Asteroseismology of HD 23734, HD 68703, and HD 73345 using K2-TESS Space-based Photometry and High-resolution Spectroscopy

TL;DR

This study combines space-based photometry and high-resolution spectroscopy to analyze three stars, revealing pulsation, rotation, and potential binarity, and challenges previous classifications of these stars as chemically peculiar.

Contribution

It provides the first detailed pulsation and chemical analysis of these stars, demonstrating they are likely chemically normal and identifying their pulsation modes using TESS data.

Findings

Detection of rotational modulation and pulsation in all three stars.

Identification of radial pulsation modes for each star.

Evidence suggesting HD 73345 is part of a long-period binary system.

Abstract

In this paper, we present a comprehensive study of three stars, HD 23734, HD 68703, and HD 73345, which were previously observed as chemically peculiar candidates within the Nainital-Cape survey and reported as null results for the pulsational variability. Frequency analyses of \ktwo\ and \tess\ time-series photometric data reveal the co-existence of rotational modulation and pulsation. We use the spectrum synthesis technique to determine fundamental parameters and chemical composition, which shows that all the three stars are likely to be chemically normal. The evolutionary status of the target stars corresponds to the main-sequence phases and places them within the $\delta$ Scuti instability strip of the Hertzsprung-Russell diagram. The line profile variability is observed in all three stars, especially intriguing in HD\,68703 and a typical signature of the non-radial pulsation, demands further detailed examination. Using \tess\ photometry, we identified the radial modes of orders $n$=3 and 4 for HD\,23734, $n$=1, 3, and 4 for HD\,68703, and $n$=3,4 and 5 for HD\,73345. In addition to the presence of pulsation and rotation, HD\,73345 exhibits a steady increase in radial velocity that we interpret as the star being likely to be part of a long-period binary system. Finally, we propose an extended campaign aimed for the in-depth spectroscopic and spectropolarimetric study of selected pulsating stars monitored under the Nainital-Cape survey project.

Tables

Table 1. Table 1: Summary of the observational details for the target stars observed by the K2  and TESS  space missions, including the available campaigns/sectors and the respective cadences for each star.

Star	Mission	Campaigns/	Cadence
		Sectors	(s)
HD 23734	K2	4	1800
	TESS	42, 43, 44	120
	TESS	70, 71	200
HD 68703	K2	5, 18	1800
	TESS	44, 45, 46	120
	TESS	71, 72	200
HD 73345	K2	5, 18	1800
	TESS	44, 45, 46	120
	TESS	72	200

Table 2. Table 2: Overview of the spectroscopic observations acquired from various ground-based facilities. Asterisks denote the epochs when the time-series spectra were obtained; the listed parameters for those entries represent the values averaged across all individual exposures.

Object	Telescope	Diameter	Spectrograph	Date	BJD	Resolution	Integration	SNR	RV	$\upsilon \sin i$
		(m)		(UT)	(2400000+)	($\lambda /\Delta \lambda$)	Time (sec)	(@5500 Å)	(km s-1)	($\pm$1 km s-1)
HD 23734	LAMOST	4.0	LRS	16 Jan 2018	58135.0181	1800	1800	140	$-1.3\pm 3.1$	-
				06 Jan 2019	58490.0631	1800	1800	227	$-5.8\pm 1.8$	-
	HCT	2.01	HESP	06 Dec 2018	58459.3276	30000	1200	137	$-4.8\pm 0.4$	133
				06 Nov 2023	60255.1806	30000	1200	40	$-4.6\pm 0.9$	134
				29 Jan 2024	60339.2102	30000	900	75	$-4.4\pm 0.7$	135
	Mercator	1.20	HERMES	04 Nov 2023	60252.5708	85000	200	60	$-3.4\pm 0.5$	132
	TNT	2.4	MRES	13 Feb 2025	60720.0171	18500	900	170	$4.0\pm 1.8$	138
HD 68703	VLT UT3	8.2	XSHOOTER	22 Dec 2022	59935.8470	11333	10	366	$0.0\pm 4.5$	-
	LAMOST	4.0	MRS	27 Dec 2017	58115.2472	7500	600	164	-	-
				28 Nov 2018	58451.3479	7500	1200	21	-	-
				19 Dec 2018	58472.2812	7500	1200	21	-	-
				27 Dec 2018	58480.3013	7500	1200	41	-	-
				11 Feb 2019	58526.1180	7500	1200	11	-	-
				04 Jan 2021	59219.2638	7500	1200	79	-	-
	HCT	2.01	HESP	29 Nov 2018	58452.4225	30000	1200	103	$-0.3\pm 0.2$	69
				26 Dec 2023	60305.2285	30000	900	222	$0.2\pm 0.2$	68
				28 Jan 2024	60338.4145	30000	900	162	$0.6\pm 0.2$	65
				07 Mar 2025	60742.1224	30000	900	146	$0.8\pm 0.2$	68
				07 Mar 2025	60742.3348	30000	900	168	$0.7\pm 0.2$	68
	TNT	2.4	MRES	18 Dec 2024∗	60663.2273	18500	410	200	$2.3\pm 0.2$	69
				19 Dec 2024∗	60664.4384	18500	389	222	$1.0\pm 0.2$	68
				13 Feb 2025	60720.0672	18500	420	200	$2.6\pm 1.1$	67
	TBL	2.0	NARVAL	12 Jan 2007∗	54113.6120	65000	600	266	$1.46\pm 0.05$	68
				17 Jan 2007∗	54118.6024	65000	600	296	$1.45\pm 0.07$	68
	Mercator	1.20	HERMES	15 Mar 2025	60750.5739	85000	300	148	$0.9\pm 0.2$	68
				15 Mar 2025	60750.5819	85000	300	173	$1.3\pm 0.2$	68
				16 Mar 2025	60751.4649	85000	300	151	$1.0\pm 0.2$	68
				16 Mar 2025	60751.5914	85000	300	134	$0.9\pm 0.2$	67
				17 Mar 2025	60752.4550	85000	300	183	$1.7\pm 0.2$	67
				17 Mar 2025	60752.5762	85000	300	159	$1.1\pm 0.1$	66
				18 Mar 2025	60753.5355	85000	300	161	$1.2\pm 0.1$	65
				20 Mar 2025∗	60755.5388	85000	180	140	$1.42\pm 0.02$	66
				23 Mar 2025	60758.5722	85000	360	119	$1.5\pm 0.1$	66
HD 73345	LAMOST	4.0	LRS	04 Jan 2016	57392.2045	1800	1800	312	$24.9\pm 2.1$	-
				27 Jan 2016	57415.1631	1800	2100	140	$28.4\pm 3.3$	-
				24 Feb 2016	57443.1606	1800	1800	255	$29.8\pm 2.2$	-
	HCT	2.01	HESP	06 Dec 2018	58459.3733	30000	1200	79	$32.5\pm 0.2$	90
				26 Dec 2023	60305.2426	30000	900	55	$32.4\pm 0.4$	89
				28 Jan 2024	60338.4302	30000	900	63	$33.0\pm 0.3$	89
	TNT	2.4	MRES	13 Feb 2025	60720.0945	18500	900	160	$37.1\pm 1.2$	90

Table 3. Table 3: Basic physical parameters of the target stars retrieved from the SIMBAD database (Columns 2–4). The rest of the columns list parameters estimated from photometric calibrations. The distance d d is calculated using the Gaia  DR3 parallax (Gaia Collaboration et al., 2023 ) . Mean photometric values for each star are indicated with an asterisk.

Star	${\alpha }_{\mathrm{J2000}}$	${\delta }_{\mathrm{J2000}}$	$V$	$A_V$	$M_v$	$d$	$T_{\mathrm{eff}}$	$\log g$	[M/H]
	(${}_{}{}^h{}_{}{}^m{}^s$)	(${}_{}{}^{\circ }{}_{}{}^{\prime }{}^{\prime \prime }$)	($\pm$0.01 mag)	($\pm$0.001 mag)	($\pm$0.01 mag)	($\pm$1 pc)	($\pm 250$ K)	($\pm 0.20$ dex)	($\pm 0.20$ dex)
HD 23734	03 48 10.59	+21 19 44.66	7.96	0.086	2.56	$120$	76231	4.091	0.121
							77002	-	-
							7660∗	4.09∗	0.12∗
HD 68703	08 14 11.14	+17 40 33.43	6.47	0.025	1.55	$96$	73401	3.861	0.321
							71802	-	-
							71803	4.023	0.323
							7230∗	3.93∗	0.32∗
HD 73345	08 38 37.86	+19 59 23.09	8.14	0.039	1.82	$184$	77101	3.991	0.261
							73002	-	-
							79803	4.493	0.253
							7660∗	4.24∗	0.26∗

Table 4. Table 4: Summary of stellar parameters derived from spectroscopy.

Star	$T_{\mathrm{eff}}$	$\log g$	${\xi }_{\mathrm{mic}}$	[M/H]
	(K)	[cm s-2]	(km s-1)	(dex)
HD 23734	$7670\pm 160$	$3.98\pm 0.15$	$2.7\pm 0.5$	$-0.31\pm 0.10$
HD 68703	$7160\pm 250$	$3.40\pm 0.15$	$2.7\pm 0.3$	$+0.12\pm 0.10$
HD 73345	$7670\pm 220$	$4.08\pm 0.15$	$3.0\pm 0.3$	$-0.14\pm 0.12$

Table 5. Table 5: Individual chemical abundances determined for the target stars using HERMES (HD 23734 and HD 68703), and MRES (HD 73345) spectra. The last column lists the solar abundances (Asplund et al., 2021 ; Magg et al., 2022 ) . The abundances are expressed as log ⁡ ( N el / N tot ) \log(N_{\rm el}/N_{\rm tot}) with typical uncertainties ( σ ​ ( log ⁡ N / N tot ) \sigma(\log N/N_{\rm tot}) ) between 0.10 and 0.35 dex, except for least accurate values marked with a colon (:).

