Rotation of Low-mass Stars in Taurus with K2

Stars in the Taurus Molecular Cloud were observed in two different K2 campaigns, Campaign 4 (C4; 2015 February 7–2015 April 24) and Campaign 13 (C13; 2017 March 8–2017 May 27), with the majority of Taurus members coming from C13; see Figure 1. As in our earlier papers, we start by considering all possible cluster members and then narrow the sample to high-confidence and lower-confidence members (see Section 2.2); results for the likely NMs are listed in the Appendix for reference. There are ∼850 candidate Taurus members with K2 LCs from either campaign and a few with K2 data from both campaigns (see Table 1). All of the LCs used here were observed in the long-cadence (∼30 minutes cadence) mode.

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Our analysis (see Section 2.2 below) focused on the 156 highest-quality Taurus members, 23 possible members, and 38 foreground objects that are young (but likely older than the Taurus molecular cloud population). Figure 1 shows the distribution of these objects with K2 LCs on the sky, in context with other reference points. The area defined as encompassing "Taurus" by, e.g., Esplin & Luhman (2019) goes further north (and east) than the K2 region, such that the K2 observations cover about 30% of the members from Esplin & Luhman (2019). Assuming that there should be no spatial dependence of stellar rotation rate on location in the cluster, there should be no bias in our distribution of periods resulting from the incomplete coverage of the cluster. However, specifically because the K2 region extends over a larger area to the south and west, it encompasses a larger area than has been studied most intensively for potential Taurus members, and enables LC collection from a more dispersed population of candidate young stars.

There are very few stars considered to be Taurus members of any confidence level that have LCs in both the C4 and C13 campaigns. Of these, just two are in the set of possible Taurus members (EPIC 210689309 = AG+18339; EPIC 210689130 = HD 28150), and one is in the foreground population (210662824 = HD 285778). All three of these are periodic in both campaigns. There are an additional 10 field stars with two sets of LCs, and four of them have periods in both campaigns. For all stars in common between C4 and C13 (whether or not they are members), the periods derived separately from both campaigns are the same within ∼4% accuracy, suggesting that the effective astrophysical uncertainty on the periods is likely very low, at least for stars without disks.

Our analysis follows the same approach discussed in our earlier papers (Papers I–V) and is briefly summarized here. For each target, we selected the best (see Paper I) LC from several different available LC versions: (1) the pre-search data conditioning (PDC) version generated by the Kepler project⁷ and obtained from the Mikulski Archive for Space Telescopes (MAST); (2) a version using custom software developed by co-author A.M.C.; (3) the "self-flat-fielding" approach used by Vanderburg & Johnson (2014) and the K2SFF pipeline as obtained from MAST; (4) the LCs from the EVEREST2 pipeline (Luger et al. 2016, 2018), which uses pixel-level decorrelation, as obtained from MAST; and (5) the EVEREST2 pipeline LCs, where large-scale structure is removed via a least-squares (Savitzky–Golay) polynomial smoothing filter (e.g., Press et al. 1992), as implemented in the IDLastro library.⁸ We removed any data points corresponding to thruster firings and any others with bad data flags set in the corresponding data product. Any periodic signals are generally unambiguous and are generally detected in all of the LC versions. The spacecraft slowly drifts and then repositions regularly every 0.245 day, so we particularly scrutinized any detected periods near 0.245 day.

K2 has a relatively large pixel size (398 × 398). To identify sources subject to confusion, we inspected the region around each target with the Finder Chart tool⁹ from NASA's Infrared Science Archive (IRSA). We also incorporated the diagnostic information provided by the various K2 data reduction pipelines. For those targets where source confusion is a concern, we either took the existing LC most likely to be centered on the target given the diagnostic information provided by the corresponding pipelines or re-reduced the data using the Cody approach but with a small, fixed aperture.

We omitted two of the highest-quality members (see Section 2.2): EPICs 247031436 (HD 28867B; confused with nearby sources) and EPIC 247989931 (2MASS J04412464+2543530; too faint). For completeness, we note that EPIC 211068851 (HD 26212) is too bright and EPIC 210893410 is too faint, but both are also unlikely to be Taurus or foreground members.

There are a few targets that are either erroneously listed as distinct targets in the EPIC catalog or could be a faint source next to a brighter source; in either case, a good LC cannot be obtained. HL Tau (EPIC 210690913) and XZ Tau AB (EPIC 210690892) are high-quality members and close together in the sky, though resolvable; the XZ Tau binary itself is not resolved. An additional target is listed as EPIC 210690886, but it is too faint and/or close to XZ Tau to measure independently. Given its location, position matching with literature data (see Section 2.3 below) accidentally picks up several matches that should have been matched to XZ Tau AB. As a result, EPIC 210690886 is explicitly removed from our database as effectively a duplicate. DR Tau (EPIC 246923113) is also a high-quality member. EPIC 246923117 is 022 away from DR Tau and is explicitly removed as effectively a duplicate. EPIC 246926943 is a real though optically faint target near a brighter source. The LC is not easily distinguishable from that of its bright neighbor. This target is listed as an NM as a result.

2.2.1. Summary

The details of our membership selection process are given in Appendix A. To summarize, we have selected 156 of the "highest-confidence" Taurus members, 23 "possible" Taurus members, and 38 stars that constitute an older (∼30 Myr) "foreground" population. The highest-confidence members are those objects listed as Taurus members in Esplin & Luhman (2019). The possible members are additional objects selected individually by us from the available literature and Gaia DR2 kinematic data as Taurus members; these are generally more dispersed than the highest-confidence members. The ∼30 Myr foreground population includes (but is not limited to) members of Group 29 (Oh et al. 2018; Luhman 2018); some stars might potentially belong to Mu Tau (M. Gagne et al. 2020, in preparation; Liu et al. 2020) or possibly Cas-Tau (e.g., Hartmann et al. 1991; de Zeeuw et al. 1999; Luhman 2018; also see the appendix of David et al. 2018 and references therein).

