RAMBO I: Project introduction and first results with uGMRT

The Rigidly-Rotating Magnetosphere (RRM) model, introduced by Townsend & Owocki (2005), has been successfully applied to explain Balmer line and photometric variability in magnetic hot stars. A key component of the RRM model is stellar rotation, which supports the stellar wind material in the magnetosphere. The co-rotation of this material leads to the variability in observable diagnostics. However, amongst several remaining questions, the mass removal from centrifugal magnetospheres is still an unresolved problem. Both leakage and breakout scenarios have been proposed (Owocki & Cranmer, 2018; Owocki et al., 2020). The Centrifugal Breakout model considers that when a critical plasma density is reached, the magnetic field lines cannot confine the plasma anymore and will open up to release this material. From analytical considerations, the characteristic surface density is cast in the form of:

with $B_{K}$ the magnetic field strength at the distance of the Kepler co-rotation radius $R_{K}$, $G$ the gravitational constant, and $M_{\star}$ the mass of the star. The MHD-modified scaling by Owocki et al. (2020) invokes a stronger $R_{K}$ dependence. The plasma build-up in the centrifugal magnetosphere is a function of the obliquity angle (Townsend & Owocki, 2005). The confined mass is maximum when the rotation and magnetic axes are aligned ($\beta=0^{\circ}$), whereas the confined mass is minimum when the two axes are perpendicular ($\beta=90^{\circ}$). ud-Doula et al. (2023) performed detailed 3D simulations with oblique rotators, indeed finding plasma distribution in a warped disc or a “wing” shape along the magnetic equator.

The gyrosynchrotron radio emission observed from the magnetospheres of early-type stars is attributed to relativistic electrons gyrating along magnetic field lines. Earlier models, such as those by Trigilio et al. (2004) and Leto et al. (2006), proposed that these electrons are accelerated in the outer magnetosphere, where the stellar wind stretches magnetic field lines into a current sheet (CS) between regions of opposite polarity. In particular, Leto et al. (2006) extended the CS framework by introducing a radiation belt-like structure, where wind-driven plasma accumulates and powers emission through electron spiraling. While these models provided a foundation for understanding magnetospheric radio emission, they assumed that the stellar wind dynamics alone drove electron acceleration, excluding any significant role for stellar rotation.

Subsequent observations, however, firmly established that the strength of radio emission correlates with stellar rotation rates¹¹1Though, empirically already evidenced in smaller samples (e.g., Linsky et al., 1992)., challenging wind-driven paradigms (Leto et al., 2021; Shultz et al., 2022). This realization led to the development of rotation-centric models, such as the CBO framework (Owocki et al., 2022), which identifies stellar rotation as the primary driver of electron acceleration. In magnetic stars with centrifugal magnetospheres, plasma accumulates near the Kepler co-rotation radius, where centrifugal forces balance gravity. When the plasma density exceeds a critical threshold (Equation 3), magnetic tension can no longer confine the material, triggering centrifugal breakout events. These events trigger magnetic reconnection, releasing stored magnetic energy that accelerates electrons to relativistic speeds. These high-energy electrons then spiral along magnetic field lines, generating the observed gyrosynchrotron emission.

The CBO model offers several advantages over earlier approaches. It explains the observed strong dependence of radio luminosity on both the stellar rotation rate and magnetic field strength. Unlike the CS models, which rely solely on wind dynamics, the CBO framework places stellar rotation as the main energy source powering radio emission. A key refinement to the CBO model emphasizes the quasi-steady-state nature of magnetospheres in these stars (Shultz et al., 2022). Instead of sporadic, large-scale breakouts, the magnetosphere appears to self-regulate near the critical breakout density, allowing for continuous, small-scale centrifugal breakout events. This quasi-continuous process sustains the production of relativistic electrons through localized reconnection, maintaining steady gyrosynchrotron emission over time. The framework also reconciles the long-term stability of magnetic fields with their role as a conduit for rotational energy. Together, these models underscore the evolving understanding of magnetospheric processes, with CBO-driven reconnection emerging as a robust explanation for observed radio emission.

