Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Precise Dynamical Masses and Orbital Fits for $\beta$ Pic b and $\beta$
  Pic c   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 $8.3\pm 1.0\,M_{\rm
Jup}$ 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 orvara's 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 c's
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.

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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn