A low-mass planet candidate orbiting Proxima Centauri at a distance of 1.5 AU, Hacker News

and orbital periods out to days. It was because of the RV technique that the temperate, low-mass planet Proxima b, orbiting at a distance of ∼0. 0006 AU, was discovered (**********************************

9. M dwarfs have high occurrence rates of small planets (1.0 to 2.8R

⊕, 3.5 times more than main-sequence FGK stars (

**********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************); Therefore, systems with multiple, small, low-mass planets are expected to be common around them. With their RV dataset, including measurements with the HARPS (High Accuracy Radial Velocity Planet Searcher) and UVES (Ultraviolet and Visual Echelle Spectrograph) spectrographs, Anglada-Escudéet al

. ( ()

(9) ********** () ************************************ could not rule out the presence of an additional super-Earth in the system with orbital periods longer than that of Proxima b and with Doppler semi-amplitude smaller than 3 ms (1) . For the sake of an independent confirmation of the existence of Proxima b and to search for additional low-mass companions, Damasso and Del Sordo (**************************************) analyzed the same RV measurements using a model that treats the imprint of the stellar activity in a different way than the method adopted in (9

. This analysis uncovered correlated variability in the RV data ascribable to the stellar activity and modulated over the known stellar rotation period. By treating the stellar activity signal with a quasi-periodic model, they could not unambiguously detect a low-mass companion with an orbital period longer than that of Proxima b. The search for additional planets in this system did not stop, and it was at the origin of the Red Dots (RD) initiative (********************************** https: // reddots. space /), which also focused on other nearby stars, and recently led to the discovery of a candidate super-Earth orbiting Barnard’s star close to the snowline ( () ************** 26). Because of the RD campaign, additional RVs of Proxima were collected with the HARPS spectrograph, extending the time span by 000592 days with respect to the dataset analyzed in ( ()(9) ********** (). ***************************************

In this work, we present the results from the analysis of the extended RV dataset carried out within the framework outlined in () and aimed at searching for additional low-mass planetary companions to Proxima. The conclusions of this study are supported by the analysis of spectroscopic activity diagnostics and of a photometric light curve with a baseline longer than the time span of the RV dataset. (**************************************** (***************************************** (MATERIALS AND METHODS)

RV extraction

The RVs from HARPS spectra were extracted using the TERRA (Template-Enhanced Radial velocity Re-analysis Application (pipeline)

and represent an updated dataset with respect to that published in (

************************************************************ ()(9) **********. As in previous works, all observations taken before (various programs) and after [including the Pale Red Dot 2016 (9) and Red Dots 2017 campaigns] the HARPS fiber upgrade in May 2015 were treated as coming from a separate instrument to account for the reported offset introduced by the fiber change. HARPS / ESO (European Southern Observatory) reduced spectra have a known “residual” systematic effect with a ~ 1-year periodicity caused by a small pixel size difference every 551 pixels on the detector, often called the “stitching problem,” coupled to the barycentric motion of the Earth, which implies that some spectral lines go across these pixels (

. As detailed in (

), we masked ± 45 pixels around each of these 549 stitches and rerun the RV velocity measurements for both pre- and post-fiber upgrade datasets. Despite the fact that this removes about (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************% of the useful Doppler pixels, a bit higher random noise is desirable compared to systematic excursions beating with the yearly sampling. All barycentric corrections were applied as in ( (******************), and secular geometric acceleration was also removed from the final RVs using the known astrometry of the star (DR2). Because we are interested in testing for the presence of longer period signals, we computed nightly weighted means and added 1 ms – 1in quadrature to the formal errors given by the pipeline to account for some unrealistically small uncertainties in some high signal-to-noise (S / N) spectra.

The RV dataset extracted from the UVES spectra, collected between and (*************************************************************************************************************************************************************************************************************************************************************************************************************************************, is an improved version of that used in ( (**************** (9) ****************

), obtained after changes have been applied to the pipeline for processing all the spectra homogeneously. We reanalyzed the entire dataset starting from the raw images and using the associated calibration frames. We reduced the raw images to one-dimensional spectra with our custom reduction package and generated velocities from our precision velocity package. After this full reduction, the root mean square (RMS) of the nightly binned RVs of Proxima has been reduced from 2. (to 2.) *********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (m / s)

*************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

. The final dataset that we analyzed consists of (HARPS RVs) before the fiber upgrade) and nightly binned UVES RVs, with a time span of (days.) ************************************** (******************************************************************** Photometry ********************************************************************

In this work, we used a long time span dataset of ASAS -3 and ASAS-4 V-band observations ( () ************** 30

. The light curve was an extension of that shown in ( Fig. 3

) (

), with a time span increased by 1343 days. We used magnitudes measured with the photometric aperture-labeled MAG2 (appropriate to brightness and crowding of the field) in the ASAS data file and considered only high-quality data (flags A and B). Last, we binned the data on a nightly basis. Their dispersion is 0. 046 mag, and the median uncertainty is 0.0 049 mag. The data are listed in table S2. (

Spectroscopic activity diagnostics (******************************************************************************************** (In addition to photometry, we inspected activity indicators extracted from spectra as the full width at half maximum ( only for HARPS) and those based on the chromospheric CaII H K and Hα emission lines. Because the S / N corresponding to CaII H K (as measured from HARPS spectra) is generally less than 1 (median value, 0.5), we selected only the Hα index for a reliable analysis. A key point to address to search for long-term, periodic modulations due to activity (to be eventually compared with any significant long-period signal found in the RVs) is to deal with indexes extracted homogeneously both from the UVES and HARPS spectra, covering the whole time span of the observations. To do so, we used the UVES activity indexes already published in (9) **************, and then we extracted the Hα index from HARPS spectra following the recipe used in (

9

[astro-ph.EP] ************************************** by adapting the code ACTIN). The time series of the Hα index measured from HARPS spectra is listed in table S3.We excluded outliers potentially due to powerful flares through a 3σ clipping of the data, resulting in two epochs removed from the UVES dataset and three epochs removed from the HARPS dataset, therefore with a very limited impact on the analysis. Then, we binned the Hα index extracted from the HARPS spectra on a nightly basis. Last, because there is not one-to-one correspondence between the Hα index and RV datasets (some of the latter missing because the corresponding spectra were discarded by the TERRA pipeline), we searched for and selected those epochs that are in common between the two time series to perform a correct correlation study (this caused 10 RVs to be excluded from the correlation analysis).

Although we used the same recipe fo r both UVES and HARPS, we noted that an offset between the two datasets still exists by comparing the Hα values ​​taken at a similar epoch (BJD=2, (**************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************, 234) and at two consecutive epochs (HARPS, BJD=2,

, 813; UVES, BJD=2, 482, 1306). It is reasonable to expect an instrumental offset when combining data extracted with the same method from spectra collected with different instruments. To produce a complete UVES HARPS dataset free from offset, we subtracted the average value 1. from the UVES Hα index dataset, as determined from measurements at the epochs indicated above. (****************************************

******************************** (RESULTS

We analyzed the enlarged RV dataset spanning ~ 19 years by performing Monte Carlo (MC) analyzes in a Bayesian framework using models based on Gaussian process (GP) regression, as described in detail in the Supplementary Materials. Initially, our model included only the orbital equation of the planet Proxima b combined with the GP term describing the stellar activity contribution to the RVs. The best-fit values ​​of the one-planet model parameters are shown in table S1. Then, we subtracted from the complete RV time series the best-fit solution for planet b (eccentric orbit), a secular acceleration term, and the RV offsets (thus, without removing any activity-related signal), and we analyzed the generalized Lomb -Scargle (GLS) periodogram (of the RV residuals. We found a clear peak with the highest power atP

∼ days, with a false alarm probability of 0. (****************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************% as derived by a bootstrap (with replacement) analysis of 13, (randomly generated RV samples)

Fig. 1 (**********************************************************************************************************************************

    

(=days. Middle and bottom: GLS and BGLS periodograms of the residuals. For the GLS periodogram, we calculated the false alarm probability thresholds, indicated by the dashed horizontal lines, through a bootstrap analysis. For clarity, the inset plot shows a zoom-in view of the low-frequency region, with the highest peak atP=2000 days marked by a vertical dotted line. The second highest peak in both periodograms occurs atP

~ days, which is the 1-year alias of the candidate planetary signal. Bottom: Window function of the RV time series. The inset plot shows a zoom-in view of the low-frequency region, with the periodP=days marked by a dotted vertical line.

“data-hide-link-title=” 0 “data-icon-position=” “href=” https://advances.sciencemag.org/content/advances/6/3/eaax / / F1.large.jpg? Width=the height=600 & carousel=1 “rel=” gallery-fragment-images –“title=” Frequency analysis of the RV residuals. Top: RV residuals after subtracting from the original dataset the spectroscopic signal induced by Proxima b, the instrumental offsets, and a secular acceleration term, as fitted by a global model including a GP quasi-periodic term and only the eccentric orbital equation for Proxima b . The residuals still include a stellar activity term. The red line corresponds to the best-fit sinusoid as derived with GLS (P=********************************************************************************************************************************************************************************************************************************************************************************************************************* days). Middle and bottom: GLS and BGLS periodograms of the residuals. For the GLS periodogram, we calculated the false alarm probability thresholds, indicated by the dashed horizontal lines, through a bootstrap analysis. For clarity, the inset plot shows a zoom-in view of the low-frequency region, with the highest peak at P=2000 days marked by a vertical dotted line. The second highest peak in both periodograms occurs at P ~ days, which is the 1-year alias of the candidate planetary signal. Bottom: Window function of the RV time series. The inset plot shows a zoom-in view of the low-frequency region, with the period P=days marked by a dotted vertical line. “>

          (Fig. . 1 Frequency analysis of the RV residuals.Top: RV residuals after subtracting from the original dataset the spectroscopic signal induced by Proxima b, the instrumental offsets, and a secular acceleration term, as fitted by a global model including a GP quasi-periodic term and only the eccentric orbital equation for Proxima b. The residuals still include a stellar activity term. The red line corresponds to the best-fit sinusoid as derived with GLS (P

(=days. Middle and bottom: GLS and BGLS periodograms of the residuals. For the GLS periodogram, we calculated the false alarm probability thresholds, indicated by the dashed horizontal lines, through a bootstrap analysis. For clarity, the inset plot shows a zoom-in view of the low-frequency region, with the highest peak atP=2000 days marked by a vertical dotted line. The second highest peak in both periodograms occurs atP

~ days, which is the 1-year alias of the candidate planetary signal. Bottom: Window function of the RV time series. The inset plot shows a zoom-in view of the low-frequency region, with the periodP=days marked by a dotted vertical line. (************************************************************************************************************** (****************************************************************************************************************

Evolution of the long-period signal o ver time (************************************************************************************************************ before investigating the nature of this signal in detail, we checked its evolution and stability over time by analyzing the stacked Bayesian GLS (SBGLS) () periodogram o f the one-planet RV residuals (we show the BGLS periodogram of the full dataset in Fig. 1. SBGLS (available online at the Web page (https://anneliesmortier.wordpress.com/sbgls/) allows us to check the variability and incoherence with time of a signal — both properties expected to be detected if it is due to the stellar activity — as it calculates BGLS periodograms for subsets of RV data by adding sequentially one data point per time, until the whole dataset is analyzed. We show the SBGLS periodogram for the RV residuals in Fig. 2 . It can be seen that the long-period signal is emerging after ~ RV measurements. We note that the signal appearing atP

~ 307 days is the 1-year alias of the ~ – day signal, whose significance decreases after(N) ~ RV measurements, while that of the ~ – day signal increases. From the logarithm of the posterior probabilities, we can calculate the relative probability of the two peaks in the BGLS periodogram for the full RV dataset. We find that the period of the candidate planet signal is at least ∼ 16 (********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (times (log [P₁/P₂] ∼) more probable than the following highest peak. The bottom panel ofFig. 2 shows the evolution, with the increasing number of RVs over time, of the values ​​of the orbital period, semi-amplitude, and phase of the candidate planetary signal, obtained from a least squares fit (we remark that the stellar activity contribution has not been removed from these RVs). We see, in particular, that the semi-amplitude and phase of the long-period signal remain constant within the error bars, indicating that it is stable and coherent over time forN>(measurements.) ******************************************************************************************************************************************************

    

Stability and coherence of the long-period signal in the RVs. (************************************************************************************************************************ Top: SBGLS periodograms of the RV residuals (same data as in************************************************************************************** (Fig. 1) ******************************************* Middle East: Zoomed-in view of the top plot, starting from the th RV measurement. The vertical dashed line marks the orbital periodP

~ days of the candidate planet to guide the eye. Bottom: Evolution of the orbital period, semi-amplitude, and phase of the candidate planet signal with increasing number of RV points, as calculated by GLS through a least squares fit. (********************************************************************************************************

“data-hide-link-title=” 0 “data-icon-position=” “href=” https://advances.sciencemag.org/content/advances/6/3/eaax79425 / F2.large.jpg? Width=& height=& carousel=1 “rel=”gallery-fragment-images – “title=” Stability and coherence of the long-period signal in the RVs. Top: SBGLS periodograms of the RV residuals (same data as in Fig. 1). Middle: Zoomed-in view of the top plot, starting from the th RV measurement. The vertical dashed line marks the orbital period P ~ 1900 days of the candidate planet to guide the eye. Bottom: Evolution of the orbital period, semi-amplitude, and phase of the candidate planet signal with increasing number of RV points, as calculated by GLS through a least squares fit. “>(**************************************************************************************************** [𝒰(20–6500) days] **********************************

**********************************            Fig **************** 2 (Stability and coherence of the long-period signal in the RVs.) ************************************* Top: SBGLS periodograms of the RV residuals (same data as in (Fig. 1) . Middle: Zoomed-in view of the top plot, starting from the th RV measurement. The vertical dashed line marks the orbital periodP

~ days of the candidate planet to guide the eye. Bottom: Evolution of the orbital period, semi-amplitude, and phase of the candidate planet signal with increasing number of RV points, as calculated by GLS through a least squares fit. (**************************************************************************************************************

(******************************************************************************************************************************

RV modeling with activity and planetary signals

******************************************************************************************************************** We inves tigated the nature of this signal by introducing a second orbital equation in the global model (GP Keplerians) and running a new analysis. As a first exploratory run, we adopted large uniform priors on the orbital period of the second Keplerian ( (to) ****************************************************************************************************************************************************************************************************************************************************************************************************************************** days, the upper limit corresponding nearly to the time span of the data) and on the GP hyperparameters λ (0 to (*****************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************, days (and θ (************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************ (to) days), representing the evolutionary timescale of the stellar active regions and the stellar rotation period, respectively. This analysis showed that the majority of the samples piled up around the orbital periodP(∼ days (fig. S2), confirming the results of the GLS / BGLS periodograms; ie, the existence in the data of a second coherent signal as shown by the existence of well-localized solutions for the time of inferior conjunctionTc, conj

, each spaced by ~ 1907 days. The best-fit semi-amplitude of the additional Keplerian orbit isK

(c) **************** (.31.3 ms) – 1. By assuming that this signal is real and can be modeled reliably by a Keplerian, we inferred the final set of best-fit values ​​of the fitted and derived system parameters through a second run of MC analyzes, this time using restricted intervals for some of the priors (which are still treated as uniform / noninformative) and testing two different models (ie, both planets on circular or eccentric orbits). We geteb) *************************** (=****************************** (0.) **********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

********** – (0.) ************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************* () ******************************************** (0.)

************************************************************************( e

************ b**********

************** c) **************************=(****************************** (0.)–********************************** (0.)

************************

****************

.

**********************************************************

(e

(c) **************** (

31); Thus, the results do not allow us to constrain the eccentricities. Moreover, the comparison of the Bayesian evidences do not favor the eccentric model [ ln (Z_circ/Z_ecc)∼ 0.8]; Therefore, the orbits can be assumed being circular according to our data. However, we note that the median of the posteriors fore

bequals the maximum a posteriori value, suggesting a real nonzero eccentricity for planet b, and that our estimatee

_b

=0. is not too different fromb (=0.) ************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************ given in (

************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** () ****************

. The posterior distributions of the free parameters of our model with two circular planets are shown in fig. S3. Our adopted best-fit solution is summarized in (Table 1) **********************************************, andFig. 3 Shows the phase-folded RV curves for planet b and candidate planet c. We note that our fit resulted in small values ​​of the uncorrelated jitter for each instrument, and instrumental offsets are consistent with zero. The results for the model with two planets on eccentric orbits are summarized in table S1. According to the adopted model, the candidate planet Proxima c has orbital period

******************************P.c

****************

(

**************************** () **************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (**********************-

**************** 200**********************************

(****************************** (**********************************

(****************************************days (corresponding to more than three complete orbits over the time span of the observations), semi-major axis a

a ********** c=1. (± 0.) ****************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** AU, minimum mass ************ m

csin (i

(c) ***************** (=5.8 ± 1.9) ************** (M)

⊕

, and equilibrium temperature (********************

********************

****************** T) ************************* (eq)=

(********************************

**************************** –

**********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

************************** 30

**********************

(************************************K. The difference between the Bayesian evidences of the two -planet circular model and that including only one circular planet (for which we used the same priors for all the parameters in common) is Δln Z=1.6, corresponding to a weak-to-moderate evidence in favor of the two-planet model according to the scale given in (

****************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

). We note that the Bayesian evidence does not favor the two-planet circular model over the one-planet circular model when a much larger prior on

P

is adopted [𝒰(20–6500) days]. In that case, Δln Z∼ −5.8. The sensitivity of the statistical evidence from the choice of the prior range for

P

cimplies that the data place weak constraints on the model evidences and that additional observations are necessary over the next years to cover more orbits of the candidate companion and make the Bayesian statistics less dependent from the prior range in a GP framework. However, as discussed above, the existence of the ~ 1900 – day signal in our present dataset appears justified. We show in fig. S4 the best-fit solution for the stellar activity term as fitted by the GP regression.

(Table 1) ************************************************Results of the GP regression analysis applied to RVs, including two circular orbital equations, and to ASAS photometry. (************************************** (************************************************************************************************************************************ [𝒰(20–6500) days]     

Top: RV curves of Proxima b and of the candidate planet Proxima c, phase-folded to the orbital periods listed in (Table 1) ***********************************************. The red curves represent the best-fit orbital solutions, and the red points are phase-binned RV values. Bottom: Distributions of the number of measurements along the planets

‘orbits.

“data-hide-link-title=” 0 “data-icon-position=” “href=” https://advances.sciencemag.org/content/advances/6/3/eaax7467 /F3.large.jpg?width=& height=& carousel=1 “rel=” gallery-fragment-images – “title=” Phase-folded spectroscopic orbits for Proxima b and c. Top: RV curves of Proxima b and of the candidate planet Proxima c, phase-folded to the orbital periods listed in Table 1. The red curves represent the best-fit orbital solutions, and the red points are phase-binned RV values. Bottom: Distributions of the number of measurements along the planets’ orbits. “>

**************************************************************************************************************************************

**********************************************************************************************

************************************          Fig. 3 (Phase-folded spectroscopic orbits for Proxima b and c.) *************************************Top: RV curves of Proxima b and of the candidate planet Proxima c, phase-folded to the orbital periods listed in (Table 1) **********************************************. The red curves represent the best-fit orbital solutions, and the red points are phase-binned RV values. Bottom: Distributions of the number of measurements along the planets

‘orbits. (************************************************************************************************ We also tested a more complex model including an additional circular Keplerian orbit, with the orbital period of a possible third companion explored up to 1600 days (using uniform priors in both linear and logarithmic scales). We did not find evidence for any significant additional signal in the data. We only note that the posterior for the orbital period for the third Keplerian gives hints for a signal at ∼ 328 days, which we also detected in the periodogram of the RV residuals (after removing only the signals of the two planets; see fig. S4) and that of the Hα activity indicator (see the next section).

