Ivo Saviane, Oana Sandu, Lars Lindberg Christensen, Richard Hook and the personnel at La Silla
(ESO) for making the Pale Red Dot campaign possible. The authors acknowledge support from fund-
ing grants; Leverhulme Trust/UK RPG-2014-281 (HRAJ, GAE, MT), MINECO/Spain AYA-2014-
54348-C3-1-R (PJA, CRL, ZMB, ER), MINECO/Spain ESP2014-54362-P (MJLG), MINECO/Spain
AYA-2014-56637-C2-1-P(JLO, NM), J.A./Spain 2012-FQM1776 (JLO, NM), CATA-Basal/Chile
PB06 Conicyt (JSJ), Fondecyt/Chile project #1161218 (JSJ), STFC/UK ST/M001008/1 (RPN, GALC,
GAE), STFC/UK ST/L000776/1 (JB), ERC/EU Starting Grant #279347 (AR, LS, SVJ), DFG/Germany
Research Grants RE 1664/9-2(AR), RE 1664/12-1(MZ), DFG/Germany Colloborative Research
Center 963(CJM, SD), DFG/Germany Research Training Group 1351(LS), and NSF/USA grant
AST-1313075 (ME). Based on observations made with ESO Telescopes at the La Silla Paranal Ob-
servatory under programmes 096.C-0082 and 191.C-0505. Observations were obtained with ASH2,
which is supported by the Instituto de Astrof´ısica de Andaluc´ıa and Astroimagen company. This
work makes use of observations from the LCOGT network. We acknowledge the effort of the
UVES/M-dwarf and the HARPS/Geneva teams, which obtained a substantial amount of the data
used in this work.
Author contributions. GAE led the PRD campaign, observing proposals and organized the manuscript.
PJA led observing proposals, and organized and supported the IAA team through research grants.
MT obtained the early signal detections and most Bayesian analyses. JSJ, JB, ZMB and HRAJ par-
ticipated in the analyses and obtained activity measurements. Zaira M. Berdi˜nas also led observing
proposals. HRAJ funded several co-authors via research grants. MK and ME provided the extracted
UVES spectra, and RPB re-derived new RV measurements. CRL coordinated photometric follow-
up campaigns. ER led the ASH2 team and related reductions (MJLG, IC, JLO, NM). YT led the
LCOGT proposals, campaign and reductions. MZ obtained observations and performed analyses on
HARPS and UVES spectra. AO analysed time-series and transit searches. JM, SVJ and AR ana-
lyzed stellar activity data. AR funded several co-authors via research grants. RPN, GALC, SJP, SD
& BG did dynamical and studied the planet formation context. MK provided early access to time-
series from the ASAS survey. CJM and LFS participated in the HARPS campaigns. All authors
contributed to the preparation of observing proposals and the manuscript.
Reprints and permissions information is available at
www.nature.com/reprints
.
The authors declare that they do not have any competing financial interests.
Correspondence and requests for materials should be addressed to Guillem Anglada-Escud´e,
g.anglada@qmul.ac.uk
9
Table 1: Stellar properties, Keplerian parameters, and derived quantities. The estimates are the
maximum a posteriori estimates and the uncertainties are expressed as 68% credibility intervals.
We only provide an upper limit for the eccentricity (95% confidence level). Extended Data Table1
contains the list of all the model parameters.
Stellar properties
Value
Reference
Spectral type
M5.5V
2
Mass
∗
/Mass
Sun
0.120 [0.105,0.135]
21
Radius
∗
/R
Sun
0.141 [0.120,0.162]
2
Luminosity
∗
/ L
Sun
0.00155 [0.00149, 0.00161]
2
Effective temperature [K]
3050 [2950, 3150]
2
Rotation period [days]
∼ 83
3
Habitable zone range [AU]
∼ 0.0423 – 0.0816
22
Habitable zone periods [days]
∼ 9.1–24.5
22
Keplerian fit
Proxima b
Period [days]
11.186 [11.184, 11.187]
Doppler amplitude [ms
−1
]
1.38 [1.17, 1.59]
Eccentricity [-]
<0.35
Mean longitude
λ = ω + M
0
[deg]
110 [102, 118]
Argument of periastron
w
0
[deg]
310 [0,360]
Statistics summary
Frequentist false alarm probability
7 × 10
−8
Bayesian odds in favour B
1
/B
0
2.1 × 10
7
UVES Jitter [ms
−1
]
1.69 [1.22, 2.33]
HARPS pre-2016 Jitter [ms
−1
]
1.76 [1.22, 2.36]
HARPS PRD Jitter [ms
−1
]
1.14 [0.57, 1.84]
Derived quantities
Orbital semi-major axis
a [AU]
0.0485 [0.0434, 0.0526]
Minimum mass
m
p
sin i [M
⊕
]
1.27 [1.10, 1.46]
Eq. black body temperature [K]
234 [220, 240]
Irradiance compared to Earth’s
65%
Geometric probability of transit
∼1.5%
Transit depth (Earth-like density)
∼0.5%
10
Methods
1
Statistical frameworks and tools
The analyses of time-series including radial velocities and activity indices were performed by fre-
quentist and Bayesian methods. In all cases, significances were assessed using model comparisons
by performing global multi-parametric fits to the data. Here we provide a minimal overview of the
methods and assumptions used throughout the paper.
1.1
Bayesian statistical analyses.
The analyses of the radial velocity data were performed by applying posterior sampling algorithms
called Markov chain Monte Carlo (MCMC) methods. We used the adaptive Metropolis algorithm
31
that has previously been applied to such radial velocity data sets.
15, 32
This algorithm is simply a
generalised version of the common Metropolis-Hastings algorithm
33, 34
that adapts to the posterior
density based on the previous members of the chain.
Likelihood functions and posterior densities of models with periodic signals are highly multi-
modal (i.e. peaks in periodograms). For this reason, in our Bayesian signal searches we applied
the delayed rejection adaptive Metropolis (DRAM) method,
16
that enables efficient jumping of the
chain between multiple modes by postponing the rejection of a proposed parameter vector by first
attempting to find a better value in its vicinity. For every given model, we performed several pos-
terior samplings with different initial values to ensure convergence to a unique solution. When we
identified two or more significant maxima in the posterior, we typically performed several additional
samplings with initial states close to those maxima. This enabled us to evaluate all of their relative
significances in a consistent manner. We estimated the marginal likelihoods and the corresponding
Bayesian evidence ratios of different models by using a simple method.
35
A more detailed descrip-
tion of these methods can be found in elsewhere.
36
1.2
Statistical models : Doppler model and likelihood function.
Assuming radial velocity measurements
m
i,INS
at some instant
t
i
and instrument INS, the likelihood
function of the observations (probability of the data given a model) is given by
L
=
INS
i
l
i,INS
(1)
l
i,INS
=
1
2π (σ
2
i
+ σ
2
INS
)
exp
−
1
2
ǫ
2
i,INS
σ
2
i
+ σ
2
INS
,
(2)
ǫ
i,INS
=
m
i,INS
−
γ
INS
+ ˙γ∆t
i
+ κ(∆t
i
) + MA
i,INS
+ A
i,INS
,
(3)
∆t
i
=
t
i
− t
0
(4)
where
t
0
is some reference epoch. This reference epoch can be arbitrarily chosen, often as the
beginning of the time-series or a mid-point of the observing campaigns. The other terms are:
11