© The Authors 2025

1 Introduction

M dwarfs, also known as “red dwarfs”, are the most common stars in the solar neighborhood (e.g., Reylé et al. 2021), and they are expected to preferentially host close-in rocky planets (Sabotta et al. 2021; Ribas et al. 2023). The discovery of Proxima b, an Earth-sized rocky planet within the habitability zone of its star Proxima Centauri (Anglada-Escudé et al. 2016), boosted the interest of the astronomical community, and the study of exoplanets and their potential habitability has blossomed in the past decade thanks to space-based missions (e.g., Kepler, TESS) as well as to the exploitation of data taken with ground-based telescopes.

The discovery of the majority of exoplanets around M dwarfs, including rocky ones, has been done using radial velocity and transit measurements, while their discovery in the radio has been elusive despite decades of relentless efforts. The detection of auroral radio emission from an exoplanet would confirm the existence of such an exoplanet and would inform us of its intrinsic magnetic field. Significantly, this latter piece of information cannot be provided by other means, which makes radio observations unique. Unfortunately, Earth and super-Earth exoplanets with plausible magnetic field strengths of up to a few Gauss would result in auroral radio emission from such exoplanets at frequencies below the Earth’s ionospheric cutoff of ~10 MHz, therefore making this radio emission undetectable from Earth. However, if an exoplanet is close enough to its host star that it is in the sub-Alfvénic regime, that is, when the plasma speed relative to the exoplanet, v, is smaller than the Alfvén speed at the planet position, v_A, then energy and momentum can be transported upstream and back to the star by Alfvén waves. Jupiter’s interaction with its Galilean satellites is a well-known example of sub-Alfvénic interaction, and it results in copious auroral radio emission (Zarka 2007). The mechanism responsible for this emission is the electron-cyclotron maser (ECM) instability, which is a coherent mechanism yielding strong, variable highly polarized emission. The typical energies of the electrons involved in auroral radio emission are around 1 keV (Wu & Lee 1979), and for the case of the Io-Jupiter decameter emission, the range of energies can go up to about 20 keV (e.g., Lamy et al. 2022). In the case of magnetic star-planet interaction (SPI), the radio emission arises from the upper layers of the atmosphere of the host star, induced by the exoplanet moving through the stellar magnetosphere, and thus the relevant magnetic field is that of the star, B_⋆, not the exoplanet magnetic field. This makes a huge difference regarding the frequency that should be searched to find this radio emission.

Notably, M dwarfs are excellent candidates to detect SPI at radio wavelengths since they have surface magnetic fields of a few hundred Gauss, or even kilogauss (Shulyak et al. 2019; Kochukhov 2021; Reiners et al. 2022), so the fundamental frequency of the cyclotron emission falls into the detection capabilities of existing radio interferometers. Sub-Alfvénic interaction is expected to yield detectable periodic radio emission via the ECM mechanism as long as the Alfvén wave connects back to the star (e.g., Zarka 2007; Saur et al. 2013; Turnpenney et al. 2018; Vedantham et al. 2020; Pérez-Torres et al. 2021). The confirmation of this radio emission would provide a completely new method of exoplanet detection. Namely, one would expect to detect strong, highly circularly polarized radio emission at an observing frequency close to or below the maximum cyclotron frequency and showing a periodic signal that correlates with the orbital period of the planet, P_orb, or the synodic period, $P_{\text{syn\hspace{0.17em}}}^{-1}=P_{\text{rot\hspace{0.17em}}}^{-1}-P_{\text{orb\hspace{0.17em}}}^{-1}$, where P_rot is the rotation period of the host star, although we note that the geometry of the system can result in a more complex relation.

In recent years, there have been several claims of exoplanet induced radio emission (GJ 1151b – Vedantham et al. 2020; Proxima b – Pérez-Torres et al. 2021; YZ Cet b – Pineda & Villadsen 2023; Trigilio et al. 2023), but a solid confirmation is still lacking for those cases. For example, Narang et al. (2024) recently reported non-detections of GJ 1151 with the uGMRT at 150,218, and 400 MHz. In this paper, we present the results from the longest monitoring radio campaign on the star-exoplanet M dwarf system GJ 486–GJ 486b using the upgraded Giant Metrewave Radio Telescope (uGMRT; Gupta et al. 2017). Our overall aim is to characterize the radio emission from this system, with the main goal of detecting radio emission due to magnetic SPI. We describe the GJ 486–GJ 486b system in Section 2 and our observations and data analysis in Section 3. We present our results in Section 4 and discuss them in Section 5.

2 The GJ 486–GJ 486b system

GJ 486 is a cool nearby M3.5V star (Caballero et al. 2022; see also Table 1). It rotates at a rate of roughly half of that of the Sun, and given its mass, it is very likely an almost fully convective star. Trifonov et al. (2021) reported the existence of an exoplanet, GJ 486b, using radial velocity (RV) measurements from the CARMENES survey (Quirrenbach et al. 2016) and TESS photometry (Ricker et al. 2014). GJ 486b has a radius and a mass slightly larger than the Earth, straddling the boundary between Earth-like planets and super-Earths. However, its bulk density (ρ ≈ 7.0 g cm⁻³) favors a massive terrestrial planet rather than an ocean one (Trifonov et al. 2021). Given the proximity of the GJ 486 system (8.1 pc from Earth) and the small separation of the planet to its host star (≲0.02 au), GJ 486 showed promise for detecting radio emission arising from star-planet interaction.

