On the long-term correlation between the flux in the Ca II H & K and Halpha lines for FGK stars
J. Gomes da Silva, N. C. Santos, I. Boisse, X. Dumusque, C. Lovis
AAstronomy & Astrophysics manuscript no. paper˙refcorr˙nohypref c (cid:13)
ESO 2018November 9, 2018
On the long-term correlation between the flux in the Ca ii H & K andH α lines for FGK stars J. Gomes da Silva , , N.C. Santos , , I. Boisse , X. Dumusque , , and C. Lovis Centro de Astrof´ısica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugale-mail:
[email protected] Departamento de F´ısica e Astronomia, Faculdade de Ciˆencias, Universidade do Porto, Portugal Observatoire de Gen`eve, Universit´e de Gen`eve, 51 ch. des Maillettes, CH-1290 Versoix, SwitzerlandReceived date / Accepted date
ABSTRACT
The re-emission in the cores of the Ca ii H & K and H α lines, are well known proxies of stellar activity. However, these activityindices probe di ff erent activity phenomena, the first being more sensitive to plage variation, while the other one being more sensitiveto filaments. In this paper we study the long-term correlation between log R (cid:48) HK and log I H α , two indices based on the Ca ii H & K andH α lines respectively, for a sample of 271 FGK stars using measurements obtained over a ∼ ff ects.We found a great variety of long-term correlations between log R (cid:48) HK and log I H α . Around 20% of our sample has strong positivecorrelation between the indices while about 3% show strong negative correlation. These fractions are compatible with those found forthe case of early-M dwarfs. Stars exhibiting a positive correlation have a tendency to be more active when compared to the median ofthe sample, while stars showing a negative correlation are more present among higher metallicity stars.There is also a tendency for the positively correlated stars to be more present among the coolest stars, a result which is probablydue to the activity level e ff ect on the correlation. Activity level and metallicity seem therefore to be playing a role on the correlationbetween log R (cid:48) HK and log I H α . Possible explanations based on the influence of filaments for the diversity in the correlations betweenthese indices are discussed in this paper. As a parallel result, we show a way to estimate the e ff ective temperature of FGK dwarfsexhibiting a low activity level by using the H α index. Key words.
Keywords should be given
1. Introduction
Stellar activity is one of the main limitations to the detectionof low-mass and / or long-period planets using the radial-velocitymethod (e.g. Saar & Donahue 1997; Santos et al. 2000; Quelozet al. 2001; Boisse et al. 2009, 2011; Dumusque et al. 2011b;Lovis et al. 2011; Gomes da Silva et al. 2012). Fortunately, theradial-velocity noise induced by these e ff ects can, in some cases,be corrected for example if the activity is simultaneously mea-sured using activity indices (e.g. Dumusque et al. 2011a, 2012).Therefore, understanding the behaviour of activity indices andtheir relation with radial-velocity is vital to reduce the impactof activity in radial-velocity measurements and thus improve itssensitivity to planetary signals.The re-emission in the Ca ii H & K lines are widely usedproxies of activity induced signals in radial-velocity measure-ments. However, for solar-type stars, the relation between thisindex and H α is not well understood. Since these two activityindices are a ff ected by di ff erent activity phenomena in di ff erentways (the emission in the centre of the Ca ii and H α lines arenot formed at the same temperature in the chromosphere), un-derstanding their relationship and di ff erences might bring newinsights not only to stellar physics but also to the detection andcharacterisation of extrasolar planets.It is known that there is a long-term correlation betweenthe emission in the Ca ii H & K and H α lines that follow theSun’s 11-year activity cycle (Livingston et al. 2007). Other au- thors have suggested that the correlation is also present in otherstars (Giampapa et al. 1989; Robinson et al. 1990; Strassmeieret al. 1990; Pasquini & Pallavicini 1991; Montes et al. 1995).However, when Cincunegui et al. (2007) measured simultane-ously the flux in the two lines for a sample of 109 southernFGK and M stars, they found a large scatter in correlations, fromvery strong positive correlations to negative ones. They also sug-gested that the mean values of the flux in the Ca ii and H α linesare correlated due to the e ff ect of stellar colour on both fluxes.Meunier & Delfosse (2009) studied the contribution ofplages and filaments to the emission in Ca ii and H α lines dur-ing a solar cycle. In their work, plages contributes to an increasein emission in both fluxes while filaments increases absorptionin H α only. They found that the contribution of filaments to H α can be responsible for the decrease in the correlation coe ffi cientbetween the two fluxes depending on their spatial distributionand contrast compared to those of plages. They also noted thatat higher activity levels (e.g. cycle maxima), the filament fillingfactor saturates and the correlation between the two fluxes in-creases. Other factors contributing to a decrease in the measuredcorrelation can be the time-span of observations, cycle phase atwhich they are measured, and stellar inclination angle. For ex-ample, if the time-span is less than the cycle period (or the ac-tivity range is not well spanned) the correlation will probably beunderestimated.Santos et al. (2010) studied the long-term activity of 8 FGKstars using the Ca ii H & K based S MW and H α indices and found a r X i v : . [ a s t r o - ph . S R ] N ov . Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars a general long-term correlation between the two. However theirsample was not large enough to have any statistical significance.Gomes da Silva et al. (2011) expanded the comparison betweenthese two activity sensitive lines to early-M dwarfs. Similarlyto Cincunegui et al. (2007) they detected a large variety of cor-relation coe ffi cients, including anti-correlations for the least ac-tive stars in their sample. The most active stars were all, how-ever, positively correlated. They also found hints that in somecases the H α index was following an ”anti-cycle” relative totheir S -index, i.e., the maxima and minima measured in the twoindices were anti-correlated. However, their time-span was notlong enough to detect full cycles and confirm this e ff ect.In this paper, we analyse the behaviour of the flux in Ca ii H& K and H α lines in FGK stars via two activity indices correctedfor the e ff ects of photospheric flux. We describe our sample anddata in Sect. 2. The activity indices derivation, statistics, corre-lations between mean values, and activity cycle detectability arepresented in Sect. 3 and Appendix A. The correlations betweenthe two indices are discussed in Sect. 4. The distribution of thecorrelations in mean values of activity are discussed in Sect. 5.The e ff ects of metallicity on the correlation are studied in Sect.6, and the distribution of the correlations in e ff ective tempera-ture is presented in Sect. 7. We discuss possible causes for theexistence of positive correlations and anti-correlations, and com-pare our results with those found for early-M dwarfs in Sect. 8,and finally conclude in Sect. 9. A possible use of the H α indexto estimate the e ff ective temperature of low activity level FGKdwarfs is proposed in Appendix B.
2. Sample and data
The sample comes from the ∼
400 FGK stars HARPS (spectralresolution =
115 000) high-precision sample already used byLovis et al. (2011) to study the long-term activity of FGK starsand its e ff ect on the measurement of precise radial velocities. Adescription of the sample is presented in their paper. The spec-tra used in this work were obtained between February 2003 andFebruary 2012. We used e ff ective temperature, metallicity, andsurface gravity that were already calculated for this sample bySousa et al. (2008). Absolute magnitude and luminosity wereboth obtained from the Hipparcos catalogue.We selected only spectra with S / N ≥
100 at spectral order 56( ∼ + ∼ ff ective temperaturefrom 4595 to 6276 K, and in metallicity from − .
84 to + .
3. The activity indices
The log R (cid:48) HK index, which is already corrected for the photo-spheric flux (Noyes et al. 1984), and respective errors were di-rectly obtained from the HARPS DRS. This index is based onthe S -index which is calculated as the sum of the flux in two 0.6Å bands centered at the calcium H (3968.47 Å) and K (3933.66 Å) lines divided by two 20 Å reference bands centered at 3900and 4000 Å (see e.g. Boisse et al. 2009).The H α index and errors were calculated as in Gomes daSilva et al. (2011). We used a 1.6 Å band centered at 6562.808Å and divided the flux in the central line by the flux in tworeference bands of 10.75 and 8.75 Å centered at 6550.87 and6580.31 Å, respectively. The flux errors were calculated as thephoton noise in the line core, √ N , where N is the number ofphotons in the band. The activity indices errors were obtainedvia error propagation. The calibration of H α for the e ff ects ofphotospheric flux is presented in Appendix A and results in the I H α index. log R (cid:48) HK index Our sample, which is biased towards inactive stars in order toincrease the chances of finding low-mass planets, has a me-dian log R (cid:48) HK of − .
