CHARACTERIZING K2 PLANET DISCOVERIES: A SUPER-EARTH TRANSITING THE BRIGHT K DWARF HIP 116454

HIP 116454 and nearly 2,000 other stars were observed by the Kepler spacecraft from 2014 February 4 until 2014 February 12 during the Kepler Two-Wheel Concept Engineering Test. After the first 2.5 days of the test, Kepler underwent a large, intentional adjustment to its pointing to move its target stars to the center of their apertures, where they stayed for the last 6.5 days of the test. We downloaded the full engineering test data set from the Mikulski Archive for Space Telescopes (MAST) and reduced the Kepler target pixel files as described in VJ14.

In brief, we extracted raw aperture photometry and image centroid positions from the Kepler target pixel files. Raw K2 photometry is dominated by jagged events corresponding to the motion of the spacecraft, as Kepler's pointing drifts because of solar radiation pressure and is periodically corrected with thrusters. For the last 6.5 days after the large pointing tweak, we removed the systematics due to the motion of the spacecraft by correlating the measured flux with the image centroid positions measured from photometry. We essentially produced a "self flat field" (SFF) similar to those produced by, for instance, Ballard et al. (2010), for analysis of Spitzer photometry. We fit a piecewise linear function to the measured dependence of flux on centroid position, with outlier exclusion to preserve transit events, and removed the dependence on centroid position from the raw light curve. Similar to VJ14, we excluded data points taken while Kepler's thrusters were firing from our reduced light curves because these data were typically outliers from the corrected light curves. For HIP 116454, the median absolute deviation (MAD) of the 30-minute-long cadence data points improved from ≃ 500 parts per million (ppm) for the raw light curve to ≃50 ppm for the SFF light curve.

Visual inspection of light curves from the ≃2000 targets observed during the engineering test revealed a 1 millimagnitude (mmag) deep candidate transit in photometry of HIP 116454, designated EPIC 60021410 by the Kepler team. HIP 116454's photometric and astrometric measurements are summarized in Table 1. Raw and corrected K2 photometry for HIP 116454 are shown in Figure 1. We fit a Mandel & Agol (2002) model to the transit and measured a total duration of approximately 2.25 hr and a planet-to-star radius ratio of approximately 0.03. Unfortunately, the data point during transit ingress happened during a thruster firing event and was excluded by our pipeline. This particular data point does not appear to be anomalous, but we choose to exclude it to minimize risk of contaminating the transit with an outlier. Slow photometric variability, presumably due to starspot modulation, is evident in the K2 light curve at the subpercent level.

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We also performed a similar SFF correction to the data taken in the 2.5 days of data before the large pointing tweak. Even though the resulting data quality is somewhat worse, we are able to confidently exclude any other events of a similar depth during that time.

Because K2 only observed one transit event, we were not able to measure a precise orbital period for the planet candidate. Nonetheless, we were able to put rough constraints on the orbital period from our knowledge of the transit duration and estimates of the stellar properties. The 9 day time baseline of the K2 observations allowed us to constrain the period of the candidate transiting planet to be greater than 5 days. To put a rough upper bound on the allowed planet period, we compared the transit duration of the candidate transit around HIP 116454 to the distribution of transit durations from the ensemble of Kepler planet candidates (retrieved from the NASA Exoplanet Archive; Akeson et al. 2013). We found that of the 413 Kepler planet candidates with transit durations between 2 and 2.5 hr, 93% had orbital periods shorter than 20 days. Because transit duration is a function of the mean stellar density, we repeated this calculation while restricting the sample to the 64 planet candidates with transit durations between 2 and 2.5 hr and host-star effective temperatures within 200 K of HIP 116454. We find similarly that 94% of these candidates had orbital periods shorter than 20 days.

2.2.1. Archival Imaging

We used a combination of modern and archival imaging to limit potential false-positive scenarios for the transit event. HIP 116454 was observed in the National Geographic Society–Palomar Observatory Sky Survey (POSS-I) on 1951 November 28. HIP 116454 has a proper motion of 303 mas yr⁻¹ (van Leeuwen 2007) and therefore has moved nearly 20 arcsec with respect to background sources since being imaged in POSS-I. Inspection of the POSS-I image reveals no background objects within the K2 aperture used in our photometric reduction. We show the POSS-I blue image overlaid with the K2 photometric aperture in Figure 2(a). The POSS-I survey has a limiting magnitude of 21.1 in the blue bandpass (Abell 1955), 10 mag fainter than HIP 116454. The depth of the detected transit is 0.1%, so if a background eclipsing binary were responsible, the depth would correspond to a total eclipse of a star 7.5 mag fainter. A low-proper-motion background star such as that would have readily been detected in POSS-I imaging. We conclude that our aperture is free of background objects whose eclipses could masquerade as planet transits.

