Nature  Letter
A terrestrial planet candidate in a temperate orbit around Proxima Centauri
 Guillem AngladaEscudé^{1}^{, }
 Pedro J. Amado^{2}^{, }
 John Barnes^{3}^{, }
 Zaira M. Berdiñas^{2}^{, }
 R. Paul Butler^{4}^{, }
 Gavin A. L. Coleman^{1}^{, }
 Ignacio de la Cueva^{5}^{, }
 Stefan Dreizler^{6}^{, }
 Michael Endl^{7}^{, }
 Benjamin Giesers^{6}^{, }
 Sandra V. Jeffers^{6}^{, }
 James S. Jenkins^{8}^{, }
 Hugh R. A. Jones^{9}^{, }
 Marcin Kiraga^{10}^{, }
 Martin Kürster^{11}^{, }
 Marίa J. LópezGonzález^{2}^{, }
 Christopher J. Marvin^{6}^{, }
 Nicolás Morales^{2}^{, }
 Julien Morin^{12}^{, }
 Richard P. Nelson^{1}^{, }
 José L. Ortiz^{2}^{, }
 Aviv Ofir^{13}^{, }
 SijmeJan Paardekooper^{1}^{, }
 Ansgar Reiners^{6}^{, }
 Eloy Rodríguez^{2}^{, }
 Cristina RodrίguezLópez^{2}^{, }
 Luis F. Sarmiento^{6}^{, }
 John P. Strachan^{1}^{, }
 Yiannis Tsapras^{14}^{, }
 Mikko Tuomi^{9}^{, }
 Mathias Zechmeister^{6}^{, }
 Journal name:
 Nature
 Volume:
 536,
 Pages:
 437–440
 Date published:
 DOI:
 doi:10.1038/nature19106
 Received
 Accepted
 Published online
Abstract
At a distance of 1.295 parsecs^{1}, the red dwarf Proxima Centauri (α Centauri C, GL 551, HIP 70890 or simply Proxima) is the Sun’s closest stellar neighbour and one of the beststudied lowmass stars. It has an effective temperature of only around 3,050 kelvin, a luminosity of 0.15 per cent of that of the Sun, a measured radius of 14 per cent of the radius of the Sun^{2} and a mass of about 12 per cent of the mass of the Sun. Although Proxima is considered a moderately active star, its rotation period is about 83 days (ref. 3) and its quiescent activity levels and Xray luminosity^{4} are comparable to those of the Sun. Here we report observations that reveal the presence of a small planet with a minimum mass of about 1.3 Earth masses orbiting Proxima with a period of approximately 11.2 days at a semimajoraxis distance of around 0.05 astronomical units. Its equilibrium temperature is within the range where water could be liquid on its surface^{5}.
At a glance
Figures
Tables
Main
The results presented here consist of an analysis of previously obtained Doppler measurements (pre2016 data) and the confirmation of a signal in a specifically designed followup campaign in 2016. The Doppler data come from two precision radial velocity instruments, both at the European Southern Observatory (ESO): the High Accuracy Radial velocity Planet Searcher (HARPS) and the Ultraviolet and Visual Echelle Spectrograph (UVES). HARPS is a highresolution stabilized echelle spectrometer installed at the ESO 3.6 m telescope (La Silla Observatory, Chile), the wavelength of which is calibrated using hollow cathode lamps (ThAr). HARPS has demonstrated radial velocity measurements at approximately 1 m s^{−1} precision over timescales of years^{6}, including measurements of lowmass stars^{7}. All of the HARPS spectra were extracted and calibrated with the standard ESO Data Reduction Software and radial velocities were measured using a leastsquares template matching technique^{7}. HARPS data are separated into two data sets. The first set includes all of the data obtained before 2016 by several programmes (HARPS pre2016). The second HARPS set comes from the more recent Pale Red Dot campaign (PRD hereafter), which was designed to eliminate period ambiguities using new HARPS observations and quasisimultaneous photometry. The HARPS PRD observations consisted of one spectrum obtained almost every night between 19 January and 31 March 2016. The UVES observations used the iodine cell technique^{8} and were obtained in the framework of the UVES survey for terrestrial planets around Mclass dwarfs between 2000 and 2008. The spectra were extracted using the standard procedures of the UVES survey^{9} and new radial velocities were obtained using uptodate iodine reduction codes^{10}. As systematic calibration errors produce correlations among the observations for each night^{11}, we consolidated the Doppler measurements through nightly averages to present a simpler and more conservative signal search. This led to 72 UVES, 90 HARPS pre2016 and 54 HARPS PRD epochs. The PRD photometric observations were obtained using the Astrograph for the South Hemisphere II telescope (ASH2 hereafter^{12}, with S ii and Hα narrowband filters) and the Las Cumbres Observatory Global Telescope network^{13} (with Johnson B and V band filters), over the same time interval and similar sampling rates as the HARPS PRD observations. Further details about each campaign and the photometry are detailed in Methods. All of the time series used in this work are available as Supplementary Data.
The search and assessment of the statistical significance (see below and Methods for more details) of the signals were performed using frequentist^{14} and Bayesian^{15} methods. The periodograms in Fig. 1 represent the improvement of a reference statistic as a function of trial period, with the peaks representing the most probable new signals. The improvement in the logarithm of the likelihood function ΔlnL is the reference statistic used in the frequentist framework, and its value is then used to assess the falsealarm probability (FAP) of the detection^{14}. An FAP below 1% is considered suggestive of periodic variability, and anything below 0.1% is considered to be a significant detection. In the Bayesian framework, the signals are first searched using a specialized sampling method^{16} that enables the exploration of multiple local maxima of the posterior density (the result of this process is the red lines in Fig. 1), and the significance of the signals is then assessed by obtaining the ratios of evidences of the models. In a Bayesian context, the evidence B_{m} of a model m is the integral of its Bayesian posterior density. A more detailed description and references are provided in Methods. If the evidence ratio between two models exceeds some threshold (for example, B_{1}/B_{0} > 10^{3}), then the model in the numerator (with one planet) is favoured against the model in the denominator (no planet).
An isolated peak at about 11.2 d was recovered when all of the night averages in the pre2016 data sets were averaged (Fig. 1a). Despite the significance of the signal, the analysis of the pre2016 subsets produced slightly different periods depending on the noise assumptions and which of the subsets were considered. Confirmation or refutation of this signal at 11.2 d was the main driver for the proposal of the HARPS PRD campaign. The analysis of the HARPS PRD data revealed a single significant signal at approximately the same 11.3 ± 0.1 d period (Fig. 1b), but this period coincidence alone does not prove consistency with the pre2016 data. Final confirmation is achieved when all of the data sets are combined (Fig. 1c)—the statistical significance of the signal at 11.2 d then increases dramatically (FAP < 10^{−7}, Bayesian evidence ratio B_{1}/B_{0} > 10^{6}). This implies that not only the period, but also the amplitude and phase are consistent during the 16 years of accumulated observations (see Fig. 2). All of the analyses performed with and without correlatednoise models produced consistent results. A second signal in the range of 60–500 d was also detected, but its nature is still unclear due to stellar activity and inadequate sampling.
Stellar variability can cause spurious Doppler signals that mimic planetary candidates, especially when combined with uneven sampling^{9, 17}. To address this, the time series of the photometry and spectroscopic activity indices were also searched for signals. After removing occasional flares, all four photometric time series show the same clear modulation with a period of P ≈ 80 days (Fig. 3b–e), which is consistent with the previously reported photometric period of approximately 83 d (ref. 3). Spectroscopic activity indices were measured on all of the HARPS spectra, and their time series were also investigated. The width of the spectral lines (measured as the variance of the mean line, or m_{2}) follows a time dependence that is almost identical to the light curves, a behaviour that has already been reported for other M dwarf stars^{18}. The time series of the indices that are based on chromospheric emission lines (for example, Hα) do not show evidence of periodic variability, even after removing the data points that are likely to be affected by flares. We also investigated possible correlations of the Doppler measurements with the activity indices by including linear correlation terms in the Bayesian model of the Doppler data. Although some indices do show hints of correlation in some campaigns, including them in the model produces lower probabilities, owing to overparameterization. Flares have very little effect on our Doppler velocities, as has already been suggested by previous observations of Proxima^{19}. More details are provided in Methods and Extended Data Fig. 8. As the analysis of the activity data failed to identify any stellar activity feature that is likely to generate a spurious Doppler signal at 11.2 d, we conclude that the variability in the data is best explained by the presence of a planet (Proxima b, hereafter) orbiting the star. All of the available photometric light curves were searched for evidence of transits, but no obvious transitlike features were detectable in our light curves. We used optimal boxLeastSquares codes^{20} to search for candidate signals in data from the All Sky Automatic Survey^{3}. No significant transit signal was found down to a depth of about 5%. The most likely orbital solution and the putative properties of the planet and transits are given in Table 1.
