A Flare-type IV Burst Event from Proxima Centauri and Implications for Space Weather

Solar type II, type III, and type IV bursts have the following characteristics and interpretations: type II bursts last several minutes and exhibit a relatively slow drift from high to low frequencies, and are produced by CME shock fronts or flare blast waves propagating outward through the corona—see Cairns et al. (2003) and Cairns (2011) for a review of type II bursts in the context of solar system shocks. There have been several efforts toward detecting stellar type II bursts, with no positive detections (Crosley et al. 2016; Crosley & Osten 2018a, 2018b; Villadsen & Hallinan 2019). Type III bursts are short-lived (∼0.1 s), rapidly drifting bursts driven by relativistic electron beams escaping from the corona along open magnetic field lines—see (Reid & Ratcliffe 2014) for a review. Type IV bursts are long-duration bursts that occur during and after the decay phase of large flares (Takakura 1963), and are thought to be driven by continuous injection of energetic electrons into post-flare magnetic structures following CMEs (Cliver et al. 2011; Salas-Matamoros & Klein 2020). We do not expand upon solar type I and type V bursts here as they are not relevant to space weather studies (White 2007), but refer the reader to texts such as Kundu (1965) and Wild et al. (1963) for overviews and detailed definitions of solar radio bursts and other emissions.

Type IV bursts are particularly important in solar space weather studies, because they are associated with space weather events such as CMEs and solar energetic particle (SEP) events, and because they indicate ongoing electron acceleration following large flares (e.g., Kahler & Hundhausen 1992). For example, Robinson (1986) argued that CMEs are a necessary condition for the generation of type IV bursts, and Cane & Reames (1988a) also argued that type IV bursts occur with CMEs, which also explains their association with SEPs (Kahler 1982). Cane & Reames (1988b) found that 88% of type IV bursts are associated with type II bursts, with almost all interplanetary type II bursts associated with CMEs (Cairns et al. 2003). In addition, solar type II and type IV bursts are strongly associated with Hα flares (Cane & Reames 1988b). Type IV bursts show a wide range of features, and consist of several subclasses (Pick 1986). Of particular interest here are the "decimetric type IV bursts" (type IVdm) (Benz & Tarnstrom 1976), which have a frequency range spanning ∼200–2000 MHz (Cliver et al. 2011), covering the frequency range accessible with current low and mid-frequency radio facilities. These bursts have long delays (>30 minutes) from the microwave continuum emission peak, and are composed of several subcomponents lasting tens of minutes to several hours (Pick 1986). The early component is often complex, showing a variety of frequency drifts (Takakura 1967). In addition, they often exhibit high degrees of circular polarization (up to 100%), fractional bandwidths Δν/ν ∼ 0.1–1 (Benz & Tarnstrom 1976; Cliver et al. 2011), and intensities reaching up to 10⁶ sfu (10¹⁰ Jy), making them among the most intense solar radio bursts recorded (Cliver et al. 2011). The associated brightness temperatures are very high (between 10⁸ K and 10¹⁵ K), with brightness temperatures in excess of 10¹² K requiring a coherent mechanism (Kellermann & Pauliny-Toth 1969). At the lower range of brightness temperatures (≲10¹¹ K) additional properties such as narrow spectral features and high degrees of circular polarization may indicate a coherent emission mechanism, though incoherent gyrosynchrotron emission is regularly invoked for bursts at this lower range of brightness temperatures lacking these indicators of coherence (Morosan et al. 2019). If the bursts exhibit a frequency drift, it is usually small (drift rates $| \dot{\nu }| \leqslant 100$ kHz s⁻¹), and may indicate a gradually expanding source region with decreasing magnetic field strength and/or plasma density (Takakura 1963).

The detection of solar-like radio bursts holds great potential for understanding coronal particle acceleration processes in M-dwarf flares, and for diagnosing the space weather environment around these stars. For example, solar type IV bursts are associated with space weather events such as CMEs and SEP events (Robinson 1986; Cane & Reames 1988b; Salas-Matamoros & Klein 2020), and probe ongoing electron acceleration in magnetic structures following large flares (Wild et al. 1963; Cliver et al. 2011; Salas-Matamoros & Klein 2020).

However, there have been few unambiguous identifications of solar-like low-frequency bursts from M-dwarfs or other stellar systems to date. Kahler et al. (1982) detected a strong radio burst from the dM4.0e star YZ Canis Minoris in time-series data with the Jodrell Bank interferometer at 408 MHz, beginning ∼17 minutes after flaring activity in optical and X-ray wave bands. Owing to the delayed onset of the burst, Kahler et al. (1982) identified this radio event as a type IV burst. Other early low-frequency detections were made with time-series data from single-dish telescopes, making them susceptible to terrestrial interference (Bastian 1990; Bastian et al. 1990). For example, Spangler & Moffett (1976) and Lovell (1969) detected several M-dwarf radio bursts with intensities ranging from hundreds of millijansky to several jansky, coincident with optical flaring activity. However, low-frequency interferometric observations of active M-dwarfs have struggled to detect bursts of similar intensities or at similar rates as recorded in early single-dish observations (Davis et al. 1978; Lynch et al. 2017; Villadsen & Hallinan 2019), casting doubt on the reliability of these early detections. A recent exception to this trend of faint, low-duty cycle bursts at low radio frequencies is the detection of a 5.9 Jy burst from dM4e star AD Leonis at 73.5 MHz reported by Davis et al. (2020). Although the signal-to-noise ratio of this detection is fairly low, future interferometric detections at these very low frequencies (<100 MHz) may provide some validation for early single-dish detections.

