Wrinkles in Time. I. Rapid Rotators Found in High-eccentricity Orbits

Recent space-based missions have ushered in a new era of observational astronomy, where high-cadence photometric light curves for thousands to millions of stars in the solar neighborhood can be used to test and apply stellar age-dating methods, including gyrochronology. Combined with precise kinematics, these data allow for powerful new insights into our understanding of the Milky Way’s dynamical history. Using TESS data, we build a series of rotation period measurement and confirmation pipelines and test them on 1560 stars across five benchmark samples: the Pleiades, Pisces–Eridanus, Praesepe, the Hyades, and field stars from the MEarth Project. Our pipelines’ recovery rates across these groups are, on average, 89%. We then apply these pipelines to 4085 likely single stars with TESS light curves in two interesting regions of Galactic action space. We identify 141 unique, rapidly rotating stars in highly eccentric orbits in the disk, some of which appear as rotationally young as the 120 Myr old Pleiades. Pending spectroscopic analysis to confirm their youth, this indicates that these stars were subject to fast-acting dynamical phenomena, the origin of which will be investigated in later papers in this series.


Introduction
With new, nearly all-sky astrometric, spectroscopic, and photometric observational surveys, we have the opportunity to understand the Milky Way dynamics impacting the solar neighborhood, using stellar ages as an additional probe.Gyrochronology is a robust age-dating method for younger, low-mass stars (2 Gyr, 1.3 M e ), particularly G-type stars.Upon measuring stellar rotational velocities and activity levels for stars in the Pleiades and Hyades open clusters and the Sun, Skumanich (1972) famously found that stars slow their rotation as they age.This relationship between a star's rotation period (P rot ) and its age (t) follows a trend described by a simple power law: µ Today, one of the best ways to measure stellar rotation is using photometry to observe modulation in stellar brightness as a result of starspots rotating in and out of our view.NASA's Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) provides the ability to make such measurements for hundreds of thousands of nearby, bright stars.These data pair well with astrometry from the Gaia mission (Gaia Collaboration et al. 2016) and spectroscopy from surveys like GALactic Archaeology with HERMES (GALAH; De Silva et al. 2015) and the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017) of stars in the local volume.
This paper is the first in a series where we focus on young stars in highly eccentric Galactic orbits.It is generally assumed that stars are born on near-circular orbits.Over the lifetime of a star, its orbit can be dynamically perturbed to a more eccentric state (e.g., Sellwood 2014 and references therein).We can explore exceptions to this trend with gyrochronological ages and precise kinematics.

More on Gyrochronology and Its Caveats
Since 1972, many research groups have used observations of stellar populations with known ages to empirically calibrate the gyrochronology age-rotation relation.The power-law exponent is typically found to be 0.50-0.65,close to Skumanich's original 0.50 value (Barnes 2007;Mamajek & Hillenbrand 2008;Meibom et al. 2009;Angus et al. 2015Angus et al. , 2019;;Douglas et al. 2019;Curtis et al. 2020).Ultimately, this relation is intended to be inverted to obtain precise and reliable ages for field stars of unknown ages.
Gyrochronology is not applicable for all lower-mass stars of all ages.As low-mass stars are interacting with their circumstellar disks and contracting onto the main sequence, they start at a range of P rot .They eventually converge to a single P rot for a given age and temperature (Barnes 2007), with the timescale for convergence being mass-dependent.Gyrochronology is only applicable after this convergence occurs.At ≈700 Myr, K dwarfs temporarily stall and only resume spinning down at 2 Gyr (Curtis et al. 2019a(Curtis et al. , 2020)).The M dwarfs have different dynamos from their G-and K-type counterparts and likely do not follow the same power law for age-dating (Newton et al. 2016;Rebull et al. 2018;Popinchalk et al. 2021).
Thus, using gyrochronology solely on G dwarfs is advantageous due to their favorable timescales for convergence (≈100 Myr; see Rebull et al. 2016;Gillen et al. 2020;Boyle & Bouma 2023), little to no stalling, and the relative abundance and Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
brightness of these stars.This is feasibly done with TESS.TESS follows in the footsteps of Kepler (Borucki et al. 2010) and K2 (Howell et al. 2014), providing high-cadence, high-precision photometric data that can be used to measure P rot for large numbers of stars.Large-scale P rot measurements (R. Angus 2022; private communication) and age-rotation relation calibration efforts (e.g., Kounkel et al. 2022) using TESS have already begun and will be incorporated into future analyses.
It is worth noting that the short ∼27 day baseline for most TESS observations limits the longest P rot we can reliably measure in this study to 13 days (determined in Appendix A), setting the upper age limit to 1.3 Gyr for stars of 1.3 M e according to age-rotation relations.

Interpreting Galactic Action Space
In this paper, we are interested in identifying young stars in orbits that are typically associated with older populations, namely, high-eccentricity orbits.Rather than reconstructing orbits using each star's 6D position and velocity coordinates, we approximate their orbital size and eccentricity by projecting these kinematics into galactocentric actions.Action space is a natural space when analyzing orbital properties and can be calculated by assuming a reasonable gravitational potential for stars in the local volume (e.g., Binney & Tremaine 2008;Trick et al. 2019).
Assuming a cylindrical symmetry for disk kinematics with the z-axis oriented perpendicular to the plane of the disk, the azimuthal action, J f , is equal to the orbital angular momentum in the z-direction, L z .Stars with higher values for J f will also have larger mean orbital radii and thus larger orbits.Radial action, J R , is related to orbital eccentricity.In a disk with a flat rotation curve, the radial action can be approximated by J R ∝ E R /κ, where κ is the epicyclic frequency, and E R is the energy associated with the orbit's noncircular motion.In this approximation, the value of , where E is the total orbital energy, E c is the energy for a circular orbit, and each is evaluated at the angular momentum L z for that orbit.For the remainder of this work, we will use L z and J R .
We calculated the radial and azimuthal action for each star in our catalog following Trick et al. (2019) using the Pythonbased galaxy modeling package galpy v1.7 (Bovy 2015). 6or these calculations, we approximate the underlying potential using the default settings for the MWPotential14 and use the Stäckle-Fudge approximation (Binney 2012).Our orbital analysis is described in Section 2.4.
The distribution of actions for stars in our catalog within 200 pc of the Sun is shown in Figure 1; our catalog uses data from Gaia DR3, GALAH DR3, and APOGEE DR16 (see Section 2).The horizontal axis shows orbital angular momentum L z , where orbits with larger mean orbital sizes will be found to the right of this plot.The vertical axis shows the square root in radial action, J R .The distribution in the solar neighborhood broadly fills in an inverted triangle.Stars in circular orbits (low values for J R ) have angular momenta close to the value of the Sun's, L z,e , located at the lower point of the triangular distribution.Stars on highly eccentric orbits (high values for J R ) may be interlopers in the solar neighborhood from other parts of the disk and thus may have angular momenta much smaller (or larger) than that of the Sun and will appear in the upper left (or upper right) of Figure 1.
While an equilibrium distribution free of dynamical perturbations would appear smooth, Trick et al. (2019) first identified the diagonal, elongated substructures in the L z − J R plane at high values of J R , which we refer to hereafter as "wrinkles."These are also sometimes referred to as corrugations or simply kinematic groups, and they motivate our age investigation of stars in this space.

