A Mass for γ Cep Ab^*

We analyze γ Cep astrometry secured with HST Fine Guidance Sensor 1r, informed by an AB orbit determined primarily from radial velocities and archival ground-based astrometry (Neuhäuser et al. 2007; Torres 2007; Endl et al. 2011). Our goals include a parallax for γ Cep and a mass for a perturbing companion, γ Cep Ab. We have described the combined radial velocity and astrometry analysis used to produce system parallax, proper motion, and component mass in detail (Benedict et al. 2007, 2011, 2016, 2017; McArthur et al. 2010, 2014; Benedict & Harrison 2017). The astrometric reference frame for γ Cep consists of eight stars. At each of 18 epochs we measured a subset of reference stars (typically four, depending on spacecraft roll) 1–3 times, and γ Cep 4–5 times.

Single-field parallax astrometry depends on prior knowledge of the reference stars, and sometimes, but less ideally, of the science target. Catalog proper motions with associated errors, lateral color corrections, estimates for reference star parallax (and for γ Cep cross-filter corrections) are entered into the modeling as quasi-Bayesian priors, data with which to inform the final solved-for parameters. Details for each kind of prior can be found in Benedict et al. (2017), Section 4.1.1, and in Benedict & Harrison (2017), Section 2.1.1. We include priors as observations with associated errors. The model adjusts the corresponding parameter values within limits defined by the data input errors to minimize χ², yielding the most accurate parallax and proper motion for the prime target, γ Cep, and the best opportunity to measure any reflex motion due to the companion, Ab, detected by RV. From positional measurements we determine the scale, rotation, and offset "plate constants" relative to an arbitrarily adopted constraint epoch for each observation set. We employ GaussFit (Jefferys et al. 1988) to minimize χ². We used a six parameter model including two perturbers, Ab and B, constraining the astrometry and RV through α sin i/π_abs = PK (1 − e²)^1/2/2π × 4.7405 (Benedict et al. 2017). We constrained P_Ab = 9050, _Ab = 0.08, T_Ab = 24532481^d, ω_Ab = 86°, and K_Ab = 32.4 m s⁻¹, more recent unpublished values provided by Endl, obtaining P_AB = 27041^d ± 341^d, K_AB = 1.956 ± 0.007 km s⁻¹, _AB = 0.401 ± 0.007, ω_AB = 1619 ± 02, T_AB = 2448502^d ± 8^d, α_AB = 336 ± 5 mas, i_AB = 1011 ± 15, and Ω_AB = 142 ± 08.

For the Ab perturbation we find α_Ab = 1.1 ± 0.1 mas, i_Ab = 1695 ± 11, and Ω_Ab = 47° ± 6°. Histograms of the FGS astrometric residuals exhibit residuals with Gaussian distributions and dispersions σ ∼ 0.8 mas. The reference frame "catalog" from FGS 1r astrometry in ξ and η standard coordinates had average uncertainties, $\langle {\sigma }_{\xi }\rangle =0.30$ and $\langle {\sigma }_{\eta }\rangle =0.34$ mas. The average residual for the ground-based astrometry (in Figure 1) is $\langle \sigma \rangle =102.4$ mas, an improvement over the Torres (2007) value, $\langle \sigma \rangle =117.3$ mas. Other derived parameters are parallax, π_abs = 73.95 ± 0.14 mas, and proper motion, μ_R.A. = −64.5 ± 0.3 μ_decl. = 148.0 ± 0.2 mas yr⁻¹. To obtain an estimate for the mass of γ Cep Ab we solve for an ${{ \mathcal M }}_{b}$ that satisfies the mass function, $f({ \mathcal M })=\tfrac{{\alpha }^{3}}{{{\rm{P}}}^{2}}=\tfrac{{{ \mathcal M }}_{b}^{3}}{{\left({{ \mathcal M }}_{A}+{{ \mathcal M }}_{b}\right)}^{2}}$. Adopting ${{ \mathcal M }}_{A}=1.18\,{{ \mathcal M }}_{\odot }$ (Torres 2007), we find ${{ \mathcal M }}_{b}={9.4}_{-1.1}^{+0.7}\,{{ \mathcal M }}_{\mathrm{Jup}}$.

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The orbits and residuals plotted in Figure 1 are the perturbation induced by the presence of γ Cep B and (insert) the perturbation to component A induced by component b. With an Ab separation of 1.94 au, and the γ Cep AB—Aa non-coplanarity (mutual inclination, Φ = 70° ± 13°), system stability remains an unresolved issue (e.g., Bazsó et al. 2017). See Benedict & Harrison (2017) for acknowledgements.