The CBO model predicts that the observable non-thermal radio luminosity from a magnetic hot star should scale with the CBO luminosity $L_{\rm CBO}$, which can be cast in the form of:

with $\dot{M}$ the mass-loss rate, $\Omega$ the surface angular velocity, $R_{\star}$ the stellar radius, $\eta_{c}$ the centrifugal magnetic confinement parameter, and $p$ the multipole index (Eq. 13 of Owocki et al. (2022)). For a dipole, $p=2$, and for a split monopole field, $p=1$. Interestingly, in the latter case, $\dot{M}$ cancels out and the CBO luminosity scales as $L_{\rm CBO}\propto B^{2}R_{\star}^{4}P_{\rm rot}^{-2}$, with $B$ the surface magnetic field strength and $P_{\rm rot}$ the rotation period of the star. This scaling was indeed found by Leto et al. (2021) and supported by Shultz et al. (2022). Thus, it is empirically well-established that both magnetic field strength and rotational velocity scale positively with the observed radio luminosity²²2The rotation period, the inverse of the rotational velocity, scales with a negative power..

The key success of the CBO model is the first, theoretical interpretation of stellar rotation as the energy source behind radio emission. However, Eq. 2 is a purely theoretical quantity, which has been equated with the observable radio luminosity. Some corrections are therefore necessary to be incorporated. Firstly, Shultz et al. (2022) and Owocki et al. (2022) invoke a large $10^{-8}$ scaling down of the CBO luminosity to equate it with the radio luminosity. The origin of the scaling factor is only broadly attributed to plasma heating, which would consume most of the CBO luminosity. These contributions urgently need to be disentangled for more accurate predictions. Furthermore, some observationally-motivated corrections are yet to be described in the CBO model. On the one hand, Shultz et al. (2022) and Owocki et al. (2022) found that including the obliquity angle and re-introducing the mass-loss rate dependences improve the fit to the observed sample. However, the role of the obliquity angle is only discussed in terms of the plasma distribution in the magnetosphere (following the RRM model). There is nonetheless also an impact of the obliquity angle on the radio emission in terms of the magnetosphere’s alignment towards the observer. This is also evidenced by the variable gyrosynchrotron radio emission, when available over the entire rotation cycle. Though this variation of gyrosynchrotron emission is expected to be small (a factor of two to three) in comparison to peaks caused by ECME (an order of magnitude increase). Indeed, the variation of gyrosynchrotron emission is found to be about a factor of two in one star over its entire rotation cycle (showing minimum gyrosynchrotron emission at magnetic nulls, Das et al. 2022c).

While the mass-loss rates, somewhat surprisingly, vanish from the formal CBO scaling for a split-monopole, it is clear that self-absorption in the magnetosphere can attenuate radio emission. This correction, particularly to explain O-type stars, is yet to be quantitively incorporated into the model.

Insofar, it remains to be explored whether magnetic hot stars would also emit non-thermal radio emission if they rotate slowly. This would point to a different mechanism powering the radio emission. Some works also discuss the potential to establish a more general scaling relation for ordered magnetospheres, including hot magnetic stars, ultracool dwarfs, planets such as Jupiter, and exoplanets (e.g., Leto et al., 2021; Owocki et al., 2022). However, before these broader goals can be investigated, it is crucial to confront the CBO model with improved and more extended data sets of magnetic hot stars and incorporate physically motivated roles of obliquity and mass loss. To further advance with these goals, we introduce the RAMBO project.

The detailed physical characterization of massive stars is essential to entangle the evolutionary pathways that lead to various kinds of supernovae, compact objects and their mergers, and hence astrophysical transients, such as gravitational waves, gamma-ray bursts and fast radio bursts (FRBs). The study of magnetic massive stars can provide a bridge to understanding the conditions that give rise to magnetars. Recent discoveries suggest that magnetars are the origin of some FRBs, producing brief but intense bursts of radio waves (e.g., CHIME/FRB Collaboration et al., 2020; Bochenek et al., 2020; Zanazzi & Lai, 2020). Therefore, the characterization of their progenitors could improve the formation channel and population synthesis studies. Radio observations of hot stars directly probe into their magnetospheres, where accelerated particles generate non-thermal emission. By extension, these observations may also offer complementary insights into the mechanisms behind magnetar-produced FRBs.

