Magnetic star-disk interaction

Claudio Zanni

Laboratoire d’Astrophysique de Grenoble

5th JETSET School January 8th – 12th 2008 Galway - Ireland

• 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 (> 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?

Observational evidences

A simple model …

• 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

… 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

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:

- Truncation radius Rt - Corotation radius Rco - Outer radius Rout

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

The truncation 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)

(Arons 1993, Wang 1996, Ostriker & Shu 1995)

(Bessolaz et al. 2008)

Can a “weak” (» 100G) dipolar component truncate a disk accreting at 10-8 Msun yr-1?

Probably not…

(N.B. located below corotation radius)

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

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

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)

Typical initial conditions• Dipolar field aligned with the rotation axis of the star

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

• “star” (M* = 0.5Msun, R* = 2Rsun) modeled as

perfect conductor rotating with a 4.5 days period (* = 0.1k, Rco = 4.6 R*)

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

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

In 2D…

As seen in 3D…

Movies…

Disk truncation

Rin

Pth

Pmag

Pram

• Disk truncated in equipartition

conditions

• Pram = vr2 < Pth

• Magnetosphere represents a “magnetic wall” for such an accretion flow

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

Funnel flow dynamics

rPth

ggrav

FLorentz

v/r

Fmag

Fkin

• 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 = rVVp) at the base of the funnel and by magnetic torque (Fmag = rBBp) at the star surface

Star-disk torques: general ideas

• Accretion torque ( ) can only spin up the star rotation (which is still contracting anyway)

• 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)

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

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

Interaction regimes

(Matt & Pudritz 2004)

“Accretor”

“Propeller”

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

• Extended magnetosphere (Rin < Rco < Rout) disk can extract angular momentum (“disk locked” state)

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

• 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.

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

State 1: “compact magnetosphere”( = 0.1 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.

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?

State 2: “extended magnetosphere”( = 1 B* » 800 G)

Magnetic braking: stellar wind

• Mwind » 8 £ 10-11 Msun yr-1

• Strongly magnetized ( » 10-3)

• Lever arm RA/R0 » 15

• Propeller regime…

• The trucation criterium ( » 1) valid also beyond corotation…

• Can be this state maintained for long timescales?

State 3a: “propeller”( = 1 B* » 1.6 kG)

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

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

• Problems: non-orthogonal metric, interpolation between 6 sectors

Koldoba et al. (2003)

Romanova et al. (2003, 2004)

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

Romanova et al. (2003)

• 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

= 15o = 60o

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

Romanova et al. (2004)

• = 15o

• Kinetic energy flux on the star converted in radiation

• One peak of intensity during one period for i < 60o

• Two peaks for i > 60o

Long et al. 2007

• Accretion on inclined quadrupolar+dipolar field