Moreover, we also used a different model based on the sum of sinusoids to treat the stellar activity. Details and results are described in the Supplementary Materials.

Is the candidate planetary signal actually linked to the stellar activity?To investigate whether the signal can be attributed to a planetary companion, or it is possibly due to a long-term stellar magnetic activity cycle, we searched ancillary data for evidence of a periodicity close to ~ days. The best dataset for our purpose is represented by the ASAS-3 – ASAS-4 V-band light curve, first analyzed in ( (**************

). In this work, we used a larger dataset, as detailed in the Supplementary Materials, which now covers days. This very extended ASAS light curve represents an invaluable dataset, because it allows to study the photometric evolution of Proxima activity over almost the whole time span of the RVs. The ASAS photometric time series is shown in

Fig. 4 (top). With respect to the data analyzed in (

********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

), the star’s brightness is observed increasing starting around the epoch HJD 2, 458, 551. We reassessed the average periodicity of the activity cycle identified in (

**********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

******************************************** () with the older light curve ( (±) days) by performing an MC fit, which takes into account both the rotational and long-period activity cycle modulations. We used a model composed of two sinusoidal functions (one modeling the rotation and one modeling the activity cycle) and of one quadratic term to model the long-term trend seen in Fig. 4 . For the rotation periodP

******** (rot, we used a uniform prior in the range of (to) ********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** days, while for the average activity cycle period(P)act. cycle, we used a uniform prior in the large range of (to days. The best-fit model is represented by the red curve in the top plot of Fig. 4 , corresponding to an average period of the activity cycle ********************

************************** (P) ******************************************** (act) **************************** (cycle) =****************************(********************************-****************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (******************************

************************ ( )

*********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (************************************************

(**************************************

**************************** days and to a rotation period  P

rot=± 0. 16 days. In the bottom panel ofFig. 4 , we show the ASAS light curve, after removing the – day rotational signal and the quadratic long-term trend, folded at the best-fit period of the activity cycle. Our newly determined value for the mean

P

_{act. cycle}is nearly************************************************************************************************************************************************************************************************************************************************************************************************************************************************************ days shorter than that estimated in (

**********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

. It differs from our best-fit orbital period for the candidate planet c ( (P) c

**************

************************************=******************************** (********************************

–

************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (

236******************************************** ((************************************************(days) by (±) **************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** days, ie, the two periods differ by 4.5σ. Even if these results could be influenced by the different sampling of the datasets, the currently available ASAS dataset indicates that the period of our candidate planetary signal is significantly distinct from that of the activity cycle; Therefore, it presently does not support the interpretation of the ∼ 1900 – day signal in terms of stellar activity. This conclusion certainly needs a more robust confirmation through a photometric follow-up extended over the next years. We also performed a GP regression analysis of the ASAS light curve by adopting the same quasi-periodic kernel used for the RV time series and large priors ( (Table 1) ************************************, ******** without including any other term in the model. Our results show that the stellar rotation period θ is well recovered and the timescale of the correlations λ attains a value close to that estimated for the RVs. This suggests that photometry and RVs contain quasi-periodic activity-related signals with similar properties, and this is particularly suggestive by taking into account that the datasets have different length, time span, and sampling. (********************************************************************************************************************************************************************

    

