigoSYcK9Vx7Ei7CZaaEU5nhW6saITJGA9px2CIA6ou/AmLVIpukh4wQ2fG9NFASPNCjdLq7+EEB0pNA890BliP1LI3L/7ndWI9qLgJC6NY05AsFg1ijrRA8zSQzyQlmk8NYCKZ+TYiIywx0SazgsnDWb5+FZqXZccuOw9XpeptlkweTuAUzsGBa6jCPdShAQQkPMMLvFpP1pv1bn0sWnNWNnMMf2R9/gDDnJYN</latexit> <latexit sha1_base64="Qx6B5oAZkTr4aexN7DRjylTUHuU=">AAACAHicbZC7SgNBFIbPxluMt6ilzWAQLCTsimAaIWhjE4hgLpBswuzsJBkyu7PMzAbCksansNXKTmx9EwvfxclmC038YeDj/Odw5vxexJnStv1l5dbWNza38tuFnd29/YPi4VFTiVgS2iCCC9n2sKKchbShmea0HUmKA4/Tlje+m/utCZWKifBRTyPqBngYsgEjWJtSr3bj2L0KqvW7whe6XyzZZTsVWgUngxJkqveL311fkDigoSYcK9Vx7Ei7CZaaEU5nhW6saITJGA9px2CIA6ou/AmLVIpukh4wQ2fG9NFASPNCjdLq7+EEB0pNA890BliP1LI3L/7ndWI9qLgJC6NY05AsFg1ijrRA8zSQzyQlmk8NYCKZ+TYiIywx0SazgsnDWb5+FZqXZccuOw9XpeptlkweTuAUzsGBa6jCPdShAQQkPMMLvFpP1pv1bn0sWnNWNnMMf2R9/gDDnJYN</latexit> <latexit sha1_base64="Qx6B5oAZkTr4aexN7DRjylTUHuU=">AAACAHicbZC7SgNBFIbPxluMt6ilzWAQLCTsimAaIWhjE4hgLpBswuzsJBkyu7PMzAbCksansNXKTmx9EwvfxclmC038YeDj/Odw5vxexJnStv1l5dbWNza38tuFnd29/YPi4VFTiVgS2iCCC9n2sKKchbShmea0HUmKA4/Tlje+m/utCZWKifBRTyPqBngYsgEjWJtSr3bj2L0KqvW7whe6XyzZZTsVWgUngxJkqveL311fkDigoSYcK9Vx7Ei7CZaaEU5nhW6saITJGA9px2CIA6ou/AmLVIpukh4wQ2fG9NFASPNCjdLq7+EEB0pNA890BliP1LI3L/7ndWI9qLgJC6NY05AsFg1ijrRA8zSQzyQlmk8NYCKZ+TYiIywx0SazgsnDWb5+FZqXZccuOw9XpeptlkweTuAUzsGBa6jCPdShAQQkPMMLvFpP1pv1bn0sWnNWNnMMf2R9/gDDnJYN</latexit> <latexit sha1_base64="Qx6B5oAZkTr4aexN7DRjylTUHuU=">AAACAHicbZC7SgNBFIbPxluMt6ilzWAQLCTsimAaIWhjE4hgLpBswuzsJBkyu7PMzAbCksansNXKTmx9EwvfxclmC038YeDj/Odw5vxexJnStv1l5dbWNza38tuFnd29/YPi4VFTiVgS2iCCC9n2sKKchbShmea0HUmKA4/Tlje+m/utCZWKifBRTyPqBngYsgEjWJtSr3bj2L0KqvW7whe6XyzZZTsVWgUngxJkqveL311fkDigoSYcK9Vx7Ei7CZaaEU5nhW6saITJGA9px2CIA6ou/AmLVIpukh4wQ2fG9NFASPNCjdLq7+EEB0pNA890BliP1LI3L/7ndWI9qLgJC6NY05AsFg1ijrRA8zSQzyQlmk8NYCKZ+TYiIywx0SazgsnDWb5+FZqXZccuOw9XpeptlkweTuAUzsGBa6jCPdShAQQkPMMLvFpP1pv1bn0sWnNWNnMMf2R9/gDDnJYN</latexit> black hole mass L ~ 1010 Lsun ~ 1 MEarth c2 every 3 hours t↵ = r 2r3 GM <latexit sha1_base64="fFmtX36tm9atRuDsVqb2YWracH8=">AAACF3icbVC7SgNBFJ2NrxhfUUubwSBYSNiNgjZC0EIbIYJ5QHYNs5PZZMjsw5m7gbDsB/gJfoWtVnZia2nhvzhJttDEAwOHc87lzj1uJLgC0/wycguLS8sr+dXC2vrG5lZxe6ehwlhSVqehCGXLJYoJHrA6cBCsFUlGfFewpju4HPvNIZOKh8EdjCLm+KQXcI9TAlrqFEvQSWzpY89L8Tm21YOExPYkoUlF3h+nydVNmuqUWTYnwPPEykgJZah1it92N6SxzwKggijVtswInIRI4FSwtGDHikWEDkiPtTUNiM/UUXfIIzWhTjK5K8UH2uxiL5T6BYAn6u/hhPhKjXxXJ30CfTXrjcX/vHYM3pmT8CCKgQV0usiLBYYQj0vCXS4ZBTHShFDJ9bcx7RPdCugqC7oPa/b6edKolC2zbN2elKoXWTN5tIf20SGy0CmqomtUQ3VE0SN6Ri/o1Xgy3ox342MazRnZzC76A+PzB+TEn+8=</latexit> <latexit