Open Access
Issue
A&A
Volume 670, February 2023
Article Number A65
Number of page(s) 16
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/202245396
Published online 08 February 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model.

Open Access funding provided by Max Planck Society.

1 Introduction

In the last decade, several long-period giant planets have been detected using the radial velocity (RV) method thanks to the increasing temporal baselines of different surveys (Mayor et al. 2011; Wittenmyer et al. 2020; Rosenthal et al. 2021). Yet, a precise determination of the orbital parameters and mass of the planets is very difficult when the orbital period is much larger than the RV time baseline. As a consequence, the radial distribution of planets beyond 8–10 au – such as those found by Fernandes et al. (2019) and Fulton et al. (2021) based on the results of the two long RV surveys of Mayor et al. (2011) and Rosenthal et al. (2021), respectively – are questionable. This unfortunately prevents an accurate comparison with formation model outputs from being made.

Combining RV data with other methods such as relative or absolute astrometry can, in principle, improve the orbital characterization of these companions. Furthermore, it can also remove the uncertainty of the orbital inclination and then allow us to determine the true mass of the planets.

Coupling RV data with relative astrometry from direct imaging (DI) or interferometry has been, however, limited to very few cases since high-contrast imaging (HCI) or interferometry observations favor young systems to minimize the flux contrast between the star and its companion while RV observations favor old and inactive stars which produce low RV jitters. However, when possible, such a coupling is very efficient. An illustration is the HD 7449 system for which the outer companion was first reported as a planet candidate using only RV data (Mayor et al. 2011; Wittenmyer et al. 2019), and it was then identified as a low-mass star by combining RV data with HCI observations (Rodigas et al. 2016).

In the 2000s, the combination of RV data and absolute astrometry, thanks to the fine guidance sensor on board the Hubble Space Telescope, also allowed for the inclination of a few stellar systems to be constrained and a few candidate planets to be confirmed (Benedict et al. 2002, 2006), while others were finally identified as brown dwarfs or low-mass stars (Bean et al. 2007; Benedict et al. 2010). Today, the position and proper motion measurements obtained with the telescopes HIPPARCOS (Perryman et al. 1997; van Leeuwen 2007) and Gaia (Gaia Collaboration 2020) allow us to combine the RV data and more precise absolute astrometry for a large number of systems. Since the publication of the first Gaia data release (DR1), a few studies have proven the efficiency of combining RV data with absolute and/or relative astrometry to improve the constraints on the orbital parameters and mass of a companion (Grandjean et al. 2019; Brandt et al. 2019, 2021a,b; Damasso et al. 2020; Lagrange et al. 2020; Nielsen et al. 2020; Venner et al. 2021; Kiefer et al. 2021; Li et al. 2021; Feng et al. 2022).

In this paper, we focus on seven long-period single companions detected by the RV method, and combine the available RV data with HIPPARCOS and Gaia early data release 3 (EDR3) absolute astrometry and, when available, relative astrometry, to improve the orbital parameters and determine the true mass of these companions. In Sect. 2, we describe our target selection method and present the RV, HCI, and astrometric data used in our study. Section 3 presents the method used to perform the orbital fitting and, there, we provide the new orbital parameters and mass found for each target. Finally, we discuss the results in Sect. 4.

Table 1

Observing logs.

2 Target selection and data

2.1 Target selection

We first selected the planetary systems in the exoplanet.eu catalog (Schneider et al. 2011) for which a single companion has been reported with a semi-major axis greater than 5 au using the RV method. Twenty-five companions were found with such criteria. For nine of them (HD 13724 B, HD 25015 b, HD 181234 b, and HD 219828 B Feng et al. 2022; HD 92987 B Venner et al. 2021; HIP 36985 B Biller et al. 2022; and HD 98649 b, HD 196067 b, and HD 221420 B Li et al. 2021), the orbital parameters and the true mass have already been properly determined in previous studies. We, therefore, do not consider them in the present study.

We first discarded the HD 95872 system because no HIPPARCOS data were available. We then discarded four systems for which the available RV time series did not cover both extrema of the RV variations and the orbital period could not be properly determined (HD 26161, HD 120066, HD 150706, and HD 213472). In those four cases, the combination of RV and absolute astrometry did not allow us to constrain the orbital parameters, the orbital inclination, or the true mass of the companion. Finally, we discarded four systems for which the orbital period was well covered by the RV data, but the coupling with absolute astrometry did not allow us to constrain the orbital inclination (HD 136925, HD 190984, HD 220773, and HD 238914). Indeed, the variations in position and acceleration of the proper motion of these stars were too small to constrain the orbital inclination of the companion due to the low mass of the companion (<~2 MJup) and/or the distance of the system.