For these reasons, the “RAdio Magnetospheres of B and O stars” (RAMBO) project aims to help currently ongoing efforts to study magnetospheric physics in hot ($T_{\rm eff}\sim 10-40$ kK), high-mass ($M_{\star}>2$ M_⊙) stars. Primarily those radio facilities are used that have demonstrated capabilities of observing magnetic hot stars in the sub-GHz and few GHz bands, such as uGMRT, jVLA, and MeerKAT. Our explicit goal is to have a critical investigation of the origin and physical nature of radio emission from ordered magnetospheres, both on observational and theoretical grounds. The RAMBO project has three main objectives.

1. 1.

   Detect gyrosynchrotron radio emission from those stars that are in the physically preferred parameter space according to the CBO model.

2. 2.

   Monitor magnetic hot stars over their entire rotation periods and study the variability of radio flux. Identify ECME pulses and scrutinize their properties.

3. 3.

   Propose a theoretical explanation and critically evaluate the CBO model with improved data.

For the uGMRT campaign, our goal is to detect radio emitters for the first time, that is, to identify gyrosynchrotron emission³³3It is also possible that in given phases, the stars would display ECME. This could only help the identification of these objects as radio emitters since ECME typically has an order of magnitude higher radio flux than gyrosynchrotron emission. from magnetic hot stars. Our targets are in the ”preferred” parameter space of the magnetic field strength-rotation diagram, therefore, on a theoretical basis, they should show radio emission. More specifically, from the overall target selection, we further constrain the parameter space to stars with magnetic field strengths above 3 kG and rotation periods less than 3 days (shown with grey area in Figure 1). According to the CBO model, the 12 stars with previous non-detections should be radio emitters. Their expected radio flux should be similar to other stars in this parameter range. We received time allocation to observe some of these targets with uGMRT. In the present paper, we discuss 5 stars from the first set of observations (ID: 45_013, PI: Keszthelyi). Further observations and results will be presented in a forthcoming publication (Kurahara et al., in prep.).

The uGMRT is located in Pune, India, and consists of 30 antennas. We conducted band 4 (550–750 MHz) observations of the targets. We specifically requested band 4 because this range has been proven successful in identifying radio bright sources (Chandra et al., 2015; Shultz et al., 2022). The observations were performed in parallel using both narrow-band and wide-band modes. We utilize the wind-band data. The use of the GWB backend system of uGMRT allows for wider bandwidth data, in comparison to the older GSB backend system. This results in an improved signal-to-noise ratio (S/N) compared to earlier observations. The central frequency was 650 MHz with a total bandwidth of 200 MHz. We obtained full-Stokes polarization data.

The observations were carried out over five sessions from December 3 to 5 and December 24, 2023. Each scheduling block alternated between target objects. At the beginning and the end of each observing session, we observed 3C138 and 3C84 for 10 minutes as flux density, bandpass, and polarization calibrators. The gain calibrator, J0706-231, was observed for 5 minutes every 30 minutes. According to the observation logs, 26 or 27 antennas were used during the sessions. When the scheduled calibrators had already set, 3C147 was used as a substitute (applied only to the first sessions observing HD55522 and HD36668). The details of the observations are summarized in Table 1.

We used SPAM (Source Peeling and Atmospheric Modeling; Intema et al. 2017), which is based on the Astronomical Image Processing System (AIPS), for data reduction. SPAM utilizes AIPS version 31DEC13 and is controlled via ParselTongue version 2.3 (with Python 2.7). Since there were several bright compact sources in the field of view, and the beam pattern of these bright sources was clearly visible in the dirty image, direction-dependent calibration (DDC; Intema et al. 2017) was applied to improve the dynamic range of the final image. For direction-dependent calibration, the Tata Institute of Fundamental Research (TIFR) GMRT Sky Survey (TGSS; Intema et al. 2017) source catalog was used. Imaging in SPAM was performed with a Briggs robustness parameter of -1.0.

For the analysis of the wide-band data, the dataset was divided into 4 sub-bands from 550 MHz to 750 MHz with 50 MHz increments. Each sub-band was analyzed individually and then combined using WSClean (w-stacking clean; Offringa et al. 2014) to produce the full-bandwidth (200 MHz) radio image, centered at 650 MHz. Since all the targets were point sources located at the center of the field of view, advanced techniques such as multi-scale cleaning and primary beam correction were not employed. We used auto-mask and no negative options. For HD22470, lower bandwidth data was used because RFI severely impacted the observations. This means that the effective integration bandwidth was halved compared to the other targets. Since the stars are effectively point sources, i.e., the beam size is comparable to the measurement area, we equate the intensity measurement ($I$ [Jy/beam]) with the flux density at the central wavelength ($F_{\nu=650\rm MHz}$ [Jy]).

