Active galactic nuclei and blazars

Active galactic nuclei and blazars

Slides from a set of lectures about active galactic nuclei (AGNs) and blazars for advanced undergraduate and graduate students in physics and astronomy. Prepared and taught by Prof. Rodrigo Nemmen. The slides give a broad overview of observations and theory of AGN, with some emphasis on jetted AGNs (blazars) and high-energy electromagnetic radiation

The following topics are covered:
1. Historical perspective
2. Black hole physics
3. Observed AGN zoo
4. The ins of BHs: accretion
5. The outs: jets
6. Blazars

This was presented in two lectures with a total duration of 3 hours at the high energy astrophysics school in ICTP-SAIFR 2019. I was not able to cover all material available in the slides. https://www.ictp-saifr.org/school-on-high-energy-astrophysics/

To cite this presentation, please use: Nemmen 2019.
DOI: 10.6084/m9.figshare.9467927

Credit for the slides and figures belongs to Rodrigo Nemmen, unless otherwise stated. If you use my slides in your presentation, please include the proper credit.
https://rodrigonemmen.com

C5ca9433e528fd5739fa9555f7193dac?s=128

Rodrigo Nemmen

August 09, 2019
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Transcript

  1. 2.

    Content of lectures Broad overview: observations and theory of active

    galactic nuclei (AGN) Some emphasis on jetted AGNs (blazars) and high-energy EM radiation
  2. 3.

    Outline of lectures 1.Historical perspective 2.Black hole physics 3.Observed zoo

    4.The ins of BHs: accretion 5.The outs: jets 6.Blazars
  3. 4.

    References: theory Physical processes in active galactic nuclei. Blandford, R.

    in Active galactic nuclei Saas-Fee lecture notes Black holes, white dwarfs and neutron stars. Shapiro, S. L. & Teukolsky, S. A. (ch. 12, 14) More details Foundations of black hole accretion disk theory. Fragile, C. & Abramowicz, M. The Formation and Disruption of Black Hole Jets. Contoupoulos, I. et al. (ch. 3, 6, 7)
  4. 5.

    References: observations Active galactic nuclei. Beckmann V. & Schrader, C.

    An introduction to active galactic nuclei: Classification and unification. New Ast. Rev. Tadhunter, C. Relativistic jets in active galactic nuclei. ARAA. Blandford, R. arXiv:1812.06025 Gamma-Ray Observations of Active Galactic Nuclei. ARAA. Madejski, G. & Sikora, M.
  5. 7.
  6. 8.
  7. 10.

    What physics is necessary? general relativistic MHD (GRMHD) at low

    accretion rates: general relativistic kinetic theory (GRK)
  8. 11.

    Nature of AGNs: Accreting black holes • enormous free energy

    • can be extracted by particles/fields Gravitational energy source
  9. 13.
  10. 14.

    AGNs: multifaceted phenomenon (challenge #1) Depending on how you observe,

    AGNs look different Appearance varies with EM energy band (radio to gamma-rays)
  11. 15.

    AGNs: multifaceted phenomenon (challenge #1) Depending on how you observe,

    AGNs look different Appearance varies with EM energy band (radio to gamma-rays) radio jet! thermal UV! dusty torus! hard X-rays! broad lines! rapid variability!
  12. 16.

    Quasar light curves imply Δtvar < 1 light-week Size of

    system must satisfy size < cΔtvar variability timescale light-crossing radius ≈0.01 pc ~ 1000 AU
  13. 17.

    Supermassive black holes (SMBHs) are extremely small on the sky

    Very hard to observe (challenge #2) SMBH Grapefruit <10-4 pc >10 kpc event horizon size galaxy size ~109
  14. 18.

    AGNs easily outshine their host galaxies (challenge #3) this image:

    z ~ 0.2 dL ~ 1 Gpc Hubble Space Telescope Bahcall+1997
  15. 19.

    Steven Weinberg When I received my undergraduate degree — about

    a hundred years ago — the physics literature seemed to me a vast, unexplored ocean, every part of which I had to chart before beginning any research of my own. How could I do anything without knowing everything that had already been done? Fortunately, in my first year of graduate school, I had the good luck to fall into the hands of senior physicists who insisted, over my anxious objections, that I must start doing research, and pick up what I needed to know as I went along. It was sink or swim. To my surprise, I found that this works. I managed to get a quick PhD — though when I got it I knew almost nothing about physics. But I did learn one big thing: that no one knows everything, and you don’t have to. Another lesson to be learned,to continue work of many theoretical and experimental physicists has been able to sort it out, and put everything (well, almost everything) together in a beautiful theory known as the standard model.My advice is to go for the messes — that’s where the action is. My third piece of advice is probably the hardest to take. It is to forgive yourself for wasting time. Students are only asked to solve problems that their professors (unless unusually cruel) know to be solvable. In addition,it doesn’t matter ifthe problems are scientifically important — they have to be solved to pass the course. But in the real world,it’s very hard to know which problems are important, and you never know whether at a given moment in history a problem is solvable. At the beginning of the twentieth century,several leading physicists,including Lorentz and Abraham, were trying to work out a theory of the electron. This was partly in order to understand why all attempts to detect effects of Earth’s motion through the to spending most of your time not being creative, to being becalmed on the ocean of scientific knowledge. Finally, learn something about the history ofscience,or at a minimum the history ofyour own branch of science. The least important reason for this is that the history may actually be of some use to you in your own scientific work. For instance, now and then scientists are hampered by believing one of the over- simplified models of science that have been proposed by philosophers from Francis Bacon to Thomas Kuhn and Karl Popper. The best antidote to the philosophy of science is a knowledge ofthe history ofscience. More importantly, the history of science can make your work seem more worthwhile to you. As a scientist, you’re probably not going to get rich. Your friends and relatives Four golden lessons Scientist Advice to students at the start of their scientific careers. (1979 Nobel Prize, Physics) 1. Learn to swim as you try not to drown. — No one knows everything, and you don’t have to. 2. Aim for the rough water (messes). — that’s where the action is. 3. Forgive yourself for wasting time. 4. Learn the history of science. — at least of your own field. 2003 Nature slide by Ken Nagamine
  16. 20.

    Historical perspective on AGNs 1783: Newtonian “dark stars” predicted 1915:

    Einstein publishes his field equation 1916: black hole solution derived from GR 1918: "curious straight ray" in galaxy M87, "connected with the nucleus by a thin line of matter”—jets discovered 1963: strong optical point source found at 3C 273 nucleus—quasars discovered Early 1990s: HST finds SMBHs at centers of nearby galaxies Late 1990s: stellar orbits at Galactic Center— strongest BH case until 2015 (Sagittarius A*, 4×106 M⦿ ) Curtis 1918 Schmidt+1963 Ford+1994; Harms+1994; Ferrarese & Ford 2004 Michell 1783 Schwarzschild 1916 Einstein 1915 Genzel & Gillessen 2010
  17. 21.

    Historical perspective on AGNs Late 1990s, early 2000s: M-σ relation—SMBHs

    and host galaxies are tightly connected 2000: SMBHs disturb thermodynamics of entire galaxy clusters 2003: Sloan Digital Sky Survey (SDSS) finds >100k AGNs 2015: direct observation of gravitational waves from stellar-mass BHs 2018a: 1st multimessenger observation from AGNs (blazar TXS 0506+056) 2018b: GRAVITY resolves orbit at r = 7M (Sgr A*) 2019: EHT images event horizon (M87*) McNamara+2000; Fabian 2012 Abazajian+2003 IceCube, Fermi LAT Collaborations Magorrian+1998; Kormendy & Ho 2013 Abbott+2015 Abuter+2018 EHTC
  18. 23.

    Pace of discovery is accelerating Future: immense discovery space awaiting

    We entered 2nd golden age of black hole (astro)physics General lessons from history
  19. 25.

    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 R μν − 1 2 g μν R = 8πG c4 T μν Solution to field equation gives Line element Metric
  20. 26.

    What is a black hole? Remarkable prediction of general relativity

    Normal object Black hole surface event horizon singularity from black hole primer for undergrads
  21. 27.

    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 Gravitational radius: R g ≡ GM c2 Useful scale
  22. 28.

    Growth of black holes If particles fall into the black

    hole M increases Schwarzschild radius RS = 2M increases surface area increases
  23. 29.

    Growth of black holes If particles fall into the black

    hole M increases Schwarzschild radius RS = 2M increases surface area increases There is no limit to how big a BH can grow. From astrophysics: Mmin = 3.6 MSun Mmax ~ 1010 MSun
  24. 30.

    What is a black hole? Once inside, nothing escapes Massive,

    compact astronomical object: gravity so strong that it traps everything that falls inside the event horizon
  25. 31.

    What is a black hole? Massive, compact astronomical object: gravity

    so strong that it traps everything that falls inside the event horizon Once inside, nothing escapes Father-in-law Mother- in-law
  26. 32.

    What is a black hole? Massive, compact astronomical object: gravity

    so strong that it traps everything that falls inside the event horizon Once inside, nothing escapes
  27. 33.

    What is a black hole? Massive, compact astronomical object: gravity

    so strong that it traps everything that falls inside the event horizon Once inside, nothing escapes
  28. 34.

    A black hole has no hair All black hole solutions

    of Einstein’s equation completely characterized by only three externally observable classical parameters: Mass M Spin: angular momentum J Charge Q J ≡ a GM2 c −1 ≤ a ≤ 1 spin parameter No-hair theorem All other information (“hair”=metaphor) disappears behind the event horizon, therefore permanently inaccessible to external observers
  29. 35.

    Types of black holes Mass M Spin a Charge Q

    Schwarzschild spacetime Kerr spacetime Reissner–Nordström spacetime
  30. 36.

    Schwarzschild black hole Simplest black hole Spherically symmetric spacetime Relatively

    “easy” to handle analytically ds2 = − ( 1 − 2M r ) dt2 + ( 1 − 2M r ) −1 dr2 + r2 (dθ2 + sin2 θdϕ2 ) Schwarzschild geometry in Schwarzschild coordinates
  31. 37.

    Kerr black hole Conservation of angular momentum leads to spinning

    black holes Rotational energy deforms spacetime → Kerr spacetime Kerr metric considerably more complex than Schwarzschild ds2 = − ( 1 − 2Mr ρ2 ) dt2 − 4Mar sin2 θ ρ2 dϕdt + ρ2 Δ dr2 + ρ2dθ2 + ( r2 + a2 + 2Mra2 sin2 θ ρ2 ) sin2 θdϕ2 a ≡ J/M, ρ2 ≡ r2 + a2 cos2 θ, Δ ≡ r2 − 2Mr + a2 Boyer-Lindquist coords.
  32. 38.

    Main parameters for astrophysical BHs Gravity Mass M Spin a∗

    Magnetic flux Φ Predict Energy output in all forms (erg/s or LEdd) (M⦿ = 2×1033 g) (1 = max spin) units Accretion Mass accretion rate (M⦿ /yr or ) ˙ MEdd <latexit sha1_base64="Nypma/3UTN6LX4HB+ocabo8Fi/o=">AAACBXicdVDLSgMxFM3UV62vVpdugkVwIUNmbLXdFUVwI1SwD2iHksmkbWjmQZKplGHWfoVbXbkTt36HC//F9CGo6IELh3PuTe49bsSZVAi9G5ml5ZXVtex6bmNza3snX9htyjAWhDZIyEPRdrGknAW0oZjitB0Jin2X05Y7upj6rTEVkoXBrZpE1PHxIGB9RrDSUi9f6HqhSq7TXtIVPrz0vLSXLyIT2ZVyyYbItMuoalU1KSOrelqClolmKIIF6r38h36DxD4NFOFYyo6FIuUkWChGOE1z3VjSCJMRHtCOpgH2qTz2xiySM+oksytSeKhND/ZDoStQcKZ+H06wL+XEd3Wnj9VQ/vam4l9eJ1b9ipOwIIoVDcj8o37MoQrhNBLoMUGJ4hNNMBFMrw3JEAtMlA4up/P4Ohr+T5q2aZ2Y9k2pWDtfJJMF++AAHAELnIEauAJ10AAE3IEH8AiejHvj2XgxXuetGWMxswd+wHj7BMUUmPA=</latexit> ˙ M <latexit sha1_base64="HQd3eZtYcOzotJK1XRc4H26PyLY=">AAAB+XicdVDLSgMxFM3UV62vqks3wSK4kCEzbbHdFd24ESrYB7RDyWTSNjSTGZJMoQz9CLe6cidu/RoX/ovptIKKHggczrmHe3P8mDOlEXq3cmvrG5tb+e3Czu7e/kHx8KitokQS2iIRj2TXx4pyJmhLM81pN5YUhz6nHX9yvfA7UyoVi8S9nsXUC/FIsCEjWBup0w8ind7OB8USsut1VKlUIbKryHXdmiGo7NbqDnRslKEEVmgOih8mSZKQCk04VqrnoFh7KZaaEU7nhX6iaIzJBI9oz1CBQ6ougimLVUa9NLt8Ds+MGcBhJM0TGmbq93CKQ6VmoW8mQ6zH6re3EP/yeoke1ryUiTjRVJDlomHCoY7gogYYMEmJ5jNDMJHMnA3JGEtMtCmrYPr4+jT8n7Rd2ynb7l2l1LhaNZMHJ+AUnAMHXIIGuAFN0AIETMADeARPVmo9Wy/W63I0Z60yx+AHrLdP1nGUnQ==</latexit>
  33. 41.

    Eddington luminosity LEdd p e- r Luminosity L from central

    object When is the radiation strong enough to prevent accretion of particles? photon field
  34. 42.

    F rad = F g Prad = Frad A =

    F c ) Frad = FA c ) Frad = L 4⇡r2 T c <latexit sha1_base64="arGTwTMi9W1wqBf6QwkC+1NwIOE=">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</latexit> Solve this to get LEdd: radiation force on an electron flux area
  35. 43.