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The POSS-I imaging also reveals a companion star about 8 arcsec to the southwest of HIP 116454. The companion is not fully resolved in POSS-I because the photographic plate was saturated by the bright primary star, but an asymmetry in the stellar image is visible. HIP 116454 was also observed during the Second Palomar Observatory Sky Survey (POSS-II) on 1992 August 31. Improvements in photographic plate technology over the previous 40 yr allowed the companion star to be resolved. The companion shares a common proper motion with the primary at a projected distance of ≃ 500 AU, so we conclude that the two stars are a gravitationally bound visual binary system.

2.2.2. Modern Imaging

2.2.3. Adaptive Optics Imaging

HIP 116454 was observed nine times for the Carney–Latham Proper Motion Survey (Latham et al. 2002) with the CfA Digital Speedometer spectrograph over the course of 9.1 yr from 1982 until 1991. The Digital Speedometer measured radial velocities to a precision of approximately 0.3 km s⁻¹and detected no significant RV variations or trends in the velocities of HIP 116454. When corrected into an absolute RV frame, the Digital Speedometer measurements indicate an absolute RV of −3.06 ± 0.12 km s⁻¹ and when combined with proper motion, a space velocity of (U, V, W) = (− 86.7, −0.2, 4.5) ± (7.6, 1.2, 0.5) km s⁻¹. This somewhat unusual space velocity corresponds to an elliptical orbit in the plane of the galaxy, indicating that HIP 116454 originated far from the stellar neighborhood. A detailed analysis of HIP 116454's elemental abundances could reveal patterns that are dissimilar to stars in the solar neighborhood.

We obtained three observations of HIP 116454 in June of 2014 with the Tillinghast Reflector Echelle Spectrograph (TRES) on the 1.5 m Tillinghast Reflector at the Fred L. Whipple Observatory. The spectra were taken with a resolving power of R = 44, 000 with a signal-to-noise ratio (S/N) of approximately 50 per resolution element. When corrected into an absolute RV frame, the TRES spectra indicate an absolute RV for HIP 116454 of −3.12 ± 0.1 km s⁻¹. When combined with the absolute radial velocities from the Digital Speedometer, there is no evidence for a RV variation of greater than 100 m s⁻¹ over the course of 30 yr. The three individual radial velocities from the TRES spectra revealed no variability at the level of 20 m s⁻¹ over the course of 8 days. We also find no evidence for a second set of stellar lines in the cross-correlation function used to measure the radial velocities, which rules out many possible close companions or background stars. When the adaptive optics constraints are combined with a lack of RV variability of more than 100 m s⁻¹ over 30 yr and the lack of a second set of spectral lines in the cross-correlation function, we can effectively exclude any close stellar companions to HIP 116454.

We obtained 44 spectra of HIP 116454 on 33 different nights between July and October of 2014 with the HARPS-N spectrograph (Cosentino et al. 2012) on the 3.57 m Telescopio Nazionale Galileo (TNG) on La Palma Island, Spain, to measure precise radial velocities and determine the orbit and mass of the transiting planet. Each HARPS-N spectrum was taken with a resolving power of R = 115000, and each measurement consisted of a 15 minute exposure, yielding an S/N of 50–100 per resolution element at 550 nm, depending on weather conditions. The corresponding (formal) RV precision ranged from 0.90 m s⁻¹ to 2.35 m s⁻¹. Radial velocities were extracted by calculating the weighted cross-correlation function of the spectrum with a binary mask (Baranne et al. 1996; Pepe et al. 2002). In some cases, we took one 15 minute exposure per night, and in other cases, we took two 15 minute exposures back-to-back. In the latter case we measured the two consecutive radial velocities individually and report the average value.

The HARPS-N RV measurements are listed in Table 2. A periodic RV variation with a period of about 9 days and a semiamplitude of about 4 m s⁻¹ is evident in the RV time series. We checked that we identified the correct periodicity by calculating a Lomb–Scargle periodogram (Scargle 1982), shown in Figure 3. We found a strong peak at a period of 9.1 days and an aliased peak of similar strength with a period close to 1 day, corresponding to the daily sampling alias of the 9.1 day signal (e.g., Dawson & Fabrycky 2010). We estimated the false alarm probability of the RV detection by scrambling the RV data and recalculating the periodogram numerous times and counting which fraction of the scrambled periodograms have periods with higher power than the unscrambled periodogram. We found that the false alarm probability of the 9.1 day periodicity is significantly less than 10⁻⁴.

