Journal of Atmospheric and Solar-Terrestrial Physics 102 (2013) 185191Contents lists available at SciVerse ScienceDirectJournal of Atmospheric and Solar-Terrestrial Physics1364-68http://d

n Tel.:E-mjournal homepage: www.elsevier.com/locate/jastpThe dispersion analysis of drift velocity in the study of solar wind flows

Maryna Olyak n

Institute of Radio Astronomy, National Academy of Sciences of Ukraine, 4, Chervonopraporna St., Kharkiv 61002, Ukrainea r t i c l e i n f o

Article history:Received 10 April 2013Received in revised form21 May 2013Accepted 23 May 2013Available online 31 May 2013

Keywords:Solar wind flowsScintillation cross spectrumVelocity dispersion26/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.jastp.2013.05.016

+380 954314831.ail address: marinaolyak@gmail.coma b s t r a c t

In this work I consider a method for the study of the solar wind flows at distances from the Sun morethan 1 AU. The method is based on the analysis of drift velocity dispersion that was obtained from thesimultaneous scintillation observations in two antennas. I considered dispersion dependences fordifferent models of the solar wind, and I defined its specificity for each model. I have determined thatthe presence of several solar wind flows significantly affects the shape and the slope of the dispersioncurve. The maximum slope angle is during the passage of the fast solar wind flow near the Earth. If a slowflow passes near the Earth, the slope of the dispersion curve decreases. This allows a more precisedefinition of the velocity and flow width compared to the traditional scintillation method. Using thecomparison of experimental and theoretical dispersion curves, I calculated the velocity and width of solarwind flows and revealed the presence of significant velocity fluctuations which accounted for about 60%of the average velocity.

& 2013 Elsevier Ltd. All rights reserved.1. Introduction

The scattering phenomenon of radio waves from cosmic radiosources by interplanetary plasma is widely used for determiningthe solar wind velocity. Intensity fluctuations (or scintillations) areoften measured in such experiments (see, for example, Shishovand Shishova, 1978; Bovkoon and Zhouck, 1982; Falkovich et al.,2006). These observations allow us to determine the perpendicu-lar component of the solar wind velocity averaged over the lengthof the scattering region. At the same time, analysis of data from thespacecraft near the Earth's orbit showed the presence of the solarwind flows with different velocities and significant velocityfluctuations (e.g. Sorriso-Valvo et al., 1999; Burlaga and Lazarus,2000; Richardson and Cane, 2012), and it may cause appreciabledistortions in the observed scintillations. Ground-based observa-tions, including tomography, also confirmed the presence of thesolar wind flow structure (e.g. Jackson et al., 1998; Kojima et al.,1998; Lotova et al., 2000; Hayashi et al., 2003).

To determine the presence of various velocities along the line ofsight one can use a cross-correlation analysis of interplanetaryscintillation. This method is based on studying the cross-correlation function, measured at two or more observation points(see, e.g., Armstrong and Coles, 1972; Lotova and Chashey, 1973;Kakinuma et al., 1973; Bourgois et al., 1985). The relative motionsof the inhomogeneities lead to asymmetry in the cross-correlationfunction. This allows us to estimate not only the average velocityll rights reserved.of the solar wind, but also its random component. For example,Coles and Kaufman (1978) analyzed observations made at afrequency of 74 MHz in three and four observation points, andfound that the values of a random component was about 40% ofthe average solar wind velocity during this period. Measuring theasymmetry of the temporary cross-correlation function at dis-tances from the Sun about 0.10.3 AU was discussed by Chasheiet al. (2000). Obtained values of the asymmetry were higher forthe fast solar wind than for slower. Tokumaru et al. (2012) arediscussing measurements of solar wind velocity at distances from13 to 37 solar radii. The authors have conducted the cross-correlation analysis of interplanetary scintillations observed attwo antennas separated by a distance much larger than theFresnel zone.

Methods of interpreting observations that consider passing theline of sight through several flows give good results at elongationangle o901 (see, e.g., Coles, 1996; Canals et al., 2002; Bisi et al.,2007). Fallows et al. (2008) used a three-stream model of solarwind to analyze the auto- and cross-correlation functions obtainedfrom EISCAT-MERLIN observations. The first results of observationson two radio telescopes of the solar wind flows at 901 arepresented by Falkovich et al. (2010).