Coherent radio bursts from M-dwarfs detected with modern interferometric facilities have shown properties at odds with solar observations. Foremost, the majority of observations show poor association between radio bursts and multiwavelength flaring activity (Haisch et al. 1981; Kundu et al. 1988; Bastian 1990; Crosley & Osten 2018a), with the exception of the results from Kahler et al. (1982) described above. Another key contrast is that there have been no morphological classifications of solar-like radio bursts to date, although some stellar radio bursts have shown spectro-temporal features consistent with solar radio bursts—e.g., "sudden reductions" or "quasiperiodic pulsations" (Bastian et al. 1990). A final point of difference is that coherent radio bursts from M-dwarfs consistently exhibit high degrees of circular polarization (f_C ∼ 50%–100%; Villadsen & Hallinan 2019), whereas only some solar radio bursts, such as type I, type IV, and decimetric spike bursts, are highly polarized (Kai 1962, 1965; Aschwanden 1986)—other solar radio bursts exhibit only mild degrees of polarization.

These differences have hampered efforts to understand M-dwarf radio activity based on our more complete understanding of the Sun (Villadsen & Hallinan 2019). In addition, recent studies have shown that the low-frequency variability of active (Zic et al. 2019) and inactive (Vedantham et al. 2020) M-dwarfs may arise from auroral processes in their magnetospheres. These phenomena are driven by ongoing field-aligned currents in the strong, large-scale magnetic field of the star, rather than flaring activity associated with localized active regions. This suggests that in general, the physical driver of many low-frequency radio bursts from M-dwarfs may be decoupled from the flares probed by optical and X-ray wave bands—in stark contrast to the Sun.

In this article, we report the detection of several radio bursts from Proxima Centauri (hereafter Proxima Cen) associated with a large optical flare. In Section 2, we detail the multiwavelength observations and data reduction. In Section 3, we describe the detections of the flare and radio bursts. We discuss these detections in light of the solar paradigm, and possible implications for space weather around Proxima Cen. In Section 4, we summarize our findings.

NASA's TESS (Ricker et al. 2015) observed Proxima Cen during the period of 2019 April–May in its Sector 11 observing run. Observations were taken through the broad red bandpass spanning 5813–11159 Å on the TESS instrument (the TESS band). We downloaded the calibrated TESS light curves for Proxima Cen from the Mikulski Archive for Space Telescopes.¹³ Light curves are available in a Simple Aperture Photometry (SAP) or Pre-search Data Conditioning Simple Aperture Photometry (PDCSAP) formats. Because PDCSAP light curves are optimized to detect transit and eclipse signals, and remove other low-level variability that may be astrophysical in origin, we opted instead to use the SAP light curve. We normalized the SAP light curve by dividing by the median value long after the flare decay (MBJD 58605.6–58605.7).

The Zadko Telescope (Coward et al. 2017) is a 1 m f/4 Cassegrain telescope situated in Western Australia. For this campaign, its main instrument, an Andor IkonL camera, was replaced by a MicroLine ML50100 camera from Finger Lakes Instrumentation. The new camera allowed for a faster readout and thus a better temporal resolution of the light curve. The CCD is 8k × 6k, but we used it with a binning of 2 × 2 to increase the signal-to-noise ratio, giving a pixel scale of 1.39'' pixel⁻¹.

We used the Sloan g' filter (spanning 3885–5640 Å) for the observations, which started as soon as possible after dusk, and lasted until Proxima Cen was too low on the horizon to safely operate the telescope. Each image was taken with a 10 s exposure, and needed 13.32 s for the readout and preparation of the next exposure. Thus, our observation cadence for that night was about 23.3 s. We took 20 bias and dark frames prior to the beginning of observations for calibration. During the observation night the conditions were good, with no visible clouds on the images. The stable temperature and calm wind allowed for fair observations.

We applied standard photometric data reduction procedures using ccdproc (Craig et al. 2015). Twenty 10 s dark exposures were bias corrected and median combined to remove effects of cosmic rays in the calibration frame. Bias and dark correction were applied to 180 s flat-field exposures taken several nights after the observing campaign, and these flat-field frames were median combined. Raw target exposures were dark and bias corrected, and the corrected flat-field image was used to correct for spatial variations in the CCD sensitivity. Images were aligned using astroalign (Beroiz et al. 2020) to correct for slight drifts in the telescope pointing throughout the night. We used SExtractor (Bertin & Arnouts 1996) to perform aperture photometry on Proxima Cen and nearby reference stars using a 12 pixel diameter (16.7'') aperture. We corrected the raw Proxima Cen light curve for systematic variations in flux over the course of the night by median normalizing the raw light curves of nearby neighboring stars around Proxima Cen, with similar colors (Gaia B_p − R_p > 2; B_p − R_p = 3.796 for Proxima Cen). We median combined these normalized light curves to produce a systematic reference light curve, and divided the Proxima Cen light curve by the systematic trend to produce a corrected light curve. Finally, we divided the Proxima Cen light curve by its median post-flare (MBJD 58605.6–58605.7) value to produce a light curve in relative intensity.