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In addition to the 9.1 day signal, we also found evidence for a weaker 45 day periodic RV variation. To help decide whether to include the second periodicity in our RV modeling, we fit the HARPS-N radial velocities with both a one-planet and a two-planet Keplerian model. The one-planet model was a Keplerian function parameterized by log (P), time of transit, log (RVsemiamplitude), $\sqrt{e}\sin (\omega)$, and $\sqrt{e}\cos (\omega)$, where P is the planet's orbital period, e is the orbital eccentricity, and ω is the argument of periastron. We also fit for a RV zero point and a stellar jitter term, for a total of seven free parameters. We fit each of these parameters with an unbounded uniform prior, except for $\sqrt{e}\sin (\omega)$ and $\sqrt{e}\cos (\omega)$, which had uniform priors over the interval between −1 and 1. The two-planet model was the sum of two Keplerian functions, each of which was parameterized by log (P), time of transit, log (RVsemiamplitude), $\sqrt{e}\sin (\omega)$, and $\sqrt{e}\cos (\omega)$. Once again, we also fit for a RV zero point and stellar jitter term, for a total of 12 free parameters. We fit each of these parameters with an unbounded uniform prior except for $\sqrt{e}\sin (\omega)$ and $\sqrt{e}\cos (\omega)$, which had uniform priors over the interval between -1 and 1, and for log P₂, the period of the outer planet, which we constrained to be between the period of the inner planet and 1,000 days. We performed the fits using emcee (Foreman-Mackey et al. 2013), a Markov chain Monte Carlo (MCMC) algorithm with an affine invariant ensemble sampler. We note that upon exploring various different periods for the outer planet, our MCMC analysis found the 45 day period to be optimal. We calculated the Bayesian information criterion (BIC, Schwarz 1978) to estimate the relative likelihoods of the two models. Although the BIC does not provide a definitive or exact comparison of the fully marginalized likelihoods of the models, it allows us to roughly estimate the relative likelihoods. Upon calculating the BIC, we estimate that the two-planet model is favored over the one-planet model with confidence P ∼ 0.03. From here on, we therefore model the RV observations as the sum of two Keplerian functions. We show our HARPS-N measurements and our best-fitting model in Figure 4.

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For both periods, we find an amplitude consistent with that of a transiting super-Earth. The 9 day periodicity in the RVs is consistent with the orbital period we estimated from the duration of the K2 transit event. We "predicted" the time of transit for the 9 day period planet during the K2 observations and found that the HARPS-N measurements alone constrain the expected time of transit to better than 1 day, and we find that the K2 transit event is consistent with the transit ephemeris predicted by only the HARPS-N RVs at the 68.3% (1σ) level. We show the K2 light curve with the transit window derived from only the HARPS-N RVs in Figure 5. Thus, the 9.1 day periodicity is consistent with being caused by a transiting planet. The more tenuous 45 day periodic variation, on the other hand, may be due to an outer planet, but it may also be caused by stellar variability.

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The HARPS-N spectra include regions used to calculate activity indicators, such as the Mount Wilson S_HK index and the R$^\prime _{\rm HK}$ index (e.g., Wright et al. 2004). We calculated the S_HK index for each HARPS-N spectrum and found a mean value of 0.275 ± 0.0034 and an associated $\log _{10}{R^{\prime }_{\rm HK}}= -4.773 \;{\pm}\; 0.007$. There were no obvious correlations between the S_HK index and either the measured RV or the residuals to either a one- or two-planet Keplerian fit.

2.5.1. WASP

2.5.2. MOST

After detecting the K2 transit, we obtained follow-up photometric observations with the MOST (Walker et al. 2003) space telescope during August and September of 2014. MOST observed HIP 116454 during three nearly continuous time spans: 13 days from 2014 August 3 to 2014 August 16, 18 days from 2014 August 21 to 2014 September 9, and 3.5 days from 2014 September 15 to 2014 September 18. During the first segment of the MOST data, observations of HIP 116454 were interleaved with observations of other stars during the satellite's orbit around Earth, but for the second and third segments MOST observed HIP 116454 continuously. During the first and third segments, the exposure time for individual data points was 1 s, and during the second segment, the exposure time was 2 s.

We processed the MOST data using aperture photometry techniques as described in Rowe et al. (2006). Background scattered light (modulated by the 101 minute orbital period of MOST) and interpixel sensitivity variations were removed by subtracting polynomial fits to the correlations between the stellar flux, the estimated background flux, and the centroid coordinates of the star. At each stage, outlying data points were excluded by either sigma clipping or hard cuts. The resulting precision of the MOST light curve was approximately 0.2% per 2 s exposure.

