We present comprehensive orbital analyses and dynamical masses for the substellar companions Gl~229~B, Gl~758~B, HD~13724~B, HD~19467~B, HD~33632~Ab, and HD~72946~B. Our dynamical fits incorporate radial velocities, relative astrometry, and most impo
rtantly calibrated Hipparcos-Gaia EDR3 accelerations. For HD~33632~A and HD~72946 we perform three-body fits that account for their outer stellar companions. We present new relative astrometry of Gl~229~B with Keck/NIRC2, extending its observed baseline to 25 years. We obtain a $<$1% mass measurement of $71.4 pm 0.6,M_{rm Jup}$ for the first T dwarf Gl~229~B and a 1.2% mass measurement of its host star ($0.579 pm 0.007,M_{odot}$) that agrees with the high-mass-end of the M dwarf mass-luminosity relation. We perform a homogeneous analysis of the host stars ages and use them, along with the companions measured masses and luminosities, to test substellar evolutionary models. Gl~229~B is the most discrepant, as models predict that an object this massive cannot cool to such a low luminosity within a Hubble time, implying that it may be an unresolved binary. The other companions are generally consistent with models, except for HD~13724~B that has a host-star activity age 3.8$sigma$ older than its substellar cooling age. Examining our results in context with other mass-age-luminosity benchmarks, we find no trend with spectral type but instead note that younger or lower-mass brown dwarfs are over-luminous compared to models, while older or higher-mass brown dwarfs are under-luminous. The presented mass measurements for some companions are so precise that the stellar host ages, not the masses, limit the analysis.
We present htof, an open-source tool for interpreting and fitting the intermediate astrometric data (IAD) from both the 1997 and 2007 reductions of Hipparcos, the scanning-law of Gaia, and future missions such as the Nancy Grace Roman Space Telescope
(NGRST). htof solves for the astrometric parameters of any system for any arbitrary combination of absolute astrometric missions. In preparation for later Gaia data releases, htof supports arbitrarily high-order astrometric solutions (e.g. five-, seven-, nine-parameter fits). Using htof, we find that the IAD of 6617 sources in Hipparcos 2007 might have been affected by a data corruption issue. htof integrates an ad-hoc correction that reconciles the IAD of these sources with their published catalog solutions. We developed htof to study masses and orbital parameters of sub-stellar companions, and we outline its implementation in one orbit fitting code (orvara, https://github.com/t-brandt/orvara). We use htof to predict a range of hypothetical additional planets in the $beta$~Pic system, which could be detected by coupling NGRST astrometry with Gaia and Hipparcos. htof is pip installable and available at https://github.com/gmbrandt/htof .
HR 8799 hosts four directly imaged giant planets, but none has a mass measured from first principles. We present the first dynamical mass measurement in this planetary system, finding that the innermost planet HR~8799~e has a mass of $9.6^{+1.9}_{-1.
8} , M_{rm Jup}$. This mass results from combining the well-characterized orbits of all four planets with a new astrometric acceleration detection (5$sigma$) from the Gaia EDR3 version of the Hipparcos-Gaia Catalog of Accelerations. We find with 95% confidence that HR~8799~e is below $13, M_{rm Jup}$, the deuterium-fusing mass limit. We derive a hot-start cooling age of $42^{+24}_{-16}$,Myr for HR~8799~e that agrees well with its hypothesized membership in the Columba association but is also consistent with an alternative suggested membership in the $beta$~Pictoris moving group. We exclude the presence of any additional $gtrsim$5-$M_{rm Jup}$ planets interior to HR~8799~e with semi-major axes between $approx$3-16,au. We provide proper motion anomalies and a matrix equation to solve for the mass of any of the planets of HR~8799 using only mass ratios between the planets.
We present a comprehensive orbital analysis to the exoplanets $beta$ Pictoris b and c that resolves previously reported tensions between the dynamical and evolutionary mass constraints on $beta$ Pic b. We use the MCMC orbit code orvara to fit fifteen
years of radial velocities and relative astrometry (including recent GRAVITY measurements), absolute astrometry from Hipparcos and Gaia, and a single relative radial velocity measurement between $beta$ Pic A and b. We measure model-independent masses of $9.3^{+2.6}_{-2.5}, M_{rm Jup}$ for $beta$ Pic b and $8.3pm 1.0,M_{rm Jup}$ for $beta$ Pic c. These masses are robust to modest changes to the input data selection. We find a well-constrained eccentricity of $0.119 pm 0.008$ for $beta$ Pic b, and an eccentricity of $0.21^{+0.16}_{-0.09}$ for $beta$ Pic c, with the two orbital planes aligned to within $sim$0.5$^circ$. Both planets masses are within $sim$1$sigma$ of the predictions of hot-start evolutionary models and exclude cold starts. We validate our approach on $N$-body synthetic data integrated using REBOUND. We show that orvara can account for three-body effects in the $beta$ Pic system down to a level $sim$5 times smaller than the GRAVITY uncertainties. Systematics in the masses and orbital parameters from orvaras approximate treatment of multiplanet orbits are a factor of $sim$5 smaller than the uncertainties we derive here. Future GRAVITY observations will improve the constraints on $beta$ Pic cs mass and (especially) eccentricity, but improved constraints on the mass of $beta$ Pic b will likely require years of additional RV monitoring and improved precision from future Gaia data releases.