2.1 Electron-cyclotron maser frequency and magnetic field of GJ 486

If radio emission is produced on a planet via the ECM instability, then the intrinsic planetary magnetic field can be directly measured. The maximum cyclotron frequency is given by $${\nu }_c[\mathrm{M}\mathrm{H}\mathrm{z}]=s\times 2.8B,$$(1)

where B is the local magnetic field, in Gauss, and s is the harmonic number of the cyclotron frequency. The ECM emission is observed essentially from the fundamental (s = 1) (Melrose & Dulk 1982). However, the detection of radio emission from SPI could be feasible if the planet is in the sub-Alfvénic regime, as mentioned in Sect. 1. In this case, the relevant local magnetic field in Eq. (1) is that of the star, B_⋆. Using high-resolution spectral measurements with CFHT/ESPaDOnS, Moutou et al. (2017) determined a total surface magnetic field value of B_⋆ f = 1.6 ± 0.3 kG for GJ 486, where f is the filling factor (the fraction of the stellar surface covered with magnetic field). Two filling factors could be considered here, namely, the Stokes I and V filling factors, f_I and f_V respectively (Morin et al. 2008). However, the relevant one is f_V, which refers to the fraction of the field that manifests as a large-scale surface magnetic field, as opposed to f_I, which also takes into account the smaller-scale field that may cancel out at larger scales and is much more poorly constrained. From spectropolarimetric observations of a sample of mid M dwarf stars of spectral types from M3 to M4.5, Morin et al. (2008) found that f_V is in the range of 0.10 to 0.15, with typical uncertainties of 0.03 in those values. Here, we use f = 0.15, which results in an average stellar magnetic field value of B_⋆ = 240 ± 45 G. With this value of B_⋆, the maximum cyclotron frequency would then be ν_c = 2.8 B_⋆ = 672 ± 126 MHz and ν_c = 1344 ± 252 MHz for s = 1 (fundamental ECM emission) and s = 2 (second harmonic), respectively. We note that since B_⋆ = 240 ± 45 G is the average value of the magnetic field in the surface of the star, the value near the (magnetic) poles of the star, where the ECM is most likely produced, has a larger value. On the other hand, ECM emission can be generated at some height above the stellar surface, where the local magnetic field would be smaller. We therefore assumed a nominal value of B_⋆ = 240 G and carried out observations with the uGMRT in band 4 (550–900 MHz), which covers the relevant frequency range to search for ECM radio emission that could arise from SPI in the GJ 486 system.

Fig. 1 Coverage of our uGMRT observations of the GJ 486 system folded to the orbital period of GJ 486 b of 1.47 d. Each epoch is shown with a different color. Each point corresponds to the central time of each observing epoch, with the horizontal side of the surrounding rectangle being the time span of the epoch. The vertical axis has no real meaning, and the epochs are simply offset so they do not overlap.

2.2 X-rays from GJ 486

Stellar X-ray and radio (quiescent) activity correlate well (Güdel et al. 1993). Hence, host stars that are strong X-ray emitters would be expected to also be strong radio emitters, which could jeopardize the search for radio emission from SPI.

GJ 486 was not detected in X-rays with ROSAT (upper limit of f_x = 5.37 × 10⁻¹⁴ erg s⁻¹ cm⁻²; Stelzer et al. 2013). However, recent XMM-Newton observations by Sanz-Forcada et al. (2025) resulted in a clear detection of GJ 486 in X-rays, with a flux at Earth of f_x = 4.05 × 10⁻¹⁵ erg s⁻¹ cm⁻², which is consistent with the recently reported detections by Diamond-Lowe et al. (2024). Using the relationship between radio and X-ray luminosities for M dwarf stars from Güdel et al. (1993), the X-ray luminosity of GJ 486 would result in a corresponding radio flux density of the star of a few μJy. Therefore, the expected quiescent radio emission from the star should be negligible.

3 Observations and data processing

We observed GJ 486 with uGMRT on 30 October 2021; 7, 9, 14, 16, 19, and 20 November 2021; and 14 January and 22 February 2022. We show in Fig. 1 the orbital phase coverage of our observations, which span almost the entire orbital phase of GJ 486band spread out over more than two full rotation periods of the star.

We observed GJ 486 at a central frequency of 650 MHz using a bandwidth of 200 MHz and a standard integration time of 10.7 s. We used 2048 channels in total, for a channel width of 97.7 kHz. Given the high proper motion of GJ 486 (Table 1), we centered all of our observations at α(J2000.0) = 12h47m56.00s and δ(J2000.0) = 09°45′05.00″. Each observing epoch lasted typically three to four hours, and we used a duty cycle of about 35 minutes, with 30 minutes on our target and 5 minutes on the quasar 3C 286, which we used as a bandpass, flux, and phase calibrator. The angular distance between this calibrator and GJ 486 is of ≈23°.

We performed all calibration steps using the Common Astronomy Software Application (CASA; McMullin et al. 2007; The CASA Team 2022), version casa-6.2.1-7-pipeline-2021.2.0.128. First, we used the task flagdata to flag edge frequency channels of the observing band as well as frequency channels affected by strong radio frequency interference (RFI). Following this step, we flagged dead antennas as well as 10 seconds at the start and end of each scan. We performed this initial flagging on both 3C 286 and out target field, GJ 486. Afterward, we performed an initial delay, bandpass, and gain calibration using 3C 286. First, we ran the task gaincal to perform the delay calibration, using the entire bandwidth. We then carried out a time-dependent gain calibration using gaincal again but just over a small part of the RFI-free band in order to minimize any frequency dependence. After applying the delay and time dependent gain solution on the fly, we estimated the frequency dependent gain solutions using the task bandpass. After these initial calibration steps, we implemented automated flagging using the tfcrop and rflag tasks on the residual visibilities to remove any low-level RFI and repeated the previous calibration steps. After three rounds of calibration and flagging, we found that the residual visibilities of 3C 286 looked clean. Finally, we applied the calibration solutions of the final round to our target, GJ 486. We then performed one round of automated flagging using tfcrop and rflag on the corrected visibilities of the target field. Since the central square antennas of the uGMRT have strong correlated RFIs, we performed this automated flagging step on the central square baselines and other baselines, separately.

We performed the imaging and self-calibration of our calibrated data with a modified version of the CAsa Pipeline-cum-Toolkit for Upgraded Giant Metrewave Radio Telescope data REduction (CAPTURE) package (Kale & Ishwara-Chandra 2021). Since we needed to obtain both Stokes I and V products for our science purposes, we modified the pipeline scripts. In particular, since CAPTURE only uses the Stokes I model for self-calibration, which is not suitable for Stokes I and V imaging, we made separate RR and LL models and used them during the self-calibration steps. We could perform self-calibration since there were several compact and bright-enough sources on the field of view. We first carried out four rounds of phase-only self-calibration with solution intervals of 8, 4, 2, and 1 min, followed by another four rounds of amplitude and phase calibration using solution intervals of 4,2, and 1 min for the last two rounds to obtain the final image at each observing epoch.