948 and a mean of − . R (cid:48) HK ≥ − .
75, lying on the higher activity region above the”Vaughan-Preston gap” (Vaughan & Preston 1980).The star with the highest activity level is HD224789, withlog R (cid:48) HK = − .
433 and the most inactive star is HD181433 withlog R (cid:48) HK = − . R (cid:48) HK index is 0.003, or in relative terms, 0.06% around themean. In terms of variability, the median standard deviation ofthe sample is 0.0154 (0.3% around the mean), with HD177758being the least variable star with σ (log R (cid:48) HK ) = . σ (log R (cid:48) HK ) = .
08 (1.6% around the mean). log I H α index In terms of log I H α , our sample has a median value of − . − . I H α meanvalue is HD85119, with an activity level of − . I H α = − . I H α index is 0.0002, or inrelative terms, 0.01% around the mean. As stated before, we areonly considering photon noise as a source of errors, and sincethe H α line is in a brighter area of the spectrum compared tothe Ca ii H & K lines, we expect the photon noise to be lowerfor I H α than for R (cid:48) HK . In terms of variability, the median standarddeviation of the sample is 0.0019 (0.11% around the mean), withHD74014 being the least variable star with σ (log I H α ) = . σ (log I H α ) = . R (cid:48) HK ismore sensitive to activity variations than log I H α . While log R (cid:48) HK has a median standard deviation of 0.3% of the mean, log I H α only has a median standard deviation of 0.1% of the mean, whichmeans that log R (cid:48) HK will have a more noticeable variation. Our activity indices are corrected for the e ff ects of photosphericflux, and can, if they are not dependent on other factors otherthan chromospheric flux, be used to compare the activity levelsbetween di ff erent stars. Figure 1 (upper panel) shows the corre-lation between the mean values of log R (cid:48) HK and log I H α . Thesemean values were calculated by averaging the two indices overall our nightly measurements, and represent the average activitylevel of each star. Open triangles are stars with correlation coef-
2. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars log I Hα >5.25.15.04.94.84.74.64.54.4 < l og R H K > N = 2711.95 1.90 1.85 1.80 1.75 1.70 1.65< log Hα >0.90.80.70.60.50.40.30.20.1 < l og S M W > N = 271
Fig. 1:
Upper panel:
Relationship between log R (cid:48) HK and log I H α mean activity levels. Open triangles are stars with positive cor-relation between the two indices with ρ ≥ ρ ≤ − .
5, and dots stars with nocorrelations.
Lower panel:
Relationship between the logarithmsof S MW and H α indices.ficient, ρ ≥ .
5, squares are stars with ρ ≤ − .
5, and dots starswith no strong correlations. There is a correlation between theindices, with a correlation coe ffi cient of 0 .
53, but the scatter islarge and the relation appears not to be linear (c.f. Cincuneguiet al. 2007, Fig. 12). However, if we choose only the positivelycorrelated stars (open triangles), they show a slightly more welldefined relationship for the mean values with a correlation coef-ficient of 0 .
65. When Cincunegui et al. (2007) studied the corre-lation between the mean values of the flux in Ca ii and H α theyconcluded that the correlation between them is due to the depen-dence of the mean fluxes on stellar colour. Indeed, when we plotthe logarithm of the mean indices S MW vs. H α (without colourcorrection), we have a stronger correlation with ρ = .
79 (Fig.1, lower panel). We can therefore confirm that stellar colour isplaying a role in the correlation between the mean flux levels ofthe Ca ii and H α lines. F r e q u e n c y N = 271
Fig. 2: Distribution of correlation coe ffi cients between log R (cid:48) HK and log I H α for the whole sample (black line). The grey filledhistogram shows the distribution of correlations for the 101 starsin Cincunegui et al. (2007) sample that have their correlationscalculated. To detect activity cycles we fitted sinusoids to the time-series ofthe two activity indices. The significance of the fitting processwas addressed by using an F-test where F = σ const /σ sin to com-pare the fitting of a sinusoid with that of a constant model with σ being the standard deviation of the residuals of the fitted model.The probability p ( F ) will give the probability that the data is bet-ter fitted by a constant model than a sinusoidal function. We se-lected stars with cycles as the ones where probabilities, p ( F ) HK and p ( F ) H α , are lower than 0.05 and, similarly to Lovis et al.(2011), we searched for periods in the region between 2 and 11years.Based on this selection criteria and using log R (cid:48) HK , we de-tected 69 stars (26%) with significant activity cycles with peri-ods varying between 2.0 and 10.8 years. The log I H α index, how-ever, is not so sensitive at detecting magnetic cycles. Only 9 stars(3.3%) showed significant cycles with periods varying between3.9 and 9.5 years. As a comparison, Robertson et al. (2013) de-tected activity cycles with periods longer than one year in 5%of their sample of 93 K5-M5 stars using an H α index similar toours. In their study of activity cycles based on this sample butwith a di ff erent selection criteria, Lovis et al. (2011) found that,out of their 284-star sample, 99 stars (35% ) showed long-termactivity cycles in their log R (cid:48) HK index. Their slightly higher frac-tion of stars with cycles is probably due to the fact that they use adi ff erent selection criteria with a di ff erent restriction on the num-ber of data points (some of their stars with detected cycles haveless than 10 observations), we use only data with S / N ≥
3. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars
4. Correlations between log R (cid:48) HK and log I H α For all stars we calculated the Pearson correlation coe ffi cient be-tween log R (cid:48) HK and log I H α . As was detected by Cincunegui et al.(2007) for the flux in the Ca ii H & K and H α lines, we alsofind a great variety of correlation coe ffi cients between log R (cid:48) HK and log I H α , in the range − . ≤ ρ ≤ .
95 (Fig. 2). Althoughthere is a tendency for the stronger correlations to be positive,we found a few cases of anti-correlations with ρ ≤ − . ii H & K and H α lines, we made a new selection of stars with good quality datathat we are going to describe in the following section. We are interested in measuring the long-term Pearson correlationcoe ffi cient ( ρ ) between the log R (cid:48) HK and log I H α indices. We needtherefore to ensure that we have (a) a long time-span to certifythat we are measuring long-term variations , (b) variability inthe long-term so that we are not measuring correlations due tonoise, (c) no short-term variations that can interfere with or hidethe long-term ones, (d) enough quantity of points to calculatea significant ρ , and (e) strong correlations. To achieve this, weperform the following selection criteria on our 271-star sample:1. All data was binned into 100-day averages, each bin with atleast three nights of observations, where the errors were cal-culated as the standard error on the mean, σ/ (cid:112) ( N ), where σ is the standard deviation of the observations and N the num-ber of observations. This will reduce the variation inducedby short-term activity modulated by stellar rotation.2. We selected stars with at least four bins. This selection en-sures that we have enough points to calculate ρ and that thetime span is at least 400 days.3. Only stars that showed long-term variability in log R (cid:48) HK wereselected. This will ensure that we are not detecting ran-dom variations due to noise. We performed an F -test on thebinned data where F = σ e / (cid:104) σ i (cid:105) , with σ e the standard de-viation of the binned data and (cid:104) σ i (cid:105) the mean of the errorson the bins (e.g. Zechmeister et al. 2009). We calculated theprobability of the F -test, P ( F ), that the variations are due tothe internal errors of the binned data, and selected stars with P ( F ) ≤ .
05 (95% probability that the variability in not dueto the internal errors).4. We also applied the variability F -test for the log I H α index ina similar way as described above.5. To select significant correlation coe ffi cients between log R (cid:48) HK and log I H α we calculated the False Alarm Probability (FAP)of having absolute values of ρ higher than the ones obtainedfor each star by bootstrapping the binned data and calcu-lating the fraction of cases with higher | ρ | values. We used10000 permutations per star to calculate the FAP values.Only stars with FAP ≤ .
05 (95% significance level) wereselected. We should note that for 165 stars they do not find cycles but theycannot exclude cycles either. In their conclusions they arrive at a finalvalue of 61% of stars with cycles when they exclude these stars fromthe fraction. Since this sample derives from a planet hunt selection of stars, ac-tive stars with log R (cid:48) HK ≥ − .
