11institutetext: Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112,
21029 Hamburg, Germany
11email<EMAIL_ADDRESS>22institutetext: Departamento de
Astronomia, Universidad de Guanajuato, Mexico 33institutetext: Kimmel fellow,
Department of Earth and Planetary Science, Weizmann Institute of Science,
Rehovot, Israel

# Chromospheric activity and photospheric variation of $\alpha$ Ori during the
great dimming event in 2020

M. Mittag 11 K.-P. Schröder 22 V. Perdelwitz 3311 D. Jack 22 J.H.M.M. Schmitt
11

(Received …; accepted …)

###### Abstract

Aims. The so-called great dimming event of $\alpha$ Ori in late 2019 and early
2020 sparked our interest in the behaviour of chromospheric activity during
this period. $\alpha$ Ori was already part of the long-term monitoring program
of our TIGRE telescope to study the stellar activity of giant stars, and
therefore regular measurements of $\alpha$ Ori have been taken since 2013.

Methods. In the context of this study, we determined the TIGRE S-index values
and, using a set of calibration stars, converted these to the Mount Wilson
S-index scale, which allows us to combine our TIGRE activity measurements with
the SMWO values taken during the landmark Mount Wilson program some decades
earlier and to compare that extended time series with the visual and V
magnitude photometric data from the AAVSO database. In addition, we determined
the absolute and normalised excess flux of the Ca II H&K lines. To understand
the activity in absolute terms, we also assessed the changes in effective
temperature using the TiO bands covered by our TIGRE spectra.

Results. We find a clear drop in effective temperature by about 80 K between
November 2019 and February 2020, which coincides with the minimum of visual
brightness. In addition, the effective (luminous) photospheric area of
$\alpha$ Ori also shrank. This might be related to a temporary synchronisation
of several large convective cells in cooling and sinking down. During the same
period, the S-index increased significantly, yet this is a mere contrast
effect, because the normalised excess flux of the Ca II H&K lines did not
change significantly. However, the latter dropped immediately after this
episode. Comparing the combined SMWO values and visual magnitude time series,
we find a similar increase in the S-index during another noticeable decrease
in the visual magnitude of $\alpha$ Ori which took place in 1984 and 1985.
These two episodes of dimming therefore seem to share a common nature. To
probe the dynamics of the upper photosphere, we further analysed the closely
neighbouring lines of V I and Fe I at 6251.82 Å and 6251.56 Å respectively.
Remarkably, their core distance varies, and once converted to radial velocity,
shows a relation with the great dimming event, as well as with the
consecutive, weaker dimming episode in the observing season of 2020 and 2021.
This type of variation could be caused by rising and sinking cool plumes as a
temporary spill-over of convection on $\alpha$ Ori.

Conclusions. As the effective temperature of $\alpha$ Ori is variable, the
S-index, computed relative to a near-ultraviolet (NUV) continuum, is only of
restricted use for any monitoring study of the chromospheric activity of
$\alpha$ Ori. It is therefore important to consider the effective temperature
variability and derive the normalised Ca II H&K flux to study the
chromospheric long-term changes in absolute terms. In fact, the Ca II H&K
normalised excess flux time series shows that the chromospheric emission of
$\alpha$ Ori did not change significantly between November 2019 and February
2020, but then beyond the great dimming minimum it does vary. Hence, this
delay of the chromospheric reaction suggests that the cause for the great
dimming is located in the photosphere. An investigation of the long-term
spectroscopic and photometric time series of $\alpha$ Ori suggests that the
great dimming in 2019 and 2020 does not appear to be a unique phenomenon, but
rather that such dimmings do occur more frequently, which motivates further
monitoring of $\alpha$ Ori with facilities such as TIGRE.

###### Key Words.:

Stars: activity; Stars: chromosphere; Stars: supergiants

##  1 Introduction

The red supergiant $\alpha$ Ori (HD 39801, Betelgeuse) is one of the brightest
stars in the sky and showed an unusual decrease in its brightness in the
winter between 2019 and 2020. Normally, the brightness of $\alpha$ Ori
typically varies between $\sim$0.2 and $\sim$1 mag in the Johnson V band, as
demonstrated by a light curve available in the AAVSO (American Association of
Variable Star Observers) database111Kafka (2021),https://www.aavso.org.
However, in February 2020, the brightness of $\alpha$ Ori decreased
extraordinarily to a mere V$\sim$1.6, an event that was consequently dubbed
the ‘great dimming event’. In December 2019, Guinan et al. (2019) raised
public awareness of this event, and an ESO press
release222https://www.eso.org/public/news/eso2003/ showed VLT/SPHERE (Very
Large Telescope)/(Spectro-Polarimetric High-contrast Exoplanet REsearch
instrument) observations of $\alpha$ Ori by Montargès, comparing its state in
January 2019 with that in December 2019; this VLT/SPHERE image confirmed the
significant darkening of Betelgeuse in comparison to an image taken in January
2019.

As to the cause of the unusual decrease in brightness, two main hypotheses
were put forward: the first interprets the cause of the dimming to be a
decrease in effective temperature, that is, a photospheric effect, while the
alternative hypothesis argues that the photospheric emission had been shielded
by material from some ejection or increased mass-loss event, thus located
further out and not directly related to the photosphere.

Levesque & Massey (2020) studied low-resolution spectra of $\alpha$ Ori; while
finding a small drop in effective temperature, the authors argue that this
decrease is too small to explain the great dimming and suggest instead a mass
ejection as an explanation for the observed decrease in brightness. This
scenario is supported by Dupree et al. (2020), who analysed the mid-
ultraviolet (MUV) flux in 2400-2700 Å and Mg II h&k lines with spectra taken
with HST/STIS (Hubble Space Telescope)/(Space Telescope Imaging Spectrograph),
and found that both fluxes, as measured in September 2019, October 2019, and
November 2019, were larger than in February 2020 at the maximum of the great
dimming event. Therefore, Dupree et al. (2020) argue that a great mass
ejection occurred in October 2019 leading to the formation of a dust cloud in
the following weeks, which eventually darkened $\alpha$ Ori. Dust dimming of
$\alpha$ Ori is also supported by the work of Montargès et al. (2021), who
analysed VLT/SPHERE images taken in January 2019, December 2019, January 2020,
and March 2020.

On the other hand, the dust cloud theory was disputed by Dharmawardena et al.
(2020), who investigated submillimetre (submm) data taken with the James Clerk
Maxwell Telescope and Atacama Pathfinder Experiment. While Dharmawardena et
al. (2020) also found $\alpha$ Ori to be about 20% fainter in the submm range,
their radiative modelling suggests that the dimming event was caused by some
photospheric change. More specifically, a change in effective temperature
during the great dimming was also demonstrated by Harper et al. (2020), who
present a TiO band light curve; based on these observations, the derived
effective temperature time series shows a significant drop, which coincides
well with the great dimming event as observed in the V band.

In this paper we present our $\alpha$ Ori observations obtained with the 1.2m
TIGRE telescope (for more details, see Schmitt et al. (2014); González-Pérez
et al. (2022) and below), an instrument designed primarily for the study of
stellar chromospheric activity. However, before we present our respective
results in more detail, we need to address the changes in effective
temperature, because these imply physical changes of the photosphere leading
to changes in the spectral fluxes, which are used as a reference in many
activity indicators. Consequently, the drop in temperature around February
2020 has a direct impact on the interpretation of the observed activity
indicators, such as the calibrated Mount Wilson S-index, as well as the
derivation of the absolute Ca II H&K line flux of $\alpha$ Ori. Thereafter, we
present a combined time series of the Mount Wilson S-index and compare its
behaviour to photometric data.

Furthermore, we derive the absolute and excess Ca II H&K line flux, which show
a remarkably different relation with the V-band light curve. Also, we present
the significant line depth and radial-velocity (RV) variations of the unequal
neighbouring line pair of V I 6251.82 Å and Fe I 6252.56 Å. These lines form
in different depths of the photosphere and are indicative of a height-
dependent dynamical behaviour of the photosphere apparently associated with
the great dimming event. Finally, we summarise our results and present our
conclusion about the possible physical causes for this dimming event.

##  2 TIGRE spectroscopic monitoring and data reduction

TIGRE (Telescopio Internacional de Guanajuato Robótico Espectroscópico) is a
fully robotic spectroscopic telescope with an aperture of 1.2 m, located at
the La Luz Observatory of the University of Guanajuato, Mexico, designed for
long term monitoring programs. The two-spectral-channel, fibre-fed Échelle
spectrograph HEROS (Heidelberg Extended Range Optical Spectrograph) is located
in a thermally and mechanically isolated room. The spectral resolving power of
the HEROS spectrograph is R$\approx$20,000, which is relatively uniform over a
wavelength range from 3800 Å to 8800 Å with a minor gap around 5800 Å between
the two spectral channels caused by the dichroic beam splitter; the TIGRE
facility and the realisation of its robotic operation is described in more
detail by Schmitt et al. (2014) and González-Pérez et al. (2022).

The TIGRE/HEROS spectra used here were reduced with the TIGRE automatic
standard reduction pipeline v3.1 written in IDL based on the reduction package
REDUCE (Piskunov & Valenti 2002). This latter pipeline includes all required
reduction steps for an Échelle spectrum; a detailed description of the first
version of the TIGRE reduction pipeline is given by Mittag et al. (2010), and
additional information can be found in Hempelmann et al. (2016) and Mittag et
al. (2016).

The TIGRE observing plan includes a monitoring program of the chromospheric
activity of giant stars, providing a study of the variations of the Ca II H&K
lines. One target of this program is the red supergiant $\alpha$ Ori. Until
November 2019, with the goal of studying long-term variability, $\alpha$ Ori
was for the most part observed with a monthly cadence; However, in December
2019, we started covering $\alpha$ Ori more frequently to better monitor the
stellar activity during the great dimming event. In Table 1, we list the
number of observations taken in each observing season and the range of the
signal-to-noise ratio (S/N) at 4000 Å per season.

Table 1: $\alpha$ Ori observations by observing season (September-April) Epoch | No. |  $\langle\rm{S/N}\rangle$ range
---|---|---
2013/14 | 15 | 39-98
2014/15 | 4 | 180-272
2015/16 | 3 | 173-207
2016/17 | 1 | 311
2017/18 | 2 | 526-554
2018/19 | 2 | 407-448
2019/20 | 15 | 103-554
2020/21 | 32 | 22-399

##  3 Assessment of long-term effective temperature variations

Before discussing the chromospheric activity of $\alpha$ Ori, we try to
quantify the possible variations of the effective temperature during the great
dimming event in order to consider this in our quantitative analysis of the
chromospheric activity at this point in time. To begin with, we used the
publicly available photometric data from the AAVSO database as a reference to
the timing of the great dimming event. Various colour indices provide an
indicator of the effective temperature. However, since their variation could
in principle be caused partly by extinction from dust, we also use TiO bands
here to estimate the effective temperature from our TIGRE/HEROS spectra by
comparing the TiO bands of each TIGRE/HEROS spectrum with best-matching
PHOENIX atmospheric model spectra.

###  3.1 Time series of photometric data and colour indices

Starting with epoch 2018.5, in Fig. 1 we show the daily brightness in the B,
V, R, I, J, and H bands, as listed in the AAVSO database. In all bands, the
light curves show a variation apparently caused by a pulsation cycle, its
amplitude being smaller in the J and H bands. Next, we computed the $B-V$,
$V-R$, $R-I,$ and $J-H$ colour indices for every day with available data; to
ensure that any variation is real, we only provide values with a relative
error of lower than 5% of the respective index. These values are shown in Fig.
2, which demonstrates that variations occur in all four colour indices; the
times and values of these changes are consistent with the effective
temperature variation shown by Harper et al. (2020).

Figure 1: Light curves of the B, V, R, I, J, and H bands, beginning with
2018.5. The upper panel depicts the J and H magnitudes, and the lower panel
shows the B, V, R, and I bands. Figure 2: Colour index time series. The top
panel shows the $B-V$ values, the second displays the $V-R$ values, the third
the $R-I$ values, and the lowest panel depicts the $H-J$ values. Black dots
represent values with a relative error of lower than 2$\%$, whereas red data
points those lower than 5$\%$.

The colour indices $R-I$ and $J-H$ increase during the great dimming event,
which shows a minimum in the light curve in each band. Both indices show the
behaviour expected, that is, a decrease in the effective temperature, which
manifests as an increase in these two indices; see Sect. B. However, the
colour index $V-R$ shows strong scatter during the minimum of the light
curves, without any clear trend, and the $B-V$ colour index actually decreases
during the great dimming event.

While over a large temperature range in cool stars the B-V index increases
with decreasing effective temperature, this is not the case here —the coolest
stars form an exception. In fact, $B-V$ values calculated from PHOENIX spectra
of an effective temperature of less than 3600 K show the same behaviour. Above
3600 K, with rising effective temperature, the $B-V$ values also decrease from
their maximum value there, but very slowly at first. The $B-V$ values based on
PHOENIX spectra (Husser et al. 2013) are shown in Fig. 24 and further
explanation of their derivation is given in Sect. B. This inverted $B-V$
behaviour was also found in the super giant star HD 156014 ($\alpha$ Her A).
This object has a $B-V$ colour of only 1.164 mag (ESA 1997), but an effective
temperature as low as 3271 K (taken from the PASTEL catalogue, Version
2020-01-30; (Soubiran et al. 2016)). Interestingly, a similar trend inversion
was shown by Lançon et al. (2007) for the $H-K$ index, calculated from PHOENIX
spectra for red supergiants and giants.

###  3.2 Effective temperature assessment based on TiO bands

To perform a quantitative assessment of any effective temperature variations,
we now use the TiO bands; these bands become stronger in cooler stars and
thereby provide a good effective temperature indicator in their own right.
Examining the TiO band at 7054 Å, in Fig. 3 we compare four TIGRE spectra
taken before, during, and after the great dimming event and indeed find a
decrease in their normalised fluxes during the great dimming; this finding
indicates that the effective temperature dropped during the great dimming
event.

Figure 3: TiO band at 7054 Å taken on four different dates: 11 November 2019
(blue), 24 January 2020 (red), 27 February 2020 (magenta), and 26 April 2020
(black).

To quantify the effective temperature based on the TiO bands strength, we
compared four normalised TiO bands at 4954 Å, 5450 Å, 6154 Å, and 7054 Å in
the TIGRE spectra with normalised PHOENIX spectra of the Göttingen University
database created by Husser et al. (2013), in a temperature range from 3300 K
to 3900 K (with a step size of 100 K, a log g of 0.0, and solar metallicity).
For this comparison, the rotational line-broadening (v$\cdot$sin(i)) and a
spectral resolving power of R$\approx$20000 are considered in the PHOENIX
spectrum.

To estimate the differences between observed spectra and PHOENIX spectra, and
to find the best matches, we computed the $\chi^{2}$ values of the residuals
for this effective temperature range of the PHOENIX models. The effective
temperatures determined in this way for each band and each TIGRE spectrum are
shown in the upper panel of Fig. 4. Ideally, these different temperatures
should agree, but systematic differences illustrate the remaining shortcomings
of the models in extreme non-local thermodynamic equilibrium (non-LTE)
conditions under very low gravity and in very extended and possibly non-
spherically symmetric atmospheres; inaccuracies in the opacities may also
influence the agreement here. In order to nevertheless be able to derive a
single effective temperature for each spectrum, the results for the four TiO
bands were simply averaged, and the standard error of the mean is used as
uncertainty for the resulting value of the effective temperature. In this way,
we may at least have the best-possible account of the temperature variations
on a relative scale; these results are shown in the lower panel of Fig. 4.

Figure 4: Effective temperature time series obtained from TIGRE/HEROS spectra:
Upper panel: Effective temperatures obtained from four TiO bands. Lower panel:
Respective averaged effective temperatures.

Figure 4 clearly suggests that the effective temperature indeed dropped during
the great dimming, with a minimum at epoch 2020.1, and a subsequent increase.
For the observation of 11 November 2019, at the onset of the great dimming, we
derive an effective temperature of 3627$\pm$16 K, well below the level of
around 3700 K observed in previous years. The TiO-band-derived effective
temperature then decreases further to its minimal value of 3547$\pm$11 K in
the TIGRE spectrum of 27 February 2020. This is then followed by a clear
increase in temperature, with a small temperature drop in November 2020. For
completeness, the mean effective temperature for all TiO band measurements was
computed. We obtained a mean effective temperature of 3649$\pm$6 K with a
standard deviation of 48 K for $\alpha$ Ori over the past 6 years.

Our work shows fair agreement with the work of Harper et al. (2020, Fig.1),
which is based on TiO band photometry, simply by visual comparison of the
respective effective temperature time series. Harper et al. (2020) mention two
effective temperature values, one for September 2019 of 3645$\pm$15 K, and
another for February 2020 of 3520$\pm$25 K. The latter value compares directly
with our measurement of 27 February 2020, which is in the same time range of
the seven-day bins used by Harper et al. (2020). This comparison shows that
our derived effective temperatures agree to within the errors with the values
obtained by Harper et al. (2020). The same conclusion can be drawn from a
comparison of the September value of Harper et al. (2020) with our November
observation.

In addition, we note that, if there were contributions from regions of
different temperature, the flux weighting would always favour the hotter
regions, in the sense that a cool patch would have a much smaller impact on
the overall value of the effective temperature than suggested by its area
fraction. Consequently, the non-uniformity of the dynamic photosphere of
$\alpha$ Ori may imply much larger local temperature variations than the ones
found here on a global scale.

Based on the evidence given by the colour indices and our effective
temperature values derived from the TiO bands, we conclude that the effective
temperature of $\alpha$ Ori is indeed variable, as is the spectral energy
distribution of $\alpha$ Ori as a consequence. This is a particularly critical
point for UV and extreme-UV (EUV) continuum fluxes far down the short-
wavelength tail end of the spectral energy distribution of this very cool
supergiant and therefore this flux depends on the effective temperature by a
very large power ($o(10)$). Consequently, this result is very important for
the quantification of the chromospheric activity, which is presented below.

##  4 Chromospheric activity

A well-known and commonly used indicator for stellar chromospheric activity is
the line emission of the Ca II H&K doublet line at 3968.47 Å and 3933.66 Å,
which is characterised by the so-called S-index. During the great dimming
event of $\alpha$ Ori, our TIGRE observations show strong changes in the
observed S-index, which we present in this section. These measurements,
combined with historical Mount Wilson S-measures, provide a long-term time
series for $\alpha$ Ori, which yields an interesting comparison to the
available photometric data. Finally, we discuss the significant temperature
impact on the S-values and present an analysis of the Ca II H&K fluxes in
absolute terms.

###  4.1 Ca II K variation during the great dimming

Upon visual inspection of the Ca II K line spectra taken by TIGRE during the
great dimming event we see a strong increase in the line core relative to the
surrounding photospheric profile. For a closer comparison, all spectra were
normalised to unity at the (photospheric) wavelength point 3925 Å and 3942.32
Å in order to give an equal relative scale to the Ca II K line cores of
different observing dates.