We computed the dynamic spectra using the dftdynspec function from the pwkit¹ package (Williams et al. 2017). This function yields the dynamic spectrum of a point source by applying a discrete Fourier transform to its visibilities. Subsequently, we re-binned the dynamic spectra into frequency bins of 0.4 MHz to explore the presence of faint structures that might remain undetected with the native channel width (97.7 kHz).

4 Results

We summarize our main results in Table 2 and Figs. 2 and 3 (with additional information in Fig. D.1). The main outcome is the non-detection of any steady radio emission above the 3σ level, where σ is the rms noise of the image, in any of our observing epochs, neither in Stokes I nor in Stokes V, at the position of GJ 486 (Table 2 and Fig. 2). We calculated the image rms within a 60 arcsecond-wide squared region centered on the position of GJ 486 (green square in Fig. 2). The rms value in the images varied from epoch to epoch, ranging from 17.6 to 39.4 μJy/b and from 9.9 to 15.2 μJy/b in Stokes I and V, respectively. We note that the rms in the Stokes V images is significantly smaller than in the Stokes I images, as the field is essentially depleted of sources emitting in Stokes V, unlike in Stokes I. We also generated an image combining all the observing epochs, which also yielded non-detections. The rms of the stacked image is 16.7 μJy/b and 8.7 μJy/b for Stokes I and V, respectively.

The rms values in Table 2 and the images in Fig. 2 correspond to the averages over the entire observing epoch, both in time and frequency. Hence, it is possible that our observations might have missed relatively bright, very short radio emission flares whose signal could have been washed out by averaging the data. We therefore obtained the dynamic spectra for all of our observing epochs, both in Stokes I and V. The dynamic spectra confirmed that there was no bursting radio emission in any of our observing epochs. As an illustration, we show in Fig. 3 the dynamic spectra for our observations on 30 October 2021.

While the dynamic spectrum of the Stokes I data seems to show some structure on the emission, the dynamic spectrum of the Stokes V shows no signal across the entire frequency and time domain, indicating that even if the features seen in the Stokes I dynamic spectrum were real, their signals were not circularly polarized and therefore were not of an ECM origin. Most likely, the apparent structure in the Stokes I data is due to artifacts and/or sidelobe contributions from other sources that were not perfectly removed from the field after the uv subtraction. We show in Fig. D.1 the rest of the Stokes V dynamic spectra. As mentioned above, there is no sign of bursting emission in Stokes V, except for a single possible burst in the 20 November observation, which is due to an instrumental effect (see Appendix D for details).

Fig. 2 Stokes I wide-field image centered on GJ 486 from band 4 (central frequency of 648 MHz) uGMRT observations on 30 October 2021. The image covers a region of ~8′ × 8′, centered at the position of GJ 486 (green cross). The synthesized beam is shown as a green solid ellipse in the bottom left. The green square corresponds to a region of 60 × 60 arcsec squared, which we have used to estimate the local rms.

Fig. 3 Dynamic spectrum of the Stokes I and V (upper and lower panels, respectively) emission from the GJ 486–GJ 486b system for our 30 October 2021 uGMRT observations in band 4, averaged in frequency (Δ ν = 0.4 MHz). The time interval used is 10.7 s (which is the integration time). There is no apparent detection of radio emission above the noise. Blank regions correspond to times when we observed the phase calibrator. The spectra at the top and right of the dynamic spectrum result from collapsing all channels (top) and times (right). For a box located on a time range from 2:00 to 2:20 and a frequency range from 0.68 to 0.72 GHz. The rms values are 13.5 and 8.4 mJy for the Stokes I and V spectra, respectively.

5 Discussion

In this section, we discuss the scenarios that could have led to the non-detection of radio emission from magnetic SPI between GJ 486b and its host star, GJ 486, and its implications for the physical and geometrical parameters of the system. First, ECM emission is intrinsically time variable, so it is possible that nature did conspire against detecting it during our observations. However, our essentially full coverage of all orbital phases of GJ 486 makes this very unlikely. We also note that since our observing campaign took place over several months, we cannot rule out that we could have missed bursting emissions between two observing epochs related to, for example, coronal mass ejections impacting the planet. Second, we cannot exclude completely the possibility that the ECM fundamental frequency fell down below our observing frequency. In fact, since the relevant magnetic field for ECM emission is the local magnetic field, if the emission took place at a significant height above the surface of the star, the field may have been significantly smaller than the one initially estimated, and our observing frequency may have been too high to detect the emission at the fundamental frequency. We note that although emission at the second harmonic could potentially have been detected by our observations, it is generally less intense than emission at the fundamental frequency and rarely observed (Melrose & Dulk 1982).

In the remaining parts of this section, we discuss the implications of the non-detections due to a too low intensity of the radio emission and/or to anisotropic radio beaming toward directions different from the observer’s. We address the former case by using a simple model to estimate the radio emission expected to arise from the (sub-Alfvénic) magnetic interaction between the star and its planet, which sets constraints on the stellar wind density at the orbit of GJ 486 b and on its planetary magnetic field 5.1. We address the latter scenario (anisotropic radio beaming) using the MASER code (Kavanagh & Vedantham 2023) to constrain the geometry of the system. MASER predicts the visibility of radio emission induced on a star via magnetic SPI as a function of time (Sect. 5.3).

5.1 Modeling the planet-induced radio emission from sub-Alfvénic interaction in GJ 486–GJ 486b

If a planet is in the sub-Alfvénic regime (M_A = v/v_A < 1), energy can be transported upstream back to the star along the stellar magnetic field line connecting to the planet (Saur et al. 2013). The key aspect, from an observational viewpoint, is that if this energy is dissipated via the ECM instability, the frequency of the emission should lie in the range of ~100 MHz to ~3 GHz, as the relevant magnetic field is B_⋆, which for M dwarfs manifest with strengths ranging from ~10 G to ~1 kG (Morin et al. 2008, 2010; Lehmann et al. 2024), which correspond to cyclotron frequencies in the above range.

The energy powering the observed ECM (radio) emission comes from the Poynting flux, S_Poynt, generated at the orbit of the planet. More specifically, it is $S_{\text{\hspace{0.17em}Poynt\hspace{0.17em}}}\propto R_{\text{eff\hspace{0.17em}}}^2{v}_{\text{rel\hspace{0.17em}}}{B}_{\perp }^2$, where R_eff is the effective radius of the planet, given by Eq. (4) below (Zarka et al. 2001; Zarka 2007) (or equal to the planet radius if the planet is not magnetized); v_rel is the relative velocity between the stellar wind flow and the planet; and B_⊥ is the component of the stellar wind magnetic field, perpendicular to the plasma velocity at the location of the planet.