6. Stars with strong correlations were selected as the ones hav-ing | ρ | ≥ . R (cid:48) HK , 51 stars (39.5%)show long-term variability in log I H α , and 45 stars (34.9%)show long-term variability on both indices. Out of the 45 starsthat show variability on both indices, 12 stars (26.7%) showstrong positive correlations between the indices, 10 of them(22.2%) having positive correlations while two (4.4%) havinganti-correlations.Table 1 shows the variability and correlations data for the 12stars with strong long-term correlations, where N bins the numberof bins for each star, ρ the correlation coe ffi cient value, FAP thefalse alarm probability of ρ , and the parameters of the F -testsfor both activity indices. The time series of log R (cid:48) HK , log I H α ,and their respective correlations for these 12 stars are shownin Fig. B.2. We also tried to fit sinusoids to these stars (seeSect. 3.4) using the binned data of both indices to check if thesestars have significant activity cycles. These fits appear in Fig.B.2 if the p ( F ) HK of the fit is lower than 0.05 (95% significancelevel). Two stars, HD100508 and HD78612, only have four binsand therefore do not have enough free parameters to calculatethe probability of the fit. From the stars with more than fourbins, three have p ( F ) values lower than 0.05 for the log R (cid:48) HK in-dex, namely HD4915, HD63765, and HD88742. These are allstars with strong positive correlations. The 7 stars with signifi-cant cycles in log R (cid:48) HK have periods in the range 1528 to 10665days, and 5 of them could be fitted in log I H α with the sameperiod found for log R (cid:48) HK and a p ( F ) H α value lower than 0.05(HD13808, HD154577, HD215152, HD7199, and HD85512).For this sample, no star showed a period in log I H α that was notfound also in log R (cid:48) HK , and at a higher significance.To try to understand why some stars have positive correla-tions while others have negative, we compared the correlationswith the basic stellar parameters shown in Table 2. The twostars with negative correlations are shown in bold. First, we ob-serve that the two stars with the negative correlations are two ofthe most inactive in terms of both log R (cid:48) HK and log I H α . Second,while all the stars with positive correlation coe ffi cient have neg-ative metallicity (median value of − .
20 dex), the two stars withnegative correlations have positive metallicity (median value of0.34 dex).Although we can se hints that activity level and metallicitycould be influencing the correlation between the two indices, thesmall number of stars we are using is insu ffi cient to clearly showa solid trend between these parameters. We therefore chose torelax our selection criteria to increase the number of stars in oursample and check if the trends with activity level and metallicityare maintained. To increase the number of stars in our study we discarded thevariability tests, FAPs on the correlation coe ffi cients and used thefull data sets based on the nightly averaged data. The correlationcoe ffi cient limit was also decreased to | ρ | ≥ .
5. This produced alarger sample which will include weaker correlations that can bedue to a lower number of data points, shorter time-spans, and / ordue to short-term variations. We shall therefore take this part ofthe study as an indication and not as a proof. However we willnow be able to do statistical tests to this sample.Using this selection, we found that out of the 271 stars inour original sample, 58 (21.4% of the sample) have positive
4. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars Table 1: Variability and correlations using binned data for the stars with strong long-term correlations.
Star N bins T span ρ FAP log R (cid:48) HK log I H α [days] σ e (cid:104) σ i (cid:105) P ( F ) σ e (cid:104) σ i (cid:105) P ( F )HD100508 4 766 − .
93 0.047 0.0199 0.0034 0.0082 0.00102 0.00031 0.040HD13808 13 2245 0.97 0.0001 0.0794 0.0043 < − < − HD154577 7 2117 0.92 0.0014 0.0302 0.0030 0.00001 0.00242 0.00047 0.00046HD209100 7 829 0.92 0.0021 0.0278 0.0048 0.00022 0.00282 0.00088 0.0062HD215152 9 1160 0.83 0.0034 0.0322 0.0028 < − < − − .
82 0.0009 0.0758 0.0071 < − < − < − < − HD88742 5 1729 0.93 0.015 0.0323 0.0043 0.00089 0.00308 0.00086 0.015
Table 2: Stellar parameters of the stars with strong long-term correlations.
Star (cid:104) log R (cid:48) HK (cid:105) (cid:104) log I H α (cid:105) [Fe / H] T e ff log g M V B − V P rot [K] [cm s − ] [days] HD100508 − . − . . ± .
05 5449 ±
61 4 . ± .
09 5.16 0.83 48.4HD13808 − . − . − . ± .
03 5087 ±
41 4 . ± .
08 6.08 0.87 42.8HD154577 − . − . − . ± .
02 4900 ±
37 4 . ± .
08 6.70 0.89 41.3HD209100 − . − . − . ± .
04 4754 ±
89 4 . ± .
19 6.89 1.06 37.2HD215152 − . − . − . ± .
04 4935 ±
76 4 . ± .
14 6.45 0.97 42.0HD4915 − . − . − . ± .
01 5658 ±
13 4 . ± .
03 5.26 0.66 20.4HD63765 − . − . − . ± .
01 5432 ±
19 4 . ± .
03 5.53 0.74 25.0HD71835 − . − . − . ± .
02 5438 ±
22 4 . ± .
04 5.38 0.77 35.2
HD7199 − . − . . ± .
03 5386 ±
45 4 . ± .
08 5.29 0.85 45.9HD78612 − . − . − . ± .
01 5834 ±
14 4 . ± .
02 4.06 0.61 21.7HD85512 − . − . − . ± .
03 4715 ±
102 4 . ± .
28 7.43 1.16 47.3HD88742 − . − . − . ± .
01 5981 ±
13 4 . ± .
02 4.60 0.59 11.4
Notes.
The average values of log R (cid:48) HK and log I H α were calculated using the binned data. correlations between log R (cid:48) HK and log I H α , and 8 (3.0% of thesample) have anti-correlations. Table B.1 shows the 66 starswith | ρ | ≥ . ffi cient betweenthe two indices. Stars with correlations coe ffi cients in the range − . < ρ < . ρ ≤ − .
5) havelow log R (cid:48) HK activity levels with a median value of − .
97 anda median super-solar metallicity with a value of 0.20. The 58stars with positive correlations ( ρ ≥ .
5) have log R (cid:48) HK with amedian value of − .
81 and a median sub-solar metallicity with avalue of − .
16. This ”relaxed” selection appears to maintain thetrends found in Section 4.1. In the next sections we will studythese trends for this sample of stars.
5. Mean activity level and correlations
Here we investigate the distribution of the positively and neg-atively correlated stars in terms of log R (cid:48) HK and log I H α activitylevels.Figure 3 (upper panel) shows the distribution of activity asmeasured by the log R (cid:48) HK index. The black line is the histogramof the selected sample of 271 main sequence stars. We can ob-serve the selection bias against active stars as the great major-ity of the sample lies between − . − . − .
95 dex. The hatched and filled grey histograms showthe distribution in average activity level of the stars with posi-tive and negative log R (cid:48) HK –log I H α correlations, respectively. The median of the negatively correlated stars is close to the medianof the full sample (but with a tendency to be less active) witha value of − .
97 dex, while the median of the positively corre-lated stars lies in a higher activity zone, with a value of − . R (cid:48) HK = − . R (cid:48) HK and log I H α . The relative histogram in Fig. 3 (lower panel) illus-trates very well this tendency.The separation between positively and negatively correlatedstars is further confirmed by the Kolmogorov-Smirnov (K-S) testthat shows that the two populations are distinct with a p -value of0.002 and a D value of 0.664. A similar distribution was foundfor log I H α (Fig. 4). The correlation between the two indices havedi ff erent distributions according to activity level, with negativelycorrelated stars being the least active ones and the positively cor-related stars increasing in number with I H α activity level. In thiscase, the K-S test have a D = .
513 and p -value = I H α are very wellconstrained between − .
73 and − .
70, and only a few cases ofhigher activity stars exists beyond these values. Note that, in the The K-S D value is the highest value of the di ff erence between thecumulative distributions of the two populations. The p -value gives theprobability that the two populations come from the same parent distri-bution. 5. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars log R HK F r e q u e n c y N = 2715.2 5.1 5.0 4.9 4.8 4.7 4.6 4.5 4.4 log R HK R e l a t i v e f r e q u e n c y Fig. 3:
Upper panel:
Distribution on log R (cid:48) HK activity for the fullsample (black), stars with positive correlation coe ffi cient higherthan 0.5 (hatched grey), and stars with negative correlation coef-ficient lower than − . Lower panel:
Same as the upper panel but usingrelative distribution on log R (cid:48) HK , i.e., the values in each bin aredivided by the total number of stars in the respective bin.relative histogram (lower panel) the ”hole” in the region between − .
