MOBSTER - II. Identification of rotationally variable A stars observed with \emph{TESS} in Sectors 1 to 4

TL;DR

This study analyzes TESS light curves of A-type stars from sectors 1 to 4, identifying 134 candidates with rotational variability, including 60 new detections, and compares properties of chemically peculiar and non-peculiar stars.

Contribution

First large-scale identification of rotationally variable A-type stars using TESS data, including new candidate detections and comparative analysis of their properties.

Findings

134 candidate rotational variables identified, 60 new.

Ap stars tend to have longer rotation periods and higher amplitudes.

Non-Ap stars show shorter periods and lower amplitudes.

Abstract

Recently, high-precision optical 2~min cadence light curves obtained with \emph{TESS} for targets located in the mission's defined first four sectors have been released. The majority of these high-cadence and high-precision measurements currently span $\sim28\,{\rm d}$, thereby allowing periodic variability occurring on timescales $\lesssim14\,{\rm d}$ to potentially be detected. Magnetic chemically peculiar (mCP) A-type stars are well known to exhibit rotationally modulated photometric variability that is produced by inhomogeneous chemical abundance distributions in their atmospheres. While mCP stars typically exhibit rotation periods that are significantly longer than those of non-mCP stars, both populations exhibit typical periods $\lesssim10\,{\rm d}$; therefore, the early \emph{TESS} releases are suitable for searching for rotational modulation of the light curves of both mCP and non-mCP stars. We present the results of our search for A-type stars that exhibit variability in their \emph{TESS} light curves that is consistent with rotational modulation based on the first two data releases obtained from sectors 1 to 4. Our search yielded $134$ high-probability candidate rotational variables -- $60$ of which have not been previously reported. Approximately half of these stars are identified in the literature as Ap (mCP) stars. Comparisons between the subsample of high-probability candidate rotationally variable Ap stars and the subsample of stars that are not identified as Ap reveal that the latter subsample exhibits statistically (i) shorter rotation periods and (ii) significantly lower photometric amplitudes.

Tables

Table 1. Table 1: Parameters associated with the 134 134 134 identified high probability candidate rotational variables. Columns (1) through (8) list the TIC identifiers, alternative identifiers, spectral types, V 𝑉 V magnitudes, maximum photometric amplitudes associated with the rotational modulation signals ( Δ ​ T max Δ subscript 𝑇 max \Delta T_{\rm max} where the 1 or 2 subscript indicates whether Δ ​ T max Δ subscript 𝑇 max \Delta T_{\rm max} corresponds to f 1 subscript 𝑓 1 f_{1} or f 2 subscript 𝑓 2 f_{2} ), rotation periods inferred from the TESS light curves, published rotation periods, and notes. The numbers in parentheses in rotation periods indicate the uncertainty in the value ( 3 ​ σ 3 𝜎 3\sigma uncertainties are listed for both Δ ​ T max Δ subscript 𝑇 max \Delta T_{\rm max} and P rot subscript 𝑃 rot P_{\rm rot} ). We note the confidence with which any reported magnetic field measurements in the literature have been obtained: definite detections (DD), marginal detections (MD), and null detections (ND). Additionally, we note whether each star is identified as a spectroscopic binary (SB), visual binary (VB), δ 𝛿 \delta  Scuti pulsator, roAp star, and if the amplitude of the rotational modulation is found to vary over time (amplitude modulation, AMod). Those stars without P rot , pub subscript 𝑃 rot pub P_{\rm rot,pub} values are considered new rotational variables; similarly, those δ 𝛿 \delta  Scuti and roAp identifications that are not accompanied with references are considered new classifications. The full table appears only in the electronic version of the paper.

TIC	Alt. ID	Sp. Type	$V$	$\Delta T_{\max }$	$P_{\mathrm{rot}}$	$P_{\mathrm{rot},\mathrm{pub}}$	Notes
			(mag)	(mmag)	(d)	(d)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
7624182	HD 27342	A2/3V	8.8	$0.62{\left(2\right)}^1$	1.720(1)
7780491	HD 28430	ApEuCrSr	8.2	$3.50{\left(2\right)}^2$	1.8763(3)
10863314	HD 10653	A1IV	7.7	$2.06{\left(2\right)}^2$	2.1345(6)
12359289	HD 225119	ApSi	8.2	$5.14{\left(3\right)}^2$	3.0644(5)	2.944a, 3.06395(41)b
12393823	HD 225264	A0IV	8.3	$0.83{\left(1\right)}^1$	1.4237(6)	1.42353(23)b	SB+c NDd
24186142	HD 5601	ApSi	7.6	$2.47{\left(3\right)}^1$	9.85(2)	1.110e	DDf
24225890	HD 5823	ApSrEu(Cr)	10.0	$6.88{\left(6\right)}^2$	5.007(3)	1.245e
27985664	HD 3885	ApSi	9.8	$11.99{\left(9\right)}^2$	1.8144(3)	1.815e
29432990	HD 198966	A9V	9.2	$0.11{\left(2\right)}^1$	1.267(3)
29666185	HD 199917	A2III/IV	7.1	$0.50{\left(1\right)}^1$	1.0594(5)		AMod
29755072	HD 200299	A3III	7.7	$0.97{\left(1\right)}^2$	6.180(4)
29781099	HD 27997	A2mA5-A9	8.1	$0.392{\left(7\right)}^2$	2.8749(9)
32035258	HD 24188	ApSi	6.3	$11.40{\left(2\right)}^1$	2.2303(1)	2.230e, 2.23047(4)b	DDd
38586082	HD 27463	ApEuCr(Sr)	6.3	$12.59{\left(3\right)}^1$	2.8349(2)	2.835750g, 2.8349(1)b	$\delta$ Scutib
41259805	HD 43226	ApSr(Eu)	9.0	$11.23{\left(3\right)}^1$	1.71450(4)	1.714e, 1.71441(11)b	roAph
42055368	HD 10038	A2mA5-F0	8.1	$3.18{\left(2\right)}^2$	2.3120(4)
44627561	HD 215559	A7V	9.3	$21.1{\left(1\right)}^1$	3.1284(6)	1.563140g	$\delta$ Scuti, AMod
44678216	HD 25267	ApSi	4.6	$7.5{\left(2\right)}^1$	3.861(4)	1.210e	DDi
44889961	HD 26726	ApSr	9.8	$18.66{\left(3\right)}^1$	5.3818(9)	5.382e
52368859	HD 10081	ApSr(Eu)	9.6	$9.47{\left(4\right)}^2$	1.57052(9)	1.570e, 1.57056(6)b	AMod
$+$: $P_{\mathrm{orb}}=5.400945\left(40\right)d$
${}^a$Catalano, Leone & Kroll (1998), ${}^b$Cunha et al. 2019 (submitted), ${}^c$Pourbaix et al. (2004), ${}^d$Bagnulo et al. (2015)
${}^e$Netopil et al. (2017), ${}^f$Kudryavtsev et al. (2006), ${}^g$Oelkers et al. (2018), ${}^h$Borra & Landstreet (1980)

Table 2. Table 2: Fundamental parameters associated with the 134 identified high probability candidate rotational variables. Columns (1) through (7) list the TIC identifiers, distances ( d 𝑑 d ), effective temperatures listed in the TIC ( T eff , TIC subscript 𝑇 eff TIC T_{\rm eff,TIC} ), effective temperatures ( T eff , SED subscript 𝑇 eff SED T_{\rm eff,SED} ), luminosities ( log ⁡ L SED / L ⊙ subscript 𝐿 SED subscript 𝐿 direct-product \log{L_{\rm SED}/L_{\odot}} ), and radii ( R SED subscript 𝑅 SED R_{\rm SED} ) derived through the SED fitting analysis, and the masses ( M 𝑀 M ) derived from comparisons with evolutionary models. The full table appears only in the elctronic version of the paper.

TIC	$d$	$T_{\mathrm{eff},\mathrm{TIC}}$	$T_{\mathrm{eff},\mathrm{SED}}$	$\log \left(L_{\mathrm{SED}}/L_{\odot }\right)$	$R_{\mathrm{SED}}$	$M_{\mathrm{SED}}$
	(pc)	(K)	(K)		$\left(R_{\odot }\right)$	$\left(M_{\odot }\right)$
(1)	(2)	(3)	(4)	(5)	(6)	(7)
7624182	$461\pm 7$	$8666\pm 229$	$8450\pm 200$	$1.68\pm 0.04$	$3.24\pm 0.15$	$2.42\pm 0.15$
7780491	$218\pm 2$	$8030\pm 220$	$7700\pm 100$	$1.29\pm 0.01$	$2.48\pm 0.05$	$1.96\pm 0.12$
10863314	$256\pm 5$	$8968\pm 234$	$9050\pm 100$	$1.69\pm 0.02$	$2.85\pm 0.08$	$2.45\pm 0.14$
12359289	$672\pm 31$		$12300\pm 250$	$2.56\pm 0.07$	$4.19\pm 0.28$	$3.95\pm 0.20$
12393823	$226\pm 5$	$9433\pm 241$	$10250\pm 100$	$1.45\pm 0.03$	$1.68\pm 0.05$	$2.27\pm 0.09$
24186142	$272\pm 6$		$11200\pm 150$	$1.95\pm 0.04$	$2.51\pm 0.08$	$2.94\pm 0.18$
24225890	$390\pm 8$	$7163\pm 207$	$7300\pm 100$	$1.08\pm 0.02$	$2.18\pm 0.06$	$1.75\pm 0.12$
27985664	$872\pm 75$		$11550\pm 200$	$2.07\pm 0.10$	$2.69\pm 0.27$	$3.12\pm 0.20$
29432990	$224\pm 4$	$7115\pm 207$	$6750\pm 100$	$0.89\pm 0.02$	$2.03\pm 0.07$	$1.58\pm 0.11$
29666185	$123\pm 1$	$7975\pm 219$	$8200\pm 100$	$1.27\pm 0.02$	$2.14\pm 0.03$	$1.97\pm 0.13$
29755072	$232\pm 4$	$8292\pm 224$	$7800\pm 100$	$1.54\pm 0.03$	$3.21\pm 0.09$	$2.23\pm 0.16$
29781099	$204\pm 1$	$8362\pm 225$	$8100\pm 100$	$1.28\pm 0.02$	$2.22\pm 0.05$	$1.97\pm 0.12$
32035258	$160\pm 2$		$13650\pm 200$	$2.20\pm 0.03$	$2.26\pm 0.06$	$3.57\pm 0.14$
38586082	$126\pm 7$	$8669\pm 229$	$9050\pm 100$	$1.63\pm 0.05$	$2.65\pm 0.19$	$2.38\pm 0.14$
41259805	$243\pm 2$	$8034\pm 220$	$8050\pm 100$	$1.07\pm 0.01$	$1.76\pm 0.03$	$1.79\pm 0.11$
42055368	$174\pm 1$	$7362\pm 210$	$7600\pm 100$	$1.11\pm 0.01$	$2.07\pm 0.06$	$1.79\pm 0.11$
44627561	$408\pm 11$	$6451\pm 198$	$6700\pm 100$	$1.42\pm 0.03$	$3.79\pm 0.18$	$1.94\pm 0.15$
44678216	$93.6\pm 1.9$	$12503\pm 87$	$13000\pm 350$	$2.38\pm 0.04$	$3.06\pm 0.15$	$3.70\pm 0.16$
44889961	$442\pm 8$	$8823\pm 232$	$8150\pm 100$	$1.23\pm 0.02$	$2.07\pm 0.07$	$1.93\pm 0.12$
52368859	$787\pm 26$	$9076\pm 235$	$9300\pm 100$	$1.89\pm 0.04$	$3.39\pm 0.14$	$2.72\pm 0.16$

Table 3. Table 3: Parameters associated with the 134 134 134 identified high probability candidate rotational variables. Columns (1) through (8) list the TIC identifiers, alternative identifiers, spectral types, V 𝑉 V magnitudes, maximum photometric amplitudes associated with the rotational modulation signals ( Δ ​ T max Δ subscript 𝑇 max \Delta T_{\rm max} where the 1 or 2 subscript indicates whether Δ ​ T max Δ subscript 𝑇 max \Delta T_{\rm max} corresponds to f 1 subscript 𝑓 1 f_{1} or f 2 subscript 𝑓 2 f_{2} ), rotation periods inferred from the TESS light curves, published rotation periods, and notes. The numbers in parentheses in rotation periods indicate the uncertainty in the value ( 3 ​ σ 3 𝜎 3\sigma uncertainties are listed for both Δ ​ T max Δ subscript 𝑇 max \Delta T_{\rm max} and P rot subscript 𝑃 rot P_{\rm rot} ). We note the confidence with which any reported magnetic field measurements in the literature have been obtained: definite detections (DD), marginal detections (MD), and null detections (ND). Additionally, we note whether each star is identified as a spectroscopic binary (SB), visual binary (VB), δ 𝛿 \delta  Scuti pulsator, roAp star, and if the amplitudes of the rotational modulation is found to vary over time (amplitude modulation, AMod). Those stars without P rot , pub subscript 𝑃 rot pub P_{\rm rot,pub} values are considered new rotational variables; similarly, those δ 𝛿 \delta  Scuti and roAp identifications that are not accompanied with references are considered new classifications. The full table appears only in the electronic version of the paper.

TIC	Alt. ID	Sp. Type	$V$	$\Delta T_{\max }$	$P_{\mathrm{rot}}$	$P_{\mathrm{rot},\mathrm{pub}}$	Notes
			(mag)	(mmag)	(d)	(d)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
7624182	HD 27342	A2/3V	8.8	$0.62{\left(2\right)}^1$	1.720(1)
7780491	HD 28430	ApEuCrSr	8.2	$3.50{\left(2\right)}^2$	1.8763(3)
10863314	HD 10653	A1IV	7.7	$2.06{\left(2\right)}^2$	2.1345(6)
12359289	HD 225119	ApSi	8.2	$5.14{\left(3\right)}^2$	3.0644(5)	2.944a, 3.06395(41)b
12393823	HD 225264	A0IV	8.3	$0.83{\left(1\right)}^1$	1.4237(6)	1.42353(23)b	SB+c NDd
24186142	HD 5601	ApSi	7.6	$2.47{\left(3\right)}^1$	9.85(2)	1.110e	DDf
24225890	HD 5823	ApSrEu(Cr)	10.0	$6.88{\left(6\right)}^2$	5.007(3)	1.245e
27985664	HD 3885	ApSi	9.8	$11.99{\left(9\right)}^2$	1.8144(3)	1.815e
29432990	HD 198966	A9V	9.2	$0.11{\left(2\right)}^1$	1.267(3)
29666185	HD 199917	A2III/IV	7.1	$0.50{\left(1\right)}^1$	1.0594(5)		AMod
29755072	HD 200299	A3III	7.7	$0.97{\left(1\right)}^2$	6.180(4)
29781099	HD 27997	A2mA5-A9	8.1	$0.392{\left(7\right)}^2$	2.8749(9)
32035258	HD 24188	ApSi	6.3	$11.40{\left(2\right)}^1$	2.2303(1)	2.230e, 2.23047(4)b	DDd
38586082	HD 27463	ApEuCr(Sr)	6.3	$12.59{\left(3\right)}^1$	2.8349(2)	2.835750g, 2.8349(1)b	$\delta$ Scutib
41259805	HD 43226	ApSr(Eu)	9.0	$11.23{\left(3\right)}^1$	1.71450(4)	1.714e, 1.71441(11)b	roAph
42055368	HD 10038	A2mA5-F0	8.1	$3.18{\left(2\right)}^2$	2.3120(4)
44627561	HD 215559	A7V	9.3	$21.1{\left(1\right)}^1$	3.1284(6)	1.563140g	$\delta$ Scuti, AMod
44678216	HD 25267	ApSi	4.6	$7.5{\left(2\right)}^1$	3.861(4)	1.210e	DDi
44889961	HD 26726	ApSr	9.8	$18.66{\left(3\right)}^1$	5.3818(9)	5.382e
52368859	HD 10081	ApSr(Eu)	9.6	$9.47{\left(4\right)}^2$	1.57052(9)	1.570e, 1.57056(6)b	AMod
55400261	HD 30296	A9V	8.7	$1.08{\left(1\right)}^1$	4.606(2)		$\delta$ Scuti, AMod
66646031	HD 16145	ApCrEuSr	7.7	$13.65{\left(3\right)}^2$	4.4751(4)	2.238e
67650835	HD 7676	ApSrCrEu	8.4	$14.72{\left(2\right)}^1$	5.0979(5)	5.098e
70525154	HD 13709	A0V	5.3	$0.332{\left(8\right)}^1$	0.5457(1)		AMod
79272047	HD 201801	A9V	8.8	$0.20{\left(2\right)}^1$	5.23(3)
79394646	TYC 8793-01478-1	A5IV-V	4.4	$1.48{\left(1\right)}^1$	4.132(4)		$\delta$ Scuti, AMod
89545031	HD 223640	A0VpSiSr	5.2	$9.06{\left(2\right)}^1$	3.7342(5)	3.735e, 3.72251(97)b	NDd
92705248	HD 200623	ApSrEuCr	9.1	$9.49{\left(4\right)}^1$	2.1576(2)	2.200e, 2.1577(2)b
102090493	HD 7454	A5IV	9.5	$8.8{\left(1\right)}^2$	1.4585(2)	0.729208g	$\delta$ Scuti
129636548	HD 203585	ApSi	5.8	$1.385{\left(7\right)}^1$	3.1082(5)	3.11016(56)b	VB++j
136843852	HD 9335	A5/7III	7.5	$4.12{\left(1\right)}^2$	1.8595(1)
140044682	HD 208489	A0V	8.7	$5.85{\left(2\right)}^1$	0.92045(5)
140204398	HD 24825	ApCrEu(Sr)	6.8	$11.25{\left(2\right)}^1$	6.795(1)
141028198	HD 35361	ApCrEu	9.9	$5.06{\left(3\right)}^2$	6.306(1)	6.3035(9)b
141610473	HD 41613	ApEuCr	9.7	$3.08{\left(3\right)}^2$	4.0947(6)	4.0954(4)b	AMod
144069014	HD 213230	A5/6V	7.7	$0.49{\left(1\right)}^1$	1.3559(7)		$\delta$ Scuti
147086189	HD 203898	A9V	9.3	$1.34{\left(2\right)}^1$	1.0394(3)		$\delta$ Scuti, AMod
150250959	HD 44532	A2V	8.8	$0.52{\left(2\right)}^1$	2.859(5)
153742460	HD 28299	ApSi	7.6	$4.94{\left(2\right)}^2$	3.3639(4)
155945483	HD 1948	A2/3V	8.1	$0.14{\left(1\right)}^1$	6.10(3)
159834975	HD 203006	ApCrEuSr	4.8	$5.469{\left(8\right)}^2$	2.12199(6)	2.122e, 2.12230(9)b	DDk
161270578	HD 215789	A2IVn	3.5	$0.088{\left(4\right)}^1$	0.7910(7)		NDd
161334416	HD 216485	A1V	8.9	$1.90{\left(2\right)}^1$	1.5264(4)
161570223	HD 31973	ApSrCrEu	9.4	$1.19{\left(3\right)}^2$	2.705(1)
182909257	HD 6783	ApSi	8.0	$2.87{\left(2\right)}^1$	3.137(1)	3.14108(82)b
183802606	HD 8700	ApSi	9.6	$2.64{\left(2\right)}^1$	2.2701(3)	2.27015(17)b
183802904	HD 8783	ApSrCrEu	7.8	$10.30{\left(1\right)}^1$	19.384(7)	19.396e, 19.408(17)b	NDd
200441087	HD 30335	ApSrCrEu	9.7	$7.35{\left(6\right)}^1$	5.094(2)	5.100e, 5.096320g
200783972	HD 21360	A0V	6.5	$0.272{\left(9\right)}^1$	1.786(2)	27.151800g
201923258	HD 17450	A0IV/V	8.9	$0.84{\left(2\right)}^1$	2.396(2)
204293493	HD 217448	A8V+(G/K)	9.6	$0.17{\left(2\right)}^1$	2.162(7)
204314449	TYC 6397-01365-2		6.8	$0.34{\left(1\right)}^2$	1.5095(5)		AMod
206648435	HD 215983	ApSrEuCr	9.7	$8.89{\left(3\right)}^1$	5.157(2)	5.1094(22)b
206663039	HD 216336	A0VpSrCrEu	4.5	$0.548{\left(7\right)}^1$	2.542(1)
207143419	HD 18796	A1V	8.8	$0.64{\left(2\right)}^1$	1.900(2)		AMod
207208753	HD 20505	ApCrSr	9.8	$9.01{\left(5\right)}^1$	2.0436(4)	2.044e, 2.04334(19)b
211404370	HD 203932	ApSrEu	8.8	$0.55{\left(2\right)}^1$	6.64(3)	6.442(12)b	roApl MDd
219118940	HD 214582	A2II	9.5	$7.99{\left(8\right)}^1$	0.7927(1)	0.792111g	$\delta$ Scuti, AMod
219234021	HD 27211	ApSrCrEu	9.4	$3.23{\left(3\right)}^1$	1.1634(2)	1.163440g
219990936	HD 12671	A8III	8.5	$2.02{\left(3\right)}^1$	0.7140(1)		$\delta$ Scuti, AMod
220035931	HD 34631	ApSi	7.0	$19.66{\left(4\right)}^1$	2.20280(9)	1.822620g, 2.203e
220414891	HD 30609	A2IV/V	8.8	$0.23{\left(1\right)}^2$	6.92(1)
220565429	HD 19398	A9III/IV	8.8	$0.21{\left(1\right)}^1$	0.5566(3)
220570020	HD 19695	A9V	9.4	$0.09{\left(1\right)}^1$	1.345(3)
231813751	HD 38471	ApSi	7.6	$5.59{\left(9\right)}^1$	2.4192(9)		AMod
231844926	HD 10840	ApSi	6.8	$24.863{\left(6\right)}^1$	2.097679(7)	2.098e, 2.0971(1)b	MDd
231864288	HD 1860	A0V	7.3	$0.127{\left(8\right)}^1$	1.4968(9)	32.372898g, 8.634e
232066526	HD 11090	ApSr	10.8	$6.74{\left(4\right)}^2$	2.9195(2)	2.91982(16)b
234346165	HD 16504	ApSi	9.1	$6.14{\left(4\right)}^1$	3.3041(4)	3.3040(3)b
235007556	HD 221006	ApSi	5.7	$15.62{\left(1\right)}^1$	2.31475(5)	2.31206(36)b, 27.151800g	DDm
237336864	HD 218495	ApEuSr	9.4	$12.92{\left(2\right)}^2$	4.2006(3)	4.2006(1)b	roApn DDd
259587315	HD 30849	ApSrCrEu	8.9	$4.72{\left(3\right)}^1$	7.489(8)	15.864e	roAp
262613883	HD 63728	ApEuCr	9.4	$24.78{\left(6\right)}^1$	1.8402(1)	1.84015(17)b, 1.840e
269857621	HD 31230	A1V	8.6	$4.15{\left(1\right)}^1$	1.12324(2)
270250508	HD 209133	A9V	8.3	$0.15{\left(1\right)}^1$	0.7901(4)
270304671	HD 209605	ApSrEuCr	9.6	$13.09{\left(3\right)}^1$	7.822(2)	7.8896(50)b, 7.813e
270406421	HD 13467	A2IV	6.7	$2.64{\left(5\right)}^2$	0.58326(6)		$\delta$ Scuti, AMod
272316843	HD 66082	A0/1V	9.3	$0.25{\left(2\right)}^1$	1.265(2)
277688819	HD 208217	ApSrEuCr	7.2	$12.89{\left(1\right)}^1$	8.4464(9)	8.3200(84)b, 8.445e	DDo
277748932	HD 208759	ApSrEuCr	10.0	$2.38{\left(4\right)}^2$	4.452(3)	4.4501(19)b
278804454	HD 212385	ApSrEuCr	6.8	$6.99{\left(1\right)}^1$	2.5084(2)	2.5062(2)b, 2.480e	DDd
279573219	HD 54118	ApSi	5.1	$8.01{\left(3\right)}^1$	3.2743(4)	27.151800g, 3.275e	DDp
280095777	HD 19782	A1IV/V	9.5	$6.46{\left(2\right)}^1$	1.7862(1)
281668790	HD 3980	A3VpSrCr	5.7	$16.09{\left(1\right)}^2$	3.95165(9)	3.9517(1)b, 27.151800g	DDq
284196481	HD 54558	A1V	7.8	$0.113{\left(9\right)}^1$	0.33273(4)
287329624	HD 57642	A8IV/V	8.5	$0.31{\left(1\right)}^1$	7.529(8)
287428184	HD 69784	A0V	8.7	$4.76{\left(2\right)}^2$	0.65973(1)
289731700	HD 15144	A3VpSrCrEu	5.9	$2.43{\left(2\right)}^1$	2.992(1)	2.998e	DDr
300162713	TYC 9179-01409-1		9.2	$0.76{\left(3\right)}^1$	1.623(2)
301345974	HD 21799	ApSrCrEu	9.3	$13.7{\left(1\right)}^1$	5.069(3)	5.121e
301481939	HD 22378	ApSi	9.3	$5.24{\left(3\right)}^1$	2.2051(5)
301795354	HD 204367	A(pSrEuCr)	7.8	$0.14{\left(1\right)}^1$	9.17(8)
304096024	HD 11346	ApSrEuCr	9.9	$3.16{\left(3\right)}^2$	7.049(2)	7.116(6)b
304101379	HD 11620	A4III	8.6	$8.36{\left(4\right)}^2$	3.2123(4)
306573201	HD 66195	ApSrCrEu	8.7	$6.74{\left(3\right)}^1$	4.8982(6)	4.88938(63)b
306893839	HD 68561	ApSi	8.0	$17.40{\left(2\right)}^1$	4.2340(2)	4.233e, 4.23415(16)b
307288162	HD 71006	ApSi	9.2	$7.00{\left(3\right)}^1$	1.5207(1)	1.52073(26)b
307642246	HD 72634	ApCrEuSr	7.3	$6.63{\left(5\right)}^2$	1.8608(3)	1.8607(2)b, 0.931e	AMod
307784098	HD 73373	A0V	8.2	$0.11{\left(1\right)}^1$	5.17(3)
308085294	HD 74388	ApSi	7.0	$1.31{\left(1\right)}^1$	4.318(3)	4.3063(19)b	AMod
309148260	HD 69862	ApSrEuCr	10.1	$13.85{\left(3\right)}^1$	13.291(7)	13.3519(107)b, 0.519e
309402106	HD 70623	A8IV	8.7	$1.99{\left(3\right)}^1$	5.600(5)		$\delta$ Scuti
309792043	HD 35402	A3V	7.1	$0.558{\left(9\right)}^1$	4.096(5)	15.491900g
316913639	HD 222638	ApSrEuCr	8.7	$3.35{\left(2\right)}^2$	2.3469(1)	2.34691(26)b
326185137	HD 6532	A2Vp	8.4	$6.79{\left(2\right)}^1$	1.9451(2)	1.945e	roAps MDd
326358579	HD 206497	A3V	8.6	$0.15{\left(1\right)}^2$	1.472(2)
327597288	HD 206653	ApSi	7.2	$29.76{\left(4\right)}^1$	1.78698(6)	1.787e, 1.786898(58)b	NDd
327724630	HD 209468	A1V	7.6	$0.06{\left(1\right)}^1$	1.189(3)
332518087	HD 220455	A0V	7.8	$0.62{\left(2\right)}^1$	3.705(8)		AMod
336731635	HD 214985	ApSi	11.1	$1.25{\left(5\right)}^2$	2.770(3)	2.77342(219)b, 1.385e
339673256	HD 58292	ApSi	7.9	$16.04{\left(1\right)}^1$	2.9607(2)	2.960e
340006157	HD 60435	ApSr(Eu)	8.9	$5.66{\left(9\right)}^1$	3.805(6)	7.6793(6)t	roApl DDd
348898673	HD 54399	ApSr(CrEu)	9.7	$6.47{\left(3\right)}^1$	5.0045(5)	4.9910(11)b, 2.501e
349409844	HD 58448	ApSi	6.9	$5.062{\left(8\right)}^2$	0.83090(1)	0.831(3)u, 0.83088(5)b	NDd
349972600	HD 61968	A3V	9.2	$0.38{\left(2\right)}^1$	0.24544(2)		$\delta$ Scuti
350146296	HD 63087	A7IV	9.4	$1.31{\left(2\right)}^1$	2.6637(2)		roApb
350146577	HD 63204	ApSi	8.3	$48.57{\left(1\right)}^1$	1.837488(9)	1.838e
350519062	HD 38719	ApCrSrEu	7.5	$6.07{\left(2\right)}^1$	4.0232(4)	4.0237(4)b, 4.021070g
358467700	HD 65712	ApSi	9.3	$14.11{\left(4\right)}^1$	1.9457(1)	1.946e, 1.94639(54)b	DDd
364323133	HD 39979	A6IV	7.9	$1.29{\left(3\right)}^1$	4.103(7)		$\delta$ Scuti
364424408	HD 30374	ApSrEuCr	10.1	$8.63{\left(3\right)}^1$	1.55632(6)	1.556e, 1.55682(14)b
365332561	HD 19228	A0	9.3	$1.40{\left(3\right)}^1$	2.115(2)
382044382	HD 34870	A2V	9.8	$2.66{\left(2\right)}^1$	2.5652(5)		AMod
382512330	HD 64369	ApSi	8.8	$9.01{\left(3\right)}^1$	0.89112(2)	0.891e, 0.8912(1)b
387515681	TYC 0640-00521-1	A5	9.4	$3.49{\left(3\right)}^1$	3.387(2)
389922504	HD 40277	ApSrCr(Eu)pec	8.3	$6.27{\left(1\right)}^2$	0.849584(6)	0.849585(8)b
391927730	HD 56981	ApSr	9.6	$0.44{\left(2\right)}^1$	3.788(4)	3.7843(18)b
392761412	HD 207259	ApEuSrCr	8.8	$8.15{\left(3\right)}^1$	2.1558(2)	2.1557(2)b, 2.200e
394230660	HD 20434	A3V	9.5	$0.17{\left(2\right)}^1$	5.66(6)		$\delta$ Scuti
396696863	HD 27952	A4mA7-A9	9.4	$2.79{\left(3\right)}^1$	0.8218(1)		AMod
410451752	HD 66318	A0pEuCrSr	9.7	$0.31{\left(4\right)}^1$	0.777(1)	0.77688(52)b	DDd
423663684	HD 2957	ApCrEu	8.5	$10.48{\left(2\right)}^1$	4.633(1)	4.633e	DDf
431380369	HD 20880	ApSr(EuCr)	8.0	$2.83{\left(3\right)}^1$	5.221(6)	5.2434(26)b	roApb
469948764	HD 6208	A0V	9.4	$0.85{\left(2\right)}^1$	1.3006(7)	4.433e
$+$: $P_{\mathrm{orb}}=5.400945\left(40\right)d$, $++$: $P_{\mathrm{orb}}=464.66\mathrm{yrs}$
${}^a$Catalano, Leone & Kroll (1998), ${}^b$Cunha et al. 2019 (submitted), ${}^c$Pourbaix et al. (2004), ${}^d$Bagnulo et al. (2015)
${}^e$Netopil et al. (2017), ${}^f$Kudryavtsev et al. (2006), ${}^g$Oelkers et al. (2018), ${}^h$Borra & Landstreet (1980)
${}^i$Malkov et al. (2012), ${}^j$Sikora et al. (2019a), ${}^k$Kurtz (1984), ${}^l$Bohlender, Landstreet & Thompson (1993)
${}^m$Martinez & Kurtz (1990), ${}^n$Mathys et al. (1997), ${}^o$Borra & Landstreet (1975), ${}^p$Maitzen, Weiss & Wood (1980)
${}^q$Aurière et al. (2007), ${}^r$Kurtz & Kreidl (1985), ${}^s$Kurtz, van Wyk & Marang (1990), ${}^t$Manfroid & Renson (1983)

