ULTRA-SHORT-PERIOD PLANETS IN K2 SUPERPIG RESULTS FOR CAMPAIGNS 0–5

, , and

Published 2016 August 4 • © 2016. The American Astronomical Society. All rights reserved.
, , Citation Elisabeth R. Adams et al 2016 AJ 152 47 DOI 10.3847/0004-6256/152/2/47

Download Article PDF

Article metrics

1187 Total downloads

Share this article

Author e-mails

adams@psi.edu

Author affiliations

1 Planetary Science Institute, 1700 E. Ft. Lowell, Suite 106, Tucson, AZ 85719, USA; adams@psi.edu

2 Department of Physics, Boise State University, 1910 University Drive, Boise ID 83725, USA

3 McDonald Observatory, The University of Texas at Austin, Austin, TX 78712, USA

Dates

  1. Received 2016 March 18
  2. Revised 2016 May 17
  3. Accepted 2016 May 20
  4. Published

Check for updates using Crossmark

Keywords

planetary systems; planets and satellites: detection; planets and satellites: dynamical evolution and stability

Journal RSS
Create or edit your corridor alerts

What are corridors?opens in new tab

1538-3881/152/2/47

ABSTRACT

We analyzed data from Campaigns 0–5 of the K2 mission and report 19 ultra-short-period candidate planets with orbital periods of less than one day (nine of which have not been previously reported). Planet candidates range in size from 0.7 to 16 Earth radii and in orbital period from 4.2 to 23.5 hr. One candidate (EPIC 203533312, Kp = 12.5) is among the shortest-period planet candidates discovered to date ($P=4.2$ hr), and, if confirmed as a planet, must have a density of at least $\rho =8.9\ {\rm{g}}\,{\mathrm{cm}}^{-3}$ to not be tidally disrupted. Five candidates have nominal radius values in the sub-Jovian desert (${R}_{P}=3\mbox{--}11\,{R}_{\oplus }$ and $P\leqslant 1.5$ days) where theoretical models do not favor their long-term stability; the only confirmed planet in this range is thought to be disintegrating (EPIC 201637175). In addition to the planet candidates, we report on four objects that may not be planetary, including one with intermittent transits (EPIC 211152484) and three initially promising candidates that are likely false positives based on characteristics of their light curves and on radial velocity follow-up. A list of 91 suspected eclipsing binaries identified at various stages in our vetting process is also provided. Based on an assessment of our survey's completeness, we estimate an occurrence rate for ultra-short-period planets among K2 target stars that is about half that estimated from the Kepler sample, raising questions as to whether K2 systems are intrinsically different from Kepler systems, possibly as a result of their different galactic location.

Export citation and abstract BibTeX RIS

Previous article in issue
Next article in issue

1. INTRODUCTION

Planets with orbital periods of less than a day present real challenges to theories of planet formation and evolution, and yet numerous objects with periods as short as a few hours have been found. So close to their host stars that some are actively disintegrating (Sanchis-Ojeda et al. 2015a), these planets' origins remain unclear, and even modified models for planet formation and evolution with significant inward migration have trouble accounting for their periods. They thus present an important test for theories of planetary origins and evolution.

The existence of such a population was suggested by several groups. For instance, Jackson et al. (2009), among others, suggested that orbital decay driven by tides raised on the host star could drive planets into very short-period orbits, but how they arrived within orbits susceptible to tidal decay is unclear. Raymond et al. (2008) explored different possibilities, from in-situ formation to Type-1 gas disk migration. That study suggested that the orbital architectures of the systems, along with the physical properties of the planets, could help distinguish between the possible origin scenarios. For instance, Type-1 migration would be expected to move multiple small planets together into short-period orbits, with the planets forming a chain of mean-motion (or near mean-motion) resonances (MMRs). The magnetosphere of a young star is thought to clear a cavity within a few stellar radii of the star, and so the inward migration is expected to cease shortly after entering that cavity, depositing a migrating planet into an orbital period of a few days (Lin et al. 1996).

Among the discoveries reported in Sanchis-Ojeda et al. (2014) are several multi-planet systems, and in some cases the outer pairs of planets are close to MMRs. For example, the KOI-1843 system includes two outer planets, with $P\approx 4$ and six days, within 1% of the 3:2 MMR. The innermost planet, KOI-1843.03, has an orbital period P = 4 hr, which is more than 75 Hill radii from its nearest sibling, and so presumably is dynamically decoupled. However, tidal decay could potentially explain KOI-1843.03's present precarious orbit, especially if interactions with the other two planets excited its orbital eccentricity and enhancing driving tidal decay (Van Laerhoven 2014). Indeed, KOI-1843.03 is so close to its host star ($\approx 2$ stellar radii) that the planet currently orbits within a space originally occupied by its host star early in the system's history. Thus, it must have arrived at its present orbit long after the system's formation. Many of the ultra-short-period (USP) planets and candidates occupy similar orbits, and therefore tidal damping seems likely to have played a role in shaping their orbits.

Whatever the planets' origins, the properties of the host stars seem related to the planets' occurrence rate. Sanchis-Ojeda et al. (2014) found marginal evidence that M dwarfs are about 10 times as likely as F dwarfs to host a planet with a radius twice that of the Earth and P ≤ 24 hr. This trend is qualitatively similar to, but more pronounced than, the trend discussed in Howard et al. (2012), but it disagrees with that discussed in Fressin et al. (2013), who found no dependence of the occurrence rate on stellar type; however, neither study considered USP planets.

Presumably, the properties of host stars play a role in the planet formation process, but probably also shape the evolution of the planetary system. For instance, if stars of all types were equally likely to host a planet, then tidal decay of a planet's orbit should occur more quickly for more massive, larger stars. The influence of the tide raised on the star rapidly increases with stellar radius, and the influence of the tide raised on the planet scales with stellar mass. On the other hand, if Type-1 migration is, indeed, responsible for bringing small planets close-in, then planets orbiting M dwarfs might start their tidal journey closer to the star, and therefore be more susceptible to tidal decay.

Unfortunately, the small sample size of USP planetary candidates reported in Sanchis-Ojeda et al. (2014) around M dwarfs (six) and F-dwarfs (nine) makes it difficult to draw statistically robust inferences regarding the dependences of the USP planet occurrence rate. Thankfully, the reincarnation of the Kepler Mission as K2 provides an ideal opportunity to continue the search for USP planets. Although K2's 80 day dwell time on each target field makes finding longer-period planets difficult, USPs are easily detectable because a transiting planet with $P=4$ hr occults its host star almost 480 times in 80 days.

In this paper we report on the ongoing efforts of the Short-Period Planets Group (SuPerPiG, http://www.astrojack.com/research/superpig/) to find additional short-period planets in the K2 mission data, using the light curve products produced by the k2sff pipeline of Vanderburg & Johnson (2014). In Section 2, we detail how we processed the K2 data and our transit search and model-fitting. In Section 3, we present our candidates, and discuss their occurrence rate and the properties of their host stars. In Section 4, we quantify our survey's completeness. In Section 5, we discuss future prospects and the possibilities for follow-up observations.

2. DATA CONDITIONING AND TRANSIT SEARCH

The process applied here closely follows the one in Jackson et al. (2013), and we verified its efficacy by recovering the disintegrating planet EPIC 201637175b reported in Sanchis-Ojeda et al. (2015a). Figure 1 illustrates our data conditioning and transit search process as applied to that data set. We also recovered the synthetic transits we injected into the data to test our survey's completeness, as described in Section 4. The complete flowchart of our search and vetting process is shown in Figure 2.

Figure 1.

Figure 1. Our data conditioning and transit search process as applied to the EPIC 201637175 data set from the K2 Campaign 1, which was first identified by Sanchis-Ojeda et al. (2015a). (a) The raw k2sff data. (b) The k2sff data after applying a median boxcar filter with width of one day. (c) The resulting EEBLS spectrum with the best-fit period hightlighted by a dashed, red line. (d) The detrended data from (b), folded on the best-fit period and binned into 200 bins for display. Note (a) and (b) share x-axes, but (c) and (d) do not.

Download figure:

Standard image High-resolution image
Figure 2.

Figure 2. Flowchart of the transit candidate search and vetting process.

