The Habitable-zone Planet Finder Detects a Terrestrial-mass Planet Candidate Closely Orbiting Gliese 1151: The Likely Source of Coherent Low-frequency Radio Emission from an Inactive Star

Pope et al. (2020) obtained time-series Doppler spectroscopy of GJ 1151 using the HARPS-N spectrometer (Cosentino et al. 2012) at Telescopio Nazionale Galileo (TNG). The HARPS-N time series consists of 21 observations compiled over a time baseline of approximately 3 months between 2018 December and 2019 February.

The standard HARPS-N RV pipeline did not offer sufficient Doppler precision for a star as cool as GJ 1151, so Pope et al. (2020) extracted their own RVs using the wobble (Bedell et al. 2019) spectral analysis code. From the 21 HARPS-N spectra, Pope et al. (2020) provided 19 wobble RVs; one spectrum (BJD = 2,458,475.75494602) was explicitly excluded for having low signal-to-noise ratio (S/N), while another (BJD = 2,458,491.64178017) was excluded for unspecified reasons. The wobble RVs exhibit an rms scatter of 3.8 m s⁻¹, with a mean single-measurement error of 2.9 m s⁻¹.

In our analysis, we have incorporated the wobble RVs as presented by Pope et al. (2020). For our analysis of stellar magnetic activity (Section 3.2), we have also used the 1D extracted HARPS-N spectra from the TNG archive to derive the Ca ii H and K (S_HK; Vaughan et al. 1978; Gomes da Silva et al. 2011) and Hα (I_Hα ; Robertson et al. 2013) activity indices.

HPF is a stabilized fiber-fed NIR spectrograph on the 10 m Hobby–Eberly Telescope (HET) covering the z, Y, and J bands from 810 to 1280 nm at a spectral resolution of R ∼ 55,000. To enable precise RVs in the NIR, HPF is actively temperature stabilized to the millikelvin level (Stefansson et al. 2016). HET is a fully queue-scheduled telescope (Shetrone et al. 2007), and all of the observations presented here were executed as part of the HET queue.

HPF uses a Laser-Frequency Comb (LFC) calibrator (Metcalf et al. 2019) to provide long-term accurate and precise instrument drift correction and monitoring. We did not obtain simultaneous LFC observations, to minimize the possibility of contaminating the target spectrum, but performed the drift correction using LFC frames obtained throughout the night. We have previously demonstrated that we can achieve a drift-corrected precision at the <30 cm s⁻¹ level (Stefansson et al. 2020) using this technique.

We used the HxRGproc (Ninan et al. 2018) package to perform bias, nonlinearity, and cosmic-ray corrections, along with slope and variance image generation of the raw HPF up-the-ramp data. Following the slope and variance image generation, the HPF 1D spectra were extracted using the methods and algorithms discussed by Ninan et al. (2018), Kaplan et al. (2018), and Metcalf et al. (2019). To extract RVs from the 1D HPF spectra, we used an adapted version of the SpEctrum Radial Velocity AnaLyzer (SERVAL; Zechmeister et al. 2018) code, which is further described by Metcalf et al. (2019) and Stefansson et al. (2020). Briefly, SERVAL uses the template-matching method (Anglada-Escudé & Butler 2012) to extract precise RVs. For the RV extraction, we followed Stefansson et al. (2020), using the eight HPF orders cleanest of tellurics covering the wavelength ranges of 854–889 nm and 994–1076 nm. Following Metcalf et al. (2019) and Stefansson et al. (2020), we masked tellurics and sky emission lines, to minimize their effect on the RV determination. To further minimize the impact of sky emission lines on the RV determination, we subtracted the sky background estimated using the dedicated HPF sky fiber. Barycentric correction of our RVs was performed using barycorrpy (Kanodia & Wright 2018). barycorrpy also corrects for secular acceleration (Kürster et al. 2003), which for GJ 1151 is 0.61 m s⁻¹ yr⁻¹. The secular acceleration is negligible across the baseline of the HARPS-N RVs but significant for our HPF velocities.

