11institutetext: JD Digital
11email<EMAIL_ADDRESS>
# SEBERTNets: Sequence Enhanced BERT Networks for Event Entity Extraction
Tasks Oriented to the Finance Field

Congqing He 11 Xiangyu Zhu 11 Yuquan Le 11 Yuzhong Liu Jianhong Yin 1111

###### Abstract

Event extraction lies at the cores of investment analysis and asset management
in the financial field, and thus has received much attention. The 2019 China
conference on knowledge graph and semantic computing (CCKS) challenge sets up
a evaluation competition for event entity extraction task oriented to the
finance field. In this task, we mainly focus on how to extract the event
entity accurately, and recall all the corresponding event entity effectively.
In this paper, we propose a novel model, Sequence Enhanced BERT Networks
(SEBERTNets for short), which can inherit the advantages of the BERT,and while
capturing sequence semantic information. In addition, motivated by
recommendation system, we propose Hybrid Sequence Enhanced BERT Networks
(HSEBERTNets for short), which uses a multi-channel recall method to recall
all the corresponding event entity. The experimental results show that, the F1
score of SEBERTNets is 0.905 in the first stage, and the F1 score of
HSEBERTNets is 0.934 in the first stage, which demonstarate the effectiveness
of our methods.

###### Keywords:

Event Extraction BERT Finance.

##  1 Introduction

Event Extraction, a challenging task Information Extraction, aims at detecting
and typing events, and extracting different entity from texts. Event
extraction lies at the cores of investment analysis and asset management in
the financial field, and thus has received much attention. However, most of
research is rarely involved in the finance field. For this purpose, the 2019
China conference on knowledge graph and semantic computing (CCKS) challenge
sets up a evaluation competition for event entity extraction task oriented to
the finance field. The goal of the evaluation is to extract the event entity
according to a given real news corpus and event type.

To this end, Liu et al. [5] proposed to exploit argument information
explicitly for event detection via supervised attention mechanisms. There are
still several questions. (1) How to extract the event entity accurately and
effectively. (2) How to recall all the corresponding event entity effectively
when there exists multiple event entity in a text. Motivated by these, we
propose a novel model, Sequence Enhanced BERT Networks, which can inherit the
advantages of the BERT [1], and while capturing sequence semantic information.
In addition, motivated by recommendation system, we propose Hybrid Sequence
Enhanced BERT Networks , which uses a multi-channel recall method to recall
all the corresponding event entity.

Our mainly contributions are shown as follows:

(1) We propose a novel model, Sequence Enhanced BERT Networks, which can
inherit the advantages of the BERT,and while capturing sequence semantic
information.

(2) We propose Hybrid Sequence Enhanced BERT Networks , which uses a multi-
channel recall method to recall all the corresponding event entity.

(3) The experimental results show that, the F1 score of SEBERTNets is 0.905 in
the first stage, and the F1 score of HSEBERTNets is 0.934 in the first stage,
which demonstarate the effectiveness of our methods.

##  2 Our Methods

Figure 1 describes the architecture of SEBERTNets, which primarily involves
the following four components: (i) Input layer, (ii) BERT layer, (iii)
Sequence layer, (iv) Output layer.

Figure 1: The architecture of SEBERTNets.

###  2.1 Input Layer

The description of text can be seen as a char sequence
$\text{x}={\\{x_{1},\cdots,x_{n}\\}}$, and the corresponding event type can be
seen as a char sequence $\text{t}={\\{t_{1},\cdots,t_{m}\\}}$. We first remove
irregular punctuation, special text, etc, and contact them together. The
description of text x and the corresponding event type t are then encoded as
input.

###  2.2 BERT Layer

Inspired by Devlin et al [1], BERT obtains new state-of-the-art results on
lots of natural language processing tasks. We introduce BERT as the layer of
SEBERTNets, to produce sequence semantic representation, and capture global
semantic representation.

${l_{1},l_{2},\cdots,l_{n+m}}=\textbf{BERT}(x_{1},\cdots,x_{n},t_{1},\cdots,t_{m})$
(1)

Where $l_{i}\in\mathbb{R}^{d}$, 111In our experiment, d=768. and $i$
represents $i-th$ element.

###  2.3 Sequence Layer

Since the BERT layer only captures the position information of the text
through the position vector, then the SEBERTNets introduces the Sequence
layer, which captures the sequence semantic information of the text, and
enhances the semantics of the text sequence based on the BERT layer. In
addition, the Sequence layer introduces a mask operation. Since the text is
usually indefinitely long, the introduction of a mask can effectively
alleviate the bias caused by the text filling.

$\displaystyle f_{t}=\sigma(W_{f}l_{t}+U_{f}h_{t-1}+b_{f}),$ (2)
$\displaystyle i_{t}=\sigma(W_{i}l_{t}+U_{i}h_{t-1}+b_{i}),$ (3)
$\displaystyle o_{t}=\sigma(W_{o}l_{t}+U_{o}h_{t-1}+b_{o}),$ (4)
$\displaystyle\widetilde{c}_{t}=tanh(W_{c}x_{t}+U_{c}h_{t-1}+b_{c}),$ (5)
$\displaystyle c_{t}=f_{t}\odot c_{t-1}+i_{t}\odot\widetilde{c}_{t},$ (6)
$\displaystyle h_{t}=o_{t}\odot tanh(c_{t}).$ (7)

Where $l_{t}$ represents the input of the recurrent layer at time step $t$.
$f_{t}$, $i_{t}$ and $o_{t}$ means forget gate, input gate, and output gate
respectively. $\odot$ denotes element-wise multiplication of two vectors. To
consider forward and backward contextual representation of the text, we use
BiLSTM instead of LSTM as fact encoder in advance. The BiLSTM generates
${h_{t}}_{\\{t=1,\cdots,T\\}}$ by concatenating a forward LSTM and a backward
LSTM.

###  2.4 Output Layer

The BERT layer and the Sequence layer can capture the global semantic
information and sequence semantic information of the text. Based on the text
and event type, the SEBERTNets model predicts the beginning and end of the
text of the event body. Finally, it is decoded by the start position and the
end position to obtain the corresponding event body.