	HD 23734	HD 68703	HD 73345	Sun
C	$-4.23$ (:)	$-3.65$	$-3.45$	$-3.47$
O	$-2.97$ (:)	$-2.96$ (:)	$-2.91$ (:)	$-3.26$
Na	$-5.25$	$-5.44$	$-5.47$	$-5.81$
Mg	$-4.63$	$-4.22$	$-4.39$	$-4.48$
Al	$-6.09$ (:)	$-5.37$	$-5.61$ (:)	$-5.60$
Si	$-4.41$	$-4.40$	$-4.42$	$-4.44$
S	-	$-4.74$	-	$-4.91$
Ca	$-5.64$	$-5.22$	$-5.60$	$-5.66$
Sc	$-9.29$	$-8.30$	$-8.75$	$-8.89$
Ti	$-7.19$	$-6.81$	$-7.12$	$-7.06$
V	$-8.02$ (:)	-	$-7.63$	$-8.13$
Cr	$-6.42$	$-6.21$	$-6.39$	$-6.41$
Mn	$-6.74$	$-6.74$	$-6.79$	$-6.61$
Fe	$-4.71$	$-4.45$	$-4.61$	$-4.52$
Co	-	-	$-6.76$ (:)	$-7.09$
Ni	$-6.13$ (:)	$-5.67$	$-5.82$	$-5.79$
Cu	-	$-8.15$	-	$-7.85$
Zn	$-7.77$ (:)	$-7.67$	$-7.61$	$-7.47$
Sr	$-11.05$ (:)	$-8.48$ (:)	-	$-9.20$
Y	$-9.92$	$-9.26$	$-9.48$	$-9.82$
Zr	-	-	$-9.44$ (:)	$-9.44$
Ba	$-9.24$	$-8.75$	$-9.67$	$-9.76$
La	-	$-10.30$	$-10.59$ (:)	$-10.92$

Table 6. Table 6: Estimated and calculated fundamental parameters derived from the evolutionary status, inferred from the Échelle diagram and best-fitting asteroseismic models for HD 23734, HD 68703, and HD 73345. The parameters reported in the literature are also provided for comparison to the parameters inferred from the present study. The identified frequencies F ​ n Fn corresponds to the radial fundamental ( n = 1 n=1 ) and higher overtones ( n > 1 n>1 ) modes.

		HD 23734			HD 68703			HD 73345
	Present Study			Present Study			Present Study
Parameters	Calculated/	Seismology	Literature	Calculated/	Seismology	Literature	Calculated/	Seismology	Literature
	H-R diagram			H-R diagram			H-R diagram
$\Delta \nu$ (d-1)	6.17 $\pm$0.47	6.96		$3.00\pm 0.33$	$3.25$		$4.14\pm 0.41$	$5.20$	5.01b
$\overline{\rho }/{\overline{\rho }}_{\odot }$	0.43$\pm$0.07	0.57		$0.09\pm 0.02$	$0.11$		$0.18\pm 0.04$	$0.30$
$R_L/R_{\odot }$	1.57$\pm$0.08	-	-	$2.79\pm 0.22$	-	-	$2.17\pm 0.15$	-	-
$M/M_{\odot }$	1.67 $\pm$0.10	-	-	$1.96\pm 0.10$	-	-	$1.85\pm 0.10$	-	-
$\log \left(L/L_{\odot }\right)$	$0.89\pm 0.01$	0.841 $\pm$0.050	-	$1.27\pm 0.01$	$1.175\pm 0.100$	1.29d	$1.17\pm 0.01$	$1.120\pm 0.050$	1.17g
$\log$($T_{\text{eff}}$)	3.88$\pm$0.01	3.881$\pm$0.010	-	$3.85\pm 0.02$	$3.854\pm 0.020$	3.86d	$3.88\pm 0.01$	$3.899\pm 0.010$	3.90g
Age (Gyr)	0.5 $\pm$ 0.3	0.327$\pm$0.010	0.832c	$1.17\pm 0.10$	$1.290\pm 0.200$	-	$1.05\pm 0.10$	$0.863\pm 0.100$	0.759a
$\left[\mathrm{Fe}/H\right]$	$-0.19$	-	-0.12c	$0.07$	-	0.352f	$-0.09$	-	0.26g
F1 (d-1)	-	-		9.5603 $\pm$ 0.0007	$9.56\pm 0.10$	-	-	-
F2 (d-1)	-	-	-	-	-	-	-	-	-
F3 (d-1)	32.93878 $\pm$ 0.00009	33.01 $\pm$ 0.50	-	15.29221 $\pm$ 0.00002	$15.38\pm 0.20$	-	24.7246 $\pm$ 0.0005	$24.83\pm 0.02$	-
F4 (d-1)	38.94782 $\pm$ 0.00006	39.01 $\pm$ 0.40	-	18.57798 $\pm$ 0.00001	$18.46\pm 0.20$	-	29.50692 $\pm$ 0.00005	$29.49\pm 0.01$	-
F5 (d-1)	-	-	-	-	-		34.3951 $\pm$ 0.0007	$34.25\pm 0.80$	-

Table 7. Table 7: The frequencies, corresponding amplitudes, and signal-to-noise ratios (SNRs) for HD 23734 derived from three consecutive sectors (42, 43, and 44) of TESS  time-series data. The frequency solution based on the K2  data from Campaign 4 is also listed. Pulsation constants ( Q Q ) are provided for the identified radial modes. Only the short-cadence TESS  data were used in this analysis to avoid aliasing effects and to resolve frequencies beyond the Nyquist (Nyq) limit inherent to K2  long-cadence data. The column ‘Comb. Freqs.’ indicates the identified radial modes, rotational frequency, and their combinations.

		TESS					K2
	$f$	Amp	SNR	Q-value	Comb.		$f$	Amp	SNR
	(d-1)	($\pm$0.003 mmag)		(days)	Freqs.		(d-1)	($\pm$0.1 mmag)
$f_{T1}$	22.90016$\pm$0.00001	1.727	309.8	-	-	$f_{K1}$	22.9001$\pm$0.0007	1.1	22.0
$f_{T2}$	25.60789$\pm$0.00003	0.936	175.4	-	-	2Nyq-$f_{K2}$	25.608$\pm$0.001	0.5	10.7
$f_{T3}$	16.13569$\pm$0.00004	0.662	126.6	-	-	$f_{K3}$	16.136$\pm$0.002	0.5$\pm$0.1	9.1
$f_{T4}$	38.94782$\pm$0.00006	0.446	75.7	0.017 $\pm$ 0.003	F4	-	-	-	-
$f_{T5}$	30.78033$\pm$0.00008	0.308	58.4	-	-	-	-	-	-
$f_{T6}$	38.79358$\pm$0.00009	0.286	49.0	-	-	-	-	-	-
$f_{T7}$	32.93878$\pm$0.00009	0.265	42.1	0.02 $\pm$ 0.004	F3	-	-	-	-
$f_{T8}$	42.4168$\pm$0.0001	0.246	44.3	-	-	-	-	-	-
$f_{T9}$	22.5310$\pm$0.0001	0.221	40.8	-	-	-	-	-	-
$f_{T10}$	25.7210$\pm$0.0001	0.208	39.4	-	-	-	-	-	-
$f_{T11}$	42.9315$\pm$0.0001	0.185	31.1	-	-	-	-	-	-
$f_{T12}$	33.0666$\pm$0.0002	0.160	24.3	-	-	-	-	-	-
$f_{T13}$	29.8766$\pm$0.0002	0.165	29.6	-	-	-	-	-	-
$f_{T14}$	42.2087$\pm$0.0002	0.164	29.5	-	-	-	-	-	-
$f_{T15}$	22.0017$\pm$0.0002	0.160	28.8	-	-	-	-	-	-
$f_{T16}$	19.2192$\pm$0.0002	0.156	30.8	-	-	-	-	-	-
$f_{T17}$	32.2210$\pm$0.0002	0.141	22.2	-	-	-	-	-	-
$f_{T18}$	33.9091$\pm$0.0002	0.131	24.4	-	-	-	-	-	-
$f_{T19}$	39.5157$\pm$0.0002	0.124	20.6	-	-	-	-	-	-
$f_{T20}$	41.7995$\pm$0.0002	0.128	23.1	-	-	-	-	-	-
$f_{T21}$	49.9145$\pm$0.0002	0.117	18.6	-	-	-	-	-	-
$f_{T22}$	26.0984$\pm$0.0002	0.101	18.5	-	-	-	-	-	-
$f_{T23}$	44.0720$\pm$0.0003	0.096	16.3	-	-	-	-	-	-
$f_{T24}$	22.4092$\pm$0.0003	0.091	16.6	-	-	-	-	-	-
$f_{T25}$	49.0387$\pm$0.0003	0.087	12.3	-	-	-	-	-	-
$f_{T26}$	37.7358$\pm$0.0003	0.086	15.7	-	-	-	-	-	-
$f_{T27}$	36.3113$\pm$0.0003	0.082	12.6	-	-	-	-	-	-
$f_{T28}$	27.5403$\pm$0.0003	0.080	15.0	-	-	-	-	-	-
$f_{T29}$	42.0281$\pm$0.0003	0.078	14.0	-	-	-	-	-	-
$f_{T30}$	31.1892$\pm$0.0003	0.074	13.6	-	-	-	-	-	-
$f_{T31}$	54.7124$\pm$0.0003	0.074	12.5	-	-	-	-	-	-
$f_{T32}$	34.3933$\pm$0.0004	0.070	11.6	-	-	-	-	-	-
$f_{T33}$	24.9947$\pm$0.0004	0.064	11.2	-	-	-	-	-	-
$f_{T34}$	46.4479$\pm$0.0004	0.063	9.9	-	-	-	-	-	-
$f_{T35}$	40.8229$\pm$0.0004	0.056	10.3	-	-	-	-	-	-
$f_{T36}$	43.8136$\pm$0.0004	0.056	9.1	-	-	-	-	-	-
$f_{T37}$	52.5559$\pm$0.0005	0.054	9.0	-	-	-	-	-	-
$f_{T38}$	29.2187$\pm$0.0004	0.056	11.9	-	-	-	-	-	-
$f_{T39}$	29.0548$\pm$0.0005	0.053	11.1	-	-	-	-	-	-
$f_{T40}$	49.5389$\pm$0.0005	0.053	8.1	-	-	-	-	-	-
$f_{T41}$	28.3355$\pm$0.0005	0.051	10.9	-	-	-	-	-	-
$f_{T42}$	21.6257$\pm$0.0005	0.051	9.7	-	-	-	-	-	-
$f_{T43}$	18.7759$\pm$0.0005	0.046	9.2	-	-	-	-	-	-
$f_{T44}$	33.3351$\pm$0.0005	0.045	7.0	-	-	-	-	-	-
$f_{T45}$	54.5173$\pm$0.0006	0.045	7.2	-	-	-	-	-	-
$f_{T46}$	18.3873$\pm$0.0006	0.044	8.8	-	-	-	-	-	-
$f_{T47}$	30.3839$\pm$0.0006	0.045	8.3	-	-	-	-	-	-
$f_{T48}$	29.6660$\pm$0.0006	0.044	8.5	-	-	-	-	-	-
$f_{T49}$	31.7962$\pm$0.0006	0.043	7.0	-	-	-	-	-	-
$f_{T50}$	46.0459$\pm$0.0006	0.041	6.9	-	-	-	-	-	-
$f_{T51}$	10.3633$\pm$0.0006	0.041	9.7	-	-	-	-	-	-
$f_{T52}$	37.0475$\pm$0.0006	0.040	7.6	-	-	-	-	-	-
$f_{T53}$	41.4372$\pm$0.0006	0.039	7.1	-	-	-	-	-	-
$f_{T54}$	36.1861$\pm$0.0006	0.039	5.8	-	-	-	-	-	-
$f_{T55}$	56.1051$\pm$0.0006	0.038	6.5	-	-	-	-	-	-
$f_{T56}$	50.8394$\pm$0.0006	0.039	7.2	-	-	-	-	-	-
$f_{T57}$	37.4168$\pm$0.0006	0.038	6.9	-	-	-	-	-	-
$f_{T58}$	21.6767$\pm$0.0006	0.039	7.2	-	-	-	-	-	-
$f_{T59}$	47.1537$\pm$0.0007	0.037	6.4	-	-	-	-	-	-
$f_{T60}$	12.3188$\pm$0.0007	0.037	7.1	-	-	-	-	-	-
$f_{T61}$	18.9915$\pm$0.0007	0.037	7.4	-	-	-	-	-	-
$f_{T62}$	52.8368$\pm$0.0007	0.036	5.6	-	-	-	-	-	-
$f_{T63}$*	2.3406$\pm$0.0007	0.034	4.8	-	Frot	-	-	-	-
$f_{T64}$*	4.660$\pm$0.001	0.018	3.5	-	2Frot	-	-	-	-

Table 8. Table 8: Same as Table  7 , but for HD 68703. In this case, we combined the consecutive TESS  sectors 44, 45, and 46, along with the K2  light curves from Campaigns 5 and 18. No frequencies beyond the K2  Nyquist limit were detected in this analysis.

	TESS					K2
	$f$	Amp	SNR	Q-value	Comb.		$f$	Amp	SNR
	(d-1)	($\pm$0.002 mmag)		(d)	Freqs.		(d-1)	($\pm$0.006 mmag)
$f_{T1}$	18.57798$\pm$0.00001	1.032	246.9	0.016$\pm$0.003	F4	$f_{K4}$	18.577989$\pm$0.000006	0.0189	69.9
$f_{T2}$	15.29221$\pm$0.00002	0.783	179.3	0.020$\pm$0.003	F3	$f_{K1}$	15.292443$\pm$0.000004	0.737	119.6
$f_{T3}$	19.36695$\pm$0.00002	0.641	145.0	-	-	$f_{K3}$	19.366866$\pm$0.000006	0.481	63.1
$f_{T4}$	14.55409$\pm$0.00003	0.365	106.9	-	-	$f_{K6}$	14.55414$\pm$0.00001	0.268	48.7
$f_{T5}$	12.85130$\pm$0.00003	0.358	127.5	-	F1+3Frot	$f_{K8}$	12.85119$\pm$0.00001	0.207	48.3
$f_{T6}$	16.70863$\pm$0.00004	0.326	83.2	-	-	$f_{K5}$	16.709372$\pm$0.000007	0.385	50.9
$f_{T7}$	16.63107$\pm$0.00004	0.328	82.9	-		$f_{K2}$	16.632078$\pm$0.000004	0.645	84.5
$f_{T8}$	17.92033$\pm$0.00007	0.188	47.8	-	-	$f_{K7}$	17.92044$\pm$0.00001	0.213	35.4
$f_{T9}$	16.17536$\pm$0.00009	0.139	33.0	-	-	$f_{K9}$	16.17520$\pm$0.00002	0.180	22.4
$f_{T10}$	21.0273$\pm$0.0002	0.077	17.1	-	2F3-F1	-	-	-	-
$f_{T11}$	16.4889$\pm$0.0002	0.072	17.9	-	-	-	-	-	-
$f_{T12}$	17.3132$\pm$0.0002	0.065	18.5	-	-	$f_{K13}$	17.31204$\pm$0.00004	0.078	10.6
$f_{T13}$	19.9153$\pm$0.0002	0.050	11.4	-	-	-	-	-	-
$f_{T14}$	20.1599$\pm$0.0002	0.052	12.6	-	-	-	-	-	-
$f_{T15}$	13.6909$\pm$0.0003	0.046	16.8	-	-	$f_{K18}$	13.69112$\pm$0.00005	0.058	11.4
$f_{T16}$	22.8251$\pm$0.0003	0.044	12.7	-	-	-	-	-	-
$f_{T17}$	0.9242$\pm$0.0003	0.042	7.0	-	-	-	-	-	-
$f_{T18}$	0.6464$\pm$0.0003	0.039	6.3	-	-	-	-	-	-
$f_{T19}$	19.9664$\pm$0.0003	0.041	9.4	-	-	-	-	-	-
$f_{T20}$	0.4850$\pm$0.0003	0.042	6.7	-	-	-	-	-	-
$f_{T21}$	6.7560$\pm$0.0003	0.040	11.8	-	-	-	-	-	-
$f_{T22}$	2.1989$\pm$0.0003	0.039	9.4	-	2Frot	-	-	-	-
$f_{T23}$	7.4194$\pm$0.0003	0.038	12.2	-	-	-	-	-	-
$f_{T24}$	17.3882$\pm$0.0003	0.036	10.0	-	-	-	-	-	-
$f_{T25}$	16.1046$\pm$0.0003	0.039	9.3	-	-	-	-	-	-
$f_{T26}$	1.0995$\pm$0.0004	0.033	5.9	-	Frot	-	-	-	-
$f_{T27}$	17.8126$\pm$0.0004	0.032	8.6	-	-	-	-	-	-
$f_{T28}$	21.4722$\pm$0.0004	0.030	7.1	-	-	-	-	-	-
$f_{T29}$	19.8069$\pm$0.0004	0.031	7.3	-	-	$f_{K17}$	19.80777$\pm$0.00005	0.061	8.4
$f_{T30}$	19.6983$\pm$0.0004	0.030	7.3	-	F4+Frot, F3+4Frot	-	-	-	-
$f_{T31}$	3.2738$\pm$0.0005	0.027	7.6	-	3Frot, F4-F3	-	-	-	-
$f_{T32}$	4.5788$\pm$0.0005	0.027	6.8	-	-	-	-	-	-
$f_{T33}$	20.5333$\pm$0.0005	0.027	6.0	-	-	-	-	-	-
$f_{T34}$	17.5449$\pm$0.0005	0.027	7.2	-	-	-	-	-	-
$f_{T35}$	23.6716$\pm$0.0005	0.023	6.6	-	-	-	-	-	-
$f_{T36}$	9.5603$\pm$0.0007	0.018	6.5	0.031$\pm$0.005	F1	-	-	-	-
-	-	-	-	-	-	$f_{K15}$	16.58560$\pm$0.00004	0.076	9.8
-	-	-	-	-	-	$f_{K16}$	19.13116$\pm$0.00004	0.063	8.9

Table 9. Table 9: Same as Table  7 , but for HD 73345. The frequency solution is given here is on combining the consecutive TESS  sectors 44, 45, and 46 and K2  time-series for the Campaigns 5 and 18.