675 and − .
660 is due to lack of data.
6. Metallicity and correlations
Is stellar activity the only variable playing a role in the defi-nition of the correlation or anti-correlation observed? In TableB.1, it is noticeable that there is a tendency for the eight starswith negative correlation between the log R (cid:48) HK and log I H α in-dices to have super-solar metallicity. We plotted the histogramof the two populations, the ones with a positive and a negativecorrelation, against metallicity (Fig. 5). Symbols and colours arethe same as the ones presented Fig. 3. In Fig. 5 (upper panel)the median of the negatively correlated stars is not coincidentwith de medians of both the sample and the positively correlatedstars. The histogram shows that, again, there seems to be two log I Hα F r e q u e n c y N = 2711.74 1.72 1.70 1.68 1.66 log I Hα R e l a t i v e f r e q u e n c y Fig. 4:
Upper panel:
Distribution on log I H α activity for the fullsample (black), stars with positive correlation coe ffi cient higherthan 0.5 (hatched grey), and stars with negative correlation coef-ficient lower than − . Lower panel:
Same as the upper panel but usingrelative distribution on log I H α .distinct populations of stars: the majority of the stars with pos-itive correlations have negative metallicity while the negativelycorrelated stars appear to be of super-solar metallicity (mainlyif compared to the overall sample). The sample median is − . − .
15 dex, butthe negatively correlated star’s median is at a metallicity of 0.20dex. This is further corroborated by the K-S test, which gives aprobability of 0.04% that the two populations are indistinct (witha K-S D value of 0.733). The relative histogram of Fig. 5 (lowerpanel) confirms this with the negatively correlated stars peakingat the super-solar metallicity while the positively correlated starspeaking at the sub-solar metallicity. Nevertheless, there are somestars with negative correlation that have sub-solar metallicity andstars with positive correlation with super-solar metallicity. Weplotted metallicity histograms for two bins where there is super-position of positively and negatively correlated stars in activityin the region − . ≤ log R (cid:48) HK ≤ − .
6. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars F r e q u e n c y N = 2711.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6[Fe/H]0.000.050.100.150.200.250.300.350.400.45 R e l a t i v e f r e q u e n c y Fig. 5:
Upper panel:
Distribution of metallicity for the full sam-ple (black), stars with positive correlation coe ffi cient higher than0.5 (hatched grey), and stars with negative correlation coe ffi cientlower than − . Lower panel:
Same as the top panel but for relativedistributions. The K-S test gives a p-value of 0.01% for the prob-ability that the two populations are drawn from the same distri-bution.stars with higher metal content to have negative correlations ismaintained in each activity bin. In the lower panel of the figure,for the three stars with metallicity between − . − . / H] = − .
20 dex, while thetwo negatively correlated stars have [Fe / H] = − .
16 and [Fe / H] = − .
15 dex. These plots show that for a given activity range,metallicity is still having an impact on the correlation betweenlog R (cid:48) HK and log I H α .Our analysis was based on a small number of anti-correlatedstars, and our conclusions can be a consequence of small-numberstatistics. Also, as was stated before, this sample is not rigorousin terms of long-term variability of the stars or the significanceof the correlations used. Further studies with a larger numberof metal-rich stars would be crucial to confirm or refute theseresults. F r e q u e n c y − .
90 log R HK − . F r e q u e n c y − .
00 log R HK − . Fig. 6:
Upper panel:
Distribution of metallicity for stars withpositive correlation coe ffi cient higher than 0.5 (hatched grey),and stars with negative correlation coe ffi cient lower than − . − . ≤ log R (cid:48) HK ≤ − . Lower panel:
Same as the top panel but for stars with activity inthe range − . ≤ log R (cid:48) HK ≤ − .
7. Effective temperature and correlations
We also analysed what would be the e ff ect of temperature on thecorrelations between log R (cid:48) HK and log I H α . Figure 7 (upper panel)shows the distributions of the correlations for the full sample(black), the positively correlated stars (hatched grey), and nega-tively correlated stars (filled grey). Black vertical line is the me-dian of the full sample with a value of 5604 K, dashed verticalline the median of the positively correlated stars with a value of5243 K, and dotted line the median of the negatively correlatedstars with a value of 5386 K. There is an observational bias to-ward brighter stars and therefore hotter ones. However, the posi-tively correlated stars seem very well distributed across the tem-perature range, which implies that, relative to the full sampledistribution, there are more cooler stars having positive correla-tions than hotter stars. This can be easily observed in the lowerpanel of Fig. 7. Stars with negative correlations appear also welldistributed in e ff ective temperature, but are only restricted to therange between ∼ ∼
7. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars fect is probably due to the fact that, in our sample, cooler starshave a tendency to be more active than the hotter ones (Fig. 8).All the stars in our sample with log R (cid:48) HK > − . ff ectivetemperatures lower than 5500 K. And as we saw before in Sect.5, all stars with activity higher than − . . < B − V < .
8. Discussion
So, why we sometimes see stars with anti-correlations (and”anti-cycles”) when we measure the flux in the H α line? Meunier& Delfosse (2009) studied the contribution of plages and fila-ments to the S MW and H α indices for the case of the Sun. Theynoted that the emission in the Ca ii lines increases in the presenceof plages but is almost una ff ected by filaments (their contributionis negligible). On the other hand, filaments contribute to the ab-sorption in the flux of H α while plages contributes to emission.However, the filling factor of filaments saturates at a given activ-ity level while plages filling factor continues to increase as theactivity level increases further. This saturation will contribute toan increase of the correlation between the flux in the two linecores for higher activity levels. For the Sun, the filaments are notonly found in active regions. They explain that the positive cor-relation between the two indices is due to the fact that as activitygets stronger (higher emission in the Ca ii lines), for the H α in-dex, which is more sensitive to filaments than the Ca ii lines, thecontribution of plages becomes more important than the contri-bution coming from filaments, because their contribution satu-rates at a certain activity level. This will produce the observedstrong positive correlation between the two indices for higheractivity stars as observed in Fig. 3 and 9. On the other hand, thelow-activity stars with anti-correlation between the emission inCa ii and H α , which appear in Fig. 3 and 9, can be explained ifthese stars have the filaments with a strong contrast (comparedto plages) and which not reach the saturation limit.The occurrence of positively correlated stars at higher activ-ity levels and negatively correlated stars at lower activity levelsthat we observe in Section 5 can then be explained by the e ff ectof filaments on the flux of the H α line.If the positively and negatively correlated stars are two di ff er-ent populations in terms of metallicity as discussed in Section 6,and if the ratio of the contrast / filing factor of filaments to plages T eff F r e q u e n c y N = 2714500 5000 5500 6000 6500 T eff [K]0.00.10.20.30.40.50.60.70.8 R e l a t i v e f r e q u e n c y Fig. 7:
Upper panel:
Distribution of e ff ective temperature forthe full sample (black), stars with positive correlation coe ffi cienthigher than 0.5 (hatched grey), and stars with negative correla-tion coe ffi cient lower than − . Lower panel:
Same as the toppanel but for relative distributions.is responsible for the anti-correlation between the flux in the Ca ii H & K and H α lines, then metallicity might have an e ff ect on thepresence of filaments (or their contrast and / or filling factor) inthe stellar corona. This could be used to predict the correlationbetween these two indices and to forecast the presence, contrast,and / or filling factor between plages and filaments for a givenstar. In a previous work, Gomes da Silva et al. (2011) studied thelong-term activity of 30 M0-M5 dwarfs and found hints of H α ”anti-cycles” (inverted in comparison to the log R (cid:48) HK cycles) onsome stars of their sample. The potential maxima and minima ofsome stars were anti-correlated. This can be an indication thatthe physical mechanisms responsible for the anti-correlation,and thus ”anti-cycles”, between the two indices are present both
8. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars T eff [K]5.25.15.04.94.84.74.64.54.4 l og R H K Fig. 8: Activity level measured by log R (cid:48) HK against e ff ective tem-perature. Triangles are stars with ρ ≥ . ρ ≤ − . S -index activity allM-dwarfs in their sample have positive correlations, and founda case of an anti-correlation with correlation coe ffi cient valuelower than − . S -index was not correctedfor the e ff ects of photospheric flux, and therefore there is a tem-perature contribution to the mean index values that will varyfrom star to star. Nevertheless, their distribution of correlationsis compatible with ours in the sense that after a certain levelof activity all active stars have positive correlations, and thereare some cases of low activity stars with anti-correlations (Fig.9). Since both FGK and early M stars have radiative cores withconvective envelopes, their activity phenomena might not be toodi ff erent (contrary to later M dwarfs which are fully convective).Therefore, if the contribution of filaments to the H α absorptionis the sole responsible to the anti-correlation between the flux inthe Ca ii and H α lines, then it is possible that this phenomenonis occurring in a similar way for the two types of stars.Further studies of the correlations between the two indicesfor later M dwarfs would be interesting to understand how thebehaviour of the two indices evolve in spectral type and inferabout the presence of filaments in fully convective stars.
9. Conclusions
We studied the correlation between the flux in the Ca ii H & Kand H α lines via two activity indices, R (cid:48) HK and I H α , correctedfor photospheric flux. A sample of 271 low activity FGK stars,observed during ∼ ff ect. This study wasthe larger scale study (in both sample number and time-span)of the correlation between these two chromospheric indices forsolar-type stars.We detected significant activity cycles in 69 stars (26% ofour sample) using the log R (cid:48) HK index, but only in 9 stars (3.3%)using log I H α . The H α line is not so sensitive at measuring long-term variations as the Ca ii lines. We also found a great variety ofcorrelation coe ffi cients, in the range − . ≤ ρ ≤ .
95, similarto what was found by Cincunegui et al. (2007). Possible expla-nations for this variety are given by Meunier & Delfosse (2009) log R HK >1.00.50.00.51.0 ρ ( R H K , I H α ) Fig. 9: Correlation coe ffi cient of the relation between log R (cid:48) HK and log I H α against mean log R (cid:48) HK level. The vertical line atlog R (cid:48) HK = − . ff erence in contrast offilaments relative to plages.To study the correlation between the log R (cid:48) HK and log I H α in-dices we first selected only the stars showing ”strong” long-termcorrelations between the two indices by applying a rigorous se-lection criteria based on variability F-tests, using FAPs on thecorrelation coe ffi cients and binning the data to 100-day bins.This selection criteria returned a sample of 12 stars where twoof them have anti-correlations and the rest positive correlations.We observed that the two stars with anti-correlations have ten-dency to have lower activity levels and super-solar metallicitywhen compared to the positively correlated stars.Since this rigorous selection returned a small number ofstars, we relaxed the selection criteria to increase our sampleand study the trends found with the rigorous selection. Usingthis selection criteria we found that: –
58 stars (21% out of 271) have positive correlations (with ρ ≥ .
5) and 8 stars (3% out of 271) show anti-correlations(with ρ ≤ − . I H α : negative activity cycles whencompared to those measured by log R (cid:48) HK . – The stars with positive correlation between the two indiceshave a tendency to be more active than those with negativecorrelations. In fact, all the stars with log R (cid:48) HK ≥ − . α line by filaments saturates, and only plages contribute toemission in both Ca ii and H α . – We also found a tendency for the stars with negative corre-lations to be more metal rich than the rest of the sample andthat this holds for stars of similar activity level. – The distribution of the correlations in e ff ective temperaturewas also studied, and we detected that, in relative terms,there are more cooler stars showing positive correlations thanhotter stars. This is because, in our sample, cooler stars are in
9. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars general more active than hotter ones, and there is a tendencyfor the more active stars to have positive correlations. – As a parallel result, we found that our H α index can be usedto estimate the e ff ective temperature of a low-activity FGKstar.These results might a ff ect planet detections since activity isone of the main source of errors in radial velocity (and photo-metric) measurements. It would be interesting to compare thecorrelation between the flux in the Ca ii H & K and H α lineswith the measured radial velocity and see if this correlation hasany e ff ect on the observed radial velocity signal. Acknowledgements.
This work has been supported by the European ResearchCouncil / European Community under the FP7 through a Starting Grant, as wellas in the form of a grant reference PTDT / CTE-AST / / / BD / / / MCTES (Portugal) andPOPH / FSE (EC). I.B. also acknowledges the financial support given by FCT inthe form of grant reference SFRH / BPD / / References
Baliunas, S. L., Donahue, R. A., Soon, W. H., et al. 1995, ApJ, 438, 269Barklem, P. S., Stempels, H. C., Allende Prieto, C., et al. 2002, A&A, 385, 951Boisse, I., Bouchy, F., H´ebrard, G., et al. 2011, A&A, 528, A4 + Boisse, I., Moutou, C., Vidal-Madjar, A., et al. 2009, A&A, 495, 959Bouchy, F., Queloz, D., Deleuil, M., et al. 2008, A&A, 482, L25Cincunegui, C., D´ıaz, R. F., & Mauas, P. J. D. 2007, A&A, 469, 309do Nascimento, Jr., J. D., Canto Martins, B. L., Melo, C. H. F., Porto de Mello,G., & De Medeiros, J. R. 2003, A&A, 405, 723Dumusque, X., Lovis, C., S´egransan, D., et al. 2011a, A&A, 535, A55Dumusque, X., Pepe, F., Lovis, C., et al. 2012, Nature, 491, 207Dumusque, X., Santos, N. C., Udry, S., Lovis, C., & Bonfils, X. 2011b, A&A,527, A82Fuhrmann, K., Axer, M., & Gehren, T. 1993, A&A, 271, 451Giampapa, M. S., Cram, L. E., & Wild, W. J. 1989, ApJ, 345, 536Gomes da Silva, J., Santos, N. C., Bonfils, X., et al. 2011, A&A, 534, A30 + Gomes da Silva, J., Santos, N. C., Bonfils, X., et al. 2012, A&A, 541, A9Livingston, W., Wallace, L., White, O. R., & Giampapa, M. S. 2007, ApJ, 657,1137Lovis, C., Dumusque, X., Santos, N. C., et al. 2011, ArXiv e-printsMeunier, N. & Delfosse, X. 2009, A&A, 501, 1103Montes, D., Fernandez-Figueroa, M. J., de Castro, E., & Cornide, M. 1995,A&A, 294, 165Noyes, R. W., Hartmann, L. W., Baliunas, S. L., Duncan, D. K., & Vaughan,A. H. 1984, ApJ, 279, 763Pasquini, L. & Pallavicini, R. 1991, A&A, 251, 199Queloz, D., Henry, G. W., Sivan, J. P., et al. 2001, A&A, 379, 279Reiners, A. & Mohanty, S. 2012, ApJ, 746, 43Robertson, P., Endl, M., Cochran, W. D., & Dodson-Robinson, S. E. 2013, ApJ,764, 3Robinson, R. D., Cram, L. E., & Giampapa, M. S. 1990, ApJS, 74, 891Saar, S. H. & Donahue, R. A. 1997, ApJ, 485, 319Santos, N. C., Gomes da Silva, J., Lovis, C., & Melo, C. 2010, A&A, 511, A54 + Santos, N. C., Mayor, M., Naef, D., et al. 2000, A&A, 361, 265Santos, N. C., Pont, F., Melo, C., et al. 2006, A&A, 450, 825Schr¨oder, K.-P., Mittag, M., Hempelmann, A., Gonz´alez-P´erez, J. N., & Schmitt,J. H. M. M. 2013, A&A, 554, A50Sousa, S. G., Santos, N. C., Mayor, M., et al. 2008, A&A, 487, 373Sozzetti, A., Torres, G., Charbonneau, D., et al. 2007, ApJ, 664, 1190Sozzetti, A., Torres, G., Charbonneau, D., et al. 2009, ApJ, 691, 1145Strassmeier, K. G., Fekel, F. C., Bopp, B. W., Dempsey, R. C., & Henry, G. W.1990, ApJS, 72, 191Vaughan, A. H. & Preston, G. W. 1980, PASP, 92, 385Wright, J. T. 2004, AJ, 128, 1273Zechmeister, M., K¨urster, M., & Endl, M. 2009, A&A, 505, 859
10. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars , Online Material p 1 H α σ ( Hα ) = 0.0004N = 271 Fig. A.1: Calibration of H α index as a function of ( B − V ) colour.The solid curve line is the best fit to the data and the dashed linescorrespond to the 1– σ limits. l og I H α N = 271
