EPIC 228735255b - An eccentric 6.57 day transiting hot Jupiter in Virgo

TL;DR

This paper reports the discovery of EPIC 228735255b, a hot Jupiter with a 6.57-day orbit around a G-type star, detected via K2 photometry and ground observations, notable for its eccentricity and moderate inflation.

Contribution

First detection of an eccentric hot Jupiter with a period over 6 days using K2 data, demonstrating K2's capability to find longer-period transiting giants.

Findings

Planet has a mass of 1.019 M_Jup and radius of 1.095 R_Jup.

Orbit is eccentric with e=0.12.

Host star's rotation period is 16.3 days.

Abstract

We present the discovery of EPIC 228735255b, a P= 6.57 days Jupiter-mass (M$_P$=1.019$\pm$0.070 M$_{Jup}$) planet transiting a V=12.5 (G5-spectral type) star in an eccentric orbit (e=$0.120^{+0.056}_{-0.046}$) detected using a combination of K2 photometry and ground-based observations. With a radius of 1.095$\pm$0.018R$_{Jup}$ the planet has a bulk density of 0.726$\pm$0.062$\rho_{Jup}$. The host star has a [Fe/H] of 0.12$\pm$0.045, and from the K2 light curve we find a rotation period for the star of 16.3$\pm$0.1 days. This discovery is the 9th hot Jupiter from K2 and highlights K2's ability to detect transiting giant planets at periods slightly longer than traditional, ground-based surveys. This planet is slightly inflated, but much less than others with similar incident fluxes. These are of interest for investigating the inflation mechanism of hot Jupiters.

Tables

Table 1. Table 1: Parameters of EPIC 228735255

Parameter	Units	Value	Source
EPIC ID		228735255	H16*
2MASS ID		2MASS J12323296-0936274	H16*
R.A. ($\alpha$)	hh:mm:ss	$12:32:32.96$	H16*
Dec. ($\delta$)	dd:mm:ss	$-09:36:27.5$	H16*
gGAIA	mag	$12.393$	GAIA∘
B	mag	$13.349\pm 0.030$	APASS⋆
V	mag	$12.624\pm 0.030$	APASS⋆
g	mag	$12.930\pm 0.060$	APASS⋆
r	mag	$12.426\pm 0.020$	APASS⋆
i	mag	$12.292\pm 0.050$	APASS⋆
J	mag	$11.421\pm 0.026$	APASS⋆
H	mag	$11.068\pm 0.021$	APASS⋆
Ks	mag	$10.995\pm 0.021$	2MASS∙
Kep	mag	$12.483$	H16*
W1	mag	$10.985\pm 0.024$	AllWISE+
W2	mag	$11.030\pm 0.021$	AllWISE+
W3	mag	$10.891\pm 0.119$	AllWISE+
W4	mag	$8.898\pm -$	AllWISE+
Distance	pc	$340.24\pm 11.58$	†
Age	Gyr	$4.22\pm 0.95$	†
Spectral Type		$\mathrm{G5}$	†
MV	mag	${4.965}_{-0.066}^{+0.069}$	†
$\left[\mathrm{Fe}/H\right]$	dex	$0.12\pm 0.045$	†
Teff	K	$5654\pm 55$	†
log(g)	dex	${4.452}_{-0.009}^{+0.010}$	†
vsini	km s-1	$3.8\pm 0.2$	†
Prot	days	$16.3\pm 0.1$	†
M∗	M☉	${1.005}_{-0.020}^{+0.021}$	†
R∗	R☉	${0.987}_{-0.011}^{+0.011}$	†
${\rho }_{\ast }$	${\rho }_{☉}$	$1.048\pm 0.041$	†
$L_{\ast }$	$L_{☉}$	${0.893}_{-0.048}^{+0.049}$	†
${\mu }_{1,\mathrm{K2}}$		${0.341}_{-0.079}^{+0.084}$	†
${\mu }_{2,\mathrm{K2}}$		${0.441}_{-0.079}^{+0.111}$	†
${\mu }_{1,\mathrm{LCO}}$		${0.56}_{-0.16}^{+0.18}$	†
${\mu }_{2,\mathrm{LCO}}$		${0.38}_{-0.17}^{+0.20}$	†
RV residuals (CORALIE)	km s-1	$0.0184$	†
RV residuals (HARPS)	km s-1	$0.0097$	†
* Huber et al. (2016), ∘ Gaia Collaboration et al. (2016a, b),
⋆ Henden & Munari (2014),∙ Skrutskie et al. (2006),
+ Wright et al. (2010); Mainzer et al. (2011), † This work

