Detection of 2–4 GHz Continuum Emission from epsilon Eridani

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Published 2020 November 27 © 2020. The American Astronomical Society. All rights reserved.
, , Citation A. Suresh et al 2020 ApJ 904 138 DOI 10.3847/1538-4357/abc004

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0004-637X/904/2/138

Abstract

The nearby star epsilon Eridani has been a frequent target of radio surveys for stellar emission and extraterrestrial intelligence. Using deep 2–4 GHz observations with the Very Large Array, we have uncovered a 29 μJy compact, steady continuum radio source coincident with epsilon Eridani to within 0farcs06 (≲2σ; 0.2 au at the distance of the star). Combining our data with previous high-frequency continuum detections of epsilon Eridani, our observations reveal a spectral turnover at 6 GHz. We ascribe the 2–6 GHz emission to optically thick, thermal gyroresonance radiation from the stellar corona, with thermal free–free opacity likely becoming relevant at frequencies below 1 GHz. The steep spectral index (α ≃ 2) of the 2–6 GHz spectrum strongly disfavors its interpretation as stellar-wind-associated thermal bremsstrahlung (α ≃ 0.6). Attributing the entire observed 2–4 GHz flux density to thermal free–free wind emission, we thus derive a stringent upper limit of 3 × 10−11 M yr−1 on the mass-loss rate from epsilon Eridani. Finally, we report the nondetection of flares in our data above a 5σ threshold of 95 μJy. Together with the optical nondetection of the most recent stellar maximum expected in 2019, our observations postulate a likely evolution of the internal dynamo of epsilon Eridani.

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1. Introduction

Radio surveys of stellar systems have garnered renewed interest in the past two decades, motivated partly by searches for exoplanetary radio emission. Among the targets in early radio searches for extraterrestrial intelligence (Drake 1961; Henry et al. 1995; Tarter 1996) and microwave coronal emission (Gary & Linsky 1981) is epsilon Eridani (hereafter epsilon Eri), a K2V dwarf at a distance of 3.2 pc (Gaia Collaboration et al. 2018). With a mass-loss rate at least 30 times (Wood et al. 2002) that of the Sun, epsilon Eri displays more vigorous chromospheric and coronal activity levels than the present Sun. Properties of epsilon Eri are summarized in Table 1.

Table 1.  Properties of epsilon Eri

Property Value References
Spectral type K2V (1)
Age (Myr) 200–800 (2)
Distance (pc) 3.20 ± 0.03 (3)
Mass (M) 0.83 ± 0.01 (4)
Radius (R) 0.74 ± 0.01 (4)
Effective temperature (K) 5100 ± 16 (4)
Surface magnetic field (G) 186 ± 47 (5)
X-ray luminositya (erg s−1) 1028.5 (6)
Radio luminosityb (erg s−1) 1012 (7)

Notes.

aX-ray luminosity in the 0.2–20 keV band. bRadio luminosity in the 4–8 GHz band.

References. (1) Keenan & McNeil (1989), (2) Mamajek & Hillenbrand (2008), (3) Gaia Collaboration et al. (2018), (4) Bonfanti et al. (2015), (5) Lehmann et al. (2015), (6) Johnson (1981), (7) Bastian et al. (2018).

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epsilon Eri hosts an adolescent (200–800 Myr; Mamajek & Hillenbrand 2008) planetary system that has aroused great scientific interest over the past decades. The confirmed members of this system include a Jovian-mass exoplanet, epsilon Eri b, with a semimajor axis, a ≃ 3.4 au (Hatzes et al. 2000; Mawet et al. 2019), and an outer debris disk (Greaves et al. 2014; Chavez-Dagostino et al. 2016) at a ≃ 64 au. Additional planets (Quillen & Thorndike 2002), warm inner disks at a ∼ 3 au and ∼20 au (Backman et al. 2009), and in situ dust-producing belts (Su et al. 2017) at a ≤ 25 au have also been proposed, but are not conclusively established.

