MHD Waves as a Source of Heating in Accretion Disks Aline A. - PowerPoint PPT Presentation

Outline Introduction Our Model Results Conclusions MHD Waves as a Source of Heating in Accretion Disks Aline A. Vidotto Vera Jatenco-Pereira Astronomy Dept. University of S˜ ao Paulo, Brazil Transformational Science with ALMA June 22-24, 2007 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Introduction 1 Angular Momentum Transport in Accretion Disks The Magneto-Rotational Instability Our Model 2 Alfv´ en Wave Damping Disk Initial Conditions Results 3 Initial Parameters Temperature Profiles The Dead Zone Conclusions 4 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Angular Momentum Transport in Accretion Disks Our Model The Magneto-Rotational Instability Results Conclusions Introduction: Angular momentum transport ~0.1 AU Disk Star Disk Understanding � L transport is the first step towards an understanding of accretion Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

✂ Outline Introduction Angular Momentum Transport in Accretion Disks Our Model The Magneto-Rotational Instability Results Conclusions The magneto-rotational instability MRI: differential rotation energy → turbulence (Balbus, Hawley) the magnetic field (c) destabilizes the disk ∂ 2 � ξ ∂ t 2 = − ( � v A ) 2 � k · � ξ �✁�✂ �✁� MHD turbulence arises (b) radial transport of � L → accretion of particles (a) Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Angular Momentum Transport in Accretion Disks Our Model The Magneto-Rotational Instability Results Conclusions The magneto-rotational instability Keys to the mechanism existence weak magnetic field differential rotation (e.g. Keplerian rotation) (partially) ionized plasma Minimum ionization fraction − → coupling between magnetic field and disk particles Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Angular Momentum Transport in Accretion Disks Our Model The Magneto-Rotational Instability Results Conclusions The magneto-rotational instability Keys to the mechanism existence weak magnetic field differential rotation (e.g. Keplerian rotation) (partially) ionized plasma Minimum ionization fraction − → coupling between magnetic field and disk particles Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Alfv´ en Wave Damping Our Model Disk Initial Conditions Results Conclusions Our model We know... disks are magnetized systems dust grains are present usually grains immersed in a plasma are charged charged grains can damp Alfv´ en waves Aim: Determine if the dissipation of Alfv´ en waves due to the interaction with grains is a significant source of heating. Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Alfv´ en Wave Damping Our Model Disk Initial Conditions Results Conclusions Dust-cyclotron damping mechanism Illustrative movie of Alfv´ en waves in the solar wind (S. Cranmer) broad band of resonance frequencies Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Alfv´ en Wave Damping Our Model Disk Initial Conditions Results Conclusions Dust-cyclotron damping mechanism Illustrative movie of Alfv´ en waves in the solar wind (S. Cranmer) broad band of resonance frequencies Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Alfv´ en Wave Damping Our Model Disk Initial Conditions Results Conclusions Disk initial conditions steady-state and axisymmetric optically thick geometrically thin Keplerian rotation � � 1 / 2 � K ˙ F ν = 3Ω 2 � R i M 1 − Energy used to heat the disk: 8 π R F tot = F ν + F A = σ T 4 � H / 2 F A F A = L dz 0 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Alfv´ en Wave Damping Our Model Disk Initial Conditions Results Conclusions Disk initial conditions steady-state and axisymmetric