Circular Polarization in Magnetized Wind

Recombination Lines

Kenneth GayleyUniv. of Iowa

the solar analogyimpact on star formationtransport of angular momentumcircumstellar and wind dynamicsend stages: SN, GRB

Why wonder if hot-starwinds have B fields?

lack of large surface convection zonesoften fast rotators with strong windsradii of order 10 times solar, diluting B

Why hot-star winds shouldnot have B fields

fossil fields (global?)buoyant above core convective zoneshear instabilities near surfaceX-rays (from confined coronae?)equipartition with wind energy (~100 G)

Why hot-star winds shouldhave B fields

observed in young Ae/Be starsobserved in chemically odd Ap/Bp starsexplain line profiles from sigma Ori Ehot stars certainly have bright E&M

Why hot-star windsdo have B fields

Rigidly rotating magnetospheremodel for sigma Ori E

Line emitting plasma is confined and forced to corotate with the tilted dipole field. Model by Townsend and Owocki (2004).

global configurations (dipole or radial)rotational modulation of starspotssmall-scale loops and CIRs–- X-rays?microscopic and stochastic (E&M)

Scales of the magneticfield in time and space

global configurations (dipole or radial)rotational modulation of starspotssmall-scale loops and CIRs–- X-rays?microscopic and stochastic (E&M)

-- B fields propagate E fields to Earth

Scales of the magneticfield in time and space

global configurations (dipole or radial)rotational modulation of starspotssmall-scale loops and CIRs–- X-rays?microscopic and stochastic (E&M)

-- B fields propagate E fields to Earth -- B fields drive the wind (classically)

Scales of the magneticfield in time and space

typical O-star stochastic B is ~ 100 Gstochastic E is the same (E&M)both stochastic, but correlated tightly

-- E field jiggles, Lorentz force drives -- Lorentz force is mostly on bound e

How do B fields (classically) drive a hot-star wind?

How stochastic (E&M) B fields drive free electrons

Radiative reaction causes the damping that allows the E field to do work against the velocity, requiring a phase angle that in turn creates a Lorentz force that drives the wind

How stochastic (E&M) B fieldsdrive bound electrons

When there is an elastic binding force, driving at the resonant frequency allows the binding force to provide the circular acceleration, leaving the E force free to do work in phase with v, creating a huge v and a huge outward Lorentz force

How a constant shifts the resonance frequency

oB

At resonance, v is perpendicular to the binding force, so the Lorentz force of the constant alters the binding force and changes the resonant frequency by half the cyclotron frequency (classically)

oB

Summary of how B fields yield Zeeman shifts

the Lorentz force from a radial B helps/hinders the atomic bindingthe effect alters the binding resonance frequency, similar to how motion gives a Doppler shiftthe classical shift is half the cyclotron frequencyshift is ~1 km/s at 1000 G

The problem with magnetic detection in wind lines

cancellation of circular polarization due to Doppler mixing yields B/v residualsurviving signal is ~ 0.1% for B in 100 G and v in 100 km/swinds are where the v is higher and B is lower than at the surfaceif the lines go effectively thick, they will form too far out, and I(x) will swamp V(x)

WR stars: we see only the windB field effects in winds: X-ray generationtorque and spindown happens in the windas with MDI of surface fields, spectral resolution gives spatial informationunlike MDI, radial information allows non-potential field extrapolation

The value of magnetic detection in winds

Current and Planned Observationsof B Fields in Massive Stars

Tau Sco mapped with ESPaDOnS

The MiMeS project: the search for magnetic massive stars

“Heartbeat” polarization for radial B proportional to v

% Circular polarization for 100G at 100 km/s (effectively thin lines, homogeneous expansion,

split monopole field)

Polarization affects:

formation depth (“gradient effect”)

width of radial bin (“stretching effect”)

angle to the radial (“angle effect”)

shape/size of resonance zone (“morphing effect”)

V(x) is antisymmetric if stellar-disk effects are small, i.e., for strong emission linesThin lines give V(x) signal that integrates to zero on each side of the profileradial B fields mimic a change in the velocity law:

I(x+) = [1-B/v] I( [1-B/v]x )then V(x) ~ B/v times [I(x) + xI’(x)]“heartbeat” waveform helps distinguish signal from noise

What are the signatures of radially swept fields?

