Main final dvi
Yüklə 354,89 Kb. Pdf görüntüsü
|
2 5 10 20 50 100 300 1000
Period [days] 0 5 10 15 20 25 ∆
1% FAP ~ 170 days S-index - HARPS pre-2016 a 2 5 10 20 50 100 300
1000 Period [days] 0 5 10 15 20 25 ∆
1% FAP ~2.14 days S-index - HARPS PRD b Extended Data Figure 6: Signal searches on the chromospheric S-index. Likelihood-ratio pe- riodogram of S-index from the HARPS pre-2016 (panel a) and HARPS PRD (panel b) campaigns. No signals detected above 1% threshold. doublet lines. They did not report any significant 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 compilation of a number of observations to reliably identify outliers caused by flares. 5.7 Signal searches in H α
Our likelihood-ratio periodograms for H α (Extended Data Figure 7) only show low significance peaks in the 30-40 days period range. It is important to note that the analyses described above have been performed on multiple versions of the dataset, in the sense that we analysed the full dataset 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 peaks in periodograms changes somewhat depending on how stringent the cuts are, no emerging peaks were seen close to an 11 day period. Concerning UVES H α measurements, our likelihood-ratio periodogram did not detect any significant signal. 5.8 Further tests on the signal. It has been shown 65 that at least some of the ultraprecise photometric time-series measured by 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 the same paper 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 non-analytic does not hold with the information available. Though the null hypothesis cannot be definitively rejected, at least until more data is gathered, our results are consistent with the hypothesis that a 26
2 5 10 20 50 100 300 1000
Period [days] 0 10 20 ∆
1% FAP ~23.8 days H α
a 2 5 10 20 50 100 300
1000 Period [days] 0 5 10 15 20 25 ∆
1% FAP ~37 days H α
b Extended Data Figure 7: Signal searches on the spectroscopic H α
riodogram searches of H α intensity from the UVES (panel a), HARPS pre-2016 (panel b) and HARPS PRD (panel c) campaigns. No signals detected above 1% threshold. harmonic component is present in the Doppler time-series. 27
0.5 0.6 0.7 0.8 0.9 -10
-5 0 5 10 RV [m/s] a 0.5 0.6 0.7 0.8 0.9 -8 -7 -6 -5 -4 -3 -2
H α
0.6 0.7 0.8 0.9 -1.0
-0.5 0.0
0.5 EW [A] NaD1 NaD2 0.5 0.6 0.7 0.8 0.9 Time [days] 0 10 20 30 40 CaII H+K [S-index] S-index b c d Extended Data Figure 8: Radial velocities and chromospheric emission during a flare. Radial velocities (panel a) and equivalent width measurements of the H α (panel b), Na Doublet lines (panel c), and the S-index (panel d) as a function of time during a flare that occurred the night of May 5th, 2013. Time axis is days since JD=245417.0 days. No trace of the flare is observed on the RVs. 5.9 Flares and radial velocities. Among the high-cadence data from May 2013 with HARPS, two strong flares are fully recorded. During these events, all chromospheric lines become prominent in emission, H α 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 RVs will be described elsewhere in detail. Relevant to this study, we show th at the typical flares on Proxima do not produce correlated Doppler shifts (Extended Data Figure 8). This justifies the removal of obvious flaring events when investigating signals and correlations in the activity indices. 28
Extended Data Figure 9: Probability distributions for the activity coefficients versus signal amplitude. Marginalized posterior densities of the activity coefficients versus the semi-amplitude of the signal for UVES (panel a), HARPS pre-2016 (panels b,c,d,e,f), HARPS PRD campaign (panels g,h,i,j,k) and the photometric FF ′ indices for the PRD campaign only (panels l, m, 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 (1- σ) in red. The blue bar shows the zero value of each activity coefficient. Only C F ′ is found to be significantly different from zero. 6 Complete model and Bayesian analysis of the activity coeffi- cients. A global analysis including all the RVs and indices was performed to verify that the inclusion of correlations would reduce the model probability below the detection thresholds. Equivalently, the Doppler semi-amplitude would become consistent with zero if the Doppler signal was to be de- scribed by a linear correlation term. Panels in Extendent Data Figure 9 show marginalized distribu- tions of linear correlation coefficients with the Doppler semi-amplitude K. Each subset is treated as a separate instrument and has its own zero-point, jitter and Moving Average term (coefficient) and its activity coefficients. In the final model, the time-scales of the Moving Average terms are fixed to ∼ 10 days because they were not contrained within the prior bounds, thus compromising the convergence of the chains. The sets under consideration are • UVES : 70 radial velocity measurements and corresponding H α emission measurements. • HARPS pre-2016 : 90 radial velocity measurements obtained between 2002 and 2014 by several programmes and corresponding spectroscopic indices : m 2
m 3 , S-index, and the intensities of the H α and HeI lines as measured on each spectrum. 29 • HARPS PRD : 54 Doppler measurements obtained between Jan 18th-Mar 31st, 2016, and the same spectroscopic indices as for the HARPS pre-2016. The values of the F, F ′ and FF
′ indices were obtained by evaluating the best fit model to the ASH2 SII photometric series at the HARPS epochs (see Section 5.3). An activity index is correlated with the RV measurements in a given set if the zero value of its activity coefficient is excluded from the 99% credibility interval. Extended Data Figure 9 shows the equiprobability contours containing 50%, 95%, and 99% of the probability density around the mean estimate, and the corresponding 1- σ uncertainties in red. Only the F ′ index (time derivative of the photometric variability) is significantly different from 0 at high confidence (Extended Data Figure 9, bottom row, panel m). 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 RV 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 the free parameters in the model including activity coefficients for each dataset.
