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gotzon
18-1-95
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TOWARD THE DETERMINATION OF MAGNETIC FIELD
DISTRIBUTION OF THE QUIET SUN: VISIBLE VS. INFRARED
SPECTROPOLARIMETRY
E. Khomenko(1, 2) A. Lagg (3), S. K. Solanki (3), S. Shelyag (3), A. Vögler (3).
(1) Main Astronomical Observatory, Kyiv, Ukraine;
(2) Instituto de Astrofísica de Canarias, Tenerife, Spain, [email protected];
(3) Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany.
SUMMARY
There is a systematic difference in the characteristic magnetic
field strength in the quiet Sun inter-network regions obtained
from the observations in visible and infrared spectral lines
[1,2,4]. We investigate the origin of this difference with the
help of recent realistic 3-D simulations of solar
magnetoconvection. The Stokes profiles of the FeI
lines
6301.5, 6302.5, 15648 and 15652 A are synthesized and
smeared to simulate the effects of a telescope and atmospheric
seeing. A number of strategies is applied to the synthetic
profiles in order to recover back the magnetic field distribution.
The recovered magnetic field strength and flux are compared
with the 'true' ones existing in the simulations. It follows that:
(1) Gaussian fitting procedure applied to the FeI 15648, 15652
Stokes V profiles overestimates the abundance of the fields in
the range 300-900 G in comparison to the original distribution
(Fig. 1).
MHD SIMULATIONS AND SPECTRAL SYNTHESIS
We have used a 3D MHD code called MURAM (MPAe/University of
Chicago RAdiative MHD). The code includes non-grey radiative
transfer, full compressibility, and the effects of partial ionization
for the 11 most abundant chemical elements [6]. The size of the
computational domain is 6000 by 6000 by 1400 km3. The horizontal
resolution is 20 km. The atmosphere extends 600 km above the
level t5000=1. The snapshots used here have a bi-polar structure of
the magnetic field with an average (unsigned) strength <B> = 30,
and 140 G.
MAGNETOGRAMS
The effective magnetic field strength Beff is defined in the
following way [7]:
V (l ) = C (l ) × B
dI (l )
C (l ) = kg L l0
dl
2
åV (l )C (l )
=
å C (l )
i
BEFF
i
i
2
i
The Stokes spectra of FeI 15648, 15652, 6301 and 6302 A
lines were calculated under LTE in 1.5D approach for every vertical
column of the simulation box. For simplicity, no noise was added to
the profiles. The profiles are smeared with the PSF to make the
resolution close to the observations.
i
(2) The average effective magnetic field strength Beff derived
from the FeI 6301, 6302 lines decreases twice with decreasing
spatial resolution from 20 km to 0."6 (Fig. 2).
(3) The ratio between the Beff derived from the Fe I 6301 A and
Fe I 6302 lines increases with decreasing spatial resolution and
becomes larger that 1. In the case of the complex magnetic
fields in simulations, this ratio does not seem to reflect the
overabundance of strong kG fields but rather the level of
contamination of the signal due to the spatial smearing (Fig. 2).
(4) The inversion procedure applied to the Stokes spectra with
original resolution recovers almost perfectly the distribution of
the magnetic field independently on the spectral region (Fig. 3).
(5) An inversion applied to the Stokes spectra at 1" resolution,
does not recover the strong-field part of the probability density
function (PDF) of B (about 1% of the total). It recovers only 1/3
of the total flux present in the simulation (Fig. 4).
(6) The PDF of B recovered from the inversion of the FeI
15648-52 and FeI 6301-2 lines at 1" resolution are very similar
to each other and to the 'true' PDF existing in the simulations
(Fig. 4).
Fig.1. Histograms of the magnetic field strength. Black line:
from MHD snapshot with <B> = 30 G at log t = - 0.4. Green line:
calculated from the Gaussian fitting to Stokes V with the original
resolution of 20 km. Blue line: calculated from Gaussian fitting to
Stokes V with 1" resolution. Red line: observations of the Fe I
1.56 mm lines with the Tenerife Infrared Polarimeter [4]. Note,
that the observations have almost 5 times larger probability for
the fields in the range 800-1500 G than MHD snapshot.
Fig. 2. Upper panels: Beff obtained from the FeI 6302 A line.
Middle panels: ratio of the magnetic field strengths from FeI 6301
and 6302 lines. Bottom panels: histograms of the previous quantity.
Panels on the left: original resolution of 20 km; panels on the right:
resolution of 0."6. The average Beff(6302) decreases from 20 to 10
G with decreasing spatial resolution. At the same time, the average
ratio Beff(6301)/Beff(6302) increases from 0.96 to 1.10.
Fig.3. Maps of the magnetic field for the <B>=140 G snapshot. Upper left: recovered from
the SIR [5] inversion of the IR lines with the original resolution. Upper middle: recovered
from the visible lines. Upper right: original from MHD at log t = - 0.4. Lower panel:
histograms of the magnetic field strength. Black line: original from MHD, red line: from
the visible lines, green line: from the IR lines.
REFERENCES:
(1) J. Sanchez Almeida & B. Lites, 2000, ApJ, 532, 1215
(2) H. Socas-Navarro & J. Sanchez Almeida, 2002, ApJ, 565, 1323
(3) B. Lites & H. Socas-Navarro 2004, ApJ
(4) E. Khomenko, M. Collados, S. K. Solanki, A. Lagg and J. Trujillo Bueno, 2003, A&A, 408, 1115
(5) B. Ruiz Cobo & J. C. Del Toro Iniesta, 1992, ApJ, 398, 375
(6) A. Vogler, 2003, Three-dimensional simulations of magnetoconvection in the solar atmosphere, PhD thesis, Univ. Gottingen.
(7) I. Dominguez Cerdena, J. Sanchez Almeida and F. Kneer, 2003, A&A, 407, 741
Fig.4. Same as Fig.3, but for the profiles at 1" resolution and snapshot with <B>=30 G. The
inversion recovers the average unsigned flux of 7 G (from the IR) and 11 G (from the visible).
These values are closed to the observed ones [3, 4].