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Stellar Winds, MHD and Disks
Asif ud-Doula
Penn State Worthington Scranton
Outline Stellar Winds
Gas pressure driven winds
Radiative driving
Magnetic Confinement
Rotation/Disks/Spindown
O,
Whirlpool Galaxy
Massive stars
dominate the
light from
galaxies
Mass Loss from Stars
Stars like the sun lose very little mass (~10-14 MSun/yr)
Solar wind is driven by gas pressure gradient
All stars lose mass, the continuous outflow is called
the Stellar Wind
Hot stars (O and B type) lose enormous amount
of material (10-9~10-5 MSun/yr)
Hot star winds are driven by scattering of
radiation by resonance lines of heavy ions.
Sound speed; thermal pressure has little
significance.
Solar corona & wind
Solar corona
high T => high Pgas
scale height H ≤ R
breakdown of hydrostatic equilibrium
pressure-driven solar wind expansion
How does magnetic field alter this?
closed loops => magnetic confinement
open field => coronal holes
source of high speed solar wind
Hydrostatic Scale Height
Scale Height:2
6
14
TH a R
R GM
1
2000
H
Rsolar photosphere: 6 0.006T
2
2
1GM dP a
r dr H
Hydrostatic
equilibrium:
1
7
H
Rsolar corona:
6 2T
2P a
Failure of hydrostatic equilibrium
for hot, isothermal corona2
20
GM a dP
r P dr
hydrostatic
equilibrium:
( )exp 1
o
P r R R
P H r
0log 12ISM
P
Pobservations :
# decades of
pressure decline:6
6log logoP R
eP H T
expR
for rH
Solar corona T6 ~ 2, pressure too high => corona must expand!
Spherical Expansion of Isothermal Solar Wind
Momentum and Mass Conservation:2
2
vv
dr
d GM a d
r dr
2v0
d r
dr
Combine to eliminate density:2 2
2 2
a v 2a1- v
v dr
d GM
r r
RHS=0 at “critical” radius:22
c
GMr
a2 2
2 2
4v v-ln 4ln c
c
rrC
a a r r
Integrate for
transcendental soln:
v cr a3C => Transonic soln:c sr r sonic radius
Solution topology for isothermal wind
How about massive star wind?
Stellar Photosphere
high luminosity, UV heating => isothermal
low T => low sound speed
line-driven stellar wind expansion
Light transports energy (& information)
But it also has momentum, p=E/c
Usually neglected, because c is very high
But becomes significant for very bright stars,
Key question: how big is force vs. gravity??
Light’s Momentum
Light As a Driving Mechanism
Free Electron (continuum) Scattering
Bound Electron (line) Scattering
• Can be much stronger than free electron scattering
details
Driving by free e scattering
Gravitational
ForceRadiative
Force
24
ee
L
crg
ege
g
eL / 4 r2c
GM / r2eL
4 GMc
50/
/2 1 S F
eu
e
n
Sun
L L
M M
2
GM
r
for hot stars
~0.5
Driving by Line-Opacity: Thin Lines
Q~ ~ 1015 Hz * 10-8 s ~ 107
Q ~ Z Q ~ 10-4 107 ~ 103
for high Quality Line Resonance,
cross section >> electron scattering
~lines eQ3~ 10lines elg g
~ ~1000thin e eQ
The Other Extreme: Optically Thick Line-Absorption
in an Accelerating Stellar Wind
1 v~ ~thin
thick
g dg
drv
v /
th
d dr
Lsob
For strong,optically thick lines:
*
v~
v
th R
<< R*
Line Force From an Ensemble of Lines
in CAK theory
e
elines
Qc
drdv
cr
LQg
/
4 2
If we take into account all available thick and thin lines,
the line force is:
Free e- scattering
details, the fraction of thick lines compared to thin lines
CAK Line-Driven Wind for OB stars
lines ~Q
1
~ ~ 1Q
M
(1 )/
2~
1
L QM
c 6~ 10 SunM
yr
( ) (1 / )V r V R r
combination of
thin and thick lines
~ ~escV V g
Hydrodynamic Equations
0
1grav lines
Dv
Dt
Dvp g g
Dt
Mass conservation
Momentum
Assume isothermal wind: energy equation redundant
Add: Finite Disk Correction factor
Simulations: Steady &
spherically symmetric
1D CAK Solutions vs Observations
Using AMRVAC
1D CAK Model of ZPup
well characterized by
)/1()( * rRvrv
Discrete Absorption Features
HD 64760
(B Star)
CAK Line-Driven Wind for OB stars
(1 )/
2
( )( ) ~
1
F Qm
c
( ) ~ ( ) ~ ( )escV V g
Mass flux can be latitude dependent
( )effg
Gravity Darkening
increasing stellar rotation
the gravity and the flux the highest at the poles
Effect of gravity darkening on line-
driven mass flux
2 ( )~
( )eff
F
g 1/ 2
e.g., for
w/o gravity darkening,
if F( )=const.
1~
( )effg( )m highest at
equator
~ ( )Fw/ gravity darkening,
if F( )~geff( )
( )m highest at
pole
1/
1/ 1
( )( ) ~
( )eff
Fm
g
Recall:
Effect of rotation on flow speed
( ) ~ ( ) ~ ( )eff effV V g
/ crit *
1
0.9
2 2( ) ~ 1effg Sin
Eta Carinae
Magnetic Effects on Solar Coronal Expansion1991 Solar Eclipse
Coronal
streamers
SOHO Extreme ultraviolet (171 Angstrom)
Pneuman and Kopp (1971)
MHD model for base dipole
with Bo=1 G
Iterative scheme
Our Simulation
Fully dynamic, time dependent
Maxwell’s equations
Induction
no mag. monopoles
1 BE
c t
0B
4 eE
Coulomb
4 1 EB J
c c tAmpere
2
1v
Oc
Frozen Flux theorem
Bv B
tIdeal MHD induction eqn.:
F B dA
implies flux F through any material surface
0dF
dt
does not change in time, i.e. is “frozen”:
Magnetohydrodynamic (MHD)
Equations
0D
vDt
Mass Momentum
mag Induction Divergence free B
1( )
4lines grav
Dvp B B g g
Dt
Bv B
t0B
Energy Ideal Gas E.O.S.
.T const2P a
Magnetohydrodynamic (MHD)
Equations
0D
vDt
Mass Momentum
mag Induction Divergence free B
2 ( 1)P a e2 ( )M
ee P H n T
tv v
1( )
4lines grav
Dvp B B g g
Dt
Bv B
t0B
Energy Ideal Gas E.O.S.
Wind confinement in magnetic B-stars
Shore & Brown 1990
Wind confinement in magnetic B-stars
Shore & Brown 1990
Magnetically Confined Wind-Shocks
Babel & Montmerle 1997
Magnetic Ap-Bp stars
B* ~ 300 G for Pup
but for O-stars, to get *~ 1, need:for solar wind, *~ 40
2
2
/ 8( )
/ 2
Br
v
2 2 22 20
. .
( / )( )
(1 ( / ))
nB R r RB rr
R rMv M v
2 2 2 20 100 12
. .
6 8
0.4B R B R
M v M v
magnetic energy density
kinetic energy density
= *
Wind Magnetic Confinement
295 G ; * = 1
Final state of Pup isothermal models
2950 G ; * = 100930 G ; * = 10520 G ; * = 3.2
165 G ; * = 0.3293 G ; * = 0.1
Basic Results
Alfven Radius
determines wind modulation
RA)=1
RA= *1/4R*
(For dipole)
Wind Magnetic Confinement Parameter
*<<1 : radial outflow and field.
*>>1 : strong confinement, infall
* ~ 1 : at equator, high density, low speed
Can explain X-ray from 1 Ori C
Magnetic confinement vs.
Wind + Rotation
RA *
1/4R*
Alfven radius
RK W 2/3R*
Kepler radius
WVrot
GM / R*
Rotation vs. critical
B*2R*
2
M.
V
Wind mag. confinement
Alfven vs. Kepler Radius
when RA > RK :
Magnetic spin-up => centrifugal support & ejection
Kepler co-rotation Radius, RK:
GM/ RK2 = V 2/RK
RK = w 2/3 R*w=Vrot/Vcrit Vcrit
2 = GM/R*
= Vrot2RK/R*
2
Alfven radius: (RA)=1
RA = *1/4 R*
e.g, for dipole field,
~ 1/r 4
Rotating Wind with High *
*=100
W=0 W=1/4 W=1/2
zoom in
Can these form disks?
Mais bien sûr …
But NOT Keplerian
Instead Rigidly Rotating Disks are formed
Subject to episodic ejections/flares
Radial Mass Distribution
Time evolution of Radial distribution of
equatorial disk mass* = 100 & Vrot/Vcrit =1/2
RK
RA
Time (ksec)
Rad
ius
(R*)
Two Parameter Study
Stronger Magnetic Confinement --->
Mo
re R
apid
Ro
tati
on
--
->
Radial Distribution of equatorial disk
mass
Stronger Magnetic Confinement --->
Mo
re R
apid
Ro
tati
on
--
->
52
Angular Momentum Loss
22
3AJ M R
Angular Momentum Loss
Contribution from the field
( , )sin
4
r
B
B B rJ r dA
Contribution from gas
singas rJ v v r dA
Total losstot B gasJ J J
22
3to At RJ M
As if gas co-rotates to RA
Weber and Davis
Need to
compute
Computing Alfven Radius
/
*
1
*
2AR
R
For a monopole n=1
2( / )
( )(1 ( / ))
nr R
rR r
/
*
1
*
4AR
R
For a dipole n=2
( ) 1AR
For hot stars, ~1
Alfven radius
22*3
J M R 22*3
J M R
Angular Momentum Loss: Sims
Dead Zone Lives!
Angular Momentum Loss
Magnetic Field Gas Total+ =
Time-Averaged Angular Momentum
LossJdot/Jdot_WD Dipole
Angular Momentum Loss
Weber and Davis
Spindown
22
3ARJ M contribution from both field and gas
32
2
1spin
IJ M
J M MR
32
mass
k
0.15spin
mass
For Dipole
Spindown Time
W=1/2 W=1/4
Spindown Time
ud-Doula et al. 2009
Ori E
Rotational Braking of Ori E
Townsend et al. 2010
Predicted
spin=1.40 Myr
Measured
spin=1.34 Myr
Angular momentum loss / RA2
Spindown time ~ Mass time /
breakout events: J stored and released
Quick Summary of J loss
J
B gasJ J
* ~ 600, Vrot=Vcrit/2
Model with Full Energy Equation
~ 4-5 kev X-ray flares, as seen
in Ori E: reconnection?
(ud-Doula et. al 2006)
log Tlog
Magnetic Bp Stars
Ori E (B2p V)
Prot = 1.2 days => vrot/vcrit ~ 1/2
Bobs ~ 104 G => * ~ 107 !
=> VAlfven very large => Courant time very small
=> Direct MHD impractical
Instead treat fields lines as Rigid guides
Torque up wind outflow
Hold down disk material vs. centrifugal force
Eff. Grav.+Centrifugal Potential
Rigidly Rotating Magnetosphere
Townsend & Owocki (2005)
Ori E
RRM Model H Observations
Summary
Magnetic field + hot star wind:
* >10: channel wind into shock (MCWS)
explains X-rays from 1 Ori C
spin up wind past Kepler co-rotation radius
confine material against centrifugal
Rigidly Rotating Magnetosphere (RRM)
explains H- vs. rot. phase in Ori E
mass build up => centrifugal breakout
reconnection => T >~ 108 K
can explain hard X-ray flares in Ori E
“centrifugally driven reconnection”
Current & Future Work
3D MHD of MCWS
lateral structure scale, tilted field case
Comparison with observations
Chandra & XMM
X-rays from shocks and flares
Optical photometry, spectroscopy, polarimetry
Application to other types of magnetospheres?
RRM shock as site for Fermi acceleration??
Could produce up to TeV Gamma Rays!
