Magnetic star-disk interaction

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Magnetic star-disk interaction

• Claudio Zanni
• Laboratoire dAstrophysique de Grenoble

5th JETSET School January 8th 12th
2008 Galway - Ireland
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Observational evidences

• CTTS 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?

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A simple model

• The flow is channelled into funnel flows
  terminating with an accretion shock on the star
  surface

• Accretion disk is truncated at a few stellar
  radii by the interaction with the (dipolar)
  stellar magnetosphere.

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with some limitations

• Spectropolarimetric observations of CTTs suggest
  that the stellar field is more complex than
  dipolar.
• Ex. V2129 Oph (Donati et al. 2007)
• - octupole 1.2 kG
• - dipole 0.35 kG

• 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

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The ingredients of the problem

• Outer accretion disk
• (torque viscous, disk wind)

• Stellar magnetosphere
• connecting the rotating star and
• the disk

• Accretion columns

• Outflows disk winds, reconnection driven
  outflows, stellar winds

• System characterized by three radii

- Outer radius Rout
- Truncation radius Rt
- Corotation radius Rco
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What analytical models can do?

• No analytical model which takes into account all
  the elements of the scenario (accretion disk,
  accretion columns, stellar magnetosphere,
  outflows) is currently (and probably it will
  never be) available.

• Parts of the problem can be solved separately
• - Localization of the truncation radius Rt
• - Structure of the accretion columns
• - Structure of the magnetically torqued
  accretion disk
• - Angular momentum exchange between the
  star and the disk
• . with some approximation

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The truncation radius
(N.B. located below corotation radius)

• Alfvén radius (Elsner Lamb 1977)
• (ram pressure of a spherical envelope accreting
  at free-fall speed magnetic pressure of a
  dipole)

• The constant k

(Ghosh Lamb 1979, Konigl 1991, Long 2005)
Can a weak ( 100G) dipolar component truncate
a disk accreting at 10-8 Msun yr-1? Probably not
(Arons 1993, Wang 1996, Ostriker Shu 1995)
(Bessolaz et al. 2008)
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Accretion columns

• Trans-sonic solutions can be calculated (ex.
  Koldoba et al. 2002)

• Passage of the sonic point and therefore
  accretion is controlled by thermal pressure at
  the base of the accretion column
• Thermal energy greater than what is available in
  a thin accretion disk

• Limitations sub-Alfvenic flow, force-free
  dipolar fieldlines

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Torqued disk structure

• It is possible to calculate the effects of the
  magnetospheric torques on the structure of the
  disk (ex. Kluzniak Rappaport 2007)

• The magnetospheric torque brakes down the disk
  rotation inside the corotation radius and forces
  the disk to co-rotate with the star

• Limitations vertically averaged disk model,
  a-priori hypothesis on B?

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Putting the pieces together numerical simulations

• Many numerical simulations do not have strong
  enough magnetic fields to truncate the disk and
  produce accretion columns (Hayashi et al. 1996,
  Miller Stone 1997, Kuker et al. 2003)

Kuker et al. (2003)

• First accretion columns simulated in 2002
  (Romanova et al. 2002) assuming a magnetic field
  in equipartition with the disk energy ( 1 kG)

Romanova et al. (2002)
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Typical initial conditions

• Dipolar field aligned with the rotation
• axis of the star

• Resistive (viscous) Keplerian accretion disk
• Resistivity (viscosity)

• Field in equipartition with the thermal
• pressure of the disk at the initial
• truncation radius Rin
• dominant magnetic torque

• star (M 0.5Msun, R 2Rsun) modeled as
• perfect conductor rotating with a 4.5 days
• period (? 0.1?k, Rco 4.6 R)

• MHD fluid equations solved with the PLUTO code
  (Godunov CT method)

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Movies
As seen in 3D
In 2D
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Disk truncation

• Disk truncated in equipartition
• conditions

• Pram ? vr2 lt Pth

• Magnetosphere represents a magnetic wall for
  such an accretion flow

• Confirms analytical results contained in
  Bessolaz et al. (2008)

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Funnel flow dynamics

• Thermal pressure gradient uplifts matter at Rin
  into the funnel flow and slows down matter fall
  pressure comes from the compression
  against the magnetic wall
• 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

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Star-disk torques general ideas

• How it is possible to extract this excess
  angular momentum?

