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ISSN 01902717, Bulletin of the Crimean Astrophysical Observatory, 2010, Vol. 106, pp. 26–30. © Allerton Press, Inc., 2010. Original Russian Text © E.A. Isaeva, V.F. Melnikov, L.I. Tsvetkov, 2010, published in Izvestiya Krymskoi Astrofizicheskoi Observatorii, 2010, Vol. 106, pp. 42–48.

Dependence of the SCR Proton Flux Estimate on Radio Burst Parameters E. A. Isaevaa, *, V. F. Melnikovb, and L. I. Tsvetkova, † a

Laboratory of Radio Astronomy, Crimean Astrophysical Observatory, Yalta, Crimea, 98688 Ukraine *email: isaeva[email protected] bPulkovo Astronomical Observatory, Russian Academy of Sciences, Pulkovskoe sh. 65, St. Petersburg, 196140 Russia Received November 10, 2009

Abstract—We present results suggesting that the accuracy of estimating the solar cosmicray (SCR) proton flux from μburst parameters is much higher for proton events characterized by a low level of postburst increase (PBI) in the μburst flux, a powerful decametric (DCM) component, and a small time shift (Δt < 9 min) of the DCM burst maximum relative to the μburst maximum. These three parameters are probably related between themselves, since events characterized by a small Δt have a very low PBI level. We show that the accuracy of estimating the proton flux depends to a greater extent on Δt than on the intensity of the DCM component. For approximately half of the events from the investigated sample, the accuracy of estimating the proton flux approaches the maximum possible accuracy from μburst parameters. Key words: Sun, proton events, radio bursts DOI: 10.3103/S0190271710010043 †

INTRODUCTION

neous number of electrons in the source over the burst time and Tμ, the effective burst duration, characterizes the injection duration and lifetime of the electrons in the flare loop. The quantity ϕ = (9/fm)α depends on the magnetic field strength B in the source and character izes the μemission efficiency, which decreases greatly with decreasing B (decreasing ϕ). The quantity ϕ F dt ≡ N e dt = Netτe, where Net is the total number

Prediction of proton events is one of the topical problems of solar radio physics. Currently available methods for the prediction of proton events are based on the correlation of solar cosmicray (SCR) parame ters with radio burst parameters (Akin’yan et al. 1977, 1978; Chertok 1982; Chertok et al. 1987; Melnikov and Epifanov 1979; Melnikov et al. 1986, 1991). Pro ton events have a characteristic Ushaped radio fre quency spectrum with maxima in the centimeter and meter wavelength ranges (Podstrigach and Fasakhova, 1981). It is well known that the total number of accel erated particles and their energy spectrum can be esti mated from the parameters of microwave (μ) bursts (Chertok 1982), while the conditions for the escape of accelerated particles into interplanetary space can be judged by the parameters of metric and decametric ones (Akin’yan et al. 1977). Melnikov et al. (1986, 1991) showed that the strong correlation between the moderately relativistic SCR electron flux and the microwave burst fluence suggested that the SCR elec trons and the radioburstgenerating electrons were accelerated by a single process. A maximum correla tion coefficient is reached when a generalized micro wave index is used, ϕ F dt, where F dt ≡ FmTμ and

∫

∫

∫

of accelerated electrons, Ne is the instantaneous num ber of electrons in the loop, and τe is the lifetime of the electrons in the radio source. Melnikov et al. (1986, 1991) showed that the electrons and protons are accel erated in a single process, which makes it possible to estimate the accelerated proton flux from microwave burst parameters. Within the gyrosynchrotron emis sion generation mechanism, it is natural to expect the radio emission parameters to correlate better with the electron flux. This is actually the case as long as the degree of correlation is estimated for the parameters containing information about the μemission power (Fm and F dt ). However, as soon as the time parame

∫

ter Tμ is included in the radio index, the influence of Tμ on Ip becomes stronger than its influence on Ie. The correlation between the proton flux Ip and the effective

∫

ϕ = (9/fm)α, where α ≈ 1.5 and fm is the frequency at which the μemission reaches a maximum. The μ burst flux Fm characterizes the maximum instanta

2

duration Tμ is nonlinear, Ip ≡ T µ , while for the elec tron flux Ie it is linear. The existence of a much stron ger correlation between Ip and Tμ explains the enrich ments by SCR protons compared to electrons as the

† Deceased.