Download figure:

Standard image High-resolution image

We retrieved the k2sff publicly available data generated by the pipeline described in Vanderburg & Johnson (2014) for all 99423 targets from the MAST archive for campaigns 0–5, C0–C5. (Two objects in C0, 202093417 and 202137146, were not used because the flux returned from MAST was uniformly −1.) The search includes targets of all object type, although only one ultimate candidate (202094740) is listed as "None" rather than "STAR" in MAST. An advantage to using the Vanderburg & Johnson (2014) pipeline is that it corrects for the pointing drift of the K2 spacecraft and generates light curves for several different photometric apertures, with a "best aperture" corresponding to the aperture giving the smallest rms variation in the final light curve. Only long-cadence data with a 30 minute exposure time was searched. For our initial search, we used the best aperture light curves (the "BESTAPER" extension in the FITS files) for the targets available (7746 in C0, 21,647 in C1, 13,401 in C2, 16,375 in C3, 24,475 in C4, and 15,779 in C5). The processed data for EPIC 201637175 from C1 (previously discovered by Sanchis-Ojeda et al. 2015a) are shown in Figure 1(a).

These light curves still exhibit a variety of astrophysical and instrumental variations that act as sources of noise for our analysis, but most of that variability is on timescales longer than the periods of interest for our search. To mitigate these variations, we applied a median boxcar filter with a width of one day. The original data have an almost regular observing cadence of 30 minutes with a few small gaps, so we first linearly interpolated the light curves to a grid with a completely regular sampling of 30 minutes, and then calculated the median value for all points within a one-day window of each regularly gridded point to generate our filter. We then interpolated this filter back to the time grid of the original data, restoring the original time gaps, and subtracted this interpolated filter from the original data. To improve detection efficiency for the shallowest transits, we masked out the handful of data points lying more than 10σ from the data set median, where the standard deviation $\sigma \equiv 1.4826\ \times $ the median absolute deviation (Leys et al. 2013). (For deeper transits where a 10σ cutoff removes real data from in-transits, the truncated transits are still easily detected and the light curves were regenerated with the noise filter set to 50σ before fitting to get the correct transit parameters.) The resulting detrended data for EPIC 201637175 are shown in Figure 1(b).

Using these data, we searched for short-period planetary transits with the EEBLS algorithm (Kovács et al. 2002). Briefly, the EEBLS algorithm folds and bins data on trial orbital periods and, after considering all relevant phases for a given period, returns the best fit to a square wave at that period. (The original EEBLS algorithm report best-fit periods correspond to positive or negative square waves; i.e., it does not care whether the best-fit signal is a dip or a blip. We modified the algorithm slightly to report best-fit periods only for dips.) We started searching for transit signals with periods P between 3 hr (an orbit near the surface of the Sun) and 3 days (although we are only interested in periods of 1 day or less, the longer initial search threshold is useful to avoid aliases). We used 10,000 trial periods—data folded on a trial period were binned into 100 bins—and sought transits with durations between 1% and 50% of the trial orbital period. With so many trial periods, the results at one period are not linearly independent from one another (cf. Kovács et al. 2002), but that consideration does not affect whether we recover a transit. Moreover, given the short durations expected ($\lesssim 1$ hr), such a fine gridding is required to recover transits. This analysis produced an EEBLS spectrum for each target, an example of which is shown for EPIC 201637175 in Figure 1(c) with a clear peak at $P\approx 9$ hr.

Figure 3 shows the best-fit periods for candidate transit signals from all 13,401 EEBLS spectra in C2 (other campaigns are similar) and the strength of the EEBLS signal at the peak as scaled by each spectrum's σ. The thruster on-board the Kepler spacecraft fires to maintain pointing as needed, with firings occurring at multiples of ${P}_{{\rm{thruster}}}=5.88460$ hr. Because of the problems that thruster firing causes for identifying short-period planets (Vanderburg & Johnson 2014), we masked it out by removing points flagged "MOVING" in the k2sff data. However, in all campaigns even after masking the thruster points, there remains a strong peak at 47 hr (or eight times the thruster period), as well as a peak at the thruster period itself. These spurious signals do not pass into the final candidate pool, however, because they do not pass the S/N and duration threshholds.

Figure 3.

Figure 3. Distribution of best-fit transit periods (3–72 hr) from EEBLS, shown for Campaign 2, with the strength of the EEBLS signal at the peak as scaled by each spectrum's σ. The red dashed line shows the 10σ cutoff used to identify candidates. Only signals between 3 and 24 hr were the subject of this analysis. Residual effects of the thruster firing period can be seen in an artificial pileup at 47 hr (8×), and spurious signals, which do not resemble actual transit light curves, remain in all campaigns at multiples (typically 1× and 8×) of the thruster period.

Download figure:

Standard image High-resolution image

To identify candidate transiting planets, we focused on those with EEBLS spectral peaks ≥ 10σ and periods less than 1 day, giving 757, 505, 1251, 419, 1480, and 1032 candidates in C0–C5, respectively, as shown in Figure 4. We then applied a generous first-pass depth requirement, requiring transit depths $D\leqslant 0.25$, which corresponds to the largest-known planet ($2\,{R}_{J}$) transiting a $0.4\,{R}_{\odot }$ M dwarf. All initial detections with depths from 0.02 to 0.25 (about 10 per campaign) proved on inspection to be either clear eclipsing binaries or else misidentified stellar noise. We also required durations τ short enough to be consistent with FGK host star main-sequence densities ${\rho }_{* }$ (Seager & Mallén-Ornelas 2003):

Equation (1)

Equation (2)

with ${\rm{\Gamma }}=0.00363$ (Jackson et al. 2013). An extra hour (or two K2-long-cadence exposure times) was added to the maximum duration (τ) to account for the distortion introduced into the light curves by K2's 30 minute observing cadence, which artificially extends the apparent transit duration and makes the transits more V-shaped than is typical for planetary transits. This threshold gives rise to an apparent cut-off in durations in Figure 4 longward of ∼1 hr. The origin of other patterns in the figure (in particular the clustering of points near durations of 10 hr) is unclear, but may arise from instrumental effects. In any case, none of our candidates have such long durations.

Figure 4.

Figure 4. Transit durations τ and depths D (in parts-per-million; ppm) from the EEBLS search. All 99,423 detections from C0-5 above the S/N threshhold are plotted in small gray points, while the 5444 larger red points are those with plausible-enough depths and durations relative to the period to warrant further inspection. The 19 planet candidates that survived subsequent scrutiny are marked by black stars, with the four suspect candidates shown as white stars. For comparison, the 91 eclipsing binaries we identified are shown as gray pluses, and generally, though not exclusively, cluster toward deeper depths.

Download figure:

Standard image High-resolution image

2.1. Initial Vetting

The candidates that meet the depth and duration cutoffs (91, 42, 177, 47, 152, and 134 for C0–C5) were inspected by hand. Candidates were vetted in the following manner: first, obvious sinusoids and light curves that were clearly just noise were rejected, leaving 7, 18, 15, 20, 24, and 37 candidate transits or eclipsing binaries per campaign, respectively. Obvious eclipsing binaries (two transit signals of different depths, occurring about half an orbital period apart) were set aside at this point; although see Table 1 for the EPIC number and period for likely eclipsing binaries identified throughout the search. Candidates with deep transits were rerun through EEBLS with a more permissive noise filter (50σ) to correct our estimate of the transit depth before proceeding. A few other light curves (zero, zero, two, two, one, and two, respectively) with odd patterns of photometric or stellar noise were investigated by hand to be sure they were not missed transits (none were). The stellar parameters for all remaining planet candidates are shown in Table 2, with one, four, two, five, seven, and four candidates, in C0–C5, respectively; four candidates (all in C4) that have some questionable features are listed separately in Table 3.