Overall, we obtained 50 high-resolution spectra with HPF in 25 visits with HPF, obtaining two spectra per visit with an exposure time of 969 s per exposure. The spectra cover a time baseline of 458 days from 2019 March 15 to 2020 June 25. The median S/N of the HPF spectra was 217 per 1D extracted pixel at 1 μm. We excluded from our analysis two of the spectra owing to low S/Ns of 28 and 38 due to poor weather, which left 48 high-quality spectra obtained in 24 visits. Following Stefansson et al. (2020), we binned the resulting RV points per HET visit, resulting in a median RV error of 2.7 m s⁻¹ and an effective exposure time of 32 minutes. The HPF RVs are shown alongside the HARPS-N velocities in Figure 1. The RVs and associated activity indicators used in this work are provided in machine-readable format as "Data behind Figure 1."

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As part of its all-sky survey for transiting exoplanets, TESS (Ricker et al. 2015) observed GJ 1151 for 27 days during Sector 22 (2020 February 18–March 18) of the mission in two orbits (Orbits 51 and 52). GJ 1151 is listed as TIC 11893637 in the TESS Input Catalog (TIC; Stassun et al. 2018, 2019). TESS pixel data surrounding GJ 1151 were averaged into 2-minute stacks, which were reduced to light curves by the Science Processing Operations Center (SPOC) at NASA Ames (Jenkins et al. 2016), which we retrieved using the lightkurve package (Lightkurve Collaboration et al. 2018). We analyzed the Presearch Data Conditioning Single Aperture Photometry (PDCSAP) light curve, which contains systematics-corrected data using the algorithms originally developed for the Kepler data analysis pipeline. The PDCSAP light curve uses pixels chosen to maximize the S/N of the target and has removed systematic variability by fitting out trends common to many stars (Smith et al. 2012; Stumpe et al. 2014). Data from Gaia demonstrate that there are no nearby stars within 1 that are within 5 TESS magnitudes of GJ 1151, resulting in minimal dilution of the TESS light curve.

To clean the available TESS data, we removed all points with nonzero quality flags (4563 in total), which indicate known problems (e.g., Tenenbaum & Jenkins 2018). We removed an additional six points that we identified as 4σ outliers, leaving a total of 14,050 points that we used for subsequent analysis, with a median error bar of 1392 ppm. The median-normalized TESS PDCSAP light curve is discussed in Section 3.4.

From the TESS Data Release Notes for Sector 22, "momentum dump" events—when the TESS reaction wheel speeds are reset by removing angular momentum through thruster firing to keep the pointing of the telescope stable—occurred every 6.625 and 6.75 days in Orbits 51, and 52, respectively. These events are known to impact the photometry (see, e.g., Huang et al. 2018), and we specifically highlight those events in Figure 2.

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When analyzing the combined HARPS-N+HPF RVs with frequency analysis tools such as periodograms, we consistently find evidence for a periodic signal near 2 days. For the sake of brevity, we will present results from the Bayes factor periodogram (BFP; Feng et al. 2017). The BFP is particularly useful for this analysis, as it offers an unambiguous measure of a signal's statistical significance, which is crucial when attempting to detect a low-amplitude exoplanet with a small number of observations. However, other periodograms such as the generalized Lomb–Scargle (GLS; Zechmeister & Kürster 2009) or Bayesian Lomb–Scargle (BGLS; Mortier et al. 2015) offer qualitatively similar results.

The BFP works by comparing the Bayesian information criterion (BIC) of a periodic signal at each candidate frequency with that of a noise model. Periodogram peaks with a Bayes factor $\mathrm{ln}({BF})\geqslant 5$ are considered statistically significant. While the Agatha implementation of this algorithm from Feng et al. (2017) offers the option to account for correlated noise using one or more moving average terms, the model selection feature of Agatha prefers a white-noise model for our data. Our BFPs were all evaluated for periods $-0.3\lt {\mathrm{log}}_{10}(P)\lt 3$ with an oversampling factor of 15.

