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Stellar Magnetospheres part deux: Magnetic Hot Stars. Stan Owocki. Key concepts from lec. 1. MagRe# --> inf => “ideal” => frozen flux breaks down at small scales: reconnection Lorentz force ~ mag. pressure + tension plasma b ~ P gas /P mag ~ (a/V A ) 2

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Stellar magnetospheres part deux magnetic hot stars

Stellar Magnetospherespart deux: Magnetic Hot Stars

Stan Owocki


Key concepts from lec 1
Key concepts from lec. 1

  • MagRe# --> inf => “ideal” => frozen flux

  • breaks down at small scales: reconnection

  • Lorentz force ~ mag. pressure + tension

  • plasma b ~ Pgas/Pmag ~ (a/VA)2

  • press. scale ht. H << R (except in corona)

  • wind mag. conf. h ~B2R2/Mdot*V¥


Wind magnetic confinement

e.g, for dipole field,

q=3; h ~ 1/r 4

h*

for OB SG, to get h*~1, need B* ~ 100 G

Wind Magnetic Confinement

Ratio of magnetic to kinetic energy density:

Alfven Radius: h( RA) º 1

For dipole (q=3): RA = h*1/4 R*


Hot stars vs sun
Hot Stars vs. Sun

  • Luminous Radiative Envelope (not conv.)

  • Radiatively Driven Wind (line scatt.)

    • Twind ~= Teff

    • Mdot ~ 10-7 MO/yr >> Mdot,sun

  • Detected B-fields often steady, dipole

  • Rotation can be rapid Vrot ~< Vcrit

  • NOT a (direct) solar Coronal analog!


Light s momentum
Light’s Momentum

  • Light transports energy (& information)

  • But it also has momentum, p=E/c

  • Usually neglected, because c is so high

  • But becomes significant for very bright stars,

  • Key question: how big is force vs. gravity??

  • Ge=ge/g < 1 (near but below “Edd. limit”)

  • “CAK” wind model: Glines = glines/g > 1


Aside radiation pressure vs gas pressure
Aside: Radiation Pressure vs. Gas Pressure

  • Force depends on gradient of Pressure

  • grad Prad comes from opacityk

  • Deep interior (t>>1), Prad nearly isotropic

    • Prad + Pgas act together => Hr=a2/g(1-G)

  • But near surface (t ~1) radiation “beamed”

  • wind is not “Radiation Pressure Corona” H ~< R


Radiative force

if k gray

e.g., compare electron scattering force vs. gravity

s

L

Th

g

2

k

4

r

c

L

p

m

e

e

el

G

º

=

=

g

4

GM

c

p

GM

grav

2

r

  • For sun, GO ~ 2 x 10-5

  • But for hot-stars with L~ 106 LO ; M=10-50 MO

.

.

.

G<1

~

Radiative force


Optically thick line absorption in an accelerating stellar wind

Lsob

Optically Thick Line-Absorption in an Accelerating Stellar Wind

<< R*

For strong,

optically thick

lines:


Cak force for power law line ensemble
CAK force for power-law line ensemble




Magnetohydrodynamic (MHD) Equations

Mass

Momentum

Energy

Ideal Gas E.O.S.

Divergence free B

mag Induction


Magnetohydrodynamic (MHD) Equations

Mass

Momentum

Energy

Ideal Gas E.O.S.

Divergence free B

mag Induction


Mhd simulation of wind channeling
MHD Simulation of Wind Channeling

IsothermalNo Rotation

Confinement parameter

h*=1/3

A. ud Doula

PhD thesis 2002


Mhd simulation of wind channeling1
MHD Simulation of Wind Channeling

IsothermalNo Rotation

Confinement parameter

h*=1


Mhd simulation of wind channeling2
MHD Simulation of Wind Channeling

IsothermalNo Rotation

Confinement parameter

h*= 3


Mhd simulation of wind channeling3
MHD Simulation of Wind Channeling

IsothermalNo Rotation

Confinement parameter

h*=10


Mhd simulation of wind channeling4

RA~ h*1/4 R*

MHD Simulation of Wind Channeling

IsothermalNo Rotation

Confinement parameter

h*=10


RA~ h*1/4 R*

IsothermalNo Rotation

Confinement parameter

h*=1000 !

!


Final state of isothermal models

295 G ; h* = 1

93 G ; h* = 0.1

165 G ; h* = 0.32

Final state of isothermal models

520 G ; h* = 3.2

930 G ; h* = 10

1650 G ; h* = 32


Q 1 ori c
Q1 Ori C


Mhd simulation for q 1 ori c o7 v
MHD simulation for Q1 Ori C (O7 V)

  • Bobs ~ 1100 G + Prot = 14 days

  • Mdot~ 10-7 Msun/yr

  • h*~= 14

  • Magnetic Confined Wind Shock (MCWS)

  • kev X-rays => match Chandra obs.


