# Study of Chemically Peculiar Stars-I : High-resolution Spectroscopy and K2
Photometry of Am Stars in the Region of M44

Santosh Joshi1, Otto Trust2, E. Semenko3,4, P. E. Williams5, P. Lampens 6, P.
De Cat6, L. Vermeylen6, D. L. Holdsworth7, R. A. García8,9, S. Mathur10,11, A.
R. G. Santos12,13, D. Mkrtichian3, A. Goswami14, M. Cuntz15, A. P. Yadav16, M.
Sarkar1, B. C. Bhatt14, F. Kahraman Aliçavuş17,18, M. D. Nhlapo19, M. N.
Lund20, P. P. Goswami14, I. Savanov21, A. Jorissen22, E. Jurua2, E.
Avvakumova23, E. S. Dmitrienko24, N. K. Chakradhari25, M. K. Das26, S.
Chowdhury17, O. P. Abedigamba19,27, I. Yakunin4, B. Letarte19, and D.
Karinkuzhi28
Affiliations are listed at the end of the paper E-mail<EMAIL_ADDRESS>mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present a study based on the high-resolution spectroscopy and K2 space
photometry of five chemically peculiar stars in the region of the open cluster
M44. The analysis of the high-precision photometric K2 data reveals that the
light variations in HD 73045 and HD 76310 are rotational in nature and caused
by spots or cloud-like co-rotating structures, which are non-stationary and
short-lived. The time-resolved radial velocity measurements, in combination
with the K2 photometry, confirm that HD 73045 does not show any periodic
variability on timescales shorter than 1.3 d, contrary to previous reports in
the literature. In addition to these new rotational variables, we discovered a
new heartbeat system, HD 73619, where no pulsational signatures are seen. The
spectroscopic and spectropolarimetric analyses indicate that HD 73619 belongs
to the peculiar Am class, with either a weak or no magnetic field considering
the 200 G detection limit of our study. The Least-Squares Deconvolution (LSD)
profiles for HD 76310 indicate a complex structure in its spectra suggesting
that this star is either part of a binary system or surrounded by a cloud
shell. When placed in the Hertzsprung-Russell diagram, all studied stars are
evolved from main-sequence and situated in the $\delta$ Scuti instability
strip. The present work is relevant for further detailed studies of CP stars,
such as inhomogeneities (including spots) in the absence of magnetic fields
and the origin of the pulsational variability in heartbeat systems.

###### keywords:

Stars: chemically peculiar– stars: individual (HD 73045, HD 73574, HD 73618,
HD 73619, HD 76310) – stars: rotation, techniques – photometry, spectroscopy,
spectropolarimetry

††pubyear: 2021††pagerange: Study of Chemically Peculiar Stars-I : High-
resolution Spectroscopy and K2 Photometry of Am Stars in the Region of M44–43

##  1 Introduction

The chemically peculiar (CP) stars are a group of main sequence (MS) B-, A-,
and F-type stars having peculiar surface elemental abundances; they are
characterized by abnormal spectral lines strengths (Preston, 1974). The
chemical anomalies in these stars are thought to be confined to the outer
stellar layers and to arise from gravitational settling and radiative
levitation of certain elements, a process known as atomic diffusion (Michaud,
1970; Michaud et al., 1981). The present study is confined to one subset of CP
stars, the metallic-lined A (Am) stars, which are generally non-magnetic in
nature and characterized by under-abundances of some light elements such as Ca
and Sc, but slight/moderate over-abundances of iron peak elements, e.g., Zn,
Sr, Y, Zr, and Ba. The projected rotational velocities of these stars are
generally smaller than for ordinary A stars ($v\sin i$ typically $<$ 120 km
s-1), with the majority of the Am stars being members of close binary systems.
Rotational braking through tidal interaction is regarded as a possible cause
of the low rotational velocities.

Using four years of high-precision photometry from the nominal Kepler mission
and the K2 campaigns, Balona et al. (2015) investigated the light variations
in 29 Am stars and found that most of the Am stars in the Kepler field have
light curves with the characteristics of rotational modulation arising from
star spots or co-rotating structures. The origin of spots in Am stars seems to
be different from solar-like spots as these stars do not show any signs of
intense magnetic fields able to produce such magnetic features. Magnetic
fields on the order of sub-Gauss strengths have been reported in some Am
stars, e.g., Sirius A (Petit et al., 2011), Vega (Böhm et al., 2015), $\beta$
UMa, and $\theta$ Leo (Blazère et al., 2015), Alhena (Blazère et al., 2016)
and $\rho$ Pup (Neiner et al., 2017). It is thought that for the majority of
these stars that convective flows in the atmospheres may disrupt any spot-like
features (Kupka, 2003). Hence, the rotational modulation in some Am stars
indicates that either a weak magnetic field may lead to surface
inhomogeneities in the form of spots across the stellar surface or,
alternatively, there is some unknown mechanism(s) producing those spots. If a
weak magnetic field is indeed present, then the basic processes operating in
Am stars would need to be revisited since magnetic fields have been omitted
from the diffusion models attempting to explain their unusual chemical
abundances (Guzik, 2021).

Stars showing variable amplitudes or harmonics in their light curves provide
the best cases for identifying rotational modulation. However, it is extremely
difficult to distinguish between rotation and binarity at low frequencies,
noting that the amplitude of the periodic variation due to co-rotating star
spots changes in a relatively short time-scale (perhaps a few months).

Short-term variability, similar to that seen in $\delta$ Scuti stars, has been
reported in many Am stars and is understood to arise from pulsations driven by
the $\kappa$-mechanism operating in the He ii ionization zone (Pamyatnykh,
2000) combined with turbulent pressure in the H/He i ionization zone (Smalley
et al., 2017; Antoci et al., 2019). In the context of the present study, Joshi
et al. (2015) suspected a short-term pulsational variability in HD 73045;
hitherto awaiting confirmation.

In close binary systems, stellar pulsations may also be tidally induced (Kumar
et al., 1995; Thompson et al., 2012); e.g., KOI-54 (Welsh et al., 2011; Fuller
& Lai, 2012; Burkart et al., 2012; O’Leary & Burkart, 2014) and KIC 3230227
(Guo et al., 2017). Highly eccentric ($e>0.3$) binary systems with orbital
periods between a fraction of a day and tens of days showing a sudden increase
in brightness at periastron passage, on the order of several parts-per-
thousand (ppt), are known as heartbeat (HB) stars (Handler et al., 2002;
Maceroni et al., 2009; Hambleton et al., 2013; Beck et al., 2014; Hambleton et
al., 2016, 2018; Kołaczek-Szymański et al., 2020). The name stems from the
resemblance of the light curve to a heartbeat in an electrocardiogram. About
180 heartbeat stars have been discovered to date. Due to the small-amplitude
light variations and their short orbital periods, these targets were mainly
detected using space missions such as Kepler (Hambleton et al., 2013; Kirk et
al., 2016; Hambleton et al., 2016; Fuller, 2017; Hambleton et al., 2018; Guo
et al., 2020). The Am stars are often part of binary systems (Carquillat &
Prieur, 2007), though Am stars in heartbeat systems have not been reported in
the literature yet, thus the discovery of a new heartbeat beat system in one
of the CP stars HD 73619 would be significant.

In the present work, we revisit all stars previously observed as part of the
Nainital-Cape survey project (Ashoka et al., 2000; Martinez et al., 2001;
Joshi et al., 2003, 2006; Joshi et al., 2009; Joshi et al., 2010, 2012, 2016,
2017) with data in the Kepler and K2 archives. It is our aim to search for low
frequency, high-precision, and photometric variability. No stars from the
Nainital-Cape survey were observed in the nominal Kepler field, whilst eight
stars were found in the K2 archive. In the current paper, we present the
results on extrinsic (rotational and heartbeat) variables, as well as the
results for stars where variability could not be ascertained.

##  2 Observations and Data Reduction

The photometric observations were obtained using both ground- and space-based
telescopes while spectroscopy and spectropolarimetry were performed through
ground-based telescopes. The specifications of the telescopes and state-of-art
instruments used for the observations are listed in Table 1.

Table 1: The specifications of the telescopes and back-end instruments used for the photometric and spectroscopic observations. Category | Name of | Diameter | Location | Detector/ | FoV/
---|---|---|---|---|---
| Telescope | (m) |  | Spectrograph | Resolution
Ground-based | DFOT | 1.30 | Devasthal (India) | Andor’s DZ436 | 18${}^{{}^{\prime}}\times 18^{{}^{\prime}}$
Photometry |  |  |  | Andor’s iXon EM+ DU-897 | 4.7${}^{{}^{\prime}}\times 4.7^{{}^{\prime}}$
| ST | 1.04 | Nainital (India) | 2k Wright CCD | 13 ${}^{{}^{\prime}}\times 13^{{}^{\prime}}$
| MASTER-II-URAL | 0.40 | Ural Federal University (Russia) | U16M CCD | 2${}^{\circ}\times 4^{\circ}$
| PROMPT-8 | 0.60 | CTIO (Chile) | Apogee, F42 | 26.6${}^{{}^{\prime}}\times 22.6^{{}^{\prime}}$
Space-based | K2 | 0.95 | Space | e2v CCD90s | 10.25 ${}^{\circ}\times 10.25^{\circ}$
Photometry |  |  |  |  |
Spectroscopy | BTA | 6.00 | Nizhniy Arkhyz (Russia) | NES,MSS | 39 000, 15 000
| TNO | 2.40 | Chiang Mai (Thailand) | MRES | 17 000
| HCT | 2.00 | Hanle (India) | HESP | 30 000
| Mercator | 1.20 | La Palma (Spain) | HERMES | 85 000

###  2.1 Ground-Based Differential Photometry of HD 73045

To investigate the variability of the single-lined spectroscopic binary (SB1)
HD 73045, as suspected by Joshi et al. (2015), this object was extensively
monitored photometrically with the 1.3-m Devasthal Fast Optical Telescope
(DFOT; Sagar et al. 2011), the 1.04-m Sampurnanand Telescope (ST; Sinvhal et
al. 1972), the 2$\times$0.40-m MASTER-II-URAL telescope (Lipunov et al.,
2010), and the 0.6-m Panchromatic Robotic Optical Monitoring and Polarimetry
Telescope (PROMPT-8; Burdanov et al. 2014). These instruments are introduced
in Table 1.

All observations were carried out through a Johnson B and/or V filter.
Calibration frames were acquired during each night for the correction of
background and pixel sensitivity. The science frames were processed by
subtracting master bias and dark frames before normalising them with a median
flat-field frame from which the cosmic rays were removed. The instrumental
magnitudes of HD 73045 and the comparison stars (BD $+19^{\circ}2046$ and TYC
1395-855-1) were obtained through aperture photometry using the in-built
daophot package of IRAF (Davis, 1994). The characteristics of the ground based
photometric observations are given in Table 10 and the individual light curves
and power spectra are presented in Figs. 15 and 16. The top and bottom panels
of Fig. 1 show the combined amplitude spectra of HD 73045 in the B and V
filters, respectively.

Figure 1: The amplitude spectra of HD 73045 using the combined data from
ground-based observations in B (top panel) and V (bottom panel) filters. There
are no significant frequencies with signal-to-noise ratio (SNR) above 4 (0.048
mag for B-filter and 0.051 mag for V-filter), hence the star is classified as
non-variable. The blue dashed vertical lines represent the short-term
periodicity as suspected by Joshi et al. (2015).

###  2.2 K2 Space Photometry

Our target stars were observed by the K2 mission that operated in a long
cadence (LC; 29.4 min) and a short cadence (SC; 58.8 s) mode (Howell et al.,
2014). K2 pointed towards the Praesepe (Beehive) cluster (M44) during the
campaigns C05 (2015/04/27–2015/07/10), C16 (2017/12/07–2018/02/25), and C18
(2018/05/12–2018/07/02). The K2 observations of our targets are summarized in
Table 2.