In Figure 1(a), we show the BFP for the combined HARPS-N+HPF time series. The RV periodogram shows two distinct sets of peaks. The first occurs at around 2 days, with peaks at 2.02 and 1.98 days. The second feature sits at approximately 0.7 days. These peaks are all aliases of each other; specifically, each frequency is separated by 1 day⁻¹. The "1-day alias" problem is common to time-series Doppler searches (Dawson & Fabrycky 2010). Interestingly, the ambiguity between 1.98 and 2.02 days is extremely similar to the alias observed for YZ Ceti b, another low-mass exoplanet orbiting a mid-M dwarf (Robertson 2018). The periodograms suggest that 2.02 days is the true signal period, a hypothesis we confirm via model comparison in Section 3.3.

The HPF RVs alone show statistically significant power near 2 days. The HARPS-N velocities alone do not show significant power at any period, but the strongest peak occurs near the 0.7-day alias of the 2-day period. While the power in the combined periodogram is approximately equal to that of the HPF power spectrum, the appearance of at least one alias of the same signal in HARPS-N, as well as the consistency of the HARPS-N RVs with the 2-day signal (Figure 1(c)), would appear to rule out instrumental systematics as the origin of the signal.

Magnetic features such as starspots and plage can create periodic RV signals (e.g., Boisse et al. 2011; Robertson et al. 2014), and the 2-day period of our candidate signal would be consistent with many young, rapidly rotating M dwarfs (Newton et al. 2016). However, we find instead that GJ 1151 appears to be quiet and slowly rotating, and that its rotation should not be the astrophysical origin of the signal.

By all indications, GJ 1151 is a slow rotator. Newton et al. (2016) estimated its rotation period to be 117.6 days based on MEarth photometry. Reiners et al. (2018) placed an upper limit on its rotational velocity of <2 km s⁻¹, which we agree with based on our own $v\sin i$ analysis of the high-resolution HPF spectra, from which we also obtain an upper limit of $v\sin i\lt 2\,{\mathrm{kms}}^{-1}$. Its X-ray luminosity L_X = 5.5 × 10²⁶ erg s⁻¹ (Foster et al. 2020) implies a stellar age of approximately 5 Gyr and a rotation period between 70 and 90 days, according to the empirical relationship of Engle & Guinan (2011). Furthermore, data from TESS, HARPS-N, and HPF disfavor a short rotation period. For the HARPS-N and HPF time series, we performed periodicity searches for four spectral activity indicators: S_HK and I_Hα from HARPS-N, and the chromatic index (CRX) and differential line width (dLW) from HPF (Zechmeister et al. 2018). We see no evidence for periodic astrophysical variability in any of the spectral activity tracers. Likewise, the TESS light curve shows no evidence for a stellar rotation period of P ≤ 15 days. Finally, the complete absence of detectable flares in the TESS light curve and the lack of emission in chromospheric lines such as Hα are inconsistent with GJ 1151 being young and active. Further still, the kinematics of this star are consistent with an older age as would be expected for a slow rotator: UVW = (−26.9, −65.0, −33.4) km s⁻¹, placing it at the boundary of thin- and thick-disk membership.

Aside from arguments related to the difference between the star's likely rotation period and the RV period, the RV data themselves are inconsistent with activity-driven variability. The RVs show no correlations with any of the spectral activity indicators. Also, if we model the 2.02-day signal using the optical HARPS-N RVs and NIR HPF RVs separately, we find consistent amplitudes. On the other hand, if the signal were created by starspots, we would expect a smaller amplitude at NIR wavelengths (e.g., Marchwinski et al. 2015). Thus, we conclude that it is extremely unlikely that the observed 2-day Doppler signal is caused by stellar variability.