Figure 5: Normalised Ca II K line spectra taken on different dates: 29 January
2019 (blue), 11 November 2019 (green), 24 January 2020 (red), 27 February 2020
(magenta), 9 April 2020 (black), and 11 January 2021 (yellow).

In Fig. 5, we compare these normalised Ca II K line spectra taken on 29
January 2019 (TIGRE SII_MWO=0.554), 11 November 2019 (TIGRE SII_MWO=0.697), 24
January 2020 (TIGRE SII_MWO=0.800), 27 February 2020 (TIGRE SII_MWO=0.748),
and 9 April 2020 (TIGRE SII_MWO=0.601). In addition, the TIGRE spectrum of 11
January 2021 (SII_MWO=0.492) serves as a reference for a Ca II K line core of
low activity. This comparison, at face value, shows that the normalised Ca II
K line flux increased until 24 January 2020 and thereafter decreased again.
The same behaviour is seen in the measured S-values; the method for deriving
S-values on the Mount Wilson scale is described in the following subsection
(Sect. 4.2.2 & 4.2.3).

Furthermore, we want to draw attention to the fact that the spectrum around
the K1V and K1R points is also variable; these points are marked in Fig 5, and
form in the transition from photosphere to chromosphere (see (Vernazza et al.
1981)). These variations may indicate a changing photospheric contribution,
which is consistent with the results of our temperature study of $\alpha$ Ori;
see Sect. 3.

###  4.2 S-index calculation for giants

The Mount Wilson program (described in detail by Wilson 1982) contains S-index
measurements of giants. These were obtained with a wider bandpass filter for
the line cores than the triangular bandpass with a FWHM of 1.09 Å (used for
main sequence stars) in order to accommodate, at least to some extent, the
widening of the emission lines in giants (caused by the so-called Wilson Bappu
effect). To compare the TIGRE raw S-index measurements of giants (SII_TIGRE)
with the historical Mount Wilson data, the transformation onto the Mount
Wilson scale was derived from a large set of observations of different giants
with a wide bandpass, which were also observed by the Mount Wilson group.

####  4.2.1 The Mount Wilson S-index for giants

The commonly used Mount Wilson S-index is defined as (Vaughan et al. 1978)

$\displaystyle
S_{\rm{MWO}}=\alpha\left(\frac{N_{H}+N_{K}}{N_{R}+N_{V}}\right),$ (1)

where NH and NK are the flux counts in the line cores of the Ca II H&K lines
in a triangular bandpass with a FWHM of 1.09 Å, and NH and NK are the flux
counts of two 20 Å wide pseudo-continuum bandpasses, centred at 3901.07 Å and
4001.07 Å, which serve as a reference for the photospheric spectrum. In this
fashion, the S-index value obtained is independent of the transparency of the
night sky, and the factor $\alpha$ is merely a scaling factor (Vaughan et al.
1978; Duncan et al. 1991) used to compare different generations of master-
built four-channel S-measurement units on Mount Wilson.

However, as already mentioned above, the Ca II H&K line cores of giant stars
are wider than those of main sequence (MS) stars. Therefore, Wilson (1982)
introduced a wider line bandpass for S-measurements of giants. This band pass
has a trapezoidal shape with a FWHM of 1.5 Å and the top has a width of 1 Å.
However, the wide continua bandpasses are the same as those used for the
normal S-index (Choi et al. 1995). For our giant S-value measures on TIGRE
spectra, we adopted a rectangular 2 Å line profile. This choice loses even
less emission from supergiants than the Mount Wilson trapezoidal profile, and
the calibrated transformation handles the different throughput.

Figure 6 shows the two different line-core bandpasses of the Mount Wilson
S-indices plotted over a TIGRE spectrum of the Ca II K line of the giant HD
29139 ($\alpha$ Tau). The triangular bandpass is outlined by the black dashed
line, and the wider trapezoidal bandpass by the red dashed line.

Figure 6: TIGRE spectra of the Ca II K line of two giants (HD 29139 (LC III)
and $\alpha$ Ori (LC I)) are shown with the line bandpasses of the different
S-indices: The black dashed line outlines the triangular bandpass, sufficient
in width for MS stars, and the red dashed line shows the wider trapezoidal
bandpass used for giants. The magenta dashed line shows the rectangular
bandpass used for the raw STIGRE index; see Sect. 4.2.2.

A visual comparison of both bandpasses shows that even the wider triangular
bandpass is too small to capture the full line-core emission. Rutten (1984)
provides a more detailed comparison and discussion of the S-values obtained
with both of these bandpasses; his main conclusion is that the wider band pass
for index SII_MWO becomes too narrow already for luminosity class (LC) I-II
giants. The S-index can then only be used for variability monitoring, and is
not useful for quantitative studies. We emphasise this point by superimposing
the trapezoidal bandpass over the Ca II K line of $\alpha$ Ori, an LC I star,
in Fig. 6.

####  4.2.2 The TIGRE SII-index for giants

We define the raw, uncalibrated TIGRE S-index for giants in the form

$\displaystyle
S_{\rm{II\\_TIGRE}}=\left(\frac{N_{H}+N_{K}}{N_{R}+N_{V}}\right),$ (2)

where $N_{*}$ are the counts in the individual bandpasses. While we used the
same continuum bandpasses ($N_{R}\leavevmode\nobreak\
\rm{and}\leavevmode\nobreak\ N_{V}$) as for the Mount Wilson S-index, our
TIGRE Ca II H&K line bandpasses (for $N_{H}\leavevmode\nobreak\
\rm{and}\leavevmode\nobreak\ N_{K}$) are simply rectangular with a width of 2
Å (see Fig. 6). This choice gives the same width at the foot of the profile,
but produces less count losses compared to the trapezoidal Mount Wilson
profile.

Measuring the SII_TIGRE index requires three main steps, which are illustrated
in Fig. 7. The first step concerns the values of the pseudo-continua, where
the calibration fluxes $N(R)$ and $H(V)$ are measured. The standard
normalisation process for TIGRE spectra may result in incorrect ratios between
the fluxes of those reference bands. In the upper panel, a normalised TIGRE
spectrum of the Ca II H&K lines is shown. A matching (by effective temperature
and gravity) PHOENIX spectrum of models by (Hauschildt et al. 1999) is now
required to estimate the true flux ratios between the fluxes of those
reference bands.

We normally use averages of the Teff and log g values in the PASTEL catalogue
(Version 2020-01-30; (Soubiran et al. 2016)), except in the case of the
variable effective temperature of $\alpha$ Ori. Instead, we adopt the values
derived by our approach. According to those Teff and log g values, the
corresponding PHOENIX spectrum is selected from the spectral database (Husser
et al. 2013). To match the observed TIGRE/HEROS spectrum, we consider the
rotational line-broadening (v$\cdot$sin(i)) and a spectral resolving power of
R$\approx$20000 in the PHOENIX spectrum. The PHOENIX spectrum adapted in this
way is then used to estimate the real spectral flux slope in the Ca II H&K
region in the TIGRE spectrum; this approach was taken from Hall & Lockwood
(1995) and guarantees consistency in the flux counts of the large reference
bandpasses of the pseudo-continua, which form the denominator of the S-index.

The second step in deriving SII_TIGRE is the assessment of the exact RV shift
of the Ca II H&K region of the respective spectrum by means of a cross
correlation with the PHOENIX spectrum (see middle panel Fig. 7). Subsequently,
the TIGRE spectral fluxes are also re-normalised to the physical spectral
slope seen in the PHOENIX spectrum (lower panel Fig. 7). Fortunately, by the
wise foresight of O.C. Wilson, the bandpasses of the S-index are symmetric,
meaning that any remaining mismatches of the flux slope and the effective
temperature are cancelled out in the resulting S-index.

Figure 7: Steps of the re-normalisation of spectra for TIGRE SII_MWO
estimation: Upper panel shows the Ca II H&K region of HD 29139 taken with
TIGRE on December 27 2019; the middle panel shows the continuum-normalised
spectra of the TIGRE spectrum as a black line and the selected and continuum-
normalised PHOENIX spectrum as a red line, and the lower panel shows the re-
normalised TIGRE spectrum as a black line and the PHOENIX spectrum in a
relative flux scale (flux divided by the maximal flux).

Finally, the counts in the four bandpasses, depicted in the lower panel of
Fig. 7, are obtained by integration, and the ratio between the sum of the two
line bandpasses and the sum of the two continuum bandpasses is computed
according to Eq. 2. The error estimation of SII_MWO follows the method used
for STIGRE and described by Mittag et al. (2016). Indeed, apart from the
continuum flux re-normalisation and line-core profiles, both indices are
obtained in a very similar manner.

####  4.2.3 Transformation of SII_TIGRE to the Mount Wilson scale

The transformation between the TIGRE and the Mount Wilson giant S-index scales
takes care of any instrumental effects. However, because of the large epoch
difference, a larger number of giants needs to be considered to average out
any individual changes in their activity levels. To do so, we chose giants
both observed by TIGRE and contained in the Mount Wilson sample published by
Radick & Pevtsov (2018). In total, we use 25 objects to derive the
transformation, of which the SII_MWO values were measured by the present
authors more than ten times.

Figure 8: SII_MWO vs. STIGRE transformation: Upper panel: SII_MWO vs.
SII_TIGRE. The solid line presents the transformation relation. Lower panel:
Residuals of the used transformation relation. Table 2: Giants used for the
transformation of the SII_TIGRE into the Mount Wilson scale.

Object |  Teff [K] |  $\log$(g) |  SII_MWO |  No. of SII_MWO |  SII_TIGRE |  TIGRE SII_MWO |  No. of SII_TIGRE |  Difference [$\%$]
---|---|---|---|---|---|---|---|---
HD4128 | 4800 | 2.5 |  0.38$\pm$0.04 | 486 |  0.0167$\pm$0.0013 |  0.422$\pm$0.033 | 29 | 11.0
HD6805 | 4600 | 2.5 |  0.229$\pm$0.005 | 35 |  0.0089$\pm$0.0003 |  0.238$\pm$0.011 | 37 | 3.9
HD6860 | 3800 | 1.5 |  0.536$\pm$0.01 | 45 |  0.0212$\pm$0.0013 |  0.528$\pm$0.034 | 35 | -1.4
HD8512 | 4700 | 2.5 |  0.217$\pm$0.006 | 45 |  0.008$\pm$0.0003 |  0.216$\pm$0.01 | 32 | -0.4
HD27371 | 5000 | 2.5 |  0.325$\pm$0.043 | 774 |  0.0126$\pm$0.0008 |  0.326$\pm$0.022 | 57 | 0.4
HD27697 | 5000 | 2.5 |  0.251$\pm$0.011 | 777 |  0.0095$\pm$0.0006 |  0.253$\pm$0.017 | 56 | 1.1
HD28305 | 4900 | 2.5 |  0.228$\pm$0.006 | 741 |  0.0092$\pm$0.0009 |  0.245$\pm$0.022 | 32 | 7.4
HD28307 | 5000 | 3.0 |  0.361$\pm$0.02 | 725 |  0.0122$\pm$0.0005 |  0.317$\pm$0.015 | 33 | -12.3
HD29139 | 3900 | 1.0 |  0.446$\pm$0.026 | 204 |  0.0169$\pm$0.0005 |  0.428$\pm$0.016 | 35 | -4.1
HD31398 | 4200 | 1.5 |  0.459$\pm$0.021 | 320 |  0.0181$\pm$0.0011 |  0.457$\pm$0.028 | 28 | -0.6
HD39801 | 3600 | 0.0 |  0.542$\pm$0.07 | 292 |  0.0212$\pm$0.0018 |  0.528$\pm$0.045 | 73 | -2.6
HD71369 | 5200 | 2.5 |  0.258$\pm$0.003 | 398 |  0.0099$\pm$0.0003 |  0.263$\pm$0.011 | 71 | 1.8
HD81797 | 4100 | 1.5 |  0.351$\pm$0.029 | 66 |  0.0135$\pm$0.0003 |  0.348$\pm$0.013 | 41 | -0.8
HD82210 | 5300 | 3.5 |  0.643$\pm$0.042 | 503 |  0.0272$\pm$0.0015 |  0.671$\pm$0.04 | 79 | 4.4
HD96833 | 4600 | 2.5 |  0.23$\pm$0.003 | 44 |  0.0085$\pm$0.0002 |  0.228$\pm$0.009 | 69 | -0.8
HD109379 | 5100 | 2.5 |  0.264$\pm$0.005 | 99 |  0.01$\pm$0.0003 |  0.265$\pm$0.011 | 42 | 0.4
HD111812 | 5600 | 3.0 |  0.727$\pm$0.022 | 322 |  0.0299$\pm$0.0008 |  0.735$\pm$0.027 | 32 | 1.1
HD115659 | 5100 | 2.5 |  0.278$\pm$0.012 | 331 |  0.0106$\pm$0.0003 |  0.279$\pm$0.012 | 67 | 0.5
HD164058 | 3900 | 1.5 |  0.407$\pm$0.008 | 15 |  0.0139$\pm$0.0017 |  0.357$\pm$0.041 | 23 | -12.4
HD124897 | 4300 | 1.5 |  0.247$\pm$0.004 | 917 |  0.0091$\pm$0.0004 |  0.243$\pm$0.012 | 72 | -1.4
HD159181 | 5200 | 1.5 |  0.69$\pm$0.032 | 611 |  0.0296$\pm$0.0006 |  0.728$\pm$0.024 | 70 | 5.6
HD186791 | 4200 | 1.5 |  0.505$\pm$0.04 | 461 |  0.0196$\pm$0.0006 |  0.492$\pm$0.019 | 28 | -2.5
HD202109 | 4900 | 2.5 |  0.241$\pm$0.011 | 222 |  0.0087$\pm$0.0003 |  0.234$\pm$0.01 | 68 | -3.0
HD205435 | 5100 | 3.0 |  0.477$\pm$0.029 | 461 |  0.0164$\pm$0.0012 |  0.417$\pm$0.031 | 66 | -12.7
HD209750 | 5200 | 1.5 |  0.486$\pm$0.024 | 543 |  0.0197$\pm$0.0011 |  0.494$\pm$0.03 | 52 | 1.7

333The listed Teff [K] and $\log$(g) are the values for the PHOENIX spectrum
that used for the TIGRE S-index estimation.

These giants —with their physical parameters and median S values, with the
standard deviation of the median as error— are listed in Table 2. The rounded
Teff and log g values are those of the selected PHOENIX reference spectra.

Figure 8 gives the distribution of SII_MWO vs. SII_TIGRE (average values) for
all 25 giants. Here, a linear trend is very obvious and we derive the
following transformation relation via an orthogonal distance regression, which
is represented in the same figure by a solid line:

$\displaystyle S_{\rm{II\\_MWO}}=(0.0280\pm 0.0063)+(23.63\pm
0.61)\rm{S}_{\rm{II\\_TIGRE}},$ (3)

which yields a standard deviation of the residuals of 0.024. In addition, we
compute the percentage deviations (listed in Table 2) between the Mount Wilson
reference S-values and the transformed TIGRE S-values, and obtain an averaged
deviation of 5.6%. This is mainly an effect of long-term changes in the
activity levels between the very different epochs of the observations, but is
also attributable, to a much lesser extent, to observational error.

###  4.3 Long-term time series: joining TIGRE and Mount Wilson S-index values

We now exploit the fact that the red supergiant $\alpha$ Ori is both part of
our TIGRE giants observation program and contained in the Mount Wilson program
(see Radick & Pevtsov (2018)), with available data reaching back into the
1980s. These data allow us to examine whether or not a similar behaviour of
the S-index as observed during the great dimming in the winter between 2019
and 2020 —with a simultaneous significant increase in the S-index anti-
correlated with the V-band luminosity— has already occurred before.

The combined, long-term S-index time series is shown in the lower panel of
Fig. 9. The Mount Wilson data are represented by black points and cover the
period of September 1983 to March 1995. The TIGRE observation of $\alpha$ Ori
started in September 2013 once TIGRE went into operation. Only S-index values
based on spectra with an S/N larger than 25 at 4000 Å are shown (as blue
points). In total, a period of 38 years is covered, from 1983 to 2021, albeit
with a gap of 18 years between 1995 and 2013. As can be seen from Fig. 9, the
median of the $\alpha$ Ori S-value is 0.539 over the whole period.

Figure 9: Long-term time series: Comparison of the visual (upper) and V band
(middle) magnitudes of the AAVSO database with S-values of the Mount Wilson
scale (lower panel). The dashed lines mark the periods with increased
S-values.

At least three episodes of strongly increased S-index values occurred during
those 38 years. The first one took place around 1984 with a maximum S-value of
0.7811 on 25 March, 1984, which is 45% larger than the long-term median
S-value, with a phase of increased S-index level continuing until 1985. The
second event took place in 1989 with a maximum S-value of 0.6879 on 1 October,
1989, which is 28% above the median S-index value. The third and most
significant event is the ‘great dimming’ in 2020 with a maximum S-index value
of 0.800 reached on 24 January, 2020, which is 48% larger than the median
S-value of 0.539. To see whether the earlier two events are of a similar
nature to the 2020 event, we now need to look at the correlation with
photometric data.

###  4.4 Comparing S-index and photometric variations

The latest 2020 increase in S-index values showed a good anti-correlation and
synchronisation with the great dimming event in 2020. To take a look further
back in time, we again employ the photometric data taken from the AAVSO
database. Figure 9 shows the light curve of the visual band magnitude in the
upper panel, and the V band magnitude (Johnson V-band) versus time in the
middle panel. To ease this comparison, the above-mentioned periods of
increased S-values are marked by dashed vertical lines. The visual magnitude
light curve does show a dimming in 1985, slightly delayed against the maximum
increase in S-index values around 1984. However, we caution that the decrease
in the visual magnitude in 1984 and 1985 was established by only two observers
and very few brightness estimates were made. However, the anti-correlation
with the S-index supports the idea that we have an event similar to the great
dimming in the winter between 2019 and 2020.

Unfortunately, V-band photometric data of before $\approx$1988 are quite rare,
and so we need to use the more abundant visual magnitude estimates for our
comparison with the older S-index time series. In the case of the S-increase
around 1 October, 1989, the decrease in visual brightness is not as strong as
during the 2020 great dimming event, but neither is the increase in S-index in
1989. From the few V-band data available, the brightness decrease can be
confirmed and can therefore be considered as real. As mentioned above, the
evidence for the 1984 and 1985 variation is less clear, yet there seems to be
a recurrent pattern; namely that when the S-index rises, the visual brightness
decreases. Such events last only $o(1)$yr, but lie several or even many years
apart.

A simple explanation for this anti-correlation of S-index and V-mag lies in
the definition of the S-index, according to which the near-ultraviolet (NUV)
continuum fluxes of the reference windows form the denominator. As now seen
very clearly in the recent great dimming event, when the brightness, and with
it the temperature, decrease (see Gray (2008), Harper et al. (2020) and this
work), the denominator of the S-index formula decreases, and consequently the
S-index of $\alpha$ Ori increases, even if the chromospheric emission remains
constant on an absolute scale. In addition, Dupree et al. (2020) present
radial velocity data that indicate a variation of the stellar radius, adding
to the effect of reduced continuum flux during such a dimming event. All these
observations show that the photosphere of $\alpha$ Ori is not at all stable,
and that in such a case the S-index is as sensitive to photospheric variations
as it is to chromospheric emission changes.

###  4.5 The absolute scale: Ca II H&K flux

To obtain the true activity level of $\alpha$ Ori based on the S-index, the
latter has to be transformed into physical emission line fluxes on an absolute
scale. Given the photospheric variability, there is no single relation for
$\alpha$ Ori to achieve this. Instead, we need to consider all components of
S, the absolute NUV-continuum fluxes, and the line emission individually and
for each spectrum separately.

To accomplish this we use the method developed by Linsky et al. (1979), which
was originally designed to derive the absolute Ca II H&K flux for $\alpha$
Ori. However, this approach requires the removal of the instrumental and
atmospheric effects on the spectral flux distribution. For this purpose, part
of the TIGRE observing schedule on each night is an observation of at least
one spectrophotometric standard star to create the instrumental (and
atmospheric) response function for each night. Hence, for 73 $\alpha$ Ori
spectra, we were actually able to obtain this spectrophotometric calibration.

After applying the nightly instrumental response function, the count ratio is
calculated for observations with a sufficient S/N (larger than 25 at 4000 Å),
following the definition by (Linsky et al. 1979), that is,

$\displaystyle I_{HK}=\left(\frac{N_{H1}+N_{K1}}{N_{3925-3975}}\right),$ (4)

where $N_{H1}$ and $N_{K1}$ are the spectral flux counts between the so-called
K1 and H1 points of the Ca II H&K lines, respectively, and $N_{3925-3975}$ is
the count in a continuum bandpass of 50 Å in width centred at 3950 Å. In the
case of $\alpha$ Ori, we assumed a distance of 3 Å between the K1 and H1
points. The positions of the K1 points of the Ca II K line are labelled in
Fig. 5. The H1 point positions of the Ca II H line are similar to those for Ca
II. In total, we were able to derive this count ratio $I_{HK}$ for 72 TIGRE
spectra, which are shown in the upper panel of Fig. 10.

Not surprisingly, given the similarities in definition, the $I_{HK}$ time line
shows a similar behaviour as the S-index values in Fig. 9. After all, both
indices are based on a ratio between the flux counts in the H&K line cores and
a UV reference continuum window, with the latter amplified by a change of the
stellar radius, changing with a high power with decreasing effective
temperature during the great dimming event.

Figure 10: Ca II H&K fluxes in relative and absolute flux scale: Upper panel
shows the count ratio $I_{HK}$ vs. time, middle panel the estimated absolute
Ca II H&K flux, and the lower panel the estimated Ca II H&K flux excess
$R^{\prime}_{HK}$.

To convert the $I_{HK}$ values into the absolute Ca II H&K fluxes, we then
follow the relation given by (Linsky et al. 1979), that is,

$\displaystyle\mathcal{F}_{\rm{H\&K}}=I_{HK}\mathcal{F}(\Delta\lambda)*50,$
(5)

where, $\mathcal{F}(\Delta\lambda)$ relation is given by Linsky et al. (1979):

$\displaystyle\mathcal{F}(\Delta\lambda)=8.264-3.076(V-R).$ (6)

To do so, we perform a transformation of the effective temperatures (as
derived above) into $V-R$ colours using Eq. 10; see Sect. C. The result is
shown in the middle panel of Fig. 10. Comparing these two panels, one
immediately notices the entirely different behaviours of the two time series:
while $I_{HK}$-values (just like the S-indices) increase during the great
dimming event, the derived absolute fluxes decrease, and their temporal
behaviour is more comparable with that of the effective temperature; see
Appendix A.

In this context, we must recall that some part of the H&K line-core emission
is the underlying photospheric contribution, which —like the UV reference
fluxes— strongly decreased during the great dimming event as well, driven by
the decreasing effective temperature and the stellar radius. To evaluate the
pure chromospheric activity of $\alpha$ Ori on an absolute scale, the latter
has to be separated from the photospheric contribution and to be normalised by
the corresponding bolometric flux.

This type of activity index was introduced by Linsky et al. (1979), who
defined an $R^{\prime}_{\rm{HK}}$-index through

$\displaystyle R^{\prime}_{\rm{HK}}$ $\displaystyle=$
$\displaystyle\frac{\mathcal{F}_{\rm{HK}}-\mathcal{F}_{\rm{HK,phot}}}{\sigma\leavevmode\nobreak\
T_{\rm{eff}}^{4}}.$ (7)

A brief description of the estimation of photospheric flux
($\mathcal{F}_{\rm{HK,phot}}$) is given in Sect. C, and the resulting
$R^{\prime}_{\rm{HK}}$ time series is presented in the lower panel of Fig. 10.
Again, there is a remarkable difference compared to the two panels above. From
the beginning of the dimming event to its brightness minimum,
$R^{\prime}_{\rm{HK}}$ remains constant within its uncertainties. Then, with
the recovery of the brightness of $\alpha$ Ori, $R^{\prime}_{\rm{HK}}$
(meaning the pure Ca II H&K flux, or line core ‘flux excess’) decreases. It
therefore appears that any variation of the pure chromospheric emission, and
so the magnetic heating, started only after the great dimming event had
reached its full strength; however, given the large errors of
$R^{\prime}_{HK}$, caused mainly by the uncertainty in the effective
temperatures, this result has to be regarded with some caution.

###  4.6 The space view: Mg II h&k flux

Valuable additional observations of the chromospheric activity during the
great dimming of $\alpha$ Ori were presented by Dupree et al. (2020), who
performed measurements of spatially resolved Mg II h&k lines and MUV fluxes in
2400-2700 Å taken on eight different days in 2019 and 2020 with the HST/STIS.
These data suggest a strong increase in flux in the period of 18 September to
28 November 2019, with a maximum on 6 October 2019.

Unfortunately, individual flux values are not listed in the paper by Dupree et
al. (2020), but these values can be reasonably estimated (within their
measurement uncertainties) from Fig. 5 of Dupree et al. (2020). The summed Mg
II h&k line and summed MUV fluxes in 2400-2700 Å for each day, as well as
their ratio, are shown here in the upper, middle, and lower panels of Fig. 11,
respectively. As expected, the upper panel reproduces the increase in the Mg
II h&k line emission described by Dupree et al. (2020); this is similar to the
behaviour of our derived Ca II H&K fluxes over time (see middle panel of Fig.
10).

Figure 11: Summed Mg II h&k spectral line flux (upper panel), the summed MUV
fluxes in 2400-2700 Å (middle panel), both as obtained from Fig. 5 of Dupree
et al. (2020), and their ratio (lower panel).

Forming the ratio of the Mg II h&k line emission over the MUV flux in
2400-2700 Å should then have a similar effect, as seen in the S-index and
$I_{HK}$ time series, because in principle the photospheric flux part in the
measured MUV flux in 2400-2700 Å, much like the UV flux in the reference bands
of the S-index, is strongly temperature dependent.

Indeed, the lower panel of Fig. 11 does also show an increase in the Mg II h&k
line flux relative to its MUV flux in 2400-2700 Å during the great dimming
event. This demonstrates that there is no discrepancy between the
observational evidence presented here regarding the chromospheric Ca II H&K
line emission and the respective Mg II h&k data presented by Dupree et al.
(2020). Both emissions should be, and indeed are, behaving in a very similar
way during the great dimming event. The only difference is seen in the
evidence for changes in the effective temperature, which is an issue we
discuss below.

##  5 Dynamical behaviour of the photosphere

We also detected significant variations and shape differences in other
spectral lines: here we specifically focus on the wavelength range from 6251 Å
to 6263.4 Å, which contains the V I 6251.82 Å and Fe I 6252.56 Å lines; the
line-depth ratio of these lines depends on the effective temperature in cool
giants (Gray & Brown 2001).

Figure 12: Normalised spectra in the wavelength range from 6251 Å to 6263.4 Å
taken before, during, and after the great dimming event. The different colours
mark the different elements and the red dashed lines indicate the laboratory
wavelengths.

First, the spectra were normalised and RV corrected as described in Sect 5.1.
In Fig. 12, we compare the normalised spectra taken before, during, and after
the great dimming event to demonstrate the spectral changes. Figure 12 also
demonstrates that the degree of blending of the involved spectral lines varies
with time. To disentangle those changes, we performed a multiple Gaussian fit
to better determine the true line centres as well as the width and the depth
of each line; to ensure robust results we considered only low-noise spectra
with a mean S/N of at least 100 in the considered wavelength range. From the
derived true line centres, and using the laboratory wavelengths as listed in
the NIST Atomic Spectra Database (Kramida et al. 2021), we then determined the
respective rest frame RVs, which are presented in this section.

###  5.1 Mean RV variations

First, we had to determine a reference photospheric RV value to which we
compare each $\alpha$ Ori spectrum; for this, we used the line of Fe I at
6254.26 Å. The RV values for the other spectra were then determined by cross
correlation with that iron line in the first spectrum, and we estimate the
uncertainty of this procedure to be about $\pm$0.4 km s-1 based on the
assumption that the shift between two spectra can be determined with a sub-
pixel accuracy of $\pm$0.1 pixel.

