  Even though it was discovered more than a decade ago, LSR1610-0040 remains an
enigma. This object has a peculiar spectrum that exhibits some features
typically found in L subdwarfs, and others common in the spectra of more
massive M dwarf stars. It is also a binary system with a known astrometric
orbital solution. Given the available data, it remains a challenge to reconcile
the observed properties of the combined light of LSR1610-0040AB with current
theoretical models of low-mass stars and brown dwarfs. We present the results
of a joint fit to both astrometric and radial velocity measurements of this
unresolved, low-mass binary. We find that the photocentric orbit has a period
$P = 633.0 \pm 1.7$ days, somewhat longer than previous results, with
eccentricity of $e = 0.42 \pm 0.03$, and we estimate that the semi-major axis
of the orbit of the primary is $a_1 \approx 0.32$ AU, consistent with previous
results. While a complete characterization of the system is limited by our
small number of radial velocity measurements, we establish a likely primary
mass range of $0.09 - 0.10 M_\odot$ from photometric and color-magnitude data.
For a primary mass in this range, the secondary is constrained to be $0.06 -
0.075 M_\odot$, making a negligible contribution to the total I-band
luminosity. This effectively rules out the possibility of the secondary being a
compact object such as an old, low-mass white dwarf. Based on our analysis, we
predict a likely angular separation at apoapsis comparable to the resolution
limits of current high-resolution imaging systems. Measuring the angular
separation of the A & B components would finally enable a full, unambiguous
solution for the masses of the components of this system.