Magnetically confined wind shocks
Magnetically Confined Wind-Shocks

Babel & Montmerle 1997

Magnetic Ap-Bp stars


Magnetically confined wind shock
Magnetically Confined Wind Shock

log T

still no rotation

but now with

Radiative

Cooling

~ 2 kev X-rays fit Chandra spectrum

for Q1 Ori C


Q 1 ori c1
Q-1 Ori C

Gagne et al. 2005, ApJ, 528, 986

Prot = 13 days


Q 1 ori c2

Q1 Ori C

b ~ 45o

i ~ 45o



Magnetically torqued disk mtd
Magnetically Torqued Disk (MTD)

Cassinelli et al. 2002


Alfven vs kepler radius

Kepler co-rotation Radius, RK:

GM/ RK2 =Vf2/RK

=Vrot2RK/R*2

RK= w-2/3R*

w=Vrot/Vcrit

Vcrit2 = GM/R*

Alfven radius: h(RA)=1

RA = *1/4 R*

e.g, for dipole field,

 ~ 1/r 4

Alfven vs. Kepler Radius

when RA > RK :

Magnetic spin-up => centrifugal support & ejection


Keplerian spin up vs escape
Keplerian spin-up vs. escape

sqrt(h*) ~B

vf > vesc

vf< vkep

w = Vrot/Vcrit


Mhd sims of field aligned rotation

RK

RA

RK

RA

MHD Sims of Field-Aligned Rotation

h*=10 ; vrot=250 km/s (w=1/2)

Vf/Vrigid

Density


Field aligned rotation
Field aligned rotation

again

isothermal, but now with

Vrot=250 km/s

= Vcrit/2

RK

RA


Magnetically torqued disk

Owocki & ud-Doula 2003

Magnetically Torqued Disk

Cassinelli et al. 2002


S ori e
s Ori E


Magnetic bp stars
Magnetic Bp Stars

  • s Ori E (B2p V)

    • Prot = 1.2 days => vrot/vcrit ~ 1/2

    • Bobs ~ 104 G => h* ~ 107 !

    • => VAlfvenvery large => Courant time very small

    • => Direct MHD impractical

  • Instead treat fields lines as “Rigid”


Strong field limit b h
Strong field limit: B*,h* --> ∞

  • Field lines act asrigid guides for wind outflow

    • Torqueup wind outflow

    • Holddown disk material vs. centrifugal force

  • Problem: VAlfven ->∞ => can’t do MHD

  • But can model semi-analytically

    • Rigidly Rotating Magnetosphere (RRM)

    • gas accumulates at minima in grav+cent. potential



R igidly r otating m agnetosphere
Rigidly Rotating Magnetosphere

Townsend & Owocki (2005)


Accumulation surface
Accumulation Surface

Townsend & Owocki (2005)


Rrm model for s ori e
RRM model for s Ori E

B*~104 G

h*~106 !

tilt ~ 55o


Em b field

RRM model for s Ori E

photometry

EM +B-field

B*~104 G

=> h*~106 !

tilt ~ 55o

Ha

polarimetry



S ori e1

Ha Observations

s Ori E

RRM Model



Mhd sim of centrifugal breakout
MHD sim of centrifugal breakout

log(r)

h*= 620

vrot=vcrit/2


Centrifugally driven reconnection flare
Centrifugally Driven Reconnection Flare

log T

h*= 620

vrot=vcrit/2

~ 4-5 kev

X-ray

flares,

as seen in

s Ori E


Model grid for 2 parameter study rotation magnetic confinement
Model grid for 2-Parameter study: Rotation & Magnetic Confinement


Isothermal v rot v crit 2 h 100

RK

RA

Isothermal, vrot=vcrit/2, h*=100


Isothermal v rot v crit 2 h 1000

RK

Isothermal, vrot=vcrit/2, h*=1000

RA~7R*



Equatorial mass distribution dm e dr
Equatorial mass distribution dme/dr

5

h*=100

W=1/2

Radius (R*)

1

0

Time (Msec)


Equatorial mass distribution dm e dr1
Equatorial mass distribution dme/dr

5

h*=100

W=0

Radius (R*)

1

0

Time (Msec)


Parameter study rotation magnetic confinement
Parameter study: rotation & magnetic confinement


Between rrm and full mhd r igid f ield h ydro d ynamics rfhd

Between RRM and full MHD: “Rigid Field Hydro-Dynamics” RFHD

Solve time-dependent hydro along completely rigid individual field lines




Summary
Summary

  • Magnetic field + hot star wind:

    • h* >10: channel wind into shock (MCWS)

      • explains X-rays from Q1 Ori C

    • spin upwind past Kepler co-rotation radius

    • confine material against centrifugal

      • Rigidly Rotating Magnetosphere (RRM)

      • explains H-a vs. rot. phase in s Ori E

    • mass build up => centrifugal breakout

      • reconnection => T >~ 108 K

      • can explain hard X-ray flares in s Ori E

      • “centrifugally driven reconnection”


Current future work
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

      • Rotation Spin-Down??

    • VLTI to resolve disk

  • Application to other types of magnetospheres?

  • RRM shock as site for Fermi acceleration??

    • Could produce up to TeV Gamma Rays!


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