This Work
In this work, we build pipelines to measure P rot and test them on stars of known P rot to assess their performance.We then apply these pipelines to regions in high-eccentricity phase space.In Section 2, we discuss the light curves used to measure P rot , the literature we test our P rot pipelines on, and the data sets we use to estimate actions for stars.In Section 3, we outline the design of our P rot pipelines.We compare our P rot measurements to literature measurements from five benchmark samples in Section 4. In Section 5, we show a preliminary P rot distribution for stars in a selection of high-eccentricity orbits.We conclude in Section 6 with a summary of this work and discussion of future plans for this paper series.

Measuring P rot with TESS Photometry
We use TESS photometry to measure P rot , which is the foundation for determining gyrochronological ages.TESS is a nearly all-sky survey searching the nearest and brightest stars for transiting exoplanets (Ricker et al. 2015).Each observational period, or sector, lasts ≈27 days for a field of view that is 24°× 96°.The mission obtained 2 minute cadence photometry for 200,000 stars that were of high priority for its exoplanet science goals and supplied full-frame images (FFIs) from each sector at a cadence of 30 minutes.Now in its extended mission, it is continuing to provide observations based on guest investigator proposals and supply FFIs with a cadence of 200 s.We start with photometry from the FFIs, since the shortercadence data are limited to certain targets.If the star does not have a light curve from the FFI-reduction pipeline we use, we check the short-cadence data.
All of the stars observed by TESS are listed in the TESS Input Catalog (TIC) with their respective stellar parameters based on the second data release from Gaia (Gaia Collaboration et al. 2018) and have an associated TIC identification number (Stassun et al. 2019).We used data accessed in 2023 January, which includes all sectors through sector 57.
Instrument systematics can affect the TESS photometry.This includes pointing jitter, the spacecraft's 14 day orbit, crowding from neighboring stars due to the cameras' large pixels, momentum dumps, and scattered light from the Earth and Moon (e.g., Smith et al. 2012;Stumpe et al. 2012;Jenkins 2020).Various teams have developed light-curve reduction pipelines to mitigate these effects, including the reduction pipeline from the mission itself, the TESS Science Processing Operations Center (TESS-SPOC; Caldwell et al. 2020).
TESS-SPOC light curves are generated from the FFIs for all stars with a TESS magnitude (T mag ) 13.5 using simple aperture photometry (SAP).Here the pixels are summed within an aperture optimized for the signal-to-noise ratio (S/N) of the particular target star (Morris et al. 2017).The resulting SAP light curve is then corrected with a set of background pixels.Given the instrument systematics discussed above, additional corrections are made by modeling and removing timedependent instrumental signatures.Corrections to the light curve are also made to account for crowding from other stars.These light curves are known as the presearch data conditioning SAP light curves, or PDC-SAP light curves.In this analysis, we measure P rot using the PDC-SAP light curves from the TESS-SPOC pipeline as the default.If the star does not have a TESS-SPOC light curve, we also check for SPOC light curves, which are generated the same way but for the 2 minute cadence targets (Jenkins et al. 2016); these stars can have T mag 13.5.

Literature P rot Measurements from Kepler, K2, and MEarth
We build and test our P rot measurement pipelines on samples of stars with previously measured P rot .While we are interested in age-dating young stars (likely 0.5-1 Gyr), high-eccentricity phase space is predominantly made up of field stars (see Section 2.4) with P rot that are too long to measure with TESS.We choose a mix of young stars and old field stars with known P rot to ensure that our pipelines can robustly measure the P rot they are supposed to and do not detect P rot when they should not.We crossmatch each of the P rot catalogs used with the TIC and Gaia DR3 to obtain information such as the TESS contamination ratio (CR) and Gaia astrometric information that may indicate that the star is a binary (Section 3.3).
For young stars, we look at four associations, three of which are open clusters of known ages.This includes the 120 Myr old Pleiades (Rebull et al. 2016), 670 Myr old Praesepe (Rampalli et al. 2021), and the 730 Myr old Hyades (Douglas et al. 2019).The community has studied rotation in these clusters for more than a decade using observations with longer baselines (particularly the K2 mission, which had an 80 day baseline and conducted multiple campaigns covering Praesepe and the Hyades), making these good laboratories in which to test P rot recovery.
We also test our pipeline on stars in the Pleiades-aged Pisces-Eridanus stellar stream (Meingast & Alves 2019; called Meingast 1 by Ratzenböck et al. 2020).The literature P rot from Curtis et al. (2019b) were derived from light curves generated from TESS FFI using SAP and measured by visually confirming Lomb-Scargle (LS) periodograms.While our analysis also utilizes TESS data, the light curves we use are generated and confirmed with a different approach.
For the field star population, we use the MEarth M dwarf sample, which contains a broad range of rapid and slow rotators (Newton et al. 2016(Newton et al. , 2018)).This catalog provides a sample where some periods are known to be too long for rotational modulation to be apparent over 27 days.We use stars with the most reliable signatures of rotation, designated in those works as "grade a" or "grade b" rotators.
We list further information on the benchmark samples used in Table 1.