Thus, we were left with seven systems for which the addition of absolute astrometry and/or new RV measurements and/or relative astrometry measurements allowed us to determine the exact nature of the companion: Epsilon Indi Ab, HD 13931, HD 1159554, HD 211847, HD 219077, HD 222155, and HIP 70849. For three of these companions (Epsilon Indi Ab, HD 211847 B, and HD 219077 b), a first estimation of their orbital inclination and true mass has been obtained by combining RV data and absolute astrometry. Yet, thanks to additional data or more precise astrometric measurements, we obtained more precise and significantly different results from those reported in the previous studies for six of these companions. In the case of HD 219077 b, the differences were mainly found for the mass of the companion. They are mainly due to the uncertainties as to the host star’s mass.

2.2 RV data

The RV data used in this study were obtained with different spectrographs between 1997 and 2021. The HARPS (Mayor et al. 2003) data were taken from the ESO archives; the ELODIE (Baranne et al. 1996) and SOPHIE (Perruchot et al. 2008) data were retrieved from the OHP archives; and the CORALIE (Queloz et al. 1999), the HIRES (Vogt et al. 1994), the UVES (Dekker et al. 2000), the AAT (Diego et al. 1990), the CES (Enard 1982) long camera (LC), and the CES very long camera (VLC) data were taken from the literature.

As instrument upgrades can lead to new RV offsets, the same instrument before and after a major upgrade is considered as two different instruments. Consequently, HARPS data obtained before and after the optical fiber upgrade in 2015 (Lo Curto et al. 2015) are referred to as H03 and H15, respectively. The SOPHIE data obtained before and after the spectrograph upgrade in 2011 (Bouchy et al. 2013) are referred to as SOPHIE and SOPHIE+, respectively. The HIRES data obtained before and after the upgrade of the spectrograph in 2004 (Tal-Or et al. 2019) are referred to as Hir94 and Hir04, respectively. Finally, the CORALIE spectrograph had two major upgrades in 2007 (Ségransan et al. 2010) and in 2014. The data obtained before 2007 and after 2014 are referred to as C98 and C14, respectively, and the data obtained between 2007 and 2014 are referred to as C07.

2.3 Direct imaging data

In three cases, HCI data are available in the SPHERE archive and can provide relative astrometry. The three targets were observed in angular (and spectral) differential imaging (A(S)DI, Marois et al. 2006) using the telescope in pupil tracking mode. The standard observing mode of SPHERE was used, with IRDIS (Dohlen et al. 2008) dual band images at H2 and H3 (K1 and K2, respectively) and IFS (Claudi et al. 2008) data covering the YJ (YJH, respectively) bands. The observing log is given in Table 1. Whenever possible, the robust PACO A(S)DI algorithm (Flasseur et al. 2020a,b) was used. The processing step takes advantage of the developments made to the COBREX data center pipeline (the prereduction improvement as well as the improvement of the detection capability of PACO). If a dataset did not sufficiently cover the field-of-view rotation to apply ADI-based algorithms, the SPECAL (Galicher et al. 2018) No-AdI algorithm was used.

In those three systems, only one companion was detected (HD 211847 B). The detected companion is characterized in Table 2. No detection above 5a was found around HD 219077. Six sources were detected around HIP 70849 but, given their position in a color-magnitude diagram and their separations, they are likely background sources.

Table 2

Relative astrometry for HD 211847 companion.

2.4 Absolute astrometry

We used measurements from HIPPARCOS obtained around epoch 1991.25 and from Gaia EDR3 (Gaia Collaboration 2016, 2021) obtained around epoch 2016.0. For each target, the stellar acceleration was determined from the proper motion and the position values were measured by HIPPARCOS and Gaia with an interval of about 25 yr. We considered the proper motion values published by Brandt (2021) in the HIPPARCOS-Gaia Catalog of Accelerations (HGCA). Moreover, a more accurate tangential proper motion (μHip–EDR3) was estimated by the difference between the position measurements obtained by HIPPARCOS and Gaia divided by the time interval between the two measurements (~25 yr). The proper motion values used for each star are given in Table A.1.