Table 1.  Eclipsing Binaries with Original EEBLS Periods from 3 to 24 hr

EB Campaign Period Notes EB Campaign Period Notes EB Campaign Period Notes
    days       days       days  
202073210 C0 1.024979 AB 202083924 C0 0.37845 AB 202087156 C0 1.893746 A
202088191 C0 1.662009 AB 202091545 C0 1.857576 AB 202103762 C0 1.327711 AB
201182911 C1 1.993038 AB 201184068 C1 1.588528 AB 201523873 C1 1.240377 AB
201563164 C1 0.37491 AC 201607088 C1 0.53093 B 201649211 C1 0.199731 ⋯
201680569 C1 0.784835 AB 201691826 C1 0.899402 AB 201740472 C1 0.958733 ⋯
201810513 C1 1.646639 AB 201843069 C1 1.096823 AB 201848566 C1 0.956863 AD
201893576 C1 0.929699 AB 201903318 C1 0.390019 A 202828096 C2 1.436287 AB
202971774 C2 0.471778 A 203027459 C2 0.530881 ⋯ 203633064 C2 0.709932 B
204429688 C2 0.410635 ⋯ 204470067 C2 1.846896 A 204538608 C2 0.914888 AB
204822463 C2 1.208611 A 205068000 C2 0.686159 ⋯ 205129673 C2 0.955311 B
205377483 C2 0.787653 A 205899208 C3 0.289449 A 205910324 C3 0.25624 A
205934874 C3 1.236054 A 205962262 C3 0.849755 B 205978103 C3 0.64287 AB
205996447 C3 1.600526 AB 206045146 C3 0.233232 ⋯ 206050740 C3 0.198387 ⋯
206100943 C3 1.601195 AB 206109113 C3 1.323701 AB 206139574 C3 0.673044 B
206315178 C3 0.635412 A 206489474 C3 1.516983 AB 210404228 C4 1.119943 AB
210434247 C4 0.453837 B 210574135 C4 0.929409 B 210593417 C4 1.062117 AB
210659779 C4 0.469356 A 210662654 C4 0.159109 B 210663545 C4 0.300752 A
210664740 C4 0.414948 ⋯ 210675130 C4 1.377904 AB 210754505 C4 1.741556 A
210821360 C4 1.467197 AD 210843708 C4 0.704035 ⋯ 210863062 C4 0.644008 B
210932768 C4 0.151526   210941737 C4 1.154352 AB 210954667 C4 0.325575 A
211012889 C4 1.7392 A 211315506 C5 0.884559 ⋯ 211380136 C5 1.753621 AB
211389268 C5 0.28499 AB 211518347 C5 1.871362 AB 211526186 C5 0.455062 B
211578677 C5 0.554273 AB 211580526 C5 1.758335 A 211604668 C5 0.515911 B
211613886 C5 0.958809 AB 211623903 C5 1.615615 AB 211631904 C5 0.442015 B
211685048 C5 0.769125 B 211719362 C5 0.402237 AB 211719484 C5 0.721766 AB
211796803 C5 0.277589 A 211797674 C5 1.323035 A 211822953 C5 1.549424 AB
211833449 C5 0.534773 AB 211833616 C5 0.534745 AB 211906940 C5 0.17545 ⋯
211931594 C5 0.320086 AD 211953866 C5 1.788937 AB 211978865 C5 0.907764 B
211995966 C5 0.558524 AB 211999656 C5 1.948462 AB 212066407 C5 1.643616 AD
212069706 C5 0.273843 A 212083250 C5 0.518772 B 212155299 C5 0.901706 B
212158225 C5 0.266589 A ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯

Note. A: Initial EEBLS period was half the period listed here. B: Object is listed in Kepler EB catalog (Third Revision Beta) http://keplerebs.villanova.edu/. C: Identified as a disintegrating minor planet around a white dwarf by Vanderburg et al. (2015). D: Object is listed at half correct period in Kepler EB catalog (Third Revision Beta) http://keplerebs.villanova.edu/.

Download table as:  ASCIITypeset image

Table 2.  Parameters for Stars Hosting Candidate Planets

Candidate Campaign R.A. decl. Kp ${R}_{\star }$ (${R}_{\odot }$) ${T}_{{\rm{eff}}}$ (K) [Fe/H] $\mathrm{log}(g)$ u1 u2 Source
202094740 C0 100.46312 27.0972 11.5 1.08 ± 0.04 6481.0 0.0 4.0 0.297 0.3126 TESS-Vanderbilt
201264302 C1 169.598013 −2.991577 13.88 0.26 ± 0.05 3299.0 0.155 5.106 0.4168 0.3719 EPIC
201606542 C1 170.311881 2.144426 11.92 0.82 ± 0.05 5540.0 0.03 4.81 0.4843 0.1926 McDonald, A
201637175 C1 169.482818 2.61907 14.93 0.54 ± 0.07 3830.0 0.03 4.65 0.5976 0.157 S15b
201650711 C1 172.044052 2.826891 12.25 0.69 ± 0.05 4340.0 −0.81 4.25 0.5126 0.2191 McDonald, B
203533312 C2 243.955378 −25.818471 12.16 1.15 ± 0.08 6620.0 0.09 4.19 0.2967 0.3076 McDonald
205152172 C2 245.180008 −19.14414 13.49 0.66 ± 0.1 4202.0 −0.04 4.758 0.7146 0.0666 EPIC
206103150 C3 331.203044 −12.018893 11.76 1.15 ± 0.04 5565.0 0.43 4.29 0.5247 0.1718 S15a
206151047 C3 333.71501 −10.769168 13.43 0.89 ± 0.06 5928.0 −0.169 4.247 0.3879 0.2573 EPIC
206169375 C3 344.016383 −10.332234 12.56 0.95 ± 0.07 6167.0 −0.168 4.16 0.3258 0.2987 EPIC
206298289 C3 337.357688 −8.266702 14.69 0.5 ± 0.06 3724.0 0.017 4.942 0.355 0.3581 EPIC
206417197 C3 337.133466 −6.347505 13.35 0.77 ± 0.04 5007.0 −0.063 4.587 0.5711 0.1407 EPIC
210414957 C4 64.325266 13.804842 12.65 0.87 ± 0.05 5838.0 0.3 4.12 0.4643 0.2162 McDonald
210754505 C4 64.64493 19.179056 13.19 0.88 ± 0.05 5875.0 0.04 4.04 0.4326 0.2302 McDonald
210605073 C4 65.62329 17.037875 17.89 1.42 ± 0.54 7020.0 0.0 4.0 0.2948 0.2825 Photometry
210707130 C4 59.464394 18.465254 12.1 0.71 ± 0.05 4462.0 −0.28 4.17 0.6686 0.0897 McDonald
210954046 C4 60.903766 22.249157 12.44 0.94 ± 0.1 6125.0 0.0 3.0 0.3583 0.2623 McDonald, C
210961508 C4 59.920104 22.365984 13.56 0.76 ± 0.04 4925.0 −0.06 3.42 0.5599 0.1535 McDonald
211152484 C4 60.069895 25.48 12.14 0.96 ± 0.05 6188.0 −0.12 4.12 0.341 0.2782 McDonald
211357309 C5 133.23263 10.944721 13.15 0.42 ± 0.06 3563.0 0.097 5.004 0.3986 0.3402 EPIC
211685045 C5 123.359621 15.713759 14.98 0.54 ± 0.13 3832.0 −0.058 4.9 0.4294 0.2983 EPIC
211995325 C5 131.207598 20.177694 18.22 0.62 ± 0.22 4071.0 −0.202 4.838 0.4525 0.259 EPIC
212150006 C5 128.169544 23.031999 14.7 0.82 ± 0.05 5528.0 −0.281 4.482 0.4385 0.23 EPIC

Note. ${T}_{{\rm{eff}}}$, $\mathrm{log}(g)$, and [Fe/H] are taken from the source listed; EPIC 202094740 and 210605073 assumed $\mathrm{log}(g)=4.0$ and $[\mathrm{Fe}/{\rm{H}}]=0$. Quadratic limb darkening parameters u1 and u2 are derived from Claret & Bloemen (2011). A: Double-peaked spectra (planetary parameters are strongly diluted, possible false positive). B. McDonald guide camera companion at 1'' and a few magnitudes fainter (planetary parameters are diluted, possible false positive). C: McDonald guide camera companion at 2''; also strong nightly RV variation (confirmed false positive). S15b: Sanchis-Ojeda et al. (2015a) S15a: Sanchis-Ojeda et al. (2015b).

Download table as:  ASCIITypeset image

Table 3.  Candidate Planet Parameters

EPIC Period (days) T0 (BJD) ${R}_{p}/{R}_{* }$ Rp (R⊕) $a/{R}_{* }$ i (deg) ${\sigma }_{\mathrm{odd}\mbox{--}\mathrm{even}}$ Notes
202094740 0.689647 ± 0.00052 2456775.19753 ± 0.001 ${0.0558}_{-0.003}^{+0.005}$ 6.58 ± 0.66 ${3.1}_{-0.9}^{+0.7}$ ${78.0}_{-11.1}^{+8.2}$ 0.4 ⋯
201264302 0.212194 ± 0.000026 ${2456812.40015}_{-0.00063}^{+0.00064}$ ${0.0271}_{-0.002}^{+0.004}$ 0.77 ± 0.18 ${3.6}_{-0.8}^{+0.9}$ ${83.3}_{-8.9}^{+4.8}$ 0.6 V16
201606542 0.444372 ± 0.000042 ${2456817.74445}_{-0.00109}^{+0.001}$ 0.0136 ± 0.002 1.22 ± 0.23 ${8.3}_{-3.8}^{+5.5}$ ${86.9}_{-6.9}^{+2.3}$ 0.6 V16, A
201637175 0.381087 ± 0.000041 ${2456867.13946}_{-0.00032}^{+0.00031}$ ${0.0731}_{-0.004}^{+0.014}$ 4.31 ± 0.98 ${4.2}_{-1.7}^{+0.6}$ ${83.0}_{-13.6}^{+5.0}$ 0.2 S15
201650711 0.259669 ± 0.000041 ${2456885.22582}_{-0.00117}^{+0.00126}$ ${0.0102}_{-0.001}^{+0.002}$ 0.77 ± 0.14 ${3.1}_{-0.8}^{+1.3}$ ${82.1}_{-10.3}^{+5.7}$ 0.4 V16
203533312 0.17566 ± 0.000183 2456933.98649 ± 0.00038 0.0248 ± 0.001 3.11 ± 0.24 ${1.7}_{-0.2}^{+0.1}$ ${76.6}_{-11.2}^{+9.4}$ 0.5 ⋯
205152172 0.980414 ± 0.000096 2456959.30915 ± 0.0014 ${0.0219}_{-0.002}^{+0.004}$ 1.58 ± 0.36 ${5.3}_{-1.9}^{+1.1}$ ${83.7}_{-8.8}^{+4.7}$ 0.7 V16
206103150 0.789693 ± 0.000082 ${2457042.1466}_{-0.00162}^{+0.00159}$ 0.0143 ± 0.001 1.79 ± 0.13 ${3.0}_{-0.5}^{+0.3}$ ${81.8}_{-7.7}^{+5.9}$ 0.3 B15
206151047 0.358378 ± 0.00006 ${2456983.06634}_{-0.00093}^{+0.00071}$ ${0.017}_{-0.001}^{+0.002}$ 1.65 ± 0.18 4.9 ± 1.0 ${85.4}_{-5.5}^{+3.3}$ 0.5 V16
206169375 0.367453 ± 0.000039 ${2457004.52447}_{-0.00068}^{+0.00052}$ ${0.0246}_{-0.001}^{+0.002}$ 2.55 ± 0.25 ${5.2}_{-1.0}^{+0.9}$ ${85.3}_{-5.1}^{+3.4}$ 0.6 V16
206298289 0.434827 ± 0.000298 ${2456987.60012}_{-0.0009}^{+0.00083}$ ${0.0297}_{-0.002}^{+0.004}$ 1.62 ± 0.28 ${5.2}_{-1.4}^{+1.3}$ ${84.8}_{-6.2}^{+3.7}$ 0.3 V16
206417197 0.442094 ± 0.000086 ${2457007.48414}_{-0.00134}^{+0.00138}$ 0.0138 ± 0.001 1.16 ± 0.13 ${3.2}_{-0.7}^{+0.6}$ ${81.6}_{-10.0}^{+6.1}$ 0.1 V16
210605073 0.567055 ± 0.000145 2457127.43651 ± 0.00056 ${0.1047}_{-0.004}^{+0.007}$ 16.22 ± 6.26 ${5.7}_{-1.3}^{+0.7}$ ${85.7}_{-5.0}^{+3.1}$ 0.5 B
210707130 0.684575 ± 0.000143 ${2457077.68807}_{-0.00052}^{+0.00063}$ ${0.0181}_{-0.001}^{+0.002}$ 1.4 ± 0.2 ${6.2}_{-1.6}^{+0.7}$ ${85.9}_{-5.6}^{+2.9}$ 0.0 ⋯
210961508 0.349935 ± 0.000042 ${2457087.65251}_{-0.00041}^{+0.00043}$ ${0.0263}_{-0.001}^{+0.003}$ 2.18 ± 0.25 ${3.4}_{-1.0}^{+0.5}$ ${81.8}_{-11.0}^{+5.7}$ 0.0 ⋯
211357309 0.46395 ± 0.000118 ${2457201.45767}_{-0.00107}^{+0.00102}$ ${0.0186}_{-0.002}^{+0.003}$ 0.85 ± 0.18 ${4.7}_{-1.6}^{+1.9}$ ${84.0}_{-9.6}^{+4.4}$ 0.3 ⋯
211685045 0.769057 ± 0.00052 ${2457201.38352}_{-0.00186}^{+0.00189}$ ${0.035}_{-0.002}^{+0.003}$ 2.06 ± 0.52 ${3.3}_{-0.7}^{+0.4}$ ${82.9}_{-8.8}^{+5.0}$ 0.4 ⋯
211995325 0.279258 ± 0.00015 ${2457154.45219}_{-0.00174}^{+0.00175}$ ${0.1243}_{-0.011}^{+0.021}$ 8.41 ± 3.31 ${2.2}_{-0.3}^{+0.7}$ ${79.8}_{-11.7}^{+7.3}$ 1.1 ⋯
212150006 0.898216 ± 0.000135 ${2457190.28605}_{-0.00068}^{+0.00067}$ ${0.0449}_{-0.002}^{+0.009}$ 4.02 ± 0.82 ${6.3}_{-3.2}^{+1.2}$ ${85.1}_{-12.2}^{+3.6}$ 0.3 ⋯
Vanishing transits
211152484 0.702084 ± 0.000335 ${2457091.55232}_{-0.00147}^{+0.00151}$ 0.016 ± 0.001 1.68 ± 0.12 ${3.0}_{-0.6}^{+0.3}$ ${81.3}_{-8.5}^{+6.1}$ 0.9 C
False positives?
210414957 0.970016 ± 0.000514 ${2457069.9496}_{-0.00049}^{+0.00048}$ ${0.0663}_{-0.005}^{+0.003}$ 6.29 ± 0.61 ${3.3}_{-0.4}^{+1.2}$ ${77.4}_{-3.7}^{+9.1}$ 0.1 D
210754505 0.870775 ± 0.000223 ${2457077.07917}_{-0.00057}^{+0.00054}$ ${0.0414}_{-0.003}^{+0.004}$ 3.97 ± 0.47 ${4.3}_{-1.4}^{+1.9}$ ${80.0}_{-8.1}^{+7.8}$ 0.7 D
210954046 0.950356 ± 0.000177 ${2457128.33024}_{-0.00113}^{+0.00111}$ ${0.0677}_{-0.006}^{+0.008}$ 6.94 ± 1.08 ${2.9}_{-0.8}^{+1.3}$ ${74.3}_{-9.5}^{+11.6}$ 0.1 D, E

Note. V16: first reported in Vanderburg et al. (2016). S15: the "disintegrating planet" first reported in Sanchis-Ojeda et al. (2015a). B15: first reported Becker et al. (2015), also known as WASP-47e. A: Companion star detected with McDonald observations; planetary parameters are diluted, possible false positive. B. Stellar temperature and radius from photometry (similar to F0 star). C: Variable depth/disappearing transits (possible false positive). Fit to all parameters assumes average transit depth is ${R}_{p}/{R}_{* }=0.0156\pm 0.001$ and ${R}_{p}=1.7\pm 0.19\,{R}_{\oplus }$. D: Potential eclipsing binary from light curve variability. E: RV measured stellar-level variations.

Download table as:  ASCIITypeset image

The focus of this paper is on the shortest period planets (less than one day). However, it is common for planets with slightly longer periods to be misidentified at a shorter alias if only the shortest periods are examined. To account for this aliasing, we ran the initial EEBLS search for periods from 3 to 72 hr, but folded and binned the data using the period with the largest BLS spectral peak, and that was less than 24 hr. This process eliminated the cases of misidentified transiting planet candidates, although about half of the eclipsing binary signals proved to be aliases on closer examination. To ensure we had identified the correct period, we also folded all candidates' data at 0.5, 2, and 4 times the initial period. We then refined the orbital periods by running a finer search of 10,000 trial periods between 98% and 102% of the initial period to find the values listed in Table 3; see Section 2.3 for the derivation of the period errors.

2.2. Follow-up Observations

We obtained reconnaissance spectra for nine candidates from C1, C2, and C4 with the Tull Coudé spectrograph (Tull et al. 1995) at the Harlan J. Smith 2.7 m telescope at McDonald Observatory from 2015 December to 2016 March. The exposure times ranged from 1200 to 4800 s, resulting in signal-to-noise ratios (S/N) from 32 to 50 per resolution element at 5650 Å. We determined stellar parameters for the host stars with the spectral fitting tool Kea (Endl & Cochran 2016). We also determined absolute RVs by cross-correlating the spectra with the RV-standard star HD 50692. Our results are summarized in Table 4. We obtained two observations on different nights of the relatively bright EPIC 210954046, finding large RV variations (over 20 km s−1) and indicating a likely stellar rather than planetary companion. Two other objects were found to have companions. EPIC 201606542 shows a double-peaked, cross-correlation function peak, indicating an SB2 binary star; with an unknown binary period, the likely options are (a) a false positive or (b) a planet around one star with diluted (underestimated) planetary radius parameters due to the light of the second star. EPIC 201650711 has a fainter companion at 1'' separation, as estimated from the guide camera, and also has likely diluted planetary parameters.