Membership status is used in Table 1 for the sample breakdown and is included in Table 2. The highest-confidence sample is listed as distinct from the possible member sample. The highest-confidence and possible member samples are combined into one sample listed as the ∼3 Myr member sample. The foreground population is a distinct sample with different kinematics and mean distance, and it is likely significantly older than the Taurus population. For completeness, Table 1 also includes the NM sample. Appendix A.2 lists individually the information on stars in the probable NMs.

Table 2.  Contents of Table: Periods and Supporting Data for Taurus Members with K2 Light Curves

Number	Column	Contents
1	EPIC	Number in the Ecliptic Plane Input Catalog (EPIC) for K2
2	Coord	R.A. and decl. (J2000) for target
3	OName	Alternate name for target
4	Gaia	Gaia DR2 ID
5	V mag	V magnitude (in Vega mags), if observed
6	Ks mag	magnitude (in Vega mags), if observed
7	(V − Ks)o	, as directly observed (in Vega mags), if V and exist
8	(V − Ks)u	used, in Vega mags (observed or inferred; see the text)
9	E(V − Ks)	E(V − Ks) adopted for this star (in mags; see Section 2.5)
10	Ks mag0	dereddened Ks,0 magnitude (in Vega mags), as inferred (see Section 2.5)
11	(V − Ks)0	, dereddened (in Vega mags), as inferred (see Section 2.5; rounded to nearest 0.1 to emphasize the relatively low accuracy)
12	Uncert	two-digit code denoting origin of and  (see Sections 2.3 and 2.5): First digit (origin of ): 1 = V measured directly from the literature (including SIMBAD) and Ks from 2MASS; 2 = V from APASS and Ks from 2MASS; 3 =  inferred from Gaia g and Ks from 2MASS (see Section 2.3); 4 =  inferred from Pan-STARRS1 g and Ks from 2MASS (see Section 2.3); 5 =  inferred from membership work (see Section 2.2; rare); 6 = V inferred from well-populated optical SED and Ks from 2MASS (see Section 2.3); −9 = no measure of . Second digit (origin of leading to ): 1 = dereddening from JHKs diagram (see Section 2.5); 2 = dereddening back to expected for spectral type; 3 = used median E(V − Ks) = 0.7 (see Section 2.5); −9 = no measure of E(V − Ks)
13	P1	Primary period, in days (taken to be rotation period in cases where there is >1 period)
14	P2	Secondary period, in days
15	P3	Tertiary period, in days
16	P4	Quaternary period, in days
17	Member	Highest-quality member, possible member, foreground young star (see Section 2.2)
18	IR excess	Whether an IR excess is present or not (see Section 4)
19	IRexStr	Minimum wavelength at which the IR excess is detected or the limit of our knowledge of where there is no excess (see Section 4)
20	Slope	Slope of SED fit to all available detections between 2 and 25 μm
21	Class	SED class (I, flat, II, III)
22	Dip	LC matches dipper characteristics (see Section 6.2)
23	Burst	LC matches burster characteristics (see Section 6.2)
24	Sin/mult	single- or multi-period star
25	dd	LC and power spectrum matches double-dip characteristics (see Section 6.2)
26	ddmove	LC and power spectrum matches moving double-dip characteristics (see Section 6.2)
27	Shape	LC matches shape changer characteristics (see Section 6.2)
28	Beat	LC has beating visible (see Section 6.2)
29	Complex	power spectrum has a complex, structured peak and/or has a wide peak (see Section 6.2)
30	Closep	power spectrum has resolved close peaks (see Section 6.2)
31	Distp	power spectrum has resolved distant peaks (see Section 6.2)
32	Pulse	power spectrum and LC match pulsator characteristics (see Section 6.2)

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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Unless explicitly indicated, the subsequent analysis in this paper uses the 156 most confident members (typically colored green in the figures) plus the 23 possible members (typically colored yellow-orange in the figures) as the member sample. The 38 stars in the foreground older population are colored blue in the figures.

2.2.2. Sample Statistics

The literature on stars in (or around or near) Taurus is rich indeed. Aiming for uniform consistency rather than completeness, rather than scouring the literature for individual photometric measurements, we assembled information on each target from several all-sky or large-scale surveys. We matched by position to each catalog with typical matched positions within an arcsecond.

The optical data came from several catalogs. We searched in Gaia DR1 (Gaia Collaboration et al. 2016) for the G magnitude consistent with our prior analyses, and DR2 (Gaia Collaboration et al. 2018) for the more recent G, R_p, and B_p photometry, in addition to parallaxes and proper motions. The kinematic data provided by Gaia DR2 are particularly useful in identifying members (Section 2.2 includes the Gaia DR2 ID; see Table 1 for fractions of samples with Gaia parallaxes). The distances we used here are those provided by Bailer-Jones et al. (2018). Additional optical data were obtained from the AAVSO Photometric All-Sky Survey (APASS; Henden et al. 2016), specifically, V magnitudes. We used both Pan-STARRS1 (Chambers et al. 2016) and the Sloan Digital Sky Survey (e.g., Ahn et al. 2012) for multiband optical data. Every star here has several optical measurements.

