11institutetext: INAF-Osservatorio Astronomico di Padova, Vicolo
dell’Osservatorio 5, Padova, Italy, 35122-I
School of Physical Sciences, Faculty of Science, Technology, Engineering and
Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA
INAF-Osservatorio Astronomico di Palermo, Piazza del Parlamento, 1, I-90134,
Palermo, Italy
Jesus College, University of Cambridge, Jesus Lane, Cambridge, CB5 8BL, UK
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3
OHA, UK
LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université,
Université de Paris, 5 place Jules Janssen, F-92195 Meudon, France
Max-Planck-Institut für Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
Department of Astronomy, Stockholm University, AlbaNova, University Center,
109 91 Stockholm, Sweden
Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille)
UMR 7326, 13388 Marseille, France
CRAL, UMR 5574, CNRS, Université de Lyon, Ecole Normale Superieure de Lyon, 46
Allée d’Italie, 69364 Lyon Cedex 07, France
Observatoire Astronomique de l’Université de Geneve, 51 Ch. des Maillettes,
1290 Versoix, Switzerland
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA
Nucleo de Astronomia, Facultad de Ingenieria y Ciencias, Universidad Diego
Portales, Av. Ejercito 441, Santiago, Chile
Escuela de Ingenieria Industrial, Facultad de Ingenieria y Ciencias,
Universidad Diego Portales, Av. Ejercito 441, Santiago, Chile
SUPA, Institute for Astronomy, University of Edinburgh, Blackford Hill,
Edinburgh EH9 3HJ, UK
Centre for Exoplanet Science, University of Edinburgh, Edinburgh, UK
Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
5Center for Space and Habitability, University of Bern, CH-3012 Bern,
Switzerland
Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park
904, 1098 XH Amsterdam, The Netherlands
Space Telescope Science Institute, Baltimore 21218, MD, USA
Geneva Observatory, University of Geneva, Chemin des Mailettes 51, 1290
Versoix, Switzerland
University of Cote d’Azur, Cote d’Azur Observatory, CNRS, Lagrange Laboratory,
France
STAR Institute, Université de Liege, Allee du Six Aout 19c, 4000 Liege,
Belgium
ESO Vitacura, Alonso de Cordova 3107, Vitacura, Casilla 19001, Santiago de
Chile, Chile
Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany

# Constraining masses and separations of unseen companions to five
accelerating nearby stars††thanks: Based on observation made with European
Southern Observatory (ESO) telescopes at Paranal Observatory in Chile, under
programs ID 095.C-0298(A), 095.C-0298(B), 096.C-0241(A), 096.C-0241(G),
097.C-0865(A), 097.C-0865(D), 1100.C-0481(F), 1100.C-0481(N), 1100.C-0481(P)

D. Mesa 11 M. Bonavita 1122 S. Benatti 33 R. Gratton 11 S. Marino 4455 P.
Kervella 66 V. D’Orazi 11 S.Desidera 11 T. Henning 77 M. Janson 88 M. Langlois
991010 E. Rickman 11111212 A. Vigan 99 A. Zurlo 1313141499 J.-L. Baudino 66 B.
Biller 7715151616 A. Boccaletti 66 M. Bonnefoy 1717 W. Brandner 77 E. Buenzli
77 F. Cantalloube 99 D. Fantinel 11 C. Fontanive 181811 R. Galicher 66 C.
Ginski 1919 J. Girard 20201717 J. Hagelberg 2121 T. Kopytova 77 C. Lazzoni 11
H. Le Coroller 99 R. Ligi 2222 M. Llored 99 A.-L. Maire 232377 D. Mouillet
1717 C. Perrot 66 S. Rochat 1717 C. Romero 17172424 D. Rouan 66 M. Samland
7788 T.O.B. Schmidt 662525 E. Sissa 11 F. Wildi
11111122334455667788991010111112121313141415151616171718181919202021212222232324242525

(Received / accepted )

###### Abstract

Aims. This work aims at constraining the masses and separations of potential
substellar companions to five accelerating stars (HIP 1481, HIP 88399, HIP
96334, HIP 30314 and HIP 116063) using multiple data sets acquired with
different techniques.

Methods. Our targets were originally observed as part of the SPHERE/SHINE
survey, and radial velocity (RV) archive data were also available for four of
the five objects. No companions were originally detected in any of these data
sets, but the presence of significant proper motion anomalies (PMa) for all
the stars strongly suggested the presence of a companion. Combining the
information from the PMa with the limits derived from the RV and SPHERE data,
we were able to put constraints on the characteristics of the unseen
companions.

Results. Our analysis led to relatively strong constraints for both HIP 1481
and HIP 88399, narrowing down the companion masses to 2-5 MJup and 3-5 MJup
and separations within 2-15 au and 3-9 au, respectively. Because of the large
age uncertainties for HIP 96334, the poor observing conditions for the SPHERE
epochs of HIP 30314 and the lack of RV data for HIP 116063, the results for
these targets were not as well defined, but we were still able to constrain
the properties of the putative companions within a reasonable confidence
level.

Conclusions. For all five targets, our analysis has revealed that the
companions responsible for the PMa signal would be well within reach for
future instruments planned for the ELT (e.g., MICADO), which would easily
achieve the required contrast and angular resolution. Our results therefore
represent yet another confirmation of the power of multi-technique approaches
for both the discovery and characterisation of planetary systems.

###### Key Words.:

Instrumentation: spectrographs - Methods: data analysis - Techniques: imaging
spectroscopy - Stars: planetary systems, Stars: individual: HIP1481, HIP30314,
HIP88399, HIP96334, HIP116063

##  1 Introduction

In the last decade the direct imaging (DI) technique has allowed for the
detection of a growing number of planetary mass objects orbiting nearby young
stars, such as 51 Eri b (Macintosh et al. 2015), HIP 65426 b (Chauvin et al.
2017b), PDS 70 b (Keppler et al. 2018), and PDS 70 c (Haffert et al. 2019).
This was made possible in particular thanks to a new generation of high-
contrast imagers mainly devoted to this aim, like the Gemini Planet Imager
(GPI; Macintosh et al. 2014), VLT/SPHERE (Beuzit et al. 2019), and CHARIS
(Groff et al. 2015).