Fig. A.2: Dependence of the log I H α index on stellar colour. Appendix A: The I H α hydrogen line based activityindex The H α index is calculated from the fraction of the flux in the H α line centreto the flux in two continuum reference bands, one bluer other redder than thehydrogen line. This is su ffi cient if we are interested in determining the activityevolution over time for a star. However, stars with di ff erent colours have di ff erentamounts of flux in the continuum, and this will make the average H α level notcomparable between di ff erent stars due to a systematic error introduced by thephotospheric flux interference in the measurements (e.g. Cincunegui et al. 2007).To be able to compare the average H α index between di ff erent stars thephotospheric contribution to the index need to be taken into account. Figure A.1shows the calibration of H α to the e ff ects of stellar colour. We fitted H α to ( B − V )using a cubic polynomial which resulted in a standard deviation of the fit of0 . I H α activity index is then (A.1) I H α = H α + . B − V ) − . B − V ) + . B − V ) . Figure A.2 shows that the resulting index is not dependent on ( B − V ) and cantherefore be used to compare the activity level of stars of di ff erent colour. Thiscalibration is valid for main sequence stars with ( B − V ) colour between 0.5 and1.2, and mean H α activity levels between 0.012 and 0.021. α >45005000550060006500 T e ff [ K ] ρ = − . , σ ( omc ) = K N = 249
Fig. B.1: Calibration of T e ff by using H α activity index for allmain sequence stars except the most active (log I HK ≥ − . Appendix B: Estimating effective temperatureusing the flux in H α line The H α line wings are known to be a proxy of e ff ective temperature (e.g.Fuhrmann et al. 1993; Barklem et al. 2002) and are sometimes used to confirmmore accurate results by other methods. For example, Bouchy et al. (2008) usedthe wings of the H α line to derive a temperature of 5450 ±
120 K for the starCoRoT-Exo-2. Sozzetti et al. (2007) compared the H α wings to those of syn-thetic spectra to obtain a temperature region of 5750-6000 K for TrES-2 (otherauthors that used the same technique as a rogue estimate of temperature includeSantos et al. 2006; Sozzetti et al. 2009).We found that our H α activity index is also a good proxy of T e ff . FigureB.1 shows a quadratic fit to the correlation between these parameters. Activestars (open circles) were not used due to their contribution to a larger scatter. Weobtained an rms of the T e ff residuals of σ =
68 K, and a correlation coe ffi cientof ρ = − .
96. The calibrated T e ff is of the form (B.1) T e ff = − (2109 H α − .
65 H α + . . This equation can be used for dwarfs with log I HK ≤ − .
70, mean H α activity inthe range 0 . ≤ H α ≤ . ff ective temperatures in the range 4600 ≤ T e ff ≤ . Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars , Online Material p 2 l og R H K HD1005083000 3500 4000 4500 5000BJD - 2450000 [days]0.0070.0060.0050.0040.0030.0020.0010.000 l og I H α log I Hα l og R H K l og R H K HD138083000 3500 4000 4500 5000 5500 6000BJD - 2450000 [days]1.7201.7151.7101.705 l og I H α log I Hα l og R H K Fig. B.2: Time-series of log R (cid:48) HK , log I H α , and correlation be-tween the two for the 12 stars with ”strong” correlations. Greydots are nightly averaged data, black points are binned data.Error bars are the standard errors on the mean. Black lines arebest fit to the binned data. A sinusoid will appear in the time-series if well fitted, i.e., having p ( F ) ≤ . l og R H K HD1545773500 4000 4500 5000 5500BJD - 2450000 [days]1.7101.7051.7001.6951.690 l og I H α log I Hα l og R H K l og R H K HD2091003000 3500 4000 4500 5000 5500BJD - 2450000 [days]1.7241.7221.7201.7181.7161.7141.7121.7101.708 l og I H α log I Hα l og R H K Fig. B.2: Continued. . Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars , Online Material p 3 l og R H K HD2151523500 4000 4500 5000 5500 6000BJD - 2450000 [days]1.7241.7221.7201.7181.7161.7141.7121.7101.708 l og I H α log I Hα l og R H K l og R H K HD49153000 3500 4000 4500BJD - 2450000 [days]1.7101.7081.7061.7041.7021.7001.6981.696 l og I H α log I Hα l og R H K Fig. B.2: Continued. l og R H K HD637653000 3500 4000 4500 5000BJD - 2450000 [days]1.7121.7101.7081.7061.7041.7021.7001.6981.696 l og I H α log I Hα l og R H K l og R H K HD718353000 3500 4000 4500 5000 5500BJD - 2450000 [days]1.7241.7221.7201.7181.7161.714 l og I H α log I Hα l og R H K Fig. B.2: Continued. . Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars , Online Material p 4 l og R H K HD71993000 3500 4000 4500 5000 5500BJD - 2450000 [days]1.7321.7301.7281.7261.7241.7221.7201.718 l og I H α log I Hα l og R H K l og R H K HD786123000 3500 4000 4500 5000 5500 6000BJD - 2450000 [days]1.7261.7241.7221.7201.7181.7161.7141.712 l og I H α log I Hα l og R H K Fig. B.2: Continued. l og R H K HD855123000 3500 4000 4500 5000 5500 6000BJD - 2450000 [days]1.7151.7101.7051.7001.6951.690 l og I H α log I Hα l og R H K l og R H K HD887423000 3500 4000 4500BJD - 2450000 [days]1.7121.7101.7081.7061.7041.7021.7001.6981.696 l og I H α log I Hα l og R H K Fig. B.2: Continued. . Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars , Online Material p 5
Table B.1: Parameters for the 66 stars with | ρ | ≥ . Star N obs T span ρ [Fe / H] T e ff (cid:104) log R (cid:48) HK (cid:105) σ (log R (cid:48) HK ) (cid:104) log I H α (cid:105) σ (log I H α )[days] [K]HD105837 21 2651 0 . − . ± .
01 5907 ± − .
825 0.019 − . . − . ± .
03 5059 ± − .
867 0.065 − . . − . ± .
02 5134 ± − .
938 0.033 − . . − . ± .
01 5613 ± − .
874 0.019 − . − .
55 0 . ± .
04 5172 ± − .
850 0.073 − . − . − . ± .
01 6069 ± − .
920 0.015 − . . − . ± .
02 5160 ± − .
691 0.020 − . . − . ± .
01 5584 ± − .
828 0.037 − . − .
59 0 . ± .
07 5007 ± − .
959 0.052 − . . − . ± .
02 5162 ± − .
897 0.043 − . .
60 0 . ± .
03 5255 ± − .
825 0.061 − . . − . ± .
06 4898 ± − .
841 0.022 − . . − . ± .
06 4740 ± − .
498 0.026 − . . − . ± .
03 5087 ± − .
908 0.074 − . .
63 0 . ± .
01 5610 ± − .
711 0.032 − . . − . ± .
02 5425 ± − .
659 0.031 − . − .
51 0 . ± .
02 5914 ± − .
073 0.019 − . . − . ± .
01 5958 ± − .
773 0.014 − . . − . ± .
06 4958 ± − .
660 0.041 − . . − . ± .
02 4900 ± − .
888 0.030 − . . − . ± .
01 5540 ± − .
792 0.033 − . . − . ± .
02 5343 ± − .
693 0.030 − . . − . ± .
02 5422 ± − .
706 0.031 − . . − . ± .
01 5500 ± − .
774 0.020 − . .
67 0 . ± .
02 5457 ± − .
616 0.039 − . . − . ± .
02 5241 ± − .
585 0.015 − . . − . ± .
04 4786 ± − .
804 0.055 − . . − . ± .
01 5477 ± − .
904 0.018 − . . − . ± .
04 4624 ± − .
882 0.033 − . . − . ± .
01 5577 ± − .
890 0.022 − . .
53 0 . ± .
02 5396 ± − .
738 0.051 − . . − . ± .
01 5608 ± − .
860 0.029 − . . − . ± .
01 5703 ± − .
806 0.032 − . . − . ± .
03 5199 ± − .
489 0.020 − . . − . ± .
04 4754 ± − .
782 0.028 − . . − . ± .
03 5137 ± − .
825 0.049 − . . − . ± .
