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We determine the mass of the nuclear black hole ($M$) in NGC 3706, an earlytype galaxy with a central surface brightness minimum arising from an apparentstellar ring, which is misaligned with respect to the galaxy's major axis atlarger radii. We fit new HST/STIS and archival data with axisymmetric orbitmodels to determine $M$, mass-to-light ratio ($\Upsilon_V$), and dark matterhalo profile. The best-fit model parameters with 1$\sigma$ uncertainties are $M= (6.0^{+0.7}_{-0.9}) \times 10^8\ M_{\scriptscriptstyle \odot}$ and$\Upsilon_V = 6.0 \pm 0.2\ M_{\scriptscriptstyle \odot}\ L_{{\scriptscriptstyle\odot},V}^{-1}$ at an assumed distance of 46 Mpc. The models are inconsistentwith no black hole at a significance of $\Delta\chi^2 = 15.4$ and require adark matter halo to adequately fit the kinematic data, but the fits areconsistent with a large range of plausible dark matter halo parameters. Thering is inconsistent with a population of co-rotating stars on circular orbits,which would produce a narrow line-of-sight velocity distribution (LOSVD).Instead, the ring's LOSVD has a small value of $|V|/\sigma$, the ratio of meanvelocity to velocity dispersion. Based on the observed low $|V|/\sigma$, ourorbit modeling, and a kinematic decomposition of the ring from the bulge, weconclude that the stellar ring contains stars that orbit in both directions. Weconsider potential origins for this unique feature, including multiple tidaldisruptions of stellar clusters, a change in the gravitational potential fromtriaxial to axisymmetric, resonant capture and inclining of orbits by a binaryblack hole, and multiple mergers leading to gas being funneled to the center ofthe galaxy.

The Black Hole Mass and the Stellar Ring in NGC 3706