11institutetext: Astronomical Institute of the Czech Academy of Sciences,
Fričova 298, CZ-25165 Ondřejov, Czech Republic
11email<EMAIL_ADDRESS>22institutetext: Department of Theoretical Physics
and Astrophysics, Masaryk University, Kotlářská 2, CZ-61137 Brno, Czech
Republic 33institutetext: Variable Star and Exoplanet Section of the Czech
Astronomical Society, Vsetínská 941/78, 757 01 Valašské, Meziříčí, Czech
Republic 44institutetext: Hvězdárna Jaroslava Trnky ve Slaném, Nosačická 1713,
Slaný 1, CZ-27401 Slaný, Czech Republic

# Periodic variable A-F spectral type stars in the southern TESS continuous
viewing zone††thanks: Table 4 is only available in electronic form at the CDS
via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/

I. Identification and classification

M. Skarka 112233 Z. Henzl 3344

(Received May 16, 2022; accepted July 21, 2022)

###### Abstract

Aims. Our primary objective is to accurately identify and classify the
variability of A-F stars in the southern continuous viewing zone of the TESS
satellite. The brightness limit was set to 10 mag to ensure the utmost
reliability of our results and allow for spectroscopic follow-up observations
using small telescopes. We aim to compare our findings with existing
catalogues of variable stars.

Methods. The light curves from TESS and their Fourier transform were used to
manually classify stars in our sample. Cross-matching with other catalogues
was performed to identify contaminants and false positives.

Results. We have identified 1171 variable stars (51 % of the sample). Among
these variable stars, 67 % have clear classifications, which includes $\delta$
Sct and $\gamma$ Dor pulsating stars and their hybrids, rotationally
variables, and eclipsing binaries. We have provided examples of the typical
representatives of variable stars and discussed the ambiguous cases. We found
20 pairs of stars with the same frequencies and identified the correct source
of the variations. Additionally, we found that the variations in 12 other
stars are caused by the contamination with the light of faint nearby large-
amplitude variable stars. To compare our sample with other variable star
catalogues, we have defined two parameters reflecting the agreement in
identification of variable stars and their classification. This comparison
reveals intriguing disagreements in classification ranging from 52 % to 100 %.
However, if we assume that stars without specific types are only marked as
variable, then the agreement is relatively good, ranging from 57 % to 85 %
(disagreement 15-43 %). We have demonstrated that the TESS classification is
superior to the classification based on other photometric surveys.

Conclusions. The classification of stellar variability is complex and requires
careful consideration. Caution should be exercised when using catalogue
classifications.

###### Key Words.:

Stars: variables: general – Stars: oscillations – Stars: rotation – Methods:
data analysis – Catalogs

##  1 Introduction

In order to study the physical origin of stellar variability, it is necessary
to investigate groups of stars that have similar observational
characteristics. This means that we need clear observational criteria to
accurately classify the type of variability being observed. Since the stellar
variability is most prominent in the brightness variations, the usual and
natural way of the classification is based on the shape and amplitude of the
light curves and typical time scales of the variations (Samus et al., 2009;
Watson et al., 2006). However, even for stars with well-defined classification
parameter spaces, such as those with large amplitudes of brightness variations
and typical light-curve shapes like eclipsing binaries or RR Lyrae stars,
classification can be a challenging task. This calls for the need of visual
inspection and utilization of additional information and various analytical
methods (e.g. Soszyński et al., 2016, 2019; Prša et al., 2022; Iwanek et al.,
2022).

Classification of stars that exhibit low-amplitude variations caused by high-
order radial and non-radial pulsations, spots of various types, deformation of
the spherical shape of stars, and stellar activity is a challenging task. This
is because these effects have similar amplitudes and time scales, thereby
making it difficult to distinguish between them. The situation is further
complicated by a combination of different mechanisms that can be present
simultaneously, especially for stars with intermediate masses of $1-3$ M⊙ (F-A
spectral-type stars).

Moreover, the classification of stars becomes more complicated with the
availability of ultra-precise space observations from the Kepler (Borucki et
al., 2010) and TESS satellites (Ricker et al., 2015). These observations have
revealed new phenomena with similar amplitudes as the intrinsic stellar
variations, which are related to the contamination with nearby stars,
instrumental effects, and trends induced into the observations by the data
reduction procedures. Especially in the mmag and sub-mmag regime, the human
supervision can be biased and subjective, making even manual classification at
least partially questionable.

In some cases, the frequency limits that are commonly accepted for classifying
stars by their variability are not firmly established or cannot be generally
applied. For instance, Balona (2022) argues that there is no need for the roAp
class (rapidly oscillating Ap stars, Kurtz, 1982) because there is no
frequency limit that differentiates roAp and $\delta$ Sct (DSCT) stars.
Similarly, the commonly accepted limit of 5 c/d (Grigahcène et al., 2010) that
differentiates $\gamma$ Dor (GDOR) and DSCT stars can be questionable since
DSCT frequencies can appear below this limit and GDOR frequencies can be above
5 c/d (Grigahcène et al., 2010).

Lastly, our limited understanding of the physics behind stellar variability
does not allow for precise constraints on the physical limits of different
physical mechanisms. These limits, in addition, cannot be generalized and are
different for every particular star. For example, the position of the
empirical DSCT instability strip (IS) borders is different than the
theoretical limits, and there are non-pulsating stars inside the IS and
pulsating stars outside this region (see figures in e.g. Murphy et al., 2019;
Antoci et al., 2019).

