ULTRA-SHORT-PERIOD PLANETS IN K2 WITH COMPANIONS: A DOUBLE TRANSITING SYSTEM FOR EPIC 220674823

As part of our analysis, we searched for transit timing variations in the fits to both planet candidates (Figure 3). The transit light curves for the smaller planet, p1, do not have sufficient signal-to-noise ratio (S/N) to allow us to robustly fit the mid-transit time of each transit. Instead, we folded together ${N}_{\mathrm{tr}}=3$ consecutive transits to increase the S/N and fit a linear ephemeris to each stacked trio, giving one point for every 1.7 days (Jackson et al. 2013). We also explored the effect of stacking together more consecutive transits and found similar fits for the ephemeris (modulo the loss of time resolution). For p2 each individual transit was fit. For both objects, the observed minus calculated (O–C) plots are consistent with no variation.

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Reconnaissance spectra were obtained of EPIC 220674823 with the Tull Coudé spectrograph (Tull et al. 1995) at the Harlan J. Smith 2.7 m telescope at McDonald Observatory on three nights during 2016 August–October. The exposure times ranged from 600 to 1600 s, resulting in S/Ns from 30 to 60 per resolution element at 5650 Å. We determined stellar parameters for the host stars with the spectral fitting tool Kea (Endl & Cochran 2016), which compares high-resolution, low-S/N spectra of stars to a massive grid of synthetic stellar spectral models in order to determine the fundamental stellar parameters of the Kepler target stars. We also determined absolute RVs by cross-correlating the spectra with the RV-standard star HD 50692. The stellar parameters from each observation and our adopted values of ${T}_{\mathrm{eff}}$, log(g), and [Fe/H] are shown in Table 2. No RV differences were seen within uncertainties (Figure 4). We used the observed ${T}_{\mathrm{eff}}$ and the models of Boyajian et al. (2012) to estimate the ${R}_{\star }$, and the stellar mass was estimated from those using the Dartmouth models and assuming a stellar age of 5 Gyr (Dotter et al. 2008).

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Table 2.  Spectra of EPIC 220674823

UT	HJD	Teff	[Fe/H]	log(g)	$v\sin (i)$	RV (km s−1)	Notes
2016 Aug 15 09:46:54	2457615.9038	5580 ± 86	0.040 ± 0.03	4.62 ± 0.16	2.62 ± 0.18	−15.86 ± 0.13	McDonald
2016 Sep 08 09:17:37	2457639.9016	5600 ± 55	0.010 ± 0.02	4.50 ± 0.10	2.23 ± 0.23	−16.01 ± 0.10	McDonald
2016 Oct 11 07:27:13	2457672.8187	5660 ± 60	−0.010 ± 0.02	4.62 ± 0.07	3.08 ± 0.21	−15.798 ± 0.28	McDonald
		5590 ± 51	0.025 ± 0.02	4.56 ± 0.09			Adopted average
		5814 ± 181	−0.283 ± 0.25	4.409 ± 0.085			EPIC (Huber et al. 2016)

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With an rms error of 110 m s⁻¹, we can place an upper limit on the planets' masses of ${M}_{{\rm{p}}1}\lt 0.43$ ${M}_{\mathrm{Jup}}$ and ${M}_{{\rm{p}}2}\lt 1.22\,{M}_{\mathrm{Jup}}$ (Jupiter masses) using Equation (14) from Lovis & Fischer (2010, pp. 27–53). If we assume that the planets are entirely rocky, we can estimate the approximate masses using the mass–radius relation from Lopez & Fortney (2014): ${M}_{{\rm{p}}}/{{\rm{M}}}_{\odot }\approx {({R}_{{\rm{p}}}/{{\rm{R}}}_{\odot })}^{4}$, which yields masses of 4.5 and 41 M_⊕ for p1 and p2, respectively. The large radius for p2 suggests that it likely harbors a substantial gaseous envelope (Rogers 2015) and, following the mass–radius relationship described in Adams et al. (2008), would have a mass of about 20 M_⊕, depending on the core composition and gas fraction. So we also provide an estimated RV signal if both planets had substantial volatiles, using half the core-only estimates, or 2.3 and 20.5 M_⊕ for p1 and p2, respectively. The RV half-amplitude estimates are 3.5 and 11 ${\rm{m}}\,{{\rm{s}}}^{-1}$ for p1 and p2, respectively, for the larger masses, and 1.7 and 5.5 ${\rm{m}}\,{{\rm{s}}}^{-1}$ respectively, for the smaller masses, as shown in Figure 4. Even the smaller mass estimate is within reach of the best world-class instruments today.

