A Preliminary Mass for Proxima Centauri C^*

An investigation using astrometry secured with HST Fine Guidance Sensor 3 (Benedict et al. 1999) established a Proxima Centauri (hereafter Proxima) companion mass detection upper limit (${ \mathcal M }$_p < 0.8 ${{ \mathcal M }}_{\mathrm{Jup}}$) with an upper period limit, P < 1000 days. In response to the discovery with precision radial velocity measurements (Damasso et al. 2020) of the long-period Proxima c companion (P ∼ 1900 days) we re-analyze Proxima astrometry, now informed by that orbit. Our goals include a refined parallax for Proxima and a mass for the perturbing companion, Proxima c.

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; McArthur et al. 2010; Benedict et al. 2011; McArthur et al. 2014; Benedict et al. 2016, 2017; Benedict & Harrison 2017). The astrometric reference frame for Proxima consists of eight stars. At each of 65 epochs we measured a subset of reference stars (typically six, depending on spacecraft roll) each 1–3 times, and Proxima Centauri 1–4 times for a total of 105 measurements of Proxima, spanning 2031 days.

Departing significantly from our previous analysis, we adopt Gaia DR2 (Gaia Collaboration et al. 2018) parallax and proper motion priors for the reference stars. In Benedict et al. (1999) these came from ground-based spectrophotometery. We also include the Damasso et al. (2020) orbital elements; period, P, time of inferior conjunction, T_conj, and RV amplitude, K_c as priors. Damasso et al. (2020) assumed an eccentricity, _c = 0. We include all priors as observations with associated errors, arbitrarily assuming an error on the eccentricity of 0.1.

We used a six parameter model including parallax, proper motion, and an orbit for the perturber, Proxima c (Benedict et al. 2010, Equations (4), (5)). Histograms of the FGS astrometric residuals exhibit residuals with Gaussian distributions and dispersions σ ∼ 0.95 mas. The reference frame "catalog" from FGS 1r astrometry in ξ and η standard coordinates had average uncertainties, $\langle {\sigma }_{\xi }\rangle =0.15$ and $\langle {\sigma }_{\eta }\rangle =0.15$ mas. We constrained the astrometry with the Damasso et al. (2020) RV results through $\alpha \,\sin \,i/{\varpi }_{\mathrm{abs}}={PK}{(1-{e}^{2})}^{1/2}/2\pi \times 4.7405$ (see Pourbaix & Jorissen 2000; Benedict et al. 2017; Benedict & Harrison 2017). We obtained the orbital elements and other astrometric parameters listed in Figure 1, which contains the derived orbit, and residual normal points (NP) of epochs of observation with corresponding residuals. The initial 48 observational epochs each contained only one observation of Proxima. Hence, the first six NP each span 100 days. The remaining 14 NP averaged five observations of Proxima acquired during each observational sequence (typically 40 minutes).

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For an estimate for the mass of Proxima c we solve for an ${ \mathcal M }$_c that satisfies the mass function, $f({ \mathcal M })=\displaystyle \frac{{\alpha }^{3}}{{{\rm{P}}}^{2}}=\tfrac{{{ \mathcal M }}_{{\rm{c}}}^{3}}{{\left({{ \mathcal M }}_{{\rm{A}}}+{{ \mathcal M }}_{{\rm{c}}}\right)}^{2}}$, where component A is Proxima. Adopting ${ \mathcal M }$ ${}_{A}=0.11$ ${{ \mathcal M }}_{\odot }$ (Benedict et al. 1999), we find ${ \mathcal M }$ ${}_{c}=18\pm 5$ ${{ \mathcal M }}_{\oplus }$. With a combination of the Hipparcos catalog and Gaia DR2, Kervella et al. (2019) detected a deviation from a purely linear tangential proper motion in the Proxima tangential velocity, significant at 1.8σ. More recently their reanalysis (Kervella et al. 2020) yields a more precise mass estimate. Our preliminary mass determination for Proxima c is compatible with both their initial prediction of a planet with true mass 10–20 ${{ \mathcal M }}_{\oplus }$ with a semimajor axis of 1–2 au and their more recent measurement, ${ \mathcal M }$ ${}_{c}={12}_{-5}^{+12}$ ${{ \mathcal M }}_{\oplus }$. Assuming a coplanar system, Proxima b would have ${ \mathcal M }$ ${}_{b}=3\pm 0.3$ ${{ \mathcal M }}_{\oplus }$. Gaia will eventually provide better companion masses.

See Benedict & Harrison (2017) for acknowledgments.