Orbiting Clouds of Material at the Keplerian Co-rotation Radius of Rapidly Rotating Low-mass WTTs in Upper Sco

For the first three K2 campaigns, the K2 Science Center did not produce detrended light curves. Instead, what was provided was the raw CCD pixel data for each star at each epoch. We (Cody et al. 2017) therefore created our own detrended light curves. We produced two primary versions—one where the aperture centers were held fixed over the course of the K2 campaign and another where a new center was derived at each epoch. For each flavor of reduction, photometry was produced with 2- and 3-pixel radius apertures. For each of these four light-curve versions, we then applied a version of the detrending routine described in Aigrain et al. (2016) to remove the short-term, non-astrophysical trends in the data.

After we had begun writing this paper, two other light-curve reductions became publicly available for Campaign 2, the Vanderburg reduction (Vanderburg & Johnson 2014) and the EVEREST reduction (Luger et al. 2016). We downloaded light curves for each of the stars that we considered as possibly relevant to this paper.

For each star addressed in this paper, we examined all of the light-curve variants that we had available and chose the one that appeared to have the least non-astrophysical contribution (when several variants were about the same, we simply adopted our own detrended light curve). In all cases, the unusual features that caused us to include the star in our paper were present in multiple light-curve variants. In a few cases, one of the light-curve variants did not have the same signature. We believe this indicates that the detrending algorithm employed in that version removed some real astrophysical signature, or that the aperture size used in that version or the centering algorithm in that version resulted in the light curve being dominated by light from a different star. We made special effort in these cases to closely examine all the available data (finding charts, literature, all light-curve variants, and different aperture sizes) in order to make sure that the light curve we present here is the best available for that star.

The Ecliptic Plane Input Catalog (EPIC; Huber et al. 2016), available at MAST, provides accurate coordinates for all of the stars in our sample. Using those coordinates, we downloaded all available near and mid-IR photometry for our stars from the 2MASS (Skrutskie et al. 2006), WISE (Wright et al. 2010), Spitzer (Werner et al. 2004) SEIP¹⁰ and FEPS (Meyer et al. 2006), AKARI (Murakami et al. 2007), and SDSS (e.g., Ahn et al. 2014) archives as well as B- and V-band photometry from APASS (Henden & Munari 2014). We also downloaded grizy photometry for most of our stars from the PAN-STARRS database (Flewelling et al. 2016). Spectral types were available in the literature (Preibisch et al. 2002; Erickson et al. 2011; Lodieu et al. 2011; Luhman & Mamajek 2012; Rizzuto et al. 2015) for 80% of our stars; for most of the stars, those same references also provided Hα and lithium (6708 Å) equivalent widths. We have used our own Keck HIRES spectra to provide a small amount of new spectral information, as described in the Appendix.

One goal for the ancillary data was to provide a color–magnitude diagram that would include all of the stars in our sample, and for that we decided to attempt to determine estimated $V-{K}_{s}$ colors for every star. Because only a small fraction of the Upper Sco members have published V-band photometry, this required transforming photometry or colors obtained at other optical bands. As the first step in that process, we downloaded G-band photometry for all of our stars from the newly released Gaia DR1 archive (Gaia Collaboration et al. 2016). We then derived a formula to convert $G-{K}_{s}$ colors to $V-{K}_{s}$ colors based on a large sample of low-mass stars with published $V-{K}_{s}$ colors in Praesepe (L. Rebull et al. 2017, in preparation). For the stars lacking Gaia photometry, we obtained I magnitudes from the Deep Near-Infrared Survey of the Southern Sky (DENIS; Epchtein et al. 1997) and derived a conversion formula in a similar way between ${I}_{(\mathrm{DENIS})}-{K}_{s}$ and $V-{K}_{s}$.

We used all of the available photometry and spectral types to produce spectral energy distributions (SEDs) for each star (the individual SEDs are shown in the Appendix). From those SEDs, we identified stars with possible IR excesses. For each of the sources thought to have an IR excess, we looked at the images, where available, to assess the quality of the photometry. The longest wavelength data we have is either WISE 22 μm or, for just four stars Spitzer 24 μm. In several cases, the 22 μm point from WISE, in particular, was not a secure detection, and the apparent IR excess therefore vanished. Only one star in our final sample has a relatively secure, though small IR excess (only at 24 μm), and that is EPIC 205024957. Carpenter et al. (2009) also determined that EPIC 205024957 has a 24 μm excess and identified it as a debris disk. For the stars where our longest wavelength detection is at 12 μm, the lack of an excess at that wavelength precludes them from having primordial disks. Because of the paucity of good data longward of 12 μm for most of our stars, a larger fraction could harbor debris disks.

The first step in our sample selection was to eliminate stars with active accretion (CTTs) from the Upper Sco and ρ Oph K2 sample, since the accretion process in CTTs and interactions with the primordial circumstellar disk can produce unusual light curves of many types, and addressing those types of variabilities was beyond the scope we wanted here (but see Cody et al. 2017). None of the stars we retained for this paper have SEDs consistent with Class I or II primordial disks (see the SED plots in the Appendix, and compare, for example, to the SEDs of Class I and II sources in Upper Sco shown in Cody et al. 2017 or similar sources in Taurus, as shown in Rebull et al. 2010). Two of the stars are considered as ρ Oph members in the literature (EPIC 203962559 and EPIC 203927435); all of the others are considered as members of Upper Sco.

Once we identified the full set of Upper Sco weak-lined T Tauri (WTTS) members with K2 data, three of the authors (T.J.D., L.M.R., A.M.C.) independently examined the data for each star, including each of the light-curve variants described above. They also independently searched for periodicities in those light curves and examined the phased light curves. Those efforts were aimed primarily at identifying possible planet transits, eclipsing binary candidates, or variability related to accretion or circumstellar disk structure or in compiling stellar rotation periods. During the course of those efforts, a few dozen stars were identified as having light curves that were not easily explained by any of those mechanisms. In those cases, further analysis was done and other members of the team were brought in to perform more manual detrending of the light curves. This more detailed analysis resulted in some of these light curves being ascribed to artifacts in the data or to allowing them to fit into one of the established light-curve classes. However, 23 of these stars survived. These stars are listed in Table 1.

Table 1.  List of Upper Sco Stars with Unusual Periodic Light Curves

EPIC ID	Namea	R.A.	Decl.	Ks	$V-{K}_{s}$ b	$[W1]-$[W3]	${\lambda }_{\max }$ c	SpTd	Hα EqW	Li EqW	P1e	P2e	Classf
		(deg)	(deg)	(mag)	(mag)	(mag)	(μm)		(Å)	(Å)	(days)	(days)
204918279	RIK-21	239.1046	−20.2711	9.86	6.90d	0.38	12	M5.0	−10.2	0.61	0.4594	0.4665*	1
204066898	UScoCTIO 80A	239.6509	−23.8005	10.19	5.59	0.27	12	M3	−9.9	⋯	0.3956*	0.5386	1
203462615	RIK-42	239.9086	−26.0565	10.25	6.13	0.47	12	M5.5	−16.2	0.81	0.5201*	0.4421	1
204897050	UScoCTIO 56	240.4208	−20.3689	10.86	7.16d	0.42	12	M5	⋯	⋯	0.2639	⋯	1
202724025	RIK-90	242.2373	−28.5993	9.63	5.78	0.33	12	M4.5	−10.2	0.21	0.2595*	0.2795	1
204117263	LHJ-65	242.7589	−23.5973	10.95	6.42	0.35	12	M5	−11.6	⋯	0.6423	⋯	1
204367193	LHJ-77	242.9766	−22.6137	13.30	8.33	⋯	4.6	M6.3	−10.3	⋯	0.4835	⋯	1
203534383	⋯	243.5125	−25.8148	11.71	7.73	0.73	12	M4:	−9.5	⋯	0.2784*	0.3234	1
205110559	⋯	243.8322	−19.3520	10.46	7.74	0.61	12	⋯	⋯	⋯	0.4031	⋯	1
203050730	RIK-246	247.7741	−27.4295	10.53	5.87	0.53	12	M4.5	−9.1	0.38	0.4865*	0.7740	1
203185083	RIK-253	248.6464	−26.9675	10.48	6.62	0.18	12	M4.5	−27.1	0.54	0.4400	⋯	1
204364515	⋯	240.3398	−22.6240	10.05	6.84	0.34	24	M4	−8.4	0.55	3.0863	1.456*	2
203849738	RIK-100	242.4703	−24.6982	10.93	6.69d	0.37	12	M5.5	−15.1	0.40	0.6190	⋯	2
203692610	⋯	242.6318	−25.2671	11.60	5.92	0.28	12	M4	−3.0	0.54	1.821	⋯	2
205374937	⋯	242.8255	−17.9580	9.33	6.35	0.34	24	M4	−4.8	0.55	0.6345*	0.5436	2
202873945	⋯	245.4164	−28.0518	11.24	8.21	0.75	12	⋯	⋯	⋯	0.6258	⋯	2
204296148	⋯	246.2158	−22.8952	10.99	8.06k	0.10	12	⋯	⋯	⋯	0.5314*	0.4717	2
203962559	AOC 64	246.7103	−24.2312	10.80	8.83d	⋯	8	M4	−6.0	⋯	1.5402	⋯	2
203927435	WMR 2–23	247.1794	−24.3812	10.14	9.11d	0.13	12	M4.5	−6.8	0.76	0.4820*	0.4162	2
205024957	⋯	242.5459	−19.7678	11.38	6.53	0.46	24+	M5	−4.4	0.56	1.6656	⋯	3
205046529	⋯	242.6099	−19.6642	10.40	6.52k	0.35	24	M4	−4.4	0.54	2.5619	1.8358*	3
204143627	LHJ-120	243.9969	−23.4934	11.31	6.29	0.13	12	M5	⋯	⋯	1.125	⋯	3
205483258	RIK-210	245.8523	−17.2909	9.65	5.04	0.37	12	M2.5	−5.3	0.59	5.667	⋯	3

Notes.

^aSources of the names are: RIK: Rizzuto et al. (2015); UScoCTIO: Ardila et al. (2000); LHJ: Lodieu et al. (2007); AOC: Alves de Oliveira & Casali (2008); WMR: Wilking et al. (2005). ^b $V-{K}_{s}$ estimated preferentially using a conversion based on the Gaia DR1 "G" magnitudes and 2mass K_s values. A "d" is appended if instead the $V-{K}_{s}$ estimate is based on Denis "I" magnitudes and 2mass K_s. A "k" is appended if the K2 count rate itself was used to estimate V. ^cLongest wavelength at which there is a secure detection, in μm. A plus sign indicates if there is a plausible, small IR excess. ^dSpectral type, Hα equivalent width, and Li equivalent width for EPIC 203534383 and 203692610 are from our own HIRES spectra. The Li equivalent widths for EPIC 203849738, 204364515, 205024957, and 205046529 are also from our own HIRES spectra. See the discussion in the Appendix. ^eAn asterisk is attached to the period (P1 or P2) to designate which star in a binary has the unusual light curve that is discussed in this paper. All of the binary companions have normal, spotted-star light-curve morphologies. ^fLight-curve classes: 1 = scallop shell; 2 = persistent short-duration flux dip; 3 = transient short-duration flux dip.

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We have sorted our unusual light curves into three classes in order to facilitate our discussion of their properties. We acknowledge that this sorting is probably imperfect, and that the boundaries between classes are indistinct. An alternative view is that all of our stars belong to a single group and their differing light-curve morphologies arise due to a range in our view angle to their rotation axes or to a range in their rotation rates (e.g., because that affects the location of the Keplerian co-rotation radius relative to the sublimation radius) or to some other hidden parameter. After assembling the data we had available, we nevertheless felt it was helpful to sort the stars into the three groups in order to emphasize the shared properties within each group.

