The Many-faceted Light Curves of Young Disk-bearing Stars in Taurus as Seen by K2

Young stars are photometric variables (Joy 1945; Herbig 1954; Walker 1954) on timescales that range from hours to weeks, with a typical timescale of 1–2 days (Costigan et al. 2014; Findeisen 2015). The variability is observed over a broad range of wavelengths (e.g., Carpenter et al. 2001; Herbst et al. 2002; Rebull et al. 2014; Venuti et al. 2015). In the optical range, the dominant effects associated with the star are due to rotational modulation of active "starspot" regions in the photosphere, as well as magnetically induced chromospheric activity at higher altitudes in the atmosphere. However, for those young stars still surrounded by circumstellar material, there is also variability due to unsteady accretion from the inner circumstellar disk onto the star (causing brightening), and in some cases, due to changes in line-of-sight extinction (causing dimming).

Modeling efforts aimed at understanding the morphologies observed in high-cadence light curves of young disk-bearing stars include those by Kesseli et al. (2016) and Robinson et al. (2021), among others. Much of the accretion-related and extinction-related variability originates in the star–disk interaction region. This zone encompasses the accretion shock on the surface of the star, the magnetosphere in which accreting gas and dust are entrained, and the innermost regions of the highly irradiated circumstellar disk.

Empirically, the diversity of light curve shapes for young stars, and their characteristic timescales, has been appreciated only with the availability of high-cadence and very high-precision photometric observations from spacecraft, specifically CoRoT (Baglin et al. 2006), MOST (Matthews et al. 2000), and K2 (Howell et al. 2014). Cody et al. (2014) defined a classification scheme to characterize young variables using a scale from strictly periodic, to quasiperiodic, to entirely stochastic, on one axis, and on the other, quantifying primarily bursting, symmetric, and primarily fading/dipping behavior. These metrics, dubbed Q and M, were developed assuming high-quality photometric times series data.

CoRoT provided the first such high-cadence, high-precision studies of young stars. The NGC 2264 region was observed over 22 days in 2008 and 39 days in 2011, sampling ∼175 young cluster members (Cody et al. 2014; Stauffer et al. 2014, 2015; McGinnis et al. 2015; Stauffer et al. 2016; Sousa et al. 2016; Venuti et al. 2017). The next opportunity came with coverage of the Upper Scorpius and ρ Ophiuchus regions in K2 Campaigns 2 and 15. These observations provided light curves over ∼80 days for ∼1300 (C2) and ∼400 (C15) young cluster members, respectively (Cody et al. 2017; Ansdell et al. 2018; Cody & Hillenbrand 2018; Rebull et al. 2018). K2 data are also available for the Lagoon Nebula Cluster, although mainly for higher-mass stars (Venuti et al. 2021).

We present here the fourth young region with space-based optical light curves. Our study uses K2 Campaign 4 and 13 coverage of the northern portion of the Taurus region, with ∼70 and ∼80 days of photometric time series data, respectively. A total of 181 young cluster members were targeted (not all of which have high-quality data).

We note that the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) is also now contributing high-cadence, high-precision light curves of young stars. Its all-sky coverage encompasses many young clusters, including the extended Taurus regions, albeit to brighter limiting magnitudes than the K2 or CoRoT data sets described above.

The greater Taurus region has been the subject of many previous photometric monitoring studies over the past eight decades, conducted using ground-based telescopes. There is a rich literature concerning the variability properties of individual stars on timescales from days to decades. The entire history of such studies is too vast to review here, but includes long-term monitoring programs, e.g., by Herbst et al. (1994) and Grankin et al. (2007). Wide-field imaging survey results were first provided by Slesnick et al. (2006) based on Palomar/QUEST data, then by Xiao et al. (2012) based on TrES data, followed by Rodriguez et al. (2017), who used KELT data. The opportunity presented by the K2 mission, however, is the first possible investigation of the young Taurus population with precision photometry. Only a few of the Taurus members have benefited previously from such high-quality data, via observations with MOST (Cody et al. 2013).

From the same set of K2 data in Taurus that we are using, (Rebull et al. 2020, hereafter "R20") presented the sample of periodic sources, and analyzed the period–color diagram in the context of stellar rotational evolution during the pre-main sequence. In addition, Roggero et al. (2021) have analyzed in detail the subset of K2 Taurus "dipper" stars—those that display fading events in their light curves characteristic of dust occultation. K2 photometry of Taurus members has also appeared in several other papers on individual objects. van Dam et al. (2020) studied the evidence for an eclipsing substellar companion to the binary V928 Tau, a weak-line T Tauri system. Pouilly et al. (2020) studied the early-type accreting star Tau and Pouilly et al. (2021) focused on the late-type dipper variable V807 Tau. Biddle et al. (2021) studied the classical T Tauri star CI Tau, Kóspál et al. (2018) investigated the accreting young binary DQ Tau, and Paudel et al. (2018) examined flares associated with brown dwarf CFHT-BD-Tau 4.

In this paper, we focus on the disk-bearing sample of Taurus. We perform an analysis similar to that in Cody & Hillenbrand (2018), classifying the light curve behaviors into morphological groups that are related to the influences of rotation, accretion, and circumstellar dust on the time-dependent photometric brightness of the sources. We also compare our results for Taurus to our previous findings for disk-bearing samples of young stellar objects in NGC 2264, ρ Oph, and Upper Sco.

The Kepler Space Telescope observed Taurus as part of its 4th and 13th K2 Campaigns from 2015 February 7 to 2015 April 23, and 2017 March 8 to May 27, respectively. While many known Taurus members from the literature were deliberately included in the campaigns, a handful of previously unknown young stars also fell within the K2 field of view.

We began with a list of 216 known and candidate Taurus members compiled as part of our Campaign 13 target request that had been submitted to the mission. Once the approved targets from all observing programs were released, we recognized that there may be additional young stars serendipitously included as K2 targets by other groups, e.g., as planet search targets. Consequently, R20 used the Gaia mission second data release (Gaia DR2) to mine the complete set of all stars observed by K2 in Campaigns 4 and 13 for colors, magnitudes, parallaxes, and proper motions consistent with Taurus membership. They ultimately published a set of 156 Taurus members observed by K2, along with 23 additional candidates of less certain status. This same sample serves as the basis set for the current study.

In this work, we are interested in assessing the variability of stars whose inner circumstellar disks have not yet dissipated. Here, we have adopted the disk selection criteria of R20, who used spectral energy distributions to identify objects in the member and candidate member samples with infrared excesses. Based on their assessment, we find a total of 99 disk-bearing stars in the K2 Taurus sample, of which 93 have definitive inner disks, and the remaining six have smaller excesses that may also indicate circumstellar dust. Stars in this latter group are included as disk-bearing "candidates" and are noted as such in Table 1.

Relative to previous samples with high-cadence, high-precision light curve data sets, the K2 Taurus sample is slightly smaller: ρ Oph had 123 stars observed with K2 (Cody & Hillenbrand 2018), NGC 2264 had 176 stars observed with CoRoT (Cody et al. 2014), and Upper Sco had 217 stars observed with K2 (Cody & Hillenbrand 2018).

We have divided each of these data sets into disk classes based on spectral energy distribution (SED) slope, α. Following Lada (1987), $\alpha =d\mathrm{log}(\lambda {F}_{\lambda })/d\mathrm{log}(\lambda )$ for flux F_λ as a function of wavelength λ. The slope is adopted from R20, who fit it to all available photometric data points between 2 and 25 μm. We consider objects with α > −1.6 to be disk-bearing sources. Those with −1.6 < α < −0.3 are labeled as class II, whereas SEDs with −0.3 < α < 0.3 are flat, and those with greater slopes are class I (α > 0.3). The majority of disks for each set are class II.

For the Taurus sample, 70 sources are class II, 11 are flat, and four are class I. The remaining objects are class III disk candidates, with possible infrared excesses apparent on visual examination of the SED. Class I objects are the most rare, with 10 in ρ Oph, four in Taurus, three in NGC 2264, and one in Upper Sco. These numbers are a reflection of the relative ages of these clusters (Reipurth 2008), with the ρ Oph population being the youngest, on average, at ∼1 Myr, the Taurus and NGC 2264 regions at 1–5 Myr, and Upper Sco the oldest at ∼5–10 Myr.

A histogram of the spectral type distribution for ρ Oph, Taurus, and Upper Sco is shown in Figure 1. The spectral type—and correspondingly, the mass range—for each of these samples is similar: low-mass K and M stars predominate at ∼85%–95% of the stars. In Taurus, spectral types for all but three of our stars (EPIC 247027353, EPIC 247590222, and EPIC 248038058) have been determined by Luhman (2018); we adopt all of his values here, except for that of EPIC 247992575, which we find to be a B5 star, based on the work of Mooley et al. (2013).

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Starting with the sample described in Section 2, we obtained K2 data for each disk-bearing Taurus member observed during the mission. These data were in the form of target pixel files ("TPFs"), which consist of stacks of small (∼8 × 8 pixels or ∼32'' × 32'') images, each taken 30 minutes apart. We performed aperture photometry on each image within a TPF, with circular aperture radii ranging from one to four pixels. Aperture placement was determined by computing a flux-weighted centroid. We then output the background-subtracted summed flux. This is subject to intrapixel positional jitter due to spacecraft drift, with corrective thruster firings approximately every six hours. The resulting photometry displays a sawtooth pattern with amplitude up to 10%, depending on source brightness. Fortunately, this systematic effect can be largely removed with detrending algorithms. To clean our light curves, we used the k2sc package (Aigrain et al. 2016) to remove position-correlated flux variations. This software simultaneously models stellar variability and pointing systematics. It also identifies flux outliers as part of this process. The outputs of k2sc are a "position-dependent" trend (i.e., systematics) and a "time-dependent" trend (i.e., real variability). We remove the former to produce our final, variability-preserved light curves, while we also subtract the latter in efforts to assess the intrinsic noise levels of the photometry, as described below and illustrated in Figure 2.

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We were then left with four detrended light curves (one for each aperture), along with a set of outlier flags. Each light curve was visually inspected, and an optimal aperture was chosen based on noise level and stellar crowding. For isolated stars, we picked the light curve with the lowest standard deviation after subtraction of intrinsic variability patterns (as provided by k2sc's time-dependent trend output). We then checked whether the particular aperture enclosed flux from any neighboring stars; if so, we opted for a smaller aperture, typically one pixel in radius. Finally, we again used visual inspection to identify cases for which stellar flares were flagged as outliers, and we manually removed the flags on those data points. After outlier removal, we normalized all light curves by their median flux level. These final cleaned light curves will be available as a high-level science product (HLSP) within the Mikulski Archive for Space Telescopes (MAST).

The underlying photometric noise level of our light curves is challenging to measure because of the high levels of astrophysical variability in the majority of targets. We have obtained a rough estimate of precision versus magnitude by analyzing the noise levels of the variability-detrended light curves output by k2sc. We estimated the Kepler magnitudes (K_p ) by adopting the relation between raw instrumental magnitude (i.e., −2.5 $\mathrm{log}(\mathrm{flux})$) and K_p derived for our Campaign 2 work on Upper Sco and ρ Oph (Cody & Hillenbrand 2018) based on the photometry of quiet field stars. The resulting magnitude versus noise trend is shown in Figure 2. We have overplotted the standard deviations of each light curve to illustrate the significant brightness fluctuations in the majority of sources.