    F rad = F g Prad = Frad A =

    F c ) Frad = FA c ) Frad = L 4⇡r2 T c <latexit sha1_base64="arGTwTMi9W1wqBf6QwkC+1NwIOE=">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</latexit> Solve this to get LEdd: radiation force on an electron flux area
  36. 44.

    F rad = F g Prad = Frad A =

    F c ) Frad = FA c ) Frad = L 4⇡r2 T c <latexit sha1_base64="arGTwTMi9W1wqBf6QwkC+1NwIOE=">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</latexit> Solve this to get LEdd: radiation force on an electron F g = GM(m e + m p ) r2 ≈ GMm p r2 flux area why?
  37. 45.

    F rad = F g Prad = Frad A =

    F c ) Frad = FA c ) Frad = L 4⇡r2 T c <latexit sha1_base64="arGTwTMi9W1wqBf6QwkC+1NwIOE=">AAACf3icjZFPa9swGMZlr1vTtNvS7diLaCgtbAQ7K7Q7FJIORg89pCP/IM7Ma0VORCXbSPJGEP4a/WC99bvsMCUxbZrusBcED7/30b/njTLOlPa8B8d9tfX6zXZlp7q79/bd+9r+h75Kc0loj6Q8lcMIFOUsoT3NNKfDTFIQEaeD6Pbboj/4RaViadLV84yOBUwTFjMC2qKwdtcJTSAFljApLoJYAjHfn0hh2o+0MKTAwQ82nWmQMv2N13z4Apcu3P4v33VhTnGQMSx/NouSBYpNBYTdxQFhre41vGXhl8IvRR2V1Qlr98EkJbmgiSYclBr5XqbHBqRmhNOiGuSKZkBuYUpHViYgqBqbZX4FPrJkguNU2pVovKTrOwwIpeYisk4BeqY2ewv4r94o1/H52LAkyzVNyOqiOOdYp3gxDDxhkhLN51YAkcy+FZMZ2DC0HVnVhuBvfvml6Dcb/pdG8+a03ros46igA3SITpCPzlALXaEO6iGC/jiHzifns+u4x27D9VZW1yn3fETPyv36F4Dmwm0=</latexit> Solve this to get LEdd: radiation force on an electron F g = GM(m e + m p ) r2 ≈ GMm p r2 L Edd = 4πGMm p c σT = 1.3 × 1038 ( M M⊙ ) erg s−1 flux area why?
  38. 47.

    Eddington luminosity: importance A system radiating at L > LEdd

    can halt mass accretion due to strong radiation pressure Roughly maximal luminosity that can be powered by accretion (if spherical symmetry) Useful luminosity unit in BH astrophysics
  39. 48.

    Eddington accretion rate • Assume an engine radiating at L

    = LEdd • If it were converting mass to radiative energy with efficiency η
  40. 49.

    L Edd = η · M Edd c2 ⇒ ·

    M Edd ≡ L Edd ηc2 • Assume an engine radiating at L = LEdd • If it were converting mass to radiative energy with efficiency η usually η = 0.1 Eddington accretion rate
  41. 50.

    L Edd = η · M Edd c2 ⇒ ·

    M Edd ≡ L Edd ηc2 • Assume an engine radiating at L = LEdd • If it were converting mass to radiative energy with efficiency η = 3 ( 0.1 η ) ( M 108M⊙ ) M ⊙ yr−1 Useful accretion rate unit in BH astrophysics usually η = 0.1 Eddington accretion rate
  42. 51.

    Eddington time tEdd · M = dM dt = ·

    M Edd ⇒ dM dt = M tEdd Assume BH accreting at Eddington rate also known as Salpeter time tS
  43. 52.

    Eddington time tEdd · M = dM dt = ·

    M Edd ⇒ dM dt = M tEdd Assume BH accreting at Eddington rate t Edd ≡ ηcσ T 4πGmp = 4 × 107 ( η 0.1 ) yr Useful timescale also known as Salpeter time tS
  44. 53.

    Useful websites and apps for grad students arxiv.org ui.adsabs.harvard.edu sci-hub.tw

    voxcharta.org Find papers Manage papers Mendeley, bibdesk, Papers, Jabref
  45. 54.

    Pro tips Organize papers using convention: 1. Folders named after

    categories 2. Filename: <Last name of first author><publication year> 3. Use a desktop search app to find (spotlight, cerebro, albert)
  46. 55.
  47. 56.
  48. 58.

    Misner, Thorne & Wheeler Effective potential for orbits around a

    Schwarzschild black hole E = 1 2 ( dr dτ) 2 + V eff V eff r/M effective potential face-on view of accretion disk innermost stable circular orbit 6M edge-on view
  49. 59.

    Misner, Thorne & Wheeler Effective potential for orbits around a

    Schwarzschild black hole E = 1 2 ( dr dτ) 2 + V eff V eff r/M effective potential innermost stable circular orbit face-on view of accretion disk face-on view of accretion disk risco
  50. 60.

    Important radii risco: Innermost stable circular orbit from now on,

    G = c = 1 r isco = 6M for a ∗ = 0 rc: photon capture radius also called photon sphere or photon ring r c = 3M seen from ∞ 27M apparent radius for a ∗ = 0
  51. 64.

    Important timescales Light-crossing t l = r c = 2

    ( r 104M ) ( M 108M⊙ ) months as a function of distance r from 108 M⦿ BH Sound-crossing t s = r cs = 700 ( r 104M ) ( M 108M⊙ ) ( T 105K ) −1/2 years Accretion t acc = r vr = 107 ( α 0.1 ) −4/5 ( r 104M) 5/4 ( M 108M⊙ ) 3/2 ( · M 0.1 · MEdd ) −3/10 years ~ viscous time Free-fall t ff = ( GM 2r3 ) −1/2 = 23 ( r 104M) 3/2 ( M 108M⊙ ) years ~ dynamical time
  52. 65.

    Gravitational sphere of influence of SMBHs r sph ≈ GM

    σ2 = 5 ( M 108M⊙ ) ( σ 300 km s−1 ) −2 pc stellar velocity dispersion (bulge)
  53. 66.

    Gravitational sphere of influence of SMBHs r sph ≈ GM

    σ2 = 5 ( M 108M⊙ ) ( σ 300 km s−1 ) −2 pc stellar velocity dispersion (bulge) rS / rsph = 10-6 Some size ratios rgal / rsph > 104 rbulge / rsph = 200
  54. 67.

    Efficiency of release of free energy from BH accretion disks

    r → ∞ How much orbital energy lost by particle when it disappears behind event horizon? 1st order estimate of Lacc
  55. 68.

    How much orbital energy lost by one particle? E acc

    = U(r → ∞) − U(r surface ) gravitational potential energy = GMm rsurface
  56. 69.

    E acc = U(r → ∞) − U(r surface )

    How much orbital energy lost by one particle? gravitational potential energy = GMm rsurface Energy lost by continuous inflow of particles? · m = dm dt dE acc dt = GM · m rsurface ⇒ L = GM · m rsurface
  57. 70.