We observed EPIC 220674823 in i' band with Robo-AO at Kitt Peak (Baranec et al. 2014; Salama et al. 2016) on 2016 September 19 and 25. Each observation comprised a sequence of full-frame-transfer detector readouts of an electron-multiplying CCD camera at the maximum rate of 8.6 Hz for a total exposure time of 90 s. Individual frames are dark- and flat-field corrected before being registered to correct for the dynamic image displacement of the target that cannot be measured with the laser guide star, and co-added. We detected no stellar companions within 2 mag at 02, nor within 4.5 mag at 10 of the primary target.

We made additional observations with the NIRC2 camera behind the Keck II adaptive optics system in natural guide star mode on 2016 October 16. We obtained six frames, 2 × 15 s exposures at each of three different dither positions in the Kp filter. After sky subtraction and flat-field calibration, the frames were co-added into a single image based on the automatic detection of the location of the target star in each dither frame. Using the same methodology of Ziegler et al. (2016), a custom locally optimized point-spread function was subtracted from the image, which was run through an automatic companion detection pipeline. This allowed even tighter constraints to be placed: there are no companions as faint as ${\rm{\Delta }}M=2$ at a separation of 008 and ${\rm{\Delta }}M=8$ at 1'' and beyond. A plot of the full Keck detection constraints is shown in Figure 5. A full description of the methodology for the automated search and the generation of the contrast curve can be found in Sections 3.5 and 3.6 of Ziegler et al. (2016).

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We used the freely available vespa package to validate the planetary system (Morton 2012, 2015). To place a limit on secondary events, we subtracted the transit model of both planets from the photometry and then searched for the strongest periodic signal within 0.001 days of the planetary orbital period using EEBLS. This placed an upper limit on secondary events of 30 and 80 parts per million (ppm) for p1 and p2, respectively. Using the nondetection of secondaries, publicly available photometry from the ExoFOP,⁷ and our observational constraints, vespa returned a false-positive probability (FPP) of 4 × 10⁻⁵ for p1 and 6 × 10⁻⁶ for p2, with each planet considered separately. Since they are part of a multitransiting system, the odds of a false positive are even lower (Lissauer et al. 2012). Thus, we consider EPIC 220674823 p1 and p2 to be validated and suggest that they be referred to as EPIC 220674823 b and EPIC 220674823 c, respectively.

We have identified another USP that is part of a multiplanet system. We know of at least 12 confirmed systems of USPs with one to four additional planets each (see Figure 6), including the new EPIC 220674823 system. While USPs have high geometric transit probabilities (10%–50%), the transit probabilities for their sibling planets, with orbital periods of 1–45 days, drop below a few percent. In 10 of the 12 systems, all of the known planets transit. For the WASP-47 system, two of the three companions transit, and the outermost planet was identified in RV only. The remaining system, 55 Cnc, was discovered via RV observations, with the innermost planet, 55 Cnc e, originally identified at the wrong period of P = 2.8 days (McArthur et al. 2004). Once the true period of less than 1 day was recognized, the transit probability for 55 Cnc e was revised upward to 25% (Dawson & Fabrycky 2010), and its transit was observed (Demory et al. 2011; Winn et al. 2011), although no other planet in the system has been shown to transit to date.

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Are USPs statistically more likely to exist in multiplanet systems than as singletons? We can estimate the likelihood with a simple heuristic argument. If we take the 11 USPs with at least one known transiting companion, we find that the sibling planet nearest the USP has a period $P=1.2\mbox{--}45$ days and a transit detection probability of 2%–10%. If we assume that every USP has at least one companion (transiting or not) that falls within the same orbital period range, then for the 175 USP systems listed at exoplanets.org in 2016 October, we would expect to have discovered 9.8 ± 0.3 companions (based on 10,000 random draws from the geometric probabilities of the known planets). This is nearly the same as the known number of 11 multiplanet USP systems. Thus, the current rate of detection of multiplanet systems is consistent with every USP having at least one additional companion within $P\lt 45$ days. Note that half of the USP multiplanet systems have one additional companion, while the other half have two to four planets, but we have only considered the odds of the first, closest companion.

The argument above makes no assumption about whether planets preferentially have aligned orbital planes, which has the known effect of increasing the transit probabilities for the additional planetary companions. In the case of the triple system Kepler-18, Cochran et al. (2011) showed that assuming that the mutual inclination of the planets is less than a few degrees increases the transit probability for the second planet by a factor of 2. We can incorporate into our heuristic calculation above the assumption that the next-nearest planet to a USP has an orbital inclination within a few degrees of the USP. This assumption roughly doubles the transit probabilities, resulting in an expected 19.6 ± 0.6 detections (instead of the actual 11 detected). Thus, if the next-nearest planets in USP systems are nearly coplanar to the USP, we find that between 47% and 66% of USP systems should host at least one additional planet, rather than 100%. (Note that none of these arguments account for biased detection efficiencies.)

The truth probably lies between these two scenarios, since coplanarity cannot be assumed for all systems. Substantial misalignments have been reported in the literature: the USP 55 Cnc e has an inclination of ${i}_{e}=83\buildrel{\circ}\over{.} 4$, while astrometric measurements of the outermost planet, 55 Cnc d, found that ${i}_{d}=53^\circ$ (McArthur et al. 2004). Some origin theories, particularly those invoking scattering, produce wide ranges of inclinations. Ultimately, the number of planets in multiple systems and the types of orbits the companion planets occupy will be a powerful constraint on planet formation theories.

Among the 24 known companion planets to USPs in 12 systems, 21 are small, ranging from sub-Earths to Neptune-sized, or ${R}_{{\rm{p}}}=0.57\mbox{--}3.6\ {R}_{\oplus }$ (Kepler-42 d and WASP-47 d, respectively), with a median value of ${R}_{{\rm{p}}}=2.3\ {R}_{\oplus }$. The 12 USPs themselves are much smaller than their more distant companions, with an average radius of $1.3\ {R}_{\oplus }$, and a range of radius values from ${R}_{{\rm{p}}}=0.59\mbox{--}2.1\ {R}_{\oplus }$ (KOI-1843 d and 55 Cnc e, respectively). This could indicate the difference between the extreme environment of Sun-grazing worlds, which have been stripped of their gases, and orbits just outside the most extreme zone.

Only three companion planets have larger radius values: the RV planets 55 Cnc d (P = 5169 days) and 55 Cnc b (P = 14.7 days), which do not transit, but have sufficiently high masses (3.8 and 0.8 ${M}_{\mathrm{Jup}}$, respectively) that standard mass–radius relationships predict radii substantially larger than that of Neptune, and the transiting Hot Jupiter WASP-47 b (P = 4.2 days), which has ${R}_{{\rm{p}}}=1.15$ ${R}_{\mathrm{Jup}}$. Both of these systems are atypical in that (1) they are the only two systems that were identified from the ground, rather than through Kepler or K2 photometry, and (2) all of the planets in these two systems are larger than the planets in the other 10 multiplanet systems. We stress that there may well be more distant companions like 55 Cnc d around other systems, since most USP-hosting stars have not been systematically monitored for long-term RV signals.

The upshot of all these considerations is that the known planets in systems that host USPs tend to be smaller than Neptune. This tendency is unlikely to be due to observational biases since they would skew detections toward larger planets.

Despite their modest masses, USPs should be high-priority targets for precision RV observations, since the RV amplitude is a function of orbital distance. To date, the smallest planet measured with RV is Kepler-78 b, a USP with P = 0.35 days and a mass of $M=1.69\mbox{--}1.85\,{M}_{\oplus }$ (Howard et al. 2013; Pepe et al. 2013). Another advantage is that observations made over a few nights will span several orbital periods, allowing detections on a short timescale. The orbital periods of these objects are also well separated from the typical stellar variability period, decreasing potential confusion (Boisse et al. 2011). Detecting the more distant companion planets in systems with USPs may also be possible with longer-term monitoring and could test theories of USP origins.

An advantage of K2 is that the average planet candidate is several magnitudes brighter than the typical Kepler target, putting them within easier reach of RV measurements. Among the multiplanet systems, the USP in three of the brightest five systems was first identified with K2 (HD 3167, V = 8.9; WASP-47, V = 11.0; and EPIC 220674823, V = 11.958), with Kepler responsible for one (Kepler-10, V = 11.157) and the last identified with RV from the ground because its star was so bright (55 Cnc, V = 5.95).

Understanding the USP population has implications for the Transiting Exoplanet Survey Satellite (TESS), scheduled to launch in 2017, which will look for short-period rocky planets around ∼500,000 nearby, bright stars. Roughly 0.1% of Sun-like stars host USPs, so TESS should find hundreds of bright USPs. These planets would be ideal for follow-up, and a clear framework for their origins would motivate and guide additional TESS observations.