The Doppler semiamplitude of Proxima b (approximately 1.4 m s^{−1}) is not particularly small compared with other reported planet candidates^{6}. The uneven and sparse sampling combined with the longerterm variability of the star seem to be the reasons why the signal could not be unambiguously confirmed with pre2016 data rather than the total amount of data accumulated. The corresponding minimum planetary mass is about 1.3 Earth masses (M_{⊕}). With a semimajor axis of approximately 0.05 au, it lies squarely in the centre of the classical habitable zone for Proxima^{5}. As mentioned earlier, the presence of another superM_{⊕} planet cannot yet be ruled out at longer orbital periods and Doppler semiamplitudes of <3 m s^{−1}. By numerical integration of some putative orbits, we verified that the presence of such a planet would not compromise the orbital stability of Proxima b.
The habitability of planets like Proxima b—in the sense of sustaining an atmosphere and liquid water on its surface—is a matter of intense debate. The most common arguments against habitability are tidal locking, strong stellar magnetic fields, strong flares and high ultraviolet and Xray fluxes; but none of these have been proved definitive. Tidal locking does not preclude a stable atmosphere via global atmospheric circulation and heat redistribution^{21}. The average global magnetic flux density of Proxima is 600 ± 150 G (ref. 22), which is quite large compared with that of the Sun (1 G). However, several studies have shown that planetary magnetic fields in tidally locked planets can be strong enough to prevent atmospheric erosion by stellar magnetic fields^{23} and flares^{24}. Because of its close orbit to Proxima, Proxima b suffers from Xray fluxes that are approximately 400 times that experienced by Earth, but studies of similar systems indicate that atmospheric losses can be relatively small^{25}. Further characterization of such planets can also inform us about the origin and evolution of terrestrial planets. For example, the formation of Proxima b from in situ disk material is implausible because disk models for small stars would contain less than 1M_{⊕} of solids within a distance of 1 au. There are three possibilities: the planet migrated in via type I migration^{26}; planetary embryos migrated in and coalesced at the current planet’s orbit; or pebbles/small planetesimals migrated via aerodynamic drag^{27} and later coagulated into a larger body. Although migrated planets and embryos that originate beyond the iceline would be rich in volatiles, pebble migration would produce much drier worlds. A warm terrestrial planet orbiting Proxima offers the opportunity to attempt further characterization via transits (ongoing searches), by direct imaging and highresolution spectroscopy in the next decades^{28}, and possibly robotic exploration in the coming centuries^{29}.
Methods
Statistical frameworks and tools
The analyses of time series including the radial velocities and activity indices were performed by frequentist and Bayesian methods. In all cases, the statistical significance was assessed using model comparisons by performing global multiparametric fits to the data. Here we provide a minimal overview of the methods and assumptions used throughout the Letter.
Bayesian statistical analyses. The analyses of the radial velocity data were performed by applying posterior sampling algorithms called Markov chain Monte Carlo methods. We used the adaptive Metropolis algorithm^{31}, which has previously been applied to such radial velocity data sets^{15, 32}. This algorithm is simply a generalized version of the common Metropolis–Hastings algorithm^{33, 34} that adapts to the posterior density based on the previous members of the chain.
The likelihood functions and posterior densities of models with periodic signals are highly multimodal (that is, they have peaks in the periodograms). For this reason, in our Bayesian signal searches we applied the delayed rejection adaptive Metropolis (DRAM) method^{16}, which 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 posterior samplings with different initial values to ensure convergence to a unique solution. When we identified two or more substantial maxima in the posterior density, we typically performed several additional samplings with initial states close to those maxima. This enabled us to evaluate their relative importance 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 description of these methods can be found in elsewhere^{36}.
Doppler model and likelihood function. Assuming that the ith radial velocity measurements is m_{i,INS} obtained at some instant t_{i} from an instrument INS, the likelihood function of the observations (probability of the data given a model) is given by
where t_{0} is some reference epoch. This reference epoch can be arbitrarily chosen, often as the beginning of the time series or a midpoint of the observing campaigns. The other terms are:
(1) ϵ_{i,INS} are the residuals to a fit. We assume that each ϵ_{i,INS} value is a Gaussian random variable with a zero mean and a variance of , where is the reported uncertainty of the ith measurement and is the jitter parameter and represents the excess white noise not included in .
(2) γ_{INS} is the zeropoint velocity of each instrument. Each INS can have a different zero point depending on how the radial velocities are measured and how the wavelengths are calibrated.
(3) is a linear trend parameter caused by a longterm acceleration.
(4) The term κ(Δt_{i}) is the superposition of k Keplerian signals evaluated at Δt_{i}. Each k depends on five parameters: the orbital period P_{p}, the semiamplitude of the signal K_{p}, the mean anomaly M_{0,p}, which represents the phase of the orbit with respect to the periastron of the orbit at t_{0}, the orbital eccentricity e_{p} that goes from 0 (circular orbit) to 1 (unbound parabolic orbit) and the argument of periastron ω_{p}, which is the angle on the orbital plane with respect to the plane of the sky at which the star goes through the periastron of its orbit (the planet’s periastron is at ω_{p} + 180°). Detailed definitions of the parameters can be found elsewhere^{37}.
(5) The moving average term
is a simple parameterization of the possible correlated noise that depends on the residual of the previous measurement ϵ_{i−1,INS}. As for the other parameters related to noise in our model, we assume that the parameters of the MA function depend on the instrument; for example the different wavelength ranges used will cause different properties of the instrumental systematic noise. Keplerian and other physical processes also introduce correlations into the data, therefore some degree of degeneracy between the MA terms and the signals of interest is expected. As a result, including an MA term always produces more conservative statistical significance estimates than a model with uncorrelated random noise only. The MA model is implemented through a coefficient ϕ_{INS} and a timescale τ_{INS}. ϕ_{INS} quantifies the strength of the correlation between the i and i − 1 measurements. It is bound between −1 and 1 to guarantee that the process is stationary (that is, the contribution of the MA term does not arbitrarily grow over time). Exponential smoothing is used to decrease the strength of the correlation exponentially as the difference t_{i} − t_{i−1} increases^{38}.