We used infrared data from three all-sky surveys: the Two-Micron All Sky Survey (2MASS; Skrutskie et al. 2006) at J, H, and K_s; the Widefield Infrared Survey Explorer (WISE; Wright et al. 2010) at 3.5, 4.6, 12, and 22 μm; and AKARI (Murakami et al. 2007) data at 9, 18, 65, 90, 140, and 160 μm. WISE and AKARI have some similar wavelengths, but they have very different sensitivities. We also used infrared data from two pointed missions (as opposed to all-sky surveys). For the Spitzer Space Telescope (Werner et al. 2004), we started with data from the Spitzer Enhanced Imaging Products (SEIP)¹⁰ at 3.6, 4.5, 5.8, 8, and 24 μm, which aggregates all data from the cryogenic portion of the Spitzer mission. The SEIP only includes objects with high signal-to-noise ratio detections; when flux densities did not appear in the SEIP for our targets, we used catalog data from the Spitzer Taurus project (Rebull et al. 2010) for any bands between 3.6 and 70 μm (note that 70 μm was not included in the SEIP, so all 70 μm data come from the Spitzer Taurus project). Most of the members have a Spitzer counterpart; a relatively low fraction of the NMs have a Spitzer counterpart (see Table 1). Relatively few stars in the sample have a Spitzer/MIPS counterpart at 24 or 70 μm. Herschel data cover a portion of the Taurus region. Analogous to the SEIP, the Herschel Space Observatory (Pilbratt et al. 2010) Highly Processed Data Products for PACS 70, 100, and 160 μm (Marton et al. 2017) incorporate all of the data from the mission. Very few targets have a PACS counterpart, but a higher fraction of the members are detected (a rate that is biased by the observations that targeted known members). K2 generally monitored optically bright stars, thereby selecting against embedded stars bright in the mid- and far-infrared.

In general, there is a steep drop off in counterpart numbers as wavelength increases. Table 1 includes the numbers and fractions of stars in several membership categories (Section 2.2) for several representative infrared bands. However, the fraction of Taurus member stars (not foreground, not NM) that are detected out to long wavelengths is much higher than the fraction of NM stars, as expected—Taurus member stars are more likely to have an IR excess and, thus, be detected in these various infrared data sets.

We used all of these photometric data to assemble a spectral energy distribution (SED) for each target. If the data from one catalog were obviously inconsistent with the rest of the SED, then we removed the data points from that catalog for that source on the assumption that the positional match failed. We also used the IRSA Finder Chart tool (as well as its sister tool, IRSA Viewer) to investigate source mismatches.

Our earlier papers use as a proxy for mass, so to better enable inter-cluster comparisons, we continue to do that here. All of the stars have measured , leaving us to find or calculate V. A substantial fraction of the targets have measured V magnitudes that we could assemble from the literature above, but several stars still lack V measurements. If a Gaia G magnitude is available (from DR1), then (V − K_s) was interpolated from (G − K_s) as in Paper IV (which used DR1 Gaia data to establish this relationship); we estimate errors on these estimates to be ∼0.017–0.085 mag. For stars redder than (V − K_s) ∼ 5, the relation from Paper IV is linearly extrapolated to (V − K_s) ∼ 8. Similarly, if no Gaia G mag is available, but a Pan-STARRS1 g is available, then (V − K_s) can be calibrated via an empirical relation between (g − K_s) and ; errors on these estimates are probably comparable to those from Gaia-derived colors. As a last resort, for those stars still missing a V estimate, since the SED is well populated in the optical using literature photometry, a V magnitude is linearly interpolated from the SED. All of the targets thus have a measured or inferred .

Table 2 includes, for the most likely members, possible members, and foreground population (identified in Section 2.2), the relevant supporting photometric data, including the observed or interpolated , plus the periods we derive (in Section 3.1) and the IR excess assessments (Section 2.4). A similar table with all of the likely NMs appears in Appendix A.2.

Most of the Taurus members have spectral types in the literature (Table 1). We assembled spectral types largely from Luhman et al. (2017), Luhman (2018), and Esplin & Luhman (2017, 2019). Some individual sources have spectral types not collected in these papers, and we assigned those spectral types individually based on the literature.

For those stars with spectral types, we used the spectral types as part of the process for identifying disks (see Section 2.4) and determining the best value of reddening (see Section 2.5). For those stars with spectral types, we used a Kurucz–Lejeune (Kurucz 1993; Lejeune et al. 1997) model corresponding to that spectral type and normalized to the data at the J band. We extended a Rayleigh–Jeans line from the longest wavelength model data point to beyond 24 μm. Using the reddening law from Mathis (1990), we reddened the models for a grid of A_J values, calculated a reduced chi-sq () comparing the model to the data at all optical bands (U, if available) through J. We selected the best fit based on the smallest . These model fits to the SED are not meant to be rigorous but to instead "guide the eye."

A substantial fraction of the Taurus members have an IR excess, from which we can infer the presence of a circumstellar disk (see summary statistics in Table 1). In the context of this paper (as for Paper V), we wish to have a complete list of disks, as opposed to an unbiased list; we identify a star as a disk candidate if it has a plausibly real excess at any IR wavelength (at which we have a detection) in the catalog we assembled. The wavelength at which the IR excess begins is included in Table 2 (and in the Appendix in Table B1 for the NMs).

Because WISE has a lower spatial resolution than Spitzer, we used IRSA's Finder Chart tool to inspect the WISE images to see if the detections in the catalog reflect what can be seen in the images. Again following Paper V, to identify disks, we looked at the significance of any putative IR excess at 12, 22, and 24 μm where available (with χ calculated as described in Paper V), taking into account that for the latest types, the expected photospheric colors may be >0. We used the empirical photospheric infrared color [W1]–[W3] as a function of from Paper V. We then assessed the ensemble of information available for all sources (e.g., all points ≥2 μm, the shape of SED, the results of the simple model fit discussed in Section 2.3 above, etc.). For each source, we have an assessment of whether it has a disk, and if so, the shortest wavelength likely contributing to an IR excess.

In this fashion, as for Paper V, we identified unambiguous disk candidates and non-disk candidates (at least, non-disks given the available data, which often extend at least to 12 or 22 μm), with a few percent of ambiguous (possible) disks noted as such. Table 1 includes the number and sample fraction for each of the relevant samples. More than half of the Taurus members have disks; there is just one high-confidence (and one more possible) disk candidate among the foreground (∼30 Myr) population. Note that the disk excess criteria are conservative and that the non-disked sample will likely have contamination from weaker (<5–10σ excess) disks. Note also that the lowest-mass bin is likely incomplete in the non-disks due to sensitivity issues (stars with excesses are more likely to be detected at long wavelengths than stars without excesses). While this sample draws from many surveys and wavelengths, in order to be considered at all, there must be an observation in K2, which requires targeting of the source by a human, and therefore, the sample is affected not only by extinction but pixel mask selection.

