Coronal scattering under strong regular refraction. Alexander Afanasiev Institute of Solar-Terrestrial Physics Irkutsk, Russia.
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Institute of Solar-Terrestrial Physics
The problemof accounting for the combined influence exerted by the regular inhomogeneity of background corona and by random coronal inhomogeneities upon the propagation of radio emission has beenstudiedinsufficiently. Itisquiteclear, however, thatinsomecasesregularrefractionthatleadstomultipathingandfocusingofradiowaves, mustinfluencethescatteringprocessandpromoteneweffectsduringthepropagationofradioemissionthrough a randomly-inhomogeneouscorona.
presenceoflarge-scaleelectrondensity inhomogeneities in
at small elongations
Schematic plot of ray trajectories in
a regular (i.e. without random inhomogeneities) spherically-symmetric solar corona
When a spacecraft is at rather
small angular distance from the
Sun, the observer on the Earth
may be in the ‘illuminated’
zone, close to the caustic or
may get in the caustic ‘shadow’
The interference integral method
(proposed by Yu. I. Orlov in 1972)
The scalar wave field U (for example, a component of the electric vector)
at any given point r is represented as an integral over partial waves:
is the eikonal in the absence of statistical inhomogeneities;
is an addition introduced into the eikonal by the inhomogeneities;
In the shadow zone near the caustic boundary, the following expression
for the energy spectrum R()can be obtained:
is the parabolic cylinder function;
are the statistical
Energy spectra for different depths of entry into the shadow zone
Turbulent inhomogeneity parameters:
the density perturbation σN=1%;
the outer scale l0=106 km;
the inner scale q0=104 km;
the radial velocity of inhomogeneities
l0=5 105km (curve 2)
l0=105km (curve 3)
the energy spectrum
with a change of the
velocity Vr of travel of
Vr=300 km/s (curve 1)
Vr=800 km/s (curve 2)
Energy spectra for
different outer scales l0
For investigating the properties of the
near-solar plasma, natural distant
radio sources when they are occulted
by the corona, are also used. In
particular, pulsars that are virtually
point pulsed sources are applied for
Coronal inhomogeneities cause the
temporal broadening of the pulses and
distort their shapes. Therefore the
mean time profile of the pulse is
a useful characteristic that contains
information on coronal turbulent
Qualitative ray picture of radio
emission propagation from
a pulsar through the corona
Ofinterest is to calculate the mean pulse profile in
the neighborhood of the regular caustic to analyse
the possibilities for the coronal turbulence diagnostics.
If the radiated (initial) pulse from a pulsar is specified by the Gaussian form, the following expression for the mean pulse profile in the neighborhood of the caustic boundary can be obtained:
d is the depth of entry into the shadow zone
Mean pulse profiles for different points of observation in the caustic shadow zone
σN = 1%
σN = 3%
Turbulent inhomogeneity parameters:
the outer scale l0=106 km;
the inner scale q0=103 km.
The initial pulse parameters:
the carrier frequency f = 111 MHz;
the initial pulse half-width T = 1.510-3 s.
Using the asymptotic representation for the parabolic cylinder function
one can obtain an expression for estimating the variance of relative
fluctuations in the electron density:
where J(d1)andJ(d2)are the values of the maxima of the mean pulse
profile in the caustic shadow zone at distances d1andd2 from
the caustic point;
(σa2) is a calculatedstatistical trajectory characteristic.
By measuring the maxima J(d1) andJ(d2) at the points d1andd2, and
calculating (σa2), one can estimate the value of the variance of
coronal plasma electron density fluctuations.
Ofspecialinterestisthecombinedinfluenceofscatteringandstrongregularrefractiononcharacteristicsofradioemissionfromcoronalsources. Itisknownthataroundsuchsourcestherecanexistdifferentlarge-scaleregularelectrondensitystructures (coronalarches, streamers, andothers). Thesestructuresmaygiverisetoregularcausticsandmultipathingofradioemission.
Examples of spikes
(Δf / f < 1%) flashesofsubsecondduration,whichaccompanysolarflares. Theyareobservedindifferentwavelengthrangesfromcentimetrictodecametric.
coronal arch top and emits a δ-pulse
Geometry ofthe problem
Ray pattern of the field (f = 100 MHz)
for different values of the density perturbation σN
(numerical modeling results)
σN = 1%
σN = 0.2%
σN = 2%
σN = 4%
The analysis of the event has shown that it is associated with
a coronal mass ejection which could be responsible for the
complex temporal structure of the pulses.
Time profile at 408 MHz of the radio burst observedwith the Trieste
Solar Radio System (Trieste Astronomical Observatory) on 15 April 2000 by J. Magdalenic, B. Vrsnak, P. Zlobec, and H. Aurass.
regular refraction due to large-scale regular electron density
structures such as coronal arches can lead to the formation of
multipathing and regular caustics. These phenomena promote
formation of a multi-component mean time profile of the radio spikes.
profiles of spikes associated with the propagation effects, it is
necessary to consider the data concerning the large-scale structure
of the solar corona (CME, arches, etc). This would create the
conditions for a more correct investigation of spike generation caused
by physical processes occurring within the solar radio source.
One important feature of type IIId radio bursts
(which was revealed by Abranin, Baselyan, and Tsybko [Astron. Rep. 1996, V. 40, 853] during the solar observations with the UTR-2 radio telescope) is that as the burst source approaches the central solar meridian, a temporal splitting of the bursts is developed and thus an additional burst component is produced.
Examples of time profiles
of type IIId bursts
Time profiles of some type IIId burst events contain several additional components.
What is more, position observations showed that
the positions of visible sources of the initial burst
and its additional component usually do not
coincide and can be spaced by a distance
comparable to the Sun’s optical diameter.
To explain this observational evidence, Abranin, Baselyan, and Tsybko suggested that the additional components represent echoes of the original burst in the corona, which are produced due to strong regular refraction of radio emission on large-scale structures lying at heights of the middle corona.
explained by the production of additional radio emission propagation
modes within a ‘transverse’ refraction waveguide arising between the
localized electron density nonuniformity and deeper layers in the corona.
As these additional modes are reflected from the streamers, they can
reach the Earth.
Ray pattern illustrating formation of the refraction waveguide in the corona
(f = 25 MHz)
Mean time profiles for the radio pulse for different values of intensity of
the large-scale localized nonuniformity forming the refraction waveguide
f = 25 MHz
The results of the theoretical analysis and numerical
modeling, presented here reveal the importance of the
regular refraction phenomenon in the solar corona.
On the one hand, analysing statistical characteristics of
radio emission from distant non-solar sources in the
neighborhood of the regular caustic is useful for coronal
turbulence diagnostics. On the other hand, strong regular
refraction due to large-scale coronal structures can
influence substantially the emission from Sun’s own radio sources.