(6) Linear correlations with activity indices can also be included in the model in the following manner
where ξ runs over all of the activity indices used to model each INS data set (for example, m_{2}, m_{3}, Sindex and so on, whose descriptions are provided below). To avoid any confusion with other discussions about correlations, we call these C_{ξ,INS} activity coefficients. Note that each activity coefficient C_{ξ,INS} is associated with one activity index (ξ_{i}) obtained simultaneously with the ith radial velocity measurement (for example, chromospheric emission from the Hα line, the second moment of the meanline profile, the interpolated photometric flux and so on). When fitting a model to the data, an activity coefficient substantially different from 0 indicates evidence of Doppler variability correlated with the corresponding activity index. Formally speaking, these C_{ξ,INS} correspond to the coefficient of the firstorder Taylor expansion of a physical model for the apparent radial velocities as a function of the activity indices and other physical properties of the star.
A simplified version of the same likelihood model is used when analysing time series of activity indices. That is, when searching for periodicities in series other than Doppler measurements, the model will consist of the γ_{INS} zero points, a linear trend term and a sum of n sinusoids
where each kth sinusoid has three parameters A_{k}, B_{k} and P_{k} instead of the five Keplerian ones. Except for the period parameters and the jitter terms, this model is linear with all the other parameters, which allows a relatively quick computation of the likelihoodratio periodograms.
Bayesian prior choices. As in any Bayesian analysis, the prior densities of the model parameters have to be selected in a suitable manner (for example see ref. 39). We used uniform and uninformative distributions for most of the parameters apart from a few, possibly important, exceptions. First, as we used a parameter l = lnP in the Markov chain Monte Carlo samplings instead of the period P directly, the uniform prior density π(l) = c for all l ∈ [lnP_{0}, lnP_{max}], where P_{0} and P_{max} are some minimum and maximum periods, does not correspond to a uniform prior in P. Instead, this prior corresponds to a period prior such that π(P) ∝ P^{−1} (ref. 40). We made this choice because the period can be considered a scale parameter for which an uninformative prior is one that is uniform in lnP (ref. 41). We selected the parameter space of the period such that P_{0 }= 1 d and P_{max} = T_{obs}, where T_{obs} is the time baseline of the combined data sets.
For the semiamplitude parameter K, we used a π(K) = c for all K ∈ [0, K_{max}], where K_{max} was selected as 10 m s^{−1} because the r.m.s. of the Doppler series did not exceed 3 m s^{−1} in any of the sets. Following previous works^{40, 42}, we chose the prior for the orbital eccentricities as , where e is bound between zero (circular orbit) and 1. We set this to penalize high eccentricities while keeping the option of high e if the data strongly favours it.
We also used an informative prior for the excess white noise parameter of σ_{INS} for each instrument. Based on analyses of a sample of M dwarfs^{15}, this stellar jitter is typically very close to a value of 1 m s^{−1}. Thus, we used a prior such that the parameters were selected as μ_{σ} = σ_{σ} = 1 m s^{−1}. Uniform priors were used in all the activity coefficients C_{ξ} ∈ [−C_{ξ,max}, C_{ξ,max}]. For practical purposes, the time series of all activity indices were mean subtracted and normalized to their r.m.s. This choice allows us to select the bounds of the activity coefficients for the renormalized time series as = 3 m s^{−1}, so that adding correlation terms does not dramatically increase the r.m.s. of the Doppler time series over the initially measured r.m.s. of <3 m s^{−1} (same argument as for the prior on K). This renormalization is automatically applied by our codes at initialization.
Search for periodicities and statistically significant signals in a frequentist framework. Periodograms are plots that represent a figure of merit derived from a fit against the period of a newly proposed signal. In the case of unevenly sampled data, a very popular periodogram is the Lomb–Scargle periodogram^{43, 44} and its variants, such as the Floatingmean periodogram^{45} or the Fratio periodogram^{46}. In this work we use likelihood ratio periodograms, which represent the improvement of the likelihood statistic when adding a new sinusoidal signal to the model. Owing to intrinsic nonlinearities in the Keplerian/radial velocity modelling, optimizing the likelihood statistic is more computationally intensive than the classic Lomb–Scarglelike periodograms^{45, 47}. On the other hand, the likelihood function is a more general and well behaved statistic that, for example, allows for the optimization of the noise parameters (such as jitter and the fit correlated noise models at the signal search level). By wellbehaved we mean that it has less intrinsic variance compared with other statistics that do not include parameters for the noise such as the χ^{2} statistic. Once the maximum likelihood of a model with one additional planet is found (the highest peak in the periodogram), its FAP can then be easily computed^{14, 48}. In general, an FAP of 1% is needed to claim hints of variability, and a value below 0.1% is considered necessary to claim a statistically significant detection.
Spectroscopic data sets
New reduction of the UVES Mdwarf programme data. Between 2000 and 2008, Proxima was observed in the framework of a precision radial velocity survey of M dwarfs in search for extrasolar planets with UVES installed in the Very Large Telescope unit 2. To attain highprecision radial velocity measurements, UVES was selfcalibrated with its iodine gas absorption cell operated at a temperature of 70 °C. Image slicer number 3 was chosen, which redistributes the light from a 1″ × 1″ aperture along the chosen 0.3″wide slit. In this way, a resolving power of R = 100,000–120,000 was attained. At the selected central wavelength of 600 nm, the useful spectral range containing iodine (I_{2}) absorption lines (500−600 nm) falls entirely on the betterquality detector of the mosaic of two 4 K × 2 K CCDs. More details can be found in the several papers from the UVES survey^{9, 45, 49}.
The extracted UVES spectra include 241 observations taken through the iodine cell, three template (no iodine) shots of Proxima and three spectra of the rapidly rotating B star HR 5987 that are also taken through the iodine cell and almost consecutive to the three template shots. The B star has a smooth spectrum devoid of spectral features and it was used to calibrate the three template observations of the target. Ten of the iodine observations of Proxima were eliminated due to low exposure levels. The remaining 231 iodine shots of Proxima were taken on 77 nights, typically 3 consecutive shots per night.
The first steps in the processing of the I_{2}calibrated data consists of constructing the high signaltonoise template spectrum of the star without iodine: (1) a custom model of the UVES instrumental profile is generated on the basis of the observations of the B star by forward modelling the observations using a higherresolution (R = 700,000–1,000,000) template spectrum of the I_{2} cell obtained with the McMath Fourier Transform Spectrometer (FTS) on Kitt Peak; (2) the three template observations of Proxima are then coadded and filtered for outliers; and (3) on the basis of the instrument profile model and wavelength solution derived from the three B star observations, the template is deconvolved with our standard software^{10}. After the creation of the stellar template, the 231 iodine observations of Proxima were then run through our standard precision velocity code^{8}. The resulting standard deviation of the 231 unbinned observations is 2.58 m s^{−1}, and the standard deviation of the 77 nightly binned observations is 2.30 m s^{−1}, which already suggests an improvement compared to the 3.11 m s^{−1} reported in the original UVES survey reports^{49}. All of the UVES spectra (raw) are publicly available in their reduced form via the ESO’s archive at http://archive.eso.org/cms.html. Extracted spectra are not produced for this mode of UVES operation, but they are available upon request from the corresponding author.
HARPS GTO. The initial HARPSGuaranteed Time Observations programme was led by M. Mayor (ESO ID: 072.C0488). 19 spectra were obtained between May 2005 and July 2008. The typical integration time ranges between 450 s and 900 s.