Table 2 summarizes detections of continuum emission from epsilon Eri over 2–300 GHz (Lestrade & Thilliez 2015; MacGregor et al. 2015; Chavez-Dagostino et al. 2016; Booth et al. 2017; Bastian et al. 2018; Rodríguez et al. 2019). While the millimeter-wave emission is attributed to optically thick chromospheric thermal emission (MacGregor et al. 2015; Booth et al. 2017), the remarkably flat 6–50 GHz spectrum is believed to be produced either via optically thin, thermal free–free emission from a stellar wind (Rodríguez et al. 2019), or through a combination of optically thick, thermal free–free and thermal gyroresonance radiation (Bastian et al. 2018) from the stellar corona. Aside from these continuum emissions, Bastian et al. (2018) also serendipitously detected a 5 minute-long, 1 mJy flare at 2–4 GHz. While the identification of epsilon Eri as a moderately active star favors a stellar origin for their observed flare, its ∼1'' separation from epsilon Eri raises the possibility of a nonstellar provenance.

Table 2.  Summary of Continuum Emission Detected from epsilon Eri at Different Frequency Bands

Instrument Epoch Band Flux Density χca Reference
    (GHz) (μJy) (%)  
VLA 2019 Aug 3 2–4 30.3 ± 3.1 <25 This paper
VLA 2019 Sep 5 2–4 28.4 ± 4.9 <25 This paper
VLA 2016 Mar 1 2–4 <65b Bastian et al. (2018)
VLA 2016 Jan 21 4–8 83 ± 16.6 <50 Bastian et al. (2018)
VLA 2013 May 18 8–12 66.8 ± 3.7 <14 Bastian et al. (2018)
VLA 2013 May 19 8–12 70.3 ± 2.7 <10 Bastian et al. (2018)
VLA 2013 Apr 20 12–18 81.2 ± 6.6 <20 Bastian et al. (2018)
VLA 2017 Jun 15 29–37 70 ± 11 <22 Rodríguez et al. (2019)
ATCA 2014 Jun 25 to Aug 5 42–46 66.1 ± 8.7 MacGregor et al. (2015)
SMA 2014 Jul 28 to Nov 19 217–233 1060 ± 300 MacGregor et al. (2015)
ALMA 2015 Jan 17 to Jan 18 226–234 820 ± 68 Booth et al. (2017)
IRAM 2007 Nov 16 to Dec 4 210–290 1200 ± 300 Lestrade & Thilliez (2015)
LMT 2014 Nov 1 to Dec 31 245–295 2300 ± 300 Chavez-Dagostino et al. (2016)

Notes.

a2.5σ upper limit on circular polarization fraction, χc = ∣V∣/I. b2.5σ upper limit on continuum flux density.

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With the intent of localizing analogous flares and conclusively associating these with a stellar, planetary, or alternate origin, we performed high spatial resolution interferometric observations of epsilon Eri. Our observations mark the first detection of 2–4 GHz quiescent continuum emission from epsilon Eri, although we find no flares in our data. Section 2 describes our observing setup and data analysis methods. We present our results in Section 3, and discuss their physical implications in Section 4. Finally, in Section 5, we summarize our findings and present the conclusions from our study.

2. Observations and Data Processing

Observations of epsilon Eri in the 2–4 GHz frequency band were acquired using the Karl G. Jansky Very Large Array (VLA) on 2019 August 3 (epoch 1) and 2019 September 5 (epoch 2). During these epochs, the VLA was in its most extended configuration, yielding an angular resolution of ≃0farcs5 at 2–4 GHz. Each observation spanned 6 hours, of which nearly 5 hours were spent on epsilon Eri. 3C138 was the flux density and bandpass calibrator, while the VLBA source J0331−1051 (Beasley et al. 2002) was the complex gain calibrator in our observations. To enable precise astrometry, every 10 minute scan (phase center: α(FK5 J2000) = 03h32m55fs84, δ (FK5 J2000) = −09° 27'29farcs73) on epsilon Eri was interleaved between 1 minute scans on J0331−1051. Since our calibration cycles are shorter than the typical VLA cycle time of 15 minutes at 2–4 GHz, we expect our VLA observations to yield more accurate gain phase solutions in comparison to a standard VLA observing program.

