Wavelet-based Characterization of Small-scale Solar Emission Features at Low Radio Frequencies

The horizontal features are instrumental artifacts that are due to the poor instrumental response at the edges of coarse spectral channels and need to be removed. These artifacts are corrected for by performing linear interpolation across the systematics-affected channels. As the coarse channel edges at the very start and end of the observing band cannot be corrected by interpolation, these are simply discarded. Recording glitches sometimes affect the beginning and end of data recording. To avoid contamination from such issues, we routinely discard the first six and the last nine time slices of data as well.

Although the MWA is located in a region with very little radio frequency interference (RFI), radio waves reflected from aircraft can occasionally interfere with the radio signals picked up by a tile and thereby corrupt the data collected. Manual RFI-flagging followed by linear interpolation across RFI-affected segments of the DS is carried out to ensure an RFI-free DS for efficient feature detection. The left panel of Figure 2 displays an instrumental artifact-free version of the DS shown in Figure 1.

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The solar radiation can be thought of as a superposition of sporadic nonthermal radio features with a spectrally varying broadband background continuum. Spectral variations in the background flux density can often distort the spectral profiles of features in the DS. To improve our efficiency at picking up small-scale features from the DS, it is therefore necessary to distinguish spectral flux density variations arising from these features from the variations associated with the background.

As the day of our observations was characterized by medium levels of solar activity, it seems reasonable to expect that the thermal quiet-Sun emission forms the dominant component of the background continuum emission in our data. We find the temporal variation of the background flux density to be negligible over the duration of individual observing scans of four minutes each. This allows us to then ignore the time dependence of the background flux density and treat it as as a function of frequency alone. As the flux densities of the weakest radio bursts detected in our data sets are only a few percent of the background flux, an accurate and robust means of determining and subtracting out the spectral variation of the background component is required.

In this work, the Gaussian Mixtures Model (GMM) routine provided by Scikit-Learn (Pedregosa et al. 2012) is applied to estimate the background flux density $({S}_{\odot ,B})$ as a function of frequency. As the background is expected to vary smoothly, the DS is divided into contiguous groups of four fine spectral channels each. The data in each of these groups are then decomposed as a sum of Gaussians using the GMM routine. As there exists no unique way of representing a given function as a sum of Gaussians, the Bayesian information criterion (Burnham & Anderson 2002) has been employed to determine the optimum number of Gaussians required to fit the data. Since the thermal quiet-Sun component forms the baseline emission level on top of which nonthermal radio emission is detected, it is reasonable to assume that the Gaussian corresponding to this background continuum must be the one with the lowest mean and the highest weight. For every group of fine spectral channels, the value of the mean of this Gaussian is noted as the background flux density (S_GMM (ν)) at the respective frequency and is shown by the red circles in the top sub-panels in Figure 3. Strong frequent radio bursts that outshine the background component in a DS degrade the ability of the GMM to determine a value of the background flux at each observing frequency. Our observations were taken on a day with moderate solar activity, allowing for the use of the GMM to determine the background flux density at several frequencies in most data sets.

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A degree-4 polynomial is then used to fit the large-scale smooth spectral trend in the background flux density and is subtracted from the DS. The right panel in Figure 2 depicts the DS obtained after background removal from the DS depicted in the left panel. The suitability of a degree-4 polynomial fit to the background can be quantified by estimating the residual percentage between ${S}_{\mathrm{GMM}}(\nu )$ and the flux densities (S_fit (ν)) predicted from the best-fit polynomial at the same frequency. The residual percentage is given by

$\begin{eqnarray}&&\mathrm{Residual} \% (\nu )=\displaystyle \frac{{S}_{\mathrm{GMM}}(\nu )-{S}_{\mathrm{fit}}(\nu )}{{S}_{\mathrm{GMM}}(\nu )}\times 100 \% .\end{eqnarray} \tag{ 1 }$

Figure 3 depicts the degree-4 polynomial fits to the estimated background fluxes for a few of the DS used in our study. A degree-4 polynomial is adequate to describe the spectral variation observed in the background flux to within a mean absolute error of 3%–4%.