Independent of the disk candidate status, we performed a simple ordinary least-squares linear fit to all available photometry (with errors, but just detections, not including upper or lower limits) between 2 and 24 μm, inclusive. In the spirit of Wilking et al. (2001), we define , where α > 0.3 for a Class I, 0.3 to −0.3 for a flat-spectrum source, −0.3 to −1.6 for a Class II, and <−1.6 for a Class III. The slope and the class are both available in Table 2 (and Table B1, where it is assumed that the IR excess is due to a circumstellar disk, which may not be a good assumption).

For completeness, we note two items. First, Table 1 indicates that there are NM with IR excesses. These objects include evolved stars with dusty winds or envelopes, distant Be stars, and a few extragalactic objects (active galactic nuclei, quasi-stellar objects). Second, Tables 2 and B1 indicate the onset of IR excess for each target. Since the IR excess could affect the bands, which could cause an overestimation of A_V in the methods described below, we note that such targets are a minority here; >80% of the highest-quality members have disks that start at longer than 3 μm.

The reddening in the direction of Taurus can be substantial and patchy. As noted above, we obtained spectral types from the literature. In order to deredden the colors, we followed the same approach as in Paper V (specifically for ρ Oph), with some modifications.

We can place essentially all of the stars on a J − H versus diagram. We can deproject much of the sample back along the reddening law derived by Indebetouw et al. (2005) to the expected JHK_s colors for young stars from Pecaut & Mamajek (2013) or the T Tauri locus from Meyer et al. (1997). Note that there is a discontinuity between the end of the Pecaut & Mamajek relation and the beginning of the T Tauri locus (noted in Meyer et al. 1997 and Paper V); this results in a small gap in the dereddened distribution between ∼0.9 and ∼1.0. The reddening so derived can be converted to via (Cardelli et al. 1989). This approach worked well for Upper Sco in Paper V, but it did not work as well in ρ Oph, primarily because there is significantly higher reddening. Similarly, there is high reddening toward some of the stars in Taurus, and there is a lot of scatter, even in the NIR colors.

Another approach used in Paper V (and preferred in ρ Oph) was to take the spectral type, compare the observed colors to those expected for that type from Pecaut & Mamajek (2013), and calculate the resultant reddening. Consequently, any distribution of colors for stars dereddened in this fashion will be quantized, because, e.g., all stars of type M1 are assigned to have the same color. Due to the high fraction of spectral types for Taurus members, we can calculate reddening following the above prescription for most of the members.

Because there is patchy reddening and a lot of scatter in the JH diagram (much more than for USco, for example), we took the reddening estimate from the spectral type first. If that value was unphysical (e.g., <0), then we took the value derived from the JHK_s diagram. Some of those values were still unphysical or insufficient (e.g., was still >8 or 10). So, for those stars with spectral types, we used the Kurucz–Lejeune model grid fitting described above (Section 2.3) to estimate the reddening in a third way. For several of the foreground population lacking spectral types, the reddening derived from the JH diagram was substantially discrepant from the SED fitting having guessed a spectral type based on the observed . In those cases, we selected the best reddening from the SED fitting. As a fourth and last resort, we assigned a star the modal reddening of E(V − K_s) ∼ 0.46 determined via the comparison of observed values to that expected from the spectral type for the ensemble.

Table 1 includes the numbers and sample fractions for each of these approaches. The value used for most stars comes from either of the first two approaches (spectral type or JHK_s diagram). For relatively few stars do we have to fall back to the most likely reddening.

The dereddened we used for each object is included in Table 2 for the members and in Appendix A.2 for the NMs. However, to emphasize the net uncertainty, the "vmk0" column in Table 2 has been rounded to the nearest 0.1 mag. The values used in the plots here can be recovered by using the E(V − K_s) ("ev-k") and ("vk-used") columns.

The net errors are hard to quantify after all of these steps. Table 2 (and its analogous Table B1 for NMs) include a two-digit code indicating the origin of the  value and the method by which the was dereddened to (see Table 2 or B1 for specific definitions). The reddening can be large and a significant source of uncertainty. Via internal comparisons and uncertainties not just on the assumed photospheric colors but also uncertainties in spectral typing, we estimate that the typical uncertainty for Taurus members could be as much as 1 magnitude in E(V − K_s). To quantify this further, for the highest-quality members, we compared the reddening values derived from the JH diagram, from spectral types, and from SED fitting. The reddening derived from the SED is well matched to that from the JH diagram; that from the spectral type has systematic offsets with respect to the others in the sense that the reddening from the spectral types is lower on average but also negative (e.g., unphysical) far more often. In all cases, a Gaussian fit to the distribution of fractional differences suggests that a scatter of ∼0.5 mag in E(V − K_s) is typical. Most of the JHK_s measurements come from 2MASS, where the measurements should have been roughly simultaneous for the three bands, so intrinsic variability alone cannot account for the scatter. It is not the case that emission from the disk is affecting the JH, because the K2 sample is biased toward optical sources, and as noted above, most (>80%) of these disks become apparent at 3.5 μm or longer. The large uncertainty in reddening is real but evidently unavoidable.

Our approach for finding periods was identical to that used in Papers I, II, IV, and V. In summary, we used the Lomb–Scargle (Scargle 1982) approach as implemented by the NASA Exoplanet Archive Periodogram Service¹¹ (Akeson et al. 2013). We also used the IRSA Time Series Tool¹² , which employs the same underlying code as the Exoplanet Archive service but allows for interactive period selection. We looked for periods between 0.05 and 35 days, with the upper limit being set by roughly half the campaign length. Because the periods are typically unambiguous, false alarm probability (FAP) levels are calculated as exactly zero for most of the periods we present here (and the remaining FAP levels are typically <10⁻⁴).