Given the evidence that GJ 1151 is a quiet, slowly rotating star, we modeled the 2-day variability as a Keplerian exoplanet orbit. We used the Markov Chain Monte Carlo (MCMC) orbit-fitting code radvel (Fulton et al. 2018) to compute the model. We adopted mostly uninformative priors for the model parameters, although for the additional white-noise terms ("jitters", ${\sigma }_{\mathrm{HARPSN}/\mathrm{HPF}}$) we adopted the jitter prior suggested by Ford & Gregory (2007) with a "reference value" σ₀ = 1 m s⁻¹ and maximum ${\sigma }_{{\rm{\max }}}=100$ m s⁻¹. This prior was chosen to facilitate Bayesian model comparison, particularly to a zero-planet model, for which a uniform prior can allow the noise terms to grow enough to absorb real astrophysical variability. We fixed the planet's eccentricity to zero, both because our data are not numerous enough to constrain it and because we expect a planet so close to the star to be tidally circularized (e.g., Rasio & Ford 1996).

For each model considered, we compared to a zero-planet model in which we account for the RV variability using only a zero-point offset and a jitter term for each instrument. We performed model selection using the Bayes factor $\mathrm{ln}{BF}=\tfrac{{\rm{\Delta }}\mathrm{BIC}}{2}$, where BIC is the Bayesian information criterion, which scales a model's log-likelihood value to include a complexity penalty for models with more free parameters (Kass & Raftery 1995).

Our preferred model is for an exoplanet with P = 2.02 days. When compared to the zero-planet model, it has a Bayes factor $\mathrm{ln}{BF}=12.7$, indicating a high level of significance. This Bayes factor also agrees well with the result of our periodogram analysis. While the alias of the 2.02-day period at P = 1.98 days appears as a strong peak in our periodogram analysis, if we choose a period prior tightly constrained at 1.98 days, the posterior distribution still prefers the 2.02-day period. Additionally, we also note that while a model treating the signal as a Keplerian with P = 0.7 days is also favored over the zero-planet model, its Bayes factor is significantly lower than that of the 2-day model, and we therefore conclude that it is simply an alias of the true period.

Given the multimodal nature of the period posterior, we additionally fit the RV data sets using the dynesty dynamic nested sampler (Speagle 2020) available in the juliet (Espinoza et al. 2018) package. Nested samplers are efficient at accurately exploring multimodal solutions (Speagle 2020). From the nested sampler, we observe a clear highest mode at 2.02 days ($P={2.0183}_{-0.0008}^{+0.0084}\,\mathrm{days}$), with a significantly smaller mode seen at 1.98 days. To quantify the preference for the 2.02-day solution over the 1.98-day solution, we ran two sets of six RV fits each in juliet to get an accurate view of the resulting variance in log evidence values ($\mathrm{ln}Z$ values). To sample the 2.02-day solution, we ran the first set with a uniform prior on the period from 2.0 to 2.04 days, and to sample the 1.98-day solution, we ran the second set with a uniform prior from 1.96 to 2.0 days on the period. In doing so, we obtain a $\mathrm{ln}Z=-136.22\pm 0.37$ and $\mathrm{ln}Z=-139.27\pm 0.22$ for the 2.02-day and 1.98-day solutions, respectively, where we report the values as the median value from the six independent fits and the error as the standard deviation from the six fits. We adopt the 2.02-day solution, given the ${\rm{\Delta }}\mathrm{ln}Z=3$ (20-to-1 posterior odds) statistical preference for that solution over the 1.98-day solution.

The planet candidate presented here is fully consistent with the expected planet occurrence around mid-M dwarfs: Hardegree-Ullman et al. (2019) suggest a planet occurrence of ${1.4}_{-1.0}^{+2.3}$ for small (0.5R_⊕ to 2.5R_⊕), short-period (P < 10 days) planets around M4–M4.5 dwarfs. There remains a possibility that further planets orbit in the system. However, as seen from Figure 1 with the current RVs, we do not see clear evidence of additional periodic signals. Additional precise RVs could shed further constraints on any additional planets in the system.

The prior distributions and adopted posterior values of the planet's orbital model are shown in Table 1. Additionally, we show the orbit superimposed over the RV data in Figure 1.