To localize our targets in the sky, we used publicly available optical and infrared data from SDSS and 2MASS, respectively. The fits files were downloaded from the SkyView portal⁴⁴4https://skyview.gsfc.nasa.gov/. Since the targets are bright stars, they are saturated in the SDSS images. Therefore we use the 2MASS K-band images to determine the area within which we measure the radio flux. Upon inspecting the images, we also used the SIMBAD Astronomical Database⁵⁵5https://simbad.cds.unistra.fr/simbad/ to cross-match the radio observations with any known radio sources in the field of view.

The H$\alpha$ profiles provide information on the centrifugal magnetospheres, while the Stokes $V$ parameter reflects on the magnetic characteristics. Therefore, with the goal of visual inspection of the H$\alpha$ and Stokes $V$ profiles, we also reviewed optical spectropolarimetric observations of our targets, which were retrieved from the PolarBase portal ⁶⁶6https://polarbase.irap.omp.eu/ (Petit et al., 2014).

CPD-271791 is a helium-strong early B-type star (Garrison et al., 1977; Walborn, 1983). The effective temperature determined by Zboril & North (1999) and Shultz et al. (2022) are $T_{\rm eff}=22.7$ kK and $T_{\rm eff}=23.8\pm 1.6$ kK, respectively. The magnetic field measurements were reported by Järvinen et al. (2018). Since the optical spectropolarimetric data does not cover the entire rotation period of the star, the line-of-sight magnetic field strength indicates a minimum value of the assumed dipolar magnetic field with $B_{\rm p}>3.9$ kG. We adopt this value in our calculations, keeping in mind that the real value might be higher and that the geometry might differ from a pure dipole. The rotation period was determined by phasing the optical photometric variability. This yielded $P_{\rm rot}=2.641$ d (Järvinen et al., 2018). The star is reported as an H$\alpha$-bright source by Shultz et al. (2020). They calculated a Kepler co-rotation radius of $R_{K}=4.1\pm 0.2$ R_⋆. Although, the obliquity angle (tilt of the magnetic axis compared to the rotation axis in a clockwise direction), $\beta$, cannot be constrained from the single spectropolarimetric data, Shultz et al. (2020) argue that based on the shape of the H$\alpha$ profile, a high obliquity angle is likely. Therefore we assume $\beta=90^{\circ}$ in our calculations. Furthermore, based on previous inferences on the projected rotational velocity and rotation period, Shultz et al. (2020) infer an inclination angle of the rotation axis compared to the observer of $i=35\pm 10^{\circ}$.

Previously, radio observations with VLA were conducted in the 5 GHz range (Drake et al., 1987; Linsky et al., 1992). The non-detection is constrained with a 180 $\mu$Jy upper limit on the radio flux. To our knowledge, there has not been newer radio observation specifically focused on this star. In particular, the GMRT archive search revealed no previous observation of this target.

From our observations with uGMRT at a central frequency of 650 MHz, we conclude a non-detection since the root-mean-square (rms) flux density is below the standard deviation. To provide a 3$\sigma$ upper limit, we report the value of the standard deviation times three. This standard deviation is measured in a radio-quiet area near the source (within 2 arcmin of the source in the 60 arcmin-size image). The upper limit is 91 $\mu$Jy.

For CPD-271791, the absence of long-term spectropolarimetric monitoring means that the full rotational phase curve of the magnetic field is unconstrained. As a result, the inclination and obliquity angles cannot be reliably inferred, limiting the ability to model the magnetospheric geometry. Similarly, phase-resolved radio observations are unavailable for this star, precluding an assessment of variability over the rotation cycle, which may include critical features such as variability in gyrosynchrotron emission or peaks associated with auroral radio emission.