Table 2. Table 2: Photometry for EPIC 228735255

BJD-2450000	Flux	Flux Error	Filter	Instr.
7582.5906314203	1.00002094	0.00008399	kep	K2
7582.6110636177	1.00006507	0.00008393	kep	K2
7582.6314957142	1.00000389	0.00008385	kep	K2
7582.6519277110	1.00001766	0.00008376	kep	K2
7582.6723599071	1.00000462	0.00008369	kep	K2
7582.6927920026	0.99998520	0.00008362	kep	K2
7582.7132239980	1.00001908	0.00008351	kep	K2
7582.7336561931	0.99992969	0.00008342	kep	K2
7582.7540882872	1.00015249	0.00008331	kep	K2
7582.7745202812	0.99993307	0.00008323	kep	K2
…	…	…	…	…
* Note: partial list – full table available in electronic form.

Table 3. Table 3: Radial Velocities for EPIC 228735255b  in chronological order

BJD-2450000	RV	RV error	BIS	Instrument
	km s-1	km s-1
7804.751722	1.25803	0.02389	-0.03886	CORALIE
7806.7167899	1.1231	0.0333	-0.019	HARPS
7814.792453	1.20384	0.02344	-0.08219	CORALIE
7815.668909	1.31119	0.02967	-0.03487	CORALIE
7817.678137	1.27255	0.03227	-0.06864	CORALIE
7818.723682	1.15348	0.02183	-0.01804	CORALIE
7820.754834	1.14137	0.02247	0.02071	CORALIE
7821.852054	1.29300	0.02745	0.03278	CORALIE
7823.874191	1.29414	0.02778	0.02189	CORALIE
7832.714263	1.10465	0.03093	-0.06040	CORALIE
7836.681188	1.31122	0.03383	0.00470	CORALIE
7850.717632	1.22394	0.02820	-0.05072	CORALIE
7851.823385	1.09243	0.03450	-0.00820	CORALIE
7866.6826602	1.1911	0.0086	0.02	HARPS
7867.699734	1.2876	0.0111	-0.009	HARPS
7868.7574426	1.3382	0.0137	0.003	HARPS
7869.6828912	1.3354	0.0111	0.039	HARPS
7871.7285204	1.1362	0.0102	0.0	HARPS

Table 4. Table 4: Parameters of EPIC 228735255b

Parameter	Units	Value	Priors*
Period	days	${6.569300}_{-0.000020}^{+0.000017}$	$𝒩(6.569,0.01)$
T0	days	${2457588.28380}_{-0.00014}^{+0.00014}$	$𝒩(2457588.28544,0.01)$
T14	hours	$4.56\pm 0.29$
T23	hours	$3.49\pm 0.26$
T12=34	hours	$0.53\pm 0.19$
RP/R∗		${0.1140}_{-0.0012}^{+0.0015}$	$𝒰(0.05,0.2)$
b		$0.33\pm 0.14$
i	$°$	${88.51}_{-0.53}^{+0.69}$	$𝒰(80,90)$
a∗	AU	$0.0591\pm 0.0034$	$𝒰(3.0,30.0)$ [R∗]
K	km s-1	${0.1112}_{-0.0073}^{+0.0076}$	$𝒩(0.1,0.1)$
${\gamma }_{\mathrm{CORALIE}}$	km s-1	${1.2170}_{-0.0092}^{+0.0089}$	$𝒩(1.22,0.05)$
${\gamma }_{\mathrm{HARPS}}$	km s-1	${1.2435}_{-0.0070}^{+0.0068}$	$𝒩(1.24,0.05)$
CORALIE jitter	km s-1	${0.0041}_{-0.0037}^{+0.0127}$	$𝒥(0.0001,0.1)$
HARPS jitter	km s-1	${0.0037}_{-0.0033}^{+0.0144}$	$𝒥(0.0001,0.1)$
Incident flux <F>	${10}^8$ erg s-1 cm-2	$2.565\pm 0.105$
e		${0.120}_{-0.046}^{+0.056}$	$\beta (0.867,3.03)$
$\omega$	$°$	${98.88}_{-4.16}^{+3.85}$	$𝒰(0.0,180.0)$
MP	MJup	$1.019\pm 0.070$
RP	RJup	$1.095\pm 0.018$
log gP	dex (cgs)	$3.324\pm 0.033$
${\rho }_P$	${\rho }_{\mathrm{Jup}}$	$0.726\pm 0.062$
Teq.	K	$1114\pm 34$
* $𝒩(\mu ,\sigma )$ is a normal distribution with mean $\mu$ and standard deviation $\sigma$; $𝒰(a,b)$ is a uniform distribution between
values a and b; $𝒥(a,b)$ is a Jeffrey’s distribution with a lower limit of a and b; and $\beta (a,b)$ is a Beta distribution
with parameters a and b as described by Kipping (2013a).

