On the viewing angle effect on Hα-line impact polarization in
solar flaring phenomena
1
V.V Zharkova and L.K. Kashapova
2
1
2
Bradford University, Bradford BD7 1DP, UK
[email protected]
Institute of Solar-Terrestrial Physics, P.O. Box 4026, Irkutsk, 664033, Russia
[email protected]
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. According
to 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 polarization
degree 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 angle
effect on impact polarization observation conditions in more large-scale emission phenomena – solar flares.
Conclusions
Introduction
Observations of linear polarisation in spectral lines from solar flares provide a unique information on the directions of energy transport from
the corona to deeper layers during these highly dynamic events. The
Hα-line is the most observable line in solar flares with the ground-based
instruments, and significant properties of energy transfer process can be
derived from the measurements of its polarisation vector.The linear Hα
polarisation is not very often observed in large solar flares but more regular in the flaring events of much smaller scales called moustaches, or
Ellerman bomb (EB) with the extended wings in the Hα line profile.
These events have sizes from 500 down to the size the diffraction limit
of modern (1-meter class) solar telescopes. Their resemblance in many
spectral aspects with the type II white-light flares assumed the Hα line
moustaches to be the small-scale appearances of the impulsive heating
similar to larger solar flares caused by electron beam precipitation and
non-thermal excitation of a hydrogen atom.
Theoretical predictions
In the current contribution the effect of a viewing angle is investigated
for the hydroden Hα-line impact polarisation caused by precipitating
beam electrons injected with energy power-law spectra into flaring atmospehers. The polarisation is considered for a 3 level plus continuum
hydrogen atom affected by Zeeman’s splitting in a moderate magnetic
field while the depolarising effects of diffusive radiation and collisions
with thermal electrons are also taken into account (Zharkova and Syniavskii, 2000). The resulting polarisation plane is defined by the orts nk
and n⊥ with the former being parallel to the vector BxK and the latter
is perpendicular to BxK, where B is a magnetic field vector and K is
a direction of the emitted photon. This polarisation plane is projected
onto a viewing angle ψ being a superposition of the flare location on a
solar disk and the magnetic field deviation from a local vertical position.
In detail the method of simulation described in Zharkova & Kashapova
(2005).
• Hα-line linear polarisation, caused by moderate electron beams, varies
in the range of 2−15% and can be either negative or positive depending
on 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 is
negative increasing up to −10% towards the smaller angles of 20o.
• For viewing angles bigger than 60o the measured impact polarisation
becomes positive sharply increasing up to 15% towards the limb and
beyond. In the zone 50 − 60o the observed polarisation degree crosses
a zero point despite the actual presence of beam electrons in a flaring
atmosphere.
Figure 3: The Hα linear polarisation as a function of a position
angle 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 are
the observations of different moustaches by Kashapova (2003).
The integrated Hα-line linear impact polarisation caused by intense electron beams with soft (γ = 6) and hard (γ = 3) energy spectra calculated
taking into account its projection onto the direction to the observer, or
a 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 is
maximal.
The results of observations
For a comparison with the theoretical predicitions above the profiles of
Stokes parameters Q/I and U/I of moustaches in the Hα hydrogen line
obtained in the summer 1999 from the Large Solar Vacuum Telescope
(Fig 4).This data was previously analyzed by Kashapova (2003) without
consideration of the moustache locations on a solar disk. From Table 1
one can see that the number of moustaches with a noticeable polarization
degree varies significantly with the distance from a solar disk centre (or
on the moustaches position on the solar sphere).
The Stokes parameters Q/I are converted from the slit coordinate system to the coordinate system related the object-to-observer direction
according to the layout shown in Figure 2. It can be seen from the plot
0
b in Figure 2 that the angles β0 and β are related to a viewing angle ψ
and latitude angle ϕ as:
0
ψ = β0 + β − (90◦ − ϕ)
Figure 1: A position of the polarisation plane of a photon emitted in the vertical magnetic loop at pitch angle of ξ and azimuthal
angle η. A viewing angle ψ is the angle between the local Cartesian
system XYZ and the system X’Y’Z’ associated with the solar sphere
centre. The viewing angle along with the loop position on a solar
disk, i.e the angle δ in Figure 2, define the projection of the polarisation plane in XYZ system onto the observational plane OX’Z’
occuring in the point O of the axis X’ for an arbitrary electron
momentum P and photon momentum K vectors.
(1)
Here ψ 0 is an angle from the north-south vertical towards the slit on a flat
solar image, under which the angle arch CS with a length ψ is seen on
the spherical solar surface. This is close to a viewing angle ψ presented
in Figure 1 within the applicability of flat disk coordinates instead of the
spherical ones, because of the triangles C’OS’ and C’O’S’ similarity in
the planes ZX and ZY (compare the plots a and b in Figure 2. The angle
ϕ is a polar angle on the solar disk that corresponds to a heliolatitude
with its sign in the relevant hemispheres.
Figure 4: The two examples of Stokes parameters I (intensity, the
left panels) and Q/I (linear polarisation, the right panels) measured
in moustaches with insignificant polarization (the top panel) and
the noticeable polarization (the bottom panel).
Table 1. A relative number of moustaches with the polarization less than
2%.
Figure 2: The layout of a slit position during the observations
in the planes Z’X’ (see Figure 1) where the observer is located and
Z’Y’ (the observing plane with a flat solar image) where β0 is an
angle between the slit and the object-to-disk center direction, β 0 is
an angle between the slit and the object-to-limb direction and ψ is
a viewing angle.
Distance f rom the solar centre,
Rust&Keil
present paper
(1992)
10◦ ± 10◦ 30◦ ± 10◦ 50◦ ± 10◦ 70◦ ± 10◦
Rate,% 69
57
85
59
87
• This allows to produce the constraints onto the slit and moustache
locations that allows to observe the measurable impact polarisation
signatures if they occur in these events, i.e. the slit positioning angles
β0 and β 0 are to be restricted to β0 + β 0 + ϕ ≥ 150◦ or β0 + β 0 + ϕ ≤
140◦, where β0 and β 0 are the slit angles towards the solar center and
limb, respectively, and ϕ is a heliolatitude.
• The theoretical predictions fit remarkably well the available observations of the Hα-line linear polarisation in moustaches, or Ellerman
bombs, located in different positions on a solar disk. This fit allows
the observers to estimate the parameters of an electron beam causing
this polarisation and compare them with those derived from hard Xray bremsstrahlung emission(Zharkova et al., 1995) that can provide
important information on the energy transport mechanisms in flaring
events on the Sun.
Acknowledgments
This work was supported by grant GR/R/53449/01 of the UK Engineering and Physical Sciences Research Council (VZ), grant NSh-733.2003.2
and Federal Scientific and Technical Program ”Astronomy - 1104” of
the Ministry of Education and Science of the Russian Federation (LK).
Dr. L.K. Kashapova acknowledges European Astronomical Society for
the supporting of participation in JENAM-2004 and the Russian Foundation of Basic Research (the travel grant 04-02-27018).
References
Kashapova, L.K. 2003, Solar polarization 3 ASP Conference Series,
307, 474
Rust, D.M. & Keil, S.L. 1992, Sol. Phys., 140, 55
Zharkova, V.V. and Kashapova, L.K. 2005, A&A, accepted
Zharkova, V.V. and Syniavskii, D.V. 2000, A & A, 354, 714
Zharkova, V.V., Brown, J.C. and Syniavskii, D.V., 1995, A & A, 304,
284 (Paper II)