The identification and classification of variable stars is a complex task, as
there are many factors that can affect the accuracy of automatic
classification using modern computational methods (e.g. Audenaert et al.,
2021; Audenaert & Tkachenko, 2022). Additional information, such as
multicolour photometric, spectroscopic, and astrometric observations, are
often needed to ensure reliable classification. In a recent study by Skarka et
al. (2022, hereafter S22), they discussed the challenges of identifying and
classifying bright A-F stars in the northern TESS continuous viewing zone
(CVZ) based on TESS photometric data. We proposed a conservative
classification scheme and compared the results with previous studies.

This paper presents a similar analysis for A-F stars in the southern TESS CVZ,
using the same criteria and methods as the previous study. We provide
conservative samples of variable stars that are suitable for follow-up
spectroscopic observations with small telescopes and that can serve as a
starting point for further detailed studies.

##  2 Sample selection and data retrieval

We used the same methodology as in S22. Initially, we selected a sample of
337798 point sources located within a 15-degree circle around the southern
ecliptic pole (RA=6h00m00s, Dec.=-66∘33’00”) from the TESS Input Catalogue
(TIC) v8.0 (Stassun et al., 2019). From this sample, we filtered out duplicate
stars and selected only 2302 stars with a record in the SIMBAD database
(Wenger et al., 2000) that have a temperature range of 6 000$<$$T_{\rm
eff}$$<$10 000 K and a brighter than 10 mag in Johnson $V$. The temperature
distribution of the stars is shown in Tab. 1. Most of the stars are fainter
than 8 mag (2043 stars), with only 17 stars being brighter than 6 mag.

Table 1: Number of stars in particular temperature ranges (based on temperatures from TIC (Stassun et al., 2019)). $T_{\rm eff}$ (K) | N
---|---
$6000-7000$ | 1308
$7000-8000$ | 603
$8000-9000$ | 222
$9000-10000$ | 169

We obtained all available data, which was processed by the TESS Science
Processing Operations Center (SPOC; Jenkins et al., 2016) and the quick-look
pipeline (QLP; Huang et al., 2020a, b), using the Lightkurve software
(Lightkurve Collaboration et al., 2018; Barentsen & Lightkurve Collaboration,
2020). We extracted the pre-search data conditioning simple aperture
photometry (PDCSAP) flux with long-term trends removed (Twicken et al., 2010)
and transformed the normalized flux to magnitudes. We did not apply any
additional de-trending or data filtering to preserve possible variability.

However, it was not possible to download data from all observed sectors for
some stars using Lightkurve. Therefore, for some stars, only one sector was
available despite being observed in multiple sectors. We analyzed data from
Cycles 1 (sectors 1-13) and 3 (sectors 27-39) in this paper. The SPOC routine
provided 2-minute and 20-second cadence data (SC) for cycles 1 and 3,
respectively, and 30- and 10-minute cadence data (LC) for cycles 1 and 3,
respectively. The QLP routine only provided LC data.

The Table 2 presents an overview of the available data sets in different
routines and their statistics. It is clear from the table that data for all
the sample stars were available in QLP, while SC SPOC data are missing for
more than 300 stars. The data from more than 20 sectors are available for most
of the stars in SPOC LC and QLP routines, whereas about half of the stars have
SC data only in 13 sectors. Additionally, the LC routines generally provide a
larger time span than is available for the SC data.

Table 2: Statistics of the analysed data sets.

| SC SPOC | LC SPOC | QLP
---|---|---|---
Stars | 1978 | 2249 | 2302
med Pts | 202441 | 48078 | 53095
Sect | 1-26 | 1-26 | 4-26
med Sect | 13 | 23 | 23
TS (d) | 22-1064 | 24-1064 | 296-1064
med TS (d) | 901 | 1064 | 1064
111Column ‘Stars’ gives the number of stars, ‘med Pts’ gives the median of
points, ‘Sect’ gives the range of available sectors, ‘med Sect’ gives the
median of available sectors, ‘TS’ and ‘med TS’ are the time span of the data
and its median, respectively.

##  3 Classification of the variable stars

We followed the same approach as discussed in S22, mainly in their sects. 3
and 4. The QLP data products have improved since the publication of S22 and
are of comparable quality to the SPOC LC data. However, we used QLP data only
when no SPOC data were available. The LC SPOC and QLP data contain various
artificial signals and they provide only integrated brightness over a longer
period, significantly reducing the amplitude of fast variations. Therefore, we
used SPOC SC data whenever possible for the analysis. We used SPOC LC and QLP
data only when there was a lack of SC data or when we needed to complement SC
data with data having a longer time base.

We carefully examined each light curve, analyzing the most prominent frequency
in the frequency spectrum, and the overall characteristics of the frequency
peaks, including their position, content, and morphology. Our classification
system is based on the criteria described in detail in tables 2-4 in S22. For
a better orientation among the variability types used in this work, we give
their basic description in Table 3.

Table 3: Description of variability types used in this work together with the
basic light-curve and frequency spectra characteristics. Binarity
---
ECL (eclipsing binary of unclear type) | Apparent minima | Harmonics of the basic frequency
EA, EP (Algol type, exoplanet) | Constant light in maximum, clearly defined minima | Many well defined harmonics of the basic frequency
EB ($\beta$ Lyr type) | Variation in maximum light, well defined minima | Many well defined harmonics of the basic frequency
EW (W UMa type) | Smooth brightness variations | Well defined harmonics of the basic frequency
ELL (ellipsoidal variables) | Regular, smooth brightness variations | One or two harmonics of the basic frequency
Rotation
ROTM (magnetic rotators) | Regular, smooth brightness variations | A few harmonics of the basic frequency
ROTS (Solar-like rotator) | Semi-regular variations | Unresolved peaks close to harmonics of the basic frequency
ROT (non-specified rotator) | Repeating stable features | A few harmonics of the basic frequency
Pulsations
RRL, DCEP (RR Lyr, Cepheids) | Fast rise to maximum, large amplitude | A few harmonics of the basic frequency
GDOR ($\gamma$ Dor, g-mode pulsators) | (ir)regular variations, beating, bumps | two and more independent peaks below 5 c/d
DSCT ($\delta$ Sct, p-mode pulsators) | (ir)regular variations, beating, bumps | two and more independent peaks above 5 c/d