The periods we derive appear in Table 2 for all members and in Appendix A.2 for the NMs.

In Papers I, II, and IV, we described in detail the LC and periodogram shapes we observed in the older Pleiades and Praesepe clusters; Paper V included an additional section on the physical interpretation of the LCs of younger stars in USco and ρ Oph. Here, we briefly summarize and refer the reader to those earlier papers for more detail.

Including both C4 and C13, 81% (127 stars) of the highest-confidence Taurus member sample stars have at least one identifiable period in their LC. We retain up to four periods; 32 (21%) have more than one period. Nearly all of the foreground population has at least one period. More than 95% of the sample we focus on here (members of Taurus or belonging to the foreground) have LCs consistent with a surface spot origin. For stars with two (or more) periods that we believe are due to rotation, we plot only one point at the period we believe corresponds to the actual rotation period of the star dominating the measurement. In those cases, particularly among the M stars, where there are two (or more) periods that are not close together, we believe the star to be a likely binary (or other multiple); see Papers II and IV, and Stauffer et al. (2018a).

In a few stars, just two of the possible members, there is a forest of very short period peaks in the periodogram. We take these to be pulsators.

There are seven stars in the entire sample that have little or no IR excess but have periodic LC shapes with scallop shell or flux dip morphologies, which cannot be due to spots or pulsation; see Stauffer et al. (2018b, 2017) for a discussion of these types of LC morphologies. Of these stars, three of them are highest-quality members (EPIC 246938594, EPIC 246969828 = Cl*Melotte25LH19, and EPIC 247794636 = 2MASS J04321786+2422149), three are possible members (EPIC 246676629 = UCAC 4522-000989, 246682490 = UCAC 4522-009859, 247343526 = 2MASS J04405340+2055471), and one is part of the foreground population (EPIC 246776923). Because the primary period in these cases is likely to either be a rotation period or strongly related to a rotation period, these were retained as rotation periods.

As in other young clusters, there are LCs with dipper or burster morphologies (see, Figure 2 and, e.g., Paper V; Cody et al. 2014; Stauffer et al. 2014, 2015, 2016a; Cody & Hillenbrand 2018). All of the LCs we identified as dippers (21 members) or bursters (25 members) also have disks, and all are members of some sort (Table 1). These are identified in the corresponding tables (Table 2 and Appendix A.2). Note that the period we report as the rotation period is often but not always also the period of the dips/bursts; sometimes the dips/bursts align with the sinusoidal modulation, and sometimes they do not. N. Roggero et al. (2020, in preparation) will explore the dipper population in Taurus.

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We categorize "timescales" for LCs that seem to have a repeating pattern, but the pattern does not seem to be due to starspots or other rotation-related phenomena and, therefore, are not taken as periodic; see Appendix B.

A detailed comparison between periods in the literature (consisting of a few to tens of stars per study) and periods we derive from K2 data is given in Appendix C.

In summary, we conclude that we are recovering most of the periods reported in the literature. The results are a mix of excellent agreement, likely harmonics reported in the literature, and, for a few, significant disagreement with the periods derived from the high-quality K2 data.

The study with which we have the most disagreement is the Kilodegree Extremely Little Telescope (KELT) analysis (Rodriguez et al. 2017b), where 19/26 do not match. Our analysis of other clusters in common with KELT produced a much better match in periods. Perhaps this is not surprising, in particular for those stars still actively accreting or where the distribution of spots may be changing on relatively short timescales; changes in the LC shape of an accreting object can reasonably be expected to change on ∼year timescales even though the stellar rotation rate itself does not change on short timescales.

In any event, for each mismatched period, we investigated the prior period and believe that the period(s) we report is/are the correct periods for these stars during the K2 campaign(s).

As discussed above in Section 2.2, it is likely that the relatively low fraction of Taurus members with periods in the K2 data is due to disk contributions to the LCs, making periods difficult to extract. To determine whether or not this results in a bias in our derived period (P) distribution, we compared our periods with the projected rotational velocities () from the literature. We started with the compilations in Rebull et al. (2004) and Güdel et al. (2007) and then added those from Nguyen et al. (2009).

Out of the Taurus members or the foreground population with K2 LCs, there are 51 with measurements or limits in the literature. Figure 3 compares the and the periods measured here. For stars with multiple measured periods, the measured  in the literature may not correspond to the period we have taken as the rotation period. Thus, those stars with multiple periods are indicated in the plot. Disks and stars lacking periods in the K2 data are indicated.

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In the left panel of Figure 3, we recover the expected relationship in that stars with fast P have large . Stars with disks lack shorter periods (<2 days; see Section 4 below). In the right panel of Figure 3, there is no obvious trend for the stars lacking periods to have systematically higher or lower than those with periods. We conclude that our sample with periods is not significantly biased by omitting the ∼20% of (member) stars (nearly all of which have disks) that do not have periods, and comparisons to other, older clusters should be straightforward.

Figures 4–6 are various versions of the / CMD for the entire sample with each highlighting the stars of interest: the most likely Taurus members, the possible Taurus members, and the older foreground population. Figure 4 shows the observed CMD, and Figures 5 and 6 show dereddened CMDs. Figures 4 and 5 include apparent and absolute , but not every star has a Gaia distance (see statistics in Table 1), so Figure 6 shows just apparent magnitudes. Figure 6 also distinguishes the periodic from the disked stars. By inspection of these CMDs, we primarily see that reddening is important, and the foreground population is older than the Taurus members.

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3.5.1. Taurus Members

3.5.2. Foreground Population

Figure 8 shows P versus . The left panel has the foreground older population; the others have both the highest-confidence members and the possible members. Overall, the slowest rotators are found in the early M stars and the fastest rotators are found in both the highest masses, A stars and F stars, and in the lowest masses we have here, mid-M stars. Despite the far fewer stars available from the foreground population, it can be seen, on average, that they are rotating more quickly than the (younger) Taurus members, consistent with their older ages. The disked stars are, on average, rotating more slowly than the disk-free Taurus members, consistent with disk locking (see Section 4 above). The latest M stars in Taurus are the youngest M stars yet studied with high-quality LCs.