3 Updated orbital parameters and mass

3.1 Orbit fitting

Orbits were fitted using a custom Markov chain Monte Carlo (MCMC) tool, based on the emcee 3.0 python package (Foreman-Mackey et al. 2013). It uses a mixture of move functions (such as the differential evolution move function) to alleviate potential multimodality issues. The HIPPARCOS/Gaia data processing uses the HTOF package (Brandt et al. 2021c) and borrows large sections of the orvara code (Brandt et al. 2021d) for the likelihood computation. The HTOF package (Brandt et al. 2021c) was used to fit the intermediate astrometric data (IAD) from HIPPARCOS, based on the 1997 (Esa 1997) and 2007 (van Leeuwen 2007) reductions and from Gaia, thanks to the Gaia Observation Forecast Tool (GOST) which allowed us to obtain the estimated Gaia observations and scan angles for each target, in order to reproduce proper motion and position of each observation. Using the HIPPARCOS and Gaia positions and the temporal baseline, the algorithm derived a tangential proper motion value that allowed us to better constrain the orbital fit when combined with RV data.

We considered ten free parameters for each system: the semimajor axis (a), the eccentricity, the orbital inclination (i), the host star mass, the companion mass, the longitude of ascending node (Ω), the argument of periastron (ω), the phase, a stellar jitter, and the distance of the system. In addition, to combine data from different instruments, we added an instrumental offset for each instrument as a free parameter of the model (see above). Finally, we considered uniform priors for all fitting parameters, except for the host star mass and the distance of the system for which we considered Gaussian priors.

3.2 Results

3.2.1 Epsilon Indi A

Epsilon Indi is a triple system with a 0.76 ± 0.04 M, K2V star (Epsilon Indi A) and a binary composed of a 75.0 ± 0.8 MJup, T1.5 brown dwarf (Epsilon Indi B) and a 70.1 ± 0.7 MJup, T6 brown dwarf (Epsilon Indi C) separated by about 2.6 au (Dieterich et al. 2018). The projected separation between the binary brown dwarfs and the star is about 1460 au. Combining RV data and absolute astrometry based on HIPPARCOS and the Gaia data release 2 (DR2) measurements, Feng et al. (2019) reported a giant planet with a semi-major axis of au, a mass of , an inclination of , and an eccentricity of Yet, the Gaia EDR3 proper motion and position measurements are significantly more precise compared to the Gaia DR2 measurement and they significantly improve the characterization of Epsilon Indi Ab.

We used 4278 RV measurements obtained with the HARPS spectrograph between 2003 and 20161, 163 RV measurements obtained with the UVES spectrograph between 1996 and 2017, 72 RV measurements obtained with the LC spectrograph between 1992 and 1997, and 53 RV measurements obtained with the VLC spectrograph between 2000 and 2006. We also combined these RV data with absolute astrometry based on HIPPARCOS and the Gaia EDR3 measurements (Fig. 1). We found significantly different orbital parameters with a semi-major axis of au, a mass of 3.0 ± 0.1 MJup, an inclination of , and an eccentricity of 0.48 ± 0.01. The posteriors obtained for each free parameter are reported in Table 3. It is important to note that if we consider only the 539 HARPS RV data with a signal-to-noise ratio greater than 110 and thus remove the high cadence observations made in August 2011, we find similar solutions.

3.2.2 HD 13931

HD 13931 is a 1.02 ± 0.05 M (Rosenthal et al. 2021), G0V star. Based on 66 RV measurements obtained with the HIRES spectrograph between 1998 and 2019, Rosenthal et al. (2021) reported a giant planet with a semi-major axis of 5.323 ± 0.091 au, a minimum mass of , and an eccentricity of .

We combined these RV data with absolute astrometry (Fig. 2). As the RV baseline is much larger than the orbital period, the orbital parameters are well-constrained. As expected, we found a semi-major axis and an eccentricity very close to those reported by Rosenthal et al. (2021) with a = 5.33 ± 0.09 au and e < 0.04. Using, in addition, the absolute astrometry, we found an orbital inclination of either or and a true mass of . The posteriors obtained for each free parameter are reported in Table 3.

3.2.3 HD 115954

HD 115954 is a 1.18 ± 0.06 M, G0V star (Demangeon et al. 2021). Based on four RV measurements obtained with the ELODIE spectrograph between 2004 and 2005 and 45 RV measurements obtained with the SOPHIE spectrograph between 2009 and 2018, Demangeon et al. (2021) reported a giant planet with a semi-major axis of au, a minimum mass of , and an eccentricity of .