In cases where it was difficult to determine the variability type, but the
star was clearly variable, we designated it as ‘VAR’. These stars typically
exhibit probable harmonics (which can include eclipsing binaries, ROT, ROTS,
ELL, ROTM, RRL, etc.) and additional peaks with unclear nature (panels d-h in
Fig. 1). Some VAR stars display a single peak or low-frequency (0-0.5 c/d) and
low-amplitude ($<0.1$ mmag) peaks that may be of instrumental origin. Some of
the stars classified as STABLE (panels a-c in Fig. 1) can be VAR in fact, but
the decision about the variability and/or the true source of variability was
impossible either due to the small amplitude of the variations (mostly
apparent only in the Fourier transform) or due to number of contaminants. The
complete classification is provided in Table 4.

Table 4: Classification of stars in our sample.

TIC | RAJ2000 | DEJ2000 | CR | Blends | Type |  $V$ (mag) |  $T_{\rm eff}$ (K) |  $L$ (L⊙)
---|---|---|---|---|---|---|---|---
25078674 | 60.18200711 | -71.16679809 | 0.0002 | 0 | VAR | 6.60 | 9150 | 26.3
25117240 | 61.65684312 | -69.26155744 | 0.3208 | 2 | GDOR | 9.40 | 6743 | 15.4
25117273 | 61.38801709 | -69.40047833 | 0.0005 | 0 | DSCT+LF | 9.52 | 7175 | 10.4
25117406 | 61.51260808 | -69.87130832 | 0.0006 | 0 | DSCT+GDOR | 7.45 | 7231 | 36.7
25117492 | 61.58357233 | -70.24478618 | 0.0015 | 1 |  | 9.80 | 8197 | 17.3
25118797 | 61.93961418 | -69.05238972 | 0.5487 | 1 |  | 9.86 | 6122 | 3.4
25132222 | 62.00132424 | -68.36099381 | 0.0105 | 0 |  | 9.73 | 6064 | 3.3
25132314 | 62.12780124 | -68.70223768 | 0.0006 | 0 | GDOR | 8.38 | 6867 | 7.1
25133052 | 62.13967593 | -71.63984666 | 0.0016 | 2 |  | 8.64 | 6315 | 2.7
25153007 | 62.8648749 | -70.73842226 | 0.0024 | 0 | ROT | 9.22 | 7109 | 5.3
… | … | … | … | … | … | … | … | …

222The full table that is available at CDS. The ‘CR’ column gives the
contamination ratio (Paegert et al., 2021), ‘Blends’ give the number of stars
with magnitude difference less than 5 mag from the target stars, values of
$V$, $T_{\rm eff}$ and $L$ are taken from Stassun et al. (2019).

Figure 1: Examples of frequency spectra of stable stars and stars marked as
VAR with unclear classification. The horizontal axis shows frequency in c/d,
while the vertical axis shows brightness in mmag. The numbers given in the
labels are the TIC numbers.

###  3.1 Stars with well defined equidistant peaks

Periodic variations associated with rotation (classes ROT, ROTM, ROTS),
orbital motion (EA, EB, EW, ELL), or non-sinusoidal pulsations (e.g., DCEP,
RRL) produce peaks at the fundamental frequency and its harmonics, resulting
in an equidistant pattern in the frequency spectrum. This pattern is easy to
recognize. However, the classification of these variations is not
straightforward.

Identifying and classifying eclipsing binaries is usually an easy task due to
prominent eclipses. However, the binary stars can be confused with other
possible classes if the eclipses are shallow and/or deformed, and not
distinct. Distinguishing non-eclipsing binary stars with tidally deformed
components (ellipsoidal variables and contact binaries) from spotted
chemically peculiar stars (class ‘ROTM’) based on a single-channel TESS
photometry can be an extremely difficult task, as discussed in S22. Both
classes show a dominant frequency and usually one well-defined harmonic in the
frequency spectrum (see the four upper panels of Fig. 2). The contamination of
ELL stars with ROTM stars is likely not too high because the incidence rate of
the spotted chemically peculiar stars of Ap type is small, only about 10 %
among the A-spectral type stars (Sikora et al., 2019b).

The light curves of ELL (ellipsoidal) stars can be distorted by various
effects like Doppler beaming, reflection effects, and spots (Faigler & Mazeh,
2011). Therefore, we decided to use a more conservative approach and classify
such stars as ‘ROTM—ELL’, instead of distinguishing between ROTM (rotational
modulation) and ELL. In the example shown in Fig. 2, only TIC 270573916 is an
ELL star with high probability. To make a final decision between ROTM and ELL
classes, spectroscopic observations are necessary. In a study by Green et al.
(2023), only 50% of 97 suspected ellipsoidal variables showed clear radial
velocity variations upon spectroscopic observation, indicating possible
contamination with spotted stars. We have also included stars that exhibit
apparent simple variability with a single peak in the frequency spectrum to
the ROTM—ELL class.

Figure 2: Examples of rotationally variable stars. The horizontal axis shows
frequency in c/d, while the vertical axis shows brightness in mmag. The insets
show the data in 5 days (four upper panels) and 10 days, respectively. The
numbers given in the labels are the TIC numbers.

It is important to note that there can be confusion between rotation and
pulsations in stars that exhibit temperature spots similar to our Sun. These
stars belong to a category called ‘ROTS’ and their frequency spectra can be
similar to GDOR pulsators. Active stars of the solar-like type show groups of
peaks around harmonics with rotational frequency due to differential rotation.
In Fig. 2, the four bottom panels show typical examples of such stars with TIC
33910266 being a bit questionable, showing five harmonics with gaps at
4$f_{\rm rot}$ and $6f_{\rm rot}$.

Stars that exhibit sharp, isolated peaks and their harmonics in the frequency
spectra, which cannot be classified accurately, are categorized as ‘ROT’.
These stars can be of various types such as ELL, ROTM, ROTS, RRL, DCEP,
eclipsing binaries, and others that display equidistant frequency peaks.
Therefore, the classification of ‘ROT’ stars should be considered only as
preliminary and rough similarly to stars in the VAR class. The frequency
spectra of VAR stars shown in panels f-h in Fig. 1 can be considered as
belonging to the ROT class.

Rotationally variable stars can be false positives because their light can be
contaminated with the light of far-away-located large-amplitude pulsating
stars (for example, RR Lyr and Cepheids) or eclipsing binaries. Such stars and
systems can have periods of variations similar to rotational periods of A-F
stars and show harmonics in their frequency spectra. In cases of
contamination, the amplitude and number of detectable harmonics are strongly
reduced. Examples of the contaminants are discussed in Sect. 3.3.

###  3.2 Pulsating stars

Assigning a star with GDOR (gravity-mode, g-mode pulsators), DSCT (pressure-
mode, p-mode pulsators), GDOR+DSCT and DSCT+GDOR (hybrid pulsators) classes
can also be challenging task. The first difficulty arises with the definition
of the GDOR class, specifically concerning the frequency content and pattern
in the frequency spectra. The gravity-mode pulsations of GDOR stars are
excited by the convective flux blocking mechanism (Guzik et al., 2000; Dupret
et al., 2005). This type of pulsation does not produce equally spaced
structures in the frequency domain (harmonics are possible). The GDOR
frequencies are usually between 0.3 and 3 c/d (Kaye et al., 1999; Henry et
al., 2011) with the most likely position being approximately 1.2-1.3 c/d (see
fig. 1 in Tkachenko et al., 2013). However, when shifted by the rotation, the
frequencies can reach up to 5 or even more cycles per day (Grigahcène et al.,
2010). The usually accepted limit to distinguish between g-mode and p-mode
pulsators is 5 c/d (Uytterhoeven et al., 2011), but other limits, such as 4
c/d (Antoci et al., 2019), are also being utilised.

The frequency pattern that is characteristic for the GDOR stars is a comb of
close, sometimes unresolved, peaks (for example, Balona et al., 2011;
Uytterhoeven et al., 2011; Tkachenko et al., 2013, our Fig. 3) that can also
be found around harmonics (see fig. 3 in Saio et al., 2018, and our Fig. 3).
This can cause a confusion with spotted solar-type stars which is best
apparent in TIC 393491490 in the bottom right panel of Fig. 3. On the other
hand, the peaks can also be randomly distributed (e.g., Uytterhoeven et al.,
2011; Balona et al., 2011, and TIC 350444342 in the bottom left panel of Fig.
3). We classified stars as GDOR when several peaks were present in the range
of approx. 0.3-5 c/d. At the same time, the frequency pattern did not comply
the requirements for the rotationally variable stars (see Sect. 3.1). In
addition, the amplitude of the frequency peaks has to be larger than 0.1 mmag.

Figure 3: Examples of GDOR stars. The horizontal axis shows frequency in c/d,
while the vertical axis shows brightness in mmag. The insets show the data in
10 days. The numbers given in the labels are the TIC numbers.

It is important to note that we do not differentiate between slowly-pulsating
B stars (SPB stars Waelkens et al., 1998; De Cat & Aerts, 2002) and GDOR stars
as SPB stars are hotter and may contaminate our sample at high temperatures.
Additionally, we do not distinguish between low- and high-amplitude GDOR stars
(HAGDOR, Paunzen et al., 2020) because the boundary between the two is not
well-defined, and amplitudes in TESS data may not be reliable due to
contamination and data processing. TIC 167008868 is an excellent candidate for
HAGDOR (top left panel of Fig. 3) with one of the largest peak-to-peak
amplitudes ever observed in HAGDOR (about 0.4 mag in TESS pass band, SPOC
routine).

The second important class of pulsating stars among A-F spectral type stars
are DSCT pulsators. The pulsations in these low-radial-order p-mode pulsators
are excited by the $\kappa$ mechanism operating in the HeII ionisation zone
and by turbulent pressure (Breger, 2000; Antoci et al., 2014). As already
mentioned, five cycles per day are usually taken as the border between GDOR
and DSCT pulsations (Uytterhoeven et al., 2011). However, some authors use 4
c/d (Antoci et al., 2019). The upper limit is also not firmly defined. Balona
(2022) stated that there is no sharp transition between roAp (Kurtz, 1982) and
DSCT stars and that the roAp class should be dropped. In fact, DSCT and roAp
stars are different objects and such a comparison concerns only the frequency
content (Holdsworth et al., 2024). Nevertheless, we marked a star as a DSCT
pulsator if it shows at least one strong peak above 5 c/d. Due to the faster
cadence in Cycle 3, the Nyquist reflections are not a significant problem
since the Nyquist frequency is 72 c/d which is well above the dominant
frequency for most of the DSCT stars.

The variety of DSCT frequency spectra has been shown many times (e.g.
Grigahcène et al., 2010; Uytterhoeven et al., 2011). Examples of frequency
spectra of DSCT stars in our sample are in Fig. 4. We can see stars with a
single dominant pulsation mode (e.g. TIC 350522254), stars with a comb of
peaks (e.g. TIC 149991210) but also stars with peaks across the whole
frequency range (e.g. TIC 299802315).

Figure 4: Examples of frequency spectra of DSCT stars. The horizontal axis
shows frequency in c/d, while the vertical axis shows brightness in mmag. The
numbers given in the labels are the TIC numbers.

The ultra-precise space observations revealed that basically, all DSCT and
GDOR stars show peaks in both regimes (Grigahcène et al., 2010; Uytterhoeven
et al., 2011; Balona, 2014). Balona (2014) also showed that most of the low
frequencies observed in the DSCT stars cannot be explained by the non-linear
combination of the DSCT modes and by rotation. Thus, the vast majority of
stars showing peaks in both DSCT and GDOR regimes, are likely hybrids.

The only situation when it is difficult to identify hybrid pulsators is in
stars where the amplitudes of the frequency peaks are different or the
frequency content is poor and the frequency peaks cannot be properly
interpreted. There is no commonly accepted amplitude threshold specifying that
a particular star is a pure GDOR or DSCT pulsator or a hybrid. The ratio of
the amplitudes in both regimes used by Uytterhoeven et al. (2011) and Bradley
et al. (2015) are only empirical thresholds (factor 5-7 in amplitude ratio)
not saying anything about the hybrid nature. In addition, each author uses a
different amplitude limit for considering the frequencies for the
classification. All of the mentioned problems add ambiguity to the
classification.

As each data set is unique, we did not adopt any amplitude threshold because
even peaks in the sub-mmag regime can be significant. We cannot avoid mixing
hybrids with pure DSCT or GDOR stars showing combination peaks without
detailed frequency analysis, which is out of the scope of this paper. However,
this will be the case in only a minority of stars. For instance, TIC 177035603
(top right-hand panel of Fig. 4) can be classified as a hybrid pulsator with
similar probability as pure DSCT. Similarly, TIC 350444342 in the bottom left
panel of Fig. 3 can be also considered as a hybrid pulsator, not a pure GDOR
star. Examples of frequency spectra of hybrid pulsators are shown in Fig. 5.
The least reliable classification among the shown stars is in TIC 41590715
because the peaks are grouped around 5 c/d and the classification can be all
of pure GDOR, pure DSCT, or hybrid pulsator. We give ‘DSCT+LF’ classification
to more than 60 % of the DSCT stars showing low-amplitude peaks below 5 c/d
meaning DSCT stars with low-frequency (LF) peaks with unclear interpretation.
Some of these stars can be hybrid stars, but some can also be rotationally
variable.

Figure 5: Examples of frequency spectra of hybrid GDOR+DSCT stars. Frequency
on the horizontal axis is in c/d, while brightness on the vertical axis is in
mmag. The numbers given in the labels are the TIC numbers. The upper four
panels show GDOR-dominating hybrids, while the four bottom panels show DSCT-
dominating hybrids. The vertical red dash-dotted lines indicate 5 c/d.

###  3.3 Contamination and identification issues

The southern TESS CVZ includes the Large Magellanic Cloud (LMC), where many
stars are strongly affected by contamination. This is especially problematic
due to the low angular resolution of TESS, which is 21 ”/px (Ricker et al.,
2015). Contamination can cause several issues such as distortion of the light
curve, mixing of variability, and decrease of the brightness amplitude. The
new data releases of Gaia catalogues (Gaia Collaboration et al., 2018, 2023)
led to the identification of redundant entries in the TICv8.0 catalogue
(Stassun et al., 2019). In TICv8.2, Paegert et al. (2021) identified ”phantom”
stars, which arise from diffraction spikes around bright stars, mismatches
between different catalogues, and from a combination of two or more fainter
stars mimicking one target.

We have found 13 such duplicate entries in our sample by comparing TIC8.0 and
TIC8.2 catalogs. The numbers of the duplicates are followed with a ‘p21’
suffix in the ‘Type’ column of Table 4. We also adopted the contamination
ratio from Paegert et al. (2021) in column CR, which gives the ratio of
contaminating flux and flux of the target star. Furthermore, we have cross-
matched the positions from TIC8.0 with the Gaia DR3 catalogue (Gaia
Collaboration et al., 2023) within a distance of 105” (5 px). The number of
blending stars with a magnitude difference less than 5 mag from the target
star is given in the ‘Blend’ column of Table 4. This information can at least
help to identify problematic targets. The most contaminated target is TIC
372913472, which has 13 contaminants. Automatic procedures for identifying the
true source of the variation signal (e.g., Higgins & Bell, 2023) are not
effective in our case, as they do not work well with a single frequency.
Therefore, each target would require a detailed investigation of the frequency
spectrum to get reliable and unambiguous results, which is beyond the scope of
this paper.

We also compared the strongest identified frequencies of categorized stars and
visually examined the frequency content to identify any obvious contaminants.
We considered a star with a larger amplitude peak as the real variable, while
the other star with the same frequency but lower amplitude was deemed a
duplicate contaminated by the variable star. In Table 4, we provide the TIC
number of the real variable (the contaminant) in the ‘Type’ column. There are
20 such cases.

It is important to note that there may be nearby large-amplitude variables,
such as eclipsing binaries or Cepheids, located just a few pixels away from
the target star. Even when the brightness difference is quite large (more than
5 mag), these variables can contaminate the light of the target and cause
false identification of variability. Two examples of this are TIC 358460464
and TIC 277293156, as shown in Fig. 6. The contaminants are approximately 3
and 2 pixels away from TIC 358460464 and TIC 277293156, respectively.
Additionally, the contaminants are 6.2 and 7.3 mag fainter than their
respective target stars.

Figure 6: Two identified variable stars that are actually not variable and
their light is contaminated by nearby stars. The numbers show the TIC
identification, variability type, magnitude difference ($\Delta m$) between
the contaminant and target star, distance of the target from the contaminant
($\Delta r$) and the contamination ratio (CR). In the charts generated with
Tpfplotter (Aller et al., 2020) in the bottom part of the figure, the
contaminating stars are numbers 4 and 6 in the left and right-hand panels,
respectively.

The contaminant of TIC 358460464 is an EW ASAS-SN J075559.67-644238.3 which is
a 15.2-mag star. Only the second and third harmonics of the orbital frequency
are apparent in the frequency spectrum of TIC 358460464, thus, we classified
it as DSCT (top panel of Fig. 6). On the other hand, three harmonics of the
pulsation frequency of ASAS-SN J053737.66-702553.4 (DCEP star, 15.62 mag) are
apparent in the frequency spectrum of TIC 277293156 (bottom panel of Fig. 6),
which makes it to belong to the ROT category.

In both cases, the classification is wrong, although the contamination ratio
is as low as 0.34 % in TIC 358460464 (in TIC 277293156 it is 10 %). Such
wrongly identified stars add noise to the statistics when investigating common
characteristics of the stars in particular variability classes. After this
finding, we cross-matched our sample with Gaia DR3 variable star catalogue
(Rimoldini et al., 2023) and ASAS-SN variable star catalogue (Jayasinghe et
al., 2018) within a 100 arcseconds (5 px) radius and compared the frequencies
(and their harmonics) from the catalogues with frequencies identified by us.
This helped us to identify 12 contaminants (Table 5), which are typically
eclipsing binaries and pulsating stars. We have therefore classified our
contaminated stars mostly as eclipsing binaries, DSCT and VAR. Such stars are
marked with an additional ‘-C’ in the column type in Table 4.

Table 5: Identification of the contaminating stars.

TIC | Type | G (mag) | Type-Cont | ID ASAS-SN |  ID Gaia DR3 |  $\Delta r$ (arcsec) |  $\Delta m$ (mag) |  $f_{\rm TESS}$ (c/d) |  $f_{\rm Literature}$ (c/d)
---|---|---|---|---|---|---|---|---|---
30469454 | VAR | 9.7 | EW | J045847.67-661118.7 |  | 85.0 | 4.1 | 0.7569 | 1.5138
141484981 | DSCT—EW | 9.3 | EW | J054857.15-733629.1 | 4650219988274730000 | 62.4 | 5.0 | 2.9631 | 5.9262
177022232 | DSCT—EW | 8.8 | EW | J064932.91-674043.5 | 5281603511044130000 | 64.7 | 7.0 | 3.6288 | 7.2574
260127863 | DSCT+LF | 9.9 | EW | J060839.75-582809.0 | 5494885264769510000 | 75.8 | 4.5 | 3.5486 | 7.0970
260160453 | VAR | 7.9 | ECL |  | 5482506511890750000 | 67.7 | 5.4 | 1.6843 | 3.3685
308538268 | VAR | 9.0 | EW | J080338.45-603047.4 | 5290787834752610000 | 77.4 | 4.7 | 2.2401 | 4.4810
340312485 | VAR | 8.9 | EW | J073934.70-595741.0 |  | 50.2 | 5.8 | 4.4852 | 8.9682
349647697 | GDOR | 8.8 | RRC | J072849.42-643817.6 |  | 78.5 | 7.5 | 3.6138 | 1.8951
358460464 | DSCT+LF | 9.0 | EW | J075559.67-644238.3 | 5275843994260360000 | 62.8 | 6.2 | 3.3086 | 6.6174
358465355 | EB | 9.6 | EB | J075605.94-601606.3 | 5290937849368120000 | 48.9 | 4.5 | 1.7528 | 3.5050
372911993 | DSCT+GDOR | 9.0 | ECL |  | 5289793459627240000 | 51.3 | 5.6 | 2.8177 | 5.6355
410452496 | VAR | 9.6 | EW | J075944.49-612807.4 | 5289891938931840000 | 85.9 | 4.5 | 2.3923 | 4.7846
333The column ‘Type-Cont’ gives the type of the contaminant from literature.
If both ASAS-SN and Gaia DR3 designations are given, the contaminant was known
to both ASAS-SN and Gaia DR3 variable stars catalogues (Jayasinghe et al.,
2018; Rimoldini et al., 2023).

This exercise underscores the risks of misidentifying and misclassifying
variable stars, which is far more common than we previously realized. In the
Gaia DR3 variable star catalogue, only 20 % of stars in the vicinity of our
target stars have had their frequencies determined. Identifying the true
variable star is further complicated by the fact that there may be multiple
stars within 100 arcseconds of the target (we only considered the brightest
one). Additionally, bright stars can contaminate the light from even larger
distances than 5 pixels. As a result, we can expect that the number of
contaminants is much larger than the 12 cases we list in Table 5.

Finally, there is high probability that many of the sample stars are bound in
physical binary or multiple systems. In such cases, the observed variability
is a combination of variability of system components. This can also lead to
miss-classification of the variability type.

##  4 Results and discussion

We have found that 50.9 % of the 1171 stars in our sample (excluding 33
duplicates) show clear variability. This is in agreement with the percentage
of variable stars in the northern TESS CVZ (51 %, S22). We were able to
determine the type of variability in 67.2 % of the stars, which is a better
performance than in S22, where only 60 % of stars were unambiguously
classified. Remaining 372 variable stars were unclassified444Considering
ROTM—ELL stars as categorized stars.. The higher number of data points, longer
time span, and more sectors observed may have contributed to our better
performance in classifying the stars.

The numbers of the classified variable stars are shown in Fig. 7. We have
identified a total of 503 pulsating stars, which includes DSCT, GDOR and their
hybrids plus one RRAB star (43 % of the variable stars). This count is about
22 % less than that of the northern TESS CVZ (S22). We can only speculate
about the reasons for the discrepancy.