However, even with such sophisticated instruments, direct detection is limited
to giant gaseous companions at large separation (more than 10 au) from the
host star. Such limitation mainly arises from the challenge of resolving
extremely faint sources (with contrast of the order of $10^{-6}$) at
relatively close angular separations (a physical separation of 10 au
corresponds to 0.2′′ for a star at a distance of 50pc)

In addition, recent studies have pointed out the relative paucity of giant
planets (masses larger than 1 MJup) at large separations (Nielsen et al. 2019;
Vigan et al. 2021) which, combined with the increasing planetary occurrence
rate between 0.1 and 1 au obtained through radial velocity (RV) surveys (see
e.g., Fulton et al. 2021) implies that the expected peak for the distribution
of giant planets should reside between 1 and 10 au (e.g., Meyer et al. 2018).

While the bulk of the giant planet population therefore appears to be out of
reach from current direct imaging surveys, it will likely be the main focus
for the future instrumentation of the under construction extremely large
telescopes (ELT; see e.g., Perrot et al. 2018). There are, however, ways to
push the discovery space of the current facilities towards the peak of the
giant planet population, and enhance our comprehension of the formation
process of such objects. Concentrating on the nearest stars is an obvious
solution, but it is also possible to carry on focused programs concentrating
the efforts on stars that have higher probability to host detectable
companions. So far the most successful selection methods for such programs
have been those based on proper motion anomalies (PMa or accelerations, see
e.g. Brandt 2018; Kervella et al. 2019) defined as the difference between the
short-term and the long-term proper motion measured for a star. While these
trends have been in the past only used to select targets for binary stars
searches, the precision on the proper motion measurements achieved by Gaia
(Gaia Collaboration et al. 2016) now allows to push towards signals pointing
to much smaller companions, down to the sub-stellar and even planetary regime.

Several groups (see e.g. Kervella et al. 2019, 2022; Brandt 2018, 2021) have
recently shared PMa catalogues, including the Hipparcos and $Gaia$ DR2/eDR3
proper motions, as well as a $Gaia$-Hipparcos scaled positional differences,
placing all proper motions at the epochs of Gaia DR2 and eDR3, respectively,
with re-calibrated uncertainties for hundred of thousand of stars. For our
work, we choose to use the catalogue from Kervella et al. (2022) and,
following their approach, we define as accelerating those stars with a PMa
signal-to noise ratio (SNR) larger than 3. As shown by several recent results,
accelerating stars have high probability of hosting companions ranging from
low mass stars to sub-stellar companions, including objects close to planetary
mass (see e.g., Bonavita et al. 2022; Currie et al. 2020; Steiger et al. 2021;
Chilcote et al. 2021). Even in case of non-detection, the combination of DI
data with the information on the PMa can be used to put constraints on the
nature of the possible unseen companions causing the acceleration. In
addition, the availability of radial velocity data provides additional
information on closer companions. For example, this approach was used by Mesa
et al. (2021) to study the disk hosting star HD 107146, leading to the
conclusion that the measured PMa should be due to the presence of a companion
with a mass of 2-5 MJup at a separation of 2-7 au. Results like this one show
how such an analysis is therefore crucial to understand the structure of
planetary systems around these stars and can also be used to define a sample
of optimal targets for future observations with ELT instruments.

In this paper we present the results of our analysis for five stars with
strong accelerations pointing towards the presence of a low mass companion and
for which DI observations were available from SHINE (Chauvin et al. 2017a;
Desidera et al. 2021; Langlois et al. 2021; Vigan et al. 2021). While no
companion was retrieved from the SHINE observations, they have been used to
constrain their presence at separation between 2 and 10 au also using mass
limits from archive RV data. A detailed description of each of our targets is
provided in Section 2, while Section 3 presents the various data sets used for
our analysis. Our results are presented in Section 4 and discussed in Section
5. Finally, Section 6 provides some concluding remarks.

##  2 Sample selection

Table 1: Main Characteristics of the target stars. Individual references for
the stellar ages (expressed as $Age^{max}_{min}$) and masses are provided in
Section2. Parallaxes and Proper Motion values are from eDR3, from which we
also show the RUWE. The values of the proper motion anomaly (PMa), PMa SNR and
tangential velocity ($\@vec{\Delta v_{\mathrm{tan}}}$) with the corresponding
position angle are from Kervella et al. (2022).