HD22470 (20 Eri) is a chemically peculiar (Si) Bp star. Netopil et al. (2008) obtained an effective temperature of $T_{\rm eff}=13.8\pm 0.3$ kK, while Paunzen et al. (2021) found $T_{\rm eff}=12.6\pm 0.3$ kK. The magnetic field of the star was first measured by Borra et al. (1983). Given the coverage of the optical spectropolarimetric data, a line-of-sight magnetic field phase curve could be established (Bychkov et al., 2021). Shultz et al. (2020) found a dipolar magnetic field strength of $B_{\rm p}=7.5$ kG. Based on photometric observations, the rotation period of the star was constrained and refined by several authors over the years (Renson & Manfroid, 1981; Adelman & Boyce, 1995; Adelman, 2000a; Dubath et al., 2011; Bernhard et al., 2020; Pyper & Adelman, 2021). Shultz et al. (2020) found that the $P_{\rm rot}=1.929$ d rotation period provides a good phasing for both the photometric and spectropolarimetric data. Shultz et al. (2020) calculate an inclination angle of $i=44^{\circ}$. A high obliquity angle is inferred for this star with $\beta=87^{\circ}$ (Glagolevskij, 2010; Shultz et al., 2020).

5-GHz radio observations of HD22470 are reported by Drake et al. (1987) and Linsky et al. (1992). The non-detection is constrained with an upper limit of 360 $\mu$Jy. The GMRT archive search yields one previous observation that contained this star in the field of view with 18 min on-source time at 325 MHz frequency band (ID: 14HSA01, PI: Shukla).

At the position of the sky associated with the target according to the 2MASS image, we find that the rms radio flux is below the standard deviation. Therefore, from our uGMRT observations, we report a 3$\sigma$ upper limit of 657 $\mu$Jy for a non-detection in HD22470.

HD36668 (V* V1107 Ori) is a helium-weak chemically peculiar (Si) B-type star (Topil’Skaya, 1993; Adelman, 2000b) with an effective temperature of $T_{\rm eff}=$13.5 kK (Romanyuk et al., 2017). The first magnetic field measurements were obtained by Borra (1981). The line-of-sight magnetic field strength shows a quasi-sinusoidal variation. The dipolar field strength is estimated to be 4.5 kG (Romanyuk et al., 2021; Shultz et al., 2022). Notably, Shultz et al. (2022) infer a magnetic field strength that may contain a significant quadrupolar contribution. From TESS light curve analysis, Romanyuk et al. (2021) obtained $P_{\rm rot}=2.1204$ days. Since this rotation period does not provide a coherent phasing for the line-of-sight magnetic field variability, Shultz et al. (2022) also inspected the TESS light curve and refined the rotation period to $P_{\rm rot}=2.1192$ days, concluding that further observations are required to better constrain both the magnetic field strength and the rotation period of this star. Shultz et al. (2022) reported an obliquity angle of $\beta=80^{\circ}$. From the known stellar and rotational parameters, we estimate an inclination angle of $i=60^{\circ}$.

According to Shultz et al. (2022), Drake et al. constrained the radio flux with an upper limit of 210 $\mu$Jy at 10 GHz. While GMRT observations that contain HD36668 in the field of view exist (ID: 27_048  PI: Chandra and ID: 40_069, PI: Bhattacharyya), to our knowledge, they were not analyzed and reported previously in the context of aiming to detect radio emission from this target. We report a non-detection with a 3 $\sigma$ upper limit of 92 $\mu$Jy for HD36668 from our new uGMRT observations.

HD49333 (12 CMa) is an $\alpha^{2}$ CVn variable, helium-weak Bp star with an effective temperature of $T_{\rm eff}=15.8\pm 0.1$kK (Netopil et al., 2008). It shows variable helium and silicon lines (e.g., Pedersen & Thomsen, 1977; Farthmann et al., 1994; Bailey & Landstreet, 2013; Monier, 2023). The star’s magnetic field has been studied by Borra et al. (1983); Bohlender et al. (1993). Shultz et al. (2022) concluded a dipolar magnetic field strength of $B_{\rm p}=3.6$ kG. A rotation period of $P_{\rm rot}=2.180$ d was constrained by several authors (Pedersen, 1979; Bohlender et al., 1993; Adelman, 2000a; Renson & Catalano, 2001). Shultz et al. (2022) used this rotation period to phase the line-of-sight magnetic field variability (see also Bychkov et al., 2021), and found a magnetic obliquity angle of $\beta=85^{\circ}$. This is consistent with the discussion of Bohlender et al. (1993). While Farthmann et al. (1994) estimated an inclination angle between 25 and 55^∘, based on the newer stellar and rotational parameters we obtain $i=65^{\circ}$.

Linsky et al. (1992) conducted radio observations of the star, finding an upper limit of 220 $\mu$Jy for the non-detection at 5 GHz. There is no record of observations of this target in the GMRT archive. From our uGMRT observations, we find a non-detection with a 3$\sigma$ upper limit of 159 $\mu$Jy.

HD55522 (*26 CMa) is a helium-strong B-type star with an effective temperature of $T_{\rm eff}=17.4\pm 0.4$kK (Briquet et al., 2004; Petit et al., 2013). The radial velocity variations hint at pulsations rather than binarity (De Cat & Aerts, 2002; Gontcharov, 2006; Aerts et al., 2014; Bodensteiner et al., 2018)). Recently, Stochastic Low-Frequency variability (Bowman et al., 2019; Bowman & Dorn-Wallenstein, 2022) was also reported in this star (Shen et al., 2023). The line-of-sight magnetic field variations are well-established (Kochukhov & Bagnulo, 2006; Bagnulo et al., 2015), and indicate a dipolar structure with strength of $B_{\rm p}=$3.1 kG (Shultz et al., 2018, 2019a). A rotation period of $P_{\rm rot}=2.7292$ d is obtained, which fits well the optical photometric and spectropolarimetric datasets (Briquet et al., 2004; Shultz et al., 2018). The inclination angle reported by Briquet et al. (2004) is $i=80\pm 10^{\circ}$, while Shultz et al. (2019a) find $i=61\pm 8^{\circ}$. We adopt the latter value. A magnetic obliquity angle of $\beta=89^{\circ}$ is found by Shultz et al. (2019b, 2022).

X-ray observations yielded no detection in this star (Nazé et al., 2014). Previous radio observations were obtained with GMRT (ID: 25_045, PI: Bhattacharyya and IDs: 27_048, 28_075, PI: Chandra). Shultz et al. (2022) analyzed the observations from 2015 September 15 (HJD: 2457280.57) and concluded a non-detection with an upper limit of 223 $\mu$Jy (in their Table B1, but 370 $\mu$Jy in their Table D1).

We observed this target two times in December 2023. On December 3, 2023, we observed HD55522, which led to detection, with the rms flux density higher than three times the standard deviation in the measured region. The region was determined from the K-band 2MASS image. We detect radio emission of $F_{\nu=650\rm MHz}=(164\pm 26)$ $\mu$Jy, and we associate it with the star (Figure 3). We determine the flux density as the peak within the measured region (see Figure 3), while the uncertainty is adopted as the standard deviation of the image. Given the observation and analysis strategy, the uncertainty for radio detections is expected to be of the order of 10% of the measured flux (Kurahara et al., 2023). Indeed, adopting the worst-case consideration, that is, considering the standard deviation of the image as the measurement uncertainty, the uncertainty is 16% of the measured flux density.

On December 5, 2023, we re-observed this star. This led to a non-detection, which we constrain with a 3$\sigma$ upper limit of 96 $\mu$Jy. This is consistent with the expectation that the gyrosynchrotron emission weakens by a factor of a few between different rotational phases. We further elaborate on this in Section 6 regarding data quality and phase constraints.

Figure 6 illustrates the observed phases of four of the five stars in our current observational sample, showing the rotational modulation of their line-of-sight magnetic field ($B_{z}$). Observed phase curves are an essential diagnostic tool in magnetospheric studies of hot stars, as they provide insights into the geometry and temporal behavior of a star’s magnetic field over its rotation period, which are crucial for evaluating phenomena such as CBO and the origin of gyrosynchrotron emission.

For the present study, we were able to reconstruct phase curves for HD22470, HD36668, HD49333, and HD55522, based on the long-term spectropolarimetric monitoring data from Bohlender et al. (1993), Shultz et al. (2020), and Shultz et al. (2022). These observations allow us to map the rotational modulation of $B_{z}$ for each of these stars, which is presented as a sinusoidal curve. In contrast, CPD-271791 has not yet been subject to long-term monitoring, therefore its phase curve remains unconstrained. Establishing phase curves for all targets would be valuable in future campaigns to enable a full analysis of each star’s magnetospheric behavior.