We combined these RV data with the absolute astrometry data (Fig. 3). We found a semi-major axis compatible with Demangeon et al. (2021) with au and an eccentricity of 0.46 ± 0.03. Using, in addition, the absolute astrometry, we found an orbital inclination of and a true mass of . The posteriors obtained for each free parameter are reported in Table 3.

Table 3

Summary of posteriors obtained with our MCMC algorithm.

thumbnail Fig. 1

Orbital fits for Epsilon Indi Ab. Top: fit of the Epsilon Indi A RV data corrected from the instrumental offset (V0). Bottom: fit of the Epsilon Indi A astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia EDR3 (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

3.2.4 HD 211847

HD 211847 is a 0.94 ± 0.04 M, G5V star (Sahlmann et al. 2011). Sahlmann et al. (2011) reported a brown dwarf candidate orbiting around HD 211847 based on 31 RV measurements obtained with the CORALIE spectrograph between 2002 and 2009. However, only one minimum of the HD 211847 B RV curve was covered by the dataset. Thus, the orbital parameters and minimum mass reported in this study are poorly constrained. Using the Levenberg-Marquardt method, they found ranges corresponding to a 3σ confidence interval for the semi-major axis, the eccentricity, and the minimum mass of 4.6–42 au, 0.48–0.95, and 16.3–24.3 MJup, respectively. Moutou et al. (2017) obtained one HCI detection with SPHERE of HD 211847 B for a projected separation of 11.3 au. Using the BT-Settl models (Allard 2014), they fit the HD 211847 B spectrum and found a low stellar mass of 155 ± 9 MJup assuming an age of 3 Gyr for the host star. Based on the result of Sahlmann et al. (2011), Moutou et al. (2017) estimated the inclination of the companion orbit to be around seven°. Recently, combining the CORALIE RV measurement and the absolute astrometry, Feng et al. (2022) reported HD 211847 B as a brown dwarf with a semi-major axis of au, a mass of , an inclination of , and an eccentricity of .

We combined the RV dataset used by Sahlmann et al. (2011), the relative astrometry observation obtained with SPHERE in June 2015, and the absolute astrometry (Fig. 4). Adding one relative astrometry observation allowed us to properly constrain the orbital parameters and the mass of HD 211847 B with results significantly different from those reported by Feng et al. (2022). We found a semi-major axis of 6.78 ± 0.08 au and an eccentricity of . Using, in addition, the absolute astrometry, we found an orbital inclination of and a true mass of 148 ± 5 MJup. The posteriors obtained for each free parameter are reported in Table 3. We note that by taking only RV data and absolute astrometry into account, we found very poorly constrained solutions with large uncertainties as to the semi-major axis (16–30 au) and mass (80–140 MJup). Moreover, the solutions found are not in agreement with those reported by Feng et al. (2022) or with the solutions found when adding the HCI data.

thumbnail Fig. 2

Orbital fits for HD 13931 b. Top: fit of the HD 13931 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 13931 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

3.2.5 HD 219077

Based on 63 CoRALIE RV measurements obtained between 1999 and 2012 and 30 HARPS RV measurements obtained between 2003 and 2012, Marmier et al. (2013) reported a very eccentric giant planet with a semi-major axis of 6.22 ± 0.09 au and a minimum mass of 10.39 ± 0.09 MJup. It is important to note that the RV data used by Marmier et al. (2013) are not publicly available. Based on 72 pieces of RV data obtained with the AAT spectrograph between 1998 and 2015, Kane et al. (2019) reported slightly different properties for HD 219077 with a semi-major axis of au and a minimum mass of . These differences are probably due to the different assumptions on the mass of the star. Indeed, Marmier et al. (2013) used the values reported by HIPPARCOS (M= 1.05 ± 0.02 M) while Kane et al. (2019) used the values reported in (Valenti & Fischer 2005; M= 1.51 ± 0.13 M). Recently, Feng et al. (2022) combined the AAT RV measurements used by Kane et al. (2019) and 33 HARPS RV measurements obtained between 2003 and 2012 with the absolute astrometry based on HIPPARCOS and the Gaia EDR3 measurements and found a semi-major axis close to Marmier et al. (2013), an orbital inclination of , and a true mass of MJup. The prior on the mass of the star is not given.

For this study, as the data used by Marmier et al. (2013) are not available, we considered the HARPS and AAT RV measurements used on Feng et al. (2022) and the 65 CoRALIE RV measurements available on the DACE archive2 obtained between 1999 and 20123. For the mass of the star, we considered the value given by Kervella et al. (2022) based on the Gaia DR3 results (M = 1.15 ± 0.06 M). We combined the RV data with the absolute astrometry (Fig. 5). We found a semi-major axis and an eccentricity close to those reported in the previous studies with a = 6.4 ± 0.1 au and e = 0.769 ± 0.002 and an orbital inclination close to that of Feng et al. (2022) with either i = 83 ± 3° or i = 97 ± 3°. Considering the star mass found by Kervella et al. (2022), we found a planetary mass at 11.3 ± 0.4 MJup. The posteriors obtained for each free parameter are reported in Table 3. However, considering that the mass used in Valenti & Fischer (2005) would lead to a mass close to the deuterium-burning limit, Mb = 13.6 ± 0.5 MJup. Due to the uncertainties on the mass of the host star, it is not possible to determine the exact nature of HD 219077 b.

thumbnail Fig. 3

Orbital fits for HD 115954 b. Top: fit of the HD 115954 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 115954 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

thumbnail Fig. 4

Orbital fits for HD 211847 B. Top left: fit of the HD 211847 RV data corrected from the instrumental offset (V0). Top right: fit of HD 211847 relative astrometry data. The red cross corresponds to the measurement obtained with SPHERE. Bottom: fit of the HD 211847 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different| fits plotted.

thumbnail Fig. 5

Orbital fits for HD 219077 b. Top: fit of the HD 219077 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 219077 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

3.2.6 HD 222155

HD 222155 is a 1.13 ± 0.11 M, G2V star (Boisse et al. 2012). Based on 44 RV measurements obtained with the ELODIE spectrograph between 1997 and 2005 and 67 RV measurements obtained with the SOPHIE spectrograph between 2007 and 2011, Boisse et al. (2012) reported a giant planet with a semi-major axis of au, a minimum mass of MJup, and an eccentricity of .

We considered 31 additional pieces of SOPHIE RV data obtained between 2011 and 2016. We combined the RV data with the absolute astrometry (Fig. 6). We found orbital parameters within the error bars associated with the values found by Boisse et al. (2012) with a = 4.7 ± 0.1 au and e = 0.34 ± 0.09. As the RV baseline is now much larger than the orbital period, the orbital parameters are better constrained. Using, in addition, the absolute astrometry, we found an orbital inclination of either or and a true mass of MJup. The posteriors obtained for each free parameter are reported in Table 3.

thumbnail Fig. 6

Orbital fits for HD 222155 b. Top: fit of the HD 222155 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 222155 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

3.2.7 HIP 70849

HIP 70848 is a 0.63 ± 0.03 M, K7V star (Ségransan et al. 2011). Ségransan et al. (2011) reported the first detection of HIP 70849 b based on 18 RV measurements obtained with the HARPS spectrograph between 2006 and 2010. However, only one minimum of the HIP 70849 b RV curve was covered by the dataset. The observations carried out by Ségransan et al. (2011) led to poorly constrained orbital parameters and minimum mass. Using a genetic algorithm followed by MCMC simulations, they reported a semi-major axis between 4.5 and 36 au, a minimum mass between 3 and 15 MJup, and an eccentricity between 0.47 and 0.96 with ranges corresponding to a 3σ confidence interval.

We considered 39 additional pieces of HARPS RV data obtained between 2011 and 2021. We combined the RV data with the absolute astrometry (Fig. 7). With these additional observations, the dataset then covered two minimum and one maximum of the RV curve of HIP 70849 b and this allowed us to properly constrain the properties of the companion. We found a semi-major axis of au and an eccentricity of . Using, in addition, the absolute astrometry, we found an orbital inclination of 96 ± 16° and a true mass of MJup. The posteriors obtained for each free parameter are reported in Table 3.

thumbnail Fig. 7

Orbital fits for HIP 70849 b. Top: fit of the HIP 70849 RV data corrected from the instrumental offset (V0). Bottom: fit of the HIP 70849 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