ID | Age${}^{max}_{min}$ | Mass | SpType | Kmag | Parallax | Proper Motion | PMa (HIP-eDR3) |  $\@vec{\Delta v_{\mathrm{tan}}}$ (HIP-eDR3) | RUWE | SNRPMa
---|---|---|---|---|---|---|---|---|---|---
| (Myrs) | ($M_{\odot}$) |  |  | (mas) | (RA: mas/yr) | (Dec: mas/yr) | (RA: mas) | (Dec: mas) | (m/s) | (PA: deg) |  |
HIP 1481 | 45${}^{50}_{35}$ | 1.16 | F8V | 6.15 | 23.36 $\pm$ 0.02 | 90.05 $\pm$ 0.02 | -59.21 $\pm$ 0.02 | -0.10 $\pm$ 0.02 | 0.04 $\pm$ 0.02 | 22.13 $\pm$ 6.40 | 290.07 $\pm$ 12.07 | 0.994 | 3.46
HIP 30314 | 149${}^{180}_{100}$ | 1.11 | G1V | 5.05 | 41.89 $\pm$ 0.01 | -11.43 $\pm$ 0.02 | 64.68 $\pm$ 0.02 | -0.04 $\pm$ 0.02 | 0.10 $\pm$ 0.02 | 12.52 $\pm$ 3.51 | 336.98 $\pm$ 11.05 | 0.874 | 3.57
HIP 88399 | 24${}^{29}_{19}$ | 1.29 | F6V | 5.91 | 20.29 $\pm$ 0.02 | 2.33 $\pm$ 0.02 | -86.23 $\pm$ 0.02 | 0.11 $\pm$ 0.03 | -0.09 $\pm$ 0.02 | 32.66 $\pm$ 8.21 | 130.94 $\pm$ 10.17 | 1.093 | 3.98
HIP 96334 | 150${}^{220}_{70}$ | 1.00 | G3V | 6.3 | 26.20 $\pm$ 0.02 | -4.04 $\pm$ 0.01 | -176.05 $\pm$ 0.02 | 0.04 $\pm$ 0.02 | 0.13 $\pm$ 0.02 | 25.13 $\pm$ 5.43 | 14.63 $\pm$ 7.53 | 0.995 | 4.63
HIP 116063 | 300${}^{500}_{200}$ | 0.80 | G1V | 5.65 | 33.05 $\pm$ 0.02 | 183.28 $\pm$ 0.02 | -122.68 $\pm$ 0.02 | -0.07 $\pm$ 0.03 | 0.09 $\pm$ 0.03 | 16.54 $\pm$ 5.45 | 324.67 $\pm$ 12.73 | 1.107 | 3.04

The starting point for the target selection was the catalogue by Kervella et
al. (2022), which lists the value of the proper motion anomaly (PMa), defined
as the difference in proper motion between Hipparcos and Gaia eDR3 (Gaia
Collaboration et al. 2021), for $\sim$11000 Hipparcos stars. From a initial
list of targets with PMa with SNR higher than three, we selected the objects
with renormalised unit weight error (RUWE; for a more detailed definition and
description of its use see Lindegren et al. 2021) higher than 1.4, to avoid
the effects of possible degradation of the astrometric parameters. Moreover, a
large value of the RUWE parameter is often caused by stellar binarity as
discussed in Kervella et al. (2022). We then restricted our sample to stars
within 50 parsecs, in order to make sure possible companions responsible for
the PMa would be accessible with direct imaging. The final list of 498 targets
was then cross-correlated with the list of targets observed during the SHINE
survey (Desidera et al. 2021; Langlois et al. 2021). After the exclusion of
objects for which the presence of a bound stellar companion was known and able
to explain the PMa signal, we were left with five targets: HIP 1481, HIP
88399, HIP 96334, HIP 30314 and HIP 116063. Their main characteristics are
summarised in Table 1 and described in detail in the following Sections.

###  2.1 HIP 1481

HIP 1481 (HD 1466) is an F8 star (Torres et al. 2006) with a mass of 1.16 M⊙
(Desidera et al. 2021), located at a distance of 42.82$\pm$0.03 pc from the
Sun (Gaia Collaboration et al. 2021). It has been recognised as member of the
Tucana-Horologium moving group (Bell et al. 2015). From this membership
Desidera et al. (2021) deduced an age of $45_{-10}^{+5}$ Myr.

The presence of a debris disk around HIP 1481 was inferred by Chen et al.
(2014) using Spitzer observations. They modelled the SED with a double black
body with temperatures of 97 and 374 K hinting for a double belt structure for
the disk. Using these results Lazzoni et al. (2018) found for the inner belt a
radius of 0.7 au and for the outer belt a radius of $\sim$52 au with a gap
between the two belts of around 40 au. Using dynamical models they then
concluded that to explain this disk configuration the presence of at least a
planet less massive than 3 MJup and with high eccentricity was required.

The PMa retreived from Kervella et al. (2022) has a SNR of 3.46, making the
presence of a companion very likely. They estimated a mass of 3.20 MJup for a
companion on a 3 au orbit and of 2.55 MJup for a companion on a 10 au orbit.

###  2.2 HIP 30314

HIP 30314 (HD 45270) is a G1 star (Torres et al. 2006) with a mass of 1.11 M⊙
(Desidera et al. 2021), located at a distance of 23.87$\pm$0.01 pc. It is part
of the AB Dor association (Zuckerman et al. 2011; Gagné et al. 2018) and it
has an estimated age of $149_{-49}^{+31}$ Myr (Desidera et al. 2021). The SNR
of the PMa for HIP 30314 is 3.57 and Kervella et al. (2022) estimated a mass
of 1.66 MJup for an object orbiting at 3 au from the star and of 1.40 MJup for
a companion orbiting at 10 au from the star.

###  2.3 HIP 88399

HIP 88399 (HD 164249) is a F6 star (Torres et al. 2006) with a mass of 1.29 M⊙
(Zúñiga-Fernández et al. 2021), located at a distance of 49.30$\pm$0.06 pc
from the Sun (Gaia Collaboration et al. 2021). It is part of the $\beta$
Pictoris moving group (e.g., Messina et al. 2017) and has an estimated age of
24$\pm$5 Myr (Desidera et al. 2021). HIP 88399 has a known companion, HD
164249 B, an M2 star with an estimated mass of 0.54 M⊙ (Zúñiga-Fernández et
al. 2021) and a separation of $\sim$6.5′′ corresponding to $\sim$323 au at the
distance of the system (Pawellek et al. 2021). IR excess was detected using
both WISE (Wright et al. 2010), Spitzer (Chen et al. 2014) and Herschel (Eiroa
et al. 2013) data, hinting toward the presence of debris disk. The disk was
finally resolved through ALMA observations by Pawellek et al. (2021) that
estimated for the disk a radius of 63 au and an inclination lower than
$49^{\circ}$.