###  2.5 Optimization

Although Adam [4] performed well at the beginning of model training,
SGDStochastic gradient descent (SGD) [6] was superior to the Adam method in
the later stages of training. Therefore, we introduce a new method, SWATS [3]
, which first starts training with the Adam method and switches to SGD when
appropriate. Verification on the real data set of the evaluation game, this
method can achieve better performance than the Adam optimization method.

##  3 Experiments

###  3.1 Dataset

CCKS 2019 evaluation task consists of 17,815 training sets, 3,500 validation
sets (preliminary test datasets) and 135,519 test sets (rematch test
datasets). Each dataset includes a given text description, event type, and
event entity respectively.

###  3.2 Evaluation

Following [2] , we use F1 score to evaluate the performance of our methods.
The F1 score is computed as follows:

$F1=\frac{2PR}{P+R}$ (8)

Where $P$ means that number of correctly identified event entities divided by
the total number of identified event entities, $R$ represents that number of
correctly identified event entities divided by the total number of annotated
event entities.

###  3.3 Hyper-parameter Setting

Since all the text descriptions and event types have been employed for char
segmentation and set each text maximum length to 140. We use character-based
Chinese BERT model
222https://storage.googleapis.com/bert_models/2018_11_03/chinese_L-12_H-768_A-12.zip
and character-based Chinese BERT-wwm model
333https://drive.google.com/open?id=1RoTQsXp2hkQ1gSRVylRIJfQxJUgkfJMW to
training SEBERTNets and variant SEBERTNets models. In addition, GRU is adopted
to Sequence layer and the hidden unit is set to 200. The batch size is set to
32 for SEBERTNets and variant SEBERTNets models.

##  4 Results

###  4.1 Main Results

Table 1: F1 score of models on preliminary test datasets. Number of entities | Top 1 | Top 2 | Top 3 | Top 4 | Top 5
---|---|---|---|---|---
BERT | 0.871 | 0.887 | 0.893 | 0.901 | 0.902
SEBERTNets | 0.905 | 0.915 | 0.918 | 0.921 | 0.923
HSEBERTNets | 0.914 | 0.922 | 0.926 | 0.931 | 0.934

In this section, we conduct experiments on preliminary test datasets to
demonstrate the effectiveness of the proposed approach. Table 1 shows the
performance of our methods on preliminary test datasets.

Overall, we can find the SEBERTNets model outperforms BERT model with a
significant margin on preliminary test datasets. SEBERTNets model obtains
$2.5\%$ average absolutely considerable improvements on preliminary test
datasets, which demonstrates the effectiveness of SEBERTNets model for event
entity extraction.

Additionally, we propose HSEBERTNets model to recall all the corresponding
event entity. Compared to the SEBERTNets model, HSEBERTNets model achieves
better performance, especially, in multiple event entities. The results
demonstrates the effectiveness of HSEBERTNets model for multiple event entity
extraction.

###  4.2 Visualization

Figure 2: Visualization of BERT layer.

In this section, we select several representative cases to give an intuitive
illustration of how the BERT layer help to promote the performance of event
entity extraction. As shown in Figure 2, red color means that the correct
entities extracted by SEBERTNets model, and yellow color means that the
incorrect entites extracted by SEBERTNets model. In these cases, we can find
that BERT layer focus on the entity of the text well. Several entities are not
belonging to the corresponding event type, and BERT layer can be well
observed. From this figure, we observe that the BERT layer can capture key
entities relevant to current event type.

## References

  * [1] Devlin, J., Chang, M.W., Lee, K., Toutanova, K.: BERT: Pre-training of deep bidirectional transformers for language understanding. In: Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers). pp. 4171–4186. Association for Computational Linguistics, Minneapolis, Minnesota (Jun 2019). https://doi.org/10.18653/v1/N19-1423, https://www.aclweb.org/anthology/N19-1423
  * [2] Hong, Y., Zhang, J., Ma, B., Yao, J., Zhou, G., Zhu, Q.: Using cross-entity inference to improve event extraction. In: Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies-Volume 1. pp. 1127–1136. Association for Computational Linguistics (2011)
  * [3] Keskar, N.S., Socher, R.: Improving generalization performance by switching from adam to sgd. arXiv preprint arXiv:1712.07628 (2017)
  * [4] Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
  * [5] Liu, S., Chen, Y., Liu, K., Zhao, J., et al.: Exploiting argument information to improve event detection via supervised attention mechanisms (2017)
  * [6] Robbins, H., Monro, S.: A stochastic approximation method. The annals of mathematical statistics pp. 400–407 (1951)


11institutetext:  Max Planck Institute for Extraterrestrial Physics,
Giessenbachstraße 1, 85748 Garching, Germany 22institutetext: LESIA,
Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université
de Paris, 5 place Jules Janssen, 92195 Meudon, France 33institutetext: Univ.
Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France 44institutetext: European
Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
55institutetext: Max Planck Institute for Astronomy, Königstuhl 17, 69117
Heidelberg, Germany 66institutetext: 1st Institute of Physics, University of
Cologne, Zülpicher Straße 77, 50937 Cologne, Germany 77institutetext: CENTRA -
Centro de Astrofísica e Gravitação, IST, Universidade de Lisboa, 1049-001
Lisboa, Portugal 88institutetext: Universidade de Lisboa - Faculdade de
Ciências, Campo Grande, 1749-016 Lisboa, Portugal 99institutetext: European
Southern Observatory, Casilla 19001, Santiago 19, Chile 1010institutetext:
Universidade do Porto, Faculdade de Engenharia, Rua Dr. Roberto, Frias,
4200-465 Porto, Portugal 1111institutetext: Department of Astrophysical &
Planetary Sciences, JILA, Duane Physics Bldg., 2000 Colorado Ave, University
of Colorado, Boulder, CO 80309, USA 1212institutetext: Faculdade de
Engenharia, Universidade do Porto, rua Dr. Roberto Frias, 4200-465 Porto,
Portugal 1313institutetext: Hamburger Sternwarte, Universität Hamburg,
Gojenbergsweg 112, 21029 Hamburg, Germany 1414institutetext: Departments of
Physics & Astronomy, Le Conte Hall, University of California, Berkeley, CA
94720, USA 1515institutetext: Max Planck Institute for Astrophysics, Karl-
Schwarzschild-Straße 1, 85748 Garching, Germany 1616institutetext: Max Planck
Institute for Radio Astronomy, auf dem Hügel 69, 53121 Bonn, Germany
1717institutetext: ORIGINS Excellence Cluster, Boltzmannstraße 2, 85748
Garching, Germany 1818institutetext: Department of Physics, Technical
University of Munich, 85748 Garching, Germany 1919institutetext: Dublin
Institute for Advanced Studies, 31 Fitzwilliam Place, D02,XF86 Dublin, Ireland
2020institutetext: School of Physics, University College Dublin, Belfield,
Dublin 4, Ireland 2121institutetext: Institute of Astronomy, University of
Cambridge, Madingley Rd., Cambridge CB3 0HA, UK