• Extended magnetosphere, connected beyond Rco
  (Ghosh Lamb 1978) does not work due to limited
  size of magnetosphere (Matt Pudritz 2005)

• X-wind extracting the disk angular momentum
  BEFORE it falls onto the star surface (Shu et al
  1994) is a wind like that possible?

• Stellar wind accretion powered stellar wind
  (Matt Pudritz 2005), reconnection X-Wind
  (Ferreira et al. 2000)

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Interaction regimes

• Compact magnetosphere (Rin lt Rout lt Rco)
• no braking torques are present
• except for outflows

Accretor

• Extended magnetosphere (Rin lt Rco lt Rout)
• disk can extract angular momentum
• (disk locked state)

• Propeller (Rin gt Rco)
• disk truncated beyond corotation, no
• accretion columns, only spin-down
• torques

Propeller
(Matt Pudritz 2004)
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State 1 compact magnetosphere
(? 0.1 B 800 G)

• All fieldlines beyond corotation magnetic
  surface (yellow line) are opened
• The opened stellar and disk fieldlines are
  separated by a strong current sheet along which
  numerical reconnection phenomena can occur as
  well as episodic mass outflows
• CME-like ejection site close to the base of the
  accretion column. No X-winds.

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State 1 compact magnetosphere
(? 0.1 B 800 G)

• After initial strong transients the accretion
  rate (and hot spot luminosity) shows
• an almost stationary behavior
• Variability may occur on the longer accretion
  time-scale
• The magnetic torque measured on the closed
  fieldlines really small (weak
• accretion rate)
• The star is always braked along the opened field
  lines

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State 2 extended magnetosphere
(? 1 B 800 G)

• Magnetosphere stays connected up to a radius
  2.5 (Rco 1.6)
• The current sheet is located further from the
  star and the episodic outflows are weaker
• The disk viscosity is efficient enough in the
  connected region in order to remove radially both
  the disk and the stellar angular momentum as to
  provide mass to the accretion columns.

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State 2 extended magnetosphere
(? 1 B 800 G)

• Accretion rate (and hot spot luminosity)
  regularly oscillates with a 1.5-2 P period
  (mismatch between magnetospheric and viscous
  torque)
• Even if part of the disk magnetically connected
  to the star beyond Rco the disk-locked torque
  always spins up the star
• The star is always braked along the opened field
  lines zero-torque state?

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Magnetic braking stellar wind

• Mwind 8 10-11 Msun yr-1
• Strongly magnetized (? 10-3)
• Lever arm RA/R0 15

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State 3a propeller
(? 1 B 1.6 kG)

• Propeller regime
• The trucation criterium (? 1) valid also
  beyond corotation
• Can be this state maintained for long timescales?

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State 3a propeller
(? 1 B 1.6 kG)

• The star is braked both along the closed and
  opened field lines
• The accretor solutions are in an almost
  zero-torque condition
• The propeller solution always spins-down the
  star

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Beyond dipoles and axisymmetry 3D simulations

• Technical issue curvilinear geometries
  (cylindrical, spherical) introduce singularities
  cartesian geometry cannot describe correctly the
  surface of the star and the disk (putting a
  sphere in a cube)
• Optimal solution cubed sphere

Koldoba et al. (2003)

• Problems non-orthogonal metric, interpolation
  between 6 sectors

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Romanova et al. (2003, 2004)

• Inclined dipole varying the angle ? between the
  rotation axis and the magnetic moment ?

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Romanova et al. (2003)
? 15o
? 60o

• Two streams funnel flow
• FF located 30o downstream (FF rotates faster
  than the star)
• Warped accretion flow perpendicular to ?

• Funnel flow more complicated
• Direct accretion on the poles
• Disk depleted of material

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Romanova et al. (2003)

• Higher accretion rate for higher ?

• Torque on the star always positive
• Higher initially for higher ? but then less
  matter is accreted in outer part of the disk

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Romanova et al. (2004)

• ? 15o
• Kinetic energy flux on the star converted in
  radiation
• One peak of intensity during one period for i lt
  60o
• Two peaks for i gt 60o

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Long et al. 2007

• Accretion on inclined quadrupolardipolar field