  The young (~16 Myr) pre-main-sequence star in Sco-Cen 1SWASP
J140747.93-394542.6, hereafter referred to as J1407, underwent a deep eclipse
in 2007 April, bracketed by several shallower eclipses in the surrounding 54 d.
This has been interpreted as the first detection of an eclipsing ring system
circling a substellar object (dubbed J1407b). We report on a search for this
companion with Sparse Aperture Mask imaging and direct imaging with both the
UT4 VLT and Keck telescopes. Radial velocity measurements of J1407 provide
additional constraints on J1407b and on short period companions to the central
star. Follow-up photometric monitoring using the PROMPT-4 and ROAD
observatories during 2012-2014 has not yielded any additional eclipses. Large
regions of mass-period space are ruled out for the companion. For circular
orbits the companion period is constrained to the range 3.5-13.8 yr (a ~
2.2-5.6 au), and masses greater than 80 M_Jup are ruled out at 3 sigma
significance over these periods. The complex ring system appears to occupy more
than 0.15 of its Hill radius, much larger than its Roche radius and suggesting
a ring structure in transition. Further, we demonstrate that the radial
velocity of J1407 is consistent with membership in the Upper Cen-Lup subgroup
of the Sco-Cen association, and constraints on the rotation period and
projected rotational velocity of J1407 are consistent with a stellar
inclination of 68+-10 degrees.
