Coronal scattering under strong regular refraction

Alexander AfanasievInstitute of Solar-Terrestrial Physics

Irkutsk, Russia

The problem of 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 been studied insufficiently. It is quite clear, however, that in some cases regular refraction that leads to multipathing and focusing of radio waves, must influence the scattering process and promote new effects during the propagation of radio emission through a randomly-inhomogeneous corona.

Questions

• Coronal sounding with spacecraft radio signals at small elongations

• Coronal sounding with a pulsar at small elongations

• Scattering of radio emission from a solar source in the presence of large-scale electron density inhomogeneities in the corona

Coronal sounding with spacecraft radio signals 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’ zone.

spacecraft

The interference integral method (proposed by Yu. I. Orlov in 1972)

daaikaAU ,exp, rrr

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:

a is a parameter that characterizes a partial wave

k is the wave number in a vacuum;

),( ar is the complete integral of the eikonal equation:

),()( 2 r

),( aA r is the solution of the transport equation:

.02 AA

where is dielectric permittivity of plasma, and)(r

(1)

In the presence of electron density inhomogeneities in the solar corona the integral representation for the wave field can be written in the form:

dataikaAtU )],,(~exp[),(),(~

rrr (2)

In the shadow zone near the caustic boundary, the following expression for the energy spectrum R() can be obtained:

4

)],([

2

)(exp)],([

)()(

2

22

20

2/1222

0 dF

kdFD

RR

ata

Sun

shadow zone

point ofcaustic d

Earth’s orbit

)(xD is the parabolic cylinder function;

0110~;~~ The perturbation theory:

is the eikonal in the absence of statistical inhomogeneities;

is an addition introduced into the eikonal by the inhomogeneities;0

1~

d is the depth of entry into the shadow zone; are the statistical trajectory characteristics depending on turbulent inhomogeneity parameters.

at and ,a ,

Some numerical modeling results

Energy spectra for different depths of entry into the shadow zone(for λ=3m)

rad1010 6d

rad1020 6d rad1060 6d

rad01 6d

Turbulent inhomogeneity parameters:the density perturbation σN=1%;

the outer scale l0=106 km;

the inner scale q0=104 km;

the radial velocity of inhomogeneitiesVr=300 km/s.

Distortion of the energy spectrumwith a change of the velocity Vr of travel of coronal inhomogeneities

Vr=300 km/s (curve 1)

Vr=800 km/s (curve 2)

Energy spectra for different outer scales l0 of turbulent inhomogeneities

l0=106 km (curve 1)

l0=5 105 km (curve 2)

l0=105 km (curve 3)

λ=3 m

σN=1%;

l0=106 km;

q0=104 km;

rad01 6d

λ=3 m

σN=1%;

q0=104 km;

Vr=300 km/s

rad01 6d

Conclusion

• The form of the energy spectrum in the caustic shadow zone differs from a Gaussian and depends critically on the properties of the turbulent inhomogeneities. Therefore measurements of the radio energy spectrum in the neighborhood of the caustic can be used for the coronal plasma diagnostics.

Coronal sounding with a pulsar at small elongations

For investigating the properties of the near-solar plasma, natural distant radio sources when they are occultedby the corona, are also used. In particular, pulsars that are virtuallypoint pulsed sources are applied for this purpose. 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 inhomogeneities.

Of interest is to calculate the mean pulse profile in the neighborhood of the regular caustic to analyse the possibilities for the coronal turbulence diagnostics.

Qualitative ray picture of radioemission propagation from a pulsar through the corona

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:

4

)],([),(exp)],([)(

21

212/10

dtFdtFdtFCDJtJ

Mean pulse profiles for different points of observation in the caustic shadow zone

d is the depth of entry into the shadow zone

The initial pulse parameters: the carrier frequency f = 111 MHz;the initial pulse half-width T = 1.510-3 s.

Turbulent inhomogeneity parameters:the outer scale l0=106 km;the inner scale q0=103 km.

σN = 1% σN = 3%

Using the asymptotic representation for the parabolic cylinder function

, as 4

exp)(2

2/12/1

xx

xxD

one can obtain an expression for estimating the variance of relative fluctuations in the electron density:

where J(d1) and J(d2) are the values of the maxima of the mean pulse profile in the caustic shadow zone at distances d1 and d2 from the caustic point;(σa

2) is a calculated statistical trajectory characteristic.

By measuring the maxima J(d1) and J(d2) at the points d1 and d2, andcalculating (σa

2), one can estimate the value of the variance of coronal plasma electron density fluctuations.

)()(

ln)(2

)(

2

1

2/1

2

12

21

22

2

dJdJ

dd

ddk

a

2N 2/

~NN

Conclusion

• The variation of the pulsar’s pulse energy in the caustic shadow zone can be treated as an indicator for turbulent inhomogeneity intensity in the solar corona

Scattering of radio emission from a solar source in the presence of large-scale electron density

inhomogeneities in the coronaOf special interest is the combined influence of scattering and strong regular refraction on characteristics of radio emission from coronal sources. It is known that around such sources there can exist different large-scale regular electron density structures (coronal arches, streamers, and others). These structures may give rise to regular caustics and multipathing of radio emission.

The appearing refraction effects should be taken into account in the analysis of the emission structure of solar radio bursts and their generation mechanisms.

There are currently a number of models for the mechanism of radio spike generation. Nevertheless, the question regarding the origin of spikes remains to be conclusively answered. One difficulty is that it is not fully clear as to the particular influence exerted by an inhomogeneous propagation medium upon observed characteristics of radio spikes.

Among the great variety of solar radio bursts, millisecond spike bursts represent one of the less understood solar phenomena. Spike bursts are intense narrowband (Δf / f < 1%) flashes of subsecond duration, which accompany solar flares. They are observed in different wavelength ranges from centimetric to decametric.

Part I. Solar millisecond spike bursts

Consideration of the propagation effects usually assumes that the solar corona is spherically-symmetric in general, the influence of regular refraction is negligible, and the spike characteristics are determined by the scattering and diffraction of the waves by turbulent coronal inhomogeneities.

On the other hand, radio spikes can be generated by sources located in high coronal arches. Not only the scattering but also strong regular refraction of radio emission in the arch structure can be important in this case.

Examples of spikes

A point radio source is located at the coronal arch top and emits a δ-pulse

Ray pattern of the field (f = 100 MHz)

Geometry of the problem

Mean profile of the pulse after its passing through the coronafor different values of the density perturbation σN

(numerical modeling results)

σN = 0.2% σN = 1%

σN = 2% σN = 4%

Time, s

Inte

nsity

Time, s

Inte

nsity

Inte

nsity

Time, s Time, s

Time profile at 408 MHz of the radio burst observed with the TriesteSolar Radio System (Trieste Astronomical Observatory) on 15 April 2000 by J. Magdalenic, B. Vrsnak, P. Zlobec, and H. Aurass.

Time (UT)

Flux density (SFU)

The analysis of the event has shown that it is associated witha coronal mass ejection which could be responsible for the complex temporal structure of the pulses.

Conclusions

• When the spike emission is propagating in the solar corona, strong 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.

• To understand the causes of formation of the complex time 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.

Part II. Type IIId solar decameter radio bursts with echo-components

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. 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.

DB

DB Examples of time profiles of type IIId bursts f=25 MHz

additionalcomponent

The observed radio burst echo-components with long delays can be 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.

photospheresource

directsignal

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 ofthe large-scale localized nonuniformity forming the refraction waveguide

direct signal

echo-components

f = 25 MHz

Conclusions

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 theneighborhood 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.