NLTE polarized lines and 3D structure of magnetic fields
P.Mein, N.Mein, M.Faurobert, V.Bommier, J-M.Malherbe, G.Aulanier
Magnetic fields cross canopy regions, not easily investigated by
extrapolations, between photosphere and chromosphere.
Full knowledge of the 3D structure implies diagnostics extracted from
strong NLTE lines.
Fortunately, the domain of ‘’weak field ’’ approximation is more
extended for such lines (smaller Lande factor, broad lines).
The data analysed below are obtained with THEMIS / MSDP and MTR in
589.6 NaI (D1)
610.27 CaI
630.2 FeI (for comparison)
1) D1 line and facular magnetic flux tubes
Problems of filling factor, vertical gradients, MHD models
Simulation of line profiles
MULTI code with field free assumption, 1D model
Instrumental profile included
- Quiet Sun = VAL3C model
- Circular polarization: I -V profile
-Solid line: flux tube, dashed: quiet
-Bisector for = +/-8, 16, 24, 32 pm
-Weak field assumption
B//
1 - 2D model flux tube compensating horizontal components of Lorentz forces
Magnetic field
Bz(0,z) ~ exp(-z/h)
Bz(x,z) ~ cos2(x/4d(z))
d(z) by constant flux
Bx(x,z) by zero divergence
P(x,z) compensates
Lorentz horiz. comp.
Departures from equilibrium
Formation altitudes of B// for
 = +/- 8, 16, 24, 32 pm
Vertical accelerations exceed
solar gravity at high levels
Simulation
No smoothing by seeing effects
Smoothing by seeing effects
convol cos2(x/4s) s=400 km
wings
core
wings
B// from tube center at  = 8, 16, 24, 32 pm
Points at half maximum values
(crosses) are in the same order
as tube widths at corresponding
formation altitudes
Seeing effects ~ filling factor effects
hide vertical magnetic gradients at
tube center
core
Filling factors and slope-ratios of profiles flux-tube/quiet-sun
I-V
Stokes Vobs = f Stokes Vtube
Tube
Quiet
Sun
Zeeman shift of I -V profile:
Zobs (dI/d)obs = f Ztube (dI/d)tube
If f << 1, from core to wings
Zobs = f
dI/d
Ztube
(dI/d)tube / (dI/d)QS
Tube
QS
Decrease of
observed B//
in the wings
Different models for tube and quiet sun !
2 - Model flux tube closer to magneto-static equilibrium
Magnetic field
Bz(0,z)2/20 ~ Pquiet(z)
Bz(x,z) ~cos2(x/4d(z))
d(z) by constant flux
Bx(x,z) by zero divergence
P(x,z) = Pquiet – Bz(x,z)2/20
Departures from equilibrium
Formation altitudes of B//
 = +/- 8, 16, 24, 32 pm
Departures from
equilibrium never exceed
solar gravity
Observation
Average of 6 magnetic structures
Faculae near disk center (N17, E18)
Simulation
With seeing effects s=500 km
core
wings
core
wings
Sections for = 8, 16, 24, 32 pm
Qualitative agreement only:
- tube thinner in line wings
- apparent B// smaller in line wings (seeing effects)
But impossible to increase the magnetic field and/or the width
of the tube without excessive departures from equilibrium
3 - Conglomerate of flux tubes
Magnetic field
Departures from equilibrium
Observation
Simulation
Seeing effects s = 700 km
Better qualitative agreement (tube width)
But magnetic field still too low
Coronal magnetic field outside the structure?
MHD models, including temperature and velocity fluctuations…?
P. Mein, N. Mein,M. Faurobert, G. Aulanier and J-M. Malherbe,
A&A 463, 727 (2007)
2) Fast vector magnetic maps with THEMIS/MSDP
UNNOFIT inversions
NLTE line 610.27 CaI + 630.2 FeI
- Examples of fast MSDP vector magnetic maps and comparison with MTR results
- How to reconcile high speed and high spectral resolution by compromise
with spatial resolution in MSDP data reduction
- Capabilities expected from new THEMIS set-up (32) and EST project (40)
- Departures between 610.3 CaI and 630.2 FeI maps
Gradients along LOS? sensitivity of lines? filling factor effects?