Continuous wavelet transform (CWT) provides a natural way of obtaining a time-frequency representation of a non-stationary signal through the use of a wavepacket with finite oscillation, i.e., a wavelet. In this work, our signal is the 2D MWA DS containing the features of interest. The efficiency of CWT at reliable detection of features from the DS depends upon our choice of the 2D mother wavelet and is maximized for a mother wavelet that closely matches the shape of the spectral and temporal profiles of these features.

3.3.1. Choice of Mother Wavelet

From the right panel in Figure 2, it can be seen that while features exist that appear isolated in the DS, several features in the DS appear to be bunched together. Figure 4 depicts the spectral and temporal profiles of one seemingly isolated feature indicated by a red circle in the background-subtracted DS depicted in Figure 2. A close look at such isolated features in the DS reveals a characteristic smooth unimodal nature to their temporal and spectral profiles. Assuming that each atomic feature in a DS possesses unimodal spectral and temporal profiles, any multi-modal spectral or temporal distribution of flux densities observed can be interpreted as a superposition of contributions from constituent unimodal distributions. This allows for a 2D Ricker wavelet to be employed as a suitable mother wavelet for CWT. Measured in pixel units, the features of interest usually have axial ratios of about 10–50. To best match features of this nature, we use a variable separable version of a 2D Ricker (also called the Mexican hat) wavelet with analytical form 

$\begin{eqnarray}&&R(t,\nu )=\displaystyle \frac{4}{3\sqrt{\pi }}((1-{t}^{2}){e}^{-\tfrac{{t}^{2}}{2}})((1-{\nu }^{2}){e}^{-\tfrac{{\nu }^{2}}{2}})\end{eqnarray} \tag{ 2 }$

as the mother wavelet. From this mother wavelet, scaled wavelets are constructed according to the definition given by Antoine et al. (2004) as follows:

$\begin{eqnarray}&&{R}_{{s}_{t},{s}_{\nu },{\tau }_{t},{\tau }_{\nu }}(t,\nu )=\displaystyle \frac{1}{\sqrt{{s}_{t}{s}_{\nu }}}R\left(\displaystyle \frac{t-{\tau }_{t}}{{s}_{t}},\displaystyle \frac{\nu -{\tau }_{\nu }}{{s}_{\nu }}\right).\end{eqnarray} \tag{ 3 }$

The peak of a 2D scaled Ricker wavelet is located at (t, ν) = (τ_t, τ_ν). The scales s_ν and s_t correspond to half the support of its positive lobe along the frequency and time directions, respectively. Using the scaled 2D Ricker wavelets, wavelet coefficients of the DS are then computed according to the following definition:

$\begin{eqnarray}&&\gamma ({s}_{t},{s}_{\nu },{\tau }_{t},{\tau }_{\nu })={\iint }_{\nu ,t}{DS}(t,\nu ){R}_{{s}_{t},{s}_{\nu },{\tau }_{t},{\tau }_{\nu }}(t,\nu ){dtd}\nu .\end{eqnarray} \tag{ 4 }$

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For ease of notation, let us denote the wavelet coefficients $\gamma ({s}_{t},{s}_{\nu },{\tau }_{t},{\tau }_{\nu })$ by the symbol $\gamma ({s}_{t},{s}_{\nu },t,\nu )$. For a given feature peaked at (t, ν) in the DS, γ(s_t, s_ν, t, ν) is maximized when s_ν and s_t match the spectral and temporal extents of the feature, respectively. Thus, the 2D Ricker wavelet acts as a peak and support detection filter. This then enables us to determine the peak flux densities as well as the temporal and spectral extents of features in the DS.