We performed time-resolved spectroscopy with the Wide-Field Spectrograph (WiFeS) on board the ANU 2.3 m Telescope at Siding Spring Observatory (Dopita et al. 2007). WiFeS is an integral-field spectrograph that uses an image slicer with 25 1'' × 38'' slitlets, resulting in a field of view of 25'' × 38''. Conditions at the observatory on 2019 May 2 were poor, resulting in high levels of cloud absorption and intermittent observational coverage during rainy periods. Seeing varied between 1.3'' and 2.0''. We took spectra with the U7000 and R7000 gratings in the blue and red arms of the instrument, respectively, using the RT480 dichroic. We took 90 s exposures of Proxima Cen using half-frame exposures, which resulted in a faster readout time of ∼30 s, and resulted in a reduced field of view of 12.5'' × 38''. The corresponding wavelength ranges after calibration were 3500–4355 Å and 5400–7000 Å, at a resolution of R ∼ 7000.

For the calibration, we took bias, internal flat field (with a Quartz-Iodine lamp), wire, and arc frames (with a neon-argon lamp), using 5 × 5 s exposures for the red arm and 5 × 90 s exposures for the blue arm where appropriate. We took 3 × 90 s exposures of the standard star LTT4364 to calibrate for the bandpass response across wavelength for each grating.

We used the PyWiFeS pipeline (Childress et al. 2014) to derive and apply calibrations to each exposure. To summarize the PyWiFeS calibration process, we performed overscan subtraction, bad pixel repair and cosmic ray rejection, and co-addition of bias frames, which we then subtracted from science frames. We co-added the internal flat-field frames, and derived wavelength and spatial (y-axis) zero-point solutions using the arc and wire frames respectively. To derive the spectral flat-field response, we used the wavelength solution and the co-added flat-field frames, and applied the derived flat-field correction to each sky exposure. To derive the bandpass sensitivity response and flux scale, we extracted the spectrum of the standard star LTT4364 from a rectified (x, y, λ) grid, and determined the corrections by comparing the extracted spectrum to a spectro-photometrically calibrated reference spectrum. We applied the flux and bandpass corrections to each of the corrected Proxima Cen data cubes, before converting the telescope-frame (x, y, λ) cubes to the sky frame (α, δ, λ), where α, δ denote J2000 R.A. and decl., respectively. To preserve the temporal resolution of our observation, we did not co-add any of the Proxima Cen exposures during the data reduction process. We extracted sky-subtracted spectra from the final calibrated spectral cubes using a custom script adapted from the internal PyWiFeS code.

Due to cloudy conditions, accurately determining the continuum and line fluxes was not possible. We divided each exposure with the R7000 grating by the median value between 6000 and 6030 Å, selected because it was free of any prominent emission or absorption features that may vary significantly with flaring activity. Prominent [O i] sky lines could not be readily subtracted due to the cloudy conditions. Similarly, we divided each exposure with the U7000 grating by the median value between 4150 and 4300 Å. However, significantly higher cloud absorption in the 3500–4355 Å U7000 band, and the intrinsically lower flux of Proxima Cen in this band means that the continuum estimates are even more uncertain than the R7000 band.

We used the specutils package¹⁴ to measure line equivalent widths in the extracted calibrated spectra.

We observed Proxima Cen with ASKAP (McConnell et al. 2016) on 2019 May 2 09:00 UTC (scheduling block 8612) for 14 hr with 34 antennas, a central frequency of 888 MHz with a 288 MHz bandwidth, 1 MHz channels, and 10 s integrations. We observed the primary calibrator PKS B1934−638 for 30 minutes (scheduling block 8614) immediately following the Proxima Cen observation. To calibrate the frequency-dependent XY-phase, an external noise source (the "on-dish calibrator" system) was employed on each of the ASKAP antennas. This system measures the XY-phase of each dual-polarization pair of phased-array feed beams, and adjusts the phase of the Y-polarization beamformer weights so that the XY-phase approaches zero. Further details of the ASKAP on-dish calibration system are provided in Chippendale & Anderson (2019) and Hotan et al. (2020).

We reduced the data using the Common Astronomy Software Applications (casa) package version 5.3.0–143 (McMullin et al. 2007). We used PKS B1934−638 to calibrate the flux scale, the instrumental bandpass, and polarization leakage. We performed basic flagging to remove radio-frequency interference that affected approximately 20% of the data, primarily from known mobile phone bands.