04 4935 ± − .
870 0.033 − . . − . ± .
08 4723 ± − .
720 0.042 − . . − . ± .
01 5482 ± − .
907 0.017 − . . − . ± .
03 5029 ± − .
798 0.049 − . . − . ± .
04 4780 ± − .
958 0.037 − . .
56 0 . ± .
01 5648 ± − .
813 0.055 − . . − . ± .
01 5774 ± − .
848 0.028 − . . − . ± .
02 5185 ± − .
433 0.020 − . . − . ± .
03 5004 ± − .
756 0.015 − . .
75 0 . ± .
01 5767 ± − .
756 0.018 − . . − . ± .
02 5169 ± − .
895 0.062 − . . − . ± .
03 4977 ± − .
948 0.056 − . . − . ± .
03 5071 ± − .
591 0.029 − . . − . ± .
01 5658 ± − .
796 0.037 − . . − . ± .
01 5432 ± − .
742 0.039 − . . − . ± .
04 4802 ± − .
999 0.034 − . − . − . ± .
01 5891 ± − .
908 0.018 − . .
69 0 . ± .
01 6051 ± − .
798 0.033 − . . − . ± .
02 5438 ± − .
898 0.035 − . − .
78 0 . ± .
03 5386 ± − .
988 0.081 − . . − . ± .
01 5243 ± − .
920 0.027 − . . − . ± .
03 5233 ± − .
670 0.042 − . − .
54 0 . ± .
05 5283 ± − .
040 0.030 − . . − . ± .
02 5425 ± − .
440 0.015 − . . − . ± .
03 4715 ± − .
905 0.041 − . − . − . ± .
01 5502 ± − .
986 0.011 − . . − . ± .
01 5981 ± − .
699 0.045 − . . − . ± .
02 5164 ± − .
945 0.039 − . . − . ± .
01 5824 ± − .
861 0.024 − . . − . ± .
01 5773 ± − .
875 0.041 − . ii H & K and H α lines for FGK stars , Online Material p 6
Table B.2: Parameters for the 205 stars with | ρ | ≤ . Star N obs T span ρ [Fe / H] T e ff (cid:104) log R (cid:48) HK (cid:105) σ (log R (cid:48) HK ) (cid:104) log I H α (cid:105) σ (log I H α )[days] [K]HD10002 12 838 0 .
08 0 . ± .
03 5313 ± − .
083 0.013 − . − .
31 0 . ± .
05 5449 ± − .
049 0.030 − . − .
08 0 . ± .
01 5911 ± − .
006 0.013 − . − . − . ± .
02 5629 ± − .
944 0.010 − . − . − . ± .
01 5560 ± − .
950 0.008 − . . − . ± .
02 5023 ± − .
960 0.011 − . . − . ± .
05 4969 ± − .
742 0.025 − . − .
13 0 . ± .
02 5477 ± − .
042 0.021 − . − . − . ± .
01 5692 ± − .
954 0.010 − . − .
31 0 . ± .
01 5680 ± − .
023 0.011 − . . − . ± .
01 5310 ± − .
959 0.006 − . .
08 0 . ± .
01 5775 ± − .
019 0.017 − . .
08 0 . ± .
02 5801 ± − .
067 0.009 − . .
05 0 . ± .
01 6098 ± − .
002 0.005 − . − . − . ± .
01 5705 ± − .
935 0.017 − . − . − . ± .
01 5752 ± − .
000 0.005 − . − .
20 0 . ± .
02 5711 ± − .
116 0.013 − . − . − . ± .
01 5558 ± − .
990 0.010 − . . − . ± .
01 5649 ± − .
900 0.015 − . . − . ± .
01 5889 ± − .
947 0.006 − . .
22 0 . ± .
02 5667 ± − .
060 0.004 − . . − . ± .
01 5982 ± − .
015 0.007 − . − .
02 0 . ± .
03 5338 ± − .
097 0.011 − . . − . ± .
02 5395 ± − .
992 0.010 − . . − . ± .
01 5700 ± − .
980 0.009 − . − . − . ± .
02 5443 ± − .
995 0.011 − . .
02 0 . ± .
01 6036 ± − .
873 0.024 − . − . − . ± .
01 5638 ± − .
981 0.007 − . . − . ± .
01 5551 ± − .
916 0.007 − . . − . ± .
04 5026 ± − .
962 0.019 − . .
30 0 . ± .
03 5027 ± − .
017 0.015 − . − . − . ± .
01 5679 ± − .
874 0.016 − . . − . ± .
01 5418 ± − .
841 0.033 − . − .
13 0 . ± .
01 5966 ± − .
000 0.009 − . − .
07 0 . ± .
02 5633 ± − .
082 0.008 − . .
41 0 . ± .
01 5865 ± − .
881 0.027 − . − . − . ± .
01 5664 ± − .
949 0.005 − . − .
33 0 . ± .
05 4994 ± − .
795 0.038 − . − . − . ± .
02 5412 ± − .
995 0.005 − . .
01 0 . ± .
02 5868 ± − .
760 0.026 − . .
36 0 . ± .
03 5240 ± − .
894 0.049 − . .
18 0 . ± .
01 5582 ± − .
828 0.044 − . . − . ± .
01 5954 ± − .
979 0.007 − . . − . ± .
03 4728 ± − .
999 0.051 − . − . − . ± .
01 5775 ± − .
946 0.005 − . . − . ± .
02 5085 ± − .
952 0.022 − . . − . ± .
02 5417 ± − .
916 0.011 − . − .
06 0 . ± .
01 5765 ± − .
020 0.013 − . − .
20 0 . ± .
01 5818 ± − .
928 0.025 − . − . − . ± .
01 5516 ± − .
945 0.018 − . . − . ± .
01 5530 ± − .
990 0.006 − . − . − . ± .
01 5665 ± − .
961 0.005 − . .
01 0 . ± .
02 5457 ± − .
038 0.004 − . − .
35 0 . ± .
03 5179 ± − .
916 0.038 − . .
04 0 . ± .
03 5374 ± − .
064 0.015 − . − . − . ± .
04 4723 ± − .
820 0.050 − . .
06 0 . ± .
02 5451 ± − .
996 0.036 − . . − . ± .
01 6027 ± − .
969 0.010 − . .
26 0 . ± .
01 5676 ± − .
014 0.006 − . . − . ± .
01 5977 ± − .
936 0.007 − . . − . ± .
01 5560 ± − .
911 0.021 − . .
09 0 . ± .
02 5616 ± − .
032 0.006 − . − . − . ± .
01 6090 ± − .
973 0.010 − . .
04 0 . ± .
04 5339 ± − .
085 0.014 − . . − . ± .
03 5127 ± − .
734 0.026 − . . − . ± .
01 5518 ± − .
965 0.008 − . − . − . ± .
01 5983 ± − .
980 0.009 − . − .
17 0 . ± .
11 4751 ± − .
814 0.061 − . . − . ± .
01 5655 ± − .
906 0.017 − . − .
23 0 . ± .
04 5216 ± − .
929 0.041 − . .
06 0 . ± .
03 5018 ± − .
835 0.024 − . . − . ± .
01 5898 ± − .
863 0.028 − . .
33 0 . ± .
01 5627 ± − .
939 0.041 − . . − . ± .
02 5862 ± − .
929 0.003 − . . Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars , Online Material p 7
Table B.2: Continued.
Star N obs T span ρ [Fe / H] T e ff (cid:104) log R (cid:48) HK (cid:105) σ (log R (cid:48) HK ) (cid:104) log I H α (cid:105) σ (log I H α )[days] [K]HD17970 19 2962 0 . − . ± .
04 5040 ± − .
008 0.012 − . − . − . ± .
01 6013 ± − .
925 0.004 − . .
07 0 . ± .
13 4962 ± − .
144 0.014 − . .
14 0 . ± .
01 5803 ± − .
987 0.008 − . − . − . ± .
07 4595 ± − .
907 0.049 − . − .
10 0 . ± .
02 5570 ± − .
043 0.014 − . − . − . ± .
01 5623 ± − .
967 0.013 − . . − . ± .
01 5726 ± − .
916 0.016 − . .
42 0 . ± .
02 5846 ± − .
810 0.041 − . .
02 0 . ± .
03 5604 ± − .
095 0.010 − . − . − . ± .
02 5430 ± − .