3.3.2. Construction of a Composite Matrix

Because the 2D CWT introduces two additional degrees of freedom through transformation from a 2D DS space to a 4D wavelet-coefficient space, a large number of wavelet coefficients computed for a given DS carry redundant information. The non-orthogonality of a set of scaled Ricker wavelets further preserves this redundancy. This aspect can then be exploited to reconstruct the DS using a basis different from the set of scaled wavelets. Torrence & Compo (1998) give an explicit expression for 1D signal reconstruction from the wavelet coefficients using a basis of δ-functions. Extending this formula to the 2D CWT used here, a composite matrix, A(t, ν), of wavelet coefficients that exactly reconstructs the DS, barring a constant normalization factor, is given by

$\begin{eqnarray}&&A(t,\nu )=\displaystyle \sum _{{s}_{\nu }\gt 0}\,\displaystyle \sum _{{s}_{t}\gt 0}\displaystyle \frac{\gamma ({s}_{t},{s}_{\nu },t,\nu )}{\sqrt{{s}_{t}{s}_{\nu }}}.\end{eqnarray} \tag{ 5 }$

As the wavelet coefficients are nothing but a convolution of the DS with the scaled wavelets, it is expected that A(t, ν) should be a smooth reconstruction of the DS. Local maxima in A(t, ν) then correspond to peaks of features in the actual DS. However, there are two issues with using A(t, ν) for feature identification. At small scales, our measurements are dominated by noise. As Equation (5) involves a sum over all values of s_ν and s_t, it also tries to incorporate the measurement noise in A(t, ν). Furthermore, bunching of features that leads to overlapping spectral and temporal profiles of adjacent features in the DS can hinder the ability of the CWT to resolve two closely spaced features from one another at high values of s_ν and s_t. It is therfore necessary to work with an intermediate range of scales to construct a composite matrix, M(t, ν), that captures details of the features of interest while it avoids being influenced by the inherent measurement noise at small scales and bunching of features at large scales. M(t, ν) is therefore constructed using the following expression:

$\begin{eqnarray}&&M(t,\nu )=\displaystyle \sum _{{s}_{\nu }={s}_{\nu ,\mathrm{lower}}}^{{s}_{\nu ,\mathrm{upper}}}\displaystyle \sum _{{s}_{t}={s}_{t,\mathrm{lower}}}^{{s}_{t,\mathrm{upper}}}\displaystyle \frac{\gamma ({s}_{t},{s}_{\nu },t,\nu )}{\sqrt{{s}_{t}{s}_{\nu }}}.\end{eqnarray} \tag{ 6 }$

In the time domain, the features of interest are already present at the resolution of the data, forcing us to set ${s}_{t,\mathrm{lower}}$ to 0.5 s. Careful visual inspection of a large number of DS revealed that a few features with bandwidths less than 0.5 MHz exist, leading us to a choice of 0.5 MHz for ${s}_{\nu ,\mathrm{lower}}$. Again, guided by careful visual inspection of several DS, we set ${s}_{t,\mathrm{upper}}=3\,{\rm{s}}$ and ${s}_{\nu ,\mathrm{upper}}=5\,\mathrm{MHz}$ in order to provide both the ability to detect atomic features present within a bunch of features and the capability to identify relatively long-lived or broadband features. The values chosen for ${s}_{t,\mathrm{upper}}$ and ${s}_{\nu ,\mathrm{upper}}$ in fact enable us to reliably reconstruct features with spectral and temporal extents as large as 26.04 MHz and 15 s, respectively. M(t, ν) is then computed using the choices of scales mentioned above. Local maxima picked up from M(t, ν) correspond to locations of the peak flux densities of different features contained in the DS. Figure 5 illustrates the ability of the CWT to distinguish between closely spaced features despite overlaps in their flux density profiles along the frequency and time axes.

