ON LOW-FREQUENCY TYPE III SOLAR RADIO BURSTS OBSERVED IN INTERPLANETARY SPACE

The Astrophysical Journal, 605:503 510, 2004 April 10 # 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A. ON LOW-FREQUENCY TYPE III SOLAR RADIO BURSTS OBSERVED IN INTERPLANETARY SPACE C. S. Wu, 1,2 M. J. Reiner, 3 P. H. Yoon, 2 H. N. Zheng, 1 and S. Wang 1 Received 2003 August 7; accepted 2003 December 18 ABSTRACT This article puts forth an alternative theory of interplanetary type III radio bursts, based on the cyclotron-maser instability. The model suggests that the radio emission is not generated in local interplanetary space but originates much closer to the corona. It postulates that the radiation remains trapped inside the density-depleted duct until it emerges out into free space at the end of the duct, which is located in the interplanetary space. With this model a number of outstanding problems associated with interplanetary type III bursts can be naturally resolved. Termination of type III bursts at low frequency can be explained by the fact that the ratio of plasma- to gyrofrequency, f p =f g, in the source region exceeds the maximum allowable value for the maser instability. The low starting frequency can be explained by the fact that the parameter f p =f g in the source region falls below the minimum allowable value for the maser instability to operate. The rapid increase of temporal width of the dynamic spectrum near the termination frequency may be due to the low group speed associated with waves trapped inside the duct. Subject headings: interplanetary medium Sun: corona Sun: radio radiation 1. INTRODUCTION In an earlier paper (Wu et al. 2002, hereafter W02), we proposed a cyclotron-maser scenario to explain the generation of meter- and decameter-wave type III solar radio emission in the low corona. It stems from the notion that near solar active regions the ambient magnetic field is generally much stronger and consequently might play a dominant role in the emission process. On the other hand, all previous theories (cited in W02) assume that the magnetic field effect on the generation process is unimportant. Here we also note that standard theories mainly grew out of the plasma emission scenario, reviewed, in a historical context, by Melrose (1985). In addition to W02, the cyclotron-maser theory is complemented by the ray-tracing study by Yoon, Wu & Wang (2002, hereafter Y02). It is understood that their theory is not directly applicable to explain low-frequency type III emission observed with spacecraft in interplanetary space (e.g., Kellogg 1980; Lin et al. 1981, 1986; Reiner & Stone 1988, 1989, 1990; Reiner, Stone & Fainberg 1992; Hoang, Dulk & Leblanc 1994; Ergun et al. 1998; Reiner & Kaiser 1999; Reiner 2001; Dulk 2000), because the magnetic field in the solar wind is weak. Our first thought was that for this low-frequency emission, the plasma-emission scenario might be more appropriate. However, we find that there are some outstanding problems for which no theoretical explanation has been offered at all in the literature. These issues, which are explained in xx 2.1 and 2.2, are peculiar to interplanetary type III emission. A preliminary study leads us to believe that the cyclotron-maser theory may offer some explanations. In this paper, we report the findings of our latest investigations. In x 2, relevant observational results as well as specific issues are discussed. We then describe our proposed explanations 1 Department of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China. 2 Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742. 3 Center for Solar Physics and Space Weather, The Catholic University of America, Washington, DC 20064; and NASA Goddard Space Flight Center, Greenbelt, MD 20771. 503 in xx 3 and 4. Finally, our conclusions and a discussion are given in x 5. 2. OBSERVATIONS AND UNEXPLAINED FEATURES Spacecraft observations of type III bursts show that the emission can have kilometer (or even longer) wavelengths. As an example, in Figure 1 we present a dynamic spectrum of the radio emissions observed by the radio experiment WAVES aboard the Wind spacecraft on 2002 October 20. This figure plots the observed radio intensity as a function of frequency ( y-axis) andoftime(x-axis). The radio data were obtained from three separate receivers and cover the frequency range from 10 khz to 13.825 MHz, which includes the kilometerto decameter-wavelength regimes. The observational time period is from 00:00 to 24:00 UT. The nearly vertical frequency-drifting features on this dynamic spectrum are the low-frequency