    E acc = U(r → ∞) − U(r surface )

    How much orbital energy lost by one particle? gravitational potential energy = GMm rsurface Energy lost by continuous inflow of particle? · m = dm dt dE acc dt = GM · m rsurface ⇒ L = GM · m rsurface Luminosity released from accretion L = η · mc2 ⇒ η = L · mc2 = GM rsurface c2 maximized for compact objects
  58. 71.

    E acc = U(r → ∞) − U(r surface )

    How much orbital energy lost by one particle? gravitational potential energy = GMm rsurface Energy lost by continuous inflow of particle? · m = dm dt dE acc dt = GM · m rsurface ⇒ L = GM · m rsurface Luminosity released from accretion L = η · mc2 ⇒ η = L · mc2 = GM rsurface c2 maximized for compact objects
  59. 72.

    For a Schwarzschild BH η = 0.5 incorrect Newtonian value

    Correct GR result η = V eff (∞) − V eff (6M) = − V eff (6M) = 1 18 = 0.06
  60. 73.

    Itaipu Dam − 14 GW ⌘ = mgh mc2 =

    10 14 ✓ h 100 m ◆
  61. 75.

    face-on view of accretion disk ISCO radius depends on the

    BH spin face-on view of accretion disk a * = 0 a * = 0.998 Disk is: hotter larger surface area higher velocities edge-on view
  62. 76.

    UO aim o 0.2 0.5 0.7 0.6 0.9 0.95 0.96

    1 mO. (3.12) Fig.3.2. Efficiency of energy release by gas accreting through a thin accretion disk onto a spinning black hole. The quantity plotted is 1 - em. as a function of the hole angular η Blandford 1990 a * η=0.42 at a∗ =0.998
  63. 78.
  64. 79.

    Supermassive 106-1010 solar masses one in every galactic nucleus 5-80

    solar masses ~107 per galaxy Stellar black holes black holes
  65. 80.

    Supermassive 106-1010 solar masses one in every galactic nucleus 5-80

    solar masses ~107 per galaxy Stellar black holes ~1 Mpc ~100 kpc Active galactic nuclei Quasars Radio galaxies black holes Gamma- ray bursts Microquasars 1 pc = 3×1013 km Blazars Binary systems
  66. 81.

    Phenomenology of active galactic nuclei 8 m VLT reveals a

    um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering based on Tadhunter+08 Nuclear lum inosity Radio power Broad / Narrow lines
  67. 82.

    Phenomenology of active galactic nuclei 8 m VLT reveals a

    um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering based on Tadhunter+08 Nuclear lum inosity Radio power Broad / Narrow lines Type I Type II
  68. 83.

    λ (Angstrom) AGNs with and without broad emission lines BH’s

    gravity accelerating the gas to v>1000 km/s but half of AGNs show narrower lines Flux (arbitrary units)
  69. 84.

    λ (Angstrom) 6.7. AGN unification 139 Ionization cone Radio jet

    NLR clouds illuminated by central source Black hole accretion disk And BLR Clumpy dusty torus Type-II AGNs Radio loud Radio quiet Type-I AGNs Radio loud Radio quiet Blazars Type I Type II Unified model of AGNs
  70. 85.

    Phenomenology of active galactic nuclei 8 m VLT reveals a

    um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering Nuclear lum inosity Radio power Broad / Narrow lines
  71. 86.

    Phenomenology of active galactic nuclei 8 m VLT reveals a

    um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering Nuclear lum inosity Radio power Radio-quiet Radio-loud Radiogalaxies (FRI, FRII) radio-loud quasar blazars (BL Lac, FSRQ) Seyferts Radio-quiet quasar
  72. 87.

    Phenomenology of active galactic nuclei 8 m VLT reveals a

    um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering Nuclear lum inosity Radio power Radio-quiet Radio-loud 10% of AGNs are radio-loud
  73. 88.

    Phenomenology of active galactic nuclei based on Tadhunter+08 8 m

    VLT reveals a um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering Nuclear lum inosity Radio power Broad / Narrow lines
  74. 89.

    Phenomenology of active galactic nuclei based on Tadhunter+08 8 m

    VLT reveals a um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering Nuclear lum inosity Radio power Broad / Narrow lines Low- luminosity AGNs
  75. 90.

    Phenomenology of active galactic nuclei based on Tadhunter+08 8 m

    VLT reveals a um of the elliptical mplication is that cted in scattered cases, spectropo- ontrast of the scat- m and narrow line trum in polarized en et al., 1999). ons are static over a Sy1). However, ve only been pos- od is short relative 07 to 108 yr). Thus ons over their life- nt over the short e AGN are known mescales of years of NGC4151 and een Sy1 and Sy2 and Perez, 1984; nuclei have been similar timescale 1996). By analogy we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering Nuclear lum inosity Radio power Broad / Narrow lines Low- luminosity AGNs Quasars
  76. 91.

    ken on the 8 m VLT reveals a llar continuum

    of the elliptical A further complication is that may be detected in scattered ight. In such cases, spectropo- nhance the contrast of the scat- ar continuum and narrow line tic Sy1 spectrum in polarized d, 1985; Cohen et al., 1999). t classifications are static over Sy1 always a Sy1). However, ts of AGN have only been pos- is time period is short relative of AGN ($ 107 to 108 yr). Thus e classifications over their life- eing apparent over the short n fact, some AGN are known hanges on timescales of years the cases of NGC4151 and anged between Sy1 and Sy2 ars (Penston and Perez, 1984; me LINER nuclei have been eristics on a similar timescale ower et al., 1996). By analogy ry systems, we must also be the diversity in their properties, some of the most important in- sights into the nature of AGN have been gained by considering ? ˙ M / ˙ M E dd Phenomenology of active galactic nuclei based on Tadhunter+08 orientation orientation TOR = f( ˙ M) Nuclear lum inosity Radio power Broad / Narrow lines spin a magnetic flux Φbh
  77. 93.

    Current compilation of spin constraints D    

      0.(.0h)     Many rapidly spinning BHs. More slowly spinning population may emerge at higher masses. Reynolds (2013; arXiv:1302.3260) … also see Sesana et al. (2014) BH spin distribution from X-ray spectroscopy (only radio quiet AGN) 106 107 108 109 Black hole mass (MSun) cf. also Brenneman+13; King+13 Reynolds+13 Spin a XMM-Newton + Suzaku Why no jets?
  78. 94.

    Sikora+2007 log Lbol/LEdd (radio loudness) BLRG RL quasars FR I

    PG quasars Sy + LINER The BH knows about its host galaxy Radio louds Radio quiets
  79. 95.

    log Lbol/LEdd (radio loudness) Radio quiets ellipticals spirals spin~1? spin<0.3

    ? Wilson & Colbert 95 Moderski+96,98 Tchekhovskoy+10 Radio louds Sikora+2007 The BH knows about its host galaxy
  80. 97.

    D⇢ Dt + ⇢r · v = 0 ⇢ Dv

    Dt = rp ⇢r + r · T ⇢ D(e/⇢) Dt = pr · v + T2/µ Conservation of 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 Equations of Newtonian hydrodynamics Plus: equation of state opacity description viscosity taken from accretion lecture at “bh gastrophysics” course Rate of change “following the fluid”
  81. 98.