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Panel (a) in Figure 5 depicts a comparison between a spectral slice taken from both the DS and M(t, ν) at the same time. The locations of the peaks of features in the M(t, ν) spectral profile closely agree with their corresponding peaks in the DS. For a given feature, we find that its spectral extent is matched well by the distance between the two local minima in the M(t, ν) spectral slice that straddle its peak. We use the distance between these local extrema as the spectral extent of the feature. The lower extremum is then taken to be the start frequency (ν_start) of the feature. The temporal extent and start time (t_start) of a feature are similarly estimated. In order to obtain estimates of a quantity similar to the half-power width of a feature, we define the spectral and temporal widths of a feature respectively as

$\begin{eqnarray*}{\rm{\Delta }}\nu & = & 0.5\,\times \,\mathrm{Spectral}\,\mathrm{extent}\,\mathrm{of}\,\mathrm{feature}\\ {\rm{\Delta }}t & = & 0.5\,\times \,\mathrm{Temporal}\,\mathrm{extent}\,\mathrm{of}\,\mathrm{feature}.\end{eqnarray*}$

For the purpose of quantifying any symmetry present in the spectral profile of a feature with a peak at frequency ν, we define its spectral symmetry parameter as follows:

$\begin{eqnarray}&&{\chi }_{\nu }=\displaystyle \frac{\nu -{\nu }_{\mathrm{start}}}{2{\rm{\Delta }}\nu }.\end{eqnarray} \tag{ 7 }$

The value of this parameter lies in the range from 0 to 1. A spectral symmetry parameter value of 0.5 for a feature represents a perfectly symmetric frequency profile, while departures from 0.5 indicate skewness in the spectral profile. The temporal symmetry parameter (χ_t) of a feature is similarly defined.

As seen from panel (a) in Figure 5, peaks of features picked up from M(t, ν) do not always coincide with their counterparts in the DS. However, since M(t, ν) peaks lie close to their corresponding DS peaks, this discrepancy is easily corrected for by first growing a region around an M(t, ν) peak and then identifying the DS peak within this region. The admissibility criterion used to grow a region S starting from an M(t, ν) peak is that the wavelet coefficient of the neighboring pixel under consideration is within a minimum threshold (T) percentage of the peak wavelet coefficient. The region-growing algorithm terminates when no more pixels on the boundary of S satisfy this criterion. Since M(t, ν) is only an approximation to the actual DS, the temporal and spectral profiles of a feature in the DS are reproduced exactly only within a small neighborhood around its M(t, ν) peak. Hence, a value of T as high as 95% has been chosen to ensure that all pixels contained in the region S around the peak of a feature actually belong to this feature. For the features detected from all DS used in this work, M(t, ν) peaks show average offsets of 0.16 s and 0.57 MHz from their corresponding DS peaks. After peak correction, the peak flux density of a feature is obtained from the flux density at the location of its peak in the background-subtracted DS.

Since M(t, ν) only approximates the DS, it is possible for it to contain some spurious peaks that do not correspond to real features in the DS. Only a peak in M(t, ν) with a corresponding peak in the DS is regarded to be a real feature. In order to weed out false peaks, the root mean square flux density (σ) is estimated across quiet patches in the DS as a function of frequency. A signal-to-noise ratio (S/N) for every peak is then defined as the ratio of the peak flux density to the root mean square background noise at the frequency corresponding to the location of the peak. The spectral and temporal profiles of all peaks detected in M(t, ν) were visually examined using figures similar to Figure 5 to check for a corresponding peak in the DS. We find false detections to constitute about 24% of the total number of peaks detected in M(t, ν), all of which have peak flux densities, ${S}_{\odot ,F}\lt 5\sigma$. In all, about 26% of our detections lie below the 5σ threshold. In order to eliminate all false positives, we reject all peaks with ${S}_{\odot ,F}\lt 5\sigma$.

Figure 6 depicts the locations of the peaks of all features detected using this automated wavelet-based approach. In order to estimate the efficiency of this approach at picking up features reliably from the DS, eight laypersons were presented with plots of different background-subtracted DS similar to Figure 6 and requested to estimate the false-positive and false-negative rates. According to their estimates, the CWT pipeline successfully picks up features from the DS with a zero false-positive rate, but with a false-negative rate of about 4%–6%. A total of 14,177 features were detected from 67 background-subtracted DS used for this work.