Table 2: The K2 campaigns concerning our programme stars. Star Name | EPIC Number |  K2 Observation Campaigns
---|---|---
|  | C05 | C16 | C18
|  |  $\sim$79 d |  $\sim$80 d |  $\sim$50 d
|  | LC | SC | LC | SC | LC | SC
HD 73045 | 211910450 | ✓ | - | - | - | ✓ | ✓
HD 73574 | 211989558 | ✓ | - | - | - | ✓ | -
HD 73618 | 211955190 | ✓ | - | ✓ | - | ✓ | -
HD 73619 | 211954496 | ✓ | - | ✓ | - | ✓ | -
HD 76310 | 212082764 | ✓ | - | ✓ | - | ✓ | -

These photometric data sets were downloaded from the Barbara A. Mikulski
Archive for Space Telescopes (MAST)
database111https://archive.stsci.edu/k2/epic/search.php. Each target pixel
file (TPF) was checked for the presence of additional stars. As HD 73045, HD
76310, and HD 73574 were the sole stars in their TPF images, their respective
K2 FITS light curve files were directly downloaded in the PDC_SAP format
(Stumpe et al., 2012; Smith et al., 2012), having undergone pre-search data
conditioning (PDC) processing of their simple aperture photometry (SAP) flux
data. The underlying position-dependent artifacts were removed by processing
the data through the K2SC algorithm (Aigrain et al., 2015). The TPF images of
HD 73618 and HD 73619 showed the presence of nearby stars (Fig. 2), which had
to be masked out to isolate the flux of these target stars. The remaining
images were averaged and a custom mask was produced to isolate the target
star. This mask was applied to each image of the campaign and the total flux
for each image was deduced, producing a light curve similar to the available
SAP flux data. These data sets were further processed with the K2SC algorithm.
Fig. 3 (top-left, in blue) shows an example light curve for the C18
observation of HD 73045. A detailed discussion of our analysis is given in
Appendix B. A periodogram produced by the Lomb-Scargle algorithm is shown in
Fig. 3 (bottom, in blue). The frequency-varying artifact in the light-curve is
due to the roll-angle variation (Aigrain et al., 2016), reversing twice near
10 and 40 days respectively. This artifact is not prevalent in the
periodogram, but is distributed between 0.25 – 2 days (0.5 – 4 d-1).

Figure 2: Target pixel images from the C18 time-series of HD 73618 (left) and
HD 73619 (right). Note that each star appears in both images. The red border
signifies the boundary of a custom mask within which the pixels are isolated
and summed to produce a single simple aperture photometry flux data point.
Figure 3: Top left: Time-series illustrating photometric flux variation (in
mmag) of HD 73045 for the LC 2018 K2 Campaign 18. The data (blue points)
include intrinsic signals as well as systemic and noise artifacts. The
sinusoidal model, with parameters given in Table 3, is shown as the red line.
Top right: The photometric data (blue points) phase folded on the dominant
variation period of 12.2 d. The red line represents the best-fit to this data.
The data is repeated over two periods for clarity of presentation. Bottom:
Linear-log periodogram of spectral amplitudes (blue line), in mmag. The
components of the sinusoidal model are shown by the red stems. The black
dotted line corresponds to a False Alarm Probability of $10^{-8}$, and the
periodogram peaks above this line are considered to be confirmed signals.

Using a multi-component sinusoidal model, frequencies, periods, amplitudes,
and phases, relating to the variability detected in the K2 light curves, are
derived, and are tabulated in Table 3. Fig. 3 (top-left, in red) illustrates
such a model of the HD 73045 C18 light curve, for which the derived amplitudes
and frequencies of the components are included in the periodogram (Fig. 3,
bottom) as red stems. The light curve data is phase-folded on the period with
the largest amplitude and overplotted with that period’s sinusoidal component
(Fig. 3, top-right). Similar figures for the remaining campaigns of all
targets are given in Appendix C (Figs. 21–32).

Table 3: Parameters of the sinusoidal component (ordered by amplitude), related to the variations observed within the analysed flux data, as derived from the fitting process. For each data set, these components have been summed to produce a model of their respective light curves. Star Name | Campaign | Frequency | Period | Amplitude | Phase
---|---|---|---|---|---
|  | (d-1) | (d) | (mmag) | (rad)
HD 73045 | C05 | 0.0783 $\pm$ 0.0002 | 12.77 $\pm$ 0.03 | 0.113 $\pm$ 0.003 | 1.44 $\pm$ 0.03
|  | 0.1555 $\pm$ 0.0005 | 6.43 $\pm$ 0.02 | 0.035 $\pm$ 0.002 | -0.47 $\pm$ 0.06
|  | 0.0640 $\pm$ 0.0005 | 15.6 $\pm$ 0.1 | 0.030 $\pm$ 0.002 | -2.38 $\pm$ 0.07
|  | 0.1395 $\pm$ 0.0006 | 7.17 $\pm$ 0.03 | 0.026 $\pm$ 0.002 | -1.31 $\pm$ 0.08
|  | 0.1668 $\pm$ 0.0008 | 6.00 $\pm$ 0.03 | 0.020 $\pm$ 0.002 | -0.9 $\pm$ 0.1
| C18 | 0.0791 $\pm$ 0.0005 | 12.64 $\pm$ 0.08 | 0.039 $\pm$ 0.002 | -0.008 $\pm$ 0.05
|  | 0.1535 $\pm$ 0.0008 | 6.51 $\pm$ 0.03 | 0.023 $\pm$ 0.002 | -0.54 $\pm$ 0.07
HD 76310 | C05 | 0.2165 $\pm$ 0.0002 | 4.618 $\pm$ 0.004 | 0.50 $\pm$ 0.01 | 2.81 $\pm$ 0.02
|  | 0.2039 $\pm$ 0.0002 | 4.905 $\pm$ 0.005 | 0.320 $\pm$ 0.008 | -1.39 $\pm$ 0.03
|  | 0.2290 $\pm$ 0.0002 | 4.367 $\pm$ 0.005 | 0.197 $\pm$ 0.007 | 0.19 $\pm$ 0.03
|  | 0.1863 $\pm$ 0.0003 | 5.366 $\pm$ 0.008 | 0.149 $\pm$ 0.006 | -0.84 $\pm$ 0.04
|  | 0.4198 $\pm$ 0.0004 | 2.382 $\pm$ 0.002 | 0.106 $\pm$ 0.005 | -2.56 $\pm$ 0.05
|  | 0.1668 $\pm$ 0.0004 | 5.99 $\pm$ 0.01 | 0.099 $\pm$ 0.004 | -2.75 $\pm$ 0.05
| C16 | 0.2089 $\pm$ 0.0002 | 4.786 $\pm$ 0.004 | 0.40 $\pm$ 0.01 | -2.22 $\pm$ 0.02
|  | 0.1856 $\pm$ 0.0002 | 5.388 $\pm$ 0.005 | 0.315 $\pm$ 0.008 | -0.65 $\pm$ 0.02
|  | 0.0756 $\pm$ 0.0004 | 13.23 $\pm$ 0.07 | 0.099 $\pm$ 0.006 | 0.90 $\pm$ 0.06
|  | 0.4302 $\pm$ 0.0004 | 2.325 $\pm$ 0.002 | 0.084 $\pm$ 0.005 | -2.51 $\pm$ 0.06
|  | 0.9699 $\pm$ 0.0004 | 1.0310 $\pm$ 0.0005 | 0.080 $\pm$ 0.005 | -2.25 $\pm$ 0.06
|  | 0.0573 $\pm$ 0.0005 | 17.4 $\pm$ 0.2 | 0.065 $\pm$ 0.005 | 2.95 $\pm$ 0.08
| C18 | 0.2065 $\pm$ 0.0002 | 4.843 $\pm$ 0.006 | 1.09 $\pm$ 0.02 | -1.05 $\pm$ 0.02
|  | 0.1841 $\pm$ 0.0005 | 5.43 $\pm$ 0.02 | 0.25 $\pm$ 0.01 | -2.47 $\pm$ 0.04
|  | 0.4270 $\pm$ 0.0006 | 2.342 $\pm$ 0.003 | 0.18 $\pm$ 0.01 | -2.4 $\pm$ 0.06
HD 73574 | C05 | 0.0700 $\pm$ 0.0004 | 14.28 $\pm$ 0.08 | 0.85 $\pm$ 0.04 | 2.87 $\pm$ 0.05
|  | 0.0925 $\pm$ 0.0008 | 10.8 $\pm$ 0.1 | 0.36 $\pm$ 0.04 | 1.7 $\pm$ 0.1
| C18 | 0.092 $\pm$ 0.002 | 10.8 $\pm$ 0.2 | 0.047 $\pm$ 0.007 | 0.4 $\pm$ 0.1
HD 73618 | C05 | 0.2644 $\pm$ 0.0002 | 3.782 $\pm$ 0.003 | 0.40 $\pm$ 0.01 | 1.89 $\pm$ 0.03
|  | 0.2055 $\pm$ 0.0002 | 4.867 $\pm$ 0.006 | 0.248 $\pm$ 0.008 | 0.90 $\pm$ 0.03
|  | 0.4100 $\pm$ 0.0004 | 2.439 $\pm$ 0.002 | 0.136 $\pm$ 0.007 | 2.98 $\pm$ 0.05
|  | 0.2531 $\pm$ 0.0005 | 3.951 $\pm$ 0.008 | 0.094 $\pm$ 0.006 | 2.78 $\pm$ 0.07
|  | 0.4287 $\pm$ 0.0005 | 2.333 $\pm$ 0.003 | 0.092 $\pm$ 0.006 | 1.00 $\pm$ 0.07
|  | 0.1766 $\pm$ 0.0006 | 5.66 $\pm$ 0.02 | 0.077 $\pm$ 0.006 | -1.81 $\pm$ 0.08
| C16 | 0.2609 $\pm$ 0.0002 | 3.833 $\pm$ 0.003 | 0.32 $\pm$ 0.009 | 1.28 $\pm$ 0.03
|  | 0.2052 $\pm$ 0.0002 | 4.874 $\pm$ 0.004 | 0.268 $\pm$ 0.007 | 2.74 $\pm$ 0.03
|  | 0.4013 $\pm$ 0.0003 | 2.493 $\pm$ 0.002 | 0.151 $\pm$ 0.005 | -2.03 $\pm$ 0.04
|  | 0.2244 $\pm$ 0.0003 | 4.456 $\pm$ 0.005 | 0.125 $\pm$ 0.005 | 2.86 $\pm$ 0.04
|  | 0.4167 $\pm$ 0.0003 | 2.399 $\pm$ 0.002 | 0.099 $\pm$ 0.004 | 2.51 $\pm$ 0.05
|  | 0.2365 $\pm$ 0.0003 | 4.228 $\pm$ 0.006 | 0.085 $\pm$ 0.004 | -2.90 $\pm$ 0.05
|  | 0.2877 $\pm$ 0.0004 | 3.476 $\pm$ 0.005 | 0.066 $\pm$ 0.004 | -0.23 $\pm$ 0.06
|  | 0.4471 $\pm$ 0.0005 | 2.237 $\pm$ 0.002 | 0.062 $\pm$ 0.004 | 1.49 $\pm$ 0.06
| C18 | 0.2656 $\pm$ 0.0003 | 3.765 $\pm$ 0.004 | 0.60 $\pm$ 0.01 | -1.54 $\pm$ 0.02
|  | 0.2120 $\pm$ 0.0004 | 4.717 $\pm$ 0.009 | 0.224 $\pm$ 0.008 | 1.47 $\pm$ 0.04
|  | 0.1951 $\pm$ 0.0005 | 5.13 $\pm$ 0.01 | 0.174 $\pm$ 0.007 | -0.80 $\pm$ 0.04
|  | 0.4180 $\pm$ 0.0004 | 2.392 $\pm$ 0.002 | 0.173 $\pm$ 0.007 | 2.89 $\pm$ 0.04
|  | 0.2373 $\pm$ 0.0005 | 4.22 $\pm$ 0.01 | 0.113 $\pm$ 0.006 | 2.11 $\pm$ 0.05
|  | 0.2941 $\pm$ 0.0005 | 3.401 $\pm$ 0.006 | 0.111 $\pm$ 0.005 | -0.38 $\pm$ 0.05
HD 73619 | C05 | 0.0771 $\pm$ 0.0002 | 12.97 $\pm$ 0.03 | 0.394 $\pm$ 0.009 | -2.01 $\pm$ 0.02
|  | 0.1548 $\pm$ 0.0002 | 6.46 $\pm$ 0.01 | 0.208 $\pm$ 0.007 | -2.91 $\pm$ 0.03
|  | 0.2326 $\pm$ 0.0003 | 4.300 $\pm$ 0.005 | 0.144 $\pm$ 0.006 | 2.52 $\pm$ 0.04
|  | 0.3104 $\pm$ 0.0005 | 3.221 $\pm$ 0.005 | 0.085 $\pm$ 0.005 | 1.45 $\pm$ 0.06
|  | 0.3882 $\pm$ 0.0006 | 2.576 $\pm$ 0.004 | 0.059 $\pm$ 0.005 | 0.77 $\pm$ 0.09
|  | 0.465 $\pm$ 0.001 | 2.152 $\pm$ 0.005 | 0.033 $\pm$ 0.005 | 0.3 $\pm$ 0.1
|  | 0.545 $\pm$ 0.001 | 1.834 $\pm$ 0.005 | 0.025 $\pm$ 0.005 | -2.1 $\pm$ 0.2
| C18 | 0.0775 $\pm$ 0.0003 | 12.92 $\pm$ 0.05 | 0.344 $\pm$ 0.01 | -1.27 $\pm$ 0.03
|  | 0.1525 $\pm$ 0.0004 | 6.46 $\pm$ 0.02 | 0.179 $\pm$ 0.007 | -0.9 $\pm$ 0.04
|  | 0.2294 $\pm$ 0.0006 | 4.36 $\pm$ 0.01 | 0.113 $\pm$ 0.006 | -0.81 $\pm$ 0.05
|  | 0.3063 $\pm$ 0.006 | 3.265 $\pm$ 0.008 | 0.074 $\pm$ 0.005 | -0.77 $\pm$ 0.07
|  | 0.384 $\pm$ 0.001 | 2.607 $\pm$ 0.007 | 0.049 $\pm$ 0.005 | -0.6 $\pm$ 0.1
|  | 0.462 $\pm$ 0.002 | 2.16 $\pm$ 0.01 | 0.023 $\pm$ 0.005 | -0.5 $\pm$ 0.2
|  | 0.540 $\pm$ 0.003 | 1.85 $\pm$ 0.01 | 0.017 $\pm$ 0.005 | -0.2 $\pm$ 0.3

###  2.3 High-Resolution Spectroscopic and Spectropolarimetric Observations

High-resolution spectroscopy provides an opportunity of deriving a wide range
of information on the target stars, such as basic stellar parameters like the
effective temperature ($T_{\textrm{eff}}$), surface gravity ($\log g$), and
metallicity ([M/H]). The high-resolution spectra of our targets were gathered
with four spectrographs: (1) the Hanle Échelle Spectrograph (HESP; Chanumolu
et al. 2015; Sriram et al. 2018) at the 2.01-m Himalayan Chandra Telescope
(HCT) of IIA, Bengaluru, (2) the Middle Resolution Échelle Spectrograph (MRES)
at the 2.4-m telescope of the TNO (Thailand), (3) the High Efficiency and
Resolution Mercator Échelle Spectrograph (HERMES; Raskin et al. 2011) at the
1.2-m Mercator telescope, and (4) the Nasmyth Échelle Spectrometer (NES;
Panchuk et al. 2017) at the 6-m Bolshoi Teleskop Alt-azimutalnyi (BTA) of the
Special Astrophysical Observatory (SAO; Russia).

For HD 73619, we also used the Main Stellar Spectrograph (MSS; Chountonov
2004; Panchuk et al. 2014) at the 6-m BTA for measuring stellar magnetic field
strengths. Our target was observed along with two standard stars, i.e., HD
52711 (non-magnetic) and 53 Cam (magnetic). These spectropolarimetric
observations were carried out in a series of paired exposures obtained in two
orthogonal orientations of a retarder.

Data reduction was performed using the pipeline developed for each particular
spectrograph that generally involves overscan correction, averaged bias
subtraction, flat-field correction, and wavelength calibration. The
spectropolarimetric data reduction was performed using the zeeman package
developed within the ESO MIDAS environment for the specific format of CCD
spectra taken with an image slicer (Kudryavtsev et al., 2006).

##  3 Radial Velocity Measurements

We measured the radial velocities (RVs) of all target stars using the Least-
Squares Deconvolution (LSD) technique (Kochukhov et al., 2010). For HD 73045,
the obtained RV time-series data were analysed using the standard Discrete
Fourier Transform (DFT) technique. The results of the RV analysis for HD 73045
obtained from HERMES and MRES are shown in Figs. 17 and 18, respectively. The
frequency spectra at different epochs do not show any significant peak with
SNR $>$ 4\. Therefore, we conclude that in the observational limit
($3\sigma\sim 300$ m s-1), HD 73045 does not vary spectroscopically on a short
time scale. The RV of HD 73045 was also measured from the single spectrum from
NES. All RV measurements are plotted with the orbital parameters given by
Carquillat & Prieur (2007), see Fig. 19. Based on the residuals shown in the
bottom panel of Fig. 19, our results are consistent with the known orbital
solution (with an orbital period of 435.57 days).

Table 4: Summary of the high-resolution spectroscopic observations.
Spectropolarimetric observations are listed in the last row (MSS BTA).
Spectrograph Telescope
---
Star | HJD (2 450 000+) | Total No. | Spectral | SNR
| (day) | Spectra | Range (nm) |
MRES @ TNT
HD 73045 | 7007.391 – 7007.467 | 38 | 406 – 879 | 33 – 310
| 7009.408 – 7009.470 | 29 |  | (@ 572 nm)
| 7011.365 – 7011.470 | 31 |  |
HD 76310 | 8954.116 | 1 |  |
NES @ BTA
HD 73045 | 7350.462 | 1 | 409 – 686 | 300
|  |  |  | (@ 555 nm)
HERME @ Mercator
HD 73045 | 7490.375–7490.496 | 30 | 390 – 893 | 40 – 45
| 7491.377 – 7491.425 | 10 |  | (@ 650 nm)
| 7512.375 – 7512.460 | 22 |  |
HESP @ HCT
HD 73574 | 8473.186 | 1 | 350 – 1000 | 143
HD 73619 | 8473.223 | 1 |  | 96
HD 76310 | 8473.261 | 1 |  | 100
HD 73618 | 8555.074 | 1 |  | 220
|  |  |  | (@ 550 nm)
MSS @ BTA
HD 73619 | 8578.300 – 8578.330 | 3 | 444 – 498 | 150 – 200
| 8579.293 – 8579.314 | 3 |  | 100 – 250
|  |  |  | (@ 455 nm)

For HD 73619, the RV measurements based on the MSS and HESP spectra (see Table
5) are fitted well using the orbital parameters (with an orbital period of
12.91 days) derived by Debernardi et al. (2000). Fig. 4 shows the orbital
solution of HD 73619 where the observations are compared to the model. Our RV
observations for both HD 73045 and HD 73619 agree with the known orbital
parameters; hence, we did not re-derive them.

Table 5: Basic parameters of the components of HD 73619 and HD 76310 obtained
through high-resolution spectroscopy. The numbers 1 and 2 are assigned to the
primary and secondary component, respectively. The spectral coverage was 430 –
680 nm. We assumed equal light factors for both components of HD 73619,
whereas for HD 76310, a light ratio ($l_{1}$) of 0.887 was used. The stars HD
73045, HD 73574, and HD 73618 are assumed to be single stars, as either they
are truly single, or the secondary star does not contribute significantly to
the lines of the spectrum.

Star | Spectrograph | RV | $T\rm_{eff}$ | $\log g$ | $v\sin i$
---|---|---|---|---|---
|  | (km s-1) | (K) | (cgs) | (km s-1)
|  | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2
HD 73619 | HESP | -8.6 $\pm$ 0.1 | 77.5 $\pm$ 0.1 | 7150 $\pm$ 90 | 7220 $\pm$ 100 | 3.28 $\pm$ 0.60 | 3.02 $\pm$ 0.12 | 14.5 $\pm$ 0.5 | 13.3 $\pm$ 0.8
| MSS | 30.2 $\pm$ 4.8 | 46.8 $\pm$ 3.3 | 7410 $\pm$ 370 | 7200 $\pm$ 280 | 3.90 $\pm$ 0.13 | 3.54 $\pm$ 0.22 | 17.0 $\pm$ 2.0 | 19.5 $\pm$ 0.5
|  | 12.3 $\pm$ 1.5 | 62.4 $\pm$ 1.2 | 7380 $\pm$ 390 | 7080 $\pm$ 260 | 4.0 | 4.0 | 16.3 $\pm$ 4.0 | 17.3 $\pm$ 3.8
HD 76310 | HESP | 18.9 $\pm$ 2.3 | 10.1 $\pm$ 1.8 | 7420 $\pm$ 210 | 6220 $\pm$ 180 | 4.0 | 4.0 | 96 $\pm$ 7 | 9 $\pm$ 1
| MRES | 27.4 $\pm$ 1.8 | 19.8 $\pm$ 2.8 | 7030 $\pm$ 170 | 6470 $\pm$ 220 | 4.0 | 4.0 | 103 $\pm$ 8 | 20.3 $\pm$ 3.4
HD 73045* | ESPaDOnS | 27.9 | - | 7570 $\pm$ 200 | - | 4.05 $\pm$ 0.2 | - | 10 $\pm$ 0.5 |
HD 73574 | HESP | 29.2 $\pm$ 2.8 | - | 7700 $\pm$ 160 | - | 4.12 $\pm$ 0.21 | - | 99 $\pm$ 5 |
HD 73618* | ESPaDOnS | 15.1 | - | 8170 $\pm$ 200 | - | 4.00 $\pm$ 0.19 | - | 47 $\pm$ 3 |
| HESP | 39.2 $\pm$ 0.5 | - | 7960 $\pm$ 180 | - | 3.76 $\pm$ 0.19 | - | 56 $\pm$ 3 |

*Fossati et al. (2007)

Figure 4: Radial velocity measurements of HD 73619 derived from both the HESP
and MSS spectra are plotted together with the orbital solution given by
Debernardi et al. (2000). Blue and red symbols represent the measured RV of
the primary and secondary component, respectively.

##  4 Atmospheric Parameters

Much of the success of astronomy and astrophysics relies on the accurate
knowledge about the basic parameters and structure of stars. Using high-
resolution spectroscopic data, HD 73045 has been extensively studied by
Fossati et al. (2007, 2008); hence, we refrained from re-deriving its
atmospheric parameters. To determine the relevant atmospheric parameters,
e.g., $T_{\textrm{eff}}$, $\log g$, etc., for the remaining targets, we used
two approaches, namely, photometric calibrations and high-resolution spectral
data. We obtained the fundamental atmospheric parameters from photometry using
the Geneva, $uvby\beta$, and 2MASS photometric systems (Cutri et al., 2003),
as well as via data obtained from the General Catalogue of Photometric Data222
http://obswww.unige.ch/gcpd/indexform.html (Mermilliod et al., 1997). The
reddening parameters $E({\rm B-V})$ and $E({\rm B2-V1})$ were obtained using a
3-D dust-map (Green, 2018; Green et al., 2019) and ratios of total-to-
selective absorption computed by Crawford & Mandwewala (1976), respectively.
In Table 6, we compiled the known and derived parameters of the programme
stars based on multi-colour photometry.

Table 6: Basic parameters of the studied stars extracted from various online
databases. We list the atmospheric parameters ($T_{\rm eff}$, $\log g$, and
[M/H]) computed from the three photometric systems (Geneva, uvby$\beta$ and
2MASS) as well as log$\left(L_{\star}/{\rm L_{\odot}}\right)$ as calculated
from the Gaia parallaxes.

Star | Va | $\pi\rm^{b}$ | $E{\rm(B-V)}$ | $E{\rm(B2-V1)}$ | $T\rm_{eff}$ | [M/H] | $T_{\rm eff}$ | $\log g$ | [M/H] | $T_{\rm eff}$ | log$\left[L_{*}/{\rm L_{\odot}}\right]$ | Sp. Typec | Peculiarity
---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  | Geneva | Geneva | uvbyβ | uvbyβ | uvbyβ | 2MASS |  |  |
| (mag) | (mas) | (mag) | (mag) | ($\pm 70$ K) | $\pm 0.08$ | ($\pm 200$ K) | ($\pm 0.10$ cgs) | $\pm 0.13$ | ($\pm 190$ K) |  |  |
HD 73045 | 8.62 | 3.7587 | 0.035 | 0.0272 | 7440 | 0.44 | 7470 | 4.28 | 0.37 | 7390 | 1.29 $\pm$0.10 | A7 | Am
HD 73574 | 7.75 | 5.7064 | 0.018 | 0.0138 | 7870 | 0.16 | 7660 | 3.91 | 0.15 | 7730 | 1.24 $\pm$ 0.17 | A3 | -
HD 73618 | 7.30 | 6.9834 | 0.015 | 0.0118 | 7940 | 0.33 | 8090 | 3.90 | 0.39 | 7910 | 1.27 $\pm$ 0.13 | A0 | Amd,e
HD 73619 | 7.52 | 5.4033 | 0.015 | 0.0120 | 7670 | 0.52 | 7890 | 4.17 | 0.47 | 7860 | 1.20 $\pm$ 0.06 | A0 | Amf
HD 76310 | 8.52 | 5.6101 | 0.015 | 0.0117 | 7310 | 0.14 | 7470 | 4.09 | 0.25 | 7320 | 0.94 $\pm$ 0.11 | A2 | Amg

aHøg et al. (2000), bGaia Collaboration (2018), cCannon & Pickering (1993),
dBertaud (1960), eRebeirot (1966), fBidelman (1956), and gCowley & Cowley
(1965a)

The fundamental atmospheric parameters determined from photometry were used as
initial input to facilitate further analyses. Spectroscopic parameters were
derived by comparing observed spectra with synthetic ones computed for the
adopted atmospheric parameters by using the $\chi^{2}$-minimisation method
(see Trust et al. 2021 for more detail). The used the radiative transfer code
MOOG (Sneden et al., 2012), together with the line-list version 5 of the Gaia-
ESO Survey (GES) (wavelength range of 475 – 685 nm) (Heiter et al., 2015), the
solar abundances by Asplund et al. (2009), and the ATLAS9333
http://www.stsci.edu/hst/observatory/crds/castelli_kurucz_atlas.html
atmospheric models of Castelli & Kurucz (2003) through an integrated software
iSpec (Blanco-Cuaresma et al., 2014; Blanco-Cuaresma, 2019). The atmospheric
parameters estimated from the best fits between the calculated and observed
spectra are listed in Table 5. The synthetic spectra based on the values of
the atmospheric parameters fit the observed spectra well, as shown in Fig. 5.

Figure 5: Hβ region of the spectra used for the determination of the
respective stellar effective temperature. The synthetic spectrum (red) is
over-plotted with the observed spectrum (black).

For HD 73619, the HESP and MSS spectra clearly show the presence of two
components (see Fig. 6 and the LSD profiles of Fig. 7). We derived the
atmospheric parameters from HESP and MSS spectra using the two-dimensional
version of the girfit code developed by Frémat et al. (2006). We reconstructed
the composite spectra by searching for the best pair of Doppler shifts and
synthetic spectra, one for each component, with solar-like composition in the
spectral regions 439 – 450 nm, 450 – 470 nm, 470 – 500 nm, and 510 – 550 nm.
Fig. 6 shows a portion of the HESP spectrum (black) and the fit (red) using a
two-component model. The radial velocities as well as the derived atmospheric
parameters are listed in Table 5.

Figure 6: Hβ section of the MRES spectrum (black) for HD 73619 and the fit
(red) using a two-component model and the 2-D version of girfit.

##  5 Magnetic Field Measurement of HD 73619

Magnetic field determinations allow us to distinguish between the two types of
CP stars of interest, namely Ap and Am stars. Though spots are thought to
occur in the presence of intense magnetic fields, Balona (2013) attributed the
photometric variability observed in some A-type stars as due to rotational
modulation of stellar surfaces with inhomogeneities in cases where the
magnetic field is either weak or absent. The magnetic field can be detected
through the Zeeman effect where the left and right circular polarization
spectra are shifted with respect to each other with the shift being
proportional to the longitudinal magnetic field averaged over the stellar disk
(Joshi et al., 2012, and references therein).

We used three techniques to measure the magnetic fields: center of gravity,
regression, and LSD. A mean value of 1.23 was adopted for the effective Landé
factor that is slightly higher than the corresponding parameter in the
original paper by Bagnulo et al. (2002). An example of the intensity and
circularly polarized LSD profiles of HD 73619 is depicted in Fig. 7. The
magnetic field measurements are summarized in Table 7.

Figure 7: The intensity and circularly polarized LSD profiles of HD 73619.
Table 7: Summary of measurements of longitudinal magnetic field in HD 73619
and the standard stars. The third, fourth, and fifth columns represent the
magnetic field measured using classical center of gravity, regression and LSD
profiles, respectively. The errors of the magnetic field are given by
$\sigma$, $n$ is a number of measured lines.

Star Name | HJD (2 450 000+) | $B_{z}^{\mathrm{g}}\pm\sigma(n)$ | $B_{z}^{\mathrm{r}}\pm\sigma$ | $B_{z}^{\mathrm{LSD}}\pm\sigma$
---|---|---|---|---
| (day) | (G) | (G) | (G)
HD 73619 | 8578.300 |  $125\pm 50$ (215) | $120\pm 30$ | $70\pm 50$
| 8579.293 |  $-150\pm 50$ (82) | $-115\pm 30$ | $-30\pm 30$
|  |  $-180\pm 50$ (74) | $-110\pm 25$ |
HD 52711 | 8578.321 |  $3\pm 50$ (267) | $10\pm 20$ | $0\pm 40$
| 8579.307 |  $170\pm 50$ (244) | $150\pm 40$ | $110\pm 30$
53 Cam | 8578.330 |  $-4960\pm 150$ (204) | $-3730\pm 80$ | $-2837\pm 50$
| 8579.314 |  $-3640\pm 150$ (204) | $-2680\pm 90$ | $-2170\pm 50$

Besides the target star HD 73619, during the same nights we also observed HD
52711 and 53 Cam as non-magnetic and magnetic standard stars, respectively.
For each standard star, two spectra were obtained, one per night of
observation. Within the observational uncertainties, the measured values of
the magnetic field in 53 Cam are consistent with the published results (e.g.,
Hill et al., 1998; Kochukhov et al., 2004; Martínez-Arnáiz et al., 2010).
Unlike the magnetic standard stars, a solar-type star such as HD 52711 should
not manifest a magnetic field within the typical $B_{z}$ measurement
uncertainties. A spurious signal of circular polarisation in one spectrum of
HD 52711 obtained during the second night, is attributable to instrumental
effects.

This signal, in combination with an incomplete separation of lines in the
spectrum of HD 73619, is the apparent cause for the measured negative
longitudinal magnetic field of the star. To check the reliability of this
result, we constructed a mask of not-blended lines belonging to the different
components and measured the signal only within the mask. Taking into account
this finding, we conclude that both components of the HD 73619 system do not
possess a magnetic field above 200 G. Nevertheless, in light of multiple
observations of the extremely weak magnetic fields seen in some Am stars, we
propose additional high-resolution spectropolarimetric observations prior to
any confirmation of magnetic field strengths at the sub-hundred Gauss level.

##  6 Surface Rotation

As a part of the Nainital-Cape survey, a total of 337 Ap and Am stars were
monitored to search for photometric variability and most of them turned out to
be non-variables. The most plausible reason is because the light variations
(if any) are of low amplitude, and thus undetectable from the ground. Using
the high-precision space-based K2 data, we confirm the presence of sub-milli-
magnitude amplitude light variability in HD 73045, HD 73574, HD 73618, HD
73619, and HD 76310, which were previously classified as non-variable stars as
part of the Nainital-Cape survey. In the following subsections, we discuss the
possible sources of light variation.

###  6.1 Rotational Modulation

Rotational modulation in the light curve of a periodic variable is an
indication of the presence of star spots or co-rotating clouds. The
periodogram associated with rotational modulation can be characterized by the
presence of harmonics of the rotation period (e.g., Santos et al., 2017).
However, rotational variables may not always exhibit detectable harmonics
besides the fundamental period. Therefore, at low frequencies, it becomes
increasingly difficult to distinguish between binarity and rotation.
Nevertheless, the amplitude of light variations due to co-rotating star spots
may change in time because of spot evolution, whereas the amplitude of light
variations due to orbital motion is expected to remain unchanged during the
time of observation.

In order to understand the nature of low-frequency variations in A-type stars,
Balona (2011) assumed that the frequency of highest amplitude in the frequency
range $0.1$ d${}^{-1}<f<5.0$ d-1 is the rotation frequency. There are two ways
of validating that the variability is due to rotational modulation. One way is
to demonstrate that there is a relationship between the projected rotational
velocities, $v\sin i$, and the predicted equatorial rotational velocities,
$v_{\rm rot}$. Since sin $i\leq 1$, the expectation is that in a plot of
$v\sin i$ as a function of $v_{\rm rot}$, all points will lie below or (less
frequent) on the line $v\sin i$ $=$ $v_{\rm rot}$, subject to measurement
errors (Balona, 2017). Another method is to show that for stars in the main-
sequence band the distribution of $v_{\rm rot}$, derived from the rotational
frequency $f_{\rm rot}$ and from an estimate of the stellar radius, matches
the distribution of $v_{\rm rot}$ derived from spectroscopic measurements of
$v\sin i$ for stars in the same stellar effective temperature range (Balona,
2013).

Fig. 8 shows the distribution of $v\sin i$ as a function of the $v_{\rm rot}$.
From this figure, it is evident that two stars, namely HD 73045 and HD 76310,
are located below the line corresponding to the inclination angle $i=90$ °.
Therefore, the observed variations are compatible with an interpretation of
spot-like features. Based on the two observations available to us, we classify
HD 73045 and HD 76310 as rotational variables. For the remaining two stars, HD
73574 and HD 73618, positioned above the diagonal line, the source of
variability is unknown, thus demanding further investigations. We did not
include HD 73619 in Fig. 8 because its dominant signal is clearly of orbital
origin.

Figure 8: The projected rotational velocity $v\sin i$ as a function of
predicted equatorial rotational velocity $v_{\rm rot}$ for the target stars.
The blue, green, and black dashed lines correspond to the inclination angle
$i=90$°, 60°, and 30°, respectively. Note that HD 73619 is not included in
this diagram because its photometric signal is orbital in nature.

###  6.2 Surface Mapping

In order to confirm the presence and locations of spots on stellar surfaces,
the phased light curves were transformed into stellar images using the
inversion technique developed by Savanov & Strassmeier (2008). The surface
mapping was performed for HD 73045 and HD 76310, classified as rotational
variables in Section 6.1. The data for the other stars contain many artefacts
that are most likely spacecraft-related (the regular thruster firings to
maintain pointing), hence the poor quality data prevent us to construct high-
precision spot maps.

The time-series data were divided into different observational data sets, each
covering one rotational period of the star. Hence, we analysed 43 and 8 data
sets for HD 76310 and HD 73045, respectively. The stellar surface was divided
into a grid of 6° $\times$ 6° pixels of unit area and the values of the
filling factor were determined for each grid pixel. The temperature
inhomogeneity maps were constructed for inclination angle $i$= 45°.

Fig. 9 shows the surface temperature inhomogeneity maps of HD 73045. There are
obvious concentrations of spots at two longitudes registered as two
independent spotted regions. The positions of the spots on the surface of HD
73045 vary rapidly on time-scales of one rotational period of about 13 days.
The maps clearly reveal that spots are continuously changing their location in
longitudinal direction, a clear indication of rotation. For HD 76310 (Fig.
20), there is typically only one spotted region at longitudes corresponding to
phases 0.5 – 0.7, but for the map numbers from 10 to 15, 29, 32, and 35, two
spot-like structures are visible. Furthermore, the light curves become more
flattened. The spot shape in most of the maps is elongated; one can also
assume that for maps from 10 to 15, a single spotted region is split into two
regions. This result supports our previous detailed analysis of spot activity
for several Am stars (Savanov, 2018) exhibiting complex behaviours depending
on the positions of spots on the stellar surfaces.

Figure 9: Temperature inhomogeneity maps of HD 73045 constructed for eight
data sets. All maps use the same scale. Darker areas imply a higher spot
filling factor (i.e., darkest regions correspond to a filling factor of about
0.994). The abscissa denotes the longitude in degrees and the ordinate denotes
the latitude in degrees. The phase diagrams show both the observed and the
model reconstructed light curves.

###  6.3 Wavelet Analysis

Akin to sunspots, the star spots are well-established tracers of stellar
rotation, but their dynamic behaviour may also be used to analyze other
relevant phenomena, such as stability, stellar magnetic activity, and cycles
(García et al., 2010; Mathur et al., 2014). Similar to sunspots, the size and
location of star spots also change; sometimes they suddenly appear or vanish.
One might expect the same behaviour for spots on A-type stars, leading to
variations in the amplitude of the frequencies. In order to investigate the
change in frequency, we constructed time–frequency diagrams for the K2 data
sets of each star based on the wavelet technique that allows a better
interpretation of the physical features (such as spots) prior to their
consideration for period refinement (Torrence & Compo, 1998; Mathur et al.,
2010).

For a given signal, this technique permits the analysis of frequency (or
period) variations with time (non-stationary signals). The Morlet wavelet,
which is interpreted as the convolution of a sinusoidal and a Gaussian
function, was used as the reference wavelet (Goupillaud et al., 1984;
Holschneider et al., 1989). For a given frequency, we calculated the
correlation between the mother wavelet and the data by sliding the wavelet
along the time axis of the light curves, resulting in a wavelet power spectrum
(WPS). The WPS was then projected on the period axis to obtain the global
wavelets power spectrum (GWPS). The time–frequency plots of the studied stars
are shown in Fig. 10 and Figs. 33– 42. The black and blue colours in the maps
indicate regions of high and low power, respectively.

Figure 10: Wavelet map of HD 73045 using the C05 data. The top left panel
shows the light curve while on the top right is the associated power density
spectrum as a function of period between 0.5 and 50 d. The left panel of the
second row depicts the wavelet power spectrum (WPS) computed using a Morlet
wavelet between 0.5 and 50 d on a logarithmic scale and the associated global
wavelet power spectrum (GWPS) is in right panel of the second row. The black
and blue colours correspond to high and low power, respectively. The black-
crossed area is the cone of influence corresponding to the unreliable results.
The panel on the third row shows the autocorrelation function (ACF) of the
full light curve plotted between 0 and 50 d. Finally, the composite spectrum
(Ceillier et al., 2016, 2017) is shown in the bottom panel. The black dashed
lines mark the respective rotation period estimates.

In all these cases, the variable (non-stationary) signal is noticeable. The
variable signals in HD 73045 and HD 76310 could be due to the drifting of
spot-like features or spot growth and decay. For HD 73574, HD 73618 and HD
73619, variable signals are detected but do not seem to be of rotational
origin (spots). To confirm the nature of the signal in HD 73574, a light curve
of longer timescale is required while that in HD 73618 seems to originate from
the beating of close frequencies. The rotation periods ($P_{\rm GWPS}$)
extracted from the GWPS are 12.5 $\pm$ 1.05 d and 4.8 $\pm$ 0.45 d for HD
73045 and HD 76310, respectively. The detected periods $P_{\rm GWPS}$ for HD
73574, HD 73618, and HD 73619 are 14.0 $\pm$ 1.05 d, 3.8 $\pm$ 0.44 d, and
12.5 /12.7 $\pm$ 1.04 d, respectively. The error in the periods are derived
from the error in the frequencies, which are equivalent to the HWHM of the
peaks in the GWPS.

###  6.4 Autocorrelation Function Analysis

The surface mapping and the time-frequency analysis imprint the existence and
evolution of spots on the surface of rotational variables. We autocorrelated
the time-series data at a given time lag to reveal the spots possibly co-
rotating with the stars (McQuillan et al., 2013, 2014; García et al., 2014;
Santos et al., 2019). The positive and normalised resultant autocorrelation
functions (ACFs) have local maxima and minima that show the presence of spots
on these stars; they mimic the displacement equation for an under-damped
simple harmonic oscillator (uSHO) (Giles et al., 2017). In each ACF, the first
local maximum represents the dominant period ($P\rm_{ACF}$). The $P\rm_{ACF}$
values for HD 73045, HD 73574, HD 73618, and HD 76310 are 12.8 d, 13.5 d, 4.1
d, and 4.7 d, respectively for the K2 C05 data. These values are in good
agreement with the periods derived from the amplitude spectra, wavelet maps
and composite spectra (e.g., Fig. 10, and Table 8).

Table 8: The approximate spot radius ($R\rm_{spot}$) as derived from the amplitude, period ($P\rm_{ACF}$), and variation time-scale ($\tau_{\rm VT}$) as estimated from the autocorrelation functions and the rotation periods ($P\rm_{GWPS}$). The composite spectrum power estimate ($P\rm_{CS}$) is obtained from the respective global wavelet power spectrum and composite spectrum.  Star | Campaign | $R\rm_{spot}$ | $P\rm_{ACF}$ | $\rm\tau_{VT}$ | $P\rm_{GWPS}$ | $P\rm_{CS}$
---|---|---|---|---|---|---
Name |  | ($R\rm_{E}$) | ($\rm d$) | (d) | (d) | (d)
HD 73045 | C05 | 3.44 $\pm$ 0.18 | 12.8 | 18.67 $\pm$ 0.38 | 12.5 $\pm$ 1.04 | 12.7 $\pm$ 0.61
| C18 | 2.02 $\pm$ 0.17 | 12.8 | 16.07 $\pm$ 0.24 | 12.5 $\pm$ 1.05 | 12.8 $\pm$ 0.57
HD 73574 | C05 |  | 13.5 |  | 14.0 $\pm$ 1.05 | 13.8 $\pm$ 0.75
HD 73618 | C05 |  | 4.1 |  | 3.8 $\pm$ 0.44 | 3.9 $\pm$ 0.21
| C16 |  | 4.3 |  | 4.1 $\pm$ 0.44 | 4.3 $\pm$ 0.23
| C18 |  | 3.9 |  | 3.8 $\pm$ 0.44 | 3.8 $\pm$ 0.20
HD 73619 | C05 |  | 12.9 |  | 12.7 $\pm$ 1.04 | 12.8 $\pm$ 0.50
| C18 |  | 12.8 |  | 12.5 $\pm$ 1.04 | 12.7 $\pm$ 0.57
HD 76310 | C05 | 5.04 $\pm$ 0.27 | 4.7 | 19.31 $\pm$ 0.13 | 4.6 $\pm$ 0.45 | 4.7 $\pm$ 0.21
| C16 | 4.49 $\pm$ 0.26 | 4.9 | 18.55 $\pm$ 0.27 | 4.8 $\pm$ 0.45 | 4.9 $\pm$ 0.23
| C18 | 7.44 $\pm$ 0.30 | 4.8 | 21.68 $\pm$ 0.13 | 4.8 $\pm$ 0.45 | 4.8 $\pm$ 0.22

The values of the spot variation time-scale ($\tau_{\rm VT}$; related to the
time of visibility of the spot on the stellar disk) obtained from fitting the
ACF (C05) with an uSHO model are 18.67 $\pm$ 0.38 d for HD 73045 and 19.31
$\pm$ 0.13 d for HD 76310. We note, however, that the dominant frequencies in
the target stars, HD 73045 and HD 76310, are sustained for a duration longer
than the $\tau_{\rm VT}$ as estimated from the ACF analysis. Santos et al.
(2021) demonstrated that the $e$-folding time of the uSHO systematically
underestimates the characteristic spot time-scale. Moreover, the length of the
observations drastically limits the retrieved timescale (Santos et al., 2021).
As a result, the length of the K2 time-series might be insufficient to
constrain spot lifetimes through the ACF. Nevertheless, we list the values for
$\tau_{\rm VT}$, which should be considered as lower limits, and we advise
caution while interpreting the retrieved $\tau_{\rm VT}$. The additional
values of $\tau_{\rm VT}$ obtained using the remainder of the campaigns are
listed in Table 8.

Assuming that the amplitude of the rotational frequency is produced by a black
circular spot, the scenario is identical to the determination of exoplanet
sizes from a transit. Using K2 C05 data for HD 73045 and HD 76310,
respectively, the minimum spot radius ($R\rm_{spot}$) — as derived from the
photometric amplitude following a procedure described by Trust et al. (2020) —
are 3.44 $\pm$ 0.18 $R_{\rm E}$ and 5.04 $\pm$ 0.27 $R_{\rm E}$, respectively
(where $R_{\rm E}$ denotes Earth’s radius). The rest of the $R\rm_{spot}$
values obtained through other campaigns, when available, are given in Table 8.
The $\tau_{\rm VT}$ of the spotted regions in these stars is of the order of a
few weeks. Although, as discussed above, $\tau_{\rm VT}$ might not be a good
constraint for the spot lifetimes due to the length of the observations, these
results might point towards weak or non-existing magnetic fields in the
program stars. The origin and nature of spots on such stars is a topic that
will require detailed future modelling in consideration of that, e.g., a star
like HD 73045 known to be non-magnetic (Fossati et al., 2007) shows
unequivocal evidence of spots.

The composite spectrum (CS) combines the time-frequency analysis and the ACF,
while being the product of the normalized GWPS and the normalized ACF
(Ceillier et al., 2016, 2017). The period estimate, $P_{\text{CS}}$, including
the respective uncertainty, corresponds to the central period and HWHM of the
Gaussian function that fits the highest peak in the CS. The results from the
wavelet maps, and the ACF and CS analyses are listed in Table 8.

##  7 An observational H-R diagram

In order to infer the evolutionary status, the location of the target stars
within the H-R diagram needs to be precisely determined. Therefore, accurate
values for the effective temperature $T_{\textrm{eff}}$ and the luminosity
$L_{\star}$ need to be obtained; note that a typical error of 150 K in
$T_{\textrm{eff}}$ (as given by many traditional methods) entails an error of
about 0.2 mag in the bolometric magnitude (Neiner & Lampens, 2015).
Fortunately, high-resolution spectroscopy allows to deduce accurate values of
$T_{\textrm{eff}}$ and $\log(L_{\star}/{\rm L_{\odot}})$ as this method takes
into account line blanketing caused by the chemical peculiarities.

The values of $\log(L_{\star}/{\rm L_{\odot}})$ of the programme stars have
been calculated using the standard relation as discussed in Balona (2018). The
bolometric corrections for the Sloan Digital Sky Survey (SDSS) ugriz
photometric system were obtained from Girardi et al. (2004). For the
derivation of the absolute magnitude, the Gaia EDR3 parallaxes (Gaia
Collaboration et al., 2021) were used. Combining all these values yielded
adequate $\log(L_{\star}/{\rm L_{\odot}})$ values, which are presented in
Table 6.

Based on the derived $T_{\textrm{eff}}$ and $\log(L_{\star}/{\rm L_{\odot}})$
values, we placed the programme stars in the H-R diagram and their location is
shown in Fig. 11. On inspection of their position, we conclude that all stars
moved away from the ZAMS and are heading towards the Terminal Age Main
Sequence (TAMS). Considering the error boxes, all targets lie within the
$\delta$ Scuti observational instability strip as determined by Murphy et al.
(2019).

Figure 11: Location of the target stars in the H-R diagram. The solid green
lines represent the theoretical evolutionary tracks for the masses from 1.4
$M_{\odot}$ to 2.1 $M_{\odot}$ taken from Murphy et al. (2019). The blue and
red edges of the observational $\delta$ Scuti instability strip are over-
plotted with blue and red lines, respectively. The black dashed line
represents the ZAMS.

##  8 Comments on Individual Stars

Capitalizing on the unprecedented quality of photometric data obtained from
space missions, searches for photometric variability followed by
determinations of the various stellar physical properties using high-
resolution spectroscopy help us to ascertain the various stellar properties
and activities such as chemical peculiarities, spots, pulsation, and rotation.
The following subsections provide a brief summary and discussion about
individual stars along with information on their basic physical properties.

###  8.1 HD 73045/KW 538 (Praesepe)

HD 73045 is classified as an Am star by Bidelman (1956) and Bertaud (1960)
with a spectral type A7.2 (Kraus & Hillenbrand, 2007) and classified as an SB1
(Debernardi et al., 2000; Carquillat & Prieur, 2007). This star was
extensively studied by Fossati et al. (2007, 2008) who derived the basic
physical parameters, chemical composition. They reported that the star is of
non-magnetic nature.

HD 73045 was photometrically analysed using the HI-1A photometer of the
Heliospheric Imager (Eyles et al., 2009) aboard the STEREO spacecraft
(Driesman et al., 2008) — a study done by Paunzen et al. (2013) who reported a
variability period of 1.25 d. However, this variation was a consequence of the
pixel response function (PRF) of HD 73045 blending with that of its visual
neighbor BD+19°2046 (P. E. Williams, 2019, private communication). The blended
PRFs vary in shape and periodically bleed outside of the circular collection
aperture as the sources track across the instrument’s field-of-view. The
sources were found to shift from one $y$-pixel to the next with a period of
1.25 d, coinciding with the period reported by Paunzen et al. (2013). Our
analysis did not find any evidence for a periodicity of 1.25 d in the long
cadence as well as the short cadence K2 data, hence contradicting the findings
of the variability of 1.25 d reported by Paunzen et al. (2013).

Applying the analyses described in Section 2.2 to the LC K2 data, the
photometric variation exhibits a dominant component close to 12.65 d (12.68 d
for C05 and 12.64 d for C18). Both data sets also show similar secondary
signals at 6.42 d and 6.51 d, respectively. The WPS and GWPS (Fig. 10) also
shows an excess of power at around the half of the dominant period. These
secondary signals are close to harmonics of the dominant components. However,
they do not correspond exactly to harmonics as can be seen in the irregular
characteristic of the light curve, highlighted by the models (e.g., Fig. 3,
top-left, red), whereas a harmonic signal would exhibit a repetitive period-
to-period structure. This observed feature is also visible in other stars such
as HD 174356 (Bowman et al., 2018) and, with more complexity, in Atlas in the
Pleiades (White et al., 2017). Based on the surface map, time-frequency and
the ACF analyses, the origin of the periodic variability in HD 73045 could be
attributable to star spots situated at different latitudes on a star
exhibiting differential rotation. Particularly, the rotational modulation in
Fig. 3 shows a double dip feature which indicates the presence of at least two
dominant spots.

Analysing the C18 SC data (Fig. 22, top), the two main components described
above are observed. The main goal in studying these data, however, was to
confirm short-term variability (i.e., 16, 28.8, and 36 d-1) as previously
suspected by Joshi et al. (2015). However, as revealed in the Lomb-Scargle
spectral frequency distribution (Fig. 22, bottom), the range of interest (as
shown in the inset) exhibits no clear signals above the noise level that would
meet the FAP threshold criterion. In addition, the time-resolved radial
velocity analysis did not reveal any short-term variability. Therefore, within
the given photometric and spectroscopic detection limits, we conclude that HD
73045 is pulsationally stable. The RV values derived from our observations
agrees well with the previous measurements by Carquillat & Prieur (2007).
Indeed, the radial velocities, after being averaged over each series, are in
good agreement with theoretical predictions based on the published stellar
orbital parameters.

###  8.2 HD 73574/KW 203 (Praesepe)

HD 73574 is classified as A5V and A5III by Bidelman (1956) and Rebeirot
(1966), respectively. Fossati et al. (2008) determined the values for
$T\rm_{eff}$, $\log g$ and $\rm[F_{e}/H]$ as 7662 K, 4.00 (cgs) and 0.10,
respectively. This star was identified as a moderate rotator with $v\sin i$ of
120 km s-1 (McGee et al., 1967). The K2 C05 data set exhibits two periods,
namely, 10.8 d and 14.27 d (see Fig. 23). From the time-frequency as well as
the ACF and CS analyses of the K2 C05 data set, it is found that HD 73574
shows a periodicity of about 13.8 d (Fig. 34).

Using the spectroscopic observations, we derived values of $T\rm_{eff}$, $\log
g$, [M/H], $\rm\xi$, $\rm\nu$ sin $i$ and RV as $7700\pm 160$ K, $4.12\pm
0.21$ (cgs), $0.07\pm 0.11$, $2.12\pm 0.17$ km s-1, $99\pm 5$ km s-1, and
$29.2\pm 2.8$ km s-1, respectively.

###  8.3 HD 73618/KW 224 (Praesepe)

HD 73618 is classified as A0 spectral type (Cannon & Pickering, 1993). It is
also referred to as an Am star (Bidelman, 1956; Bertaud, 1960; Rebeirot,
1966). The $v\sin i$ value for this star was reported as 51 km s-1 (Abt &
Willmarth, 1999) and 44 km s-1 (Debernardi et al., 2000).

Mason et al. (1993) identified this star as the primary component of a SB1
binary system in which the flux of the secondary star does not significantly
influence the combined total flux spectrum. There are various studies about
the atmospheric parameters. Based on those determinations, $T_{\rm eff}$,
$\log g$, and $\rm[F_{e}/H]$ are given as 8060 K, 3.87 (cgs), and 0.46 by Hui-
Bon-Hoa et al. (1997), 8100 K, 4.00 (cgs), and 0.50 by Burkhart & Coupry
(1998), and 8170 K, 4.00 (cgs), and 0.46 by Fossati et al. (2007),
respectively. Fossati et al. (2007) did not find any detectable magnetic
field.

The K2 C05 data set (Fig. 25) shows a dominant peak at 3.78 d. In the C16 data
set (Fig. 26), the three peaks are given as 3.83 d, 4.87 d, and 2.49 d,
whereas in the C18 data set (Fig. 27), they are given as 3.76 d, 4.81 d, and
2.37 d. These main features are accompanied by lower amplitude, seemingly
unrelated, components, producing a rather complex time-series. The time-
frequency, ACF and CS analyses suggest a periodic variability of about 4 d
with its origin still undetermined.

An attempt was made to analyse the C16 and C18 time-series together, in a
$\sim$208-day dataset that includes a non-centered gap extending across 36 per
cent of the temporal baseline. While issues arise when applying Fourier
methods to gapped data (Munteanu et al., 2016), the Lomb-Scargle algorithm did
produce a periodogram with a frequency resolution of 0.05 d-1. Applying
oversampling to the Lomb-Scargle process introduced sidelobes that completely
corrupting the periodogram.

Based on our spectroscopic analysis, the derived parameters are given as
$T\rm_{eff}=7960\pm 180\,K$, $\log g$ $\rm=3.76\pm 0.19$ (cgs),
$\rm[M/H]=0.34\pm 0.11$, $\rm\xi=2.77\pm 0.16$ km s-1, $v\sin i$ $=56\pm 3$ km
s-1, and RV $=39.5\pm 0.5$ km s-1. Based on age and metallicity, Ahumada &
Lapasset (2007) classified HD 73618 as a blue straggler; hence, it can be
considered an ideal object for testing current models of collisionally formed
blue stragglers. The wide and detailed knowledge available on this star and
its environment should allow us to test the reliability of current models and
provide important constraints for future model development.

###  8.4 HD 73619/KW 229 (Praesepe)

HD 73619 is a member of the Praesepe open cluster (Sanford, 1931). Bidelman
(1956) identified this star as a classical Am star, with a spectral type given
as A4 and F0 III based on Ca ii K and metallic lines, respectively. Abt &
Willmarth (1999) and Debernardi et al. (2000) identified the projected stellar
rotational velocity as 20 and 11.2 km s-1, respectively.

The light curve of HD 73619 shown in the upper-left panel of Fig. 28 is
similar to that of a heartbeat star (Thompson et al., 2012; Fuller, 2017;
Hambleton et al., 2018; Wheeler & Kipping, 2019; van Kooten et al., 2020).
Analysis of the frequency spectrum provided orbital periodicities of 12.97 and
12.91 d from the C05 and C18 data, respectively. These values were confirmed
by using time-domain autocorrelation and box fitting (Kovács et al., 2002)
methods. Although HD 73619 was observed during Campaign 16 of the K2 mission,
its image was blended with HD 73598; thus, these C16 observations have been
excluded from this study.

A thorough search for any pulsational variability induced by tidal interaction
requires an accurate model to be constructed and subtracted from the light
curve, and the residuals analysed. While conservative sinusoidal models were
produced from a limited number of components (Table 3), many more components
would be required to reconstruct accurately the light curve. None of these
components relate to pulsational signals. Construction of a detailed model was
also attempted using the PHOEBE package (Prša & Zwitter, 2005), but the
procedure failed to converge. However, two other methods were performed to
probe the existence of pulsational phenomena.

One method involved separating the heartbeat light curve into separate intra-
period segments. Each segment was fit with an eighth-order polynomial, which
was subsequently subtracted from the data, resulting in respective sets of
residuals (Fig. 12, top left). These residual data-sets were analysed with the
LS algorithm to produce a frequency spectrum (Fig. 12, top right). While an
instrumental artifact appeared in the third and fourth segments of the C05
data, neither evidence of pulsation was observed nor any such evidence was
seen in the C18 data (Fig. 43). The other method involved using the K2SC
algorithm previously applied to clean SAP light curves. This process also
produced a de-trended residual data-set with the dominant heartbeat signal
removed (Fig. 12, middle). Again, the data-sets were analysed using the LS
algorithm with no evidence of pulsation signals neither in the C05 (Fig. 12,
bottom) nor the C18 (Fig. 43, middle and bottom) found. In conclusion, within
the limits of our analysis, HD 73619 shows no evidence of pulsational
variability.

Figure 12: The top five rows illustrate the residual light curve (left) and
amplitude spectrum (right) of HD 73619 after removing the heartbeat signal
from five segments of the C05 time-series. The $\sim$0.5 d-1 spectral peak in
segments 3 and 4 are related to an instrumental artifact. The middle panel
shows the complete time-series after being de-trended by the k2sc algorithm
with its respective amplitude spectrum in the bottom panel. Neither analysis
indicates any evidence for the existence of pulsation phenomena.

Based on the parameters given in Table 5, we ratify that the two components of
the heartbeat system have similar characteristics. From Fig. 4, our revised
radial velocities support the orbital solution determined by Debernardi et al.
(2000). Moreover, Debernardi et al. (2000) reported an orbital period of
12.91124 $\pm$ 0.00004 d. This implies that the dominant 12.91 d signal
detected in both K2 data sets is orbital in nature. The spectropolarimetric
analysis indicates that, within the observational uncertainty of 200 G,
magnetic fields in HD 73619 are either weak or absent.

###  8.5 HD 76310

Cowley & Cowley (1965b) classified HD 76310 as an Am star. The projected
rotational velocity $v\sin i$ as a function of the predicted equatorial
rotational velocity $v_{\rm rot}$ for the target stars. The blue, green, and
black dashed lines correspond to the inclination angle $i=90$°, 60°, and 30°,
respectively. Note that HD 73619 is not included in this diagram because its
photometric signal is orbital in nature.

All three K2 data sets tend to be dominated by two components at $\sim$4.7 d
and $\sim$5.4 d, with variation around those values across the campaigns.
These close frequencies result in well-pronounced beating effects in C05 (Fig.
30) and C16 (Fig. 31), but less interaction between the components during C18
(Fig. 32) where the shape of the time-series varies across the periods. The
level of these interactions are defined by the ratio of their amplitudes. Also
note that overtones of the $\sim$4.8 d feature seem to exist, although they do
not always clear the FAP threshold and, in some cases, are obscured by the
background noise. Finally, it is noteworthy that the modeling of the C05 time-
series failed to produce a good fit to the data when the single component
relating to the dominant 4.622 d peak was included, and two other components
at around $\pm$0.3 d either side of the peak were required to better fit the
data. From the time-series analysis of the K2 data, the surface map, the
wavelet, the ACF, and the composite spectrum, a dominant period close to 4.7 d
was obtained. Given that the photometric amplitude of HD 73610 changes
significantly within only a few dozen variability cycles, we may not rule out
the possibility of having unresolved multiperiodic pulsational signals, for
instance of the $\gamma$ Doradus type. An attempt to analyse the combined
time-series of C16 and C18, corresponding to that for HD 73618, was performed
with a similar outcome.

On investigating the $v\sin i$ vs. $v_{\rm rot}$ diagram in Fig. 8, HD 76310
was found to be positioned below the line of sin $i=1$. Based on the surface
maps, wavelet, and ACF, we thus categorise this star as a rotational variable.
The LSD profiles shown in Fig. 13 indicate a complex structure. The RV values
obtained at different epochs (December 2018 and April 2020) are the same
within the observational uncertainty (i.e., $20.13\pm 0.40$ km s-1 and
$20.22\pm 0.83$ km s-1, respectively). The similarity between the shapes of
the LSD profile of HD 76310 and the CCF profile of KIC 11572666 (Lampens et
al., 2018) implies that the system is an SB2 system. We fitted the MRES
spectrum of HD 76310 with a composite model using the 2D version of girfit in
spectral regions around Hγ (430 – 440 nm), Hβ (470 – 500 nm), Hα (630 – 680
nm), and the Mg i triplet (510 – 520 nm). We treated the component $T_{\rm
eff}$, $v\sin i$, RV and the luminosity ratio as free parameters while keeping
$\log g$ fixed at 4.0 (cgs).

Figure 13: The LSD profiles for HD 76310 based on HESP (red) and MRES (black)
data.

The composite spectrum was fitted well (e.g., see Hβ line in Fig. 14); thus,
we adopted the mean values of the stellar parameters from these spectral
regions. The obtained values are: effective temperature of $T_{\rm
eff1}=7030\pm 170$ K and $T_{\rm eff2}=6470\pm 220$ K, $v\sin i$ of $97.1\pm
0.4$ km s-1 and $9.3\pm 0.7$ km s-1, RV of $27.4\pm 1.8$ km s-1 and $19.8\pm
2.8$ km s-1, respectively, with a light ratio $l_{1}$ of $0.887\pm 0.023$ (see
Table 5).