Table 4.  Spectral Observations Of Candidates

EPIC HJD S/N RV ${T}_{{\rm{eff}}}$ [Fe/H] $\mathrm{log}(g)$ $v\ \sin i$ Notes
  days   km s−1 K   cm s−2 km s−1
201606542 2457462.81892 35 0.00 ± 0.00 5540 ± 108 0.030 ± 0.04 4.81 ± 0.12 13.23 ± 0.53 SB2 (double peaked), A
203533312 2457462.96524 38 18.56 ± 1.50 6620 ± 86 0.090 ± 0.05 4.19 ± 0.12 23.85 ± 0.83  
201650711 2457463.81728 43 5.52 ± 0.43 4340 ± 103 −0.810 ± 0.08 4.25 ± 0.42 2.31 ± 0.40 Comp. star at 1''
210414957 2457373.91896 32 43.76 ± 0.40 5838 ± 102 0.300 ± 0.07 4.12 ± 0.14 8.25 ± 0.28  
210707130 2457374.67776 47 −4.123 ± 0.37 4462 ± 84 −0.280 ± 0.10 4.17 ± 0.18 1.92 ± 0.34  
210754505 2457374.79139 36 −1.82 ± 0.32 5875 ± 103 0.040 ± 0.05 4.04 ± 0.19 8.75 ± 0.22  
210954046 2457373.65486 38 40.57 ± 3.91 6062 ± 274 0.000 ± 0.16 3.00 ± 0.58 55.00 ± 2.89 Large RV variation
  2457374.84919 50 18.83 ± 1.96 6188 ± 298 0.000 ± 0.16 3.00 ± 0.58 53.33 ± 3.55 Large RV variation
210961508 2457375.65275 42 −58.53 ± 0.22 4925 ± 45 −0.060 ± 0.07 3.42 ± 0.08 2.42 ± 0.15  
211152484 2457374.82461 44 −49.55 ± 0.23 6188 ± 67 −0.120 ± 0.06 4.12 ± 0.15 8.42 ± 0.15  

Note. A: The parameters for 201606542 have larger uncertainties than quoted, due to the presence of a secondary set of lines.

Download table as:  ASCIITypeset image

2.3. Fitting Candidate Transits

Light curves were fit assuming a transiting planet model. The light curves were fit in Python using the algorithm from Mandel & Agol (2002), as implemented by the Batman package (Kreidberg 2015).4 We used the pymodelfits5 and PyMC packages to conduct a Markov Chain Monte Carlo transit analysis using 100,000 iterations (discarding as burn-in the first 1000 iterations and thinning the sample by a factor of 10). The results are shown in Table 3, with the quoted 1σ error bars containing 68.3% of the posterior values. With very short transit durations, there are only a few observations per transit, resulting in considerable averaging point-to-point in the observed light curves. The solution is to fit the light curves using supersampling, where each model point is an average of several points spanning the half-hour exposure time. Because the time to run each fit scales directly with the number of points used in supersampling, we chose to use 7 points for candidates with $4\leqslant P\leqslant 24$ hr periods and 11 points for the very shortest with $P\lt 4$ hr.

Accurate stellar parameters are key to getting accurate planetary parameters. When possible, we used values for stellar Teff, $\mathrm{log}(g)$, and [Fe/H] from spectral observations (either our own at McDonald or from the literature). Next, in order of preference, was the revised EPIC catalog (Huber et al. 2015), which had 20 of the 23 targets of this paper (1 of which was observed from McDonald). For EPIC 202094740, we used the the K2-TESS Stellar Properties Catalog6 for stellar temperature, and assumed that $\mathrm{log}(g)=4.0$ and [Fe/H] = 0. For EPIC 210605073, which is very faint, we estimated the stellar type as F0 from photometric ugriz colors (see Section 3.3), and assigned a temperature of 7020 K, as well as $\mathrm{log}(g)=4.0$ and $[\mathrm{Fe}/{\rm{H}}]=0$.

For EPIC 206103150 (also known as, WASP-47), we used the published stellar radius of Mortier et al. (2013). For all other stars we derived stellar radii from ${T}_{{\rm{eff}}}$ using Boyajian et al. (2012; their Equation (4) and Table 10). Where available, we compared these radius values to the EPIC values and found significant differences for only two stars: EPIC 210414957 (one of the likely false positives; EPIC ${R}_{* }=2.319\pm 0.233\,{R}_{\odot }$, whereas we calculated ${R}_{* }=0.806\pm 0.041\,{R}_{\odot }$), and EPIC 210961508 (EPIC ${R}_{* }=2.589\pm 0.512\,{R}_{\odot }$, whereas we calculated ${R}_{* }=0.773\pm 0.045\,{R}_{\odot }$). The calculated errors on the stellar radius are included in the estimates of planetary radius. We calculated the quadratic limb darkening coefficients for the Kepler bandpass using Claret & Bloemen (2011), where we fixed microturbulent velocity = 2 km s−1 and used the available [Fe/H] and $\mathrm{log}(g)$ values, except as noted previously.

To estimate uncertainties on each candidate's orbital period, we fit for the transit ephemeris. Because there are too few points in any individual light curve to constrain a transit fit, consecutive transits were folded and binned on a number n of orbital periods, with n large enough to give the resulting binned transits sufficient S/N to be analyzed. (We required n between 11 and 31 orbits for our candidates.) Then each folded/binned transit was fit with a linear ephemeris, and the errors on the orbital periods were assigned based on these fits. (There was no evidence of transit-timing variations for any of our candidates.) We used a similar procedure in Jackson et al. (2013) and were able to recover the ephemerides assumed for synthetic transits injected into real data from the Kepler mission.

Because a blend scenario with similarly sized eclipsing binary stars can resemble a transiting planet with half the true period of the system, we separately fit the odd- and even-numbered transits, and compared the radius ratios derived for each (Batalha et al. 2010). The difference between the depth of the odd and even transits, expressed in terms of the errors, is shown in Table 3 as ${\sigma }_{\mathrm{odd}\mbox{--}\mathrm{even}}$. All candidates with odd–even ratios greater than 3σ were assigned to be eclipsing binaries.

To further investigate the possibility of blend scenarios for our candidates, we looked for correlations between photometric centroids and flux variations—in-transit shifts of the photocenter may indicate blending with objects near the target star in the sky (Batalha et al. 2010). For C0-2 we used the positions calculated by A. Vanderburg (private communication), while for C3-5 we used the values for MOM_CENTR1 and MOM_CENTR2 provided with the standard mission light curves from MAST, which we downloaded separately for each of our candidates. We found no statistically significant (3σ) photocenter variations in the centroid position during transit compared to out-of-transit for any of our candidates.

3. CANDIDATES

3.1. EPIC 206103150, a.k.a. WASP-47

EPIC 206103150 is the WASP-47 system, where a 4 day hot Jupiter (Hellier et al. 2012) was recently found to be accompanied by a super-Earth at 0.8 days (the candidate identified by this survey) and another transiting planet at 9 days (Becker et al. 2015), as well as a Jupiter-sized, non-transiting planet at ∼572 days (Neveu-VanMalle et al. 2016). Clear evidence of the outer two transiting planets is seen in the folded light curve for the inner planet in Figure 5. This system provided a check on our detection and characterization algorithms, particularly for multiples; we saw no signs of additional planets among our other candidate systems. Our radius of $1.79\pm 0.13\,{R}_{\oplus }$ is very similar to the value of 1.829 ± 0.070 from Becker et al. (2015), which used the higher-precision short-cadence (1 minutes) data.

Figure 5.

Figure 5. Transiting planet-like candidates. The blue lines show the best-fit models to the planet parameters without binning over K2ś observing cadence, while the red lines are the model calculated with binning (supersampling). Residuals between the binned model fits and the data are shown below each light curve. Candidates with their names in red show signs of being eclipsing binaries or otherwise potentially non-planetary; see individual discussions in Section 3.

Download figure:

Standard image High-resolution image

3.2. Sub-Jovian Desert Candidates: EPIC 201637175, 202094740, 203533312, 212150006, and 211995325

No confirmed planets with radii between about 3 and 11 R⊕ are known below a period of about 1.5 days, and that radius range is underpopulated out to about 3 days. This region in period-radius space has been referred to as the sub-Jovian desert (Beaugé & Nesvorný 2013; Matsakos & Königl 2016), and corresponds to the size range in which a planet would need to have significant volatiles to match the observed radius, which might be difficult for the planets to retain. One candidate for the sub-Jovian desert is EPIC 201637175, the disintegrating planet candidate of Sanchis-Ojeda et al. (2015a).

Membership in the sub-Jovian desert is highly dependent on the precision with which the stellar parameters are known. EPIC 211995325 is around a very faint star (${Kp}=18.2$), and the large errors on its radius (${R}_{{\rm{p}}}=8.41\pm 3.31\,{R}_{\oplus }$) are due to both the low S/N light curve and the uncertain stellar size (${R}_{* }=0.62\pm 0.22\,{R}_{\odot }$).

The remaining three candidates—EPIC 202094740, 203533312 and 212150006—are prime targets for follow-up, even though they have strong a priori odds of being false positives (see Colón et al. 2015). Many initially promising candidates in this size range turn out to be deeper eclipses that have been diluted to appear planetary in size—this is likely the case for the three objects discussed in Section 3.3.1. We note that although EPIC 212150006 is in the Kepler EB catalog online, it appears with erroneous values (see Section 3.4), so its status is uncertain. Any confirmed planets would be of great value for understanding the stability and evolution of planets in this size range. The shortest-period candidate in this paper is EPIC 203533312, which is around a bright star (${Kp}=12.5$) with $P=4.2$ hr and ${R}_{p}=3.11\pm 0.24\,{R}_{\oplus }$, placing it at the lower edge of the sub-Jovian desert. Following the work of Rappaport et al. (2013), we can estimate a minimum mass for the planet by requiring it to be just exterior to its Roche limit. We find ${M}_{p}\geqslant 48.5\,{M}_{\oplus }$, with a density of $\rho =8.9\,{\rm{g}}\,{\mathrm{cm}}^{-3}$.

3.3. EPIC 210605073

Candidate 210605073 is a 1% deep transit around an extremely faint star (${Kp}=17.9$), with no stellar parameters (e.g., ${T}_{{\rm{eff}}}$ and R⊙) listed in the EPIC or TESS/Vanderbilt catalogs. Based on the broadband Sloan photometry provided on the K2 ExoFOP (https://exofop.ipac.caltech.edu/k2/edit_target.php?id=210605073), the star has very neutral to slightly blue colors ($g-r=-0.037$, $g-i=-0.145$, and $g-z=-0.266$). Using Pinsonneault et al. (2012; their Table 1) to estimate ${T}_{{\rm{eff}}}$ from Sloan colors, we find that the colors are just above the high-mass end of their fiducial models, suggesting that the star is a bit larger than $1.5\,{M}_{\odot }$. We note however that no measurements of the metallicity, log g, or photometric extinction are available to better constrain the estimate. An F0 star with ${M}_{* }=1.7\,{M}_{\odot }$ and ${R}_{* }=1.3\,{R}_{\odot }$ implies a candidate radius of 14 R⊕, while (for comparison) an M dwarf with a stellar radius of 0.4 R⊙ implies a radius of 5 R⊕. Both radius values are large enough that the candidate would probably have a significant volatile component (Adams et al. 2008), and Roche-lobe overflow (Valsecchi et al. 2015) and/or photoevaporative mass loss (Lopez & Fortney 2013) would likely have removed the atmosphere of such a planet in a 13 hr orbital period. Thus, it seems a priori unlikely that this candidate is a planet, although additional (and not likely forthcoming) data would be required to make a definitive judgment.

3.3.1. Likely EBs: Out-of-transit Variability for EPIC 210414957, 210754505, and 210954046

Although there are no signs of odd–even depth variations for any of the objects presented in this paper, three show variability in the out-of-transit portion of their light curves, which is probably explained by a false-positive scenario. For EPIC 210414957 and 210754505, the out-of-transit portion shows a sinusoidal pattern at twice the period of the candidate transits, with transits occurring at both peaks and troughs as seen in Figure 6 panels (a) and (b). Such variability is typically due to ellipsoidal variations, although for large, hot planets a similar pattern could be due to phase-curve variations (e.g., υ And; Harrington et al. 2006). If the undulation were due to the phase variability of a large planet rotating through view, we would expect that the transits would only occur at the same point in the variation (typically the troughs, when no emission from the planet is seen). Both objects are also in the so-called sub-Jovian desert, where the stability of their atmospheres is questionable.

Figure 6.

Figure 6. Questionable candidates. (a)–(b) Two candidates, EPIC 21041957 and 201754505, folded to four times the orbital period, have significant out-of-transit variation and the transits occur at different points in the sinusoidal pattern; this is a common feature of similar-sized eclipsing binary light curves. (c) EPIC 210954046, folded to the orbital period, has a sinusoidal pattern with a minimum suggestive of a secondary around 0.5 orbital phase; coupled with the large RV signature, this is a confirmed false positive. (d) EPIC 211152484, showing only intermittent transit-like signals in the raw time series. The gray line shows a transit model with the parameters in Table 3, scaled to the depth of the deepest point (radius ratio = 0.035), which occurs around T = 2457082; the red dashed horizontal line shows the approximate time range during which transit-like signals most frequently occurred.

Download figure:

Standard image High-resolution image

The third object, EPIC 210954046, has out-of-transit variability that more closely resembles a shallow secondary eclipse (see Figure 6 panel (c)). Follow-up RV observations revealed an RV shift of more than 20 km s−1, which indicates that this candidate is a false positive (see Table 4); the host star is also a fast rotator. In addition, a nearby star at 2'' separation was seen in the McDonald guide camera, lending more support to the idea that the nominal $6\,{R}_{\oplus }$ transit is actually a diluted binary star.

3.3.2. Variable and Disappearing: EPIC 211152484

The importance of examining the full time series, not just the binned composite transit, is illustrated by EPIC 211152484. Although the period signal in Figure 5 strongly resembles a transiting planet, it does so only intermittently. There are no transits for about half the period of observation (see Figure 6), and when transits are visible, they have variable depths. The best fit reported in Table 3 is a fit to all the data and is thus an average of transit depths; the deepest point (at $T=2457082.4$) corresponds to a radius ratio of 0.035, or double the average. Possible explanations include some kind of stellar variability, a rapidly precessing cloud of debris, or a disintegrating comet. A full examination of this interesting object is beyond the scope of this work. Additional data may be forthcoming as part of the GO proposal from Charbonneau and colleagues to characterize and provide masses for planets smaller than 2.5 R⊕ (http://keplerscience.arc.nasa.gov/data/k2-programs/GO4029.txt).

3.4. Eclipsing Binaries

In the process of identifying transiting planet candidates, 91 likely eclipsing binary stars were also identified (Table 1). Eclipsing binaries with strongly dissimilar depths were obvious on first visual inspection of the transit light curves, while those with more similar transit depths were often initially identified by EEBLS at an alias of half the true period. Table 1 lists the EPIC number and period for all eclipsing binaries, along with a note for which were found at an alias of the true period. Because we focused on objects with periods of under a day, the list of eclipsing binaries is not complete for $P\gt 1$ day, and everything listed with a period of one day or more was originally identified at a shorter alias. It is also possible that some eclipsing binaries with periods less than one day were missed if they more closely resembled sinusoidal noise.

We cross-correlated our list of eclipsing binaries with the Kepler EB catalog (http://keplerebs.villanova.edu/), which has been extended to include K2 targets in the online Third Revision (Beta) updated 2015 October 26. Out of the 91 EBs listed in Table 1, 58 appear in that catalog (although 4 appear at half the period we identify), while 33 are new. Only two of the USP transiting planet candidates in Table 3 appeared in the Kepler EB catalog, and it is unclear if either truly belongs there: for EPIC 211685045, the secondary marked appears to be a glitch (three points of noise that happen to lie half an orbital phase from the transit; see http://keplerebs.villanova.edu/overview/?k=211685045). EPIC 212150006 (which is a sub-Jovian desert candidate) has a secondary depth and width of −1 (likely an error). Nonetheless, the possibility of these and other targets being undetected eclipsing binary blends remains, and requires follow-up RV observations and high-resolution images to be fully resolved.

4. SURVEY COMPLETENESS

4.1. Detectability Calculations

To test the completeness of our survey, we injected a grid of synthetic transits into a representative sample of light curves. We sorted all light curves from a given campaign by the median noise of the detrended light curve and took 10 light curves at each decile (median noise for C0-5, respectively: 540, 1090, 700, 490, 440, and 460 ppm), as well as the least ($\approx 1$ ppm) and most ($\approx {10}^{6}$ ppm) noisy curves for each campaign. Into each of these representative light curves we inserted transits with radius ratios from 0.0025 to 0.25 and with periods between 3.5 and 23.5 hr. Each synthetic light curve was run through our EEBLS detection pipeline, and a transit was declared detected if it was recovered within 0.1% of the injected period and within a factor of two on depth. The completeness as a function of the input radius ratio and light curve noise is shown in Figure 7, while the completeness as a function of period and radius is shown in Figure 8.

