Modelling the radio pulses of an ultracool dwarf

Context. Recently, unanticipated magnetic activity in ultracool dwarfs (UCDs, spectral classes later than M7) has emerged from a number of radio observations. The highly (up to 100%) circularly polarized nature and high brightness temperature of the emission have been interpreted as requiring an effective amplification mechanism of the high-frequency electromagnetic waves - the electron cyclotron maser instability (ECMI). Aims. We aim to understand the magnetic topology and the properties of the radio emitting region and associated plasmas in these ultracool dwarfs, interpreting the origin of radio pulses and their radiation mechanism. Methods. An active region model was built, based on the rotation of the UCD and the ECMI mechanism. Results. The high degree of variability in the brightness and the diverse profile of pulses can be interpreted in terms of a large-scale hot active region with extended magnetic structure existing in the magnetosphere of TVLM 513-46546. We suggest the time profile of the radio light curve is in the form of power law in the model. Combining the analysis of the data and our simulation, we can determine the loss-cone electrons have a density in the range of 1.25 × 10⁵-5 × 10⁵ cm^-3 and temperature between 10⁷ and 5 × 10⁷ K. The active region has a size <1 R _Jup, while the pulses produced by the ECMI mechanism are from a much more compact region (e.g. ∼0.007 R_Jup). A surface magnetic field strength of 7000 G is predicted. Conclusions. The active region model is applied to the radio emission from TVLM 513-46546, in which the ECMI mechanism is responsible for the radio bursts from the magnetic tubes and the rotation of the dwarf can modulate the integral of flux with respect to time. The radio emitting region consists of complicated substructures. With this model, we can determine the nature (e.g. size, temperature, density) of the radio emitting region and plasma. The magnetic topology can also be constrained. We compare our predicted X-ray flux with Chandra X-ray observation of TVLM 513-46546. Although the X-ray detection is only marginally significant, our predicted flux is significantly lower than the observed flux. Further multi-wavelength observations will help us better understand the magnetic field structure and plasma behavior on the ultracool dwarf.