HARPS Mdwarfs. Led by X. Bonfils and collaborators, this programme consists of ESO programmes 082.C0718 and 183.C0437. It produced 8 and 46 measurements, respectively, with integration times of 900 s in almost all cases^{50}.
HARPS highcadence. This programme consisted of two 10night runs (May 2013, and December 2013, ESO ID: 191.C0505) and was led and executed by several coauthors of this work. Proxima was observed on two runs:
(1) May 2013: 143 spectra obtained on three consecutive nights between 4 May and 7 May and 25 additional spectra between 7 May and 16 May with exposure times of 900 s.
(2) December 2013: 23 spectra obtained between 30 December and 10 January 2014 also with 900 s exposure times.
For simplicity in the presentation of the data and analyses, all HARPS data obtained before 2016 (HARPS GTO, HARPS Mdwarfs, and HARPS highcadence) are integrated in the HARPS pre2016 set. The longterm Doppler variability and sparse sampling makes the detection of the Doppler signal more challenging in such a consolidated set than, for example, separating it into subsets of contiguous nights. The latter strategy, however, necessarily requires more parameters (offsets, jitter terms, correlated noise parameters) and arbitrary choices on the sets to be used, producing strong degeneracies and aliasing ambiguities in the determination of the favoured solution (11.2 d was typically favoured, but alternative periods caused by a nontrivial window function at 13.6 d and 18.3 d were also found to be possible). The data taken in 2016 exclusively correspond to the new campaign specifically designed to address the sampling issues.
HARPS PRD campaign. The PRD campaign was executed between 18 January and 30 March 2016. Interruptions of a few nights were anticipated to allow for technical work and other timecritical observations with HARPS. Of the 60 scheduled epochs, we obtained 56 spectra for 54 nights (two spectra were obtained on two of those nights). Integration times were set to 1,200 s, and observations were always obtained at the very end of each night. All of the HARPS spectra (raw, extracted and calibrated frames) are publicly available in their reduced form via ESO’s archive at http://archive.eso.org/cms.html.
Spectroscopic indices. Stellar activity can be traced by features in the stellar spectrum. For example, changes in the lineprofile shapes (symmetry and width) have been associated with spurious Doppler shifts^{18, 51}. Chromospheric emission lines are tracers of spurious Doppler variability in the Sun and they are expected to behave similarly for other stars^{52}. We describe here the indices measured and used in our analyses.
Measurements of the mean spectral line profiles. The HARPS Data Reduction Software provides two measurements of the meanline profile shapes derived from the crosscorrelation function (CCF) of the stellar spectrum with a binary mask. These are called the bisector span (or BIS) and fullwidthathalfmaximum (or FWHM) of the CCF^{50}. For verylatetype stars like Proxima, all of the spectral lines are blended, producing a nontrivial shape of the CCF and thus the interpretation of the usual lineshape measurements is not nearly as reliable as in earliertype stars. We applied the leastsquares deconvolution (LSD) technique^{53} to obtain a more accurate estimate of the spectral mean line profile. This profile is generated from the convolution of a kernel, which is a model spectrum of line positions and intensities, with the observed spectrum. A description of our implementation of the procedure, applied specifically to crowded M dwarf spectra is described in ref. 54. The LSD profile can be interpreted as a probability function distribution that can then be characterized by its central moments^{55}. We computed the second (m_{2}) and third (m_{3}) central moments of each LSD profile for each observation. More details of these indices and how they compare with other standard HARPS crosscorrelation measurements can be found in ref. 11. To eliminate the correlation of the profile moments with the slope of the spectral energy distribution^{11}, we corrected the spectral energy distribution and blaze function to match the same spectral energy distribution of the highest signaltonoise ratio (or S/N) observation obtained with HARPS. Uncertainties were obtained using an empirical procedure as follows: we derived all the m_{2} and m_{3} measurements of the highcadence night of 7 May 2013 and fitted a polynomial to each time series. The standard deviation of the residuals to that fit was then assumed to be the expected uncertainty for a S/N ≈ 20 (at reference echelle aperture number 60), which was the typical value for that night’s observations. All other errors were then obtained by scaling this standard deviation by a factor of for each observation.
Chromospheric indices. Chromospheric emission lines are tracers of spurious Doppler variability in the Sun and they are expected to behave similarly for other stars^{52}. We describe here the indices computed and used in our analyses.
Chromospheric Ca ii H+K Sindex. We calculated the Ca ii H+K fluxes following standard procedures^{56, 57}, both the PRD data and the pre2016 data were treated the same. Uncertainties were calculated from the quadrature sum of the variance in the data used within each bandpass.
Chromospheric Hα emission. This index was measured in a similar way to the Sindices, in that we summed the fluxes in the centre of the lines, calculated to be 6,562.808 Å, this time using square bandpasses of 0.678 Å not triangular shapes, and those were normalized to the summed fluxes of two square continuum band regions surrounding each of the lines in the time series. The continuum square bandpasses were centred at 6,550.870 Å and 6,580.309 Å and had widths of 10.75 Å and 8.75 Å, respectively. Again the uncertainties were calculated from the quadrature sum of the variance of the data within the bandpasses.
Photometric data sets
ASH2. The ASH2 telescope is a 40 cm robotic telescope with a CCD camera STL11000 2.7 K × 4 K, and a fieldofview (FOV) of 54 × 82 arcmin. Observations were obtained in two narrowband filters centred on the Hα and S ii lines, respectively (Hα is centred on 656 nm, S ii is centred on 672 nm, and both filters have a Gaussianlike transmission with a FWHM of 12 nm). The telescope is at SPACEOBS (San Pedro de Atacama Celestial Explorations Observatory), at 2,450 m above sea level, located in the northern Atacama Desert in Chile. This telescope is managed and supported by the Instituto de Astrofísica de Andalucía (Spain). During the present work, only subframes with 40% of the total FOV were used, resulting in a useful FOV of 21.6 × 32.8 arcmin. Approximately 20 images in each band of 100 s of exposure time were obtained per night. In total, 66 epochs of about 100 min each were obtained during this campaign. The number of images collected per night was increased during the second part of the campaign (to about 40 images in each filter per night).
All CCD measurements were obtained by the method of synthetic aperture photometry using a 2 × 2 binning. Each CCD frame was corrected in a standard way for dark and flatfielding. Different aperture sizes were also tested to choose the best one for our observations. A number of nearby and relatively bright stars within the frames were selected as check stars to choose the best ones to be used as comparison stars. After checking their stability, C2 = HD 126625 and C8 = TYC 901030291, were selected as main comparison stars.
The basic photometric data were computed as the differences in magnitude of the S ii and Hα filters for VarX and C2X, with Var = Proxima and X = C2+C8)/2. Typical uncertainties of each individual data point are about 6.0 mmag, for both S ii and Hα filters. This usually leads to error bars of about 1.3 mmag in the determination of the mean levels of each epoch, assuming 20 points per night once occasional strong activity episodes (such as flares) are removed for the analysis of periodicities. For the analyses, these magnitudes were transformed to relative flux measurements normalized to the mean flux over the campaign.