HIP 88399 has a PMa SNR of 3.98 providing a strong indication of the presence
of a substellar object at short separation from the star or of a larger mass
companion at larger separation.

###  2.4 HIP 96334

HIP 96334 (HD 183414) is a G3 star (Torres et al. 2006) with a mass of 1.00 M⊙
(Vigan et al. 2017) at a distance of 38.16$\pm$0.03 pc from the Sun (Gaia
Collaboration et al. 2021). It is not part of any known young moving group.
Its age has been evaluated of $150_{-80}^{+70}$ Myr (Vigan et al. 2017). This
star was a target both for direct imaging (see e.g., Chauvin et al. 2010;
Nielsen et al. 2019) and RV (see e.g., Grandjean et al. 2020) with no
detection of low mass stellar or substellar companion.

Kervella et al. (2022) lists a PMa SNR of 4.63 that makes the presence of a
companion very probable.

###  2.5 HIP 116063

HIP 116063 (HD 221231) is a G1 star (Torres et al. 2006) with a mass of 0.8 M⊙
(Vigan et al. 2017) located at a distance of 30.25$\pm$0.02 pc from the Sun
(Gaia Collaboration et al. 2021). Its age is $300_{-100}^{+200}$ Myr (Desidera
et al. 2015). A wide companion for this star is known (TYC-9339-2158-1;
Desidera et al. 2015) but its large separation (36.3′′ corresponding to more
than 1100 au) and mass (0.80 M⊙) are not compatible with the detected PMa. The
value of the PMa SNR for HIP 116063 is 3.04, just above the threshold hinting
toward the presence of a possible companion.

##  3 Observations and data reduction

Table 2: List and main characteristics of the SPHERE observations used for
this work.

Target | Date | Obs. mode | Coronograph | DIMM seeing | $\tau_{0}$ | wind speed | Field rotation | DIT | Total exp.
---|---|---|---|---|---|---|---|---|---
HIP 1481 | 2015-10-26 | IRDIFS | N_ALC_YJH_S | 1.08′′ | 1.4 ms | 1.77 m/s | $25.1^{\circ}$ | 64 s | 4096 s
HIP 1481 | 2016-09-18 | IRDIFS | N_ALC_YJH_S | 0.80′′ | 5.0 ms | 9.95 m/s | $25.1^{\circ}$ | 64 s | 5120 s
HIP 30314 | 2016-01-16 | IRDIFS | N_ALC_YJH_S | 1.73′′ | 1.5 ms | 10.93 m/s | $27.2^{\circ}$ | 64 s | 4096 s
HIP 88399 | 2015-05-10 | IRDIFS | N_ALC_YJH_S | 1.86′′ | 1.2 ms | 2.63 m/s | $34.5^{\circ}$ | 64 s | 3584 s
HIP 88399 | 2015-06-01 | IRDIFS | N_ALC_YJH_S | 1.25′′ | 1.1 ms | 2.48 m/s | $34.1^{\circ}$ | 64 s | 4096 s
HIP 88399 | 2016-04-17 | IRDIFS | N_ALC_YJH_S | 1.58′′ | 1.5 ms | 14.73 m/s | $37.2^{\circ}$ | 64 s | 3776 s
HIP 88399 | 2018-04-11 | IRDIFS | N_ALC_YJH_S | 0.52′′ | 5.6 ms | 7.45 m/s | $32.0^{\circ}$ | 96 s | 3840 s
HIP 88399 | 2019-09-07 | IRDIFS | N_ALC_YJH_S | 1.14′′ | 1.9 ms | 12.75 m/s | $40.7^{\circ}$ | 96 s | 4896 s
HIP 96334 | 2019-05-19 | IRDIFS | N_ALC_YJH_S | 0.47′′ | 4.6 ms | 8.73 m/s | $32.8^{\circ}$ | 96 s | 6144 s
HIP 116063 | 2019-09-07 | IRDIFS | N_ALC_YJH_S | 2.06′′ | 1.5 ms | 18.23 m/s | $31.6^{\circ}$ | 64 s | 4032 s

###  3.1 Direct imaging data

All our objects were observed as part of the SPHERE/SHINE program. Table 2
shows the main characteristics of the observations, all performed using the
IRDIFS SPHERE observing mode, that uses both IFS (Claudi et al. 2008)
operating in Y and J spectral bands between 0.95 and 1.35 $\mu$m on a
$1.7\hbox{${}^{\prime\prime}$}\times 1.7\hbox{${}^{\prime\prime}$}$ field of
view (FOV) and IRDIS (Dohlen et al. 2008) covering in the H spectral band
using the H23 filter pair (wavelength H2=1.593 $\mu$m; wavelength H3=1.667
$\mu$m; Vigan et al. 2010) on a circular FOV of $\sim$5′′. All the
observations were performed exploiting the SPHERE adaptive optics system SAXO
(Fusco et al. 2006).

At all epochs we acquired frames with satellite spots symmetrical with respect
to the central star just before and just after the science sequence, used to
precisely define the position of the star behind the coronagraph (Langlois et
al. 2013). To obtain photometric calibration we also observed each star
without the coronagraph, using an appropriate neutral density filter to avoid
the saturation of the detectors

As detailed in Table 2, multiple epochs were available for HIP 1481 and HIP
88399. Unfortunately, only one the five data-sets available for HIP 88399 was
taken in good enough weather conditions (2018-04-11). The same is true for HIP
1481, for which the conditions were significantly better in second night
(2016-09-18). Therefore we will only use these data sets for our analysis of
these two objects.