type III radio bursts. These radio bursts are often associated with reported solar flares and subflares and are believed to be generated by electrons accelerated deep in the corona near the flare site. However, there is some recent evidence that suggests that the bursts may originate from electrons accelerated high in the corona (2 R ; Lin et al. 1996). Their characteristic frequency drift is evident in Figure 1, especially in the lower frequency range from 20 to 1000 khz. The temporal duration of these bursts at high frequencies is quite short (a few minutes) but can become very long at lower frequencies (several hours). At the lower frequencies, some of these observed type III bursts are actually a superposition of two or more type III bursts, as is evidenced from the high-frequency observations. In some cases, these superposed bursts originate from different active regions on the Sun. We also see in Figure 1 that the individual type III bursts observed during this period have a variety of different starting and termination frequencies. The radio emissions for some of these bursts extend to the highest WAVES frequency of 14 MHz (and presumably beyond), while for others, the radio emissions appear to start only at frequencies well below 14 MHz. These type III radio bursts also exhibit a variety of different termination frequencies, which are generally significantly higher than the local plasma

504 WU ET AL. Vol. 605 Fig. 1. Dynamic spectrum of the low-frequency radio data observed by the WAVES experiment aboard the Wind spacecraft on 2002 October 20. The frequency range is from 10 khz to 13.825 MHz. A large number of type III bursts were observed from two main active regions on the Sun. See text for the characteristic features of these type III radio bursts. frequency at the spacecraft. Some of these bursts are observed in Figure 1 down to only a few hundred khz, while a few extend nearly to the local plasma frequency, which at the time of the observation in Figure 1, was unusually low (18 khz). These diverse observed spectral features of the type III radio bursts are what we attempt to explain in this paper. During this time period, there were many reported solar flares and subflares that were associated with two main solar active regions on the near side of the Sun. One of these active regions was near the east limb in the northern hemisphere and the other was in the southern hemisphere somewhat to the west of central meridian. As expected, we found that many of the individual type III radio bursts in Figure 1 were associated with these flares. For the most intense type III bursts, there was usually a reported flare. However, as is also usual, for many of these type III bursts there were no reported flares. In some cases, it might be that the flare was simply not observed or that the type III burst was not associated with any flare. However, in some cases it is quite likely that the observed type III burst originated from a flare on the back-side of the Sun (Dulk et al. 1985). For many of the intense type III bursts in Figure 1, there were flares reported at about the same time from both the eastern and western active regions. In these cases, we could usually determine the originating active region of the type III burst from the direction-finding analysis of the radio signal, which makes use of the spin modulation produced by the spinning Wind spacecraft. For example, the first intense type III burst that started at 00:40 UT occurred at the time of flares from NOAA Active Region 10162 located at N27,E61 and from NOAA AR 10160 located at S18,W17 (Solar Geophysical Data Reports). The direction-finding results from Wind indicated that the direction of arrival of the radio emissions was from 2 to the east of central meridian. Thus, we concluded that this type III burst must have originated from the eastern 1F flare from NOAA AR 10162. In this way, we found that the majority of the type III bursts in the dynamic spectrum in Figure 1 were associated with flares from the eastern active regions; however, a few were associated with the active regions on the western hemisphere. The local plasma frequency at the Wind spacecraft is delineated in Figure 1 by the so-called quasi-thermal noise line (Meyer-Vernet 1979). Because the plasma density was unusually low at this time (4 cm 3 ), the radio emission delineating this line is not so evident in Figure 1. However, during this time period there were a large number of Langmuir waves observed at the plasma frequency (bursty features), most likely produced from Earth s electron foreshock (Filbert & Kellogg 1979). As is evident from Figure 1, the local plasma frequency at the spacecraft during this entire time period was somewhat below 20 khz. In the following subsections we list some of the outstanding issues raised by these spacecraft observations. 2.1. Termination of Emission at Low Frequencies A very important feature of the observed dynamic spectra is that in almost every case, the emission terminates at certain characteristic frequencies. The paper by Leblanc, Dulk & Hoang (1995) addresses this issue. Their study is based on

