Surface Rotation and Photometric Activity for Kepler Targets. II. G and F Main-sequence Stars and Cool Subgiant Stars

The measurement of the rotation of solar-like stars (i.e., stars with an external convective envelope) has been at the center of many studies in stellar physics. Internal rotation modifies the mixing of elements inside stars. During the main sequence, rotation refuels the hydrogen content in the stellar core from the upper layers, extending the main-sequence lifetime of faster rotators compared to slower rotators (e.g., Aerts et al. 2019). Asteroseismology, i.e., the study of stellar oscillations (e.g., García & Ballot 2019), provides a unique way to infer stellar properties, including internal rotation. Unfortunately, only for evolved stars has it been possible to measure the core rotation (e.g., Beck et al. 2012; Deheuvels et al. 2012, 2014; Gehan et al. 2018; Mosser et al. 2018). For main-sequence solar-like stars, asteroseismology can only provide reliable constraints on rotation of the outermost layers and for a small number of stars (e.g., Benomar et al. 2015, 2018). Alternatively, surface rotation can be measured from long-term brightness variations due to magnetic features corotating with the stellar surface.

As shown by Skumanich (1972), there is a tight relation between stellar age and surface rotation for low-mass solar-like stars: stars spin-down as they evolve owing to magnetic braking. This inspired the so-called gyrochronology (e.g., Barnes 2003, 2007; Meibom et al. 2011a, 2011b, 2015; Mamajek & Hillenbrand 2008), which could allow us to estimate stellar ages for large samples of field stars with high precision. However, the validity of the Skumanich spin-down law throughout the main sequence has been subject to debate. On the one hand, the recent results by Lorenzo-Oliveira et al. (2019, 2020) are consistent with a steady spin-down, supporting gyrochronology as reliable. On the other hand, other studies invoke a weakening of the magnetic braking to explain the discrepancy found between the asteroseismic ages and those predicted by gyrochronology (e.g., Angus et al. 2015; van Saders et al. 2016; Metcalfe & Egeland 2019; Hall et al. 2021). Therefore, the determination of reliable rotation periods is crucial to understand the spin-down evolution and derive precise stellar ages where applicable.

Thanks to the advent of planet-hunting space missions, like CoRoT (Convection, Rotation et Transits planétaires; Baglin et al. 2006), Kepler (Borucki et al. 2010), K2 (Howell et al. 2014), and TESS (Transiting Exoplanets Survey Satellite; Ricker et al. 2014), such measurements are possible for an extraordinary number of targets (e.g., Mosser et al. 2009; Nielsen et al. 2013; García et al. 2014a; McQuillan et al. 2014; Santos et al. 2019; Reinhold & Hekker 2020; Gordon et al. 2021).

In this work, we focus on the analysis of the 4 yr Kepler data, which correspond to the longest continuous high-precision photometric survey obtained so far for hundreds of thousands of stars. In the near future, no other ongoing or planned space mission will provide a better data set in terms of continuous long-term photometric monitoring. Here, we estimate rotation periods following the same methodology as in Santos et al. (2019, hereafter Paper I), which combines three different rotation diagnostics for different calibrated time series. Paper I reported the detection of new rotation periods for 4431 stars in comparison to McQuillan et al. (2014, hereafter McQ14) for main-sequence K and M stars, according to the stellar properties of Mathur et al. (2017). The current work, the second of this series, extends the analysis to solar-like stars of spectral type G and F, as well as solar-like subgiants. Because the target sample of this work is several times larger than that of Paper I, we use a machine-learning (ML) algorithm (ROOSTER—Random fOrest Over STEllar Rotation; Breton et al. 2021) to reduce the amount of visual inspections with respect to those carried out in Paper I.

The manuscript is organized as follows. Section 2 describes the target selection and data calibration. Although the original target selection was done according to the stellar parameters from Mathur et al. (2017), we adopt for the remainder of the analysis the recent stellar properties catalog by Berger et al. (2020). For continuity of Paper I, the title of the current work reflects the stellar classification by Mathur et al. (2017), i.e., a target sample of F and G main-sequence stars and subgiants. Nevertheless, the majority of the targets in the current analysis are indeed consistent with mid-F to G main-sequence or subgiant stars also according to Berger et al. (2020). The rotation pipeline, used to retrieve rotation-period candidates, and the photometric magnetic activity proxy are described in Sections 3.1 and 3.2. Reliable rotation periods are then selected through the implementation of an ML algorithm, automatic selection, and supplementary visual inspection (Section 3.3). The results are finally presented and discussed in Sections 4 and 5.

2.1. Data Preparation

2.2. Sample Selection

The target samples for Paper I and for the current study were originally defined with the Kepler Stellar Properties Catalog for Data Release 25 (Mathur et al. 2017, hereafter DR25), which was the latest update to the Kepler stellar properties available at the time for Paper I. In Paper I, we analyzed Kepler stars that were classified as K and M main-sequence stars according to DR25 (cooler than T_eff = 5200 K). Here, we analyze the remainder of the Kepler main-sequence and subgiant targets expected to be solar-like stars, i.e., stars with convective outermost layers. According to DR25, the current work focuses on main-sequence stars from spectral type mid-F to G, as well as subgiant stars from spectral type mid-F to K. Nonetheless, for the current analysis we decide to embrace the new update to the Kepler stellar properties, i.e., the recent Gaia-Kepler Stellar Properties Catalog (Berger et al. 2020, hereafter B20). As follows, in light of B20, the current classification differs from that considered in Paper I (see below). The detailed comparison between the two stellar properties catalogs is presented in B20. In Appendices B–D, we discuss some of the differences relevant for the targets in our sample.

Figure 1 shows the target samples of Paper I and the current study according to DR25 (left) and B20 (right). We adopt the classical instability strip (diagonal solid line in Figure 1; Bowman & Kurtz 2018; Dupret et al. 2005) to select the targets expected to have convective envelopes. To avoid potential red giants, we consider a flat cut at $\mathrm{log}g$ = 3.5 (horizontal solid line). We then remove contaminants from the target sample: δ Scuti, γ Doradus, and hybrids (Uytterhoeven et al. 2011; Bradley et al. 2015; Van Reeth et al. 2018; Murphy et al. 2019; Li et al. 2019b, 2019a); RR Lyrae stars (Benkő et al. 2010; Nemec et al. 2011, 2013; R. Szabó et al. 2021, in preparation); misclassified red giant stars (R. A. García et al. 2021, in preparation, and references therein); and eclipsing binaries (Villanova Kepler Eclipsing Binary Catalog; Kirk et al. 2016; Abdul-Masih et al. 2016). In total we remove 8209 known contaminants that are within the parameter space of the target sample of this work.

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The top panels of Figure 1 show in color the targets that are main-sequence or subgiant stars in both stellar properties catalogs (DR25 and B20). The target sample of Paper I, used in this work as part of the training for the ML algorithm (Breton et al. 2021), is plotted in blue. The targets colored in shades of red belong to the target sample for the rotational analysis of this work (121,749 targets—subsample I), after removing the contaminants listed above. The bottom panels of Figure 1 show the targets whose classification, in terms of being solar-like, disagrees between the two catalogs that are still considered in the rotational analysis: main-sequence or subgiant solar-like stars in DR25 but not in B20 (green; 9265 targets—subsample II), and main-sequence or subgiant solar-like stars in B20 but not in DR25 (red; 1907 targets—subsample III). In total, the target sample considered for the rotational analysis in this work comprises 132,921 stars (subsamples I, II, and III).

For the remainder of the analysis, we prioritize the stellar properties from B20, which are listed in Tables 1 and 2. When not available (part of subsample III), we adopt the stellar properties from DR25. Accordingly, in Tables 1 and 2, we also provide a flag indicating the stellar properties source.

Table 1. Stellar Properties for Stars with Successfully Recovered Rotation Period

KIC	Kp	Q	Teff	$\mathrm{log}g$	Mass	Prot	Sph	CP/CB	Subsample	Binary	KOI	Source
			(K)	(dex)	(M⊙)	(days)	(ppm)	Cand.		flag
757099	13.152	1–17	${5364.9}_{-84.9}^{+102.7}$	${4.318}_{-0.029}^{+0.037}$	${0.873}_{-0.039}^{+0.054}$	0.38 ± 0.02	15463.8 ± 1668.0	1	1	0	⋯	0
757450	15.264	1–17	${5301.2}_{-103.1}^{+111.0}$	${4.432}_{-0.044}^{+0.045}$	${0.914}_{-0.057}^{+0.062}$	19.11 ± 1.50	3756.4 ± 118.7	⋯	1	0	0	0
891916	14.799	1–17	${5650.8}_{-137.7}^{+131.9}$	${4.132}_{-0.254}^{+0.224}$	${1.008}_{-0.112}^{+0.164}$	5.45 ± 0.42	3409.6 ± 199.2	⋯	1	⋯	⋯	0
892195	13.757	1–17	${5333.4}_{-84.2}^{+101.3}$	${4.372}_{-0.029}^{+0.039}$	${0.862}_{-0.040}^{+0.057}$	21.78 ± 2.90	212.9 ± 4.7	⋯	1	0	⋯	0
892713	12.082	0–17	${6238.9}_{-129.8}^{+123.4}$	${3.548}_{-0.037}^{+0.066}$	${1.731}_{-0.087}^{+0.219}$	5.78 ± 0.76	390.4 ± 11.9	⋯	1	0	⋯	0
893209	13.087	1–17	${6051.4}_{-107.2}^{+110.0}$	${4.031}_{-0.053}^{+0.037}$	${1.263}_{-0.117}^{+0.071}$	4.58 ± 0.44	605.3 ± 20.8	⋯	1	0	⋯	0
893286	15.345	1–17	${5297.1}_{-98.5}^{+103.4}$	${4.522}_{-0.044}^{+0.034}$	${0.853}_{-0.057}^{+0.047}$	24.54 ± 2.23	1079.3 ± 36.1	⋯	1	0	⋯	0
893383	14.281	1–17	${5680.9}_{-102.2}^{+105.1}$	${4.526}_{-0.031}^{+0.020}$	${0.912}_{-0.051}^{+0.036}$	21.19 ± 2.58	967.2 ± 31.5	⋯	1	0	⋯	0
893505	14.248	3–16	${5920.4}_{-118.5}^{+123.8}$	${3.896}_{-0.044}^{+0.058}$	${1.239}_{-0.075}^{+0.143}$	10.81 ± 0.81	617.9 ± 34.1	⋯	1	0	⋯	0
893507	12.517	2–16	${5447.0}_{-124.5}^{+121.8}$	${3.580}_{-0.039}^{+0.028}$	${1.510}_{-0.095}^{+0.075}$	10.98 ± 0.86	7019.0 ± 293.3	⋯	1	0	⋯	0
893559	15.818	1–17	${5095.3}_{-88.7}^{+95.2}$	${4.546}_{-0.041}^{+0.033}$	${0.808}_{-0.049}^{+0.044}$	14.69 ± 1.06	2183.0 ± 87.9	⋯	1	0	⋯	0
893676	15.310	1–17	${5260.0}_{-72.5}^{+81.3}$	${4.211}_{-0.037}^{+0.037}$	${0.881}_{-0.024}^{+0.031}$	24.37 ± 2.73	1227.7 ± 39.9	⋯	1	1	⋯	0
1025986	10.150	0–17	${5662.1}_{-100.1}^{+101.7}$	${4.425}_{-0.042}^{+0.039}$	${0.912}_{-0.064}^{+0.066}$	9.68 ± 0.73	5940.1 ± 245.0	⋯	1	0	1	0
1026838	13.897	1–17	${6056.9}_{-101.9}^{+101.3}$	${4.399}_{-0.030}^{+0.020}$	${1.133}_{-0.056}^{+0.041}$	15.56 ± 1.85	361.9 ± 16.1	⋯	1	0	⋯	0
1027536	12.886	0–17	${5944.4}_{-105.9}^{+117.2}$	${4.304}_{-0.038}^{+0.033}$	${1.139}_{-0.069}^{+0.066}$	16.35 ± 4.43	74.4 ± 5.0	⋯	1	0	⋯	0

Note. T_eff, $\mathrm{log}g$, and mass from B20 when available, otherwise DR25 (Mathur et al. 2017; Berger et al. 2020). The rotation-period and photometric activity estimates are obtained in this work. CP/CB candidate flag: (1) Type 1 CP/CB candidate. Subsample: (1) targets in subsample I; (2) targets in subsample II; and (3) targets in subsample III. Binary flag: (0) single stars in Berger et al. (2018) or in Simonian et al. (2019); (1) targets flagged as binary candidates in Berger et al. (2018); (2) targets flagged as binary candidates in Simonian et al. (2019) according to their inclusive threshold; (3) binary candidates in both Berger et al. (2018) and Simonian et al. (2019). KOI flag: (0) confirmed planet hosts; (1) candidate planet hosts; (2) and false positives. Source for stellar properties: (0) B20; (1) DR25.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 2. Stellar Properties for Stars without Rotation-period Estimate