Table 1 provides a list of all 23 stars we identified as belonging to these three classes, along with some of their overall defining properties. Spectral types are known for 20 of these stars; all are M dwarfs, with 17 of the 20 having spectral types between M4.0 and M5.5. Most of the Upper Sco K2 sample are M dwarfs, but the stars in Table 1 are predominantly weighted toward later M subtypes (this is also reflected in their CMD locations—see Figure 23). Eighteen of the stars in Table 1 have known Hα equivalent widths, all but one of which have equivalent widths appropriate for WTTS (−3.0 Å < EqW < −16 Å). Thirteen of the stars in Table 1 have measured Li 6708 Å equivalent widths, all of which are ∼0.5 Å, also as appropriate for WTTS mid-to-late M dwarfs (the spectral types for two stars and the lithium data for six stars are from our own HIRES spectra, as described in the Appendix).

Eleven of 23 (48%) of the stars in Table 1 have two Lomb–Scargle periods (i.e., are apparent binaries), which seems high. From the full sample of K2 M dwarf WTTs with 2 < P < 8 days (∼280 stars), only 16% are apparent binaries by the same measure. However, for the ∼140 K2 M dwarfs with P < 1 day, 38% are apparent binaries. Thus, the stars in Table 1 may have a high binary fraction simply because the rapidly rotating low-mass stars in Upper Sco are often binaries. This is consistent with the conclusion from Stauffer et al. (2016) that M dwarfs in the Pleiades with two Lomb–Scargle peaks are both more rapidly rotating and the two periods are closer together than would have been true if their periods were drawn at random from the single star population.

Figure 1 shows phased light curves for two examples of each of the three classes; phased light curves for all members of the scallop shell and persistent flux-dip classes are provided in the Appendix, along with a description of the processing we have done to the original light curves. The class definitions are as follows.

• 1.  
  Scallop shells—phased light curves that look like the rim of a scallop shell. They have many wave-shaped undulations in their phased light curves. Usually the shape remains nearly constant for the entire K2 campaign, but in some cases it changes over time. Peak-to trough amplitudes from a few percent to more than 10%; periods always less than 0.65 days. Eleven of our Upper Sco stars fall in this category.
• 2.  
  Persistent flux-dip class—discrete triangularly shaped flux dips, generally covering less than 0.15 in phase (for each of up to 4 dips). The flux dips are often more or less stable in depth over the K2 campaign, with dip depths generally a few percent. Outside of the dips, the phased light curves are either nearly flat or consistent with sinusoidal variation due to cool star spots. Periods range from 0.5 to 1.8 days. A half dozen rapidly rotating, late M dwarf members of the Pleiades with this light-curve signature were identified from K2 Campaign 4 data (Rebull et al. 2016, Section 3.6; A.Collier Cameron et al. 2017, in preparation). Eight of our Upper Sco stars fall in this category.
• 3.  
  Transient, narrow dip class—more or less triangularly shaped flux dips, narrow in phase, but always variable in depth, on both short and long timescales, over the 78-day K2 campaign. Only one prominent dip is present in the phased light curve. Dip depths are generally a few percent, but up to 20% for EPIC 205483258 (RIK-210). All four stars also show a spotted-star waveform, whose period is identical to the dip period within our uncertainties. Periods ranging from 1 to 5.5 days.

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In the next sections, we discuss specific examples of these categories.

EPIC 204066898 (a.k.a. UScoCTIO 80A¹¹ ; Kraus & Hillenbrand 2009 = KH2009; Kraus & Hillenbrand 2012 = KH2012) is an M3 member of Upper Sco with no apparent IR excess. It has been identified as a wide binary, with separation about 13'' and ${\rm{\Delta }}{K}_{s}=1.9$ mag (Kraus & Hillenbrand 2009 = KH2009). KH2012 also identified UScoCTIO 80A as a close (005), nearly equal mass binary (see their Table 3). We find two independent peaks in the Lomb–Scargle periodogram with periods of 0.3956 and 0.5386 days. We experimented with 1-pixel and 1.5-pixel apertures for the light-curve extraction in order to assess the contribution of UScoCTIO 80B to the EPIC 204066898 light curve; our conclusion is that the two Lomb–Scargle peaks are both correctly associated with UScoCTIO 80A (UScoCTIO 80B is also EPIC 204066097, for which we derive a period of 0.36d). We thus assume the two stars associated with the two Lomb–Scargle peaks are also the close binary pair identified in KH2012. The longer period system for EPIC 204066898 (which we designate as the secondary component) has a more or less sinusoidal light curve with about 1% peak-to-trough amplitude. After removing the signal from this system and phasing the remaining signal to the 0.3956-day period of the primary component, the light-curve shape for this star (Figure 2) is fairly typical of the scallop-shell class, with a full amplitude of about 5% and multiple peaks and troughs in its phased light curve.

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There are no published spectra for EPIC 205110559, but its colors suggest it is a mid-to-late M dwarf. Its light curve (Figure 3) is also fairly typical of the scallop-shell class, with a full amplitude of about 5% and multiple peaks and troughs in its phased light curve. For phase 0.45–1.0, the waveform is relatively stable over the duration of the campaign. However, as emphasized in the second panel of Figure 3, the waveform shows considerable evolution over the campaign for the phase range 0–0.45. The primary shift in waveform shape appears to occur almost exactly at the boundary between the first window (day 2060–2099) and the second window (day 2099.2–2107.5).¹² The third panel of Figure 3 shows an expanded view of the time frame when the waveform changed state, which reveals that a strong flare occurred at day 2099. This is by far the strongest flare for this star during the K2 campaign and it occurs at exactly the point that the waveform made its state transition. This latter point is illustrated in the last panel in Figure 3. The "excess" flux at phase ∼0.15 gradually declines, returning to approximately the pre-flare level by day ∼2128. We conclude that there is very likely a physical link between the occurrence of the flare and the change in morphology of the phased light curve.

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The K2 light curve for EPIC 204918279 has a beating appearance and the Lomb–Scargle periodogram shows two strong peaks at very similar periods, 0.4594 and 0.4665 days, which we interpret as indicating that it is a binary with the two components having nearly the same period.