When we search the MOST light curve at the predicted times of transits from a simultaneous analysis of the K2 and HARPS-N data, we detect a weak signal with the same depth, duration, and ephemeris as the K2 transit. The MOST light curve is shown in Figure 6. The MOST data refine our estimate of the transiting planet period to a precision of roughly 30 s. We take this detection as confirmation that the 9.1 day period detected in radial velocities is in fact caused by the transiting planet. From here on, we refer to the 9.1 day period planet as HIP 116454 b.

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3.1.1. Spectroscopic Parameters of the Primary

3.1.2. Stellar Mass and Radius

3.1.3. Stellar Rotation Period

We attempted to measure the rotation period of HIP 116454 using photometric measurements from WASP, MOST, and K2 to see if stellar activity might contribute to the possible 45 day periodicity in the RV measurements. A constraint or measurement of the rotation period consistent with the possible 45 day periodicity in radial velocities could affect our interpretation of the signal. We only used photometric measurements for our analysis given the relatively short time coverage and sparseness of the spectroscopic observations.

We first started by analyzing the WASP data only because its time baseline far exceeded that of the K2 and MOST data. We binned the WASP data into nightly data points, calculated a Lomb–Scargle periodogram, and Fourier transformed the resulting power spectrum to obtain an autocorrelation function. The resulting periodograms and autocorrelation functions are shown in Figure 7. We performed this analysis on each season of WASP data individually. In the first season (2008) of WASP data, we found a moderately strong peak in both the autocorrelation function and the Lomb–Scargle periodogram at a period of about 16 days. We evaluated the significance of this peak by scrambling the binned data, recalculating the Lomb–Scargle periodograms, and counting the number of times the maximum resulting power was greater than the power in the 16 day peak. We found a false alarm probability of 2% for the peak in the first season. We did not find any convincing signals in the second (2009) or third (2010) observing seasons. A possible explanation for the inconsistency between observing seasons is that HIP 116454 experienced different levels of starspot activity, but it is also possible that the 16 day period detected in the first season is spurious. We concluded that the WASP data showed a candidate rotation period at 16 days, but the relatively high false alarm probability and lack of consistency between observing seasons precluded a confident detection.

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After our analysis of the WASP data yielded suggestive yet ambiguous results, we attempted to measure the rotation period of HIP 116454 by fitting all of the photometric data with a Gaussian process noise model. Stochastic yet time-correlated processes such as the variability produced by rotation in stellar light curves can be modeled as a Gaussian process by parameterizing the covariance matrix describing the time correlation between data points with a kernel function and inferring kernel hyperparameters from the data. We use a quasi-periodic kernel function for the specific problem of measuring a rotation period from a light curve. This in principle is better suited to inferring the rotation period of a star than a periodogram analysis because the variability produced by active surface regions on a rotating star is typically neither sinusoidal nor strictly periodic. The Gaussian process analysis also allows us to simultaneously model multiple data sets and to take advantage of data sets (like K2 and MOST) with relatively short time coverage.

We conducted our analysis using george (Foreman-Mackey et al. 2014), a Gaussian process library that employs Hierarchical Off-Diagonal Low Rank Systems (HODLR), a fast matrix inversion method (Ambikasaran et al. 2014). We used the following kernel function in our analysis:

$$\begin{equation} k_{ij} = A^2\exp \left[{\frac{-(x_i-x_j)^2}{2l^2}}\right]\exp \left[\frac{-\sin ^2\left(\frac{\pi (x_i-x_j)}{P}\right)}{g_q^2}\right], \end{equation} \tag{ 1 }$$

where A is the amplitude of correlation, l is the timescale of exponential decay, g_q is a scaling factor for the exponentiated sinusoidal term, and P is the rotation period. An additional hyperparameter s was used to account for additional white noise in the time series, where s is added to the individual measurement uncertainties in quadrature.

We modeled the three continuous periods of MOST data, the three seasons of WASP data, and the K2 photometry simultaneously, with A, l, g_q, and P constrained to be the same across all seven data sets and with s allowed to take a different value for each. We used emcee to explore the posterior distributions of the hyperparameters. The resulting posterior distribution was not well constrained, with significant power at essentially all rotation periods greater than about 8 days and less than about 50 days. There were a few periods that seemed to be preferred to some extent in the posterior distribution: a strong peak at 12 days, and weaker peaks at 16, 20, and 32 days.