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Figure 9 puts the P versus for Taurus and the foreground population in context with the other young clusters that have periods we derived from K2 LCs: ρ Oph (∼1 Myr; Paper V), USco (∼8 Myr; Paper V), Pleiades (∼125 Myr; Papers I–III), and Praesepe (∼790 Myr; Paper IV).

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There are relatively few stars in Taurus (and even fewer foreground stars) in comparison with the older clusters. The shortest periods in all of these clusters are on the order of hours and are limited by breakup (see discussion in Paper V). The longest periods found in the youngest clusters are those of early M stars and are ∼10–20 days; there are many periods longer than ∼10 days in Praesepe, encompassing K and early M stars. At older ages, there are two well-defined sequences: rotation period increasing (slower rotation) to lower mass for FGK stars, and a second sequence where rotation period decreases sharply (faster rotation) as mass decreases among the M dwarfs. These two trends (particularly the latter) appear to already be in place by Taurus's age (∼3 Myr). For higher-mass stars ( ≲ 3), the trend is for higher masses to have faster rotation rates (smaller P), and lower masses to have slower rotation rates, although there are very few stars available. For low-mass ( ≳ 3) stars, there are shorter periods at lower masses. Such trends are harder to see in the ρ Oph sample, perhaps because of larger uncertainties in the colors (due to larger and more variable reddening). It does seem to be there in the Taurus foreground sample as well (∼30 Myr). There is an apparent decrease in the range of periods at a given color/mass as a function of age; this is at least partially (perhaps completely) due to the larger uncertainties in the inferred colors at younger ages. The colors are more uncertain in the youngest clusters due to the larger extinction corrections, possibly the influence on from the disk (this is relatively rare in this sample), and possibly due to variable extinction or accretion (and the non-simultaneity of the observed or inferred V and measured ). The Taurus distribution is not as organized as USco, but it is also not as disorganized as ρ Oph. The Taurus distribution is starting to resemble the USco distribution, but it still has a lot of scatter, particularly in the M stars, more like ρ Oph. The Taurus foreground distribution is sparse indeed but consistent with the Pleiades distribution.

The influence of disks can be seen in Figure 9; the top panels show all primordial disks, and the "pile-up" at ∼2 days is obvious in USco but less so in the younger clusters (see Section 4 above). The disks in the Pleiades are all debris disks; the debris disk sample is likely incomplete among the M stars in Pleiades and Praesepe, since the more subtle IR excesses indicative of debris disks are harder to find among the fainter stars.

We included in Papers I (Pleiades) and IV (Praesepe) information about the variability amplitude, where we define amplitude as the difference in magnitude between the 10th and the 90th percentile of the flux distribution for a given LC. We did not include such a discussion in Paper V (USco and ρ Oph) because the systematics in that campaign (C2) were large and hard to manage (e.g., the fraction of the variability due to the instrument or due to the star is hard to determine). In most cases, however, the amplitudes we measured for the "best" LC for the periodic sources in USco and ρ Oph are probably usable in the ensemble, especially given the relatively large uncertainty in . The instrumental systematics in the Taurus campaigns are much lower than that in C2, so here again, the amplitudes are probably due primarily to the astrophysical source.

Figure 10 shows the amplitudes of periodic variability (10th to 90th percentiles) as a function of color and period for our K2 young clusters. As in Figure 9, the echoes of structures seen in the older and more populated cluster plots can be seen in the younger clusters. The average LC amplitude decreases with cluster age.

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Stars with primordial disks have larger amplitudes, on average, though disked and non-disked stars both have a wide range of amplitudes in the youngest three clusters (ρ Oph, Taurus, and USco). The variability amplitudes for the Taurus disked stars primarily measure the larger amplitude variability due to accretion bursts ("bursters") or variable extinction ("dippers"). The variability amplitudes for the non-disked stars (and for the low-mass stars in the older clusters in Figure C1) primarily measure non-axisymmetrically distributed spots as they rotate into and out of our line of sight.

The earliest spectral type stars sampled here (A and F stars) have lower amplitudes, on average, than their same-age counterparts among the G, K, and M stars. This makes sense since the A and F stars are expected to have substantially less fractional spot coverage than the G, K, and M stars at any given age.

We expected that longer period rotators might have lower amplitudes on average, due to lower levels of activity. That is very roughly the case at the ages of Praesepe and perhaps Pleiades; it might be the case at the age of USco, and it seems to not be the case for disk-free younger stars.

There is obvious substructure seen in the amplitude distribution against color or period in Praesepe (and more subtle echoes of it in the Pleiades) as a function of , some of which may be selection effects in that the longest periods may require larger amplitudes for detection (Paper IV). The substructure seen in the amplitude distribution in the Pleiades and Praesepe is not obvious in the clusters <100 Myr—perhaps the behavior is not yet organized enough, or there are not enough stars for comparison. That lack of structure could be explained in the plot by invoking the likely large uncertainties in for the young clusters, but the uncertainty in P is likely small, so the relative lack of substructure in the distributions as a function of P for the younger stars is likely real, though greatly complicated by the range of masses included at any given P (or amplitude).

In Papers II, IV, and V, we classified the LC and periodogram morphologies for the Pleiades, Praesepe, USco, and ρ Oph; see these references for discussion of the classes (e.g., double-dip, scallop, etc.). Table 3 includes statistics on these classifications for all of the clusters, now including Taurus.

A high fraction of the Taurus stars are periodic, 83%. As for nearly all of the other clusters, ∼70% of the periodic Taurus members have only one period; about 30% of the periodic sample has at least two real periods. The Taurus foreground has different proportions, but it is likely biased/incomplete.

