Carrington cycle 24: The solar chromospheric emission in a historical and stellar perspective

TL;DR

This study presents a detailed record of solar chromospheric Ca II H&K emission during cycle 24, revealing unusually deep minimum and low maximum activity, with implications for understanding solar UV flux variations and their impact on Earth's atmosphere.

Contribution

It provides the first high-resolution, calibrated S-index record of cycle 24 using moonlight, enabling direct comparison with historical data and other stars, highlighting unique solar activity features.

Findings

Cycle 24 had an unusually deep and long minimum in 2008/09.

The cycle 24 maximum was notably low compared to previous cycles.

Chromospheric emission variations differ from coronal and sunspot activity.

Abstract

We present the solar S-index record of cycle 24, obtained by the TIGRE robotic telescope facility and its high-resolution spectrograph HEROS (R$\approx$20,000), which measures the solar chromospheric Ca II H&K line emission by using moonlight. Our calibration process uses the same set of standard stars as introduced by the Mt. Wilson team, thus giving us a direct comparison with their huge body of observations taken between 1966 and 1992, as well as with other cool stars. Carrington cycle 24 activity started from the unusually deep and long minimum 2008/09, with an S-index average of only 0.154, by 0.015 deeper than the one of 1986 (<S>=0.169). In this respect,the chromospheric radiative losses differ remarkably from the variation of the coronal radio flux F10.7cm and the sunspot numbers. In addition, the cycle 24 S-amplitude remained small, 0.022 (cycles 21 and 22 averaged: 0.024), and so resulted a very low 2014 maximum of <S>=0.176 (cycles 21 and 22 averaged: 0.193). We argue that this find is significant, since the Ca II H&K line emission is a good proxy for the solar far-UV flux, which plays an important role in the heating of the Earth's stratosphere, and we further argue that the solar far-UV flux changes change s with solar activity much more strongly than the total solar output.

Equations

$$S_{\mathrm{MWO}}=\alpha \left(\frac{N_H+N_K}{N_R+N_V}\right),$$

$$S_{\mathrm{MWO}}=(0.029\pm 0.004)+(19.8\pm 0.6)S_{\mathrm{HRT}}$$

$$S_{\mathrm{MWO}}=(0.036\pm 0.003)+(20.0\pm 0.4)S_{\mathrm{TIGRE}}.$$

Full text

††pagerange: Carrington cycle 24: The solar chromospheric emission in a historical and stellar perspective††thanks: based on TIGRE spectra, the NASA OMMNI data base, SORCE data provided by the LASP of the University of Colorado and SOLIS data obtained by the NSO–Carrington cycle 24: The solar chromospheric emission in a historical and stellar perspective††thanks: based on TIGRE spectra, the NASA OMMNI data base, SORCE data provided by the LASP of the University of Colorado and SOLIS data obtained by the NSO

1 Introduction

The period between approximately 1650 and 1715 has long been known for its paucity and/or absence of sunspots, first described by Spörer (1890) and Maunder (1894). For a long time, it had been thought that this apparent absence of sunspots was due to a lack of suitable observations, until Eddy (1976) convincingly demonstrated that this apparent absence of sunspots is really an actual absence of sunspots and not merely an absence of observations; Eddy (1976) also introduced the name “Maunder Minimum” for this period of time. Ever since, the question has been around of what made the Sun enter and eventually leave this ”Maunder Minimum” phase and what the properties of the Sun were at that time; unfortunately except for sunspot numbers no physical information is available from that period.

The current Carrington Cycle 24 of the Sun follows the extraordinarily long and deep minimum of 2008/09. Schröder et al. (2012) showed that there were ”zero-active” minimum days, when the chromospheric emission was at its entirely inactive, basal flux level. The Sun was entirely void of activity regions, not even showing plages or faculae, which are a common sight on a “normal minimum”, i.e., ”zero-sunspot” day, yet the random magnetic fine structure (unrelated to any magnetic activity region) is still present in those same days of zero-activity and not reduced at all, as seen in the respective SOHO images; as shown by Vögler and Schüssler (2007), it is a simple by-product of convection (dubbed “local dynamo”).

Various solar activity data suggest that the maximum of Carrington cycle 24 occurred in the second half of 2014. The cycle was remarkably weak and even in the maximum year one day was recorded without any sunspots present on the solar surface (i.e., July 17, 2014). By now, the Sun has already gone well beyond its peak activity in the current cycle and is approaching a new minimum. It is therefore appropriate to put the current solar cycle in its proper historical and stellar perspective.

2 TIGRE-observations of solar chromospheric activity

2.1 Overview and context

We use our TIGRE 1.2 m robotic telescope located in Guanajuato, central Mexico, and its HEROS spectrograph (spectral resolution $\approx$ 20000, with a spectral coverage of $\approx$ 3800 Å to 8800 Å); this facility is described in detail by Schmitt et al. (2014).

For a consistent treatment of the echelle order sampling, assessment of their sensitivity functions, wavelength calibration and straylight removal, a data-reduction pipeline is used. The echelle order sampling parameters are recalibrated each time the spectrograph passes maintenance (typically once a year), while flatfields, white-light and ThAr lamp emission line spectra are taken each night at least twice, before and after the observations. In addition, a spectrum of Vega or other suitable standard star is taken to get a reliable, yet only relative flux-calibration.

Lunar light is used to obtain full-disk solar (i.e., Sun as a star) spectra typically twice a week whenever possible. In this way we study the Sun with the same equipment as used for a set of standard stars (and program stars of our stellar chromospheric activity survey), originally defined by O.C. Wilson (see Baliunas et al. 1995, and Duncan et al. 1991 and references therein). Specifically, the surface area of the Moon sampled by the fiber of the adapter unit channeling the light in the TIGRE spectrograph, has a size of 3 arcseconds in diameter, and is thus only slightly larger than the average seeing disk of a star.

Consequently, we can directly compare the integrated solar emission to a huge body of stellar activity data gathered during the last five decades.

2.2 Definition of the S-index

The original Mt. Wilson index is defined through the expression (Vaughan et al. 1978)

[TABLE]

where $\alpha$ is an instrument-dependent calibration factor, used to put data taken with different equipment on the same scale, $N_{H}$ and $N_{K}$ are the counts measured in a 1 Å wide window, each centred on the Ca II H&K line cores, and $N_{R}$ and $N_{V}$ are the counts in two 20 Å wide, “quasi-continuum” reference bands centred on 3901 Å and 4001 Å, conveniently encompassing the two Ca II lines in between. In this way any variable atmospheric opacity and its possibly variable slope in the near UV automatically cancel out. In the original four-photomultiplier set-up used at Mt. Wilson, the line-centred channels had an approximately triangular transmission profile, while we nowadays obtain digital records of spectra and use a rectangular profile; the small differences between the two are taken care of in the calibration process.

2.3 Calibration of the TIGRE S-index

For each instrumental setup, including our TIGRE facility, the calibration process has to be carried out continuously and must be monitored carefully. For this purpose, TIGRE regularly observes a set of stars, listed in Baliunas et al. (1995) and Hall et al. (2007) as a reference to all occurring levels of activity, and selected for their relative low degree of variation.

Here, we show results from two different observation campaigns and setups. The first campaign was undertaken in the season 2008/09 with TIGRE still located at the Hamburg Observatory, then called Hamburg Robotic Telescope (HRT). The second campaign refers to the observations carried out at the La Luz Observatory since 2013. Therefore, we use two separate S-index calibrations to handle possible longterm instrumental drifts, such as residual under- or overcorrection for the echelle stray light in the line cores, which is accounted for with a zero-point small offset in the linear regression of TIGRE’s raw S-values over the respective original Mt. Wilson S-indices for our set of calibration stars. The calibration data for the period 2008/09 is shown in Fig. 2, and in Fig. 2 for the data taken in La Luz data since 2013. It is obvious from both figures that a linear relation describes the transformation into the Mount Wilson scale very well; specifically the calibration relation for 2008/09 data is given by (cf., Mittag et al. 2011):

[TABLE]

and for the data taken since 2013 (cf., Mittag et al. 2016):

[TABLE]

These relations are represented by a solid line in Fig. 2 and Fig. 2 together with the fit residuals. We note that especially at low activity levels (critical for the Sun in low activity states) the residuals are very small indeed, because here the calibration stars show nearly no long-term variability. Furthermore, the slope of the regression is the same in both periods to within the errors, which demonstrates that the sample of calibrations stars as a whole does not significantly vary over longer timescales.

2.4 TIGRE S-index of the Sun

In Fig. 3 we show the solar S-index measurements so far obtained with TIGRE. While our TIGRE observations of the past solar minimum in 2008/09 were obtained from the preliminary telescope setup at Hamburg Observatory and published by Mittag et al. (2011) and Schröder et al, (2012), the maximum of Carrington cycle 24 was covered from Aug. 2013 onwards, after the installation of TIGRE at the La Luz Observatory near Guanajuato. The best and simplest way to obtain the S-index of the Sun are observations of lunar light, where the Moon is used as a ”mirror” for the incident solar radiation. Such observations provide an unbiased measure of the light of the integral solar disk and therefore such spectra record “the Sun as a star” with the disk-integration coming for free.

To test Olin Wilson’s idea that the sunlight reflected by the Moon is a very good proxy for direct sunlight and to check how well our reduction pipeline deals with the echelle blaze functions, we compare the respective near-UV spectral range with the flux-calibrated, high-resolution KPNO FTS Solar Flux Atlas (see http://kurucz.harvard.edu/sun/fluxatlas/fluxatlastext.tab). This atlas provides a very high SNR spectrum of integrated sunlight with a spectral resolution of several hundred thousand. Furthermore, the FTS straylight and resulting solar spectrum dynamics are very well calibrated, and in the near UV the residual uncertainty is believed to be 0.2%.

In Fig. 4 we compare the TIGRE lunar spectra (black histograms) with the corresponding FTS spectra (red histograms) for the four spectral ranges (V, K, H, R) relevant for the S-index determination; note that the much higher spectral resolution FTS data was ”blurred” to the TIGRE resolution of $\sim$ 20000. Fig. 4 shows that the spectra agree very well, and outside the cores of the Ca II lines we find variations between our moon-light spectra and the FTS direct sun-light spectrum of under 1-2%, which appear on short scales and which we attribute to our broadening procedure. In the cores of the Ca II H&K lines the FTS spectra are at a much higher level, which is not surprising given they were taken at the time of solar maximum.

We therefore conclude that our TIGRE Moon spectra represent a very good approximation to the ”true” solar spectrum in the Ca II region, and consequently our determinations of the solar S-index should have a very small systematic error at worst. Since – a benefit of our approach – we use the same equipment and calibration for the Sun and for the stars, there is no instrumental or methodological bias at all and consequently, the solar chromospheric activity recorded by means of the Mt. Wilson S-index is directly comparable with the S-index records of stars.

The method described above has been used for the data taken since 2013 at the La Luz site. However, in the observations taken in 2008/09 at Hamburg, only two direct Moon spectra could be obtained. The majority of the Hamburg observations uses sky-scattered sunlight. The physical processes involved in sunlight scattering include Rayleigh scattering, Mie scattering, as well as rotational Raman scattering off the N2 and O2 molecules in the Earth’s atmosphere. The latter process is particularly relevant for our Ca II H&K data, since it leads to the so-called “Ring-effect”, first described by Grainger & Ring (1962). Rotational Raman scattering is inelastic leading to a a frequency redistribution of the scattered light, which leads to a fill-in of the stronger solar lines from the adjacent continuum. Specifically, for the Ca II H&K lines, the Ring effect reaches well over 1% of the solar continuum intensity and will therefore strongly affect the measurement of the S-index; for a more recent, quantitative study of the Ring-effect we refer to Sioris et al. (2002).

The Ring-effect is naturally also present in the 2008/09 TIGRE data. In Fig. 5 we compare a solar spectrum (of the core of the Ca II K line) taken from the Moon and form the day sky (left panel) and demonstrate that our scattering corrections removes the Ring-effect (right panel). We normalize the sky-scattered sunlight Ca II K line profile by the deeper profile obtained from the direct sunlight obtained from the Moon spectra; our resultant correction of the sky-scattered sunlight spectra is of the same order as predicted by the modelling of Sioris et al. (2002).

2.5 Further S-data-sets

The gap in time between the original Mount Wilson S-measurements and our TIGRE measurements has been filled by several initiatives, most notably from Lowell Observatory (J. Hall and colleagues) and the National Solar Observatory (NSO). However, the different calibration and instrumental issues still need a more detailed debate than the one we can give below.

Using the late Mount Wilson, NSO/Sacramento Peak, Lowell and Lick S-values, Egeland et al. (2017) find that already cycle 23 was quite weak, deriving maximum and minimum S-value of 0.178 and 0.163 respectively. Inspecting their full data set of S-index values, which is provided online and also covers cycle 24, we find good agreement with our S-index values for the time since 2013. However, for the past minimum, their S-index values are larger than ours, while their S-index values for the early 1990ies (cycle 22) are systematically lower than the measurements presented by Baliunas et al. (1995), to which we calibrated our S-index values shown in Fig. .

Egeland et al. (2017) argue that our TIGRE measurements taken in 2008/09 are affected by an incorrect correction for the Ring effect described above. However, first, we argue that our corrections are correct, and second, we point out the S-index values obtained from two direct moonlight spectra (without any Ring effect) in 2008, are also low. In addition, the S-index time series presented by Egeland et all (2017) does not appear to reflect, what is shown by all other solar activity indicators (see Section 2.6 and Section 3: SOLIS Ca II K 1-Å, radio flux, sunspot numbers): that the 2008/09 minimum is lower than the minima in 1986 and 1997.

Further evidence is available from the fact that the Sun is the only star with a directly observable surface. Egeland et al. (2017) inspected SOHO MDI magnetograms on two specific dates (Jan, 28th 1997 and Oct, 9th 2009), since for both days they obtain relatively low S-index values, of 0.1593 and 0.1596 respectively. The first value was measured with the original Mount Wilson HKP-2 instrument, while the second value was transformed from the NSO/Sacramento Peak Ca II K 1-Å emissions index. While Egeland et al. (2017) state, that they find a low activity on either day, a closer inspection of the MDI magnetogram from Jan, 28th 1997 (see Fig. 7) reveals the presence of a small region of chromospheric activity, while by contrast, on Oct 9th 2009 the Sun was entirely void of any activity. Yet the S-index quoted by Egeland et al (2017) for that day is not any lower than the one measured by Mount Wilson for the slightly active day Jan 28th 1997.

We carried out the same exercise for Mar 8th 2009, since on this day we obtained one of the two Moon light spectra from Hamburg with a very low S-index of 0.152$\pm$0.006. In Fig. 7 we shows the respective SOHO MDI magnetogram taken on that day, and just as is the case for Oct 9th 2009 there is absolutely no activity region visible on the surface. By this, admittedly limited but yet very representative probe, our S-index values appear to be consistent with the Mount Wilson measurements during the past minimum period.

2.6 Other solar data sets

In the mid-seventies the National Solar Observatory (NSO) began taking regular observations of the disk-integrated solar Ca II K line at Sacramento Peak, measuring in particular the so-called 1-Å Ca II K emission index, defined as the equivalent width of a band with a width of 1-Å centered on the K-line core. After October 1, 2015, the measurements were continued using the Integrated Sunlight Spectrometer (ISS) on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) facility. The ISS has actually been in operation since late 2006 at NSO/Kitt Peak, so that there is an overlap of about eight years between the two time series.

Interestingly, the two time series differ and Bertello et al. (2017) provide a detailed discussion of these discrepancies and develop a procedure to unify the two time series. Specifically, Bertello et al. (2017) correct the NSO/Sacramento Peak measurements and empirically rescale them to the SOLIS data, which are not affected by sky-scattered light and the afore-mentioned Ring effect. In Fig. 8 we show the monthly medians of their re-calibrated data; obviously, the minimum in NSO 1-Å Ca II K emission index time series is clearly lower in 2008/09 than in the minimum in 1997, consistent with the TIGRE S-index data. Unfortunately, SOLIS is not able to measure the S-index directly and cannot perform measurements of stars, therefore the stellar dimension is missing from those measurements.

3 Solar activity during Carrington cycle 24

The last solar minimum and the ongoing Carrington cycle 24 are unusual not only w.r.t. the solar UV emission, but also in many respects, which we briefly demonstrate in this section.

3.1 Radio emission and sun spot number

To provide a wider context we show in Fig. 9 the monthly averaged sunspot numbers (upper panel, taken from the Belgian SIDC website) for the Carrington cycles 20 to 24 and values of the F10.7 cm radio flux (medium panel, NR Canada website). One recognizes, first, the very close correlation between these so different activity indicators, and, second, that in the present cycle 24 maximum, both these indicators reached only half of their levels of the maxima of 1980 and 1991, or about their level of early 2003.

3.2 Total solar irradiance

The total solar irradiance (TSI) has been continuously monitored by various space-based instruments since 1978. Since the zero-points of the individual instruments do not fully agree, it is a non-trivial task to combine the results of different missions into a definitive record of the solar TSI. BenMoussa et al. (2013) and Fröhlich (2012) discuss the various problems in extensive detail and provide a summary of the TSI measurements during the last three cycles (i.e., Carrington cycles 21 to 23). As discussed by Fröhlich (2012), even the TSI may have dropped during the 2008/09 minimum below the TSI values recorded during any of the previous minima, albeit only by a very small margin, probably smaller than $\Delta$TSI/TSI $\approx(10^{-4})$, but long-term drifts and calibration differences between the different TSI missions prevent the derivation of more accurate numbers.

3.3 Far UV-emission

We next use the SOLSTICE data of the SORCE mission, provided by the Laboratory for Atmospheric and Space Physics (LASP) of the University of Colorado. These far UV spectral irradiance measures are of special interest, because a “haze” of metal lines (Anderson & Athay 1989) should reveal magnetic chromospheric heating by radiative losses, similar to the S-index, and like the latter, SOLSTICE data are star-calibrated, with the consequence that they do not suffer from calibration lamp and/or electronics degradation problems (see the discussion by Lockwood 2011 and references therein).

We integrate spectral irradiance over the wavelength range of 200 to 280 nm, which by wavelength and intensity is the relevant spectral window for stratospheric warming by photodissociation of molecules such as ozone and show (in Fig. 10) the averages obtained for periods of half a year, to minimize the impact of short-term fluctuations of the solar activity, covering the time-span of 2003 to 2016. Although this mission missed the maximum of cycle 23 by two years, it is evident from Fig. 10 that the maximal far-UV irradiation in cycle 24 is, like the S-index, again exceptionally low: With a total variation of only 1.4%, the cycle 24 maximum level compares with the cycle 23 decline of late 2004. That is about 1% lower than the far-UV irradiation of early 2003, with which time the cycle 24 maxima of F10.7 and sunspot numbers compare.

4 The historical solar and stellar perspective

4.1 The solar perspective

The hitherto most complete description of the Mt. Wilson H&K monitoring project was presented by Baliunas et al. (1995). Recently, these data have become publicly available, covering the period of 1966 to 1992 with rather unequal but sufficient sampling of the chromospheric activity maxima of 1980 and 1991 (S-index of one-year-averages around maxima: 0.193, extreme: 0.215), as well as of the minimum in 1986 (between cycles 21 and 22, S-index one-year-average: 0.169, extreme: 0.162). Superimposed in Fig. 11 we plot (with dashed lines) the extreme S-index values observed by TIGRE in 2008 and 2014, i.e., 0.150 and 0.180 (cf., Fig. 2.5).

We therefore conclude that the minimum in 2008 (average: 0.154) reached significantly below the minimum of 1986 (by 0.015 in one-year-averages), and the cycle 24 maximum observed by TIGRE (S-index one-year-average of 0.176) is much lower (by 0.017) than the cycle 22 maximum; it is in fact closer to the minimum of 1986.

Hence, the change is not so much a smaller cycle 24 S-index amplitude between the one-year-averages around maximum and minimum (0.022, as compared to 0.024 in cycles 21 and 22). Rather, chromospheric activity has now settled for a 0.015 deeper starting level. This is what makes the S-index underscore, on a relative scale, what the already low cycle 24 records of sunspot numbers and F10.7cm flux let expect.

4.2 The stellar perspective

We next move on to the stars and compare – in Fig. 12 – the solar S-index values reported by Baliunas et al. (1995; blue data points) and our TIGRE S-indices (cf., Fig. 2.5, red data points) with a larger number of S-index measurements of solar-like stars (taken from Mittag et al. 2013, triangular data points). Clearly, the TIGRE values reproduce very well the lower cut-off (at around 0.15), observed for solar-like stars already by Duncan et al. (1991). We are therefore confident that our TIGRE calibration is accurate, especially for stars of relatively low activity, and argue that during the extended solar minimum in 2008/09 the Sun was actually close to the minimal S-index values observed for solar-like stars and hence very close to the state it had during the ”Maunder Minimum” period.

5 Discussion and Conclusions

The now outgoing Carrington cycle 24 is not only much weaker than its three predecessors in terms of sunspot numbers and F10.7cm coronal radio flux (see Fig. 9), the average S-index of chromospheric emission was even more reduced. According to our TIGRE observations presented here, its amplitude between one-year-averages of the S-index measurements was only 0.022 (rather than 0.024, which was typical of cycles 21 and 22). Most remarkably, however, the activity cycle started from a minimum deeper by 0.015, see Fig. 11), meaning that the extraordinary decrease of the S-index has a timescale longer than a single cycle.

The same behavior is seen in the averaged, integrated spectral far-UV flux in the wavelength range 200 to 280 nm (cf., Fig. 10), according to the star-calibrated SOLSTICE/SORCE data available for the timespan of 2003 to 2016. Importantly, in both, the cycle 24 minimum (cf., Lockwood 2011) and maximum (compare Fig. 3 with Fig. 2) far-UV irradiation is lower by about 1% against the projected cycle variation of the F10.7cm and sunspot number records. The cycle 24 amplitude of the far-UV averaged irradiation is 1.4%.