Based on the variability detrended light curves, the brightest sources (K_p ∼ 10) in our sample have photometric precisions of ∼0.15% in normalized flux. In contrast, fainter stars (K_p ∼ 15–16) have lower precisions of ∼0.65%. In Figure 2, we have shifted the noise curve up by a factor of five to generate a threshold for variability detection. All stars with standard deviations lying above this shifted curve are considered to be variable. There are then only 11 stars (black triangles in Figure 2) that do not immediately qualify as variable, of which four are of uncertain disk status ("M" in Table 1). We have run these stars through periodicity detection algorithms as part of the statistics computations described in Section 4, and we find each to have one or more significant periodicities. Therefore, we are left with no nonvariable objects in the entire data set of 99 young stars.

Because of the large Kepler pixel size (∼4'' ), a number of our targets are blended with companion stars. We cannot separate the photometry for most of these, and therefore have noted their status in Table 1. Blends include both visual companions and spectroscopic or photometric binary systems drawn from the literature. The light curves for blended sources contain contributions from both stars, and should therefore be considered with caution.

We display the full set of disk-bearing light curves in Appendix A. In each panel, we show the available light curve, from either Campaign 4 or Campaign 13. Spatial overlap between these campaigns was minimal (two of 84 CCD channels), and so no disk-bearing stars appeared in both sets. Labeling indicates the light-curve variability class, and the quantitative Q and M metrics developed below.

4.1. Q − M Classification

Visual inspection and statistical analysis of the K2 Taurus light curve sample revealed that 100% of our inner disk-bearing stars are variable. To further probe the nature of the variability, we applied several statistical metrics introduced in our previous work on young stars observed with CoRoT and Kepler. In particular, we defined two metrics, "Q" and "M," which reflect the degrees of periodicity and flux symmetry, respectively (Cody et al. 2014; Cody & Hillenbrand 2018). Although alternative statistics exist in the literature (e.g., Antille et al. 1982), we have found that these metrics work well for capturing the range of young star variability behavior. Recently, they have also been applied to a ground-based data set (Hillenbrand et al. 2022) where extra care is needed given the larger photometric errors and lower sampling relative to space-based photometry.

Q values range from zero to one, where Q = 0 indicates a perfectly periodic light curve, and Q = 1 is obtained for a light curve with no repeating patterns. Intermediate values of Q apply to flux behavior that is somewhat repetitive but does not display the same shape or amplitude from one cycle to the next. The M statistic is a measure of light curve symmetry, where M = 0 is retrieved for a light curve with flux equally distributed above and below the median. Positive M values indicate a tendency toward fading events, whereas negative values indicate predominantly brightening behavior. For more discussion and the exact definition of Q and M, we refer the reader to Cody et al. (2014) and Cody & Hillenbrand (2018).

Using the derived statistics, we have classified the disk-bearing variables of Taurus into eight different categories, as defined in Cody et al. (2014) and shown in Figure 3. In accordance with our analysis of other K2 young star light curves (Cody & Hillenbrand 2018), the categories, their shorthand denotation, and their Q and M ranges are:

• 1.  
  burster (B) M < −0.25;
• 2.  
  purely periodic symmetric (P) Q < 0.15 and − 0.25 <M < 0.25;
• 3.  
  quasiperiodic symmetric (QPS) 0.15 < Q < 0.85 and − 0.25 < M < 0.25;
• 4.  
  purely stochastic (S) Q > 0.85 and − 0.25 < M < 0.25;
• 5.  
  quasiperiodic dipper (QPD) 0.15 < Q < 0.85 and M >0.25;
• 6.  
  aperiodic dipper (APD) Q > 0.85 and M > 0.25;
• 7.  
  long timescale (L);
• 8.  
  variable but unclassifiable (U).

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The first six categories are the same as those used in our other K2 young star analyses in the ρ Oph/Upper Sco region (Cody & Hillenbrand 2018) and in NGC 6530, the Lagoon Nebula cluster (Venuti et al. 2021). We note that Venuti et al. (2021) additionally included categories for multiperiodic and eclipsing binary light curves, which we do not find here. Our final two categories are reserved for "long-term" variables that showed a trend on >30 day timescales, as well as "unclassifiable" sources with unknown light curve form but high enough standard deviations to be selected as variable. As noted in Section 3, we do not have any nonvariable sources in this sample.

The distribution of Q and M values for all disk-bearing Taurus stars observed by K2, as well as those in ρ Oph and Upper Scorpius, is displayed in Figure 4. In those plots, we illustrate the established divisions in Q and M, but emphasize that these should be viewed more so as transition regions from one variability type to another, rather than as sharp boundaries.

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In Taurus, the Q distribution spans the whole range from zero to one. The results for the M statistic indicate that 40% of Taurus stars exhibit asymmetric flux behavior, tending to either preferentially fade or to brighten. There are no eclipsing binary systems in our sample; instead, the fading events are associated with dippers (17% prevalence). The remaining 23% of asymmetric flux sources are bursters.

We list the variability status of all disk-bearing stars (illustrated in Appendix A) in Table 2, including the metrics regarding the degree of periodicity and flux asymmetry about the mean value, the inferred variability type, and the light-curve amplitude and its timescale. The derivation of the last two quantities is discussed in Section 5 below.