We used a mask excluding a 4' square region centered on Proxima Cen to allow modeling of the field sources without removing the time- and frequency-dependent effects of Proxima Cen. The large exclusion window around the target also ensured that the flux density present in strong point spread function (PSF) sidelobes during burst events were not modeled as point sources and removed during deconvolution, ensuring that its total flux density was preserved. We used the task tclean to perform deconvolution with a Briggs weighting and a robustness of 0.0. We used the mtmfs algorithm (with scales of 0, 5, 15, 50, and 150 pixels and a cell size of 2.5'') to account for complex field sources, and used two Taylor terms to model sources with non-flat spectra. We imaged a 6000 × 6000 pixel field (250' × 250') to include the full primary beam and first null, and deconvolved to a residual of ∼3 mJy beam⁻¹ to minimize PSF side-lobe confusion at the location of Proxima Cen. We subtracted the field model from the visibilities with the task uvsub, and vector-averaged all baselines greater than 200 m to generate the dynamic spectra for each of the instrumental polarizations. We show a deconvolved image of the full 250' field over the 14 hr ASKAP observation in Figure 1.

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We formed dynamic spectra for the four Stokes parameters (I, Q, U, V) following Zic et al. (2019), such that they were consistent with the IAU convention of polarization. To improve the signal-to-noise ratio in the dynamic spectra, we averaged the Stokes I and V products by a factor of 3 in frequency to produce final dynamic spectra with a resolution of 3 MHz in frequency and 10 s in time. Similarly, we averaged the Stokes Q and U dynamic spectra by a factor of 6 in frequency, giving these products a resolution of 6 MHz in frequency and 10 s in time. We produced radio light curves by averaging the dynamic spectra across frequency. The rms sensitivity of our dynamic spectra is 12 mJy for Stokes I, and 11 mJy for Stokes Q, U, and V, calculated by taking the standard deviation of the imaginary component of the dynamic spectra visibilities. In a similar way, we calculated the rms sensitivity of the light curves, finding 1.4 mJy for Stokes I and 1.1 mJy for Stokes Q, U, and V.

We present the photometric light curves in the bottom panel of Figure 2. These observations show the large, long-duration flare on MBJD 58605, which had a duration of approximately 1 hr.

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We determined the radiated flare energy as follows. The flare energy E_f,p through a photometric passband p is given by E_f,p = ED × L_p, where ED is the "equivalent duration" of the flare, and L_p is the total quiescent luminosity of the star in passband p. The equivalent duration is given by

$$\begin{eqnarray}&&\mathrm{ED}={\int }_{{t}_{0}}^{{t}_{1}}\left(\displaystyle \frac{{I}_{f}(t)-{I}_{0}}{{I}_{0}}\right){dt},\end{eqnarray} \tag{ 1 }$$

which we evaluate using Simpson's rule. Here, t₀ and t₁ are the start and end times of the flare, estimated by visual inspection of the light curve, I_f(t) is the intensity of the flare as a function of time, and I₀ is the median quiescent intensity. To compute the quiescent luminosity of the star, we obtained the flux-calibrated spectrum of Proxima Cen presented in Ribas et al. (2017), multiplying by 4πd² to obtain the spectral luminosity L_λ. We estimate the total quiescent luminosity through passband p as L_p ≈ 〈L_λ,p〉Δλ_p, where 〈L_λ,p〉 is the mean quiescent spectral luminosity in passband p, and Δλ_p is the bandwidth of passband p. We evaluated the mean quiescent spectral luminosity using

$$\begin{eqnarray}&&\langle {L}_{\lambda ,p}\rangle =\displaystyle \frac{{\int }_{0}^{\infty }{L}_{\lambda }{T}_{p}(\lambda )\lambda d\lambda }{{\int }_{0}^{\infty }{T}_{p}(\lambda )\lambda d\lambda },\end{eqnarray} \tag{ 2 }$$

where T_p(λ) is the filter transmission curve for passband p. This quantity is independent of any global scaling factors of the transmission curve, enabling a more reliable estimate of the total quiescent luminosity through passband p. To measure the the bandwidth Δλ_p, we computed the equivalent rectangular width,

$$\begin{eqnarray}&&W=\displaystyle \frac{{\int }_{0}^{\infty }{T}_{p}(\lambda )d\lambda }{\max ({T}_{p}(\lambda ))},\end{eqnarray} \tag{ 3 }$$

which is the width of a rectangle of height 1 and area equal to the total area beneath the filter transmission curve T_p(λ). Applying these calculations to the TESS and Sloan g' passbands, we obtain quiescent luminosities of 1.1 × 10³⁰ erg s⁻¹ and 2.3 × 10²⁸ erg s⁻¹ respectively. TESS observations cover the full duration of the flare, albeit with relatively low temporal resolution (2 minute cadence), enabling us to compute a TESS-band flare equivalent duration of 31.2 ± 0.3 s, yielding a TESS-band flare energy E_f,TESS = 3.38 ± 0.03 × 10³¹ erg. To estimate the bolometric flare energy, we follow Osten & Wolk (2015) and adopt a 9000 K flare blackbody profile, and evaluate the fraction of energy radiated within the TESS and Sloan g' passbands, respectively, finding E_f,TESS/E_bol = 0.21 and ${E}_{f,{g}^{{\prime} }}/{E}_{\mathrm{bol}}=0.22$. Using the TESS observation, which covers the full duration of the flare, we calculate a bolometric flare energy of 1.64 ± 0.01 × 10³² erg. We note that the quoted uncertainties in this section are statistical only, and factors such as the light-curve normalization, accurate determination of quiescent luminosity, and choice of flare blackbody temperature introduce systematic uncertainties, which we estimate contribute to errors on the order of 10% of the quoted values.