# Astrometric detection of a Neptune-mass candidate planet in the nearest
M-dwarf binary system GJ65 with VLTI/GRAVITY

GRAVITY Collaboration,: R. Abuter  GRAVITY is developed in a collaboration by
MPE, LESIA of Paris Observatory / CNRS / Sorbonne Université / Univ. Paris
Diderot and IPAG of Université Grenoble Alpes / CNRS, MPIA, Univ. of Cologne,
CENTRA - Centro de Astrofisica e Gravitação, and ESO. 44 A. Amorim 8877 M.
Benisty 33 J.P. Berger 33 H. Bonnet 44 G. Bourdarot  Corresponding authors: G.
Bourdarot (bourdarot@mpe.mpg.de), P. Kervella<EMAIL_ADDRESS>& O.
Pfuhl (opfuhl@eso.org). 11 P. Bourget 44 W. Brandner 55 Y. Clénet 22 R. Davies
11 F. Delplancke-Ströbele 44 R. Dembet 22 A. Drescher 11 A. Eckart 661616 F.
Eisenhauer 111818 H. Feuchtgruber 11 G. Finger 11 N.M. Förster Schreiber 11 P.
Garcia 121277 R.Garcia-Lopez 19192020 F. Gao 1313 E. Gendron 22 R. Genzel
111414 S. Gillessen 11 M. Hartl 11 X. Haubois 99 F. Haussmann 11 T. Henning 55
S. Hippler 55 M. Horrobin 66 L. Jochum 99 L. Jocou 33 A. Kaufer 99 P. Kervella
⋆⋆ 22 S. Lacour 22 V. Lapeyrère 22 J.-B. Le Bouquin 33 C. Ledoux 99 P. Léna 22
D. Lutz 11 F. Mang 11 A. Mérand 44 N. More 11 M. Nowak 2121 T. Ott 11 T.
Paumard 22 K. Perraut 33 G. Perrin 22 O. Pfuhl ⋆⋆ 44 S. Rabien 11 D. C.
Ribeiro 11 M. Sadun Bordoni 11 J. Shangguan 11 T. Shimizu 11 J. Stadler 1515
O. Straub 1717 C. Straubmeier 66 E. Sturm 11 L.J. Tacconi 11 K.R.W. Tristram
99 F. Vincent 22 S. von Fellenberg 1616 F. Widmann 11 E. Wieprecht 11 J.
Woillez 44 S. Yazici 11 G. Zins 44

(Received 8 February 2024 / Accepted 20 March 2024)

The detection of low-mass planets orbiting the nearest stars is a central
stake of exoplanetary science, as they can be directly characterized much more
easily than their distant counterparts. Here, we present the results of our
long-term astrometric observations of the nearest binary M-dwarf Gliese 65 AB
(GJ65), located at a distance of only 2.67pc. We monitored the relative
astrometry of the two components from 2016 to 2023 with the VLTI/GRAVITY
interferometric instrument. We derived highly accurate orbital parameters for
the stellar system, along with the dynamical masses of the two red dwarfs. The
GRAVITY measurements exhibit a mean accuracy per epoch of 50-60
microarcseconds in 1.5h of observing time using the 1.8m Auxiliary Telescopes.
The residuals of the two-body orbital fit enable us to search for the presence
of companions orbiting one of the two stars (S-type orbit) through the reflex
motion they imprint on the differential A-B astrometry. We detected a Neptune-
mass candidate companion with an orbital period of $p=156\pm 1\,\mathrm{d}$
and a mass of $m_{p}=36\pm 7\,M_{\oplus}$. The best-fit orbit is within the
dynamical stability region of the stellar pair. It has a low eccentricity,
$e=0.1-0.3$, and the planetary orbit plane has a moderate-to-high inclination
of $i>30^{\circ}$ with respect to the stellar pair, with further observations
required to confirm these values. These observations demonstrate the
capability of interferometric astrometry to reach microarcsecond accuracy in
the narrow-angle regime for planet detection by reflex motion from the ground.
This capability offers new perspectives and potential synergies with Gaia in
the pursuit of low-mass exoplanets in the solar neighborhood.

###### Key Words.:

astrometry – exoplanet – M-dwarfs – binary – long-baseline interferometry

##  1 Introduction

Figure 1: Orbit of GJ65 AB, combining WDS, NACO and GRAVITY data., shown on
the left. The residuals of the stellar orbit are on the right.

M-dwarfs are favorable targets in the search for signatures of planets thanks
to their low stellar masses ($0.1-0.25\,M_{\odot}$), as the presence of
planets induces a significantly larger reflex motion on the parent star than
for sun-like stars. This makes them ideal targets both for radial velocity and
astrometric searches. In our close solar neighborhood, M-dwarfs represent 80%
of the stellar population (Winters et al. 2019; Chabrier & Baraffe 2000).
Thus, the characterization of the properties of the stellar host and their
monitoring are of key interest. In that respect, radial velocity and
astrometry probe complementary parameter spaces. Radial velocity (RV)
measurements are most sensitive to close-in planets, but are ultimately
limited to a precision of a few m/s in M-dwarfs due to stellar variability and
flaring events (Meunier 2021). Conversely, astrometry probes planetary
companions at larger separation (typically 0.1 to a few astronomical units,
au) and is less sensitive to flare activity, with a typical noise contribution
of 10$\mu$au for M-type stars (Eriksson & Lindegren 2007; Lagrange et al.
2011). In addition, in the case of M stars, the flux contribution of flares
decreases by two orders of magnitude in the K band
($2.0\,\mu\mathrm{m}-2.4\,\mu\mathrm{m}$) compared to the UV and optical
(Davenport et al. 2012), favoring the infrared domain for precision astrometry
for these objects. The typical astrometric signature of a planet with a few
Earth-mass on a 0.1 au orbit around an M dwarf located at 1pc is on the order
of 1-10 $\mu$as, below the present limit of space and ground based astrometric
instrumentation.

Parameter |  Value
---|---
Orbital parameters: |
Period $P$ (yr) |  $26.38\pm 0.002$
$a$ (AU) |  $5.459\pm 0.002$
$i$ (deg) |  $128.0\pm 0.1$
$e$ |  $0.6172\pm 0.0001$
$\Omega$ (deg) |  $325.9\pm 0.1$
$\omega$ (deg) |  $103.2\pm 0.1$
$T_{0}$ (mjd) |  $41333\pm 8$
Masses: |
$m_{A}$ ($M_{\odot}$) |  $0.122\pm 0.002$
$m_{B}$ ($M_{\odot}$) |  $0.116\pm 0.002$
$m_{A}+m_{B}$ ($M_{\odot}$) |  $0.238\pm 0.003$
Parallax1 (mas) |  $371.92\pm 0.42$
Table 1: Orbital parameters of GJ65 A and B obtained with GRAVITY. 1 from
Kervella et al. (2022)

In this context, narrow-angle astrometry with interferometry (Eisenhauer et
al. 2023) provides a powerful technique for monitoring stellar orbits with
very high precision. Shao & Colavita (1992) first discussed the potential of
micro-arcsecond precision from the ground with long-baseline interferometry to
observe two objects contained in the same isopistonic area. This technique was
first demonstrated at PTI (Colavita et al. 1999), achieving 100$\mu$as
accuracy (Muterspaugh et al. 2010), but put on hold after the cancellation of
the large space-based NASA mission SIM (Unwin et al. 2008) and first-
generation ground-based instruments (Keck/ASTRA, Woillez et al. (2010);
VLT/PRIMA, Delplancke et al. (2006)). The full potential of dual-field
interferometry was finally reached with GRAVITY (GRAVITY Collaboration et al.
2017), routinely achieving an accuracy of a few $10\,\mu$as on 8m class
telescopes for objects as faint as $m_{K}$=19.5mag (GRAVITY Collaboration et
al. 2018, 2022).

In the following, we present the astrometric monitoring of GJ65 AB (also known
as: Luyten 726-8, UV Ceti+BL Ceti, WDS J01388-1758 AB) we conducted with
VLTI/GRAVITY on the 1.8m VLTI Auxiliary Telescopes between 2016 and 2023. GJ65
AB is a binary star located at $d=2.67\,\mathrm{pc}$, and one of the Sun’s
nearest neighbors. GJ65 is the class prototype of UV Ceti Type stars (Luyten
1949; Joy & Humason 1949). The separation of the binary ($a=5.4\,\mathrm{au}$)
is wide enough to neglect magnetic and tidal interactions between the stars,
but its orbital period $P=26.38\,\mathrm{yr}$ is short enough to allow for an
extremely accurate determination of the orbital parameters (Kervella et al.
2016). This makes GJ65 a prime target in determining the masses of the two
stellar components. The stars’ properties are very similar to Proxima Centauri
(Kervella et al. 2016). The components A and B in GJ65 have nearly identical
masses ($\simeq 0.12M_{\odot}$). No RV detection of a planet has been
reported, due to the fast rotation of the two stars and their strong
variability through flaring events that limit the accuracy of RV measurements.
In astrometry, indications of the presence of a third body from the proper
motion anomaly were found from Gaia DR2 and EDR3 but with no clear planet
signature (Kervella et al. 2019, 2022). Understanding planet formation in
close binary systems is still challenging and models show that it is hindered
by the dynamical excitation and gravitational instability (Holman & Wiegert
1999; Marzari & Thebault 2019). Therefore, obtaining accurate measurements of
the stellar orbit and constraining the presence of potential companions is
imperative to testing these models.

The outline of the paper is as follows. Section 2 describes the observations
of our monitoring program and Section 3 presents the principle of dual-field
observations used for narrow-angle astrometry with long baseline
interferometry, and the performance achieved in the program. In Section 4, we
present the orbital parameters and the analysis of the residuals of the
astrometry of GJ65. Finally in Section 5, we discuss the properties and the
dynamical stability of this system, and offer an outlook for future studies.

##  2 Observations

We observed GJ65 from 2016 to 2023 with GRAVITY/ATs, with typically 15h of
observations per semester. The individual epochs have a total observing time
ranging from 1h to 3.3h including overheads. All data were acquired in medium
resolution ($R=500$) and SPLIT polarization mode to separate the stellar light
in two linear polarizations. Each observation consists of a series of field
swaps of about 20 min each, during which the two fibers observe each star
successively in order to extract the differential astrometric signal. The
principle of measurement in dual-field observations and of swap measurement is
detailed in Section 3. The observation sequence does not require an
interferometric transfer function calibrator given that the visibility
amplitudes are not used in dual-field astrometry and the phases are self-
calibrated by the swapping procedure.

##  3 Phase-referenced astrometry

Narrow-angle astrometry is enabled by the dual-field design of GRAVITY
(GRAVITY Collaboration et al. 2017). In this mode, the interferometric beam
combiner is able to simultaneously observe two separated interferometric field
of view, with two fibers for each telescope, thereby providing two
interference patterns for each baseline. The angular separation of the two
objects is measured from the optical path difference (OPD) between the white
light fringe of these two fringe patterns, delivering astrometry with a high
level of precision that is defined by the interferometric baseline. In order
to compensate for additional perturbations on the path between these two
channels, a metrology system was implemented (Gillessen et al. 2012; Lippa et
al. 2016) that measures the OPD from the two-beam combiner to the top of the
telescopes. The relevant baseline in astrometric observations is the narrow
angle baseline (Woillez & Lacour 2013; Lacour et al. 2014), defined by the end
of the metrology point, located on the secondary mirror spider arms of each
telescope. The relation between the phase measured by GRAVITY and the angular
separation between the targets is then (Lacour et al. 2014):

$\displaystyle\phi$
$\displaystyle=(\phi_{SC}-\phi_{FT})-\phi_{\mathrm{MET}}-\frac{2\pi}{\lambda}D(\lambda_{m},\lambda)\,$
(1)
$\displaystyle=\frac{2\pi}{\lambda}(\overrightarrow{s}_{B}-\overrightarrow{s}_{A})\cdot\overrightarrow{B}_{NAB}+\phi_{0}(\lambda)$

with $\phi_{SC}$ as the phase measured on the science channel of GRAVITY,
$\phi_{FT}$ the phase measured on the fringe-tracker, $\phi_{\mathrm{MET}}$
the differential OPD measured by the metrology, $\overrightarrow{B}_{NAB}$ the
narrow-angle baseline, $D(\lambda_{m},\lambda_{SC})$ the dispersion between
the wavelength of the metrology and of the starlight, $\overrightarrow{s}_{A}$
and $\overrightarrow{s}_{B}$ the position vector of stars A and B in the plane
of sky, $\lambda$ the wavelength of the science channel and
$\phi_{0}(\lambda)$ the zero point of the metrology.

To carry out the phase astrometry, it is necessary to remove
$\phi_{0}(\lambda)$, the constant internal offset of the metrology. In dual-
field observations, this can be done either by choosing a reference point to
the observations, which will be used as phase reference and subtracted from
the astrometry (GRAVITY Collaboration et al. 2018, 2019) or by measuring this
zero-point independently by the means of successive swaps between the two
fibers. The latter option is used in the case of GJ65. We detail the
methodology of the measurement in Appendix A.

We implemented this method and applied it on the standard reduced files
produced by the GRAVITY reduction pipeline (Lapeyrere et al. 2014). The output
of the process is finally the relative angular separation
$\overrightarrow{s}_{B}-\overrightarrow{s}_{A}$ of the A and B components.

##  4 Analysis

Figure 2: Generalized Lomb-Scargle periodogram. Top: Periodogram in RA
(orange) and DEC (blue) computed for the residuals of the binary orbit.
Bottom: Residuals after the subtraction of the planet candidate at
$p=156\,\mathrm{d}$.

###  4.1 Stellar orbit

We started by fitting the orbital elements of the stellar binary based on the
astrometric data. The orbital fit includes our new GRAVITY data, complemented
by archival astrometry data from WDS catalog and NACO published in Kervella et
al. (2016). The result of the fit is dominated by the GRAVITY data, as shown
in Figure 1 given the much higher accuracy on these points, roughly a factor
100 compared to the archival data. For each GRAVITY point, the uncertainty and
the degree of correlation of the error in RA and DEC are provided as part of
the GRAVITY data reduction. The covariance matrix can be reconstructed from
these quantities and is integrated in the orbital fit. The result of the fit
is shown in Table 1. We expressed the orbital parameters following the same
convention as used in Gaia Collaboration et al. (2023); Halbwachs et al.
(2023), and shown in Appendix B. The dynamical mass of the binary is
constrained by the combination of the GRAVITY astrometry with UVES radial
velocity retrieved from ESO public archive, whose joint fit with the
astrometry is shown on Figure 7 and 8. This study refines the initial estimate
without dual-field astrometry data given in Kervella et al. (2016), with which
they agree. We note the discrepancy in the value of the inclination in
Kervella et al. (2016) due to the difference of convention used in our current
paper, which is the same as in Gaia DR3.

Figure 3: Orbital solution for the best period, $p=156\,\mathrm{d}$ (left). Phase-folded orbit (right) with the average data displayed as coloured dots.  Parameter |  Star B |  Star A
---|---|---
Period (day) |  $156\pm 1$ |  $156\pm 1$
Mass ($M_{\oplus}$) |  $36\pm 6$ |  $39\pm 7$
a (AU) |  $0.274\pm 0.002$ |  $0.283\pm 0.002$
$e$ |  $0.27\pm 0.21$ |  $0.33\pm 0.30$
$i$ (deg) |  $89\pm 9$ |  $88\pm 6$
$\Omega$ (deg) |  $9^{\star}\pm 7$ |  $8^{\star}\pm 7$
$\omega$ (deg) |  $230\pm 36$ |  $248\pm 30$
Table 2: Orbital parameters of the planet for the best period (reduced chi-
square $\chi^{2}_{r}=1.03$). The host star is indicated for both solutions.
⋆ Both values ($\Omega,\Omega+180^{\circ}$) are compatible with this parameter
given that it is degenerated (see text).

###  4.2 Periodogram

We computed a generalized Lomb-Scargle periodogram (Zechmeister & Kürster
2009) on the residuals of the astrometry of the stellar orbit. The
periodograms of the residuals in right ascension (RA) and declination (DEC)
were first computed independently, taking into account their error bars. In
addition, we computed the joint periodogram of the signal following the
methodology described by Catanzarite et al. (2006), which consists of summing
the periodograms in RA and DEC, however the detection is mainly driven by the
signal in DEC. The result is shown in Figure 2. We used a bootstrapping
approach to compute the false alarm probability (FAP) and the detection
threshold. To do so, a large number ($N=10^{4}$) of random periodograms in RA
and DEC was generated, then drawn with replacement at the measurement epochs
of our sample and following a normal distribution with a zero mean and a
standard deviation corresponding to the $1\sigma$ uncertainty of that point.
For each draw, a periodogram was generated in RA and DEC. The FAPs were
finally estimated by computing the 10%, 1% and 0.15% quantiles of the set of
generated periodograms.

Finally, in order to distinguish the impact of the temporal sampling on the
final periodogram, we computed the periodogram of the sample replaced by
constant values, superimposed on Figure 2 (gray curve). This ”blank”
periodogram shows the typical frequencies of our sampling, with a distinct
peak at $p=365\,\mathrm{d}$ for the one-year annual periodicity of the
program.