LCOGT network. The LCOGT is an organization dedicated to timedomain astronomy^{13}. To facilitate this, LCOGT operates a homogeneous network of 1 m and 2 m telescopes on multiple sites around the world. The telescopes are controlled by a single robotic scheduler, which is capable of orchestrating complex responsive observing programmes, using the entire network to provide uninterrupted observations of any astronomical target of interest. Each site hosts between one and three telescopes, which are configured for imaging and spectroscopy. The telescopes are equipped with identical instruments and filters, which allows for network redundancy. This means that observations can be seamlessly shifted to alternate sites at any time if the scientific programme requires it, or in the event of poor weather.
Observations for the PRD campaign were obtained on the 1 m network every 24 h in the B and V bands with the Sinistro (4 K × 4 K Fairchild CCD486) cameras, which have a pixel scale of 0.38 arcsec and a FOV of 27 × 27 arcminutes. In addition, B and V observations were taken every 12 h with the SBIG (4 K × 4 K Kodak KAF6303E CCD) cameras, with a pixel scale of 0.46 arcsec and a FOV of 16 × 16 arcminutes. Exposure times ranged between 15 and 40 s and a total of 488 photometrically useful images were obtained during the campaign.
The photometric measurements were performed using aperture photometry with AstroImageJ^{58} and DEFOT^{59}. The aperture sizes were optimized during the analysis with the aim of minimizing the measurement noise. Proxima and two nonvariable comparison stars were identified in a reference image and used to construct the detrended light curves. As with the ASH2 curves, the LCOGT differential magnitudes were transformed to normalized flux to facilitate interpretation and later analyses (see Fig. 3).
Signals in time series
In this section we present a homogeneous analysis of all of the time series (Doppler, activity and photometric) presented in this Letter. In all of the periodograms, the black curve represents the search for a first signal. If one first signal is identified, then a red curve represents the search for a second signal. In the few cases where a second signal is detected, a blue curve represents the search for a third signal. The period of Proxima b is marked with a green vertical line.
Module of the window function. We first present the socalled window function of the three sets under discussion. The window function is the Fourier transform of the sampling^{60}. Its module shows the frequencies (or periods) where a signal with 0 frequency (or infinite period) would have its aliases. As shown in Extended Data Fig. 1, both the UVES and HARPS PRD campaigns have a relatively clear window function between 1 and 360 d, meaning that the peaks in periodograms can be interpreted in a very straightforward way (no aliasing ambiguities). For the UVES case, this happens because the measurements were uniformly spread over several years without severe clustering, producing only strong aliases at frequencies beating caused by the usual daily and yearly sampling (peaks at 360, 1, 0.5 and 0.33 d). The window of the PRD campaign is simpler, which is the result of a shorter time span and the uniform sampling of the campaign. On the other hand, the HARPS pre2016 window function (Extended Data Fig. 1b) contains numerous peaks between 1 and 360 d. This means that signals (for example, activity) in the range of a few hundred days will inject severe interference in the period domain of interest, and explains why this set is where the Doppler signal at 11.2 d is detected with a lower confidence (see Extended Data Fig. 2).
Radial velocities. Here we present likelihoodratio periodogram searches for signals in the three Doppler time series separately (PRD, HARPS pre2016 and UVES). They are analysed in the same way as the activity indices to enable direct visual comparison. They differ from the ones presented in the main Letter in the sense that they do not include MA terms and the signals are modelled as pure sinusoids to mirror the analysis of the other time series as close as possible. The resulting periodograms are shown in Extended Data Fig. 2. A signal at 11.2 d was close to detection using UVES data only. However, let us note that the signal was not clearly detectable using the Doppler measurements as provided by the UVES survey^{45}, and it only became obvious when new Doppler measurements were rederived using uptodate iodine codes (see Methods subsection ‘New reduction of the UVES Mdwarf programme data’). The signal is weaker in the HARPS pre2016 data set, but it still appears as a possible second signal after modelling the longerterm variability with a Keplerian at 200 d. Subsets of the HARPS pre2106 data taken on consecutive nights (for example, HARPS highcadence runs) also show strong evidence of the same signal. However splitting the data into subsets adds substantial complexity to the analysis and the results become quite sensitive to subjective choices (how to split the data and how to weight each subset). The combination of UVES with all the HARPS pre2016 (Fig. 1a) already produced an FAP of 1%, but a dedicated campaign was deemed necessary given the caveats with the sampling and activity related variability. The HARPS PRD campaign unambiguously identifies a signal with the same period of approximately 11.2 d. As discussed earlier, the combination of all the data results in a very high significance (FAP < 10^{−7}), which implies that the period, but also the amplitude and phase are consistent in all three sets.
Photometry signals and calculation of the FF′ index. The nightly average of the four photometric series was computed after removing the measurements clearly contaminated by flares (see Fig. 3). This produces 43 LCOGT epochs in the B and V bands (80 nights), and 66 ASH2 epochs in both S ii and Hα bands (100 nights covered). The precision of each epoch was estimated using the internal dispersion within a given night. All four photometric series show evidence of a longperiod signal that is compatible with a photometric cycle at 83 d (probably the rotation) reported before^{3}. See periodograms in Extended Data Fig. 3.
In the presence of spots, it has been proposed that spurious variability should be linearly correlated with the value of the normalized flux of the star F, the derivative of the flux F′, and the product of FF′ (ref. 61) in what is sometimes called the FF′ model. To include the photometry in the analysis of the Doppler data, we used the best model fit of the highestquality light curve (AHS2 S ii, which has the lowest postfit scatter) to estimate F, F′ and FF′ at the instant of each PRD observation. The relation of F, F′ and FF′ to the Doppler variability is investigated later in the Bayesian analysis of the correlations.
Width of the mean spectral line as measured by m_{2}. The m_{2} measurement contains a strong variability that closely mirrors the measurements from the photometric time series (see Fig. 3). As in the photometry, the rotation period and its first harmonic (approximately 40 d) are clearly detected in the PRD campaign (see Extended Data Fig. 4). This apparently good match needs to be verified on other stars as it might become a strong diagnostic for stellar activity in M stars. The analysis of the HARPS pre2016 data also shows very strongly that m_{2} is tracing the photometric rotation period of 83 d. The modelling of this HARPS pre2016 requires a second sinusoid with P_{2 }≈_{ }85 d, which is peculiar given how close it is to P_{1}. We suspect this is caused by photospheric features on the surface changing over time.
Asymmetry of the mean spectral lines as monitored by m_{3}. The periodogram analysis of m_{3} of the PRD run suggests a signal at 24 d, which is close to twice the Doppler signal of the planet candidate (see Extended Data Fig. 5). However, line asymmetries are expected to be directly correlated with Doppler signals, not at twice nor integer multiples of the Doppler period. In addition, the peak has an FAP of 5%, which makes it not significantly different from white noise. When looking at the HARPS pre2016 data, strong beating is observed at 179 and 360 d, which is probably caused by a poorly sampled signal at that period or longer (possibly a magnetic cycle), or some residual systematic effect (possibly contamination by tellurics). In summary, m_{3} does not show evidence of any stable signal in the range of interest.