Figure 7.

Figure 7. Detectability of injected transits by radius ratio and noise of light curve. Ten light curves at the highest and lowest noise levels, and at each intervening decile, were tested for a suite of injected planets with periods from 3.5 to 23.5 hr and radius ratios of 0.0025 to 0.25. Black represents no detection, while the grayscale represents the fraction of samples (averaged over each of the 10 light curves per point and all orbital periods) that were detected. The radius ratios of a 1 R⊕ planet around G, K, and M dwarfs are also indicated. Sensitivity improved between the first three campaigns (C0–C2) and the last three (C3–C5).

Download figure:

Standard image High-resolution image
Figure 8.

Figure 8. Detectability of injected transits by radius ratio and orbital period. Ten light curves at the highest and lowest noise levels, and at each intervening decile, were tested for a suite of injected planets with periods from 3.5 to 23.5 hr and radius ratios of 0.0025 to 0.25. The sampled grid is shown as small black dots, while the background contours show that grid interpolated onto an evenly spaced grid. Black represents no detection, with the color-bar shading to light to represent the fraction of samples (averaged over each of the 10 light curves per point and all noise levels) that were detected. The approximate locations of a 1 R⊕ planet around G, K, and M dwarfs are also indicated (lower left). Candidates are shown with error bars (white points are likely false positives); note that one candidate from C5, 211995325, which orbits a tiny, late M dwarf, is off the scale with a radius ratio of ${R}_{p}/{R}_{* }=0.1558$.

Download figure:

Standard image High-resolution image

As expected, detectability is a strong function of the radius ratio. Detectability also varied by campaign, with C0–C2 less sensitive to small transits than C3–C5. In C0-2 only about 10% of light curves would have been sensitive to a 1 R⊕ planet around a G star (radius ratio of 0.01), compared to 30% for K stars and 50% M dwarfs. For C3–C5, the detectable fraction of Earth-sized planets is roughly 30%, 50%, and 65%, respectively. We detected three sub-Earth-sized candidates (i.e., 201264302, 201650711, and 211357309) and seven candidates with $1\leqslant {R}_{p}\leqslant 2\,{R}_{\oplus }$ (i.e., 201606542, 205152172, 206103150, 206151047, 206298289, 206417197, 210707130), all around stars smaller than the Sun (Table 2).

By the time the radius ratio reaches 0.035, the detection probability saturates at 80%–85% of all injected transits, indicating that 15%–20% of K2 light curves are unlikely to detect transits of any size. Unlike in the analysis of Sanchis-Ojeda et al. (2014) of the Kepler field, we did not find a strong detectability trend with orbital period, although there is a modestly increased likelihood of finding closer planets.

4.2. Comparison to Published Occurrence Rates

Sanchis-Ojeda et al. (2014) provided robust estimates of the USP occurrence rate for the Kepler field, and we calculated the estimated number of candidates assuming that the same occurrence applies to C0-5 K2 targets. For this purpose, we used the effective temperatures of the K2 target stars as provided by the K2-TESS catalog, and the occurrence rates and period distribution for USPs from Sanchis-Ojeda et al. (2014). We also note that Sanchis-Ojeda et al. (2014) found no candidates larger than $\sim 2\,{R}_{\oplus }$, so we separated our candidates into two bins, using $2.2\,{R}_{\oplus }$ as the cutoff because that is the first zero-object bin in their Figure 9.

Figure 9.

Figure 9. Known exoplanets with periods under two days are taken from http://exoplanet.eu (queried 2016 January) and shown as small gray circles. Candidates from the K2 ExoFOP (https://exofop.ipac.caltech.edu/k2/, queried 2016 April 13) are shown as open black circles. The 19 planet candidates of this paper are shown in red (some of which were previously reported elsewhere), and the 4 problematic objects in this paper are shown as open circles. Dashed lines indicate the regions in which few planets have been confirmed: the sub-Jovian desert, between about $3\mbox{--}11\,{R}_{\oplus }$, which has no confirmed planets with $P\leqslant 1.5\,{\rm{day}}$, and Hot Jupiters with periods shorter than that of WASP-19b at $P=0.788\,\mathrm{day}$. The "disintegrating planet" of Sanchis-Ojeda et al. (2015a) is shown as a filled red star just above the sub-Jovian desert line, while the object with "vanishing transits" (EPIC 211152484; this work) is shown as an open red star well below the line.

Download figure:

Standard image High-resolution image

We first estimated the expected number of planets based on the occurrence rate, which varies by stellar type. We considered all stars inferred to be dwarf stars and divided them by stellar type (based on their effective temperatures) to estimate the total number of USPs in orbit around all stars of that type. For example, Sanchis-Ojeda et al. (2014) estimated an occurrence rate among M dwarfs of 1.1 ± 0.4%. In C2, there are 1030 such stars, leading us to expect between 7 and 15 USPs orbiting M dwarfs in that field. We generated a hypothetical population of USPs for each field and for each stellar type, with a random number distributed normally about the mean expected number and with a standard deviation given by the error bars on the occurrence rates. We assigned each hypothetical USP an orbital period between 3 and 24 hr, with a probability distribution given by the one inferred for USPs in Sanchis-Ojeda et al. (2014). We selected as many stars of the type under study, drawing a random effective temperature, and converted that temperature to a stellar radius and mass using the empirical fits from Boyajian et al. (2012). (This conversion involves extrapolation slightly above the range of temperatures considered in that study.) We used the stellar mass and period hosting each USP to calculate a semimajor axis and, combined with the stellar radius, a transit probability (Barnes 2007). We considered that USP to transit if a random number uniformly distributed between 0 and 1 lay below the transit probability. We applied this procedure several times for each field and for each stellar type to achieve robust statistics and estimated uncertainties as the standard deviation of our resulting yields. This number is the "Expected" field in Table 5, and varies from 5 to 14 planets per campaign.

Table 5.  Ultra-short-period Planet Yield from this Survey

Field ${N}_{\mathrm{Cand}.}$ Nest ${N}_{\mathrm{Expected}}$ a ${N}_{\mathrm{Cand}.}$ ${N}_{\mathrm{est}}$ b
  ($\leqslant 2.2\,{R}_{\oplus }$)     ($\gt 2.2\,{R}_{\oplus }$)  
C0 0 0 5 ± 2 1 1–2
C1 3 7 9 ± 3 1 1–2
C2 1 5 8 ± 3 1 1–2
C3 4 11 10 ± 3 1 1–2
C4 2 5 11 ± 3 1 1–2
C5 2 3 14 ± 4 2 2–4
Total 12 31 57 ± 7 7 7–14

Notes.

aBased on the occurrence rate for smaller planets of Sanchis-Ojeda et al. (2014). bNo occurrence rate is available for larger planets because Sanchis-Ojeda et al. (2014) detected none; some of these candidates are likely false positives. The estimated population assumes no false positives and a completeness of 50%–80% for larger USPs (${R}_{p}\gt 2.2\,{R}_{\oplus }$ and $P\lt 1$ day).

Download table as:  ASCIITypeset image

Next we estimated the fraction of targets that our survey would have detected (using the survey completeness calculation of Section 4), assuming the same occurrence rate as in Sanchis-Ojeda et al. (2014). The occurrence rate calculations were expressed in terms of planetary radius and only covered planets from $0.84\leqslant \,{R}_{{\rm{p}}}\leqslant 2.2\,{R}_{\oplus }$; the survey completeness was in terms of radius ratio and covered a broader range of planetary radii, while not taking the stellar radius into account. To reconcile the two, we first found the fraction of planets from Sanchis-Ojeda et al. (2014) as a function of planetary radius between $0.84\leqslant \,{R}_{{\rm{p}}}\leqslant 2.2\,{R}_{\oplus }$ (taken from their Figure 9). We used the same log bins they did, centered at 0.92, 1.09, 1.3, 1.55, and 1.84 R⊕; all of their bins from 2.2 R⊕ up were empty. We assumed (as they did) that stellar type did not affect the occurrence rate of planets as a function of planetary radius, although the detectability of planets would depend on the stellar radius. To factor that in, we calculated the radius ratio of each radius bin if the object were around a nominal F, G, K, or M star (assumed to have radius values of 1.2, 1, 0.7, and 0.5 R⊙, respectively). We then found a single function for the detectability of a planet as a function of radius ratio by integrating the completeness grid (Figure 8) over all periods, and taking the mean over all campaigns. Now, for each stellar type we had the detectable fraction of planets in each radius bin (which ranged from 15% of the 0.92 R⊕ bin around an F dwarf to 81% of the 1.84 R⊕ bin around an M dwarf). We then convolved that with the fraction of F, G, K, and M stars per field to get the total fraction of planets from $0.84\leqslant {R}_{p}\leqslant 2.2\,{R}_{\oplus }$ around any stellar type that we would have found, resulting in an integrated detection rate of 37%–42% of objects in that size range, depending on the field. This integrated detection rate was multiplied by the number of candidates in that size range in each campaign, resulting in the Nest column in Table 5, ranging from 0 to 11 objects per campaign.