Table 1. Priors and One-dimensional Posterior Distributions for the Orbital and Instrumental Parameters for Our One-planet RV Model to GJ 1151

Parameter	Prior	Posterior
Orbital Parameters
Period P (days)	${\mathscr{N}}(2.016,0.1)$	2.0180 ± 0.0005
Time of inferior conjunction TC (BJD −2,458,400)	${\mathscr{U}}(72.6655,74.6835)$	73.691 ± 0.07
$\sqrt{e}\sin \omega$	⋯	0 (fixed)
$\sqrt{e}\cos \omega$	⋯	0 (fixed)
RV semiamplitude K (m s−1)	${\mathscr{U}}(0,100)$	4.1 ± 0.8
Instrument Parameters
HARPS-N zero-point offset ${\gamma }_{\mathrm{HARPSN}}$ (m s−1)	${\mathscr{U}}(-20,20)$	0.7 ± 0.7
HPF zero-point offset γHPF (m s−1)	${\mathscr{U}}(-20,20)$	−0.4 ± 0.7
HARPS-N jitter ${\sigma }_{\mathrm{HARPSN}}$ (m s−1)	$\propto {(\sigma +{\sigma }_{0})}^{-1}$	${0.4}_{-0.4}^{+1.0}$
HPF jitter σHPF (m s−1)	$\propto {(\sigma +{\sigma }_{0})}^{-1}$	1.8 ± 1
Inferred Parameters
Minimum mass $m\sin i$ (M⊕)		2.5 ± 0.5
Semimajor axis a (au)		${0.01735}_{-0.00070}^{+0.00065}$
Semimajor axis a (a/R*)		18.5 ± 0.9

Note. ${\mathscr{N}}(a,b)$ denotes a normal prior with median value a and standard deviation b; ${\mathscr{U}}(a,b)$ denotes a uniform prior with lower-limit value a and upper-limit value b.

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3.4.1. Transit Search

3.4.2. Periodogram Analysis

3.4.3. Starspot Modulation

To study the Alfvén interaction of the planet candidate and estimate the resulting Poynting fluxes, we broadly follow Vedantham et al. (2020), using the model frameworks of Saur et al. (2013) and Turnpenney et al. (2018) and that of Lanza (2009) to describe the energetics of the SPIs. These models assume that the planet is a conductive perturber orbiting in a magnetized expanding stellar corona described as a Parker wind (Parker 1958). For the Parker wind, we assumed a coronal temperature of T_corona = 2 × 10⁶ K, which results in a sound speed of c_s ∼ 129 km s⁻¹. Following Vedantham et al. (2020), we assumed a base number density of n_base = 10⁶ g cm⁻³, which we scaled as n ∝ d⁻², where d is the distance from the star.

To determine whether our planet candidate satisfies the criterion for sub-Alfvénic interactions, we estimate the Alfvén Mach number of the planet, which is given by

$$\begin{eqnarray}&&{M}_{A}={v}_{\mathrm{rel}}/{v}_{A},\end{eqnarray} \tag{ 1 }$$

where v_rel is the relative velocity of the stellar wind as seen by the orbiting planet and v_A is the Alfvén speed. Assuming a circular orbit with a period of P = 2.02 days, the planet has a Keplerian orbital velocity of v_orb ∼ 94 km s⁻¹ at its orbital distance of a/R_* = 18.5. As the magnetic field of GJ 1151 is not currently well constrained, if we adopt the nominal value of B_* = 0.01 T assumed by Vedantham et al. (2020), we obtain an Alfvén speed of v_A ∼ 11, 800 km s⁻¹ and an Alfvén Mach number of M_A = 0.026 at the orbital distance of the planet. As the Mach number is less than 1, the planet is capable of sub-Alfvénic interactions with its host star. We further note that the planet also satisfies the second criterion for sub-Alfvénic interactions—that the radial wind speed is less than the radial component of the Alfvén speed, which is a necessary condition so that one of the two Alfvén wings points toward the star (see discussion in Saur et al. 2013).