Figure 7: Types of stars identified in our sample.

The diagram in Fig. 8 shows that DSCT and hybrid stars are evenly distributed
throughout the empirical instability strip from Murphy et al. (2019). Pure
GDOR stars, on the other hand, are clustered within the theoretical GDOR
instability strip from Dupret et al. (2005), although they can also be found
across the entire temperature range. At the hotter end of the scale, GDOR and
DSCT stars are likely to mix with SPB and $\beta$ Cep stars.

As expected, the ROTS stars are found at the lowest temperatures between
6000-7000 K, while ROTM—ELL stars are spread out across the entire temperature
range. This indicates that the population of ROTM—ELL is a mix of ELL and ROTM
stars. The ROT stars tend to prefer temperatures around the cooler GDOR edge
but can also be found spread out up to 10000 K, similar to the distribution
found in S22.

Figure 8: Hertzsprung-Russell diagram showing our categorized stars. The
dashed line shows the zero-age main sequence, while the evolutionary tracks
are shown with the dash-dotted lines. The empirical boundaries of the DSCT
instability strip are shown with blue and red continuous lines. The ZAMS,
evolutionary tracks and instability strip boundaries are taken from Murphy et
al. (2019). The GDOR instability region (Dupret et al., 2005) is shown with
the shaded area limited by the dotted lines. All the stars in our sample
including non-variable stars are shown with the grey dots.

We cross-matched our sample with other catalogues within the distance of 21”
(1 px) from our targets to compare the classifications. We used Topcat
(Taylor, 2005) and CDS X-Match service (Boch et al., 2012; Pineau et al.,
2020) to cross-match the catalogues. We can use two parameters describing the
agreement of the two catalogues. The first parameter is the Classification
Agreement Percentage (CAP), which gives the percentage of stars with the same
classification in both catalogues. The second parameter is the Detection
Agreement Percentage (DAP), which gives the fraction of stars identified and
classified as VAR and other variability types in our sample while being
assigned with the same variability type or as VAR in the other catalogue.

For instance, if we classify a star as DSCT and the catalogue identifies it as
VAR (and vice versa), it will count towards DAP. However, if we classify a
star as DSCT and the catalogue identifies it as EW, it will not count.
Similarly, if the catalogue gives a variability type, and we do not detect any
variability, it will not count. DAP is useful in reflecting the uncertainty in
the classification, as it gives a chance that the classification is correct in
at least one of the compared catalogues.

There are 97 sample stars present in the VSX catalogue (Watson et al., 2006).
This catalogue is a compilation of variable stars identified in various sky
surveys and projects but also by individual observers (for example, NSVS
(Woźniak et al., 2004), ZTF (Chen et al., 2020), CzeV catalogue (Skarka et
al., 2017)). However, only 85 of these 97 stars have been categorized. In 15
of the VSX-declared variables, we did not notice any variation. Out of the
remaining 82 stars that have been classified in the VSX catalogue, we agree
with the classification of only 26 stars (32 %). The CAP for our
classification and VSX is, therefore, 26 out of 97 (27 %).

We show examples of where our classification differs from that of the VSX
catalogue in Fig. 9. Specifically, we have classified TIC 31925242 (CR Hyi) as
a GDOR variable, whereas it is classified as ELL in the VSX catalogue (see the
top panel of Fig. 9). Similarly, TIC 350522254 (XY Pic) is classified as DSCT
by us555The variability type DSCT of XY Pic was already discussed by Dall
(2005)., while it is classified as EW in the VSX catalogue. The data of TIC
350522254 show a beating caused by the presence of two close frequencies at
about 6.7 c/d (Fig. 9). For the VSX catalogue, the DAP 77 %.

Figure 9: Stars with wrong classification in the catalogues. The left panels
show the frequency spectra with the part of the time series (the catalogue
classification is given together with the TIC number), while the right-hand
panels show the data phase-folded with the dominant frequency together with
the correct variability type.

Out of the 84 stars in our sample, 80 are classified as VAR in the ASAS-SN
catalogue (Jayasinghe et al., 2018, 2019), while only four are categorized.
Among the four categorized stars, one star is classified as GCAS (our
ROTM—ELL, TIC 348898673, see Fig. 9), and another star is listed as ROT (our
EA, TIC 349480507). However, we did not detect any variation in the remaining
two stars that should be classified as GCAS according to Jayasinghe et al.
(2018, 2019). Furthermore, we did not detect variation in 9 of the declared
variable stars. It is worth noting that there is no agreement between our
classification and the ASAS-SN catalogue (CAP$=0$ %). The DAP for our
classification and the ASAS-SN catalogue is 85 %, but this is only because
most of the stars are labelled as VAR in the ASAS-SN catalogue.

We crossmatched our sample of stars also with the Gaia DR3 variables
(Rimoldini et al., 2023) within a 21” radius, and found 219 entries for our
stars666By omitting three stars that are apparent blends with other stars in
our sample.. The CAP parameter is 48 % while DAP is 57 %. The high value of
CAP is because most stars in our sample have a broad variability type
classification in Rimoldini et al. (2023). For example, Gaia DR3
classification ACV—CP—MCP—ROAM—ROAP—SXARI complies with our ROT, ROTS,
ROTM—ELL stars, SOLAR LIKE complies with our ROTS, ROT and ROTM—ELL classes,
DSCT—GDOR—SXPHE complies with our GDOR, DSCT and their hybrid classes. We
found no variability in 35 stars declared as variables in Rimoldini et al.
(2023).

