We have obtained a series of high-resolution optical spectra for the brown dwarf 2MASSW J1207334-393254 (2M1207) using the ESO Very Large Telescope with the UVES spectrograph during two consecutive observing nights (time resolution of ~12 min) and the Magellan Clay telescope with the MIKE spectrograph. Combined with previously published results, these data allow us to investigate changes in the emission line spectrum of 2M1207 on timescales of hours to years. Most of the emission line profiles of 2M1207 are broad, in particular that of Halpha, indicating that the dominant fraction of the emission must be attributed to disk accretion rather than to magnetic activity. From the Halpha 10% width we deduce a relatively stable accretion rate between 10^(-10.1...-9.8) Msun/yr for two nights of consecutive observations. Therefore, either the accretion stream is nearly homogeneous over (sub-)stellar longitude or the system is seen face-on. Small but significant variations are evident throughout our near-continuous observation, and they reach a maximum after ~8 h, roughly the timescale on which maximum variability is expected across the rotation cycle. Together with past measurements, we confirm that the accretion rate of 2M1207 varies by more than one order of magnitude on timescales of months to years. Such variable mass accretion yields a plausible explanation for the observed spread in the accretion rate vs. mass diagram. The magnetic field required to drive the funnel flow is on the order of a few hundred G. Despite the obvious presence of a magnetic field, no radio nor X-ray emission has been reported for 2M1207. Possibly strong accretion suppresses magnetic activity in brown dwarfs, similar to the findings for higher mass T Tauri stars.
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