The Hyades Binaries θ¹ Tauri and θ² Tauri: The Distance to the Cluster and the Mass-Luminosity Relation

We report new spectroscopic observations of the close binaries θ¹ Tauri and θ² Tauri in the Hyades. Our radial velocities for the primary component of θ¹ Tau, supplemented with other velocities from the literature and existing astrometric information (speckle observations and lunar occultation measurements), have enabled us to solve for an astrometric-spectroscopic orbit giving a period of 16.3 yr and a nearly edge-on configuration on the sky.

We have analyzed our echelle spectra of θ² Tauri with TODCOR, a two-dimensional cross-correlation technique, and have derived a new spectroscopic orbit for this difficult system, including the orbital velocity amplitude of the rapidly rotating secondary component. We then combine this spectroscopic orbit with a published astrometric orbit from the Mark III interferometer and solve for the individual masses and the orbital parallax. Our analysis technique should eliminate the distortion in the velocity amplitude of the primary that has plagued previous studies by fully accounting for the presence of the secondary in the spectrum.

Using proper motions for a representative sample of cluster members, along with the orbital parallax of θ² Tau, we obtain a new estimate for the distance modulus of the Hyades of m - M = 3.39 ± 0.08 (47.6 ± 1.8 pc), in excellent agreement (1%) with similar estimates from two other Hyades binaries (51 Tau and ϕ342), as well as with results from other methods.

We also derive individual masses for θ¹ Tau using the distance information from θ² Tau, transferred via relative proper motions. There are now nine main-sequence stars in the Hyades with directly determined masses and with known individual distances. We compare the empirical mass-luminosity relation from these data with recent theoretical isochrones and show that they are in good agreement. This provides a stringent test of stellar evolution models that does not invoke arbitrary shifts, as is usual in the main-sequence fitting technique for clusters.