	TESS					K2
	$f$	Amp	SNR	Q-value	Comb.		$f$	Amp	SNR
	(d-1)	($\pm$0.003 mmag)			Freqs			($\pm$0.006 mmag)
$f_{T1}$	31.56558$\pm$0.00003	0.694	154.0	-	-	2Nyq-$f_{K1}$	31.56564$\pm$0.00001	0.285	107.2
$f_{T2}$	30.24686$\pm$0.00005	0.473	108.4	-	-	2Nyq-$f_{K3}$	30.24688$\pm$0.00001	0.203	77.0
$f_{T3}$	29.50692$\pm$0.00005	0.458	112.1	0.014 $\pm$ 0.002	F4	2Nyq-$f_{K2}$	29.50709$\pm$0.00001	0.331	130.0
$f_{T4}$	31.89596$\pm$0.00006	0.372	80.8	-	-	2Nyq-$f_{K7}$	31.89610$\pm$0.00004	0.064	22.6
$f_{T5}$	27.8107$\pm$0.0001	0.191	42.0	-	-	2Nyq-$f_{K8}$	27.80985$\pm$0.00006	0.048	19.7
$f_{T6}$	26.5554$\pm$0.0002	0.123	27.2	-	-	2Nyq-$f_{K6}$	26.55562$\pm$0.00004	0.066	24.8
$f_{T7}$	21.4556$\pm$0.0003	0.089	22.8	-	-	$f_{K5}$	21.45574$\pm$0.00003	0.081	32.6
$f_{T8}$	36.7432$\pm$0.0003	0.081	20.3	-	-	-	-	-	-
$f_{T9}$	1.1119$\pm$0.0004	0.055	8.1	-	Frot	-	-	-	-
$f_{T10}$	25.3400$\pm$0.0004	0.051	11.7	-	-	2Nyq-$f_{K13}$	25.34047$\pm$0.00008	0.032	10.5
$f_{T11}$	23.4880$\pm$0.0005	0.047	11.3	-	-	$f_{K9}$	23.48595$\pm$0.00008	0.035	12.2
$f_{T12}$	24.7246$\pm$0.0005	0.047	10.8	0.017 $\pm$ 0.002	F3	2Nyq-$f_{K10}$	24.72477$\pm$0.00008	0.035	11.8
$f_{T13}$	38.6261$\pm$0.0005	0.046	9.8	-	-	-	-	-	-
$f_{T14}$	23.2674$\pm$0.0005	0.045	10.8	-	-	-	-	-	-
$f_{T15}$	34.3951$\pm$0.0007	0.034	6.4	0.012 $\pm$ 0.002	F5	2Nyq-$f_{K12}$	34.39525$\pm$0.00008	0.034	10.7
$f_{T16}$	33.0620$\pm$0.0007	0.034	7.0	-	-	-	-	-	-
$f_{T17}$	43.2062$\pm$0.0007	0.033	7.6	-	-	-	-	-	-
$f_{T18}$	37.5039$\pm$0.0008	0.030	7.2	-	-	-	-	-	-
$f_{T19}$	36.5739$\pm$0.0008	0.029	7.4	-	-	-	-	-	-
$f_{T20}$	35.7724$\pm$0.0009	0.027	5.8	-	-	-	-	-	-
$f_{T21}$	10.095$\pm$0.001	0.022	5.6	-	-	-	-	-	-
$f_{T22}$	14.360$\pm$0.001	0.022	5.4	-	3F4-3F3	$f_{K19}$	14.2104$\pm$0.0001	0.022	7.0
-	-	-	-	-	-	$f_{K4}$	15.03217$\pm$0.00001	0.210	67.9
-	-	-	-	-	-	$f_{K11}$	19.25318$\pm$0.00008	0.035	14.1
-	-	-	-	-	-	$f_{K15}$	18.8381$\pm$0.0001	0.025	9.3
-	-	-	-	-	-	$f_{K16}$	8.1570$\pm$0.0001	0.023	6.0

Equations

$${\nu }_{n,\ell }=\Delta \nu (n+\ell /2+ϵ),$$

$$\frac{\Delta \nu }{\Delta {\nu }_{\odot }}=0.776{\left(\frac{\bar{\rho }}{{\bar{\rho }}_{\odot }}\right)}^{0.46},$$

$${\chi }^2={\left(\frac{f_t-f_o}{{\sigma }_{f_o}}\right)}^2,$$

Full text

††pubyear: 2024

1 Introduction

About 10% of upper main-sequence (MS) stars with spectral types ranging from B to F exhibit anomalous intensities of spectral features compared to normal stars of similar spectral types, ages, and populations. Owing to the observed photospheric overabundances of silicon (Si), chromium (Cr), strontium (Sr), europium (Eu), and many other heavy elements, and are classified as chemically peculiar or CP stars (Ghazaryan et al., 2018).

The CP stars are traditionally divided into four subgroups based on their effective temperature, strength of absorption lines, and magnetic field properties: Am/Fm (CP1), Bp/Ap (CP2), HgMn (CP3), and He-weak (CP4) stars (Preston, 1974; Paunzen et al., 2021). As our study focuses primarily on Am (metallic-line A-type) and Ap (peculiar A-type) stars, we briefly introduce these two subtypes within the context of the present work.

The Am/Fm stars are non-magnetic objects characterised by deficiencies in light elements (e.g., C, N, O, Ca, Sc) and/or overabundances of Fe-peak elements (e.g., Fe, Cr) and rare-earth elements (Conti, 1970; Catanzaro et al., 2019). These A- or early F-type MS stars occupy the same region of the Hertzsprung–Russell (H-R) diagram as chemically normal A-F stars, with effective temperatures in the range of 7000-9000 K. Most of the Am stars are slow rotators with projected rotational velocities ($\upsilon\sin i$) below 150 km s*-1* and are commonly found in binary systems with orbital periods ($P_{\rm orb}$) exceeding 1.2 days (Iliev & Budaj, 2008).

The Ap stars possess strong magnetic fields and exhibit pronounced overabundances of elements such as Si, Sr, Cr, and Eu. The magnetic fields of Ap stars are generally organised as dipoles and can reach strengths of several tens of kilogauss (Bychkov et al., 2021), often varying with rotational period (Babcock, 1947; Aurière et al., 2007). Although the origin of these fields remains uncertain, they are thought to be fossil in origin, retained from the process of star formation (Braithwaite & Spruit, 2004; Aurière et al., 2007).

The axial rotation of CP stars has a powerful impact on various stellar properties. The chemical peculiarities of Am and Ap stars are believed to arise from processes like atomic diffusion, which can work only in a stabilised environment. It is the slow rotation and magnetic field that suppress convective mixing and allow for the selective levitation or gravitational settling of chemical elements in stellar interiors (Michaud, 1970; Richer et al., 2000). Slow rotation as the main factor of emerging atomic diffusion in Am stars is typically associated with tidal synchronisation in binary systems, while in Ap stars it is attributed to strong magnetic fields (Abt & Snowden, 1973; Shore & Adelman, 1974; Ghazaryan & Alecian, 2016). Nonetheless, in certain instances, abnormally high rotational velocities have been noted (e.g., Mikulášek et al., 2022). The rotational properties of a few hundred magnetic CP stars have recently been examined in open star clusters by Netopil et al. (2017), and the authors found that the evolution of rotational periods is consistent with the conservation of angular momentum during the main sequence (MS) phase. The coexistence of pulsations, surface chemical inhomogeneities, moderate rotation, and magnetic fields makes Am and Ap stars exceptional laboratories for asteroseismic modelling, offering valuable insights into internal stellar structure and evolutionary processes (Mikulášek et al., 2010; Krtička et al., 2013).

Several ground-based surveys have been conducted in the past to study CP stars, including the Cape and Nainital-Cape Surveys (Martinez et al., 1991; Martinez et al., 2001), the SuperWASP111SuperWASP : Super Wide Angle Search for Planets Survey (Smalley et al., 2011), ASAS-3222ASAS : All Sky Automated Survey (Bernhard et al., 2015), ${\it 2MASS}$3332MASS : Two Micron All-Sky Survey (Herdin et al., 2016), LAMOST444LAMOST : Large Sky Area Multi-Object Fiber Spectroscopic Telescope (Hümmerich et al., 2020; Labadie-Bartz et al., 2023), ATLAS Sky Survey (Bernhard et al., 2021), and the ZTF555ZTF : Zwicky Transient Facility Survey (Hümmerich et al., 2024), to name a few. Thanks to the high-precision, continuous photometric data obtained from space missions such as BRITE666BRITE : BRIght Target Explorer (Paunzen, 2024a), Kepler (Hümmerich et al., 2018), GAIA777GAIA : Global Astrometric Interferometer for Astrophysics (Paunzen, 2024c), and TESS888TESS : Transiting Exoplanet Survey Satellite (Kobzar et al., 2020), where the data acquired by these missions have led to the detection of multi-periodic pulsations in numerous CP stars covered by the $\delta$ Sct instability strip in the H-R diagram (Smalley et al., 2017; Holdsworth et al., 2021; Dürfeldt-Pedros et al., 2024), providing valuable data for modelling the pulsation (Joshi & Joshi, 2015; Paunzen, 2024b). The CP stars have also been searched for and studied in open star clusters by various authors, as they provide strong constraints on their ages and metallicity given that they are assumed to have originated from the same molecular clouds (Faltová et al., 2025). One of the intriguing findings on CP stars in open clusters is that they are of very young ages (log $t>6.90$) and located at galactocentric distances up to 11.4 kpc (Paunzen et al., 2005, 2014).

A class of pulsating variables known as $\delta$ Scuti ($\delta$ Sct) stars are located near the intersection between the classical instability strip and the main sequence. They span effective temperatures of 6300 $<$ T_{\textrm{eff}}$$< 9000 K, luminosities of 0.6 $<$ $\log(L/L_{\odot})$ $<$ 2.0 dex, and masses (M) between 1.5 and 2.5 M⊙. These stars can be found in pre-main sequence stages or just evolving off the main sequence and exhibit low-order pressure ($p$) modes with pulsation periods ranging from $\sim$15 minutes to $\sim$8 hours (e.g., Rodríguez & Breger, 2001; Buzasi et al., 2005; Guzik, 2021). The primary excitation mechanisms include the $\kappa$-mechanism in the He ii ionization zone (Baker & Kippenhahn, 1962; Steindl et al., 2022) and turbulent pressure in the H ionization layer (Antoci et al., 2014). The $\delta$ Sct pulsators represent a particularly intriguing class of variable stars due to their location in the transition region between stars with convective envelopes (M $<$ 2 M⊙) and those with radiative envelopes (M $>$ 2 M⊙). This transitional nature makes them ideal targets for probing the structure of stellar envelopes. However, understanding the mechanisms that drive pulsations and determining mode selection in $\delta$ Sct stars remains a significant unresolved challenge in stellar astrophysics, as their masses fall within a regime where convective zones persist in the outer stellar layers. In binary systems, tidal interactions may further influence the pulsation patterns and rotation rates, producing observable effects in light curves and spectra.

The “Nainital–Cape Survey” (N-C Survey), a collaborative effort between the Aryabhatta Research Institute of Observational Sciences (ARIES) in India and the South African Astronomical Observatory (SAAO) in South Africa, was initiated in the late 1990s to search for short-period pulsations in CP stars belonging to the northern and southern hemispheres and led to the discovery and detailed study of the first far-northern roAp star, HD 12098 (Girish et al., 2001; Kurtz et al., 2024). Subsequent time-resolved photometric and spectroscopic observations revealed anomalous pulsations in half a dozen CP stars (Joshi et al., 2003, 2006; Joshi et al., 2009; Joshi et al., 2010, 2012, 2016, 2017). In the era of space-based photometry, Joshi et al. (2022) discovered HD 73619 as the first CP heartbeat star, lacking tidally induced pulsations. Recently, Sarkar et al. (2024) conducted an asteroseismic analysis of HD 118660 using TESS light curves. A series of Non-Local Thermodynamic Equilibrium (NLTE) analyses of hot CP stars using data from HESP and HERMES spectrographs was also carried out by Trust et al. (2020, 2021, 2023). Furthermore, Dileep et al. (2024) revisited the variability classification of N-C Survey stars using TESS data. To address the spatial resolution limitations of TESS, we have also initiated a ground-based search for pulsating CP stars in open clusters (Dileep et al., 2025). These efforts have now expanded into a global collaboration within the field of asteroseismology through various international bilaterals (e.g. BINA 999BINA : Belgo-Indian Network for Astronomy and Astrophysics) and multilaterals research cooperation (e.g. SAPTARISI101010 SAPTARISI : Search and Follow-up Studies of Time-domain Astronomical Sources using Sky Surveys, BRICS Telescopes and Artificial Intelligence).

In this study, we perform asteroseismic investigation of three multi-periodic $\delta$ Scuti stars, HD 23734, HD 68703, and HD 73345, using combined space-based photometric observations from the K2 and TESS missions, complemented by multi-epoch spectroscopy from ground-based facilities. The manuscript is organised as follows. The criteria for the selection of the sample are given in Section 2. The Section 3 describes the photometric observations and frequency analysis, along with an overview of spectroscopic data acquisition and reduction. Section 4 presents a detailed photometric and spectroscopic analysis to derive fundamental parameters and chemical abundances, along with the evolutionary status of the stars. In Section 5, we identify the observed radial pulsation modes, while Section 5.2 provides details on seismic modelling to constrain the basic stellar parameters. Finally, Section 6 summarises the conclusions drawn from the present study.

2 Target Selection

The N-C Survey comprises 381 stars, and none of them were observed by the Kepler space mission. However, K2 data are available for eight targets. Of these, five have been classified as rotational variables (Joshi et al., 2022), and three stars – HD 23734, HD 68703, and HD 73345 – have been identified as pulsating stars in the present study.

HD 23734 was listed as a member of the Pleiades cluster based on Gaia DR2 and APOGEE radial velocity data (Poovelil et al., 2020). Joshi et al. (2006) considered this star as a CP candidate based on Strömgren photometric indices. The age and metallicity of this cluster are reported as $\log(\mathrm{Age})=8.920$ and [Fe/H] = $-0.12\pm 0.06$ (Dias et al., 2021). However, using the Gaia DR3 data, Alfonso & García-Varela (2023) excluded HD 23734 from membership of the Pleiades.

HD 68703 is included in the General Catalogue of Ap and Am stars (Renson & Manfroid, 2009), where it is listed as an Am star (Mendoza et al., 1978) with the spectral type A8-dD (with "dD" denoting a $\delta$ Delphini-type star (Cowley & Crawford, 1971)). Its metallicity, derived from LAMOST medium-resolution spectroscopy is [Fe/H] = 0.352 (Zong et al., 2020). Later, HD 68703 has been classified as a non-magnetic star by Kudryavtsev et al. (2006), with a spectral type of F1IV (Abt & Morrell, 1995), and it exhibits $\rho$ Puppis-type peculiarity — characteristic of evolved, pulsating Am stars. Fundamental parameter derived by Dürfeldt-Pedros et al. (2024) are: $T_{\textrm{eff}}$ = 7192 K, $\log g$ = 3.8 dex, and $\log(L/L_{\odot})$ = 1.29. The same authors investigated its TESS light curves and detected five radial pulsation modes, although these remain unidentified.

HD 73345, also known as CY Cnc, is a $\delta$ Sct star with a reported pulsation period of 0.1 d (Lopez de Coca et al., 1990) while based on the time-series analysis of the TESS data, Pamos Ortega et al. (2023) reported 26 frequencies. This is a confirmed member of the Praesepe cluster, which has an estimated age of 759 million years (Pamos Ortega et al., 2023). HD 73345 was identified as a candidate CP star in the catalogue of Hauck & Mermilliod (1998). Gray & Corbally (2002) reported this star as a mildly-peculiar star with slightly strong Ca II K. However, Fossati et al. (2008) listed the fundamental parameters of the star as $\log(L/L_{\odot})$ = 1.17, $T_{\textrm{eff}}$ = 7993 K, $\log g$ = 3.96 dex and [Fe/H] = 0.26, their abundance analysis concluded that the star is a chemically normal A7V spectral type star.

3 Observations and Data Reduction

3.1 K2 and TESS Photometry

The K2 (Kepler two-wheel; February 4, 2014 – September 26, 2018) mission surveyed a $105^{\circ}\times 105^{\circ}$ region along the ecliptic plane by observing each field for approximately 80 days across 20 different pointings (Howell et al., 2014). The mission provided two data types: short-cadence (1-minute) and long-cadence (30-minute) photometry, with an angular resolution of 4 arcsec  per pixel, thereby reducing contamination from nearby stars.

The TESS  (Ricker et al., 2015), launched in 2018, is an all-sky photometric survey operating primarily in the Cousins I band. It covers 90% of the sky, originally excluding a narrow band along the ecliptic. During its primary mission, TESS observed 26 sectors – each spanning $24^{\circ}\times 96^{\circ}$ – dividing each hemisphere into 13 sectors and monitoring them sequentially over one year, with each sector observed for approximately 27.4 days. With an angular resolution of 21 arcsec per pixel, TESS data may suffer from spatial blending and contamination from nearby stars. Sector overlaps at high ecliptic latitudes enable the repeated observation of some stars across multiple sectors. The primary data products include short-cadence (2-minute) observations for pre-selected targets and full-frame images (FFIs) captured every 30 minutes for all stars within the field of view. The extended TESS mission, initiated on July 4, 2020, introduced higher temporal resolutions, including 20-second, 200-second, and 10-minute cadences, allowing for a more detailed re-observation of all sectors.

The details of the data available from different TESS sectors and K2 campaigns are presented in Table 1. The photometric data products were retrieved using the Python package lightkurve (Lightkurve Collaboration et al., 2018), sourced from the Barbara A. Mikulski Archive for Space Telescopes (MAST)111111https://archive.stsci.edu/. For both the missions, we utilised the Pre-search Data Conditioning Simple Aperture Photometry (PDCSAP) flux, which has been corrected for instrumental systematics using Co-trending Basis Vectors (CBVs). Outliers were identified and removed through a combination of visual inspection and sigma clipping. The resulting light curves were then converted to relative milli-magnitudes (mmag) and normalised by subtracting the mean magnitude level to centre them around zero.

3.1.1 Frequency Analyses

The frequency analysis of the light curves was performed using the Period04 programme (Lenz & Breger, 2005). Periodograms were computed over a frequency range from zero to the Nyquist frequency, which is considered to be the maximum frequency resolvable in a frequency spectrum and defined as $\nu_{\mathrm{Nq}}=\frac{1}{2\Delta t}$, where $\Delta t$ represents the time sampling interval. For long ($\Delta t=29.43$ min) and short ($\Delta t=120$ sec) cadence data, the Nyquist frequencies are approximately 24.27 d*-1* and 360 d*-1*, respectively. To minimise aliasing, we combined contiguous sectors while avoiding large gaps in the time-series data. The resulting frequency spectra were iteratively prewhitened by fitting the frequency, amplitude, and phase of the highest peak using a sinusoidal model. Each identified frequency was successively subtracted from the light curve, and this process was repeated until the signal-to-noise ratio (SNR) of the residual peaks fell below the significance thresholds, namely SNR $<$ 5.2 for TESS data (Baran & Koen, 2021), and SNR $<$ 5.7 for K2 data (Baran et al., 2015). Frequency and amplitude uncertainties were estimated using the formalism described by Montgomery & O’Donoghue (1999). Frequencies separated by less than 2.5 times the Rayleigh resolution ($1/\Delta T$) were considered unresolved (Loumos & Deeming, 1978).

