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

A Sample Simulation

RK RA

W=1/2

*=10

RE

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)

Oblique-Dipole RRM

Not a cartoon!!

Analytic result.

Ori E

RRM Model H Observations

Rigid Field – Hydro Model

Townsend , Owocki and ud-Doula (2007)

Compare (3D)

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!