Evidence for the Keplerian orbit of a close companion around a giant star

TL;DR

This study directly detects Keplerian motion of a close-in companion to an AGB star, π1 Gru A, by combining two-epoch ALMA continuum imaging with archival Hipparcos and Gaia astrometry. A Bayesian two-body framework links the observed sky-plane motion to orbital elements, favoring a nearly circular inner orbit with $m_1\approx1.12\,M_\odot$, $m_2\approx1.18\,M_\odot$ at $a\approx6.8$ au and $P_{\rm orb}\approx11.8$ yr, while radial-velocity checks help resolve geometric degeneracies. Hydrodynamic and stellar-evolution modelling show wind-RLOF accretion forming a compact disk around the companion with $R_{\rm disk}\approx0.83$ au and a modest disk dust mass, compatible with mm-continuum emission. The results provide a crucial benchmark for tidal-interaction physics and binary evolution on the TP-AGB, and demonstrate the potential of multi-epoch (sub)mm interferometry combined with optical astrometry to map binary orbits in evolved stars. This work also highlights tensions between observed circularization and some theoretical expectations, motivating refined tidal dissipation models and future UV/X-ray constraints to pin down the companion's nature and the system's long-term fate.

Abstract

Close companions influence stellar evolution through tidal interactions, mass transfer, and mass loss effects. While such companions are detected around young stellar objects, main-sequence stars, red giants, and compact objects, direct observational evidence of close-in companions around asymptotic giant branch (AGB) stars has remained elusive. Here, we present (sub)millimeter time-domain imaging spectroscopy revealing the Keplerian motion of a close-in companion around the AGB star pi1 Gruis. The companion, slightly more massive than the AGB star, is likely a main-sequence star. Unlike more evolved stars with companions at comparable distances, pi1 Gru's companion follows a circular orbit, suggesting an eccentricity-generating mechanism late- or post-AGB. Our analysis suggests that model-predicted circularization rates may be underestimated. Our results highlight the potential of multi-epoch (sub)millimeter interferometry in detecting the Keplerian motion of close companions to giant stars and open avenues for our understanding of tidal interaction physics and binary evolution.

Figures (48)

• Figure 1: Proper motion of the $\boldsymbol{\pi^1}$ Gru system. Panel (a): 2019 ALMA C6 and 2023 ALMA C10 data with white contours at (3, 10, 30, 50, 100, 300)$\times$ the continuum rms value. The ALMA beam sizes are shown in orange (2019 C6) and yellow (2023 C10) at the bottom. Data are corrected for the parallactic shift. The red cross marks the Gaia 2016.0 position of $\pi^1$ Gru A. The grey arrow ($\mu^{G}$) indicates the proper motion of the binary system's center of mass (CoM, $G_\star$). The white, pink, and grey crosses mark the barycentre's position at the 2019, 2023, and Gaia 2016.0 epochs, respectively. The dashed white line shows the orbit of $\pi^1$ Gru A ($M_1$), while the dotted white line shows the orbit of $\pi^1$ Gru C ($M_2$), both in the ICRS frame based on Bayesian best-fit parameters. Panel (b): Similar to (a), but also including the Hipparcos 1991.25 position of $\pi^1$ Gru A (green cross). ALMA contour levels are omitted for clarity. In both panels, observed proper motion is in yellow, predicted motion in orange, with vectors representing 1-year (panel a) and 3-year (panel b) intervals. The orange vector is nearly indistinguishable due to the almost perfect fit with the observed motion. An accompanying video is in Suppl. Video \ref{['Video:pi1_gru']}.
• Figure 1: ALMA continuum observations of the $\boldsymbol{\pi^1}$ Gru system. 2019 ALMA C6 and 2023 ALMA C10 data are shown with white contours drawn at (3, 10, 30, 50, 100, 300)$\times$ the continuum rms value of 0.05 mJy and 0.15 mJy, respectively. The ALMA beam sizes for the 2019 C6 and 2023 C10 data are depicted at the bottom of the figure in orange and yellow, respectively, positioned below their corresponding images. White crosses indicate the astrometric position of the primary ($\pi^1$ Gru A, or '$M_1$'), while silver crosses mark the position of the companion ($\pi^1$ Gru C, or '$M_2$') at both epochs.
• Figure 1: Video showing the proper motion of $\boldsymbol{\pi^1}$ Gru A and $\boldsymbol{\pi^1}$ Gru C over time, spanning from 1984.5 to 2030. The video can be found on: .
• Figure 1: Orbital plane and focal reference frames illustrated for the equivalent one-body problem. The Cartesian orbital plane frame, $(X_p, Y_p, Z_p)$, is shown in blue, while the focal reference frame, $(X, Y, Z)$, is depicted in black. The position vector $\vec{r}$, representing the location of object $M_2$ relative to $M_1$, is defined by the orbital elements: $\Omega$ (longitude of the ascending node), $i$ (inclination), $\omega$ (argument of periapsis/periastron), $a$ (semi-major axis), $e$ (eccentricity), and $T_0$ (time of periapsis/periastron passage). The focal frame is related to the orbital plane through the angles $i$, $\Omega$, and $\omega$, which are indicated in brown, alongside the true anomaly $f$. The section of the orbit from the ascending to the descending node is depicted with a solid line, while the segment from the descending to the ascending node is shown with dotted lines. This figure presents a general illustration of orbital elements, while the specific visualization for the $\pi^1$ Gru system, with its retrieved orbital parameters, is provided in Extended Data Fig. \ref{['fig:schematic']}.
• Figure 2: Time evolution of stellar parameters for a 1.7 M$_{\odot}$ model near the end of the thermally-pulsing AGB, compared to observed values for $\boldsymbol{\pi^1}$ Gru A. We include models with two different values for the overshoot parameter in pressure scale heights, $N_{\rm ov}$, of $2.0$ (dotted lines) and $2.5$ (solid lines). The panels show from top to bottom: (a): total (lines) and core masses (grey shaded region), (b): luminosity, (c): first overtone mode period, (d): amplitude growth rates for the first overtone mode (orange) and fundamental mode (blue) and (e): C/O ratio; all with respect to time since the onset of the TP-AGB phase. Also included are the measurements for $\pi^1$ Gru A (red dashed lines and shaded regions): luminosity of 7,300 L$_{\odot}$, period of $195.5$ d and C/O ratio of $0.97$ (between $0.75$ and $1$). In the top panel, we plot the derived masses from both agnostic and Gaussian priors on $m_1$, which are $1.12$ and $1.27$ M$_{\odot}$ respectively. The period, luminosity and total mass are consistent with the final few thermal pulses of this model, though the higher mass using the Gaussian prior is favoured for this model mass. The first overtone mode is also dominant at these model times (i.e. the growth rate is higher), which is consistent with the observed pulsation mode of $\pi^1$ Gru A.