On the viewing angle effect on Hα-line impact polarization insolar flaring phenomena

V.V Zharkova1 and L.K. Kashapova 2

1 Bradford University, Bradford BD7 1DP, UK

v.v.zharkova@brad.ac.uk2 Institute of Solar-Terrestrial Physics, P.O. Box 4026, Irkutsk, 664033, Russia

lkk@iszf.irk.ru

Abstract

The authors compare the observation of Hα-line linear polarization in moustaches or Ellerman bombs, located in different positions on a solar disk, with the theoretical predictions of impact polarization caused by beams of electrons. Accordingto the results of theoretical calculations, within the viewing angles 50–60◦ the observed impact polarization should approaches zero values despite the electron beam presence. The number distribution of moustaches with different polarizationdegree and located at the different distances from the solar disk center, showed that the rate of moustaches with polarization more then 2% was the minimum at the viewing angle about 50–60◦. We discuss role of the revealed viewing angleeffect on impact polarization observation conditions in more large-scale emission phenomena – solar flares.

Introduction

Observations of linear polarisation in spectral lines from solar flares pro-vide a unique information on the directions of energy transport fromthe corona to deeper layers during these highly dynamic events. TheHα-line is the most observable line in solar flares with the ground-basedinstruments, and significant properties of energy transfer process can bederived from the measurements of its polarisation vector.The linear Hα

polarisation is not very often observed in large solar flares but more reg-ular in the flaring events of much smaller scales called moustaches, orEllerman bomb (EB) with the extended wings in the Hα line profile.These events have sizes from 5′′ down to the size the diffraction limitof modern (1-meter class) solar telescopes. Their resemblance in manyspectral aspects with the type II white-light flares assumed the Hα linemoustaches to be the small-scale appearances of the impulsive heatingsimilar to larger solar flares caused by electron beam precipitation andnon-thermal excitation of a hydrogen atom.

Theoretical predictions

In the current contribution the effect of a viewing angle is investigatedfor the hydroden Hα-line impact polarisation caused by precipitatingbeam electrons injected with energy power-law spectra into flaring at-mospehers. The polarisation is considered for a 3 level plus continuumhydrogen atom affected by Zeeman’s splitting in a moderate magneticfield while the depolarising effects of diffusive radiation and collisionswith thermal electrons are also taken into account (Zharkova and Syni-avskii, 2000). The resulting polarisation plane is defined by the orts n‖and n⊥ with the former being parallel to the vector BxK and the latteris perpendicular to BxK, where B is a magnetic field vector and K isa direction of the emitted photon. This polarisation plane is projectedonto a viewing angle ψ being a superposition of the flare location on asolar disk and the magnetic field deviation from a local vertical position.In detail the method of simulation described in Zharkova & Kashapova(2005).

Figure 1: A position of the polarisation plane of a photon emit-ted in the vertical magnetic loop at pitch angle of ξ and azimuthalangle η. A viewing angle ψ is the angle between the local Cartesiansystem XYZ and the system X’Y’Z’ associated with the solar spherecentre. The viewing angle along with the loop position on a solardisk, i.e the angle δ in Figure 2, define the projection of the po-larisation plane in XYZ system onto the observational plane OX’Z’occuring in the point O of the axis X’ for an arbitrary electronmomentum P and photon momentum K vectors.

Figure 2: The layout of a slit position during the observationsin the planes Z’X’ (see Figure 1) where the observer is located andZ’Y’ (the observing plane with a flat solar image) where β0 is anangle between the slit and the object-to-disk center direction, β′ isan angle between the slit and the object-to-limb direction and ψ isa viewing angle.

Figure 3: The Hα linear polarisation as a function of a positionangle ψ caused by electron beams with a spectral index γ = 7,F0 = 1010 erg/cm2/s (dashed line with triangles ), γ = 7, F0 =1012 (dashed line with circles ), γ = 4, F0 = 1011 erg/cm2/s(solid line with squares). The crosses, diamonds and triangles arethe observations of different moustaches by Kashapova (2003).