The total radio power emitted from one hemisphere of the star is P_R = β S_Poynt, where β corresponds to the efficiency factor in converging Poynting flux to ECM radio emission. The value of β is not known, but it is expected to be in the range from 0.0001 to 0.01 for the planets of the Solar System (Zarka 2018). The radio flux density coming from the star can then be expressed as $$F_R=\frac{P_R}{\mathrm{\Omega }{D}^2\mathrm{\Delta }\nu },$$(2)

where Ω is the solid angle into which the ECM radio emission is beamed, D is the distance to the star from Earth, and Δν is the total bandwidth of the ECM emission. Observations of the Io-DAM emission indicate that the beaming solid angle of a single flux tube is of about 0.16 sr (Kaiser et al. 2000; Queinnec & Zarka 2001). However, various characteristics can lead to a larger solid beam of about a few times that value, including a thick emission cone wall, a planetary plasma wake, or a distorted stellar magnetic field. On the other hand, there is no reason to consider a full auroral oval around the star, which in the case of Jupiter yields a solid beam angle of 1.6 sr (see, e.g., Zarka et al. 2004). We therefore used a value of Ω = 0.5 sr in our simulations, corresponding to a few times the size of a single magnetic flux tube. We made the standard assumption that ECM radio emission has Δν = ν_g, where ν_g ≈ 2.8 B_⋆ MHz is the cyclotron frequency, and B_⋆ is the average surface magnetic field strength of the star.

We followed the prescriptions in Appendix B of Pérez-Torres et al. (2021) to estimate the observed radio emission arising from the sub-Alfvénic star-planet interaction in the GJ 486–GJ 486b system, and we considered a closed dipolar geometry for the stellar magnetic field. We computed the predicted radio emission using the Zarka/Saur/Turnpenney model².

We approximated the stellar wind of GJ 486 as an isothermal fully ionized hydrogen plasma (Parker 1958), which is characterized by the sound speed, or equivalently, the coronal temperature, T_c. We used log $T_{\mathrm{c}}={6.67}_{-0.09}^{+0.40}$ for GJ 486 from the work by Sanz-Forcada et al. (2025), who utilized XMM-Newton X-ray data to determine coronal temperatures for 21 CARMENES stars.

The stellar wind density (ρ_sw) at the orbit of GJ 486 b is not known beforehand. We therefore parameterized it via the stellar mass-loss rate, ${\dot{M}}_{\star }$: $${\rho }_{\mathrm{s}\mathrm{w}}=\frac{{\dot{M}}_{\star }}{4\pi d^2{v}_{\mathrm{s}\mathrm{w}}},$$(3)

which follows from the mass conservation equation for a time-independent stellar wind with constant ${\dot{M}}_{\star }$. Here, d is the semi-major axis of the orbit of the planet (see Table 1) and v_sw is the stellar wind speed at the planet position. The stellar wind number density is n_sw = ρ_sw/μm_p, and since we assumed a fully ionized purely hydrogen plasma, μ = 1/2.

The main difference with respect to the modeling in Pérez-Torres et al. (2021) is that here we also take into account the effect of free-free absorption. While for the nominal value of T_c its impact is negligible, for the lower limit it can significantly impact the amount of transmitted radio signal if the stellar wind mass-loss rate is very high (see Fig. 4). We show the modeling of this effect in Appendix B.

The effective obstacle radius of the planet is given by the magnetopause standoff distance of the planet, R_mp, which we obtained by assuming a pressure balance between the stellar wind pressure (dynamic, thermal, and magnetic pressures) and the planetary pressure (magnetic pressure): $$R_{\mathrm{m}\mathrm{p}}=k_{\mathrm{m}\mathrm{p}}^{1/3}{\left[\frac{{\left(B_{pl}/2\right)}^2/8\pi }{p_{\mathrm{d}\mathrm{y}\mathrm{n},\mathrm{s}\mathrm{w}}+p_{\mathrm{t}\mathrm{h},\mathrm{s}\mathrm{w}}+B_{\mathrm{s}\mathrm{w}}^2/8\pi }\right]}^{1/6}{R}_{\mathrm{p}\mathrm{l}},$$(4)

where k_mp is the factor by which the magnetopause currents enhance the magnetospheric magnetic field at the magnetopause, which is a value between two and three. For simplicity, we adopted k_mp = 2. The term B_pl is the intensity of the (dipolar) planetary magnetic field at the poles; p_dyn,sw = ρ v_rel² and p_th,sw = n_swk_BT_c are the dynamic and thermal components of the stellar wind pressure, respectively; B_sw is the magnetic field intensity of the stellar wind; and R_pl is the planetary radius. We note that Eq. (4) is an approximation of the actual value of the magnetopause standoff distance, and it does not take into account effects such as the topology or the reconnection of the interplanetary magnetic field (IMF) with the magnetic field of the planet. For instance, the tilt of the magnetic field of the planet with respect to the IMF can increase the value of R_mp for a Proxima b-like planet by a factor of up to seven (Peña-Moñino et al. 2024).

Finally, we estimated the magnetic field of the planet using Sano’s scaling law (Sano 1993). This resulted in a value of B_pl ≃0.85 G (see Appendix A), which is around 40% larger than the magnetic field of the Earth at the poles. We show in Fig. 5 the effective radius and magnetopause standoff distance as a function of the magnetic field of the planet. If B_pl ≲ 0.35 G, then the effective radius is that of the planet itself. For B_pl= 0.85 G, the nominal value of the magnetic field, the effective radius is about 40% larger than the physical radius of the planet.

Fig. 4 Fraction of transmitted SPI flux due to the effect of free-free absorption for Tc values of 1 (dot-dashed black line), 1.5 (blue dashed line), 2.5 (orange dotted line), and 4.7 (green solid line) MK.

Fig. 5 Magnetopause standoff distance, Rmp, and effective radius, Reff, as a function of the magnetic field of the planet, Bpl. If Bpl ≳ 0.35 G, Reff = Rmp; otherwise Reff = Rpl. The vertical dashed line corresponds to the nominal value of the magnetic field of 0.85 G.