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(a) 1000 100 10 1 0.1 0.01 0.001 0.1 1 10 100 1000 Iρμ, cm–2 s–1 sr–1

Ip (Ep >25 MeV), cm–2 s–1 sr–1

Ip (Ep >25 MeV), cm–2 s–1 sr–1

DEPENDENCE OF THE SCR PROTON FLUX ESTIMATE

27

(b) 1000 100 10 1 0.1 0.01 0.01 0.001 0.01 0.1 1 10 100 1000 Iρμ, cm–2 s–1 sr–1

Fig. 1. Scatter diagrams between the observed, Ip, and calculated, Ipμ, proton fluxes: (a) σ2 ≈ 0.85 and r ≈ 0.69 for the investigated sample of proton events; (b) σ ≈ 0.63 and r ≈ 0.82 for the reference sample of proton events.

effective duration Tμ of μbursts increases (Melnikov et al. 1991; Lipatov et al. 2002). The enrichment by SCR protons compared to electrons can be explained without invoking the second proton acceleration phase if the differences in electron and proton dynam ics in flare loops of different sizes are taken into account. The fraction of the escaped electrons and protons is largely determined by the escape conditions. The intensity (Akin’yan et al. 1977) and duration (Melni kov and Epifanov 1979) of the metric component are known to play an important role as predictive factors in estimating the proton flux from the radio emission. The presence of an intense metric–decametric emis sion is indicative of favorable conditions for the escape of particles high into the corona and further out into interplanetary space. Melnikov et al. (1991) showed the escape conditions for electrons and protons to be strongly correlated. Hence, it follows that the accu racy of predicting the proton flux Ip in interplanetary space can be further improved based on metric–deca metric emission characteristics, which are an indica tor of the escape of accelerated electrons into high coronal layers. Therefore, it seems necessary to corre late the flux of electrons and protons in the interplan etary medium with various metric and decametric emission characteristics. Previously, the best accuracy of estimating the SCR proton flux was achieved based on the generalized microwave index at the frequency of the spectral micro wave maximum (Melnikov et al. 1991), where the resid ual variance σ2 and correlation r between the observed, Ip, and calculated, Ipμ, proton fluxes were σ2 ≈ 0.63 and r ≈ 0.82. Melnikov et al. (1991) provided arguments indicating that a further increase in the accuracy of esti mating the proton flux from the parameters of micro wave (μ) bursts would be related to a quantitative taking into account the accelerated proton escape conditions based on the parameters of metric and DCM bursts.

Therefore, in this paper, we made an attempt to ascertain the extent to which an taking into account the parameters of the DCM component affected the accuracy of esti mating the proton flux from the parameters of μbursts. For this purpose, we used an independent sample of solar proton events for which the original records of solar radio emission in the frequency range 25–15400 MHz (http://www.ngdc.noaa.gov/stp/SOLAR/ftpsolarradio. html) and data on the proton fluxes in the energy range 0.8–500 MeV recorded at the GOES10 International Space Station from 1991 to 2005 (http://www. ngdc.noaa.gov/data.avg/) were available. RESULTS The independent sample includes 64 proton events recorded in solar cycles 22 and 23 (Fig. 1a). The accu racy of estimating the proton flux from the parameters of μbursts was compared with the previously achieved accuracy for a reference sample (see Fig. 1b) of 53 pro ton events recorded in solar cycle 21 (Melnikov et al. 1991). The first stage of our comparative analysis of the proton flux estimation accuracy consisted in finding linear regression models for the (1) reference and (2) investigated samples that related the SCR proton flux Ip to the parameters of μbursts, where Ipμ is the calcu lated proton flux, Fm and Tμ are the maximum μburst flux and effective duration at the frequency of the spectral microwave maximum fm: log I pµ = 1.2 log F m + 2.0 log T µ – 2.0 log f m – 3.4, (1) log I pµ = 1.0 log F m + 1.0 log T µ – 0.8 log f m – 3.2. (2) Figure 1 presents scatter diagrams of the proton flux for the reference and investigated samples, where the residual variance σ2 and correlation r between the observed proton flux Ip and the proton flux Ipμ calcu lated from the parameters of μbursts were σ2 ≈ 0.63 and r ≈ 0.82 for the reference sample and σ2 ≈ 0.85 and

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(b)

0.80 0.70 0.60 0.50 0.40 2 4 6 8 10 12 14 Fm/Fpbi, rel. units

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20

1000 100 10 1 0.1 0.01

Ip (Ep > 25 MeV), cm–2 s–1 sr–1

Variance σ2 (Ip, Ipµ)

Correlation r (Ip, Ipµ)

(a) 0.90

0.01 0.1 1 10 100 1000 Ipμ, cm–2 s–1 sr–1

2 4 6 8 10 12 14 Fm/Fpbi, rel. units

Fig. 2. SCR proton flux estimation accuracy versus PBI intensity: (a) the correlation between the observed, Ip, and calculated, Ipμ, proton fluxes; (b) the variance between the observed, Ip, and calculated, Ipμ, proton fluxes; (c) the scatter diagram between the observed, Ip, and calculated, Ipμ, proton fluxes for events with a PBI level Fpbi ≤ 0.1Fm, for which σ2 ≈ 0.55 and r ≈ 0.85.

r ≈ 0.69 for the investigated one. The filled symbols denote the proton fluxes derived from worldwide solar patrol network data. The open symbols denote the proton fluxes calculated from the solar radio emission observations at the RT22 Crimean Astrophysical Observatory (CrAO) radio telescope performed with a 4wavelength polarimeter. We see from Fig. 1 that the six events recorded at RT22 fall nicely on the previously derived dependence. The radio bursts associated with proton events were recorded at RT22 on July 22, 1991, in the interval 09:45–10:05 UT, on July 24, 1991, in the interval 11:40– 11:55 UT, on July 28, 1991, in the interval 06:30– 06:40 UT, on July 12, 2000, in the interval 10:00–10:35 UT, on July 14, 2000, in the interval 10:15–10:45 UT, and on September 24, 2001, in the interval 09:30– 11:30 UT. Note that the accuracy of estimating the proton flux for the investigated sample is much lower than that for the reference one. This was the reason why we carried out detailed studies to establish the possible causes of such significant differences in model param eters for the reference and investigated samples. Our comparative analysis showed that the types of proton events from radio burst parameters represented in the investigated sample have a great effect on the accuracy of estimating the proton flux. As the parameters that characterized the accuracy of estimating the proton flux from radio bursts, we chose the following three parameters: the intensity of postburst increase (PBI) in the μburst flux Fpbi expressed in units of the maxi mum μburst flux, the intensity of the DCM compo nent F dec dt, and the parameter Δt that characterizes

∫

the time shift of the DCM burst maximum relative to the μburst maximum. Our detailed studies of the dependence of the accu racy of estimating the proton flux from the parameters of μbursts on the PBI intensity Fpbi showed that this accuracy is much higher for events with a low PBI

level, Fpbi ≤ 0.1Fm, for which the residual variance σ2 and correlation r between the observed, Ip, and calcu lated, Ipμ, proton fluxes are σ2 ≈ 0.55 and r ≈ 0.85, while for events with a high PBI level, Fpbi ≥ 0.1Fm, σ2 ≈ 0.90 and r ≈ 0.55 (Fig. 2). Moreover, for events with a low PBI level, Fpbi ≤ 0.1Fm for the investigated sample, the regression model parameters virtually coincide with those for the reference sample (1). Thus, the significant differences in the accuracy of estimat ing the proton flux from the parameters of μbursts for the reference and investigated samples were related to the presence of a large number of events accompanied by an intense PBI and GRF (gradual rise and fall) bursts in the sample in the microwave range, while events with a low PBI are mainly represented in the reference sample. The accuracy of estimating the proton flux from the parameters of microwave bursts depends to a large extent on the conditions for escape into the uppermost layers of the solar corona. Previously, the presence and absence of an intense metric–decametric component in continuum bursts were shown to be indicative of favorable and unfavorable escape conditions, respec tively (Akin’yan et al. 1977). In this paper, we made attempts to quantitatively allow for the escape condi tions based on the parameters of DCM bursts. Figure 3 presents the results of our numerical estimation of the SCR proton escape conditions from the parameters of DCM bursts. Our studies showed (see Fig. 3) that the accuracy of estimating the proton flux from the parameters of μ bursts is much higher for events with a powerful DCM component. As the parameter that characterized the intensity of the DCM component, we used the DCM burst fluence at the frequency of the spectral DCM maximum. For events with a powerful DCM compo nent, for which F dec dt > 10000, the residual variance