Table 5. Table 5: K2 Discovered warm and hot Jupiters with precise measurements (20%) on the masses and radii.

Planet	Porb (d)	Mass (MJup)	Radius (RJup)	Reference
K2-29b	$3.2588321\pm 0.0000019$	$0.73\pm 0.04$	$1.19\pm 0.02$	Santerne et al. (2016)
"	$3.2589263\pm 0.0000015$	${0.613}_{-0.026}^{+0.027}$	${1.000}_{-0.067}^{+0.071}$	Johnson et al. (2016)
K2-30b	$4.098503\pm 0.000011$	${0.579}_{-0.027}^{+0.028}$	${1.039}_{-0.051}^{+0.050}$	Johnson et al. (2016)
"	$4.098513\pm 0.000018$	$0.625\pm 0.030$	$1.197\pm 0.052$	Lillo-Box et al. (2016b)
"	${4.09849}_{-0.00002}^{+0.00002}$	${0.589}_{-0.022}^{+0.023}$	${1.069}_{-0.019}^{+0.023}$	Brahm et al. (2016a)
K2-31b	$1.257850\pm 0.000002$	$1.774\pm 0.079$	$0.71-1.41$	Grziwa et al. (2016b)
K2-34b	${2.9956675}_{-0.000071}^{+0.0000075}$	$1.649\pm 0.098$	$1.217\pm 0.053$	Lillo-Box et al. (2016b)
"	$2.995654\pm 0.000018$	$1.773\pm 0.086$	$1.44\pm 0.16$	Hirano et al. (2016)
"	${2.995629}_{-0.000006}^{+0.000006}$	${1.698}_{-0.050}^{+0.061}$	${1.377}_{-0.13}^{+0.14}$	Brahm et al. (2016a)
K2-60b	$3.00265\pm 0.00004$	$0.426\pm 0.037$	$0.683\pm 0.037$	Eigmüller et al. (2017)
K2-97b	$8.4016\pm 0.0015$	$1.10\pm 0.11$	$1.31\pm 0.11$	Grunblatt et al. (2016)
K2-99b	$18.249\pm 0.001$	$0.97\pm 0.09$	$1.29\pm 0.05$	Smith et al. (2017)
K2-107b	$3.31392\pm 0.00002$	$0.84\pm 0.08$	$1.44\pm 0.15$	Eigmüller et al. (2017)

Full text

††pubyear: 2017††pagerange: EPIC 228735255b – An eccentric $\rm 6.57$ day transiting hot Jupiter in Virgo–EPIC 228735255b – An eccentric $\rm 6.57$ day transiting hot Jupiter in Virgo

1 Introduction

Transiting exoplanets offer the best insight into worlds outside our Solar System, as we can determine the mass, radius, and obtain information regarding the planetary atmosphere. Traditional ground-based surveys such as HAT-Net (Bakos et al., 2004), WASP (Pollacco et al., 2006) and KELT (Pepper et al., 2007) are predominately sensitive to very short period transiting giant planets (P$\sim 3$d). Longer period transiting systems have proved much more difficult to detect. Some advantage has been gained using multi-site surveys, with HATSouth (Bakos et al., 2013) detecting planets in periods as long as 16 days (Brahm et al., 2016b). However, the continuous monitoring enabled by space-based telescopes has allowed for a dramatic increase in the number of longer period transiting systems. The Kepler mission (Borucki et al., 2010; Koch et al., 2010; Jenkins et al., 2010), with 4 years of near-continuous coverage, has uncovered a host of transiting planets with longer periods, however many of these transit stars that are too faint to allow for planetary mass determination via radial velocities. In 2013, after 4 years of observations, the second of Kepler’s four reaction wheels failed. From this, the K2 mission was born (Howell et al., 2014). Unlike the original mission, which observed a single region of the sky, K2 observes proposed targets within a series of fields lying along the ecliptic continuously for $\sim 80$ days. The adverse impact of the two failed reaction wheels has been minimised, but there is now a 6-hour roll effect affecting K2 light curves. This causes brightness changes as stars move from pixel to pixel on the CCD. However, there have been many different attempts to calibrate this effect and remove it from the light curves allowing for transiting exoplanet searches (Vanderburg & Johnson, 2014; Armstrong et al., 2015; Aigrain et al., 2016). Additionally, the continuous observations for 80 days still allows for longer period systems to be discovered, e.g. EPIC 201702477b (40.736d, Bayliss et al., 2017b). Additionally a number of more typical hot Jupiters have been discovered, e.g. K2-30b (4.099d), K2-34b (2.996d) (Lillo-Box et al., 2016a) and K2-31b (1.258d, Grziwa et al., 2016a).

In this paper we report the discovery of EPIC 228735255b, a $\rm 6.57$  day hot Jupiter. In §2 we outline the observations that led to the discovery. In §3 we describe the analysis of the data which determined its properties. In §4, we discuss the properties and the planet’s position with respect to other known hot Jupiters, and in §5 we summarise the discovery.

2 Observations

In this section we set out the observations made to detect and characterise the transiting exoplanet EPIC 228735255b.

2.1 K2 Photometry

The light curve for EPIC 228735255  came from Campaign 10 of the K2 mission. This campaign observed 41607 targets in Long Cadence (30 minutes) and 138 in Short Cadence (1 minute) in the ecliptic plane centered around RA 12h 27m 07.07s Dec -04$\degree\,$01’ 37.77”. Due to a pointing error (targets were off by 12 arcseconds meaning many fell outside their apertures) this campaign was split into two data releases, C10a and C10b. C10a lasted 6 days between 2016 July 6 19:45:29 UTC and 2016 July 13 01:19:55 UTC. The second release, C10b, was observed for 69 days. However there was a data gap of 14 days after 7 days of observing due to module 4 of the telescope failing which powered off the photometer.

After the public release of the data on 2016 December 20, the light curves reduced by the K2 Science team were downloaded and analysed for planetary signals (light curve data listed in Table 2). This analysis required long term variations to be removed from the light curve. This was done by fitting a sliding polynomial, which fits locally a polynomial to a small section (‘stepsize’) of the light curve using a significantly larger section (‘window’) of the surrounding light curve, and dividing it out. For the sliding polynomial, we used a 3rd order polynomial with a stepsize of 0.1 days and a window size of 5 days. To ensure the result is not jagged, the stepsize must be significantly smaller than the window size and to ensure that the transit is not accidentally fitted and removed by the process, to ensure the transit is left intact requires outlier rejection from the polynomial fit – this was done with a strict cut of positive outliers and a looser negative outlier cut. To search for planetary transits, we used a python-wrapped111https://github.com/dfm/python-bls version of the BLS routine (Kovács et al., 2002) to initially search for any significant signals and then a second time focused on the signal of interest to determine the transit parameters as accurately as possible. We then phase fold and output the light curve for visual inspection. This transit search found many candidates, which included EPIC 228735255 – a $\rm 6.57$  day planet with a 1.26 per cent transit signal (Fig. 1).

Additionally, as can be seen in Fig. 1, there is some evidence of aliasing in the cadence. This is due to the observed rotation period being a half integer multiple of the cadence of K2.

2.2 Radial Velocities

We observed EPIC 228735255 using the CORALIE spectrograph (Queloz et al., 2000) on the 1.2 m Euler Telescope at La Silla Observatory in Chile. CORALIE is a fibre-fed, high resolution (R=60,000) echelle spectrograph capable of delivering <6 m s*-1* accuracy. Observations were made between 2017 February 20 and 2017 April 8. Additionally, EPIC 228735255 was observed using the High Accuracy Radial Velocity Planet Searcher (HARPS, Mayor et al., 2003) mounted on the ESO 3.6m telescope in La Silla Observatory in Chile, on February 22 and between April 23 and 28. The spectra, which have a resolution R = 115000, were reduced using the Collection of Elemental Routines for Echelle Spectra (CERES, Brahm et al., 2017a).

The associated errors with each instrument vary significantly. In the case of CORALIE, the initial errors are higher than HARPS primarily because the star is relatively faint. As a test for the errors, we also calculated the root-mean-square of the data points from the fitted model (see § 3.2) and they were comparable to the measured errors (see Tab. 1).

The radial velocities are plotted in Fig. 2, along with the best fit model determined by the joint fit described in § 3.2. The radial velocities are also presented in Table 3.

In order to check radial velocity variation induced by a blended spectrum, we computed the bisector slope of the cross-correlation function for each observation in the manner described in (Queloz et al., 2001). In Fig. 3 we find no correlation between the bisector slope and the measured radial velocity. If the signal detected was due to a blended eclipsing binary, then we may expect to see a strong correlation between the bisectors and radial velocity measurements. The bisector values are presented with the radial velocities in Table 3.

2.3 LCO photometry

In order to refine the ephemeris, check for TTVs, and check for a colour-dependent transit depth (signifying a probable blend), we performed ground-based photometric follow-up using the Las Cumbres Observatory (LCO) 1-m telescope network (Brown et al., 2013). On 2017 March 18 we monitored the transit in the i-band using the three LCO 1-m telescopes situated at South Africa Astronomical Observatory at Sutherland, South Africa (Fig. 4). The observations were taken using the “Sinistro” camera with exposure times of 120 s and the telescope defocused (2.0mm) to avoid saturation and spread the stellar point-spread function over more pixels – reducing the impact of flat-fielding uncertainties. The images were reduced using the standard LCO reduction pipeline (BANZAI), and then aperture photometry was performed using an automated pipeline (Espinoza et al., 2017, in prep). These observations were made as part of a wider LCO Key Project222http://web.gps.caltech.edu/~shporer/LCOKP/ to characterize transiting planets using the LCO 1-m network (see Bayliss et al., 2017b). They are listed in Table 2.

2.4 High Angular Resolution Imaging

High angular resolution imaging of the target was obtained using the Robo-AO instrument (Baranec et al., 2013, 2014) mounted on the Kitt Peak 2.1m telescope, on the night of 2017 April 15 using the long-pass “lp600" filter (Baranec et al., 2014) with a seeing of 1.5" with a resulting Strehl ration of 2.7%. The raw rapid read-out data from the Robo-AO visual camera were processed using Robo-AO’s reduction pipelines described briefly below. A more detailed description can be found in Jensen-Clem et al. (2017).

First, the “bright star" pipeline generates a windowed data cube centered on an automatically selected guide star. The windowed region is bi-cubically up-sampled and cross correlated with the theoretical PSF to give the center coordinates of the guide star’s PSF in each frame. The nightly dark and dome flat exposures are then used to calibrate the full-frame, unprocessed images. The calibrated full frames are aligned using the center coordinates identified by the up-sampled, windowed frames, and co-added via the Drizzle algorithm.

Next, the “high contrast imaging pipeline" generates a 3.5” frame windowed about the star of interest in the final science frame from the bright star pipeline. A high pass filter is applied to the windowed frame to reduce the contribution of the stellar halo. To whiten correlated speckle noise at small angular separations from the target star, a synthetic PSF generated by the Karhunen-Loève Image Processing (KLIP) algorithm is subtracted from the frame. The KLIP algorithm is based on the method of Principal Component Analysis. The PSF diversity needed to create this synthetic image is provided by a reference library of Robo-AO observations — a technique called Reference star Differential Imaging.