B fields exist and do interesting things in hot-star windsclassical pictures are useful for understanding what the fields doobservational capabilities are just now coming online: ESPaDOnS and NARVALsignal will be weak, theory is “proof”

Conclusions about magnetic fields in hot stars and winds

B fields exist and do interesting things in hot-star winds

classical treatments are useful for understanding what the fields do

observational capabilities are just now coming online: ESPaDOnS and NARVAL

signal is so weak that theoretical support is crucial

Conclusions about magnetic fields in hot stars and winds

set by B/v in the deepest visible regions, about 0.1% for B=100 G and v=100 km/sa radial B effectively increases/decreases the wind velocity for the two polarizationsantisymmetric V(x) globally regular Bthen V(x) ~ B/v times [I(x) + xI’(x)]“heartbeat” waveform helps distinguish signal from noise

V profile in strong but effectively thin emission lines

Emission line profiles from spherically symmetric winds

When the winds are spherically symmetric, it is helpful to take the point of view of the emitting gas, and integrate over the observers, rather than the other way around

Split monopole B fields allowa similar symmetry simplification

In a strong wind, the B field should be radial, but the sign must reverse to avoid net flux– that would break spherical symmetry, but we can return it if the magnitude is symmetric:split monopole

in dense winds, like WR, the star simply looks much bigger at line frequenciesthis is often how lines appear in emissionif light escapes the zone where it was born, it escapes the whole windthe line formation is essentially a collision process, if zones are “effectively thin”

Wind emission lines and the “big star” effect

I(x) and V(x) / I(x) for splitmonopole with linear expansion

Hot Stars: live fast and die young

Galactic luminosity, chemical enrichment, energetic flows, and cosmic rays are all largely due to hot, massive stars, up to a hundred times more massive and a million times more luminous than our Sun.

Evidence for large-scale circumsolar magnetism

http://solar-heliospheric.engin.umich.edu/hjenning/Corona.html

Hot emission from confinedgas in solar magnetic loops

Convective regions in different mass stars

For radio:• ultra low attenuation• excellent spatial resolution• thermal free-free signatures• nonthermal diagnostics of acceleration

For X-rays:• fairly low attenuation• important energy channel for hot gas• temperature-sensitive spectral lines

The Good News

For radio:• uncertainty in acceleration and B fields• thermal emission is a weak energy component• density-squared sensitivity to clumping

For X-rays:• self-absorption may remove some sources• trace energy channel when nearly adiabatic• again the density-squared clumping sensitivity

The Not-So-Good News:

Cluster outflows with are expected to be primarily adiabatic.

The good news:• energy bookkeeping is made easier• gas gets hot enough to emit X-rays• high pressure resists clumpingThe bad news:• bulk of energy is not directly observable• radiative efficiency becomes a critical

parameter which is sensitive to clumping and ionization

Good/Bad News for Adiabaticity

3-2- cm10en

Importance of clumping motivates a better understanding of compression and turbulence:

• Patterned compression (standing shocks, slowly propagating working surfaces) could yield geometry dependence and intermittency

• Compressible turbulence involving scale-invariant perturbations gives a log-normal density profile

But either way, the potential for strong clumping implies that a tiny fraction of the mass may be responsible for the observed emission

Patterns and Turbulence

In general:

Density Distributions

EMddVd 2

Define characteristic densities:

2EM

dρdVd 2

0

EM

MddVd

VddVd

V

0 2V

ddVd

ρ

|||||||||||

2M

ddVd

M

0

mass filling factor:

Contrast with Single Filling Factor

emission filling factor:

MME VV

VM

VV

M

M

VEM

VV

EM2

EM

||||||

single filling factor: but for log-normal:

so in this case:and therefore:

M3

EM VV

4 !

one-component clumps:

Scaling with Filling Factor

log-normal clumps:

0

||||||||||

scales as:

21

scales as:

scales as:

21M

MEM

1

221

V scales as: 0 2

If emission measure (EM) and volume (V) are observed:

Zeeman splitting in molecular clouds gives

synchrotron emission from cluster outflowsB affects dynamics when , so when

may matter close to star where , or far from cluster core whereMay explain radio filaments (Yusef-Zadeh 2003), and might also alter outflow dynamics (Ferriere, Mac Low, & Zweibel 1991)

B Fields vs. Ram Pressure

G3

10B

vvA

n106B 4GB 210 3-2-

e cm10n

Dipole Field Effects on Wind

From ud-Doula & Owocki (2002)

Resonant character of nonthermal radio lets it trace particle distribution (but… relativistic tail only)Thermal radio is a high-density diagnostic (but… is insensitive to T and oversensitive to clumping)Thermal X-ray is a good diagnostic of both density and T for hot gas (but… is also sensitive to clumps)Radiative efficiency is a key issue in adiabatic limitOne-component clumping factor is likely too naiveBlowouts and leaky shells reduce thermal energy and limit bubble sizeB fields may affect winds close to stars and flows far from cluster, and light up nonthermal filaments

Conclusions