Table 2. Variability Properties of Young Disk-bearing Stars in K2 Campaign 2

EPIC	2MASS	Variability	Variability	Amplitude	Timescale	Additional	Q	M
ID	ID	(primary)	(secondary)	(Norm. Flux)	(d)	period (d)
210683818	J04313407+1808049	L		0.17	109.31		1.0	0.14
210689083	J04313747+1812244	B		0.77	7.58		0.65	−0.76
210690598	J04313613+1813432	S		0.47	25.25		0.86	−0.5
210690735	J04300399+1813493	APD		0.84	5.52		0.9	0.15
210690892	J04314007+1813571	S		0.5	46.85		1.0	−0.13
210690913	J04313843+1813576	S		0.25	22.80		1.0	−0.3
210699670	J04315968+1821305	B		1.36	16.67		0.81	−0.6
210699801	J04315779+1821380	B		0.07	4.03		0.77	−0.25
210725857	J04285053+1844361	QPS	APD	0.14	2.07		0.64	0.12
210777988	J04215943+1932063	QPS		0.12	2.81		0.65	−0.07
210780789	J04221332+1934392	P		0.1	1.33		0.18	0.23
210865655	J04102834+2051507	B		0.19	8.06		0.74	−0.6
211104793	J04124068+2438157	B		0.2	5.81		0.77	−0.46
246859790	J04440164+1621324	QPS	APD	0.08	2.17		0.66	0.18
246923113	J04470620+1658428	S		0.75	12.50		0.87	−0.03
246925324	J04465305+1700001	B	QPS	0.31	15.62	3.01	0.54	−0.87
246929818	J04465897+1702381	APD		0.58	10.87		0.75	0.5
246942563	J04542368+1709534	APD		0.17	5.07		0.85	0.16
246963876	J04343128+1722201	B		0.21	78.62		1.0	−0.56
246989752	J04384725+1737260	QPD		0.15	1.62		0.79	0.27
246990243	J04384502+1737433	B		0.2	2.50		0.83	−0.76
247027353	J04332789+1758436	B		0.67	8.33		0.84	−0.32
247031423	J04333297+1801004	MP		0.01	3.09	3.29	0.52	0.1
247035365	J04335283+1803166	QPS		0.02	2.60		0.22	0.54
247046059	J04324107+1809239	QPS		0.02	2.00		0.8	0.06
247047380	J04334871+1810099	B		0.24	7.35		0.82	−0.43
247051861	J04321606+1812464	P		0.08	2.66		0.15	−0.02
247078342	J04322210+1827426	QPD		0.2	1.92		0.79	0.85
247103541	J04363081+1842153	APD		0.07	23.44		0.96	0.35
247520207	J04391779+2221034	QPD		0.53	5.81		0.79	0.69
247534022	J04333905+2227207	QPS		0.06	13.16		0.36	0.16
247573157	J04332621+2245293	MP		0.06	9.62	4.55	0.42	0.17
247575425	J04331907+2246342	S		0.68	37.90		0.87	0.08
247575958	J04330945+2246487	QPS		0.25	3.47		0.72	−0.01
247583818	J04354733+2250216	QPS	APD	0.12	2.43		0.56	0.02
247584113	J04335200+2250301	S		0.37	17.33		1.0	0.04
247585465	J04322415+2251083	B		0.09	2.48		0.69	−0.53
247589612	J04324911+2253027	APD	QPS	0.16	47.65	2.21	0.94	0.99
247590222	J04331650+2253204	S		0.53	51.22		1.0	−0.09
247591534	J04355760+2253574	QPS		0.23	7.81		0.67	0.18
247592103	J04355415+2254134	MP		0.08	1.20	1.22	0.43	−0.02
247592463	J04355277+2254231	APD		0.26	42.09		0.89	0.68
247592919	J04355684+2254360	B		0.23	21.56		0.88	−0.37
247593952	J04355209+2255039	P		0.06	0.85		0.15	0.06
247596872	J04335252+2256269	MP		0.08	1.41	4.10	0.18	0.24
247601658	J04345693+2258358	P		0.2	2.02		0.08	0.23
247604953	J04305028+2300088	S		0.62	56.45		0.93	−0.12
247763883	J04330622+2409339	QPS		0.38	2.50		0.83	0.03
247764745	J04330664+2409549	QPD		0.11	4.39		0.51	0.32
247788960	J04323058+2419572	QPS		0.11	6.94		0.71	−0.24
247789209	J04323176+2420029	B		0.39	35.27		1.0	−0.38
247791801	J04333456+2421058	QPD		0.6	4.63		0.37	0.19
247792225	J04333405+2421170	S		0.54	7.14		0.82	0.01
247794636	J04321786+2422149	MP		0.05	1.72	2.60	0.45	0.1
247799571	J04315056+2424180	QPS		0.31	3.29		0.72	0.11
247805410	J04302961+2426450	APD		0.31	34.16		1.0	0.3
247810494	J04345542+2428531	S		1.3	55.47		1.0	−0.3
247810751	J04321540+2428597	S		0.51	25.87		0.92	0.1
247820507	J04292373+2433002	S		0.16	13.63		1.0	−0.22
247820821	J04295950+2433078	QPS		0.96	2.38		0.46	0.19
247827638	J04293606+2435556	P	APD	0.23	3.91		0.12	−0.24
247837468	J04293008+2439550	B		0.32	11.90		0.55	−0.48
247842020	J04305171+2441475	L		0.24	115.36		1.0	−0.24
247843485	J04305137+2442222	B		0.17	4.17		0.56	−0.59
247885481	J05023985+2459337	APD	QPS	0.06	2.98		0.82	0.32
247890584	J05010116+2501413	P		0.07	8.62		0.09	−0.1
247915927	J04442713+2512164	QPS	APD	0.15	4.46		0.35	0.45
247923794	J04423769+2515374	QPS		0.55	3.68		0.57	−0.04
247932205	J04403979+2519061	MP		0.03	0.94	0.85	0.74	−0.32
247935061	J04430309+2520187	APD		0.2	18.35		0.9	0.25
247935696	J04422101+2520343	QPS		0.08	1.89		0.36	−0.05
247941378	J04420548+2522562	MP		0.19	4.90	2.66	0.15	0.01
247941930	J04420777+2523118	S		0.87	8.33		0.8	−0.2
247968420	J04414825+2534304	QPS		0.54	2.91		0.41	−0.05
247986526	J04270280+2542223	B		0.4	15.62		0.81	−0.48
247991214	J04390396+2544264	QPS		0.22	3.12		0.54	−0.4
247992574	J04392090+2545021	QPS		0.89	5.81		0.73	−0.1
247992575	J04395574+2545020	L		0.77	66.20		1.0	0.53
248006676	J04404950+2551191	QPD		0.27	3.33		0.38	0.64
248009353	J04324282+2552314	QPS		0.33	3.79		0.67	−0.02
248015397	J04411078+2555116	QPD		0.6	3.91		0.77	0.25
248017479	J04410826+2556074	S		0.35	6.76		0.8	−0.15
248018164	J04413882+2556267	S		0.61	30.03		1.0	0.08
248018652	J04305718+2556394	U		0.25	27.87		0.96	−0.1
248023915	J04380083+2558572	MP		0.06	0.66		1.0	0.0
248029373	J04304425+2601244	S		1.23	32.63		1.0	−0.01
248029954	J04394748+2601407	B		0.12	2.98		0.78	−0.19
248030407	J04394488+2601527	QPS	APD	0.16	3.47		0.3	0.01
248038058	J04400800+2605253	B		0.35	34.53		0.86	−0.32
248040905	J04295156+2606448	QPS	APD	0.99	6.58		0.78	−0.13
248044306	J04300724+2608207	B		0.27	3.82		0.9	−0.12
248046139	J04382134+2609137	QPS		0.99	2.66		0.44	0.3
248047443	J04333678+2609492	QPD		0.13	7.58		0.6	0.23
248049115	J04383528+2610386	P		0.1	4.54		0.16	−0.22
248049475	J04382858+2610494	B		1.06	61.27		0.9	−0.67
248051303	J04381486+2611399	B		0.19	5.95		0.84	−0.45
248055184	J04335470+2613275	QPS		0.09	2.75		0.52	0.05
248057096	J04331435+2614235	QPS		0.18	11.9		0.52	0.0
248058354	J04334465+2615005	QPS		0.46	5.81		0.7	−0.06

Note. Variability properties for Taurus stars with inner disks observed in K2 Campaigns 4 and 13. Variability types are determined by eye and supported by statistical measures. The types consist of the following: "P" is for strictly periodic behavior, "MP" is reserved for stars with multiple distinct periods, "QPD" is for quasiperiodic dippers, "QPS" means quasiperiodic symmetric (i.e., quasiperiodic stars that neither burst nor dip), "APD" are aperiodic dippers, "B" is for bursters, "S" is for stochastic stars, and "L" is the label for long-timescale behavior that does not fall into the other categories.

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4.2. Hybrid Classes

4.3. Summary of Source Classification

Table 3 shows the breakdown of the Taurus classification. We find 21 bursters, 16 stochastic objects, nine aperiodic dippers, eight quasiperiodic dippers, 26 quasiperiodic symmetric objects, seven periodic stars, eight multiperiodic sources, and three long-timescale variables. Uncertainties on the fractional make-up for each group were determined based on binomial distributions (see, e.g., the Appendix of Burgasser et al. 2003). We also compare in Table 3 the Taurus fractions to those for other clusters we have studied, and discuss these results in Section 7.

Table 3. Variability Types among Young Disk-bearing Stars

Morphology Class	Taurus	Oph	Sco	Sco/Oph	NGC 2264
				Composite
	%	%	%	%	%
Categories based on periodicity and stochasticity
All bursters	${21}_{-3}^{+5}$	${14}_{-3}^{+5}$	${13}_{-2}^{+3}$	${14}_{-2}^{+2}$	${13}_{-2}^{+3}$
Aperiodic symmetric (stochastic)	${16}_{-3}^{+5}$	${12}_{-3}^{+4}$	${6}_{-1}^{+2}$	${8}_{-2}^{+2}$	${13}_{-2}^{+3}$
Quasiperiodic symmetric	${26}_{-4}^{+5}$	${20}_{-4}^{+5}$	${29}_{-3}^{+3}$	${26}_{-2}^{+3}$	17 ± 3
Aperiodic dippers	${9}_{-2}^{+4}$	${9}_{-2}^{+5}$	${18}_{-2}^{+3}$	${16}_{-2}^{+2}$	${11}_{-2}^{+3}$
Quasiperiodic dippers	${8}_{-2}^{+4}$	${14}_{-3}^{+5}$	${18}_{-2}^{+3}$	${17}_{-2}^{+2}$	${10.5}_{-2}^{+3}$
Periodic symmetric	${7}_{-2}^{+4}$	${6}_{-2}^{+4}$	${7}_{-2}^{+2}$	${7}_{-2}^{+1}$	${3}_{-1}^{+2}$
Other categories
Multiperiodic	${8}_{-2}^{+4}$	${7}_{-2}^{+4}$	${4}_{-1}^{+2}$	${5}_{-1}^{+2}$	${1}_{-1}^{+2}$
Long timescale	${3}_{-1}^{+3}$	${8}_{-2}^{+4}$	${0}_{-0}^{+2}$	${3}_{-1}^{+1}$	${1}_{-1}^{+2}$
Unclassifiable	${0}_{-0}^{+2}$	${2}_{-0}^{+3}$	${0}_{-0}^{+2}$	${1}_{-1}^{+1}$	${11}_{-2}^{+3}$
Nonvariable	${0}_{-0}^{+2}$	${6}_{-2}^{+4}$	${3}_{-1}^{+2}$	${4}_{-1}^{+1}$	19 ± 3

Note. Fraction of young stars in each light curve morphology group, as defined by eye but generally supported by the statistical measures Q and M (Section 5). There are eight variability categories, plus one more for nonvariable sources.