The 2 minute cadence of the TESS light curve undersamples the impulsive rise phase of the flare. To obtain a more informed estimate of the flare onset time, we modeled the temporal morphology of the flare using the following piecewise model, adapted from the empirical flare template presented in Davenport et al. (2014):

$$\begin{eqnarray}&&{\rm{\Delta }}I=\displaystyle \frac{{I}_{f}-{I}_{0}}{{I}_{0}}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}=\,A\times \left\{\begin{array}{ll}{A}_{0}^{(t-{t}_{p})/({t}_{0}-{t}_{p})} & t\lt {t}_{p}\\ (1.0-{A}_{g}){e}^{(t-{t}_{p})/{\tau }_{i}} & \\ +{A}_{g}{e}^{(t-{t}_{p})/{\tau }_{g}} & t\geqslant {t}_{p}\end{array}\right.,\end{eqnarray} \tag{ 5 }$$

where A is the peak fractional amplitude above quiescence, t_p is a the time at flare peak relative to the ASKAP observation start time MBJD 58605.38154, A₀ is the relative pre-flare amplitude in the last TESS exposure at a set time MBJD t₀ = 58605.44678 (93.94 minutes after the beginning of the ASKAP observation at MBJD 58604.38154), τ_i is the impulsive decay timescale, and A_g and τ_g are the gradual decay amplitude and timescales. We model the impulsive rise with an exponential rather than the quartic model of Davenport et al. (2014) to reduce the number of free parameters to determine from the low-resolution TESS light curve. We used emcee to estimate the parameters and sample their posterior probability distributions, first evaluating each candidate model on a high-resolution time grid before resampling the candidate model onto the lower-resolution (2 minute cadence) TESS time series. We set uniform priors on each parameter, constraining A₀ > 0, τ_i, τ_g < 0, and A > 0.03. The resulting central parameter estimates and 64% confidence limits are as follows: ${t}_{p}={96.61}_{-0.17}^{+0.23}$ minutes, $A={0.26}_{-0.08}^{+0.19}$, ${A}_{0}={2.2}_{-1.3}^{+1.9}\times {10}^{-3}$, ${A}_{g}={0.13}_{-0.05}^{+0.06}$, τ_g = −12.6 ± 0.2 minutes, and τ_i = −0.5 ± 0.2 minutes. The best-fitting model is shown in Figure 3, alongside the photometric light curve from TESS and the radio light curve from ASKAP.

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Spectroscopic monitoring with the WiFeS on board the ANU 2.3 m Telescope (Dopita et al. 2007) shows broadening and intensification of the Balmer lines, and the appearance of other chromospheric emission lines (e.g., He I λλ4026, 5876, 6678 Å) during this flare (Figures 4 and 5). This indicates substantial energy deposition by accelerated particles into the stellar chromosphere. Unfortunately, these observations were affected by poor weather, making it difficult to reliably detect variability in chromospheric emission line strength over the whole night. Along with the appearance of higher-order Balmer lines (up to H14 λ 3721 Å), Figure 5 also shows a continuum enhancement toward the blue end of the spectrum. Figure 2 shows that the equivalent width of the Hα line is well correlated with the gradual decay of the flare continuum, consistent with previous observational results (e.g., Hawley & Pettersen 1991).

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Observations with ASKAP (McConnell et al. 2016) centered at 888 MHz show three successive bursts, which we denote as ASKAP Bursts 1, 2, and 3 (AB1, AB2, and AB3, respectively). Figure 2 shows the total intensity (Stokes I) dynamic spectrum and full-Stokes light curves in their multiwavelength context, and the full-Stokes dynamic spectra of the bursts are shown in Figures 6 and 7. Figure 1 shows two 10 s snapshot images, taken 20 s prior to (bottom left) and at the peak of AB1 (bottom right). Table 1 summarizes the important burst properties. The important observational characteristics of these bursts include high flux densities (peak flux density >100 mJy, high degree of circular polarization (∣V/I∣ > 50%), presence of moderate degrees of linear polarization for AB1 and AB2 (∼40%), and narrow-band and sharp-cutoff spectral features. To measure fractional polarizations, we masked insignificant values (signal-to-noise ratio <1) in the dynamic spectra for each Stokes parameter, before averaging over frequency and taking quadrature sums where relevant. This mitigated positive biases toward the fractional polarization due to the Ricean statistics of quadrature-summed signals.