In Fig. 13, we plot the resulting RV values. For the observing season between
2019 and 2020, these RVs are consistent with the RV values shown by Dupree et
al. (2020). Additionally, we plot the average RV value of $\alpha$ Ori of
21.56$\pm$0.58 km s-1 given by (Kharchenko et al. 2007), in order to better
visualise the RV variations. As evident from Fig. 13, the RV variations range
from $\sim$14 km s-1 to $\sim$26 km s-1, and we note that for the observation
season from 2020 to 2021, the RV values are larger than the long-term average
RV, except for the first two values, indicating a redshifted photosphere until
the end of the year 2020. Subsequently, the RV values decrease until
approximately 2021.1 and we see a blueshifted photosphere; later, the RV
values increase again.

Figure 13: Estimated RV values vs. time. The red dashed line marks the long-
term average RV value for $\alpha$ Ori of 21.56$\pm$0.58 km s-1 given by
(Kharchenko et al. 2007).

###  5.2 Line RV variations

Visual inspection of the spectra, as shown in Fig. 12 reveals some variations
of the line centres. Some are blueshifted and others are redshifted. These
variations include shifts of one line core with respect to another, suggesting
a non-uniform motion of their slightly different geometrical origins.

In order to gauge the reality of this dynamical picture, we first checked the
stability of the wavelength solution of our TIGRE spectra in this wavelength
range. To do so, we determined the line centres of various lines in this
wavelength region with respect to the RV standard star of that night, which is
always taken for quality-control purposes (cf. the TIGRE
webpage444https://hsweb.hs.uni-hamburg.de/projects/TIGRE/DE/
hrt_user/spec_redu_info_rv_log.php). Each line centre was determined via a
multiple Gaussian fit, in the same way as done for comparing the $\alpha$ Ori
lines to one another as described above.

With respect to the RV standard stars, we find no significant trends in the
lines cores, confirming the stability of our wavelength solution. The standard
deviation of the rest RV variation of the respective lines (with a line depth
of at least one-tenth of the normalised continuum) suggests a small scatter,
ranging from 0.07 km s-1 for the Fe I line at 6254.26 Å to 0.55 km s-1 for the
Ti I line at 6261.10 Å. We also checked in this fashion the stability of the
line distances; here, we find a scatter of less than 0.02 Å.

Figure 14: Rest RV values over observing epoch. The grey area marks the range
of the scatter as expected from the line RV examination with respect to the RV
standard stars.

Following this quality check, we restricted our analysis to spectra with rest-
frame RV errors of below 2 km s-1, and considered only RV data more recent
than epoch 2019.5, because the earlier observing cadence was not sufficiently
dense. The derived time series of rest-frame RV (hereafter, rest RV) values of
the V I at 6251.82 Å, Fe I lines at 6252.56 Å and 6254.26 Å, Ti I line at
6261.10 Å, and La II line at 6262.30 Å are shown in Fig. 14. In these time
series, we observe some residual variation in the rest RV values. Also, these
time series show a different trend in the rest RV values. To check whether
these variations could be caused by residual errors in the wavelength solution
of the TIGRE Échelle spectra, we check the line distances in this wavelength
range in the RV standard stars observed on the same nights. Here, we do not
find any significant scatter in the line distances and therefore we conclude
that the observed variations are not caused by an erroneous wavelength
solution.

To visualise the different trends in the time series of the rest RV values, we
computed the rest RV differences for four line combinations and list our
results in Table 3; to this end, we normalised the rest RV by subtracting the
mean rest RV value and computed the differences of these rest RV values. These
RV differences ($\Delta$RVnorm_rest) values are shown in Fig. 15, which
demonstrates a clear wave-like variation in the time range 2019.5-2020.5
during the great dimming. Figure 15 also shows that the variations during the
great dimming were much stronger than those observed during the following
season. To quantify the strength of these variations, the standard deviation
of these variations is computed for these two observation epochs and also for
both individual seasons, with the results being listed in Table 3.

Table 3: Standard deviations of the difference of the rest RV values for
different line combinations

|  $\sigma$ of $\Delta$ RVnorm_rest in different epochs
---|---
Line combination | 2019.5-2021.5 | 2019.5-2020.5 | 2020.5-2021.5
V I6251.82Å \- Fe I6252.56Å | 1.31 | 2.43 | 0.83
Fe I62521.56Å \- Fe I6254.26Å | 1.53 | 2.49 | 0.55
Fe I6254.26Å \- Ti I6261.10Å | 1.93 | 2.70 | 1.09
Ti I6261.10Å \- La II6262.30Å | 2.62 | 4.29 | 0.93

Figure 15: Normalised rest RV value vs. time. The different signs and colour
codes mark the different line pairs.

In summary, we exclude that the variations in the rest RV values are an
artifact created by an uncertain wavelength solution. Rather, we assume these
variations to be a sign of additional motions, suggesting that the behaviour
of the variations in the rest RV values indicates a difference in motion
between the mean regions where the different lines are formed.

###  5.3 Variation of the line depths and widths

The strong line variability during the great dimming event is evident from
Fig. 12. To visualise this significant variation in lines, we plot the line
depths and the line widths obtained from the Gaussian fits against observing
epoch in Figs. 16 and 17 for the lines of Fe I at 6252.56 and 6256.36 Å, the V
I lines at 6251.82 Å and 6256.90 Å, and for the Ti I lines at 6261.10 Å.

Both line parameters show clear variations with a wave-like shape reminiscent
of the effective temperature time series shown in Fig.4. Furthermore, the
strengths of the variations in the line depths are about the same, while the
strengths of the variations in the line widths are clearly different. The
differences in the variation of the line widths indicate differences in the
extent of thermal broadening between the respective mean regions of the
respective line origins. Again, the variations in depth and width of the lines
presented here suggest that the photosphere is always dynamic; however, during
the great dimming event, the resulting changes were extraordinarily large.

Figure 16: Line depths vs. time shown. Figure 17: Line FWHM vs. time shown.

###  5.4 Temperature sensitive line-depth ratio of V I 6251.82 Å over Fe I
6252.56 Å

Gray & Brown (2001) demonstrated that the line-depth ratio (LDR) of the lines
of V I at 6251.82 Å and Fe I at 6252.56 Å can be used to estimate the
effective temperature for cool giants. The LDR is determined by the expression

$\displaystyle LDR$ $\displaystyle=$
$\displaystyle\frac{line\leavevmode\nobreak\ depth\leavevmode\nobreak\
of\leavevmode\nobreak\ {V\textsc{I}}_{\leavevmode\nobreak\
6251.82\AA}}{line\leavevmode\nobreak\ depth\leavevmode\nobreak\
of\leavevmode\nobreak\ {Fe\textsc{I}}_{\leavevmode\nobreak\ 6252.56\AA}}.$ (8)

Gray (2008) used this LDR to study the variations of $\alpha$ Ori and showed
it to correlate with the V magnitude. However, Gray (2008) thought that a
conversion of the LDR values into $\alpha$ Ori temperatures is not possible in
absolute terms in the absence of an established relation. However, it is
plausible that such a relation exists in physical terms, as we see below.

In this work, we measured the LDR of the V I 6251.82 Å and Fe I 6252.56 Å
lines to see whether any significant variations occurred during the great
dimming event and how these compare to the normal variations of $\alpha$ Ori.
For this purpose, we used the line depths obtained from the amplitudes of the
Gaussian line fits above to compute the depth ratios of these lines; we show
our results in Fig. 19. We see that the LDR values do indeed vary with time
and behave much like our derived effective temperature; see Sect. 3.2.

Figure 18: Time series of the line-depth ratio of the V I 6251.82 Å and Fe I
6252.56 Å lines

Figure 19: Teff over the line-depth ratio. The solid line represents their
mean relation.

These results suggest a consistent relation between our effective temperature
values and the LDR (see Fig. 19), with a simple linear behaviour, which is
represented in the same figure by the solid line:

$\displaystyle T_{\rm{eff}}=(3736.7\pm 7.8)K-(328.5\pm 25.3)K(LDR-1).$ (9)

The scatter of this relation is small: we obtain a standard deviation of the
residuals of only 24 K.

##  6 Summary and conclusions

In this study, we performed a multi-wavelength analysis of the variations
observed during the great dimming event of $\alpha$ Ori and in the subsequent
observation season of 2020 to 2021. To provide an overview, we plot the
derived time series of the V magnitude, the well observed and temperature-
dependent colour index $R-I$, our effective temperature values, the RVrest km
s-1 of the line-core variation, our S-index time series, the derived
$R^{\prime}_{HK}$ values, and the ratio between the absolute Mg II h&k line
flux and the MUV flux in 2400-2700 Å shown in Dupree et al. (2020) in Fig. 20;

Figure 20: Summary of the time series to show the main variation results. From
top to bottom, we show the V band, $R-I$ colour index, the effective
temperature, the RVrest variation of the Ti I line at 6261.1 Å and the TIGRE
SII_MWO, the $R^{\prime}_{HK}$, and the ratio between the absolute Mg II h&k
line flux and the MUV flux in 2400-2700 Å shown in Dupree et al. (2020).

as a reference of the long-term variability, the values of the V band
magnitude are instructive and therefore, we show them here in the upper panel
of Fig. 20.