969 0.012 − . . − . ± .
01 5215 ± − .
954 0.006 − . . − . ± .
03 5166 ± − .
991 0.040 − . − . − . ± .
01 5979 ± − .
933 0.016 − . . − . ± .
01 5720 ± − .
002 0.015 − . . − . ± .
01 5415 ± − .
918 0.025 − . .
23 0 . ± .
01 5926 ± − .
052 0.014 − . . − . ± .
01 5765 ± − .
895 0.005 − . − .
37 0 . ± .
02 5973 ± − .
012 0.019 − . − .
25 0 . ± .
02 5494 ± − .
988 0.040 − . .
19 0 . ± .
02 5645 ± − .
858 0.057 − . . − . ± .
01 5866 ± − .
899 0.007 − . .
03 0 . ± .
02 5776 ± − .
019 0.017 − . − .
13 0 . ± .
01 6033 ± − .
976 0.009 − . . − . ± .
03 5056 ± − .
952 0.030 − . . − . ± .
02 5442 ± − .
016 0.006 − . .
32 0 . ± .
01 5937 ± − .
903 0.030 − . .
30 0 . ± .
01 5666 ± − .
006 0.010 − . − . − . ± .
02 5256 ± − .
035 0.011 − . . − . ± .
01 5774 ± − .
919 0.015 − . − . − . ± .
01 5401 ± − .
981 0.006 − . − .
44 0 . ± .
02 5556 ± − .
028 0.010 − . . − . ± .
01 5866 ± − .
881 0.013 − . . − . ± .
01 5826 ± − .
957 0.011 − . − . − . ± .
01 5923 ± − .
874 0.004 − . − . − . ± .
01 5755 ± − .
002 0.015 − . . − . ± .
01 5850 ± − .
919 0.023 − . − . − . ± .
04 4671 ± − .
840 0.022 − . − .
34 0 . ± .
02 5681 ± − .
076 0.014 − . .
26 0 . ± .
01 5555 ± − .
957 0.010 − . . − . ± .
01 5532 ± − .
909 0.013 − . − . − . ± .
01 5654 ± − .
924 0.016 − . .
02 0 . ± .
02 5430 ± − .
909 0.055 − . . − . ± .
01 5778 ± − .
939 0.007 − . − . − . ± .
03 5144 ± − .
022 0.016 − . .
02 0 . ± .
01 5698 ± − .
052 0.010 − . − . − . ± .
03 6112 ± − .
919 0.004 − . .
13 0 . ± .
01 5894 ± − .
863 0.022 − . − . − . ± .
01 5436 ± − .
975 0.013 − . . − . ± .
02 5857 ± − .
908 0.007 − . . − . ± .
01 6178 ± − .
909 0.010 − . . − . ± .
03 5153 ± − .
944 0.034 − . − . − . ± .
02 5157 ± − .
949 0.011 − . . − . ± .
01 5745 ± − .
991 0.021 − . − . − . ± .
01 5710 ± − .
986 0.012 − . . − . ± .
01 5660 ± − .
975 0.013 − . − . − . ± .
02 5394 ± − .
006 0.013 − . .
43 0 . ± .
02 5529 ± − .
074 0.013 − . . − . ± .
01 5898 ± − .
955 0.006 − . . − . ± .
01 6042 ± − .
865 0.007 − . . − . ± .
01 5818 ± − .
032 0.013 − . − . − . ± .
02 5274 ± − .
972 0.035 − . . − . ± .
01 5848 ± − .
883 0.013 − . . − . ± .
03 4928 ± − .
799 0.037 − . − . − . ± .
06 4647 ± − .
872 0.040 − . . − . ± .
01 5916 ± − .
992 0.006 − . − . − . ± .
01 6030 ± − .
976 0.006 − . − .
24 0 . ± .
03 5507 ± − .
082 0.013 − . − . − . ± .
01 6022 ± − .
988 0.007 − . − . − . ± .
01 5871 ± − .
019 0.007 − . − . − . ± .
01 5733 ± − .
918 0.013 − . − .
07 0 . ± .
01 6016 ± − .
972 0.013 − . . − . ± .
02 5205 ± − .
951 0.014 − . . − . ± .
01 5527 ± − .
013 0.009 − . . Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H α lines for FGK stars , Online Material p 8
Table B.2: Continued.
Star N obs T span ρ [Fe / H] T e ff (cid:104) log R (cid:48) HK (cid:105) σ (log R (cid:48) HK ) (cid:104) log I H α (cid:105) σ (log I H α )[days] [K]HD44120 18 3019 0 .
33 0 . ± .
01 6052 ± − .
070 0.017 − . .
14 0 . ± .
02 5818 ± − .
036 0.024 − . . − . ± .
01 5999 ± − .
977 0.015 − . − .
01 0 . ± .
01 5840 ± − .
004 0.020 − . .
24 0 . ± .
01 5869 ± − .
905 0.026 − . . − . ± .
01 5717 ± − .
033 0.008 − . − . − . ± .
01 5434 ± − .
959 0.022 − . − .
28 0 . ± .
02 5675 ± − .
051 0.009 − . − . − . ± .
04 4870 ± − .
974 0.032 − . . − . ± .
01 5358 ± − .
982 0.020 − . − .
43 0 . ± .
02 5914 ± − .
999 0.020 − . − .
17 0 . ± .
01 5618 ± − .
996 0.012 − . . − . ± .
01 5722 ± − .
946 0.010 − . . − . ± .
03 5076 ± − .
954 0.035 − . − . − . ± .
01 5945 ± − .
914 0.010 − . − .
04 0 . ± .
02 5635 ± − .
058 0.020 − . . − . ± .
01 6082 ± − .
877 0.014 − . .
26 0 . ± .
03 5215 ± − .
728 0.036 − . − .
03 0 . ± .
02 5965 ± − .
879 0.015 − . . − . ± .
01 5961 ± − .
943 0.009 − . − . − . ± .
01 5694 ± − .
987 0.010 − . . − . ± .
01 5940 ± − .
949 0.005 − . − .
14 0 . ± .
01 6026 ± − .
040 0.015 − . − .
35 0 . ± .
02 5449 ± − .
087 0.009 − . − .
07 0 . ± .
02 5640 ± − .
090 0.015 − . .
07 0 . ± .
01 6091 ± − .
061 0.013 − . − .
12 0 . ± .
01 6017 ± − .
002 0.017 − . − .
29 0 . ± .
02 5561 ± − .
072 0.010 − . . − . ± .
01 6024 ± − .
850 0.015 − . − .
24 0 . ± .
01 5760 ± − .
927 0.029 − . . − . ± .
01 5711 ± − .
974 0.009 − . . − . ± .
01 5834 ± − .
005 0.017 − . − . − . ± .
01 5778 ± − .
921 0.008 − . . − . ± .
02 5522 ± − .
990 0.013 − . . − . ± .
03 4820 ± − .
943 0.032 − . − .
04 0 . ± .
04 5104 ± − .
955 0.044 − . . − . ± .
01 5902 ± − .
970 0.009 − . . − . ± .
01 5726 ± − .
856 0.009 − . . − . ± .
03 5186 ± − .
959 0.026 − . . − . ± .
04 4903 ± − .
806 0.020 − . − . − . ± .
02 5507 ± − .
953 0.006 − . . − . ± .
01 5766 ± − .
973 0.009 − . . − . ± .
02 5403 ± − .
996 0.010 − . .
46 0 . ± .
01 5728 ± − .
701 0.029 − . . − . ± .
01 5599 ± − .
947 0.006 − . .
38 0 . ± .
03 5444 ± − .
004 0.034 − . − .
07 0 . ± .
01 5977 ± − .
988 0.007 − . .
02 0 . ± .
01 5583 ± − .
974 0.031 − . − .
08 0 . ± .
02 6276 ± − .
982 0.019 − . .
05 0 . ± .
01 5711 ± − .
035 0.013 − . − . − . ± .
01 5845 ± − .
948 0.011 − . . − . ± .
01 5883 ± − .
998 0.009 − . . − . ± .
01 5410 ± − .
015 0.009 − . − .
35 0 . ± .
01 6023 ± − .
974 0.007 − . . − . ± .
02 5179 ± − .
874 0.025 − . . − . ± .
01 5716 ± − .
902 0.007 − . . − . ± .
02 5381 ± − .
887 0.027 − ..