All data were reduced using the SPHERE data center (Delorme et al. 2017). The
first step was to apply the appropriate calibrations following the data
reduction and handling pipeline (DRH; Pavlov et al. 2008). For IRDIS the
required calibrations include the creation of the master dark and of the
master flat-field frames and the definition of the star center. For IFS it was
also necessary to define the position of of each spectra on the detector as
well as the wavelength calibration and the application of the instrumental
flat that takes into account the different response of each lenslet of the IFS
array. On the reduced data we then applied speckle subtraction using both
angular differential imaging (ADI; Marois et al. 2006) and spectral
differential imaging (SDI; Racine et al. 1999). These methods were implemented
using both the principal components analysis (PCA; Soummer et al. 2012) and
the TLOCI (Marois et al. 2014) algorithms. They are applied to the SPHERE case
as described in Zurlo et al. (2014) and in Mesa et al. (2015) and they are
currently implemented through the SpeCal pipeline (Galicher et al. 2018).

###  3.2 RV data

Radial velocity data, acquired with the HARPS specrograph, were available from
Trifonov et al. (2020) for HIP 1481 (24 data points), HIP 30314 (27 data
points), HIP 88399 (38 data points) and HIP 96334 (71 data points).
Unfortunately no RV data, taken with HARPS or any other RV instrument, were
available for HIP 116063. The retrieved RV data were used to obtain mass
limits (shown in Fig. 6) for possible companions at low separations from the
host stars using the Exoplanets Detection Map Calculator (EXO-DMC; Bonavita
2020) and following the method described in Mesa et al. (2021).

###  3.3 PMa data

All the PMa data used for this work were obtained from the catalogue by
Kervella et al. (2022) (see Table 3.3). Following their approach we considered
as probable companion hosting stars all the targets with a PMa SNR larger than
3. Using the method described in Kervella et al. (2019) we were able to
estimate the mass of the companions compatible with the PMa signal as a
function of the separation from the host star (see their Equation 1). The
resulting limits are shown in Fig 6 (blue solid lines). It is important to
note that the mass is calculated assuming a circular orbit while a statistical
distribution for its inclination is taken into account following the method
devised in Kervella et al. (2019). The values obtained should therefore be
regarded as a minimum mass for the object causing the PMa signal. Moreover the
possible positions of the companion generating the PMa signal can be further
limited using the position angle (PA) of the velocity anomaly vector
$\@vec{\Delta v_{\mathrm{tan}}}$, as shown by Bonavita et al. (2022). We will
discuss the resulting constraints in Sec. 6.

##  4 Results

###  4.1 Candidate companions

Figure 1: Final IRDIS image for HIP 88399 obtained from data taken on 2018-04-11. The four candidate companions are marked as cc1, cc2, cc3 and cc4, respectively. The known stellar companion HD 164249 B is partially visible at the eastern edge of the image. Table 3: Astrometry for the four candidate companions in the IRDIS FOV of HIP 88399 retrieved from the first and last SPHERE data sets.  cc | Obs. date | Sep. RA (mas) | Sep. Dec (mas) | Total sep. (mas) | PA (∘)
---|---|---|---|---|---
1 | 2015-05-10 | -661.50$\pm$6.13 | -1115.98$\pm$6.13 | 1297.30$\pm$8.66 | 210.7$\pm$0.1
1 | 2019-09-07 | -649.25$\pm$6.13 | -758.28$\pm$6.13 | 998.25$\pm$8.66 | 220.6$\pm$0.1
2 | 2015-05-10 | 2130.28$\pm$6.13 | -2757.48$\pm$6.13 | 3484.50$\pm$8.66 | 142.3$\pm$0.1
2 | 2019-09-07 | 2142.53$\pm$6.13 | -2418.15$\pm$6.13 | 3230.77$\pm$8.66 | 138.5$\pm$0.1
3 | 2015-05-10 | -3173.98$\pm$6.13 | -2878.75$\pm$6.13 | 4285.01$\pm$8.66 | 227.8$\pm$0.1
3 | 2019-09-07 | -3150.70$\pm$6.13 | -2527.18$\pm$6.13 | 4039.00$\pm$8.66 | 231.3$\pm$0.1
4 | 2015-05-10 | -3197.25$\pm$6.13 | 4120.90$\pm$6.13 | 5125.77$\pm$8.66 | 322.2$\pm$0.1
4 | 2019-09-07 | -3186.23$\pm$6.13 | 4477.38$\pm$6.13 | 5495.35$\pm$8.66 | 324.6$\pm$0.1
Figure 2: Common proper motion analysis of all the candidate companions identified for HIP 88399. In all panels, the solid black line shows the motion of a background object relative to the target, based on the eDR3 parallax and proper motion of the primary over the same time frame. The filled circles show the measured separation and position angle of the companions at the first (red) and second (blue) epoch. The blue cross indicates the expected position of a background object at the second epoch. Figure 3: Final IRDIS image for HIP 96334. The candidate companion is indicated by the white arrow in the upper part of the image. The position of the star behind the coronagraph is indicated by a white cross. Table 4: Astrometry of the candidate companion to HIP 96334 for the two epochs considered in this work, obtained from NACO and SPHERE observations.  Obs. date | Instrument | Pixel scale (mas) | Sep. RA (mas) | Sep. Dec (mas) | Total sep. (mas) | PA (∘)
---|---|---|---|---|---|---
2007-06-09 | NACO | 27.15 | -2793.74$\pm$13.58 | 3529.50$\pm$13.58 | 4501.37$\pm$19.20 | 321.6$\pm$0.2
2019-05-19 | SPHERE/IRDIS | 12.25 | -2793.00$\pm$6.13 | 5503.93$\pm$6.13 | 6172.04$\pm$8.66 | 333.1$\pm$0.1
Figure 4: Common proper motion analysis for the candidate companion to HIP
96334. The solid black line shows the motion of a background object relative
to the target, based on the eDR3 parallax and proper motion of the primary
over the same time frame. The filled circles show the measured separation and
position angle of the companions at the first (red) and second (blue) epoch.
The blue cross indicates the expected position of a background object at the
second epoch.