Clearly, the values of effective temperature are important for a complete
understanding of the chromospheric activity of $\alpha$ Ori in absolute terms.
We analysed the variations in different colour indices using the photometric
data of the AASVO, as well as of the LDR of the V I 6251.82 Å and Fe I 6252.56
Å lines; as an example, we refer to the $R-I$ index time series in the third
panel of Fig. 20. This and the LDR time series do indicate changes in the
effective temperature, especially during the great dimming event. To assess
the effective temperature and its changes, we use four TiO bands covered by
the TIGRE spectra and derive clear temperature variations of $\alpha$ Ori over
time, in full agreement with Harper et al. (2020).

Next, we study the magnetic activity of $\alpha$ Ori, starting with the Ca II
K line during the great dimming event. We find a strengthening of the
chromospheric line-core emission relative to the photospheric spectrum in the
months leading up to the brightness minimum, and afterwards a weakening of the
relative Ca II K line-core brightness. We then compare the wider 2Å S-indices
taken with TIGRE with the respective values obtained by the Mount Wilson
program in the 1980s for giants, including $\alpha$ Ori. To this end, we
needed to derive a transformation equation between those two scales based on a
larger number of giants observed by the present authors and Mount Wilson in
order to average out most individual activity changes between those two
epochs. Our analysis then shows that the current TIGRE measurements of the Ca
II lines can be related to Mount Wilson S-index data taken much earlier and to
the photometric data available from the AAVSO database over the past four
decades. We used these relations to construct a long-term light curve of
$\alpha$ Ori that extends over almost 40 years, thus providing a very much
extended perspective of the great dimming event.

Upon subsequent inspection of the combined 2Å S-index time series, we note
three larger increases in the S-values, each lasting less than a year,
occurring in 1984-1985, 1989 (both Mount Wilson data), and 2020 (TIGRE); the
latter coincides with the great dimming event and is shown here in the fifth
panel of Fig. 20. A comparison with the V-band light curve shows a clear
brightness decrease over the same period, suggesting a correlation between the
decrease in brightness and the increase in the S-values. This correlation
indicates that the debated former dimming in 1984 and 1985 was a real event
—even though only two observers recorded this event in the visual band—
because it coincided with the first 2Å S-increase observed by Mount Wilson.

Next, we estimated the Ca II H&K line flux in absolute terms, applying the
method by Linsky et al. (1979) to $\alpha$ Ori. The time series of the
absolute Ca II H&K line flux obtained in this way shows, in stark contrast to
the S-value time series, that at the beginning of the great dimming event
there was clearly a larger chromospheric emission than at the brightness
minimum. The time series rather follows the shape of the effective temperature
graph during the great dimming, which is no surprise, because the continuum
flux —used as a reference to estimate the line flux— depends very strongly on
the effective temperature in this NUV spectral range. Ignoring this effect
would be like comparing the fluxes of two different stars, because the
effective temperature of $\alpha$ Ori changes notably during the great dimming
event.

We also estimated the excess of the normalised Ca II H&K line flux,
$R^{\prime}_{HK}$. Interestingly, this excess flux does not change
significantly at the beginning of the great dimming event (see sixth panel of
Fig. 20), and only starts to vary after the dimming event. Also, comparing the
absolute Ca II H&K line flux with the absolute Mg II h&k line flux, our
results and those of Dupree et al. (2020) are comparable. We therefore
conclude that in order to remove the temperature effect on the latter, we need
to involve the ratio between the absolute Mg II h&k line flux and the MUV flux
in 2400-2700 Å (shown in Dupree et al. (2020); see Figs. 11 and the seventh
panel of Fig. 20). This ratio shows a behaviour that is comparable to that
seen in our $R^{\prime}_{HK}$ time series during the great dimming.

This finding implies that the chromospheric activity did not change much at
the beginning of the observed brightness minimum; however, as seen in the time
series of $R^{\prime}_{HK}$, there is a decrease in chromospheric activity
after the brightness minimum in February 2020. Therefore, our interpretation
contradicts that of Dupree et al. (2020), at least as far as the cause of the
dimming is concerned. Whatever started this chain of events does not seem to
be located in the outer atmosphere.

This conclusion is supported by the observed variations in different lines,
which display strong changes during the great dimming event, both in their
ratio of line strength, which are caused by the impact of the effective
temperature changes, and also in their width and respective RV; an example is
shown in the fourth panel of Fig. 20. This dynamical behaviour indicates a
strong variation in the photosphere of $\alpha$ Ori.

In agreement with previous studies, our results demonstrate that $\alpha$ Ori
is a highly variable star, which is reflected in all parameters illustrated in
Fig. 20. This leads us to the interesting question of how these variations
provide support to the two main hypotheses for the cause of the great dimming
event. The decrease in the mean effective temperature, as demonstrated here,
in combination with a reduction in the effective luminous area of the
photosphere —which may not necessarily be a radius change— supports scenarios
(see Freytag et al. (2019)) where a large cool area forms temporarily, while a
much smaller number of warm convection cells rise. Such temporary quasi-
synchronisation of several large convection cells may go hand in hand with
shock- or density waves. The down-flow of such a large, temporary cool area,
which greatly reduces both the effective luminous area of the photosphere and
the effective temperature, would not appear as obvious changes in RV; cooler
regions are under-represented in the observed line profiles, because cooler
gas contributes much less to the total emergent flux, and we would rather
expect changes on a differential scale between lines with different formation
temperatures, as reported here. Thus, all these ideas point to the photosphere
and its convection as the main driver of the great dimming event.

The other prominent hypothesis, put forward by Dupree et al. (2020), assumes
veiling by dust related to an observed mass ejection in October 2019. This
idea is also based on the stronger absolute Mg II h&k line flux and MUV flux
in 2400-2700 Å seen in October 2019 compared to the respective fluxes during
the brightness minimum in February 2020 reported by the same authors. In our
study we too find that the absolute Ca II H&K line flux was clearly larger in
November 2019 than during the brightness minimum in February 2020. However,
the significant changes in effective temperature and luminous area must be
accounted for in order to correctly assess the chromospheric energy output on
an absolute scale as shown above. As a consequence, the apparent large
chromospheric emission increase that was observed to take place simultaneously
with the beginning of the great dimming event disappears, and it is not until
after the bolometric brightness minimum that the chromosphere reacts to it in
absolute terms.

Thus, the corrected timing of the different events disagrees with the
assumption of a strong mass ejection in October 2019, and any subsequent
veiling by dust is therefore an unlikely cause of the great dimming; it would
rather be a consequence and serve as an enhancement. Further evidence in
favour of an origin of the chain of events in the photosphere and its
convection, forming sometimes larger cool plumes, is provided by the
recurrence of such an event; we show the similarities between the available
data from 1984-1985 and those from 2020-2021. Given the extremely large size
and therefore small number of convection cells under the extremely low gravity
of $\alpha$ Ori, any temporary chance synchronisation and plume formation on
the earth-facing side should indeed not be a particularly unique event.

###### Acknowledgements.

We are grateful to our anonymous referee for the kind report.– We particularly
wish to thank our colleague Bernd Freytag of the Theoretical Astrophysics
Department, Uppsala University, for enlightening discussions of how to
interpret the complex information gained from our observations. – We
particularly acknowledge use of the public HK_Project_v1995_NSO data base of
the Mount Wilson Observatory HK Project, which was supported by both public
and private funding through the Carnegie Observatories, the Mount Wilson
Institute, and the Harvard-Smithsonian Center for Astrophysics, running from
1960ies over more than three decades. These data are the result of the
dedicated work of O. Wilson, A. Vaughan, G. Preston, D. Duncan, S. Baliunas,
and many others. We are also very grateful for using the AAVSO International
Database, photometric data on $\alpha$ Ori contributed by observers worldwide.
– Furthermore, the VizieR catalogue access tool, CDS, Strasbourg, France (see
the original description of the VizieR service: A&AS 143, 23) was helpful to
this research, as well as the SVO Filter Profile Service
(http://svo2.cab.inta-csic.es/theory/fps/) supported from the Spanish MINECO
through grant AYA2017-84089. – Finally, our research and international
collaboration between Germany and Mexico, as well as the operation of TIGRE,
has benefited significantly from travel money by the Conacyt-DFG bilateral
projects No. 207772 and 278156, and by the institutional support given by the
universities of Hamburg and Guanajuato (UG: by DAIP funding from its project
003/2022 and CAP programs) over the past decade.

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##  Appendix A Variation of the calculated radius and calculated $\log(g)$

Dupree et al. (2020) presented RV measurements of $\alpha$ Ori during the
great dimming event. These were variable and are correlated with the observed
V mag variation. If there are real radius changes, the question therefore
arises as to which changes we address here in terms of the calculated radius.
Indeed, the photometric variation cannot be explained by the effective
temperature changes alone and implies changes in the calculated radius.
However, we cannot distinguish whether these reflect physical radius changes
or simply changes in the effective luminous area. A reduced calculated radius
could also result from the temporary presence of a large dark patch on the
photosphere, such as that seen when there is a rising or sinking cooled plume
formed in the course of some chance synchronisation of the few large granules
on the observable side of this supergiant.

To estimate such changes in the stellar radius of $\alpha$ Ori in absolute
terms, the luminosity of $\alpha$ Ori can be used: assuming spherical
symmetry, it is proportional to $R^{2}T_{eff}^{4}$. For a quantification of
the stellar luminosity of $\alpha$ Ori, we adopted the distance of 168 pc
given by (Joyce et al. 2020). In addition, we used the V magnitude data from
the AAVSO database of the days where we were able to derive an effective
temperature.