optically thick geometrically thin Keplerian rotation � � 1 / 2 � K ˙ F ν = 3Ω 2 � R i M 1 − Energy used to heat the disk: 8 π R F tot = F ν + F A = σ T 4 � H / 2 F A F A = L dz 0 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Alfv´ en Wave Damping Our Model Disk Initial Conditions Results Conclusions Disk initial conditions steady-state and axisymmetric optically thick geometrically thin Keplerian rotation � � 1 / 2 � K ˙ F ν = 3Ω 2 � R i M 1 − Energy used to heat the disk: 8 π R F tot = F ν + F A = σ T 4 � H / 2 F A F A = L dz 0 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Alfv´ en Wave Damping Our Model Disk Initial Conditions Results Conclusions Disk initial conditions steady-state and axisymmetric optically thick geometrically thin Keplerian rotation � � 1 / 2 � K ˙ F ν = 3Ω 2 � R i M 1 − Energy used to heat the disk: 8 π R F tot = F ν + F A = σ T 4 � H / 2 F A F A = L dz 0 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Initial parameters Star & disk T Tauri star: M ⋆ = 0 . 5 M ⊙ � � ( δ B ) 2 � R ⋆ = 2 R ⊙ f = M = 10 − 8 M ⊙ / yr ˙ B F z =0 ∝ v A ( fB ) 2 Grain characteristics A a 1 = 0 . 005 µ m a 2 = 0 . 250 µ m ρ gas /ρ dust = 100 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Initial parameters Star & disk T Tauri star: M ⋆ = 0 . 5 M ⊙ � � ( δ B ) 2 � R ⋆ = 2 R ⊙ f = M = 10 − 8 M ⊙ / yr ˙ B F z =0 ∝ v A ( fB ) 2 Grain characteristics A a 1 = 0 . 005 µ m a 2 = 0 . 250 µ m ρ gas /ρ dust = 100 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Results: temperature profiles 1000 T ∝ R − q f=0.00 f=0.05 f=0.10 f=0.20 f = 0 . 00 q = 0 . 75 f = 0 . 05 q = 0 . 71 T (K) 100 f = 0 . 10 q = 0 . 69 f = 0 . 20 q = 0 . 67 α -model q = 3 / 4 MMSN q = 1 / 2 Andrews & Williams 10 (2007) 0.1 1.0 10.0 100.0 r (AU) Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Results: temperature profiles 1000 T ∝ R − q f=0.00 f=0.05 f=0.10 f=0.20 f = 0 . 00 q = 0 . 75 MMSN f = 0 . 05 q = 0 . 71 T (K) 100 f = 0 . 10 q = 0 . 69 f = 0 . 20 q = 0 . 67 α -model α -model q = 3 / 4 MMSN q = 1 / 2 Andrews & Williams 10 (2007) 0.1 1.0 10.0 100.0 r (AU) Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Results: temperature profiles 1000 T ∝ R − q f=0.00 f=0.05 f=0.10 f=0.20 f = 0 . 00 q = 0 . 75 MMSN f = 0 . 05 q = 0 . 71 T (K) 100 f = 0 . 10 q = 0 . 69 f = 0 . 20 q = 0 . 67 α -model α -model q = 3 / 4 MMSN q = 1 / 2 Andrews & Williams 10 (2007) 0.1 1.0 10.0 100.0 r (AU) Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Results: temperature profiles 500 Viscous Alfvenic 200 T (K) 100 anomalous Alfvenic viscosity 50 20 10 0.1 1.0 10.0 r (AU) Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Results: simple estimate of the dead zone size Following Gammie (1996) ( x � 10 − 13 ): Σ � 100 g cm − 2 T � 10 3 K Size of the dead zone: 0 . 1 � r ( AU ) � 6 Considering Alfv´ en waves: 0 . 65 � r ( AU ) � 3 . 7 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Initial Parameters Our Model Temperature Profiles Results The Dead Zone Conclusions Results: simple estimate of the dead zone size Following Gammie (1996) ( x � 10 − 13 ): Σ � 100 g cm − 2 T � 10 3 K Size of the dead zone: 0 . 1 � r ( AU ) � 6 Considering Alfv´ en waves: 0 . 65 � r ( AU ) � 3 . 7 Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Conclusions Dissipation of Alfv´ en waves flattens the temperature profile of the disk compared to the α -model and causes a more significant increase in T at large distances from the star reduces the size of the dead zone (simple estimates) The region we study in this work will be accessible with ALMA, whose observations will place hard constraints on the disk structure. Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks