Issue 
A&A
Volume 621, January 2019



Article Number  A136  
Number of page(s)  7  
Section  Stellar structure and evolution  
DOI  https://doi.org/10.1051/00046361/201834319  
Published online  18 January 2019 
Discovery of shortterm activity cycles in Ftype stars
^{1}
Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
email: mmittag@hs.unihamburg.de
^{2}
Department of Astronomy, University of Guanajuato, Mexico
Received:
25
September
2018
Accepted:
16
November
2018
Previous studies have revealed a 120 day activity cycle in the Ftype star τ Boo, which represents the shortest activity cycle discovered until now. The question arises as to whether or not shortterm activity cycles are a common phenomenon in Ftype stars. To address this question, we analyse Sindex time series of Ftype stars taken with the TIGRE telescope to search for periodic variations with a maximal length of 2 years using the generalised LombScargle periodogram method. In our sample, we find four Ftype stars showing periodic variations shorter than one year. However, the amplitude of these variations in our sample of Fstar type stars appears to be smaller than that of solartype stars with welldeveloped cyclic activity, and apparently represents only a part of the total activity. We conclude that among Fstars, the timebehaviour of activity differs from that of the Sun and cooler main sequence stars, as shortterm cyclic variations with shallow amplitude of the cycle seem to prevail, rather than cycles with 10+ years periods and a larger cycle amplitude.
Key words: stars: activity / stars: atmospheres / stars: chromospheres / stars: latetype
© ESO 2019
1. Introduction
While the 11year activity cycle of our Sun was already discovered by Schwabe (1844), the systematic search for activity cycles in main sequence stars only started with the Mount Wilson HK program (Wilson 1978; Baliunas et al. 1995), which began in 1966 and terminated at the end of the last century. In a landmark paper Baliunas et al. (1995) presented the time series of 112 stars from the Mount Wilson HK program, including the Sun observed as a star, and found activity cycles in 46 stars. Depending on the false alarm probability (FAP), Baliunas et al. (1995) assigned a grade to each of the determined cycles and labelled the cycles as “excellent” (FAP ≤10^{−9}), “good” (10^{−9}< FAP ≤10^{−5}), “fair” (10^{−5}< FAP ≤ 10^{−2}), and “poor” (10^{−2}< FAP ≤10^{−1}).
In nine stars, Baliunas et al. (1995) also found a secondary cycle, while the shortest reported activity cycle (for the Gtype star HD 76151) has a period of 2.52 yr with a FAP grade “fair”. Ten of the 46 stars with a determined activity cycle are Ftype stars with cycles being assigned only the FAP grade “fair” or “poor”. The shortest cycle among the investigated Ftype stars is 3.56 yr with the FAP grade “fair” for the star HD 100180. The remaining stars without any significant period were categorised by Baliunas et al. (1995) into four classes, namely “flat”, “flat?”, “long” or “var” depending on the ratio of the scatter and mean Svalue. Those stars categorised as “flat” have σ_{S}/S < 1%−1.5%, “flat?” have σ_{S}/S ≈ 1.5%−2.%, “var” have σ_{S}/S > 2% without a significant periodic signal in the time range from 1 to 25 years, and “long” refers to stars with variability on a timescale longer than 25 years.
As far as solartype, pronounced (“excellent” or “good” in the nomenclature of Baliunas et al. 1995) cycles of a period of approximately 10 yr or more are concerned, by placing the Mount Wilson sample stars in the HR diagram, Schröder et al. (2013) found that the Sun seems to be near the upper end of such detections on the main sequence, while most other pronounced cycles are found among somewhat cooler, less massive stars (see Fig. 4 in that paper). Consequently, Fstars do not show the same form of solartype activity with long, pronounced cycles. What therefore is their activity like in the timedomain?
In the bright Ftype star τ Boo (HD 120136), Baliunas et al. (1995) report an activity cycle with a length of 11.6 yr; however, with the FAP grade “poor”. Baliunas et al. (1997) also mention a 116 day “variation” in their Ca II data for τ Boo without providing any details for the estimation and nature of this variation. In new and independent Sindex data, Mengel et al. (2016) and Mittag et al. (2017) found an activity cycle ≈117 days and ≈122 days, respectively. Simultaneously, Schmitt & Mittag (2017) reanalysed the Mount Wilson Sindex time series of τ Boo in detail and confirmed the presence of such a shortperiod cycle over the past 40 years. Mittag et al. (2017) also showed that Xray data support a periodicity of about 120 days. As far as shortterm activity cycles in Ftype stars are concerned, we note that Metcalfe et al. (2010) found a 1.6 yr activity cycle for ι Hor (HD 17051; spectral type F8) and García et al. (2010) report an indication for at least a 120 day cycle for HD 49933 (spectral type F3). Thus the question arises as to how common shortterm cycles in Ftype stars are.