Table 4. Table 4: Fundamental parameters associated with the 134 identified high probability candidate rotational variables. Columns (1) through (7) list the TIC identifiers, distances ( d 𝑑 d ), effective temperatures listed in the TIC ( T eff , TIC subscript 𝑇 eff TIC T_{\rm eff,TIC} ), effective temperatures ( T eff , SED subscript 𝑇 eff SED T_{\rm eff,SED} ), luminosities ( log ⁡ L SED / L ⊙ subscript 𝐿 SED subscript 𝐿 direct-product \log{L_{\rm SED}/L_{\odot}} ), and radii ( R SED subscript 𝑅 SED R_{\rm SED} ) derived through the SED fitting analysis, and the masses ( M 𝑀 M ) derived from comparisons with evolutionary models.

TIC	$d$	$T_{\mathrm{eff},\mathrm{TIC}}$	$T_{\mathrm{eff},\mathrm{SED}}$	$\log \left(L_{\mathrm{SED}}/L_{\odot }\right)$	$R_{\mathrm{SED}}$	$M_{\mathrm{SED}}$
	(pc)	(K)	(K)		$\left(R_{\odot }\right)$	$\left(M_{\odot }\right)$
(1)	(2)	(3)	(4)	(5)	(6)	(7)
7624182	$461\pm 7$	$8666\pm 229$	$8450\pm 200$	$1.68\pm 0.04$	$3.24\pm 0.15$	$2.42\pm 0.15$
7780491	$218\pm 2$	$8030\pm 220$	$7700\pm 100$	$1.29\pm 0.01$	$2.48\pm 0.05$	$1.96\pm 0.12$
10863314	$256\pm 5$	$8968\pm 234$	$9050\pm 100$	$1.69\pm 0.02$	$2.85\pm 0.08$	$2.45\pm 0.14$
12359289	$672\pm 31$		$12300\pm 250$	$2.56\pm 0.07$	$4.19\pm 0.28$	$3.95\pm 0.20$
12393823	$226\pm 5$	$9433\pm 241$	$10250\pm 100$	$1.45\pm 0.03$	$1.68\pm 0.05$	$2.27\pm 0.09$
24186142	$272\pm 6$		$11200\pm 150$	$1.95\pm 0.04$	$2.51\pm 0.08$	$2.94\pm 0.18$
24225890	$390\pm 8$	$7163\pm 207$	$7300\pm 100$	$1.08\pm 0.02$	$2.18\pm 0.06$	$1.75\pm 0.12$
27985664	$872\pm 75$		$11550\pm 200$	$2.07\pm 0.10$	$2.69\pm 0.27$	$3.12\pm 0.20$
29432990	$224\pm 4$	$7115\pm 207$	$6750\pm 100$	$0.89\pm 0.02$	$2.03\pm 0.07$	$1.58\pm 0.11$
29666185	$123\pm 1$	$7975\pm 219$	$8200\pm 100$	$1.27\pm 0.02$	$2.14\pm 0.03$	$1.97\pm 0.13$
29755072	$232\pm 4$	$8292\pm 224$	$7800\pm 100$	$1.54\pm 0.03$	$3.21\pm 0.09$	$2.23\pm 0.16$
29781099	$204\pm 1$	$8362\pm 225$	$8100\pm 100$	$1.28\pm 0.02$	$2.22\pm 0.05$	$1.97\pm 0.12$
32035258	$160\pm 2$		$13650\pm 200$	$2.20\pm 0.03$	$2.26\pm 0.06$	$3.57\pm 0.14$
38586082	$126\pm 7$	$8669\pm 229$	$9050\pm 100$	$1.63\pm 0.05$	$2.65\pm 0.19$	$2.38\pm 0.14$
41259805	$243\pm 2$	$8034\pm 220$	$8050\pm 100$	$1.07\pm 0.01$	$1.76\pm 0.03$	$1.79\pm 0.11$
42055368	$174\pm 1$	$7362\pm 210$	$7600\pm 100$	$1.11\pm 0.01$	$2.07\pm 0.06$	$1.79\pm 0.11$
44627561	$408\pm 11$	$6451\pm 198$	$6700\pm 100$	$1.42\pm 0.03$	$3.79\pm 0.18$	$1.94\pm 0.15$
44678216	$93.6\pm 1.9$	$12503\pm 87$	$13000\pm 350$	$2.38\pm 0.04$	$3.06\pm 0.15$	$3.70\pm 0.16$
44889961	$442\pm 8$	$8823\pm 232$	$8150\pm 100$	$1.23\pm 0.02$	$2.07\pm 0.07$	$1.93\pm 0.12$
52368859	$787\pm 26$	$9076\pm 235$	$9300\pm 100$	$1.89\pm 0.04$	$3.39\pm 0.14$	$2.72\pm 0.16$
55400261	$183\pm 1$	$7173\pm 208$	$7000\pm 100$	$0.90\pm 0.01$	$1.91\pm 0.03$	$1.60\pm 0.10$
66646031	$250\pm 5$	$9100\pm 236$	$8900\pm 100$	$1.65\pm 0.03$	$2.81\pm 0.09$	$2.40\pm 0.14$
67650835	$241\pm 3$	$8944\pm 233$	$8650\pm 100$	$1.30\pm 0.02$	$1.98\pm 0.07$	$2.02\pm 0.13$
70525154	$96.8\pm 1.7$	$9977\pm 92$	$10000\pm 100$	$1.90\pm 0.02$	$2.96\pm 0.08$	$2.76\pm 0.16$
79272047	$170\pm 1$	$6782\pm 70$	$6850\pm 100$	$0.83\pm 0.01$	$1.84\pm 0.05$	$1.54\pm 0.10$
79394646	$29.4\pm 0.2$	$8655\pm 229$	$8350\pm 250$	$1.06\pm 0.02$	$1.61\pm 0.13$	$1.82\pm 0.10$
89545031	$101\pm 3$		$13150\pm 250$	$2.17\pm 0.06$	$2.35\pm 0.11$	$3.48\pm 0.11$
92705248	$273\pm 10$	$8808\pm 231$	$8600\pm 100$	$1.15\pm 0.04$	$1.68\pm 0.08$	$1.90\pm 0.11$
102090493	$360\pm 4$	$6830\pm 203$	$7100\pm 150$	$1.24\pm 0.03$	$2.76\pm 0.08$	$1.90\pm 0.13$
129636548	$120\pm 10$		$11450\pm 300$	$2.01\pm 0.09$	$2.57\pm 0.31$	$3.04\pm 0.20$
136843852	$137\pm 1$	$7626\pm 214$	$7600\pm 100$	$1.16\pm 0.02$	$2.20\pm 0.03$	$1.84\pm 0.11$
140044682	$276\pm 5$	$9726\pm 246$	$9700\pm 100$	$1.36\pm 0.03$	$1.69\pm 0.05$	$2.18\pm 0.09$
140204398	$250\pm 2$	$9400\pm 241$	$10000\pm 200$	$2.07\pm 0.02$	$3.63\pm 0.15$	$3.02\pm 0.18$
141028198	$782\pm 21$	$8192\pm 222$	$7700\pm 100$	$1.72\pm 0.04$	$4.09\pm 0.17$	$2.30\pm 0.19$
141610473	$423\pm 12$	$7183\pm 208$	$6900\pm 100$	$1.25\pm 0.03$	$2.94\pm 0.12$	$1.90\pm 0.15$
144069014	$124\pm 1$	$7520\pm 212$	$7600\pm 150$	$1.00\pm 0.03$	$1.82\pm 0.05$	$1.71\pm 0.11$
147086189	$204\pm 2$	$7050\pm 206$	$7100\pm 100$	$0.82\pm 0.02$	$1.71\pm 0.04$	$1.55\pm 0.10$
150250959	$226\pm 3$	$8072\pm 220$	$7700\pm 100$	$1.10\pm 0.03$	$1.99\pm 0.06$	$1.79\pm 0.11$
153742460	$362\pm 7$		$13050\pm 250$	$2.32\pm 0.04$	$2.83\pm 0.09$	$3.63\pm 0.15$
155945483	$197\pm 2$	$7909\pm 218$	$7950\pm 150$	$1.26\pm 0.03$	$2.24\pm 0.06$	$1.94\pm 0.12$
159834975	$54.7\pm 1.7$	$8790\pm 231$	$9750\pm 150$	$1.57\pm 0.04$	$2.14\pm 0.11$	$2.37\pm 0.16$
161270578	$41.4\pm 0.5$	$7900\pm 210$	$8550\pm 250$	$1.73\pm 0.02$	$3.34\pm 0.28$	$2.48\pm 0.15$
161334416	$431\pm 18$	$8126\pm 221$	$8100\pm 100$	$1.59\pm 0.04$	$3.17\pm 0.16$	$2.30\pm 0.16$
161570223	$378\pm 8$	$8345\pm 224$	$8350\pm 150$	$1.29\pm 0.04$	$2.10\pm 0.08$	$1.99\pm 0.13$
182909257	$285\pm 5$		$12350\pm 250$	$1.95\pm 0.04$	$2.06\pm 0.08$	$3.08\pm 0.15$
183802606	$680\pm 18$	$8754\pm 231$	$9250\pm 100$	$1.82\pm 0.03$	$3.16\pm 0.14$	$2.62\pm 0.16$
183802904	$318\pm 5$	$8648\pm 229$	$8300\pm 100$	$1.77\pm 0.02$	$3.72\pm 0.17$	$2.53\pm 0.18$
200441087	$451\pm 7$	$8683\pm 229$	$8500\pm 100$	$1.33\pm 0.02$	$2.12\pm 0.05$	$2.04\pm 0.12$
200783972	$122\pm 1$	$9068\pm 235$	$10000\pm 100$	$1.62\pm 0.01$	$2.15\pm 0.02$	$2.45\pm 0.15$
201923258	$628\pm 21$	$8936$	$9200\pm 100$	$2.00\pm 0.03$	$3.94\pm 0.15$	$2.87\pm 0.21$
204293493	$218\pm 3$	$6490\pm 83$	$6950\pm 100$	$0.76\pm 0.03$	$1.66\pm 0.05$	$1.40\pm 0.04$
204314449	$101\pm 1$	$7880\pm 218$				$1.88\pm 0.22$
206648435	$400\pm 10$	$8184\pm 222$	$8350\pm 100$	$1.24\pm 0.03$	$1.99\pm 0.07$	$1.95\pm 0.12$
206663039	$62.3\pm 1.8$		$10500\pm 250$	$1.88\pm 0.05$	$2.64\pm 0.16$	$2.78\pm 0.17$
207143419	$225\pm 2$	$8123\pm 221$	$8150\pm 100$	$1.07\pm 0.02$	$1.73\pm 0.03$	$1.81\pm 0.10$
207208753	$544\pm 13$	$9310\pm 239$	$9450\pm 200$	$1.49\pm 0.05$	$2.08\pm 0.09$	$2.27\pm 0.15$
211404370	$201\pm 57$	$7544\pm 213$	$7350\pm 100$	$0.97\pm 0.25$	$1.89\pm 0.55$	$1.67\pm 0.20$
219118940	$219\pm 3$	$7172\pm 208$	$7150\pm 100$	$0.78\pm 0.02$	$1.59\pm 0.04$	$1.53\pm 0.09$
219234021	$536\pm 12$	$9531\pm 243$	$10000\pm 100$	$1.67\pm 0.03$	$2.29\pm 0.08$	$2.50\pm 0.16$
219990936	$152\pm 1$	$7313\pm 209$	$7300\pm 100$	$0.86\pm 0.01$	$1.68\pm 0.03$	$1.59\pm 0.09$
220035931	$261\pm 3$		$12950\pm 250$	$2.29\pm 0.05$	$2.77\pm 0.06$	$3.58\pm 0.14$
220414891	$230\pm 2$	$8377\pm 225$	$8300\pm 150$	$1.10\pm 0.02$	$1.72\pm 0.04$	$1.84\pm 0.10$