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Figure 7 shows the histogram of the peak flux densities (${S}_{\odot ,F}$) of the features. While this histogram extends up to nearly 307 SFU at its upper end, it touches peak flux densities as low as 0.6 SFU at its lower end. This makes the detected small-scale features about 1.6 times weaker than the type-I bursts studied by Ramesh et al. (2013) and hence places them among the weakest reported bursts in literature. A least-squares power-law $({dN}/{{dS}}_{\odot ,F}\propto {{S}_{\odot ,F}}^{\alpha })$ fit to this histogram yields a power-law index α = −2.23 over the 12–155 SFU range. The flux range for this power-law fit overlaps with that of the power-law fits to the flux density profile reported in Mercier & Trottet (1997). The upper end of this flux range approaches the lower end of the flux range for the power-law fits by Saint-Hilaire et al. (2013). The value of α obtained here is intermediate between the corresponding values obtained by Saint-Hilaire et al. (2013) (α ≈ −1.66 to −1.8) and Mercier & Trottet (1997) (α ≈ −2.9 to −3.6). Iwai et al. (2014), in their observational studies of type-I bursts, also report a power-law index of −2.9 to −3.3. The value of α obtained here is also much lower than the power-law index of −3.5 predicted for the low-energy part of the statistical flare spectrum by Vlahos et al. (1995). However, it agrees well with the the power-law indices α ≈ −2.5 obtained by Mugundhan et al. (2016) and α ≈ −2.2 to −2.7 obtained by Ramesh et al. (2013) in separate studies of type-I bursts observed using the Gauribidanur Radio Observatory.

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We note that the residuals to the power-law fit in Figure 7 are non-Gaussian, implying the inadequacy of the power-law model to fit these data. The uncertainty in the best-fit power-law slope is, however, only about 1%, implying that it still provides a reasonable, if sub-optimal, description of the distribution. While a higher order polynomial in log–log space would provide a better fit, we have chosen to use a power-law model as it renders itself to an interesting physical interpretation from a coronal heating perspective (Section 5.1) and provides a point of comparison with earlier literature in the field. We note that the distribution of peak flux densities depicted in Figure 7 suffers from incompleteness at low flux densities and limited statistics at high flux densities. We have, hence chosen to fit the power law to an intermediate range of flux densities where the obtained histogram is expected to resemble the true distribution. Although the numerical value of the power-law index depends on the exact choice of endpoints chosen for the power-law fit, the index is found to be lower than −2 regardless of this choice in the flux density range ∼10–160 SFU, where we expect the distribution to be complete.

Figure 8 shows a 2D histogram of the distributions of the peak flux densities and the peak frequencies (ν) of the features. While the peak flux densities of a majority of features appear to be independent of ν, a sub-population of them seem to show a frequency-dependent variation in the peak flux density. For this sub-population, the peak flux density appears to increase with ν from 100 to 150 MHz, remains nearly constant with ν between 150 and 200 MHz, and then declines for ν ≥ 200 MHz.

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Figure 9 depicts histograms of the spectral and temporal widths of features. Both Δν and Δt follow smooth unimodal distributions. The Δν distribution peaks at about 4–5 MHz, well above the 40 kHz frequency resolution of our data. On the other hand, the peak in the Δt distribution lies at 1–2 s, quite close to the 0.5 s temporal resolution of these data. Figure 9(c) further shows that the distributions of Δν and Δt arrange themselves in a single well-formed cluster peaking at about 4–5 MHz and 1–2 s. While the bandwidths of these features are two orders of magnitude smaller than the bandwidth for type-III bursts, they are comparable to the typical frequency span, Δν ≲ 10 MHz (Mercier & Trottet 1997), reported for type-I bursts.