∫

σ2 and correlation r between the observed, Ip, and cal


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0.90 0.80 0.70 0.60 0.50 0.50 0.40

Ip (Ep > 25 MeV), cm–2 s–1 sr–1

0.80

(c) 1000 100 10 1 0.1 0.01



0.90 0.70 0.60 0.50 0.50 0.40 10000

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∫ Fdec dt , rel. units

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0.01 0.1 1 10 100 1000

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∫ Fdec dt , rel. units

Ipμ, cm–2 s–1 sr–1

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0.90 0.85 0.80 0.75 0.70

0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15

10 20 30 40 Δt, min

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1000 100 10 1 0.1 0.01

(c)

Ip (Ep > 25 MeV), cm–2 s–1 sr–1

0.95



Fig. 3. SCR proton flux estimation accuracy versus DCM burst intensity: (a) the correlation between the observed, Ip, and calcu lated, Ipμ, proton fluxes; (b) the variance between the observed, Ip, and calculated, Ipμ, proton fluxes; (c) the scatter diagram between the observed, Ip, and calculated, Ipμ, proton fluxes for events with a powerful DCM component, Fdec ≥ 10000, for which σ2 ≈ 0.32 and r ≈ 0.89.

10 20 30 40 Δt, min

0.01 0.1 1 10 100 1000 Ipμ, cm–2 s–1 sr–1

Fig. 4. SCR proton flux estimation accuracy versus time shift Δt of the DCMburst maximum relative to the μburst maximum: (a) the correlation between the observed, Ip, and calculated, Ipμ, proton fluxes; (b) the variance between the observed, Ip, and calculated, Ipμ, proton fluxes; (c) the scatter diagram between the observed, Ip, and calculated, Ipμ, proton fluxes for events with a small Δt ≤ 9 min, for which σ2 ≈ 0.20 and r ≈ 0.94.

culated, Ipμ, proton fluxes are σ2 ≈0.32 and r ≈ 0.89. We see that the proton flux estimation accuracy increased considerably with respect to the complete sample of proton events, because the residual variance decreased significantly, from 0.85 to 0.32. It is interesting to determine the accuracy of esti mating the proton flux from the parameters of μbursts as a function of the temporal DCMcomponent char acteristics, namely, the parameter Δt that characterizes the time shift of the DCMburst maximum relative to the μburst maximum (see Fig. 4). We see from Fig. 4 that the proton flux estimation accuracy is much higher for events with small time shifts of the DCM max imum relative to the μburst maximum (Δt ≤ 9 min). The dependence of the proton flux estimation accuracy on Δt is considerably stronger than that on the DCM intensity. For half of the events from the investigated sample, for which the time shift of the DCMburst maximum relative to the μburst maximum does not exceed 9 min, the proton flux estimation accuracy

approaches the maximum possible accuracy from the parameters of radio bursts. For these events, the residual variance σ2 and cor relation r between the observed proton flux Ip and the flux Ipμ calculated from the parameters of μbursts are σ2 ≈ 0.20 and r ≈ 0.94. These correlation parameters are close to the maximum achievable accuracy (σ2 ≈ 0.19) of predicting the SCR proton fluxes from radio bursts estimated by Melnikov et al. (1991) using the intensity of the SCR electron component as a quantity that characterized the efficiency of the escape of accelerated protons into interplanetary space. This result indicates that the decametric emission from solar flares can serve as an effective quantitative indi cator of the escape conditions. DISCUSSION AND CONCLUSIONS The above three parameters affecting the accuracy of estimating the SCR proton flux from the parameters of microwave bursts are probably related between


