We present multi-epoch radio and optical observations of the M7 dwarf 2MASS J13142039+1320011 .
We detect a \sim 1 mJy source at 1.43 , 4.86 , 8.46 and 22.5 GHz , making it the most luminous radio emission over the widest frequency range detected from an ultracool dwarf to date .
A 10 hr VLA observation reveals that the radio emission varies sinusoidally with a period of 3.89 \pm 0.05 hr , and an amplitude of \approx 30 \% at 4.86 GHz and \approx 20 \% at 8.46 GHz .
The periodicity is also seen in circular polarization , where at 4.86 GHz the polarization reverses helicity from left- to right-handed in phase with the total intensity .
An archival detection in the FIRST survey indicates that the radio emission has been stable for at least a decade .
We also detect periodic photometric variability in several optical filters with a period of 3.79 hr , and measure a rotation velocity of v { sin } i = 45 \pm 5 km s ^ { -1 } , in good agreement with the radio and optical periods .
The period and rotation velocity allow us to place a lower limit on the radius of the source of \gtrsim 0.12 R _ { \odot } , about 30 \% larger than theoretical expectations .
The properties of the radio emission can be explained with a simple model of a magnetic dipole mis-aligned relative to the stellar rotation axis , with the sinusoidal variations and helicity reversal due to the rotation of the magnetic poles relative to our line of sight .
The long-term stability of the radio emission indicates that the magnetic field ( and hence the dynamo ) is stable on a much longer timescale than the convective turn-over time of \sim 0.2 yr .
If the radio emission is due to the electron cyclotron maser process , the inferred magnetic field strength reaches at least 8 kG .