As the planet is capable of sub-Alfvénic interactions and has a small Alfvén Mach number, we estimate the total Poynting flux of the system with

$$\begin{eqnarray}&&{S}_{\mathrm{total}}=2\pi \displaystyle \frac{{v}_{\mathrm{rel}}{R}_{\mathrm{eff}}^{2}{B}_{0}^{2}}{{\mu }_{0}}\varepsilon ,\end{eqnarray} \tag{ 2 }$$

where v_rel is the relative velocity of the stellar wind as seen by the orbiting planet, B₀ is the total magnetic field at the position of the planet, μ₀ is the vacuum permeability constant, and R_eff is the effective radius of the planet. The ε parameter describes the efficiency of the SPIs, and its parameterization differs in the model of Saur et al. (2013) and Turnpenney et al. (2018) (hereafter the ST model) and the model of Lanza (2009) (hereafter the Lanza model). In the ST model the ε parameter is given by

$$\begin{eqnarray}&&\varepsilon ={M}_{A}{\bar{\alpha }}^{2}{\sin }^{2}(\theta ),\end{eqnarray} \tag{ 3 }$$

where M_A is the Alfvén Mach number of the system, θ is the angle between the total magnetic field B₀ at the position of the planet and the total stellar wind velocity, and $\bar{\alpha }$ is a parameter denoting the sub-Alfvénic interaction efficiency, where we follow Vedantham et al. (2020) and assume that it is equal to unity.

In the model of Lanza (2009), ε is given by

$$\begin{eqnarray}&&\varepsilon =\gamma /2,\end{eqnarray} \tag{ 4 }$$

where γ is a parameter ranging from 0 to 1. Here we follow Vedantham et al. (2020) and assume γ = 0.5.

To estimate the effective radius of the planet, given our mass estimate of $m\sin i=2.5\pm 0.5{M}_{\oplus }$, we use the forecaster (Chen & Kipping 2017) mass–radius relations to predict a likely minimum radius of the planet of ${R}_{p}={1.35}_{-0.29}^{+0.53}{R}_{\oplus }$. If the planet has an inherent magnetic field, this will increase the effective radius R_eff of the interaction (see Equation (57) in Saur et al. 2013) by

$$\begin{eqnarray}&&{R}_{\mathrm{eff}}={R}_{\mathrm{exo}}{\left(\displaystyle \frac{{B}_{\mathrm{exo}}}{{B}_{0}}\right)}^{1/3}\sqrt{3\cos \left(\displaystyle \frac{{{\rm{\Theta }}}_{M}}{2}\right)},\end{eqnarray} \tag{ 5 }$$

where R_exo is the radius of the planet, B_exo is the equatorial magnetic field of the planet, and Θ_M is the angle between the planet magnetic moment and the stellar magnetic field at the location of the planet. We follow Vedantham et al. (2020) and assume that the planet has a magnetic field of 1 G and that the magnetic moment nominally has a Θ_M = 90° angle with the stellar magnetic field, resulting in $\sqrt{3\cos (\tfrac{{{\rm{\Theta }}}_{M}}{2})}\sim$ 1.46. As planets on short-period orbits are expected to be tidally locked to their stars, we make the assumption that the planet rotation period is equal to its orbital period, which we use to scale the resulting planetary magnetic field.

From these model input parameters, we obtain a Poynting flux of S_total,ST ∼ 8 × 10¹⁴ W and S_total,Lanza ∼ 9 × 10¹⁶ W for the ST and Lanza models, respectively. Assuming a Poynting-flux-to-radio-emission conversion efficiency of _r = 1%, we obtain a Poynting radio power of P_radio,ST = 8 × 10¹² W and P_radio,Lanza = 9 × 10¹⁴ W for the two models. Given the distance of d = 8.04 pc to the host star, we can also calculate the resulting spectral flux density of F_radio,ST = 0.5 mJy and F_radio,Lanza = 52 mJy, where we followed Vedantham et al. (2020) assuming a bandwidth of Δν equal to the electron gyrofrequency on the surface of the star and a beam solid angle Ω = 0.1 sr. These spectral flux densities broadly agree with the observed LOFAR value of ∼ 0.9 mJy from Vedantham et al. (2020). As a comparison to other M-dwarf systems, this spectral flux density is similar to—but somewhat higher than—the spectral flux density of ∼0.3 mJy for the M4-dwarf planet GJ 876 b as estimated by Turnpenney et al. (2018).