No. 1, 2004 LOW-FREQUENCY TYPE III SOLAR RADIO BURSTS 505 Fig. 2. Dynamic spectrum of the low-frequency radio data observed by the WAVES experiment aboard the Wind spacecraft on 2001 December 13. The frequency range is from 20 khz to 13.825 MHz. A number of well-separated type III bursts were observed that exhibited well-defined termination frequencies (see text). 1028 individual type III events observed by Ulysses. The authors find that in the majority of these cases, termination frequencies, which vary from event to event, are much higher than the plasma frequency at the spacecraft. On the basis of observational evidence, Leblanc et al. (1995) favor the conclusion that the low-frequency termination is intrinsic to the emission mechanism. Type III radio storms, which can last for days or weeks and consist of many thousands of individual type III bursts per day, by contrast often show fairly uniform termination frequencies between 100 and 200 khz (Bougeret, Fainberg, & Stone 1984). We have already mentioned above, in reference to Figure 1, that type III bursts have different termination frequencies, which are generally well above the local plasma frequency. Since there were so many closely spaced type III bursts observed during the time period shown in Figure 1, this characteristic of the termination frequency was somewhat obscured. A somewhat clearer example is presented in the dynamic spectrum from 12:00 to 24:00 UT on 2001 December 13, shown in Figure 2. This example shows a number of wellseparated type III bursts, thereby making their terminal frequencies easier to discern. A detailed examination of the intensity time profiles in the various frequency channels reveals that the first burst, starting at about 12:30 UT, extends to a frequency of about 200 khz and that the second burst, starting at 13:35 UT, extends to about 100 khz. The intense burst starting at 14:25 UT was observed to about 70 khz. The next two bursts had termination frequencies of about 80 and 100 khz, respectively. No solar flares were reported for the first two type III bursts. However, the intense third burst starting at 14:25 UT was associated with an X6.2 flare from NOAA AR 9733, located at N16,E09, i.e., very near the central meridian. The next two bursts starting at 16:05 and 18:00 UT were associated with subflares from NOAA AR 9727, located at S18,W61. The local plasma frequency, as indicated by the quasi-thermal noise line in Figure 2, was very constant at 34 khz during the entire day, well below the lowest type III termination frequency of 70 khz. Dulk et al. (1996) studied 303 type III bursts observed simultaneously by Wind and Ulysses. They find that even though the positions of the two spacecraft were separated by nearly 180, the termination of the observed frequencies are statistically similar. Their discussion illustrates the dynamic spectra of a type III storm on 1994 December 21 22, which consisted of 20 bursts. The plasma frequency at Ulysses was 9 khz, while the plasma frequency at Wind was between 15 and 25 khz (Dulk et al. 1996, Fig. 1). In spite of the difference in local conditions, the authors report that the termination frequencies observed by both spacecraft are generally the same and generally several times higher than the local plasma frequencies. One might attempt to explain the frequency termination on the basis of the plasma-emission model. For instance, the conventional wisdom is that the storms are produced by lower energy electrons (2 kev) than for the normal type III bursts (>10 kev). As the low-energy electrons diffuse out from the Sun far into the corona and interplanetary space, it becomes difficult to maintain the bump-on-tail distribution, so the plasma emission gets turned off at a certain point. The other explanation may involve the propagation effect, i.e., that the radio source turns away from the two spacecraft in such a way that it produces a fortuitously similar termination frequency. While these scenarios are plausible, we propose an alternative explanation below.

