Download Circular Polarization in Magnetized Wind Recombination Lines

Circular Polarization in
Magnetized Wind
Recombination Lines
Kenneth Gayley
Univ. of Iowa
Why wonder if hot-star
winds have B fields?
the solar analogy
impact on star formation
transport of angular momentum
circumstellar and wind dynamics
end stages: SN, GRB
Why hot-star winds should
not have B fields
lack of large surface convection zones
often fast rotators with strong winds
radii of order 10 times solar, diluting B
Why hot-star winds should
have 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)
Why hot-star winds
do 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 E&M
Rigidly rotating magnetosphere
model for sigma Ori E
Line emitting
plasma is confined
and forced to
corotate with the
tilted dipole field.
Model by Townsend
and Owocki (2004).
Scales of the magnetic
field in time and space
global configurations (dipole or radial)
rotational modulation of starspots
small-scale loops and CIRs–- X-rays?
microscopic and stochastic (E&M)
Scales of the magnetic
field in time and space
global configurations (dipole or radial)
rotational modulation of starspots
small-scale loops and CIRs–- X-rays?
microscopic and stochastic (E&M)
-- B fields propagate E fields to Earth
Scales of the magnetic
field in time and space
global configurations (dipole or radial)
rotational modulation of starspots
small-scale loops and CIRs–- X-rays?
microscopic and stochastic (E&M)
-- B fields propagate E fields to Earth
-- B fields drive the wind (classically)
How do B fields (classically)
drive a hot-star wind?
typical O-star stochastic B is ~ 100 G
stochastic 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 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 fields
drive 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 Bo shifts the
resonance frequency
At resonance, v is
perpendicular to the
binding force, so the
Lorentz force of the
constant Bo alters the
binding force and
changes the resonant
frequency by half the
cyclotron frequency
(classically)
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
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)
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 nonpotential field extrapolation
Current and Planned Observations
of 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”)
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/v]x )
then V(x) ~ B/v times [I(x) + xI’(x)]
“heartbeat” waveform helps distinguish signal
from noise
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”
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
V profile in strong but effectively
thin emission lines
set by B/v in the deepest visible regions,
about 0.1% for B=100 G and v=100 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
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 allow
a 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
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”
I(x) and V(x) / I(x) for split
monopole 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://solarheliospheric.engin.umich
.edu/hjenning/Corona.ht
ml
Hot emission from confined
gas in solar magnetic loops
Convective regions in
different mass stars
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
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
Good/Bad News for Adiabaticity
n
Cluster outflows with e  10 cm 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
-2
-3
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
Density Distributions
In general
:



dV
d
 V
d
dV
M
d
d
dV 2
d   EM
d
| Define characteristic densities:
|
|
|
|
|
|
|
|
|
|
V


dV
M

d

0 d  2
dV
V

dρ
d 2
0
M

EM
EM
dV
2
d dρ   2
0
Contrast with Single Filling Factor
emission filling factor:
mass filling factor:
VEM EM

 2
V
EM V
VM M
 
V MV
single filling factor:
VEM  VM
and therefore:
 
|
|
|
|
|
|
but for log-normal:
VEM   VM
3
so in this case:
 4 !
Scaling with Filling Factor
If emission measure (EM) and volume (V) are observed:

V

M
EM
M
one-component clumps: | log-normal clumps:
|
scales as:
|
scales as:
scales as:
scales as:
0
1
2
 1
2

1
2

0

2

1

2
|
|
|
|
|
|
|
B Fields vs. Ram Pressure
Zeeman splitting in molecular clouds gives
3
B  10 G
synchrotron emission from cluster outflows
B affects dynamics when vA  v , so when
4
B  610
n
may matter close to star where B  10 G ,
-2
-3
or far from cluster core where ne  10 cm
May explain radio filaments (Yusef-Zadeh
2003), and might also alter outflow dynamics
(Ferriere, Mac Low, & Zweibel 1991)
2
Dipole Field Effects on Wind
From ud-Doula & Owocki (2002)
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