Building a Kinematics Catalog with Gaia, GALAH, and APOGEE
The Gaia mission was launched in 2013 with the goal of creating the largest and most precise 3D catalog of objects in the sky (Gaia Collaboration et al. 2016).It is equipped with three instruments: the astrometry instrument (ASTRO) to measure positions, the photometric instrument (BP/RP) to measure luminosities, and the radial velocity spectrometer (RVS) to determine line-of-sight radial velocities (RVs).The third and latest data release, DR3, provides full astrometric solutions for over 1.46 billion stars in the galaxy and RVs for 33 million stars (Gaia Collaboration et al. 2023).
While Gaia has spectroscopic capabilities, the resolution of RVS is not very high (R = 11,000) given that spectroscopy is not a primary science goal of the mission.Furthermore, the precession of the Gaia spacecraft prevents the measurement of truly precise RVs, with an average RV precision of 1.3 km s −1 (Katz et al. 2023).However, a number of ground-based surveys provide accompanying higher-resolution spectroscopic observations for stars Gaia has observed.Two such efforts are GALAH (R = 28,000) and APOGEE (R=22,500); both have RV precisions of around 0.1 km s −1 (Nidever et al. 2015;Zwitter et al. 2021).GALAH observes stars of all ages and locations in the Milky Way for Galactic archeology purposes (De Silva et al. 2015), while APOGEE is a near-infrared survey designed to primarily measure spectra for red giant stars in the inner disk and bulge (Majewski et al. 2017).When available, we use the more precise RVs from GALAH DR3 (Buder et al. 2021) and APOGEE DR16 (Jönsson et al. 2020).
We recreate the action space plot from Trick et al. (2019) based on the most recent phase space information for 3.9 million stars observed by the Gaia mission (Gaia Collaboration et al. 2021, 2023;Katz et al. 2023), which we supplement with RVs from GALAH and APOGEE.This is shown in Figure 1.We first query Gaia DR3 for all stars within 200 pc that have a measured RV and parallax errors of less than 10%, yielding 731,961 stars.We then crossmatch these results with GALAH and APOGEE RVs, limiting stars with APOGEE RVs to an RV S/N of >10, as suggested by the survey.This resulted in 16,937 and 47,432 crossmatches, respectively.For stars that have RVs in each survey, we calculate the zero-point offset among surveys using GALAH as our standard.We find an offset of −0.1 ± 5.9 km s −1 between Gaia and GALAH and −0.5 ± 6.8 km s −1 between APOGEE and GALAH, which is reasonable given the errors associated with each survey.7If the star does not have a GALAH RV, we use the APOGEE RV; otherwise, we use the Gaia RV.

Action Space Calculations
As outlined by Trick et al. (2019), to calculate actions for our 731,961 stars, we convert the 6D observed kinematics to Galactic heliocentric Cartesian coordinates (X, Y, Z) and the corresponding heliocentric velocities (UHC, VHC, WHC) using the coordinate transformations in galpy (Bovy 2015).
Here U defines the radial direction toward the Galactic center, V defines the rotational direction of the galaxy, and W defines the vertical direction toward the Galactic north pole.We incorporate the Sun's motion with respect to the local standard of rest (LSR), (U, V, W) = (11.1,12.24, 7.25) km s −1 (Schönrich et al. 2010).Then we convert (UHC, VHC, WHC) to (ULSR, VLSR, WLSR) assuming that the Sun's distance to the Galactic center is 8 kpc, its circular velocity is 220 km s −1 , and its height above the Galactic plane is 25 pc (Jurić et al. 2008;Bovy et al. 2012;Bovy 2015).We transform (X, Y, Z, ULSR, VLSR, WLSR) to galactocentric cylindrical coordinates (R, f, z, vR, vT, vz).Assuming the Stäckle-Fudge Galactic potential (Binney 2012), we find each star's orbital actions using galpy.We remove any stars with J 14.4 R > kpc km s −1/2 , as these are likely stars in the halo.We simulate the propagation of parallax and RV errors in our action calculations for 1000 random stars.We find that a 10% error on the parallax has a minimal effect (1%) on the action calculations.Radial actions begin to significantly change for RV errors of 5-10 km s −1 .The average change in J R was always <0.1 kpc km s −1/2 , but the standard deviations were 0.7 kpc km s −1/2 for RV errors of 8-10 km s −1 .Based on the scales of the wrinkles, we choose stars with RV errors of 7 km s −1 , which gives an average change in J R of 0.07 ± 0.6 kpc km s −1/2 .8Angular momentum changes are small (<1%).
In subsequent works, we will explore how combining ages and kinematics can significantly deepen our interpretation of kinematic structures in action space.For this work, we choose a vertical and a horizontal slice in high J R on which to run our P rot pipelines.The locations of these were in part motivated by where benchmark clusters fall in action space.In Figure 2, we see that younger clusters like the Pleiades, Pisces-Eridanus, the Hyades, and Praesepe are at lower J R , while the 2.7 Gyr old Ruprecht 147 cluster sits a bit higher (Curtis et al. 2020).Note that Ruprecht 147, which is not one of the clusters we study in this work, is at a distance of 302 pc, beyond our 200 pc limit.We have plotted its members (using membership cuts suggested by Curtis et al. 2020) for demonstration of where an older group of stars falls in action space.We also note that there is an elongation in most of the clusters.While exploring the reason for this morphology is beyond the scope of this work, we posit that this could be the result of tidal effects (e.g., Röser & Schilbach 2019;Röser et al. 2019), the presence of binaries and their effects on the measured RVs, or interloping nonmembers.However, because we use rotation-based catalogs, the latter is unlikely.
Both slices were selected using Glue (Beaumont et al. 2015).Glue is an interface that allows "linked-view" visualizations of astronomical image or catalog data.For example, users can draw an arbitrary shape on a plot with an associated table of data that will filter the particular data lying within the drawn boundaries.We recreate Figure 1 in the Glue interface and manually highlight the two slices, which in turn creates a subtable with the selected stars.The vertical slice contains 8834 stars, and the horizontal slice contains 3952 stars, with 238 stars overlapping.We choose the vertical slice of action space as 6 kpc km s −1/2   J 14 R kpc km s −1/2 , 1655 kpc km s −1  L z  1700 kpc km s −1 , as shown in Figure 2. The J R lower bound begins at the location of Ruprecht 147, since its presence indicates that stars in that region are likely over 1 Gyr old and implies that finding young stars there would be anomalous.This slice also captures part of a wrinkle structure (discussed in Section 1).Our horizontal slice is of a similar thickness located at 11 kpc km s −1/2   J 11.5 R kpc km s −1/2 , 1300 kpc km s −1  L z  2050 kpc km s −1 .This slice also captures a part of two wrinkles.

