LETTERS https://doi.org/10.1038/s41550-018-0561-6 The mass of the young planet Beta Pictoris b through the astrometric motion of its host star I. A. G. Snellen* and A. G. A. Brown The young massive Jupiters discovered with high-contrast Beta Pic is included in the second data release16 (DR2) of Gaia imaging1–4 provide a unique opportunity to study the formation and covers 32 observations for this star, between 1 October 2014 and early evolution of gas giant planets. A key question is to and 19 April 2016, of which 30 were used for the astrometric solu- what extent gravitational energy from accreted gas contributes tion. The individual measurements are not provided in DR2. For to the internal energy of a newly formed planet. This has led to most stars observed by Hipparcos, Gaia is expected to eventually a range of formation scenarios from ‘cold’ to ‘hot’ start mod- achieve a precision that is 100 times better17. However, β Pic is els5–8. For a planet of a given mass, these initial conditions gov- such a bright star (apparent visual magnitude, V =​ 3.86) that its ern its subsequent evolution in luminosity and radius. Except images in the Gaia data are saturated, substantially degrading the for upper limits from radial velocity studies9,10, disk modelling11 achieved positional accuracy, resulting in DR2 uncertainties of and dynamical instability arguments12, no mass measurements 0.3 mas in each positional direction and parallax, and 0.7 mas yr−1 of young planets are yet available to distinguish between in proper motion. However, since the Hipparcos and Gaia mis- these different models. Here, we report on the detection of sions span a baseline of 24 yr, the combined positional data pro- the astrometric motion of Beta Pictoris, the ~21-Myr-old host vide a long-term proper-motion measurement16 with a precision star of an archetypical directly imaged gas giant planet, around of 0.02 mas yr−1 (Table 1). the system’s centre of mass. Subtracting the highly accurate Figure 2 shows the heliocentric Hipparcos positional data after Hipparcos13,14 and Gaia15,16 proper motion from the internal 3 yr subtraction of the 24 yr Hipparcos–Gaia baseline. The residual Hipparcos astrometric data reveals the reflex motion of the proper motion is governed by the reflex motion of β Pic around star, giving a model-independent planet mass of 11 ± 2 Jupiter the centre of mass of the system. The planet β Pic b is in a nearly masses. This is consistent with scenarios in which the planet is edge-on orbit at a position angle of 212° (ref. 18), consistent with formed in a high-entropy state as assumed by hot start mod- the observed motion of the star in the Hipparcos data. The planet’s els. The ongoing data collection by Gaia will soon lead to mass discovery was announced in 2009 from high-contrast images taken measurements of other young gas giants and form a great in 20032,3. Only after the planet reappeared on the other side (south- asset to further constrain early-evolution scenarios. west) of the star, it started to be intensely monitored, in particu- The European Space Agency’s Hipparcos13 (1989–1993) and lar with the new generation of high-contrast imaging instruments Gaia15 (2013–present) astrometric space observatories use the same Gemini Planet Imager at the Gemini Observatory and SPHERE measurement principles. Both contain two telescopes with lines (Spectro-Polarimetric High-contrast Exoplanet REsearch) on the of sight perpendicular to the spin axis of a continuously rotating Very Large Telescope18–20. It means that while about half of the spacecraft, which slowly precesses while maintaining a constant orbit is well known, the orbital period is still poorly constrained to angle with respect to the spacecraft–Sun direction. The telescopes be between 20.2 yr and 26.3 yr (ref. 18). Since the reference epochs precisely time the crossing of stars in their field of view, providing of Hipparcos (1991.25) and Gaia DR2 (2015.5) are separated by accurate one-dimensional astrometric positions, which result in a 24.25 yr, the observations of the former mission fall in the well- rigid system of reference by combining the relative positions of the determined part of the planet’s orbit, but the precise orbital phase observed stars. is uncertain. Depending on the orbital period, the Hipparcos–Gaia Hipparcos observed Beta Pictoris (β Pic) 111 times between baseline also contains a small part of the stellar reflex motion. For 1990.0 and 1993.1 (Julian epochs are used throughout this Letter), example, for an orbital period of 22 yr and a planet mass of 10 distributed over 35 spacecraft orbits. Each set of ~3–5 observations Jupiter masses (MJ), the two reference epochs correspond to orbital taken during one orbit has similar telescope scanning directions. phases that differ by 0.1, resulting in a planet-induced position dif- While the initial data release delivered one position per orbit13, ference of 1.0 mas and an effect on the Hipparcos–Gaia baseline of with typical uncertainties in the range of 1.5–2.5 mas, the subse- 1.0 mas ÷​ 24.25 yr =​ 0.04 mas yr−1. This effect is taken into account in quent reprocessing of these data by van Leeuwen14 maintained the our calculations below. individual data points and delivered uncertainties in the range of Since the projected orientation of the orbit is well constrained18, 0.8–1.0 mas (see Supplementary Table 1), improving the precision so is the expected direction of stellar reflex motion. Hence, we con- by a factor of ~4. The latter analysis provides for β Pic a parallax of verted the positional data from Hipparcos into one-dimensional 51.44 ±​ 0.12 mas, corresponding to a distance of 19.44 ±​ 0.05 pc, and position measurements in this direction as a function of time, a proper motion of 4.65 ±​ 0.11 mas yr−1 and 83.10 ±​ 0.15 mas yr−1 shown in the right panel of Fig. 2. The solid curves show the best- in the right ascension (RA) and the declination (dec.) direction, fit stellar motion for several trial orbital periods, indicating that respectively (Fig. 1; Table 1). The star is the largest member of an short periods are not consistent with the Hipparcos data since these association of young stars, the β Pic moving group (BPMG), sharing would result in substantial acceleration in the stellar proper motion the same origin and motion through space. in the period 1990–1993, which is not observed. Figure 3 shows the Leiden Observatory, Leiden University, Leiden, Netherlands. *e-mail: [email protected] NatURE AstRONOMY | www.nature.com/natureastronomy LETTERS NATURE ASTRONOMY 200 β Pic reflex motion 2 4 1 1990.3 2 24 yr (mas) 23 yr 1990.9 HG 22 yr 0 1991.4 0 1991.9 Pos (mas) 21 yr Δ –1 1992.6 100 dec. – PM –2 Δ –2 –4 2 1 0 –1 –2 1989 1990 1991 1992 1993 ΔRA – PMHG (mas) Year of observation Fig. 2 | The heliocentric Hipparcos positional data after subtraction of the 24 yr Hipparcos–Gaia baseline. Left: the change in position of β Pic in 0 the Hipparcos data relative to the 24 yr Hipparcos–Gaia baseline, where dec. (mas) PMHG is the proper motion as derived from the Hipparcos–Gaia baseline. Δ The one-dimensional positions taken during 35 Hipparcos spacecraft orbits were combined into five two-dimensional astrometric positions. The shaded areas indicate the 1σ uncertainty areas (s.e.m.) with their mean epochs. The arrow shows the expected direction for the movement of the star around the centre of mass of the system. Right: the change in position, –100 Δ Pos, of the star relative to the Hipparcos–Gaia baseline in the direction of the expected reflex motion direction of the star at 212°, known from the orbital mapping of the planet. Positions averaged over a spacecraft orbit are shown, which strongly vary in accuracy (grey scaling, with the darkest greys showing the smallest errors) depending on the relative orientation of the one-dimensional astrometric measurement. Five measurements are omitted because their measurement vectors are nearly perpendicular to the reflex motion movement. The coloured lines show the best-fit velocity –200 150 100 50 0 –50 curves for orbital periods of 21–24 yr. Planet orbital periods shorter than ΔRA (mas) 22 yr are excluded since they would show substantially more curvature than the Hipparcos data allow. Fig. 1 | The astrometric motion of the young star β Pic as shown by the Hipparcos data (1990–1993). The black curve is the best-fit model to the parallax (caused by the Earth’s yearly motion around the Sun) constraints to the planet’s mass and orbital period. The green shaded area indicates the 1σ uncertainty interval for the orbital period from and the star’s proper motion, with the points indicating the modelled 18 positions for the one-dimensional Hipparcos positions (the dark blue the high-contrast imaging monitoring , and the contours indicate lines are perpendicular to the scanning direction), which are averaged the 1σ , 2σ and 3σ limits on orbital period and mass from the study presented here. The planet’s mass is constrained to 11 ± 2 MJ (1σ ), per satellite orbit for clarity and have typical error bars of < 1 mas (s.e.m.). The grey circle and line indicate the separate parallax and proper-motion and the orbital period is likely to be > 22.2 yr (2σ limit). Previous upper limits to the planet’s mass of < 20–30 MJ from radial veloc- components, respectively.