  Studying the magnetic fields of exoplanets will provide valuable information
about their interior structures, atmospheric properties (escape and dynamics),
and potential habitability. One of the most promising methods to detect
exoplanetary magnetic fields is to study their auroral radio emission. However,
there are no confirmed detections of an exoplanet in the radio despite decades
of searching. Recently, Turner et al. 2021 reported a tentative detection of
circularly polarized bursty emission from the $\tau$ Boo exoplanetary system
using LOFAR low-frequency beamformed observations. The likely source of this
emission was presumed to be from the $\tau$ Boo planetary system and a possible
explanation is radio emission from the exoplanet $\tau$ Boo b, produced via the
cyclotron maser mechanism. Assuming the emission is from the planet, Turner et
al. 2021 found that the derived planetary magnetic field is compatible with
theoretical predictions. The need to confirm this tentative detection is
critical as a conclusive detection would have broad implications for
exoplanetary science. In this study, we performed a follow-up campaign on the
$\tau$ Boo system using the newly commissioned NenuFAR telescope in 2020. We do
not detect any bursty emission in the NenuFAR observations. There are many
different degenerate explanations for our non-detection. For example, the
original bursty signal may have been caused by an unknown instrumental
systematic. Alternatively, the planetary emission from $\tau$ Boo b is
variable. As planetary radio emission is triggered by the interaction of the
planetary magnetosphere with the magnetized stellar wind, the expected
intensity of the planetary radio emission varies greatly with stellar rotation
and along the stellar magnetic cycle. More observations are needed to fully
understand the mystery of the possible variability of the $\tau$ Boo b radio
emission.