After separating the variability at those two periods, we find that the star with P = 0.4665 days has a light-curve shape that places it in the scallop-shell category at least for the first ∼60 days of the K2 campaign, as shown in the first panel of Figure 4. The phased light curve changed abruptly in shape at day ∼2123.5, as illustrated in the second and third panels of Figure 4. The state transition of the light-curve shape again appears to have been triggered by a flare; see the fourth panel of Figure 4. In this case, this is a much weaker flare than for EPIC 205110559.¹³ Nevertheless, this was the strongest flare seen in the K2 light curve for EPIC 204918279, at least during the last 60 days of the campaign. Prior to and after the flare, the light -curve shape appeared quite stable during the K2 campaign.

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EPIC 203185083 is an M4.5 YSO Upper Sco member with unusually strong Hα emission (equivalent width = −27 Å) for a WTTS of that spectral type (Rizzuto et al. 2015). However, it appears to have no IR excess, so we consider it to be a WTTS. The Lomb–Scargle periodogram indicates a period of 0.4400 days.

After phasing the light curve to the 0.44-day period, we find a waveform shape that is not plausibly explained by cool spots and that seems to evolve over the duration of the K2 campaign. After some investigation, we find the waveform evolution basically occurs at two rapid transitions on day 2093 and day 2102, as shown in the left panel of Figure 5. The first state transition of the light-curve shape again appears to have been triggered by a flare (right panel of Figure 5), though again a much weaker flare than for EPIC 205110559. Nevertheless, this was the strongest flare seen in the K2 light curve for EPIC 203185083. The second state transition appears to happen without any obvious trigger as seen from our vantage point. Finally, for both EPIC 203185083 and EPIC 204918279, the flares at the state transition seem unusual in that they have nearly symmetric shape (rather than a rapid rise and slow decay as true for most flares and for the flare on EPIC 205110559).

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The Lomb–Scargle periodogram for EPIC 204117263 shows a single strong peak at P = 0.6423 days; when phased to that period, the light curve has a scallop-shell appearance for the entire campaign. There was, however, a small, abrupt change in the phased light-curve shape at day 2080.0, as illustrated in Figure 6. In this case, the state transition in the light-curve shape does not appear to be associated with a flare (at least on the side of the star that is facing us).

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The Lomb–Scargle periodogram for EPIC 204897050 shows a dominant strong peak at a very short period of P = 0.2639 days; when phased to that period, the light curve has a scallop-shell appearance for the entire campaign. As illustrated in Figure 7, there is a small portion of the phased light curve around phase = 0.6 where the waveform shape gradually changes throughout the length of the campaign. This could be consistent with the other three stars discussed above, if there was a trigger event just prior to the beginning of Campaign 2; no significant flares are seen during the time period of our light curve.

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The stars having scallop-shell light curves have many shared characteristics, which presumably provide clues to the physical process driving their unusual light-curve morphology. Below we collect the most salient of those shared characteristics.

• 1.  
  All have periods less than 0.65 days. We do not know that this is, in fact, the stellar rotation period, but we will assume that is the case. With that assumption, their periods place them among the most rapidly rotating M dwarfs in Upper Sco (see also Section 7).
• 2.  
  All have mid-to-late M spectral types (M4 to M6.5).
• 3.  
  They have full amplitudes for their K2 light curves of 2%–10%.
• 4.  
  Six of 11 of them show relatively stable phased light-curve shapes over the entire 78 day K2 campaign.
• 5.  
  Five of them show evolving waveforms. In all but one case, there is an abrupt transition from one waveform to another with the switch happening in generally less than a day. In three cases, the phase change takes place when a strong flare occurs. In four of the five cases, the change in shape only significantly affects 20%–30% of the waveform, with the remaining waveform staying essentially constant in shape. For EPIC 205110559, the fractional flux change between states at phase = 0.1 is of order 4% (Figure 3, second panel). Any physical mechanism to explain this light-curve morphology must be able to accommodate events of this size. For all three events with triggering flares, the affected portion of the light curve brightened after the flare.
• 6.  
  The number of distinct peaks (or troughs) in their phased light curves ranges from 3 to 6.
• 7.  
  There are 83 WTTs in our sample with P < 0.65 days and $(V-{K}_{s})\gt 5$. The fraction that have scallop-shell light-curve morphologies for that period range is therefore 13%.
• 8.  
  We have also examined this WTT control group for obvious flares. Based on a simple visual check of the detrended light curves of our Table 1 stars and our WTT control group, we find no obvious difference in either the frequency or strength of flares.

Preibisch et al. (2001) first identified EPIC 205374937 as a low-mass member of Upper Sco. Carpenter et al. (2009) and Luhman & Mamajek (2012) both reported no IR excess. Using Gemini North adaptive optics (AO) imaging, Lafreniere et al. (2014) identified EPIC 205374937 as a nearly equal mass binary with a 01 separation. The K2 light curve shows two approximately equal strength close peaks, corresponding to periods of 0.6345 and 0.5436 days. We assume the two nearly equal mass components seen with the AO imaging give rise to these two periodogram peaks; we somewhat arbitrarily assign the the larger periodogram peak as the A component. The phased light curve for the A component is shown in Figure 8.

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We interpret the phased light curve for EPIC 205374937A as the superposition of a more or less sinusoidal variation due to star spots and two (or possibly three) short-duration flux dips. The two most prominent flux dips are centered at phases about 0.2 and 0.6; the full width at zero intensity (FWZI) of the dips are 0.16 and 0.12 in phase (or about 2 hr in time) and their depths are about 3% of the continuum. There is no suggestion of the dips varying in depth or width over the course of the campaign (that is, the noise level in the phased light curve appears the same inside and outside the dips). The period that phases the dips best also produces the least scatter in the rest of the light curve, indicating that the dip period is essentially the same as the spot period. Two of the other stars in this group (EPIC 204296148 and 203849738) also have both spotted-star waveforms and persistent flux dips where the periods are the same (see Figure 36).