KIC	Kp	Q	Teff	$\mathrm{log}g$	Mass	No Prot	Subsample	Binary	KOI	Source
			(K)	(dex)	(M⊙)	Flag		Flag
757280	11.901	0–17	${6856.8}_{-139.9}^{+144.4}$	${3.834}_{-0.032}^{+0.033}$	${1.715}_{-0.089}^{+0.086}$	8	2	0	⋯	0
891901	13.306	0–17	${6350.6}_{-131.7}^{+130.8}$	${3.958}_{-0.090}^{+0.098}$	${1.411}_{-0.119}^{+0.125}$	8	1	⋯	—	0
892203	13.575	0–17	${5712.8}_{-105.3}^{+108.3}$	${4.386}_{-0.044}^{+0.042}$	${0.967}_{-0.074}^{+0.073}$	⋯	1	0	⋯	0
892667	13.137	1–17	${6704.9}_{-128.8}^{+148.8}$	${3.950}_{-0.036}^{+0.034}$	${1.548}_{-0.087}^{+0.081}$	5	2	0	⋯	0
892675	13.475	1–17	${5929.4}_{-108.1}^{+108.9}$	${4.385}_{-0.043}^{+0.035}$	${1.038}_{-0.076}^{+0.066}$	0	1	0	⋯	0
892678	12.176	0–17	${5890.4}_{-114.9}^{+121.6}$	${3.574}_{-0.030}^{+0.030}$	${1.584}_{-0.062}^{+0.071}$	⋯	1	0	⋯	0
892828	13.195	0–17	${6464.3}_{-128.9}^{+137.7}$	${4.034}_{-0.034}^{+0.032}$	${1.398}_{-0.069}^{+0.071}$	5	1	0	⋯	0
892911	15.648	2–17	${5782.1}_{-112.6}^{+116.5}$	${4.295}_{-0.062}^{+0.062}$	${1.001}_{-0.077}^{+0.077}$	⋯	1	0	⋯	0
892946	15.882	4–17	${5993.8}_{-119.6}^{+122.3}$	${3.859}_{-0.113}^{+0.113}$	${1.317}_{-0.120}^{+0.157}$	0	1	0	⋯	0
892977	13.759	1–17	${6072.9}_{-116.6}^{+116.6}$	${3.937}_{-0.048}^{+0.044}$	${1.299}_{-0.090}^{+0.126}$	⋯	1	0	⋯	0
892986	15.974	4–17	${5770.8}_{-114.4}^{+115.8}$	${4.093}_{-0.090}^{+0.083}$	${1.068}_{-0.086}^{+0.101}$	0	1	0	⋯	0
893004	13.957	1–17	${6107.3}_{-115.7}^{+129.4}$	${4.171}_{-0.040}^{+0.044}$	${1.189}_{-0.091}^{+0.067}$	⋯	1	0	⋯	0
893165	13.340	0–17	${5989.1}_{-102.5}^{+115.7}$	${4.154}_{-0.042}^{+0.038}$	${1.152}_{-0.092}^{+0.073}$	1	1	0	⋯	0
893234	13.195	1–17	${6558.2}_{-141.2}^{+128.9}$	${4.112}_{-0.032}^{+0.033}$	${1.371}_{-0.060}^{+0.068}$	5	1	0	⋯	0
893468	15.439	1–17	${6016.0}_{-110.0}^{+112.0}$	${4.368}_{-0.058}^{+0.048}$	${1.067}_{-0.075}^{+0.067}$	0	1	0	⋯	0

Note. Same as in Table 1, with the exception of the no P_rot flag, which indicates the type target: (0) no rotational modulation; (1) possible rotational modulation; (2) misclassified red giant star; (3) known eclipsing binary; (4) known RR Lyrae; (5) known δ Scuti, γ Doradus, or hybrids; (6) photometric pollution in KEPSEISMIC and PDC-MAP time series; (7) photometric pollution in KEPSEISMIC time series; (8) multiple signals; (9) Type 2 CP/CB candidate; (10) Type 3 CP/CB candidate; (11) Type 4 CP/CB candidates.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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In Section 4 we present the results for the targets in subsample I according to their spectral type and evolutionary stage. There, the targets are split following B20. To separate main-sequence from subgiant stars, we take the transition between main sequence and the subgiant branch from evolutionary tracks for solar metallicity and different stellar masses obtained with MESA (Modules for Experiments in Stellar Astrophysics; Paxton et al. 2018, and references therein) and fit a linear relation shown by the dashed line in Figure 1. This cut leads to 21,665 subgiant stars in subsample I according to the originally adopted DR25. However, this cut is not appropriate for B20, as the main sequence is slightly shifted toward small $\mathrm{log}g$ values. Therefore, we shift the line by −0.12 dex in $\mathrm{log}g$ (dotted line in the right panels). Using this cut and B20 parameters leads to similar statistics, now with 22,843 subgiant stars. We consider the boundary between main-sequence G and F stars at T_eff = 6000 K.

In addition to known contaminants reported in the literature and described above (listed in Table 2), there are a number of other contaminants that may still remain in the data. Here, we do not provide rotation period for light curves with photometric pollution (e.g., when the signal is only present every four Kepler quarters) or multiple signals. These targets are listed in Table 2 with the respective flag. Multiple signals can result from photometric pollution by background stars or from unresolved multiple systems. Determining the source of the multiple signals is beyond the scope of this work. Thus, we do not consider these targets in the subsequent analysis.

Following the approach in Paper I, we flag CP/CB (classical pulsator/close-in binary) candidates. Type 1 CP/CB candidates show high-amplitude brightness variations, stable and fast beating patterns, and/or a large number of harmonics. In Paper I, we discuss the possibility of these targets being tidally synchronized binaries, which are common among rapidly rotating Kepler targets (Simonian et al. 2019; Angus et al. 2020). We provide rotation periods (Table 1 with the proper flag) for these targets, as the signal can still be related to rotation but not of single stars. The signal of Type 2 CP/CB candidates resembles that of contact binaries (e.g., Lee et al. 2016; Colman et al. 2017). Type 3 CP/CB candidates are δ Scuti and/or γ Doradus candidates or alternatively polluted by a nearby star of this type. Additionally, in this work we flag another potential type of CP/CB candidates. The signal of Type 4 CP/CB candidates resembles that of heartbeat stars or close binaries with tidally excited oscillations (e.g., Guo et al. 2020). The signatures of Type 2−4 CP/CB candidates can be mistakenly selected as rotation and are identified during visual examination. We do not provide periods for Type 2−4 CP/CB candidates; instead, these are listed in Table 2 with the respective flag.

3.1. Rotation-period Candidates

In this section, the methodology used to estimate the rotation-period candidates from the stellar brightness variations is briefly described. For more details see Paper I and Ceillier et al. (2016, 2017).

Our rotation pipeline combines a time-frequency analysis and the autocorrelation function (ACF). Using artificial data, Aigrain et al. (2015) concluded that such a combination of different rotation diagnostics, together with a performant time-series preparation, provides the most complete set of reliable rotation-period estimates (see also Appendix B in Breton et al. 2021). Compared with McQ14, in addition to a different rotation analysis, we use the full length of the Kepler observations, and we obtain and calibrate our own light curves (KEPSEISMIC) using different high-pass filters (see Section 2.1). As a result, for M and K main-sequence stars (Paper I), we were able to recover rotation periods for 4431 targets for which McQ14, using ACF alone, did not report a rotation period.

Our rotation analysis retrieves three rotation-period estimates for each light curve, i.e., nine estimates per star. We obtain the first estimate from the global wavelet power spectrum (GWPS; Figures 2(b) and (c)), which results from the wavelet decomposition (Torrence & Compo 1998). The wavelet decomposition was first adapted for the analysis of stellar light curves by Mathur et al. (2010), who adopted the correction by Liu et al. (2007). Following the method by McQuillan et al. (2013; see also García et al. 2014a), we obtain the second period estimate from the autocorrelation function of the light curve (ACF; Figure 2(d)). Finally, the third period estimate is provided by the composite spectrum (CS; Figure 2(c)), which is the product of the normalized GWPS and the normalized ACF (for its first application, see Ceillier et al. 2016, 2017). As the common periods between GWPS and ACF are highlighted by the CS, this diagnostic allows us to better distinguish the stellar rotation signals from false positives, such as instrumental modulations.

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For the final period estimate we prioritize the value provided by the GWPS, whose uncertainty is typically large accounting for the uncertainty on the period determination and partially for differential rotation.

3.2. Photometric Magnetic Activity Proxy

3.3. Rotation-period Selection

In Paper I, the selection of reliable rotation periods was made essentially in two steps. Periods were automatically selected if the rotation-period estimates agree between different diagnostics and filters, and if the height of the respective rotation peaks is larger than a given threshold (for details see Paper I). In the second step, for the targets whose period was not automatically selected, we proceeded with visual examination of the light curves, results from the rotation pipeline, and power spectrum density. We visually inspected about 60% of the target sample of Paper I, composed of 26,521 main-sequence K and M stars, according to DR25 (note that for the current analysis we adopt B20). Here, we analyze the remainder of the targets observed by Kepler expected to be main-sequence or subgiant solar-like stars. The target sample of this work is then composed of 132,921 targets. Therefore, it is crucial to reduce the number of required visual checks.

xIn order to do so, here we use an ML algorithm, ROOSTER, to identify targets with rotational modulation and select the respective period. ROOSTER and its validation are described in detail in Breton et al. (2021) and summarized in Section 3.3.2. In the context of this work, the main goal of the implementation of ML is to efficiently select reliable rotation periods while reducing the required amount of visual inspection. To that end, we also need to supply the ML algorithm with a proper training set (Section 3.3.1).

3.3.1. Training Set

For the training set of ROOSTER, we use the 26,521 solar-like stars from Paper I. At the time, these targets were classified as K and M main-sequence stars (top left panel of Figure 1). According to B20 (right panel of Figure 1), the latest stellar properties catalog, most of the stars in Paper I (95.4%) are indeed cool solar-like stars with T_eff < 5200 K. To complement the training set, namely, to account for the full range of target effective temperatures, we analyze 34,100 stars from subsamples I–III (Figure 3) in the same manner as the targets of Paper I, i.e., through automatic selection and visual inspection. The rotational signal of hotter stars, in particular F stars, differs from that of cooler stars. Thus, to avoid bias and properly train the ML tool, it is important to consider a diverse training set.

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Automatic selection.—Rotation periods are automatically selected if there is agreement between the P_rot estimates from the different diagnostics (GWPS, ACF, CS) and KEPSEISMIC light curves obtained with three different filters. Additionally, we impose a height threshold for the ACF and CS rotation peaks. See Paper I for details.

Visual inspection.—The light curves (three KEPSEISMIC and one PDC-MAP; see Section 2.1), power density spectra, and rotation diagnostics of all fast rotators (P_rot < 10 days), slow rotators (P_rot > 60 days), and targets for which the rotation period is not automatically selected are visually inspected.

The final training set is composed of 60,621 targets (Figure 3): 29,563 targets with rotation-period estimate, including Type 1 CP/CB candidates; and 31,058 targets without rotation-period estimate. This leaves 98,821 targets to be analyzed by the ML algorithm. Note that the targets analyzed in Paper I (26,521) are not part of the target sample of the current work, being only part of the training.

3.3.2. Machine-learning Algorithm: ROOSTER

Breton et al. (2021) developed an ML tool, ROOSTER, to select reliable rotation periods from the output of the rotation pipeline (Section 3.1). For each target, ROOSTER's input parameters are the nine rotation-period candidates (Section 3.1) and respective S_ph values (Section 3.2), additional control parameters from the rotation pipeline (e.g., ACF and CS peak heights), stellar fundamental properties, FliPer metric (Bugnet et al. 2018), and observation parameters (e.g., Kepler magnitude, observation length). ROOSTER employs three random forest classifiers, each one dedicated to a specific task. The first classifier selects stars with rotational modulation from the target sample. For those selected stars, the second classifier provides a flag, which identifies Type 1 CP/CB candidates (see Section 2.2). Finally, for the same selected stars, the third classifier chooses the rotation period from the nine provided estimates (Section 3.1).

The validation of ROOSTER is presented in detail by Breton et al. (2021), where the target sample was that of Paper I, which comprises mostly KM stars (see Appendix A for the full training set, i.e., stars of spectral type from mid-F to M). For the cool solar-like targets, the initial ROOSTER's global accuracy was 92.1%. In spite of the good yield, the results can still be improved through supplementary visual inspection. The main source of the ROOSTER's confusion are the targets with high-amplitude second harmonics of the rotation period, for which several of the nine period estimates provided as input parameters are half of the true rotation period. Another group of intricate targets corresponds to light curves with long-term instrumental modulations. Often the period selected by ROOSTER for these targets is between 38 and 60 days. In Section 3.3.3, we then carry out a number of steps to identify the potential ROOSTER period misselections. In fact, for the cool solar-like stars, Breton et al. (2021) concluded that the methodology's accuracy can be improved from 92.1% to 96.9% by identifying relevant targets for visual inspection.

Note that for the current analysis, which focuses on hotter solar-like stars than those in Paper I and Breton et al. (2021), we have doubled the training set (Section 3.3.1 and Appendix A). We currently train ROOSTER with stars of spectral type mid-F to M.

3.3.3. Supplementary Visual Inspection

As mentioned above, during the development and validation of the ML tool, we have identified problematic groups of targets for which ROOSTER has difficulty in selecting the correct rotation period. For this reason the ML P_rot selection is complemented with additional checks and visual inspection. Below we describe the most relevant groups of targets, rather than describe the full assessment from the visual inspection.

Targets with missing input parameters for the ML tool.—For a fraction of stars (∼1% of the sample considered for the ML), ROOSTER is unable to provide an assessment, because some of the input parameters, namely, those related to the ACF, are not determined. We visually check these targets. A significant part of the targets (∼56%) do not show rotational modulation, and only for ∼10% do we provide a final rotation period (Table 1).

Comparison with the automatic selection.—We first compare the P_rot values for targets common to the ML selection (P_rot,ML) and automatic selection (P_rot,AutoS). P_rot,AutoS always corresponds to the period recovered from the wavelet analysis. We visually inspect all the targets in disagreement, as well as the targets with P_rot,AutoS but no P_rot,ML. The targets for which the ML and the automatic selection disagree usually correspond to targets with high-amplitude second harmonics for which ROOSTER selects half of the rotation period (∼93% of the targets in disagreement). Table 3 summarizes the P_rot values finally selected after the visual inspection.

Table 3. Summary of the P_rot Detections

	# Prot	# Corrected Prot
		(>15%)
ML training set
Paper I	15,640
Additional targets	13,923
AutoS	819	2
ML+AutoS	10,693	32
ML	10,731	1099
Visual check	3,426
Total	55,232
New detection	24,182 (+311)
	(∼43.8%)

Note. Top: ML training set composed of the targets in Paper I and additional targets to complement the T_eff range. Reliable rotation periods in the training set are obtained by combination of automatic selection (AutoS) and visual inspection. Middle: summary of the results for the targets analyzed by ROOSTER (see details in Section 3.3.3). The rotation periods here are recovered by automatic selection, ML, and additional visual checks. Bottom: total number of P_rot detections and number of new detections in comparison with (McQ14; +311 corresponds to incorrect P_rot values reported in the literature). The first column shows the number of P_rot detections in each step. The second column indicates the number of P_rot values that were corrected after visual inspection for the targets in the ROOSTER analysis.

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Comparison with the literature.—Next, we cross-check the targets with P_rot,AutoS and/or P_rot,ML with the P_rot values reported by McQ14 (P_rot,McQ14). Similarly to the previous step, we visually inspect all the targets with P_rot,AutoS and/or P_rot,ML in disagreement with P_rot,McQ14. Also, we visually check the targets with P_rot,McQ14 that were not automatically selected or selected by the ML, with the exception of the known contaminants (Section 2.2). For the targets with both P_rot,AutoS and P_rot,ML in disagreement with P_rot,McQ14, our P_rot estimates are correct for ∼47% of the targets. For the remainder of the targets, their light curves often show photometric pollution (∼29%) or are CP/CB candidates (∼18%). The rotation periods selected solely by the ML (i.e., without P_rot,AutoS) in disagreement with McQ14 usually correspond to half of the true rotation periods (∼84% of the targets with discrepant P_rot,ML and P_rot,McQ14). Photometrically polluted light curves contribute to ∼13% of the disagreement between P_rot,ML and P_rot,McQ14. Targets with P_rot reported in McQ14 but not in this work correspond mostly to CP/CB candidates, light curves with instrumental modulation or photometrically polluted, and known contaminants (e.g., red giants, δ Scuti, γ Doradus). These targets are listed in Table 2.

We then proceed to identify additional wrongly selected P_rot,ML or rotation periods of targets that may have been missed by ROOSTER. The visual inspections described in the subsequent paragraphs concern targets for which P_rot was not automatically selected or reported by McQ14.

Mistaken filter choice.—We verify whether the proper filter is being selected, i.e., 20-day filter for P_rot < 23 days, 55-day filter for 23 days ≤ P_rot < 60 days, and 80-day filter for P_rot > 60 days (see Paper I for details). The objective of this choice is to ensure that the impact from instrumental modulations on the S_ph value is minimized, while P_rot is unaffected by the filtering. If the proper filter was not chosen by the ML, but the GWPS rotation period agrees within 15% of P_rot,ML, we automatically change the P_rot value to that retrieved by the GWPS in the proper filter (Table 1). If the P_rot,ML and the P_rot value in the proper filter disagree, we proceed for visual examination to decide whether there is a rotational signal and decide on the correct period. This disagreement often results from the presence of long-term instrumental modulations. Thus, ROOSTER is giving preference to the P_rot results from the 20-day filtered light curves. If the filtering does not affect P_rot, P_rot,ML is kept. We corrected the P_rot values for ∼24% of the targets in this condition, while ∼17% of the targets were demoted to no P_rot detection (Table 2).

Potential CP/CB candidates.—ROOSTER also flags Type 1 CP/CB candidates, which are typically fast rotators with P_rot < 7 days (see Paper I). Thus, we visually check the Type 1 CP/CB candidates with P_rot > 7 days: the Type 1 CP/CB flag is removed for about 29% of the targets. Second, to ensure that we are not providing rotation periods for Type 2 CP/CB candidates, we visually inspect the targets with P_rot ≤ 1.6 days (for targets in Paper I, the periodicity of the signal of all Type 2 CP/CB candidates is shorter than 1.6 days). Approximately 17% of these targets are actually affected by photometric pollution.

Potential instrumental modulation.—As mentioned in Section 3.3.2, the results from ROOSTER are affected by some confusion with instrumental-related modulations. Therefore, we visually inspect the targets with ML P_rot longer than 38 days. Approximately 87% of these targets belong indeed to the rotation table, but for ∼11% of them we choose a different P_rot after the visual inspection.

Potential harmonics.—Another problematic group of targets for ROOSTER, identified in Breton et al. (2021, Section 3.3.2), corresponds to targets with high-amplitude second harmonics. For this type of target, half of the rotation period may be reported (see, e.g., discussion in McQuillan et al. 2013, 2014). Therefore, we visually check the targets for which one or more P_rot estimates (nine for each target) are double the P_rot,ML. The ML algorithm had wrongly selected the harmonic for ∼28% of these targets. In particular, for the targets with at least three P_rot estimates being the double of P_rot,ML, ROOSTER had selected half of the correct P_rot for about 58% of the targets. The targets mentioned here exclude the half P_rot already identified in previous steps.

P_rot probability between 0.4 and 0.8.—In Breton et al. (2021), we found that there is an area of confusion where a significant number of targets without P_rot,ML exhibit rotational signal, and vice versa. This corresponds to targets with a P_rot,ML probability between 0.4 and 0.8, which we visually check. We determined that ∼61% of the targets without P_rot,ML have rotational modulation and selected the respective period. Approximately 20% of the targets in this visual inspection with P_rot,ML are corrected or demoted to no P_rot detection.

Short light curves.—Finally, we visually check light curves shorter than five Kepler quarters with a P_rot,ML estimate, to ensure that the ML algorithm decision is correct. From the targets left to visually check in this step, P_rot,ML is correct for ∼96%.

In total, we visually checked ∼26% of the 98,821 targets (i.e., 25,477 targets) analyzed by the ML algorithm. This corresponds to a significant decrease in the visual inspections in comparison with Paper I (e.g., Section 3.3).

Following the methodology described in Section 3.1, we recover average rotation periods and the respective S_ph for 39,592 targets from subsamples I–III, which comprise 132,921 targets, including part of the training set for ROOSTER. Tables 1 and 2 summarize the properties of the individual targets with and without a P_rot estimate, respectively. Table 2 also includes the known contaminants (see Section 2.2) that were not considered in the rotation analysis but are within the parameter space of subsamples I–III. The final P_rot yield is summarized in Tables 3 and 4.

Figures 4–8 summarize the results for the targets that are solar-like main-sequence and subgiant stars in subsample I, while neglecting Type 1 CP/CB candidates flagged either by ROOSTER or during the visual inspection. Among subsamples I–III, we have flagged 2251 Type 1 CP/CB candidates.

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Figure 4 shows the P_rot and S_ph distributions per type of targets (main-sequence F and G stars, and subgiants) in comparison with the distributions for the full subsample I. Note that because of the updated stellar properties, subsample I contains some K dwarfs according to B20. These are not represented individually in this section (see Appendix D instead). The dependency on effective temperature is better depicted in Figures 5 and 6, which show P_rot and S_ph as a function of T_eff, color-coded by the number of targets. For reference, Figures 5 and 6 also include the targets from Paper I with P_rot. Although less pronounced than for the cooler stars, the P_rot distribution for the hotter stars (subsample I) also shows evidence for bimodality. The S_ph distribution tends to be shifted toward smaller S_ph values for hotter stars than for cooler stars, with F stars showing lower levels of photometric activity than GKM stars. From M to G stars, the range of S_ph values becomes wider, with the upper and lower edge taking place at larger and smaller S_ph as T_eff increases, respectively. As for the subgiant stars, although their P_rot distribution is similar to the main-sequence stars of similar T_eff, there are more slower rotators among subgiants. In particular, between ∼5000 and ∼6000 K there is a group of slow-rotating subgiants, which are relatively cool and evolved subgiants (see Figure 15 in Appendix C). For cooler subgiants, the S_ph distribution is similar to the main-sequence stars' distribution. However, the hotter subgiants have distinctively low photometric activity levels.

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Figure 7 shows the S_ph as a function of P_rot for the targets in subsample I, except for the Type 1 CP/CB candidates. For main-sequence G stars, fast rotators are typically more photometrically active than slow rotators (Spearman correlation coefficient of −0.45). At relatively short P_rot, S_ph saturates. Part of the main-sequence F stars and subgiants also show the same behavior, but a new group of hot weakly active stars is apparent (Spearman correlation coefficients of −0.16 and −0.07, respectively). In particular, the weakly active fast-rotating F stars correspond mainly to targets expected to be above the Kraft break (Kraft 1967; see Appendix B).

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Finally, the relative uncertainty on P_rot is depicted in Figure 8. As described in Section 3.1, we prioritize the rotation-period estimate from the GWPS, where the width of the rotation peak reflects both the uncertainty on the rotation determination and partially differential rotation. The average uncertainty for main-sequence and subgiant solar-like stars (except Type 1 CP/CB candidates) is about 10%. The P_rot uncertainty generally increases with T_eff. Interestingly, the maximum relative P_rot uncertainty is reached around the Kraft break.

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Appendix D shows the same as Figures 5–7 but for all targets with a P_rot estimate. In particular, as described in Section 2.2, the Type 1 CP/CB candidates tend to be fast rotators with large-amplitude brightness variations. Thus, when considering Type 1 CP/CB candidates, there is an increase of fast rotators with very large S_ph, namely, values that are larger than the typical S_ph values for stars of similar T_eff. Also, Type 1 CP/CB candidates often have small P_rot uncertainties, being on average 7%.

4.1. Comparison with the Original ROOSTER Results

Figure 9 shows the comparison between the original P_rot,ML selected by ROOSTER and the final P_rot adopted after the additional visual inspection described in Section 3.3.3. For comparison purposes, in this section and Section 4.2, the final P_rot values are indicated by P_rot,final instead of simply P_rot. The total number of targets analyzed by ROOSTER is 98,821. Not accounting for known contaminants (Section 2.2), ROOSTER selected 23,547 P_rot,ML. Following the steps in Section 3.3.3, 2123 targets were demoted to Table 2, while 21,424 are among the targets with a final P_rot. From the latter, P_rot,ML agrees within 15% with the final P_rot for 20,293. These results indicate that the global ROOSTER's accuracy is 86.2%. For the targets in disagreement, 68.1% of those are related to cases where P_rot,ML is in fact the second harmonic (one-half) of P_rot. Another problematic group for ROOSTER corresponds to targets with P_rot,ML between ∼40 and ∼50 days (see, e.g., Figure 4 in Breton et al. 2021). Nevertheless, these account for only a small fraction of the targets. Finally, another group of targets in slight disagreement (still within 15%) correspond to targets with final rotation periods around midtwenties, which reflect the impact from the filtering of the light curve. As described in Section 3.3.3, for part of these targets the rotation period was automatically changed from P_rot,ML to the final P_rot value, namely, that obtained from the GWPS of the 55-day filtered light curves.

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During the visual inspection, P_rot was recovered for 3426 additional targets (out of the 98,821) for which ROOSTER did not provide a rotation period.

4.2. Comparison with McQuillan et al. (2014)

Figure 10 compares the final P_rot values determined in this work with those reported by McQ14. Among the 20,080 targets in common, there is an agreement within 15% for 99.1% of the targets. The P_rot estimates differ for 183 targets, for which we performed visual checks (Section 3.3.3) and determined that the P_rot values reported in Table 1 are correct. Part of the disagreement arises from the fact that the second peak in the ACF can have a larger amplitude than the first, while the first is actually the correct period.

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McQ14 reported P_rot for 615 known contaminants (see details in Section 2.2) within the parameter space of the target sample of this work (i.e., subsamples I–III): 553 red giants; 22 δ Scuti, γ Doradus, or hybrids; 28 eclipsing binaries; and 12 RR Lyrae stars. In addition to the known contaminants, McQ14 also reported periods for light curves with photometric pollution or instrumental modulation (for which it is not possible to disentangle the intrinsic rotation signal or that simply do not show rotational modulation) and Type 2−4 CP/CB candidates.

Considering the full sample of main-sequence and subgiant FGKM stars (this work and Paper I), we report P_rot for 31,038 targets in McQ14, with an agreement (within 15%) of 99.0%. Note that the targets for which we do not report P_rot are now known contaminants or targets for which during the visual inspection we determined that they belong to Table 2. We report P_rot for 24,182 main-sequence and subgiant FGKM stars that were not part of the periodic table of McQ14. A total of 15,088 of those were listed as nonperiodic stars in McQ14: the period assessment agrees within 15% with our final values for 55.5% of the targets. A total 3632 stars (out of 15,088) in the McQ14 nonperiodic table do not have a period candidate.

Figure 11 compares the P_rot distribution for the combined results of Paper I and the current analysis (red) with that from McQ14 (black). The bottom panels illustrate where the new P_rot detections lie in the P_rot−T_eff diagram in comparison with those in McQ14. We recover rotation periods for a larger number of fast-rotating F stars and, particularly, for a larger number of GKM slower rotators. While the new P_rot estimates alter the upper edge of the P_rot distribution, they do not alter the previous findings on the bimodal P_rot distribution in the Kepler field (e.g., McQ14), nor the subsequent gap, i.e., region of low density (see further discussion below).

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Figure 12 shows the upper edge of the P_rot distribution obtained in this work (solid black line) in comparison with that for the results of McQ14 (dashed black line). The upper edge corresponds to the 95% percentile. Within T_eff ∼ 3500 K and ∼4000 K there is a reasonable agreement between the two upper edges (the same for the DR25 catalog—Appendix D—except they are shifted toward cooler temperatures). Outside this T_eff range, we recover rotation periods for a larger number of slow rotators in comparison with McQ14 (see Figure 11). Therefore, the upper edge recovered in this work is located at longer P_rot. This result may be consistent with the model predictions by van Saders et al. (2019), which indicates a larger fraction of slow rotators than that detected by McQ14.

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The rotational modulation of light curves due to dark magnetic spots corotating with the stellar surface allows us to constrain rotation and magnetic activity properties. In this work, in order to recover average rotation periods and photometric magnetic activity, we analyze the long-cadence data collected by Kepler for 132,921 stars, which were originally selected according to DR25 (Mathur et al. 2017) as main-sequence F and G stars and late subgiant stars. This work is the second of this series, where Paper I focused the analysis to main-sequence K and M stars (according to DR25).

In this work, we decided to adopt the recent update, using Gaia data, on the stellar properties for Kepler targets (B20; Berger et al. 2020). Therefore, some of the targets in Paper I are now hotter stars (namely, G dwarfs), while some targets originally selected for the current work are K dwarfs according to B20.

Our study uses KEPSEISMIC (García et al. 2011, 2014b; Pires et al. 2015) time series obtained with three different filters with cutoff periods at 20, 55, and 80 days. The parallel analysis of the three time series aims at avoiding the long-term instrumental modulations, while retrieving the rotation period, i.e., unaffected by the filtering process. We also use PDC-MAP light curves to determine whether the measured signal could be due to photometric pollution resulting from the larger apertures employed in KEPSEISMIC data.

Rotation-period candidates are retrieved by combining the wavelet analysis with the autocorrelation function of light curves (e.g., Mathur et al. 2010; García et al. 2014a; Ceillier et al. 2016, 2017; Santos et al. 2019). The final P_rot estimates are selected by an ML algorithm (ROOSTER; Breton et al. 2021), automatic selection, and complementary visual examination. The training set for ROOSTER includes the targets of Paper I (Santos et al. 2019) and 34,100 additional targets analyzed in the current work to cover the full T_eff range. ROOSTER then searches for rotational signals and the respective rotation periods among the remaining 98,821 targets. Finally, we perform a series of cross-checks and supplementary visual checks.