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In addition to computing the Q and M statistics for each light curve, we have also assessed other features such as the variability amplitude and various timescale metrics. These measurements provide a broader picture of the flux variations, offering hints into their origins.

5.1. Amplitudes

While the photometric precision of most of our light curves is less than 1%, the observed flux excursions are typically much larger than that. To quantify the variability level and search for correlations with light curve morphology type, we measured a "peak-to-peak" amplitude. This metric was defined by first identifying the bottom and top fifth percentile of flux points, and then determining the difference between them. All amplitudes were measured on the normalized light curves. The resulting values are reported in Table 2 and plotted in Figure 5.

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The variability amplitudes range from 0.005 to 1.36 in normalized flux units (roughly 0.5% to 140%). As seen in Figure 5, the lowest amplitude objects are periodic, multiperiodic, or quasiperiodic, while those with the highest amplitudes tend to be aperiodic, though not exclusively so.

We note that the point sizes in Figures 4, 6, 7, and 8 are scaled by these light-curve amplitudes.

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5.2. Timescales

6.1. Variability and Circumstellar Disks

As described in Section 2, our sample consists of 99 disk-bearing sources. Of these, 93 have evidence for strong inner disks with α > −1.6. The remainder have weaker disks with α < −1.6 (where a photosphere would have α = −3); they are formally Class III objects interpreted as having sparsely populated inner regions.

In Figure 6, we show the photometric variability classes in a disk diagnostics plot, with α measuring infrared excess strength (and consequently disk geometry and accretion) versus equivalent width of Hα emission (where available in the literature), measuring gas accretion and outflow strength. The equivalent widths were adopted from the literature, ⁴ and are therefore not simultaneous with the K2 variability assessed here. Besides their photometric variability, the variability of Hα line profiles and line strengths is well-documented (e.g., Zsidi et al. 2022) in accreting T Tauri stars. Despite being prone to scatter, Figure 6 does show a few notable trends.

Stars with periodic signals are segregated toward lower infrared excess and smaller gas emission, as expected if we have a clear view toward the stellar photosphere, unaffected by line-of-sight dust or gas. Stars with quasiperiodic or aperiodic dipping light curves also tend to have smaller gas emission, though they span a range of infrared excess. The quasiperiodic symmetric stars typically have somewhat larger gas emission and also span a range of infrared excess. There are few bursters, but they tend toward Class II type disks, with a range of gas emission strengths.

For comparison, we also show the same diagram for the Cody & Hillenbrand (2018) sample of Upper Sco and ρ Oph stars. The larger population there exhibits similar behavior with respect to the light curve categories, though the trends described above are not quite as clear, with more overall spread. There is a well-populated concentration of quasiperiodic dippers at moderate infrared excess and low gas emission. We note that using infrared colors instead of the SED slope α typically hides the trends discussed above.

The observed variability may not only be tied to disk emission and gas accretion strength, but also to viewing geometry. It has long been hypothesized (Bouvier et al. 1999) that dipper stars must be viewed at high inclinations in order for dusty material in the inner disk to block our line of sight. This idea was recently questioned by Ansdell et al. (2020), who noted several dippers with nearly face-on measured disk inclinations. We further assess the correlation between inclination and variability type here.

To do so, we assemble an updated inclination data set from millimeter and submillimeter observations of Taurus disks. Recent high-quality disk inclinations are available for a decent fraction (∼25%) of our sample (Schaefer et al. 2009; Tripathi et al. 2017; Long et al. 2019; Aizawa et al. 2020; Ansdell et al. 2020; Villenave et al. 2020). In Figure 7, we show the inclinations as a function of our calculated Q. Of note is the fact that there is no inclination data for the periodic sources in our sample, consistent with our finding above that the periodic sources have small infrared excesses; the disks surrounding these sources are apparently weak in the millimeter and submillimeter as well, according to their infrared spectral energy distributions.

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Figure 7 also compares the Taurus inclinations and Q values to those derived for ρ Oph and Upper Sco. For the latter, the inclinations are from Barenfeld et al. (2017) and Ansdell et al. (2016); the Q data come from Cody & Hillenbrand (2018). All values are color-coded by light curve morphology type, to enable exploration of the variability properties as a function of inclination. We circle in black points for which multiple sources are blended into the light curve; in these cases, it is difficult to uniquely associate light curve behavior with geometry. For several binary systems, including DK Tau AB (EPIC 210777988), HK Tau AB (EPIC 247799571), and UZ Tau AB (EPIC 248009353), there are two very different measured disk inclinations, and we omit them from the Taurus panel.

Our main conclusion from the inclination–Q comparison is that periodic and quasiperiodic sources are almost exclusively found at moderate to high inclination (40°–90°), while the disk inclination distribution of aperiodic sources appears largely isotropic. This finding is particularly significant for the dipper stars, which split into quasiperiodic and aperiodic subtypes. The differing inclination distributions for these subtypes suggests that they may originate from distinct phenomena, or different locations, in terms of disk radius.

