The Last 40 Years of Accretion Disk Theory...(abridged)
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1 The Last 40 Yeas of Accetion Disk Theoy...(abidged) Matin Pessah Niels Boh Intenational Academy DARK Cosmology Cente - Niels Boh Institute - Januay 13, 2011 Image Cedit: NASA
2 Why Ae Accetion Disks Impotant? Cucial fo undestanding - How stas and planets fom - What powes the bightest X-ay souces in the sky - Why Active Galactic Nuclei (Quasas) shine - How to use flow dynamics to map black hole space-time Poto-sta X-ay Binay Active Galactic Nucleus Release of gavitational enegy in accetion disks esponsible fo some of the most poweful phenomena in natue!
3 Why Ae Accetion Disk so Had to Undestand? R Gavity balanced by pessue gadient along R Enegy flows along R too! Mass Momentum Enegy R Magnetic fields do not seem to influence stella stuctue significantly Mostly themal enegy Magnetic fields ae essential fo accetion disks to wok Non-themal pocesses
4 Kepleian Disks 101 Ω(R) Matte Ω 2 = GM R 3 Ω R 3/2 R
5 Impotance of Angula Momentum Tanspot l(r) Angula Momentum l R 1/2 l = v R =(ΩR)R = ΩR 2 R Gas in the disk must lose angula momentum!!!!
6 Impotance of Stess... ρ t l t +.(ρv) =0 +.(lv) = 0 Angula Mass consevation momentum is not conseved... l t +.(lv) = 1 (2 T ) If thee is no stess, angula momentum fo fluid elements in the disk is conseved and matte does not accete!
7 Solving the Angula Momentum Poblem. I Poblem I: Tanspot of Angula Momentum!!!
8 Solving the Angula Momentum Poblem. I Solution I: Assume some kind of tubulent viscosity Eddies of sie H inteacting with tunove velocity α c s t tub t obs!!! Shakua & Sunyaev 70s, α-model With this enhanced stess we can match the fast timescales obseved!
9 The Standad Accetion Disk Model Since the ealy 70 s we have used this viscosity pesciption to emove angula momentum fom the disk... Angula momentum Matte We can calculate the global stuctue of the disk Σ(),P(),T(),v (),...
10 Solving the Angula Momentum Poblem. II Poblem II: Oigin of Tubulence? - Kepleian flows ae vey STABLE to hydodynamic petubations (Hawley et al. 1999, Yi et al. 2006) - Convection? (Stone & Balbus 1996, Lesu & Ogilvie 2010) Solution II: s * Velikhov & Chandasekha ealy 60 s Balbus & Hawley in ealy 90 s B * Mechanism to disupt lamina flows * Numeical simulations confim development of MHD tubulence
11 A Piece of Physics
12 Acoustic Waves Alfven Waves P B Restoing foce: pessue gadients Restoing foce: magnetic tension δp δb k k
13 MHD Waves B
14 MHD Waves Magnetic Tension B δb
15 MHD Waves B δb
16 MHD Waves B δb
17 MHD Waves B δb
18 MHD Waves B δb
19 MHD Waves B δb
20 MHD Waves B δb
21 MHD Waves B δb
22 MHD Waves B δb
23 MHD Waves B δb
24 MHD Waves B δb
25 MHD Waves B δb
26 MHD Waves k B δb
27 MHD Waves k B δb ω 2 = k 2 v A 2 v A 2 = B2 4πρ
28 Magnetootational Instability B Diffeential otation To the black hole
29 Magnetootational Instability B δb Diffeential otation
30 Magnetootational Instability Diffeential otation
31 Magnetootational Instability Diffeential otation
32 Magnetootational Instability Diffeential otation
33 Magnetootational Instability Diffeential otation
34 Magnetootational Instability Diffeential otation
35 Magnetootational Instability Diffeential otation
36 Magnetootational Instability Magnetic Toques + Diffeential otation B δb Magnetootational Instability B δb
37 Magnetootational Instability Magnetic Toques + Diffeential otation B δb Magnetootational Instability k 2 2 v A < 2Ω 2 dlnω d ln B δb v A 2 = B2 4πρ
38 Tubulent Magnetied Accetion Disks: MRI Diffeentially otating magnetied plasmas ae unstable to the Magnetootational Instability (MRI) (Velikhov & Chandasekha, 60 s; Balbus & Hawley, 90 s) Fom J. Hawley s website Fom J. Stone s website How do we measue stesses and angula momentum tanspot fom simulations?
39 Angula Momentum Tanspot: MRI & Tubulence Angula momentum consevation l t + (lv) = 1 [2 (R M )] Reynolds Stess Maxwell Stess MRI and MHD tubulence lead to coelated fluctuations of the PROPER sign!!! Sano et al. 2004
40 Impotance & Limitations of Numeical Simulations Hubble Time 1Gy 1y Inside Hoion Mean Field Models BH Vaiability Disk Spectum BH Gowth Viscous Satuation Obital Boad Line Region 10 7 M o 1sec Numeical Simulations 0.1AU 1AU 1000AU
41 MHD Tubulent Tanspot vs. alpha-viscosity Shakua & Sunyaev ( 70s): tanspot due to tubulence Pessah, Chan, & Psaltis, 2006 Pessah, Chan, & Psaltis, 2008 Shakua & Sunyaev, 1973 Standad pesciption does not captue physics coectly! Need to undestand tubulent MHD angula momentum tanspot fom fist pinciples...
42 Satuation of MRI & MHD Tubulence -Maxwell Non-linea Reynolds Satuation MRI gowth Insets fom Sano et al. 2004
43 Compaison with Numeical Simulations Encouaging ageement with oveall featues of numeical simulations See woks by Knobloch & Julien, Umuhan et. al, Vishniac, Latte et. al, Longaetti & Lesu,...
44 Cuent Focus and Futue Pospects CK Chan & Pessah 2011 Whee ae we going? Bette mico-physics. Themodynamics. Synegy between analytical and numeical wok Davis, Stone, & Pessah 2010 Moe ealistic global simulations Beckwith et al, 2008
45 Recap: The Big Pictue Fundamental Poblem in Accetion Disks: How to get id of angula momentum Since ealy 70 s we have dealt with this poblem by using a pesciption poposed by Shakua & Sunyaev (1973) Balbus & Hawley (1991): magnetic fields ae key! Diffeentially otating, magnetied plasmas ae unstable to MRI Ensuing tubulence emoves angula momentum fom disk! Fom J. Hawley s website Massive analytical and numeical effots to undestand MHD tubulence and simulate accetion disks Fom J. Stone s website
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