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The left panel of Figure 10 shows a 2D histogram of the distributions of Δν and the peak frequency (ν). The prominent peak and valley-like structures are artifacts arising from the limited bandwidth of the observations. While valleys occur at the edges of the observing bandwidth, peaks occur at its center. There seems to be a hint of a trend for a small increase in Δν with increase in ν (≈0.02 MHz increase in Δν per unit increase in ν). The original data set has an equal number of observations at each of the observing bands. The algorithm used to determine the background continuum is designed for periods of medium or low levels of solar activity and hence worked effectively for most of the data. However, it was not suitable for about 24.3% of the data that were characterized by high solar activity (typically periods immediately following occurrences of B- and C-class flares) and hence were discarded from this analysis. This effectively leads to different observing durations for different observing bands and is reflected in the left panel of Figure 10. In order to arrive at the true spectral distribution of features, the feature occurrence rate per unit bandwidth is computed as a function of frequency. As shown in the right panel of Figure 10, the spectral distribution of features appears to remain flat in the frequency range from 140 to 210 MHz and declines at lower frequencies. Below 140 MHz, the galactic background temperature rises sharply, while the intrinsic solar emission becomes weaker (Oberoi et al. 2017). This leads to a drop in the S/N of our detections at these frequencies, and they are consequently underrepresented in the spectral distribution. The true spectral distribution of feature occurrences is expected to be flatter than the distribtuion shown in the right panel of Figure 10.

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An interesting finding about the nature of the spectral and temporal profiles of the features of interest is obtained through the histograms of χ_ν and χ_t (defined in Section 3.3.2) shown in Figure 11. While features largely appear to possess symmetric frequency profiles, their temporal profiles display no inherent symmetry. The peaks at the extremes of the χ_ν and χ_t histogram range arise as a result of features with peaks located close to the edges of the DS.

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Figure 12 shows a 2D histogram of the background flux density as a function of frequency. The background-continuum emission shows the expected monotonic increase with frequency that is due to the broadband thermal radiation from the 10⁶ K coronal plasma. RSTN (http://www.sws.bom.gov.au/World_Data_Centre) solar flux measurements estimate the median flux density on the day of our observations to be 20 SFU at 245 MHz. We also note that over the course of these observations, the spectrally smooth background flux density is observed to vary by a rather large amount.

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After estimating the peak flux, bandwidth, and duration of each feature detected in the DS, estimates of their energy can be obtained if the solid angle into which emission is radiated is known. Assuming isotropic emission for these features, $W=4\pi {D}^{2}{\rm{\Delta }}\nu {\rm{\Delta }}{{tS}}_{\odot ,F}$ gives the total energy radiated for a feature when observed from a distance D = 1 au. As this definition of W uses only the peak flux density of a feature without accounting for any reduction in flux density within its shape and assumes isotropic emission, it overestimates the actual energy of a feature. We note that while most earlier works use constant bandwidths and durations to estimate the energy radiated, we use the spectral and temporal spans corresponding to individual features for this purpose. The histogram of the total feature energies is shown in Figure 14. The typical energies of these features lie in the range of 10¹⁵–10¹⁸ erg. These features are therefore weaker than both the type-III bursts (W ≈ 10¹⁸–10²³ erg) investigated by Saint-Hilaire et al. (2013) and the type-I bursts (W ≈ 10²¹ erg) studied by Mercier & Trottet (1997).The best-fit power-law to the tail of the histogram in Figure 13 yields a power-law index of −1.98. Hudson (1991) has shown that for weak flare emissions to play a significant in coronal and chromospheric heating, the power-law distribution describing their occurrence must have an index α ≤ −2. Within the uncertainty of the fit, the features studied here meet this criterion and hence can be expected to play an interesting role in coronal heating. Subramanian & Becker (2004) have estimated the ratio of the radiative power output from noise storm continua to the total power input provided to the accelerated nonthermal electrons producing these bursts to be about 10⁻¹⁰–10⁻⁶. Using this efficiency estimate, the typical energies of the nonthermal electrons producing the features of interest lie in the range from 10²¹–10²⁸ erg. This agrees well with the estimate of 10²³–10²⁶ erg obtained by Subramanian & Becker (2004) for the energy transferred to the nonthermal electron population that cause noise storm continua. This hints at a possible correlation between the properties of these features with that of type-I bursts. On the basis of observational studies, Ramesh et al. (2013) also report nonthermal electron energies of about 10²⁰ erg for radio noise storm bursts.