How do the numbers compare? All the expected values are within 3σ of the estimated yields, although we note that the total number of objects is about half what we would expect. In particular, three campaigns (C1, C2, and C3) are within 1σ of the expected value, while C0, C4, and C5 are low by 2–3σ (and C0 has no detections). This raises the question of whether the lower detected numbers are intrinsic to (a) this survey, (b) the K2 mission (less likely without a mechanism for lower yields in particular campaigns), or (c) variability in planet occurrence rates with galactic location. The campaigns observed are a diverse sample: C0 is near the Galactic Anti-Center and C2 is near Galactic Center, while C1 and C3 are near the North and South Galactic Caps, respectively, and C4 and C5 are near clusters (the Pleiades/Hyades and the Beehive, respectively). The Kepler field, for comparison, is just off the galactic field in the Cygnus region along the Orion arm.

We also note that we found seven candidates larger than $2.2\,{R}_{\oplus }$, while Sanchis-Ojeda et al. (2014) did not find any in the Kepler data (although Sanchis-Ojeda et al. 2015a did find one in K2—the disintegrating EPIC 201637175). Some of those objects are quite likely to be false positives, and more follow-up observations are needed to confirm which, if any, are planets. For this reason, we consider it premature to calculate an occurrence rate for larger planets. We note, however, that the detectable fraction of such objects is high (50%–85% around F-M stars), so this sample is more complete than the lower-radius subgroup. Thus, the fact that there are only seven candidates larger than $2.2\,{R}_{\oplus }$ (standing in for ${N}_{\mathrm{est}}=7\mbox{--}14$ objects, assuming no false positives and a detection rate of 50%–80%), while there are twelve candidates smaller than $2.2\,{R}_{\oplus }$ (standing in for ${N}_{\mathrm{est}}=31$), is more evidence that the sub-Jovian desert is real.

4.3. Comparison to Other Surveys

Another test of survey completeness is to compare our list of detected objects to other surveys that examined the same data. Some of our candidates from C0 to C3 were reported by Vanderburg et al. (2016), which was published while this manuscript was being prepared. Our single C0 candidate was not reported by that work. In C1, all four of our candidates were reported, along with four others that are well below our cutoff S/N of 10 (with S/N = 5–7) and two that we identify as EBS (EPIC 201182911 and 201563164). In C2, we found one candidate (EPIC 203533312) that was not reported by Vanderburg et al. (2016), while they reported one target below our S/N cutoff. (That object, EPIC 203518244, had S/N = 5.8 and also had a duration longer than our generous duration cutoff, indicating a potential non-planetary source of the transit signal.) In C3, we didn't find any candidates that were not reported by Vanderburg et al. (2016), and the three candidates they reported that we did not find had S/N = 6–7, again below our cutoff. As a test, we reran our C2 search with a lower cutoff of S/N = 5, which resulted in no new planet recoveries but about twice as many light curves to sort through, indicating that our current cutoff is about as good as the current data and detection pipeline warrant.

5. DISCUSSION

Known short-period exoplanets (less than three days) tend to divide into two populations: Jupiter-sized objects (10–15 R⊕), which are known to exist down to just under 1 day periods (the shortest confirmed Hot Jupiter is WASP-19b, at 0.788 days; Hebb et al. 2010), and much smaller planets ($\leqslant 2\,{R}_{\oplus }$) that are expected to lack volatiles. The sub-Jovian desert is the region between 3 and 11 R⊕ where there are no confirmed stable planets with periods of less than 1.5 days, as shown in Figure 9, and very few with periods less than 3–4 days. The origin of this bifurcation is an active area of research. Kurokawa & Nakamoto (2014) suggest that objects with periods below a day represent represent in-migrating hot Jupiters (at the high end) and stripped remnant cores (at the low end), while Matsakos & Königl (2016) suggest the bifurcation is consistent with short-period planets originating via circularization of a high-eccentricity orbit.

It has been noted by Rogers (2015) that most planets with ${R}_{p}\gt 1.6\,{R}_{\oplus }$ are not (entirely) rocky, and must therefore contain a substantial volatile fraction. We note that, in general, for planets with radius values of 2–3 R⊕ "volatiles" does not always imply H/He gas. For example, Kepler-22b (Borucki et al. 2012) has a radius of 2.4 R⊕, with its mass constrained to below 52.8 M⊕ (Kipping et al. 2013), and may be an ocean-like world. It is not clear, however, how long such an ocean would last if Kepler-22b were moved from its current orbital period of nearly 290 days into the sub-day period regime of the planets that are the focus of this work. Nor is it likely that an object with $R\gt 3\,{R}_{\oplus }$ could achieve that size without a substantial H/He envelope (Fortney et al. 2007), which would be vulnerable to tidal stripping and/or photoevaporation.

Six of our candidates have radius values of $\gt 3\,{R}_{\oplus }$ (i.e., 202094740, 201637175, 203533312, 210605073, 211995325, and 212150006). It is entirely possible that some or perhaps all are false positives. The dearth of objects in this size range detected in other surveys makes this group highly important to pursue via follow-up observations.

We stress that our candidates are still preliminary, and require accurate follow-up observations to be certain that (a) we have the correct stellar parameters, because the planetary parameters scale directly with the stellar radius value, and (b) that we can rule out false-positive scenarios. Toward goal (a), we are continuing efforts to obtain spectra at McDonald to determine better measurements of ${T}_{{\rm{eff}}}$ and ${R}_{* }$ (for most objects). For those candidates that are bright enough, we are also pursuing (b) by acquiring radial velocity and high-resolution imaging to rule out false-positive scenarios, and to determine the fraction of starlight that might be due to nearby stars (which will affect the measured planet radius).

6. CONCLUSION

We conducted a survey for ultra-short-period candidates (less than 1 day) in K2 data. In this paper, we present 19 candidates in C0-5 of K2. Four additional objects (three likely eclipsing binaries and one odd case of vanishing transits) are also noted, as are 91 eclipsing binary systems. Among the new candidates reported is EPIC 203533312, one of the shortest-period planet candidates identified ($P=4.2$ hr), which by stability arguments must have a density of at least ρ = 8.9 g cm−13. Its star, at ${Kp}=12.5$, is a good candidate for follow-up observations. It is also one of five candidates with radius values in the sub-Jovian desert between 3–11 R⊕ and less than P = 1.5 days. An additional candidate hot Jupiter (EPIC 210605073) at P = 13.6 hr, would be the shortest-period hot Jupiter identified, although the faintness of its host star (${Kp}=17.89$) makes additional follow-up difficult. We estimated our survey completeness, which varied from 10%–85% depending on planet size, stellar type, and K2 campaign, with an average detection efficiency of about 40% for Earths and super-Earths ($0.8\leqslant {R}_{p}\leqslant 2.2\,{R}_{\oplus }$). Finally, we compared the occurrence rate of Earths and super-Earths with ${R}_{p}\leqslant 2.2\,{R}_{\oplus }$ to that of Sanchis-Ojeda et al. (2014) and find that we detected about half as many planets in K2 as they found in Kepler (31 versus 57 after adjusting for completeness). We note that that survey did not find any candidates with ${R}_{p}\geqslant 2.2\,{R}_{\oplus }$, while we found eight, indicating that (a) several of our candidates may yet prove to be false positives, and (b) larger planets are indeed rare among ultra-short-period planets.

All the data analyzed in this paper were collected by the K2 mission, funding for which is provided by the NASA Science Mission Directorate. The data were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. This study is based upon work supported by NASA under grant No. NNX15AB78G issued through the Astrophysical Data Analysis Program by Science Mission Directorate. This work has made use of the K2-TESS Stellar Properties Catalog on the Filtergraph data portal, through the TESS Science Office's target selection working group (architects K. Stassun, J. Pepper, N. De Lee, M. Paegert). The Filtergraph data portal system is trademarked by Vanderbilt University. This research used Uncertainties: a Python package for calculations with uncertainties, by Eric O. Lebigot, http://pythonhosted.org/uncertainties/. We thank Andrew Vander-burg, Daniel Huber, and an anonymous referee for helpful comments on a draft of this manuscript.

Facility: Kepler - .

Footnotes

Please wait… references are loading.
10.3847/0004-6256/152/2/47