An astrometric planetary companion candidate to the M9 Dwarf TVLM 513-46546

Astrometric observations of the M9 dwarf TVLM 513$-$46546 taken with the VLBA reveal an astrometric signature consistent with a period of 221 $\pm$ 5 days. The orbital fit implies that the companion has a mass m${}_p$ = 0.35$-$0.42 $M_J$, a circular orbit ($e\simeq 0$), a semi-major axis a = 0.28$-$0.31 AU and an inclination angle i = 71$-$88${}^{\circ }$. The detected companion, TVLM~513$b$, is one of the few giant-mass planets found associated to UCDs. The presence of a Saturn-like planet on a circular orbit, 0.3 AU from a 0.06$-$0.08 $M_{\odot }$ star, represents a challenge to planet formation theory. This is the first astrometric detection of a planet at radio wavelengths.