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The Very Large Array was used to observe the ultracool, rapidly rotating M9dwarf TVLM 513-46546 simultaneously at 4.88 GHz and 8.44 GHz. The radioemission was determined to be persistent, variable and periodic at bothfrequencies with a period of ~2 hours. This periodicity is in excellentagreement with the estimated period of rotation of the dwarf based on its v sini of ~60 km/s. This rotational modulation places strong constraints on thesource size of the radio emitting region and hence the brightness temperatureof the associated emission. We find the resulting high brightness temperature,together with the inherent directivity of the rotationally modulated componentof the emission, difficult to reconcile with incoherent gyrosynchrotronradiation. We conclude that a more likely source is coherent, electroncyclotron maser emission from the low density regions above the magnetic poles.This model requires the magnetic field of TVLM 513-46546 to take the form of alarge-scale, stable, dipole or multipole with surface field strengths up to atleast 3kG. We discuss a mechanism by which broadband, persistent electroncyclotron maser emission can be sustained in the low density regions of themagnetospheres of ultracool dwarfs. A second nonvarying, unpolarized componentof the emission may be due to depolarization of the coherent electron cyclotronmaser emission or alternatively, incoherent gyrosynchrotron or synchrotronradiation from a population of electrons trapped in the large-scale magneticfield.Comment: 30 pages, 8 figures. Accepted for publication in Ap

Rotational Modulation of the Radio Emission from the M9 Dwarf TVLM 513−46546: Broadband Coherent Emission at the Substellar Boundary?