We first inspected the reduced DI data looking for candidate companions that
could explain the PMa signal. In the case of HIP 1481, HIP 30314 and HIP
116063 we did not find any candidate within the IFS or IRDIS FOV.

Four candidates were identified in the IRDIS images of HIP 88399, all at
separations larger than 1′′ and therefore not included in the IFS images.
Figure 1 shows the IRDIS image of HIP 88399, acquired on 2018-04-11 (the night
with the best weather conditions), with the candidates highlighted in white.
The bright source at the extreme East of the IRDIS image is the known stellar
companion: HD 164249 B. Given its position, it was however not possible to
extract any astrometric value for this star as its PSF was not within the
IRDIS FoV.

Table 3 includes the values of the relative astrometry of each candidate,
obtained for the first and last epochs available (2015-05-10 and 2019-09-07),
which were used to check for common proper motion. For all the data we adopted
a rather conservative error bar of half of the IRDIS pixel scale. In Figure 2
we compare these astrometric values with the relative astrometric position of
a background object that is indicated by a blue cross. This position can be
easily calculated starting from the known proper motion and the parallax of
the host star and from the dates of the observing epochs. A background object
with no proper motion would be expected to be found at the separation and PA
indicated by the blue cross at the epoch of the second observation (indicated
by the filled blue circle). Because a background object will display some
proper motion, perfect correspondence is not expected. For the Figure 2 plots,
the filled blue circle is very near the expected position for a background
object. Hence, we disprove the assertion that these objects are
gravitationally bound to the host star. In this latter case we would expect
that the position of the filled blue circle would be almost coincident with
the relative position of the first observation (filled red circle). Indeed, in
this latter case the only source of movement should be due to orbital motion
of the companion that, because of the large separation of such objects, is
expected to be very small. Some examples showing these plots for
gravitationally bound objects could be found, e.g., in Figure 4 of Bonavita et
al. (2022). We therefore concluded that none of these objects could be the
cause of the measured PMa.

One candidate companion was also identified at the edge of the IRDIS FoV for
HIP 96334, as shown in Figure 3. Although only one SPHERE epoch was available
for this target, we were able to perform a common proper motion analysis (the
results of which are shown in Figure 4) using NaCo data available in the ESO
archive (Program ID: 079.C-0908(A); PI B. Zuckerman) taken on the 2007-06-09,
where the candidate was also visible. The astrometry values for the two epochs
is listed in Table 4. Following the same approach described above for HIP
88399 we were able to confirm that the candidate is a background source, a
conclusion strengthened by the detection of the companion in eDR3, where it is
listed with a parallax which is inconsistent with that of of HIP 96334.

###  4.2 Contrast limits

Figure 5: Contrast limits, expressed in magnitude, obtained for all of our
targets for IFS (left panel) and IRDIS (right panel) images. In case of
multiple epochs, the plotted limit is the one corresponding to the epoch with
best weather conditions. Specifically the data taken on the 2016-09-18 were
used for HIP 1481 (red line) and on 2018-04-11 for HIP 88399 (light blue
line).

For each target we calculated the contrast limits for both IFS and IRDIS,
using the method described in Mesa et al. (2015). The self-subtraction due to
the speckle subtraction method was estimated including simulated objects at
different separations from the star and consequently corrected. Finally, the
results were corrected taking into account the effect of the small sample
statistics as defined by Mawet et al. (2014). The resulting contrast limits
are shown in Figure 5. Note that for HIP 1481 and HIP 88399, for which more
than one data set was available, we choose to show only the limits obtained
using the data taken on the nights with the best weather conditions
(2016-09-18 and 2018-04-11, respectively).

###  4.3 Mass limits and comparison with PMa results

Figure 6: Plots of the mass as a function of the separation from the host star
of the companion needed to explain the PMa measurement at the Gaia eDR3 epoch
(blue lines) for HIP 1481 (top left panel), HIP 30314 (top right panel), HIP
88399 (center left panel), HIP 96334 (center right panel) and HIP116063
(bottom panel). The blue shaded areas display the $1\sigma$ confidence
interval. The violet lines represent the mass limits from RV data (assuming
95% confidence level). The DI mass limits assuming minimum, expected and
maximum ages are shown by the green, orange and red lines, respectively.
Finally, for HIP 1481 and HIP 88399, we also included the positions of the
belts (two in the cases of HIP 1481) composing the debris disk detected around
these stars. They are indicated by black dashed lines.

The contrast limits shown in Figure 5 were then converted into mass limits
using the AMES-COND evolutionary models (Allard et al. 2003) and adopting the
stellar ages listed in Table 1.

We then compared these mass limits with those obtained using the RV data (see
Section 3.2) as well as with the estimates of the mass of the companion
responsible for the PMa signal calculated as described in Section 3.3. This
allowed us to put further constraints on the mass and the separation of the
possible unseen companions. We should at this point stress once more that the
mass limits calculated in Section 3.3 assume circular orbits and therefore
only provide an indication of the order of magnitude for the mass of the
companion generating the PMa signal, rather than an exact value. The results
of the comparison are shown in Figure 6, where the limits from the PMa are
shown as solid blue lines, the RV limits as violet lines and the DI limits are
shown with green, orange and red solid lines, depending on the age used for
the conversion (minimum, adopted and maximum values, respectively). For HIP
1481 (top left panel) and HIP 88399 (center left panel) we also included black
dashed lines marking the expected positions of the known debris disks.