The periodogram shows a peak at $p=156\,\mathrm{d}$ above a FAP = 0.15%
threshold. The peak does not overlap with the test periodogram generated on
white noise at the temporal sampling of our data set, nor at a harmonic of the
one-year period associated to the main period of our program (see Figure 2).
For the moment, we have discarded the peaks with a period ¡30d, for which we
consider our temporal sampling is not sufficient.

###  4.3 Orbit fitting

In a second step, we performed an orbital fit of the residuals to obtain a
second detection of candidate, using a methodology that is different from the
Lomb-Scargle periodogram, and to determine the orbital parameters of the
companion planet. Our astrometric model describes the reflex motion of a
companion in Keplerian motion around one of the components of the system. With
respect to both our stellar orbit and the planetary orbit, the four orbital
elements ($a$, $i$, $\Omega$, $\omega$) can be replaced by a linear model
using the Thiele-Innes elements.

Firstly, we performed an orbital fit over a grid of fixed periods and fit all
the other orbital parameters. In this way, we fixed the period, which is the
most non-linear parameters of the fit. Since P is fixed, the fit is left with
only two non-linear parameter ($e$, $t_{0}$) to solve the Kepler equation, and
the four Thiele-Innes parameters (A, F, B, G), which are linear coefficients
of the elliptical rectangular coordinates ($X,Y$). This method allows us to
make the fit robust by limiting the number of non-linear parameters. The
covariance matrix of the GRAVITY data, assuming the noise is random Gaussian,
is taken into account in the fit as:

$\chi^{2}=\left(\overrightarrow{y}-\overrightarrow{y}_{\mathrm{model}}\right)^{T}\Sigma^{-1}\left(\overrightarrow{y}-\overrightarrow{y}_{\mathrm{model}}\right)$
(2)

Finally, the Campbell parameters were deduced from the Thiele-Innes
parameters, for which we again used the same convention as in Gaia
Collaboration et al. (2023); Halbwachs et al. (2023). The result of the grid
search over periods converges to the same period $p=156\,\mathrm{d}$ as the
Lomb-Scargle periodogram, as shown in Fig. 4. The final orbital solution is
obtained by allowing all parameters to vary, and converges to a Neptune-mass
planet with mass $35-40\,M_{\oplus}$. The result for the best period and the
phase folded orbit are shown on Fig 3. The orbital parameters of the planet
are shown in Table 2.

We note that the fit of the orbit is degenerate to four solutions in total:
two possible host stars, and two possible longitudes of the ascending nodes
($\Omega,\Omega+180^{\circ}$) of the planet. However, the prograde solutions
(two out of the four in total) are favored from a dynamical point of view, and
are the ones shown in Table 2. The degeneracy on the host star could be lifted
by measuring the absolute astrometry of the binary, and the degeneracy of the
longitude of the ascending nodes by measuring the radial velocity of the host
star caused by the motion of the planet. However, we note that the location of
the planet in the plane of sky is known within two possible solutions
(degeneracy of the host star), the degeneracy of the ascending node does not
affect the knowledge of the location of the planet in the plane of sky (only
$z$). The projection of the GJ65 system onto the sky is shown in Fig 6.

###  4.4 Additional companions and complementary RV data

Our orbital solution would lead to a typical RV amplitude of $\approx
20\,\mathrm{m/s}$. We used UVES data to constrain the stellar orbit (see Sec
4.1) with a typical accuracy of the order of $\pm$100 m/s; however this is not
sufficient to constrain a planetary companion. The two components of GJ65 are
difficult targets for high precision RV measurements. Firstly, their very
strong magnetic activity and fast rotation results in spotted and time-
variable apparent surfaces (Barnes et al. 2017) that affect the spectral line
profiles. Secondly, their relatively small angular separation (Fig. 1) induces
crosstalk between the two stars for ground-based, seeing-limited
spectrographs.

We note the presence of peaks at shorter periods $\approx 20\,\mathrm{d}$ both
in the Lomb-Scargle periodograms and the period search. Such an astrometric
signal would correspond to a Saturn-mass planet on a ¡ 0.1 AU orbit. Here, we
limited our analysis to the periods ¿ 30 d due to the temporal sampling of our
monitoring under one month. However, the typical RV amplitude of this signal
is $\approx 100\,\mathrm{m/s}$, which could be confirmed by RV data. As a
follow-up to the ¡30 d and the 156d candidates, additional RV observations
would provide complementary information in this system. The NIRPS high-
stability spectrograph at La Silla (Bouchy et al. 2017) could be a prime
instrument for GJ65 AB, thanks to its adaptive optics system which allows for
the flux to be isolated from each components of the binary, and in the longer
term the high-precision ELT/ANDES instrument.

##  5 Discussion

The candidate exoplanet that we detect in GJ65 is the second nearest after
Proxima Centauri’s exoplanet system at the date of
writing111exoplanetarchive.ipac.caltech.edu. It thus offers unique
opportunities for the further characterization of this exoplanet. The
astrometric detection allows for the mass, inclination and orbital parameters
of the candidate to be derived. The location of the planet can be compared
with the expected orbital stability region of test particles as derived by
Holman & Wiegert (1999) (see Eq. 1 of that paper; Appendix C). The orbital
parameters of GJ65AB in Table 1 allow us to derive a critical semi-major axis
of $a_{c}=0.46\,\mathrm{au}$. The exoplanet candidate’s orbit lies within this
region, with a semi-major axis $a\simeq 0.283\,\mathrm{au}$ for the largest
value (Table 2). This candidate could thus have formed and evolved within the
region of stability. The formation of planets at relatively short separation
binaries ($<10\,\mathrm{au}$) is challenging due the dynamical interactions in
these systems and the tidal truncation of the protoplanetary disks in early
phases of formation, as a disk truncation below the snow line prevents the
formation of giant planets (Pichardo et al. 2005). In GJ65, the snowline is
located well within the stability region of the binary $\sim
0.04\,\mathrm{au}$ (Ida & Lin 2005). This is a priori compatible with the
formation of a Neptune type planet in this region (Table 2). The current
detection thus provides an important example to study the formation mechanism
of these systems, although a complete dynamical and evolutionary study of GJ65
is out of the scope of this Letter. Interestingly, GJ65AB shares strong
similarities with Alpha Centauri AB from the standpoint of stability, since
these two systems share almost identical mass ratio and eccentricity, which
are, at first order, the sole parameters with the semi-major axis entering in
$a_{c}$. GJ65 ($a=5.45\,\mathrm{au}$) is scaled down by a factor 4.2 with
respect to Alpha Cen AB ($a=23.52\,\mathrm{au}$), which could form a basis for
theoretical long-term stability studies of these two objects (Quarles &
Lissauer 2016; Cuello & Sucerquia 2024).