To verify our complex gain solutions, we additionally performed three 2 minute scans on the VLA calibrator J0339−0146 at each epoch. However, the gain solutions derived from J0331−1051 result in a systematic error of 0farcs05–0farcs1 on the position of J0339−0146 (∼5°–10° away from J0331−1051). Considering that J0331−1051 is separated from epsilon Eri by ≲1° on the sky, we use the complex gain solutions derived from J0331−1051 to calibrate our epsilon Eri data.

The primary motivation for our study was the detection of circularly polarized flares from the epsilon Eri system. The VLA uses native circularly polarized feeds at 2–4 GHz, thereby circumventing the need for observing a polarization calibrator.

The data products analyzed in this work were processed using the standard VLA Stokes-I continuum calibration pipeline supplied with the Common Astronomy Software Applications (CASA; McMullin et al. 2007) package. No additional postpipeline processing or self-calibration was performed. Clipping bandpass edges and excising known satellite-associated radio frequency interference (RFI) in the 2.3–2.4 GHz band, approximately 90% of our 2–4 GHz bandwidth is usable across 27 and 24 "good" antennas during epochs 1 and 2, respectively. We mapped the data from each epoch out to the first null of the primary beam, and built a model composed of background sources in the field of view. Utilizing the model-subtracted visibilities (Chiti et al. 2016), series of radio images centered on epsilon Eri were then constructed over different timescales ranging from 1 minute (duration of the Bastian et al. 2018 flare) to 5 hours (net integration time on epsilon Eri per epoch).

Briggs weighting (Briggs 1995) encapsulates a smooth transition from uniform weighting (finest angular resolution, lowest sensitivity) to natural weighting (greatest sensitivity, coarsest angular resolution) of complex visibilities using a robust parameter than can be varied continuously between −2 (uniform weighting) and +2 (natural weighting). For achieving the best compromise between sensitivity and angular resolution in our images, we adopted Briggs weighting with a robust parameter of zero.

3. Results

Continuum images of the central 4'' × 4'' neighborhood of epsilon Eri were generated by integrating over the entire 2–4 GHz band (after flagging bad channels and clipping bandpass edges) and the full exposure time on epsilon Eri at each epoch. The resulting rms noise estimated from a source-free region in these 4'' × 4'' cleaned images is ${\sigma }_{{I}_{\nu }}\simeq 3.4$ μJy beam−1. As shown in Figure 1, an unresolved source of flux density, Sν ≃ 29 μJy, is evident at both observing epochs. We use the CASA task imfit to characterize the properties of this source via a 2D elliptical Gaussian fit. Table 3 summarizes the fit results, wherein we additionally incorporate the 5% flux density uncertainty of 3C138 (Perley & Butler 2017) in our quoted radio source flux density errors. We introduce the systematic errors, epsilonα = 19.2 mas and epsilonδ = −10.4 mas, to account for both the position uncertainty of the phase calibrator J0331−1051 in our VLA images and the relative tie of the J0331−1051 VLBA frame (Beasley et al. 2002) to our VLA coordinate frame. The net uncertainties on the absolute position of the radio centroid, (αcentroid, δcentroid) are computed as the quadrature sum of the internal fitting errors and the systematic errors (epsilonα, epsilonδ).

Figure 1.

Figure 1. Detection of 2–4 GHz continuum emission associated with epsilon Eri at epochs 1 (left) and 2 (right). From outer to inner, the solid gray contours label 2, 3, 4, 5, 6, 7, and 8 times the rms intensity, ${\sigma }_{{I}_{\nu }}$ = 3.4 μJy beam−1. The dotted contours mark $-3{\sigma }_{{I}_{\nu }}$ and $-2{\sigma }_{{I}_{\nu }}$ levels. The red crosshairs in each panel indicate the Gaia DR2 position (with 1σ errors) of epsilon Eri corrected for proper motion and annual parallax to the respective epochs. The black solid ellipse at the bottom left corner of each panel illustrates the VLA synthesized beam of size 0farcs63 × 0farcs44.

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Table 3.  Results of a 2D Elliptical Gaussian Fit to the 2–4 GHz Radio Counterpart of epsilon Eri

Epoch Start MJD Positions (FK5 J2000)a Flux Densityb S/Nc
    αcentroid δcentroid    
(number)   (h m s) (° ' '') (μJy)  
1 58698.45 03 32 54.573(1) −09 27 29.22(2) 30.3 ± 3.1 9.02
2 58731.37 03 32 54.568(2) −09 27 29.38(3) 28.4 ± 4.9 8.45

Notes.

aParenthesized numbers reflect uncertainties in the last significant digits. bFlux density uncertainties include not only internal fitting errors, but also a 5% flux calibration error arising from the flux density uncertainty of our amplitude calibrator 3C138. cDetection signal-to-noise ratio (S/N) is computed as the ratio of the peak spectral intensity (${I}_{\nu }^{\mathrm{peak}}$) of the 2D Gaussian fit to the rms image intensity (${\sigma }_{{I}_{\nu }}$).

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Figure 2 compares (αcentroid, δcentroid) at our two epochs with the Gaia DR2 (Gaia Collaboration et al. 2016, 2018) positions of epsilon Eri corrected for proper motion and annual parallax to the respective epochs. For a given epoch, let αoffset, δoffset, and ξ denote, respectively, the R.A. offset, the decl. offset, and the net angular separation of our radio centroid from the Gaia DR2 position of epsilon Eri. We use standard error propagation rules for estimating uncertainties on αoffset, δoffset, and ξ.

Figure 2.

Figure 2. Comparison of radio centroid locations (crosshairs showing 1σ errors) with the Gaia DR2 positions (triangular markers) of epsilon Eri at epochs 1 (red) and 2 (blue). Positions are shown as offsets relative to the fiducial coordinates, α(J2000) = 03h32m54s and $\delta ({\rm{J}}2000)=-09^\circ 27^{\prime} 29^{\prime\prime} $. The black dashed curve labels the path of epsilon Eri on the sky over a 10 month time span, accounting for proper motion and annual parallax. The black solid arrow indicates the direction of motion of epsilon Eri along its path. The Gaia DR2 positions of epsilon Eri at our observing epochs have 3 mas position uncertainties along α and δ that are not visible on the plotted axes scales.

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For epoch 1, we have

Equation (1)

Equation (2)

Equation (3)

The values of the corresponding quantities for epoch 2 are

Equation (4)

Equation (5)

Equation (6)

All of the above offsets are consistent with being zero at the 1σ–2σ level. We also consider the possibility that our detected emission is associated with the confirmed planet epsilon Eri b. According to Benedict et al. (2006), epsilon Eri b executes a ∼7 yr orbit with semimajor axis, a ≃ 3.4 au, eccentricity, e ≃ 0.7, and orbital inclination, i = 30fdg1. Therefore, at the 3.2 pc distance (Gaia Collaboration et al. 2018) of epsilon Eri, epsilon Eri b must lie at least 0farcs29 away from its host star. On the contrary, Mawet et al. (2019) favor an edge-on orbital orientation for epsilon Eri b. However, the rapid orbital phase coverage of the emission centroid between our epochs implies an orbital period of 64–114 days (assuming circular orbit in the plane of the sky), which cannot be attributed to epsilon Eri b. In the absence of evidence for an alternate close-in body within this system, we conclude that our observed emission is coincident with epsilon Eri.

3.1. Source Emission Properties

We find no evidence of Stokes-V emission associated with our 2–4 GHz continuum source, thereby constraining its circular polarization fraction, χc = ∣V∣/I ≲ 25%, at the 2.5σ level. We characterize the source spectrum by performing epoch-integrated imaging of the epsilon Eri field in four contiguous subbands covering 2–4 GHz. At each subband, we estimate the source flux density using the CASA task imfit, but with the 2D Gaussian peak constrained to the coordinates (αcentroid, δcentroid) inferred from the band-averaged image. As illustrated in Figure 3, the spectrum is consistent with being flat over 2–4 GHz at both observing epochs.

Figure 3.