The method of dispersion analysis of the drift velocity is closeto the cross-correlation techniques that are used to study thevelocity distribution in a random medium. This method wasproposed by Jones and Maude (1965) to study the movement ofirregularities in the ionosphere. It is based on the analysis of thedrift velocity dispersion dependence Vf(f) obtained from thescintillation observations at several antennas. Lotova andChashey (1973) developed the basis of this method to investigate

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d3

l2

l1

d2

d

Radio source

1st flow

2nd flow

z

3rd flow

l3

M. Olyak / Journal of Atmospheric and Solar-Terrestrial Physics 102 (2013) 185191186the interplanetary medium. The study of the distribution function ofthe solar wind velocity was carried out by Lotova et al. (1977).In contrast to the cross-correlation method, the observations of driftvelocity were made at antennas separated by a distance not exceedingthe Fresnel zone. In these works, the interpretation of the observationswas performed by using the phase screen model. The phase screenformulas do not allow us to separate the presence of different speedsin scattering area from the geometric effect of changing the velocityprojection on the plane of sky. The latter effect is associated with asignificant length of the scattering area; it is especially characteristicfor the decameter radio waves (Olyak, 2005).

The values of solar wind velocity that were obtained fromobservations at high frequencies and small elongation anglesoo901 are close to the true values. This is due to the fact thatthe length of the scattering layer, which is proportional to sin (Shishov and Shishova, 1978), does not exceed the characteristic lengthof the solar wind flow (Olyak, 2005; Falkovich et al., 2010). At thesame time, the length of the scattering layer in the decameter wavesmay reach 34 AU (Falkovich et al., 2006). The main feature of theobservations at large elongations is not only the fact that the scatteringarea is sufficiently extended, but also that the densest plasma layer islocated near the observer. In addition, the existence of differentvelocities along the line of sight can be associated not only with thefact that the line of sight crosses several flows but also with velocityfluctuations within each flow. At last, the appearance of differentspeeds on the line of sight may be due to the change of velocityprojection on the plane of sky.

The aim of this work is to study application of dispersion analysisof the drift velocity for the case of extended turbulent interplanetaryplasma with large-scale flow structure and large elongation angles.In order to demonstrate the potential of this method, I determinedvelocity and width of the solar wind flows from the observations ofdispersion dependences of drift velocity performed at the Ukrainianradio telescopes UTR-2 and URAN-2 (Falkovich et al., 2011).

2. Methods

I used the parabolic equation to describe the radio wavepropagation through random interplanetary plasma (e.g.Tatarskii, 1971). I solved the parabolic equation with the Feynmanpath-integral method (Feynman and Hibbs, 1965; Frehlich, 1987).The calculation technique for the second and fourth spacemoments for the solar wind with the large-scale flow structureis given in Olyak (2012).

I used the interplanetary scintillation observations at theUkrainian decameter radio telescopes UTR-2 (4913817N, 3615629E, the effective area is 150,000 m2) and URAN-2 (4913748N,3414920E, the effective area is 28,000 m2) to determine theparameters of the solar wind. The observations were made at afrequency of 25 MHz for large elongation angles (901). Thedistance between the radio telescopes is 152.75 km. The construc-tion technique for the experimental dispersion dependence of thedrift velocity is given in Falkovich et al. (2010, 2011).

A comparison of experimental and theoretical dispersiondependences of drift velocity was used for the determination ofthe solar wind velocity. The method of least squares (see, e.g., Afifiand Azen, 1979; Boucher et al., 1999) was applied for this purpose.I compared the calculated values of the solar wind velocity withthe data of SOHO mission (http://umtof.umd.edu/pm/).1

Sun

Earth

Fig. 1. Geometry of the solar wind flows.3. Cross spectra of interplanetary scintillations for solar windwith flow structure

Consider the following problem. Suppose that several flowsof solar wind are directed radially away from the Sun. Line of sight(z-axis) crosses these flows. The flow with a width d1 passes nearthe Earth (see Fig. 1). The length of the area occupied by the flowalong the line of sight is equal to l1. Next there are the solar windflows, which are characterized by values dk and lk, k2,..., K; K isthe total number of solar wind flows along the line of sight withinthe scattering area.

Let the radio emission from a remote cosmic source be receivedby two spatially separated antennas, which are located in theplane zconst. Let us introduce the spacetime cross-correlationfunction of the intensity fluctuations as

B b!; U r!1a ; t1Un r!1

a ; t1Un r!2a ; t2U r

!2a ; t

2U r!1a ; t1Un r

!1a ; t

1Un r!2a ; t2U r!2

a ; t2:

Here U r!1;2a ; t1;2 is the slowly varying complex amplitude ofsignal received by the antenna with the radius-vector r!1;2a attime t(1,2), b

! r!2a r!1

a is the distance between observationpoints (the baseline), and t(2)t(1), where the angle bracketsdenote averaging over the statistical ensemble. Using the methodof the Feynman path integrals, we can write the followingexpression for the received signal (Olyak, 2009, 2012):

U r!a; t Z Z

Z

d2 r!0d2 r!1d2 r!K1U0 r!0; tZ Z

Z

D s!1zD s!K z

exp i2c

K

k 1

Z LkLk1

dzd s!kz

dz

!2 k s!kz; z; t

24

359=;:

8