We conclude that with our data we cannot conclusively identify a rotation period for HIP 116454, which leaves us unable to rule out stellar activity as the cause of the 45 day signal in the radial velocities. While we do not find any strong evidence in the photometry that the rotation period is close to 45 days, we cannot conclusively rule out a 45 day rotation period. More photometric (or spectroscopic) observations will be important to determining HIP 116454's rotation period.

We conducted an analysis of the K2 light curve, the HARPS-N RV observations, the MOST light curve, and the WASP light curve to determine orbital and planetary properties. We first reprocessed the K2 data using a different method from that described in VJ14 to minimize the possibility of any bias due to using the in-transit points in the flat field. We rederived the SFF correction by fitting the K2 light curve using an MCMC algorithm with an affine invariant ensemble sampler (adapted for IDL from the algorithm of Goodman & Weare 2010; Foreman-Mackey et al. 2013). We fit the transit light curve with a Mandel & Agol (2002) model, as implemented by Eastman et al. (2013), with quadratic limb-darkening coefficients held at the values given by Claret & Bloemen (2011). We modeled the stellar out-of-transit variations with a cubic spline between 10 nodes spaced evenly in time, the heights of which were free parameters. Similarly, we modeled the SFF correction as a cubic spline with 15 nodes spaced evenly in "arclength," a one-dimensional metric of position on the detector as defined in VJ14. Upon finding the best-fit parameters for the SFF correction, we applied the correction to the raw K2 data to obtain a debiased light curve.

After rederiving the correction to the K2 light curve, we simultaneously fit a transit light curve to the K2 light curve, the HARPS-N radial velocities, and the MOST and WASP photometry using emcee. We modeled the RV variations with a two-planet Keplerian model (fitting the 9.1 day period and the 45 day period simultaneously) and modeled the transits of the 9.1 day planet with a Mandel & Agol (2002) model. For the K2 light curve, we accounted for the 29.4-minute-long cadence exposure time by oversampling the model light curve by a factor of 13 and binning. We allowed limb-darkening coefficients (parameterized as suggested by Kipping 2013) to float. We used a white-noise model for the RV observations with a stellar jitter term added in quadrature to the HARPS-N formal measurement uncertainties. For the light curves, we used a Gaussian process noise model, using the same kernel described in Equation (1). We used an informative prior on the stellar log g_⋆ from Section 3.1.2 in our fits, which we converted to stellar density to help break the degeneracy between the scaled semimajor axis and the impact parameter. Using this prior let us constrain the impact parameter, despite having only one K2 long-cadence data point during transit ingress and egress. In total, the model had 28 free parameters. We used emcee to sample the likelihood space with 500 "walkers," each of which we evolved through 1500 steps. We recorded the last 300 of these steps as samples of our posterior distribution, giving a total of 150,000 MCMC links. We calculated correlation lengths for all 28 parameters, which ranged from 5.6 to 19.0, corresponding to between 8,000 and 27,000 independent samples per parameter. We assessed the convergence of the MCMC chains using the spectral density diagnostic test of Geweke (1992) and found that the means of the two sequences are consistent for 21/28 parameters (75%) at the 1σ level, for 27/28 (96%) at the 2σ level, and 28/28 at the 3σ level. These fractions are consistent with draws from a normal distribution, which is the expected behavior for the MCMC chains having converged.

In Table 3, we report the best-fitting planet and orbit parameters and their uncertainties for HIP 116454 b by calculating the median link for each parameter and 68% confidence intervals of all links for each parameter, respectively. We summarize the priors used in the fits and the full model outputs in Table 4, including nuisance parameters like the noise model outputs. We also make our posterior samples available for download as a FITS file.

Table 3. System Parameters for HIP 116454

Parameter	Value		68.3% Confidence	Comment
			Interval Width
Orbital parameters
Orbital period, P (days)	9.1205	±	0.0005	A
Radius ratio, (RP/R⋆)	0.0311	±	0.0017	A
Transit depth, (RP/R⋆)2	0.000967	±	0.000109	A
Scaled semimajor axis, a/R⋆	27.22	±	1.14	A
Orbital inclination, i (deg)	88.43	±	0.40	A
Transit impact parameter, b	0.65	±	0.17	A
Eccentricity	0.205	±	0.072	A
Argument of Periastron ω (deg)	−59.1	±	16.7	A
Velocity semiamplitude K⋆ (m s−1)	4.41	±	0.50	A
Time of Transit tt (BJD)	2456907.89	±	0.03	A
Stellar parameters
M⋆ (M☉)	0.775	±	0.027	B, D
R⋆ (R☉)	0.716	±	0.024	B, D
ρ⋆ (ρ☉)	2.11	±	0.23	B, D
log g⋆ (cgs)	4.590	±	0.026	B
[M/H]	−0.16	±	0.08	B
Distance (pc)	55.2	±	5.4	D
Teff (K)	5089	±	50	B
Planet parameters
MP (M⊕)	11.82	±	1.33	B, C, D
RP (R⊕)	2.53	±	0.18	B, C, D
Mean planet density, ρp (g cm−3)	4.17	±	1.08	B, C, D
log gp (cgs)	3.26	±	0.08	B, C, D
Equilibrium temperature $T_{\rm eff}(\frac{R_\star }{2a})^{1/2}$ (K)	690	±	14	B, C, D, E