Figure 3. Emission spectrum (lower panels) of the radio counterpart of epsilon Eri during epochs 1 (left) and 2 (right). The light pink vertical lines and horizontal arrows in each panel highlight subband edges. Note that the RFI-affected 2.3–2.4 GHz band is excluded from our analysis. The red dotted horizontal lines in the bottom panels mark the frequency-averaged source flux density reported in Table 3. The orange band covers flux density values within ±1σ of the red dotted line. Detection S/N values (top panels) at subband center frequencies are calculated as the ratio of the peak source intensity (${I}_{\nu }^{\mathrm{peak}}$) to the rms image intensity (${\sigma }_{{I}_{\nu }}$). All plotted error bars indicate 1σ errors on their respective quantities.

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Implementing a similar procedure along the time axis, we find that the radio source displays no significant intra-epoch variability. Imaging our observations separately in 10 minute and 1 minute intervals, we find no evidence of emission above $5{\sigma }_{{I}_{\nu }}$ in our radio images, thus placing an upper limit, Sν ≤ 95 μJy, on any undetected weak flares in our data.

4. Discussions

Our VLA observations have yielded the first detection of quiescent continuum emission from epsilon Eri in the 2–4 GHz band. Assuming a source size, rs ≈ R* = 0.74 R (Bonfanti et al. 2015), at the d = 3.2 pc distance (Gaia Collaboration et al. 2018) of epsilon Eri, the observed Sν ≃ 29 μJy implies a brightness temperature

Equation (7)

Allowing for a flat spectrum over 2–4 GHz, TB ≃ 0.7–2.7 MK, which agrees with the coronal temperature, Tc ≃ 3 MK, associated with X-ray emitting regions (Drake et al. 2000) on the stellar surface. Coupled with the detected low circular polarization fraction, this comparison postulates a likely thermal nature of the observed radiation.

Figure 4 illustrates the broadband continuum spectrum of epsilon Eri using the multifrequency flux density estimates listed in Table 1. Consistent with Bastian et al. (2018), our findings confirm a sharp decline in continuum flux density below 4–8 GHz. Accounting for likely inter-epoch variability between different spectral measurements, we identify emission processes that explain general spectral trends over different frequency ranges. The millimeter-wave spectrum conforms with expectations of an optically thick, thermally emitting stellar chromosphere having T ≈ 8000 ± 2400 K (MacGregor et al. 2015). On the other hand, the observed radio spectrum is flat over 6–50 GHz, and follows a Sν ∝ ν2 scaling below 6 GHz. We note that our in-band spectral measurements at 2–4 GHz (see Figure 3) agree with our band-averaged flux estimates, and hence do not argue against a broadband ν2 scaling below 6 GHz. Bastian et al. (2018) attribute the flat 6–50 GHz spectrum to optically thick, thermal emission from active regions with a frequency-dependent filling factor. On the other hand, Rodríguez et al. (2019) propose that it is optically thin, thermal free–free emission from a stellar wind. Here, in Sections 4.1 and 4.2, we discuss the optically thick 2–4 GHz spectrum of epsilon Eri in the context of two plausible sources of thermal bremsstrahlung, respectively, a magnetically confined stellar corona, and an ionized stellar wind. Section 4.3 quantifies the significance of our flare nondetection relative to an apparent flaring rate inferred from Bastian et al. (2018).

Figure 4.

Figure 4. The 2–300 GHz spectrum of continuum emission associated with epsilon Eri. The plotted points represent different multi-epoch, multifrequency flux density estimates listed in Table 1. The gray dashed line is a smooth spectral fit that is constant above 8 GHz, and follows a Sν ∝ ν2 scaling below 4–8 GHz. The gray dotted lines indicate Sν ∝ ν2 blackbody laws for T ≈ 104 K (upper) and T ≈ 5600 K (lower). Acknowledging possible inter-epoch variability, we refrain from fitting precise power-law models separately over the 2–6, 6–50, and 100–300 GHz frequency ranges.