    General Relativistic Hydrodynamics • The general relativistic hydrodynamics equations are

    obtained from the local conservation laws of the stress-energy tensor, Tµν (the Bianchi identities), and of the matter current density Jµ (the continuity equation): rµ(⇢uµ) = 0 <latexit sha1_base64="KAlzxr4lIDT38NhaQPvnHsKSdBc=">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</latexit> <latexit 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sha1_base64="KAlzxr4lIDT38NhaQPvnHsKSdBc=">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</latexit> rµTµ⌫ = 0 <latexit 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sha1_base64="PnhcmxFqN1xgJ9g1AKaIvzgSuNk=">AAAC5HichVFNTxRBEH2MgLgKrHox8TJxwRAPmxouEoyGxItHvhZIGNjMzPauHWZ6xvnYiJP9A8abMR5MTDDhQPgZHoSbHjzwEwxHSLx4sKZ3ogJRezJdVa/rVb+uciNfJinR0YBxaXBo+PLIlcrVa6Nj49XrN1aSMIs90fBCP4zXXCcRvlSikcrUF2tRLJzA9cWqu/W4OF/tijiRoVpOtyOxETgdJdvSc1KGmtUHtis6UuXiWaaRe72KrRzXd5p2kJnLm3lhbJX1HppUsYVq/ZHZrNaoTnqZFx2rdGoo13xYPYSNFkJ4yBBAQCFl34eDhL91WCBEjG0gZyxmT+pzgR4qzM04S3CGw+gW7x2O1ktUcVzUTDTb41t8/mNmmpikr7RHJ3RA+/SNfvy1Vq5rFFq22bp9roia4y9vLX3/Lytgm+Lpb9Y/NadoY0Zrlaw90kjxCq/P7754e7I0uziZ36UPdMz6d+iIPvILVPfU210Qi+909RZz2my7bD3UuIM5R4X2EM+17+pOtH6pMzGh8yb4Hu4qD9E6P7KLzsp03aK6tTBdm3tUjnMEt3EHU1zpPubwBPNosIIdfMJnfDHaxivjtfGmn2oMlJybOLOM9z8B2Q2uUQ==</latexit> equations of motion (µ = 0, ..., 3) <latexit 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sha1_base64="wCsNStTFWtoQk6I2UFh6SF3UH3s=">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</latexit> : covariant derivative associated with the four dimensional spacetime metric rµ <latexit 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sha1_base64="nAUSOQhKnwI0Yux/jgLV6W63uy4=">AAAC1XichVE9TxRRFD2MIrCgrNiQ2GxcMMaYzR0aDQUhsaHka1kShmxmZt+uL8y8GeZjI0y2MxY2JDYWVJBQGP4ALdroD6DgJxBKTGwsvPN24hdR32Teve/ce+47714n9GScEJ0PGDduDt4aGh4pjY7dvjNevjuxFgdp5Iq6G3hBtO7YsfCkEvVEJp5YDyNh+44nGs7W8zze6IooloFaTXZCsenbHSXb0rUThprlJ5YjOlJlYjvVyONeyVK249lNy09LllCtX0LNcpVqpFflumMWThXFWgzKn2GhhQAuUvgQUEjY92Aj5m8DJgghY5vIGIvYkzou0EOJuSlnCc6wGd3ivcOnjQJVfM5rxprt8i0e/xEzK5imM3pPV/SJjumCvv21VqZr5Fp22Dp9rgib428mV77+l+WzTfDiJ+ufmhO08Uxrlaw91Ej+CrfP7+6+u1qZXZ7OHtIhXbL+Azqnj/wC1f3iHi2J5X1dvcWcNtsuWxdV7mDGp1x7gJfad3QnWj/UVTCl86b4Hu4qD9H8c2TXnbWZmkk1c2mmOj9XjHMY9/EAj7jSU8xjAYuos4K3OMEpPhgNo2e8Ml73U42BgnMPvy1j7ztMT6jH</latexit> <latexit sha1_base64="nAUSOQhKnwI0Yux/jgLV6W63uy4=">AAAC1XichVE9TxRRFD2MIrCgrNiQ2GxcMMaYzR0aDQUhsaHka1kShmxmZt+uL8y8GeZjI0y2MxY2JDYWVJBQGP4ALdroD6DgJxBKTGwsvPN24hdR32Teve/ce+47714n9GScEJ0PGDduDt4aGh4pjY7dvjNevjuxFgdp5Iq6G3hBtO7YsfCkEvVEJp5YDyNh+44nGs7W8zze6IooloFaTXZCsenbHSXb0rUThprlJ5YjOlJlYjvVyONeyVK249lNy09LllCtX0LNcpVqpFflumMWThXFWgzKn2GhhQAuUvgQUEjY92Aj5m8DJgghY5vIGIvYkzou0EOJuSlnCc6wGd3ivcOnjQJVfM5rxprt8i0e/xEzK5imM3pPV/SJjumCvv21VqZr5Fp22Dp9rgib428mV77+l+WzTfDiJ+ufmhO08Uxrlaw91Ej+CrfP7+6+u1qZXZ7OHtIhXbL+Azqnj/wC1f3iHi2J5X1dvcWcNtsuWxdV7mDGp1x7gJfad3QnWj/UVTCl86b4Hu4qD9H8c2TXnbWZmkk1c2mmOj9XjHMY9/EAj7jSU8xjAYuos4K3OMEpPhgNo2e8Ml73U42BgnMPvy1j7ztMT6jH</latexit> <latexit sha1_base64="nAUSOQhKnwI0Yux/jgLV6W63uy4=">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</latexit> gµ⌫ <latexit sha1_base64="BNW7O5bNVMUwsUGRjYcHYR5bwf4=">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</latexit> <latexit sha1_base64="BNW7O5bNVMUwsUGRjYcHYR5bwf4=">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</latexit> <latexit sha1_base64="BNW7O5bNVMUwsUGRjYcHYR5bwf4=">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</latexit> <latexit sha1_base64="BNW7O5bNVMUwsUGRjYcHYR5bwf4=">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</latexit> • The density current is given by Jµ = ⇢uµ <latexit 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sha1_base64="JGTFsNySLiGKHftr0cnUopF+Tgk=">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</latexit> <latexit sha1_base64="JGTFsNySLiGKHftr0cnUopF+Tgk=">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</latexit> <latexit sha1_base64="JGTFsNySLiGKHftr0cnUopF+Tgk=">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</latexit> is the fluid 4-velocity and is the rest-mass density in a locally inertial reference frame. uµ <latexit sha1_base64="uI+nrVkdAUAJIl9V5ZPRQ/vi9C8=">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</latexit> <latexit sha1_base64="uI+nrVkdAUAJIl9V5ZPRQ/vi9C8=">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</latexit> <latexit sha1_base64="uI+nrVkdAUAJIl9V5ZPRQ/vi9C8=">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</latexit> <latexit sha1_base64="uI+nrVkdAUAJIl9V5ZPRQ/vi9C8=">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</latexit> ⇢ <latexit sha1_base64="O69ttEf24RIjUq+GBdXhUWbOp7Q=">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</latexit> <latexit sha1_base64="O69ttEf24RIjUq+GBdXhUWbOp7Q=">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</latexit> <latexit sha1_base64="O69ttEf24RIjUq+GBdXhUWbOp7Q=">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</latexit> <latexit sha1_base64="O69ttEf24RIjUq+GBdXhUWbOp7Q=">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</latexit> slide: Yosuke Mizuno
  82. 99.

