# Variability of magnetic hot stars from the TESS observations

Shen, Dong-Xiang School of Physical Science and Technology, Xinjiang
University, Urumqi 830046, People’s Republic of China<EMAIL_ADDRESS>Li,
Gang Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven,
Belgium;  Abdusamatjan Iskandar  Xinjiang Astronomical Observatory, National
Astronomical Observatories, Chinese Academy of Sciences, Urumqi 830000, China;
<EMAIL_ADDRESS>School of Astronomy and Space Science, University of
Chinese Academy of Sciences, Beijing 100049, People’s Republic of China  Fu,
Jian-Ning Department of Astronomy, Beijing Normal University, Beijing, 100871,
People’s Republic of China  Zhu, Chun-Hua  School of Physical Science and
Technology, Xinjiang University, Urumqi 830046, People’s Republic of China;
<EMAIL_ADDRESS>Yu, Jin-Long  College of Mechanical and Electronic
Engineering, Tarim University. 843300, Alar, P.R.China  Zhang, Yu  Xinjiang
Astronomical Observatory, National Astronomical Observatories, Chinese Academy
of Sciences, Urumqi 830000, China<EMAIL_ADDRESS>L$\ddot{\rm u}$ , Guo-
Liang  Xinjiang Astronomical Observatory, National Astronomical Observatories,
Chinese Academy of Sciences, Urumqi 830000, China<EMAIL_ADDRESS>Zhai,
Nan-Nan Xinjiang Astronomical Observatory, National Astronomical
Observatories, Chinese Academy of Sciences, Urumqi 830000, China;
<EMAIL_ADDRESS>Liu, Jin-Zhong  Xinjiang Astronomical Observatory, National
Astronomical Observatories, Chinese Academy of Sciences, Urumqi 830000, China;
<EMAIL_ADDRESS>
###### Abstract

Magnetic hot stars refer to the stars, which effective temperatures
approximately in the range from 7,000 to 50,000 K, and with large-scale
globally organized magnetic fields. These magnetic fields exhibit strengths
ranging from tens of Gauss to tens of kilo-Gauss. They are key in
understanding the effects caused by magnetic fields in the stellar evolution.
However, there are only three magnetic hot stars studied via a combination of
spectropolarimetric and asteroseismic modeling. Combined with
$Transiting\;Exoplanet\;Survey\;Satellite\;(TESS)$ 1-56 sectors data sets, we
provided a photometric variability and stochastic low frequency (SLF)
variability study of 118 magnetic hot stars. 9 new rotating variable stars are
identified. Using the Bayesian Markov Chain Monte Carlo (MCMC) framework, we
fitted the morphologies of SLF variability for magnetic hot stars. Our
analysis reveals that the magnetic hot stars in our sample have $\gamma<5.5$
with the vast majority having $1\leq\gamma\leq 3$. The $\nu_{\rm char}$ is
primarily in the ranges of $0\;\text{d}^{-1}<\nu_{\rm
char}<6.3\;\text{d}^{-1}$. The amplitude of SLF variability, log$\alpha_{\rm
0}$, shows a dominant distribution ranging from 0.8 to 3. No significant
correlations are observed between the luminosity and fitting parameters,
suggesting no clear dependence of SLF variability on stellar mass for our
sample of magnetic hot stars with masses between approximately
$1.5M_{\odot}<M<20M_{\odot}$. We found a significant negative correlation
between the $B_{\rm p}$ and $\nu_{char}$. This suppression effect of magnetic
fields on $\nu_{\rm char}$ may be a result of their inhibition of
macroturbulence.

stars: early-type — stars: magnetic fields — stars: variables: general —
stars: statistics

##  1 Introduction

Magnetic hot stars have been revealed by recent large surveys (e.g. Fossati et
al., 2014; Bagnulo et al., 2015; Grunhut et al., 2017). Their effective
temperatures range from roughly 7,000 to 50,000 K (Neiner, 2021). The majority
of the detected large-scale magnetic fields of the magnetic hot stars are
stable over timespans of up to decades (e.g. Oksala et al., 2012; Sikora et
al., 2019), and have a predominantly dipole topological structure inclined to
the rotational axis, with magnetic field strengths ranging from tens of Gauss
to tens of kilo-Gauss (e.g. Shultz et al., 2018; Järvinen et al., 2021).
Strong magnetic fields have been considered to explain the particular
properties of these hot stars, such as photometric variations (e.g. Oksala et
al., 2015; Shen et al., 2022), H$\alpha$ line variations (e.g. Wisniewski et
al., 2015; Hubrig et al., 2017; Shultz et al., 2020), the UV resonance line
variations (e.g. Shore & Brown, 1990; ud-Doula et al., 2022), the X-ray
properties (e.g. Wade et al., 2012; Petit et al., 2015), and the radio
emissions (e.g. Leto et al., 2017; Shultz et al., 2022).

The strong, large-scale dipole magnetic field in a hot star could be a fossil
field from the pre-main sequence (pre-MS), or the result of a violent binary
interaction such as a merger (MacGregor & Cassinelli, 2003; Braithwaite &
Spruit, 2004; Brun et al., 2005; Braithwaite & Nordlund, 2006; Petit et al.,
2010, 2011; Cantiello & Braithwaite, 2011; Alecian et al., 2013; Jouve et al.,
2015). Theories and numerical simulations considered various effects caused by
strong magnetic fields in hot stars, i.e.: magneto-convection (e.g. Jermyn &
Cantiello, 2020), mass-loss quenching (e.g. Keszthelyi, 2019; Keszthelyi et
al., 2019), internal angular momentum transport (e.g. Rogers et al., 2013;
Moyano et al., 2023), magnetic braking (e.g. Keszthelyi et al., 2020), and
mass leakage (e.g. Owocki & Cranmer, 2018). On the other hand, observations
contributed more and more pieces of evidence of these effects (e.g. Oskinova
et al., 2011; Grunhut et al., 2012c; Henrichs et al., 2012; Fossati et al.,
2014, 2015; Shultz et al., 2020).

The number of known magnetic stars is steadily increased with the dedicated
surveys of spectropolarimetry and high-resolution spectrometry. FOcal Reducer
and low dispersion Spectrograph (FORS1) catalog include about 1500 observing
series, for a total of more than about 12 000 scientific frames, revealing
dozens of magnetic hot stars (Bagnulo et al., 2015). The B fields in OB stars
(BOB) Collaboration observed hundreds of OB-type stars to characterize the
incidence of large-scale magnetic fields in slowly rotating main-sequence
massive stars (Morel et al., 2014, 2015). Magnetism in Massive Stars (MiMeS)
Survey also observed numbers of massive stars to search magnetic hot stars
(Grunhut et al., 2017). These surveys indicate about $\sim 10\%$ of the B
stars host strong and large-scale magnetic fields, while only $\sim 6\%$ of
O-type (Grunhut et al., 2012a, 2017). Up to now, more and more magnetic hot
stars are still detected by the spectrometric or photometric surveys (e.g.
Eikenberry et al., 2014; Chojnowski et al., 2019; Jayaraman et al., 2022;
Chojnowski et al., 2022).

Despite tremendous contributions made by spectropolarimetric and high-
resolution spectrometric measurements, it is difficult to calibrate the
physical properties of stellar interiors. Asteroseismology is a powerful tool
that allows us to directly access the interiors of early-type stars and
improve the physics of stellar interiors (Bowman, 2020; Aerts, 2021). Analysis
of stellar pulsations allows deriving direct inferences of the internal
rotation and chemical stratification from the pulsation frequencies or period
spacing patterns in stars born with a convective core (Van Reeth et al., 2015;
Ouazzani et al., 2019; Li et al., 2020). Furthermore, forward seismic modeling
of the frequencies restricts the masses and ages of stars (Schmid & Aerts,
2016; Aerts et al., 2018, 2019). The high-duty cycles, long-term, near-
continuous, and high-precision data sets are necessary for asteroseismology.
The fragmented time series obtained with ground-based telescopes are
notoriously limited by their poor duty cycles which complicates mode
identification (e.g. Handler et al., 2005; Desmet et al., 2009; Daszyńska-
Daszkiewicz et al., 2013). In contrast to ground-based telescopes, the
$Transiting\;Exoplanet\;Survey\;Satellite$ ($TESS$; Ricker et al., 2015) is
designed to observe the whole sky, and provide high-precision photometric data
with a wide field of view. The asteroseismic potential of TESS is evidenced by
many studies (e.g. Pedersen et al., 2019; Bowman et al., 2020; Jayaraman et
al., 2022; Balona & Ozuyar, 2020; Burssens et al., 2023).

There have two main coherent pulsations in magnetic hot stars: one is the
gravity modes ($g$ modes) where the restoring force is buoyancy, and another
one is pressure modes ($p$ modes) where the restoring force is pressure (Aerts
et al., 2010). They are standing waves motivated by heat engine driving
mechanism (Aerts et al., 2010). Gravity modes normally associated with the
Slowly Pulsating B-type stars (De Cat & Aerts, 2002; Walczak et al., 2013;
Moravveji et al., 2015), while $p$ modes more occurred in $\beta$ Cephei
variables (Stankov & Handler, 2005). The theoretical instability strips can be
calculated using non-adiabatic calculations performed with Aarhus Pulsation
code (ADIPLS; Christensen-Dalsgaard, 2008) or GYRE (e.g. Townsend & Teitler,
2013). The stellar interior rotation profiles, temperature gradient in the
core boundary layer, and envelope mixing profiles are revealed by analyzing
the coherent pulsations (e.g. Degroote et al., 2009, 2010; Daszyńska-
Daszkiewicz et al., 2013; Szewczuk & Daszyńska-Daszkiewicz, 2018; Michielsen
et al., 2021; Szewczuk et al., 2022). The core masses and ages for a number of
OB-type stars are also constrained by the method of asteroseismology (e.g.
Dziembowski & Pamyatnykh, 2008; Daszyńska-Daszkiewicz & Miszuda, 2019;
Pedersen et al., 2021; Salmon et al., 2022; Burssens et al., 2023).

However, there are few inferences as to the magnetic field strength and
geometry within the deep interiors of stars. Only $\beta\;Cep$ (e.g.
Shibahashi & Aerts, 2000; Henrichs et al., 2013), V2052 Oph (e.g. Neiner et
al., 2012; Handler et al., 2012; Briquet et al., 2012), and HD 43317
(Buysschaert et al., 2017, 2018; Lecoanet et al., 2022) have been studied
using combined asteroseismic and magnetometric analyses. Despite the
interaction of IGWs with a magnetic field is discussed extensively using the
numerical simulations (e.g. Lecoanet et al., 2017; Ji et al., 2023; Rui &
Fuller, 2023), there only have rare observational evidences (Fuller et al.,
2015; Lecoanet et al., 2022). The lack of large samples of the pulsating
magnetic stars has impeded the exploration of pulsating variability, magnetic
fields, and stellar evolution in the magnetic hot star regime.

Apart from coherent pulsations, internal gravity waves (IGWs) are predicted to
exist in stars with convective regions, and their properties vary based on the
radial rotation profile (e.g. Pantillon et al., 2007; Rogers et al., 2013;
Mathis et al., 2014; Rogers, 2015) or the strength of the internal magnetic
field (e.g. Rogers & MacGregor, 2010, 2011; Mathis & de Brye, 2011, 2012;
Augustson et al., 2016; Lecoanet et al., 2017). The amplitudes of IGWs are
expected to scale with stellar mass, while their frequencies are predicted to
inversely scale with stellar mass on the main sequence (e.g. Samadi et al.,
2010; Shiode et al., 2013; Rogers, 2015). Although two- and three-dimensional
hydrodynamical simulations of IGWs for massive stars with $M>8\;M_{\odot}$
have also been done (e.g. Ratnasingam et al., 2023; Thompson et al., 2023;
Herwig et al., 2023), the influence of magnetic fields on these stars is still
not widely studied. Stochastic low frequency (SLF) variability is observed in
upper main sequence stars (e.g. Bowman et al., 2019a, b, 2020; Bowman & Dorn-
Wallenstein, 2022). The SLF variability is seen across a wide range in mass,
age, and metallicity in massive stars (Bowman et al., 2020, 2019b). The origin
of SLF variability is currently debated. It could be caused by the IGWs (e.g.
Edelmann et al., 2019; Bowman et al., 2019a, 2020; Bowman & Dorn-Wallenstein,
2022), or by subsurface convection zones (e.g. Blomme et al., 2011; Cantiello
& Braithwaite, 2019; Lecoanet et al., 2019; Cantiello et al., 2021). Bowman et
al. (2019b) investigated the 167 OB-type stars within Milky Way and Large
Magellanic Cloud (LMC) galaxy, and reported that SLF variability is
insensitive to the metallicity of the star. While how magnetic fields
systematically affect the presence of SLF variability in massive stars
requires the detection of this phenomenon for a large sample of magnetic hot
stars, which is currently not available. It has been confirmed that the
magnetic field has an effect on stabilizing the atmosphere and suppressing the
generation of macroturbulence, which in turn can affect the variability of SLF
caused by subsurface convection (Lecoanet et al., 2019; Sundqvist et al.,
2013). Exploring the correlation between SLF variability and the magnetic
field could provide valuable insights into the underlying mechanisms
responsible for the observed SLF variability.

In this work, we classified the variability of 118 magnetic hot stars using
short cadence target pixel files (TPFs) observed by TESS from sector 1 to
sector 56. We detected the SLF variability for each magnetic hot star within
our sample. We investigated the characteristics of SLF variability in magnetic
hot stars and explored the correlation of SLF variability and the magnetic
field. In Section 2, we presented our sample component of magnetic hot stars.
In Section 3, we introduced the methods used to extract the light curves and
analyze frequency spectra. We presented our results, and evaluated the
asteroseismic potential for multiperiodic pulsators in Section 4. We discussed
our results and drew conclusions in Sections 5 and 6, respectively.

##  2 Sample Selection

Magnetic fields in the stars can be detected through the circular polarization
and split induced in spectral lines by the Zeeman effect. The first-generation
photo-polarimeters carried out the measurements of magnetic fields in the bulk
of magnetic Ap/Bp stars (e.g. Borra & Landstreet, 1980). Dozens of magnetic
hot stars are detected with second generation instruments, such as the low-
resolution spectropolarimetric instruments FORS 1 and 2 mounted at the Very
Large Telescope (VLT) (Appenzeller et al., 1998), or high-resolution
spectrometric spectropolarimeters MUSICOS (Foing et al., 1988), ESPaDOnS
(Donati, 2003), Narval (Aurière, 2003), and HARPSpol (Piskunov et al., 2011).

The low-resolution spectropolarimeters are sensitive to the longitudinal
(line-of-sight) field component ($\langle B_{z}\rangle$), whereas high-
resolution spectroscopy detecting magnetic fields in stars by observing the
Zeeman splitting of spectral lines (Donati & Landstreet, 2009). However, a
significant number of magnetic stars claimed by the low-resolution
spectropolarimeters have not been confirmed by high-resolution spectroscopy
(Silvester et al., 2009; Shultz et al., 2012a; Grunhut et al., 2012b). Bagnulo
et al. (2012) elaborated the polarization measurements data set of the FORS 1
archive, explored the results using various data reduction pipelines, and
analyzed the sources of uncertainties. Using the new prescription for low-
resolution spectropolarimeteric data analysis, the consistency of the results
between the low-resolution spectropolarimeters and high-resolution
spectroscopy are improved significantly (e.g. Shultz et al., 2012b).

Therefore, we only considered the results based on these new detection
statuses for magnetic hot stars. We use the compilations of the magnetic hot
stars including the results of FORS1 (Bagnulo et al., 2015), B fields in OB
stars Survey (BOB/FORS2; Morel et al., 2014, 2015), and the Magnetism in
Massive Stars Survey (MiMeS; Grunhut et al., 2017) surveys. In the results of
FORS1, the mean longitudinal magnetic field ($\langle B_{z}\rangle$) of each
object is measured from the analysis carried out on the H Balmer lines, on the
metal lines, and on the combination of the two sets of lines, respectively
(Bagnulo et al., 2012, 2015). The BOB/FORS2 and MiMeS catalogs also show the
results in a similar format to FORS1. The stars which $|\langle
B_{z}\rangle|/\sigma_{\langle B_{z}\rangle}\geq 3$ in at least two sets are
selected as the samples to ensure the sigma completeness of our catalog. Other
exhaustive studies that identify hot stars with confirmed field detections are
complemented in our catalog (e.g. Petit et al., 2013; Shultz et al., 2018,
2019a, 2019b, 2020). Many magnetic hot stars show chemical abundance
peculiarities (e.g. Fossati et al., 2007; Wade et al., 2000a, b), and their
spectral data sets are not always readily available. It is difficult to ensure
completeness at the low-temperature boundary. Therefore, we consider all
magnetic hot stars with spectral type in the range of A5 and earlier. Out of
the 729 stars, 168 met our criteria and were included in the original sample.
We cross-matched the catalog consisting of the original sample with the
Mikulski Archive for Space Telescopes (MAST111https://archive.stsci.edu/)
archive, acquired the 360 TPFs of 118 magnetic hot stars, which form the basis
of our study. The galactic distribution of 118 magnetic hot stars in our
catalog is shown in Figure 1.

Figure 1: Location of the stars in our catalogue in celestial coordinates. The
galactic plane (in red) is plotted as the reference.

##  3 Methodology

###  3.1 TESS light curve extraction

The TESS space telescope observed the stars with the field of view of 24 by
96∘. A portion of the sky will be observed for a duration of 27.3 days before
TESS turns to the next position. This is referred to as a sector. To obtain
the TESS light curves, we retrieved the short cadence TPFs for Sectors 1-56
from the MAST. We performed the aperture photometry and data reduction using
the python package $Lightkurve$ (Lightkurve Collaboration et al., 2018). The
aperture mask for each sector of each star is defined using the thresholding
method
222https://docs.lightkurve.org/reference/api/lightkurve.TessTargetPixelFile.
This method selects all pixels which have a flux higher than threshold times
standard deviations above a median brightness as the photometric aperture. The
standard deviation is estimated in a robust way by multiplying the Median
Absolute Deviation (MAD) by $1.4826$. In order to minimize contamination from
nearby stars in the light curves, we meticulously optimized the aperture
masks. Because the TESS pixels are large (21 arcsec), the photometry will be
contaminated by the neighboring stars within our selected aperture masks (e.g.
Pedersen & Bell, 2023). FluxCT (Schonhut-Stasik & Stassun, 2023) is a
dedicated tool designed to identify contaminating flux in TESS TPFs. It
utilizes the Gaia EDR3 database to search for potential sources of
contamination within the corresponding regions of the aperture masks,
providing a contamination coefficient. Each pixel within the aperture masks
was individually assessed using FluxCT to calculate its contamination
coefficient. By excluding pixels with higher contamination coefficients, the
majority of stars in the sample exhibit a photometric aperture contamination
rate below 5%. For stars in crowded fields, we selected pixels with a flux
higher than 5 times the standard deviation above the median brightness as the
photometric aperture to minimize the impact of background sources.

The raw time series of the photometry are obtained by summing flux counts for
each pixel within photometric apertures. For removing the background noise, we
defined background aperture masks using the threshold method. The pixels which
are fainter than 1-sigma above the median flux will be used. To remove the
background noise, we employed the PLDCorrector
333http://docs.lightkurve.org/reference/api/lightkurve.correctors.PLDCorrector.
The outliers are removed using the sigma-clipping method, which is provided by
$Lightkurve$. Based on the quality flags contained in each individual data
cadence, the photometric data points marked with labels such as
”Argabrightening”, and ”Cosmic ray in optimal aperture” were ignored in our
study to reduce the noise in the light curves. The long-term instrumental
trends such as jumps and drifts are removed by means of a linear or low-order
polynomial fit to the light curve. We converted the corrected flux to the
magnitude and subtracted its average value for each individual TPF. The
consecutive sectors for each star are combined as one light curve. We
inspected all the combined light curves to ensure that long period trends
between each sector were correctly removed. We used Combined Differential
Photometric Precision (CDPP) metric to quantify the noise level of the
combined light curves, ensuring that no additional noise is increased in the
combined process.

In Figure 2, we demonstrated our results of the aperture photometry and data
reduction using the light curves of HD 53921 and HD 205021 as examples. The
top panel of the Figure 2 shows the light curve of the binary star HD 53921,
which resulted from combining 10 sectors (sectors 4 to 13). In the bottom
panel of the Figure 2, we presented the light curve of the pulsating star HD
205021, which resulted from combining data from 3 sectors (sectors 16 to 18).
From the Figure 2, it is evident that the long period trends in the light
curves of each sector have been properly removed.

Figure 2: The light curves of two stars in our sample. The top panel shows the
light curve of the binary star HD 53921, which resulted from combining 10
sectors (sectors 4 to 13). In the bottom panel, we shown the light curve of
the pulsating star HD 205021, which resulted from combining data from 3
sectors (sectors 16 to 18).

###  3.2 Frequency Analysis and Variability Classification

In order to analyze the coherent pulsations, we used the Discrete Fourier
Transform (DFT; Kurtz, 1985) to calculate the amplitude spectra of the
combined light curves. The Nyquist frequency refers to the highest frequency
that can be correctly resolved by the sampling process. It can be calculated
using the $f_{\mathrm{Ny}}=1/(2\Delta t)$, where $\Delta t$ represents the
time interval between consecutive samples. Thanks to the sampling interval of
short cadence being that 120 seconds, we determined the
$f_{\mathrm{Ny}}=\mathrm{359.9\,d^{-1}}$. The frequencies in the range of
$0<f<f_{\mathrm{Ny}}$ are considered in our frequency analysis thanks to they
are not undersampled for the sampling rate of TESS short cadence. We extracted
the significant frequencies from the amplitude spectra using the software
PERIOD 04 (Lenz & Breger, 2005). The parameters of the frequencies derived
from the amplitude spectra are calculated and optimized using the following
formula:

$m=m_{0}+\sum_{i}^{N}A_{i}\sin(f_{i}t+\Phi_{i}),$ (1)

where $N$ is the number of the coherent pulsations, $m_{0}$ is the zero point.
$A_{i}$, $f_{i}$, and $\Phi_{i}$ represent the amplitude, frequency, and phase
of the $i$th coherent pulsation, respectively. According to the study by
Bowman & Michielsen (2021), frequencies extracted from space photometry using
a signal-to-noise ratio (SNR) criterion of $3.5<SNR<4.0$ are indistinguishable
from high-amplitude noise. Frequencies between $4.0\leq SNR\leq 4.6$ have a
modest chance of being noise peaks. Therefore, we have adopted a conservative
significance threshold of $SNR\geq 4.6$ for determining significant
frequencies. Burssens et al. (2020) point out that the noise behavior of stars
at different evolutionary stages should be accounted for when choosing the
window size to calculate the SNR of the significant frequencies. Therefore, we
optimized the window size based on the spectral type of each star. We set the
window size with a value of 1 d-1 for the O-type stars. The window sizes of 5
d-1 are set for the early B-type dwarfs, subgiants, and giants (corresponding
with the spectral types similar to BV and BVI), while the window size values
for the B-type giants, bright giants, and supergiants (corresponding with the
spectral types similar to III, II, and I) are set as 1 d-1. For the A-type
stars, we set the window size with the value of 2 d-1. The window size values
of spectroscopic binaries are set at the value of 5 d-1. The frequency
resolution criterion is defined as $f_{\rm res}=1.5/T$, where $T$ represents
the duration of the observations (Loumos & Deeming, 1978). If the difference
between two frequencies exceeds the $f_{\rm res}$, we conclude that these two
frequencies have been resolved. So the combined light curves have the best
frequency resolution and afford the greatest precision compared with the light
curves derived from the single sector.

Based on visual inspection of the light curves and amplitude spectra, the
variability classification of each star is provided. The details of the
classification criteria that we applied as follows:

  * (1)

$\beta$ Cep ($\beta$ Cephei star): coherent $p$ modes with frequencies in the
range between 2.5 and 20 d-1 (Stankov & Handler, 2005; Balona & Ozuyar, 2020);

  * (2)

SPB (Slowly Pulsating B Star): coherent $g$ modes with frequencies below
$\sim$ 2.5 d-1 (Balona & Ozuyar, 2020; Burssens et al., 2020);

  * (3)

hybrid: a combination of $\beta$ Cep and SPB;

  * (4)

SLF: stochastic variability with broad excess in amplitude spectrum, has
periods of several hours to days, the amplitudes range from tens to hundreds
$\mu$mag (Bowman et al., 2020);

  * (5)

rot.: rotational variability caused by spots, stellar wind and/or peculiar
abundances of the elements (Netopil et al., 2017; David-Uraz et al., 2019);

  * (6)

Multi: eclipsing binary or multiple system;

  * (7)

cont.: no significant frequency is detected in the amplitude spectrum;

  * (8)

unknown: thanks to the poor quality data led to we can not identify the
classification (i.e. low duty-cycles, and the light curve is contaminated by
nearby star or instrumental periodicities).

###  3.3 Stochastic Low-frequency Variability Analysis

The stochastic low-frequency variability is typically manifested in the
amplitude spectrum as the red noise component of a stochastic signal (e.g.
Bowman et al., 2019b). To obtain the light curves that only contained the
stochastic signal caused by the stochastic low-frequency variability, the
coherent pulsations should be removed from the light curves. Inspired by the
methodology of Bowman et al. (2019a), we employed first a traditional
prewhitening for each light curve. The significant peaks are selected and
fitted using the eq.(1). The fitted functions are subtracted from the light
curves. Based on the study by Bowman & Michielsen (2021), after removing
frequencies with SNR $\geq$ 4.6, the light curves reached the noise level.
Therefore, we adopted this criterion (SNR $\geq 4.6$) to identify the
significant peaks during the prewhitening process. Using the conservative
criterion also ensures that we have reached the noise level. Finally, we
derived the residual amplitude spectra from the light curves using the DFT
method. In the Figure 3, the analysis result of coherent pulsation is shown in
the top panel. The significant peak is marked with a blue inverted triangle,
and the harmonics of the dominant frequency are marked with yellow inverted
triangle. In the bottom panel of Figure 3, the residual amplitude spectrum is
shown as the logarithmic diagram.

Figure 3: The frequency analysis result of HD 37479. In the top panel, the
significant peak is marked with a blue inverted triangle, and the harmonics of
the dominant frequency are marked with orange inverted triangle. In the bottom
panel, the residual amplitude spectrum is shown as the logarithmic diagram.

It should be noted that one sector TESS light curves are generally sufficient
to place constraints on the type of variability, but the low frequency
resolution of only one or two sectors makes the identification of rotational
splitting, harmonics, and low SNR astrophysical signal difficult, especially
in the low frequency regime and in stars with significant SLF variability
(e.g. Burssens et al., 2020; Bowman et al., 2020). For example, the bottom
panel of Figure 3 shows the obvious remnant peaks after the prewhitening. The
density of the peaks in $0.5<\mathit{f}<6\;\text{d}^{-1}$ is extremely high
(the top panel of Figure 3), low frequency resolution of only one sector is
not sufficient to resolve the beating and identify close-frequency in this
range. As a result, unresolved frequencies appear in the residual amplitude
spectrum, compromising the accuracy of the fitting parameters of SLF
variability. To address this concern, we utilized combined light curves to
improve the frequency resolution in our study.

The morphology of the SLF variability in the amplitude spectrum is normally
interpreted by the Lorentzian function as the following formula (e.g. Bowman
et al., 2020):

$\alpha(\nu)=\frac{\alpha_{\rm{0}}}{1+(\frac{\nu}{\nu_{\rm{char}}})^{\gamma}}+C_{\rm{w}},$
(2)

where $\alpha_{\rm{0}}$ represents the scaling factor and represents the
amplitude at zero frequency, $\gamma$ means the logarithmic amplitude
gradient, $\nu_{\rm{char}}$ is the characteristic frequency, and $C_{\rm{w}}$
is a white noise term. Inspired by previous efforts by Bowman et al. (2019b,
a, 2020), in this work, Bayesian Markov Chain Monte Carlo (MCMC) framework
with the Python code emcee (Foreman-Mackey et al., 2013) is applied to derive
the morphologies from the residual amplitude spectra as the eq.(2). Flat
priors and 32 parallel chains are used to fit the residual amplitude spectra.
In the iteration processing, each parallel chain used to construct a model is
evaluated with the likelihood function (Anderson et al., 1990):

$\ln\mathfrak{L}=-\sum_{i}^{N}\Bigg{\\{}{\ln[M_{i}(\boldsymbol{\theta})]}+\frac{O_{i}}{[M_{i}(\boldsymbol{\theta})]}\Bigg{\\}},$
(3)

where $N$ is the number of total data points contained in the residual
amplitude spectrum, $O_{i}$ represents the $i$th point of the residual
amplitude spectrum, $M_{i}(\boldsymbol{\theta})$ is the model with parameters
$\boldsymbol{\theta}$ of the $i$th point. The criterion from the Gelman &
Rubin (1992) is adopted to confirm the convergence of the parameters, which is
typically achieved after approximately 1000 iterations. Each star is analyzed
by the aforementioned process. As an example, the analysis results of the B2IV
star HD 121743 are shown in Figure 4. The top left panel of Figure 4 shows the
amplitude spectrum using the DFT method, we marked significant frequencies
with blue inverted triangles. The bottom left panel of Figure 4 shows the
logarithmic amplitude spectrum, and the best-fit result of Eq. (3) is shown as
a solid blue line. Red dash-dot and green dash lines represent the red noise
and white noise components, respectively. We presented the posterior
distributions from the MCMC for the parameters of the SLF variability in the
right panel of Figure 4.

Figure 4: The analysis results of HD 121743. The top left panel shows the
amplitude spectrum using the DFT method, we marked significant frequencies
with blue inverted triangles. The bottom left panel shows the logarithmic
amplitude spectrum, and the best-fit result of Eq. (3) is shown as a solid
blue line. Red dash-dot and green dash lines represent the red noise and white
noise components, respectively. The right panel shows the posterior
distributions from the MCMC for the parameters of the SLF variability.

###  3.4 Astrophysical parameters

Around half of the stars in our sample have relatively accurate stellar
parameters derived from the high resolution spectra (e.g. Grunhut et al.,
2012d; Wade et al., 2015; Shultz et al., 2019a). However, astrophysical
parameters are only available for a small number of magnetic chemically
peculiar (mCP) stars in our sample that are close to the low-temperature
boundary. Due to the abnormal colors of mCP stars, their effective
temperatures and luminosities of them cannot be determined using the usual
calibrations. We adopted the literature value of the astrophysical parameters,
which are corrected by the intensive researches (e.g. Kochukhov & Bagnulo,
2006; Netopil et al., 2008). For the mCP stars that lack of the astrophysical
parameters in our sample, we performed the spectral energy distribution (SED)
fitting to derive their effective temperatures and luminosities using a wide
range of wavelengths. The photometric bands adopted include $Gaia\;GG_{\rm
rp}G_{\rm bp}G_{\rm rvs}$ (Gaia Collaboration, 2022), $SDSS\;ugriz$ (Alam et
al., 2015), $2MASS\;JHK_{S}$ (Skrutskie et al., 2006), and $WISE$ $W_{\rm
1}W_{\rm 2}W_{\rm 3}W_{\rm 4}$ (Wright et al., 2010). We used the ATLAS9 SED
Grid (Castelli et al., 1997) for mCP stars with the effective temperatures
ranging from 8,000 to 15,000 K and surface gravities log$g$ (cgs) from 3.5 to
5. Andrae et al. (2023) have noted that the distance assessments by Bailer-
Jones et al. (2021) outperform GSP-Phot distances. Consequently, we have
determined the distances to the stars in our sample using the results derived
by Bailer-Jones et al. (2021). We estimated the instellar extinction from the
3D extinction map provided by Gontcharov (2017). Using the VO Sed Analyzer
(Bayo et al., 2008), we performed the minimum chi-squared method to compare
the observational values with SED templates as following:

$\chi_{r}^{2}=\dfrac{1}{N-n_{p}}\sum_{i=1}^{N}\left\\{\dfrac{(Y_{i,o}-M_{d}Y_{i,m})^{2}}{\sigma_{i,o}^{2}}\right\\}$
(4)

where $N$ is the number of photometric data points, $n_{p}$ is the number of
the fitted parameters for the model. $Y_{i,o}$ and $\sigma_{i,o}$ represent
the the observed flux and observational error in the flux of the $i$th point,
respectively. $Y_{i,m}$ is theoretical flux predicted by the model of the
$i$th data point. $M_{d}$ is the dilution factor.

Netopil et al. (2008) compiled the temperature calibrations for the individual
CP groups with the different photometric systems. Netopil et al. (2017)
validated the photometric temperature calibrations concluded by Netopil et al.
(2008), and pointed out they are consistent with the SED results. In order to
investigate the validity of our SED approach, we gathered the magnitudes of
Johnson $UBV$ photometric system for the mCP stars, and calculated the
astrophysical parameters from the photometric results. We derived the
effective temperatures using the Johnson $UBV$ photometric temperature
calibrations provided by Netopil et al. (2008). The luminosities are derived
using the bolometric corrections ($BC_{V}$) and extinction ($A_{\mathrm{V}}$)
evaluated from the intrinsic colour $(B-V)_{\rm 0}$. The theoretical $BC_{V}$
values are obtained using the second order fit
$BC_{V}=-5.737+18.685\theta_{\text{eff}}-15.135\theta_{\text{eff}}^{2}$, where
$\theta_{\text{eff}}=5040/T_{\text{eff}}$ (Netopil et al., 2008). We used the
relationship of $R_{V}=A_{\mathrm{V}}/E(B-V)=3.1$ (Cardelli et al., 1989) to
derive the extinction coefficient $A_{\mathrm{V}}$. Based on the distances
($r$) from the Gaia EDR 3, we obtained the absolute magnitude
$M_{v}=m_{V}+5-5\text{lg}r$. The luminosity is calculated using
$\text{log}(L/L_{\odot})=-0.4[M_{V}-V_{\odot}-31.572+(\mathrm{BC}_{V}-\mathrm{BC}_{V,\odot})]$,
where $V_{\odot}=-26.72$ and $\mathrm{BC}_{V,\odot}=-0.19$ are taken from the
previous work (Torres, 2010).

In the top panel of Figure 5, we presented the effective temperatures derived
from the SED analysis and photometry. A linear relation exists between the
results based on the SED analysis and those derived from photometry, which can
be expressed as
$\text{log}(T_{\text{eff}}/K)_{\text{(SED)}}=0.955\text{log}(T_{\text{eff}}/K)_{\text{(Photo)}}+0.194$.
Out of the 16 mCP stars, only HD 146555 shows the discrepancy in the effective
temperature that is caused by inappropriate temperature calibrations thanks to
the lack of the $U$ band magnitude. In the bottom panel of Figure 5, we
compared the luminosities derived from the SED analysis with those obtained
from the photometry. Our results indicate that a linear correlation exists
between the luminosities obtained using the two methods. This correlation can
be expressed as
$\text{log}(L/L_{\odot})_{\text{(SED)}}=0.973\text{log}(L/L_{\odot})_{\text{(Photo)}}-0.054$.
Overall, the results of the SED analysis are consistent with the photometry
results, as shown in the comparison of effective temperature and luminosity in
Figure 5.

Figure 5: We compared astrophysical parameters obtained from spectral energy
distribution (SED) analysis with those derived from photometry. The top panel
presents the effective temperatures derived from both methods, and a linear
relation is shown by the red line. In the bottom panel, we compared the
luminosities derived from SED analysis with those obtained from photometry,
and their correlation is also displayed by the red line.

##  4 RESULTS

In our sample, we definitely detected 87 variable stars, 14 constant stars,
and 17 unknown variables. All coherent pulsators and multiple systems in our
sample are identified by previous studies. 9 new rotating variable stars are
detected from our sample. On the other hand, HD 35912 is classified as a
magnetic hot star according to Bychkov et al. (2005) and Conti (1970).
However, Shultz et al. (2018) reported an inability to detect a magnetic field
in the DAO measurements. Given the inconsistent results from multiple
measurements of the magnetic field in HD 35912, the classification of this
star as a magnetic hot star is disputed. As a result, HD 35912 is removed from
our analysis. For the rotating variables, we provided more accurate rotational
periods that were only derived via spectroscopy or spectropolarimetry
observations. In Table 1, we summarized the stellar parameters and the
classification results for the stars in our sample.

###  4.1 Pulsating variables

Our sample contains 10 coherent pulsators, namely: HD 121743, HD 136504, HD
156424, HD 205021, HD 3360, HD 35912, HD 43317, HD 44743, HD 46328, and HD
96446. Among them, HD 136504 and HD 156424 are components of the binary
systems. HD 3360 was previously identified as a $\beta$ Cep star in earlier
studies (e.g. Unno et al., 1989; Telting et al., 2006). However, our results
suggest that HD 3360 is actually a hybrid star, rather than a $\beta$ Cep
star.

####  4.1.1 HD 3360

HD 3360 (TIC 240669906) is known as a nitrogen-rich B2IV star (e.g. Gies &
Lambert, 1992; Neiner et al., 2003; Nieva & Przybilla, 2012). Neiner et al.
(2003) discovered the presence of the magnetic fields in the HD 3360 using the
Musicos spectropolarimeter at T$\acute{\rm e}$lescope Bernard Lyot (TBL). The
fundamental parameters of HD 3360 have been determined by the high-resolution
spectroscopy in various studies (e.g. Briquet & Morel, 2007; Lefever et al.,
2010; Nieva & Przybilla, 2012, 2014). The spectroscopic parameters of HD 3360
include an effective temperature of $T_{\rm eff}=20.8\pm 0.2k\rm{K}$, a
luminosity of $\text{log}(L/L_{\odot})=3.82\pm 0.06$ and a surface gravity of
$\text{log}g=3.80\pm 0.05$. Nieva & Przybilla (2012) determined the
microturbulence velocity of $\xi=2\pm 1\;km\;s^{-1}$, the projected rotational
velocity of $v\text{sin}i=20\pm 2\;km\;s^{-1}$ and macroturbulence velocity of
$\zeta=12\pm 5\;km\;s^{-1}$ of the HD 3360.

The non-radial pulsation mode of $l=2\pm 1$ at the frequency
$f=0.64\;\text{d}^{-1}$ is detected in the radial velocity amplitude
variations by (Neiner et al., 2003). The rotational period ($P_{\rm
rot}=5.370447\pm 0.000078\;\text{days}$) of the HD 3360 was obtained through a
detailed study of time-resolved equivalent width measurements of the
C${}_{\rm\;IV}$, Si${}_{\rm\;IV}$ and N${}_{\rm\;V}$ lines, also conducted by
(Neiner et al., 2003). The light curve and amplitude spectrum of HD 3360 are
presented in the Figure 6. We detected four significant frequencies in the
amplitude spectrum of HD 3360. The rotational period is not present in the
amplitude spectrum. Out of four significant frequencies, two frequencies below
2.5 $\rm d^{-1}$, while the other frequencies are close to 4 $\rm d^{-1}$.
These results suggest that there are two types (corresponding to $g$-mode and
$p$-mode) of coherent pulsations in HD 3360. Therefore, the HD 3360 should be
classified as a hybrid star rather than an SPB star.

Figure 6: The light curve and frequency spectrum of HD 3360. The light curve
of HD 3360 is shown in the left panel, and the corresponding frequency
spectrum is shown in the right panel. No significant variability is observed
beyond 8 $\mathrm{d}^{-1}$. In the frequency spectrum, the significant peaks
are marked with a blue inverted triangle.

###  4.2 Rotating stars

Mainly rotating stars in our sample are members of magnetic chemically
peculiar (mCP) stars. They generally have slowly rotating velocities, and
atmospheric abundances abnormities of some chemical elements due to the
effects of radiative diffusion and gravitational settling (Preston, 1974;
Alecian & Stift, 2010; Alecian, 2015). The 54 out of the 62 rotational
variables are known as rotating variables prior to our study, we confirmed
their variabilities and rotational periods. Additionally, we have identified 8
new rotational variables in our sample: CPD-62 2124, HD 89103, HD 118913, HD
119308, HD 127453, HD 138758, HD 157751, and HD 172690. By combining the
spectra observed by previous studies with the $TESS$ light curve, we clarified
that HD 67621 is a rotating variable, rather than a young stellar object
(YSO). The fundamental frequencies of mCP stars in our sample are distributed
in the range of 0.1 $\sim$ 1.6 d-1. We determined their rotational periods,
rotational modulation, and/or coherent pulsations. The light curves and
amplitude spectra of new rotating variables are presented in Figure 7 and
Figure 8.

####  4.2.1 CPD-62 2124

CPD-62 2124 (TIC 290796936) is an evolved, He-rich star with a spectral type
of Of?p (Castro et al., 2017). Castro et al. (2017) reported the detection of
an exceptionally strong magnetic field in CPD-62 2124 with a strength of
approximately 5.2 kG, as measured by the FORS2 low-resolution
spectropolarimeter and HARPSpol spectropolarimeter. CPD-62 2124 has an
effective temperature of $T_{\rm eff}=23.6\pm 0.2\text{kK}$, a luminosity of
$\text{log}(L/L_{\odot})=3.8\pm 0.2$, a surface gravity of
$\text{log}g=4.05\pm 0.10$, and a rotational period $P_{\rm rot}=2.62809\pm
000005\;\text{days}$ (Castro et al., 2017; Shultz et al., 2019a). Using the
stellar evolutionary models, these parameters, including the mass
$M_{\star}=10.0\pm 0.4\;M_{\odot}$, radius $R_{\star}=5.6\;R_{\odot}$ are
determined by Brott et al. (2011) and Ekström et al. (2012).

The light curve and amplitude spectrum of CPD-62 2124 are shown in the middle
panel of Figure 7. We detected three significant frequencies and a harmonic
frequency in the amplitude spectrum. The most significant frequency
($\mathit{f}=0.3810113\pm 0.0000027\;\text{d}^{-1}$) is corresponding with the
rotational frequency of the CPD-62 2124. Therefore, we determined the
rotational period with the value of $2.62459\pm 0.00002\;\text{days}$, which
slightly smaller than the result derived from the spectropolarimetry. In
previous study, Shultz et al. (2020) determined the log$R_{\text{A}}/R_{\rm
K}=0.4\pm 0.2$, where $R_{\text{A}}$ is the Alfv$\acute{\rm e}$n radius, and
$R_{\rm K}$ is the $Kepler$ radius. The fact that $R_{\text{A}}>R_{\rm K}$
suggests that CPD-62 2124 has a centrifugal magnetosphere, which indecates
that the rotationally modulated light curve of CPD-62 2124 is caused by the
material trapped in closed magnetic loops. Additionally, other significant
frequencies indicate that CPD-62 2124 has coherent pulsations, possibly due to
the Z-bump effect (Saio, 1993), or other physical processes.

####  4.2.2 HD 67621

HD 67621 (TIC 238489837) is a B2IV star, and is a member star of the Vel OB2
association determined by de Zeeuw et al. (1999). Alecian et al. (2014)
reported the presence of magnetic fields, and determined the stellar
parameters of HD 67621 include an effective temperature of $T_{\rm
eff}=21.0\pm 0.6\;\text{kK}$, a surface gravity of $\text{log}g=4.18\pm 0.10$
and a luminosity of $\text{log}(L/L_{\odot})=3.3\pm 0.1$. Shultz et al. (2018)
confirmed that HD 67621 has a dipolar magnetic field with the strength of
$0.160\pm 0.004\;\text{kG}$. HD 67621 has a rotational period $P_{\rm
rot}=3.593\pm 0.001\;\text{days}$ (Alecian et al., 2014; Shultz et al., 2018).

The light curve and amplitude spectrum of the HD 67621 is shown in the second
row of Figure 7. We detected a significant frequency and 2 harmonics. The
rotational period $P_{\rm rot}=3.50695\pm 0.00006\;\text{days}$ is deduced
from the significant frequency. The rotational period determined by us is
slightly shorter than the results derived by the Alecian et al. (2014) and
Shultz et al. (2018). Cantat-Gaudin et al. (2019) determined the HD 67621 as a
YSO using the color-magnitude-diagram (CMD). This determination may have been
influenced by the abnormal color index of HD 67621, which is affected by its
chemical peculiarities. However, by combining the $TESS$ light curve with data
from previous studies (Alecian et al., 2014; Shultz et al., 2018), we
determined that HD 67621 is a rotating variable. In Shultz et al. (2018), the
authors attempted to constrain the period using $Hipparcos$ photometry.
However, the almost complete absence of variability in the data resulted in a
light curve that was dominated by noise. In contrast, the light curve obtained
from $TESS$ clearly shows variations, demonstrating the great potential of
$TESS$ for detecting variability in magnetic hot stars.

####  4.2.3 HD 89103

HD 89103 (TIC 219614759) is a B9V star (Bagnulo et al., 2015). Based on data
from the FORS1 archive, Bagnulo et al. (2015) reported the presence of
magnetic fields in HD 89103 with the strength of $\langle B_{z}\rangle=2.14\pm
0.07\;\text{kG}$. The only literature has provided the fundamental parameters
including an effective temperature of $\text{log}(T_{\rm
eff}/\text{K})=4.07\pm 0.02$ a luminosity of $\text{log}(L/L_{\odot})=1.67\pm
0.12$, and a mass of $M_{\star}=2.68\pm 0.11M_{\odot}$ (Kochukhov & Bagnulo,
2006).

The light curve and amplitude spectrum of HD 89103 are presented in the third
row of Figure 7. 2 significant frequencies and 2 harmonics are detected in the
amplitude spectrum. Using the most significant frequency
($\mathit{f}=0.4600395\pm 0.0000033\;\text{d}^{-1}$), and using this value, we
determined the rotational period of HD 89103 to be $P_{\rm rot}=2.17242\pm
0.00002\;\text{days}$.

####  4.2.4 HD 118913

HD 118913 (TIC 342995661) is an A0V star (Bagnulo et al., 2015). Bagnulo et
al. (2015) cataloged HD 118913 as an mCP star, which has the strength of
$\langle B_{z}\rangle=0.52\pm 0.03\;\text{kG}$. The only literature has
provided the fundamental parameters include an effective temperature of
$\text{log}(T_{\rm eff}/\text{K})=3.98\pm 0.01$ a luminosity of
$\text{log}(L/L_{\odot})=1.67\pm 0.14$, and a mass of $M_{\star}=2.40\pm
0.14M_{\odot}$ (Kochukhov & Bagnulo, 2006).

The light curve and amplitude spectrum of HD 118913 are presented in the
fourth row of Figure 7. We detected 4 significant frequencies and one harmonic
frequency in the amplitude spectrum. We deduced the rotational period $P_{\rm
rot}=2.45892\pm 0.00002\;\text{days}$ using the frequency of
$\mathit{f}=0.40668\pm 0.00002\;\text{d}^{-1}$. The presence of three
additional significant frequencies suggests that HD 118913 is not only a
rotating variable, but also exhibits coherent pulsations.

####  4.2.5 HD 119308

HD 119308 (TIC 305716720) is a A0V star (Bagnulo et al., 2015). The star has a
dipole magnetic field with strength of $\langle B_{z}\rangle=-0.29\pm
0.05\;\text{kG}$ (Bagnulo et al., 2015). The only literature has provided the
fundamental parameters of HD 119308 include an effective temperature of
$\text{log}(T_{\rm eff}/\text{K})=4.01\pm 0.01$, a luminosity of
$\text{log}(L/L_{\odot})=1.48\pm 0.15$, and a mass of $M_{\star}=2.30\pm
0.11M_{\odot}$ for this star (Kochukhov & Bagnulo, 2006).

The light curve and amplitude spectrum of HD 119308 are presented in the fifth
row of Figure 7. From the amplitude spectrum, we detected 1 significant
frequencies and 2 harmonics. The rotational period of $P_{\rm rot}=1.90666\pm
0.00002\;\text{days}$ is derived from the most significant frequency of
$\mathit{f}=0.524476\pm 0.000005\;\text{d}^{-1}$.

####  4.2.6 HD 127453

HD 127453 (TIC 446846414) is a B8V star (Bagnulo et al., 2015). The star has a
magnetic fields with the strength of $\langle B_{z}\rangle=-0.26\pm
0.07\;\text{kG}$ (Bagnulo et al., 2015). Using the photometric data, Kochukhov
& Bagnulo (2006) provided the fundamental parameters include an effective
temperature of $\text{log}(T_{\rm eff}/\text{K})=4.08\pm 0.01$, a luminosity
of $\text{log}(L/L_{\odot})=2.25\pm 0.17$, and a mass of $M_{\star}=3.33\pm
0.23M_{\odot}$ for this star.

The light curve and amplitude spectrum of HD 127453 are presented in the fifth
row of Figure 7. One significant frequency and 3 harmonics are detected in the
amplitude spectrum. The rotational period of $P_{\rm rot}=5.50959\pm
0.00008\;\text{days}$ is derived from the significant frequency of
$\mathit{f}=0.1815015\pm 0.0000026\;\text{d}^{-1}$. No coherent pulsation is
detected in the amplitude spectrum.

Figure 7: The light curves (left panels) and amplitude spectra (right panels)
for CPD-62 2124, HD 67621, HD 89103, HD 118913, HD 119308, and HD 127453. In
the frequency spectra, the significant peaks are marked with a blue inverted
triangle, and the harmonics of the dominant frequency are marked with orange
inverted triangles.

####  4.2.7 HD 138758

HD 138758 (TIC 425871448) is a main sequence star with the B9 spectral type
(Bagnulo et al., 2015). Using the FORS1 archive data, Bagnulo et al. (2015)
reported the presence of magnetic fields in HD 138758. Using the photometric
data, Kochukhov & Bagnulo (2006) provided the fundamental parameters include
an effective temperature of $\text{log}(T_{\rm eff}/\text{K})=4.02\pm 0.02$, a
luminosity of $\text{log}(L/L_{\odot})=1.68\pm 0.17$, and a mass of
$M_{\star}=2.51\pm 0.15M_{\odot}$ for this star.

The light curve and amplitude spectrum of HD 138758 is shown in the top row of
the Figure 8. From the amplitude spectrum, we detected a significant frequency
and a harmonic. The rotational period $P_{\rm rot}=1.100073\pm
0.000005\;\text{days}$ is determined from the significant frequency of
$\mathit{f}=0.909030\pm 0.000004\;\text{d}^{-1}$.

####  4.2.8 HD 157751

HD 157751 (TIC 160367734) has a B9V spectral type, and a large-scale magnetic
fields with the strength of $\langle B_{z}\rangle=4.10\pm 0.08\;\text{kG}$
(Bagnulo et al., 2015). Based on the calibration of the Geneva photometric
system, Kochukhov & Bagnulo (2006) provided the stellar parameters include an
effective temperature of $\text{log}(T_{\rm eff}/\text{K})=3.99\pm 0.01$, a
luminosity of $\text{log}(L/L_{\odot})=1.38\pm 0.15$, and a mass of
$M_{\star}=2.18\pm 0.10M_{\odot}$ for this star.

The light curve and amplitude spectrum of HD 157751 is shown in the middle row
of the Figure 8. Our frequency analysis detected one significant frequency and
three harmonics in the spectrum. The significant frequency
$\mathit{f}=0.370186\pm 0.000004\;\text{d}^{-1}$, corresponds to the
rotational frequency, allowing us to determine a rotational period of $P_{\rm
rot}=2.70134\pm 0.00003\;\text{days}$ for HD 157751.

####  4.2.9 HD 172690

HD 172690 (TIC 469692862) has a A0V spectral type, and a dipole magnetic field
with the strength of $\langle B_{z}\rangle=-0.25\pm 0.08\;\text{kG}$ (Bagnulo
et al., 2015). Based on the calibration of the Geneva photometric system,
Kochukhov & Bagnulo (2006) provided the stellar parameters include an
effective temperature of $\text{log}(T_{\rm eff}/\text{K})=4.06\pm 0.02$, a
luminosity of $\text{log}(L/L_{\odot})=2.05\pm 0.15$, and a mass of
$M_{\star}=3.00\pm 0.18M_{\odot}$ for this star.

The light curve and amplitude spectrum of HD 172690 is shown in the bottom row
of the Figure 8. We detected one significant frequency and four harmonics in
the amplitude spectrum of the HD 172690. The most significant frequency of
$\mathit{f}=0.5786305\pm 0.0000028\;\text{d}^{-1}$ corresponds to the
rotational frequency, allowing us to determine a rotational period of $P_{\rm
rot}=1.72822\pm 0.000008\;\text{days}$ for HD 172690.

Figure 8: The light curves (left panels) and amplitude spectra (right panels)
for HD 138758, HD 157751, and HD 172690. The markers in the amplitude spectra
have the same meaning as in Figure 7.

###  4.3 Multiple systems and Other types

Our sample contains 16 multiple systems, the majority of which have been
confirmed as spectroscopic binaries. Among these, 8 multiple systems do not
exhibit obvious eclipses in their light curves. HD 25558, HD 36485, HD 37742,
HD 47129, HD 130807, and HD 136504 exhibit complex variations in their light
curves. We presented the light curves and amplitude spectra for these systems
in Figure 9, and our analysis suggests that continued spectroscopic monitoring
will advance the discovery of magneto-asteroseismic phenomena in binary stars.

Among the variables in our sample, we were unable to definitively determine
the variability of 17 stars. CPD-60 944B and HD 66318 are severely
contaminated by nearby stars, making it impossible to obtain their light
curves. HD 101412 is reported to be a Herbig Ae star (Hubrig et al., 2010).
The observed variations in its light curve are likely caused by chemical spots
and magnetospheric accretion (Schöller et al., 2016; Järvinen et al., 2016).
HD 200775 is a well-known Herbig Be star (Alecian et al., 2008; Benisty et
al., 2013; Saha et al., 2020), and we detected a significant peak in its
amplitude spectrum. However, without additional photometry and spectroscopy
data, we are unable to determine the classifications of the remaining stars.

Figure 9: The light curves (left panels) and amplitude spectra (right panels)
of binary stars. The markers in the amplitude spectra have the same meaning as
in Figure 7.

###  4.4 Stochastic Low-Frequency (SLF) variability

Figure 10: The SLF variability analysis results of Ap/Bp stars in our sample.
The pair-wise relationships between the fitting parameters, $\alpha_{0}$,
$\nu_{char}$ and $\gamma$ in Eq. (2) are presented in top row. Each star is
color-coded by the luminosity. The arrows extending from the single colored
circle indicate the direction of variation in the fitting parameters of the
SLF variabilities, revealing trends in the fitting parameters across the
different sectors. Location of the stars within our sample in the HR diagram
are presented in bottom row. Each star is color-coded by the fitting
parameters $\alpha_{0}$ (left panel) and $\nu_{\rm char}$ (right panel). The
symbol sizes are proportional to the $\gamma$ values. Evolutionary tracks are
plotted as grey lines. A typical error bar is shown in the top-left corner.
Figure 11: The pair-wise relationships between the luminosities and fitting
parameters(log$\alpha_{\rm 0}$, $\nu_{\rm char}$, and $\gamma$) for our sample
of Ap/Bp stars. The Spearman rank-order correlation coefficients and p-values
are provided in the figures accordingly. Figure 12: The SLF variability
analysis results of upper main-sequence stars in our sample. The pair-wise
relationships between the fitting parameters, $\alpha_{0}$, $\nu_{char}$ and
$\gamma$ in Eq. (2) are presented in top row. Each star is color-coded by the
luminosity. The arrows extending from the single colored circle indicate the
direction of variation in the fitting parameters of the SLF variabilities,
revealing trends in the fitting parameters across the different sectors.
Location of the stars within our sample in the HR diagram are presented in
bottom row. Each star is color-coded by the fitting parameters $\alpha_{0}$
(left panel) and $\nu_{\rm char}$ (right panel). The symbol sizes are
proportional to the $\gamma$ values. Evolutionary tracks are plotted as grey
lines. Figure 13: The pair-wise relationships between the luminosities and
fitting parameters(log$\alpha_{\rm 0}$, $\nu_{\rm char}$, and $\gamma$) for
our sample of more massive magnetic hot stars. The Spearman rank-order
correlation coefficients and p-values are provided in the figures accordingly.

Inspired by previous efforts by Bowman et al. (2019b, a, 2020), we conducted
an analysis of the SLF variability in approximately two hundred light curves
from our sample using the MCMC framework. The fitting parameters for SLF
variability are listed in Table 2, and the logarithmic amplitude spectra and
corresponding fitting results are included in Appendix B (ranging from Figure
B1 to Figure B11). As demonstrated by Bowman et al. (2019a, 2020), excluding
eclipsing binary (EB) systems is warranted in SLF variability analysis,
because binary interaction dominates the evolution of massive stars in these
systems (Sana et al., 2012, 2014). In addition, the significant light
contributions from the secondary component in EB systems can cause modulation
of the photometric variability detected in the primary star during the binary
phase, which limits the scientific inference of SLF variability. Therefore, we
excluded EB systems from our sample in SLF variability analysis. We also
excluded stars that exhibit strong contamination from our analysis.

On the other hand, our sample includes various types of magnetic hot stars,
such as Of?p-type stars, rigidly rotating magnetosphere (RRM) stars, and Ap/Bp
stars. To explore SLF variability across a wider mass range in magnetic hot
stars, it is necessary to improve the homogeneity of both the stellar and
magnetic field structures in our sample. Ap/Bp stars often exhibit chemical
peculiarities and slow rotation (e.g. Zorec & Royer, 2012; Ryabchikova &
Romanovskaya, 2017; Netopil et al., 2017; Hümmerich et al., 2020). These stars
also display vertical stratification of the abundance of several chemical
species, indicating distinct chemical and temperature stratification in their
photospheres (e.g. Savanov & Kochukhov, 1998; Zverko et al., 2005; Khalack et
al., 2014). In contrast to more massive magnetic stars (with spectral types
earlier than B5), the magnetic field geometry and evolution of Ap/Bp stars
depend on their mass (e.g. Mathys et al., 1997; Hubrig et al., 2000;
Landstreet et al., 2007; Mathys, 2017; Hubrig & Schöller, 2021). Consequently,
we grouped Ap/Bp stars with other types of stars based on their spectral type,
resulting in two sub-samples for a systematic exploration of SLF variability
in magnetic hot stars. The first sub-sample comprises 55 magnetic Ap/Bp stars
from our original sample, and the second sub-sample comprises 45 more massive
stars from our original sample.

####  4.4.1 SLF variability of magnetic Ap/Bp stars

In the top row of Figure 10, we presented the pair-wise relationships between
the fitting parameters of SLF variability for our Ap/Bp sub-sample, each star
is color-coded by its luminosity. The arrows extending from the individual
colored circles indicate the direction of variation in the fitting parameters
of the SLF variability, revealing trends in the fitting parameters across the
different sectors. The characteristic frequency, $\nu_{\rm char}$ for magnetic
Ap/Bp stars exhibits a primary distribution between 0 and 1.5 $\text{d}^{-1}$.
The amplitude of SLF variability, log$\alpha_{\rm 0}$, shows a dominant
distribution ranging from 0.8 to 3, while $\gamma$ primarily falls between 0
and 1.5. We calculated Spearman rank-order correlation coefficients $R$ to
quantify the relationships between fitting parameters in the sample of Ap/Bp
stars and labelled them in the figures accordingly. Due to the smaller sample
sizes of Ap/Bp stars in our study, p-values were obtained using a permutation
test. A linear regression analysis reveals a strong negative correlation (R =
-0.48, p ¡ 0.01) between log$\alpha_{\rm 0}$ and $\nu_{\rm char}$ indicating
that stars with larger log$\alpha_{\rm 0}$ tend to have smaller values of
$\nu_{\rm char}$. Our statistical analysis also demonstrates a significant
correlation between log$\alpha_{\rm 0}$ and $\gamma$ (R = -0.32, p ¡ 0.02), as
well as a relationship between $\gamma$ and $\nu_{\rm char}$ (R = 0.84, p ¡
0.01). These significant correlations among fitting parameters suggest that an
Ap/Bp star with larger amplitude of SLF variability is likely to have smaller
values of $\nu_{\rm char}$ and $\gamma$.

To more accurately investigate the SLF variability of magnetic Ap/Bp stars, we
placed the Ap/Bp stars in the Hertzsprung-Russell diagram (HR diagram). In the
bottom-left and bottom-right panels of Figure 10, each Ap/Bp star in our sub-
sample is represented by a circle, which also be color-coded by the fitting
parameters $\alpha_{\rm 0}$ and $\nu_{\rm char}$, respectively. The symbol
sizes of the points are proportional to the fitting parameter $\gamma$. To
illustrate the distribution of the Ap/Bp stars in our sub-sample, we computed
the non-rotating, solar abundance evolutionary tracks for initial masses from
2 to 4.5 $M_{\odot}$ with Modules for Experiments in Stellar Astrophysics
(MESA; Paxton et al., 2019). During the computation process, the Ledoux
criterion is used for convection, the mixing-length parameter $\alpha_{\rm
MLT}$ and the efficiency parameter $\alpha_{\rm SEM}$ for semi-convection are
taken as 1.5 and 1.0, respectively (Brott et al., 2011). These evolutionary
tracks are plotted as grey lines in the Figure 10.

The relationships between the fitting parameters and the distribution in the
HR diagram for stars with masses below 20 $M_{\odot}$ are less clear due to
the limited sample size and the variability associated with the opacity
mechanism (Bowman et al., 2020). It is also challenging to identify any clear
dependence of SLF variability on mass from the two HR diagrams presented in
the bottom-left and bottom-right panels of Figure 10. However, in view of the
mass-luminosity relation of the stars, we can indirectly investigate any
potential dependence of SLF variability on stellar mass by examining the
correlation between the fitting parameters of SLF variability and luminosity.
The pair-wise relationships between the luminosities and fitting
parameters(log$\alpha_{\rm 0}$, $\nu_{\rm char}$, and $\gamma$) for the sample
of Ap/Bp stars are shown in Figure 11. The Spearman rank-order correlation
coefficients and p-values are provided in the figures accordingly. Our results
indicate that no significant correlation exists between the luminosity and the
fitting parameters, which suggests that there is no mass-dependence of SLF
variability in Ap/Bp stars with masses between approximately 1.5 $M_{\odot}$ ¡
M ¡ 4.5 $M_{\odot}$.

Magnetic Ap/Bp stars constitute approximately 10% to 15% of the intermediate-
mass and massive main-sequence stars with spectral types ranging from
approximately B8 to F0 (Hubrig & Schöller, 2021). However, it is important to
note that our sample only covers a limited section of the main sequence of
Ap/Bp stars, significantly limiting our ability to explore the dependence of
SLF variability on the stellar evolutionary stage. Furthermore, estimating the
age of Ap/Bp stars based solely on their positions in the HR diagram typically
introduces uncertainties on the order of 25% of the total main sequence
lifetime (Bagnulo et al., 2006). Consequently, the ages determined from the HR
diagram positions of the Ap/Bp stars in our sample currently have high
uncertainties, making them of limited value in constraining SLF variability in
relation to stellar age. Therefore, no sufficient constraints on the
dependence of SLF variability on stellar age are provided by our sub-sample of
Ap/Bp stars.

####  4.4.2 SLF variability of more massive magnetic hot stars

The pair-wise relationships between the fitting parameters of SLF variability
for our second sub-sample are presented in the top row of the Figure 12. We
also plotted the HR diagrams for each star in our second sub-sample in the
bottom panels of Figure 12. The markers in Figure 12 have the same meaning as
in Figure 10. The log$\alpha_{\rm 0}$ and $\gamma$ values in the sample of
more massive magnetic hot stars are primarily concentrated between 1 and 3,
which is consistent with the distribution range of log$\alpha_{\rm 0}$ and
$\gamma$ in the Ap/Bp star sample. However, $\nu_{\rm char}$ of the stars in
the sample of more massive magnetic hot stars are primarily distributed in the
range from 0 to 7 d-1, exhibiting a wider range compared to the Ap/Bp star
sample. Cantiello & Braithwaite (2019) provided detailed convective atlas for
stars of different masses during the main sequence evolution stage. For stars
below 4$M_{\odot}$, the sub-surface convection zone (CZ) predominantly
consists of H CZ, HeI CZ, and HeII CZ. On the other hand, for stars above
4$M_{\odot}$, the sub-surface CZ primarily consists of HeII CZ and Fe CZ. If
the SLF variability is caused by the stellar envelope convection, the
differences in $\nu_{\rm char}$ distribution between the sample of Ap/Bp stars
and the sample of more massive magnetic hot stars may be reflect the
variations in the number and efficiency of CZ. Furthermore, SLF variability is
expected to provide effective constraints on the efficiency of heat transport
or the mixing length parameters within the CZ of stars.

We employed the same statistical methodology as described in section 4.4.1 to
analyze the correlation of fitting parameters in the sample of more massive
magnetic hot stars. We provided the Spearman rank-order correlation
coefficients $R$ and $p$-value for each panel in the top row of Figure 12. The
$\nu_{\rm char}$ and log$\alpha_{\rm 0}$, as well as $\nu_{\rm char}$ and
$\gamma$, in the sample of more massive magnetic hot stars exhibit significant
correlations. However, there is no correlation between log$\alpha_{\rm 0}$ and
$\gamma$. This result contradicts the findings from the sample of Ap/Bp stars.
Notably, both in the sample of Ap/Bp stars and the sample of more massive
magnetic hot stars, we found a negative correlation between log$\alpha_{\rm
0}$ and $\nu_{\rm char}$. This implies that the relationship between
log$\alpha_{\rm 0}$ and $\nu_{\rm char}$ in the SLF variability of stars is
universal and independent of stellar mass. The pair-wise relationships between
the luminosities and fitting parameters (log$\alpha_{\rm 0}$, $\nu_{\rm
char}$, and $\gamma$) for our sample of more massive magnetic hot stars are
illustrated in Figure 13. The Spearman rank-order correlation coefficients $R$
and corresponding $p$-values are provided in the figures. Our results indicate
that no significant correlations are observed between the luminosities and
fitting parameters, suggesting no clear dependence of SLF variability on
stellar mass for our sample of more massive magnetic hot stars.

The surveys conducted on magnetic hot stars have indicated that probably about
7% of O-type stars with masses exceeding 18 $M_{\odot}$ and about 6% of
early-B and O stars have measurable magnetic fields (e.g. Grunhut et al.,
2017; Schöller et al., 2017). Currently, observations of magnetic hot stars
with masses above 20$M_{\odot}$ are limited to only around ten objects, and
the majority of stars with strong magnetic fields are observed in the main
sequence stage. This observational bias results in our sample primarily
consisting of stars close to the zero-age main sequence early (ZAMS), which
indicates that the current sample of magnetic hot stars still suffers from a
significant lack of completeness in terms of evolutionary stages. Therefore,
with the current sample of magnetic hot stars, our ability to investigate the
relationship between SLF variability and stellar age is limited. The
implication of previous study is that up to about 30%-50% of all massive stars
might be magnetic, and only the tip of the iceberg has been seen (Braithwaite
& Spruit, 2004; Stello et al., 2016).Therefore, an extended sample of magnetic
hot stars can be expected to be utilized in order to investigate the
dependence between SLF variability and stellar physical parameters in future.

##  5 DISCUSSION

As previously mentioned in section 3.1, we gathered all short cadence data for
stars in our sample from TESS sectors 1 to 56. Thanks to $TESS$ repeated
observations of the entire sky, the majority of stars in our sample were
observed in different sectors that were 26 sectors apart (approximately 710
days), except for stars that overlapped consecutive sectors. This allows us to
explore variations in SLF variability over time, ranging from months to years.
In the top panels of Figure 10 and Figure 12, the arrows extending from the
single point indicate the direction of variation in the fitting parameters of
the SLF variability, revealing trends in the fitting parameters across the
different sectors. The fitting parameters of SLF variability for the same star
exhibit the significant variations between the different sectors observed by
$TESS$, suggesting that the morphology of SLF variability occurred significant
changes in the time. This is consistent with the findings previously reported
by Blomme et al. (2011) and Bowman et al. (2019a), who noted that the dominant
peaks of SLF variability in stars have short lifetimes on the order of hours
and days.

The steepness $\gamma$ and characteristic frequency $\nu_{\rm char}$ are
crucial features for understanding the physical mechanism behind SLF
variability (Bowman et al., 2019a, b). Our analysis reveals that the magnetic
hot stars in our sample have $\gamma<5.5$ with the vast majority having
$1\leq\gamma\leq 3$. This is consistent with the predictions of numerical
simulations of IGWs (Rogers et al., 2013; Rogers, 2015). The $\nu_{\rm char}$
for the stars in our sample is primarily in the ranges of
$0\;\text{d}^{-1}<\nu_{\rm char}<6.3\;\text{d}^{-1}$. These results are
consistent with the findings of Bowman et al. (2019a, 2020). Previous studies
have suggested that such a broad frequency range can be explained by the
presence of an entire spectrum of IGWs (Edelmann et al., 2019; Horst et al.,
2020).

Bowman et al. (2019b) studied the SLF variability in 167 OB-type stars
observed by the K2 and TESS. They pointed out that the $\nu_{\rm char}$ and
$\gamma$ are insensitive to the metallicity of the star, while a significant
correlation is discovered between the intrinsic brightness of a star and
$\nu_{\rm char}$. Investigating the systematic effects of magnetic fields on
the occurrence of SLF variability in massive stars also requires the detection
of this phenomenon in a larger sample of magnetic hot stars. To accurately
investigate the correlation between the SLF variability and the magnetic field
strength, we selected 37 single stars within our sample of more massive
magnetic hot stars. This sample consists of the magnetic hot stars identified
by Shultz et al. (2020) and Petit et al. (2013), for which sufficient
spectroscopic and spectropolarimetric data are available to evaluate their
magnetic properties.

In the top row of Figure 14, we presented the relationship between the fitting
parameters ($\alpha_{0},\;\nu_{\rm char},\;\text{and}\;\gamma$) and the polar
strength of the surface dipole magnetic fields ($B_{\rm p}$). Each star is
represented by a circle and color-coded according to its luminosity. The
Spearman’s rank correlation coefficient, $R$, and the corresponding $p$-value
are provided in the panels. In our study, we found a significant negative
correlation between the $B_{\rm p}$ and $\nu_{char}$ ($R=-0.30,p=0.07$).
Previous studies reported a positive correlation between macroturbulent
($\nu_{\rm macro}$) and the fitting parameters of SLF variability (e.g. Aerts
& Rogers, 2015; Grassitelli et al., 2015; Simón-Díaz et al., 2017; Bowman et
al., 2020). Additionally, the magnetic field is confirmed to have an effect to
stabilize the atmosphere and suppress the generation of macroturbulence
(Lecoanet et al., 2019; Sundqvist et al., 2013). Therefore, the suppression
effect of magnetic fields on $\nu_{\rm char}$ may be a result of their
inhibition of macroturbulence. We plotted the HR diagrams in the bottom panels
of Figure 14. Each star is represented by a circle, which also be color-coded
by the polar strength of the surface dipole magnetic fields ($B_{\rm p}$). The
symbol sizes of the points are proportional to the fitting parameter
log$\alpha_{\rm 0}$ (bottom-left panel) and $\nu_{\rm char}$ (bottom-right
panel), respectively. Inferring the relationships among the fit parameters and
the strength of the magnetic fields in the HR diagram for stars are less
clear.

Figure 14: The relationship between the fitting parameters
($\alpha_{0},\;\nu_{\rm char},\;\text{and}\;\gamma$) and the polar strength
($B_{\rm p}$) of the surface dipole magnetic fields are presented in the top
panels. Each star is colour-coded by luminosity. The Spearman’s rank
correlation coefficient, R, and the corresponding p-value are also provided.
The HR diagrams of 37 magnetic hot stars are shown in bottom panels. Each star
is represented by a circle, which also be color-coded by the polar strength of
the surface dipole magnetic fields ($B_{\rm p}$). The symbol sizes of the
points are proportional to the fitting parameter log$\alpha_{\rm 0}$ (bottom-
left panel) and $\nu_{\rm char}$ (bottom-right panel), respectively.

##  6 CONCLUSIONS

Using sectors 1-56 $TESS$ short cadence photometric data, we provided a
variability study for 118 magnetic hot stars, which was confirmed using
spectropolarimeter or high-resolution spectrograph (e.g. Bagnulo et al., 2015;
Morel et al., 2014, 2015; Grunhut et al., 2017). Based on the light curves and
amplitude spectra, we determined the photometric variability classification of
the stars in our sample. As the results, we detected 87 variable stars, 14
constant stars, and 17 unknown variables. We identified 9 new rotating
variable stars in our sample. We discussed the new variable stars aided by the
available spectroscopic parameters, spectropolarimeteric parameters, and
variability. The details of our results are listed in Table 1.

Using a Bayesian MCMC method inspired by Bowman et al. (2019b, a), we derived
the fitting parameters of SLF variability from the prewhitening light curves
for the stars within our sample. We concluded that the SLF variability is
ubiquitous in magnetic hot stars, which are consistent with the findings of
Bowman et al. (2019a, 2020). The fitting parameters for SLF variabilities are
listed in Table 2. We also included all logarithmic amplitude spectra, along
with the corresponding fitting results, in Appendix B (From the Figure B1 to
Figure B11). To systematically explore SLF variability in magnetic hot stars,
we divided our sample into two groups. Our analysis reveals that the magnetic
hot stars in our sample have $\gamma<5.5$ with the vast majority having
$1\leq\gamma\leq 3$. The $\nu_{\rm char}$ for the stars in our sample is
primarily in the ranges of $0\;\text{d}^{-1}<\nu_{\rm
char}<6.3\;\text{d}^{-1}$. These results are consistent with the findings of
Bowman et al. (2019a, 2020). Furthermore, no significant correlations are
observed between the luminosities and fitting parameters, suggesting no clear
dependence of SLF variability on stellar mass for our sample of magnetic hot
stars. To accurately investigate the correlation between SLF variability and
magnetic field strength, we selected 37 single stars from our sample of more
massive magnetic hot stars. In our study, we found a significant negative
correlation between the $B_{\rm p}$ and $\nu_{char}$ ($R=-0.30,p=0.07$). This
suppression effect of magnetic fields on $\nu_{\rm char}$ may be a result of
their inhibition of macroturbulence. It should be noted that our results are
affected by observational selection effects. Therefore, future studies should
employ an expanded sample of magnetic hot stars to investigate the
relationship between SLF variability and stellar physical parameters in more
detail.

Finally, our results are valuable for guiding future magneto-asteroseismic
studies of massive stars, such as the multiple systems, hybrid, and $\beta$
Cep. In the future, we will expand the photometric variables catalog for the
magnetic hot stars, and combine it with the spectroscopic databases, such as
the IACOB, Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST),
and Sloan Digital Sky Survey (SDSS) to explore the variability more
accurately.

##  Appendix A Appendix A

Table 1: Identification numbers, physical parameters and variability
classifications of the 118 magnetic hot stars.

Name | TIC | Sp.type | log($\rm L/L_{\odot}$) | log($T_{\rm eff}/\text{K}$) | log$\;g$ | Reference | Variability
---|---|---|---|---|---|---|---
ALS 15218 | 458859193 | O8.5Vp | 5.00 $\pm$ 0.10 | 4.53 $\pm$ 0.03 | 4.00 $\pm$ 0.20 | R1 | cont. + SLF
ALS 3694 | 37053664 | B1 | 3.80 $\pm$0.20 | 4.40 $\pm$ 0.02 | 4.00 $\pm$ 0.10 | R2 | rot. + SLF
CD-59 3239 | 390668263 | B0.5V | 4.30 $\pm$ 0.20 | 4.36 $\pm$ 0.06 | 3.60 $\pm$ 0.20 | R1 | cont. + SLF
CPD-28 2561 | 129361218 | O6Ifp | 5.50 $\pm$ 0.20 | 4.54 $\pm$ 0.02 | 4.00 $\pm$ 0.20 | R1 | unknown + SLF
CPD-60 944B | 358467049 | B8III | 2.26 $\pm$ 0.02 | 4.18 $\pm$ 0.03 | 4.75 $\pm$ 0.25 | this work | unknown
CPD-62 2124 | 290796936 | B2IV | 3.80 $\pm$ 0.20 | 4.37 $\pm$ 0.00 | 4.05 $\pm$ 0.10 | R2 | rot. + SLF
HD 101412 | 320547523 | B9 | 1.65 $\pm$ 0.01 | 4.00 $\pm$ 0.04 | 4.10 $\pm$ 0.40 | this work | unknown + SLF
HD 105382 | 333670665 | B6III | 3.00 $\pm$ 0.20 | 4.26 $\pm$ 0.01 | 4.13 $\pm$ 0.07 | R1 | rot. + SLF
HD 108 | 406893156 | O6f?p-O8fp | 5.70 $\pm$ 0.10 | 4.54 $\pm$ 0.02 | 3.50 $\pm$ 0.20 | R1 | Multi + SLF
HD 121743 | 359762838 | B2IV | 3.60 $\pm$ 0.20 | 4.32 $\pm$ 0.03 | 4.02 $\pm$ 0.12 | R1 | hybird + SLF
HD 125823 | 167480388 | B7IIIp | 3.20 $\pm$ 0.20 | 4.28 $\pm$ 0.05 | 4.14 $\pm$ 0.12 | R1 | rot. + SLF
HD 127381 | 457686485 | B1V | 3.76 $\pm$ 0.06 | 4.36 $\pm$ 0.02 | 4.02 $\pm$ 0.10 | R1 | rot. + SLF
HD 130807 | 455309397 | B5 | 2.70 $\pm$ 0.20 | 4.23 $\pm$ 0.03 | 4.25 $\pm$ 0.10 | R1 | Multi + SLF
HD 136504 | 147226597 | B2IV-V | 3.70 $\pm$ 0.20 | 4.31 $\pm$ 0.01 | 3.97 $\pm$ 0.15 | R1 | Multi + $\beta$ Cep + SLF
HD 149277 | 229331994 | B2IV/V | 3.50 $\pm$ 0.20 | 4.30 $\pm$ 0.04 | 3.75 $\pm$ 0.15 | R3 | Multi + SLF
HD 149438 | 205175750 | B0.2V | 4.50 $\pm$ 0.10 | 4.50 $\pm$ 0.01 | 4.00 $\pm$ 0.10 | R1 | unknown + SLF
HD 156324 | 153805844 | B2V | 3.80 $\pm$ 0.60 | 4.34 $\pm$ 0.06 | 4.00 $\pm$ 0.30 | R2 | Multi + SLF
HD 156424 | 154190068 | B2V | 3.50 $\pm$ 0.40 | 4.30 $\pm$ 0.07 | 3.99 $\pm$ 0.10 | R4 | Multi + $\beta$ Cep + SLF
HD 175362 | 113272022 | B5V | 2.60 $\pm$ 0.10 | 4.25 $\pm$ 0.01 | 4.24 $\pm$ 0.10 | R1 | rot. + SLF
HD 176582 | 120355394 | B5IV | 2.90 $\pm$ 0.10 | 4.23 $\pm$ 0.03 | 4.00 $\pm$ 0.10 | R2 | rot. + SLF
HD 189775 | 303247444 | B5V | 2.90 $\pm$ 0.10 | 4.24 $\pm$ 0.01 | 4.12 $\pm$ 0.08 | R2 | rot. + SLF
HD 191612 | 378273410 | O6f?p | 5.40 $\pm$ 0.20 | 4.54 $\pm$ 0.01 | 3.50 $\pm$ 1.00 | R1 | unknown + SLF
HD 200775 | 387813185 | B1 | 4.00 $\pm$ 0.30 | 4.25 $\pm$ 0.05 | 3.40 $\pm$ 0.20 | R1 | unknown + SLF
HD 205021 | 321818578 | B1IV | 4.30 $\pm$ 0.10 | 4.40 $\pm$ 0.02 | 3.80 $\pm$ 0.15 | R1 |  $\beta$ Cep + SLF
HD 23478 | 26432264 | B3IV | 3.20 $\pm$ 0.20 | 4.30 $\pm$ 0.04 | 4.20 $\pm$ 2.00 | R2 | rot. + SLF
HD 25558 | 407615454 | B3V | 2.80 $\pm$ 0.30 | 4.23 $\pm$ 0.02 | 4.20 $\pm$ 0.20 | R1 | Multi + SLF
HD 306795 | 290682018 | B2V | 3.20 $\pm$ 0.30 | 4.25 $\pm$ 0.05 | 3.90 $\pm$ 0.20 | R1 | unknown + SLF
HD 3360 | 240669906 | B2IV | 3.82 $\pm$ 0.06 | 4.32 $\pm$ 0.00 | 3.80 $\pm$ 0.05 | R1 |  $\beta$ Cep + SLF
HD 345439 | 424048289 | B2IV | 4.00 $\pm$ 0.30 | 4.36 $\pm$ 0.04 | 4.29 $\pm$ 0.19 | R2 | rot. + SLF
HD 35298 | 269118344 | B3Vw | 2.40 $\pm$ 0.10 | 4.20 $\pm$ 0.02 | 4.25 $\pm$ 0.12 | R1 | rot. + SLF
HD 35502 | 4289780 | B5V | 3.00 $\pm$ 0.10 | 4.26 $\pm$ 0.01 | 4.30 $\pm$ 0.20 | R2 | Multi + SLF
HD 35912 | 464839773 | B1.5Ve | 3.30 $\pm$ 0.30 | 4.25 $\pm$ 0.02 | 4.00 $\pm$ 0.10 | R1 | SPB + SLF
HD 36485 | 50743458 | B2Ve | 3.50 $\pm$ 0.10 | 4.30 $\pm$ 0.04 | 4.00 $\pm$ 0.10 | R2 | Multi + SLF
HD 36526 | 50787573 | B8Vp | 2.30 $\pm$ 0.20 | 4.17 $\pm$ 0.06 | 4.10 $\pm$ 0.14 | R1 | rot. + SLF
HD 36982 | 427395300 | B1.5Vp | 3.00 $\pm$ 0.20 | 4.34 $\pm$ 0.04 | 4.40 $\pm$ 0.20 | R1 | unknown + SLF
HD 37017 | 427393058 | B1.5-2.5IV-Vp | 3.40 $\pm$ 0.20 | 4.32 $\pm$ 0.04 | 4.10 $\pm$ 0.20 | R2 | Multi + SLF
HD 37022 | 427394772 | O6V | 5.30 $\pm$ 0.10 | 4.59 $\pm$ 0.01 | 4.10 $\pm$ 0.10 | R1 | Multi + SLF
HD 37058 | 427393350 | B3VpC | 2.90 $\pm$ 0.10 | 4.27 $\pm$ 0.01 | 4.17 $\pm$ 0.07 | R1 | unknown + SLF
HD 37479 | 11286209 | B2Vp | 3.50 $\pm$ 0.20 | 4.36 $\pm$ 0.04 | 4.20 $\pm$ 0.20 | R2 | rot. + SLF
HD 37742 | 11360636 | O8f?p | 5.60 $\pm$ 0.10 | 4.46 $\pm$ 0.01 | 3.20 $\pm$ 0.10 | R1 | Multi + SLF
HD 37776 | 11400909 | B2Vp | 3.30 $\pm$ 0.20 | 4.34 $\pm$ 0.02 | 4.25 $\pm$ 0.20 | R2 | rot. + SLF
HD 43317 | 265080539 | B3IV | 2.95 $\pm$ 0.08 | 4.24 $\pm$ 0.00 | 4.07 $\pm$ 0.10 | R5 | hybird + SLF
HD 44743 | 34590771 | B1II/III | 4.41 $\pm$ 0.06 | 4.39 $\pm$ 0.01 | 3.78 $\pm$ 0.08 | R6 |  $\beta$ Cep + SLF
HD 46328 | 47763235 | B1III | 4.50 $\pm$ 0.10 | 4.43 $\pm$ 0.02 | 3.78 $\pm$ 0.07 | R1 |  $\beta$ Cep + SLF
HD 47129 | 220197273 | O7Vp | 5.09 $\pm$ 0.04 | 4.52 $\pm$ 0.03 | 4.10 $\pm$ 0.10 | R1 | Multi + SLF
HD 47777 | 220322778 | B3V | 3.42 $\pm$ 0.15 | 4.34 $\pm$ 0.02 | 4.20 $\pm$ 0.10 | R1 | rot. + SLF
HD 52089 | 63198307 | B1.5II | 4.35 $\pm$ 0.05 | 4.35 $\pm$ 0.01 | 3.40 $\pm$ 0.08 | R6 | unknown + SLF
HD 54879 | 177860391 | O9.7V | … | … | … | … | unknown + SLF
HD 55522 | 65403216 | B2IV/V | 3.00 $\pm$ 0.20 | 4.24 $\pm$ 0.01 | 3.95 $\pm$ 0.06 | R1 | rot. + SLF
HD 57682 | 187458882 | O7.5III | 4.80 $\pm$ 0.20 | 4.53 $\pm$ 0.01 | 4.00 $\pm$ 0.20 | R1 | unknown + SLF
HD 58260 | 284735369 | B3Vp | 3.20 $\pm$ 0.30 | 4.28 $\pm$ 0.03 | 4.20 $\pm$ 0.20 | R1 | cont. + SLF
HD 61556 | 110798652 | B5V | 3.10 $\pm$ 0.20 | 4.27 $\pm$ 0.02 | 4.10 $\pm$ 0.15 | R1 | rot. + SLF
HD 63425 | 175599737 | B0.5V | 4.49 $\pm$ 0.07 | 4.47 $\pm$ 0.01 | 4.00 $\pm$ 0.10 | R1 | cont. + SLF?
HD 64740 | 268971806 | B1.5Vp | 3.80 $\pm$ 0.20 | 4.39 $\pm$ 0.02 | 4.01 $\pm$ 0.09 | R2 | rot. + SLF
HD 66522 | 238314043 | B2III | 3.50 $\pm$ 0.20 | 4.32 $\pm$ 0.04 | 3.88 $\pm$ 0.23 | R1 | cont.? + SLF
HD 66665 | 443848410 | B0.5V | 4.70 $\pm$ 0.20 | 4.45 $\pm$ 0.02 | 3.90 $\pm$ 0.10 | R1 | cont. + SLF
HD 66765 | 238381092 | B1/B2V | 3.40 $\pm$ 0.20 | 4.30 $\pm$ 0.04 | 4.13 $\pm$ 0.20 | R2 | Multi + SLF
HD 67621 | 238489837 | B2IV | 3.30 $\pm$ 0.10 | 4.32 $\pm$ 0.01 | 4.18 $\pm$ 0.10 | R1 | rot. + SLF
HD 9289 | 136842396 | A3V | 0.94 $\pm$ 0.07 | 3.94 $\pm$ 0.02 | 4.50 $\pm$ 0.20 | this work | rot. + SLF
HD 96446 | 466675723 | B1IVp/B2Vp | 3.80 $\pm$ 0.20 | 4.36 $\pm$ 0.02 | 3.74 $\pm$ 0.10 | R1 |  $\beta$ Cep + SLF
NGC 1624 2 | 354879267 | O7V | 5.10 $\pm$ 0.20 | 4.54 $\pm$ 0.02 | 4.00 $\pm$ 0.20 | R1 | unknown + SLF
HD 184927 | 41099689 | B2Vp | 3.60 $\pm$ 0.20 | 4.34 $\pm$ 0.02 | 3.90 $\pm$ 0.23 | R1 | rot. + SLF
HD 105770 | 357310008 | B9V | 2.22 $\pm$ 0.11 | 4.12 $\pm$ 0.01 | … | R7 | rot. + SLF
HD 115226 | 394272819 | A3V | 0.86 $\pm$ 0.12 | 3.88 $\pm$ 0.01 | … | R7 | rot. + SLF
HD 117025 | 314265097 | A2V | 1.42 $\pm$ 0.05 | 3.95 $\pm$ 0.02 | … | R7 | rot. + SLF
HD 118913 | 342995661 | A0V | 1.67 $\pm$ 0.14 | 3.98 $\pm$ 0.01 | … | R7 | rot. + SLF
HD 119308 | 305716720 | A0V | 1.48 $\pm$ 0.15 | 4.0 $\pm$ 0.01 | … | R7 | rot. + SLF
HD 122983 | 329012708 | B9 | 1.75 $\pm$ 0.22 | 4.02 $\pm$ 0.01 | 4.00 $\pm$ 0.34 | this work | rot. + SLF
HD 127453 | 446846414 | B8V | 2.25 $\pm$ 0.17 | 4.08 $\pm$ 0.01 | … | R7 | rot. + SLF
HD 12932 | 268751602 | A5V | 1.07 $\pm$ 0.04 | 3.92 $\pm$ 0.02 | 3.50 $\pm$ 0.30 | this work | cont.
HD 136933 | 148822705 | A0V | … | … | … | … | rot. + SLF
HD 138758 | 425871448 | B9V | 1.68 $\pm$ 0.17 | 4.02 $\pm$ 0.02 | … | R7 | rot. + SLF
HD 146555 | 208684639 | A0V | 2.37 $\pm$ 0.12 | 4.11 $\pm$ 0.01 | 4.00 $\pm$ 0.34 | this work | rot. + SLF
HD 150562 | 44827786 | A5V | 0.86 $\pm$ 0.04 | 3.83 $\pm$ 0.03 | 3.50 $\pm$ 0.50 | this work | cont. + SLF
HD 154708 | 173372645 | A2V | 0.73 $\pm$ 0.14 | 3.83 $\pm$ 0.01 | … | R7 | rot. + SLF
HD 157751 | 160367734 | B9V | 1.38 $\pm$ 0.15 | 3.99 $\pm$ 0.01 | … | R7 | rot. + SLF
HD 161459 | 363716787 | A2V | 1.09 $\pm$ 0.04 | 3.86 $\pm$ 0.01 | 3.50 $\pm$ 0.50 | this work | rot. + SLF
HD 166473 | 368866492 | A5V | 0.98 $\pm$ 0.01 | 3.88 $\pm$ 0.01 | 4.50 $\pm$ 0.24 | this work | cont. + SLF
HD 172690 | 469692862 | A0V | 2.05 $\pm$ 0.15 | 4.06 $\pm$ 0.02 | … | R7 | rot. + SLF
HD 176196 | 387132889 | B9V | 1.81 $\pm$ 0.15 | 4.00 $\pm$ 0.01 | … | R7 | cont. + SLF
HD 187474 | 300279840 | A0V | 1.88 $\pm$ 0.08 | 4.00 $\pm$ 0.01 | … | R7 | unknown
HD 190290 | 318007796 | A0V | 0.83 $\pm$ 0.01 | 3.85 $\pm$ 0.01 | 4.00 $\pm$ 0.30 | this work | rot. + SLF
HD 19918 | 348717688 | A5V | 1.09 $\pm$ 0.01 | 3.87 $\pm$ 0.01 | 4.00 $\pm$ 0.10 | this work | cont. + SLF
HD 201018 | 115150623 | A2V | … | … | … | … | Multi + SLF
HD 203932 | 211404370 | A5V | 1.02 $\pm$ 0.01 | 3.89 $\pm$ 0.01 | 4.50 $\pm$ 0.41 | this work | unknown + SLF
HD 218495 | 237336864 | A2V | 1.00 $\pm$ 0.01 | 3.93 $\pm$ 0.01 | 0.00 $\pm$ 0.00 | this work | rot. + SLF
HD 45583 | 42884620 | B9V | 2.33 $\pm$ 0.10 | 4.20 $\pm$ 0.05 | 3.75 $\pm$ 0.25 | this work | rot. + SLF
HD 49299 | 49314893 | A0V | 2.43 $\pm$ 0.05 | 4.23 $\pm$ 0.04 | 4.00 $\pm$ 0.10 | this work | unknown + SLF
HD 53921 | 766092864 | B9III+B8V | … | … | … | … | Multi + SLF
HD 56350 | 344175577 | BV | 1.79 $\pm$ 0.08 | 4.02 $\pm$ 0.02 | … | R7 | rot. + SLF
HD 65712 | 358467700 | A0V | 1.48 $\pm$ 0.04 | 3.95 $\pm$ 0.01 | 4.00 $\pm$ 0.30 | this work | rot. + SLF
HD 65987 | 372913684 | B9V | 2.62 $\pm$ 0.06 | 4.11 $\pm$ 0.02 | 4.00 $\pm$ 0.20 | this work | rot. + SLF
HD 66295 | 410451777 | B8V | 1.62 $\pm$ 0.05 | 4.05 $\pm$ 0.08 | 4.00 $\pm$ 0.20 | this work | rot. + SLF
HD 66318 | 410451752 | A0V | 1.48 $\pm$ 0.03 | 3.93 $\pm$ 0.01 | 4.00 $\pm$ 0.10 | this work | unknown + SLF?
HD 87240 | 462162948 | B9V | 2.9 $\pm$ 0.4 | 4.1 | 3.6 | R8 | rot. + SLF
HD 89103 | 219614759 | B9V | 1.67 $\pm$ 0.12 | 4.07 $\pm$ 0.02 | … | R7 | rot. + SLF
HD 92499 | 146715928 | A2V | 1.05 $\pm$ 0.17 | 3.86 $\pm$ 0.01 | … | R7 | cont. + SLF
HD 94660 | 147622676 | A0V | 1.98 $\pm$ 0.09 | 4.03 $\pm$ 0.02 | … | R7 | rot. + SLF
HD 9672 | 54003409 | A1V | 1.25 $\pm$ 0.02 | 3.98 $\pm$ 0.01 | 4.00 $\pm$ 0.20 | this work | cont. + SLF
HD 10840 | 231844926 | B3V | 1.93 $\pm$ 0.11 | 4.07 $\pm$ 0.02 | 4.22 $\pm$ 0.20 | R9 | cont. + SLF
HD 115440 | 394308408 | B9V | 1.90 $\pm$ 0.11 | 4.08 $\pm$ 0.02 | 4.29 $\pm$ 0.20 | R9 | rot. + SLF
HD 116890 | 340963903 | B9V | 2.45 $\pm$ 0.12 | 4.11 $\pm$ 0.02 | 3.97 $\pm$ 0.21 | R9 | rot. + SLF
HD 127575 | 421348273 | B9V | 1.77 $\pm$ 0.11 | 4.08 $\pm$ 0.02 | 4.36 $\pm$ 0.20 | R9 | rot. + SLF
HD 128775 | 128886984 | B9V | 2.09 $\pm$ 0.14 | 4.07 $\pm$ 0.02 | 4.07 $\pm$ 0.24 | R9 | rot. + SLF
HD 129899 | 402517183 | A0V | 2.28 $\pm$ 0.12 | 4.03 $\pm$ 0.02 | 3.74 $\pm$ 0.22 | R9 | rot. + SLF
HD 149764 | 83824229 | A0V | 2.03 $\pm$ 0.11 | 4.11 $\pm$ 0.02 | 4.31 $\pm$ 0.20 | R9 | rot. + SLF
HD 149822 | 148207172 | B9V | 1.66 $\pm$ 0.10 | 4.02 $\pm$ 0.02 | 4.21 $\pm$ 0.20 | R9 | rot. + SLF
HD 212385 | 278804454 | A3V | 1.36 $\pm$ 0.10 | 3.93 $\pm$ 0.03 | 4.05 $\pm$ 0.22 | R9 | rot. + SLF
HD 24188 | 32035258 | A0V | 1.98 $\pm$ 0.10 | 4.10 $\pm$ 0.02 | 4.29 $\pm$ 0.18 | R9 | rot. + SLF
HD 34797 | 408217716 | B8V | 2.43 $\pm$ 0.14 | 4.12 $\pm$ 0.02 | 4.04 $\pm$ 0.26 | R9 | rot. + SLF
HD 37633 | 11295912 | B9V | 1.90 $\pm$ 0.14 | 4.11 $\pm$ 0.02 | 4.39 $\pm$ 0.23 | R9 | rot. + SLF
HD 63401 | 175604551 | B8V | 2.32 $\pm$ 0.10 | 4.13 $\pm$ 0.02 | 4.15 $\pm$ 0.18 | R9 | rot. + SLF
HD 69067 | 182362832 | B8V | 1.91 $\pm$ 0.12 | 4.09 $\pm$ 0.02 | 4.30 $\pm$ 0.21 | R9 | rot. + SLF
HD 83625 | 440537642 | A0V | 1.88 $\pm$ 0.11 | 4.07 $\pm$ 0.02 | 4.27 $\pm$ 0.20 | R9 | rot. + SLF
HD 86199 | 469253078 | B9V | 2.23 $\pm$ 0.11 | 4.10 $\pm$ 0.02 | 4.11 $\pm$ 0.20 | R9 | rot. + SLF
HD 88158 | 375583232 | B8V | 2.31 $\pm$ 0.10 | 4.11 $\pm$ 0.02 | 4.07 $\pm$ 0.19 | R9 | rot. + SLF
HD 88385 | 462877348 | A0V | 1.63 $\pm$ 0.11 | 3.99 $\pm$ 0.02 | 4.12 $\pm$ 0.22 | R9 | rot. + SLF
HD 218994 | 2055137574 | ApSr | … | … | … | R10 |  $\delta$ Sct

Note. — The variability classification and stellar parameters of the 118
magnetic hot stars. The first column is the identification names of the stars.
The TESS Input Catalog (TIC) numbers are listed in the second column. The
luminosities, effective temperatures, and surface gravity are listed in
columns 4, 5, and 6, respectively. References for spectroscopic analyses are
provided in the seventh column. In the column 7, R1 = Petit et al. (2013), R2
=Shultz et al. (2020), R3 = González et al. (2018), R4 = Shultz et al. (2021),
R5 = Shultz et al. (2019a), R6 = Shultz et al. (2018), R7 = Kochukhov &
Bagnulo (2006), R8 = Saffe et al. (2005), R9 = Netopil et al. (2017), R10 =
Kurtz et al. (2008), and ”this work” represents the stellar parameters derived
from the SED using the VOSA. In the last column, we reported the variability
classification result for each star. SPB = Slowly Pulsating B star; $\beta$
Cep = $\beta$ Cepheid variable; rot. = rotating variable; cont. = constant;
SLF = stochastic low-frequency variable; $\delta$ Sct = $\delta$ Scuti; Multi
= binary or multiple star. Unknown represents we can not identify the
classification using the amplitude spectrum and light curve.

Table 2: The SLF fitting parameters of the magnetic hot stars.

Name | Sector(s) | $\alpha_{\rm 0}$ | $\nu_{\rm chat}$ | $\gamma$ | $C_{\rm w}$ | Name | Sector(s) | $\alpha_{\rm 0}$ | $\nu_{\rm chat}$ | $\gamma$ | $C_{\rm w}$
---|---|---|---|---|---|---|---|---|---|---|---
|  | ($\mu\;$mag) |  |  | ($\mu\;$mag) |  |  | ($\mu\;$mag) |  |  | ($\mu\;$mag)
ALS 15218 | 10 - 11 | ${45.80}_{-3.16}^{+3.35}$ | ${1.35}_{-0.11}^{+0.12}$ | ${2.11}_{-0.11}^{+0.12}$ | ${9.84}_{-0.02}^{+0.02}$ | HD 127381 | 11 | ${114.22}_{-5.55}^{+5.87}$ | ${3.24}_{-0.16}^{+0.17}$ | ${1.77}_{-0.03}^{+0.03}$ | ${2.18}_{-0.01}^{+0.01}$
ALS 15218 | 36 | ${62.76}_{-6.71}^{+8.26}$ | ${1.13}_{-0.12}^{+0.14}$ | ${3.45}_{-0.34}^{+0.43}$ | ${20.17}_{-0.06}^{+0.07}$ | HD 127381 | 38 | ${86.25}_{-3.23}^{+3.40}$ | ${5.39}_{-0.20}^{+0.19}$ | ${2.58}_{-0.05}^{+0.05}$ | ${2.45}_{-0.01}^{+0.01}$
ALS 3694 | 12 | ${520.15}_{-82.72}^{+130.37}$ | ${0.31}_{-0.07}^{+0.07}$ | ${1.52}_{-0.07}^{+0.08}$ | ${26.08}_{-0.09}^{+0.10}$ | HD 127453 | 11 - 12 | ${112.81}_{-15.08}^{+20.59}$ | ${0.16}_{-0.03}^{+0.04}$ | ${0.98}_{-0.03}^{+0.03}$ | ${4.37}_{-0.02}^{+0.02}$
ALS 3694 | 39 | ${202.62}_{-22.18}^{+27.70}$ | ${0.81}_{-0.12}^{+0.12}$ | ${1.65}_{-0.09}^{+0.10}$ | ${18.06}_{-0.06}^{+0.06}$ | HD 127575 | 11 - 12 | ${84.77}_{-6.57}^{+6.33}$ | ${0.70}_{-0.06}^{+0.07}$ | ${1.43}_{-0.04}^{+0.04}$ | ${5.05}_{-0.02}^{+0.01}$
CD-59 3239 | 10 - 11 | ${295.17}_{-20.65}^{+22.82}$ | ${0.88}_{-0.07}^{+0.07}$ | ${1.82}_{-0.06}^{+0.06}$ | ${24.56}_{-0.06}^{+0.06}$ | HD $128775$ | 11 | ${74.36}_{-9.29}^{+12.05}$ | ${0.60}_{-0.13}^{+0.14}$ | ${1.07}_{-0.04}^{+0.04}$ | ${5.77}_{-0.04}^{+0.03}$
CD-59 3239 | 36 - 37 | ${107.13}_{-6.55}^{+7.33}$ | ${1.61}_{-0.11}^{+0.12}$ | ${2.61}_{-0.16}^{+0.18}$ | ${21.54}_{-0.05}^{+0.05}$ | HD 12932 | 3 | ${17.17}_{-3.22}^{+3.95}$ | ${1.18}_{-0.24}^{+0.32}$ | ${2.05}_{-0.34}^{+0.52}$ | ${16.21}_{-0.07}^{+0.06}$
CPD-28 2561 | 34 | ${948.91}_{-135.20}^{+155.43}$ | ${0.30}_{-0.04}^{+0.05}$ | ${1.62}_{-0.05}^{+0.06}$ | ${21.34}_{-0.08}^{+0.08}$ | HD 12932 | 30 | ${52.11}_{-7.77}^{+10.55}$ | ${0.58}_{-0.10}^{+0.09}$ | ${3.68}_{-1.11}^{+1.64}$ | ${15.40}_{-0.05}^{+0.05}$
CPD-62 2124 | 10 - 11 | ${243.83}_{-17.35}^{+19.21}$ | ${0.80}_{-0.07}^{+0.07}$ | ${1.53}_{-0.04}^{+0.04}$ | ${15.55}_{-0.04}^{+0.04}$ | HD 129899 | 12 | ${25.58}_{-3.89}^{+5.40}$ | ${0.43}_{-0.12}^{+0.14}$ | ${1.09}_{-0.07}^{+0.09}$ | ${4.41}_{-0.02}^{+0.02}$
CPD-62 2124 | 37 - 38 | ${245.56}_{-21.23}^{+24.68}$ | ${0.54}_{-0.06}^{+0.06}$ | ${1.45}_{-0.04}^{+0.05}$ | ${13.35}_{-0.04}^{+0.04}$ | HD 130807 | 11 | ${310.59}_{-27.16}^{+29.37}$ | ${0.84}_{-0.07}^{+0.07}$ | ${1.76}_{-0.04}^{+0.04}$ | ${4.92}_{-0.02}^{+0.02}$
HD 101412 | 37 - 38 | ${64.08}_{-4.78}^{+6.09}$ | ${0.79}_{-0.08}^{+0.08}$ | ${1.71}_{-0.07}^{+0.08}$ | ${7.53}_{-0.02}^{+0.02}$ | HD 130807 | 38 | ${270.44}_{-21.20}^{+22.70}$ | ${1.00}_{-0.06}^{+0.07}$ | ${2.06}_{-0.04}^{+0.04}$ | ${2.30}_{-0.01}^{+0.01}$
HD $105382$ | 10 | ${473.411}_{-32.79}^{+38.40}$ | ${0.61}_{-0.09}^{+0.10}$ | ${1.22}_{-0.02}^{+0.02}$ | ${3.51}_{-0.02}^{+0.03}$ | HD 136504 | 38 | ${109.04}_{-5.54}^{+5.87}$ | ${2.73}_{-0.12}^{+0.12}$ | ${2.28}_{-0.04}^{+0.04}$ | ${1.70}_{-0.01}^{+0.01}$
HD $105382$ | 37 | ${95.67}_{-6.61}^{+7.22}$ | ${0.73}_{-0.04}^{+0.05}$ | ${1.79}_{-0.06}^{+0.06}$ | ${1.57}_{-0.01}^{+0.01}$ | HD 136933 | 38 | ${5.28}_{-0.51}^{+0.61}$ | ${2.62}_{-0.41}^{+0.43}$ | ${1.53}_{-0.11}^{+0.13}$ | ${2.19}_{-0.01}^{+0.01}$
HD 105770 | 11 - 13 | ${71.74}_{-11.38}^{+14.86}$ | ${0.09}_{-0.03}^{+0.03}$ | ${0.77}_{-0.02}^{+0.02}$ | ${3.66}_{-0.02}^{+0.02}$ | HD 138758 | 12 | ${58.47}_{-8.14}^{+9.25}$ | ${0.58}_{-0.12}^{+0.16}$ | ${1.13}_{-0.05}^{+0.07}$ | ${7.39}_{-0.04}^{+0.04}$
HD 108 | 17 - 18 | ${390.77}_{-30.39}^{+33.72}$ | ${0.57}_{-0.05}^{+0.05}$ | ${1.28}_{-0.02}^{+0.02}$ | ${5.07}_{-0.02}^{+0.02}$ | HD 146555 | 39 | ${683.85}_{-112.35}^{+140.65}$ | ${0.24}_{-0.06}^{+0.08}$ | ${0.95}_{-0.04}^{+0.04}$ | ${32.49}_{-0.24}^{+0.22}$
HD 10840 | 1 - 2 | ${6.91}_{-0.63}^{+0.75}$ | ${1.14}_{-0.19}^{+0.21}$ | ${1.11}_{-0.05}^{+0.06}$ | ${2.25}_{-0.01}^{+0.01}$ | HD 149277 | 12 | ${921.01}_{-155.22}^{+212.71}$ | ${0.20}_{-0.04}^{+0.05}$ | ${1.23}_{-0.03}^{+0.04}$ | ${14.11}_{-0.07}^{+0.07}$
HD 115226 | 11 - 12 | ${47.96}_{-4.49}^{+5.30}$ | ${0.58}_{-0.08}^{+0.09}$ | ${1.23}_{-0.04}^{+0.05}$ | ${5.73}_{-0.02}^{+0.02}$ | HD 149277 | 39 | ${593.11}_{-90.88}^{+120.29}$ | ${0.24}_{-0.05}^{+0.05}$ | ${1.22}_{-0.03}^{+0.04}$ | ${10.63}_{-0.05}^{+0.05}$
HD 115226 | 38 - 39 | ${91.59}_{-9.34}^{+12.72}$ | ${0.35}_{-0.06}^{+0.06}$ | ${1.10}_{-0.03}^{+0.04}$ | ${5.67}_{-0.02}^{+0.02}$ | HD 149438 | 12 | ${334.07}_{-38.59}^{+49.14}$ | ${0.49}_{-0.08}^{+0.08}$ | ${1.22}_{-0.04}^{+0.03}$ | ${14.80}_{-0.07}^{+0.07}$
HD 115440 | 11 - 12 | ${69.41}_{-12.59}^{+19.23}$ | ${0.25}_{-0.07}^{+0.08}$ | ${1.19}_{-0.05}^{+0.06}$ | ${5.04}_{-0.02}^{+0.02}$ | HD 149438 | 39 | ${8.71}_{-0.57}^{+0.68}$ | ${2.11}_{-0.16}^{+0.16}$ | ${2.30}_{-0.13}^{+0.14}$ | ${1.42}_{-0.01}^{+0.00}$
HD 116890 | 11 - 12 | ${60.17}_{-5.98}^{+7.91}$ | ${0.37}_{-0.06}^{+0.06}$ | ${1.28}_{-0.04}^{+0.05}$ | ${3.27}_{-0.01}^{+0.01}$ | HD 149764 | 39 | ${265.65}_{-30.82}^{+38.91}$ | ${0.56}_{-0.10}^{+0.09}$ | ${1.22}_{-0.04}^{+0.03}$ | ${7.92}_{-0.04}^{+0.04}$
HD 117025 | 11 | ${70.38}_{-7.69}^{+9.05}$ | ${0.72}_{-0.10}^{+0.11}$ | ${1.54}_{-0.06}^{+0.07}$ | ${4.36}_{-0.01}^{+0.01}$ | HD 149822 | 25 | ${74.46}_{-20.72}^{+20.23}$ | ${0.15}_{-0.06}^{+0.14}$ | ${0.77}_{-0.04}^{+0.06}$ | ${4.87}_{-0.05}^{+0.07}$
HD 118913 | 11 - 12 | ${54.60}_{-4.78}^{+5.32}$ | ${0.68}_{-0.08}^{+0.10}$ | ${1.22}_{-0.04}^{+0.04}$ | ${4.92}_{-0.02}^{+0.02}$ | HD 149822 | 52 | ${39.05}_{-3.61}^{+4.19}$ | ${1.42}_{-0.17}^{+0.17}$ | ${1.82}_{-0.10}^{+0.10}$ | ${3.95}_{-0.01}^{+0.01}$
HD 119308 | 11 | ${55.83}_{-5.73}^{+7.00}$ | ${1.14}_{-0.17}^{+0.18}$ | ${1.43}_{-0.08}^{+0.08}$ | ${7.52}_{-0.03}^{+0.03}$ | HD 150562 | 12 | ${71.36}_{-11.20}^{+16.45}$ | ${0.63}_{-0.20}^{+0.24}$ | ${0.88}_{-0.06}^{+0.06}$ | ${16.22}_{-0.14}^{+0.14}$
HD 121743 | 11 | ${121.32}_{-7.31}^{+7.83}$ | ${1.88}_{-0.13}^{+0.14}$ | ${1.51}_{-0.02}^{+0.02}$ | ${2.01}_{-0.01}^{+0.01}$ | HD 150562 | 39 | ${95.96}_{-11.57}^{+15.96}$ | ${0.78}_{-0.17}^{+0.16}$ | ${1.24}_{-0.07}^{+0.08}$ | ${13.45}_{-0.07}^{+0.06}$
HD 121743 | 38 | ${84.79}_{-4.35}^{+4.37}$ | ${3.00}_{-0.14}^{+0.16}$ | ${1.89}_{-0.03}^{+0.03}$ | ${1.72}_{-0.01}^{+0.01}$ | HD 154708 | 12 | ${192.66}_{-30.73}^{+43.30}$ | ${0.20}_{-0.06}^{+0.07}$ | ${0.93}_{-0.04}^{+0.04}$ | ${10.69}_{-0.07}^{+0.06}$
HD 122983 | 38 | ${275.42}_{-39.12}^{+46.60}$ | ${0.34}_{-0.07}^{+0.08}$ | ${1.04}_{-0.03}^{+0.04}$ | ${13.36}_{-0.07}^{+0.08}$ | HD 154708 | 39 | ${200.04}_{-34.65}^{+42.06}$ | ${0.23}_{-0.06}^{+0.08}$ | ${0.97}_{-0.03}^{+0.04}$ | ${10.26}_{-0.06}^{+0.06}$
HD 125823 | 11 | ${386.76}_{-27.39}^{+29.48}$ | ${1.28}_{-0.08}^{+0.08}$ | ${1.82}_{-0.03}^{+0.03}$ | ${3.39}_{-0.01}^{+0.01}$ | HD 156324 | 12 | ${157.58}_{-19.68}^{+24.18}$ | ${0.62}_{-0.12}^{+0.14}$ | ${1.15}_{-0.05}^{+0.05}$ | ${14.95}_{-0.08}^{+0.07}$
HD 125823 | 38 | ${227.20}_{-11.39}^{+12.49}$ | ${2.20}_{-0.09}^{+0.09}$ | ${2.41}_{-0.04}^{+0.04}$ | ${2.48}_{-0.01}^{+0.01}$ | HD 156324 | 39 | ${151.88}_{-15.33}^{+18.55}$ | ${0.78}_{-0.10}^{+0.10}$ | ${1.76}_{-0.09}^{+0.09}$ | ${11.53}_{-0.04}^{+0.04}$
HD 156424 | 12 | ${295.24}_{-53.82}^{+76.45}$ | ${0.21}_{-0.07}^{+0.07}$ | ${0.93}_{-0.04}^{+0.04}$ | ${12.91}_{-0.09}^{+0.10}$ | HD 218495 | 27 - 28 | ${28.57}_{-2.88}^{+4.24}$ | ${1.23}_{-0.21}^{+0.17}$ | ${2.17}_{-0.23}^{+0.23}$ | ${8.21}_{-0.01}^{+0.02}$
HD 156424 | 39 | ${218.65}_{-42.91}^{+56.77}$ | ${0.14}_{-0.05}^{+0.07}$ | ${0.81}_{-0.03}^{+0.03}$ | ${10.47}_{-0.09}^{+0.09}$ | HD $23478$ | 42 - 44 | ${65.96}_{-7.69}^{+9.41}$ | ${0.18}_{-0.03}^{+0.04}$ | ${0.90}_{-0.02}^{+0.02}$ | ${2.44}_{-0.01}^{+0.01}$
HD 157751 | 12 | ${152.40}_{-19.09}^{+23.34}$ | ${0.48}_{-0.10}^{+0.11}$ | ${1.04}_{-0.04}^{+0.04}$ | ${8.38}_{-0.06}^{+0.05}$ | HD 24188 | 12 - 13 | ${18.06}_{-2.48}^{+3.14}$ | ${0.31}_{-0.08}^{+0.10}$ | ${0.85}_{-0.04}^{+0.04}$ | ${3.07}_{-0.01}^{+0.01}$
HD 161459 | 13 | ${174.10}_{-26.92}^{+37.96}$ | ${0.39}_{-0.09}^{+0.11}$ | ${1.09}_{-0.05}^{+0.06}$ | ${18.52}_{-0.09}^{+0.09}$ | HD 24188 | 36 - 37 | ${84.80}_{-11.10}^{+14.24}$ | ${0.16}_{-0.03}^{+0.03}$ | ${1.29}_{-0.04}^{+0.04}$ | ${2.51}_{-0.01}^{+0.01}$
HD 161459 | 39 | ${261.43}_{-45.61}^{+63.56}$ | ${0.28}_{-0.07}^{+0.09}$ | ${1.06}_{-0.04}^{+0.05}$ | ${17.09}_{-0.09}^{+0.09}$ | HD $24188$ | 6 - 7 | ${36.53}_{-3.62}^{+4.04}$ | ${0.51}_{-0.07}^{+0.08}$ | ${1.23}_{-0.04}^{+0.04}$ | ${2.72}_{-0.01}^{+0.01}$
HD 166473 | 13 | ${147.25}_{-42.07}^{+76.56}$ | ${0.06}_{-0.03}^{+0.06}$ | ${0.69}_{-0.03}^{+0.04}$ | ${7.52}_{-0.10}^{+0.08}$ | HD 25558 | 32 | ${509.66}_{-40.68}^{+45.85}$ | ${0.84}_{-0.06}^{+0.06}$ | ${1.90}_{-0.03}^{+0.03}$ | ${3.61}_{-0.01}^{+0.01}$
HD $172690$ | 12 - 13 | ${206.16}_{-19.18}^{+23.94}$ | ${0.33}_{-0.04}^{+0.04}$ | ${1.34}_{-0.03}^{+0.03}$ | ${4.85}_{-0.01}^{+0.01}$ | HD 25558 | 5 | ${839.96}_{-92.28}^{+100.57}$ | ${0.45}_{-0.04}^{+0.05}$ | ${1.58}_{-0.02}^{+0.02}$ | ${3.74}_{-0.02}^{+0.02}$
HD $175362$ | 13 | ${149.36}_{-22.39}^{+29.97}$ | ${0.28}_{-0.06}^{+0.07}$ | ${1.01}_{-0.03}^{+0.02}$ | ${3.72}_{-0.03}^{+0.03}$ | HD 306795 | 37 - 38 | ${267.72}_{-21.98}^{+26.17}$ | ${0.64}_{-0.07}^{+0.07}$ | ${1.57}_{-0.05}^{+0.06}$ | ${20.80}_{-0.05}^{+0.05}$
HD 176196 | 13 | ${49.35}_{-8.24}^{+11.59}$ | ${0.28}_{-0.08}^{+0.10}$ | ${1.00}_{-0.06}^{+0.07}$ | ${5.31}_{-0.03}^{+0.03}$ | HD 3360 | 17 | ${106.62}_{-5.74}^{+6.38}$ | ${2.72}_{-0.16}^{+0.17}$ | ${1.67}_{-0.03}^{+0.03}$ | ${2.40}_{-0.01}^{+0.01}$
HD $176582$ | 40 - 41 | ${243.64}_{-34.52}^{+46.18}$ | ${0.12}_{-0.02}^{+0.01}$ | ${1.36}_{-0.05}^{+0.07}$ | ${3.12}_{-0.01}^{+0.01}$ | HD 345439 | 54 | ${631.71}_{-131.74}^{+185.84}$ | ${0.13}_{-0.05}^{+0.06}$ | ${0.83}_{-0.03}^{+0.03}$ | ${28.82}_{-0.22}^{+0.21}$
HD $176582$ | 53 - 54 | ${212.71}_{-35.60}^{+40.10}$ | ${0.13}_{-0.01}^{+0.02}$ | ${1.37}_{-0.08}^{+0.09}$ | ${3.48}_{-0.01}^{+0.01}$ | HD 34797 | 32 | ${252.18}_{-18.48}^{+21.02}$ | ${1.19}_{-0.07}^{+0.08}$ | ${2.05}_{-0.04}^{+0.05}$ | ${4.06}_{-0.01}^{+0.01}$
HD 184927 | 40 - 41 | ${26.67}_{-2.06}^{+2.19}$ | ${0.90}_{-0.09}^{+0.09}$ | ${1.74}_{-0.07}^{+0.09}$ | ${3.87}_{-0.01}^{+0.01}$ | HD 34797 | 37 | ${238.71}_{-16.17}^{+18.03}$ | ${1.24}_{-0.07}^{+0.07}$ | ${2.14}_{-0.05}^{+0.05}$ | ${4.05}_{-0.01}^{+0.01}$
HD 187474 | 13 | ${102.49}_{-44.39}^{+46.02}$ | ${0.05}_{-0.03}^{+0.11}$ | ${0.69}_{-0.03}^{+0.04}$ | ${3.45}_{-0.03}^{+0.05}$ | HD 35298 | 32 | ${119.13}_{-10.82}^{+12.93}$ | ${1.11}_{-0.12}^{+0.13}$ | ${1.69}_{-0.06}^{+0.07}$ | ${6.72}_{-0.03}^{+0.03}$
HD 187474 | 27 | ${3.94}_{-0.49}^{+0.64}$ | ${0.83}_{-0.10}^{+0.09}$ | ${4.83}_{-1.34}^{+2.21}$ | ${2.14}_{-0.01}^{+0.01}$ | HD 35298 | 6 | ${38.62}_{-2.81}^{+3.25}$ | ${2.73}_{-0.26}^{+0.26}$ | ${2.19}_{-0.14}^{+0.15}$ | ${6.31}_{-0.02}^{+0.02}$
HD $189775$ | 16 | ${7.46}_{-0.37}^{+0.46}$ | ${8.86}_{-0.9}^{+0.78}$ | ${1.62}_{-0.04}^{+0.04}$ | ${4.50}_{-0.02}^{+0.02}$ | HD 35502 | 32 | ${138.09}_{-18.61}^{+25.19}$ | ${0.33}_{-0.07}^{+0.07}$ | ${1.13}_{-0.03}^{+0.03}$ | ${4.93}_{-0.02}^{+0.02}$
HD $189775$ | 41 | ${145.915}_{-16.50}^{+19.95}$ | ${0.12}_{-0.01}^{+0.01}$ | ${1.52}_{-0.23}^{+0.24}$ | ${4.55}_{-0.01}^{+0.01}$ | HD 35502 | 6 | ${242.10}_{-53.85}^{+91.39}$ | ${0.12}_{-0.04}^{+0.05}$ | ${1.02}_{-0.03}^{+0.03}$ | ${5.14}_{-0.03}^{+0.03}$
HD $189775$ | 56 | ${115.202}_{-22.89}^{+32.14}$ | ${0.12}_{-0.03}^{+0.03}$ | ${3.56}_{-0.24}^{+0.27}$ | ${2.88}_{-0.01}^{+0.01}$ | HD 35912 | 32 | ${587.49}_{-60.48}^{+68.52}$ | ${0.58}_{-0.06}^{+0.07}$ | ${1.43}_{-0.02}^{+0.02}$ | ${5.07}_{-0.02}^{+0.03}$
HD 190290 | 27 | ${66.11}_{-7.75}^{+9.29}$ | ${0.81}_{-0.11}^{+0.12}$ | ${2.34}_{-0.20}^{+0.23}$ | ${12.17}_{-0.04}^{+0.04}$ | HD 35912 | 6 | ${258.42}_{-19.31}^{+22.00}$ | ${1.30}_{-0.10}^{+0.10}$ | ${1.73}_{-0.03}^{+0.03}$ | ${4.08}_{-0.02}^{+0.02}$
HD 190290 | 39 | ${70.21}_{-10.16}^{+14.70}$ | ${0.54}_{-0.12}^{+0.12}$ | ${1.58}_{-0.12}^{+0.15}$ | ${12.47}_{-0.05}^{+0.04}$ | HD 36485 | 32 | ${196.60}_{-10.88}^{+11.72}$ | ${2.13}_{-0.09}^{+0.10}$ | ${3.12}_{-0.10}^{+0.10}$ | ${7.16}_{-0.02}^{+0.02}$
HD 191612 | 14 - 15 | ${219.82}_{-12.01}^{+13.16}$ | ${1.41}_{-0.10}^{+0.10}$ | ${1.40}_{-0.02}^{+0.02}$ | ${6.52}_{-0.03}^{+0.03}$ | HD 36485 | 6 | ${469.22}_{-34.26}^{+39.16}$ | ${1.35}_{-0.09}^{+0.09}$ | ${2.04}_{-0.04}^{+0.04}$ | ${6.31}_{-0.03}^{+0.03}$
HD 19918 | 12 - 13 | ${74.73}_{-9.73}^{+12.49}$ | ${0.19}_{-0.04}^{+0.05}$ | ${1.05}_{-0.05}^{+0.05}$ | ${7.82}_{-0.03}^{+0.03}$ | HD $36526$ | 32 | ${35.093}_{-2.11}^{+2.17}$ | ${2.40}_{-0.13}^{+0.12}$ | ${1.59}_{-0.05}^{+0.05}$ | ${7.22}_{-0.03}^{+0.03}$
HD 19918 | 27 - 28 | ${135.09}_{-20.17}^{+26.39}$ | ${0.19}_{-0.04}^{+0.04}$ | ${1.59}_{-0.08}^{+0.09}$ | ${7.27}_{-0.02}^{+0.02}$ | HD $36526$ | 6 | ${32.46}_{-2.32}^{+2.56}$ | ${1.81}_{-0.12}^{+0.12}$ | ${1.54}_{-0.06}^{+0.06}$ | ${7.59}_{-0.03}^{+0.03}$
HD 200775 | 24 - 25 | ${323.94}_{-7.97}^{+8.53}$ | ${5.36}_{-0.11}^{+0.11}$ | ${2.48}_{-0.03}^{+0.03}$ | ${6.22}_{-0.02}^{+0.02}$ | HD 36982 | 32 | ${88.53}_{-8.67}^{+10.25}$ | ${0.98}_{-0.13}^{+0.13}$ | ${1.46}_{-0.05}^{+0.05}$ | ${6.62}_{-0.02}^{+0.03}$
HD 201018 | 1 | ${224.77}_{-32.90}^{+48.64}$ | ${0.34}_{-0.09}^{+0.09}$ | ${0.97}_{-0.03}^{+0.03}$ | ${8.36}_{-0.05}^{+0.06}$ | HD $37017$ | 32 | ${73.08}_{-7.23}^{+7.87}$ | ${1.20}_{-0.16}^{+0.18}$ | ${1.33}_{-0.04}^{+0.04}$ | ${4.27}_{-0.02}^{+0.02}$
HD 203932 | 1 | ${197.86}_{-43.58}^{+70.31}$ | ${0.14}_{-0.05}^{+0.07}$ | ${0.95}_{-0.04}^{+0.04}$ | ${7.79}_{-0.05}^{+0.04}$ | HD $37017$ | 6 | ${14.71}_{-1.00}^{+1.15}$ | ${2.06}_{-0.20}^{+0.20}$ | ${1.90}_{-0.15}^{+0.17}$ | ${4.66}_{-0.02}^{+0.02}$
HD 203932 | 28 | ${68.52}_{-8.69}^{+10.27}$ | ${0.77}_{-0.11}^{+0.12}$ | ${2.17}_{-0.20}^{+0.23}$ | ${9.41}_{-0.03}^{+0.03}$ | HD 37022 | 32 | ${332.46}_{-25.45}^{+31.89}$ | ${1.04}_{-0.09}^{+0.09}$ | ${1.47}_{-0.02}^{+0.03}$ | ${4.74}_{-0.02}^{+0.02}$
HD $205021$ | 16 - 18 | ${123.75}_{-3.07}^{+3.11}$ | ${4.28}_{-0.10}^{+0.11}$ | ${2.06}_{-0.02}^{+0.02}$ | ${3.35}_{-0.01}^{+0.01}$ | HD 37022 | 6 | ${333.26}_{-28.51}^{+34.96}$ | ${0.88}_{-0.06}^{+0.06}$ | ${2.26}_{-0.06}^{+0.06}$ | ${3.34}_{-0.01}^{+0.01}$
HD $205021$ | 24 - 25 | ${103.70}_{-2.69}^{+2.99}$ | ${5.18}_{-0.10}^{+0.10}$ | ${3.36}_{-0.06}^{+0.06}$ | ${6.61}_{-0.01}^{+0.01}$ | HD 37058 | 32 | ${450.78}_{-47.60}^{+58.22}$ | ${0.60}_{-0.08}^{+0.08}$ | ${1.37}_{-0.03}^{+0.03}$ | ${10.15}_{-0.05}^{+0.05}$
HD 212385 | 1 | ${136.83}_{-23.70}^{+28.17}$ | ${0.30}_{-0.08}^{+0.12}$ | ${0.87}_{-0.02}^{+0.03}$ | ${4.44}_{-0.04}^{+0.04}$ | HD $37479$ | 6 | ${116.88}_{-8.26}^{+9.13}$ | ${2.47}_{-0.15}^{+0.15}$ | ${4.73}_{-0.66}^{+0.79}$ | ${36.19}_{-0.13}^{+0.13}$
HD 212385 | 28 | ${53.92}_{-7.04}^{+9.88}$ | ${0.49}_{-0.10}^{+0.10}$ | ${1.37}_{-0.07}^{+0.07}$ | ${4.51}_{-0.02}^{+0.02}$ | HD $37479$ | 32 | ${485.00}_{-35.63}^{+39.43}$ | ${2.43}_{-0.17}^{+0.18}$ | ${2.68}_{-0.11}^{+0.11}$ | ${85.59}_{-0.29}^{+0.28}$
HD 37633 | 6 | ${84.55}_{-9.49}^{+11.23}$ | ${1.03}_{-0.15}^{+0.16}$ | ${1.84}_{-0.12}^{+0.13}$ | ${9.71}_{-0.04}^{+0.04}$ | HD 65712 | 1 | ${84.14}_{-9.32}^{+11.40}$ | ${0.87}_{-0.14}^{+0.14}$ | ${1.51}_{-0.07}^{+0.07}$ | ${10.58}_{-0.03}^{+0.04}$
HD 37742 | 6 | ${3405.39}_{-383.38}^{+469.66}$ | ${0.46}_{-0.05}^{+0.05}$ | ${1.53}_{-0.02}^{+0.02}$ | ${9.96}_{-0.05}^{+0.05}$ | HD 65712 | 4 | ${202.06}_{-22.19}^{+28.10}$ | ${0.80}_{-0.12}^{+0.12}$ | ${1.55}_{-0.06}^{+0.06}$ | ${11.76}_{-0.04}^{+0.05}$
HD 43317 | 33 | ${77.00}_{-4.06}^{+4.52}$ | ${2.98}_{-0.15}^{+0.15}$ | ${2.54}_{-0.09}^{+0.10}$ | ${5.33}_{-0.02}^{+0.02}$ | HD 65712 | 7 - 8 | ${272.54}_{-16.59}^{+17.43}$ | ${1.11}_{-0.07}^{+0.08}$ | ${1.60}_{-0.03}^{+0.03}$ | ${8.15}_{-0.03}^{+0.02}$
HD 43317 | 6 | ${72.25}_{-4.84}^{+4.93}$ | ${3.20}_{-0.24}^{+0.20}$ | ${2.55}_{-0.15}^{+0.13}$ | ${6.45}_{-0.03}^{+0.03}$ | HD 65712 | 10 - 11 | ${30.70}_{-3.09}^{+3.67}$ | ${0.74}_{-0.11}^{+0.12}$ | ${1.37}_{-0.07}^{+0.07}$ | ${8.14}_{-0.02}^{+0.02}$
HD 44743 | 33 | ${63.54}_{-2.19}^{+2.23}$ | ${5.69}_{-0.15}^{+0.14}$ | ${3.57}_{-0.10}^{+0.10}$ | ${2.19}_{-0.01}^{+0.01}$ | HD 65712 | 27 - 28 | ${131.41}_{-9.32}^{+10.75}$ | ${0.96}_{-0.08}^{+0.09}$ | ${1.78}_{-0.05}^{+0.06}$ | ${8.07}_{-0.02}^{+0.02}$
HD 44743 | 6 | ${91.75}_{-5.53}^{+6.01}$ | ${3.69}_{-0.25}^{+0.26}$ | ${2.44}_{-0.12}^{+0.12}$ | ${7.12}_{-0.03}^{+0.03}$ | HD 65712 | 34 - 38 | ${124.55}_{-5.66}^{+6.18}$ | ${0.80}_{-0.04}^{+0.04}$ | ${1.60}_{-0.02}^{+0.03}$ | ${5.10}_{-0.01}^{+0.01}$
HD 45583 | 6 | ${27.20}_{-3.96}^{+5.68}$ | ${0.86}_{-0.23}^{+0.27}$ | ${1.09}_{-0.07}^{+0.07}$ | ${6.59}_{-0.04}^{+0.04}$ | HD 65987 | 1 | ${145.66}_{-15.70}^{+15.25}$ | ${0.89}_{-0.11}^{+0.12}$ | ${1.49}_{-0.04}^{+0.05}$ | ${8.32}_{-0.03}^{+0.03}$
HD $46328$ | 33 | ${26.14}_{-1.32}^{+1.52}$ | ${3.50}_{-0.22}^{+0.21}$ | ${1.83}_{-0.04}^{+0.04}$ | ${1.39}_{-0.01}^{+0.01}$ | HD 65987 | 4 | ${417.27}_{-49.46}^{+60.34}$ | ${0.57}_{-0.09}^{+0.08}$ | ${1.23}_{-0.02}^{+0.02}$ | ${7.03}_{-0.04}^{+0.04}$
HD $46328$ | 6 | ${49.65}_{-3.01}^{+3.33}$ | ${3.50}_{-0.27}^{+0.28}$ | ${1.61}_{-0.04}^{+0.04}$ | ${2.88}_{-0.02}^{+0.01}$ | HD 65987 | 7 | ${54.64}_{-6.44}^{+7.54}$ | ${0.94}_{-0.15}^{+0.17}$ | ${1.43}_{-0.07}^{+0.08}$ | ${7.45}_{-0.03}^{+0.03}$
HD 47129 | 6 | ${3553.01}_{-328.89}^{+389.57}$ | ${0.75}_{-0.06}^{+0.06}$ | ${1.75}_{-0.02}^{+0.02}$ | ${12.10}_{-0.05}^{+0.06}$ | HD 65987 | 9 - 11 | ${48.90}_{-4.05}^{+4.37}$ | ${0.54}_{-0.06}^{+0.07}$ | ${1.25}_{-0.03}^{+0.04}$ | ${4.41}_{-0.01}^{+0.01}$
HD 47777 | 33 | ${62.53}_{-8.74}^{+12.66}$ | ${0.62}_{-0.15}^{+0.17}$ | ${1.13}_{-0.06}^{+0.06}$ | ${6.69}_{-0.04}^{+0.04}$ | HD 65987 | 34 - 37 | ${79.06}_{-4.70}^{+5.12}$ | ${0.63}_{-0.04}^{+0.05}$ | ${1.48}_{-0.03}^{+0.03}$ | ${3.62}_{-0.01}^{+0.01}$
HD 47777 | 6 | ${29.23}_{-3.40}^{+4.36}$ | ${1.57}_{-0.34}^{+0.36}$ | ${1.13}_{-0.07}^{+0.08}$ | ${7.24}_{-0.05}^{+0.04}$ | HD 66295 | 4 | ${333.98}_{-31.11}^{+37.51}$ | ${0.86}_{-0.09}^{+0.09}$ | ${1.75}_{-0.06}^{+0.06}$ | ${14.92}_{-0.06}^{+0.05}$
HD 49299 | 33 | ${102.40}_{-16.07}^{+20.27}$ | ${0.50}_{-0.11}^{+0.13}$ | ${1.49}_{-0.12}^{+0.13}$ | ${19.14}_{-0.07}^{+0.07}$ | HD 66295 | 7 | ${113.58}_{-11.45}^{+14.18}$ | ${1.05}_{-0.14}^{+0.14}$ | ${1.70}_{-0.09}^{+0.10}$ | ${11.97}_{-0.05}^{+0.04}$
HD 52089 | 33 - 34 | ${284.71}_{-13.85}^{+14.73}$ | ${1.57}_{-0.08}^{+0.08}$ | ${1.70}_{-0.02}^{+0.02}$ | ${3.46}_{-0.01}^{+0.01}$ | HD 66295 | 9 - 10 | ${65.89}_{-5.92}^{+7.04}$ | ${0.69}_{-0.09}^{+0.10}$ | ${1.37}_{-0.05}^{+0.06}$ | ${8.24}_{-0.02}^{+0.02}$
HD 52089 | 6 - 7 | ${304.99}_{-16.69}^{+29.75}$ | ${1.70}_{-0.11}^{+0.09}$ | ${1.90}_{-0.02}^{+0.02}$ | ${2.38}_{-0.01}^{+0.01}$ | HD 66318 | 34 - 37 | ${71.15}_{-6.87}^{+8.24}$ | ${1.08}_{-0.13}^{+0.13}$ | ${1.71}_{-0.08}^{+0.09}$ | ${7.91}_{-0.03}^{+0.03}$
HD 53921 | 4 - 13 | ${20.85}_{-1.27}^{+1.27}$ | ${0.24}_{-0.02}^{+0.02}$ | ${1.24}_{-0.02}^{+0.02}$ | ${0.82}_{-0.00}^{+0.00}$ | HD 66318 | 35 - 36 | ${116.46}_{-14.35}^{+19.14}$ | ${0.63}_{-0.10}^{+0.10}$ | ${1.55}_{-0.07}^{+0.07}$ | ${7.91}_{-0.03}^{+0.03}$
HD 53921 | 30 - 37 | ${12.14}_{-0.65}^{+0.76}$ | ${0.41}_{-0.03}^{+0.03}$ | ${1.27}_{-0.02}^{+0.02}$ | ${0.94}_{-0.00}^{+0.00}$ | HD 66318 | 7 - 9 | ${149.87}_{-8.98}^{+9.72}$ | ${0.80}_{-0.05}^{+0.05}$ | ${1.55}_{-0.03}^{+0.03}$ | ${5.06}_{-0.01}^{+0.01}$
HD 54879 | 33 | ${33.42}_{-3.56}^{+4.34}$ | ${0.94}_{-0.11}^{+0.12}$ | ${2.23}_{-0.18}^{+0.20}$ | ${4.98}_{-0.02}^{+0.02}$ | HD 66318 | 8 - 11 | ${68.11}_{-3.35}^{+3.41}$ | ${1.10}_{-0.06}^{+0.06}$ | ${1.78}_{-0.03}^{+0.04}$ | ${5.25}_{-0.01}^{+0.01}$
HD 54879 | 7 | ${60.12}_{-6.47}^{+8.03}$ | ${0.86}_{-0.11}^{+0.10}$ | ${2.24}_{-0.16}^{+0.17}$ | ${5.80}_{-0.02}^{+0.02}$ | HD 66522 | 34 - 36 | ${34.23}_{-3.06}^{+3.74}$ | ${0.43}_{-0.07}^{+0.07}$ | ${1.07}_{-0.03}^{+0.03}$ | ${3.72}_{-0.01}^{+0.01}$
HD 55522 | 33 - 34 | ${62.97}_{-2.65}^{+2.76}$ | ${2.33}_{-0.09}^{+0.10}$ | ${2.19}_{-0.04}^{+0.05}$ | ${2.54}_{-0.01}^{+0.01}$ | HD 66522 | 7 - 9 | ${45.40}_{-3.26}^{+4.43}$ | ${0.56}_{-0.06}^{+0.05}$ | ${1.45}_{-0.04}^{+0.04}$ | ${3.48}_{-0.01}^{+0.01}$
HD 56350 | 7 - 9 | ${113.86}_{-7.78}^{+8.19}$ | ${0.61}_{-0.05}^{+0.05}$ | ${1.25}_{-0.02}^{+0.01}$ | ${2.69}_{-0.01}^{+0.01}$ | HD 66665 | 34 | ${142.57}_{-22.02}^{+25.39}$ | ${0.25}_{-0.06}^{+0.08}$ | ${0.94}_{-0.04}^{+0.04}$ | ${8.88}_{-0.06}^{+0.06}$
HD 57682 | 34 | ${177.79}_{-18.20}^{+24.94}$ | ${1.00}_{-0.17}^{+0.18}$ | ${1.13}_{-0.03}^{+0.03}$ | ${7.63}_{-0.05}^{+0.05}$ | HD 66665 | 7 | ${27.05}_{-3.80}^{+5.01}$ | ${0.97}_{-0.20}^{+0.21}$ | ${1.73}_{-0.17}^{+0.20}$ | ${7.43}_{-0.03}^{+0.03}$
HD 57682 | 7 | ${102.70}_{-6.42}^{+7.05}$ | ${2.58}_{-0.20}^{+0.21}$ | ${1.58}_{-0.04}^{+0.04}$ | ${3.94}_{-0.02}^{+0.02}$ | HD 66765 | 34 | ${80.66}_{-5.93}^{+6.82}$ | ${1.83}_{-0.18}^{+0.18}$ | ${1.55}_{-0.05}^{+0.05}$ | ${4.82}_{-0.02}^{+0.02}$
HD 58260 | 33 - 34 | ${12.55}_{-0.93}^{+1.16}$ | ${0.98}_{-0.09}^{+0.09}$ | ${2.26}_{-0.17}^{+0.18}$ | ${3.27}_{-0.01}^{+0.01}$ | HD 66765 | 7 | ${41.15}_{-2.38}^{+2.51}$ | ${3.73}_{-0.25}^{+0.28}$ | ${1.87}_{-0.06}^{+0.07}$ | ${4.59}_{-0.02}^{+0.02}$
HD 61556 | 34 | ${98.41}_{-5.34}^{+6.08}$ | ${2.61}_{-0.16}^{+0.16}$ | ${1.55}_{-0.02}^{+0.02}$ | ${2.19}_{-0.01}^{+0.01}$ | HD 66765 | 9 | ${86.43}_{-5.97}^{+6.75}$ | ${2.12}_{-0.17}^{+0.19}$ | ${1.66}_{-0.04}^{+0.05}$ | ${4.22}_{-0.02}^{+0.02}$
HD 61556 | 7 | ${15.81}_{-0.56}^{+0.54}$ | ${3.70}_{-0.10}^{+0.10}$ | ${3.32}_{-0.11}^{+0.13}$ | ${1.67}_{-0.01}^{+0.01}$ | HD 67621 | 34 | ${53.74}_{-4.65}^{+5.48}$ | ${1.56}_{-0.20}^{+0.22}$ | ${1.39}_{-0.06}^{+0.06}$ | ${4.46}_{-0.02}^{+0.02}$
HD $63401$ | 34 - 35 | ${151.30}_{-7.80}^{+8.84}$ | ${1.59}_{-0.12}^{+0.12}$ | ${1.16}_{-0.01}^{+0.01}$ | ${3.22}_{-0.02}^{+0.02}$ | HD 67621 | 7 | ${23.77}_{-0.83}^{+0.89}$ | ${6.21}_{-0.15}^{+0.14}$ | ${5.68}_{-0.40}^{+0.42}$ | ${3.97}_{-0.01}^{+0.01}$
HD $63401$ | 7 - 8 | ${24.30}_{-1.13}^{+1.20}$ | ${3.01}_{-0.18}^{+0.19}$ | ${1.83}_{-0.05}^{+0.06}$ | ${2.84}_{-0.01}^{+0.01}$ | HD 67621 | 9 | ${31.54}_{-1.78}^{+1.95}$ | ${4.05}_{-0.28}^{+0.29}$ | ${2.24}_{-0.12}^{+0.13}$ | ${4.05}_{-0.02}^{+0.02}$
HD $64740$ | 34 - 35 | ${7.02}_{-0.84}^{+0.67}$ | ${2.29}_{-0.34}^{+0.54}$ | ${1.21}_{-0.05}^{+0.07}$ | ${1.03}_{-0.01}^{+0.01}$ | HD 69067 | 7 - 8 | ${45.04}_{-3.21}^{+3.73}$ | ${1.17}_{-0.12}^{+0.12}$ | ${1.61}_{-0.06}^{+0.06}$ | ${5.63}_{-0.01}^{+0.02}$
HD $64740$ | 7 - 9 | ${16.18}_{-1.12}^{+1.28}$ | ${1.08}_{-0.12}^{+0.13}$ | ${1.15}_{-0.03}^{+0.03}$ | ${1.64}_{-0.01}^{+0.01}$ | HD 83625 | 9 - 10 | ${118.77}_{-10.79}^{+12.79}$ | ${0.50}_{-0.06}^{+0.07}$ | ${1.28}_{-0.03}^{+0.03}$ | ${4.18}_{-0.01}^{+0.01}$
HD 86199 | 9 - 10 | ${50.11}_{-3.18}^{+3.62}$ | ${1.25}_{-0.11}^{+0.11}$ | ${1.36}_{-0.03}^{+0.03}$ | ${3.65}_{-0.01}^{+0.01}$ | HD 9289 | 30 | ${99.73}_{-14.86}^{+20.03}$ | ${0.56}_{-0.14}^{+0.15}$ | ${1.35}_{-0.11}^{+0.11}$ | ${14.85}_{-0.06}^{+0.06}$
HD 87240 | 36 - 37 | ${33.47}_{-3.16}^{+3.96}$ | ${0.96}_{-0.13}^{+0.14}$ | ${1.66}_{-0.11}^{+0.12}$ | ${9.83}_{-0.02}^{+0.02}$ | HD 94660 | 36 | ${518.92}_{-115.25}^{+126.49}$ | ${0.09}_{-0.02}^{+0.04}$ | ${0.92}_{-0.02}^{+0.02}$ | ${2.91}_{-0.03}^{+0.03}$
HD 88158 | 9 - 10 | ${46.95}_{-4.33}^{+5.68}$ | ${1.07}_{-0.15}^{+0.14}$ | ${1.67}_{-0.09}^{+0.10}$ | ${5.59}_{-0.02}^{+0.02}$ | HD 94660 | 9 - 10 | ${60.63}_{-6.24}^{+7.45}$ | ${0.39}_{-0.06}^{+0.06}$ | ${1.11}_{-0.03}^{+0.03}$ | ${2.81}_{-0.01}^{+0.01}$
HD 88385 | 36 - 37 | ${18.20}_{-1.38}^{+1.44}$ | ${1.37}_{-0.13}^{+0.13}$ | ${2.46}_{-0.28}^{+0.33}$ | ${4.99}_{-0.01}^{+0.01}$ | HD 96446 | 10 - 11 | ${70.38}_{-5.76}^{+6.89}$ | ${0.59}_{-0.07}^{+0.07}$ | ${1.23}_{-0.03}^{+0.03}$ | ${4.65}_{-0.01}^{+0.01}$
HD 89103 | 9 - 10 | ${69.11}_{-23.99}^{+11.02}$ | ${0.52}_{-0.09}^{+0.41}$ | ${1.35}_{-0.05}^{+0.18}$ | ${4.63}_{-0.02}^{+0.02}$ | HD 9672 | 3 | ${8.41}_{-0.76}^{+0.88}$ | ${1.51}_{-0.14}^{+0.13}$ | ${2.90}_{-0.28}^{+0.33}$ | ${2.15}_{-0.01}^{+0.01}$
HD 92499 | 36 | ${76.89}_{-11.00}^{+13.85}$ | ${0.53}_{-0.11}^{+0.12}$ | ${1.37}_{-0.09}^{+0.13}$ | ${10.05}_{-0.04}^{+0.04}$ | HD 9672 | 30 | ${28.12}_{-4.62}^{+6.16}$ | ${0.42}_{-0.11}^{+0.13}$ | ${1.22}_{-0.08}^{+0.09}$ | ${3.58}_{-0.02}^{+0.01}$
HD 92499 | 9 - 10 | ${46.48}_{-4.30}^{+4.64}$ | ${0.64}_{-0.07}^{+0.08}$ | ${1.71}_{-0.10}^{+0.11}$ | ${6.66}_{-0.02}^{+0.02}$ | NGC 1624-2 | 19 | ${356.63}_{-66.66}^{+96.56}$ | ${0.21}_{-0.06}^{+0.07}$ | ${1.11}_{-0.05}^{+0.06}$ | ${15.86}_{-0.08}^{+0.07}$
HD 9289 | 3 | ${60.37}_{-6.13}^{+7.32}$ | ${1.31}_{-0.13}^{+0.15}$ | ${2.67}_{-0.25}^{+0.32}$ | ${11.65}_{-0.04}^{+0.04}$ |  |  |  |  |  |

Note. — The fitting parameters of SLF for the 118 magnetic hot stars. We
reported the result of the fitting parameters of SLF. The Sectors using to
derive the parameters are listed behind the identification names.

##  Appendix B Appendix B

Figure B1: The logarithmic amplitude spectra for each star in our sample. Line
styles and colours are the same as in Figure 4.  Figure B2: continued. Figure
B3: continued. Figure B4: continued. Figure B5: continued. Figure B6:
continued. Figure B7: continued. Figure B8: continued. Figure B9: continued.
Figure B10: continued. Figure B11: continued.

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