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themselves and characterize two different proton and electron acceleration processes. Proton events with a low PBI level have small time shifts of the DCMburst maximum relative to the μburst maximum and a good correlation between the SCR proton flux and μburst parameters is observed for these events. On the other hand, proton events with a high PBI level generally have large time shifts of the DCMburst maximum relative to the μburst maximum and a poor correla tion between the SCR proton flux and μburst param eters is characteristic of these events. This result prob ably suggests the simultaneous action of two widely known acceleration processes in some cases. In one process, the acceleration of protons and electrons takes place during the impulsive flare phase low in the corona, in the region of flare loops. In the other pro cess, the acceleration takes place in the corona at the front of the shock generated by a coronal mass ejection (CME). If the conditions without any significant acceleration at the CME are realized and if the condi tions for the escape of protons from the flare region are favorable, i.e., the magnetic field configuration above the flare loops is predominantly open into interplane tary space, then both protons and electrons escape rapidly. In that case, on the one hand, the time shifts between the microwave and DCMburst maxima will be small (because, in this case, the DCM emission is generated by the electrons accelerated at the impulsive microwave burst phase) and, on the other hand, there will be a good correlation between the proton flux and microwave burst parameters. If, alternatively, the conditions when the main acceleration of protons and electrons takes place at the shock ahead of the CME are realized, then the proton flux in interplanetary space can be overestimated and there will be a poor correlation between the proton and microwave burst parameters. However, since the CME reaches large heights with a significant delay (>10 min), the electrons accelerated at the shock front will also give a decametric burst delayed significantly relative to the microwave one.

Our investigation showed the following: (1) The solar radio emission data obtained on the CrAO radioastronomical facility may well be used to further improve the space weather forecast methods. (2) Taking into account the parameters of micro wave and decametric bursts significantly improves the prediction of geoeffective events. ACKNOWLEDGMENTS We are grateful to the creators of the sites http://www.ngdc.noaa.gov/ and http:/goes.ngdc.noaa/ gov/ for extensive information on the solar radio emis sion. We also thank G.N. Shlikar’, who prepared the manuscript for publication. REFERENCES 1. S. T. Akin’yan, V. V. Fomichev, and I. M. Chertok, Geomagn. Aeronom. 17, No. 1, 10 (1977). 2. S. T. Akin’yan, V. V. Fomichev, and I. M. Chertok, Geomagn. Aeronom. 18, No. 4, 577 (1978). 3. E. A. Isaeva and L. I. Tsvetkov, in Proceedings of the 19th International Crimean Conference “Microwave Engineering and Telecommunication Technology”, Sevasto pol, 2009, Vol. 2, p. 920. 4. B. I. Lipatov, V. F. Melnikov, T. S. Podstrigach, et al., Isv. VUZov, Radiofizika, 65, No. 2, 83 (2002). 5. V. F. Melnikov and O. V. Epifanova, in Proceedings of the KAPG Symposium on Solar–Terrestrial Physics (Nauka, Moscow, 1979), p. 115. 6. V. F. Melnikov, T. S. Podstrigach, V. G. Kurt, and V. G. Stolpovskii, Kosmich. Issled. 24, 610 (1986). 7. V. F. Melnikov, T. S. Podstrigach, E. I. Daibog, and V. G. Stolpovskii, Kosmich. Issled. 29, 95 (1991). 8. Yu. P. Ochelkov, Geomagn. Aeronom. 26, No. 6, 1007 (1986). 9. T. S. Podstrigach and M. A. Fasakhova, Geomagn. Aeronom. 21, No. 1, 22 (1981). 10. I. M. Chertok, Geomagn. Aeronom. 22, No.2, 182 (1982). 11. I. M. Chertok, G. A. Bazilevskaya, and A. I. Sladkova, Geomagn. Aeronom. 27, No.36, 362 (1987).


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