In each panel of Figure 6, the sinusoidal curve represents the theoretical variation in $B_{z}$ expected from a dipolar magnetic geometry, modulated by the star’s rotation period. These are well matched by the previous spectropolarimetric data. The red and purple shaded regions indicate the time span of our uGMRT radio observations, providing constraints on the magnetic field alignment during those times. By comparing the radio flux observed at different phases with the corresponding $B_{z}$ values, we can begin to assess whether phase-dependent modulation of the magnetic field influences the radio emission characteristics.

Our detection of radio emission from HD55522 is at a rotational phase close to magnetic maximum. On the other hand, we are unable to confirm detection at a subsequent rotation phase, at magnetic null. Since at the time of magnetic null the magnetic geometry has a preferential alignment to detect ECME, we inspected the data if a short burst of coherent emission could be identified.

Recently, the flux peaks caused by auroral radio emission are actively being investigated (Das et al., 2022a, b, c; Das & Chandra, 2023; Das et al., 2024; Kajan et al., 2024). In most cases, ECME is expected at times of magnetic null, though in some cases the tendency is not so clear. Since two of our targets were observed at their magnetic nulls, we have further inspected the data, searching for signs of ECME.

To obtain light curves, the data was binned into shorter time intervals. We used WSclean to create images accordingly. Considering the number of visibility data points, the -intervals-out parameter was set to 10 for HD55522 (epoch 2) and to 8 for HD222470. It is important to note that the beam size varies due to differences in uv coverage for each dataset.

For each subset of the data, the peak flux within a circular region of 4.0 arcseconds in radius (approximately equivalent to the beam major axis, BMAJ) centered on the source was measured. Additionally, the standard deviation within a circular region of 30 arcseconds in a radius centered 2 arcminutes north of the source was calculated. The S/N was determined by taking the ratio of the peak flux to the standard deviation. For cases where the S/N exceeded 5, the measured peak flux was adopted. Otherwise, three times the standard deviation was used as an upper limit.

Despite careful analysis, no clear ECME bursts were identified in the light curves of HD55522 or HD22470 at their magnetic null phases. The absence of detectable coherent emission could result from several factors. First, the emission might occur at frequencies outside our observational band. ECME often exhibits a narrow spectral range, and our observations, centered at 650 MHz, might have missed the emission if its peak lies at lower or higher frequencies. Second, the measurement sensitivity is lower than in case of the time-integrated data, potentially missing a fainter emission.

This analysis underscores the importance of phase-resolved and multi-frequency observations to comprehensively characterize ECME in magnetic hot stars. Future studies should focus on continuous monitoring over entire rotation cycles and extend coverage to both lower and higher frequencies to account for variability in ECME. The absence of ECME in our observations does not rule out its occurrence in these stars, as magnetic nulls remain the most likely phases for such emission. Detecting ECME in more magnetic hot stars will provide critical insights into the conditions that drive this emission, such as the local electron density and magnetic reconnection processes in centrifugal magnetospheres. Expanding the sample size and observing strategies will be pivotal for establishing the prevalence and properties of ECME (Das et al., 2022b). We obtained VLA and MeerKAT observations over the rotation cycle of two stars, which will be reported in forthcoming publications (Sakemi et al., in prep.).

The rms noise levels obtained from our data typically reach tens of $\mu$Jy beam^-1, which is consistent with the noise level expected from the integration time. However, the image quality is not good due to sparse uv-coverage, which results in incomplete sampling of spatial frequencies and introduces artifacts in the synthesized beam. These distortions can appear as patterns around bright sources, often resembling concentric rings or streaks, depending on the coverage and weighting scheme used. Despite the use of techniques such as source peeling and other direction-dependent calibrations to account for ionospheric distortions and antenna-based errors, we find that completely mitigating contamination from bright sources remains challenging, particularly for sources located near the target in the field of view. This contamination can elevate the local noise floor and obscure faint emissions, limiting our ability to detect weak radio signals from the targets.

