Accretion discs Geoffroy Lesur (IPAG, Grenoble, France) Les Houches
Outline Accretion discs and jets: what are they Accretion discs in nature Jets in nature Accretion disc models Hydrostatic equilibrium Angular momentum transport Linear stability A Specific application of the MRI to protoplanetary discs Nonideal MRI Direct detection of turbulence in protoplanetary discs 2
Protoplanetary discs Credit: C. Burrows and J. Krist (STScl), Artist view K. Stapelfeldt (JPL) and NASA Size 10 9 -10 13 m Central object: young star (10 30 kg) Temperature 10 3 -10 K 3
Structures in protoplanetary discs I- Vortices C Giant anticyclonic vortex [van-der Marel+ (2013)] 4
Structures in protoplanetary discs II- Rings HL tau deprojected HL tau ALMA (ESO/NAOJ/NRAO) [Brogan+2015] Press release 6 Nov. 2014 5
Compact binaries Artist view Size 10 4 -10 8 m Central object: white dwarf, neutron star, black hole (10 30 kg) Temperature 10 5 -10 3 K 6
Active galactic nuclei (blazars, quasars…) M87 Size 10 10 -10 15 m Central object: black hole (10 36 -10 39 kg=10 6 -10 9 M sun ) Temperature 10 5 -10 2 K 7
Jets in protoplanetary discs 100 AU 100 AU M87 2000 AU HH"212"(Class"I"YSO)" HH212 HH30 8
Jets in AGNs Centaurus A Quasar 3C175 9
Outline Accretion discs and jets: what are they Accretion discs in nature Jets in nature Accretion disc models Hydrostatic equilibrium Angular momentum transport Linear stability A Specific application of the MRI to protoplanetary discs Nonideal MRI Direct detection of turbulence in protoplanetary discs 10
Nonlinear evolution of the MRI 11
The shearing box model Ω H z h B i y x α = ρ v x v y − B x B y ρ Ω 2 H 2 12
Boundary conditions Use shear-periodic boundary conditions= «shearing-sheet» Allows one to use a sheared Fourier Basis periodic in y and z (non stratified box) Mean vertical and toroidal fields are conserved Courtesy T. Heinemann zero mean field mean toroidal field mean vertical field y y y z z z x x x 13
Mean vertical field case 14
Typical simulation Simulation parameters: Re=1000, Pm=1, β =1000 3D map of v y (azimuthal velocity) 0.1 0.08 α 0.06 0.04 0.02 0 2 4 6 8 10 12 14 t (orbits) 15
Zero mean field case =“MRI dynamo” 16
MRI Simulations zero mean field shearing box=dynamo Zero net flux MRI Small scale dynamo [Fromang+ 2007] [Schekochihin+ 2006] ? Rem YES NO 25000 YES YES YES NO NO 12500 YES YES NO NO 6250 NO NO NO 3125 1600 800 Re e 800 1600 3125 6250 12500 25000 Turbulent resistivity effect ? [Riols+2015] See also J. Walker’s talk on Thursday 17
MRI Simulations Global simulations Global simulations are consistent with box simulations in the same conditions α ∼ 10 − 3 —10 − 2 [Hawley+ (1995) ; Fromang & Nelson (2006) ; Sorathia+ (2012)] [Flock+ 2011] 18
Outline Accretion discs and jets: what are they Accretion discs in nature Jets in nature Accretion disc models Hydrostatic equilibrium Angular momentum transport Linear stability A Specific application of the MRI to protoplanetary discs Nonideal MRI Direct detection of turbulence in protoplanetary discs 19
The MRI in protoplanetary discs 20
Ionisation sources in protoplanetary discs Cosmic rays X-rays Far-UV Thermal ionisation ~1AU ~10AU Ionisation Fraction 0.2 − 4 − 6 0.15 z/R − 8 0.1 − 10 0.05 − 12 0 − 1 0 1 2 10 10 10 10 R (AU) Protoplanetary disc plasmas are dominated by neutrals 21
Dead zone in protoplanetary discs Cosmic rays X-rays Far-UV «Dead zone» Thermal ionisation ~1AU ~30AU 3 non ideal effects enter the scene Ohmic diffusion (collisions between electrons and neutrals) Ambipolar Diffusion (collisions between ions and neutrals) Hall Effect (drift between electrons and ions) Amplitude of these effects depends strongly on location & chemistry 22
Non-ideal protoplanetary discs [Kunz & Balbus 2003] [Armitage 2011] 0.1 AU Density at z = 4 h, e fg ective disk Midplane 1) Ambipolar temperature 10 3 temperature, 2) Hall density 3) Ohmic 1 AU 10 2 1) Ohmic T (K) 2) Hall 10 AU 3) Ambipolar 1) Hall 10 1 2) Ohmic 3) Ambipolar 10 2 AU 1) Hall 2) Ambipolar NB: strongly depends on 10 0 3) Ohmic grain size and metallically 10 –17 10 –15 10 –13 10 –11 10 –9 10 –7 10 –5 ρ (g cm –3 ) Hall effect dominates in most of the disc midplane Ambipolar diffusion dominates in the upper layer 23
weak ionisation regions Wind-driven accretion [Béthune+2017] : elec- w- that not Surface layer is sufficiently ionised to drive a wind Wind extract angular momentum and generates accretion Self organisation instead of turbulence in the midplane 24
[Béthune+2017] 25
Detecting the MRI in protoplanetary discs 26
Line broadening Emission lines from the gas are broaden by: Measuring line broadening due to Keplerian rotation turbulence requires very Thermal velocity precise measures of and Turbulence Turbulence weaker than “ideal MHD” MRI turbulence Figure 6. CO ( 3-2 ) high resolution spectra ( black line ) compared to the median model when turbulence is allowed to move toward very low values ( red dotted – dashed lines ) or when it is fi xed at 0.1 km s − 1 ( blue dashed lines ) . All spectra have been normalized to their peak fl ux to better highlight the change in shape. The models with weak turbulence provide a signi fi cantly better fi t to the data despite the fact that the turbulence is smaller than the spectral resolution of the data. [Flaherty+2015] + 27 -
Dust settling (I) Turbulent Dust mixing settling The thickness of the dust layer depends on the competition between settling and turbulent mixing 28
Dust settling (II) Assume the disc is organised into rings Thick dust disc Thin dust disc In a thick disc seen inclined, the dark bands are strongly non-axisymmetric 29
Dust settling (III) Thin disc model Thick disc model HL tau, as seen by ALMA observatory [ALMA partnership 2015] HL tau dust disc is very thin (H/R<0.01) [Pinte+2016] Very strong settling (H/R gas=0.1) low level of turbulence 30
The end thank you for your attention 31
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