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Table 1.  Properties of the Radio Bursts

Label	t + MBJD 58605	Δt	Speak	Tb,peak a	fL	fC	fP	$\dot{\nu }$
	(days)	(minutes)	(mJy)	( × 1011 K)	(%)	(%)	(%)	(MHz s−1)
AB1	0.4466	1.3	142.4 ± 1.4	2.93 ± 0.03	36.5 ± 1.1	−52.1 ± 1.3	57.1 ± 1.4	−4.70 ± 0.66
AB2	0.4715	119	24.7 ± 1.4	0.51 ± 0.02	43.3 ± 0.4	87.4 ± 0.8	98.5 ± 1.0	Complexb
AB3	0.5652	354	41.0 ± 1.4	0.84 ± 0.02	<9c	91 ± 4	91 ± 4	5.9 ± 0.3 × 10−3

Notes. Columns, from left to right: burst label, start time, duration, peak flux density, brightness temperature; fractional linear polarization; circular polarization, and total polarization, and frequency drift rate. To avoid positive biases due to Ricean statistics, fractional polarizations were measured by masking out insignificant values (signal-to-noise ratio <1) in the dynamic spectra, before averaging over frequency and taking the quadrature sum where relevant.

^aThis is a lower limit owing to the conservatively large size of the emission region used. ^bAB2 exhibits reversals in its drift direction, preventing simple characterization with a linear drift rate. ^cSome linear polarization is evident at the beginning of AB3. However, this is likely to be from the overlapping tail end of AB2.

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To measure the drift rate of ASKAP Bursts 1 and 3 (AB1 and AB3), we measured a characteristic frequency of the burst for each temporal integration. We fit the time-frequency ordinate pairs with a linear model, using emcee (Foreman-Mackey et al. 2013) to estimate the slope and intercept parameters. AB1 is broad band, and its lower spectral cutoff is below the frequency range of the observations. For this reason, we measured the upper frequency cutoff (defined as the highest frequency where the intensity exceeds a 6σ threshold of 71 mJy), and took this as the characteristic frequency. The slope in the upper frequency cutoff of AB1 is evident in Figure 6. For AB3, we took the frequency of maximum flux density for each integration as the characteristic burst frequency, since the drifting component of AB3 is contained within the bandwidth of our observation. The derived drift rates are −4.7 ± 0.7 MHz s⁻¹ for AB1 and −7.0 ± 0.2 kHz s⁻¹ for AB3.

The brightness temperature is an important diagnostic of the emission mechanism, with very high brightness temperatures indicating a coherent emission process. Conservatively assuming a source size equal to the size of the full stellar disk (R_* = 0.146R_⊙; Ribas et al. 2017), we can calculate a lower limit on the brightness temperature using Equation (14) from Dulk (1985). The lower limits on the brightness temperature for each burst are given in Table 1, and lie within the range of 10¹⁰–10¹¹ K. Due to the high brightness temperatures, the high degrees of polarization (up to 100%), and the spectral structure of the bursts (including narrow-band features and sharp frequency cutoffs), coherent emission is strongly favored. In the context of stellar radio emission, the most plausible coherent emission mechanisms are the electron cyclotron maser instability (ECMI), or plasma emission (Dulk 1985; Melrose 2017).

In the case of AB3, assuming that the drifting component with bandwidth Δν ≈ 120 MHz arises from a single ECMI source, we can estimate the length of the emitting region L_s as L_s ≈ L_BΔν/ν, where L_B = ∣B/∇B∣ is the magnetic scale height, taken to be close to the stellar radius (i.e., ∼1 × 10¹⁰ cm). For Δν = 120 MHz, ν = 950 MHz, we obtain a source length of 1.3 × 10⁹ cm. Using this as the characteristic source size, we obtain brightness temperatures in the range of 10¹³–10¹⁴ K, confirming the need for a coherent emission mechanism.

AB1 and AB2 also exhibit elliptical polarization, as can be seen in Figures 6 and 7. Possible interpretations of its origin include intrinsically elliptically polarized emission arising from a strongly rarefied duct (Melrose & Dulk 1991; Zic et al. 2019); or coupling of the extraordinary and ordinary magneto-ionic modes as the radiation traverses an inhomogeneous quasi-transverse region (Kai 1963). In the former case, only the ECMI can be responsible for the emission, while in the latter case both fundamental plasma emission or ECMI emission are plausible emission mechanisms. While both mechanisms are plausible, reversals in the frequency drift of AB2 and the lower frequency cutoff of AB3 can be more readily explained by the modulation and/or geometrical beaming effects of the ECMI mechanism, whereas plasma emission would require upward and downward motion and/or density fluctuations of an excited plasma region.

The properties of AB2 and AB3, which make up the type IV burst, can be used to infer properties of the associated post-eruptive loop system. The ∼40% degree of linear polarization in AB2 implies a strongly under-dense source region, since Faraday rotation effects, such as differential Faraday rotation and bandwidth depolarization, should be strong in a dense and highly magnetized stellar corona (Melrose & Dulk 1991; Sokoloff et al. 1998). Melrose & Dulk (1991) considered the elliptical polarization of Jovian decametric radio emission (Boudjada & Lecacheux 1991; Lecacheux et al. 1991), and argued that for the elliptical polarization to be preserved along the propagation path, mode coupling around the emission region, and along the propagation must be weak. This leads to a condition on the electron density,

$$\begin{eqnarray}&&{n}_{e}\lesssim \alpha (\nu /25\,\mathrm{MHz}),\end{eqnarray} \tag{ 6 }$$