506 WU ET AL. Vol. 605 2.2. Very Low Starting Frequencies In the past it was believed that typical type III emission has starting frequencies above 100 200 MHz. However, more recent observations carried out with spacecraft reveal that in general, type III emission may have starting frequencies much lower than those that were conceived in early years on the basis of ground observations. In a recent review article, Dulk (2000) remarks that an unpublished study of 269 radio bursts recorded by WAVES finds that 70% had starting frequencies below 3 MHz. However, many of these may have been generated by flares on the far side of the Sun, so that their higher frequency emissions are occulted by the plasma sphere (Dulk et al. 1985). As mentioned above, a number of the type III bursts in Figure 1 appear to have starting frequencies below 14 MHz. For example, radio emissions for the two type III bursts starting at about 01:35 and 02:07 UT have starting frequencies at or below 3 MHz, the two type III bursts at about 16:00 and 18:00 UT have starting frequencies below 1 MHz, and the type III burst at 22:55 UT has a starting frequency of about 4.6 MHz. The simple explanation for the low starting frequencies observed for these bursts is that these may correspond to solar back-side events. However, we believe that this possibility is very unlikely, because of the fact that most of these type III bursts are temporally well-associated with front-side flares. The type III event at 02:07 UT is temporally associated with the reported flare observed from 02:09 to 02:52 UT from NOAA AR 10160, located at S18,W17. Furthermore, the radio direction-finding from Wind indicates that the arrival direction of these radio emissions at 1 MHz were from 3 to the west of the central meridian, which is consistent with this flare association. Likewise, the weak type III bursts at about 16:00 and 18:00 UT were also found to lie to the west of the central meridian and therefore can be positively identified with flares observed from the western active regions NOAA AR 10158 (W27 ) and AR 10154 (W52 ), respectively. For the type III burst at 23:00 UT, the direction-finding indicates an origin to the west, but the only reported flare at that time was on the east. Thus, for this case it is likely that the flare was not reported, but we cannot rule out the possibility that this could be a back-side event. In Figure 1, it can be seen that there are many other type III bursts that start well below 14 MHz, but there were no reported associated flares. Again, it is likely that many of these flares were simply missed and that many of these type III bursts with low starting frequencies originated in the nearside active regions. On the other hand, it is also likely that some of these type III bursts were back-side events. Even those type III bursts that do extend beyond the WAVES upper frequency of 14 MHz may not extend up to hundreds of MHz. For example, several of these type III bursts were also observed at higher frequencies by the Bruny Island Radio Spectrometer, which observes in the frequency range from 10 to 60 MHz (Erickson 1997). For example, the initial type III bursts starting at about 05:06 UT have starting frequencies of between 35 and 55 MHz. The intense eastern type III event starting at about 06:12 UT appears to start at about 25 MHz. The point we wish to make here is that at least some of these type III bursts with low starting frequencies are consistent with front-side flares, which indicates to us that the low starting frequencies observed for many of these bursts are intrinsic to the type III emissions and do not result from occulting of the high-frequency emissions from any plasma structures. 2.3. Rapid Increase of Duration near the Termination Frequencies In general, a dynamic spectrum of type III bursts reflects the effects of time delay among emitted waves with different frequencies associated with a moving source. For meter, decameter, and even hectometer waves, the emission time covered in a dynamic spectrum is about several tens of seconds. According to the conventional interpretation, the observed frequency drift depends on the density gradient in the source region and the speed of the radio source. A very interesting feature that deserves attentionandappearsinmanylowfrequency dynamic spectra is the broadening of the temporal width of the spectrum near the termination frequency. This is quite evident in Figure 1, especially for those intense type III bursts that extend to very low frequencies, such as the type III bursts that began at 02:07, 05:30, 11:25, and 14:15 UT. The intensity versus time plots measured at 40 khz, which correspond to a horizontal slice through the dynamic spectrum, show rapidly rising and slowly decaying profiles that last for more than 3, 6.5, 2.5 and 4.5 hr, respectively. Although most of these involve the superposition of two type III bursts, this is not the main reason for these prolonged durations, since usually one or the other of these bursts dominates at the lower frequencies. Such prolonged durations are also observed for many well-isolated type III bursts. The lowfrequency durations of the type III bursts shown in Figure 2 was on the order of 1 hr. In this regard, it is worthwhile to mention recent work on beam-beam cannibalism by Li et al. (2003), which shows that multiple bursts are not necessarily simply superposed but may steal one another s energy. 