(****************************************, “data-hide-” link-title=”0″ data-icon-position=”” href=”https://advances.sciencemag.org/content/advances/6/3/eaax79425 / F4.large.jpg? Width=& height=600 & carousel=1 “rel=” gallery-fragment-images – “title=” Analysis of the light curve of Proxima Centauri. Top: ASAS light curve of Proxima (gray dots). The red curve represents our best-fit model of the photometric data, which includes two sinusoids (for the rotational and activity cycle modulations) and a quadratic term to take into account the rise in brightness particularly evident after the epoch HJD 2, 457, 551. Bottom: ASAS light curve, after removing the – day rotational signal and the quadratic long-term trend, folded at the best-fit period of the activity cycle. The best-fit sinusoid modeling the activity cycle is represented by the red curve. The epoch corresponding to phase 0 is HJD 2, 512, **************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** “>*************************************** [𝒰(20–6500) days] ************************************            Fig. 4 (Analysis of the light curve of Proxima Centauri.) ********************************** Top: ASAS light curve of Proxima (gray dots). The red curve represents our best-fit model of the photometric data, which includes two sinusoids (for the rotational and activity cycle modulations) and a quadratic term to take into account the rise in brightness particularly evident after the epoch HJD 2, 457, 551. Bottom: ASAS light curve, after removing the – day rotational signal and the quadratic long-term trend, folded at the best-fit period of the activity cycle. The best-fit sinusoid modeling the activity cycle is represented by the red curve. The epoch corresponding to phase 0 is HJD 2, 512, **************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (**************************************************************************************************************************************************************** collins *************** et al

. (

****************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

analyzed (years of spectroscopic and photometric observations and derived (**************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************. 1 days for the stellar rotation period of Proxima based on Hα activity index, in agreement with the period of (days calculated in (************** 4)) with Hubble Space Telescope (HST) photometry and confirmed in (20,************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************. Robertson

et al

. (

*************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************

) did not find anything relevant on longer timescales, likely as a consequence of the stochastic nature of the microflaring activity of Proxima, which dominates the Hα line emission and makes the analysis of this index very complex in the time domain, as already pointed out in ( (**************** (8) **************

. We performed an analysis of activity diagnostics extracted from UVES and HARPS spectra to search for evidence of a long-term activity cycle and correlations with the RV time series that could explain the candidate planetary signal alternatively in terms of activity. Concerning indexes derived from chromospheric emission lines, we consider here only that derived from the Hα line (see Materials and Methods), for which the median S / N is 52 compared to a median S / N of 0.5 of the index based on the CaII H K lines. Figure S5 shows the time series of the Hα index, the GLS periodogram, and correlation diagrams with the RV residuals (after subtracting from the original dataset the spectroscopic signal induced by Proxima b, the instrumental offsets, and a secular acceleration term, thus still including activity-related signals). The main peak in the periodogram occurs at days, and no long-term activity cycle is detected, neither in the original dataset nor in the residuals after pre-whitening the data by subtracting the – day signal. The same result is obtained when analyzing data extracted from HARPS spectra only. The correlation between the Hα index and the RV residuals is not significant for both the complete UVES HARPS and only HARPS datasets (Spearman’s correlation coefficients are ρ=0. and ρ=0. 25, respectively).

(Very recently, Pavlenko) et al

. (

) analyzed the temporal variations of some chromospheric emission lines from the same HARPS optical spectra of our sample. Their analysis focused on the pseudo-equivalent widths and profiles of the emission lines, and they found that all the lines show short timescale variability (at least********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************** (min). We do not report about long-period activity cycles detected in the time series of the analyzed indexes. We calculated the GLS periodogram of their Hα index dataset (after removing five outliers) and found that the main peak is located at days , with no evidence of significant signals with long periods, ie, a result very similar to that obtained with our dataset. (********************************************************************************************************************************************************************** In conclusion, our analysis of activity diagnostics, as the long time span photometric and the Hα index datasets, did not reveal the exis tence of a periodicity similar to that of our 5.2-year candidate planet and of correlations that would explain the long-period signal detected in the newly extracted RV dataset in terms of stellar activity. Therefore, we affirm to the best of our knowledge that the signal may be due to an additional planet in the system, Proxima c. Nonetheless, the lack of correlation between Hα index and RVs does not entirely exclude that the ~ 1905 – day signal is linked to the activity. Still, little is known about the impact of activity cycles on the RV measurements for slowly rotating cool dwarfs as Proxima. Moreover, because the statistical significance of our GP 2 planets model is not high with the present dataset, and due to the long period and small semi-amplitude of the signal, its real nature needs to be further investigated with additional extensive RV and photometric follow-up, by using alternative models and data analysis methods to treat the stellar activity, and with different detection techniques. How we will show in the next section, a decisive contribution to this regard is expected to come from Gaia astrometric observations.