sha1_base64="fFmtX36tm9atRuDsVqb2YWracH8=">AAACF3icbVC7SgNBFJ2NrxhfUUubwSBYSNiNgjZC0EIbIYJ5QHYNs5PZZMjsw5m7gbDsB/gJfoWtVnZia2nhvzhJttDEAwOHc87lzj1uJLgC0/wycguLS8sr+dXC2vrG5lZxe6ehwlhSVqehCGXLJYoJHrA6cBCsFUlGfFewpju4HPvNIZOKh8EdjCLm+KQXcI9TAlrqFEvQSWzpY89L8Tm21YOExPYkoUlF3h+nydVNmuqUWTYnwPPEykgJZah1it92N6SxzwKggijVtswInIRI4FSwtGDHikWEDkiPtTUNiM/UUXfIIzWhTjK5K8UH2uxiL5T6BYAn6u/hhPhKjXxXJ30CfTXrjcX/vHYM3pmT8CCKgQV0usiLBYYQj0vCXS4ZBTHShFDJ9bcx7RPdCugqC7oPa/b6edKolC2zbN2elKoXWTN5tIf20SGy0CmqomtUQ3VE0SN6Ri/o1Xgy3ox342MazRnZzC76A+PzB+TEn+8=</latexit> <latexit sha1_base64="fFmtX36tm9atRuDsVqb2YWracH8=">AAACF3icbVC7SgNBFJ2NrxhfUUubwSBYSNiNgjZC0EIbIYJ5QHYNs5PZZMjsw5m7gbDsB/gJfoWtVnZia2nhvzhJttDEAwOHc87lzj1uJLgC0/wycguLS8sr+dXC2vrG5lZxe6ehwlhSVqehCGXLJYoJHrA6cBCsFUlGfFewpju4HPvNIZOKh8EdjCLm+KQXcI9TAlrqFEvQSWzpY89L8Tm21YOExPYkoUlF3h+nydVNmuqUWTYnwPPEykgJZah1it92N6SxzwKggijVtswInIRI4FSwtGDHikWEDkiPtTUNiM/UUXfIIzWhTjK5K8UH2uxiL5T6BYAn6u/hhPhKjXxXJ30CfTXrjcX/vHYM3pmT8CCKgQV0usiLBYYQj0vCXS4ZBTHShFDJ9bcx7RPdCugqC7oPa/b6edKolC2zbN2elKoXWTN5tIf20SGy0CmqomtUQ3VE0SN6Ri/o1Xgy3ox342MazRnZzC76A+PzB+TEn+8=</latexit> <latexit sha1_base64="fFmtX36tm9atRuDsVqb2YWracH8=">AAACF3icbVC7SgNBFJ2NrxhfUUubwSBYSNiNgjZC0EIbIYJ5QHYNs5PZZMjsw5m7gbDsB/gJfoWtVnZia2nhvzhJttDEAwOHc87lzj1uJLgC0/wycguLS8sr+dXC2vrG5lZxe6ehwlhSVqehCGXLJYoJHrA6cBCsFUlGfFewpju4HPvNIZOKh8EdjCLm+KQXcI9TAlrqFEvQSWzpY89L8Tm21YOExPYkoUlF3h+nydVNmuqUWTYnwPPEykgJZah1it92N6SxzwKggijVtswInIRI4FSwtGDHikWEDkiPtTUNiM/UUXfIIzWhTjK5K8UH2uxiL5T6BYAn6u/hhPhKjXxXJ30CfTXrjcX/vHYM3pmT8CCKgQV0usiLBYYQj0vCXS4ZBTHShFDJ9bcx7RPdCugqC7oPa/b6edKolC2zbN2elKoXWTN5tIf20SGy0CmqomtUQ3VE0SN6Ri/o1Xgy3ox342MazRnZzC76A+PzB+TEn+8=</latexit> free-fall timescale
57. Hercules A Black holes also produce relativistic jets of particles Size of the galaxy
58. Hercules A 3C 31 ~1 Mpc ~100 kpc M87 Cosmic particle accelerators! Black holes also produce relativistic jets of particles
59. 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 Black hole binaries (microquasars) ~1 pc 1E1740.7-2942 ~1 Mpc ~100 kpc Active galactic nuclei ~10-4 pc? Tidal disruption events
60. if t>45’: goto slide 88 do not use goto when coding!