[31] Haario, H., Saksman, E. & Tamminen, J. –. Bernouilli 7, 223 (2001). [32] Tuomi, M. et al. Signals embedded in the radial velocity noise. Periodic variations in the τ Ceti velocities. Astron. Astrophys. 551, A79 (2013). [33] Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. & Teller, E. Equations of State Calculations by Fast Computing Machines. JChPh 21, 1087–192 (1953). [34] Hastings, W. K. Monte carlo sampling methods using markov chains and their applications.
http://www.jstor.org/stable/2334940 . [35] Newton, M. A. & Raftery, A. E. –. JRSS B 56, 3– (1994). [36] Tuomi, M. A new cold sub-Saturnian candidate planet orbiting GJ 221. Mon. Not. R. Astron. Soc 440, L1–L5 (2014). [37] Wright, J. T. & Howard, A. W. Efficient Fitting of Multiplanet Keplerian Models to Radial Velocity and Astrometry Data. Astrophys. J. Suppl. 182, 205–215 (2009). [38] Scargle, J. D. Studies in astronomical time series analysis. I - Modeling random processes in the time domain. Astrophys. J. Suppl. 45, 1–71 (1981). [39] Tuomi, M. Evidence for nine planets in the HD 10180 system. Astron. Astrophys. 543, A52 (2012). 30
[40] Tuomi, M. & Anglada-Escud´e, G. Up to four planets around the M dwarf GJ 163. Sensitivity of Bayesian planet detection criteria to prior choice. Astron. Astrophys. 556, A111 (2013). [41] Berger, J. O. Statistical Decision Theory and Bayesian Analysis (Springer, 1980). [42] Anglada-Escud´e, G. et al. A dynamically-packed planetary system around GJ 667C with three super-Earths in its habitable zone. Astron. Astrophys. 556, A126 (2013). [43] Lomb, N. R. Least-squares frequency analysis of unequally spaced data. AP&SS 39, 447–462 (1976). [44] Scargle, J. D. Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data. Astrophys. J. 263, 835–853 (1982). [45] Zechmeister, M., K¨urster, M. & Endl, M. The M dwarf planet search programme at the ESO VLT + UVES. A search for terrestrial planets in the habitable zone of M dwarfs. Astron.
[46] Cumming, A. Detectability of extrasolar planets in radial velocity surveys. Mon. Not. R. Astron. Soc 354, 1165–1176 (2004). [47] Ferraz-Mello, S. Estimation of Periods from Unequally Spaced Observations. Astron J. 86, 619 (1981). [48] Baluev, R. V. Accounting for velocity jitter in planet search surveys. Mon. Not. R. Astron. Soc 393, 969–978 (2009). [49] Baluev, R. V. The impact of red noise in radial velocity planet searches: only three planets orbiting GJ 581? Mon. Not. R. Astron. Soc 420 (2012). [50] Endl, M. & K¨urster, M. Toward detection of terrestrial planets in the habitable zone of our closest neighbor: proxima Centauri. Astron. Astrophys. 488, 1149–1153 (2008). [51] Queloz, D. et al. No planet for HD 166435. Astron. Astrophys. 379, 279–287 (2001). [52] Robertson, P., Mahadevan, S., Endl, M. & Roy, A. Stellar activity masquerading as planets in the habitable zone of the M dwarf Gliese 581. Science 345, 440–444 (2014). [53] Bonfils, X. et al. The HARPS search for southern extra-solar planets. XXXI. The M-dwarf sample. Astron. Astrophys. 549, A109 (2013). [54] Donati, J.-F. & Brown, S. F. Zeeman-Doppler imaging of active stars. V. Sensitivity of maxi- mum entropy magnetic maps to field orientation. Astron. Astrophys. 326, 1135–1142 (1997). [55] Barnes, J. R. et al. Red Optical Planet Survey: a new search for habitable earths in the southern sky. Mon. Not. R. Astron. Soc 424, 591–604 (2012). 31
[56] Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. Numerical recipes in FORTRAN. The art of scientific computing (Cambridge: University Press, —c1992, 2nd ed., 1992).