In their study, Fetherolf et al. (2023) created a comprehensive list of
variable stars from the TESS prime mission by searching for periodicity and
variability using the Lomb-Scargle periodogram (Lomb, 1976; Scargle, 1982).
Since we used the same data and analysis method, we expected to obtain similar
results. Our sample overlapped with 1141 stars from Fetherolf et al. (2023)
catalogue, including 16 duplicates and 9 false positives (stars that were
blends with faint large-amplitude variables). Unfortunately, Fetherolf et al.
(2023) did not provide a classification of the variable stars, so we could
only calculate the DAP, which was only 63 %. Most of the stars that we
disagreed on did not exhibit apparent variability and displayed low-frequency
peaks similar to those shown in panel (c) of Fig. 1. The frequencies of
variable stars found by Fetherolf et al. (2023) perfectly matched with
frequencies found by us (including our VAR stars). However, in stars that we
marked as stable, the frequencies identified by (Fetherolf et al., 2023)
differed from the frequencies identified by us. This is an additional argument
against assigning these stars as variable.

Fourty-four stars from our sample are listed in the binary-star catalogue by
Prša et al. (2022). However, we classified three of them not as eclipsing
binaries but as ROTM—ELL (TIC 382512330, 306578324, and 141127435) and TIC
142148228 and 150187916 as VAR stars. The CAP and DAP with Prša et al. (2022)
are both 89 %. This result is no surprise since variations of eclipsing
binaries are characteristic and usually have large amplitudes.

Regarding rotational variable stars, 29 stars from our sample appear in Sikora
et al. (2019a). The variations are connected with rotation or orbital motion
only in 16 of them. The rotational nature of the 13 rest stars is ambiguous.
The CAP and DAP are both 55 %.

Twelve of our sample stars are listed in Antoci et al. (2019) which deals with
DSCT stars. Nine of them were identified as DSCT (or hybrids) also by us, and
one of the stars was found as constant in agreement with Antoci et al. (2019).
In TIC 260416268, which was identified as rot/binary Am star by Antoci et al.
(2019), we detected no variability. The same applies to the roAp candidate TIC
238185398. The CAP and DAP are both 83 %.

The discrepancies between our results and results from literature arise from
the superior characteristics of the TESS data compared to other catalogues
meaning better precision, cadence and often also the time span. The agreement
in classification with previous studies and catalogues is summarized in Table
6.

Table 6: Agreement (1st column) in per cent of our classification with the large catalogues and dedicated studies. CAP/DAP (%) | Type | Catalogue
---|---|---
27/77 | General | VSX (Watson et al., 2006)
0/85 | General | ASAS-SN (Jayasinghe et al., 2018)
48/57 | General |  Gaia DR3 (Rimoldini et al., 2023)
-/63 | General | TESS PM (Fetherolf et al., 2023)
89/89 | Binaries | (Prša et al., 2022)
55/55 | ROT | (Sikora et al., 2019b)
83/83 | DSCT | (Antoci et al., 2019)

##  5 Conclusions

We carefully classified variable stars using data from TESS from Cycles 1 and
3. This data is useful for detecting fast variations, such as DSCT pulsations,
as well as variations that occur over several days. We discussed the
limitations of our classifications, including the general shortcomings in
variable stars classification. Furthermore, we compared our results with
existing databases and variable star catalogues.

We confirm the previous issues with the classification of rotationally
variable stars and hours- to days-long pulsations of GDOR type. It is also
often difficult to distinguish between ellipsoidal and/or contact binary
variables and spotted stars without additional information. Additionally, the
classification can be influenced by nearby stars, and the level of
contamination depends on the distance of the contaminating star, the amplitude
of variations, and the difference in brightness. This mainly affects the
classification of rotationally variable stars and stars that show a
combination of different types of variation.

We found intriguing discrepancies in the classification in variable stars
catalogues that can be up to 100 %. To address this issue, we have introduced
two parameters - CAP and DAP. CAP reflects the classification, while DAP
concerns the detection of variability without a specific variability type. Our
results show that we have a relatively good agreement with the Gaia catalogue
(CAP$=48$ % Rimoldini et al., 2023). The best agreement was with the studies
dedicated to particular variability types. For instance, the agreement of our
classification was almost 90 % with the database of eclipsing binaries (Prša
et al., 2022) and 83 % in case of DSCT variables (Antoci et al., 2019).
Surprisingly, the agreement of our results with a study by Fetherolf et al.
(2023), that was also based on the TESS data, was only 63 %. We have also
demonstrated that large-amplitude variables can contaminate the light of the
target stars up to 100 arcseconds from the star, which can lead to incorrect
identification and classification.

It has been shown that classifying variable stars is a complex task and may
produce ambiguous or incorrect results. It is not advisable to blindly use
samples of variable stars without individually checking each star. This is
especially important in usage of samples based on automatic classifiers. To
create reliable catalogues of variable stars, it is necessary to analyze not
only single-channel photometric observations but also multi-color and
spectroscopic observations, and to estimate reddening and distance.
Additionally, one must be very careful in handling contamination. Only then
can we be confident that the variations of specific objects are caused by the
proposed effect(s).

The first PLATO mission field (LOPS2, Nascimbeni et al., 2022) will include
the southern TESS CVZ. Our classification represents a good starting point for
the studies of stellar variability in the PLATO field.

###### Acknowledgements.

MS acknowledges the support by Inter-transfer grant no LTT-20015. This paper
includes data collected with the TESS mission. Funding for the TESS mission is
provided by the NASA Explorer Program. Funding for the TESS Asteroseismic
Science Operations Centre is provided by the Danish National Research
Foundation (Grant agreement no.: DNRF106), ESA PRODEX (PEA 4000119301) and
Stellar Astrophysics Centre (SAC) at Aarhus University. We thank the TESS team
and staff and TASC/TASOC for their support of the present work. We also thank
the TASC WG4 team for their contribution to the selection of targets for 2-min
observations. The TESS data were obtained from the MAST data archive at the
Space Telescope Science Institute (STScI).

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