Date post: | 20-Dec-2015 |
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Wind-Fed Magnetospheres:Mass Budget & Spindown
Stan OwockiUniversity of DelawareNewark, 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?
Wind Magnetic Confinement
€
η(r) ≡B2 /8π
ρv 2 /2Ratio of magnetic to kinetic energy density:
e.g, for dipole
q=3; η ~ 1/r 4 =B*
2R*2
M•
v∞
(r / R*)2−2q
(1− R* / r)β
η*
Alfven Radius: η( RA) ≡ 1
For dipole (q=3) with beta=0: RA = η*1/4 R*
Magnetic confinement vs. Wind + Rotation
RA =η*1/4R*
Alfven radius
RK =W−2/3R*
Kepler radius
W ≡Vrot
GM / R*
Rotation vs. critical
η∗≡B*
2R*2
M.
V∞
Wind mag. confinement
Field-aligned rotation
η*=100RA=3.2R*
Vrot/Vorb=1/2RK=1.6 R* QuickTime™ and a
BMP decompressorare needed to see this picture.
RK RA
Strong Field + Rapid rotationη*=100 W=1/2
QuickTime™ and aBMP decompressor
are needed to see this picture.
RK RA
Time evolution of Radial distribution of equatorial disk mass
η* = 100 & Vrot/Vcrit =1/2
RK
RA
Time (ksec)
Rad
ius
(R*)
Temporal evolution of radial distribution of equatorial disk mass
Stronger Magnetic Confinement --->More
Rap
id R
ota
tion
--
->
r=1-5
t=0-3 Msec
13
QuickTime™ and aBMP decompressor
are needed to see this picture.
Strongest MHD sim
η*=1000W=1/2
RK RA
16
Breakout time & Asymptotic mass
tb (r) ≈η* tff
R*RK3
r(r3 −RK3 )
but for sigOriE, eta* ~106,
tb (2RK ) ≈100 yr
M∞ ≈10−7 Me
for MHD sims with eta* =100,
tb (2RK ) ≈106 sec~10 day ≈3 ×10−9M e
B32R12
2
g4
Independent of Mdot!
M∞ ≈0.2M
g
η* tff(for W=1/2)
19
Weber & Davis 1967
j =Vφr −BφBrrρVr
j =ΩRA2
At r= RA, MA=1 implies
Tot. equat. Ang. mom/mass jgas ≡Vφr =
jMA2 −Ωr2
MA2 −1
=>
Bφ
Br
=Ωr −Vφ
Vr &
Frozen flux
gas field
30
Spindown age
P =Poe−t/τspin Po ≈ fPc
Pc =0.21d R RM ⇒ Po ~ day
e.g. HD191612, with Po = 0.5 to 1 day:
τ age ≈ 6.3 → 6.9 τ spin ≈ 2.5 → 2.9 Myr
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 Mtot
– breakout analysis predicts Mtot indep of Mdot!
• Wind Magnetic Spindown– tspin ~ tmass/Sqrt[eta*] for aligned dipole– complex field => slower spindown?– need 3D sims to confirm!