EPIC 203692610 is an essentially anonymous red star with proper motion consistent with Upper Sco membership. Our own Keck HIRES spectra for this star shows it to have a spectral type of about M4, with weak Hα emission (equivalent width = −3.0 Å) and strong lithium absorption (equivalent width = 0.54 Å), typical of Upper Sco M dwarfs. The Lomb–Scargle periodogram for its K2 light curve shows a single strong peak at P = 1.821 days.¹⁴ When the light curve is phased to that period, it shows a relatively flat continuum with three sharp triangular-shaped flux dips (Figure 9). The dip depths are about 3% to 7%, and the FWZI for each dip is about 0.1 in phase. Close examination of the light curve shows that the dip depths vary in time, with the time dependence being somewhat different for each dip, as illustrated in the top-right panel of Figure 9. The left-most dip is more or less stable in its depth until day 2119, when it essentially disappears. The central dip is more or less stable in depth until day 2131, when it too disappears. The strongest (right-most) dip is quite deep until day 2089; from 2089 to 2131 it is about half as deep (and somewhat shifted in phase), and at day 2131 it becomes significantly weaker again. There are no strong flares in the K2 light curve for this star. However, the strongest flare-like event (or events) occurs at the time of the first state transition of the flux dips at day 2089, as illustrated in the bottom-left panel of Figure 9. There are no obvious flares of any sort at the other two state-transitions. Finally, we note that the dip properties and the general appearance of the phased light curve for EPIC 203692610 are quite similar to the K2 light curve for HHJ 135, one of the six late M dwarfs with persistent, short-duration flux dips identified in the Pleiades by Rebull et al. (2016).

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While EPIC 203962559 has been identified as a ρ Oph member (Wilking et al. 2005); it appears to have no IR excess and has relatively weak Hα emission, from which we conclude it is a WTTS. The Lomb–Scargle periodogram shows one strong, real peak at P = 1.5402 days. When phased to that period and examined closely, the light curve appears to undergo a major change in shape at about day 2106. This is illustrated in Figure 10. Prior to that day, there were four well-defined flux dips in the light curve; after that day, only two flux dips remain, and one of those is significantly narrower and less deep. We are unable to determine if there was a flare at day ∼2106 because that date also is when Mars transited the K2 FOV (near the position of EPIC 203962559), corrupting its light curve for ∼10 hr. We can think of no possible way for the Mars transit to induce systematic flux errors in a specific phase range in the extracted light curve for this star, so we assume this was a bizarre coincidence.

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EPIC 203927435 has also been identified as a ρ Oph member (Wilking et al. 2005); it too appears to have no IR excess and relatively weak Hα emission (equivalent width −6.8 Å). The Lomb–Scargle periodogram shows two resolved peaks, with periods of 0.4817 and 0.4162 days. After removing the signal from the star with P = 0.4162 days (which we refer to as the B component), we find that the phased light curve for the A component shows a waveform that is not explainable by cold spots, but that also shows some evolution during the K2 campaign. The first panel of Figure 11 shows the phased light curve for the first 63 days of the campaign; the light curve for the last 13 days of the campaign is shown in the second panel of Figure 11. A very strong flare occurred at the transition point—third panel of Figure 11—on day 2123.3; this was by far the strongest flare for this star during the K2 campaign. Prior to that day, there were four well-defined flux dips in the light curve; after the flare, only one (weaker) dip remains. In this case, the transition between states took place over about 3 days. During the middle of that transition period, a second weaker flare-like event occurred; see the last panel of Figure 11. That event, however, has a symmetrical shape (as was the case for the triggering events for EPIC 204918279 and EPIC 203185083).

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Bouy et al. (2006) showed that EPIC 204364515 is a possible resolved triple system, consisting of a close, equal brightness pair with a 015 separation and a fainter possible companion at a separation of about 1'' (with its ∼4'' pixels, the K2 light curve includes light from all three stars). The Lomb–Scargle periodogram for EPIC 204364515 shows two dominant periods of 3.0863 and 1.456 days. After removal of the light from the star with P = 3.086 days, the phased light curve for the star with P = 1.456 days shows four well-defined flux dips. Figure 12 shows the phased light curve, where we have split the data into two windows of time (black for day 2060–2105; red for day 2105–2139). The two strongest flux dips appear to be approximately stable in position, shape, and depth. The flux dip at phase ∼0.2, however, appears to shift in phase by about 0.03 in phase (10 degrees in azimuth) between the two windows. The fourth flux dip at phase ∼0.75 appears to become considerably deeper in the second time window.

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We measured widths and depths for all the prominent flux dips in these eight stars; see Table 2. The widths we provide are full-width, zero-intensity values, FWZI, in units of fraction of the period—meaning that they are intended to indicate the entire duration of the event (rather than, for example, a FWHM). Most of the dips have FWZI of 0.1–0.15 in phase; for a typical star with P = 0.6 days, a FWZI of 0.12 corresponds to about 1.7 hr. The depths are the difference in counts between a nearby "continuum" level and the bottom of the dip relative to the continuum level, expressed as a percent. Most of the dips have depths of 1%–3.5%, with the strongest being 7% (the deepest dip for EPIC 203692610).

Additional shared characteristics of these stars include the following.

• 1.  
  All eight of these stars have $P\lt 2$ days. Five of them have $P\lt 0.65$ days. In three cases, the period derived for the flux dips agrees with the period inferred from a spotted-star waveform, confirming that the dip period is also the stellar rotation period. For the other five, we believe it is likely that the dip period is the rotation period, but that is not proven.
• 2.  
  All have mid-to-late M dwarf spectral types (M4 to M5.5).
• 3.  
  The deepest flux dips for each star have depths from 2% to 7%; their widths (FWZI) are generally 0.1 to 0.15 in phase, corresponding to about 1–5 hr duration in time.
• 4.  
  They have two to four discrete flux dips in their phased light curves (at the sensitivity level of the K2 data).
• 5.  
  For four of these stars, the dip depths appear fairly stable over the duration of the K2 campaign. In three of the other stars, one or more of the flux dips disappears abruptly (or becomes markedly weaker) during the course of the campaign. At least two of the abrupt changes in flux-dip depth occurs immediately following a flare (or flare-like event).