The inclination of the planet’s orbit can be compared to the inclination of
the stars’ rotation axes and that of the binary star orbit. The inclinations
of the rotation axes of GJ65A and GJ65B were measured through spectro-
polarimetric observations by Barnes et al. (2017), who derived inclinations of
$i_{A}=60\pm 6^{\circ}$ and $i_{B}=64\pm 7^{\circ}$ ($0<i<90^{\circ}$),
respectively, modulo $180^{\circ}$. They can therefore be either
$i=60^{\circ}$ or $i=180-60=120^{\circ}$. The first scenario ($i=60^{\circ}$)
would indicate a $\approx 180^{\circ}$ misalignment between the spin and the
orbital plane of the binary, that is, a retrograde orbital configuration. This
appears particularly unlikely in GJ65AB, considering that both stars are fast
rotators with consistent rotation axis inclinations. We therefore favor an
inclination of $120^{\circ}$ for the stellar rotation axes, as it corresponds
to a spin-orbit alignment of star and the binary. In this configuration, the
inclination of the planet’s orbital plane ($i_{P}\approx 90^{\circ}$; Table 2)
with respect to the binary star’s and the two stars’ equatorial plane is
$\Delta i\approx 30\pm 10^{\circ}$. A similarly high relative inclination is
known in several multi-planet systems between planet orbits as, for instance,
$\pi$ Men (De Rosa et al. 2020; Hatzes et al. 2022), $\nu$ And (McArthur et
al. 2010) or Kepler-108 (Mills & Fabrycky 2017). While the configuration is
different in GJ65 with two stars A and B instead of multiple planets, the high
eccentricity of their orbit ($e\approx 0.62$; Table 1) could induce the Kozai-
Lidov effect, thereby raising the planet’s inclination (Naoz 2016; Kozai 1962;
Lidov 1962). Testing this hypothesis would benefit from follow-up observations
to improve the precision of the inclination of the planetary orbit, as well as
complementary measurements of the position angle and inclination of the stars’
rotation axes, for example, using spectro-interferometry (Le Bouquin et al.
2009).

The immediate vicinity of GJ65 raises the question of characterizing this
system with direct imaging. The age of the system was estimated to
approximately $\sim 1\,\mathrm{Gyr}$ from mass-luminosity isochrones by
Kervella et al. (2016), based on the evolutionary models for low-mass stars in
Baraffe et al. (2015). Given this system is relatively old, the intrisic
emission of the planet will be extremely low. The luminosity of the planet
will be given by the reflected light contrast
$\mathrm{c}=g(\phi)\cdot\,A\cdot\left(\frac{R_{p}}{a}\right)^{2}$ with $A$ as
the albedo, $g(\phi)$ the phase function on the orbit, and $R_{p}$ the planet
radius. The estimated contrast is $\mathrm{c}=10^{-6.3}$ at a projected
separation of 90mas, assuming $g(\phi).\,A=0.4$, and $R_{p}=7\,R_{\oplus}$
based on the mass-radius relation of Chen & Kipping (2017). This value of
contrast is at the limit of current observation capabilities, but could be a
prime target for direct high-contrast observations with VLTI/GRAVITY+ and its
planned extreme adaptive optics (Gravity+ Collaboration et al. 2022), as well
as the upcoming ELT instruments (Davies et al. 2018; Carlotti et al. 2022;
Palle et al. 2023). In addition, the knowledge of the orbital parameters of
the planet would allow for an astrometry-informed pointing for GRAVITY+ and
direct imaging observations from ground and space. Gaia DR4 will be useful to
further constrain this system and potentially provide absolute astrometry to
lift the degeneracy which of the two stars host the candidate planet. However,
the astrometric performance may be more affected by flares in the visible
compared to infrared observations. The monitoring of GJ65 with follow-up
GRAVITY observations will be important in further constraining the orbital
parameters of the candidate planet and the possible presence of additional
planets. These observations demonstrate the ability to use astrometry to
detect planets around low-mass stars, and could be applied to the monitoring
of nearby $<25$pc system to constrain the presence of giant planets down to
Neptune mass. In the longer term, the extension of ground-based
interferometers to micro-arcsecond precision could enable to probe Earth-mass
planets in our close solar neighborhood.

###### Acknowledgements.

We thank the anonymous referee for his comments which improved the content of
this Letter. We are very grateful to our funding agencies (MPG, ERC, CNRS
[PNCG, PNGRAM], DFG, BMBF, Paris Observatory [CS, PhyFOG], Observatoire des
Sciences de l’Univers de Grenoble, and the Fundação para a Ciência e
Tecnologia), to ESO and the Paranal staff, and to the many scientific and
technical staff members in our institutions, who helped to make GRAVITY a
reality. P.K. has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program
(projects CepBin, grant agreement 695099, and UniverScale, grant agreement
951549). A.A. and P.G. acknowledge the financial support provided by
FCT/Portugal through grants PTDC/FIS-AST/7002/2020 and UIDB/00099/2020. F.W.
has received funding from the European Union’s Horizon 2020 research and
innovation programme under grant agreement No 10100471. This research has made
use of the Jean-Marie Mariotti Center Aspro service. Based on observations
collected at the European Southern Observatory under ESO programme(s):
099.C-2017(A), 099.C-2017(B), 099.C-2017(C), 0100.C-0597(A), 0100.C-0597(B),
0100.C-0597(C), 0100.C-0608(A), 0100.C-0608(B), 0101.C-0121(A),
0101.C-0121(B), 0101.C-0121(C), 0102.C-0205(A), 0102.C-0205(B),
0102.C-0205(C), 0102.C-0211(A), 0102.C-0211(B), 0102.C-0211(C),
0103.C-0183(A), 0103.C-0183(B), 0103.C-0183(C), 0103.C-0192(A),
0103.C-0183(A), 0103.C-0183(B), 0103.C-0183(C), 0104.C-0161(A),
0104.C-0161(B), 0104.C-0161(C), 0104.C-0161(D), 105.20KT.001, 105.20KT.002,
105.20KT.003, 106.215T.001, 106.215T.002, 106.215T.003, 109.2310.001,
109.2310.002, 109.2310.003, 109.2310.004, 110.23TC.001, 110.23TC.002,
110.23TC.003, 111.24KS.001, 111.24KS.002, 111.24KS.003, 111.24KS.004,
111.24KS.005, 111.24KS.006, 112.25GN.001, 112.25GN.002, 112.25GN.003. This
research has made use of Astropy222Available at http://www.astropy.org/, a
community-developed core Python package for Astronomy (Astropy Collaboration
et al. 2013, 2018), the Numpy library (Harris et al. 2020), the Scipy library
(Virtanen et al. 2020) and the Matplotlib graphics environment (Hunter 2007).