Figure 14: The Hβ MRES spectrum for HD 76310 (black) and the composite model
spectrum (red) obtained using the 2D version of girfit.

Based on the rotational velocities and periods of HD 76310, the source of the
stellar photometric variability, as indicated, could be the sharp-lined and
cooler component, thus favouring the stellar binarity hypothesis. It is also
noteworthy that HD 76310 is included in the Washington Double Star Catalogue
(Mason et al., 2001) as a system consisting of two equally bright stars
separated by $0.1$ arcsec. Nevertheless, there is still the possibility that
HD 76310 is a single star surrounded by a cloud shell (Slettebak, 1986; Fekel
et al., 2003). Future observations would be crucial for exploring the
variability and possible binarity nature of this object (Welsh & Montgomery,
2013).

##  9 Conclusions and Future Prospects

Based on the time-series photometry obtained from the ground, the K2 mission
and from contemporaneous high-resolution spectroscopy and spectropolarimetry,
we arrived at the following conclusions:

  * •

All targets in the study sample, previously part of the Nainital-Cape survey
and classified as constant stars, are now (potentially) identified as
variables. Our analysis suggests that HD 73045 and HD 76310 are rotational
variables. The LSD profiles of HD 76310 indicates that this star is part of
binary system or surrounded by a cloud shell. The light variation recorded for
HD 73619 is consistent with orbital signals and likely to be the first
chemically peculiar Am star in a heartbeat system without tidally induced
pulsations. As we could not ascertain the origin of the variability of HD
73574 and HD 73618, further time-domain studies are needed to apprehend the
nature of these objects.

  * •

Within the detection limits of the K2 photometry and radial velocity
measurements, we conclude that HD 73045 is pulsationally stable contrary to
the previous prediction by Joshi et al. (2015). Similarly, the analysis of the
K2 data revealed the absence of a periodicity of 1.25 d previously reported by
Paunzen et al. (2013); it is confirmed as previously erroneous.

  * •

High-resolution spectroscopy measurements obtained with two spectrographs at
different epochs revealed that the HD 73619 system is comprised of two stars
with similar properties. The individual radial velocities of HD 73619 at the
different epochs are in good agreement with the orbital solution by Debernardi
et al. (2000). The spectropolarimetric data analysis indicates that HD 73619
may possess a weak magnetic field, hence additional high-resolution
spectropolarimetric observations would be essential for confirmation.

  * •

The atmospheric parameters of the target stars have been derived using high-
resolution spectroscopy. Considering observational uncertainties, it is found
that all the studied stars are evolved away from the ZAMS and located within
the $\delta$ Scuti instability strip.

The potential presence of a weak magnetic field in HD 73619, and the surface
spots seen on HD 73045 and HD 76310, constitute further evidence that magnetic
fields cannot be disregarded when exploring the origin of the peculiar
chemical abundances in Am stars. The magnetic fields leading to the formation
of the surface spots might not be stable, suggesting that they may be
dominated by the dynamo effect. It is unclear if (or how) magnetic fields
would affect the diffusion model for the formation of the peculiar chemical
abundances in these stars, or whether alternative formation mechanism(s) would
be needed to explain these phenomena.

The origin of weak magnetic fields in metallic line (Am) stars and even in
normal $\delta$ Sct stars (hotter than Sun) are fossil or related to a dynamo
effect is still largely an unsolved problem, although copious valuable
contributions for A-type stars have previously been made (e.g., MacDonald &
Mullan, 2004). A detailed study of the various underlying processes,
particularly the diverse theoretical aspects require more attention. Future
studies are relevant to the bigger picture of stellar and galactic evolution,
in consideration of the significance of massive stars, notably for the
production and proliferation of heavy elements as well as the overall galactic
chemistry (e.g., Matteucci, 2021, and references therein).

Our overall long-term goal of this work is to continue the study of stellar
structure and atmospheres of CP stars as well as of magnetic fields,
inhomogeneities (such as spots), and tidal interaction. In the framework of
our ongoing research, our future plan is to extend the detailed analysis of
heretofore unstudied CP stars with TESS data in combination with future high-
resolution spectroscopic and spectropolarimetric observations.

## Acknowledgments

The work presented here is supported by the Belgo-Indian Network for Astronomy
and astrophysics (BINA), sanctioned by Department of Science and Technology
(DST, Govt. of India; DST/INT/Belg/P-09/2017) and the Belgian Federal Science
Policy Office (BELSPO, Govt. of Belgium; BL/33/IN12). OT and EJ thank the
International Science Programme (ISP) of Uppsala University and African
Astronomical Society (AfAS) for financial support. DLH acknowledges financial
support from the Science and Technology Facilities Council (STFC) via grant
ST/M000877/1. AG, DM, and SJ are grateful for the support received from the
Indo-Thailand Programme of co-operation in Science and Technology through the
Indo-Thai joint project DST/INT/Thai/P-16/2019. FKA and SC thanks the Polish
National Center for Science (NCN) for grant 2015/18/A/ST9/00578. RAG
acknowledges support from the CNES PLATO grant. SM acknowledges support from
the Spanish Ministry with the Ramony Cajal fellowship number RYC-2015-17697.
ARGS acknowledges support from NASA under Grant No. NNX17AF27G and from STFC
consolidated grant ST/T000252/1. IS thanks the Government of the Russian
Federation and the Ministry of Higher Education and Science of the Russian
Federation, grant no. 075-15-2020-780 (N13.1902.21.0039). This paper includes
data collected by the K2 mission available at Mikulski Archive for Space
Telescopes (MAST), SIMBAD and NASA’s ADS. The authors thank the anonymous
reviewer for the insightful comments and suggestions which led to the
improvement of the manuscript.

## DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the
corresponding author.

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##  Appendix A Author Affiliations

1Aryabhatta Research Institute of Observational Sciences, Manora Peak,
Nainital-263002, India
2Department of Physics, Mbarara University of Science and Technology, P.O. Box
1410, Mbarara, Uganda
3National Astronomical Research Institute of Thailand, Chiangmai 50180,
Thailand
4Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnii
Arkhyz 369167, Russia
5Affiliate Faculty, Physics and Astronomy Department, George Mason University,
Fairfax, VA 22030, USA
6Royal Observatory of Belgium, Ringlaan 3, B-1180 Brussel, Belgium
7Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1
2HE, UK
8CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France 9AIM, CEA, CNRS,
Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité,
F-91191 Gif-sur-Yvette, France
10Universidad de La Laguna (ULL), Departamento de Astrofísica, E-38206 La
Laguna, Tenerife, Spain
11Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife,
Spain
12Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
13Space Science Institute, 4765 Walnut Street, Suite B, Boulder, CO 80301, USA
14Indian Institute of Astrophysics, Koramangala, Bangalore-560034, India
15Department of Physics, University of Texas at Arlington, Arlington, TX
76019, USA
16Department of Physics and Astronomy, National Institute of Technology,
Rourkela - 769008, Odisha, India
17Copernicus Astronomical Center, Bartycka 18, PL-00-716 Warsaw, Poland
18Çanakkale Onsekiz Mart University, Faculty of Sciences and Arts, Physics
Department, 17100 Canakkale, Turkey
19 Centre for Space Research, North-West University, South Africa
20Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus
University, Ny Munkegade 120, Denmark
21Institute of Astronomy, Russian Academy of Sciences, Moscow-119017, Russia
22Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles,
Boulevard du Triomphe, 1050-Bruxelles, Belgium
23Kourovka Astronomical Observatory, Ural Federal University, Yekaterinburg,
Russia
24M. V. Lomonosov Moscow State University, P. K. Shternberg State Astronomical
Institute, Moscow, Russia
25SoS in Physics and Astrophysics, Pt. R. S. University, Raipur-492010, India
26Institute of Informatics and Communication, University of Delhi South
Campus, New Delhi, India
27Department of Physics, Kyambogo University, P. O. Box 1, Kyambogo, Kampala,
Uganda
28 Indian Institute of Science (IISc), Bengaluru, India

##  Appendix B K2 Photometric Data Analysis

We analysed the K2 data discussed in Section 2.2. From these data sets, the
flux (in e- s-1), $F_{i}$, over a set of $N$ sample times, $t_{i}$, with
indices $i=\\{0,1,2,...,N-1\\}$, was analysed to search for photometric
variability. The analysis processes, as described below, were applied to the
long cadence data of all stars. The analysis of the short cadence data
acquired for HD 73045 was performed in a similar manner.

To begin, each time step, $t_{i}$, was defined in a way that $t_{0}$ = 0; this
was done by subtracting the original Barycentric Julian Date (BJD) times,
$\tau_{i}$, by that of the first point, $\tau_{0}$, using

$t_{i}=\tau_{i}-\tau_{0},$ (1)

where $\tau_{0}$ = 2 457 139.63 days, 2 458 095.49 days, and 2 458 251.57 days
for C05, C16, and C18, respectively.

The flux data were re-calibrated as a magnitude deviation, $\Delta\it{m}_{i}$,
of each flux, $F_{i}$, from its mean, $\langle F\rangle$. For all $N$ data
points in a data set, at a corresponding time, $\it{t}_{i}$, the $i$-th
magnitude deviation data point in the series is defined by

$\Delta m_{i}=-2500\log_{10}\left(\frac{F_{i}}{\langle F\rangle}\right),$ (2)

where $\Delta\it{m}_{i}$ is calculated in mmag (hence the incorporated factor
of 1000). To prepare these data for the signal analysis process, variable
artifacts, such as those possibly left over from the PDC process were removed
by subtracting an eighth order polynomial, although it is noted that such
artifact removal may also cancel any intrinsic variability component of a
corresponding frequency. Subsequently, the signal search was focused on
periods shorter than 20 days. The median value of the data was also
subtracted. As an example, the analysed photometric light curve of HD 73045
obtained during C18 campaign is shown in Fig. 3 (top-left, blue points).

To analyse a light curve in the frequency domain, the Lomb-Scargle (LS)
algorithm (Lomb, 1976; Scargle, 1989) was applied to the time-series data,
noting that the original SAP data are irregularly sampled. The Nyquist
frequency $(2dt)^{-1}$ for LC (29.4 min cadence) and SC (58.8 s cadence)
sampling are $\sim$24.5 d-1 and $\sim$735 d-1, respectively. Each campaign
occupies its own temporal range $T$, giving in a respective frequency
resolution, $\Delta\it{f}$. For example, C18 has a temporal window of
$T=50.814$ d, providing a frequency resolution of $\Delta\it{f}$ = 0.0197 d-1
that allows an estimate for the peak frequencies and corresponding amplitudes.
To improve signal peak definition and to better estimate the peak frequencies
and amplitudes, oversampling was applied to provide a frequency domain sampled
every 0.001 d-1. Although the half-width at half-maximum (HWHM) of a peak is
often used to estimate the accuracy of the peak frequency, VanderPlas (2018)
suggests avoiding this approach through computing the false-alarm probability
(FAP) for each peak. This criterion estimates the probability that a peak was
produced by noise as opposed to an inherent signal. The lower the value of the
FAP, the more likely that a given peak is real. Furthermore, Frescura et al.
(2008) noted the subjectivity of the noise level determination in calculating
the signal-to-noise ratio, which is often used to select relevant peaks from
the background noise spectrum (Breger et al., 1993). Therefore, while the
amplitude signal-to-noise value was calculated for candidate signal peaks,
through the use of a smoothing function across the frequency spectrum to
calculate the noise spectrum, the FAP was used as the selection criterion to
determine a signal’s validity. For this study, the independent frequency
method (VanderPlas, 2018) was applied to calculate the FAPs of respective
spectral amplitudes across the frequency domain. After a provisional analysis,
a threshold FAP of $10^{-8}$ was adopted across all data sets to provide a
consistent, conservative criterion for identifying true signals amongst the
noise, which is noted by Bowman et al. (2018) to be particularly significant
at low frequencies. An example periodogram (logarithm of the period versus
amplitude) is shown in Fig. 3 (bottom, blue-line) for the C18 data set for HD
73045. The frequencies, periods, and amplitudes for peaks with FAP values of
$10^{-8}$ and below, for all stars during their respective campaigns as a
result of performing the Lomb-Scargle analysis are listed in Table 9.

Next, the time-series data were analysed to determine the frequency, $f$,
amplitude, $A$, and the phase at $t_{0}=0$, $\phi(t_{0})$, from which a model
of the light curve was constructed. Using the results of the Lomb-Scargle
analysis as initial starting points, sinusoidal components incorporating these
parameters were determined by sequentially fitting a series of components in
the form of a sinusoid plus an offset, $Z$, to the data:

$\Delta m_{i}=Z+A\sin(2\pi ft_{i}+\phi),$ (3)

where $\phi$ is the phase derived from the fit and is described below.

