Context. The LOFAR (LOw Frequency ARray) radio telescope is a giant digital phased array interferometer with multiple antennas distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization methods. Aims. Recent papers have established a clear link between the discrete nature of radio interferometry measurement and the "compressed sensing" (CS) theory, which supports sparse reconstruction methods to form an image from the measured visibilities. Empowered by proximal theory, CS offers a sound framework for efficient global minimization and sparse data representation using fast algorithms. Combined with instrumental direction-dependent effects (DDE) in the scope of a real instrument, we developed and validated a new method based on this framework. Methods. We implemented a sparse reconstruction method in the standard LOFAR imaging tool and compared the photometric and resolution performance of this new imager with that of CLEAN-based methods (CLEAN and MS-CLEAN) with simulated and real LOFAR data. Results. We show that i) sparse reconstruction performs as well as CLEAN in recovering the flux of point sources, ii) performs much better on extended objects (the root mean square error is reduced by a factor of up to 10), and iii) provides a solution with an effective angular resolution 2-3 times better than the CLEAN images. Conclusions. Sparse recovery gives a correct photometry on high dynamic and wide-field images and improved realistic structures of extended sources (of simulated and real LOFAR datasets). This sparse reconstruction method is compatible with modern interferometric imagers that handle DDE corrections (A-and W-projections) required for current and future instruments such as LOFAR and SKA.

Context. The detection of radio emissions from exoplanets will open up a vibrant new research field. Observing planetary auroral radio emission is the most promising method to detect exoplanetary magnetic fields, the knowledge of which will provide valuable insights into the planet’s interior structure, atmospheric escape, and habitability. Aims. We present LOFAR (LOw-Frequency ARray) Low Band Antenna (LBA: 10–90 MHz) circularly polarized beamformed observations of the exoplanetary systems 55 Cancri, υ Andromedae, and τ Boötis. All three systems are predicted to be good candidates to search for exoplanetary radio emission. Methods. We applied the BOREALIS pipeline that we have developed to mitigate radio frequency interference and searched for both slowly varying and bursty radio emission. Our pipeline has previously been quantitatively benchmarked on attenuated Jupiter radio emission. Results. We tentatively detect circularly polarized bursty emission from the τ Boötis system in the range 14–21 MHz with a flux density of ~890 mJy and with a statistical significance of ~3σ. For this detection, we do not see any signal in the OFF-beams, and we do not find any potential causes which might cause false positives. We also tentatively detect slowly variable circularly polarized emission from τ Boötis in the range 21–30 MHz with a flux density of ~400 mJy and with a statistical significance of >8σ. The slow emission is structured in the time-frequency plane and shows an excess in the ON-beam with respect to the two simultaneous OFF-beams. While the bursty emission seems rather robust, close examination casts some doubts on the reality of the slowly varying signal. We discuss in detail all the arguments for and against an actual detection, and derive methodological tests that will also apply to future searches. Furthermore, a ~2σ marginal signal is found from the υ Andromedae system in one observation of bursty emission in the range 14–38 MHz and no signal is detected from the 55 Cancri system, on which we placed a 3σ upper limit of 73 mJy for the flux density at the time of the observation. Conclusions. Assuming the detected signals are real, we discuss their potential origin. Their source probably is the τ Boötis planetary system, and a possible explanation is radio emission from the exoplanet τ Boötis b via the cyclotron maser mechanism. Assuming a planetary origin, we derived limits for the planetary polar surface magnetic field strength, finding values compatible with theoretical predictions. Further observations with LOFAR-LBA and other low-frequency telescopes, such as NenuFAR or UTR-2, are required to confirm this possible first detection of an exoplanetary radio signal.