[57] Jenkins, J. S. et al. An activity catalogue of southern stars. Mon. Not. R. Astron. Soc 372, 163–173 (2006). [58] Jenkins, J. S. et al. Metallicities and activities of southern stars. Astron. Astrophys. 485, 571– 584 (2008). [59] Collins, K. A., Kielkopf, J. F. & Stassun, K. G. AstroImageJ: Image Processing and Photomet- ric Extraction for Ultra-Precise Astronomical Light Curves. ArXiv e-prints (2016). [60] Southworth, J. et al. High-precision photometry by telescope defocussing - VI. WASP-24, WASP-25 and WASP-26. Mon. Not. R. Astron. Soc 444, 776–789 (2014). [61] Dawson, R. I. & Fabrycky, D. C. Radial Velocity Planets De-aliased: A New, Short Period for Super-Earth 55 Cnc e. Astrophys. J. 722, 937–953 (2010). [62] Aigrain, S., Pont, F. & Zucker, S. A simple method to estimate radial velocity variations due to stellar activity using photometry. Mon. Not. R. Astron. Soc 419, 3147–3158 (2012). [63] Gomes da Silva, J. et al. Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program . II. Activity and radial velocity. Astron. Astrophys. 541, A9 (2012). [64] Baliunas, S. L. et al. Chromospheric variations in main-sequence stars. Astrophys. J. 438, 269–287 (1995). [65] Pascual-Granado, J., Garrido, R. & Su´arez, J. C. Limits in the application of harmonic analysis to pulsating stars. Astron. Astrophys. 581, A89 (2015). 32
Extended Data Table 1: Complete set of model parameters. The definition of all the parameters is given in Section 1 of the methods. The values are the maximum a posteriori estimates and the uncertainties are expressed as 68% credibility intervals. The reference epoch for this solution is Julian Date t 0
∗ Units of the activity coefficients are ms −1 divided by the units of each activity index. Parameter Mean [68% c.i.] Units Period
11.186 [11.184, 11.187] days
Doppler Amplitude 1.38 [1.17, 1.59] ms −
Eccentricity <0.35 – Mean Longitude 110 [102, 118] deg
Argument of periastron 310 [-]
deg Secular acceleration 0.086 [-0.223, 0.395] ms − 1 yr − 1 Noise parameters σ HARPS
1.76 [1.22, 2.36] ms − 1 σ PRD 1.14 [0.57, 1.84] ms − 1 σ UVES 1.69 [1.22, 2.33] ms − 1 φ HARPS 0.93 [0.46, 1] ms − 1 φ PRD 0.51 [-0.63, 1] ms − 1 φ UVES 0.87 [-0.02, 1] ms − 1 Activity coefficients a UVES
C Hα -0.24 [-1.02, 0.54] HARPS pre-2016 C Hα -0.63 [-4.13, 3.25] C He 1.0 [-9.3, 11.4] C S -0.027 [-0.551, 0.558] C m 2 -1.93 [-6.74, 2.87] C m
0.82 [-0.60, 2.58] HARPS PRD C Hα
C He -77 [-210, 69] C S -0.117 [-0.785, 0.620] C m 2 -2.21 [-8.86, 7.96] C m 3 -0.02 [-3.67, 3.44] PRD photometry C F 0.0050 [-0.0183, 0.0284] C F ′ -0.633 [-0.962, -0.304] C FF
4.3 [-6.8, 14.8] a Units of the activity coefficients are ms − 1
33 Yüklə 354,89 Kb. Dostları ilə paylaş:
|