Signal searches in the Sindex. Although Hα^{51} and other lines such as the sodium doublet (NaD1 and NaD2)^{62} have been shown to be the best tracers for activity on M dwarfs, analysing the time series of the Sindex is also useful because of its historical use in the longterm monitoring of mainsequence stars^{63}. In Extended Data Fig. 6 we show the likelihood ratio periodograms for the Sindices of the HARPS pre2016 and PRD time series. As can be seen, no signals were found around the 11 d period of the radial velocity signal, however two peaks were found close the 1% FAP threshold with periods of approximately 170 and 340 d. To further test the reality of these possible signals, we performed a Lomb–Scargle periodogram analysis^{44} of the combined PRD and pre2016 HARPS data. This test resulted in the marginal recovery of both the 170 and 340 d peaks seen in the likelihood periodograms, with no emerging peaks around the proposed 11 d Doppler signal. The Lomb–Scargle tests revealed some weak evidence for a signal at much lower periods, around 7 and 30 d.
Given that there is evidence for substantial peaks close to periods of 1 yr, its first harmonic and the lunar period, we also analysed the window function of the time series to check if there was evidence that these peaks are artefacts from the combination of the window function pattern interfering with a real longperiod activity signal in the data. The dominant power in the window function is found to increase at periods greater than 100 d, with a forest of strong peaks found in that domain, in comparison to that of sub100 d periods, which is very flat, representing the noise floor of the time series. This indicates that there are likely to be strong interference patterns from the sampling in this region, and that the signal in the radial velocity data are also not due to the sampling of the data. A similar study in the context of the HARPS M dwarf programme was also done on Proxima^{62}. They compared several indices and finally decided to use the intensity of the chromospheric sodium doublet lines. They did not report any notable period at the time, but we suspect this was due to using fewer measurements and not removing the frequent flaring events from the series, which also requires the compilation of a number of observations to reliably identify the outliers caused by flares.
Signal searches in Hα emission. Our likelihoodratio periodograms for Hα (Extended Data Fig. 7) only show nonsignificant peaks in the 30–40 d period range. It is important to note that the analyses described above have been performed on multiple versions of the data set, in the sense that we analysed the full data set without removing measurements affected by flaring, then proceeded to reanalyse the activities by dropping data clearly following the flaring periods that Proxima went through when we observed the star. This allowed us to better understand the impact that flares and outliers have on signal interference in the activity indices. Although the distribution of the peaks in periodograms changes somewhat depending on how stringent the cuts are, no emerging peaks were seen close to an 11 d period. Concerning UVES Hα measurements, our likelihoodratio periodogram did not detect any statistically significant signal.
Further tests on the signal. It has been shown^{64} that at least some of the ultraprecise photometric time series measured by the CoRot and Kepler space missions do not have a necessary property to be represented by a Fourier expansion: the underlying function, from which the observations are a sample, must be analytic. An algorithm introduced in ref. 64 can test this property and was applied to the PRD data. The result is that, contrary to the light curves aforementioned, claims that the underlying function is nonanalytic does not hold with the information available. Although the null hypothesis cannot be definitively rejected, at least until more data are gathered, our results are consistent with the hypothesis that a harmonic component is present in the Doppler time series.
Flares and radial velocities. Among the highcadence data from May 2013 with HARPS, two strong flares are fully recorded. During these events, all of the chromospheric lines become prominent in emission, Hα being the one that best traces the characteristic time dependence of flares observed on other stars and the Sun. The spectrum and impact of flares on the radial velocities will be described elsewhere in detail. Relevant to this study, we show that the typical flares on Proxima do not produce correlated Doppler shifts (Extended Data Fig. 8). This justifies the removal of obvious flaring events when investigating signals and correlations in the activity indices.
Complete model and Bayesian analysis of the activity coefficients
A global analysis including all of the radial velocities and indices was performed to verify that the inclusion of correlations would reduce the model probability below the detection thresholds. Equivalently, the Doppler semiamplitude would become consistent with zero if the Doppler signal was to be described by a linear correlation term. Extended Data Fig. 9 shows the marginalized distributions of linear correlation coefficients with the Doppler semiamplitude K. Each subset is treated as a separate instrument and has its own zero point, jitter and MA term (coefficient) and its own activity coefficients. In the final model, the timescales of the MA terms are fixed to around 10 d because they were not constrained within the prior bounds, thus compromising the convergence of the chains. The sets under consideration are:
(1) UVES. 70 radial velocity measurements and corresponding Hα emission measurements.
(2) HARPS pre2016. 90 radial velocity measurements obtained between 2002 and 2014 by several programmes and corresponding spectroscopic indices: m_{2}, m_{3}, Sindex and the intensities of the Hα and He i lines as measured on each spectrum.
(3) HARPS PRD. 54 Doppler measurements obtained between 18 January–31 March 2016, and the same spectroscopic indices as for the HARPS pre2016. The values of the F, F′ and FF′ indices were obtained by evaluating the best fit model to the ASH2 S ii photometric series at the HARPS epochs (see Methods subsection ‘Photometry signals and calculation of the FF′ index’).
An activity index is correlated with the radial velocity measurements in a given set if the zero value of its activity coefficient is excluded from the 99% credibility interval. Extended Data Fig. 9 shows the equiprobability contours that contain 50%, 95%, and 99% of the probability density around the mean estimate, and the corresponding 1σ uncertainties in red. Only the F′ index (the time derivative of the photometric variability) is substantially different from 0 at high confidence (Extended Data Fig. 9m). Linking this correlation to a physical process requires further investigation. To ensure that such correlations are causally related, one needs a model of the process causing the signal in both the radial velocity and the index, and in the case of the photometry one would need to simultaneously cover more stellar photometric periods to verify that the relation holds over time. Extended Data Table 1 contains a summary of all of the free parameters in the model, including the activity coefficients for each data set.
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Acknowledgements
We thank E. Gerlach, R. Street and U. Seemann for their support to the science preparations. We thank P. Micakovic, M. M. Mutter (QMUL), R. Ivison, G. Hussain, I. Saviane, O. Sandu, L. L. Christensen, R. Hook and the personnel at La Silla (ESO) for making the PRD campaign possible. The authors acknowledge support from the following funding grants: Leverhulme Trust/UK RPG2014281 (H.R.A.J., G.A.E. and M.T.); MINECO/Spain AYA201454348C31R (P.J.A., C.R.L., Z.M.B. and E.R.); MINECO/Spain ESP201454362P (M.J.L.G.); MINECO/Spain AYA201456637C21P (J.L.O. and N.M.); J.A./Spain 2012FQM1776 (J.L.O. and N.M.); CATABasal/Chile PB06 Conicyt (J.S.J.); Fondecyt/Chile project #1161218 (J.S.J.); STFC/UK ST/M001008/1 (R.P.N., G.A.L.C. and G.A.E.); STFC/UK ST/L000776/1 (J.B.); ERC/EU Starting Grant #279347 (A.R., L.F.S. and S.V.J.); DFG/Germany Research Grants RE 1664/92 (A.R.); RE 1664/121 (M.Z.); DFG/Germany Colloborative Research Center 963 (C.J.M. and S.D.); DFG/Germany Research Training Group 1351 (L.F.S.); and NSF/USA grant AST1313075 (M.E.). Study based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programmes 096.C0082 and 191.C0505. Observations were obtained with ASH2, which is supported by the Instituto de Astrofísica de Andalucía and Astroimagen. This work makes use of observations from the LCOGT network. We acknowledge the effort of the UVES/Mdwarf and the HARPS/Geneva teams, who obtained a substantial amount of the data used in this work.
Author information
Affiliations