Measuring P rot
The LS periodogram is perhaps the most used form of P rot measurement given its efficiency and ability to use unevenly sampled data (Lomb 1976;Scargle 1982;Press & Rybicki 1989;VanderPlas 2018).After defining a grid of periods or frequencies, sine curves with the defined periods/ frequencies are fit to the signal.The result is an estimate of the Fourier power as a function of period/frequency.The second column of Figure 3 shows the periodograms for an example star.Visually, we can see that the P rot is ≈1.2 days (first column), and this is where the periodograms have their highest peaks.This is confirmed by phase-folding the light curve with the measured P rot , as shown in the third column.
The generalized LS (GLS) periodogram (Zechmeister & Kürster 2009) is an iteration of the LS periodogram in which the sine wave fit is more rigorous and can account for measurement errors and offsets resulting in more precise P rot measurements.It has already been used successfully with TESS data (Anthony et al. 2022).We use pyastronomys implementation (Czesla et al. 2019).
There should be at least 1.5-2 rotation cycles observed to reliably measure a P rot .For TESS's typical observational baseline of 27 days, this means we cannot trust a measured P rot beyond 13.5-18 days.We define a periodogram with periods ranging from 0.1 to 50 days with a grid spacing of 0.001 days.If a P rot 19 days is measured, we expect that it is likely a spurious signal, and our pipeline then chooses a new, shorter P rot corresponding to the next largest peak.This ultimately limits any measured P rot to 19 days, but we leave the periodogram limit at 50 days for better constraints on our periodograms' peak-width measurements (introduced in Section 3.2.1).
For our analysis in Section 4 and our injection and recovery test discussed in Appendix A, we set the reliable P rot detection limit at 13 days.This limit matches other TESS rotation pipelines and guarantees two rotation cycles in a single TESS sector.Previous attempts at automating measuring rotation using single sectors of TESS data have only been successful for P rot 13 days (Canto Martins et al. 2020;Holcomb et al. 2022;Kounkel et al. 2022), with measurements of longer periods more likely being associated with TESS systematics.
The P rot measurements may return half or double the true P rot .This can result from sampling, short baselines, stellar spot evolution, or an intrinsically double-peaked signal (e.g., Basri & Nguyen 2018).If a substantial peak (60% of the primary peak) is seen at double the period, we automatically choose this for our P rot measurement, as the code may be inadvertently folding the signal in half.If a longer harmonic is found at the pipeline P rot detection limit 19 days, we choose the shorter harmonic as the measured P rot .We also calculate the window function for each light curve following VanderPlas (2018).We discard any P rot and peak width that overlaps with the P rot returned from the primary peak of the window function, which is typically between 14 and 17 days.

Confirming P rot
Instrument systematics and spot evolution require that a candidate P rot be subject to a confirmation process.For a P rot in With TESS surveying the majority of the sky, it is necessary to develop an accurate confirmation that is at least partially automated, despite the systematics present.Automated machine-learning tools such as random forest classifiers and convolutional neural networks have been used to measure P rot in Kepler (e.g., Breton et al. 2021) and TESS data.These methods do not necessarily outperform non-machine-learning methods for nonconsecutive sectors of data at present (Claytor et al. 2022).
We develop a quasi-automated confirmation process that significantly reduces the number of stars that require by-eye inspection.This process results in three pipelines that employ varying levels of confirmation.We illustrate these pipelines in Figure 4 and outline the process below.Each subsequent pipeline includes the previous pipeline's steps, meaning that Pipeline III is the most comprehensive and thorough.Pipelines I and II are fully automated, while Pipeline III adds visual inspection in select cases.Before querying the star's light curve, we determine if the star is a candidate binary based on archival catalog information (see Section 3.3 for how this is done).If it is, we exclude the star from further analysis.If single, we check whether the star's light curve(s) displays significant periodicity by calculating two metrics for each periodogram.
First, we calculate the peak power over the median power, or S/N, of the periodogram.We show examples of a star with strong periodicity in two of three sectors (S/N > 40; Figure 3).
Second, we measure the peak width of the period detected as a diagnostic tool for P rot measurement quality within and across sectors.We use the width of the highest peak in the GLS periodogram (see fourth column of Figure 3), which we calculate by fitting a Gaussian.We discard any stars (I) that have a peak-width measurement of 25% of the candidate P rot or (II) for which the peak-width measurement has failed.If the fitting fails, this indicates that there was no peaklike feature to fit in the periodogram.This tends to happen at longer (and likely spurious) periods, where the periodogram feature is more plateau-like than peaklike.
If a star has at least one light curve with S/N 40 (see the determination of this value in Appendix A) and a peak-width measurement of <25% of the candidate P rot , we consider it a period detection for Pipeline I and continue to the next pipeline.Third column: phase-folded light curve with measured P rot .Fourth column: periodogram in frequency space with the primary peak fitted for width measurement (in black).This star has a strong S/N and small peak width in two of three sectors, which means its P rot is a Pipeline I detection that is automatically confirmed as part of Pipeline II and considered a Pipeline II/III detection.
The final P rot reported for Pipeline I is the median P rot if there are Pipeline I detections in multiple sectors for a star.If the star passes Pipeline I with at least one detection, we check whether the star has multiple sectors with Pipeline I detections.9If there are multiple sectors, we see if the P rot from each sector are within 2× the peak width including any 1/2× or 2× harmonics.This comparison is done by taking the median Pipeline I P rot detection and comparing each individual P rot measurement to the median.If there is an even number of detections, we choose the higher middle value as the median.If two-thirds of the detections match the median within the uncertainties we measured in Pipeline I, the star's median P rot is considered a Pipeline II detection and reported as the final P rot .If we find that a harmonic is present among the sectors, we report the longer P rot as the final P rot .
This form of automated confirmation is based on results from Rampalli et al. (2021) and Reinhold & Hekker (2020), who found that in spite of stellar spot evolution that occurs in stars observed with the K2 mission, it is expected that P rot can be recovered within 10%-20% across yearlong gaps between observations excluding harmonic effects.Because of the shorter observational baseline and systematics, longer TESS P rot (more than 10 days) may differ by more than 20% between sectors but still measure the same P rot .The peak-width measurement captures a similar level of uncertainty.

Pipeline III: By-eye Inspection for Stars that Did Not Pass
Pipeline II A star with a period detection from Pipeline I might not be confirmed by Pipeline II for two reasons.The first case is stars where only a single sector has a Pipeline I period detection.The second case is where there are multiple sectors with Pipeline I period detections but for which the periods do not agree.In these cases, the star is flagged for by-eye inspection in Pipeline III.To do a by-eye inspection for a star's candidate P rot , we check whether the modulation in either the light curve or the phase-folded light curve matches the measured P rot .We use the quality check system (Q) used in Rampalli et al. (2021).We assign Q = 0 for obvious detections, Q = 1 for questionable detections (usually when there are obvious modulations in the light curve but an unclear period due to systematics), Q = 2 for spurious periodicity from instrument systematics, and Q = 3 for cases where the light curve is entirely dominated by systematics.We show examples of each classification in Figure 5. Periods are considered visually confirmed for Q = 0 and 1 and discarded for Q = 3 and 4.
A star that passes either automated (i.e., Pipeline II detection) or by-eye (i.e., Pipeline III detection) inspection is considered a confirmed detection.

Candidate Binary and Subgiant Flagging
Gyrochronology is intended to be applied to single stars.Tight binary systems' rotational evolution can be significantly Starting with a star's light curve(s), we check whether it is a candidate binary using ancillary data and discard if so.Next, we check for periodicity in the periodograms and identify stars with strong periodicity (Pipeline I detections).A Pipeline II detection is one in which a star has multiple sectors that have Pipeline I detections, where the same P rot is measured.A Pipeline III detection includes Pipeline II detections plus any additional Pipeline I detections that pass a by-eye inspection.altered due to each body exerting tidal forces on the other (e.g., Meibom & Mathieu 2005;Zahn 2008).This can lead to a spinup or spin-down effect that deviates from the known single-star age-rotation relations.A companion can also contaminate the rotation we are attempting to measure from the source star.Additionally, whether or not stars are tidally interacting or even physically associated, TESS pixels are large and can contain multiple stars.These effects lead to incorrect placement on the color-period plane and imprecise age inference, so we remove binaries from our sample.
We also want to remove subgiants because, while they might have solar colors, they were likely warmer when on the main sequence and beyond the Kraft break (van Saders & Pinsonneault 2013).Thus, magnetic braking and gyrochronology may no longer apply despite the star having a rapid P rot .
We use high-precision Gaia astrometry, GALAH spectroscopy, and TESS photometry in formulating the following tests to identify binaries.

Gaia DR3 includes a number of additional catalogs
with non-single-star solutions (Gaia Collaboration 2022).This includes spectroscopic, photometric, and eclipsing binary observations.Solutions from the combinations of these observations are also provided in Eyer et al. (2023) and Halbwachs et al. (2023).We check whether our stars are listed in any of these catalogs, flag them as binaries, and discard them from future analyses.2. We examine the renormalized unit weight error (RUWE) measurement for each star.This is a goodness-of-fit measure of the single-star model fit to the source's astrometry.If a star has an RUWE of >1.4,there is a strong likelihood that it has a companion (e.g., Jorissen 2019; Belokurov et al. 2020).3. We check the GALAH DR3 catalog pre-main-sequence star/binary flag column.Although pre-main-sequence stars would be of interest given our goal of finding young The position of the detected period is indicated by the orange line.First row: Q = 0.There is a clear 9 day periodic modulation in the light curve and a strong, sharp peak in the periodogram (literature P rot : 8.7 days).Second row: Q = 1.There is evidence of modulation measured at 8.3 days in the light curve, but it is weak due to instrument systematics and the data gap (literature P rot : 7.3 days).Third row: Q = 2.The light curve shows evidence for a long-term periodic trend likely due to systematics, which the periodogram chooses as the period instead of the masked and potentially astrophysically real period at 0.16 days (literature P rot : 0.32 days).Fourth row: Q = 3. Systematics completely dominate the light-curve structure, and no astrophysical periodicity appears to be present (literature P rot : 0.43 days).
stars (despite gyrochronology not being applicable), it is more likely for the stars to be binaries.4. Each star in the TIC has a reported CR, or the ratio of flux from neighboring stars (F neighbor ) to that of the source (F source ; Stassun et al. 2019).We identify stars with a CR of >20% as visual binaries.This limit derives from the following procedure.Following Rampalli et al. (2019), the dilution (d) is equal to the contribution of F source to the total flux observed in the light curve (F total ): The CR is For a star with CR = 20%, we find using Equation (3) that d is 83% or, alternatively, that the neighboring star contributes 17% of the flux.When F source is constant and F neighbor is varying by 5% and contributes 17% of the flux, the total flux variation is 0.83 × 0 + 0.17 Failing any one of these tests is sufficient to be labeled a candidate binary or subgiant.
While we do apply these binary and subgiant cuts to stars with calculated actions, we do not apply these cuts to any of the clusters and MEarth groups when testing our pipelines, except the CR cut.This maximizes the number of stars on which we can validate our pipelines unless a star was unresolved in TESS.Whether or not a star is a binary or subgiant does not affect period detection.Rather, it is the P rot interpretation and subsequent gyrochronological age that is affected.

Training, Validation, and Testing with Literature P rot
In order to understand how well our P rot pipelines work, we divide the five literature P rot catalogs into training, validation, and testing data sets.We begin with the training sample and use the validation sample to initially test the pipelines.Based on the validation sample results, we go back and adjust on the training sample to improve performance.The testing data set is used postoptimization to report final numbers (no changes can be made to the pipeline after reviewing the results for the testing data).We have broken up the catalogs in the following manner.