The integrated Hα-line linear impact polarisation caused by intense elec-tron beams with soft (γ = 6) and hard (γ = 3) energy spectra calculatedtaking into account its projection onto the direction to the observer, ora viewing angle, is presented in Figure 3 (the solid and dashed lines)for the time of 6 seconds after the injection when the impact effect ismaximal.

The results of observations

For a comparison with the theoretical predicitions above the profiles ofStokes parameters Q/I and U/I of moustaches in the Hα hydrogen lineobtained in the summer 1999 from the Large Solar Vacuum Telescope(Fig 4).This data was previously analyzed by Kashapova (2003) withoutconsideration of the moustache locations on a solar disk. From Table 1one can see that the number of moustaches with a noticeable polarizationdegree varies significantly with the distance from a solar disk centre (oron the moustaches position on the solar sphere).The Stokes parameters Q/I are converted from the slit coordinate sys-tem to the coordinate system related the object-to-observer directionaccording to the layout shown in Figure 2. It can be seen from the plotb in Figure 2 that the angles β0 and β

′are related to a viewing angle ψ

and latitude angle ϕ as:

ψ = β0 + β′ − (90◦ − ϕ) (1)

Here ψ′ is an angle from the north-south vertical towards the slit on a flatsolar image, under which the angle arch CS with a length ψ is seen onthe spherical solar surface. This is close to a viewing angle ψ presentedin Figure 1 within the applicability of flat disk coordinates instead of thespherical ones, because of the triangles C’OS’ and C’O’S’ similarity inthe planes ZX and ZY (compare the plots a and b in Figure 2. The angleϕ is a polar angle on the solar disk that corresponds to a heliolatitudewith its sign in the relevant hemispheres.

Figure 4: The two examples of Stokes parameters I (intensity, theleft panels) and Q/I (linear polarisation, the right panels) measuredin moustaches with insignificant polarization (the top panel) andthe noticeable polarization (the bottom panel).

Table 1. A relative number of moustaches with the polarization less than2%.

Distance from the solar centre, Rust&Keilpresent paper (1992)

10◦ ± 10◦ 30◦ ± 10◦ 50◦ ± 10◦ 70◦ ± 10◦

Rate,% 69 57 85 59 87

Conclusions

•Hα-line linear polarisation, caused by moderate electron beams, variesin the range of 2−15% and can be either negative or positive dependingon the position of a flaring loop on the solar disk, i.e. its heliolongitude.For viewing angles less then 50o the Hα-line impact polarisation isnegative increasing up to −10% towards the smaller angles of 20o.

• For viewing angles bigger than 60o the measured impact polarisationbecomes positive sharply increasing up to 15% towards the limb andbeyond. In the zone 50− 60o the observed polarisation degree crossesa zero point despite the actual presence of beam electrons in a flaringatmosphere.

• This allows to produce the constraints onto the slit and moustachelocations that allows to observe the measurable impact polarisationsignatures if they occur in these events, i.e. the slit positioning anglesβ0 and β′ are to be restricted to β0 + β′+ ϕ ≥ 150◦ or β0 + β′+ ϕ ≤140◦, where β0 and β′ are the slit angles towards the solar center andlimb, respectively, and ϕ is a heliolatitude.

• The theoretical predictions fit remarkably well the available observa-tions of the Hα-line linear polarisation in moustaches, or Ellermanbombs, located in different positions on a solar disk. This fit allowsthe observers to estimate the parameters of an electron beam causingthis polarisation and compare them with those derived from hard X-ray bremsstrahlung emission(Zharkova et al., 1995) that can provideimportant information on the energy transport mechanisms in flaringevents on the Sun.

Acknowledgments

This work was supported by grant GR/R/53449/01 of the UK Engineer-ing and Physical Sciences Research Council (VZ), grant NSh-733.2003.2and Federal Scientific and Technical Program ”Astronomy - 1104” ofthe Ministry of Education and Science of the Russian Federation (LK).Dr. L.K. Kashapova acknowledges European Astronomical Society forthe supporting of participation in JENAM-2004 and the Russian Foun-dation of Basic Research (the travel grant 04-02-27018).

References

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