    rµ(⇢uµ) = 0 <latexit sha1_base64="KAlzxr4lIDT38NhaQPvnHsKSdBc=">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</latexit> <latexit sha1_base64="KAlzxr4lIDT38NhaQPvnHsKSdBc=">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</latexit> <latexit sha1_base64="KAlzxr4lIDT38NhaQPvnHsKSdBc=">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</latexit> <latexit

    sha1_base64="KAlzxr4lIDT38NhaQPvnHsKSdBc=">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</latexit> rµTµ⌫ = 0 <latexit sha1_base64="PnhcmxFqN1xgJ9g1AKaIvzgSuNk=">AAAC5HichVFNTxRBEH2MgLgKrHox8TJxwRAPmxouEoyGxItHvhZIGNjMzPauHWZ6xvnYiJP9A8abMR5MTDDhQPgZHoSbHjzwEwxHSLx4sKZ3ogJRezJdVa/rVb+uciNfJinR0YBxaXBo+PLIlcrVa6Nj49XrN1aSMIs90fBCP4zXXCcRvlSikcrUF2tRLJzA9cWqu/W4OF/tijiRoVpOtyOxETgdJdvSc1KGmtUHtis6UuXiWaaRe72KrRzXd5p2kJnLm3lhbJX1HppUsYVq/ZHZrNaoTnqZFx2rdGoo13xYPYSNFkJ4yBBAQCFl34eDhL91WCBEjG0gZyxmT+pzgR4qzM04S3CGw+gW7x2O1ktUcVzUTDTb41t8/mNmmpikr7RHJ3RA+/SNfvy1Vq5rFFq22bp9roia4y9vLX3/Lytgm+Lpb9Y/NadoY0Zrlaw90kjxCq/P7754e7I0uziZ36UPdMz6d+iIPvILVPfU210Qi+909RZz2my7bD3UuIM5R4X2EM+17+pOtH6pMzGh8yb4Hu4qD9E6P7KLzsp03aK6tTBdm3tUjnMEt3EHU1zpPubwBPNosIIdfMJnfDHaxivjtfGmn2oMlJybOLOM9z8B2Q2uUQ==</latexit> <latexit sha1_base64="PnhcmxFqN1xgJ9g1AKaIvzgSuNk=">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</latexit> <latexit sha1_base64="PnhcmxFqN1xgJ9g1AKaIvzgSuNk=">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</latexit> <latexit sha1_base64="PnhcmxFqN1xgJ9g1AKaIvzgSuNk=">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</latexit> • GRHD equations + Maxwell equations rµ ⇤Fµ⌫ = 0 <latexit sha1_base64="rXiqfRiBsm9gxqIaUvfl53i4bYQ=">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</latexit> <latexit sha1_base64="rXiqfRiBsm9gxqIaUvfl53i4bYQ=">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</latexit> <latexit sha1_base64="rXiqfRiBsm9gxqIaUvfl53i4bYQ=">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</latexit> <latexit sha1_base64="rXiqfRiBsm9gxqIaUvfl53i4bYQ=">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</latexit> where Fµν, Faraday tensor may be constructed from electric and magnetic fields Eα, Bα as measured in a generic frame as Fµ⌫ = UµE⌫ U⌫Eµ ( g) 1/2⌘µ⌫ U B <latexit sha1_base64="If1gB3MC5mQfHlayiaYRt0uwyok=">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</latexit> <latexit sha1_base64="If1gB3MC5mQfHlayiaYRt0uwyok=">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</latexit> <latexit sha1_base64="If1gB3MC5mQfHlayiaYRt0uwyok=">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</latexit> <latexit sha1_base64="If1gB3MC5mQfHlayiaYRt0uwyok=">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</latexit> where ηµνλδ: the fully-antisymmetric symbol and g : determinant of 4- metric • The dual Faraday tensor is ⇤Fµ⌫ = UµB⌫ U⌫Bµ ( g) 1/2⌘µ⌫ U E <latexit sha1_base64="kApS+ghOC5uDuhiW5Qcdv4HUVsw=">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</latexit> <latexit sha1_base64="kApS+ghOC5uDuhiW5Qcdv4HUVsw=">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</latexit> <latexit sha1_base64="kApS+ghOC5uDuhiW5Qcdv4HUVsw=">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</latexit> <latexit sha1_base64="kApS+ghOC5uDuhiW5Qcdv4HUVsw=">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</latexit> • Ideal MHD limit Fµ⌫u⌫ = 0 <latexit 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sha1_base64="rkQI2MUI5NGkN3A17VMK8F6LACM=">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</latexit> <latexit sha1_base64="rkQI2MUI5NGkN3A17VMK8F6LACM=">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</latexit> <latexit sha1_base64="rkQI2MUI5NGkN3A17VMK8F6LACM=">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</latexit> General relativistic magnetohydrodynamics slide: Yosuke Mizuno
  83. 101.

    Thermal sta (NLS1s?) Intermediat (Quasars, Se M · a Simple

    description of an accretion disk · M/ · M Edd mass accretion rate h /r disk thickness · M = 4πr2ρv r mass accr. rate related to gas density
  84. 102.

    t cool ≪ t acc h/r ⇠ 1 –8 –6

    –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) M · 0 log (L/L Edd ) a b · M/ · M Edd 1 RIAFs h/r ⌧ 1 Thin disks –6 –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) M · log (L/L Edd ) a b –8 (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) 0 Figure 7 (a) Schematic diagram showing the configuration of the accretion flow in different accretion rate ˙ MBH (panel adapted from Esin et al. 1997, Narayan & McClintock in parentheses. Red triangles indicate the hot accretion flow, whereas thick black h transition radius Rtr where the thin disk is truncated becomes smaller with increas truncated, and its inner edge is located at the ISCO. (b) Plot of the Eddington-scal from observations. The transition radii were estimated by modeling spectra of ind Yuan & Narayan 2004). Abbreviations: AGN, active galactic nuclei; BHB, black h LLAGN, low-luminosity active galactic nuclei. h/r ⇠ 1 0.01 then move on and describe consequence for efficiency q adv ≫ q − q adv ≫ q − Super-Eddington q − ≫ q adv Unified theory of black hole accretion flows L/L Edd
  85. 103.