3. A NEW SCENARIO OF INTERPLANETARY TYPE III EMISSION The discussion in this section is a further extension of work by W02 and Y02, which pertain to the type III emission generated above active regions in low corona where the magnetic field is strong. To complement their discussion, we now extend the theory to the low-frequency regime. We begin with the concept of density-depleted ducts, which are essential in the proposed scenario. 3.1. Fibrous Structure and Density-depleted Flux Tubes Observational results and theoretical analysis seem to indicate that the plasma in the solar corona behaves as a fibrous medium (Benz 1993). This is mainly because thermal pressure is much lower than magnetic pressure. Let us consider a slight deviation of the magnetic field inside a flux tube, B, fromthe mean value. The corresponding deviation of the density, n, can be estimated from the pressure balance relation, n ¼ 1 2B ; ð1þ n 0 B 0 where B 0, ¼ 8n 0 T=B 2 0,andn 0 are the mean magnetic field strength, the ratio of thermal to magnetic pressure (the plasma, andt being the temperature), and the mean density, respectively. In equation (1), B k B 0 is assumed. Evidently, when T1, a small increase in the magnetic field intensity by compression could result in a severe density depletion inside the tube. As a result, the plasma density can vary with

No. 1, 2004 LOW-FREQUENCY TYPE III SOLAR RADIO BURSTS 507 large gradients across the magnetic field while the magnetic field itself remains largely unaffected and uniform across the field lines. Because particles can move freely along open field lines, the density gradient parallel to the field lines is expected to be much smaller. Consequently, it is expected that the coronal plasma density can possess radial corrugated structures. In general, coronal fibrous structures may possess a wide range of radial dimensions. The radial size of optically observable plumes (see, e.g., Koutchmy 1977; Habbal 1992) are large, but other, much smaller flux tubes that may not be observable with the resolutions of available optical instruments may also exist. The key issue of interest is, what are the physical processes that dictate the formation of these fibrous structures? We believe that plasma conditions at the chromosphere or low corona may control the density of a flux tube. For instance, the plumes are connected to bright points where small-scale reconnections or other activities take place. Then, jets of chromospheric plasma may lead to the formation of over-dense tubes. On the other hand, in view of the complex physical situation near the surface of the Sun, one may conjecture that numerous processes of similar nature but on much smaller scales could lead to the formation of many types of smaller sized fibrous structures. Although these structures are not directly observable, their existence can be inferred from radio observations. The type III storm may be a prime example. The fact that the emission consists of many bands may indicate that energetic electrons generated from a source of large radial extent are projected out via numerous channels. It is quite reasonable to expect that the fine structure associated with the coronal flux tubes can extend farther out into interplanetary space. Since charged particles cannot easily move across the magnetic field, plasmas with different properties in adjacent regions may not intermingle while being swept outward by the solar wind to 1 AU and beyond. This idea was first discussed by Parker (1963) and is known as the spaghetti model in space physics. This point is also illustrated graphically in Figure 9 in Lecacheux et al. (1989). Their article suggests that the large-scale density structures in interplanetary space might have important effects on the lowfrequency emission observed by the Voyager and ISEE 3 spacecraft. The existence of density-depleted ducts emanating from the Sun is evidenced by observations acquired with the Ulysses spacecraft and discussed in Buttighoffer et al. (1995) and Buttighoffer (1998). They find that the channel, which has an interior density lower than that of the ambient solar wind and an interior magnetic field that is higher, can extend out to a radial distance at least 5 AU. This remarkable finding implies the existence of magnetic flux tubes with a high degree of density depletion in the low corona. 3.2. Basic Emission Process In the present theory, we propose that emission can be attributed to a cyclotron-maser process. Since the details of the instability theory are already discussed in recent articles (Chen et al. 2002; W02; Y02), we will not repeat it here. However, to facilitate our discussion it is useful to summarize the most important conclusions: 1. The extraordinary (X ) mode is in general much more important than the ordinary (O) mode. 2. Both the fundamental and harmonic X-modes (X 1and X 2, respectively) can be excited if the parameter f p =f g [where Fig. 3. Maximum growth rates of X-modes versus the ratio of plasma frequency to gyrofrequency in the source region. The parameters used are similar to those used in W02, but u 0 is set at 0:3c. f p ¼ e(n 0 =m e ) 1=2 and f g ¼ eb 0 =(2m e c) are the plasma- and gyrofrequencies, respectively] falls in the range 0:1 < f p =f g < 0:3, depending on the beam speed. 