We compute the photometric activity proxy as the standard deviation over light-curve segments of length 5× P_rot (Mathur et al. 2014). The final reported S_ph corresponds to the average of the individual S_ph values. Although S_ph is a lower limit of the true photometric activity level, depending, for example, on the stellar inclination angle and on the longitudinal and latitudinal spot distribution, S_ph has been shown to be an adequate magnetic activity proxy (Salabert et al. 2016, 2017).

We report surface rotation periods and the respective S_ph for 39,592 main-sequence and subgiant solar-like stars (out of 132,921). In comparison with Paper I, focused on cooler stars, there is a significant decrease in the detection fraction. The detection fraction in Paper I was about 60%, while the detection in this work is about 30%. A drastic decrease in the detection fraction with T_eff was also observed by McQ14. In particular, F stars seem to have rotational modulation with distinct characteristics from those of cooler stars. This motivated the expansion of the training set for ROOSTER to properly account for the different behavior of the hottest stars considered here. The change in behavior may be due to the shallow convective zones in F stars. The amplitude of rotational modulation is distinctively small, which can reflect weak magnetic activity characterized by small, less, and/or short-lived spots or active regions. We also find that the rotational signal of F stars is typically complex, with broad rotation peaks in the GWPS (relatively large P_rot uncertainties) and multiple peaks in the power spectrum. Often, in the WPS we observe a blended band of stronger rotational signal that ranges from the first harmonic (P_rot) to the third harmonic. This is in contrast with the signal of cooler stars (see, e.g., Figure 2).

A total of 2251 targets (out of 39,592) are flagged as Type 1 CP/CB candidates, as their signal also does not seem to be consistent with that of the other solar-like rotators. These targets generally have short P_rot and large S_ph (see Appendix D), being also characterized by stable fast beating in the light curve and a large number of harmonics associated with P_rot. Type 1 CP/CB candidates tend to be beyond or close to the upper edge of the S_ph distribution and the lower edge of the P_rot distribution. Interestingly, in Paper I we verified a significant overlap between the Type 1 CP/CB candidates and the synchronized binaries identified by Simonian et al. (2019), suggesting thus the possibility of the Type 1 CP/CB being close-in binaries.

For the target sample of the current work, we report P_rot of 19,732 targets for which McQ14 did not report a P_rot. For the common targets, there is an agreement of more than 99%. Note that the majority of the P_rot values reported here correspond to targets that are expected to be main-sequence solar-like stars. Therefore, even ignoring the detections for subgiant stars that were not the focus in McQ14, our analysis still yields a significantly larger number of P_rot detections. Nevertheless, McQ14 reported P_rot for 2060 targets that are considered subgiants in this work. Note also that the stellar properties (e.g., T_eff and $\mathrm{log}g$) have been updated since the study by McQ14.

The rotation period generally decreases with increasing effective temperature, with F stars being on average faster rotators than the cooler solar-like stars. This is consistent with previous findings (e.g., McQ14; García et al. 2014a).

Relative to the rotation-period distribution reported by McQ14, we recover a larger number of slow rotators. For this reason the upper edge of the P_rot distribution is located at longer periods than that in McQ14. Interestingly, the model predictions by van Saders et al. (2019) were consistent with a larger number of slower rotators than that detected by McQ14.

Similarly to the cooler targets of Paper I, the bimodal P_rot distribution is found for the targets of the current work. The bimodality in the P_rot distribution of Kepler targets was previously identified and investigated by, for example, McQuillan et al. (2013, 2014), Davenport (2017), and Davenport & Covey (2018). These studies in particular suggested that the bimodal behavior is related to two distinct episodes of stellar formation. This bimodal behavior is, however, not exclusive to the targets in the Kepler field and was also discovered for K2 targets (Reinhold & Hekker 2020; Gordon et al. 2021). An alternative origin for the bimodal P_rot distribution was suggested by Montet et al. (2017) and Reinhold et al. (2019), who concluded that the targets in the fast-rotating branch are spot dominated, in contrast with the targets in the slow-rotating branch, which are faculae dominated. Gordon et al. (2021) proposed instead that the bimodal P_rot distribution is due to a broken spin-down related to the coupling between the stellar rapidly rotating core and the envelope.

Among the subgiant stars, there is a group of slow-rotating targets with T_eff between 5000 and 6000 K. These are found to be consistent with more evolved subgiants. In particular, the slowest of these targets (P_rot > 60 days) are located close to the red giant branch.

The S_ph values for F stars are significantly smaller than those of cooler main-sequence stars. Considering also the targets of Paper I, for GKM stars, the range of measured S_ph values is wider: the S_ph value corresponding to the upper edge of the S_ph distribution generally increases with T_eff, while the S_ph value of the lower edge decreases with T_eff. For main-sequence GKM stars, S_ph increases with decreasing P_rot, which is consistent with fast rotators being more active than slower rotators (e.g., Vaughan et al. 1981; Baliunas et al. 1983). While for K stars (see Appendix D and Paper I) the bimodal P_rot distribution is visible in the S_ph−P_rot diagram through two almost parallel branches, for G stars the fast-rotating branch corresponds to a mostly saturated S_ph regime. Indeed, particularly for K stars, the transition between the two branches causes a discontinuity in the S_ph−P_rot diagram, where the slowest-rotating stars belonging to the fast-rotating branch have smaller S_ph values than the fastest-rotating stars belonging to the slow-rotating branch. For K2 targets, Reinhold & Hekker (2020) used the location of this discontinuity or kink to infer the location of the period gap in the P_rot−T_eff diagram. For main-sequence F stars and subgiants, the correlation between S_ph and P_rot is significantly reduced. In particular, the hottest targets are found to be weakly active fast rotators.

Finally, the combined output of Paper I and the current work is average P_rot and S_ph values for 55,232 main-sequence and subgiant FGKM stars (out of 159,442). These results include 24,182 new P_rot detections in comparison with McQ14.

The material is based on work supported by the National Aeronautics and Space Administration (NASA) under grant No. NNX17AF27G to the Space Science Institute (Boulder, CO, USA), which was the recipient of the grant. This paper includes data collected by the Kepler mission and obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the Kepler mission is provided by the NASA Science Mission Directorate. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 526555. The authors thank D. Bossini for providing the evolutionary tracks used in this paper to distinguish main-sequence from subgiant stars. A.R.G.S. acknowledges the support STFC consolidated grant ST/T000252/1. S.N.B. and R.A.G. acknowledge the support from PLATO and GOLF CNES grants. S.M. acknowledges support by the Spanish Ministry of Science and Innovation with the Ramon y Cajal fellowship No. RYC-2015-17697 and grant No. PID2019-107187GB-I00. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

Software: KADACS (García et al. 2011), ROOSTER (Breton et al. 2021), NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020), Matplotlib (Hunter 2007), Pandas (McKinney 2010), Scikit-learn (Pedregosa et al. 2011).