where α is a geometrical factor of order unity, which we take to be 1. Using this, we compute an electron density upper limit of ∼30 cm⁻³, corresponding to our lowest observing frequency ν = 744 MHz. This limit is derived based on the emission angle relative to the magnetic field θ satisfying ${\cos }^{2}(\theta )\ll 1$, along with assumptions that ${\nu }_{p}^{2}/{\nu }^{2}\ll 1$ and ${\nu }_{p}^{2}\sin (\theta )/2{\nu }^{2}\ll 1-{\nu }_{c}/\nu \ll 1$ close to the emission region, and ${\nu }_{p}^{2}/{\nu }^{2}\ll 1$ and ν_c/ν ≪ 1 more than about one magnetic scale length from the emission region (Melrose & Dulk 1991). The emission frequency for ECMI is close to the local electron cyclotron frequency ν_c = eB/m_ec ≈ 2.8B MHz, or its second harmonic. Assuming first harmonic emission, ECMI radiation in the ASKAP band (744–1031 MHz) corresponds to local magnetic field strengths ranging from ∼270–370 G. The low plasma density inferred from the elliptical polarization implies a local plasma frequency ν_p ≤ 100 kHz, a factor of at least ∼1000 lower than the local electron cyclotron frequency. These properties satisfy the condition ν_p/ν_c ≪ 1 for operation of the ECMI (Melrose & Dulk 1982).

Using the observed frequencies of the emission, we can estimate the vertical extent of the post-eruptive loop system. The average surface magnetic field of Proxima Cen is 600 ± 150 G (Reiners & Basri 2008). Considering that the magnetic field strength in active regions may be substantially stronger, we use a range of basal magnetic field strengths from 600–1600 G. Assuming (1) that the ECMI-emitting region fills a fraction between 0.1 and 0.5 of the length active loop (consistent with the fractional bandwidth of the bursts) from the footpoints, (2) an upper frequency cutoff for AB3 of ∼1200 MHz, and (3) a dipolar loop geometry (so that B(r) ∝ r⁻³), we estimate loop sizes from ∼0.3–1.0 stellar radii (∼0.3–1.0 × 10¹⁰ cm).

To compute the probability that the optical flare and AB1 are temporally aligned by chance coincidence, we followed the approach of Osten et al. (2005). We assume the probability distribution function of observing N flares occurring at a rate λ within a time interval Δt is

$$\begin{eqnarray}&&P{(N| \lambda ,{\rm{\Delta }}t)={e}^{-\lambda {\rm{\Delta }}t}(\lambda {\rm{\Delta }}t)}^{N}/N!\,.\end{eqnarray} \tag{ 7 }$$

If two flare events in disparate wave bands are independent, then the probability of observing both within a time interval τ of each other is just the product of their independent rate probabilities. For the optical flare, using the bolometric flare energy of ∼1.6 × 10³² erg we calculate a rate for flare of this energy and higher of ∼0.04 day⁻¹ using the cumulative flare frequency distribution model from Howard et al. (2018). The burst rate of Proxima Cen at radio frequencies is not well constrained and is likely to be frequency dependent (Villadsen & Hallinan 2019). Given the six bursts observed in 46 hr of observing time with ASKAP, we estimate an ASKAP-band radio burst rate of ∼3 day⁻¹, above a detection threshold of a few millijansky.

Using the flare temporal model described above, we determine that the time at which the flare reaches 1% of its peak intensity is ${94.59}_{-0.27}^{+0.32}$ minutes. Taking this as the flare onset time, we obtain a temporal offset between the peak of AB1 and the flare onset of ${42}_{-17}^{+19}$ s, taking the 10 s ASKAP integration time as the uncertainty around the peak of AB1. Using Equation (7) with a temporal offset of 42 s, we obtain a probability of independent, coincident events of 3.2 × 10⁻⁸, strongly indicating a causal relation. Considering there were four additional lower-energy flares detected by TESS during ASKAP observations (Vida et al. 2019b), and taking the total TESS flare rate of 1.49 day⁻¹ (Vida et al. 2019b), we obtain a conservative trials-factor corrected coincidence probability of 7.8 × 10⁻⁶. This is an overestimation, because the rate of energetic flares such as the one detected on MBJD 58605 is substantially lower than the total flare rate. This represents the first definitive association of an interferometrically detected coherent stellar burst with an optical flare in the literature.

The association of these radio bursts with the large optical flare indicates that they can be interpreted within the paradigm of solar radio bursts, which also are associated with multiwavelength activity. We interpret AB1 as a solar-like decimetric burst or an unresolved group of type III bursts. In the latter interpretation, we note that the measured frequency drift rate of −4.7 ± 0.66 MHz s⁻¹ is not compatible with the positive drift rate of individual type III bursts, and instead may represent the "envelope" of the group of bursts. Solar observations show that both decimetric spike and type II bursts are often associated with hard X-ray bursts (Stewart 1978; Trottet 1986). The occurrence of AB1 prior to the impulsive phase of the flare (see Figure 3) suggests that particle acceleration was already ongoing during this early time (Trottet 1986). This is consistent with the findings of Kundu et al. (2006), who detected decimetric bursts similar to AB1 prior to the impulsive phase of a flare, which occurred high above the impulsive flare energy release site. They suggested that these decimetric bursts indicate a destabilization of the upper coronal magnetic field, which may be connected in some way to the flare energy release in the lower corona.