3. Waves with maximum growth rates are usually excited with a quasi-perpendicular wave phase vector (defined with respect to the ambient magnetic field). This is particularly true for the X 2-mode. 4. If 0:5 f p =f g < 1:4, only the X 2-mode is excited. 5. Although the fundamental O-mode (O1) can be excited when 0 < f p =f g < 1, the saturated wave intensity is insignificant in comparison with X1- and X 2-mode intensity. 6. In general, the growth rate of the harmonic O-mode (O2) as well as all higher harmonics of both polarizations (X 3, X4, O3, O4, and so forth) are negligibly small. In Figure 3, we summarize the findings concerning the X-mode growth rate. Here we remark that since the excited waves have frequencies very close to the local electron gyrofrequency, according to the cyclotron-maser theory, the radio source can be characterized through the magnetic field, not the density, as in the plasma-emission model. In the new model, the emission of radiation takes place inside the density-depleted flux tube (where f p =f g is much lower than the surroundings). The excited waves bounce back and forth inside the tube while continuously experiencing amplification and reabsorption, but they are generally confined within the tube until the waves reach a destination where the local cutoff frequency falls below the wave frequency. The important point here is that the true source location is much closer to the Sun than the apparent source region, where the radiation emerges from the wave duct (W02). Finally, we remark that, strictly speaking, the calculated ranges of the ratio of plasma frequency to gyrofrequency for instability depend upon the velocity distribution function, as well as the beam velocity of the streaming electrons. Thus, the specific numbers mentioned in the above discussion are mainly for the sake of illustration, although they are qualitatively representative. 4. OBSERVATIONS AND OUTSTANDING ISSUES We now make use of the model considered in x 3toaddress the issues listed in x 2. First, we postulate that inside a given

508 WU ET AL. Vol. 605 Fig. 4. Various frequencies and their ratio versus radial distance R, defined from the center of the Sun, in units of solar radius. Curves labeled (i), (ii), and (iii) depict three different depletion models, 1, 2, and 3, the moderate, severe, and extreme, respectively. (a) Plots of the ratio of plasma frequency to gyrofrequency; the leftmost curve represents the frequency ratio at the outer region. (b) Plots of the cutoff frequencies; the topmost curve represents the outside value. duct the degree of density depletion may vary from case to case. To illustrate this, let us consider three cases: case (1) represents a moderate density depletion (which corresponds to the situation considered in W02), case (2) is a situation with severe depletion. Finally, case (3) is a case of extreme depletion. These three possibilities are depicted in Figure 4. In Figure 4a, we plot the frequency ratio f p =f g versus the height from the solar surface, and Figure 4b depicts the X-mode cutoff frequency corresponding to each case, plotted as a function of the radial height. In Figure 4b we also plot the gyrofrequency and its harmonic, based on the magnetic field model used in W02. Note that the cutoff frequencies inside the duct are much lower than that outside the duct, which is shown in the topmost curve. The three cases and all the intermediate situations represent physical situations, which may occur under different circumstances at different times. 4.1. Sudden Termination of Emission In x 2.1 we discuss the issue of low-frequency termination. While one may attempt explanations in the context of the standard model, it is our view that the termination frequency is primarily intrinsic to the emission mechanism, as speculated by Leblanc et al. (1995) and Dulk et al. (1996). We propose that the low-frequency termination can be intrinsically explained by the maser instability model. As discussed in x 3.2, the maser instability operates only below certain altitudes where the local parameter f p =f g reaches its limiting value of 1.5 or so. At higher altitudes, therefore, the instability would be suppressed. Obviously, the critical altitude depends upon the degree of density depletion. For example, we see from Figure 4a that it is about 2 R for case (1), while in the severely depleted case (2), the threshold is reached at 4 R. In the former case, the corresponding gyrofrequency is approximately 500 khz, and thus the cutoff frequency for X 2-mode is about 1 MHz. In the latter case, the gyrofrequency is about 60 khz and the X 2 cutoff frequency is 120 khz. In Figure 4a, the leftmost line represents the frequency ratio outside the duct, while the curves labeled (i), (ii), and (iii) represent the ratio in the duct interior. Thus, by comparing the outside curve with the interior curves, one can have a sense of the degree of density depletion. The same is true with Figure 4b in that the uppermost, unmarked curve represents the cutoff frequency outside the duct. In the extremely depleted case (3), the interior plasma