There are some aspects of the periodic LC morphologies that are common between the clusters and others that show signs of evolution with stellar age. Specifically:

• 1.  
  The fraction of double-dip stars falls substantially between Praesepe and ρ Oph. Assuming that the rate at which we find double-dip characteristics increases as rotation period decreases (e.g., Basri & Nguyen 2018), this makes sense since Praesepe is, on average, rotating much more slowly than ρ Oph.
• 2.  
  LCs of the scallop shell morphology (and related categories) continue to be rare but much more common among the younger clusters. None have disks. We note that Zhan et al. (2019) find scallop shell stars at ∼40 Myr, but there are very few by ∼125 Myr, the age of the Pleiades.
• 3.  
  LC categories suggestive of complicated spot occurrence and evolution (beater, complex peak) seem harder to find in clusters with a higher disk fraction. In contrast, shape changers (which could arise from spot/spot group emergence/evolution or from disk influence) are more common in clusters with a higher disk fraction.
• 4.  
  Resolved distant peaks (which are most likely binaries, either real or apparent) occur at comparable rates across all clusters. Pulsators are rare in all clusters, which is unsurprising, at least in the stellar mass range where our studies are focused.
• 5.  
  Dippers and bursters only occur in clusters that still have primordial disks, consistent with our physical interpretation of these phenomena as interactions with gas/dust disks. The vast majority of dippers and bursters are also disked stars; a few have little or no IR excess, though they could still have gas disks depleted in dust.

As for the other clusters, we calculated the ΔP/P_rot metric for stars with resolved multi-period peaks; see Figure 11. This metric is defined by taking the closest peak to the P_rot, subtracting the smaller from the larger, and dividing by the P_rot. For well-separated peaks and/or M stars (see Paper V and Stauffer et al. 2018a), it is very likely that the two periods are two independent periods of two components of a binary system.

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The distribution in Taurus, like that for USco/ρ Oph (Paper V) and Praesepe (Paper IV), has relatively little structure as compared to that for the Pleiades (Paper II). Here, as noted in Paper V, the ∼70 days K2 campaigns are not quite long enough to capture multiple complete cycles in order to be able to resolve two close periods. If the phasing of the two periods is favorable, we can resolve the two periods, but if the phasing is not "lucky", ∼70 days is not long enough to distinguish the periods.

Despite the fact that Taurus is close (∼140 pc) and has been studied for decades, membership is still controversial. Recent literature combines years of prior data collection with the Gaia DR2 data in an attempt to create a complete list of members (e.g., Luhman et al. 2017; Luhman 2018; Esplin & Luhman 2019; Galli et al. 2019; and references therein). Numerous approaches have sought a dispersed population of young stars (e.g., Wichmann et al. 1996; Slesnick et al. 2006; Rebull et al. 2010; Rebull et al. 2011; Kraus et al. 2017; and references therein). The net result is persistently confusing in the literature, with a subset of stars that most authors agree must be members, stars where membership evidence is mixed, and still other stars where evidence is both mixed and controversial, particularly those having several indications of youth but with distinct motions and/or distances that are apparently inconsistent with membership.

In the context of this paper, we needed to find the sample of member stars that also had K2 LCs. It is important to note three important selection effects. First, K2 LCs were only downloaded for targets submitted in advance, so completeness is limited by the submitted list of targets. Second, the K2 observations did not cover all of the sky encompassing the least controversial Taurus members (see Figure 1, in addition to discussion below). Third, since it observed in optical bands, K2 effectively selected against those Taurus members that are so embedded as to attenuate the optical data (see discussion below and Section 2.4).

Based on our experience with the other K2 clusters that we previously analyzed (Papers I–V), we knew that we had to start with an overly generous list of possible members; by starting with an expansive set, we could analyze all of the LCs in the same way, at the same time (thus reducing biases in the analysis). Subsequent membership modifications implemented late in the process then become trivial to implement.

We assembled a list of 851 EPIC-numbered targets with LCs (e.g., targets submitted in advance that had actually been observed) that could be members of Taurus with data in either of the Taurus-relevant K2 campaigns (C4 and C13). These targets originated from any of the 64 different K2 GO programs that mention in their abstract studying young stars or members of Taurus. These programs did not necessarily perform complete and thorough vetting of possible targets prior to target submission (we note that both C4 and C13 predate Gaia DR2); observers just included targets that could be Taurus members, so we likewise included them in our initial target list assembly.

We proceeded with the analysis of those ∼850 LCs in parallel with membership assessment efforts. For most of these targets (see Section 2.3 and Table 1), there are Gaia DR2 and 2MASS data. We explored a variety of parameter spaces such as vector point diagrams and CMDs. While this process was underway, Luhman (2018) was published, with similar subgroups as we had identified, but with a much more complete analysis than we had accomplished to that point. Subsequently, Esplin & Luhman (2019) and Galli et al. (2019) were published, again presenting lists of members based primarily on Gaia DR2 data. These recent analyses include all of the least controversial Taurus members. We made the decision to adopt the intersection of those targets with K2 LCs and those in Esplin & Luhman (2019) as the highest-quality members.

Note that the regions of sky encompassed by Luhman (2018), Esplin & Luhman (2019), and Galli et al. (2019) are significantly different than the region of sky observed by K2 in the two campaigns including Taurus members (Figure 1). The K2 observations cover about 30% of the Taurus members from Esplin & Luhman (2019), and the K2 observations also encompass a much larger region of the sky to the south of where the membership work was focused. Moreover, the Esplin & Luhman (2019) member list seems to have very few higher-mass G and K stars.¹³ Since that mass range proved interesting for the rotation rate distribution in Papers I–V, we wanted to be sure that we had that region of parameter space well-represented here.