The onset of AB2 is 35 minutes after the flare impulsive peak, and occurs during the gradual decay phase of the flare. This burst lasts for 119 minutes and has a complex morphology, exhibiting a variety of both positive and negative drift components. These details of AB2 are consistent with the ∼30 minute delays from solar flare peaks of the type IVdm bursts studied in Cliver et al. (2011), and of the complex early component of type IVdm bursts described in Takakura (1967). AB2 is also elliptically polarized, a property also exhibited by some type IV bursts (Kai 1963).

The radio light curves in Figure 2 show that AB3 either directly follows, or temporally overlaps with AB2, and shares the same handedness of circular polarization. This suggests that they are two components of the same event, and are likely to originate from the same region in the stellar corona. The fractional bandwidth Δν/ν ranges from 0.1–0.3, although the upper frequency cutoff is not within the ASKAP frequency range at the early stages of the burst, so the upper limit may be higher. The burst is up to 100% circularly polarized, and exhibits a gradual drift of −7.0 ± 0.2 kHz s⁻¹ over its 353 minute duration. These properties are again consistent with solar type IV bursts, which display high degrees of circular polarization (up to 100%), high brightness temperatures (∼10¹¹ K; Cliver et al. 2011), and can show relatively modest fractional bandwidths (Benz & Tarnstrom 1976). The long-duration, slowly drifting morphology of the event also closely resembles other type IVdm events from the Sun (e.g., see Figure 5(a) from Cliver et al. 2011 or Figure 4(d) from Takakura 1963).

The properties of AB2 and AB3 together, and their association with the 1.6 × 10³² erg optical/Hα flare, identify this radio event as a type IV burst. Our detection of this event with full-Stokes dynamic spectroscopy along with the suite of multiwavelength observations make this the most compelling example of a solar-like radio burst from another star to date.

As described in Section 1.1, studies of solar type IV bursts have established that these events are very closely associated with CMEs and SEPs (Robinson 1986; Cane & Reames 1988a, 1988b), and indicate ongoing electron acceleration during magnetic field reconfiguration in the wake of CMEs (e.g., Kahler & Hundhausen 1992). Recently, a systematic study of solar type IV events by Salas-Matamoros & Klein (2020) established that these bursts occur in columnar structures near the extremities of post-eruptive loop arcades, which they ascribe to the magnetic flux rope of the outgoing CME. The association of post-eruptive loop arcades and CMEs with decimetric type IV bursts has also been noted by Cliver et al. (2011)—for example, the 2002 April 21 "HF type IV" burst presented in Kundu et al. (2004) and Cliver et al. (2011) occurred at the same time as the rise of a post-eruptive loop system after an X1.5 flare (Gallagher et al. 2002). Cliver et al. (2011) argued that these bursts may be originate in low-density flux tubes, with a field-aligned potential drop driving ECMI emission. Ultraviolet imaging of the rising post-eruptive loop arcades during the 2002 April 21 event showed the presence of evacuated flux tubes (Gallagher et al. 2002), supporting this claim, and perhaps explaining the existence of small degrees of linear polarization in other solar type IV bursts (Kai 1963; Melrose & Dulk 1991). This picture, developed from multiwavelength observations of solar flares may explain the high degree of circular polarization, presence of linear polarization, and the long duration of the type IV burst from Proxima Cen. Driven by large-scale magnetic field reconfiguration associated with a post-eruptive loop arcade, the type IV burst from Proxima Cen is highly suggestive of a CME leaving the stellar corona (Robinson 1986; Cane & Reames 1988a; Tripathi et al. 2004).

If this type IV burst is indeed associated with a CME, it does not directly probe CME properties, but its exceptional nature indicates that eruptive processes on active M-dwarfs may only be associated with the most powerful flares. This is consistent with numerical simulations of CMEs and associated type II bursts by Alvarado-Gómez et al. (2020), who reported that a simulated CME with a kinetic energy of 1.7 × 10³² erg is weakly confined within a Proxima Cen-like magnetosphere. Applying a solar-like energy partition between the bolometric flare energy and CME kinetic energy (E_K,CME) of E_bol/E_K,CME = 0.3 (Emslie et al. 2012), we estimate a CME kinetic energy of ∼5.5 × 10³² erg for the putative CME indicated by our flare-type IV event. Even with a more conservative energy partition E_bol/E_K,CME = 1 (Osten & Wolk 2015) (resulting in E_K,CME = 1.6 × 10³² erg), these CME kinetic energy estimates closely match or exceed the weak CME confinement scenario explored by Alvarado-Gómez et al. (2020), depending on the flare-CME energy partition.

If energetic flares such as the 1.6 × 10³² erg flare presented here are necessary for eruptive space weather events, then their low rate (∼0.04 day⁻¹; Howard et al. 2018) indicates that the space weather environment around Proxima Cen may be less threatening to planetary habitability than predicted by solar scaling relations (Osten & Wolk 2015). However, without direct evidence for the putative CME and its influence on planetary companions, our inferences on the space weather environment around Proxima Cen also remain indirect.