Phase connecting multi-epoch radio data for the ultracool dwarf TVLM 513-46546

Context. Radio data obtained for the ultracool dwarf TVLM 513-46546 has indicated a rotation period of ≈ 1.96 h via regular radio pulses, but how stable is this period. This has major implications regarding the stability of the magnetic field structures responsible for the radio emission from the ultracool dwarf. Aims. The aim of the present work is to investigate the stability of this rotation period using two datasets taken ≈ 40 days apart, some 12 months after the first report of periodical pulses in the radio data. Methods. Here we use a Bayesian analysis method which is a statistical procedure that endeavours to estimate the parameters of an underlying model probability distribution based on the observed data. Results. Periodical pulses are detected in datasets taken in April and June 2007, with the pulses being confined to a narrow range in the rotation period. This is in contradiction to a previous report of only aperiodic activity in the April 2007 dataset, while in fact both datasets have a periodic signal with a false alarm probability < 10 ^-12. These two datasets are then used to derive a more accurate period (previously determined to be 1.96 h) of 1.96733 ± 0.00002 h. Conclusions. The similarly in the burst structure in datasets taken several weeks apart point towards the stability of an electric field structure which is somehow generated and sustained within the magnetosphere of the ultracool dwarf. The derived period of 1.96733 h is consistent with the period derived via radio and optical data taken some 12 months prior to the present observations and implies the near phase constancy of the pulsed emission. This suggest the presence of stable large-scale magnetic fields on timescales of more than 1 year. The characteristics of the pulses suggest that they are produced by the electron cyclotron maser (ECM) instability.