By simple comparison, we find that S-index and far-UV irradiation cycle variations scale approximately to 0.016 in S-index being equivalent to 1% in far-UV irradiation, making the former index a very good proxy for the latter – not requiring space-based instrumentation and having a longer track record. We extrapolate, that in cycles 21 and 22 maxima, the average far-UV irradiation must have been almost 3% larger than in 2008, while in the respective minima it was still 1% larger.

Such a lasting deficiency of the solar UV irradiance implies a decline of the magnetic chromospheric heating which lasts beyond the present cycle, thus providing further evidence that the Sun is entering again a grand minimum phase. In fact, such low activity could even been seen as the return to a long-term normal, since the two closest solar twins compare better, by their S-index values, with the low cycle 24 solar chromospheric activity (see Mittag et al. 2016).

In the context of possible TSI changes, we also analyzed how much variance of the latter would be needed to produce a 1% drop of the far-UV flux of the Sun, using PHOENIX model atmospheres (Hauschildt et al. 1999) with a very small difference in effective temperature. We find that, driven by the large UV opacities, a hypothetical decrease of the solar $T_{\rm eff}$ of as little as 1.5 K over the decade or so in question would already account for such an additional 1% decrease of the far-UV irradiation. However, this would also imply a drop in TSI by about 0.1%, probably more than observational evidence seems to suggest. Hence, we consider it more plausible that the decrease of the far-UV irradiation and Ca II line emission is entirely due to a longterm reduced magnetic heating, which is consistent with only a small extra decrease in the TSI during the past minimum.

The here presented evidence suggests that a phase of reduced solar activity (or grand minimum) has an effect mainly on the solar far-UV emission, but much less so on the TSI. That would explain (see also the discussion by Ermolli et al. 2013), why on the one hand there is only inconclusive evidence for a global cooling during the Maunder and Dalton minima but, on the other hand, there was a clear rise in the frequency of cold northern winters (as shown by Ineson et al 2012), which point to a then weaker jetstream and winter blocking situations.

The hypothesis, albeit not yet reproduceable in global climate models, is that the above far-UV spectral range ($\approx$ 200 nm to 280 nm) is responsible for the photodissociation of molecules in the Earth’s stratosphere and constitutes its main radiative heating. Temperatures there are related to the strength and behavior of the jetstream (by climate sciences referred to as NAO, North Atlantic Oscillation). Consequently, low solar activity and lower stratospheric temperatures seem to, statistically, favour a weaker jetstream with wider oscillations (see Ineson et al. 2011 and references therein), subtly allowing for more pronounced blocking situations in the northern hemisphere. A rise of colder-than-average winters during times of low solar activity is simply caused by the formation of more large, persistent bubbles of arctic air – without much affecting average world temperatures.

In this context, we need consistent chromospheric emission records over long periods, in order to test refined climate models and to obtain a clearer correlation with climate records. Since direct, well-calibrated observations of the far-UV flux only exist for about 2 decades at best, the longer time-span available with the solar Mt. Wilson-calibrated S-index records provide an important advantage. O.C. Wilson’s star-calibrated method makes present and future records directly comparable with those obtained over half a century ago, and with TIGRE we will continue the spectroscopic monitoring of solar and stellar chromospheric activity.

Acknowledgments

We acknowledge the very helpful travel support by bilateral projects CONACyT-DFG no. 192334 and PROALMEX (CONACyT-DAAD) No. 207772, as well as by CONACyT mobility grant No. 207662 (KPS), and by the DFG in several related projects. The HK_Project_v1995_NSO data on the solis.nso.edu website derive from the Mount Wilson Observatory HK Project, which ran from 1966 to 1992 and was supported by both public and private funds through the Carnegie Observatories, the Mount Wilson Institute, and the Harvard-Smithsonian Center for Astrophysics. It lived of the dedicated work of O. Wilson, A. Vaughan, G. Preston, D. Duncan, S. Baliunas, and many others. We also acknowledge discussions with Drs. R. Egeland and J. Hall, who provided their own solar S-index data set to us prior to publication, and Dr. M. Giampapa for drawing our attention to the work of Bertello and colleagues, clarifying the interpretation of the SOLIS K-index measurements. Finally, and wish to thank our referee, Dr. P. Judge, for his most helpful comments, which led to very substantial improvements.