The Lomb–Scargle periodogram for EPIC 205046529 shows two strong peaks indicating it is a binary, with P₁ = 2.5619 days and P₂ = 1.837 days. This star appeared as a close pair in the Keck/HIRES guider camera, and we assume the two spatially resolved stars seen with Keck correspond to the two periodogram peaks. After removing the signal from the longer period star and then phasing to 1.837 days, we noted the presence of an apparent flux dip in the light curve for the second star. After further processing, we determined a best-fit period to highlight the flux dip of P = 1.8358 days. Figure 13 shows the phased light curve; the dominant feature is a spotted-star waveform, superposed on which is a well-defined flux dip centered at phase ∼0.6. The flux dip, however, appears somewhat noisy either due to jitter in the individual dip depths or their timing or both. We believe this fuzziness is primarily due to variations in the depth of the dip both on short and long timescales. Figure 14 shows four 10-day windows in the light curve for EPIC 205046529B. Close examination of those traces shows that the dip depth seems to decrease slowly with time over the K2 campaign, but also varies in depth from cycle to cycle. In order to determine better the nature of the variations in the dip times and depths, we measured the depths and first-moment times of occurrence of all the dips where we could identify that a dip was present. Those times and depths are provided in Table 3. Histograms of the dip depths in two time windows (day 2060–2086 and day 2087–2106) are shown in Figure 15, demonstrating the decreasing dip depth with time. After day 2107, the flux dip was no longer detected with certainty. Figure 16 shows the phased light curves for those same two time windows, also illustrating the decrease in dip strength as the K2 campaign progressed. For both time windows, the dip profile appears to show a shallower ingress slope compared to the egress slope. For the stronger, better defined dips, we measure a mean width (FWZI) of 0.195 days, or as a fraction of the period, (dip duration)/period = 0.106.

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EPIC 205024957 is the one star in our sample that appears to have a significant 24 μm IR excess; however, as originally concluded by Carpenter et al. (2009), the lack of an excess at shorter IR wavelengths indicates that this is likely a debris disk and not a primordial disk. Its weak Hα emission (Table 1) also supports it being a WTTS and not a CTTS. The Lomb–Scargle periodogram for EPIC 205024957 shows a single strong peak at P = 1.6672 days, largely driven by a nearly sinusoidal spotted-star waveform; however, the phased light curve also shows a definite but fuzzy flux dip (Figure 17). We have analyzed the light curve for this star in the same way as for EPIC 205046529 and reached similar conclusions. That is, we believe the fuzzy appearance of the flux dip is due to both short- and long-term variations in the dip depth, with little contribution from variations in the occurrence times for the dips. Figure 18 illustrates the short- and long-term variability of the flux-dip depths with four 10-day portions of its light curve. Based on Gaussian fits to the well-detected flux dips, we derive a best period for the dips of P = 1.6656 days. For the stronger, better defined dips, we measure a mean dip width (FWZI) of 0.203 days, or as a fraction of the period, (dip duration)/period = 0.122. Times and depths for the individual flux dips we could measure are provided in Table 4. As for EPIC 205046529, in Figures 19 and 20 we also provide histograms of the dip depths and phased light curves for EPIC 205024957 in two time windows to illustrate the evolution of the dip character during the K2 campaign.

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The Lomb–Scargle periodogram for EPIC 204143627 shows a single strong peak at P = 1.125 days, largely driven by a nearly sinusoidal spotted-star waveform; however, the phased light curve also shows a definite but weak flux dip (Figure 21). We analyzed the light curve for this star in the same way as for EPIC 205046529 and reached similar, though more limited, conclusions due to the lower S/N for this star. That is, we believe the fuzzy appearance of the flux dip is due to variations in the dip depth, with little contribution from variations in the occurrence times for the dips. The four panels of Figure 21 show that the flux dip was present and well defined in the first 20 days of the K2 campaign and slowly diminished in depth over the duration of the campaign. For the first time window in Figure 21, we measure a dip width (FWZI) of 0.06 days, or relative to the period, (dip duration)/period = 0.055.

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EPIC 205483258 is a relatively anonymous (only two references in SIMBAD as of this date) Upper Sco member. Its literature name is RIK-210 (Rizzuto et al. 2015). It is both the earliest type star in Table 1 and has the longest period. Its phased light curve is dominated by a well-defined stable sinusoidal variation presumably due to a highly non-axisymmetric spot distribution. Superposed on that waveform is a single strong narrow flux dip—as shown in Figure 22. The dip width (FWZI) varies from epoch to epoch, but is about 0.4–0.5 days, or relative to the period, (dip duration)/period ∼0.08. The dips are generally asymmetric, with a shallower and more variable ingress profile.

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We have much more follow-up data for RIK-210 than for any of our other stars. In David et al. (2017), we provide a detailed examination of the K2 light curve for RIK-210 and an analysis of synoptic spectra for it, which we obtained with Keck HIRES. Radial velocities at 15 epochs exclude any EB scenario to explain the narrow flux dips. The variability in the shape, depth and duration of its flux dip can only be explained by some type of cloud of material orbiting the star at the Keplerian co-rotation radius and with physical dimension similar in size to the stellar radius. We return to the implications of these data in Section 8.

All of the stars in this class share the characteristics below.

• 1.  
  All four stars have $P\gt 1$ day. In all four cases, there is a well-defined spotted-star waveform in addition to the flux dip, and both share the same period to within the uncertainties. Therefore, for these stars, we are certain that the flux-dip period is the same as the rotation period.
• 2.  
  All have M spectral types (M2.5 to M5).
• 3.  
  In all cases, there is only one major flux dip per star. The maximum depths are 1.5%, 2.5%, 3%, and 20% (the latter for RIK-210). The widths (full width zero intensity) are on the of order 0.1 in phase or slightly less, corresponding to about 10 hr for RIK-210 and to a few hours for the other three stars.
• 4.  
  The dip depths vary significantly on both short (cycle to cycle) and long (campaign duration) timescales. From one cycle to the next, the dip can go from present and near maximum depth to absent.
• 5.  
  In one case for sure, and probably in two of the other cases, the dip shape is asymmetric, with the slope of the ingress being steeper or shallower than the slope of the egress.
• 6.  
  Of all 23 stars discussed in this paper, only one has a relatively secure IR excess and that is EPIC 205024957.