Pipeline Results
We calculate six metrics for each sample for each pipeline's definition of a detection to assess pipeline performance.In our calculations of completeness and recovery, we use P rot = 13 days as the detection limit but do not impose this cut on our results, which occasionally include detections 13 days.
1. Recovery rate for all stars.How many of our TESS P rot measurements are within 2x the measured peak width of the literature P rot , considering only stars with literature P rot < 13 days?We also consider a P rot recovered if the P rot is within 2× the measured peak width of a harmonic (1/2, 2) of the reported literature.A P rot does not have to be considered a detection by our pipeline for the correct literature P rot to be accurately measured.2. Recovery rate for pipeline detections.How many of our TESS stars had P rot detections for the particular pipeline within 2x the measured peak width of the literature P rot given the detection limit of 13 days?We also consider a P rot recovered if the P rot is within 2x the measured peak width of a harmonic (1/2, 2) of the reported literature.3. True-positive rate.How many of our TESS stars had P rot detections when a detection was expected (i.e., the true P rot was within the reliable P rot detection limit for TESS, <13 days)?The detected P rot does not have to match the true P rot .4. True-negative rate.How many of our TESS stars had P rot nondetections when a nondetection was indeed expected (i.e., the true P rot was outside the reliable P rot detection limit for TESS, >13 days)? 5. False-positive rate.How many of our TESS stars had P rot detections when a detection was not expected (i.e., the true P rot was outside the reliable P rot detection limit for TESS, >13 days)?6. False-negative rate.How many of our TESS stars had P rot nondetections when a detection was expected (i.e., the true P rot was within the reliable P rot detection limit for TESS, <13 days)?
We report these values in Table 2 for all five groups in the three pipelines.The Pipeline II results have fewer stars than the other two pipelines, since it only considers stars with multiple sectors of data, as shown in Figure 4.While we have divided these groups up for the training and validation phases, we combine the data sets used for training and validation when reporting numbers, since they were all subjected to the same analyses.We repeat this analysis with the test set: 50% of the Pisces-Eridanus, 50% of the Praesepe, and 20% of the MEarth samples.The results are shown in Table B1 in Appendix B. The numbers are very similar to those in Table 2, with an average recovery rate of 92%, true-positive rate of 92%, and true-negative rate of 89%.For all five samples, the overall recovery rate is 90%.When considering the recovery of each pipeline's detections, the rates generally remain similar, except for the Pleiades and Praesepe, whose distances of 136 and 186 pc lead to magnitude limitations for TESS light curves (discussed further below).
True-positive rates across groups and pipelines never fall below 80%.The lowest true-negative rate is 76% for MEarth after running Pipeline I; this is not unexpected, since Pipeline I has the lowest number of confirmation tests.The true-negative rate increases to 87% and then 95% for MEarth with Pipelines II and III and thus subsequent confirmation checks.The Hyades has a similar true-negative rate of 77%.The higher falsepositive rate is because many Hyades have P rot just slightly >13 days.As can be seen in Figure 6, we identify a period for many of these stars at <13 days; these stars are then counted as false positives given our imposed detection limit of 13 days.
With Pipeline I, true-positive rates are strong (83%-100%).However, when looking at the associated recovery rates for detections, or how well Pipeline I does measuring the correct P rot for detections, we see that the accuracy is somewhat lower (79%-98%).The true-negative rates are quite strong as well, with the exception of MEarth and the Hyades sample, as discussed previously.
Pipeline II only considers stars with multiple sectors of data as a means of confirming P rot .This additional confirmation test generally increases true-negative rates, indicating that it is successful in identifying bad detections.
Pipeline III, our most rigorous pipeline, includes by-eye inspection.For the Pleiades, Pisces-Eridanus, Praesepe, the Hyades, and MEarth, by-eye inspection of stars with mismatching P rot in multiple sectors occurred for 0%, 6%, 10%, 16%, and 11% of the stars in the five respective groups.By-eye inspection is also invoked for single sectors, which occurred for 98%, 7%, 7%, 13%, and 42% of the samples, respectively.
For Pipeline III, the recovery rate for detections and truepositive rates decrease slightly across all groups compared to Pipeline I. Most P rot detections in Pipeline I are labeled true positives despite potentially having inaccurately measured P rot because there are no additional confirmation steps in this pipeline; any star's light curve with a significant peak in a periodogram is deemed a detection.Adding the by-eye inspection and/or comparison of P rot across sectors decreases false positives; the trade-off is that it can move stars originally classified as true positives in Pipeline I to false negatives in Pipelines II and III.True-negative rates increase from Pipeline I, especially for MEarth and the Hyades, indicating the importance of by-eye inspection.
The overall trend going from Pipeline I to II to III is for improved true-negative rates with only modest decreases in true-positive rates.This is strongest in the MEarth sample.Given our motivations to explore the ages of stars in higheccentricity orbits (e.g., mostly old field stars with some young interlopers), the MEarth sample is our closest proxy.Thus, going forward, we will choose Pipeline II or III, which best improve the chances of eliminating false positives.
We further investigate the reasons behind the statistics of our pipeline.We show our literature-versus-TESS P rot plots for the five groups in Figure 6 for Pipeline III.In comparison to the detections found at <13 days, very few detections are found for stars with longer periods (these are primarily in Praesepe and MEarth).In the case of Praesepe and the Hyades, we measure the half-period harmonics for a fair number of the longer rotators.
In Figure 7, we project these results into the literature P rot space.These extend to the length of a TESS sector, 27 days, to illustrate where our pipeline starts failing.For MEarth, we extend the histogram out to 100 days in log space.We highlight in gray the reliable P rot detection range.We show the TESS magnitude distributions in Figure 8, highlighting in gray the TESS-SPOC magnitude regime.The targets for our period search-young G dwarfs-are generally expected to fall within the gray regions.The near-perfect recovery of Pisces-Eridanus is expected, since both use TESS data.However, the method of light-curve extraction and confirmation by Curtis et al. differs from ours, yet we measure the same P rot .This validates the automated aspects of our pipeline, since all of the P rot measured in Curtis et al. (2019b) were visually inspected, in contrast to our pipelines.
Figure 8 demonstrates that the lower period recovery rates for detections in the Pleiades and Praesepe is due to their distances.Because Praesepe has rotators beyond the 13 day limit, most of which are also faint, this further contributes to the failure to recover P rot .Less than 60% of the P rot are recovered beyond 12 days (Figure 7).The rotators beyond 13 days are Note.Percentage recovered indicates whether 1×, 2×, or 1/2× the literature P rot was recovered with each pipeline within 2× the peak width and within the reliable P rot detection limit (13 days).Percentage of detections recovered indicates whether 1×, 2×, or 1/2× the literature P rot was recovered with each pipeline for a detection within 2× the peak width and within the reliable P rot detection limit (13 days).True positive indicates a detection within the reliable P rot detection limit.
True negative indicates a nondetection outside of the reliable P rot detection limit.False positive indicates a detection outside of the the reliable P rot detection limit.
False negative indicates a nondetection within the reliable P rot detection limit.The Pleiades and Pisces-Eridanus do not have true-negative and false-positive columns, since two stars have P rot > 13 days.Pipeline II only considers stars with multiple sectors.
mostly nondetections despite the true P rot being recovered in some cases (Figure 6).This is in contrast to the Hyades, which is close by.In the Hyades, rotators beyond 13 days are mostly detected with the true P rot recovered.The recovery rate decreases by 29% from 11 to 13 days, with the sharpest drop in recovery (60%) at 15 days.The MEarth sample has a drop to <50% recovery in the same 10-15 day range.Figures 7 and  8 illustrate the motivation for our 13 day limit (see also Appendix A).
5. Testing Pipeline II on Stars in High-eccentricity Orbits

Pipeline Performance
Given the promising results from our pipelines, we remove binaries and query TESS light curves for the vertical (8834 stars) and horizontal (3952 stars) slices of action space shown in Figure 2.After applying Pipeline II to the 2887 and 1198 likely single stars with TESS-SPOC PDC-SAP light curves for multiple sectors, we are left with 302 and 60 rotators, respectively.The difference in the number of rotators found in each slice is expected, as there are more stars in the vertical slice.This region also samples a relatively lower radial action space, where young stars are more likely to populate.
We do an additional visual inspection following the quality flag guidelines outlined in Figure 5 and keep stars with Q = 0 and 1. Postinspection, we are left with 127 rotators out of 302 stars in the vertical slice, 17 rotators out of 60 stars in the horizontal slice, and three stars overlapping.This suggests a false-positive rate of ≈60%-70% and is significantly higher than the false-positive rates in the MEarth sample, which most resembles this sample of mostly field stars.We attribute this to the fact that 40% of the stars in MEarth only had one sector of data and were therefore immediately flagged for by-eye inspection, increasing the true-negative rates.While this implies that Pipeline II can be improved in the automatic vetting of multisector stars, Pipeline II has significantly reduced the number of stars normally needing by-eye inspection (from 4085 to 359).

