Peering into the formation history of β Pictoris b with VLTI/GRAVITY long-baseline interferometry

Abstract

Context. β Pictoris is arguably one of the most studied stellar systems outside of our own. Some 30 yr of observations have revealed a highly-structured circumstellar disk, with rings, belts, and a giant planet: β Pictoris b. However very little is known about how this system came into being. Aims. Our objective is to estimate the C/O ratio in the atmosphere of β Pictoris b and obtain an estimate of the dynamical mass of the planet, as well as to refine its orbital parameters using high-precision astrometry. Methods. We used the GRAVITY instrument with the four 8.2 m telescopes of the Very Large Telescope Interferometer to obtain K-band spectro-interferometric data on β Pic b. We extracted a medium resolution (R = 500) K-band spectrum of the planet and a high-precision astrometric position. We estimated the planetary C/O ratio using two different approaches (forward modeling and free retrieval) from two different codes (ExoREM and petitRADTRANS, respectively). Finally, we used a simplified model of two formation scenarios (gravitational collapse and core-accretion) to determine which can best explain the measured C/O ratio. Results. Our new astrometry disfavors a circular orbit for β Pic b (e = 0.15−0.04+0.05). Combined with previous results and with HIPPARCOS/Gaia measurements, this astrometry points to a planet mass of M = 12.7 ± 2.2 MJup. This value is compatible with the mass derived with the free-retrieval code petitRADTRANS using spectral data only. The forward modeling and free-retrieval approches yield very similar results regarding the atmosphere of β Pic b. In particular, the C/O ratios derived with the two codes are identical (0.43 ± 0.05 vs. 0.43−0.03+0.04). We argue that if the stellar C/O in β Pic is Solar, then this combination of a very high mass and a low C/O ratio for the planet suggests a formation through core-accretion, with strong planetesimal enrichment.

Dynamical Mass Estimates of the $β$ Pictoris Planetary System Through Gaussian Process Stellar Activity Modelling

“…We also include the single epoch of relative astrometry obtained with VLTI/GRAVITY by Nowak et al (2020) on September 22 2018. This data point, obtained by averaging 17 exposure files, is given by the bivariate normal distribution (∆RA, ∆DEC) ∼ N (µ, Σ).…”

“…µ is the mean relative planet-to-star position and Σ = Cov(∆RA, ∆DEC), the covariance matrix of all exposure files, gives the 1σ confidence interval. The mean coordinates and their covariance, as reported by Nowak et al (2020) (1)…”

“…We then evaluate this PDF at the coordinates of the data point to obtain the likelihood before taking its logarithm and adding it to the other two likelihoods (RV and other relative astrometry). However, the covariance matrix Σ from Equation 1, reported by Nowak et al (2020), is not positive semi-definite. This yields an invalid Pearson correlation coefficient r < −1.…”

“…Monitoring the motion of β Pic b with direct imaging has led to various constraints on its orbit. The inclination is now well constrained, excluding perfectly edge-on orbit, at i = 89.04 ± 0.04 • (Wang et al 2016;Lagrange et al 2019b;Nielsen et al 2020;Nowak et al 2020). Period and eccentricity were also constrained with direct imaging.…”

“…These last two mass measurements account for the presence of a second giant planet in the system. The addition of a VLTI/GRAVITY relative astrometric point with exquisite precision of 80 µas, but without the RVs and without accounting for a second planet, led Nowak et al (2020) to measure M b = 12.7 ± 2.2 M Jup while excluding circular orbit (e b = 0.15 +0.05 −0.04 ). From stellar RVs only, the mass and period of β Pic c were estimated to M c ∼ 8.9 M Jup (assuming the same inclination as β Pic b) and P c ∼ 1220 d (Lagrange et al 2019a), while Nielsen et al (2020) found M c = 9.18 +0.96 −0.87 M Jup , P c = 1238 +7 −11 d, and e c = 0.24 +0.11 −0.10 .…”