frequency approaches 10 khz. In this case, the instability is not quenched until one reaches near 5.5 R, where the parameter f p =f g approaches 1.5. As a consequence, the X 2-mode cutoff is approximately 30 khz. The extremely depleted case, therefore, implies a very long and extended duct. Needless to say, the existence of such a structure is only postulated and has not been observationally verified. The salient point in our model is that regardless of the degree of density depletion, the actual emission occurs much closer to the solar surface than can be inferred from apparent source location. Thus, according to our model, the so-called interplanetary emission may actually originate quite near the Sun. The crucial assumption in our model is that a sufficiently long and well-defined density-depleted duct exists in such a way that the waves emitted near the Sun can propagate all the way out to interplanetary space while being guided within the duct. The advantage of the present model is that the low-frequency termination mechanism is built within the emission process itself. 4.2. The Reason for Low Starting Frequencies As discussed in x 2.3, spacecraft observations find that type III emission may have starting frequencies that are much lower than those anticipated on the basis of ground observations. The low starting frequency implies that the emission is suppressed at low altitudes. This issue can be naturally resolved according to the maser model. As an illustration, consider the severely depleted case (ii). As already mentioned, the significant wave amplification is restricted to 0:1 < f p =f g.accordingtofigure4a, this criterion is satisfied at altitude of approximately 1 R and higher, where the gyrofrequency is about 4 MHz. Since both X1 andx 2 modes can be simultaneously excited there, one expects the highest starting frequency should be about 8 MHz. (Note that in this frequency range, the distinct fundamental-harmonic structure may not be discernable, because of overlapping intensity signatures in the frequency versus time dynamic spectrogram.) Such a finding is in qualitative agreement with that exhibited in Figure 1, in which the type III starting frequency appears to be around 5 7 MHz. Of course, the above finding is model dependent. For instance, if we chose case (1), which is the situation considered by W02, the onset height is about 0.5 R when the gyrofrequency is approximately 80 MHz. In such a case, the starting frequency should be 160 MHz. In spite of the inherent degree of freedom associated with model dependency, the important thing to note here is that the maser model intrinsically possesses the onset frequency above which no instability may operate. Here we should note that Robinson & Cairns (1998a, 1998b, 1998c) discussed the issue of why fundamental and harmonic emissions seem to have different starting frequencies, which they explained in terms of lower group delay and scattering of the F component. However, the issue we are addressing is not the relative difference in the starting frequencies between F and H components, but rather the overall limitation on the starting frequency whether the burst is F, H, or paired emission. 4.3. Long Emission Duration near Termination Frequency As described in x 2.2, it is generally observed that the temporal widths of many observed type III bursts increase

No. 1, 2004 LOW-FREQUENCY TYPE III SOLAR RADIO BURSTS 509 rapidly in low-frequency regimes, particularly near the termination frequency, usually on the order of a couple of hr. Robinson & Cairns (1994) have previously addressed the issue of the long duration of the type III burst radiation observed at low frequencies within the context of the stochastic growth model (Robinson 1992; Robinson, Willes, & Cairns 1993). Using a simple model for the propagation of the finite electron beam and the propagation of the fundamental and harmonic radiation from source to observer, they estimated the onset and termination times of the (unscattered) fundamental and harmonic emissions as a function of frequency. Comparing these times for several observed type III bursts, they found that at low frequencies (<100 khz) the observed termination times of the type III emissions persisted for some hours after the predicted end of the unscattered radiation calculated in the context of their model. They concluded that the long temporal widths of the observed electromagnetic emissions were probably the result of multiply scattered fundamental or harmonic emissions. Specifically, because the harmonic radiation is less effectively scattered than fundamental emission, they argued in favor of the observed temporal width most probably being due to multiply scattered fundamental emissions, except possibly very near the local plasma frequency, where multiply scattered harmonic emissions could dominate. In a later work, Robinson & Cairns (1998a, 1998b, 1998c) also discussed the low-frequency termination in terms of the low-density electron beam merging with the background solar wind plasma, which leads to the termination of the beam-generated Langmuir waves. In our model, two factors contribute to the observed duration: one is the size of the duct at the exit point, and the other is that the exit waves have near-zero reflective indices. Let us first discuss the former. We consider that the density-depleted flux tube is along open magnetic field lines emanating from an active region (Buttighoffer et al. 1995; Buttighoffer 1998). If the ambient magnetic field in the source region of metric waves is about 100 G and the magnetic flux tube in that region has a radius about 10 2 10 3 km, then at the exit point the radius of the same flux tube may be roughly 5 ; 10 4 5 ; 10 5 km for waves with low frequencies (100 khz or lower). (This estimate is based on conservation of magnetic flux and the assumption that in the exit region in interplanetary space the magnetic field is about 4 ; 10 4 G.) In short, according to our model the size of the apparent source is determined by the size of the cross section of the flux tube at the exit point. Thus, an observed source region of low-frequency radiation is expected to be large. This is consistent with observations (Lecacheux et al. 1989). Consequently, when a spacecraft is passing through the source region it would see a long duration of emission. If we postulate that the spacecraft is moving with a velocity of 5 10 km s 1, it would take a few hours to traverse a region of the size 10 5 km. One may raise the question that the above explanation would require a very long wave train to occur inside the duct. Here we stress that according to the cyclotron-maser scenario, the exiting waves have near-zero reflective index. Since the density gradient at 1 AU is very small, the exiting waves can have a small refraction index for a long time. These waves leave the exit region primarily because of convection by the solar wind. Certainly a quantitative comparison of beam electron velocity with the propagation speed of the waves is desirable, but it is a difficult task. For instance, the measured distribution functions of the energetic electrons are often fairly isotropic, only exhibiting a weak diffusive beam. On the other hand, the discussion of wave propagation speed in the duct is also very difficult, if not impossible. Several difficulties are apparent: (1) refraction and reflection near the wall of a density-depleted flux tube, (2) scattering on small scale structures and irregularities, (3) the geometry of the flux tubes, which are generally curved, and (4) other nonlinear processes. All these effects can significantly reduce the propagation speed of the trapped waves. 5. DISCUSSION AND CONCLUSIONS Streaming electrons can definitely excite Langmuir waves. Therefore, simultaneous observations of streaming electrons and Langmuir waves are expected. The gist of the issue is whether the observed electromagnetic waves are really generated locally via nonlinear conversion of the Langmuir waves. Our contention stems from several considerations. First, the issues of sudden termination and low starting frequencies, which are described in xx 2.1 and 2.2, cannot be explained by the plasma-emission process, whereas the maser scenario may offer a resolution. The tenuous energetic electrons, which have a density only 10 5 times that of the solar wind density, have a rather limited amount of kinetic energy to produce the radiation. In conclusion, we have put forth an alternative model of low-frequency type III emission observed in interplanetary space. The major points are: 1. The observed termination (or cutoff ) of interplanetary type III bursts at low frequency can be explained by the fact that the parameter f p =f g exceeds the maximum allowable value for the maser instability. The termination frequency has nothing to do with the local frequency at the spacecraft. 2. The low starting frequency can be explained by the fact that the plasma in the source region is severely depleted, so that the minimum value of the ratio f p =f g for onset of the maser instability occurs at high altitude. 3. Observations show that the temporal width of a type III burst increases as the frequency of radiation decreases. According to the maser scenario, the size of the apparent source is determined by the cross section of the flux tube from which that radiation exits. For low-frequency type III emission near 1 AU, the radius of the source region can be on the order of 10 5 km. It takes a couple of hours for a spacecraft to traverse the region. In the present discussion, the postulate of the existence of density-depleted magnetic flux tubes is essential, because only if these exist can the low-frequency radiation generated in the low corona leak out. Although no direct observation of such low-density ducts is possible, our postulate is supported by several indirect observations: first, the fibrous structure of optically observable plumes (Koutchmy 1977; Habbal 1992); second, the large-scale density inhomogeneity discussed in Lecacheux et al. (1989); and finally, the findings made with Ulysses discussed in Buttighoffer et al. (1995) and Buttighoffer (1998). In short, our contention is that the low-frequency type III radiation is actually produced near the Sun, rather than locally generated in interplanetary space. Indeed, this topic deserves more discussion and scrutiny. The research effort at the University of Science and Technology of China was supported by grant KJCX 2-NO8

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