As a result of the larger areal coverage and the G star deficit, we sought to reassess membership for stars with K2 LCs that were not already in the highest-quality members, in particular, stars meeting those criteria. We investigated the literature for each possible additional target in question, as well as the Gaia DR2 data. In most cases, a star had several or many papers in the literature citing it as a suspected Taurus member, and it had DR2 data consistent with belonging to Taurus, or it had very few references suggesting membership and usually DR2 data inconsistent with membership. The less likely (lower-confidence) members include targets added by our own additional star-by-star inspections, including a few from Galli et al. (2019) or Kraus et al. (2017) that were not in Esplin & Luhman (2019).

In this process, we realized that there was a subset of stars that had indications of youth but distances and/or motions incompatible with Taurus membership; these include those "controversial" members mentioned above. Many of these targets are listed in Luhman (2018) as Group 29 members (see also Oh et al. 2018). Some appear in the literature as possible members of Mu Tau (M. Gagne et al. 2020, in preparation; Liu et al. 2020) or possibly Cas-Tau (e.g., Hartmann et al. 1991; de Zeeuw et al. 1999; Luhman 2018; also see appendix of David et al. 2018). Analyses to date of this population in the literature suggest that they are ∼30 Myr (e.g., Kraus et al. 2017). Our list of Taurus foreground stars are primarily those Group 29 members, plus targets added by our own additional star-by-star inspections that might very well be Mu Tau or Cas-Tau members (see also Stauffer et al. 2020).

Much of the supporting non-survey data available in the literature (Section 2.3) is biased toward those least controversial members, and those targets nearby in projected distance. For example, a high fraction of the highest-confidence members have a Spitzer and/or Herschel counterpart (Sections 2.3 and 2.4; Table 1) because those pointed missions targeted the most well-known members. Circularly, the most reliable members also are more likely to have an IR excess and, thus, be detected in various IR data sets. Similarly, we expect members to be young and significantly spotted and, therefore, periodic more often, which is the case (Section 3.1).

After extracting the members (of any sort) out of the ∼850 in our initial sample, we are left with ∼630 nominal NMs. Among this nominal NM sample, there is an anomalously high fraction of apparent IR excesses and an anomalously high periodic fraction (Table 1). Looking at the distribution of Gaia distances from Bailer-Jones et al. (2018), many are nominally at ∼140 pc, more than would be expected for a randomly selected set of field stars. We suspect that we have been somewhat conservative in identifying members, and that some (perhaps several) legitimate members are left in the NM sample. Moreover, the set of stars with K2 LCs is biased toward objects appearing in the literature as young, which makes the entire K2 sample different than any random selection of stars.

For these NMs, we performed much of the same analysis as for our members, but they were largely ignored in the discussion in the rest of the paper. We include results from these additional stars here, should they be of use to future investigators. We provide the NMs in Table A1, which has the same contents as in Table 2 above (except for the columns on cluster membership and dippers/bursters, none of which are found among the NMs). Note that the Gaia DR2 ID is provided for easily matching parallaxes and proper motions. We focused on the analysis of the members, and as such, some of the NMs may not have been vetted as closely as the member sample.

Table A1.  Periods and Supporting Data for Taurus Likely Nonmembers with K2 Light Curves

Number	Label	Contents
1	EPIC	Number in the Ecliptic Plane Input Catalog (EPIC) for K2
2	Coord	R.A. and decl. (J2000) for target
3	OName	Alternate name for target
4	Gaia	Gaia DR2 ID
5	V mag	V magnitude (in Vega mags), if observed
6	Ks mag	magnitude (in Vega mags), if observed
7	(V − Ks)o	, as directly observed (in Vega mags), if V and exist
8	(V − Ks)u	used, in Vega mags (observed or inferred; see the text)
9	E(V − Ks)	E(V − Ks) adopted for this star (in mags; see Section 2.5)
10	Ks mag0	dereddened Ks,0 magnitude (in Vega mags), as inferred (see Section 2.5)
11	(V − Ks)0	, dereddened (in Vega mags), as inferred (see Section 2.5; rounded to nearest 0.1 to emphasize the relatively low accuracy)
12	Uncert	two-digit code denoting the origin of and  (see Sections 2.3 and 2.5): First digit (origin of ): 1 = V measured directly from the literature (including SIMBAD) and Ks from 2MASS; 2 = V from APASS and Ks from 2MASS; 3 =  inferred from Gaia g and Ks from 2MASS (see Section 2.3); 4 =  inferred from Pan-STARRS1 g and Ks from 2MASS (see Section 2.3); 5 =  inferred from membership work (see Section 2.2; rare); 6 = V inferred from well-populated optical SED and Ks from 2MASS (see Section 2.3); −9 = no measure of . Second digit (origin of E(V − Ks) leading to ): 1 = dereddening from JHKs diagram (see Section 2.5); 2 = dereddening back to expected for spectral type; 3 = used median E(V − Ks) = 0.7 (see Section 2.5); −9 = no measure of
13	P1	Primary period, in days (taken to be rotation period in cases where there is >1 period)
14	P2	Secondary period, in days
15	P3	Tertiary period, in days
16	P4	Quaternary period, in days
17	IR excess	Whether an IR excess is present or not (see Section 4)
18	IRexStr	Minimum wavelength at which the IR excess is detected or the limit of our knowledge of where there is no excess (see Section 4)
19	Slope	Slope of SED fit to all available detections between 2 and 25 μm
20	Class	SED class (I, flat, II, III)
21	Sin/mult	single or multi-period star
22	dd	LC and power spectrum matches double-dip characteristics (see Section 6.2)
23	ddmove	LC and power spectrum matches moving double-dip characteristics (see Section 6.2)
24	Shape	LC matches shape changer characteristics (see Section 6.2)
25	Beat	LC has beating visible (see Section 6.2)
26	Complex	power spectrum has a complex, structured peak and/or has a wide peak (see Section 6.2)
27	Closep	power spectrum has resolved close peaks (see Section 6.2)
28	Distp	power spectrum has resolved distant peaks (see Section 6.2)
29	Pulse	power spectrum and LC match pulsator characteristics (see Section 6.2)

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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