Using the methods of Montgomery & O'Donoghue (1999), the corresponding errors,
$\sigma(f)$, $\sigma(A)$, and $\sigma(\phi)$, were also derived using:

$\sigma(f)=\sqrt{\frac{6}{\mathcal{N}}}\frac{1}{\pi\mathcal{T}}\frac{\sigma{(\Delta
m)}}{A},$ (4)

$\sigma(A)=\sqrt{\frac{2}{\mathcal{N}}}\sigma{(\Delta m)},$ (5)

$\sigma(\phi)=\sqrt{\frac{2}{\mathcal{N}}}\frac{\sigma{(\Delta m)}}{A}.$ (6)

Here, $\mathcal{N}$ is the number of terms in a regularly sampled time series
with an interval $\Delta t$, $\mathcal{T}=\mathcal{N}\Delta t$ is the time
range of the data set, $A$ is the amplitude of the sinusoidal fit, and
$\sigma{(\Delta m)}$ is the root mean square of the flux deviation values.

To determine these sinusoidal parameters and their uncertainties, the data
were resampled at the regular 29.4-min cadence using cubic spline
interpolation. Next, the time was adjusted such that the zero point was placed
at the center of the data set by subtracting the average of the resampled time
array. Using the Lomb-Scargle results as a starting point, single sinusoids
were sequentially fit using Eqn. 3 and subtracted from the time-series, until
all components (i.e., those with Lomb-Scargle FAP values below the threshold)
were accounted for. The fitting process allowed the amplitude to vary within
20 per cent about its LS value, while the frequency was allowed to vary within
0.01 d-1 about its input value. From the resulting phase value, $\phi$, which
is determined at this central point, the phase of the first point of the fit,
$\phi(t_{0})$, was calculated.

For any component with a variation period $P$, the phase of each data point
$\phi_{i}$, at time $t_{i}$ relative to the first point in the data series at
time $t_{0}$, can be calculated using

$\phi_{i}=2\pi\left(\frac{t_{i}-t_{0}}{P}-\left\lfloor\frac{t_{i}-t_{0}}{P}\right\rfloor\right),$
(7)

which simplifies when $t_{0}=0$. From this, phase-folded plots of the time-
series were produced corresponding to the dominant period of each star for
each campaign. The C18 HD 73045 data are folded to the dominant period of
12.64 d in Fig. 3 (top-right) along with a sinusoidal fit to this component
(red-line) with the parameters given in Table 3.

Table 9: Flux variation signal properties (ordered by amplitude) derived from applying the Lomb-Scargle analysis to the all flux-deviation data sets. For HD 73045, C18, refer to the blue-line peaks of Fig. 3 (bottom). Star Name | Campaign | Frequency | Period | Amplitude | log10(FAP)
---|---|---|---|---|---
|  | (d-1) | (d) | (mmag) |
HD 73045 | C05 | 0.078 | 12.82 | 0.112 | -302
|  | 0.155 | 6.452 | 0.039 | -33
|  | 0.054 | 18.52 | 0.0309 | -18
|  | 0.138 | 7.246 | 0.029 | -17
|  | 0.171 | 5.848 | 0.022 | -8
| C18 | 0.079 | 12.66 | 0.039 | -95
|  | 0.155 | 6.452 | 0.022 | -29
HD 76310 | C05 | 0.217 | 4.608 | 0.498 | -361
|  | 0.186 | 5.376 | 0.189 | -49
|  | 0.421 | 2.375 | 0.113 | -15
|  | 0.049 | 20.41 | 0.105 | -13
|  | 0.159 | 6.289 | 0.095 | -10
| C16 | 0.209 | 4.785 | 0.398 | -331
|  | 0.187 | 5.348 | 0.333 | -231
|  | 0.076 | 13.16 | 0.104 | -19
|  | 0.430 | 2.326 | 0.089 | -13
|  | 0.969 | 1.031 | 0.081 | -11
|  | 0.058 | 17.24 | 0.072 | -8
| C18 | 0.206 | 4.854 | 1.094 | -420
|  | 0.177 | 5.650 | 0.275 | -24
|  | 0.430 | 2.326 | 0.188 | -9
HD 73574 | C05 | 0.070 | 14.29 | 0.8139 | -76
|  | 0.091 | 10.99 | 0.3827 | -14
| C18 | 0.091 | 10.99 | 0.0513 | -9
HD 73618 | C05 | 0.264 | 3.788 | 0.415 | -274
|  | 0.205 | 4.878 | 0.228 | -81
|  | 0.410 | 2.439 | 0.152 | -34
|  | 0.244 | 4.098 | 0.104 | -14
|  | 0.431 | 2.320 | 0.102 | -13
|  | 0.184 | 5.435 | 0.086 | -9
| C16 | 0.261 | 3.831 | 0.320 | -254
|  | 0.205 | 4.878 | 0.287 | -203
|  | 0.401 | 2.494 | 0.137 | -44
|  | 0.225 | 4.444 | 0.135 | -43
|  | 0.418 | 2.392 | 0.104 | -24
|  | 0.242 | 4.132 | 0.094 | -19
|  | 0.290 | 3.448 | 0.074 | -10
|  | 0.448 | 2.232 | 0.069 | -9
| C18 | 0.266 | 3.759 | 0.595 | -256
|  | 0.213 | 4.695 | 0.249 | -42
|  | 0.196 | 5.102 | 0.194 | -24
|  | 0.417 | 2.398 | 0.190 | -23
|  | 0.238 | 4.202 | 0.125 | -8
|  | 0.295 | 3.390 | 0.123 | -8
HD 73619 | C05 | 0.077 | 12.987 | 0.388 | -289
|  | 0.155 | 6.452 | 0.210 | -82
|  | 0.233 | 4.292 | 0.160 | -46
|  | 0.058 | 17.241 | 0.108 | -19
|  | 0.042 | 20.810 | 0.098 | -16
|  | 0.310 | 3.226 | 0.095 | -14
|  | 0.096 | 10.417 | 0.082 | -10
| C18 | 0.077 | 12.987 | 0.324 | -217
|  | 0.156 | 6.410 | 0.163 | -52
|  | 0.235 | 4.256 | 0.103 | -19
|  | 0.112 | 8.929 | 0.075 | -9

##  Appendix C Supplementary Materials

Table 10: Ground-based CCD photometric observations of HD 73045 obtained from various optical telescopes located at different sites. S. No. | Observatory | Telescope | Filters | Exposure Time | Total Durations | Date | HJD
---|---|---|---|---|---|---|---
|  | Diameter (m) |  | (s) | (h) | dd-mm-yyyy | (d)
1. | ARIES | 1.04 | V | 2 | 1.47 | 16-04-2014 | 2456764
2. |  |  | V | 3 | 0.92 | 20-04-2014 | 2456768
3. |  |  | B | 5 | 2.53 | 21-04-2014 | 2456769
4. | Devasthal | 1.30 | B | 5 | 1.80 | 02-11-2014 | 2456964
5. |  |  | V | 4 | 1.47 | 11-11-2014 | 2456973
6. |  |  | B | 4 | 0.17 | 30-11-2014 | 2456992
7. |  |  | V | 15 | 0.85 | 30-12-2015 | 2457387
8. |  |  | V | 10 | 0.57 | 27-01-2016 | 2457415
9. |  |  | B | 15 | 2.12 | 28-01-2016 | 2457416
10. |  |  | V | 3 | 2.02 | 19-12-2016 | 2457742
11. | MASTER-II | 0.40 | B, V | 5 | 2.92, 2.92 | 09-11-2015 | 2457336
12. | -URAL |  | B | 5 | 1.35 | 22-01-2016 | 2457410
13. |  |  | B, V | 5 | 0.13,0.13 | 13-02-2016 | 2457432*
14. |  |  | B | 5 | 4.00 | 11-03-2016 | 2457459
15. |  |  | V | 5 | 3.97 | 14-03-2016 | 2457463
16. |  |  | B, V | 5 | 3.96, 3.96 | 15-03-2016 | 2457478
17. | PROMPT-8 | 0.60 | B | 4 | 1.26 | 12-05-2014 | 2456790
18. |  |  | B | 4 | 0.27 | 14-05-2014 | 2456792
19. |  |  | B | 4 | 1.65 | 16-05-2014 | 2456794
20. |  |  | B | 15 | 1.10 | 11-01-2015 | 2457033
21. |  |  | B | 20 | 1.21 | 09-02-2015 | 2457062
Figure 15: Light curves for HD 73045 from ground-based observations with
B-filter. Figure 16: Light curves for HD 73045 from ground-observations with
V-filter. Figure 17: RV curve (panels on the left) and power spectrum (panels
on the right) of the radial velocity measurements for HD 73045 from MRES data.
The black horizontal dashed line in the power spectrum represents SNR of 4.
Figure 18:  RV curve (panels on the left) and power spectrum (panels on the
right) of the radial velocity measurements for HD 73045 from HERMES data. The
black horizontal dashed line in the power spectrum represents SNR of 4.
Figure 19: RV of HD 73045, as measured by us (blue), compared to the orbital
solution by Carquillat & Prieur (2007) (grey). Figure 20: As Fig. 9, but spot
maps for HD 76310. Figure 21: As Fig. 3, but for the LC K2 Campaign 5
observations of HD 73045. Figure 22: Top: Time series photometric variability
(in mmag) of HD 73045 from the SC 2018 K2 Campaign 18. The PDC_SAP data
includes intrinsic signals as well as systemic and noise artifacts. Bottom:
Frequency distribution of spectral amplitudes, in mmag, derived from applying
the Lomb-Scargle algorithm to the time series. The frequency range from 10 –
40 d-1 is expanded into the inset to provide more detail of that range. It can
be seen there are no signals related to those from the earlier ground-based
observations and that this range is dominated by noise. Figure 23: As Fig. 3,
but for the LC K2 Campaign 5 observations of HD 73754. Figure 24: As Fig. 3,
but for the LC K2 Campaign 18 observations of HD 73754. Figure 25: As Fig. 3,
but for the LC K2 Campaign 5 observations of HD 73618. Figure 26: As Fig. 3,
but for the LC K2 Campaign 16 observations of HD 73618. Figure 27: Time series
(top) and respective Lomb-Scargle periodogram (bottom) for the LC K2 Campaign
18 observations of HD 73618.  Figure 28: As Fig. 3, but for the LC K2 Campaign
5 observations of HD 73619. However, in contrast to the remainder of this
paper, the phase diagram is traced by two periods of the light curve model,
and not by the dominant component. Additionally, the FAP threshold criterion
has been removed, with the model being constructed from the fundamental
component and its overtones. Figure 29: Time series (top) and respective Lomb-
Scargle periodogram (bottom) for the LC K2 Campaign 18 observations of HD
73619.  Figure 30: As Fig. 3, but for the LC K2 Campaign 5 observations of HD
76310. Figure 31: As Fig. 3, but for the LC K2 Campaign 16 observations of HD
76310. Figure 32: As Fig. 3, but for the LC K2 Campaign 18 observations of HD
76310. Figure 33: The wavelet map of HD 73045 based on K2 C18 data; see Fig.
10 for description details. Figure 34: The wavelet map of HD 73574 based on
C05 data. The description follows that for HD 73045, see Fig. 10. Figure 35:
The wavelet map of HD 73618 based on C18 data. The description follows that
for HD 73045, see Fig. 10. Figure 36: The wavelet map of HD 73619 based on C18
data. The description follows that for HD 73045, see Fig. 10. Figure 37: The
wavelet map of HD 73610 based on C05 data. The description follows that for HD
73045, see Fig. 10. Figure 38: The wavelet map of HD 73618 based on K2 C05
data. The description follows that for HD 73045, see Fig. 10. Figure 39: The
wavelet map of HD 73618 based on K2 C16 data. The description follows that for
HD 73045, see Fig. 10. Figure 40: The wavelet map of HD 73619 based on K2 C05
data. The description follows that for HD 73045, see Fig. 10. Figure 41: The
wavelet map of HD 73610 based on K2 C16 data. The description follows that for
HD 73045, see Fig. 10. Figure 42: The wavelet map of HD 73610 based on K2 C18
data. The description follows that for HD 73045, see Fig. 10.

Figure 43: As Fig. 12, but for C18. Here the light curve was split into four
segments. No evidence for pulsational signals is identified based on either
method of analysis.