To visualize the sensitivity of the models to different input parameters as a function of orbital distance of the planet, we performed a Monte Carlo sampling assuming nominal input priors summarized in Table 2. Figure 3 shows the Alfvén Mach number, along with the resulting Poynting flux estimates using the ST and Lanza models, as a function of distance from the star. The solid curves show the median models, and the corresponding shaded regions show the 1σ credible intervals. From Figure 3(a), we see that for even the broad set of input parameters in Table 2 the system is sub-Alfvénic (${\mathrm{log}}_{10}({M}_{A})\lt 1$) at the orbital location of the planet. In Figure 3(b), we additionally compare our resulting Poynting flux estimates from the ST and Lanza models to the radio observation constraint from Vedantham et al. (2020) (gray shaded region in Figure 3(b)). We see that the ST and Lanza models flank the radio constraint presented by Vedantham et al. (2020), which assumes a B_* = 0.01 T, with both the ST and Lanza models being consistent with the observed radio constraint at the 1σ–2σ level for the assumed parameters. We conclude that the planet candidate we report here is compatible with being the source of the radio emission detected by Vedantham et al. (2020).

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Table 2. Summary of Input Parameters and Posterior Parameters Describing the Energetics of the Star–Planet Interactions for the ST Model (Saur et al. 2013; Turnpenney et al. 2018) and the Lanza model (Lanza 2009)

Parameter	Parameter Description	Value	Notes
Prior Parameters
R*	Stellar radius (R⊙)	${\mathscr{N}}(0.2016,0.0060)$	TICv8 (Stassun et al. 2019)
M*	Stellar mass (M⊙)	${\mathscr{N}}(0.171,0.020)$	TICv8 (Stassun et al. 2019)
Prot	Stellar rotation (days)	117	Newton et al. (2016)
TC	Temperature of stellar corona (K)	2 × 106	Adopted from Vedantham et al. (2020)
nbase	Base number density (cm−3)	1 × 106	Adopted from Vedantham et al. (2020)
B*	Stellar magnetic field (T)	${\mathscr{J}}(0.001,0.1)$	Nominal M-dwarf stellar magnetic field
Bexo	Planet magnetic field (G)	${\mathscr{J}}(0.1,10)$	Nominal planet magnetic field
Rp	Planet radius (R⊕)	${\mathscr{N}}(1.5,0.5)$	Estimated from $m\sin i$
Posterior Parameters
${\mathrm{log}}_{10}({M}_{{\rm{A}}})$	Alfvén Mach number	−1.6 ± 0.7
${\mathrm{log}}_{10}({S}_{\mathrm{total},\mathrm{ST}})$	Poynting flux, ST model (erg s−1)	${22.0}_{-0.6}^{+0.7}$
${\mathrm{log}}_{10}({S}_{\mathrm{total},\mathrm{Lanza}})$	Poynting flux, ST model (erg s−1)	${24.0}_{-0.9}^{+1.1}$

Note. ${\mathscr{N}}(a,b)$ denotes a normal prior with median value a and standard deviation b; ${\mathscr{J}}(a,b)$ denotes a log-uniform prior with lower-limit value a and upper-limit value b; ${\mathscr{U}}(a,b)$ denotes a uniform prior with lower-limit value a and upper-limit value b.

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In the near future, the Square Kilometre Array (SKA), a next-generation radio telescope, is expected to come online, which is anticipated to improve on the flux density sensitivity compared to that of LOFAR by a factor of 10–30, resulting in a flux density sensitivity of ∼ 10 μJy (Zarka et al. 2015) in the 50–250 MHz range. With its improved precision, SKA is expected to enable the detection of additional planets exhibiting coherent radio emission around nearby stars.