[Abridged] We present the first simultaneous radio, X-ray, ultraviolet, and optical spectroscopic observations of the M8.5 dwarf TVLM513-46546, with a duration of 9 hours. These observations are part of a program to study the origin of magnetic activ
ity in ultracool dwarfs, and its impact on chromospheric and coronal emission. Here we detect steady quiescent radio emission superposed with multiple short-duration, highly polarized flares; there is no evidence for periodic bursts previously reported for this object, indicating their transient nature. We also detect soft X-ray emission, with L_X/L_bol~10^-4.9, the faintest to date for any object later than M5, and a possible weak X-ray flare. TVLM513-46546 continues the trend of severe violation of the radio/X-ray correlation in ultracool dwarfs, by nearly 4 orders of magnitude. From the optical spectroscopy we find that the Balmer line luminosity exceeds the X-ray luminosity by a factor of a few, suggesting that, unlike in early M dwarfs, chromospheric heating may not be due to coronal X-ray emission. More importantly, we detect a sinusoidal H-alpha light curve with a period of 2 hr, matching the rotation period of TVLM513-46546. This is the first known example of such Balmer line behavior, which points to a co-rotating chromospheric hot spot or an extended magnetic structure, with a covering fraction of about 50%. This feature may be transitory based on the apparent decline in light curve peak during the four observed maxima. From the radio data we infer a large scale steady magnetic field of ~100 G, in good agreement with the value required for confinement of the X-ray emitting plasma. The radio flares, on the other hand, are produced in a component of the field with a strength of ~3 kG and a likely multi-polar configuration.