Rotator Distribution in Color Space
We show the rotator distribution (filled stars are from the horizontal slice, open stars are from the vertical) in color-P rot space in Figure 9 with the benchmark clusters' P rot for reference.We correct the Gaia colors for extinction, which is minimal given the proximity of the stars.We determine the A v from the calculated reddening in the Gaia bandpasses using Bayestar19 (Green et al. 2019).The rotation periods detected correspond to periods typical for Pleiades-age (120 Myr) single stars to beyond the age of NGC 6811 (1 Gyr).
While we have removed binaries, there is likely still binary contamination in our sample.The P rot work with Kepler and K2 has shown that rapid rotators with P rot 2 days largely tend to be binary stars undergoing tidal interactions (Douglas et al.   2016; Simonian et al. 2019).Following Kounkel et al. (2022), we flag stars with P rot < 2 days, and we consider the most robust region for gyrochronology to be 2 days < P rot < 13 days.While there are young G dwarfs (11%-20% for 87-120 Myr) that can have <2 day periods and be misclassified as binaries, this makes up a very small portion of the entire sample (Rebull et al. 2018;Boyle & Bouma 2023).This is also on the same timescale of convergence onto the main sequence, where gyrochronology may not yet be applicable (Bouma et al. 2023).Recall that 13 days was chosen as the upper limit to account for TESS's short observational baseline to minimize misclassifying its orbital period systematics as astrophysical periodicity and based on injection and recovery tests (Appendix A).These limits are shown as dashed horizontal lines in Figure 9.We demarcate the G dwarf regime with dashed vertical lines, where gyrochronology will work the best, since age-rotation relations are best calibrated for G dwarfs.There are 30 G dwarfs within these period and color limits that have P rot Pipeline II detections.Stars outside of this period and temperature regime may still be useful for indicating youth.For example, K dwarfs with P rot where spin-down has stalled still indicate youth, as do stars that have not yet converged to a gyrochronology track.
Though rapid rotation suggests youth, it is not a definitive indicator.We will obtain preexisting or new spectra to provide an additional check for youth with abundance and/or activity measurements.One such elemental abundance is lithium, [Li/ Fe].Lithium is one of the most sensitive elements and burns at fairly low temperatures within a star.As a low-mass star ages, its measured [Li/Fe] ratio decreases due to the burning (Sestito & Randich 2005).Using spectra from groups of coeval stars of known ages, empirical Li-age relations have been derived (Stanford-Moore et al. 2020; Jeffries et al. 2023) and used to confirm stellar ages in combination with gyrochronology (e.g., Tofflemire et al. 2021;Newton et al. 2022).
Using our kinematics catalog, we do a preliminary investigation of [Li/Fe] abundance measurements that may exist for rotators.Only 15/141 unique stars had GALAH spectra.Five of the 15 had reported Li abundances, and all were [Li/Fe] −0.25 dex, indicating that they are on the order of several gigayears old (Carlos et al. 2016).This strongly motivates the need for additional confirmations of youth and binary screening in our future work.

Rotator Distribution in Action Space
While some rotators in this sample will be identified as interloping old stars, we have found stars with rotation indicative of youth in highly eccentric orbits, as indicated by their radial actions.We show the distribution of rotators in action space in the left panel of Figures 10 and 11 color-coded by the stars' P rot , as well as the benchmark clusters plotted for reference.In the right panel of Figures 10 and 11, we show the percent fraction of rotators found in binned values of radial action (vertical slice) and angular momentum (horizontal slice) with error bars.These bins are indicated by dashed lines in the left panel insets.We do not make the cuts on P rot or color delineated in Figures 9, as we are not inferring ages for these stars just yet and are interested in examining the full rotator distribution.
In the horizontal slice, the distribution of rotators is flat considering the errors.Visually, there is a peak at L J 1600, 11 z R ~» , which corresponds to part of one of the many overdensities in action space that we call wrinkles (discussed in Section 1.2).In the right panel of Figure 11, we see a significant peak at J 6 R ~.This is an exciting region dynamically, which we will explore in depth in later papers in this series.There are older associations, like Ruprecht 147 (2.7 Gyr), whose stars could be in these orbits.This indicates that some of the rotators we have identified could be from older associations such as these.However, we also note the presence of >10 rotators that follow the Pleiades-like color-P rot distribution in Figure 9, which is unexpected this high in radial action space.This general region also includes part of a wrinkle as well.

Conclusions and Future Directions
The combination of the Gaia and TESS data offers an unprecedented opportunity to understand the dynamical history of the Milky Way using stellar ages with gyrochronology and kinematics.We build a series of TESS P rot measurement and confirmation pipelines that we test on 1560 stars with literature P rot from five groups: the Pleiades, Pisces-Eridanus, Praesepe, the Hyades, and the MEarth sample.On average, we find a recovery rate of 88%, a true-positive rate of 91%, and a truenegative rate of 89%.We find that our pipelines predominantly fail when stars are distant and thus faint like the cooler members of the Pleiades (136 pc) and Praesepe (186 pc).
Given the promising P rot pipeline results (Table 2), we apply our Pipeline II to a vertical and horizontal slice in Galactic action space, which we calculate using kinematics from Gaia DR3 and radial velocities from GALAH and APOGEE, when possible (Figure 2).Each slice contains one to two overdensities of stars in highly eccentric orbits identified by Trick et al. (2019), which we call wrinkles.We find 141 unique rotators out of the 12,786 in these selected regions.Five stars have GALAH [Li/Fe] measurements that indicate that they are interloping, several-gigayear-old stars (beyond the age where gyrochronology is applicable).When looking at the other rotators' Gaia color-P rot distributions, we see the rotation periods point to ages between 120 Myr and 1 Gyr old (Figure 9).What is especially interesting is the rotator distribution at L z ≈ 1675 and J 6 R » .This could be an area where older, ≈1 Gyr associations live but perhaps also 120 Myr stars that could have been dynamically heated to these eccentric orbits.
The identification of a rapid P rot < 13 days for stars in highly eccentric orbits motivates our future studies.We will apply our rotation pipelines to all of the stars at highly eccentric orbits (  J 6