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Our statistical analysis shows that the features of interest appear to ride on a broadband background continuum. These findings closely agree with observations of type-I bursts present against a continuum emission, giving rise to the speculation that these features might be weak type-I bursts. These results would then support the theory proposed by Benz & Wentzel (1981) and Spicer et al. (1982), which describes type-I bursts as observational signatures of scattered small-scale energy release events in the solar corona. The very electrons accelerated in such small magnetic reconnection events might give rise to the broadband background continuum (Benz & Wentzel 1981). Investigations of type-I bursts in the 160–320 MHz frequency band by De Groot et al. (1976) suggest an average frequency drift rate of −10 MHz s⁻¹ for type-I bursts. The small-scale features detected in the MWA DS appear as vertical streaks with no perceptible frequency drift. However, they might possess small frequency drifts that cannot be measured at the time resolution of the MWA data.

Figure 14 shows a 2D histogram of their peak flux densities and the background flux density at their peak frequency. The dashed and solid black lines in Figure 14 depict trends in the first quartile and third quartile, respectively, in the distribution of peak flux densities as a function of the background flux density. The 25th percentile of the distribution of peak fluxes increases from 0.76 SFU at a background flux of 2 SFU to 10.18 SFU at 38 SFU background flux. Similarly, the 75th percentile increases from 1.59 SFU to 44.39 SFU over the same range of background flux densities. This demonstrates a tendency for an increase in feature peak flux density with an increase in background flux density. Note that we are limited by statistics at background flux estimates greater than 38 SFU.

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As shown in Figure 12, the background flux density at any frequency varies by a factor of ∼2. Such large variations are seen over timescales as short as 30 minutes and are not likely to reflect changes in thermal emission from the 10⁶ K coronal plasma. The observed increase in the peak flux of the features with increase in background flux density suggests the possibility that this enhanced background continuum could arise from a superposition of a large number of features that remain unresolved at the time resolution of these data. Observations of such small-scale features with finer time resolution are required to understand them better.

Gergely & Kundu (1975) and Duncan (1981) find close similarities between sources of type-I bursts and that of decametric type-III bursts. Benz & Wentzel (1981) claim that electrons accelerated at magnetic reconnection sites, if trapped along closed field lines, produce type-I bursts and their associated continuum. If untrapped, these electrons propagate along open field lines and produce type-III storm bursts. Assuming a type-III-like emission mechanism for the small-scale features observed in the MWA data, we arrive at a one-to-one correspondence between their peak frequencies and the electron densities at their heights of production in the solar corona. We assume a 4× Newkirk (1961) density profile in the solar corona in order to translate from electron densities (Li et al. 2009) into heights (h) in the solar corona. Having computed ν_start, Δν and Δt for every feature, we can also determine a height band (Δh) and a propagation speed (v = Δh/Δt) for every feature. Assuming emission at the local plasma frequency, we find that the features of interest mostly possess propagation speeds of about (0.01–0.04)c and arise in the solar corona from within a narrow band ${\rm{\Delta }}h\approx (0.01\mbox{--}0.03){R}_{\odot }$ centered at $h\approx (0.20\mbox{--}0.50){R}_{\odot }$ above the photosphere. The typical electron speeds drop steadily with frequency, decreasing from (0.02–0.07)c at 120 MHz to (0.01–0.03)c at 220 MHz. These values are much lower than the speed of 0.33c reported for type-III bursts in the lower corona, however. As we are unable to discern any spectral drift in these features from the data, the speeds determined here are lower limits to their true speeds.

The growth and decay timescales of type-III bursts provide interesting diagnostics for the physical processes involved in their production (Reid & Ratcliffe 2014). For the small-scale features observed in the MWA DS, the mean and median values of the growth and decay timescales ( ∼ 1.5 s) are not found to be significantly different, although we note that they are likely temporally undersampled by the time resolution of these data.