Example of MSDP image (Meudon Solar Tower 2007, courtesy G. Molodij):
In each channel, x and  vary simultaneously along the horizontal direction
Compromise spatial resol / spectral resol
interpolation in x, plane
A,D
B,C
80 mA
--> E
cubic interpol --> F,G
40 mA
20 mA
Profile deduced from 16 MSDP channels
+ interpolation x,plane
610.27 CaI
THEMIS / MSDP
610.3 CaI
2006
UNNOFIT inversion
THEMIS / MTR 2006
630.2 FeI
160’’
70’’
70’’
Aug 18, NOAA 904
S13 , W35
120’’
Scatter plots Ca (MSDP) / Fe (MTR)
f B//
f Bt
THEMIS/MSDP 2007
UNNOFIT inversion
630.2 FeI
610.3 CaI
160’’
120’’
June 11, NOAA 10960
120’’
S05, W52
610.3 CaI
I
Q/I
U/I
V/I
THEMIS
MSDP
f Bx
Similar Bx and By
f By
similar f angles
THEMIS
MSDP
Bt 6103 < Bt 6302
- Gradients along line of sight ?
- B t more sensitive than B// to line
center, 6103 saturated NLTE line?
- stray-light effects?
- instrumental profile not included?
- filling factor effects?
- further simulations needed …..
- comparisons with MTR data
(not yet reduced)
Possible improvements:
- Include instrumental profile
- set-up 32 channels (2 cameras =
effective increase of potential well)
- better size of 6302 filter !
Scanning speed
for targets 100’’x160’’
9 mn
3) Problems and plans:
Gradients of B along LOS from NaD1, 610.3 Ca, 630.2 Fe, …
Weak field approximation
Disk center,
no rotation of B along LOS: Stokes U = 0
1 - Simple case: LTE, Milne Eddington,
B vector and f independent of z
V() ~ f Bl dI/d
Q() ~ f Bt2 d2I/d2
For weak fields, line profile inversions
provide only 2 quantities, f Bl and f Bt2
Bt * f
Bt * f1/2
Below a given level of c2 the range of possible solutions is
larger for (Btransverse * f ) than for (Btransverse * f ½) ?
2 – NLTE, B function of z, f = 1, given solar model (parts of spots?)
> Computation of response functions by MULTI code
V() =
Q() =
S B (z) R(,z) dz
l
SB
2
t (z)
R’(,z) dz
?
> Formation altitudes: barycenters of response functions
> Vertical gradients:
Circular polarization: Bl (0), dBl/dz
Bl = a + bz
V()=
S R(,z) (a+bz) dz
Instead of using individual points of the bisector,
integrations along line profile to optmize signal/noise ratio.
Choose functions with different weights at line-center and wings:
Examples:
SV()
S = SV()
w1() = +1 and -1 around line center, 0 elsewhere
w2() = +1 and -1 in line wings, 0 elsewhere
S1=
w1() d
2
w2() d
a, b
Linear polarization: Bt
??? Bt2 = a’+ b’z
Q()=
S R’(,z) (a’+b’z) dz
> Application: comparisons between gradients from
and
Bt2, dBt2/dz ???
full profile of 1 line
2 different lines
3 – NLTE,
B and f functions of z,
given solar model (flux tubes?)
Example: flux tubes, NaD1 line (section 1)
Bl = a + bz
f = a + bz
V() =
S R(,z) (a+bz) (a+bz) dz
Both unknown quantities b and b are present in the coefficient of z
Impossible to determine separately f and Bl
In particular, when flux tubes are not spatially resolved,
the assumption of constant flux f Bl
implies that gradients of f and Bl are compensated (b/a ~ - b/a)
MHD model necessary in case of weak fields (see section 1).
4 – Possible extension of UNNOFIT to NLTE lines close to LTE ?
Example: Analysis of depatures between UNNOFIT results and
parameters used for synthetic profiles in case of 610.3 Ca …