##  5 Discussion

Figure 7: 2D maps, obtained with FORECAST (see Bonavita et al. 2022, for
details) showing in blue the sky area compatible with the PMa reported in
Table 1. The intensity of the blue areas changes according to the dynamical
mass (in $M_{Jup}$) responsible for the PMa at a give distance; the same
logarithmic scale, shown on the bottom of the figure, was used for all stars.
The bar shows the separation corresponding to 0.3′′, expressed in au using the
distance of each system. The hashed areas show the regions excluded due to
incompatibility with the PMa (black) and using the limits from direct imaging
(orange) and radial velocity (purple), respectively (see Fig. 6).

The procedure described in the previous Sections allowed us to determine
different constraints on mass and separations for each of the targets
considered in this work.

The most promising results have been obtained for HIP 1481. As can be seen in
the upper left panel of Figure 6 the DI mass limits exclude the presence of
the companion responsible for the PMa signal at separations larger than
$\sim$15 au while at short separation the RV mass limits exclude the presence
of this companion at separations less than 2-3 au. The possible values of the
mass of this object range between 2-5 MJup with the higher masses possible
only at the lower allowed separations. The probability of a companion at
separations smaller than $\sim$1 au and at separations of 40-60 au is further
diminished by the presence of the inner and the outer belt of the debris disk
found around this star.

The constraints that we can obtain for the case of HIP 30314 are not as strong
(see the upper right panel of Figure 6). Due to the poor weather conditions
during the SPHERE observation (see Table 2) and the higher age for this
system, the DI limits are worse than those achieved for HIP 1481, especially
at short separations (see red and orange solid lines in Fig. 5), and can only
exclude companions at separations larger than $\sim$30 au. The limits produced
using the RV are also higher than in the case of HIP 1481, thus providing much
less stringent constraints at separations smaller than 1 au. The possible
masse values range between $\sim$1 MJup and 5 MJup at separation larger than 2
au while they could be as large as 10 MJup at separation lower than 2 au.

The limits on the separation for HIP 88399 from the DI data allow to exclude
the presence of the companion causing the PMa signal at separations larger
than 7-9 au (depending on the chosen value of the age). On the other hand, the
mass limits from the RV data are very low and they seem to exclude separations
lower than $\sim$3 au for the companion generating the PMa signal. The mass of
the possible companion ranges between 3 and 5 MJup with possible higher masses
(up to 8-9 MJup) at the lower end of the separations range. As discussed in
Section 2, this star has a companion with an estimated mass of 0.54 M⊙
(corresponding to $\sim$566 MJup) and a separation of $\sim$323 au. Looking at
the PMa limit in Fig. 6 (blue curve) we can see that at the separation of this
companion, the mass requested to explain the PMa signal is of 1547.4 MJup with
a lower limit of 856.3 MJup, thus well above the estimated mass for the
companion. This is true also considering higher masses found in literature
like, e.g, the value of 0.6 M⊙ corresponding to $\sim$628.6 MJup (Desidera et
al. 2021). Moreover, the separation used here for this companion is the
projected one. The real separation of this object could then be even larger,
making the difference between its mass and the one required to explain the PMa
signal more evident111Once again, we note that the determination of the mass
obtained in this way is valid under the assumption of circular orbits.
Eccentric orbits could broaden the mass distribution at the separation of the
companion.. As further confirmation, we note also that the PA of the companion
($\sim$90∘) is also not compatible with that derived by Kervella et al. (2022)
from the PMa ($130.94^{\circ}\pm 10.17^{\circ}$), with a difference larger
than 3$\sigma$ between the two values. While from each single value listed
above it is difficult to draw a conclusion because of their large
uncertainties, the combination of all these indications strongly hints toward
the exclusion of the known companion as responsible for the PMa signal. In any
case further data, both from astrometry and DI, is still needed to further
clarify the situation.

The large errors on the age for HIP 96334 lead to very different mass limits
from the DI images, and this has quite a large impact on the constraints we
could put on the nature of the PMa companion. In fact, when considering an age
of 70 Myr (green solid line in the center right panel of Figure 6), DI data
exclude companions at separations larger than $\sim$7 au. Instead, when
considering the much higher ages of 150 and 200 Myr (orange and red lines in
the center right panel of Figure 6), we could only exclude possible companions
at separations larger than $\sim$20 au. On the other hand, mass limits from
the RV allow to exclude any possible companions at separations lower than
$\sim$3 au. From the mass point of view, an age of 70 Myr would allow for
companion of 3-4 MJup while the higher ages would allow masses as high as 5-7
MJup.

The lack of RV data limited our ability to put constraints on companions
within 1 au from HIP 116063, where we cannot exclude masses as large as
$\sim$100 MJup. At larger separations, the bad quality of the DI data and the
relatively high age of the system only allowed us to exclude companions at
separation larger than 30 au with masses that can be as high as 10 MJup.

###  5.1 FORECAST maps

The limits shown in Fig. 6 were derived using the absolute value of the PMa
reported in Table 1. But as mentioned in Section 3.3, further constraints can
be put taking advantage of the vectorial nature of the PMa, and in particular
of the information on its position angle. We therefore used the FORECAST tool
(Finely Optimised REtrieval of Companions of Accelerating STars, see Bonavita
et al. 2022, for details and other uses) to isolate the region on the plane of
the sky where the companion compatible with the PMa should lie, based on the
PA values reported in Table 1.

For each target, FORECAST evaluates the position angle of each pixel in the
IFS image with respect to the center and then compares it with the PMa
position angle (PApma) retrieved from the catalogue by Kervella et al. (2022).
The optimal region (shown in blue in Fig. 7) is then identified by the X and Y
positions on the image where the position angle is within one sigma from the
PApma value, plus or minus an additional quantity which takes into account the
possible orbital motion of a companion at that separation between the SPHERE
observation and the Gaia observations.

Finally, it also associates with each point of the resulting 2D map a value of
the companion mass based on the PMa absolute value, again using the approach
from Kervella et al. (2019), similarly to what was done to obtain the PMa
limits shown in Fig. 6.