Combined frequency spectra of HD 23734, HD 68703, and HD 73345 – based on K2 campaigns and TESS sectors – are presented in Figs. 1, 2, and 3, respectively. Individual light curves and periodograms for each K2 campaign and TESS sector are shown in Figs. 9–14 (left and right panels, respectively). A total of 64, 38, and 26 frequencies were recovered in HD 23734, HD 68703, and HD 73345, respectively. It is evident that the short-cadence TESS data enabled the detection of more frequencies compared to K2. Some of the frequencies were found in one dataset (K2) but absent in the other (TESS) – or vice versa – likely due to the wavelength dependency of pulsation amplitudes. The K2 band is centred around 6400 Å  while TESS operates near 9000 Å. A comparison of the individual amplitude spectra of different K2 campaigns and TESS sectors also revealed amplitude modulations in certain frequencies, potentially caused by beating between close frequencies, non-linear mode coupling, or other non-linear effects (Bowman et al., 2016).

We further searched for possible linear combinations involving radial and rotational frequencies, adopting a relation of the form $aF_{n}\pm bF_{m}$, where $a$ and $b$ are integers between $-5$ and $+5$, and $n$ and $m$ denote the order of the parent radial modes ($1,2,3,4,...$) or rotational frequency (‘${\rm rot}$’). The identified frequencies, amplitudes, SNR, and their combinations for each target are summarised in Tables 7, 8, and 9.

3.2 Spectroscopy

For this study, we employed spectroscopic data obtained from the dedicated observing programmes and various archival sources. High-resolution spectra were acquired using the Hanle Echelle Spectrograph (HESP; Chanumolu et al. 2015; Sriram et al. 2018) of the 2.01-m Himalayan Chandra Telescope (HCT) at the Indian Astronomical Observatory (Ladakh, India) and with the High Efficiency and Resolution Mercator Échelle Spectrograph (HERMES; de Cuyper et al. 2007; Raskin et al. 2011) working with the 1.2-m Mercator Telescope (La Palma, Spain). Medium-resolution spectra were collected for all programme stars with the Medium-Resolution Échelle Spectrograph (MRES) fed by fibre from the 2.4-m Thai National Telescope (TNT) at Doi Inthanon (Chiang Mai, Thailand). One of the programme stars, HD 68703, was observed with MRES and HERMES in a time-series regime.

The raw spectra were reduced using dedicated pipelines specific to each instrument. For HESP and HERMES, those were their respective official pipelines. For the MRES data, we used the latest version of the Python-based pipeline PyYAP121212Python-based Yet Another Pipeline (PyYAP): https://github.com/ich-heisse-eugene/PyYAP.

Wavelength calibration for the medium- and high-resolution spectra was performed using Thorium-Argon (Th-Ar) reference sources, followed by correction for barycentric motion. All spectra were normalised to the continuum level using the continuum task in the Image Reduction and Analysis Facility (IRAF)131313https://iraf-community.github.io/. The signal-to-noise ratio (SNR) was calculated at a reference wavelength of 5500 Å.

The archival data were found in the European Southern Observatory (ESO) Science Portal141414https://archive.eso.org/scienceportal/home, a PolarBase archive of high-resolution spectropolarimetric stellar observations 151515https://www.polarbase.ovgso.fr/ (Petit et al., 2014), and in the Data Release 10 (DR10) of the LAMOST archive161616https://www.lamost.org/dr10/v2.0/search (Cui et al., 2012; Zhao et al., 2012). Most of these data pertained to HD 68703. This star was observed once with a multi-wavelength medium-resolution spectrograph XSHOOTER of the Very Large Telescope (VLT) of ESO under a project ID 110.248M.001. Two observations of HD 68703 resulted in a total of 16 archival spectra from NARVAL, a high-resolution spectropolarimeter of the 2-m Bernard Lyot Telescope (TBL) at the Pic du Midi Observatory, and were acquired from PolarBase. All of our target stars were observed multiple times with the LAMOST, and their spectra were publicly released as part of DR10.

The details of all spectroscopic observations are summarised in Table 2. Besides the information about the origin and time of the observation, the last three columns of the table list the signal-to-noise ratio, radial velocity (RV), and projected rotational velocity ($\upsilon\sin i$) measured from each spectrum.

4 Stellar Fundamental Parameters and Evolutionary Status

The reliable values of the fundamental stellar parameters, such as effective temperature ($T_{\textrm{eff}}$), surface gravity ($\log g$), metallicity ([M/H]), and rotational characteristics in the form of the projected rotational velocity ($\upsilon\sin i$) or period of axial rotation, are essential for any theoretical modelling. These parameters naturally restrict the range of possible solutions. The following subsections, review the observational approach to the determination of stellar parameters and its outcome for all the target stars.

4.1 Interstellar Extinction

The interstellar extinction alters the observed characteristics of the stars. High-resolution spectroscopy of stars in close proximity to the Sun, like objects in our study, is less sensitive to this effect. However, we cannot ignore the reddening when it comes to photometry, which we used for the preliminary evaluation of stellar parameters.

To account for the potential effect of reddening, we first examined the three-dimensional Bayestar dust maps (Green, 2018; Green et al., 2019). Using Gaia parallaxes (Gaia Collaboration, 2018) and Galactic coordinates from the SIMBAD database171717https://simbad.u-strasbg.fr/simbad/ (Wenger et al., 2000), the Bayestar models yielded zero reddening values for all targets in our sample. However, more recent interstellar extinction maps given by Lallement et al. (2022) and Vergely et al. (2022) indicate non-zero cumulative absorption values ($A_{\rm 5500}$, at $\lambda$ = 5500 Å) for all three stars. Since $A_{\rm 5500}$ closely approximates the commonly used extinction parameter $A_{\mathrm{V}}$, we accounted for these values in the analysis. Following them, the highest extinction $A_{\rm 5500}=0.086$ mag is observed for HD 23734, while HD 68703 and HD 73345 exhibit $A_{\rm 5500}$ equals to 0.025 and 0.039 mag, respectively. We adopted the values of $A_{\rm 5500}$ as the upper limit of interstellar reddening $A_{\mathrm{V}}$ and used them in the calculation of stellar luminosities listed in Table 3.

A more direct method of estimating reddening involves measuring the equivalent widths of interstellar Na i D1 and D2 lines in high-resolution spectra. Among the three targets, interstellar features near the Na i D1 and D2 lines were securely detected only in HD 23734. The equivalent widths of these features were measured as $W_{\lambda}$(D1) = 100 mÅ and $W_{\lambda}$(D2) = 85 mÅ. Applying the empirical calibration given by Poznanski et al. (2012), we derived the colour excess of $E_{B-V}$, which corresponds to a total extinction of $A_{\mathrm{V}}=0.06$–0.10 mag (assuming $A_{\mathrm{V}}=3.11\times$ $E_{B-V}$), in a good agreement with the $A_{\rm 5500}$ value for this star. There was no measurable interstellar Na i absorption detected in the spectra of HD 68703 or HD 73345.

4.2 Fundamental parameters and chemical composition

4.2.1 Photometry based evaluation

Before proceeding with spectroscopic analysis, we used Geneva (Golay, 1980; Rufener & Nicolet, 1988), $uvby\beta$ (Strömgren, 1963, 1966; Crawford & Mander, 1966; Hauck & Mermilliod, 1998), and 2MASS (Cutri et al., 2003) photometry to derive stellar fundamental parameters. By combining colour indices from multiple photometric systems, we aimed to minimise discrepancies arising from potential binarity, which can significantly affect the total flux of the system. Multiple $T_{\textrm{eff}}$ values derived from different indices were averaged, and the results are presented in Table 3, alongside the parameters derived from the other two photometric systems.

In our sample, Geneva photometric indices are available only for HD 68703 and HD 73345 (Paunzen, 2022). Applying the calibrations by Kunzli et al. (1997) to the $B2-V1$, $d$, and $m2$ indices, we obtained $T_{\textrm{eff}}$ = 7180 K and $\log g$ = 4.02 dex for HD 68703, and $T_{\textrm{eff}}$ = 7980 K and $\log g$ = 4.50 dex for HD 73345. For the metallicity [M/H], this calibration yields values in the range of $+$0.20 to $+$0.35 dex for both stars. Notably, HD 73345 exhibits an unusually high surface gravity.

Photometric indices of the $uvby\beta$ system are available for all three stars, as compiled by Paunzen (2015). To analyse these, we employed the calibrations developed by Moon & Dworetsky (1985) and refined by Napiwotzki et al. (1993), providing estimates of $T_{\textrm{eff}}$, $\log g$, and [M/H] for the stars under study.

From the 2MASS photometric system, we estimated stellar effective temperatures using the relations given by Casagrande et al. (2021). The photometrically-derived parameters were subsequently refined using the spectra.

4.2.2 Spectroscopic Approach

In contrast to photometry, spectroscopic analysis offers a more reliable way to determine multiple stellar parameters from just one observation. To evaluate the fundamental parameters and chemical composition of the programme stars, we employed a spectrum-fitting technique.

Our analysis utilised an IDL-based implementation of the Spectroscopy Made Easy package (SME; Valenti & Piskunov, 1996; Piskunov & Valenti, 2017) with a grid of built-in Atlas9 models to fit synthetic spectra to medium- and high-resolution observational data. Line lists were obtained from the Vienna Atomic Line Database (VALD; Piskunov et al., 1995; Kupka et al., 2000; Ryabchikova et al., 2015) based on $T_{\textrm{eff}}$ and $\log g$ values estimated from photometry.

Taking the photometric $T_{\textrm{eff}}$, $\log g$, and [M/H] as starting parameters, we refined $T_{\textrm{eff}}$ and [M/H] by fitting the LAMOST (HD 23734 and HD 73345) and XSHOOTER (HD 68703) spectra. We preferred this approach to the direct handling of high-resolution data because the Balmer lines in échelle spectra of early-type stars typically span a significant fraction of a single order, complicating accurate continuum normalisation.