61. INTERROMPEMOS A PROGRAMAÇÃO
62. MOMENTO NERD
67. Collision of neutron stars: converted 5% of Msunc2 into GWs and light Swope Foley distance = 130 million ly Soares-Santos Quasars: L~1045 erg/s Bahcall+1997 distance = 5 billion ly Hubble LIGO
68. How are relativistic jets produced by black holes? Conjecture: from spinning black holes Growing evidence that this is correct Theory/simulations Observations (?)
69. 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
70. Toy model for jet production from black hole: rotati accretion + B Semenov+04, Science 1.0 as a t rB ˙ MB) with ency d 10 able 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 ⊵
71. Kudos to Alice Harding (NASA GSFC) https://www.youtube.com/watch?v=R173dLIktsw How to make a black hole jet at home: Homopolar generator
73. Gustavo Soares PhD Artur Vemado undergrad (IC) Henrique Gubolin Msc Fabio Cafardo PhD Raniere Menezes PhD Ivan Almeida Msc https://blackholegroup.org Rodrigo Nemmen Apply to join my group Roberta Pereira undergrad (IC)
74. “Weather forecast for black holes” Virtual laboratory of numerical relativistic astrophysics Gravity: general relativity Gas (plasma) Electromagnetic fields
75. 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
76. 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 ds2 = ↵2dt2 + ij(dxi + idt)(dxj + p = ( 1)⇢✏ ;l where Tl  is the stress energy tensor. In a coordinate basis, @t ffiffiffiffiffiffiffi À g p Tt  À Á ¼ À @i ffiffiffiffiffiffiffi À g p Ti  À Á þ ffiffiffiffiffiffiffi À g p T  À ; ð4Þ where i denotes a spatial index and À  is the connection. The energy momentum equations have been written with the free index down for a reason. Symmetries of the metric give rise to conserved currents. In the Kerr metric, for exam- ple, the axisymmetry and stationary nature of the metric give rise to conserved angular momentum and energy cur- rents. In general, for metrics with an ignorable coordinate xl the source terms on the right-hand side of the evolution equation for Tt l vanish. These source terms do not vanish when the equation is written with both indices up. The stress energy tensor for a system containing only a perfect fluid and an electromagnetic field is the sum of a fluid part, Tl fluid ¼ ð þ u þ pÞulu þ pgl ð5Þ Fl; þ The rest of Maxwell’s equ and are not needed for MHD. Maxwell’s equations c by taking the dual of equ F Here FÃ l ¼ 1 2 lF is t tensor (MTW: ‘‘ Maxwel FÃl which can be proved by t The components of blul ¼ 0. Following, e.g where i denotes a spatial index and À  is the connection The energy momentum equations have been written w the free index down for a reason. Symmetries of the me give rise to conserved currents. In the Kerr metric, for exa ple, the axisymmetry and stationary nature of the me give rise to conserved angular momentum and energy c rents. In general, for metrics with an ignorable coordin xl the source terms on the right-hand side of the evolut equation for Tt l vanish. These source terms do not van when the equation is written with both indices up. The stress energy tensor for a system containing onl perfect fluid and an electromagnetic field is the sum o fluid part, Tl fluid ¼ ð þ u þ pÞulu þ pgl (here u  internal energy and p  pressure), and electromagnetic part, Tl EM ¼ Fl F À 1 4 glF F :
77. 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
78. McKinney et al. 2013, Science Black hole weather forecast
79. Moscibrodzka Jet-disk connection? Predictive model for full radiation spectrum Predictive model for dynamical evolution
80. 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
81. y x Units of GM/c2 phd, Gustavo soares Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
82. y x Units of GM/c2 Work in progress Preliminar result: Null geodesics in x-y plane around Kerr black hole
83. Chan+15a,b ApJ radio 10 GHz 1.3mm IR 2.1μm X-rays Future: Radiative transfer and GPU-accelerated ra tracing in BH spacetimes ptg
84. Remarkable connection between central black holes and host galaxies: the M-σ relation M BH = 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 9.5 1 6 7 8 9 10 M BH /M Velocity dispersion/km s–1 lo log 10 (M BH /M ) MBH = 0.002 M * All galaxies AGN: L bol /L AGN: L bol /L 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
85. Why are black holes and host galaxies connected? SMBH Grapefruit
86. Energy release from supermassive BHs impact large scale structure formation (“AGN feedback”) <10-4 pc galaxy time SMBH BH accretion outflows
87. How do supermassive black holes affect their host galaxies? What is their cosmological evolution?
88. 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
89. Gravitational waves open GWs for undergrads.key
90. 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
91. Goal of Event Horizon Telescope Credit: Warner, Paramount
92. 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 Cosmic particle accelerators Sources of gravitational waves If interested in doing research in these topics, please talk to me Soon: first image of a black hole blackholegroup.org radio-gamma light cosmic rays neutrinos GWs
93. Quiz time! https://kahoot.com/
94. Github Twitter Web E-mail Bitbucket Facebook Group figshare rodrigo.nemmen@iag.usp.br rodrigonemmen.com @nemmen rsnemmen facebook.com/rodrigonemmen nemmen blackholegroup.org bit.ly/2fax2cT