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4.1. Coronal and Chromospheric Emissions

Thermal free–free absorption and thermal gyroresonance absorption constitute the major opacity sources in the stellar corona. The thermal free–free absorption coefficient scales as ${\kappa }_{\mathrm{ff}}\propto {n}_{e}^{2}{\nu }^{-2}{T}^{-3/2}$ (Dulk 1985), where ne is the electron density. Therefore, κff(ν) dominates at low frequencies in cool, dense plasma. On the other hand, thermal gyroresonant absorption (κgr ∝ neTpBq, p, q > 1) of low harmonics (ν = sνB,e, s ≃ 2–5) of the electron cyclotron frequency (νB,e = 2.8 MHz Bgauss) becomes relevant in hot coronal plasma above active regions, particularly at high frequencies where κff(ν) is negligible. At large optical depths (τν ≫ 1), κff and κgr lead to coronal hotspots superposed on a relatively cool stellar disk with chromospheric temperature, Tch ≃ Tch,⊙ ∼ 104 K (Jordan et al. 1987). Following Villadsen et al. (2014) and Bastian et al. (2018), we constrain the filling factor (fc) of such hotspots on the stellar disk using the model

Equation (8)

Taking Tc ≃ 3 MK, our observed TB ≃ 1.2 MK necessitates fc ≈ 40% at 2–4 GHz, which is consistent with the lower fc estimates obtained by Bastian et al. (2018) at higher frequencies. Above an active region, lower frequencies correspond to weaker magnetic fields higher up from the footpoint. Magnetic flux freezing in the highly conductive coronal plasma then implies a mapping to larger projected areas for weaker fields, resulting in greater fc at lower frequencies (Lee et al. 1998). Absorption of the s = 3 harmonic of νB,e then implies B ≃ 357 G at the coronal heights from where the 2–4 GHz emission emanates.

Figure 4 shows that the stellar corona of epsilon Eri becomes optically thick below ∼6 GHz. Using constraints from recent X-ray observations (Coffaro et al. 2020) of epsilon Eri, we identify the radio frequency νff, below which κff(ν) dominates the net opacity. At any radio frequency, the free–free optical depth (τff) is given by

Equation (9)

Here, $\mathrm{EMD}=\int {n}_{e}^{2}{dV}$ is the emission measure distribution (EMD) of X-ray emitting coronal volumes. Setting EMD = 3.2 × 1050 cm−3 at T ≈ 3 MK (Coffaro et al. 2020), and fc ≳ 40% below 4 GHz based on magnetic flux freezing, we find that τff(ν) = 1 occurs at νff ≲ 1 GHz. Hence, it is likely that gyroresonance absorption renders the stellar corona optically thick to radiation in the 2–6 GHz frequency band. The observed low circular polarization fraction of the 2–4 GHz continuum emission can then be explained if the stellar corona of epsilon Eri is optically thick to both the ordinary and extraordinary modes of gryoresonance emission (Vourlidas et al. 2006). In addition, unless active regions on epsilon Eri preferentially exhibit one hand of magnetic helicity, a low circular polarization is expected for the disk-averaged radio emission.

4.2. Free–Free Emission from an Ionized Stellar Wind

The diffuse corona tied to open magnetic field lines streams into the interplanetary medium, forming the stellar wind. Radio emission from stars with high mass-loss rates (Abbott et al. 1981; Leitherer et al. 1997; Fichtinger et al. 2017) is primarily governed by free–free interactions between charged species in their ionized winds. Analytic forms of standard wind spectra (Olnon 1975; Panagia & Felli 1975; Wright & Barlow 1975) typically presume a spherically symmetric, isothermal, constant velocity (vw) outflow with a steady mass-loss rate ($\dot{M}$). These assumptions imply a wind density profile, ne(r) ∝ r−2, where r denotes the radial distance from the wind engine.

Fitting a standard wind model to the flat 6–50 GHz spectrum in Figure 4, Rodríguez et al. (2019) argue that the 6–50 GHz continuum radiation from epsilon Eri is consistent with optically thin, free–free emission from a stellar wind with $\dot{M}\simeq 6.6\times {10}^{-11}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. This $\dot{M}$ value is about 3300 times that of the Sun, and nearly 110 times larger than corresponding estimates derived by Wood et al. (2002) and Odert et al. (2017) using different methods. While Wood et al. (2002) measured $\dot{M}$ indirectly using atmospheric Lyα absorption lines, Odert et al. (2017) invoked a relation between the flare rate and the mass-loss rate from coronal mass ejections to determine $\dot{M}$ for epsilon Eri.

