Coronal scattering under strong regular refraction

1. Coronal scattering under strong regular refraction Alexander Afanasiev Institute of Solar-Terrestrial Physics Irkutsk, Russia

2. 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. Questions • Coronalsoundingwithspacecraftradio signals at small elongations • Coronalsounding with a pulsar at small elongations • Scatteringofradioemissionfrom a solarsourceinthe presenceoflarge-scaleelectrondensity inhomogeneities in thecorona

3. Coronal sounding withspacecraft 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

4. isthewavenumberinavacuum; isthecompleteintegraloftheeikonalequation: whereisdielectricpermittivityofplasma, and isthesolutionofthetransportequation: 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: (1) aisaparameterthatcharacterizesapartialwave

5. The perturbation theory: is the eikonal in the absence of statistical inhomogeneities; is an addition introduced into the eikonal by the inhomogeneities; Inthepresenceofelectrondensityinhomogeneitiesinthesolarcorona theintegralrepresentationforthewavefieldcanbewrittenintheform: (2) In the shadow zone near the caustic boundary, the following expression for the energy spectrum R()can be obtained: shadow zone is the parabolic cylinder function; d isthedepthofentryintotheshadow zone; point of caustic d Sun are the statistical trajectory characteristicsdependingon turbulentinhomogeneityparameters. Earth’sorbit

6. Some numerical modeling results Energy spectra for different depths of entry into the shadow zone (for λ=3m) 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 Vr=300 km/s.

7. l0=106km (curve 1) l0=5 105km (curve 2) l0=105km (curve 3) Distortion of the energy spectrum with a change of the velocity Vr of travel of coronal inhomogeneities Vr=300 km/s (curve 1) Vr=800 km/s (curve 2) λ=3 m σN=1%; l0=106 km; q0=104 km; Energy spectra for different outer scales l0 of turbulent inhomogeneities λ=3 m σN=1%; q0=104 km; Vr=300 km/s

8. 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.

9. Coronal sounding with a pulsar at small elongations 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 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. 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.

10. 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 = 1.510-3 s.

11. 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.

12. 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

13. Scatteringofradioemissionfromasolarsourceinthepresenceoflarge-scaleelectrondensityinhomogeneitiesinthecoronaScatteringofradioemissionfromasolarsourceinthepresenceoflarge-scaleelectrondensityinhomogeneitiesinthecorona Ofspecialinterestisthecombinedinfluenceofscatteringandstrongregularrefractiononcharacteristicsofradioemissionfromcoronalsources. Itisknownthataroundsuchsourcestherecanexistdifferentlarge-scaleregularelectrondensitystructures (coronalarches, streamers, andothers). Thesestructuresmaygiverisetoregularcausticsandmultipathingofradioemission. Theappearingrefractioneffectsshouldbetakenintoaccountin theanalysisoftheemissionstructureofsolarradioburstsand theirgenerationmechanisms.

14. PartI.Solarmillisecondspikebursts Examples of spikes Amongthegreatvarietyofsolarradiobursts,millisecondspikeburstsrepresentoneofthelessunderstoodsolarphenomena.Spike burstsareintensenarrowband (Δf / f < 1%) flashesofsubsecondduration,whichaccompanysolarflares. Theyareobservedindifferentwavelengthrangesfromcentimetrictodecametric. Therearecurrentlyanumberofmodelsforthe mechanismofradiospikegeneration.Nevertheless, thequestionregardingtheoriginofspikesremains tobeconclusivelyanswered.Onedifficultyisthatitisnotfullyclearastothe particularinfluenceexertedbyaninhomogeneouspropagationmediumupon observedcharacteristicsofradiospikes. Considerationofthepropagationeffectsusuallyassumesthatthesolarcorona isspherically-symmetricingeneral,theinfluenceofregularrefractionis negligible,andthespikecharacteristicsaredeterminedbythescatteringand diffractionofthewavesbyturbulentcoronalinhomogeneities. Ontheotherhand, radiospikescanbegeneratedbysourceslocatedinhigh coronalarches.Notonlythescatteringbutalsostrongregularrefractionofradio emissioninthearchstructurecanbeimportantinthiscase.

15. A point radio source is located at the coronal arch top and emits a δ-pulse Geometry ofthe problem Ray pattern of the field (f = 100 MHz)

16. Mean profile of the pulse after its passing through the corona for different values of the density perturbation σN (numerical modeling results) σN = 1% σN = 0.2% Intensity Intensity Time, s Time, s σN = 2% σN = 4% Intensity Time, s Time, s

17. Fluxdensity (SFU) Time (UT) 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.

18. 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.

19. DB 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. Examples of time profiles of type IIId bursts f=25 MHz DB additional component 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.

20. 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. Ray pattern illustrating formation of the refraction waveguide in the corona (f = 25 MHz) direct signal source photosphere

21. 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 direct signal echo-components

22. 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 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.