    t cool ≫ t acc h/r ⌧ 1 Thin disks

    · M/ · M Edd 1 –6 –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) M · log (L/L Edd ) a b –8 (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) 0 Figure 7 (a) Schematic diagram showing the configuration of the accretion flow in different accretion rate ˙ MBH (panel adapted from Esin et al. 1997, Narayan & McClintock in parentheses. Red triangles indicate the hot accretion flow, whereas thick black h transition radius Rtr where the thin disk is truncated becomes smaller with increas truncated, and its inner edge is located at the ISCO. (b) Plot of the Eddington-scal from observations. The transition radii were estimated by modeling spectra of ind Yuan & Narayan 2004). Abbreviations: AGN, active galactic nuclei; BHB, black h LLAGN, low-luminosity active galactic nuclei. h/r ⇠ 1 0.01 then move on and describe consequence for efficiency q adv ≫ q − q adv ≫ q − Super-Eddington Unified theory of black hole accretion flows h/r ⇠ 1 –8 –6 –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) M · 0 log (L/L Edd ) a b RIAFs radiatively inefficient accretion flow L/L Edd
  86. 104.

    h/r ⇠ 1 h/r ⌧ 1 Thin disks –8 –6

    –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) M · 0 log (L/L Edd ) a b · M/ · M Edd 1 RIAFs –6 –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) M · log (L/L Edd ) a b –8 (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) 0 Figure 7 (a) Schematic diagram showing the configuration of the accretion flow in different accretion rate ˙ MBH (panel adapted from Esin et al. 1997, Narayan & McClintock in parentheses. Red triangles indicate the hot accretion flow, whereas thick black h transition radius Rtr where the thin disk is truncated becomes smaller with increas truncated, and its inner edge is located at the ISCO. (b) Plot of the Eddington-scal from observations. The transition radii were estimated by modeling spectra of ind Yuan & Narayan 2004). Abbreviations: AGN, active galactic nuclei; BHB, black h LLAGN, low-luminosity active galactic nuclei. h/r ⇠ 1 0.01 q adv ≫ q − q adv ≫ q − Super-Eddington Unified theory of black hole accretion flows
  87. 105.

    h/r ⇠ 1 h/r ⌧ 1 Thin disks –8 –6

    –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) M · 0 log (L/L Edd ) a b · M/ · M Edd 1 RIAFs –6 –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) M · log (L/L Edd ) a b 0.01 q adv ≫ q − –8 (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) 0 Figure 7 (a) Schematic diagram showing the configuration of the accretion flow in different accretion rate ˙ MBH (panel adapted from Esin et al. 1997, Narayan & McClintock in parentheses. Red triangles indicate the hot accretion flow, whereas thick black h transition radius Rtr where the thin disk is truncated becomes smaller with increas truncated, and its inner edge is located at the ISCO. (b) Plot of the Eddington-scal from observations. The transition radii were estimated by modeling spectra of ind Yuan & Narayan 2004). Abbreviations: AGN, active galactic nuclei; BHB, black h LLAGN, low-luminosity active galactic nuclei. h/r ⇠ 1 Super-Eddington Unified theory of black hole accretion flows Adapted from Yuan & Narayan 2014, ARA&A t diffusion ≫ t acc photon
  88. 106.

    h/r ⇠ 1 h/r ⌧ 1 Adapted from Yuan &

    Narayan 2014, ARA&A Thin disks Unified theory of black hole accretion flows –8 –6 –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) M · 0 log (L/L Edd ) a b · M/ · M Edd 1 RIAFs –6 –4 –2 0 Brig C Thermal state (NLS1s?) Intermediate state? (Quasars, Seyferts?) Hard state (LLAGNs, Seyferts) M · log (L/L Edd ) a b –8 (LLAGNs, Seyferts) Quiescent state (LLAGNs, Sgr A*) 0 Figure 7 (a) Schematic diagram showing the configuration of the accretion flow in different accretion rate ˙ MBH (panel adapted from Esin et al. 1997, Narayan & McClintock in parentheses. Red triangles indicate the hot accretion flow, whereas thick black h transition radius Rtr where the thin disk is truncated becomes smaller with increas truncated, and its inner edge is located at the ISCO. (b) Plot of the Eddington-scal from observations. The transition radii were estimated by modeling spectra of ind Yuan & Narayan 2004). Abbreviations: AGN, active galactic nuclei; BHB, black h LLAGN, low-luminosity active galactic nuclei. h/r ⇠ 1 0.01 Super-Eddington radiative efficiency η ≪ 0.1 η = 0.06 − 0.4 η ≪ 0.1 L/L Edd
  89. 107.

    thin or thick. In thin disks, most of the mass

    supplied at large radii reaches the central black hole. By contrast, in thick disks, very little of the supplied mass ends up accreting into the hole. Instead, most of the mass circulates in convective motions (33, 34) or is driven away in an unbound outflow (35, 36). This in turn causes the amount of radiation from the accretion flow to decrease drastically. Because the fate of sup- plied matter depends so strongly on the mode of accretion (thin versus thick), it is likely that bright accreting black holes occupy a Jet Coronal envelope Inner torus Main disk body KDP 30 20 10 10 20 0 –10 1 SNE, GRB Radiation–trapped Bright XRBs, AGN Faint XRBs, AGN 2 2 3 log R (RS ) log R (km) log M (MEdd ) log M (g s–1) Regimes of BH accretion Super-Eddington, radiation-trapped TDE, AGN? Near-Eddington Sub-Eddington om the accretion flow to Because the fate of sup- so strongly on the mode rsus thick), it is likely black holes occupy a Main disk body KDP 30 20 10 0 SNE, GRB Radiation–trapped Bright XRBs, AGN Faint XRBs, AGN log M (MEdd ) log M (g s–1) Main disk body KDP 20 10 0 –10 1 Radiation–trapped Bright XRBs, AGN Faint XRBs, AGN 2 log R (RS ) log M (MEdd ) log M (g s–1) the central black s, very little of the ng into the hole. ates in convective way in an unbound turn causes the accretion flow to the fate of sup- ngly on the mode ick), it is likely holes occupy a KDP 30 10 20 SNE, GRB Radiation–trapped 2 3 log R (km) log M (MEdd ) log M (g s–1) Adapted from Narayan & Quataert 2005 Faint XRBs, low- luminosity AGNs Bright XRB, quasars, Seyferts log R (pc) -4 -5 ? ? slide from BASS ESO 2018 talk
  90. 108.
  91. 110.

    Hercules A 3C 31 ~1 Mpc ~100 kpc M87 Cosmic

    particle accelerators! Black holes produce relativistic jets of particles Huge powers (enough to unbind a galaxy) Aligned over long periods (millions of years)
  92. 111.

    How are relativistic jets produced by black holes? Conjecture: from

    spinning black holes Huge free energy Stable gyroscopes Growing evidence that this is correct Theory/simulations Observations (?)
  93. 112.

    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
  94. 114.

    How jets are formed large scale B + accretion +

    rotation Semenov+2004, Science magnetic flux tube ergosphere Requirements v ⊵ spinning black hole
  95. 115.