R
).Once the P rot are measured, we will age-date these stars using gyrochronology relations and confirm or refute their youth with spectroscopic observations.The confirmation of  young stars at high radial actions will, in turn, allow us to understand the dynamics that caused their orbits to become highly eccentric.injection-recovery test, the S/N of signals that are not recovered drops off beyond S/N = 20, but not as steeply.Imposing an S/N limit at 20 results in a false-negative rate of 5%, but the trade-off is a high false-positive rate of 40%.This increases the burden of by-eye inspection by 2-3×.Therefore, we choose an S/N limit of 40, which has a more even trade-off, with a false-positive rate of 25% and a false-negative rate of 10%.We can also see at S/N ≈ 20 in the top panel of Figure 3 that the periodicity is just barely, if at all, visible by eye compared to the bottom two panels with S/N > 40.
As with the simulated signals, the maximum period at which we recover >50% of the periods in the sample measurement is <15 days.We recover 61% of the signals at 13 days (compared to 70% in the injected samples), 54% at 14 days, and 44% at 15 days.Because of these large decreases in the recovery rates at longer periods in both the injection-recovery and benchmark population results, we set 13 days as the maximum period at which we can reliably recover periods.This is also a practical value to choose, as it is half the sector length of 27 days and corresponds to the 13.7 day orbital period of TESS.Note.Percentage recovered indicates whether 1, 2, or 1/2 times the literature P rot was recovered with each pipeline within both 2x the peak width and the reliable P rot detection limit (13 days).Percentage of detections recovered indicates whether 1, 2, or 1/2 times the literature P rot was recovered with each pipeline for a detection within both 2x the peak width and the reliable P rot detection limit (13 days).True positive indicates a detection within the reliable P rot detection limit.True negative indicates a nondetection outside of the reliable P rot detection limit.False positive indicates a detection outside of the reliable P rot detection limit.False negative indicates a nondetection within the reliable P rot detection limit.The Pleiades and Pisces-Eridanus do not have true-negative and false-positive columns, since two stars have P rot > 13 days.Pipeline II only considers stars with multiple sectors.

Figure 1 .
Figure1.The figure shows L z vs. J R using updated kinematics from Gaia DR3, GALAH DR3, and APOGEE DR16.A larger L z is associated with a larger orbital size in the solar neighborhood, and a larger J R is associated with a more eccentric orbit.

Figure 2 .
Figure2.Updated action plot as shown in Figure1and described in Section 1.2 with the Pleiades (pink), Pisces-Eridanus (orange), Praesepe (blue), Hyades (green), and Ruprecht 147 (red) overplotted.Vertical and horizontal slices chosen for P rot study are noted in black.As the clusters increase in age, so do their radial actions, motivating our choice for studying P rot and finding young stars at high J R .
3.2.1.Pipeline I: Two Metrics Required to Be Considered a Period Detection, No By-eye Inspection Required

Figure 3 .
Figure 3. Example of the measurement and confirmation process for a star observed in sectors 42 (top row), 43 (middle row), and 44 (bottom row) that is detected in Pipelines I, II, and III.First column: star's light curve for the sector.Second column: GLS periodogram with measured P rot associated with highest peak indicated in yellow, median power indicated in green, and calculated S/N of the highest peak.The S/Ns of the three sectors (21, 52, and 61) span our detection threshold of 40.Third column: phase-folded light curve with measured P rot .Fourth column: periodogram in frequency space with the primary peak fitted for width measurement (in black).This star has a strong S/N and small peak width in two of three sectors, which means its P rot is a Pipeline I detection that is automatically confirmed as part of Pipeline II and considered a Pipeline II/III detection.

Figure 4 .
Figure4.Flowchart of the P rot pipelines.Starting with a star's light curve(s), we check whether it is a candidate binary using ancillary data and discard if so.Next, we check for periodicity in the periodograms and identify stars with strong periodicity (Pipeline I detections).A Pipeline II detection is one in which a star has multiple sectors that have Pipeline I detections, where the same P rot is measured.A Pipeline III detection includes Pipeline II detections plus any additional Pipeline I detections that pass a by-eye inspection.

Figure 5 .
Figure 5. Examples of quality flag designations.Light curves are on the left, the corresponding periodogram in the middle, and phase-folded light curves on the right.The position of the detected period is indicated by the orange line.First row: Q = 0.There is a clear 9 day periodic modulation in the light curve and a strong, sharp peak in the periodogram (literature P rot : 8.7 days).Second row: Q = 1.There is evidence of modulation measured at 8.3 days in the light curve, but it is weak due to instrument systematics and the data gap (literature P rot : 7.3 days).Third row: Q = 2.The light curve shows evidence for a long-term periodic trend likely due to systematics, which the periodogram chooses as the period instead of the masked and potentially astrophysically real period at 0.16 days (literature P rot : 0.32 days).Fourth row: Q = 3. Systematics completely dominate the light-curve structure, and no astrophysical periodicity appears to be present (literature P rot : 0.43 days).
× 0.05 = 0.0084.A flux variation of around 0.84% has a 66% chance of detection with our pipelines (see bottom right panels in Figure A2 in Appendix A). 5. Subgiants and equal-mass binaries can also pose as single-star interlopers.They are overluminous and sit above the single-star main sequence in a color-magnitude diagram.Following Douglas et al. (2019) and Rampalli et al. (2021), we fit a sixth-order polynomial to the Gaia color, G BP − G RP , and absolute G magnitude, M g , colormagnitude diagram for the single-star rotator sequence in Praesepe.Stars that lie >0.4 mag above this fit are flagged as binary or evolved stars.

Figure 6 .
Figure 6.Literature vs. TESS P rot for Pipeline III for Pleiades (pink), Pisces-Eridanus (orange), Praesepe (blue), Hyades (green), and MEarth (purple).Pipeline III detections considered recovered are noted with black circles, and the detection limit is noted at 13 days with a vertical dashed line.

Figure 7 .
Figure 7. Literature P rot distributions for Pipeline III detections for Pleiades (pink), Pisces-Eridanus (orange), Praesepe (blue), Hyades (green), and MEarth (purple).The recovered P rot is noted by a dashed black line, and gray shaded regions indicate what we expect to detect with TESS (13 days).

Figure 9 .
Figure 9. Color-P rot distribution of likely single rotators for horizontal (filled stars) and vertical (open stars) sections of action space with benchmark clusters plotted for reference (120 Myr old Pleiades in pink, 670 Myr old Praesepe in blue, 1 Gyr old NGC 6811 in yellow, and 2.7 Gyr old Ruprecht 147 in red).The most robust region for gyrochronology (G dwarfs with reliable P rot measurements) is highlighted by the white region.

Figure 10 .
Figure 10.Left: rotator distribution in the slice of action space with benchmark clusters overplotted as shown in Figure 2. Bins from the right panel are indicated by dashed vertical lines in the inset.Right: fraction of rotators vs. all stars found in bins of angular momentum in the z-direction.

Figure 11 .
Figure 11.Left: rotator distribution in the vertical slice of action space with benchmark clusters overplotted as shown in Figure 2. Bins from the right panel are indicated by dashed horizontal lines in the inset.Right: fraction of rotators vs. all stars found in bins of the square root of radial action.

Figure A1 .
Figure A1.Distribution of recovered stars with an injected P rot as a function of S/N (top left), input P rot (top right), magnitude (bottom left), and amplitude (bottom right) in red.The distribution of stars not recovered in S/N are shown with the blue dashed line.The distribution of the entire sample of stars used in the injection analysis are shown with the black dashed line in input prot, magntidue, and amplitude.

Table 1
Literature P rot Catalogs Tested with Our P rot Pipeline

Table 2 P
rot Pipeline versus Literature P rot Catalog Results