Facilities: MAST - , Kepler Eclipsing Binary Catalog - , Exoplanet Archive. -

ROOSTER (Section 3.3.2) was developed and validated in Breton et al. (2021) with the target sample of Paper I. Breton et al. (2021) performed a training loop with 100 realizations. In each realization, 75% of the targets are randomly selected for the training set, while the remaining 25% constitutes the test set. By performing a training loop rather than a single training, one can compute the mean classification ratio for each star. As follows, ROOSTER is able to classify all the targets in the training set.

In this section, we discuss ROOSTER's results for the full training sample of the current analysis (see Section 3.3.1), which, in addition to the cooler stars of Paper I, includes hotter targets as well. From Breton et al. (2021) to the current analysis, we have more than doubled the size of the training set. This way ROOSTER is trained with targets of spectral types from mid-F to M (Figure 3). This increment is motivated by the different behavior observed in F stars in comparison to cooler solar-like stars in terms of rotational signature (see discussion in Section 5).

Figure 13 compares the rotation periods selected by ROOSTER (P_rot,ML) and the correct P_rot. The blue diamonds highlight the targets that would be selected for visual inspection or for an automatic change in the filter choice according to the selection criteria described in Section 3.3.3. The P_rot values agree within 15% for ∼95.3% of the targets. From the targets in disagreement, ∼94.6% would be selected for visual inspection (blue diamonds) and, therefore, corrected. The global accuracy of ROOSTER for the training set composed of mid-F to M stars is 95.3%. Finally, ROOSTER only selects P_rot for two targets that are found not to have rotational modulation and only misses P_rot for the targets with missing parameters, which would be selected for visual inspection following the procedure in Section 3.3.3.

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The rotation period is observed to decrease generally with increasing effective temperature (Figure 5). F stars are then typically fast rotators. For main-sequence GKM stars (Figure 7; see also Figure 9 in Paper I), faster rotators are found to be photometrically more active than slower rotators. However, for main-sequence F stars and subgiants there is a group of weakly active fast rotators. For subgiants, it is clear that those correspond to the hottest subgiant stars considered in this work (Figures 5 and 7). Figure 14 shows the S_ph−P_rot diagram for the main-sequence F stars expected to be below (red) and above (blue) the Kraft break (Kraft 1967). Note that the red data points are overplotted. The left panels show the results based on the stellar properties from DR25, while the right panels show the results based on B20 (Berger et al. 2020), where F stars usually have lower T_eff compared to DR25. Most of the fast-rotating F stars with small S_ph values are stars expected to be above the Kraft break. Additionally to the T_eff difference between the two catalogs, there is an associated uncertainty and the effect from metallicity on the convection properties, which may also contribute to the scatter in these diagrams.

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While the P_rot values for most of the subgiant stars are consistent with the P_rot distribution for the main-sequence stars of similar T_eff, there is a group of slow-rotating stars (Figure 5), which are located above the upper edge of the P_rot distribution. We select the targets with 5000 K ≤ T_eff,B20 ≤ 6000 K and P_rot > 40 days. Figure 15 shows where these slow-rotating subgiant stars are located in the $\mathrm{log}g$−T_eff diagram according to the stellar properties from DR25 (left) and B20 (right). The slowest targets (lighter colors) tend to be more evolved targets, in both DR25 and B20, relative to the target sample. However, part of slow-rotating subgiants are in the main sequence according to DR25.

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Figure 16 highlights the Type 1 CP/CB candidates, tidally synchronized binaries (Simonian et al. 2019), and Gaia binaries (Berger et al. 2018) in the P_rot−T_eff and S_ph−T_eff diagrams for the targets with a P_rot estimate in Paper I and in this work. The overlap between the target sample of the current paper and the binaries identified by Simonian et al. (2019) and Berger et al. (2018) is very small, with only 8 and 125 targets, respectively. The tidally synchronized binaries tend to have larger S_ph values and short periods in comparison to the targets with similar T_eff. The Gaia binaries have a P_rot and S_ph distribution more consistent with those of the (presumably) single targets. The targets flagged as Type 1 CP/CB candidates have generally short periods and large S_ph. In particular, they are located at or beyond the lower edge of the P_rot distribution and the upper edge of the S_ph distribution. To guide the eye, the dashed lines in Figure 16 show the lower (5th percentile) and upper (95th percentile) edges of the P_rot and S_ph distribution, respectively. The cooler end of the P_rot edge was removed because of its erratic behavior due to small sample size. Nevertheless, the gray data points show the results for the main-sequence stars in Figures 5 and 6.

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As concluded in Paper I, the tidally synchronized binaries and the Type 1 CP/CB candidates tend to occupy the same parameter space, being typically characterized by very large S_ph and short P_rot. Note, however, that data, methodology, and properties studied in Simonian et al. (2019) are distinct from those of this work and Paper I. The targets flagged as Type 1 CP/CB candidates were first identified in Paper I during the visual inspection. The behavior of the brightness variations and the respective rotation diagnostics appeared to be distinct from the remainder of the solar-like stars with rotational modulation. These targets exhibit large-amplitude brightness variations, leading to large S_ph values. The "rotational" modulation shows fast and stable beating patterns throughout the time series, which also leads to, for example, beating in the ACF. Finally, these targets often show a large number of visible harmonics of the rotation period. Part of these targets were found to be tidally synchronized binaries by Simonian et al. (2019), who concluded that the rapid-rotating regime in Kepler observations is dominated by binary systems. The overlap and the similarities between the Type 1 CP/CB candidates and the tidally synchronized binaries suggested that Type 1 CP/CB candidates might be indeed binaries, while the signal may still be related to rotational modulation. For the current work, ROOSTER was trained to flag these targets. As discussed in Breton et al. (2021), ROOSTER tends to flag more targets than those flagged by visual inspection. This may suggest that ROOSTER is flagging targets that are not Type 1 CP/CB candidates. Nevertheless, we advise caution when dealing with these targets.

Figure 17 shows the same as Figures 6 and 7 but for the stellar properties of DR25, where subgiant and main-sequence stars are separated according to $\mathrm{log}g$ from DR25 (in this figure). As discussed in B20, the effective temperatures of M stars (to be improved in a forthcoming work; see B20) are overestimated in comparison with DR25. Thus, in Figure 17 M stars are located at cooler T_eff. The slow-rotating subgiants have hotter T_eff in DR25 than in B20, while F stars are also shifted toward hotter temperatures. Note that the T_eff gaps in DR25 are due to artifacts in the stellar properties catalog.

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Figures 18 and 19 show the P_rot−T_eff, S_ph−T_eff, and S_ph−P_rot diagrams for the full target sample of Paper I and this work, including Type 1 CP/CB candidates and subsamples II and III, which were neglected in Figures 5 and 6. As discussed above, there is an increase of fast rotators, particularly with high T_eff and an increase of large S_ph values. In Figures 18 and 19, the split of the targets in terms of spectral type and evolutionary state is made according to B20 stellar properties. Note that in Paper I we used DR25.

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Finally, Figure 20 compares the upper edge of the P_rot distribution according to the T_eff values in DR25 and B20 (for comparison with the simplified Figure 12). The upper edge does not change significantly owing to the different T_eff estimates, in particular for stars hotter than 4000 K. For M stars, as mentioned above, T_eff,B20 is systematically larger than T_eff,DR25. Independently of the stellar properties catalog, our P_rot distribution is characterized by a larger number of slow rotators than that of McQ14.

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