School of Physics and Astronomy, Queen Mary University of London, 327 Mile End Road, London E1 4NS, UK
 Guillem AngladaEscudé,
 Gavin A. L. Coleman,
 Richard P. Nelson,
 SijmeJan Paardekooper &
 John P. Strachan

Instituto de Astrofísica de Andalucía – Consejo Superior de Investigaciones Científicas, Glorieta de la Astronomía S/N, E18008 Granada, Spain
 Pedro J. Amado,
 Zaira M. Berdiñas,
 Marίa J. LópezGonzález,
 Nicolás Morales,
 José L. Ortiz,
 Eloy Rodríguez &
 Cristina RodrίguezLópez

Department of Physical Sciences, Open University, Walton Hall, Milton Keynes MK7 6AA, UK
 John Barnes

Carnegie Institution of Washington, Department of Terrestrial Magnetism, 5241 Broad Branch Road NW, Washington DC 20015, USA
 R. Paul Butler

Astroimagen, C. Abad y Lasierra, 58 Bis, 62, 07800 Ibiza, Spain
 Ignacio de la Cueva

Institut für Astrophysik, GeorgAugustUniversität Göttingen, FriedrichHundPlatz 1, 37077 Göttingen, Germany
 Stefan Dreizler,
 Benjamin Giesers,
 Sandra V. Jeffers,
 Christopher J. Marvin,
 Ansgar Reiners,
 Luis F. Sarmiento &
 Mathias Zechmeister

McDonald Observatory, the University of Texas at Austin, 2515 Speedway, C1400, Austin, Texas 78712, USA
 Michael Endl

Departamento de Astronomía, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile
 James S. Jenkins

Centre for Astrophysics Research, Science & Technology Research Institute, University of Hertfordshire, Hatfield AL10 9AB, UK
 Hugh R. A. Jones &
 Mikko Tuomi

Warsaw University Observatory, Aleje Ujazdowskie 4, Warszawa, Poland
 Marcin Kiraga

MaxPlanckInstitut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
 Martin Kürster

Laboratoire Univers et Particules de Montpellier, Université de Montpellier, Place E. Bataillon—CC 72, 34095 Montpellier Cédex 05, France
 Julien Morin

Department of Earth and Planetary Sciences, Weizmann Institute of Science, 234 Herzl Street, Rehovot 76100, Israel
 Aviv Ofir