6.2. Variability and Stellar Properties

In Figure 8, we show the distribution of α measuring infrared excess slope with spectral type, again color-coded by photometric variability type. There are no clear trends in variability type with spectral type, a proxy for stellar mass in the early pre-main-sequence phase. An alternate plot using color instead of spectral type (not shown) also reveals no trends.

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We also do not see any tendency toward lower amplitude at higher mass and temperature, which was a tentative trend in the Upper Sco data set (Cody & Hillenbrand 2018) as well as a finding of Venuti et al. (2021). However, there are only a few stars in our Taurus sample earlier than spectral type K, so this is a weak conclusion. What we do see is that the collection of low-amplitude (<1%) periodic variables is clustered at low mass (e.g., purple points of spectral type M in Figure 8). This may again be a result of the lack of early-type stars in the sample, as well as the younger age of Taurus, as compared to Upper Sco.

With K2 photometry available now for more than one star-forming region dominated by low-mass YSOs, we are in a position to perform a comparison of variability properties with age. Figures 4, 5, 6, and 7 already compare Taurus, at 1–5 Myr of age, with ρ Oph (∼1 Myr) and Upper Sco (∼5–10 Myr). We find several significant differences between these clusters.

First, there is a a significantly lower fraction of low-Q (<0.4) systems in Taurus, as seen in Figure 4. There is a conspicuous gap in the Q–M diagram from Q ∼ 0.2–0.35. This gap is difficult to explain as an evolutionary effect, since it is not present in either the younger ρ Oph data set or the older Upper Sco data set.

In addition, the measured incidence of quasiperiodic dippers (QPDs) in Taurus is only about half that of ρ Oph and Upper Sco. The error bars are substantial, though, and it is possible that the younger two regions (Taurus and ρ Oph) both have a lower QPD rate of roughly 11%, while Upper Sco remains elevated at a rate of at least 16%. This trend of increasing dipper fraction at older age would be in line with the tendency for dipper behavior to occur for stars with weaker inner disks, as indicated by smaller near- and mid-infrared colors (Cody & Hillenbrand 2018).

Turning to the top portion of the Q–M diagram in Figure 4, we also see more quasiperiodic bursters (orange points with Q < 0.85) in Taurus as compared to ρ Oph and Upper Sco, but somewhat less extreme flux asymmetries (lower M) overall.

There is also a trend in overall amplitudes decreasing as a function of age. Whereas some of the ρ Oph burster light curves vary by a factor of almost three (0.5 in log space, as seen in Figure 5), the amplitudes in Taurus and Upper Sco rarely exceed 100%. Furthermore, the bottom envelope of the amplitude distribution decreases with age. Quasiperiodic targets in Upper Sco extend down to amplitudes as small as 0.001, whereas they only reach ∼0.005–0.01 in Taurus. In ρ Oph, we do not see any amplitudes smaller than 0.025.

Timescales of variability are presumably dominated by several phenomena, including accretion fluctuations and stellar rotation or inner disk orbits (at a similar timescale if at corotation). Among the three regions ρ Oph, Taurus, and Upper Sco, we do not observe a significant difference in the overall distribution of timescales (Figure 5). When broken down into individual variability types, we only detect a difference among quasiperiodic dippers. The timescales for the QPDs extend to somewhat larger values for the older population of Upper Sco than they do in ρ Oph and Taurus. The origin of this effect is unclear, but it may be connected with the disk clearing that occurs at older ages.

We also detect a stronger tendency toward periodic bursting behavior in the younger ρ Oph and Taurus populations, as compared to Upper Sco. This is evident in the rightward shift of the orange points (bursters) from the top Q–M diagram in Figure 4 to the bottom one. In Taurus, the behavior at Q > 0.5 is mostly low-M, i.e., burst-dominant, whereas in Upper Sco, we see a wide range of light curve asymmetry here.

All of the above trends are consistent with the variability patterns in younger populations being more dominated by the accretion properties of the YSOs than either the properties of the stars (which are the origin of the periodic light curve signatures indicating stellar rotation) or the properties of the optically thin layers of the disks (which are the likely origin of the dipper light curve effect). The explanation for this is that the Taurus stars have, on average, less-evolved disks than those in Upper Sco. In Upper Sco, if the accretion rates are somewhat lower and the disks somewhat more evolved, variability could be dominated by the kinematics of the rotating dust near the corotation radius. Our observations support the idea that the accretion timescale is shorter than that of inner disk dispersal, as measured by, e.g., near-infrared excess.

Young stars of the Taurus Molecular Clouds are the fourth population of <10 Myr old stars for which high-precision, high-cadence optical photometric monitoring data are available from space-based platforms. We have presented here a study of the young disk-bearing stars in Taurus observed by K2, and applied quantitative metrics to classify their light-curve behavior.

Within Taurus, we found that all of the disk-bearing stars display variability detectable above the photometric noise floor. Using the Q and M statistics developed by Cody et al. (2014), we have divided the light curves into morphology categories, as listed in Table 3. In Taurus, the dominant mode of variability is "quasiperiodic symmetric" behavior, in which a pattern that favors neither flux increases (bursts) nor decreases (dips) emerges. The second most common variability type is bursting, the majority of which in Taurus is quasiperiodic. Dipper behavior is less common in Taurus than its incidence in the other clusters. More rare variability types include strictly periodic stars and those with long-timescale trends. In general, around 70% of the light curves have repeating patterns that we label as periodic or quasiperiodic, while the remaining 30% display more erratic, and typically higher-amplitude, variability. These estimates are based on the Q values listed in Table 2 and displayed in Figure 4.

