Wind-Fed Magnetospheres: Mass Budget & Spindown Stan Owocki University of Delaware Newark, Delaware USA Collaborators Asif ud-Doula Rich Townsend

2 Questions What processes limit the build-up of mass in a wind-fed magnetosphere? –how/where does it leak? –how does total mass scale with B, vrot/vcrit, Mdot, etc. How does angular momentum loss & spindown scale with B *, Mdot, etc.? –can we explain slow rotators w/ magnetic spindown? –how to generalize for higher multipoles?

Rigid Field - Hydro Model

Wind Magnetic Confinement Ratio of magnetic to kinetic energy density: e.g, for dipole q=3;  ~ 1/r 4 ** Alfven Radius:  ( R A )  1 For dipole (q=3) with beta=0: R A =  * 1/4 R *

Magnetic confinement vs. Wind + Rotation Alfven radius Kepler radius Rotation vs. critical Wind mag. confinement

Field-aligned rotation  * =100 R A =3.2R * V rot /V orb =1/2 R K =1.6 R * RKRK RARA

Strong Field + Rapid rotation  * =100 W=1/2 RKRK RARA

Radial Mass Distribution

Time evolution of Radial distribution of equatorial disk mass  * = 100 & Vrot/Vcrit =1/2 RKRK RARA Time (ksec) Radius (R * )

Corotation Parameter  * = 100 & Vrot/Vcrit =1/2 RKRK RARA Time (ksec) Radius (R * )

Two Parameter Study Stronger Magnetic Confinement ---> More Rapid Rotation --->

Temporal evolution of radial distribution of equatorial disk mass Stronger Magnetic Confinement ---> More Rapid Rotation ---> r=1-5 t=0-3 Msec

13 Strongest MHD sim  * =1000 W=1/2 RKRK RARA

14 Strongest MHD sim, no rotation 14  * =1000 W=0

16 Breakout time & Asymptotic mass but for sigOriE, eta * ~10 6, for MHD sims with eta * =100, Independent of Mdot! (for W=1/2)

18 Angular Momentum Loss & Spindown

19 Weber & Davis 1967 At r= R A, M A =1 implies Tot. equat. Ang. mom/mass => & Frozen flux gasfield

20 Gas fraction of angular momentum WD eqn.: at large radii

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23 Time Variation of Angular Momentum Loss

24 Time variation of total Angular Momentum Loss Gas Field Total

25 Angular Momentum Loss vs. latitude & time + + = =

26 Angular Momentum Loss vs. Radius & Time GasFieldTotal

27 Angular Momentum Loss: Gas vs. Field

28 Magnetic confinement parameter =>

29 Dipole spindown times

30 Spindown age e.g. HD191612, with P o = 0.5 to 1 day:

31 Extrapolated spindown law for higher order multipoles? p=2 monopole =3 dipole =4 quadrapole... etc. => Spindown weaker for more complex fields? If so, hard to explain tau Sco by spindown?? Need 3D MHD sims to test this!

32 Summary Wind feeding of magnetosphere –balanced by inner & outer “leakage”? –observations should estimate M tot –breakout analysis predicts M tot indep of M dot ! Wind Magnetic Spindown –t spin ~ t mass /Sqrt[eta * ] for aligned dipole –complex field => slower spindown? –need 3D sims to confirm!

Alfven speed Note: Compare sound speed