Fig. 6 Predicted flux density arising at a nominal frequency of 670 MHz from SPI. The yellow (cross-hatched) areas correspond to the expected radio flux density, including (neglecting) free-free absorption from the thermal electrons in the stellar wind. The rows correspond to the expected emission for two different values of the coronal temperature, Tc= 4.7 MK (the nominal value; top row) and Tc= 2.5 MK (3σ lower limit; bottom row). The left and middle panels show the predicted flux density as a function of the stellar wind mass-loss rate for an unmagnetized planet (left) and a magnetized one with Bpl= 0.85 G (middle), with a vertical dashed line showing the nominal value, ${\dot{M}}_{\star }$ = 1.4 ${\dot{M}}_{\odot }$ (see text for details). The right panels show the predicted flux density as a function of the planetary magnetic field for the aforementioned nominal value of ${\dot{M}}_{\star }$, and a vertical dashed line corresponds to the nominal value of the magnetic field, Bpl= 0.85 G. Red areas correspond to values MA ≥ 1, that is, where the planet is in the super-Alfvénic regime; therefore model predictions are not valid. The horizontal dash-dotted lines correspond to the 3σ detection threshold of our observations (where σ = 30 μJy b−1).

5.2 Constraints from the modeling of the radio emission

In this section, we use the modeling described in Sect. 5.1 to constrain some of the physical parameters of the system in the case that the non-detections were due to the signal being too low to be detectable. We show in Fig. 6 the predicted radio emission arising from the sub-Alfvénic SPI in the GJ 486-GJ 486b system as a function of ${\dot{M}}_{\star }$ and B_pl for two different values of the coronal temperature of GJ 486: T_c = 10^6.67 = 4.7 MK (top), which corresponds to the nominal value, and T_c = 10^6.40 = 2.5 MK (bottom), which corresponds to the 3σ lower limit of the coronal temperature determined by Sanz-Forcada et al. (2025). The left panels correspond to the case of an unmagnetized planet, while the middle panels correspond to the case of a planet with B_pl = 0.85 G, which is the nominal estimated magnetic field value of GJ 486b (see Appendix A).

The vertical lines in the plots correspond to the nominal value of ${\dot{M}}_{\star }$= 1.4 ${\dot{M}}_{\odot }$, obtained by applying Eq. (7) in Johnstone et al. (2015) to the GJ 486 star and using the values in Table 1. Our predictions already take into account that the efficiency of the conversion of Poynting flux into radio emission, β, is poorly known but is very unlikely to be above 1% and possibly closer to 0.2% or even lower (Zarka 2018). This results in the yellow (cross-hatched) areas in the plots of Fig. 6, which correspond to the expected radio flux density including (neglecting) free-free absorption from the thermal electrons in the stellar wind.

The majority of M dwarfs have winds that are weaker than or comparable to that of the Sun: ${\dot{M}}_{\star }$≲ ${\dot{M}}_{\odot }$ (Wood et al. 2021; ${\dot{M}}_{\odot }$ = 2×10⁻¹⁴ M_⊙ yr⁻¹). However, Wood et al. (2021) found in their sample that two M dwarfs showed values of ${\dot{M}}_{\star }$= 30 ${\dot{M}}_{\odot }$ (YZ CMi, M4 Ve) and ${\dot{M}}_{\star }$= 10 ${\dot{M}}_{\odot }$ (GJ 15AB; M2 V + M3.5 V). Therefore, in our study of the SPI radio signal as a function of the stellar density and given our lack of knowledge of the stellar mass-loss rate of GJ 486, we used values of ${\dot{M}}_{\star }$ in the range from 0.1 up to 100 ${\dot{M}}_{\odot }$. This broad range encompasses the whole range of values inferred for M dwarfs to date (Wood et al. 2021).

Our reference case is the one shown in the top-middle panel of Fig. 6 (i.e., a magnetized planet with B_pl= 0.85 G orbiting its host star GJ 486, which has T_c= 4.7 MK). The planet is in the Sub-Alfvénic regime as long as ${\dot{M}}_{\star }$≲ 57 ${\dot{M}}_{\odot }$, so the planet-induced Poynting flux can be transferred to the star and be re-emitted as auroral ECM emission at radio wavelengths. If the stellar wind mass-loss rate were higher, the planet would always be in a super-Alfvénic regime, and there would be no emission arising from SPI. However, given the inferred value of ${\dot{M}}_{\star }$ for GJ 486, it is very unlikely that such mass-loss rates are in place. Since the (nominal) value of T_c is large, free-free absorption effects (yellow areas in the plots) are negligible, regardless of the value of ${\dot{M}}_{\star }$. For the nominal value of ${\dot{M}}_{\star }$= 1.4 ${\dot{M}}_{\odot }$, we should have clearly detected radio emission from SPI independently of the value of β. We could have expected a non-detection only if ${\dot{M}}_{\star }$ is much smaller than ${\dot{M}}_{\odot }$(${\dot{M}}_{\star }$≲ 0.3 ${\dot{M}}_{\odot }$) and, at the same time, β ≪ 0.01. If the planet is not magnetized (top-left panel), non-detections could be expected for values ${\dot{M}}_{\star }$≲ 1.2 ${\dot{M}}_{\odot }$, but this also requires small values of β. The top-right panel also shows that for the nominal value of T_c, we should have detected radio emission from SPI, whether the planet is magnetized or not, unless β ≲ 10⁻³. The bottom panels show the same set of simulations as in the top panels but for T_c= 2.5 MK. The main differences with respect to the case of T_c= 4.7 MK are the following: The planet enters the super-Alfvénic regime at much larger values of ${\dot{M}}_{\star }$(≳ 91 ${\dot{M}}_{\odot }$); and the predicted flux is about a factor of two smaller; free-free absorption effects are noticeable, since T_c is lower, albeit only for large values of ${\dot{M}}_{\star }$. The strong lower limit on T_c would have implied a detection of radio emission from SPI if ${\dot{M}}_{\star }$ ≳ 1.2 ${\dot{M}}_{\odot }$ (≳4.7 ${\dot{M}}_{\odot }$) for a magnetized (non-magnetized) planet, irrespective of the value of β. As in our reference case, non-detections imply not only very small values of ${\dot{M}}_{\star }$, but also that simultaneously the efficiency in converting Poynting flux into SPI radio emission is quite low (β ≪ 0.01). The bottom-right panel shows essentially the same results as in the top-right panel, namely that independent of whether the planet is magnetized or not, we should have expected a detection of radio emission from SPI unless β ≲ 10⁻³.