220565429	$209\pm 1$	$7194\pm 208$	$7050\pm 100$	$1.01\pm 0.01$	$2.13\pm 0.04$	$1.68\pm 0.11$
220570020	$184\pm 1$	$6824\pm 203$	$7100\pm 100$	$0.67\pm 0.02$	$1.43\pm 0.03$	$1.48\pm 0.07$
231813751	$377\pm 8$		$14150\pm 100$	$2.47\pm 0.03$	$2.86\pm 0.07$	$3.99\pm 0.13$
231844926	$194\pm 2$		$12700\pm 350$	$2.11\pm 0.05$	$2.34\pm 0.07$	$3.33\pm 0.14$
231864288	$140\pm 1$	$9232\pm 238$	$9400\pm 150$	$1.34\pm 0.03$	$1.76\pm 0.03$	$2.13\pm 0.11$
232066526	$721\pm 22$	$8750\pm 230$	$8700\pm 300$	$1.31\pm 0.05$	$1.98\pm 0.14$	$2.04\pm 0.13$
234346165	$726\pm 24$	$9480$	$10700\pm 100$	$2.20\pm 0.04$	$3.68\pm 0.15$	$3.25\pm 0.15$
235007556	$124\pm 2$		$14750\pm 250$	$2.31\pm 0.04$	$2.18\pm 0.05$	$3.84\pm 0.25$
237336864	$245\pm 2$	$8283\pm 223$	$8100\pm 100$	$0.91\pm 0.02$	$1.45\pm 0.04$	$1.62\pm 0.06$
259587315	$355\pm 5$	$8165\pm 222$	$7750\pm 100$	$1.41\pm 0.02$	$2.83\pm 0.11$	$2.09\pm 0.13$
262613883	$402\pm 6$	$9359\pm 240$	$9100\pm 150$	$1.44\pm 0.03$	$2.11\pm 0.06$	$2.19\pm 0.14$
269857621	$196\pm 2$	$9136\pm 236$	$8700\pm 100$	$1.06\pm 0.02$	$1.50\pm 0.03$	$1.72\pm 0.07$
270250508	$151\pm 1$	$6973\pm 76$	$6850\pm 100$	$0.92\pm 0.01$	$2.05\pm 0.05$	$1.62\pm 0.11$
270304671	$387\pm 6$	$8044\pm 220$	$7750\pm 100$	$1.22\pm 0.02$	$2.27\pm 0.08$	$1.90\pm 0.11$
270406421	$117\pm 1$	$7918\pm 218$	$7700\pm 100$	$1.37\pm 0.01$	$2.73\pm 0.05$	$2.05\pm 0.13$
272316843	$319\pm 4$	$8547\pm 227$	$8150\pm 150$	$1.17\pm 0.03$	$1.93\pm 0.06$	$1.88\pm 0.12$
277688819	$115\pm 2$	$8368\pm 225$	$8200\pm 100$	$1.13\pm 0.02$	$1.83\pm 0.08$	$1.85\pm 0.11$
277748932	$518\pm 14$	$8955\pm 234$	$8500\pm 100$	$1.33\pm 0.03$	$2.12\pm 0.08$	$2.04\pm 0.13$
278804454	$146\pm 3$	$8672\pm 229$	$8450\pm 100$	$1.48\pm 0.02$	$2.56\pm 0.08$	$2.18\pm 0.13$
279573219	$85.4\pm 1.4$		$11250\pm 250$	$1.93\pm 0.04$	$2.42\pm 0.10$	$2.92\pm 0.18$
280095777	$327\pm 5$	$8808\pm 231$	$8750\pm 150$	$1.13\pm 0.03$	$1.60\pm 0.06$	$1.91\pm 0.09$
281668790	$68.3\pm 0.4$	$8747\pm 230$	$8500\pm 150$	$1.28\pm 0.02$	$2.01\pm 0.08$	$2.00\pm 0.13$
284196481	$257\pm 2$	$8650\pm 229$	$8650\pm 100$	$1.62\pm 0.02$	$2.86\pm 0.05$	$2.35\pm 0.13$
287329624	$135\pm 1$	$6900\pm 94$	$7000\pm 100$	$0.76\pm 0.01$	$1.63\pm 0.02$	$1.50\pm 0.10$
287428184	$261\pm 3$	$9259\pm 238$	$9000\pm 100$	$1.30\pm 0.02$	$1.83\pm 0.03$	$2.05\pm 0.12$
289731700	$81.7\pm 1.0$	$8429\pm 226$	$8450\pm 100$	$1.37\pm 0.02$	$2.27\pm 0.06$	$2.08\pm 0.13$
300162713	$288\pm 4$	$8826\pm 232$	$8500\pm 100$	$1.14\pm 0.02$	$1.72\pm 0.05$	$1.89\pm 0.10$
301345974	$305\pm 4$	$8212\pm 222$	$7400\pm 100$	$1.12\pm 0.02$	$2.21\pm 0.09$	$1.79\pm 0.11$
301481939	$482\pm 13$	$9501\pm 242$	$11150\pm 200$	$1.77\pm 0.05$	$2.05\pm 0.07$	$2.73\pm 0.16$
301795354	$168\pm 2$	$8790\pm 231$	$8450\pm 100$	$1.23\pm 0.02$	$1.93\pm 0.04$	$1.95\pm 0.13$
304096024	$751\pm 20$	$8098\pm 221$	$7600\pm 100$	$1.65\pm 0.03$	$3.88\pm 0.14$	$2.21\pm 0.19$
304101379	$233\pm 2$	$8046\pm 220$	$7650\pm 100$	$1.19\pm 0.01$	$2.23\pm 0.05$	$1.86\pm 0.12$
306573201	$292\pm 8$		$8950\pm 100$	$1.42\pm 0.04$	$2.14\pm 0.08$	$2.16\pm 0.14$
306893839	$516\pm 9$		$12700\pm 200$	$2.47\pm 0.04$	$3.55\pm 0.12$	$3.82\pm 0.16$
307288162	$809\pm 30$		$13600\pm 200$	$2.42\pm 0.05$	$2.92\pm 0.16$	$3.83\pm 0.15$
307642246	$353\pm 36$	$8947\pm 233$	$9650\pm 100$	$2.19\pm 0.09$	$4.48\pm 0.51$	$2.99\pm 0.21$
307784098	$278\pm 3$	$8396\pm 225$	$8550\pm 100$	$1.56\pm 0.02$	$2.75\pm 0.05$	$2.28\pm 0.13$
308085294	$349\pm 5$		$13850\pm 200$	$2.62\pm 0.04$	$3.54\pm 0.16$	$4.25\pm 0.17$
309148260	$632\pm 11$	$8134\pm 221$	$7350\pm 100$	$1.43\pm 0.03$	$3.20\pm 0.09$	$2.10\pm 0.17$
309402106	$158\pm 1$	$7053\pm 206$	$7050\pm 100$	$0.76\pm 0.01$	$1.60\pm 0.02$	$1.51\pm 0.09$
309792043	$164\pm 2$	$8482\pm 226$	$8450\pm 100$	$1.52\pm 0.03$	$2.69\pm 0.06$	$2.23\pm 0.13$
316913639	$307\pm 5$	$9714\pm 245$	$9550\pm 250$	$1.47\pm 0.03$	$1.98\pm 0.09$	$2.25\pm 0.13$
326185137	$197\pm 3$	$8550\pm 227$	$8450\pm 100$	$1.11\pm 0.02$	$1.67\pm 0.05$	$1.86\pm 0.09$
326358579	$215\pm 3$	$7573\pm 213$	$7500\pm 100$	$1.12\pm 0.03$	$2.15\pm 0.05$	$1.79\pm 0.12$
327597288	$240\pm 5$		$12100\pm 500$	$2.08\pm 0.07$	$2.49\pm 0.15$	$3.20\pm 0.18$
327724630	$162\pm 2$	$8906\pm 233$	$9350\pm 100$	$1.39\pm 0.01$	$1.88\pm 0.03$	$2.16\pm 0.11$
332518087	$201\pm 2$	$9631\pm 244$	$10100\pm 250$	$1.52\pm 0.03$	$1.87\pm 0.07$	$2.36\pm 0.12$
336731635	$1640\pm 270$	$9439\pm 241$	$12150\pm 550$	$2.28\pm 0.19$	$3.13\pm 0.67$	$3.50\pm 0.17$
339673256	$409\pm 6$	$9601\pm 244$	$10450\pm 250$	$2.12\pm 0.04$	$3.52\pm 0.15$	$3.12\pm 0.18$
340006157	$245\pm 2$	$8427\pm 226$	$7800\pm 100$	$1.10\pm 0.01$	$1.93\pm 0.08$	$1.79\pm 0.11$
348898673	$700\pm 16$	$7505\pm 44$	$7300\pm 100$	$1.67\pm 0.03$	$4.26\pm 0.17$	$2.12\pm 0.04$
349409844	$159\pm 1$		$11500\pm 200$	$1.78\pm 0.03$	$1.97\pm 0.04$	$2.79\pm 0.13$
349972600	$281\pm 3$	$9540\pm 243$	$7800\pm 200$	$1.08\pm 0.03$	$1.91\pm 0.06$	$1.78\pm 0.11$
350146296	$221\pm 3$	$7690\pm 215$	$7200\pm 100$	$0.79\pm 0.02$	$1.59\pm 0.04$	$1.54\pm 0.09$
350146577	$336\pm 5$	$9737\pm 246$	$10700\pm 150$	$1.83\pm 0.03$	$2.38\pm 0.06$	$2.74\pm 0.17$
350519062	$223\pm 2$	$8937\pm 233$	$8950\pm 100$	$1.62\pm 0.02$	$2.70\pm 0.05$	$2.37\pm 0.14$
358467700	$432\pm 6$	$8768\pm 231$	$10000\pm 350$	$1.56\pm 0.04$	$2.01\pm 0.11$	$2.39\pm 0.14$
364323133	$118\pm 1$	$7578\pm 213$	$7250\pm 100$	$0.86\pm 0.02$	$1.70\pm 0.04$	$1.58\pm 0.09$
364424408	$643\pm 21$	$7608\pm 47$	$8100\pm 150$	$1.49\pm 0.05$	$2.83\pm 0.14$	$1.95\pm 0.18$
365332561	$311\pm 8$	$9470\pm 242$	$8500\pm 100$	$1.17\pm 0.03$	$1.78\pm 0.06$	$1.91\pm 0.12$
382044382	$370\pm 6$	$7917\pm 218$	$7950\pm 150$	$1.09\pm 0.03$	$1.86\pm 0.07$	$1.80\pm 0.12$
382512330	$430\pm 6$	$9042\pm 235$	$9350\pm 100$	$1.72\pm 0.02$	$2.76\pm 0.05$	$2.50\pm 0.15$
387515681		$6885\pm 9$	$6600\pm 100$
389922504	$207\pm 1$		$8750\pm 100$	$1.20\pm 0.01$	$1.73\pm 0.03$	$1.95\pm 0.09$
391927730	$230\pm 1$	$6984\pm 205$	$6750\pm 100$	$0.76\pm 0.01$	$1.75\pm 0.02$	$1.48\pm 0.11$
392761412	$304\pm 5$	$8036\pm 220$	$7850\pm 100$	$1.31\pm 0.02$	$2.45\pm 0.07$	$1.98\pm 0.11$
394230660	$320\pm 4$	$7908\pm 218$	$7950\pm 200$	$1.10\pm 0.03$	$1.86\pm 0.06$	$1.81\pm 0.11$
396696863	$208\pm 1$	$6562\pm 199$	$6800\pm 100$	$0.80\pm 0.02$	$1.81\pm 0.03$	$1.52\pm 0.11$
410451752	$509\pm 14$	$9057\pm 235$	$8900\pm 100$	$1.52\pm 0.03$	$2.41\pm 0.10$	$2.25\pm 0.14$
423663684	$327\pm 9$	$9185$	$9400\pm 100$	$1.58\pm 0.03$	$2.31\pm 0.10$	$2.35\pm 0.15$
431380369	$221\pm 5$	$8242\pm 223$	$8000\pm 100$	$1.38\pm 0.02$	$2.56\pm 0.12$	$2.06\pm 0.12$
469948764	$327\pm 7$	$8779\pm 231$	$8950\pm 100$	$1.22\pm 0.03$	$1.69\pm 0.06$	$1.99\pm 0.11$