Astronomisches RechenInstitut, Mönchhofstrasse 12–14, 69120 Heidelberg, Germany
 Yiannis Tsapras
Contributions
In the author list, after G.A.E., the authors are listed in alphabetical order. G.A.E. led the PRD campaign, observing proposals and organized the manuscript. P.J.A. led observing proposals and organized and supported the Instituto de Astrofisica de Andalucía team through research grants. M.T. obtained the early signal detections and most of the Bayesian analyses. J.S.J., J.B., Z.M.B. and H.R.A.J. participated in the analyses and obtained activity measurements. Z.M.B. also led observing proposals. H.R.A.J. funded several coauthors via research grants. M. Kuerster and M.E. provided the extracted UVES spectra, and R.P.B. rederived radial velocity measurements. C.R.L. coordinated photometric followup campaigns. E.R. led the ASH2 team and related reductions (M.J.L.G., I.d.l.C., J.L.O. and N.M.). Y.T. led the LCOGT proposals, campaign and reductions. M.Z. obtained observations and performed analyses on HARPS and UVES spectra. A.O. analysed time series and transit searches. J.M., S.V.J. and A.R. analysed stellar activity data. A.R. funded several coauthors via research grants. R.P.N., G.A.L.C., S.J.P., S.D. and B.G. did dynamical studies and studied the planet formation context. M. Kiraga provided early access to time series from the ASAS survey. C.J.M. and L.F.S. participated in the HARPS campaigns. All authors contributed to the preparation of observing proposals and the manuscript.
Competing financial interests
The authors declare no competing financial interests.
Reviewer Information
Nature thanks A. Hatzes and D. Queloz for their contribution to the peer review of this work.
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Extended data figures and tables
Extended Data Figures
 Extended Data Figure 1: Window function. (201 KB)
a–c, Window function of the UVES (a), HARPS pre2016 (b) and HARPS PRD (c) data sets. The same window function applies to the time series of Doppler and activity data. Peaks in the window function are periods at which aliases of infinite period signals would be expected. The green vertical lines mark the period of the planet candidate at 11.2 d.
 Extended Data Figure 2: Signal searches on independent radial velocity data sets. (307 KB)
a–c, Likelihoodratio periodograms searches on the radial velocity (RV) measurements of the UVES (a), HARPS pre2016 (b) and HARPS PRD (c) subsets. The periodogram with all three sets combined is shown in Fig. 1. The black and red lines represent the searches for the first and second signals, respectively. The green vertical lines mark the period of the planet candidate at 11.2 d.
 Extended Data Figure 3: Signal searches on the photometry. (348 KB)
a–d, Likelihoodratio periodograms searches for signals in each photometric ASH2 photometric band (a, b) and LCOGT bands (c, d). The two sinusoid fits to the ASH2 S ii series (P_{1} = 84 d, P_{2} = 39.1 d) are used later to construct the FF′ model to test for correlations of the photometry with the radial velocity data. The black, red and blue lines represent the search for the first, second and third signal respectively. The green vertical lines mark the period of the planet candidate at 11.2 d.
 Extended Data Figure 4: Signal searches on the width of the spectral lines. (271 KB)
a, b, Likelihoodratio periodogram searches on the width of the mean spectral line as measured by m_{2} for the HARPS pre2016 (a) and HARPS PRD data (b). The signals in the HARPS pre2016 data are comparable to the photometric period reported in the literature and the variability in the HARPS PRD run compares quite well to the photometric variability. The black, red and blue lines represent the search for the first, second and third signal, respectively. The green vertical lines mark the period of the planet candidate at 11.2 d.
 Extended Data Figure 5: Signal searches on the asymmetry of the spectral lines. (188 KB)
a, b, Likelihoodratio periodogram searches on the line asymmetry as measured by m_{3} from the HARPS pre2016 (a) and HARPS PRD (b) data sets. Signal beating at around 1 yr and 0.5 yr is detected in the HARPS pre2016 data, which is possibly related to instrumental systematic effects or telluric contamination. No signals are detected above the 1% threshold in the HARPS PRD campaign. The black and red lines represent the search for the first and second signals respectively. The green vertical lines mark the period of the planet candidate at 11.2 d.
 Extended Data Figure 6: Signal searches on the chromospheric Sindex. (155 KB)
a, b, Likelihoodratio periodogram of the Sindex from the HARPS pre2016 (a) and HARPS PRD (b) campaigns. No signals were detected above the 1% threshold. The green vertical lines mark the period of the planet candidate at 11.2 d.
 Extended Data Figure 7: Signal searches on the spectroscopic Hα index. (232 KB)
a–c, Likelihoodratio periodogram searches of Hα intensity from the UVES (a), HARPS pre2016 (b) and HARPS PRD (c) campaigns. No signals were detected above the 1% threshold. The green vertical lines mark the period of the planet candidate at 11.2 d.
 Extended Data Figure 8: Radial velocities and chromospheric emission during a flare. (301 KB)
a–d, Radial velocities (a) and equivalent width measurements of the Hα (b), Na doublet lines (c) and the Sindex (d) as a function of time during a flare that occurred the night of 5 May 2013. The time axis is days since jd = 245417.0 d. No trace of the flare is observed in the radial velocities. Error bars in the radial velocities correspond to 1σ errors. The formal 1σ errors in the equivalent width measurements are comparable to the size of the points.
 Extended Data Figure 9: Probability distributions for the activity coefficients versus the signal amplitude. (226 KB)
a–n, Marginalized posterior densities of the activity coefficients versus the semiamplitude of the signal for UVES (a), HARPS pre2016 (b–f), HARPS PRD campaign (g–k) and the photometric FF′ indices for the PRD campaign only (l–n). Each panel shows equiprobability contours containing 50%, 95% and 99% of the probability density around the mean estimate, and the corresponding standard deviation of the marginalized distribution (1σ) in red. The blue bar shows the zero value of each activity coefficient. Only C_{F′} is found to be substantially different from zero.
Extended Data Tables
Supplementary information
Zip files
 Supplementary Data (62 KB)
This zipped file contains the timeseries used in the paper. All timeseries are given as plain ASCII/CSV files (columns separated by commas) and follow the same format. See the README file within the zip folder for details.
Comments
Additional data

Extended Data Figure 1: Window function.Hover over figure to zoom

Extended Data Figure 2: Signal searches on independent radial velocity data sets.Hover over figure to zoom

Extended Data Figure 3: Signal searches on the photometry.Hover over figure to zoom

Extended Data Figure 4: Signal searches on the width of the spectral lines.Hover over figure to zoom

Extended Data Figure 5: Signal searches on the asymmetry of the spectral lines.Hover over figure to zoom

Extended Data Figure 6: Signal searches on the chromospheric Sindex.Hover over figure to zoom

Extended Data Figure 7: Signal searches on the spectroscopic Hα index.Hover over figure to zoom

Extended Data Figure 8: Radial velocities and chromospheric emission during a flare.Hover over figure to zoom

Extended Data Figure 9: Probability distributions for the activity coefficients versus the signal amplitude.Hover over figure to zoom

Extended Data Table 1: Complete set of model parametersHover over figure to zoom
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The authors would like to acknowledge useful discussions and quantitative feedback provided by Dr. Javier Pascual Granado and Prof. Rafael Garrido at IAA/CSIC on the mathematical properties of timeseries under the section "Methods. Further tests on the signal" during the preparation of the manus cript.