To summarize, if the non-detection of radio emission from SPI in GJ 486 was due to an intrinsically dim signal, this suggests that independent of whether the planet is magnetized or not, the mass-loss rate must have been small (${\dot{M}}_{\star }$≲ 0.3 ${\dot{M}}_{\odot }$) and that, concomitantly, the efficiency of the conversion of Poynting flux into radio emission was low, with values of β close to 0.001, or even lower. If the value of β had been higher, then detections would have been warranted, regardless of the values of B_pl and ${\dot{M}}_{\star }$.

5.3 Constraints on the geometry of the system

In the previous section, we discussed the constraints that can be inferred from modeling the radio emission, as described in Sect. 5.1, if the absence of a radio detection was due to the ECM signal being too faint to be detectable. Here we discuss an alternative scenario, namely that the signal might have been strong enough, but our lack of knowledge about the stellar rotation, magnetic field geometry, and/or orbital and emission cone geometry could have resulted in the emission being beamed out of the line of sight during our observations.

We used the MASER code developed by Kavanagh & Vedantham (2023) to determine whether this was the case. The MASER code takes in all key parameters pertaining to the geometry of the stellar rotation, stellar magnetic field, planetary orbit, and emission cone³, and it determines whether radio emission generated along the magnetic field line connecting the star to the planet is visible to the observer as a function of time (called a visibility light curve). We first constructed uninformed prior distributions for each parameter, which we list in Table 3. From each distribution, we drew one million samples for each parameter and computed the visibility light curve of the system during the observing windows listed in Table 2. (We note that we divided each window into 100 points). We then constructed a probability density for each parameter from the sets of samples that produced light curves with zero visibility. If any deviated from the assumed prior distribution, this implied that certain values for the parameter were more probable for the system.

Kavanagh & Vedantham (2023) found that certain configurations for the stellar rotation and magnetic axis produce emission that is visible for a large percentage of time. These configurations describe systems where the magnetic axis of the star is always inclined relative to the observer by the cone opening angle, α (see Fig. 2 in Kavanagh & Vedantham 2023). In the case of GJ 486, however, we found the opposite. In Fig. 7, we show a 2D probability density of the magnetic obliquity against the stellar inclination for systems with no visible emission. We observed a pattern that is effectively the opposite of what is shown in Figure 8 of Kavanagh & Vedantham (2023), that is, configurations where the magnetic axis never forms the angle α with the line of sight. We note that in Fig. 7, the darker the color, the more likely it is to have a non-detection of SPI in the GJ 486 system (assuming SPI is in action in the system and we have the sensitivity to detect it). We highlight the three most probable configurations for a non-detection of SPI, denoted as #1, #2 and #3. We show in Fig. 8 a sketch of the first possible configuration (#1). The region describes a configuration where the system is viewed edge-on, with a low magnetic obliquity. For completeness, we have also included to-scale sketches of the additional two most probable configurations inferred, #2 and #3, and show them in Appendix C. Those findings illustrate how non-detections of magnetic SPIs can also be informative when combined with numerical models such as MASER.

Fig. 7 Probability density for the stellar inclination and magnetic obliquity of GJ 486 given the non-detection of magnetic SPIs. The darker blue color corresponds to a higher probability of non-detection. The top and right panel shows the 1D histogram for each parameter. We note that this assumes that magnetic SPIs take place in the system and we have the sensitivity to detect them (see main text for details).

Fig. 8 To-scale sketch of the geometry for case #1, inferred for the GJ 486 planetary system based on our non-detection of SPIs at radio wavelengths. The system is viewed equator-on and has a low magnetic obliquity, meaning the magnetic dipole is aligned with the rotation axis (shown as a dot on the surface). The orbit of GJ 486 b is shown in blue, and the stellar magnetic field line connecting to the orbit is shown in red. The dashed lines on the stellar surface are lines of constant latitude, with the solid line showing the equator. We note that we found no bias toward any projected spin-orbit angle λ. For simplicity, we set λ = 0° here.

6 Summary and outlook

We have presented the results of the longest radio monitoring campaign on the GJ 486–GJ 486b system, whose star hosts an Earth-like rocky planet, aimed at finding evidence of radio emission arising from magnetic SPI. We observed GJ 486 with uGMRT in the frequency range 550 to 750 MHz (where we expected the cyclotron emission to take place since this covers a surface magnetic field ranging from 196 to 268 G) in nine different epochs between 30 October 2021 and 22 February 2022, covering almost all orbital phases of GJ 486b.

We obtained radio images of the region around GJ 486in both Stokes I (total intensity) and V (circularly polarized intensity). We did not detect any quiescent radio emission in any epoch above a 3σ noise floor of (33–96) μJy/b and (30–45) μJy/b Stokes I and Stokes V images, respectively. We obtained dynamic spectra in both Stokes I and V for all individual epochs, but we did not find any evidence of short bursty activity either. Our non-detections could have been due to four issues: (1) the time variability of the emission, (2) the cyclotron frequency being outside of our observing frequency window (~550 – 750 MHz), (3) an SPI radio signal too low to be detectable, and (4) the anisotropic radio beaming pointing to a direction away from the observer.

(1) Since we obtained almost full coverage of the orbital phases of GJ 486b and the resulting dynamic spectra showed no bursting signal at any time, it seems extremely unlikely that we missed the signal because of the putative SPI signal being time variable. (2) The frequency range where we observed was well tuned based on existing observations that indicate a magnetic field of about 240 G, although we cannot exclude that the maximum value of the cyclotron frequency fell below our lowest available frequency. This aspect suggests the need to either have stellar magnetic field estimates from Zeeman Doppler Imaging (ZDI) beforehand or set up simultaneous ZDI and radio observations.