4 Summary and concluding remarks

Combining RV measurements from various spectrographs with absolute astrometry based on HIPPARCOS and Gaia EDR3 data and, when available, relative astrometry, we determined the orbital parameters and, in particular, the orbital inclination and the true mass of seven long-period single companions detected by the RV method. Figure 8 summarizes the true mass and the semi-major axis of the companions and compares them with the previous estimations. Clearly, Gaia EDR3 data allow for a better determination of these companions' orbital parameters and mass. All of these companions have true masses of 2 MJup or more and orbit between 3.9 and 9 au from their stars. Absolute astrometry would probably help to determine the true mass of planets with a period larger than the duration of Gaia DR3 observations (P > ~1000 d) down to 1 MJup, provided the RV variations are well covered and the variations in position and acceleration of the proper motion of the star are large enough. In practice, in most cases, when the period is not well constrained by the RV data, the impact of the coupling of RV data with absolute astrometry is more limited. An illustration of this is the case of HD 211847 B for which, by combining RV data that cover only a minimum of the RV variations with absolute astrometry, Feng et al. (2022) reported a mass of about 55 MJup, corresponding to a brown dwarf. Yet, HCI revealed a companion and the fit of the RV and the relative and absolute astrometry leads to a mass of about 150 MJup instead.

We conclude that Gaia/HIPPARCOS can help to further constrain the orbital parameters of long-period RV planets, providing good coverage of the RV variations is available. Otherwise, additional information is needed, such as relative astrometry, provided by DI or interferometry.

thumbnail Fig. 8

Update of the orbital parameters and masses of the seven analyzed systems thanks to the combination of absolute astrometric and RV data and, when available, absolute astrometry data. For each system, a dotted line between two solutions was drawn to allow for the different solutions obtained to be compared.

Acknowledgements

This study was funded by a grant from PSL/OCAV. This project has also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (COBREX; grant agreement n° 885593). This work presents results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is https://www.cosmos.esa.int/gaia. The Gaia archive website is https://archives.esac.esa.int/gaia. This publications makes use of the Data & Analysis Center for Exoplanets (DACE), which is a facility based at the University of Geneva (CH) dedicated to extrasolar planets data visualisation, exchange and analysis. DACE is a platform of the Swiss National Centre of Competence in Research (NCCR) PlanetS, federating the Swiss expertise in Exoplanet research. The DACE platform is available at https://dace.unige.ch. This research has made use of the SIMBAD database and VizieR catalogue access tool, operated at CDS, Strasbourg, France. Based on data retrieved from the SOPHIE archive at Observatoire de Haute-Provence (OHP), available at atlas.obs-hp.fr/sophie. Based on spectral data retrieved from the ELODIE archive at Observatoire de Haute-Provence (OHP). Based on observations collected at the European Southern Observatory under ESO programme(s) 183.C-0972(A), 108.22KV.001, 108.22KV.002, 072.C-0488(E), 108.222V.001, 090.C-0421(A), 085.C-0019(A), 087.C-0831(A), 095.C-0551(A), 0100.C-0097(A), 0103.C-0432(A), 0101.C-0379(A), 096.C-0460(A), 0102.C-0558(A), 093.C-0409(A), 098.C-0366(A), 099.C-0458(A), 089.C-0732(A), 091.C-0034(A), 196.C-1006(A), 0102.C-0558(A), 106.21R4.001, 183.C-0972(A), 075.C-0332(A), 192.C-0852(A), 190.C-0027(A), 091.C-0936(A), 085.C-0063(A), 086.C-0284(A), 076.C-0155(A), 077.C-0101(A), 082.C-0212(A).

Appendix A Proper motion values

Table A.1

Proper motion values from HGCA.

Appendix B MCMC priors

Table B.1

Priors considered for each free parameter.

Appendix C MCMC results

thumbnail Fig. C.1

Corner plot of the posteriors’ fit of Epsilon Indi A combined RV and absolute astrometry. An offset of 39.9 km/s was added to V0, V1, V3, and V4 to improve readability.

thumbnail Fig. C.2

Corner plot of the posteriors’ fit of HD 13931 combined RV and absolute astrometry.

thumbnail Fig. C.3

Corner plot of the posteriors’ fit of HD 115954 combined RV and absolute astrometry. An offset of 14 km/s was added to V0, V1, and V2 to improve readability.

thumbnail Fig. C.4

Corner plot of the posteriors’ fit of HD 211847 combined RV, relative astrometry, and absolute astrometry. An offset of 6 km/s was subtracted to V0 and V1 to improve readability.

thumbnail Fig. C.5

Corner plot of the posteriors’ fit of HD 219077 combined RV and absolute astrometry. An offset of 30 km/s was added to V0, V1, and V2 to improve readability.

thumbnail Fig. C.6

Corner plot of the posteriors’ fit of HD 222155 combined RV and absolute astrometry. An offset of 3.9 km/s was added to V0, V1, and V2 to improve readability.

thumbnail Fig. C.7

Corner plot of posteriors fit of HIP 70849 combined RV and absolute astrometry.