In the subsequent step, we analysed the high-resolution spectra to determine the surface gravity ($\log g$), microturbulence ($\xi_{\rm mic}$), and individual elemental abundances. To do so, $T_{\textrm{eff}}$ was fixed, [M/H] was set to zero, and hydrogen lines were excluded from the fit. All steps of analysis were performed in the Local Thermodynamic Equilibrium (LTE) approach. The final best-fit spectroscopically-derived parameters are presented in Table 4. To demonstrate the goodness-of-fit, for all the target stars, by the black solid lines in Fig. 4, we plot the regions of spectra obtained with HERMES (HD 23734, HD 68703), and MRES (HD 73345) and centred at the Balmer lines Hα and Hβ. Spectra synthesised with the spectroscopically derived parameters are shown there as red lines. Within the error limits, the spectroscopic parameters agree with the photometric values listed in Table 3.

4.2.3 Stellar Rotation

The rotational broadening of spectra was estimated using the Least-Squares Deconvolution (LSD) method (Donati & Brown, 1997). The line mask required for deconvolution was constructed from VALD line lists, tailored to the derived fundamental parameters of each star. LSD profiles were fitted with a function describing rotational broadening (Gray, 2005), with some of the best-fit profiles shown in Fig. 15. Two parameters, $\upsilon\sin i$ and RV, found in this way are listed in columns 10 and 11 of Table 2. From sme spectrum fitting, the averaged $\upsilon\sin i$ values for HD 23734, HD 68703, and HD 73345 are $134\pm 5$ km s*-1*, $69\pm 2$ km s*-1*, and $88\pm 3$ km s*-1*, respectively.

The LSD profiles of HD 23734 and HD 73345 exhibit minimal line profile variability (LPV), likely due to high-order pulsation combined with significant rotational broadening. In contrast, HD 68703 shows substantial LPV which is confidently attributable to pulsational activity, making this star an excellent candidate for detailed follow-up studies.

In photometric time-series, we searched for the rotational frequencies in the range 0.1 to 5 d*-1* (Balona, 2011) as shown in Fig. 16. In this diagram, viable rotational frequencies correspond to positions below the diagonal line representing 90*∘* inclination, as $\upsilon\sin i$ must always be less than or equal to the equatorial velocity. For HD 23734, we identified a frequency of 2.3406 d*-1*, which exhibits one harmonic. Although its S/N ratio falls below the detection threshold of SNR = 5.2, we classify this as a probable rotational frequency. In the case of HD 68703, a frequency of 1.0995 d*-1* was detected with two harmonics. For HD 73345, we observed a frequency of 1.1119 d*-1*, although no harmonics were identified. To evaluate the feasibility of the identified rotational frequencies, we estimated equatorial rotational velocities from the computed stellar radii and compared them to the spectroscopic $\upsilon\sin i$ values, indicating that these rotational frequencies are physically plausible. The inferred inclinations are approximately 45*∘* for HD 23734 and HD 73345, while HD 68703 likely has a lower inclination of $\sim$25*∘*, which requires additional verification.

4.2.4 Atmospheric Abundances

The photospheric abundances of all dominant elements were evaluated from fitting multiple segments of spectra taken with HERMES (HD 23734, HD 68703) and MRES (HD 73345) and summarised in Table 5. In Fig. 5 we plotted the chemical composition of stars relative to the Sun with the reference values adopted from Asplund et al. (2021) and Magg et al. (2022). We characterise the overall composition of HD 23734 and HD 73345 as being mildly metal-deficient, unlike the third star, HD 68703, which shows a slight excess of many elements. The revealed difference in metallicity may reflect the individual specific properties of each star.

In the present study, we ignored the effect of departures from the LTE. This fact might stand behind the abnormal excess of oxygen, which was measured from the Oi 7771-7775 Å triplet (e.g. Sitnova et al., 2013). Even though the goodness-of-fit is high for the oxygen lines, we marked the derived abundance of this element as uncertain. The low accuracy of the rest of the values marked with a colon in Table 5 mostly resulted from the weakness of measured lines, their limited number, or blending with more abundant species in rotationally broadened profiles.

Our analysis indicates that neither of the programme stars shows strong anomalies typical for CP stars. This conclusion complements the negative test for the presence of a flux depression around 5200 Å (Kupka et al., 2004) in spectra taken with low resolution. We checked for such features in the flux-calibrated low-resolution spectra obtained with LAMOST for HD 23734 and HD 73345, and a medium-resolution spectrum of HD 68703 taken with XSHOOTER. Unfortunately, a flux-calibrated LAMOST spectrum of HD 68703 is unavailable in the LAMOST archive. For comparison, we used bona fide CP1 and CP2 stars with a spectral type comparable to that of the target stars. On inspecting the spectra shown in Fig. 17, one can notice that HD 23734 and HD 73345 do not possess any anomalies near 5200 Å. Furthermore, CP1 stars usually exhibit a distinctly weak Ca II K line in their spectra. This line in the spectra of our targets appears normal (Fig. 18), thereby confirming that neither of the studied stars belongs to the Am (CP1) class. In summary, our study portrays HD 23734, HD 68703, and HD 73345 as chemically normal stars.

4.2.5 Stellar Multiplicity

We measured the radial velocities (RV) from the available spectra as listed in Table 2. Among the three stars, notably, only HD 73345 showed significant variation of RV over time, suggesting it may be part of a long-period binary system. However, due to the limited temporal sampling of the available data, we were unable to determine the orbital period with confidence, and additional spectroscopic follow-up observations might therefore be essential to confirm the binary status of HD 73345.

In contrast, HD 68703 displays RV variations with a standard deviation of approximately 0.7 km s*-1*, consistently with rather pulsational variability than binarity. We therefore classify this object as a single star.

4.3 Evolutionary Status

To know the evolutionary status of the sample stars, we placed them in the H–R diagram. For this, we used luminosities derived from Gaia parallaxes and effective temperatures ($T_{\textrm{eff}}$) obtained from high-resolution spectroscopy. The absolute magnitudes ($M_{\rm V}$) were calculated from the Gaia parallaxes (Gaia Collaboration et al., 2016) using the standard relation (Cox, 2000). To compute the stellar luminosity ($\log(L/L_{\odot})$), we adopted a solar bolometric magnitude of $M_{\rm bol,\odot}=4.73$ mag (Torres, 2010). The bolometric correction (BC) was determined using an empirical relation taken from Torres (2010). The resulting values of $M_{\rm V}$ and $\log(L/L_{\odot})$, along with their associated uncertainties, are listed in Table 3 and 6, respectively.

The locations of HD 23734, HD 68703, and HD 73345 in the H–R diagram are shown in Fig. 6. It is found that position of HD 23734 is near to the zero-age main sequence (ZAMS) indicates it has recently begun core hydrogen burning. HD 68703 lies near the terminal-age main sequence (TAMS), suggesting that hydrogen in the core is nearly exhausted. HD 73345 is positioned between the ZAMS and TAMS and is likely still undergoing core hydrogen burning.

We have overplotted the stellar evolutionary tracks for masses ranging between 1.6 and 2.0 M⊙, and ages ranging from 0.1 to 1.4 Gyr, computed using the stellar evolution code CLÉS (Code Liégeois d’Evolution Stellaire; Scuflaire et al. 2008a). Theoretical $\gamma$ Dor (Dupret et al., 2004) and empirical $\delta$ Sct (Murphy et al., 2019) instability strips are overlaid for reference. An inspection of the stars’ locations within the instability strips, in combination with their frequency spectra, confirms that HD 23734, HD 68703, and HD 73345 are $\delta$ Sct-type pulsating variables. It is important to note that the observed values of the luminosity of HD 73345 can be slightly higher than the actual luminosity of the star due to its possible membership to a binary system. If the star has a companion, the combined flux could cause an observed vertical displacement in the H–R diagram, placing HD 73345 above its true evolutionary position.

5 Mode Identification

Asteroseismology leverages stellar pulsation frequencies and their corresponding amplitudes to infer fundamental stellar properties, thereby contributing significantly to our understanding of stellar structure and evolution. A crucial prerequisite for applying asteroseismic techniques is the accurate identification of pulsation modes, which remains a challenging task even when high-precision space-based data are available. (Aerts et al., 2010). In the following subsections, we outline several approaches employed for mode identification in our target stars.

5.1 Échelle Diagram

One of the robust techniques for identifying pulsation modes in asteroseismology is the Échelle diagram (ED). In an ED, for a given large frequency separation ($\Delta\nu$), the observed frequencies corresponding to the same angular degree ($\ell$) are folded into segments. Frequencies associated with low angular degrees ($\ell<2$) and high radial orders ($n\gg\ell$) of pressure modes approximately follow the asymptotic relation (Tassoul, 1980):

[TABLE]

where $n$ is the radial overtone number, $\ell$ is the angular degree, and $\epsilon$ is a constant of order unity. For higher radial orders, modes of the same degree and consecutive overtone numbers are nearly equally spaced in frequency (Bedding et al., 2020), and this regularity manifests as vertical ridges in the ED.

The large frequency separation $\Delta\nu$ is empirically related to the star’s mean density ($\bar{\rho}$) via the following relation (Suárez et al., 2014):

[TABLE]

where $\Delta\nu_{\odot}=135\,\mu$Hz $\approx 11.67$ d*-1* is the solar large frequency separation (Huber et al., 2011) and $\bar{\rho}_{\odot}$ is the mean density of the Sun. To obtain an initial estimate of $\Delta\nu$, we computed the mean stellar density using $\bar{\rho}=M/R^{3}$, where the radius $R$ was derived from the Stefan–Boltzmann law ($L\propto R^{2}T_{\rm eff}^{4}$) and the mass $M$ was estimated from theoretical evolutionary tracks. These values were then used to refine $\Delta\nu$ through the dynamic échelle interface (Hey & Ball, 2022).