We tackled the potential issue of (3) the SPI radio signal being too faint by modeling the energetics of SPI (Sects. 5.1 and 5.2). Our modeling strongly suggests that the stellar wind mass-loss rate of GJ 486 must have been small (${\dot{M}}_{\star }$≲ 0.3 ${\dot{M}}_{\odot }$), irrespective of whether the planet is magnetized or not, and that, simultaneously, the efficiency of the conversion of Poynting flux into radio emission is very low (β ≲ 0.001). If the value of β had been higher, then detections would have been warranted, regardless of the values of B_pl and ${\dot{M}}_{\star }$. We also note that free-free absorption effects are negligible, given the high value of the coronal temperature of the star (T_c= 4.7 MK), and although they are noticeable above ${\dot{M}}_{\star }$ ≈ 20 ${\dot{M}}_{\odot }$ for the strong lower limit of the coronal temperature of the star (T_c= 2.5 MK), this should not have prevented the detection of radio emission from SPI.

Finally, we discussed the alternative possibility (4) that the SPI radio signal was strong enough to be detectable but the anisotropic radio beaming could have been pointing to a direction away from our line of sight, and thus we could have missed it. To this end, we used the MASER code to constrain the geometry of the system. From our non-detections, we conclude that the magnetic obliquity and the stellar inclination are very low.

All of this illustrates how non-detections of magnetic SPIs can also be informative when combined with a numerical modeling of both the energetics giving rise to radio emission from SPI and of the geometry of the system. We emphasize the need for accurate determinations of the magnetic field strength of M stars hosting planets, for example using the ZDI method. ZDI can also provide the stellar inclination and magnetic obliquity and therefore would be an extremely useful tool to guide observing strategies at radio and other wavelengths. We also emphasize the need to obtain X-ray measurements of M dwarf stars in order to reliably determine their coronal temperatures and assess the role of free-free absorption.

We end by noting that the detection of radio emission from SPI in M dwarf systems hosting Earth-like exoplanets is proving to be very challenging, as the case of GJ 486 highlights, and the direct detection of small Earth-like exoplanets would only be viable with hypothetical space-based instruments, such as the FARSIDE initiative (Hallinan et al. 2021), among others. On the other hand, the detection of Jupiter-like planets from radio observations is more promising, as their magnetic fields are expected to be large enough to have their associated gyrofrequency above the ionosphere cutoff, and the radio emission should be much larger than that from an Earth-like planet. However, the only potential detection so far is that of τ Boo (Turner et al. 2021). While efforts at the extreme edge of low frequencies (ν ≲ 50 MHz), such as NenuFAR, are worthwhile, current low-frequency (ν ≲ 100 MHz) radio interferometers lack the necessary sensitivity and are affected by severe radio frequency interference to be able to directly detect radio emission from Jupiter-like exoplanets. Thus, we may still need to wait for LOFAR 2.0 and SKA-low to be operational.

Acknowledgements

We thank the referee, Philippe Zarka, for his thorough and insightful review, which significantly improved our manuscript. We thank Sanne Bloot for her suggestion to take into account free-free absorption effects in our modeling of the radio emission. LPM, MPT, GB, JFG, JM, GA, AA, PA, DR, MO, and JAC acknowledge financial support through the Severo Ochoa grant CEX2021-001131-S, and through the Spanish National grants PID2023-147883NB-C21, PID2020-114461GB-I00, PID2023-146295NB-I00, and PID2022–137241NB–C42, all of them funded by MCIU/AEI/ 10.13039/501100011033, LPM also acknowledges funding through grant PRE2020-095421, funded by MCIU/AEI/10.13039/501100011033 and by FSE Investing in your future. We also acknowledge the service and support of the Spanish Prototype of an SRC (SPSRC), funded by the Spanish Ministry of Science, Innovation and Universities, by the Regional Government of Andalusia, by the European Regional Development Funds and by the European Union NextGenerationEU/PRTR. GB-C acknowledges support from grant PRE2018-086111, funded by MCIN/AEI/ 10.13039/501100011033 and by ‘ESF Investing in your future’

Appendix A Planetary magnetic field

Since the planet GJ 486b has a bulk density slightly larger but close to being Earth-like, we estimated its magnetic field by assuming a Sano scaling law (Sano 1993), which is adequate for magnetized planets of the Solar System. The magnetic field moment, ℳ is then $\mathcal{M}\propto {\rho }_c^{1/2}\omega r_c^{7/2}$. Here, ρ_c is the mass density in the dynamo region, ω is the rotational speed of the planet, and r_c is the planet core radius, assumed to be ~0.55 R_pl, as in the case of the Earth. For simplicity, we assume ρ_c to be the planet bulk density, which we estimate by using the planetary mass and radius in Table 1. Since the rotational speed, ω, of GJ 486b is unknown, we assume that GJ 486b is tidally locked, so that its rotational speed is equal to the orbital speed. The surface magnetic field of GJ 486 b is then B_pl = ℳ/R_pl. Adopting B_⊕ = 0.5 G, we get B_pl = 0.85 G.

Appendix B Free-free absorption

Free-free absorption attenuates the radio signal by a factor of $e^{-{\tau }_{\nu }}$, where the optical depth, τ_ν, is defined as (Cox 2000) $${\tau }_{\nu }={\int }_{R_{\star }}^{\mathrm{\infty }}{\kappa }_{\nu }dz,$$(B.1)

We integrated along the line of sight from the site where the emission takes place, which we conservatively took as the stellar surface, to the observer (at infinity). In practice, we integrated up 10⁴ R_⋆, at which point the effect of free-free absorption became negligible in all cases. The coefficient κ_ν is (e.g., Cox 2000) $${\kappa }_{\nu }=3.692\times {10}^8(1-e^{-h\nu /k_{B}T})Z^{2}g{T}^{-1/2}{\nu }^{-3}{n}_e{n}_p[{\mathrm{c}\mathrm{m}}^{-1}],$$(B.2)

where ν is the frequency of the observed emission, h is the Planck constant, k_B is the Boltzmann constant, Z is the ionization state (+1 for a fully ionized hydrogen medium), T is the temperature of the medium (which in this case is T_c, since we assume an isothermal wind), and n_e and n_i are the electron and ion number density, respectively. All magnitudes are in cgs units. Since we have a fully ionized hydrogen plasma, n_i = n_p = n_e, where n_p is the proton density. Finally, g is the Gaunt factor, which in the radio regime is given by (Cox 2000) $$g=10.6+1.9{\log }_{10}(T)-1.26{\log }_{10}(Z\nu ).$$(B.3)

Appendix C Other geometric configurations yielding non-detections of star-planet interactions

We show in Figs. C.1 and C.2 sketches for the alternative geometric configurations # 2 and # 3 depicted in Figure 7. Those configurations maximize the probability of non-detection of SPI (see Sect. 5.3 for details).

