  We report the first direct detection of a strong, 5 kG magnetic field on the
surface of an active brown dwarf. LSR J1835+3259 is an M8.5 dwarf exhibiting
transient radio and optical emission bursts modulated by fast rotation. We have
detected the surface magnetic field as circularly polarized signatures in the
819 nm sodium lines when an active emission region faced the Earth. Modeling
Stokes profiles of these lines reveals the effective temperature of 2800 K and
log gravity acceleration of 4.5. These parameters place LSR J1835+3259 on
evolutionary tracks as a young brown dwarf with the mass of 55$\pm$4 M$_{\rm
J}$ and age of 22$\pm$4 Myr. Its magnetic field is at least 5.1 kG and covers
at least 11% of the visible hemisphere. The active region topology recovered
using line profile inversions comprises hot plasma loops with a vertical
stratification of optical and radio emission sources. These loops rotate with
the dwarf in and out of view causing periodic emission bursts. The magnetic
field is detected at the base of the loops. This is the first time that we can
quantitatively associate brown dwarf non-thermal bursts with a strong, 5 kG
surface magnetic field and solve the puzzle of their driving mechanism. This is
also the coolest known dwarf with such a strong surface magnetic field. The
young age of LSR J1835+3259 implies that it may still maintain a disk, which
may facilitate bursts via magnetospheric accretion, like in higher-mass T
Tau-type stars. Our results pave a path toward magnetic studies of brown dwarfs
and hot Jupiters.