    How jets are formed large scale B + accretion +

    rotation Semenov+2004, Science Requirements P = B2 8⇡ <latexit sha1_base64="FqfqdSJ6YeVubAYd6XxayOAVE88=">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</latexit> <latexit sha1_base64="FqfqdSJ6YeVubAYd6XxayOAVE88=">AAACDHicdVDLSsNAFJ34rPUVdSO4GSyCCwkTNdgsBNGNywrWFppaJtOJHTpJhplJoYT6CX6FW125E7f+gwv/xUmtoKIHLhzOuZd77wkFZ0oj9GZNTc/Mzs2XFsqLS8srq/ba+pVKM0lonaQ8lc0QK8pZQuuaaU6bQlIch5w2wv5Z4TcGVCqWJpd6KGg7xjcJixjB2kgde7N2HEQSk/y0E4geu94f5VUYCDbq2BXkIM/3XASR4yHXPyiI71cPPQ+6DhqjAiaodez3oJuSLKaJJhwr1XKR0O0cS80Ip6NykCkqMOnjG9oyNMExVXvdARNqTNv5+JkR3DFmF0apNJVoOFa/D+c4VmoYh6YzxrqnfnuF+JfXynRUbecsEZmmCflcFGUc6hQWycAuk5RoPjQEE8nM2ZD0sMlGm/zKJo+vp+H/5GrfcZHjXhxWTk4nyZTAFtgGu8AFR+AEnIMaqAMCbsE9eACP1p31ZD1bL5+tU9ZkZgP8gPX6AVytm2E=</latexit> <latexit sha1_base64="FqfqdSJ6YeVubAYd6XxayOAVE88=">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</latexit> <latexit sha1_base64="FqfqdSJ6YeVubAYd6XxayOAVE88=">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</latexit>
  96. 116.

    How jets are formed large scale B + accretion +

    rotation Semenov+2004, Science Requirements environment radiation GR Lense-Thirring precession Complications for theory Blandford-Znajek mechanism: Jet power rotation frequency magnetic flux ∝(ΦΩ)2 ∼ ( a M Φ BH) 2 ∼ a2 · Mc2 Jet
  97. 118.

    Best way of producing relativistic jets Compact object accreting highly

    magnetized gas magnetized accretion flow Such conditions are natural outcomes of stellar deaths and easily produced around black holes
  98. 119.

    Basic facts about jets Highly magnetized β = P gas

    Pmag < 0.1 N m s T th r in la a in u ti s o U strong synchrotron radiation ν c ∼ γ2B MHz expect to see in radio
  99. 120.

    Basic facts about jets Highly magnetized β = P gas

    Pmag < 0.1 Relativistic Γ ∼ a few − 100 v > 0.9c AGNs GRBs bulk Lorentz factor
  100. 122.

    shall Cohe discovered These are p that is, wh any

    misalig jets associa the emissio with the fa degrees or One does n less they ex radio sour v= 0.94c comoving frame ments of s shall Cohe discovered These are that is, wh any misali jets associa the emissio with the fa degrees or One does less they ex v= 0.5c ments of sm shall Cohe discovered These are p that is, wh any misalig jets associa the emissio with the fa degrees or One does n less they ex v= 0.75c shall Cohe discovered These are that is, wh any misali jets associa the emissio with the fa degrees or One does less they ex radio sour v= 0.98c observer’s frame
  101. 123.

    Basic facts about jets Highly magnetized β = P gas

    Pmag < 0.1 Relativistic Γ ∼ a few − 100 v > 0.9c Beamed: most radiated power along the propagation direction, skewed towards high frequency relativistic aberration Doppler shift
  102. 124.

    neutrinos, cosmic rays maybe show Feynman diagrams Basic facts about

    jets Collimated Highly magnetized β = P gas Pmag < 0.1 Relativistic Γ ∼ a few − 100 v > 0.9c Beamed: most radiated power along the propagation direction θ j < 10∘ collimation half-angle θ j
  103. 126.

    Launching of Active Galactic Nuclei Jets 19 toward the polar

    regions as they move away from the BH. The group of field lines highlighted in green connects to the BH and makes up the twin polar jets. The jet field lines extract BH rotational energy and carry it away to large distances. These field lines have little to no gas attached to them and are therefore highly magnetized (since disk gas cannot cross magnetic field lines and is thus blocked from getting to the polar region, the jet field lines either drain the gas to the BH or fling the gas Fig. 9 [Panel (a)]: A 3D rendering of our MAD a = 0.99 model at t = 27,015rg /c (i.e., the same time as Fig. 8d). Dynamically-important magnetic fields are twisted by the rotation of a BH (too small to be seen in the image) at the center of an accretion disk. The azimuthal magnetic field component clearly dominates the jet structure. Density is shown with color: disk body is shown ith yellow and jets with cyan-blue color; we show jet magnetic field lines with cyan bands. The s approximately 300rg ⇥800rg . [Panel (b)]: Vertical slice through our MAD a = 0.99 e and azimuth over the period, 25,000rg /c  t  35,000rg /c. Ordered, fields remove the angular momentum from the accreting gas pinning BH (a = 0.99). Gray filled circle shows the s, and gray dashed lines indicate density of the time-average magnetic s is also seen from nd with Jet sim.: Tchekhovskoy The difference between blazars and radio galaxies is orientation Blazar Radio galaxy Radio galaxy Rad
  104. 127.

    Beyond orientation: Radio loud AGNs have different states of accretion

    flow FR I FR II Radio galaxy morphology BL Lac FSRQ flux flux ADAF thin disk Blazar spectral type Wavelength (A) Wavelength (A) Low power, weak lines High power, broad lines, UV bump Accretion mode torus disappears?
  105. 128.

    Synchrotron emission Inverse Compton Isotropic Radio Emission from Slowed Plasma

    in the Lobes E. Meyer+2011 log(⌫/Hz) log(⌫L⌫/erg s 1) dp" = Pdx" As a consequence, P is a scalar invariant. We therefor relativistic generalisation of equation (2.3)for which choice is 2e2 dp" dp,. P=--<--> dr dr where r denotes the proper time. Rewriting this eq (3 = v/ c, we obtain For synchrotron radiation, the particle energy is Equation(2.6)can be re-written in the convenient for 2 2 (B2) P = 2aTCf (31. 871" Synchrotron power: Opt. thin synchrotron Synchrotron self-absorption Blazars: observing beamed power of the relativistic jet
  106. 130.

    Ghisellini 11 Swift / BAT Fermi / LAT Integral FSRQs

    BL Lacs Line strength ˙ M/ ˙ MEdd Blazar zoo: the “blazar sequence” Fossati+1998; Donato+2001
  107. 131.

    Ghisellini 11 Swift / BAT Fermi / LAT Integral FSRQs

    BL Lacs FR II FR I Continuous? Discontinuity Blazar zoo: the “blazar sequence” Fossati+1998; Donato+2001
  108. 135.
  109. 136.

    EM radiation: radio, infrared, optical, X-rays, gamma-rays neutrinos, cosmic rays

    Giant Magellan Telescope ELT LSST Cherenkov Telescope Array SKA IceCube Observatory AGNs: Powerful EM radiators, particle accelerators LISA GWs Athena
  110. 137.

    The future of AGN astrophysics is bright! You can be

    part of this! blackholegroup.org
  111. 138.

    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