Using this information we could further limit the possible positions of the
companion on the IFS field of view at the epoch of the observation. Once
again, since no information is available about eccentricity and inclination of
the orbits, this method only provides a rough indication of the position
compatible with circular and edge-on orbits. The FORECAST maps can also be
used as _finding charts_ , to identify the area where to search for possible
companions. Figure 7 displays the FORECAST maps obtained for all our targets,
considering the IFS field of view. For each panel, the distance bar
corresponds to a separation of 0.3′′, which we then converted in $au$ using
the distance of the targets. To take into account the constraints derived from
Figure 6, we highlighted the regions excluded thanks to the RV (purple) and
SPHERE limits (orange). Combined with Figure 6, Figure 7 therefore provides
further visual confirmation that while for HIP 1481 and HIP 88399 our limits
are relatively tight, for HIP 30314 and HIP 116063 the allowed positions area
is much larger.

The HIP 1481 and HIP 88399 systems presents similarities with our solar system
as both of them have a solar type central star with a debris belt at few tens
of au (similar to the Kuiper belt) and a very probable Jupiter-mass planet at
a separation comparable to that of Jupiter. For these reasons they could be
regarded as young analogues of the solar system making their study even more
interesting.

###  5.2 Probability of future detection with DI observations

The SPHERE observations for HIP 88399 and HIP 96334 were taken in good
observing conditions so that it is difficult that new observations with such
instruments could allow getting substantial improvement in the contrast (and
in the mass limits). This suggests a low probability of direct companion
detection using current high-contrast imagers. The observations for HIP 1481
were instead taken in intermediate condition (in particular strong wind, see
Table 2). Better observing conditions could improve the contrast and the mass
limits for this star helping in detecting the companion or in further
constraining its mass and separation. On the other hand, longer observations
should not be useful to improve the contrast limits as at large angular
separations from the passage at the meridian the rotation of the FOV is low
making high-contrast method like ADI less effective. Finally, the observations
for HIP 30314 and HIP 116063 were taken in bad weather conditions limiting the
contrast reached for these targets. This leaves some room for improvements in
constraining the positions and the mass of the companions with future
observations with SPHERE. In any case, the relatively high ages (larger than
100 Myr) for both of them makes very challenging the direct detection of the
companions especially if they reside at separations less than 10 au.
However, these stars should be ideal targets for future instrumentation at
ELT. We note indeed that the contrasts obtained from simulations of the
performance of ELT first generation instruments like MICADO (e.g., Perrot et
al. 2018) would allow the detection for the proposed companions for each
separation and mass as constrained by our analysis. This type of analysis
demonstrates then to be a very powerful tool to select interesting targets for
observations with ELT instruments.

##  6 Conclusions

This paper presents a detailed analysis based on the combination of DI, RV and
astrometric data for five stellar systems showing significant acceleration
(PMa) signals suggesting the presence of planetary companions within few au.
We were able to put constraints on the possible separation and mass of unseen
companions on circular orbits for each considered system.

Such constraints were particularly strong for HIP 1481, for which we were able
to limit the possible companion separations to 2-15 au and masses of the order
of few MJup. Also interesting are the cases for HIP 88399 and HIP 96334 for
which similar constraints can be obtained despite of the limits imposed by the
strong uncertainty on the age. For HIP 88399, although more data are needed
for final confirmation, our analysis seems to exclude the known wide companion
HD 164249 B as the reason of the PMa signal.

Finally, looser constraints were possible for HIP 30314 and HIP 116063. The
bad weather condition in which the DI observations were taken in both cases,
and the lack of RV data in the second case, strongly limited our capacity to
put constraints both on mass and separation. Despite such difficulties, these
targets still proved to be interesting, with a good probability of the
presence of a companion at separations between few au and up to 20-30 au.

While the characteristics of the companions compatible with the PMa strongly
limit the feasibility of a detection with current current high-contrast
instruments (e.g., SPHERE and GPI), they represent ideal targets for
observations with ELT-class telescopes, as their proposed masses and
separations perfectly fit with the estimated performance of the instruments
planned for these facilities.

###### Acknowledgements.

This work has made use of the SPHERE Data Center, jointly operated by
OSUG/IPAG (Grenoble), PYTHEAS/LAM/CeSAM (Marseille), OCA/Lagrange (Nice) and
Observatoire de Paris/LESIA (Paris). This work has made use of data from the
European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia),
processed by the Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This research has made use
of the SIMBAD database, operated at CDS, Strasbourg, France. This work has
been supported by the PRIN-INAF 2019 ”Planetary systems at young ages
(PLATEA)” and ASI-INAF agreement n.2018-16-HH.0. A.Z. acknowledges support
from the CONICYT + PAI/ Convocatoria nacional subvención a la instalación en
la academia, convocatoria 2017 + Folio PAI77170087. SPHERE is an instrument
designed and built by a consortium consisting of IPAG (Grenoble, France), MPIA
(Heidelberg, Germany), LAM (Marseille, France), LESIA (Paris, France),
Laboratoire Lagrange (Nice, France), INAF-Osservatorio di Padova (Italy),
Observatoire de Genève (Switzerland), ETH Zurich (Switzerland), NOVA
(Netherlands), ONERA (France) and ASTRON (Netherlands), in collaboration with
ESO. SPHERE was funded by ESO, with additional contributions from CNRS
(France), MPIA (Germany), INAF (Italy), FINES (Switzerland) and NOVA
(Netherlands). SPHERE also received funding from the European Commission Sixth
and Seventh Framework Programmes as part of the Optical Infrared Coordination
Network for Astronomy (OPTICON) under grant number RII3-Ct-2004-001566 for FP6
(2004-2008), grant number 226604 for FP7 (2009-2012) and grant number 312430
for FP7 (2013-2016).For the purpose of open access, the authors have applied a
Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript
version arising from this submission.

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