Non-axisymmetrically distributed spots on the surfaces of low-mass stars typically produce relatively simple and smooth phased light-curve shapes with one or two maxima and one or two minima per period. However, it is not inconceivable that some combination of spot sizes and locations might produce light-curve signatures similar to our unusual Upper Sco stars. In order to address this hypothesis, we created a spotted-star modeling routine and produced simulated light curves for a variety of spot configurations. We describe the spot simulation program and some of the tests we have run in the Appendix. Based on those simulations, it is possible to get light-curve shapes that are very similar to the scallop-shell and persistent-dip classes if one puts spots very close to the upper (or lower) limb of the star as viewed from Earth. However, the spot distributions that can mimic the light-curve shapes cannot also yield light-curve amplitudes that match our observations. For several of the scallop shells, the full amplitude is on the order of 10%, and for a number of the persistent flux-dip class, the dip depths are between 3% and 8% with FWZI < 0.2 in phase. In order to yield the very structured phased light curves of the scallop-shell class, or the very narrow (in phase) flux dips of the persistent-dip class, the spots have to be very near the edge of the visible hemisphere of the star. Because of the geometric fore-shortening and limb darkening when at the edge of the visible hemisphere, such spots yield amplitudes or dip depths less than 1%, even if the spots are assumed to be totally black. Larger spots or spots further from the "terminator" yield light curves that are smoother and do not match the morphologies we see. Therefore, we believe that cool spots on the stellar surface do not provide a suitable model to explain the light-curve morphologies for our Upper Sco stars.

There is some similarity between the light curves of some of the stars in Table 1 and some of the stars identified in recent years as "dippers" in Orion, NGC 2264, and Upper Sco (Morales-Calderon et al. 2011; Cody et al. 2014; Stauffer et al. 2015; Ansdell et al. 2016); these stars are also sometimes referred to as AA Tau analogs (Bouvier et al. 1999; Alencar et al. 2010; McGinnis et al. 2015). The light curves of AA Tau stars show a wide diversity, with most of them showing very broad and structured flux dips that are quite dissimilar from our Upper Sco stars and thus do not serve as plausible comparison objects. A small subset of them, however, do have periodic short-duration flux dips sometimes superposed on sinusoidal variations with the same period (Stauffer et al. 2015), thus superficially linking their light-curve morphology with that of the stars we have discussed in this paper. For these stars, the periodic short-duration flux dips have generally been attributed to extinction by localized structures in or above the star's inner circumstellar disk, where the inner disk rim and stellar photosphere are assumed to be locked into at least approximate co-rotation. Could some/many of the stars in Table 1 simply be another subset of this class, with the same basic physical processes producing the observing photometric variability?

We believe the answer to that question is primarily no, based on one major difference between our stars and the stars of the dipper class. All but two of the 40 dippers in Orion identified by Morales-Calderon et al. and all of the dippers identified in NGC 2264 by Cody et al. and by Stauffer et al. have strong IR excesses and SEDs appropriate for Class I or II YSOs. All of the dippers in Upper Sco identified by Ansdell et al. (2016) have strong 24 μm excesses, and all but one of them have strong 12 μm excesses. Those IR excesses arise from warm dust at or near the inner edge of their primordial circumstellar disks. As discussed in Section 2.2 and in the Appendix, with one exception, our stars do not have IR excesses and have SEDs consistent with bare photospheres. Also, for most of our stars (with P < 1 day), the Keplerian co-rotation radius lies interior to the likely dust sublimation radius and therefore any "cloud" responsible for the periodic light-curve variability should be dust free.

The CoRoT light curves for NGC 2264 are similar in quality to the K2 light curves for Upper Sco, and CoRoT light curves were obtained for more than 300 WTT cluster members (about twice as many WTTs as CTTs); however, none of those WTTs showed light-curve morphologies like our Upper Sco stars in Table 1. Could that absence somehow affect the conclusion we have just reached? Probably not. NGC 2264 is five times further away than Upper Sco, and the CoRoT limiting magnitude is brighter than for K2. Therefore, the sample of stars with good light curves in NGC 2264 contains very few stars in the mass range of the stars in our Table 1 (Venuti et al. 2017 include only two stars with $P\lt 1$ day and mass <0.4 M_☉ in their table of NGC 2264 rotation periods from CoRoT). To the extent that the light-curve signatures we see require young ages, rapid rotation, and low masses, we would not expect to have found them in NGC 2264 because we were not able to sample the needed mass range.

As discussed in Sections 7, 8.2, and in David et al. (2017), the transient short-duration flux dips found for four of our stars cannot be produced by cool spots on the stellar photosphere or by any other plausible phenomenon associated with the surface of the star. The equality of the period for the narrow flux dip and the sinusoidal waveform (which we assume is due to spots) therefore places the material responsible for the narrow flux dips at the Keplerian co-rotation radius. That material must be distributed over a region with size comparable to the star (Figure 26 and Table 5), but have low average optical depth given flux-dip depths generally just a few percent. Several recently discovered stars have light-curve properties that seem reasonably analogous to our four transient flux-dip stars. The closest analog is PTF 08–8695 (van Eyken et al. 2012; Johns-Krull et al. 2016), an M3 star in the ∼3 Myr old 25 Ori subgroup of Orion. Light curves for PTF 08–8695 show narrow flux dips with depths up to 3%, FWZI ∼ 0.18 in phase, and a period of 0.448 d. The flux-dip depths are variable and at some epochs are not present at all. The dips are superposed on a more or less sinusoidal spotted-star waveform with identical period to that for the flux dips. These properties are remarkably similar to our four Upper Sco transient flux-dip sources. Van Eyken et al. (2012) concluded that the best interpretation of the data was to ascribe the flux dips to transits of a recently formed or forming planet undergoing Roche-lobe overflow mass loss.

