Numerical modeling of magnetic stardisk interaction

1
Numerical modeling of magnetic star-disk
interaction

• Claudio Zanni (LAOG Grenoble)
• Sauze DOulx JETSET School 2007

2
Outline

• Observational evidences for magnetospheric
  accretion
• Magnetic fields, accretion speeds, accretion
  shocks
• MHD numerical simulations of a stellar (dipolar)
  magnetosphere interaction with an accretion disk
• 2.5D simulations performed with the PLUTO code
• Resistive and viscous simulations
• Physics of magnetically controlled accretion
• Accretion rates, funnel flow dynamics
• Stellar spin down
• Disk locking
• Some annoying problems

3
Observational evidences

• CTTSs have dynamically important surface
  magnetic fields B 1-3 kG (Valenti
  Johns-Krull 2004)
• Redshifted absorption features in inverse
  P-Cygni profiles of H?-? lines reveal accreting
  material at free-fall speed (gt 100 km s-1)
  (Edwards et al. 1994)
• Hot spots can be inferred from photometric and
  colour variability (Bouvier et al. 1995)
• Rotational modulation of light curves suggests
  star rotation periods around 3-10d (Bouvier et
  al. 1993) origin of stellar spin-down?

• Accretion disk is truncated at a few stellar
  radii by the interaction with the (dipolar)
  stellar magnetosphere.
• The flow is channelled into funnel flows
  terminating with an accretion shock on the star
  surface.

4
(Astro)physical scenario

• Perfectly conducting star of mass M rotating
  with ? angular speed connected through a closed
  dipolar field with a Keplarian disk
• Corotation radius Rco
• Truncation radius Rin
• correlated (?) with the magnetospheric radius
  Rm
• where
• External radius Rout
• disk disconnected from the star field
  lines open

(Matt Pudritz 2004)
5
A couple of caveats

• Generally surface magnetic fields have no
  dipolar topology dipolar component should be
  weaker ( 100 G)

(Jardine et al. 2006)

• Photometric and spectroscopic variations of AA
  Tau determined by periodic occultations of a disk
  warped by the interaction with an inclined
  dipolar magnetosphere intrinsically 3D problem

(Bouvier et al. 1999, 2003)
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2.5D simulations initial conditions

• Dipolar field aligned with the rotation axis of
  the star
• Field in equipartition with the thermal
• pressure of the disk
• at the initial truncation radius Rin 3.7 R

B 150 (300) G

• Resistive (viscous) Keplerian (accretion) disk
• Resistivity (?
  1)

• star perfect conductor rotating at ? 0.1?k
  (Rco 4.6 R)

• Boundary condition on the magnetic torque
  adv terms

• ----

• Alfven crossing time of one grid cell

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A couple of movies

• As seen in 3D

• In 2.5 dimensions

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Resistive simulations
1.5 P
Rin
Rco

• Large fraction of the disk beyond Rco still
  connected to the star

• After 2 star periods 80 of the initial mass
  below Rco has been accreted

• Need an additional mechanism to remove angular
  momentum from the disk to cross the centrifugal
  barrier beyond Rco VISCOUS
  TORQUE

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Introducing viscosity (1)

• In standard ? Keplerian accretion disks sign of
  the viscous torque on the midplane is (generally)
  positive matter is ejected on the midplane!

Conservation of mass and angular momentum
? viscosity
Radial speed on the midplane
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Introducing viscosity (2)

• Proposed solution high ? with all the
  components of viscous stress tensor

? 0.4
? 0.7
?cr 0.685
(Kluzniak Kita 1997)

• There is a critical ? below which matter is
  ejected along the midplane
• For an adiabatic disk ?cr 0.685

11
Resistive Viscous simulations
1.5 P
2.5 P

• ?v 1 ensures accretion all across the disk (
  )

• At 2.5 P first indication of an oscillating
  truncation radius and variable accretion rate

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Mass accretion rates

• Accretion at all radii (at least at longer
  timescale)
• Mass accretion rate variable both in space and
  in time
• Spatial oscillations of accretion rate due to
  the different local combination of magnetic and
  viscous torques
• Truncation radius Rin changes position

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Disk truncation

• Disk truncated where
• Such a field represents a magnetic wall for a
  subsonic accretion flow
• Pram ? vr2 lt Pth

• A field in equipartion with the rotational
  energy of the disk (B 1kG, as in Romanova et
  al.) can support free-fall
• a weaker dipolar field (B 100 G) can
  truncate the disk

14
Funnel flow dynamics
rPth
?v?/r
Fkin
Fmag
FLorentz
?ggrav

• Thermal pressure gradient uplifts matter at Rin
  into the funnel flow and slows down matter fall
• Centrifugal barrier always negligible
  matter is braked along funnel flow
• Transport of angular momentum dominated by
  advection (Fkin r?V?Vp) at the base of the
  funnel and by magnetic torque (Fmag rB?Bp) at
  the star surface

15
Stellar spin down
Jmag

• Magnetic torque dominant on the surface of the
  star
• Total magnetic torque sligthly slows down star
  rotation
• Estimated braking time 108 yrs (our star is
  already slowly rotating)

Jkin
Jmag, disk

• Braking torque associated with the fieldlines
  still connected to the disk is negligible
• need to properly model (accretion
  powered?) stellar winds !!!

16
An annoying problem
2.5 P
1 P

• Torque correctly changes sign at Rco

• Disk accelerated (star braked) down to Rin?

• Problem of (numerical) diffusion of the
  accretion column across the field lines?

17
which is not just my problem
Rco
Rco
(Long et al. 2005)

• (Magnetic) transfer of angular momentum from the
  star to the disk below Rco

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Summary

• Magnetically controlled star-disk interaction
• Resistivity introduced to control the magnetic
  star-disk coupling
• Viscous stresses introduced to allow accretion
  beyond Rco
• Not the only possible solution reconnection
  X-winds
• Accretion process variable both in time and space
• Accretion column dynamics
• Thermal pressure gradient determines mass loading
  and slows down matter fall towards the star
• Magnetic torque brakes the accreting material
• Stellar spin down
• Weak braking torque observed but the braking
  torque associated with the disk is negligible

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Perspectives

• Try to solve the problem of the sign of the
  torque below corotation
• Parameter space study ?m, ?v, ?, B
• Properly model the (accretion powered) stellar
  wind
• 3D simulations inclined dipole, non-axisymmetric
  accretion