Our longterm monitoring program of stellar activity performed with the TIGRE telescope (Schmitt et al. 2014) also contains Ftype stars, which we examined for the presence of shortterm activity cycles. Higher cadence thanks to the robotic operation of TIGRE and precise Smeasurements thanks to a high signaltonoise ratio (S/N) in line cores of the Ca II H&K lines – for example for HD 16673 a mean S/N of 100 in the 1 Å band pass – make these observational data especially suitable for this task. Here we present the results for four Fstars, namely HD 16673, HD 49933, HD 75332, and HD 100563, which show clear evidence for shortterm cycles in their activityrelated chromospheric emission.
2. Observations
Table 1 provides some details on the three stars discussed in this paper, that is, visual magnitude V and B − V colour (taken from HIPPARCOS catalogue ESA 1997) together with the total number of TIGRE Sindex measurements available. The TIGRE telescope is a fully robotic telescope with a 1.2 m aperture, located at the La Luz Observatory near Guanajuato, Mexico. Its only instrument is the twochannel fibrefed Échelle spectrograph HEROS with a wavelength range from 3800 Å to 8800 Å with a 100 Å gap at 5800 Å and a spectral resolution of R ≈ 20 000; a detailed description of the TIGRE facility is given by Schmitt et al. (2014).
Object and observational information.
The spectral data are reduced with the TIGRE/HEROS standard reduction pipeline version v3.1, implemented in IDL and based on the IDL reduction package REDUCE (Piskunov & Valenti 2002). The TIGRE/HEROS pipeline is designed as a fully automatic datareduction pipeline and includes all necessary reduction steps for Échelle spectra; a detailed description of an older TIGRE/HEROS pipeline version is given by Mittag et al. (2010) and additional general information on the pipeline is provided by Hempelmann et al. (2016) and Mittag et al. (2016).
An additional feature implemented in the TIGRE/HEROS reduction pipeline is the automatic estimation of the instrumental Sindex (S_{TIGRE}), defined as (Mittag et al. 2016)
where N_{H} and N_{K} are the Ca II H&K line intensities summed in a 1 Å wide rectangular band pass centred on the H and K lines, respectively, and N_{R} and N_{V} are the summed intensities in two 20 Åwide band passes centred on 3901.07 Å and 4001.07 Å, respectively. The instrumental S_{TIGRE} index can be converted with a linear relation into the socalled Mount Wilson Sindex (S_{MWO}), the classical and commonly used activity index, through the equation
Further general information on the automatic estimation of S_{TIGRE} and the derivation of Eq. (2) can be found in Mittag et al. (2016).
The Sindex transformation given in Eq. (2) was derived with S_{TIGRE} data taken until May 2015 and from spectra reduced with the datareduction pipeline version 1. In the meantime, the pipeline has been updated and more Svalues have been obtained for our calibration stars [see Table 2 of ][]Mittag2016. Therefore, we decided to check our Sindex calibration, but found no significant changes. Next, we tested the influence of different versions of the datareduction pipeline on our Sindex values: We first compared the mean TIGRE Sdata computed with the different reduction versions and found a mean scatter between the mean Sdata of less than 1%. In Fig. 1 we show the ratio of mean TIGRE Mount Wilson Sindex of our calibration stars obtained using different pipeline versions versus the TIGRE Mount Wilson Sindex from the last pipeline version. The upgrade of the datareduction pipeline has a larger influence on the individual Sindex than on the mean Sindex, meaning that the individual Sindex values can show more variation. An important upgrade of the pipeline was the improvement of the treatment of cosmics which can impact the Sindex calculation. To quantify this dispersion, we computed the difference between the Svalues obtained from the different reductions and determined the scatter. We find a mean scatter of 1.5% in the difference between the Sdata computed with the different reduction version and conclude that the different reduction versions have no significant influence on the mean Svalue, except for the individual Svalues at a level of 1.5% on the mean.
Fig. 1. Ratio of the mean TIGRE Sdata obtained from the reduction pipelines. 

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3. Data analysis
3.1. Period, error of the period, and falsealarm probability estimation
To search for periodic variations in our Sindex time series, we use the generalised LombScargle (GLS) method by Zechmeister & Kürster (2009). For this analysis, we used our own Python code based on the equations presented by Zechmeister & Kürster (2009). The GLS formalism assumes a sinusoidal wave form with a constant offset and calculates a χ^{2}value using the model ansatz
where A, B, and C are constants calculated from the data y_{i} with uncertainty σ_{i} at the times t_{i}, i =...N, where N denotes the number of data points. The GLS periodogram is calculated with the expression (Zechmeister & Kürster 2009)
where is the χ^{2}value from the weighted mean and is used for the normalisation of χ^{2}(ω); a detailed description and derivation of the GLS method is given by Zechmeister & Kürster (2009).
The error in the determined period is estimated using the equation (Baliunas et al. 1995)
where σ_{n} denotes the standard deviation of the residuals (O–C), P the period, T the total length of the observation interval, A the amplitude of the signal, and N the total number of data points.
For the FAP estimation, we use the method described by Zechmeister & Kürster (2009), who define the FAP as
where Prob(p > p_{0}) is the probability estimated with Eq. (7) and M the number of independent frequencies. The probability Prob(p > p_{0}) is estimated following Zechmeister & Kürster (2009) through
where p_{0} is the peak height and N the number of data points. For the estimation of the number of independent frequencies M, we follow the method described by Zechmeister & Kürster (2009). Here, the number of independent frequencies is given by
where Δf is the frequency range (f_{max} − f_{min}) and δf the frequency resolution. In our case, the frequency range Δf is equal to f_{max} because f_{max} ≫ f_{min}. For the estimation of f_{max}, the time spans (ΔT) between consecutive observations are computed and the most frequent value of ΔT is determined. This value is multiplied by a factor of two to estimate the smallest reasonable period and f_{max}, respectively. Our definition of f_{max} is comparable with the definition of the Nyquist frequency for evenly sampled time series . For the frequency resolution (δf), we compute the FWHM of a peak in the periodogram and use this value as δf.
3.2. Prewhitening analysis
To test the independence of different peaks in a periodogram we use a prewhitening procedure that removes a previously found period from the time series and then the period search is repeated for the residuals.
If the relevant peaks remain, they are independent and must be taken into account in the analysis, if not these peaks are not independent and can be attributed to aliasing effects.
4. Results
In the following section we present our TIGRE Sindex time series for the stars HD 16673, HD 49933, HD 75332, and HD 100563 and analyse them for periodic variations with the GLS formalism (see, Sect. 3.1 for details). Therefore, we used only Sindices from spectra with a minimal mean S/N of 25. For each case we present the recorded TIGRE time series in a “raw” form and folded with the most likely period. Further, we present the GLS periodogram and the window function of the observations. The results of our GLS analysis are presented in Table 2, where we list the determined periods, the derived FAPs and the amplitudes of the variations. In the following subsections, the four stars and the derived results are discussed individually in more detail.
Results of the period search.
4.1. HD 16673
HD 16673 is of spectral type F8V (Simbad database) with a rotation period of 7.40 ± 0.07 days (Baliunas et al. 1985). Mittag et al. (2018) published RV data of HD 16673 taken with the TIGRE telescope and showed the binary nature of this star; the same result is also published by Gorynya & Tokovinin (2018). Baliunas et al. (1995) list HD 16673 with a mean S_{MWO}index of 0.215 and labelled as variable star without a significant period larger than 1 yr and shorter than 25 yr. Our TIGRE S_{MWO}index time series is shown in Fig. 2; we obtain a mean S_{MWO} value of 0.219 with a standard deviation of 0.012, very much comparable to the results obtained by Baliunas et al. (1995).
Fig. 2. HD 16673 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 309.4 days. 

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The result of our LombScargle analysis is shown in the upper panel of Fig. 3. The GLS periodogram has a significant peak at 309.4 days with a FAP of 5 × 10^{−15} for this period. In the lower panel of Fig. 3, the window function of our HD 16673 Sindex time series is presented, which clearly shows the seasonal sampling of one year. However, this peak at 355 days in the window function is clearly different from the peak in the time series periodogram. We therefore conclude that the GLS period is not influenced by the seasonal sampling and is indeed highly significant.
Fig. 3. Upper panel: periodogram of the HD 16673 Sindex time series. Lower panel: window function of the HD 16673 Sindex time series. 

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The Sindex data, phasefolded with the period of 309.4 days, are shown in Fig. 4. To estimate the amplitude of the variation, we fit the data with a sine function with the most significant period, and the result is shown as a red line in Figs. 2 and 4. We find an amplitude of the variation of 0.0144 in S_{MWO}; after the removal of this variation, the standard deviation of the residuals is reduced to 0.0065.
Fig. 4. Phasefolded HD 16673 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 309.4 days. 

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4.2. HD 49933
HD 49933 is of the spectral type F3V (according to the Simbad database) and has a rotational period of 3.45 days (Mosser et al. 2009). For this star, an indication for a shortterm activity cycle of at least 120 days in the CoRoT light curve is reported by García et al. (2010). Furthermore, a Mount Wilson Sindex of 0.3 is given for HD 49933 in García et al. (2010). In the upper panel of Fig. 5 we show the TIGRE S_{MWO}index time series, from which we derive a mean Sindex value of 0.213 with a standard deviation of 0.01, clearly lower than the value reported by García et al. (2010). This difference might be due to different Sindex calibrations and/or to a longterm trend caused by a longterm activity cycle. In our TIGRE Sindex data, a longterm trend is visible (see red line in the upper panel of Fig. 5), suggesting that a part of the Sindex difference could be caused by this trend.
Fig. 5. Upper panel: HD 49933 S_{MWO} time series taken with TIGRE. The red line depicts the estimated trend. Lower panel: detrended S_{MWO} time series; the red line depicts the sinusoidal fit with the found period of 219.2 days. 

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For the LombScargle analysis, we detrend our Sindex time series (see lower panel of Fig. 5), from which we compute the LombScargle periodogram plotted in the upper panel of Fig. 6; the window function of our Sindex time series is shown in the lower panel of Fig. 6. The highest peak in the periodogram and therefore the most probable period is at 212.2 days, for which we estimate a FAP of 7 × 10^{−6}. The Sindex data are fitted with a sinusoidal curve at the determined period of 212.2 days and the result is depicted as the red line in the lower panel of Fig. 6 and in Fig. 7 for the phasefolded Sindex; from the sinusoidal fit we obtain an amplitude of this variation of 0.0063 with a standard deviation of 0.0052.
Fig. 6. Upper panel: periodogram of the HD 49933 Sindex time series. Lower panel: window function of the HD 49933 Sindex time series. 

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Fig. 7. Phasefolded HD 49933 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with the found period of 212.2 days. 

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However, the periodogram also shows two clear peaks at 170.1 and 465.7 days with a FAP of 6 × 10^{−4} and 2 × 10^{−4}, respectively. To test the significance of the peaks, we performed prewhitening for the three periods. First, the most probable period of 212.2 days is removed and the LombScargle analysis of the residuals performed. Here, the peak at 465.7 days vanishes but not the peak at 170.1 days. Next, the 465.7day period is removed and the residuals are tested. In this case, the 212.2day period remains, but the peak is no longer significant, while the peak at 170.1 days decreases slightly and a smaller peak at ∼300 days in the periodogram (see lower panel of Fig. 6) becomes the strongest peak in the periodogram of the residuals. From this test, we can conclude that the periods of 212.2 and 465.7 days are not independent. Finally, the 170.1day period is removed and the peaks at 212.2 and 465.7 days remain. Hence, the 170.1day period is interesting. It appears that this period is independent of both the 212.2day and the 465.7day periods, but to check the significance of this period, a longer and more densely sampled time series is required.
4.3. HD 75332
HD 75332 is of spectral type F7V (Simbad database) with a rotational period of 4.8 days (Vidotto et al. 2014). Baliunas et al. (1995) list HD 75332 with a mean S_{MWO}index of 0.279 as a variable star without a significant period in the range of 1–25 yr. We obtained a mean S_{MWO}index of 0.279 with a standard deviation of 0.01, again consistent with the S_{MWO} value listed by Baliunas et al. (1995).
The TIGRE S_{MWO} time series is presented in Fig. 8, and in the upper panel of Fig. 9 we show the periodogram of our TIGRE S_{MWO} time series. This periodogram has two significant peaks, the higher peak being located at 179.9 days with a FAP of 5 × 10^{−17}. The second significant peak is at 349.5 days, which is very close to one year and the samplingrelated, seasonal peak at 384.2 days, as seen in the window function (in the lower panel in Fig. 9). We cannot exclude that this second peak may be influenced by the seasonal sampling, so we disregard it.
Fig. 8. HD 75332 S_{MWO} time series taken with TIGRE; the red line depicts the sinusoidal fit with a period of 179.9 days. 

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Fig. 9. Upper panel: periodogram of the HD 75332 Sindex time series. Lower panel: window function of the HD 75332 Sindex time series. 

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In Fig. 10 the phasefolded TIGRE S_{MWO} data are presented; the Sindex data are fitted with a sine function at the main period at 179.9 days and the result of this fit is shown as a red line in Figs. 8 and 10. From this fit, we obtain an amplitude for the periodic variation of 0.0095. Also, it is clear that the fit with the period of 179.9 days describes the data in the first two seasons very well. Finally, when removing the variations from the data we obtain a standard deviation of 0.0073 for the residuals and a prewhitening test shows no remaining periodic variations. Additionally, we perform a prewhitening test with the 349.5day period. Here, the period at 179.9 days remains, but the significance of the peak is reduced significantly.
Fig. 10. Phasefolded HD 75332 S_{MWO} time series taken with TIGRE; the red line depicts the sinusoidal fit with a period of 179.9 days. 

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4.4. HD 100563
The spectral type of HD 100563 is F5.5V (Simbad database). A rotation period of 7.73 days was listed in Hempelmann et al. (2016), albeit with low significance (1σ) obtained from TIGRE data taken from 2013 to 2014. Baliunas et al. (1995) list HD 100563 with a mean S_{MWO}index of 0.202 and without a significant period. In the upper panel of Fig. 11, we show the S_{MWO} time series taken with TIGRE; we find a mean S_{MWO}index of 0.195 with a standard deviation of 0.0063, slightly lower than the value listed in Baliunas et al. (1995).
Fig. 11. HD 100563 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 222.3 days. 

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However, we see a small trend in our Sindex data, which might explain this small difference; the detrended time series is shown in the lower panel of Fig. 11. After detrending we perform the LombScargle analysis and present the result in the upper panel of Fig. 13, while the lower panel of Fig. 13 shows the window function of this time series. The highest peak in the GLS periodogram is at a period of 222.3 days with a formal FAP of only 1 × 10^{−3}. The FAP of HD 100563 is small compared to the other three objects in this work. Following the classification of the FAP grade by Baliunas et al. (1995), the cycle is only “fair”. We therefore consider this result as simply an indication of a shortterm cycle. In Fig. 12, we show the phasefolded TIGRE Sindex data together with a sine function fit to the data (using the period of 222.3 days); in Figs. 11 and 12 these fit results are depicted with the red line. For the amplitude of this variation we obtain 0.0033 and after the removal of the cycle, the standard deviation of the residuals is 0.0042.
Fig. 12. Phasefolded HD 100563 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 222.3 days. 

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Fig. 13. Upper panel: periodogram of the HD 100563 Sindex time series. Lower panel: window function of the HD 100563 Sindex time series. 

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5. Summary and conclusions
In this paper we present the Sindex time series of four Ftype stars observed with the TIGRE telescope. In each of these time series we find a significant periodic signal, which we interpret as a shortterm magnetic cycle; the amplitudes lie between 0.003 and 0.015 in Sindex values.
With the detections of three more shortterm cycles and one candidate, in addition to the already known cycle of τ Boo, we conclude that such shortterm activity cycles appear to be a common and possibly typical phenomenon in Ftype stars. The cycle lengths of the four found activity cycles are between 0.5 and 1 year, so the 120day shortterm activity cycle in τ Boo is still the shortest known, albeit by no means exceptional.
Furthermore, we find that in these four Fstars the amplitude of the cycle is not as large as commonly found with longperiod (10+ years), solartype cyclic activity. Therefore these shortterm cycles may contribute to further activity with a large spectrum of variability in the time domain, or the observed smaller amplitude may be inherent to this type of shortterm cycle.
The currently available sample is clearly too small to draw any statistically significant conclusions, but it did not escape our attention that in our four stars rotation periods and cycle lengths are roughly proportional. On the other hand, such a direct comparison does not hold in its extension to solartype stars, where the cycle periods are more than an order of magnitude longer. Brandenburg et al. (2017) derive a relation between the cycle length and rotation period using the convective turnover time as a factor in their relation. The convective turnover time depends on the colour index B − V or rather T_{eff}, and therefore one can assume a B − V dependence between the cycle length and the rotation period.
In this respect, we find the theoretical prediction of Brandenburg et al. (2017), that is, that both long and short period cycles could coexist, very interesting. In Fig. 14, we show the cycle period versus the rotational period; the blue data points (Sun with a diamond) are depicted; the data are taken from Brandenburg et al. (2017, Table 3) for F and Gtype stars of the socalled short inactive branch. The shortterm cycles found is this work with the corresponding rotational periods mentioned in the text, and also the cycle and rotational period of τ Boo taken from Mittag et al. (2017) are all displayed as red points in Fig. 14; except HD 100563 which is shown as red square. We see from Fig. 14 that the shortterm cycles (red points) seem to be consistent with the shortterm cycle branch from Brandenburg et al. (2017). We also note that ι Hor (HD 17051) is included in the Brandenburg sample (last blue data point at the low period tail) and fits in the general trend. We therefore conclude that for the study of magnetic activity of solarlike stars in a wider context, and to aid dynamo theory modelling, Ca II monitoring of Ftype stars appears to be a rewarding task, which is perfectly suited for a robotic telescope like TIGRE.
Fig. 14. Blue data points taken from Brandenburg et al. (2017; Table 3) (Sun with a diamond) for F and Gtype stars referred to as the short inactive branch. The red data point are labelled the shortterm cycles found in this work (the corresponding rotational periods are mentioned in the text) including the cycle and rotational period of τ Boo taken from Mittag et al. (2017). The red square data point marks HD 100563 where the significance of the period are comparable low and therefore, we consider this object only as a candidate for a shortterm activity cycle. 

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Acknowledgments
This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in A&AS 143, 23.
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All Tables
All Figures
Fig. 1. Ratio of the mean TIGRE Sdata obtained from the reduction pipelines. 

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In the text 
Fig. 2. HD 16673 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 309.4 days. 

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In the text 
Fig. 3. Upper panel: periodogram of the HD 16673 Sindex time series. Lower panel: window function of the HD 16673 Sindex time series. 

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In the text 
Fig. 4. Phasefolded HD 16673 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 309.4 days. 

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In the text 
Fig. 5. Upper panel: HD 49933 S_{MWO} time series taken with TIGRE. The red line depicts the estimated trend. Lower panel: detrended S_{MWO} time series; the red line depicts the sinusoidal fit with the found period of 219.2 days. 

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In the text 
Fig. 6. Upper panel: periodogram of the HD 49933 Sindex time series. Lower panel: window function of the HD 49933 Sindex time series. 

Open with DEXTER  
In the text 
Fig. 7. Phasefolded HD 49933 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with the found period of 212.2 days. 

Open with DEXTER  
In the text 
Fig. 8. HD 75332 S_{MWO} time series taken with TIGRE; the red line depicts the sinusoidal fit with a period of 179.9 days. 

Open with DEXTER  
In the text 
Fig. 9. Upper panel: periodogram of the HD 75332 Sindex time series. Lower panel: window function of the HD 75332 Sindex time series. 

Open with DEXTER  
In the text 
Fig. 10. Phasefolded HD 75332 S_{MWO} time series taken with TIGRE; the red line depicts the sinusoidal fit with a period of 179.9 days. 

Open with DEXTER  
In the text 
Fig. 11. HD 100563 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 222.3 days. 

Open with DEXTER  
In the text 
Fig. 12. Phasefolded HD 100563 S_{MWO} time series taken with TIGRE. The red line depicts the sinusoidal fit with a period of 222.3 days. 

Open with DEXTER  
In the text 
Fig. 13. Upper panel: periodogram of the HD 100563 Sindex time series. Lower panel: window function of the HD 100563 Sindex time series. 

Open with DEXTER  
In the text 
Fig. 14. Blue data points taken from Brandenburg et al. (2017; Table 3) (Sun with a diamond) for F and Gtype stars referred to as the short inactive branch. The red data point are labelled the shortterm cycles found in this work (the corresponding rotational periods are mentioned in the text) including the cycle and rotational period of τ Boo taken from Mittag et al. (2017). The red square data point marks HD 100563 where the significance of the period are comparable low and therefore, we consider this object only as a candidate for a shortterm activity cycle. 

Open with DEXTER  
In the text 
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