Equations

$$\Delta T(t)=a_0+\sum _{n=1}^{n=5}{a}_n\sin (2\pi nt/P+{\varphi }_n)$$

Full text

††pagerange: MOBSTER - II. Identification of rotationally variable A stars observed with TESS in Sectors 1 to 4–LABEL:lastpage††pubyear: 2019

1 Introduction

One fundamental property that distinguishes main sequence (MS) A-type stars with masses $1.5<M<3\,M_{\odot}$ from their lower-mass ($M\lesssim 1.5\,M_{\odot}$) counterparts is the incidence rate of inhomogeneous surface brightness distributions, which are broadly referred to as star spots. Contrary to MS A-type stars, essentially all late-F, G-, and K-type MS stars exhibit bright and/or dim star spots (Cameron, Donati & Semel, 2002; Berdyugina, 2005; Ermolli et al., 2007). The relatively small fraction of MS A-type stars that do host qualitatively similar surface structures are known as $\alpha^{2}$ CVn variables and are identified based on detections of low-frequency photometric and spectroscopic variability (Samus’ et al., 2017). While the origins of these surface structures differ, in both the spotted low-mass MS star and $\alpha^{2}$ CVn cases, the observed photometric variability is understood to be a consequence of the star’s rotation: the star’s brightness is modulated as surface features appear and disappear from view.

It is well established that $\alpha^{2}$ CVn variable stars are magnetic chemically peculiar (mCP) Ap stars (e.g. Babcock & Burd, 1952). Furthermore, the origin of surface brightness inhomogeneities that lead to photometric rotational modulation in $\alpha^{2}$ CVn stars can be traced to the presence of strong, organized magnetic fields that are visible at the stellar surface (Krtička et al., 2007, 2009, 2015). The mCP stars account for approximately $10$ per cent of all MS A-type stars with masses $\sim 3\,M_{\odot}$ (Wolff, 1968; Aurière et al., 2007; Sikora et al., 2019a). They host strong, stable, and organized magnetic fields with strengths $\sim 0.1-30\,{\rm kG}$ (Babcock, 1960; Landstreet, 1982). Recently, a small number of non-mCP MS A-type stars have been found to host ultra-weak (dubbed “Vega-like” after the prototype of the population) fields with strengths $\lesssim 1\,{\rm G}$ (Lignières et al., 2009; Petit et al., 2011a; Blazère et al., 2016). It is has been suggested that these stars may represent a new class of magnetic MS A-type stars that are distinct from the mCP stars (Lignières et al., 2014).

The Kepler (Borucki et al., 2010), K2 (Howell et al., 2014), and CoRoT (Auvergne et al., 2009) space-based photometry missions have resulted in the identification of a large number of MS A-type stars exhibiting variability that is consistent with rotational modulation (Balona, 2011; Paunzen et al., 2015; Bowman et al., 2018). In particular, Balona (2013) reported the discovery that $\sim 40$ per cent of MS A-type stars observed with Kepler may exhibit photometric rotational variability. In addition to the rotational variables, Balona (2012, 2013) also identified (i) a number of apparently flaring A-type stars and (ii) unexplained periodogram features that are characterized by nearly coincident low-frequency diffuse and narrow peaks (e.g. Fig. 6 of Balona, 2013).

Pedersen et al. (2017) carried out a detailed analysis of 33 of the A-type stars that reportedly exhibit evidence of flares in their Kepler light curves. They confirmed the presence of flares in 27 of these stars’ light curves but found that the flares associated with 14 of these cases may be attributed to contamination from nearby sources. Ultimately, these authors concluded that the flares identified by Balona (2012, 2013) are likely not intrinsic to the A stars themselves. In the case of the unexplained periodogram features, Balona (2014) suggested that the diffuse peaks may be caused by spots appearing on the surface of a differentially rotating A star while the narrow peaks are caused by close-in Jupiter-sized planets. However, Saio et al. (2018) argue for a more physically-justified explanation in that the features in the amplitude spectra of many A stars are evidence of Rossby waves (also known as r modes, Papaloizou & Pringle, 1978), which can occur in rotating $\gamma$ Dor stars. Observational evidence of this phenomenon has been previously identified by Van Reeth, Tkachenko & Aerts (2016).

If the variability identified by Balona (2013) is indeed produced by spots on the surfaces of rotating A-type stars, then what is the origin of the spots? Such variability in these particular objects is normally attributed to the presence of magnetic fields that are visible at the surface. The reported $\sim 40$ per cent incidence rate of rotationally variable A-type stars is several times higher than the incidence rate of strongly magnetic (mCP) stars; therefore, it is unlikely that all of these stars are strongly magnetic. Considering that surface spots have been detected on Vega (which hosts an ultra-weak field, Böhm et al., 2015) and that such spots may lead to photometric variability, it is plausible that a large number of the A-type stars that were found to exhibit rotational modulation by Balona (2013) may host ultra-weak fields. Recently, Cantiello & Braithwaite (2019) explored the observational consequences of convection that might produce dynamo magnetic fields at or near the surfaces of fast-rotating A- and B-type stars. Referring to similar discussions presented by Cantiello & Braithwaite (2011) in the context of more massive stars, the authors note that such magnetic fields are expected to result in both ultra-weak fields and coincident spots characterized by low temperature contrasts ($\sim 10\,{\rm K}$) being present at the stellar surface. They predict that, while all A- and late B-type stars should host these features, they are likely largely undetectable. The fraction of stars for which the temperature spots can be expected to be detected depends on the size and number of spots (Kochukhov & Sudnik, 2013), which is not well constrained.

The MS A-type stars as defined in this study partly overlap with the mercury-manganese (HgMn) group of CP stars, which exhibit a distinct and unique rotational variability. HgMn stars have masses between $2.5\,M_{\odot}$ and $\sim 5\,M_{\odot}$ and effective temperatures as low as $10\,000\,{\rm K}$ (Ghazaryan & Alecian, 2016). These stars show no evidence of either global or strong complex magnetic fields (Aurière et al., 2010; Makaganiuk et al., 2010; Kochukhov et al., 2013), with the best upper limits on the longitudinal field component currently in the $1-10\,{\rm G}$ range. Nevertheless, many of these stars show rotational line profile variability indicative of low-contrast, large-scale inhomogeneous surface abundance distributions (Adelman et al., 2002; Kochukhov et al., 2005; Folsom et al., 2010; Briquet et al., 2010; Makaganiuk et al., 2012). Unlikely stationary spots on magnetic Ap stars, surface structures on HgMn stars evolve on time scales from months to years (Kochukhov et al., 2007; Korhonen et al., 2013), suggesting a different underlying physical mechanism of their formation. A low-amplitude photometric modulation associated with chemical spots on HgMn stars is undetectable from the ground but can be identified using high-precision space photometric data (Alecian et al., 2009; Balona et al., 2011; Hodgson et al., 2017).

The MOBSTER collaboration (Magnetic $\rm{OB[A]}$ Stars with TESS: probing their Evolutionary and Rotational properties; David-Uraz et al., 2019) is focused on advancing our understanding of stellar magnetism of intermediate- and high-mass stars using TESS observations along with spectroscopic and spectropolarimetric follow-up observations. The primary goal of the study presented here, which is the second of a series of publications by the MOBSTER collaboration, is to identify new candidate rotational variable MS A-type stars based on the release of TESS observations. These stars are hypothesized to host either strong magnetic fields (similar to those associated with mCP stars) or ultra-weak fields (similar to that found on Vega, Lignières et al., 2009). Since these stars are generally much brighter than those detected by Kepler, these identifications will serve as the basis for spectropolarimetric surveys designed to detect such magnetic fields, as was proven a successful strategy with stars observed by K2 (e.g. Buysschaert et al., 2018).

In Sect. 2 we describe the TESS observations on which our study is based. In Sect. 3 we describe our sample of A-type stars and the methods by which it was constructed. In Sect. 4 we discuss how our search for rotationally modulated TESS light curves was carried out and present the results of this search. In Sect. 5, we present the fundamental parameters (i.e. effective temperatures, radii, masses, etc.) associated with our sample and describe the way in which they were derived. In Sect. 6, we discuss some of the more noteworthy targets identified as candidate rotational variables. Finally, in Sect. 7 we summarize and discuss the results of this study.

2 Observations

TESS is optimized to detect planetary transit signatures in light curves of MS dwarf stars having $I_{C}$ magnitudes of approximately $4-13$ (Ricker et al., 2015). For typical MS A-type stars, which are the focus of this study, the $I_{C}$ limits correspond to Johnson $V$ magnitudes of approximately $3-12$. The passband of the filter used by the onboard photometer has an effective wavelength of $\approx 7\,500\,{\rm\AA}$ and a width of $\approx 4\,000\,{\rm\AA}$ (Sullivan et al., 2015). In this study we used the $2\,{\rm min}$ PDC_SAP light curves processed by the TESS Science Team. These light curves are available from the Mikulski Archive for Space Telescopes (MAST)111https://archive.stsci.edu/tess/. We refer the reader to Jenkins et al. (2016) for a description of the pipeline that produces these light curves.

The TESS data considered in this study consist of targets located in sectors 1 to 4. These sectors are in the southern ecliptic and contain targets with right ascension (RA) values of ${\rm RA}<131$ degrees and ${\rm RA}>308$ degrees and declination (Dec) values of $-85<{\rm Dec}<+12$ degrees. The observations have been obtained over a period of $\approx 4\,{\rm months}$ from July 25 to November 14, 2018. Sectors 1 and 2, sectors 2 and 3, and sectors 3 and 4 partially overlap where ${\rm Dec}\lesssim-30$ degrees; the light curves associated with the targets found in only one sector (the majority of the targets) span $28\,{\rm d}$ while those associated with targets found in two sectors span $56\,{\rm d}$. The brightness measurements exhibit typical uncertainties of $\lesssim 800\,{\rm parts~{}per~{}million}$ (ppm).

3 Sample

TESS light curves of $44\,371$ targets in sectors 1 to 4 were made available during the first two data releases. In order to identify the A-type stars within this sample, we first cross-referenced this list with the SIMBAD astronomical database222http://simbad.u-strasbg.fr/simbad/ for available spectral types associated with those targets. No spectral types could be found for $20\,098$ of the $44\,371$ observed targets while a further $5\,083$ targets could not be found within SIMBAD. We identified $1\,715$ A-type stars from the $19\,190$ TESS targets with available spectral types.

We attempted to identify the A-type stars in the subset of $25\,181$ stars ($20\,098+5\,083$) without available spectral types using their effective temperatures ($T_{\rm eff}$). The TESS Input Catalogue (TIC, Stassun et al., 2018) includes $T_{\rm eff}$ values that are either derived from $(V-K_{\rm S})-T_{\rm eff}$ calibrations (Casagrande, Flynn & Bessell, 2008; Huang et al., 2015) or are taken from published spectroscopic surveys. Typical A-type stars exhibit $7\,000\lesssim T_{\rm eff}\lesssim 10\,000\,{\rm K}$; however, the colour-$T_{\rm eff}$ calibrations used for the majority of the $T_{\rm eff}$ values reported in the TIC are only applicable to stars having $T_{\rm eff}\leq 9\,755\,{\rm K}$. Out of the subset of $25\,181$ observed stars without available spectral types that are listed in the TIC, $228$ exhibit $7\,000\leq T_{\rm eff}\leq 9\,755\,{\rm K}$ and another $228$ have not been assigned $T_{\rm eff}$ values (i.e. their $T_{\rm eff}$ values could not be estimated using the $(V-K_{\rm S})-T_{\rm eff}$ calibrations and no spectroscopically determined $T_{\rm eff}$ values are available).

Johnson $B$ and $V$ magnitudes are available for $93$ of the $228$ stars without $T_{\rm eff}$ values listed in the TIC. We estimated their $T_{\rm eff}$ values using the $(B-V)-T_{\rm eff}$ calibration published by Gray (2005) for MS stars. This colour-$T_{\rm eff}$ calibration is reasonably sensitive to stars with $T_{\rm eff}\lesssim 10\,000\,{\rm K}$; the scatter associated with the calibration is estimated to be $\approx 2-5$ per cent. The $(B-V)-T_{\rm eff}$ calibration yielded $19$ stars having $7\,000\leq T_{\rm eff}\leq 10\,000\,{\rm K}$ and are therefore considered to be candidate A-type stars.

In summary, out of the $44\,371$ targets included in the first two TESS data releases, we identified a total of $1\,962$ A-type stars based on (i) published spectral types ($1\,715$ stars), (ii) the $(V-K_{\rm S})-T_{\rm eff}$ calibrations used in the TIC ($228$ stars), and (iii) $(B-V)-T_{\rm eff}$ calibrations ($19$ stars). We note that by adopting a minimum $T_{\rm eff}$ value of $7\,000\,{\rm K}$ in our search for A-type stars within the subsample of those stars without available spectral types, a number of cooler A-type stars will likely have been missed. While this is unlikely to significantly impact the broader findings of our study, it may have an impact on the results associated with the coolest and lowest mass A-type stars in our sample.

Johnson $V$ magnitudes for all but one of the $1\,962$ A-type stars included in our sample are listed in the TIC. The sample exhibits a median $V$ magnitude of $8.7\,{\rm mag}$ and ranges from $16.4$ to $2.9\,{\rm mag}$. Distances ($d$) derived from the parallax angles associated with the second Gaia Data Release (DR2) (Gaia Collaboration et al., 2016; Holl et al., 2018; Bailer-Jones et al., 2018) for $1\,906$ of the $1\,962$ sample stars are available; based on these values, the majority of the stars in the sample are relatively nearby with $90$ per cent having $d\lesssim 440\,{\rm pc}$. Out of the $1\,962$ stars in our sample, $363$ are located in overlapping sectors and thus, their light curves have a temporal baseline of $56\,{\rm d}$ while the remaining $1\,599$ appear only in one sector and have temporal baselines of $28\,{\rm d}$.

4 Rotational Modulation

4.1 Search criteria

We carried out a search for rotationally modulated variability in the set of TESS light curves by adopting the main criteria outlined by Balona (2011, 2013): (i) the frequency spectrum of the light curve (i.e. the periodogram) must exhibit a low frequency peak ($f_{1}\lesssim 3\,{\rm d^{-1}}$) that plausibly corresponds to the star’s rotational frequency and (ii) this peak must be accompanied by a first harmonic ($f_{2}=2f_{1}$). The first criterion is based on the fact that the critical rotation frequency of a zero age MS (ZAMS) A-type star ranges from $f_{\rm crit}\approx 3-3.7\,{\rm d^{-1}}$. As described by Balona (2013), the second criterion is adopted as a means of minimizing the number of stars exhibiting low frequency signals that may be caused by pulsations rather than rotational modulation (e.g. $\gamma$ Dor stars and slowly pulsating B-type stars, Cousins, Caldwell & Menzies, 1989; Waelkens, 1991; De Cat & Aerts, 2002; Henry & Fekel, 2003).

As a result of the second criterion, rotational variables may not be detected in our study if the amplitude of the first harmonic ($A_{2}$) is low. The ratio of the amplitude of the rotational frequency ($A_{1}$) to $A_{2}$ depends largely on the distribution of co-rotating surface structures (i.e. spots) and on the inclination angle, $i$, of the star’s rotational axis. We attempted to evaluate the selection effect that the second criterion has on our sample of identified rotational variables by using the analytical spot model developed by Eker (1994). The model consists of a rigidly rotating star having one or more circular surface spots positioned at various longitudes and latitudes. The inclination of the star’s rotation axis, the manner in which limb darkening is treated (i.e. whether it is neglected or described by a linear or quadratic limb darkening law), and the spot radii and contrast values are input parameters that can be modified in this model.

The expected range of the ratio $A_{1}/A_{2}$ was estimated by carrying out several Monte Carlo (MC) simulations. We generated $500$ models each for cases in which between 1 and 5 spots are present on the star’s surface. For each model, the star’s $i$ value, spot longitudes, latitudes, and angular radii (ranging from $2$ to $30$ degrees) were randomly assigned; for those models with more than one spot, the same radius was adopted for each spot. We used a linear limb darkening law with a coefficient of $u=0.589$, which is computed by Díaz-Cordovés, Claret & Gimenez (1995) in the $V$ band for a $7\,000\,{\rm K}$ star with $\log{g}=4.0\,{\rm(cgs)}$. We adopted a rotation period of $2.5\,{\rm d}$ and the light curves were then calculated during $40\,{\rm d}$ ($16$ rotational cycles) with a cadence of $2\,{\rm min}$. Lomb-Scargle (LS) periodograms (Lomb, 1976; Scargle, 1982; Press, 2007) were calculated for each synthetic light curve (the same technique was employed in the analysis of the TESS light curves, as described below) from which the values of $A_{1}$ and $A_{2}$ were extracted in units of magnitude.

In Fig. 1 we show the cumulative distribution functions for $A_{1}/A_{2}$ associated with the MC simulations carried out with 1 to 5 spots. The results suggest that stars having multiple spots are more likely to exhibit $A_{1}/A_{2}$ ratios that are $\gtrsim 2$ compared to stars with single spots. This implies that stars with complex spot distributions are less likely to satisfy the second criterion in our search for rotational modulation since, depending on the value of $A_{1}$, the value of $A_{2}$ is more likely to fall below the detection threshold. It is also noted that a non-negligible fraction ($\sim 10\,$per cent) of the models exhibiting more than one spot have $A_{1}/A_{2}<1$ and thus, the rotation frequency does not necessarily correspond to the periodogram peak with the largest amplitude.

The two criteria used to identify rotationally modulated light curves are also frequently satisfied by eclipsing binaries (EBs) and ellipsoidal variables (EVs). EBs are easily identified based on the presence of primary and secondary eclipses in their light curves; however, EVs can exhibit highly sinusoidal light curves similar to those produced by rotational modulation (e.g. Fig. 10 of Smalley et al., 2014). In order to reduce the number of EVs misclassified as rotational variables, we rejected any non-Ap rotational variable candidates with light curves exhibiting a deep local minimum followed by a shallower local minimum that are both bracketed by the system’s maximum brightness. These characteristic features of EVs are often easy to identify when the light curve is phased by the system’s orbital period since the two minima have a phase separation of $0.5$. Furthermore, the distances separating the two components of an EV system are relatively low and the inclination of the orbital plane is relatively high; therefore, radial velocity variations are often large and easy to detect (e.g. Matson et al., 2017). We searched the literature for any reported detections of radial velocity variations from which orbital periods have been derived. Those candidate rotational variables with reported orbital periods consistent with the photometric periods that were originally attributed to the star’s rotation were rejected.

The last step of the search process involved classifying the identified candidate rotational variables as either low- or high-probability candidates. In a number of cases, the rotation and first harmonic peaks were accompanied by additional low-frequency peaks with comparable amplitudes (e.g. $\gamma$ Dor stars, Henry & Fekel, 2003). These stars were considered to be low-probability candidate rotational variables due to our inability to distinguish between those peaks that are caused by rotational modulation and those which are caused by pulsations; all other candidates were assigned a high-probability status.

4.2 Application of the search criteria to the TESS sample

We found that the signatures of rotational modulation in the light curves that were reduced and made publicly available by the TESS team could be more clearly identified after they were post-processed. This involved manually removing obvious outliers and detrending instrumental systematics by subtracting a low-order polynomial. We note that this detrending process may remove long-term trends described by periods that are approximately one or more times as long as the total light curve’s timespan. First- or second-order polynomial fits are unlikely to remove short period signals that are strictly periodic; however, signals that exhibit variations between consecutive cycles (e.g. such as those which might be associated with evolving star spots) are more susceptible to being removed.

We calculated LS periodograms of these post-processed light curves using an oversampling factor of ten to ensure that peaks in a periodogram were well resolved. Statistically significant peaks were then identified using an iterative pre-whitening procedure similar to that described by Morel et al. (2011). For each iteration, the frequency of the maximum-amplitude peak ($f_{\rm max}$) appearing in the periodogram was identified and a first-order sinusoidal function having frequency $f_{\rm max}$ (i.e. $A\sin{[2\pi f_{\rm max}t+\phi]}$ where $A$, $t$, and $\phi$ correspond to the semi-amplitude, time, and phase) was fit to the light curve with $A$ and $\phi$ as free parameters. The fit was then subtracted from the light curve and the LS periodogram was recalculated. This procedure was repeated until either $50$ frequencies had been extracted or until no peaks having a statistical significance $\geq 5\,\sigma$ were found (the significance is evaluated according to Eqn. 13.8.7 of Press, 2007). Uncertainties in all the extracted frequencies and their associated amplitudes were estimated using the prescriptions described by Montgomery & O’Donoghue (1999), which involve the root mean square deviation (RMSD) of the noise inherent in the light curve ($\sigma[m]$). We estimated $\sigma(m)$ by taking the RMSD of the light curve once all of the statistically significant signals had been removed.

After extracting the frequencies as described above, we carried out an automated routine designed to identify rotation ($f_{1}$) and first harmonic ($f_{2}$) frequency pairs. The first harmonic is given by $f_{2}=2f_{1}\pm\Delta f$ where $\Delta f$ is defined as the half-width at half-maximum of the central peak of each light curve’s spectral window function corresponding to a typical value of $0.02\,{\rm d^{-1}}$. The $1\,695$ light curves exhibiting low frequency peaks with accompanying first harmonics were then inspected visually; those targets with obvious EB, EV, or pulsational (e.g. RR Lyrae stars) signatures were removed from the list of candidate rotational variables. The remaining candidates were then assigned either a low-probability or high-probability candidate rotational variable classification based on the appearance of additional low-frequency, high-amplitude peaks (described in Sect. 4.1).

Having identified periodogram peaks that are likely associated with each star’s rotation period ($P_{\rm rot}=1/f_{1}$), we refined the final $P_{\rm rot}$ values using a Levenberg-Marquardt least-squares algorithm. This involved fitting the light curves to a sinusoidal function that includes the first four harmonics:

[TABLE]

where $a_{0}$, $a_{n}$, $\phi_{n}$, and $P$ are free parameters. The $a_{1}$ and $P$ parameters are assigned initial guesses of half the range of $\Delta T(t)$ and $1/f_{1}$, respectively, while all other parameters are assigned initial guesses of zero. The uncertainties in each of the fitting parameters were estimated using a residual bootstrapping method. The refined rotation periods associated with the high-probability candidates along with the maximum amplitudes ($\Delta T_{\rm max}$, i.e. the largest $a_{n}$, which always corresponds to either $a_{1}$ or $a_{2}$) associated with the sinusoidal fitting function are listed in Table 1.

In Fig. 2, we show sample light curves and their associated periodograms of several Ap stars identified as high-probability candidate rotational variables. Similarly, Fig. 3 shows examples of stars that are classified as non-chemically peculiar (i.e. their spectral types do not contain a ‘p’ classification) in the literature and are also considered to be high-probability candidate rotational variables. The search yielded $134$ high-probability and $126$ low-probability candidate rotational variables, respectively. This corresponds to an incidence rate of $6.8\pm 0.6$ per cent. Including those stars identified as low-probability rotational variables increases this incidence rate to $13.3\pm 0.9$ per cent. Out of the $134$ high-probability candidate rotational variables, $76$ are classified as Ap stars, $3$ are classified as Am stars, $7$ have luminosity classes of II or III (i.e. they have likely evolved off the MS), and $48$ are either classified as non-chemically peculiar MS stars or are unclassified.

The distribution of the inferred rotation periods of the $134$ high-probability rotational variables is shown in Fig. 4. The longest period is $\approx 20\,{\rm d}$; $81$ per cent of the $134$ stars exhibit $P_{\rm rot}<5\,{\rm d}$. Statistically, chemically peculiar Ap stars are known to have significantly longer rotation periods compared with their chemically normal, main sequence counterparts (e.g. Wolff, 1975; Abt & Morrell, 1995). Comparing the high-probability candidate rotational variables with Ap classifications with the remainder of the high-probability candidates, we find that the Ap stars have statistically longer inferred $P_{\rm rot}$ values: this is apparent from the cumulative distribution functions shown in the inset plot of Fig. 4. We also compare the rotation periods of the $76$ Ap stars with those of the sample of nearby magnetic Ap stars studied by Sikora et al. (2019b). The TESS light curves span a period range of $\approx 30\,{\rm d}$ for the majority of the stars in our sample (i.e. for those stars that are found in only one sector), which implies that only rotation periods of $P_{\rm rot}\lesssim 15\,{\rm d}$ can be detected. Comparing the distributions of those stars in the two samples having $P_{\rm rot}<15\,{\rm d}$ – $75/76$ of the Ap stars included in this study and $43/48$ of the stars included in the survey carried out by Sikora et al. (2019b) – yields close agreement.

In Fig. 6 we show the distribution of maximum TESS photometric amplitudes ($\Delta T_{\rm max}$, i.e. the maximum of the amplitudes associated with $f_{1}$ and $f_{2}$) for the identified $134$ high-probability rotational variables. The distribution ranges from $\sim 3-52\,{\rm mmag}$ and exhibits a median value $\sim 6\,{\rm mmag}$. Comparing the distributions of $\Delta T_{\rm max}$ associated with the Ap stars and those not identified as Ap, it is evident that the sample of Ap stars tend to exhibit larger $\Delta T_{\rm max}$ values.

We searched the light curves of the identified $134$ high-probability candidate rotational variables for evidence of amplitude modulation (AMod). This was carried out by dividing each light curve into sections spanning one rotational cycle (defined by $P_{\rm rot}$); those sections having a coverage $\lesssim 80$ per cent of the rotational cycle were discarded. The sections were then individually fit using Eqn. 1 with $P$ fixed at $P_{\rm rot}$ while allowing the $a_{n}$ and $\phi_{n}$ terms to vary. Evidence of AMod is manifest as changes in the amplitudes associated with the rotation frequency and first 4 harmonics ($a_{n}$ where $n$ goes from $1$ to $5$) over time. In many cases, the variations in $a_{n}$ were found to be correlated with the level of noise throughout the light curve; those sections of the light curve that were obviously affected by the level of noise were disregarded. We identified 22 instances of clear AMod that is not obviously induced by changes in the noise level or by the detrending process that was applied to the light curves. These cases are noted in Table 1 and 3 examples of such light curves are shown in Fig. 6. In several of the light curves the detected AMod could be a beating effect caused by low-amplitude (pulsation) frequencies in a narrow frequency near the rotation frequency (e.g. Degroote et al., 2011; Bowman et al., 2016) produced by pairs of signals having narrow frequency spacings. An example of this is shown in the second panel of Fig. 6 (TIC 70525154). The apparent beating could also be induced by the presence of binary companions or background variable stars; therefore, the detected AMod may not be intrinsic to the A stars themselves. Out of the 22 stars, 3 have likely evolved off of the MS based on their luminosity classes of II or III, 1 is an Am star, 8 are Ap stars, and 10 are not identified as chemically peculiar. The inferred rotation periods of the 3 evolved stars and 1 Am star are all $<1\,{\rm d}$ while those of the 8 Ap stars and remaining 10 non-Ap stars are between $0.5$ and $4.4\,{\rm d}$.

The study recently carried out by Cunha et al. (submitted) focuses on Ap stars observed with TESS in sectors 1 and 2. It consists of 83 stars located in sectors 1 and 2; they find that 61 of these targets exhibit variability that is consistent with rotational modulation and for which rotation periods could be inferred from the TESS light curves. A total of 76 out of the 83 stars in their sample are also found in our sample while the 7 stars that are excluded have reported spectral types of either F or B and thus were filtered out during the construction of our sample. The majority of our identifications of candidate rotational variables is in agreement with those reported by Cunha et al. (submitted): only four stars that these authors identify as rotational variables are not identified as such in our survey due to the difficulty with which we were able to identify clear rotation and first harmonic frequency pairs in accordance with the search criteria outlined in Sect. 4.1. For example, TIC 394124612 exhibits a large number of low-frequency peaks in the periodogram associated with its light curve; as a result, we could not definitively attribute a single peak to the star’s rotation frequency.

5 Fundamental parameters

The TIC (Stassun et al., 2018) provides a number of fundamental stellar parameters including effective temperatures, luminosities, radii, and masses. For $12$ of the $1\,962$ stars in the sample of A-type stars the reported fundamental parameters are obtained from large spectroscopic surveys that have been compiled into the TIC. For the majority of the stars ($1\,900$ of the $1\,962$ stars in the sample) the fundamental parameters listed in the TIC have been derived using the $(V-K_{S})-T_{\rm eff}$ calibration published by Huang et al. (2015). Comparisons between the extracted spectral types of the stars in our sample with the $T_{\rm eff}$ values derived from this colour-$T_{\rm eff}$ calibration suggest that many of the temperatures may be inaccurate (e.g. TIC 13373403 is an A0/1V star with a reported $T_{\rm eff}=5\,500\,{\rm K}$ and TIC 30728476 is an A7V star with a reported $T_{\rm eff}=9\,200\,{\rm K}$). As a result, we decided to derive the fundamental parameters for our sample using several methods.

5.1 SED fitting

We derived temperatures, luminosities, and stellar radii by fitting the available photometric observations with synthetic spectral energy distributions (SEDs). The TIC contains Johnson $B$ and $V$ magnitudes for $1\,956$ of the $1\,962$ A-type stars in our sample and 2MASS $J$, $H$, and $K_{S}$ (Cohen, Wheaton & Megeath, 2003) magnitudes for $1\,959$ stars. We searched additional catalogues for available Johnson $U$ ($31$ stars, Ducati, 2002), Tycho $B_{T}$ and $V_{T}$ ($953$ stars, ESA, 1997), Strömgren $uvby$ ($537$ stars, Hauck & Mermilliod, 1997), and Geneva $UB_{1}BB_{2}VV_{1}G$ ($402$ stars, Rufener & Nicolet, 1988) magnitudes. All of the photometric measurements were converted from magnitudes to physical flux units using published Johnson, Tycho (Bessell & Murphy, 2012), Strömgren (Bessell, 2011), Geneva (Rufener & Nicolet, 1988), and 2MASS (Cohen, Wheaton & Megeath, 2003) zero points.

Colour excess values ($E[B-V]$) associated with $1\,885$ and $1\,457$ of the $1\,962$ stars in our sample are listed in the TIC and reported by Gontcharov & Mosenkov (2017), respectively. We found that de-reddening the flux measurements using the values taken from either of these catalogs prior to carrying out the SED fitting analysis yielded a large number of $T_{\rm eff}$ values that are significantly greater than is expected for A-type stars ($T_{\rm eff}>12\,000\,{\rm K}$). Furthermore, based on the distances derived from the Gaia DR2 parallax measurements (Bailer-Jones et al., 2018), many of these stars were found to be positioned well below the main sequence in the Hertzsprung-Russell Diagram. As a result, we opted to derive the fundamental parameters with $E(B-V)\equiv 0$.

We used the grid of synthetic SEDs published by Castelli & Kurucz (2003) to fit the photometric observations. The grid consists of models having $5\,000\leq T_{\rm eff}\leq 20\,000\,{\rm K}$ in increments of $250-1\,000\,{\rm K}$, surface gravities of $3\leq\log{g}\leq 5\,{\rm(cgs)}$ in increments of $0.5$, and metallicities of $-2.5\leq{\rm[M/H]}\leq+0.5$ in increments of $0.2-0.5$. The model SEDs are computed using the solar abundances published by Grevesse & Sauval (1998). The model flux associated with each photometric filter was then computed using the transmission functions obtained from the same publications from which the zero points were obtained. The grid of synthetic SEDs was linearly interpolated in $T_{\rm eff}$, $\log{g}$, and [M/H] in order to produce a uniform grid having $\Delta T_{\rm eff}=50\,{\rm K}$, $\Delta\log{g}=0.5$, and $\Delta{\rm[M/H]}=0.5$.

The best-fitting $T_{\rm eff}$, $\log{g}$, and [M/H] were derived using a grid-search $\chi^{2}$ minimization analysis that was carried out with the interpolated grid of models. The $\chi^{2}$ value associated with each grid point was calculated after deriving an angular radius ($\alpha\equiv(R/d)$, where $R$ and $d$ correspond to the star’s radius and distance, respectively); for those stars with known distances, the angular radius was used to infer the stellar radii. The distances were primarily obtained from Bailer-Jones et al. (2018), which are based on Gaia DR2 parallax measurements ($1\,906$ of $1\,962$ stars in the sample). Additional distances were obtained from the Gaia DR1 parallax measurements derived by Astraatmadja & Bailer-Jones (2016) ($9$ of $1\,962$ stars), Hipparcos parallax measurements (van Leeuwen, 2007) ($28$ of $1\,962$ stars), or Tycho parallax measurements (ESA, 1997) ($2$ of $1\,962$ stars); no distances could be obtained for $17$ of $1\,962$ stars. For $88$ stars, [M/H] values are listed in the TIC; in these cases, [M/H] was fixed at the reported values. The $T_{\rm eff}$ and $R$ values were used to derive the luminosities ($L$) of the stars in our sample based on the Stefan-Boltzmann relation. In Fig. 7, we show two examples of the obtained fits to the observed photometry. The uncertainties in $T_{\rm eff}$, $\log{g}$, [M/H], $R$, and $L$ were estimated using the residual bootstrapping method described by Sikora et al. (2019a); note that the uncertainties in $R$ and $L$ include the errors in the distances that are propagated through the scaling factor $\alpha$.

Effective temperatures were derived for $1\,913$ stars through the SED fitting analysis. Based on our bootstrapping method of estimating uncertainties, we find that $1\,765$ of these stars ($92$ per cent) exhibit $\sigma_{T_{\rm eff}}\leq 200\,{\rm K}$. For nearly all of those stars that were found to have $\sigma_{T_{\rm eff}}\geq 400\,{\rm K}$, only Johnson $B$ and $V$ and 2MASS $J$, $H$, and $K_{S}$ measurements are available (only two of the stars with more than five available measurements were found to have $\sigma_{T_{\rm eff}}\geq 400\,{\rm K}$). Overall, only moderate differences are evident between those $\sigma_{T_{\rm eff}}$ values obtained from stars with only five available measurements compared to those with more than five: we find that $\langle\sigma_{T_{\rm eff}}\rangle=150\,{\rm K}$ in the former case compared to $\langle\sigma_{T_{\rm eff}}\rangle=100\,{\rm K}$ in the latter case.

5.2 Strömgren colour-$T_{\rm eff}$ calibrations

In addition to the SED fitting, we also derived $T_{\rm eff}$, $R$, and $L$ values using Strömgren colour-$T_{\rm eff}$ calibrations for those $537$ stars with available Strömgren indices. As in the SED fitting analysis, we opted not to de-redden the colour indices prior to applying the calibrations.

Out of the $537$ stars with available Strömgren indices, $32$ are identified as Ap stars; in these cases, we applied the calibrations published by Stepień (1994). These calibrations include bolometric corrections (BCs), which were used along with the available Johnson $V$ magnitudes and distances to derive $L$ and $R$. For the remaining stars not identified as Ap, we used the calibrations incorporated into the uvbybeta IDL routine (Moon & Dworetsky, 1985). The $R$ and $L$ values were then derived using the same method as was applied to the Ap stars where the BCs were calculated from the calibration published by Flower (1996).

The adopted $T_{\rm eff}$, $R$, and $L$ values associated with the stars in our sample have been derived using five methods: (i) a spectroscopic-based analysis (Stassun et al., 2018) ($12$ stars), (ii) SED modelling ($1\,889$ stars), (iii) Strömgren colour-$T_{\rm eff}$ calibrations ($5$ stars) (iv) $(V-K_{S})-T_{\rm eff}$ calibrations ($41$ stars), and (v) a $(V-B)-T_{\rm eff}$ calibration ($8$ stars). For each star, the method that was used to obtain the final parameters was prioritized based on the order in which they are listed above. In Fig. 8, we compare the first three of these methods for those stars for which multiple methods could be applied. It is evident that, in general, the $T_{\rm eff}$ values derived from the SED modelling and the Strömgren colour-$T_{\rm eff}$ calibration are in agreement with the values listed in the TIC that were derived from $(V-K_{S})-T_{\rm eff}$ calibrations. Comparisons between $T_{\rm eff,Str\ddot{o}mgren}$ and $T_{\rm eff,SED}$ yield a median absolute deviation of $150\,{\rm K}$ while comparing $T_{\rm eff,Str\ddot{o}mgren}$ and $T_{\rm eff,TIC}$ yields a slightly higher value of $210\,{\rm K}$.

5.3 Hertzsprung-Russell diagram

The masses of the stars in our sample were computed by comparing their positions on the HRD with several non-rotating grids of model evolutionary tracks. For stars having masses $<3.5\,M_{\odot}$, we used the dense grid computed by Mowlavi et al. (2012), which has mass intervals of $0.1\,M_{\odot}$. For the small number of more massive stars in the sample, we used the grid computed by Ekström et al. (2012), which has larger mass intervals of $0.1-2\,M_{\odot}$ for the models with $M\leq 15\,M_{\odot}$. The derivation of the masses and their uncertainties was carried out using the method described by Sikora et al. (2019a).

In Fig. 9 we show the Hertzsprung-Russell diagram (HRD) generated using the sample’s derived $T_{\rm eff}$ and $L$ values. These are plotted along with the grid of model evolutionary tracks for solar metallicity, non-rotating stars published by Ekström et al. (2012). It is evident that the sample roughly spans the entirety of the MS for those stars having $1.4\lesssim M/M_{\odot}\lesssim 3$. Based on the HRD, the sample appears to include a small number of post-MS stars, which is consistent with the fact that $212$ of the stars in the sample have luminosity classes of II or III. The incidence of the high-probability candidate rotational variable stars as a function of mass is shown in Fig. 10. In Table 2, we list the derived fundamental parameters ($T_{\rm eff}$, $\log{L}$, $M$, and $R$) associated with the $134$ high-probability candidate rotational variable stars in our sample.

6 Targets of particular interest

As discussed in Sect. 4, we identified $134$ high-probability candidate rotational variables. The TESS light curves associated with these targets all exhibit low-frequency peaks in their LS periodograms that are accompanied by at least one harmonic. Here we discuss some of those targets in our sample which are particularly noteworthy.

6.1 Candidate $\delta$ Scuti and roAp stars

Fourteen of the $134$ rotational variable candidates are found to exhibit high-frequency peaks in the range $10\lesssim f\lesssim 65\,{\rm d^{-1}}$ which are associated with $\delta$ Scuti pulsators (e.g. Breger, 2000; Holdsworth et al., 2014; Bowman & Kurtz, 2018) in addition to the low-frequency peaks believed to be associated with rotation. Aside from these periodogram features, no other statistically significant peaks were detected. Only one of the $14$ stars (TIC 38586082) has been identified as a $\delta$ Scuti pulsator in the literature. Little information is available for the other $13$ new candidate $\delta$ Scuti stars.