Notes. (A) Determined from our analysis of the K2 light curve, the HARPS-N radial velocity measurements, the MOST light curve, and the stellar parameters. (B) Based on our spectroscopic analysis of the HARPS-N spectra. (C) Based on group A parameters. (D) Based on the Hipparcos parallax. (E) Assuming albedo of zero and perfect heat redistribution.

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Table 4. Summary of Combined Analysis

Parameter	Prior	50% Value	15.8%	84.2%
$\sqrt{e_1}\cos (\omega _1)$	$\mathcal {U}(-1, 1)$	0.244	−0.052	+0.049
$\sqrt{e_1}\sin (\omega _1)$	$\mathcal {U}(-1, 1)$	−0.395	−0.091	+0.109
tt, 1, [BJD]	$\mathcal {U}(-\infty, \infty)$	2456907.895	−0.037	+0.015
log (P1 day−1)	$\mathcal {U}(-\infty, \infty)$	2.210472	−0.000176	+0.000079
log (M1/MJup)	$\mathcal {U}(-\infty, \infty)$	−3.286	−0.111	+0.089
cos i1	$\mathcal {U}(-1, 1)$	−0.0296	−0.0038	+0.0023
$\sqrt{e_2}\cos (\omega _2)$	$\mathcal {U}(-1, 1)$	0.19	−0.26	+0.22
$\sqrt{e_2}\sin (\omega _2)$	$\mathcal {U}(-1, 1)$	−0.581	−0.122	+0.186
tt, 2, [BJD]	$\mathcal {U}(-\infty, \infty)$	2456930.8	−5.4	+5.7
log (P2 day−1)	$\mathcal {U}(-\infty, \infty)$	3.838	−0.082	+0.093
log (M2sin i2/MJup)	$\mathcal {U}(-\infty, \infty)$	−2.22	−0.29	+0.28
log Rp, 1/R⋆	$\mathcal {U}(-\infty, \infty)$	−3.443	−0.039	+0.042
q1	$\mathcal {U}(0, 1)$	0.37	−0.24	+0.33
q2	$\mathcal {U}(0, 1-q_1)$	0.41	−0.39	+0.29
RV zero point (m s−1)	$\mathcal {U}(-\infty, \infty)$	−0.42	−0.34	+0.33
Jitter (m s−1)	$\mathcal {U}(-\infty, \infty)$	0.45	−0.28	+0.32
log g⋆	$\mathcal {N}(4.59, 0.026)$	4.591	−0.020	+0.022
log A	$\mathcal {U}(-20, 5.5)$	−13.05	−0.33	+0.35
log l	$\mathcal {U}(-2, 8.5)$	1.33	−0.93	+1.33
log gq	$\mathcal {U}(-8, 7)$	2.7	−1.6	+1.4
log (Prot day−1)	$\mathcal {U}(2, 4)$	3.31	−0.78	+0.53
log σWASP1	$\mathcal {U}(-6.75, -1.75)$	−4.1	−1.8	+1.8
log σWASP2	$\mathcal {U}(-6.75, -1.75)$	−4.2	−1.8	+1.8
log σWASP3	$\mathcal {U}(-6.75, -1.75)$	−4.3	−1.7	+1.9
log σK2	$\mathcal {U}(-11, -6)$	−9.284	−0.044	+0.048
log σMOST1	$\mathcal {U}(-9, -3)$	−6.685	−0.059	+0.064
log σMOST2	$\mathcal {U}(-9, -3)$	−7.227	−0.051	+0.051
log σMOST3	$\mathcal {U}(-9, -3)$	−6.710	−0.122	+0.149

Notes. $\mathcal {U}(A, B)$ represents a uniform distribution between A and B, and $\mathcal {N}(\mu, \sigma)$ represents a normal distribution with mean μ and standard deviation σ. The limb-darkening coefficients q₁ and q₂ are defined according to the parameterization of Kipping (2013). All logarithms are base e. (This table is available in its entirety in FITS format.)