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##  Appendix A Swap observations

The goal of the swap sequence is to measure the phases of Eq.1 with two
opposite signs for the field component, while keeping constant the zero-point
of the metrology. This is done using the internal K-mirror of GRAVITY fiber
coupler (Pfuhl et al. 2014), which allows us to rotate the field before the
injection of light in the fibers, given the separation of the stars and the
fact that both components are equally bright and can be equally used as a
fringe-tracking star.

The two phases which are measured for each step of the swap sequence are:

$\cases{\phi}_{1}&=\frac{2\pi}{\lambda}(\overrightarrow{s}_{B}-\overrightarrow{s}_{A})\cdot\overrightarrow{B}_{NAB,1}+\phi_{0}(\lambda)\\\
\phi_{2}=\frac{2\pi}{\lambda}(\overrightarrow{s}_{A}-\overrightarrow{s}_{B})\cdot\overrightarrow{B}_{NAB,2}+\phi_{0}(\lambda){}$
(3)

For each baseline, the metrology zero point can finally be extracted from the
combination of Eq.3 pointings:

$\displaystyle\phi_{0}(\lambda)$
$\displaystyle=\frac{1}{2}\,\mathrm{arg}\left[\;\tilde{V}_{FT,1}\,e^{-\frac{2\pi}{\lambda}(\overrightarrow{s}_{B}-\overrightarrow{s}_{A})\overrightarrow{B}_{NAB,1}}\,\cdot\,\tilde{V}_{FT,2}\,e^{-\frac{2\pi}{\lambda}(\overrightarrow{s}_{A}-\overrightarrow{s}_{B})\,\overrightarrow{B}_{NAB,2}}\;\right]$
(4)
$\displaystyle=\frac{1}{2}\mathrm{arg}\left[\,\tilde{V}_{FT,1}\cdot\tilde{V}_{FT,2}\,\right]-\frac{\pi}{\lambda}\,(\overrightarrow{s}_{B}-\overrightarrow{s}_{A})\cdot\left(\overrightarrow{B}_{NAB,1}-\overrightarrow{B}_{NAB,2}\right)$

with $\tilde{V}_{FT,k}$ the complex visibility amplitude measured by the
fringe-tracker. The metrology zero-point is then included in Eq.3, which
provides the relative separation
$\overrightarrow{s}_{B}-\overrightarrow{s}_{A}$ of components A and B.

##  Appendix B Orbit fitting

The stellar orbit and the planetary orbits are both defined using the Thiele-
Innes elements, related to the four orbital orbital elements ($a$, $e$,
$\omega$, $\Omega$). We followed the convention in Gaia Collaboration et al.
(2023); Halbwachs et al. (2023):

$\cases{A}=\cos\Omega\cos\omega-\sin\Omega\sin\omega\cos i\\\
B=\sin\Omega\cos\omega+\cos\Omega\sin\omega\cos i\\\
F=-\cos\Omega\sin\omega-\sin\Omega\cos\omega\cos i\\\
G=-\sin\Omega\sin\omega+\cos\Omega\cos\omega\cos i\\\ {}$ (5)

The projected separation of the secondary with respect to the primary is then
defined as:

$\cases{\Delta}\delta=a\left(AX+FY\right)\\\
\Delta\alpha^{*}=a\left(BX+GY\right){}$ (6)

where X and Y are the elliptical rectangular coordinates:

$\cases{X}=\cos E-e\\\ Y=\left(\sin E\right)\sqrt{1-e^{2}}{}$ (7)

with $E$ as the eccentric anomaly, obtained by solving the Kepler equation.

Figure 4: Period search of GJ65 residuals, with all orbital parameters free
for each (fixed) period and including covariances, shown with inverse reduced
chi-square in y-axis. The best period, $p=156\,\mathrm{d}$, coincides with the
peak of the Lomb-Scargle periodogram.

##  Appendix C Stability domain

We use the stability criterion of test particles derived in Holman & Wiegert
(1999) (Eq. 1), which we reproduce here:

$a_{c}=\left[0.464-0.380\mu-0.631e+0.586\mu e+0.150e^{2}-0.198\mu
e^{2}\right]a_{b}$ (8)

with $a_{c}$, as the critical semi-major axis defining the outer edge of the
stability region, $\mu=m_{B}/m_{A}$ the mass ratio of the binary, $e$ the
eccentricity of the binary, and $a_{b}$ its semi-major axis. The Neptune-mass
candidate as well as the stability region of the system are shown in Figure 5.

Figure 5: Parameter space probed by GRAVITY observations. The stability region
is computed from Holman & Wiegert (1999).

##  Appendix D System architecture

Figure 6: Planet candidate and barycentric ellipsis of the A and B stars in
GJ65. The gray-shaded disk corresponds to the region of stability, shown in
the orbital plane of the binary. The blue orbit corresponds to the planet in
either star A and star B hypothesis. The inset shows the on-sky orbit around
GJ65 B and the location of the ice-line (green) in the orbital plane of the
planetary system.

Figure 7: Relative angular separation of the stars A and B in GJ65. Figure 8:
Relative radial velocity of stars A and B in GJ65.