HD 27463 (TIC 38586082) is an ApEuCr(Sr) star (Houk & Cowley, 1975) for which a number of photometrically determined rotation periods have been reported (Manfroid & Renson, 1981; Mathys & Manfroid, 1985). The $\delta$ Scuti pulsations were recently discovered by Cunha et al. (submitted) using the same TESS light curves analyzed in our study. No magnetic field measurements were found in the literature. Anomalous $\Delta a$ measurements of $26\pm 6\,{\rm mmag}$ and $28\,{\rm mmag}$ published by Vogt et al. (1998) and Paunzen & Maitzen (2005), respectively, support the star’s Ap classification. Speckle interferometry has been used to detect a companion with a separation of $0.3\pm 0.4\arcsec$ that is dimmer than the primary component by $0.9\,{\rm mag}$ in the Strömgren $y$ filter (Hartkopf, Tokovinin & Mason, 2012). It is plausible that the $\delta$ Scuti pulsation peaks are associated with this dimmer companion rather than the Ap star itself. A detailed photometric and spectroscopic analysis of HD 27463 is presented by Khalack et al. (in preparation).

In addition to the $\delta$ Scuti stars, our sample of high-probability candidate rotational variable stars also contains seven previously discovered roAp stars (TIC 41259805, TIC 211404370, TIC 237336864, TIC 326185137, TIC 340006157, TIC 431380369, and TIC 350146296), and one new candidate roAp star (TIC 259587315).

HD 30849 (TIC 259587315) is a well-known ApSrCrEu star with a reported rotation period of $\sim 16\,{\rm d}$ based on Strömgren light curves (Renson, 1979; Hensberge et al., 1981). We infer a shorter rotation period of $8.105(6)\,{\rm d}$ based on the TESS light curve. Martinez & Kurtz (1994) observed this star twice over time spans $\sim 1\,{\rm hr}$; no high-overtone pulsations typical of roAp stars were detected. Based on the TESS light curve, we detect several peaks at frequencies of $78.1\,{\rm d^{-1}}$, $80.1\,{\rm d^{-1}}$, and $82.1\,{\rm d^{-1}}$ with respective amplitudes of $0.072\,{\rm mmag}$, $0.098\,{\rm mmag}$, and $0.118\,{\rm mmag}$, which suggest that HD 30849 is likely a roAp star.

6.2 Am stars

Three Am stars were identified as being high-probability candidate rotational variables based on our analysis of their TESS light curves (TIC 29781099, TIC 42055368, and TIC 396696863). All three targets are listed in the Catalogue of Ap, HgMn and Am stars compiled by Renson & Manfroid (2009); however, no definitive information could be found in the literature regarding photometric variability, binarity, or chemical peculiarities. All three light curves and periodograms are shown in Fig. 11 of the electronic version of the paper.

The long rotation periods associated with Am stars, which allow for the formation of these stars’ defining chemical peculiarities, are believed to be the result of tidal interactions (Abt, 1961). This is consistent with the fact that Am stars are commonly found in short period binary systems (e.g. Carquillat & Prieur, 2007). Therefore, it is plausible that the periods identified in the TESS light curves may be associated with orbital motions. In this case, large radial velocity variations are expected; spectroscopic monitoring of these targets will need to be carried out in order to determine whether these targets are binaries, and that the observed low-frequency harmonics represent the orbital period.

7 Discussion & Conclusions

We have identified $134$ high-probability candidate rotational variable stars based on 2 min cadence TESS light curves among a sample of $1\,962$ A-type stars. More than half of these $134$ stars ($76$ of $134$) are identified in the literature as Ap stars, which are expected to exhibit photometric rotational modulation (e.g. Adelman, Dukes, Jr. & Pyper, 1992; Catalano, Leone & Kroll, 1998; Samus’ et al., 2017; Netopil et al., 2017). Our sample of $1\,962$ A-type stars includes $20$ Ap stars for which we did not detect low-frequency variability in their TESS light curves. These stars are relatively dim compared to the Ap stars for which low-frequency variability was detected: $75$ per cent of the variable Ap stars in our sample have brighter $V$ magnitudes than the median magnitude ($V=9.5\,{\rm mag}$) of the $20$ non-variable Ap stars. The dimmest variable Ap stars in our sample having $V>9.5\,{\rm mag}$ are found to have $\Delta T_{\rm max}>0.3\,{\rm mmag}$; therefore, it is likely that any of the dim, apparently non-variable Ap stars that exhibit photometric amplitudes $<0.3\,{\rm mmag}$ fall below our detection threshold. That being said, less than $10$ per cent of the variable Ap stars have $\Delta T_{\rm max}<0.3\,{\rm mmag}$, which suggests that only a small number of the $20$ non-variable Ap likely have $\Delta T_{\rm max}$ below this limit.

A significant number of Ap stars are known to have very long rotation periods $\gg 1\,{\rm yr}$ (e.g. Landstreet & Mathys, 2000; Mathys, 2015; Bychkov, Bychkova & Madej, 2016; Mathys et al., 2016). It is possible that several of the $20$ apparently non-variable Ap stars are variable over timescales that significantly exceed the $28-56\,{\rm d}$ temporal baseline of the TESS light curves used in this study. Alternatively, assuming that these Ap stars host strong, organized magnetic fields similar to other Ap stars and that they have $P_{\rm rot}\lesssim 14\,{\rm d}$, the lack of low-frequency variability may either be indicative of the geometry and structure of the magnetic field or simply be due to the fact that $i=0$ degrees. The Oblique Rotator Model (ORM, Stibbs, 1950; Preston, 1967) predicts that no longitudinal magnetic field variability will be observed in the case in which (i) the magnetic field is axially symmetric and (ii) the axis of symmetry is parallel to the star’s axis of rotation. Since the chemical spots which produce the non-uniform surface brightness distributions are known to be correlated with the magnetic field topology (Kochukhov et al., 2004; Silvester, Kochukhov & Wade, 2014; Kochukhov et al., 2017), the star’s rotation might lead to weak or absent photometric variability in this specific case.

The $134$ high-probability candidate rotational variable stars includes $58$ A-type stars that are not identified as Ap based on the spectral types obtained from SIMBAD. We find that these stars’ light curves are statistically distinct from the $76$ identified candidate rotational variable Ap stars both in terms of the distribution of inferred $P_{\rm rot}$ values and in terms of their distribution of photometric amplitudes, $\Delta T_{\rm max}$. The (presumably) non-Ap stars tend to exhibit much lower values of $\Delta T_{\rm max}$ than the Ap stars: $\approx 60$ per cent of the non-Ap stars have $\Delta T_{\rm max}\lesssim 1\,{\rm mmag}$ compared to $<7$ per cent of the Ap stars. The distribution of rotation periods inferred for the Ap stars in our sample is found to be in agreement with that reported by Sikora et al. (2019b) for nearby mCP stars. The non-Ap stars in our sample tend to rotate more rapidly based on the inferred rotation periods. This is to be expected from normal (i.e. non-chemically peculiar) A-type stars; nevertheless, comparing with published distributions of A star $v\sin{i}$ values (Abt & Morrell, 1995; Zorec & Royer, 2012) suggests that the inferred $P_{\rm rot}$ values are unusually long for non-CP A stars. Including those non-CP stars identified in our sample as low-probability candidate rotational variables reduces the discrepancy but does not change the conclusion that the distribution of periods is inconsistent with that of non-CP A-type stars.

The photometric variability associated with Ap stars is well understood to be associated with strong, organized, and stable magnetic fields that are visible at the stellar surface. The origin of the identified rotational variability associated with the non-Ap star light curves, however, is unclear. It is plausible that the A stars are not intrinsically variable but that the observed variability is related to late-type binary companions or late-type background stars. A similar explanation for the origin of a number of flares in Kepler light curves of A-type stars was presented by Pedersen et al. (2017). This is a distinct possibility especially considering the relatively large $21\arcsec$ pixel size of the TESS CCDs (Sullivan et al., 2015) (cf. Kepler’s $4\arcsec$ pixel size, Koch et al., 2010).

Assuming that the identified rotational variability of the non-Ap stars is intrinsic to the A stars themselves, it cannot be excluded that the variability is caused by the same mechanism that is responsible for the formation of dynamic, low-contrast chemical spots on HgMn stars. No convincing evidence of a surface magnetism has been found for HgMn stars (e.g. Shorlin et al., 2002; Wade et al., 2006; Makaganiuk et al., 2010). Consequently, it was suggested (Kochukhov et al., 2007) that their spots are not linked to magnetic fields but are formed under the influence of hydrodynamic instabilities associated with the build-up of chemical anomalies by radiative diffusion. Numerical simulations (Alecian, Stift & Dorfi, 2011; Deal, Richard & Vauclair, 2016) demonstrate possibility of such instabilities for both late-B and A-type stellar parameter ranges, though it is not clear at the moment what governs the horizontal spatial scales of these structures. A comparison of the photometric behaviour of known HgMn stars with the present non-Ap sample is necessary to assess their similarities and differences. Furthermore, detailed abundance analysis of newly discovered rotational variables is required to ascertain their status as chemically normal stars. As noted above, the rotation periods associated with our sample of non-Ap stars appear to be unusually long for non-CP A stars, which suggests that this subsample may include unrecognised chemically peculiar stars with moderate abundance anomalies (e.g. marginal Am and HgMn stars).

The detection of ultra-weak magnetic fields with strengths $\lesssim 1\,{\rm G}$ on a small but growing number of non-Ap stars such as Vega (Lignières et al., 2009; Petit et al., 2011b; Blazère, Neiner & Petit, 2016) has led to speculation that such fields may be widespread amongst the population of non-Ap stars (e.g. Petit et al., 2011a). Given that (i) chemical and/or temperature spots have been detected on the surface of Vega (Böhm et al., 2015) and that (ii) these spots exhibit a similarly complex topology to that of the detected magnetic field (Petit et al., 2010, 2017), it is plausible that the non-Ap candidate rotational variables identified in our study also host ultra-weak fields, which are responsible for the observed variability. This explanation has been put forth in response to the discovery by Balona (2013) that $\sim 40$ per cent of A-type stars observed with Kepler appear to exhibit rotational variability. Braithwaite & Cantiello (2013) have proposed that such ultra-weak fields may be so-called failed fossils – weak fields having a similar origin to the fossil fields that are widely believed to be associated with mCP stars (Cowling, 1945). The strengths of failed fossil magnetic fields are predicted to decrease as the star evolves across the MS and have strengths that are anti-correlated with $P_{\rm rot}$. While Braithwaite & Cantiello (2013) do not provide any predictions regarding photometric variability, the authors note that changes in a failed fossil (and presumably, any chemical spots that may be associated with the field) should not be detectable. Evidence of AMod was found in the light curves of 10 of the 48 high-probability candidate rotational variable non-CP MS stars in our sample, which could be indicative of evolving surface spot morphologies. Assuming that the detected AMod is intrinsic to the A stars and not the result of contamination from binary companions or background stars, these detections would be inconsistent with the failed fossil model.

Cantiello & Braithwaite (2019) explored an alternative explanation for the origin of ultra-weak fields in A- and late B-type stars, which involves dynamo fields that are generated near the stellar surface. The authors suggest that (i) all rapidly rotating A- and B-type stars possess sub-surface H and He convection zones where turbulent dynamo may generate magnetic fields and that (ii) these fields are associated with bright temperature spots similar to those predicted to exist on more massive stars (Cantiello & Braithwaite, 2011). A rotation-activity connection is known to be a key feature of any type of dynamo-powered magnetic field and associated surface activity. According to Cantiello & Braithwaite (2019), the dynamo action requires stellar rotation with periods of $0.5-1\,{\rm d}$ for a dwarf star with parameters similar to Vega. Among the 48 MS non-CP stars in our sample only $20$ have $P_{\rm rot}\leq 1.5\,{\rm d}$ and the rest are slower rotators with $P_{\rm rot}$ up to $7.5\,{\rm d}$ for which no dynamo action is anticipated. Moreover, we do not observe a clear anticorrelation between $P_{\rm rot}$ and $\Delta T_{\rm max}$, which is expected within the framework of any dynamo hypothesis. As noted above, we do find evidence of AMod in the light curves of 10 of the 48 MS non-CP stars. These 10 stars have inferred rotation periods ranging from $0.5$ to $4.6\,{\rm d}$ and all but 4 have $P_{\rm rot}\leq 1.5\,{\rm d}$. We also note that we did not find evidence of AMod for an additional 17 of the MS non-CP stars with $P_{\rm rot}\leq 1.5\,{\rm d}$.

It is likely that in order to better understand the origin of the variability associated with the non-Ap stars identified in our sample as being rotational modulation we will need to obtain high-resolution spectroscopic measurements. The measurement of chemical abundancies in the atmosphere’s of these stars is of particular interest as it may confirm our suspicion that some of the stars in our sample are at least weakly chemically peculiar. Detecting spectroscopic variability or placing constraints on the strength of such variability would also be useful in this regard. We also note that combining the TESS light curves with multi-colour long-term monitoring, such as that provided by the BRITE-Constellation mission (Weiss, 2008), may provide insight into the puzzling results presented here.

Acknowledgments

GAW acknowledges support in the form of a Discovery Grant from the Natural Science and Engineering Research Council (NSERC) of Canada. ADU and VK acknowledge support from NSERC. The research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 670519: MAMSIE). SC gratefully acknowledge funding through grant 2015/18/A/ST9/00578 of the Polish National Science Centre (NCN). OK acknowledges support by the Swedish Research Council (project 621-2014-5720) and the Swedish National Space Board (projects 185/14, 137/17).

This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This paper includes data collected with the TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the TESS mission is provided by the NASA Explorer Program. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5–26555. Funding for the TESS Asteroseismic Science Operations Centre is provided by the Danish National Research Foundation (Grant agreement no.: DNRF106), ESA PRODEX (PEA 4000119301) and Stellar Astrophysics Centre (SAC) at Aarhus University. We thank the TESS team and staff and TASC/TASOC for their support of the present work. We thank Dr. D. W. Kurtz for providing useful comments.

Appendix