Fig. 7 shows the Échelle diagrams of HD 23734, HD 68703, and HD 73345, with $\Delta\nu$ = 6.96, 3.25, and 5.20 d*-1*, respectively. We identified radial ($\ell=0$) and possibly non-radial ($\ell=1$) ridges for all three samples and are highlighted in the figure with light red shaded regions.

5.2 Seismic Modelling

Seismic modelling is an independent method for accurately measuring the age of stars based on observed frequencies. The conventional approach of employing theoretical isochrones presents considerable uncertainty, particularly near the Zero-Age Main Sequence (ZAMS), where the theoretical isochrones are closely spaced.

We adopted an iterative approach to identify the radial pulsation modes using theoretical models. Our working hypothesis assumed that the highest amplitude frequencies ($\nu^{\rm radial}_{\rm max}$) correspond to radial modes of an arbitrary radial order ($n$) in evolved main sequence stars, while they correspond to non-radial modes in less evolved stars with a higher surface gravity. To investigate this, we employed the stellar evolution code CLÉS (Code Liégeois d’Evolution Stellaire; Scuflaire et al. 2008a) to compute evolutionary models with stellar masses ranging from $1.40$ to $2.20\,M_{\odot}$, assuming solar metallicity ($Z=0.014$) and a convective core overshooting parameter of $\alpha_{\rm ov}=0.1$. For each model, we computed the radial mode frequencies ($\ell=0$) using the adiabatic stellar oscillation code OSC (Scuflaire et al., 2008b), considering various values of the radial overtone number $n$ associated with $\nu^{\rm radial}_{\rm max}$. The most likely $n$ value was determined by minimizing the seismic-$\chi^{2}$, following the formulation of Murphy et al. (2021) :

[TABLE]

where $f_{t}$ and $f_{o}$ are the theoretical and observed frequencies of the identified radial mode, respectively, and $\sigma_{f_{o}}$ is the uncertainty in the observed frequency, taken as 0.1 d*-1* (Murphy et al., 2021). The best-fitting models for each star were selected based on the minimum $\chi^{2}$ value, and are overplotted on the H-R diagram and is shown in Fig. 6, alongside evolutionary tracks for various stellar masses. The derived seismic parameters for HD 23734, HD 68703, and HD 73345 are listed in Table 6 and tagged with column Seismology.

The identified radial modes that align closely with the models are the second and third overtones for HD 23734; the fundamental, second, and third overtones for HD 68703; and the second, third, and fourth overtones for HD 73345.

5.3 Frequency Ratios

When multiple radial modes are detected in a pulsating star, the Petersen diagram (Petersen, 1973, 1978), that depicts the ratio of the higher to lower radial mode frequencies of a star, is generally used to verify the identifications. In this analysis, we compared the theoretical frequency ratios of the higher radial overtones ($n\geq 2$) to the lower radial modes or the fundamental radial mode ($n=1$) if present. Fig. 8 presents the Petersen diagram for our target stars. These results are in agreement with the mode identifications obtained through the Échelle diagrams and the seismic models.

5.4 Pulsation Constant

To validate the identified radial pulsation modes, we calculated the pulsation constant, $Q$ for each target star, following the formulation provided by Breger (1990). The $Q$ values for HD 23734, HD 68703, and HD 73345 are listed in the fifth columns of Tables 7, 8, and 9, respectively. These values fall within the expected ranges for the fundamental and overtone modes, with fractional uncertainties up to 18%. The adopted $Q$ ranges for radial modes are as follows: fundamental ($Q\geq 0.027$), first overtone ($0.021\leq Q<0.027$), second overtone ($0.018\leq Q<0.021$), and third overtone ($Q<0.018$), as given by Poro et al. (2024). The sixth columns of these tables indicate the corresponding identified pulsation modes, labelled as fundamental ($F_{1}$) and successive overtones ($F_{2}$ to $F_{5}$). It is found that HD 23734 pulsates in the second and third overtone, HD 68703 shows pulsations in the fundamental, second, and third overtones and HD 73345 exhibits radial pulsations in the second, third, and fourth overtones. The agreement among the $Q$ values, échelle diagrams, seismic models and frequency ratios supports the reliability of the identified radial pulsation modes.

6 Conclusions and Future Prospects

The primary goal of the extension of the N-C survey is to gain insights into the interplay between stellar pulsation, chemical inhomogeneities, rotation, and magnetic fields. To achieve the identified goals, we utilised state-of-the-art photometric and spectroscopic data acquired from both ground- and space-based facilities, followed by thorough analyses. Based on our investigation, we draw the following conclusions:

• (i)

Analysis of K2 and TESS photometry reveals that HD 68703 and HD 73345 are multi-periodic $\delta$ Sct pulsators, while HD 23734 is a newly identified $\delta$ Sct pulsator. In our studied stars, we have also observed evidence of the coexistence of rotational modulation in the presence of the pulsational variability.

• (ii)

We have determined the basic astrophysical parameters of HD 23734, HD 68703, and HD 73345 using photometric and spectroscopic data. The lack of anomalies in measured individual abundances, together with the absence of flux depression at 5200 Å in flux-calibrated spectra, confirms that the studied objects are likely to be chemically normal A- and F-type stars.

• (iii)

The stellar parameters of HD 68703 derived by Dürfeldt-Pedros et al. (2024) are generally consistent with our findings. The Least Squares Deconvolution (LSD) profiles of HD 68703 reveal notable line profile variations due to pulsation, making it an ideal candidate for follow-up time-series spectroscopic studies.

• (iv)

One of the targets, HD 73345, is a member of the Praesepe cluster (Pamos Ortega et al., 2023), which has an estimated age of 759 Myr. This value is relatively close to the 863 Myr derived from our asteroseismic analysis. Pamos Ortega et al. (2023) reported a large frequency separation of $\Delta\nu=58\mu$Hz (approximately 5.01 d*-1*) for HD 73345, which is in good agreement with our dynamically derived value of $\Delta\nu=5.20$ d*-1*. Further, our RV measurements suggests that HD 73345 is a likely member of a binary system, albeit, the limited phase coverage restricts to make a conclusive results, and demands additional spectroscopic observations to confirm and characterise the system.

• (v)

Through our comprehensive asteroseismic analysis, we identified the observed radial modes for all three stars. HD 23734 and HD 73345 exhibit predominant non-radial modes, whereas HD 68703 displays prominent radial modes. The observed radial pulsation modes were found to be of radial orders $n$ = 3 and 4 for HD 23734; $n=1,3,$ and $4$ for HD 68703; and $n=3,4,$ and $5$ for HD 73345. In addition to the radial modes, we also detected the probable non-radial ridge of $\ell$=1.

Among the samples observed under the N-C Survey project using ground-based facilities, we have identified several targets that have also been observed by the TESS mission (Dileep et al., 2024). These stars were previously classified as non-pulsators based on ground-based observations in the N-C Survey. Therefore, we propose a re-examination of all the objects using high-precision space-based photometry and high-resolution spectroscopy. Thus, the present study is an important step towards finding clues to understand the interactions between pulsation, rotation, binarity, and chemical peculiarities in the intermediate-mass stars.

Data availability statement

The high-resolution spectroscopic data used in this article will be shared upon reasonable request to the corresponding author. The TESS time-series flux data for the target stars are publicly available from the NASA MAST archive (https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html). This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for DPAC has been provided by national institutions, in particular those participating in the Gaia Multilateral Agreement. This research has also made use of the SIMBAD database, operated at CDS, Strasbourg, France.

Acknowledgments

The authors acknowledge the anonymous referee for providing the insightful comments. This work is supported by the Belgo-Indian Network for Astronomy and Astrophysics (BINA), approved by the International Division, 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) (BINA). SJ, SCG, and OT acknowledge the financial support received from the BRICS grant DST/ICD/BRICS/Call-5/SAPTARISI/2023(G). AD acknowledges the financial support received from the DST-INSPIRE Fellowship Programme (DST/INSPIREFellowship/2020/IF200245). OT acknowledges financial support from the Uppsala University International Science Programme (ISP), the SEISMIC project, and the Max Planck - Humboldt Research Unit, in collaboration with MPA, MPS, and Kyambogo University. SJ, APY, and SP gratefully acknowledge the financial support from the Core Research Grant (CRG/2021/007772) of the Science and Engineering Research Board (SERB), India. This paper includes data collected by the Kepler and TESS missions, available from the Mikulski Archive for Space Telescopes (MAST), operated by NASA. Based on observations made with the Mercator Telescope, operated on the island of La Palma by the Flemish Community at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. Based on observations obtained with the HERMES spectrograph, which is supported by the Research Foundation – Flanders (FWO), Belgium; the Research Council of KU Leuven, Belgium; the Fonds National de la Recherche Scientifique (F.R.S.-FNRS), Belgium; the Royal Observatory of Belgium; the Observatoire de Genève, Switzerland; and the Thüringer Landessternwarte Tautenburg, Germany. Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. The LAMOST spectra are available at https://www.lamost.org/. Part of the research is based on data obtained from the European Southern Observatory (ESO) Science Archive Facility with DOI(s): https://doi.org/10.18727/archive/24, https://doi.org/10.18727/archive/50, and https://doi.org/10.18727/archive/71 under ESO Prog ID 110.248M.001. This research has used data, tools, or materials developed as part of the EXPLORE project, which has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 101004214.

Appendix A TESS and K2 Light Curves and Amplitude Spectra

Appendix B Frequency Solutions from TESS and K2 Time-series Analysis

Appendix C LSD Profiles Variations

Appendix D Rotation

Appendix E Flux Depression and Strength of Ca-K lines