Can isotropic collisions create net circular polarization
and not only depolarization of spectral lines?
J. Štěpán1,2 and S. Sahal-Bréchot2
1 Astronomical Institute AS CR, v.v.i, Fričova 298, 25165 Ondřejov, Czech Republic
2 Observatoire de Paris, LERMA UMR CNRS 8112, 5 place Jules Janssen, 92195 Meudon Cedex, France
1 Motivation
3p3/2 -> 3d 5/2 , proton collisions at 0.05 eV
1.5x10
7
M=-1/2 -> M'=1/2
M=1/2 -> M'=-1/2
1.4x107
cross-section [a.u.]
Recent observations of net circular polarization of hydrogen lines
in prominences(López Ariste et al. 2005) are currently not understood
(for possible explanation due to presence of turbulent electric fields see Casini
& Manso Sainz 2006).
threshold effect. The importance of this mechanism is mainly due to long-range
collisions (r atomic radius).
1.3x107
1.2x107
1.1x107
0
10
20
30
40
50
B [G]
Figure 1: Observed Stokes profiles of Hα in prominences by THEMIS. The
profile are averaged along the slit with o spectral resolution of 23.5 mÅ pixel−1
and wavelength increasing toward the left. Noise has been filtered out. From
López Ariste et al. (2005).
Explanation of the symmetric Stokes-V profile: Interpretation
requires presence of atomic orientation,i.e., imbalance of populations
of the Zeeman sublevels:
N (αJM ) 6= N (αJ − M ) .
Figure 3: Comparison of the angle-averaged proton cross-sections for
3p3/2(M = −1/2) → 3d5/2(M 0 = +1/2) and 3p3/2(M = +1/2) →
3d5/2(M 0 = −1/2) transitions at the collision energy 0.05 eV (close to the
maximum cross-section value). The transitions are schematically illustrated in
Fig. 2 using the same line patterns.
4 Results
We propose this effect could be a possible explanation of the observed net
circular polarization found in solar prominences (Fig. 4).
(1)
2 Possible source of atomic orientation
h = 130 000 km
over the limb
Importance of weakly inelastic collisions with electrons and protons. The inelastic dipolar collisions
θ = 57 ο
nlJM → n l ± 1 J 0M 0
(2)
depolarize the Hα line (n = 3) (Bommier et al. 1986; Sahal-Bréchot et al.
1996; Vogt et al. 1997). Calculation of the rates of these transitions can be
done using the semiclassical perturbation theory since
|E(nlJ) − E(n l ± 1 J 0)| kT ,
(3)
(Seaton 1962; Sahal-Bréchot et al. 1996; Bommier 2006). In all these works,
Zeeman splitting was neglected because of very short duration of the individual collisions. This assumption is not valid for long-range collisions that play
a dominant role in excitation transfer in solar prominences even if the impact
approximation remains valid. Gay & Schneider (1979, and other references
therein) showed that orientation could be created by taking into account
the Zeeman splitting during the collision.
3 New calculation
We take into account in the calculation of the cross-section the
Zeeman splitting of the levels which is comparable to separation of the
nlj − nl ± 1j 0 levels.
d 5/2
5x10-6
Figure 4: The Stokes-Q and -V profiles normalized to the maximum intensity of the line. Magnetic field is supposed to be vertical with respect to solar
surface. The typical antisymmetric Zeeman-effect profile is suppressed by the
symmetric component due to presence atomic orientation. Left (right) panels:
B = 20 G (50 G), perturbers (electrons, protons) density: 0 (solid line), 1010
(dashed line), 5 × 1010 cm−3. Plasma temperature T = 8 000 K. It is worth to
mention that
5 Summary and conclusions
• This mechanism can lead to atomic orientation (i.e., net circular polarization)
if the excited levels are radiatively pumped by non-Planckian radiation.
• Perturbers density must be high enough to redistribute the radiatively unevenly populated Zeeman sublevels before their radiative decay but not too
high to establish even populations (typically 1010 cm−3).
• In contrast to linear polarization degree (that is always decreased by isotropic
collisions), the amplitude of circular polarization can be increased in typical
prominence conditions.
• This mechanism does not significantly affect linear polarization.
0
E [eV]
1.45x10-6
1.4x10
• Our results are only preliminary and deeper investigation of the conditions
of validity of our approach needs to be discussed.
p 3/2
-6
1.35x10-6
d
3/2
1.3x10-6
-5x10-6
1.25x10-6
1.2x10-6
-1x10-5
0
5
10
15
References
s1/2
p1/2
0
10
20
30
40
50
B [G]
Bommier, V. 2006, in proceedings of the 4th Solar Polarization Workshop, ed. R. Casini (ASP
Conf. Series, in press)
Bommier, V., Leroy, J. L., & Sahal-Bréchot, S. 1986, A& A, 156, 90
Figure 2: Zeeman splitting of the n = 3 fine-structure levels of hydrogen. The
energy difference leads to modification of cross-sections. See Fig. 3 for a typical
cross-section behavior.
This can lead to breaking of the symmetry of ±M → ∓M 0 cross-sections
(Fig. 3). The rate of orientation creation is only weakly related to the energy of the collider (∼ 1/ ln(ε), for thermal energies ε 1) hence it is not a
Casini, R. & Manso Sainz, R. 2006, J. Phys. B: At. Mol. Opt. Phys., 39, 3241
Gay, J. C. & Schneider, W. B. 1979, Phys. Rev. A, 20, 879
López Ariste, A., Casini, R., Paletou, F., et al. 2005, ApJ, 621, L145
Sahal-Bréchot, S., Vogt, E., Thoraval, S., & Diedhiou, I. 1996, A& A, 309, 317
Seaton, M. J. 1962, Proc. Phys. Syc., 79, 1105
Vogt, E., Sahal-Bréchot, S., & Hénoux, J.-C. 1997, A& A, 324, 1211