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1

The 3636 RV data obtained between Julian days 2455790 and 2455805 were obtained to study high-frequency oscillations of the star. These data were measured with high cadence, which led to a significantly lower signal-to-noise ratio compared to the other data.

3

The CORALIE RV data available on DACE and the HARPS RV data available on the ESO archive cover the same time base as those used by Marmier et al. (2013).

All Tables

Table 1

Observing logs.

Table 2

Relative astrometry for HD 211847 companion.

Table 3

Summary of posteriors obtained with our MCMC algorithm.

Table A.1

Proper motion values from HGCA.

Table B.1

Priors considered for each free parameter.

All Figures

thumbnail Fig. 1

Orbital fits for Epsilon Indi Ab. Top: fit of the Epsilon Indi A RV data corrected from the instrumental offset (V0). Bottom: fit of the Epsilon Indi A astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia EDR3 (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

In the text
thumbnail Fig. 2

Orbital fits for HD 13931 b. Top: fit of the HD 13931 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 13931 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

In the text
thumbnail Fig. 3

Orbital fits for HD 115954 b. Top: fit of the HD 115954 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 115954 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

In the text
thumbnail Fig. 4

Orbital fits for HD 211847 B. Top left: fit of the HD 211847 RV data corrected from the instrumental offset (V0). Top right: fit of HD 211847 relative astrometry data. The red cross corresponds to the measurement obtained with SPHERE. Bottom: fit of the HD 211847 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different| fits plotted.

In the text
thumbnail Fig. 5

Orbital fits for HD 219077 b. Top: fit of the HD 219077 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 219077 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

In the text
thumbnail Fig. 6

Orbital fits for HD 222155 b. Top: fit of the HD 222155 RV data corrected from the instrumental offset (V0). Bottom: fit of the HD 222155 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

In the text
thumbnail Fig. 7

Orbital fits for HIP 70849 b. Top: fit of the HIP 70849 RV data corrected from the instrumental offset (V0). Bottom: fit of the HIP 70849 astrometric acceleration in right ascension (left) and declination (right). The black points correspond to the measurements obtained with HIPPARCOS (1991.25) and Gaia (2016.0). In each plot, the black curve shows the best fit. The color bar indicates the log likelihood of the different fits plotted.

In the text
thumbnail Fig. 8

Update of the orbital parameters and masses of the seven analyzed systems thanks to the combination of absolute astrometric and RV data and, when available, absolute astrometry data. For each system, a dotted line between two solutions was drawn to allow for the different solutions obtained to be compared.

In the text
thumbnail Fig. C.1

Corner plot of the posteriors’ fit of Epsilon Indi A combined RV and absolute astrometry. An offset of 39.9 km/s was added to V0, V1, V3, and V4 to improve readability.

In the text
thumbnail Fig. C.2

Corner plot of the posteriors’ fit of HD 13931 combined RV and absolute astrometry.

In the text
thumbnail Fig. C.3

Corner plot of the posteriors’ fit of HD 115954 combined RV and absolute astrometry. An offset of 14 km/s was added to V0, V1, and V2 to improve readability.

In the text
thumbnail Fig. C.4

Corner plot of the posteriors’ fit of HD 211847 combined RV, relative astrometry, and absolute astrometry. An offset of 6 km/s was subtracted to V0 and V1 to improve readability.

In the text
thumbnail Fig. C.5

Corner plot of the posteriors’ fit of HD 219077 combined RV and absolute astrometry. An offset of 30 km/s was added to V0, V1, and V2 to improve readability.

In the text
thumbnail Fig. C.6

Corner plot of the posteriors’ fit of HD 222155 combined RV and absolute astrometry. An offset of 3.9 km/s was added to V0, V1, and V2 to improve readability.

In the text
thumbnail Fig. C.7

Corner plot of posteriors fit of HIP 70849 combined RV and absolute astrometry.

In the text

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