Circular Polarization in Magnetized Wind Recombination Lines

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Circular Polarization in Magnetized Wind
Recombination Lines

• Kenneth Gayley
• Univ. of Iowa

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Why wonder if hot-starwinds have B fields?

• the solar analogy
• impact on star formation
• transport of angular momentum
• circumstellar and wind dynamics
• end stages SN, GRB

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Why hot-star winds shouldnot have B fields

• lack of large surface convection zones
• often fast rotators with strong winds
• radii of order 10 times solar, diluting B

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Why hot-star winds shouldhave B fields

• fossil fields (global?)
• buoyant above core convective zone
• shear instabilities near surface
• X-rays (from confined coronae?)
• equipartition with wind energy (100 G)

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Why hot-star windsdo have B fields

• observed in young Ae/Be stars
• observed in chemically odd Ap/Bp stars
• explain line profiles from sigma Ori E
• hot stars certainly have bright EM

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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).
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Scales of the magneticfield in time and space

• global configurations (dipole or radial)
• rotational modulation of starspots
• small-scale loops and CIRs- X-rays?
• microscopic and stochastic (EM)

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Scales of the magneticfield in time and space

• global configurations (dipole or radial)
• rotational modulation of starspots
• small-scale loops and CIRs- X-rays?
• microscopic and stochastic (EM)
• -- B fields propagate E fields to Earth

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Scales of the magneticfield in time and space

• global configurations (dipole or radial)
• rotational modulation of starspots
• small-scale loops and CIRs- X-rays?
• microscopic and stochastic (EM)
• -- B fields propagate E fields to Earth
• -- B fields drive the wind (classically)

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

• typical O-star stochastic B is 100 G
• stochastic E is the same (EM)
• both stochastic, but correlated tightly
• -- E field jiggles, Lorentz force drives
• -- Lorentz force is mostly on bound e

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How stochastic (EM) 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
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How stochastic (EM) 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
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How a constant shifts the resonance
frequency
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)
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Summary of how B fields yield Zeeman shifts

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

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The problem with magnetic detection in wind lines

• cancellation of circular polarization due to
  Doppler mixing yields B/v residual
• surviving signal is 0.1 for B in 100 G and v
  in 100 km/s
• winds are where the v is higher and B is lower
  than at the surface
• if the lines go effectively thick, they will form
  too far out, and I(x) will swamp V(x)

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The value of magnetic detection in winds

• WR stars we see only the wind
• B field effects in winds X-ray generation
• torque and spindown happens in the wind
• as with MDI of surface fields, spectral
  resolution gives spatial information
• unlike MDI, radial information allows
  non-potential field extrapolation

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Current and Planned Observationsof B Fields in
Massive Stars
Tau Sco mapped with ESPaDOnS
The MiMeS project the search for magnetic
massive stars
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Heartbeat polarization for radial B
proportional to v
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Circular polarization for 100G at 100 km/s
(effectively thin lines, homogeneous expansion,
split monopole field)
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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)

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What are the signatures of radially swept fields?

• V(x) is antisymmetric if stellar-disk effects are
  small, i.e., for strong emission lines
• Thin lines give V(x) signal that integrates to
  zero on each side of the profile
• radial B fields mimic a change in the velocity
  law
• I(x) 1-B/v I( 1-B/vx )
• then V(x) B/v times I(x) xI(x)
• heartbeat waveform helps distinguish signal
  from noise

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Conclusions about magnetic fields in hot stars
and winds

• B fields exist and do interesting things in
  hot-star winds
• classical pictures are useful for understanding
  what the fields do
• observational capabilities are just now coming
  online ESPaDOnS and NARVAL
• signal will be weak, theory is proof

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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

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V profile in strong but effectively thin emission
lines

• set by B/v in the deepest visible regions, about
  0.1 for B100 G and v100 km/s
• a radial B effectively increases/decreases the
  wind velocity for the two polarizations
• antisymmetric V(x) ? globally regular B
• then V(x) B/v times I(x) xI(x)
• heartbeat waveform helps distinguish signal
  from noise

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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
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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
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Wind emission lines and the big star effect

• in dense winds, like WR, the star simply looks
  much bigger at line frequencies
• this is often how lines appear in emission
• if light escapes the zone where it was born, it
  escapes the whole wind
• the line formation is essentially a collision
  process, if zones are effectively thin

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I(x) and V(x) / I(x) for splitmonopole with
linear expansion
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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.
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Evidence for large-scale circumsolar magnetism
http//solar-heliospheric.engin.umich.edu/hjenning
/Corona.html
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Hot emission from confinedgas in solar magnetic
loops
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Convective regions in different mass stars
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The Good News

• 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

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The Not-So-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

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Good/Bad News for Adiabaticity

• 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 clumping
• The bad news
• bulk of energy is not directly observable
• radiative efficiency becomes a critical parameter
  which is sensitive to clumping and ionization

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Patterns and Turbulence

• 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

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Density Distributions

• In general

Define characteristic densities
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Contrast with Single Filling Factor

• mass filling factor

emission filling factor
but for log-normal
single filling factor
so in this case
and therefore
!
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Scaling with Filling Factor
If emission measure (EM) and volume (V) are
observed

• one-component clumps

log-normal clumps
scales as
scales as
scales as
scales as
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B Fields vs. Ram Pressure

• Zeeman splitting in molecular clouds gives
• synchrotron emission from cluster outflows
• B affects dynamics when , so when
• may matter close to star where
  , or far from cluster core where
• May explain radio filaments (Yusef-Zadeh 2003),
  and might also alter outflow dynamics (Ferriere,
  Mac Low, Zweibel 1991)

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Dipole Field Effects on Wind

From ud-Doula Owocki (2002)
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Conclusions

• 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
  limit
• One-component clumping factor is likely too naive
• Blowouts and leaky shells reduce thermal energy
  and limit bubble size
• B fields may affect winds close to stars and
  flows far from cluster, and light up nonthermal
  filaments