For days with an effective temperature value but no V mag, we interpolated the
nearest V mag data. The results of this calculation are shown in the upper
panel of Fig 21. For simplicity, the bolometric correction (BC) of -1.93 here
is based on the long-term mean effective temperature of 3649 K, but see below.
For the calculation of the latter, we apply Eq. 10.10 of Gray (2005).

Figure 21: Calculated stellar properties where BC is constant vs. time: Upper
panel: Logarithmic luminosity in solar units vs. time. Middle and lower
panels: Calculated radius in solar units and calculated gravity (calculated
$\log(g)$) on the same timescales. Here, a constant BC of -1.93 was used,
which is based on the long-term mean effective temperature.

The strong decrease in the stellar luminosity during the great dimming event
is obvious, and radius and gravity values calculated from luminosity and
effective temperature are presented in the middle and lower panels of Fig. 21.
As the luminosity drop was too large to be explained by the lower effective
temperature alone, the radius would had to decrease from $\approx$640
$R_{\odot}$ on 11 November 2019 to $\approx$500 $R_{\odot}$ on 24 January
2020, which would explain the above-mentioned variation of the RV data.

The $\log(g)$ values were then calculated using the above stellar radius
values and assuming a (constant) mean stellar mass of 17.75 $M_{\odot}$ (see
Joyce et al. (2020)). As seen in the lower panel of Fig. 21, there is an
increase in the calculated $\log(g)$ of up to $\approx$0.3 dex during the
great dimming event, which is caused by the reduction in calculated radius.

In this context, the impact of the temperature variation on the bolometric
correction (BC) now requires some consideration. For this purpose, we
calculated the BCs for the individual days (see top panel of Fig. 22) where we
had derived the effective temperature, again using the relation in Eq 10.10 of
Gray (2005). We repeated the calculation of the luminosity, radius, and
gravity to assess the impact of a time-variable BC (in the range of -1.69 to
-2.26 mag) and compared the results with those obtained assuming a constant BC
(-1.93) based on the long-term mean effective temperature of 3649 K.

Figure 22: Calculated Stellar properties where BC is variable vs. time: Upper
panel: Time-variable BC, using the derived daily effective temperatures (black
dots). The red dashed line shows the BC of the mean effective temperature of
3649 K. Second panel: Logarithmic luminosity. Third panel: Stellar radius.
Lowest panel: $\log(g)$. Black points represent the values obtained with
daily, time-variable BC (as in the top panel), and red points show the values
using the constant BC instead.

These comparisons are shown in Fig. 22.

The second panel of Fig. 22 shows the logarithm of the luminosity in solar
units versus time. the third panel depicts the calculated radius, and the
lowest panel the calculated $\log(g)$ (if the calculated radius was indeed
representative of the geometrical radius). In all panels, black points
represent the values calculated with the time-variable BC based on the daily
effective temperatures, and red points depict the values for which the
constant BC of the long-term mean effective temperature is used.

Not surprisingly, we find some differences between the use of the daily time-
variable BC and a constant mean effective temperature BC for the stellar
luminosity, calculated radius, and calculated $\log(g)$. In principle, these
differences vary with the course of the effective temperatures and amplify the
effect of the latter on all three quantities. From this test, we conclude that
all the consequences of the effective temperature changes must be considered .

##  Appendix B Theoretical colour estimation using PHOENIX model spectra

To understand, at least qualitatively, the non-linear behaviour of the
different colour indices $B-V$, $V-R$, $R-I,$ and $J-H$ mag with a variable
effective temperature in the range from 3300 K to 4000 K, we estimated these
indices from synthetic PHOENIX model spectra of different temperatures. Here
we give an example to our work, using the synthetic spectrum of the model
atmosphere for Teff = 3600 K, log(g) = 0, [Fe/H] = 0, as made available by the
University of Göttingen database of (Husser et al. 2013).

The filter functions for the B, V, R, and I bands were taken from Mann & von
Braun (2015), and for the J and H bands we used the Keck_NIRC2.J and
Keck_NIRC2.H filter functions available from SVO Filter Profile
Service555http://svo2.cab.inta-csic.es/theory/fps/ (Rodrigo et al. 2012;
Rodrigo & Solano 2020). The above-mentioned PHOENIX spectrum and these filter
functions are plotted in Fig. 23.

Figure 23: Normalised PHOENIX spectrum (Teff = 3600 K, log(g) = 0 and [Fe/H] =
0),; over-plotted are the filter functions used here.

To derive colour indices from the PHOENIX model, the synthetic spectral flux,
weighted with the filter function, is integrated over each band, and then
converted into magnitudes. For this last step, a theoretical spectral flux
reference to a ‘white’ A0 standard star, such as Vega, is required. We use the
synthetic PHOENIX spectrum with the physical parameters Teff = 9600 K, log(g)
= 4.0, and [Fe/H] = -0.5. The results of these estimations are shown in Fig.
24.

Figure 24: $B-V$, $V-R$, $R-I,$ and $J-H$ colour indices vs. effective
temperature.

Regarding the colour indices, in general the colour index increases with
decreasing effective temperature; however, as demonstrated in Fig. 24, the
values for the B-V colour index actually decrease with effective temperature
once this latter drops below 3600 K.

##  Appendix C Ca II H&K flux estimation

To estimate the Ca II H&K flux, we used the method described in Linsky et al.
(1979) and the main points of this method are given in Sect. 4.5. Here, we
want to add and discuss a few added details.

###  C.1 Spectrophotometry: counts of a 50 Å continuum window vs. airmass

For the Ca II H&K flux estimation with the method described in Linsky et al.
(1979), a spectrophotometric standard star is required to create an
instrumental response function. Unfortunately, the air mass of the target star
and the observed spectrophotometric standard star can be different, and so can
the extinction, which then causes a distortion or tilt of the derived spectral
energy distribution (SED) of each flux-corrected spectrum. To test the impact
of this problem, which should become worse at large airmass, we integrated the
counts in the 50 Å bandpass window centred at 3950 Å (where the counts in the
3 Å bandpass of Ca II H&K lines are not considered). These continuum counts
are plotted here against air mass; see Fig. 25. Fortunately, we do not find
any significant correlation between the flux-corrected continuum counts

Figure 25: Continuum counts without the counts in the 3 Å bandpass of Ca II
H&K lines vs. air mass.

and the air mass, which suggests that this possible problem is sufficiently
well controlled by our procedures.

###  C.2 $V-R$ colour index–Teff relation

In the conversion of the count ratio ($I_{HK}$; see Eq. 4), the flux depends
on the colour index $V-R$; see Eq. 6. However, the AAVSO database does not
contain $V-R$ values for the same days for which we have TIGRE spectra.
Furthermore, we did not have enough data to derive a relation between
effective temperature and $V-R$ value.

Therefore, we derived the $V-R$ colour index from PHOENIX spectra of the
University of Göttingen database of (Husser et al. 2013) as explained above,
using models of different effective temperatures with [Fe/H]=0.0 and a
$\log$(g)= 0.0; see Sect. B. Figure 26 shows these $V-R$ colours against the
respective effective temperature, represented by blue points.

Figure 26: PHOENIX $V-R$ vs. effective temperature : Blue points: $V-R$
colours derived from PHOENIX spectra over effective temperature. The solid
black line indicates the best-fit relation between the two. Black points:
$V-R$ colours from the AASVO database over our derived effective temperatures
from different days in the time line.

To derive the relation between $V-R$ and the effective temperature, we
performed a least-square fit through:

$\displaystyle V-R$ $\displaystyle=$ $\displaystyle 1.4331-2.3620\cdot
10^{-3}x$ (10) $\displaystyle+4.03\cdot 10^{-6}x-2.64\cdot 10^{-9}x,$

where $x$ is $x=T_{eff}-3300[K]$; this relation is represented by a solid
black line in Fig. 26.

To test the reality of the PHOENIX spectra $V-R$ values and their dependence
on effective temperature, we compare these with the observed $V-R$ colours
from the AASVO database, coinciding in time with some of the days (only 7) for
which we could derive an effective temperature. These observed $V-R$ values
are shown as black points in Fig. 26.

This comparison shows that the observed $V-R$ values are slightly above their
synthetic counterparts, but the latter still represent the relative changes
with effective temperature quite well. We conclude that the $V-R$ values
derived from PHOENIX models and their synthetic spectra are slightly smaller
than in reality, implying that the real Ca II H&K fluxes and flux excesses may
be a little larger than stated here.

###  C.3 Photospheric flux

In the case of $\alpha$ Ori, it is essential to remove the photospheric flux
contribution from the Ca II H&K line in order to study the true stellar
activity and prevent this latter from mimicking a false degree of variation in
stellar activity. Here, we give a brief description of how we derive that
photospheric flux contribution, following Linsky et al. (1979), who considers
its part between the Ca II K1 and H1 points of the Ca II H&K lines.

Figure 27: Ca II K line spectrum of $\alpha$ Ori. The magenta solid line shows
the fit between the assumed K1V and K1R point. The grey area shows the
photospheric contribution, and the red area represents the chromospheric
emission.

To estimate the photospheric flux contribution in the Ca II H&K lines in our
TIGRE spectra, we used the a linear trend between Ca II K1 and H1 points of
the Ca II H&K lines. These are illustrated for the Ca II K line in Fig. 27.
Here, the magenta solid line represents the linear trend which splits the line
flux into the the photospheric and chromospheric contribution. The grey area
in Fig. 27 below the solid magenta line specifies the photospheric line
contribution, and the red area in Fig. 27 above the magenta solid line shows
the pure chromospheric line emission.