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

1

Introduction Angular Momentum Transport in Accretion Disks The Magneto-Rotational Instability

2

Our Model Alfv´ en Wave Damping Disk Initial Conditions

3

Results Initial Parameters Temperature Profiles The Dead Zone

4

Conclusions

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Angular Momentum Transport in Accretion Disks The Magneto-Rotational Instability

Introduction: Angular momentum transport

Disk Star Disk ~0.1 AU

Understanding L transport is the first step towards an understanding

• f accretion

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Angular Momentum Transport in Accretion Disks The Magneto-Rotational Instability

The magneto-rotational instability

MRI: differential rotation energy → turbulence (Balbus, Hawley) the magnetic field destabilizes the disk ∂2 ξ ∂t2 = −( k · vA)2 ξ MHD turbulence arises radial transport of L → accretion of particles

(c) (a) (b) Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Angular Momentum Transport in Accretion Disks The Magneto-Rotational Instability

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 Our Model Results Conclusions Angular Momentum Transport in Accretion Disks The Magneto-Rotational Instability

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 Our Model Results Conclusions Alfv´ en Wave Damping Disk Initial Conditions

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 Our Model Results Conclusions Alfv´ en Wave Damping Disk Initial Conditions

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 Our Model Results Conclusions Alfv´ en Wave Damping Disk Initial Conditions

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 Our Model Results Conclusions Alfv´ en Wave Damping Disk Initial Conditions

Disk initial conditions

steady-state and axisymmetric

• ptically thick

geometrically thin Keplerian rotation Energy used to heat the disk: Ftot = Fν+FA = σT 4 Fν = 3Ω2

K ˙

M 8π

• 1 −

Ri R 1/2 FA = H/2 FA L dz

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Alfv´ en Wave Damping Disk Initial Conditions

Disk initial conditions

steady-state and axisymmetric

• ptically thick

geometrically thin Keplerian rotation Energy used to heat the disk: Ftot = Fν+FA = σT 4 Fν = 3Ω2

K ˙

M 8π

• 1 −

Ri R 1/2 FA = H/2 FA L dz

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Alfv´ en Wave Damping Disk Initial Conditions

Disk initial conditions

steady-state and axisymmetric

• ptically thick

geometrically thin Keplerian rotation Energy used to heat the disk: Ftot = Fν+FA = σT 4 Fν = 3Ω2

K ˙

M 8π

• 1 −

Ri R 1/2 FA = H/2 FA L dz

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Alfv´ en Wave Damping Disk Initial Conditions

Disk initial conditions

steady-state and axisymmetric

• ptically thick

geometrically thin Keplerian rotation Energy used to heat the disk: Ftot = Fν+FA = σT 4 Fν = 3Ω2

K ˙

M 8π

• 1 −

Ri R 1/2 FA = H/2 FA L dz

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Initial Parameters Temperature Profiles The Dead Zone

Initial parameters

Star & disk T Tauri star:

M⋆ = 0.5 M⊙ R⋆ = 2 R⊙ ˙ M = 10−8 M⊙/yr

Grain characteristics

a1 = 0.005 µm a2 = 0.250 µm ρgas/ρdust = 100

f =

• (δB)2

B Fz=0

A

∝ vA(fB)2

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Initial Parameters Temperature Profiles The Dead Zone

Initial parameters

Star & disk T Tauri star:

M⋆ = 0.5 M⊙ R⋆ = 2 R⊙ ˙ M = 10−8 M⊙/yr

Grain characteristics

a1 = 0.005 µm a2 = 0.250 µm ρgas/ρdust = 100

f =

• (δB)2

B Fz=0

A

∝ vA(fB)2

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Initial Parameters Temperature Profiles The Dead Zone

Results: temperature profiles

0.1 1.0 10.0 100.0 r (AU) 10 100 1000 T (K)

f=0.00 f=0.05 f=0.10 f=0.20

T ∝ R−q f = 0.00 q = 0.75 f = 0.05 q = 0.71 f = 0.10 q = 0.69 f = 0.20 q = 0.67 α-model q = 3/4 MMSN q = 1/2 Andrews & Williams (2007)

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Initial Parameters Temperature Profiles The Dead Zone

Results: temperature profiles

0.1 1.0 10.0 100.0 r (AU) 10 100 1000 T (K)

f=0.00 f=0.05 f=0.10 f=0.20

MMSN α-model

T ∝ R−q f = 0.00 q = 0.75 f = 0.05 q = 0.71 f = 0.10 q = 0.69 f = 0.20 q = 0.67 α-model q = 3/4 MMSN q = 1/2 Andrews & Williams (2007)

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Initial Parameters Temperature Profiles The Dead Zone

Results: temperature profiles

0.1 1.0 10.0 100.0 r (AU) 10 100 1000 T (K)

f=0.00 f=0.05 f=0.10 f=0.20

MMSN α-model

T ∝ R−q f = 0.00 q = 0.75 f = 0.05 q = 0.71 f = 0.10 q = 0.69 f = 0.20 q = 0.67 α-model q = 3/4 MMSN q = 1/2 Andrews & Williams (2007)

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Initial Parameters Temperature Profiles The Dead Zone

Results: temperature profiles

0.1 1.0 10.0 r (AU) 10 20 50 100 200 500 T (K)

Viscous Alfvenic

Alfvenic anomalous viscosity

Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks

Outline Introduction Our Model Results Conclusions Initial Parameters Temperature Profiles The Dead Zone

Results: simple estimate of the dead zone size

Following Gammie (1996) (x 10−13): Σ 100 g cm−2 T 103 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 Initial Parameters Temperature Profiles The Dead Zone

Results: simple estimate of the dead zone size

Following Gammie (1996) (x 10−13): Σ 100 g cm−2 T 103 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

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

Outline Introduction Our Model Results Conclusions Aline Vidotto MHD Waves as a Source of Heating in Accretion Disks