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 …