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We find that our data are best described by the presence of a planet with R_p = 2.53 ± 0.18 M_⊕ and M_p = 11.82 ± 1.33 M_⊕in a 9.1205 day orbit. While we find some evidence for an outer planet in the RV measurements, we cannot conclusively claim its existence based on the data presently at our disposal.

Figure 8 shows HIP 116454 b on a mass–radius diagram with other known transiting, sub-Neptune-sized exoplanets with measured masses and radii. We overlaid the plot with model composition contours from Zeng & Sasselov (2013). We first note that HIP 116454 b has a mass and radius consistent with either a low-density solid planet or a planet with a dense core and an extended gaseous envelope. The relatively low equilibrium temperature of the planet (T_eq = 690  ±  14 K, assuming zero albedo and perfect heat redistribution) makes it unlikely that any gaseous envelope the planet started with would have evaporated over its lifetime.

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In terms of mass and radius, this planet is similar to Kepler-68 b (8.3 M_⊕, 2.31 R_⊕, Gilliland et al. 2013) and HD 97658 b (7.9 M_⊕, 2.3 R_⊕ Howard et al. 2011; Dragomir et al. 2013), but it is likely slightly larger. HIP 116454 b and HD 97658 b (T_eq ≈ 730 K) have similar effective temperatures, but Kepler-68 b (T_eq ≈ 1250 K under the same assumptions) is somewhat hotter. Like these planets, HIP 116454 b has a density intermediate to that of rocky planets and of ice giant planets. On the mass–radius diagram, HIP 116454 b lies close to the 75% H₂O–25% MgSiO₃ curve for solid planets. It could be either a low-density solid planet with a large fraction of H₂O or other volatiles (which have equations of state similar to H₂O), or it could have a dense core with a thick gaseous layer.

We made inferences about the structure and composition of HIP 116454 b  if it indeed has a dense core and thick gaseous envelope, using analytic power-law fits to the results of Lopez & Fortney (2014). Assuming that the thick gaseous envelope is composed of hydrogen and helium in solar abundances, an equilibrium temperature calculated with perfect heat redistribution and an albedo of 0 and a stellar age of about 2 Gyr, the models predict that HIP 116454 b has a hydrogen and helium envelope making up about 0.5% of the planet's mass. The model suggests that HIP 116454 b has a 1.8 R_⊕ core with virtually all of the planet's mass, surrounded by a gaseous envelope with thickness 0.35 R_⊕, and a radiative upper atmosphere also with thickness 0.35 R_⊕. Using different assumptions to calculate the equilibrium temperature, like imperfect heat distribution and a nonzero albedo (for instance, the value of Sheets & Deming 2014), and different assumptions about the envelope's composition and age does not change the calculated thickness and mass of the gaseous envelope by more than a factor of two. We note that this envelope fraction is consistent with the population of Kepler super-Earth and sub-Neptune-sized planets studied by Wolfgang & Lopez (2014), who found the envelope fraction of these candidates to be distributed around 1% with a scatter of 0.5 dex.

We also explored the composition of HIP 116454 b  assuming it is solid and has little in the way of a gaseous envelope, using an online tool³², based on the model grids of Zeng & Sasselov (2013). We investigated a three-component model with layers of H₂O, MgSiO₃  and Fe. In this case, HIP 116454 b must have a significant fraction of either H₂O or other volatiles in an ice form like methane or ammonia. The composition in this case would be more similar to the ice giants in the solar system than the rocky planets like Earth.

We find that the pressure at the core of the planet can range from 1400 GPa for an iron-free planet to 2,800 GPa for a silicate-free planet. Assuming a ratio of iron to silicates similar to that of the Earth and other solar system bodies, we find that the core pressure of HIP 116454 b is about 2400 GPa. Under this assumption, HIP 116454 b would consist of 8% Fe, 17% MgSiO₃  and 75% H₂O by mass. Using the ratio of iron to silicates in solar system bodies is usually a relatively good assumption because this ratio is largely determined by element synthesis cosmochemistry, which does not vary greatly on the scale of 50 parsecs. However, HIP 116454's unusual space motion indicates that it might have formed elsewhere in the galaxy, so this assumption might not hold. More detailed spectral analysis, in particular measuring elemental abundances for Mg and Si compared to Fe in the parent star, could put additional constraints on the composition of HIP 116454 b  assuming it is solid.