Two main-sequence field stars with Kepler or K2 data have light-curve properties that make them somewhat analogous to our transient flux-dip stars. KIC 12557548 (Rappaport et al. 2012) is a 16th magnitude, field K dwarf with a rotation period P ∼ 23 days and hence a likely age of a few Gyr. The Kepler data show it to have asymmetric flux dips with a period of 15.7 hr; the flux dips vary irregularly in depth, with a maximum depth of about 1.3%. The FWZI of the dips is about 0.15 in phase. K2-22b (Sanchis-Ojeda et al. 2015) is a field M0 dwarf with a rotation period P ∼ 15 days and hence a likely age of about a Gyr. Its K2 light curve shows asymmetric flux dips with a period of about 9.1 hr; the flux dips are highly variable in depth, with dip depths from zero to 1.3%. The FWZI of the dips is about 0.09 in phase. The flux dips for both stars have been modeled by the above authors as arising from a planet that is in the process of disintegrating. The surface of each planet would have temperatures near 2000 K. In the Rappaport et al. (2012) model, a dusty wind from the surface generates a dust stream/tail that is responsible for the transits, with the curved geometry of the tail explaining the asymmetric dip profiles and their variability.

If the model proposed for KIC 1255b and K2-22b is correct, those planets are at a kind of fiery Goldilocks distance from their star—close enough for their surfaces to be molten, but not so close that dust grains could not survive in their planetary wind stream long enough to create a tail of sufficient extent to explain the transit duration and asymmetric shape. For our four transient flux-dip stars, using the parameters in Table 5, the surface temperature of a hypothetical planet would be in the range 1200–1500 K, and thus the specific mechanism proposed for KIC 1255b and K2-22b is not likely applicable. However, we believe the similarities in light-curve properties between these two stars and our four stars make a compelling case to ascribe the flux dips for our stars to dust associated with a planet. In our case, the distance of the planet from the star is not a function of the star's luminosity but is instead a function of its rotation period and mass. Planets at about that location could arise from orbital migration within a circumstellar disk, and then having that migration stop when the planet reaches the inner rim of the disk—which is expected to be close to the Keplerian co-rotation radius for the star (Papaloizou 2007). What is not obvious is the mechanism for creation of the dusty cloud that would cause the transits for our stars. Several possibilities are explored in David et al. (2017).

The salient features of the persistent flux-dip class are multiple short-duration flux dips with FWZI 0.1–0.15 in phase and depths of a few percent. Periods are always less than two days, usually less than 1 day. Long-term behavior is akin to the punctuated equilibrium models in evolutionary theory—long periods of stability, but often with abrupt shifts where the depth of one or more dips changes significantly. At some level, the scallop-shell class is just a more extreme version of the persistent flux-dip class—more structure in the phased light curve, shorter periods (all <0.65 days), the same or more frequent abrupt shifts in light-curve morphology. We therefore hope to find a single physical mechanism that could explain the light-curve variability of both classes.

The closest analog to these stars we can find in the literature is HHJ 135, in the Pleiades (Rebull et al. 2016). HHJ 135 is a 125 Myr, dM4.5 star; its K2 data yields a period of 0.61 days and a phased light curve showing three short-duration flux dips with a very similar appearance to our Upper Sco persistent flux-dip stars EPIC 203692610 and EPIC 204364515. This primarily tells us that extreme youth (low gravity) is not required for this morphological signature.

The next best analogy in the literature we can find for these stars is, surprisingly, an 8 M_☉ star. σ Ori E is a rapidly rotating Be star. Ground-based and MOST light curves for σ Ori E show it to have two short-duration flux dips (widths about 0.2 in phase) superposed on a wave-shaped undulation with a period of 1.19 days (Townsend et al. 2013). The light-curve shape is apparently stable over many years. The MOST light curve closely resembles that for our persistent flux-dip stars EPIC 204296148 and EPIC 205374937. Townsend & Owocki (2005) proposed that the σ Ori E light curve is a natural outcome for a rapidly rotating star with a wind and a strong magnetic dipole field. Gas from the wind accumulates in a lumpy warped disk with inner rim at the Keplerian co-rotation radius, oriented so that the normal to the disk lies between the rotation and magnetic axes. The short-duration flux dips in the light curve arise when the disk transits our line of sight. Their model (see also Ud-Doula et al. 2006) also predicts break-out events, resulting when too much mass accumulates onto the field lines. These magnetic reconnections could resemble flares (which are otherwise not predicted for B stars).

While the Townsend & Owocki (2005) model is for a high-mass star with a radiative wind, it turns out that a very similar model had been proposed to explain some properties of rapidly rotating low-mass stars. Optical spectra of AB Doradus (P = 0.51 days; Collier Cameron & Robinson 1989a, 1989b) and Speedy Mic (HD 197890; P = 0.38 days; Jeffries 1993; Dunstone et al. 2006) and other similar rapidly rotating K dwarfs show narrow Hα absorption dips that sweep through their broad quiescent Hα profiles, best explained as due to orbiting warm gas clouds at or above the Keplerian co-rotation radius that transit the observer's line of sight. Some Be stars show similar absorption dip transients (Smith & Balona 2006). In AB Dor, often as many as six individual features (i.e., individual clouds) are seen at a given epoch. Many of the Hα transients repeat from night to night for periods up to the end of a week-long campaign (Dunstone et al. 2006). Similar features have also recently been detected in a rapidly rotating (P = 0.44 days) M dwarf, V374 Peg (Vida et al. 2016). Jardine & van Ballegooijen (2005) proposed a model for these systems in which gas from the stellar (Parker) wind accumulates in a lumpy torus at or above the Keplerian co-rotation radius where net gravitational and magnetic forces vanish, with density maxima at the places where the radial component of the magnetic field changes polarity. These density maxima could be the "clouds" that give rise to the light-curve structure we see in the persistent flux-dip and scallop-shell light curves. Note that in this model, the flux dips in the K2 data arise when one of these glowing clouds is eclipsed by the star, rather than when the cloud transits the face of the star and produces the Hα absorption transients. The scallop shells may differ from the persistent flux-dip class because they have an additional source of supra-photospheric gas—gas lost through their equatorial plane because they are rotating at breakup velocity.

The above speculations are at most proof of concept. The next step is to determine if the gas in these structures have densities, ionization fractions, and temperatures consistent with that needed to generate the light-curve features we see. We intend to address those issues in a future paper (A. Collier Cameron et al. 2017, in preparation).