The standard wind spectrum assumed by Rodríguez et al. (2019) predicts Sν ∝ ν0.6 at τν ≫ 1. Such scaling is clearly disfavored by our 2–4 GHz data, suggesting minimal wind contribution to the thermal emission from epsilon Eri. Allowing for ne(r) ∝ rδ, our optically thick spectral index (Sν ∝ ναα ≃ 2) requires δ →   (Panagia & Felli 1975). Such steep density distributions are unphysical in stellar winds, where nonspherical geometry resulting from stellar rotation and magnetic fields typically yields flatter density distributions (see Schmid-Burgk 1982 for a discussion on radiative fluxes for nonspherical stellar envelopes).

Assuming a well-behaved, thermal free–free emitting wind with solar-like composition, we use our 2–4 GHz data to place a stringent upper limit on $\dot{M}$ for epsilon Eri. Equation (24) of Panagia & Felli (1975) relates $\dot{M}$ to the optically thick flux density, Sν, via

Equation (10)

As indicated in Table 4, vesc ≃ 656 km s−1 is the photospheric escape speed of epsilon Eri, and Te ∼ 106 K is the local electron temperature at the base of the wind. Setting the wind velocity, vw = vesc, and Sν < 29 μJy at ν = 3 GHz, we obtain $\dot{M}\,\lt 3\times {10}^{-11}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. The absolute ionized mass-loss rate is likely much lower depending on the fractional contribution of wind emission to the observed flux density, and the ion density at different radial distances from epsilon Eri. We note that Cranmer & Saar (2011) predict a low $\dot{M}\simeq 5\times {10}^{-14}\,{M}_{\odot }$ yr−1 using stellar wind models of cool stars driven by Alfvén waves and turbulence. This estimate is only a factor of 2 above the solar value, possibly suggesting that the $\dot{M}$ values derived by Wood et al. (2002) and Rodríguez et al. (2019) may be significant overestimates.

Table 4.  Summary of Photospheric, Chromospheric, and Coronal Properties of epsilon Eri

Property Value
Photospheric escape speed, vw (km s−1) 656
Chromospheric temperature, Tch (K) ∼104
Coronal temperature, Tc (K) × 106
Coronal filling factor at 2–4 GHz, fc(ν) ≈40%
Wind electron temperature, Te (K) ∼106

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4.3. Significance of Flare Nondetections

Stellar flares are often linked to magnetic energy release episodes in the corona, with their event rates highly dependent on stellar activity cycles. Regular monitoring of epsilon Eri over the past 50 years has revealed the simultaneous operation of two dynamos (Metcalfe et al. 2013; Coffaro et al. 2020) with cycle periods of 2.95 years and 12.7 years. For comparison, the Sun also exhibits dual dynamos with a short ∼2 yr cycle and a long 11 yr cycle (Fletcher et al. 2010). Using 2–4 GHz VLA observations close to the peak of the ∼3 yr cycle of epsilon Eri in 2016, Bastian et al. (2018) reported one ∼mJy flare in a 20 minute scan on epsilon Eri. While the exact physical origin of this flare is still uncertain, we use the apparent mean radio flaring rate, ${\lambda }_{\mathrm{radio}}=0.05\,{\min }^{-1}$, to predict a flare count for our net 10 hour exposure on epsilon Eri in 2019. We note that λradio is several orders of magnitude higher than the observed X-ray flaring rate, λX−ray ≃ 4.6 × 10−7 minute−1, inferred from the detection of four X-ray flares by Coffaro et al. (2020) over 6000 days of observing.