If solid, HIP 116454 b would be one of the "H₂O rich" planets described in Zeng & Sasselov (2014), for which it is possible to make inferences about the phase of the planet's H₂O layer, given knowledge of the star's age. Various evidence points to HIP 116454 having an age of approximately 2 Gyr. Using relations from Mamajek & Hillenbrand (2008), the $R^{\prime }_{\rm HK}$ level indicates an age of 2.7 Gyr, and the rotation indicates an age of 1.1 Gyr, if the rotation period is indeed close to 16 days. The white dwarf's cooling age, however, sets a lower limit of approximately 1.3 Gyr. Future observations, like a mass measurement of the white dwarf to estimate its progenitor's mass (and therefore age on the main sequence), could constrain the age further. If HIP 116454's age is indeed about 2 Gyr and the planet lacks a gaseous envelope, then it is likely to have water in plasma phases near its water–silicate boundary (the bottom of the H₂O layer), but if it is slightly older (∼3 Gyr or more) or has a faster cooling rate, it could have superionic phases of water.

HIP 116454 b is a promising transiting super-Earth for follow-up observations because of the brightness of its star, especially in the near infrared. We used the Exoplanet Orbit Database³³ (Wright et al. 2011; Han et al. 2014) to compare HIP 116454 b to other transiting sub-Neptune-sized planets orbiting bright stars. We found that among stars hosting transiting sub-Neptunes with R_p < 3 R_⊕, only Kepler 37, 55 Cnc, and HD 97658 have brighter K-band magnitudes.

HIP 116454 is particularly well suited for additional follow-up photometric and RV observations, both to measure the mass of the planet to higher precision and to search for more planets in the system. HIP 116454 is chromospherically inactive and has low levels of stellar RV jitter (0.45 ± 0.29 m s⁻¹). This combined with its brightness makes it an efficient RV target. Moreover, the brightness of the host star makes HIP 116454 ideal for follow-up with the upcoming CHEOPS mission (Broeg et al. 2013).

HIP 116454 b could be important in the era of the James Webb Space Telescope to probe the transition between ice giants and rocky planets. In the solar system, there are no planets with radii between 1–3 R_⊕  while population studies with Kepler data have shown these planets to be nearly ubiquitous (Howard et al. 2012; Fressin et al. 2013; Petigura et al. 2013; Morton & Swift 2014). Atmospheric studies with transit transmission spectroscopy can help determine whether these planets are in fact solid or have a gaseous envelope and give a better understanding of how these planets form and why they are so common in the Galaxy. Also of interest is the fact that HIP 116454 b is very similar to HD 97658 b in terms of its orbital characteristics (both are in ∼10 day low-eccentricity orbits), mass and radius (within 10% in radius and within 25% in mass), and stellar hosts (both orbit K dwarfs). Comparative studies of these two super-Earths will be valuable for understanding the diversity and possible origins of close-in super-Earths around Sun-like stars. This being said, despite HIP 116454's brightness, the relatively shallow transit depth will make it a somewhat less efficient target than super-Earths orbiting smaller stars (for instance, GJ 1214 b, Charbonneau et al. 2009).

HIP 116454 b has demonstrated the potential of K2 to increase the number of bright transiting planets amenable to radial velocity follow-up. Despite its degraded pointing precision, it is possible to calibrate and correct K2 data to the point where super-Earths can be detected to high significance with only one transit. Despite the increased expense of bright stars in terms of Kepler target pixels required for the aperture, K2 data is of high enough precision to produce many transiting exoplanets around bright stars.

Many K2 fields, including the engineering test field, are located such that observatories in both hemispheres can view the stars, a significant difference between K2 and the original Kepler mission. Even though all of our follow-up observations for HIP 116454 b took place at northern observatories, the star's equatorial location enables follow-up from southern facilities like the original HARPS instrument at La Silla Observatory (Mayor et al. 2003) and the Planet Finding Spectrograph at Las Campanas Observatory (Crane et al. 2010) just as easily as with northern facilities with instruments like HARPS-N or the High Resolution Echelle Spectrograph at Keck Observatory (Vogt et al. 1994).

Many Kepler planet candidates were confirmed in part thanks to precise measurements of the Kepler image centroid as the planet transited: the expected motion of the image centroid could be calculated based on the brightness and position of other stars near the aperture, and deviations from that prediction could signal the presence of a false-positive planet candidate. Such an analysis will be substantially more difficult for K2 data because the unstable pointing leads to large movements of the image centroid. In this work, we were able to exclude the possibility of background objects creating false transit signals, taking advantage of the star's high proper motion and archival imaging. This will be more difficult for more distant stars. However, the focus of the K2 mission on nearby late K and M dwarfs, which typically have high proper motions, could make this technique of background star exclusion more widely applicable than it was for the original Kepler mission.