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NLTE polarized lines and 3D structure of magnetic fields. P.Mein, N.Mein, M.Faurobert, V.Bommier, J-M.Malherbe, G.Aulanier. M agnetic fields cross canopy regions, not easily investigated by extrapolations, between photosphere and chromosphere. - PowerPoint PPT Presentation
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NLTE polarized lines and 3D structure of magnetic fields
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.
The data analysed below are obtained with THEMIS / MSDP and MTR in
589.6 NaI (D1)
610.27 CaI
630.2 FeI (for comparison)
Fortunately, the domain of ‘’weak field ’’ approximation is more extended for such lines (smaller Lande factor, broad lines).
P.Mein, N.Mein, M.Faurobert, V.Bommier, J-M.Malherbe, G.Aulanier
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 Departures from equilibrium
Formation altitudes of B// for = +/- 8, 16, 24, 32 pm
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.
Vertical accelerations exceed solar gravity at high levels
Simulation
Smoothing by seeing effects convol cos2(x/4s) s=400 km
B// from tube center at = 8, 16, 24, 32 pm
No smoothing by seeing effects
Points at half maximum values (crosses) are in the same order as tube widths at corresponding formation altitudes
wings
corewings
core
Seeing effects ~ filling factor effects hide vertical magnetic gradients at tube center
Filling factors and slope-ratios of profiles flux-tube/quiet-sun
Stokes Vobs = f Stokes Vtube
Zeeman shift of I -V profile:
Zobs (dI/d)obs = f Ztube (dI/d)tube
If f << 1, from core to wings
Zobs = f Ztube (dI/d)tube / (dI/d)QS
dI/d
Tube
Quiet Sun
Tube
QS
I - V
Decrease of observed B// in the wings
Different models for tube and quiet sun !
2 - Model flux tube closer to magneto-static equilibrium
Bz(0,z)2/20 ~ 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)2/20
Magnetic field Departures from equilibrium
Formation altitudes of B// = +/- 8, 16, 24, 32 pm
Departures from equilibrium never exceed solar gravity
Observation SimulationAverage of 6 magnetic structures
Faculae near disk center (N17, E18)
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
With seeing effects s=500 km
wings
corecore
wings
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 80 mA
B , C --> E 40 mA
cubic interpol --> F,G 20 mA
610.27 CaI
Profile deduced from 16 MSDP channels+ interpolation x,plane
THEMIS / MSDP 2006 610.3 CaI
160’’
120’’
THEMIS / MTR 2006 630.2 FeI
70’’
70’’
UNNOFIT inversion
Aug 18, NOAA 904
S13 , W35
f B// f Bt
Scatter plots Ca (MSDP) / Fe (MTR)
630.2 FeI 610.3 CaI
120’’
160’’
120’’
THEMIS/MSDP 2007 UNNOFIT inversion
June 11, NOAA 10960 S05, W52
I Q/I U/I V/I
610.3 CaI
THEMISMSDP
f Bx f By
Similar Bx and By similar angles
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 !
THEMIS MSDP
Scanning speed
for targets 100’’x160’’
9 mn
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/d2
For weak fields, line profile inversions provide only 2 quantities, f Bl and f Bt
2
3) Problems and plans:
Gradients of B along LOS from NaD1, 610.3 Ca, 630.2 Fe, …
Below a given level of 2 the range of possible solutions is
larger for (Btransverse * f ) than for (Btransverse * f ½) ?
Bt * f Bt * f1/2
2 – NLTE, B function of z, f = 1, given solar model (parts of spots?)
> Computation of response functions by MULTI code
V() = Bl(z) R(,z) dz
Q() = Bt2(z) R’(,z) dz ?
> Formation altitudes: barycenters of response functions
Bl = a + bz V()= R(,z) (a+bz) dz
Choose functions with different weights at line-center and wings:
S1= V() w1()
dS2= V() w2() d
a, b
Linear polarization: Bt
??? Bt2 = a’+ b’z Q()= R’(,z) (a’+b’z) dz Bt
2, dBt2/dz ???
integrations along line profile to optmize signal/noise ratio.
Circular polarization: Bl (0), dBl/dz
> Vertical gradients:
Instead of using individual points of the bisector,
Examples: w1() = +1 and -1 around line center, 0 elsewhere w2() = +1 and -1 in line wings, 0 elsewhere
> Application: comparisons between gradients from full profile of 1 line and 2 different lines
3 – NLTE, B and f functions of z, given solar model (flux tubes?)
Example: flux tubes, NaD1 line (section 1)
V() = R(,z) (a+bz) (+z) dz
Bl = a + bz
f = + z
MHD model necessary in case of weak fields (see section 1).
In particular, when flux tubes are not spatially resolved,
implies that gradients of f and Bl are compensated (b/a ~ - /)the assumption of constant flux f Bl
Both unknown quantities b and are present in the coefficient of z
Impossible to determine separately f and Bl
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 …