Assuming a Poisson distribution of flare numbers with flare rate λradio, the expected flare count for our VLA observations is $\left\langle N\right\rangle =30\pm 6$. This estimate markedly deviates from our findings in Section 3.1 suggesting that the flare detection by Bastian et al. (2018) was highly fortuitous. We note that our above arguments do not incorporate the intrinsic flare flux density distribution and the detection threshold of our data analysis. According to Nita et al. (2002), the cumulative peak flux density distribution of solar radio bursts at ν > 2 GHz is well described by $N(\gt {S}_{\nu })\propto {S}_{\nu }^{-1.82}$ at both solar maxima and solar minima. However, given the rapid rotation and relatively young age of epsilon Eri, a similar flux density distribution may not hold for flares originating on epsilon Eri. Moreover, using observations of chromospheric Ca ii levels, Coffaro et al. (2020) recently reported the nondetection of the latest stellar maximum expected in 2019.

Chromospheric activity is tightly linked to changes in the stellar magnetic field and, consequently, the subsurface convection zone, stellar rotation, and magnetic field regeneration via self-sustaining dynamos (Hall 2008). Hence, the nondetection of the most recent peak of the chromospheric Ca ii cycle suggests a likely change in the internal dynamo of epsilon Eri. While the coincidence of our flare nondetection with this undetected stellar maximum supports a stellar origin for the Bastian et al. (2018) flare, models of coherent emission produced through star–planet interactions (Turnpenney et al. 2018) cannot be discarded.

5. Summary and Conclusions

Using the VLA at 2–4 GHz, we have conducted the deepest radio survey of the epsilon Eri system reported to date. Our observations have revealed a 29 μJy, compact continuum source coincident with the Gaia DR2 position of epsilon Eri to within 0farcs06 (≲2σ). At our sensitivity threshold, we detected neither significant variability, nor circularly polarized emission (<25% at 2.5σ significance) associated with this source. Assuming a source size equal to the stellar radius of epsilon Eri, the source TB is comparable to the coronal temperature on epsilon Eri, suggesting a likely thermal nature of the observed emission.

Combining our 2–4 GHz data with previous high-frequency measurements (MacGregor et al. 2015; Bastian et al. 2018; Rodríguez et al. 2019), our observations confirm a spectral turnover of the continuum radiation from epsilon Eri in the 4–8 GHz band. We attribute the observed 2–6 GHz emission to thermal gyroresonance radiation from the optically thick stellar corona of epsilon Eri. Optically thick, thermal free–free emission from the stellar corona may become relevant at ν ≲ 1 GHz.

The observed steep spectral index (α ≃ 2) in the 2–6 GHz band strongly disfavors thermal free–free emission (Sν ∝ ν0.6 at τν ≫ 1) from a stellar wind as a plausible interpretation for the 2–50 GHz continuum radiation from epsilon Eri. Thus, attributing the entire observed flux density at 3 GHz to stellar-wind-associated thermal free–free emission, we derive the upper limit, $\dot{M}\lt 3\times {10}^{-11}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, for epsilon Eri at the time of our observations.

Despite scheduling our observations close to the expected maximum of the ∼3 yr magnetic cycle of epsilon Eri in 2019, we detected no flares in our data above our sensitivity limits. A comparison with the mean flaring rate inferred from Bastian et al. (2018) then reveals the extremely fortunate nature of their flare discovery in 2016. However, the optical nondetection (Coffaro et al. 2020) of the most recent stellar maximum expected in 2019 hints at a possible evolution of the internal dynamo of epsilon Eri. We encourage continued monitoring of epsilon Eri to track its activity levels and better understand its internal dynamo. Periods of high stellar activity should preferably be followed up both at 2–4 GHz and at low radio frequencies (ν < 300 MHz) to discriminate between stellar and planetary emission models for any flare recurrences.

All authors thank J. Villadsen for initial conversations that motivated this work. A.S. thanks P. Nicholson and R. J. Jennings for useful thought-provoking discussions. A.S., S.C., and J.M.C. acknowledge support from the National Science Foundation (AAG 1815242). The VLA observations presented here were obtained as part of program VLA/19A−283, PI: A. Suresh. The VLA is operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Facility: VLA. -

Software: CASA (McMullin et al. 2007), Python 3 (http://www.python.org), Astropy (Price-Whelan et al. 2018), NumPy (van der Walt et al. 2011), Matplotlib (Hunter 2007), SciPy (Virtanen et al. 2020).

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10.3847/1538-4357/abc004