We have previously discussed the origins of these different variability morphology types, and our findings in Taurus largely support a consistent picture. Several different driving mechanisms are at work, with the possibility for more than one to operate at the same time in individual stars.

The simplest variability categories to explain are the periodic and multiperiodic types. We have shown that stars with perfectly repeating (and often sinusoidal) patterns are most often class III sources with very weak disks. Thus, we are likely seeing the rotational modulation of one or more magnetic starspots, since there is little accretion or disk material to introduce other genres of flux variation.

The bursters, on the other hand, likely represent cases for which accretion flow variations and associated stellar surface hot shock regions dominate the flux changes. Ribas et al. (2014) and Fedele et al. (2010) showed that accretion rates decrease over time, and hence we would expect to see bursting behavior tapering off as stars evolve. We have detected a decrease in the quasiperiodic burster incidence from ρ Oph through Taurus to older Upper Sco that may reflect this trend. The Upper Sco sample included a population of aperiodic bursters, which could point to a shift from rotationally modulated hotspots to more erratic gas flow as YSOs age.

Long-timescale variability appears to be almost exclusively associated with class I or flat spectral energy distributions, and hence more embedded sources. We are likely observing flux changes connected with copious circumstellar material and light reflected off of it that originates on or near the stellar surface. There may be many more of these long-timescale variables, but higher levels of extinction precludes good photometric detection and precision with Kepler.

The physical driver of quasiperiodic variations remains difficult to pinpoint, as it may be a combination of spot modulation (either cool magnetic spots or hot accretion spots) and obscuration by orbiting circumstellar material near corotation. Future multicolor photometric monitoring should help distinguish the different mechanisms here.

Finally, dipper variability has typically been ascribed to occultation of the central star by elevated dusty material at or near the inner disk edge. Our data support this hypothesis but suggest that there may be different origins for quasiperiodic and aperiodic dipper behavior. This idea comes from the finding that single (i.e., nonbinary), quasiperiodic dipper stars in the ρ Oph, Taurus, and Upper Sco samples all have measured disk inclinations of at least 40° (at least for the fraction of YSOs where interferometric data is available). The set of aperiodic dippers, on the other hand, seems to have a relatively isotropic distribution of inclinations, with some targets hosting nearly face-on disks.

Few theoretical models have endeavored to explain the full suite of YSO variability elucidated in the recent continuous, high-cadence space telescope data. However, Robinson et al. (2021) demonstrated that they can populate much of the parameter space at M < 0.25 (symmetric to bursting light curves) and Q < 0.9 (not completely stochastic light curves) with magnetospheric accretion disk models of varying corotation radii; additional important parameters include the detailed configuration of the magnetic field, and the fractional area of the accretion flow on the surface of the star. The models are somewhat idealized in their geometry and spot parameters, but nevertheless provide valuable insight. Specifically, Robinson et al. (2021) create synthetic light curves for systems spanning appropriate ranges in physical and geometric parameters describing the infall of material from an inner disk region onto a central star. They then analyze noised-up versions of the light curves using the Q and M metrics. A major determinant of the behavior is source inclination, with Robinson et al. (2021) finding that the high-inclination sources have purely periodic low Q values, the intermediate inclination have quasiperiodic, intermediate Q values, and the low inclination have stochastic, high Q values, where we essentially are viewing the stochastic infall along the field lines directly, unmodulated by stellar rotation. However, these are stated as "typical" trends, with the Q values for any individual source also influenced by other parameters in the model. The M metric was stated as most influenced by parameters associated with the magnetic field strength and geometry, along with source inclination.

At this juncture, it is possible that not all of the observables required to explain different variability modes are amenable to observational constraint. For example, magnetic field strength and geometry is only available for a handful of bright targets. Through our work on YSOs observed during the K2 Mission, we have confirmed that no single stellar or circumstellar parameter determines the time domain flux properties. The light curve morphology, timescale, and amplitude are shaped by disk evolutionary state (and hence stellar age), system inclination, accretion rate, and likely magnetic properties as well. Further monitoring of both low-mass and intermediate-mass YSOs by the TESS satellite may soon help further untangle the physical drivers of variability, enabling renewed modeling efforts and constraints on the nature of the inner disk region where terrestrial planet formation may be ongoing at this epoch.

We thank the referee for constructive comments. This paper includes data collected by the K2 mission, for which funding was provided by the NASA Science Mission directorate. This work was additionally supported by K2 Guest Observer program GO13117 and NASA award 80NSSC17K0026.

In this appendix, we show light curves for disk-bearing (Figure 9) and non-disk-bearing (Figure 10) sources toward Taurus.

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View figure set (10 panels)

Tarball of figure set images

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As a check on the timescales derived for our periodic and quasiperiodic sources (e.g., those with Q < 0.85), we performed a comparison with the results of R20, who studied periodic sources in Taurus. Although ostensibly the same data set was used in the two studies, there are methodological differences, as we have used a combination of Fourier transforms and autocorrelations instead of Lomb–Scargle periodograms. In addition, the period-searched light curves adopted in R20 partially overlap those used here, but sometimes are drawn from other groups' pipelines. For these reasons, there can be differences in both the periodicity detections (or lack thereof) and the derived periods, which we detail in this section.

B.1. Discussion of Objects with Periodicities or Quasiperiodicities Reported Here but Not in R20

B.2. Discussion of Individual Objects Reported as Periodic in Both Studies

B.3. Discussion of Individual Objects with Reported Periodicities Not Recovered in This Study