Gaia Astrometry and MIKE+PFS Doppler Data Joint Analysis Reveals that HD 175167b is a Massive Cold Jupiter

HD 175167b is a long-period gas giant around a G5V star reported by Arriagada et al. (2010) using the MIKE radial velocity (RV) data taken under the Magellan Planet Search Program (Bernstein et al. 2003). The planet has a period of 1290 ± 22 days with a minimum mass of ${M}_{p}\,\sin \,i=7.8\pm 3.5\ {M}_{J}$. Recent work from Feng et al. (2022) and Xiao et al. (2023) both carried out full orbit fits with a combination of RV measurements and astrometric data from Hipparcos (Perryman et al. 1997; van Leeuwen 2007) and Gaia (Gaia Collaboration et al. 2021), enabling them to determine the true mass of the secondary. Since only two absolute astrometry measurements are available now at the epoch of Year 1991 and 2016, the derived companion mass (M_p  = 6.4 ± 1.4 M_J and 9.8 ± 1.9 M_J ) and other orbital parameters still have large uncertainties.

As part of Gaia Data Release 3 (Gaia DR3; Gaia Collaboration et al. 2023), Halbwachs et al. (2023) presented a "two-body" catalog based on Gaia observations spanning about 33 months. It includes orbital solutions for about 165,500 systems, among which 1162 sources are potential substellar objects (Holl et al. 2023). A recent work from Winn (2022) proposed a method to conduct a joint analysis of these two-body solutions and RV data, which has been used in many relevant studies (e.g., Fitzmaurice et al. 2023; Unger et al. 2023). Basically, the Gaia two-body solution is treated as a basis and MCMC sampling is performed to maximize the combined Doppler+Gaia likelihood function. Note that this approach is only valid when the system contains a single companion because the Gaia two-body solution from a single Keplerian model fit would not be robust for multicompanion systems.

With this method, Winn (2022) performed a joint analysis for the HD 175167 system using the MIKE data and the Gaia two-body solution, leading to a companion mass of 14.8 ± 1.8 M_J , a period of 1175 ± 25 days and an orbital inclination of 355 ± 23. Therefore, Winn (2022) suggested that the companion might be located in the brown dwarf mass range. However, two caveats were also pointed out by Winn (2022): (1) the Gaia orbital solution has large uncertainties, which may be due to the shorter time span of Gaia observations compared with the companion's period; (2) the periods and eccentricities are discrepant between the Gaia and Doppler solutions, which is perhaps caused by non-Gaussian uncertainties of Gaia orbital parameters.

In addition to the MIKE data, HD 175167 was also monitored by the Planet Finder Spectrograph (PFS; Crane et al. 2010) on the 6.5 m Magellan II (Clay) telescope between 2010 May 23 and 2019 August 14 (see Feng et al. 2022). A total of 22 observations were collected with a median RV uncertainty of 1.1 m s⁻¹.

Following the methodology proposed by Winn (2022), I perform a joint-fit analysis including the PFS data. The joint model has 11 free parameters including stellar mass M, companion mass m, $e\cos \omega$, $e\sin w$, the cosine of the inclination $\cos i$, the longitude of the ascending node Ω, orbital period P, time of periastron t_p , parallax ϖ and two RV offsets γ_MIKE, γ_PFS, where e is the orbital eccentricity and ω represents the argument of pericenter. The Keplerian model is built by utilizing the code radvel (Fulton et al. 2018). Since the companion is a dark body based on previous mass measurements, the flux ratio ε between the companion and the primary star is thus fixed at 0. Except for a Gaussian prior ${ \mathcal N }$ (1.00, 0.04²) adopted on the host star mass based on the value from literature (Feng et al. 2022), all the other parameters are set with uniform priors. The posterior sampling is carried out with emcee (Foreman-Mackey et al. 2013). A total of 100 walkers are initialized and run for 35,000 steps with the first 5000 steps excluded as burnt-in samples. Figure 1 presents the joint-fit results, the orbital geometry and the posterior distributions.

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After including additional RV data points, the uncertainty on the companion mass is successfully reduced. The joint-fit of Doppler velocities from MIKE and PFS along with the Gaia two-body solution reveals that the companion has a mass of 10.2 ± 0.4 M_J , an eccentricity of e = 0.529 ± 0.002 and a period of 1275.8 ± 0.4 days. The orbital period constrained by the new joint-fit is better in accord with the values 1290.0 ± 22.0, 1276.1 ± 0.7 and ${1289}_{-28}^{+8}$ days from Arriagada et al. (2010), Feng et al. (2022) and Xiao et al. (2023), compared with 1175 ± 25 days determined by Winn (2022). The best-fit orbit inclination is 386 ± 17, consistent with the result 355 ± 23 reported by Winn (2022) but different from 946 ± 237 and 60° ± 17° measured by Feng et al. (2022) and Xiao et al. (2023), which may be due to the small number of absolute astrometry measurements. Based on the updated mass measurement from the joint analysis, HD 175167b turns out to be a massive cold gas giant planet rather than a brown dwarf.

The author thanks Drs. Shude Mao, Sharon X. Wang and Joshua Winn for the useful discussions. This work is supported by the National Science Foundation of China (grant No. 12133005).

Facilities: Gaia - , Magellan/MIKE - , Magellan/PFS - .

Software: radvel (Fulton et al. 2018), emcee (Foreman-Mackey et al. 2013), Rebound (Rein & Liu 2012).