Fig. C.1 Sketch of the geometry # 2 inferred for the GJ 486 planetary system based on our non-detection of SPIs at radio wavelengths. The system is viewed pole-on and has a low magnetic obliquity.

Fig. C.2 Same as in Fig. C.1 but for our system viewed pole-on and with a magnetic obliquity close to 90° (geometry # 3).

Appendix D Stokes V dynamic spectra

We show here all Stokes V dynamic spectra for all observing epochs, but the 30 October 2021, which is shown in Fig. 3. Note that all dynamic spectra are featureless, indicating that there is no bursting emission. The only possible exception is a burst-like signature around 07:00 hr on 20 November 2021. To determine whether this feature corresponded to a real emission, we obtained the dynamic spectra using four different phase centers. The resulting spectra had always the same feature seen in the original dynamic spectrum (centered at the position of GJ 486), implying that this bursting feature is not real, but due to an instrumental effect.

Fig. D.1 Stokes V dynamic spectra for the rest of the observing sessions. Each dynamic spectra has two other spectra associated: one collapsed in frequency and the other in time.

References

All Tables

All Figures

Fig. 1 Coverage of our uGMRT observations of the GJ 486 system folded to the orbital period of GJ 486 b of 1.47 d. Each epoch is shown with a different color. Each point corresponds to the central time of each observing epoch, with the horizontal side of the surrounding rectangle being the time span of the epoch. The vertical axis has no real meaning, and the epochs are simply offset so they do not overlap.

In the text

Fig. 2 Stokes I wide-field image centered on GJ 486 from band 4 (central frequency of 648 MHz) uGMRT observations on 30 October 2021. The image covers a region of ~8′ × 8′, centered at the position of GJ 486 (green cross). The synthesized beam is shown as a green solid ellipse in the bottom left. The green square corresponds to a region of 60 × 60 arcsec squared, which we have used to estimate the local rms.

In the text

Fig. 3 Dynamic spectrum of the Stokes I and V (upper and lower panels, respectively) emission from the GJ 486–GJ 486b system for our 30 October 2021 uGMRT observations in band 4, averaged in frequency (Δ ν = 0.4 MHz). The time interval used is 10.7 s (which is the integration time). There is no apparent detection of radio emission above the noise. Blank regions correspond to times when we observed the phase calibrator. The spectra at the top and right of the dynamic spectrum result from collapsing all channels (top) and times (right). For a box located on a time range from 2:00 to 2:20 and a frequency range from 0.68 to 0.72 GHz. The rms values are 13.5 and 8.4 mJy for the Stokes I and V spectra, respectively.

In the text

	Fig. 4 Fraction of transmitted SPI flux due to the effect of free-free absorption for Tc values of 1 (dot-dashed black line), 1.5 (blue dashed line), 2.5 (orange dotted line), and 4.7 (green solid line) MK.
In the text

	Fig. 5 Magnetopause standoff distance, Rmp, and effective radius, Reff, as a function of the magnetic field of the planet, Bpl. If Bpl ≳ 0.35 G, Reff = Rmp; otherwise Reff = Rpl. The vertical dashed line corresponds to the nominal value of the magnetic field of 0.85 G.
In the text

Fig. 6 Predicted flux density arising at a nominal frequency of 670 MHz from SPI. The yellow (cross-hatched) areas correspond to the expected radio flux density, including (neglecting) free-free absorption from the thermal electrons in the stellar wind. The rows correspond to the expected emission for two different values of the coronal temperature, Tc= 4.7 MK (the nominal value; top row) and Tc= 2.5 MK (3σ lower limit; bottom row). The left and middle panels show the predicted flux density as a function of the stellar wind mass-loss rate for an unmagnetized planet (left) and a magnetized one with Bpl= 0.85 G (middle), with a vertical dashed line showing the nominal value, ${\dot{M}}_{\star }$ = 1.4 ${\dot{M}}_{\odot }$ (see text for details). The right panels show the predicted flux density as a function of the planetary magnetic field for the aforementioned nominal value of ${\dot{M}}_{\star }$, and a vertical dashed line corresponds to the nominal value of the magnetic field, Bpl= 0.85 G. Red areas correspond to values MA ≥ 1, that is, where the planet is in the super-Alfvénic regime; therefore model predictions are not valid. The horizontal dash-dotted lines correspond to the 3σ detection threshold of our observations (where σ = 30 μJy b−1).

In the text

Fig. 7 Probability density for the stellar inclination and magnetic obliquity of GJ 486 given the non-detection of magnetic SPIs. The darker blue color corresponds to a higher probability of non-detection. The top and right panel shows the 1D histogram for each parameter. We note that this assumes that magnetic SPIs take place in the system and we have the sensitivity to detect them (see main text for details).

In the text

Fig. 8 To-scale sketch of the geometry for case #1, inferred for the GJ 486 planetary system based on our non-detection of SPIs at radio wavelengths. The system is viewed equator-on and has a low magnetic obliquity, meaning the magnetic dipole is aligned with the rotation axis (shown as a dot on the surface). The orbit of GJ 486 b is shown in blue, and the stellar magnetic field line connecting to the orbit is shown in red. The dashed lines on the stellar surface are lines of constant latitude, with the solid line showing the equator. We note that we found no bias toward any projected spin-orbit angle λ. For simplicity, we set λ = 0° here.

In the text

	Fig. C.1 Sketch of the geometry # 2 inferred for the GJ 486 planetary system based on our non-detection of SPIs at radio wavelengths. The system is viewed pole-on and has a low magnetic obliquity.
In the text

	Fig. C.2 Same as in Fig. C.1 but for our system viewed pole-on and with a magnetic obliquity close to 90° (geometry # 3).
In the text

	Fig. D.1 Stokes V dynamic spectra for the rest of the observing sessions. Each dynamic spectra has two other spectra associated: one collapsed in frequency and the other in time.
In the text