In particular, some targets have nearby bright radio sources in the field of view, which limits their detectability (Figures 7-10). CPD-271719 and HD36668 have nearby uncataloged radio bright sources. The angular separation is large, clearly implying that these sources cannot be associated with the star. HD49333 has the nearby radio source NVSS J064706-210033 (Stein et al., 2021), and several uncataloged radio bright sources. One nearly overlapping source in particular could strongly affect the detectability. In the case of HD22470, the data quality was severely impacted by RFI, leading to a narrow-band measurement, in contrast to the more favorable wide-band measurements. In this case, the previous upper limit (obtained from higher frequency observations) could not be improved. It is worth revisiting this target with improved sensitivity and data quality because the obtained upper limits imply a notably lower radio luminosity than expected from the CBO relation.

For HD55522, we cannot confirm radio detection at the second epoch of observations. The data quality is broadly similar to the one obtained at the first epoch, and the same integration time was used. This suggests that the non-detection at the second epoch is perhaps more likely caused by variability in the emission. Indeed, we deem that this detection is just missed by the lower gyrosynchrotron emission due to the observed phase of the star at the second epoch (magnetic null).

These limitations suggest that our non-detections are most likely due to insufficient measurement sensitivity rather than the absence of radio emission. For these targets, achieving higher signal-to-noise ratios, particularly in fields with strong source contamination, will require longer integration times and improved observational setups, such as MeerKAT or the Square Kilometre Array (SKA).

The SKA offers an unparalleled opportunity to advance our understanding of the magnetospheres of massive stars. With its unprecedented sensitivity, broad frequency coverage, and rapid survey speed, the SKA will significantly enhance the detection and characterization of non-thermal radio emission from magnetic OB stars (Dewdney et al., 2009; Braun et al., 2015). The SKA’s ability to perform phase-resolved monitoring of gyrosynchrotron and electron cyclotron maser emission across the rotation periods of a large number of stars will be transformative. For example, while current observations often capture only snapshots of emission at specific phases, the SKA will enable precise mapping of variability patterns and distinguishing between emission mechanisms tied to the star’s magnetic geometry.

The SKA’s wide frequency range, spanning from 50 MHz to 15 GHz across its Low and Mid components, is critical for constraining the SED of magnetic hot stars. Cross-calibrated, multi-frequency observations from the SKA will refine models of particle acceleration and allow for testing predictions such as the spectral turnover and the flat SEDs assumed in scaling relations (Shultz et al., 2022). Such observations will also provide insights into the physical conditions in the magnetosphere, such as plasma density, magnetic field topology, and loss mechanisms.

For HD55522, which displays a gyrosynchrotron flux density of  160 $\mu$Jy at 650 MHz, the SKA1-Mid would achieve a signal-to-noise ratio of  70 in just 10 minutes, compared to 40 minutes with the uGMRT. The SKA’s sensitivity and speed would allow the detection of similar emissions from stars up to 10 times farther away, effectively expanding the observable sample volume by a factor of 1000. Additionally, for stars with lower radio luminosities, such as those with marginal or non-detections in the current study, the SKA would lower flux limits by more than an order of magnitude, detecting emission even from stars with dense, self-absorbing magnetospheres⁷⁷7https://www.skao.int/en/science-users/118/ska-telescope-specifications. These capabilities will not only solidify scaling relations like the CBO-radio luminosity correlation but also extend them to a broader parameter space, encompassing more diverse stellar populations (Owocki et al., 2022; Shultz et al., 2022).

The SKA’s ability to push the boundaries of sensitivity, frequency coverage, and spatial resolution will allow for a much improved statistical exploration of magnetic massive stars, revealing how their radio emission evolves with stellar parameters such as rotation, magnetic field strength, and mass-loss rates. By enabling detailed studies of individual systems and population-level trends, the SKA will bridge gaps between theory and observation, significantly advancing our understanding of magnetospheric processes and their implications for massive star evolution.

Expanding radio observations to a larger sample of magnetic massive stars could refine our understanding of how magnetospheric properties vary across different stellar parameters, such as magnetic field strength, rotation rate, and stellar wind density.

Our findings at radio frequencies underscore the need for a multiwavelength approach to fully understand magnetospheric processes in massive stars. In particular, X-ray emission has been reported in previous studies (e.g., Babel & Montmerle, 1997; Nazé et al., 2014). Combining radio data with X-ray observations could reveal complementary insights into particle acceleration mechanisms, plasma density, and magnetic reconnection events within stellar magnetospheres. High-energy X-ray follow-up observations can also test for hot plasma signatures associated with shocks or magnetic reconnection, which are anticipated by the CBO model.