The contrast curve was estimated using the Vortex Image Processing (VIP) package (Gomez Gonzalez et al., 2016) by measuring the residuals from resolution element-sized regions in the PSF-subtracted image.

The final Robo-AO image and contrast curve are shown in Fig. 5. The target is isolated down to $\Delta$mag = 4 at 0.5 arcsec and $\Delta$mag = 4.5 at 1 arcsec.

3 Analysis

3.1 Stellar Parameters

Initially, to determine the stellar parameters of EPIC 228735255  we built a pipeline for CORALIE spectra based on iSpec333http://www.blancocuaresma.com/s/iSpec (Blanco-Cuaresma et al., 2014). This tool provides a large number of options to treat high-resolution spectra (e.g., co-addition, continuum normalization) and it can derive atmospheric parameters and chemical abundances using many different model atmospheres, atomic line lists, radiative transfer codes and spectroscopic techniques (i.e., equivalent width and synthetic spectral fitting). For this study, we executed the following steps:

• •

Align and co-add all the observations taken with CORALIE (see Section 2.2) to increase the S/N.

• •

Reduce the spectrum to the optical wavelength range (480 - 680 nm).

• •

Cross-correlate with a solar template to shift the observed spectrum to the rest frame.

• •

Discard negative fluxes and estimate flux errors based on an estimated S/N.

• •

Convolve to a resolution of $R\sim 47\,000$ and homogeneously re-sample the spectrum.

• •

Ignore regions affected by telluric lines.

• •

Fit the pseudo-continuum and normalize the spectrum.

• •

Derive atmospheric parameters using the synthetic spectral fitting technique, SPECTRUM (Gray & Corbally, 1994) as radiative transfer code, atomic data obtained from VALD (Kupka et al., 2011), a line selection based on a $R\sim 47\,000$ solar spectrum (Blanco-Cuaresma et al., 2016, 2017) and the MARCS model atmospheres (Gustafsson et al., 2008).

As an output we obtained the effective temperature, surface gravity (log g) and metallicity, which is basically correlated with the iron abundance (i.e., [Fe/H]) of the star. From these, a series of isochrones were generated using stellar model generator SYCLIST444https://obswww.unige.ch/Recherche/evoldb/index/ (Mowlavi et al., 2012). A grid of ages at a given metallicity (Z=0.040) were generated and interpolated to determine the stellar age, mass, radius and luminosity.

The results of the iSpec analysis gave an effective temperature of 5732$\pm$32K, a log g of 4.29 dex and [Fe/H] = 0.32$\pm$0.03 dex.

Following a similar procedure, the individual HARPS spectra were median combined in order to construct a higher SNR template. The resulting spectrum was used as input of the Zonal Atmospheric Parameter estimator (ZASPE, Brahm et al., 2017b) for computing the stellar atmospheric parameters (Teff, log$g$, [Fe/H] and v${}_{\rm rot}\sin{i}$) by comparing it with a grid of synthetic spectra generated from the ATLAS9 model atmospheres (Kurucz, 1993).

For estimating an initial guess of the physical parameters of the star we used the Yonsei-Yale Isochrones (Yi et al., 2001) by searching for the $M_{*}$ and stellar Age of the model that would produce the observed Teff and $a/R_{*}$ values for the given [Fe/H]. For obtaining the errors in the physical parameters we performed Monte Carlo simulations where new values for Teff, $a/R_{*}$ and [Fe/H] were sampled from Gaussian distributions in each realisation.

The resulting physical parameters were used to compute a more precise value for the stellar log$g$ than the one obtained from spectroscopy. The new log$g$ value was then held fixed in a new ZASPE execution whose results are displayed in Table 1. The new atmospheric parameters were used to determine a new set of physical parameters from the Yonsei-Yale Isochrones (Fig. 6) obtaining a stellar mass of 1.005 $\pm$ 0.020 M*⊙, a stellar age of 4.2 $\pm$ 1.0 Gyr and a corresponding stellar radius of 0.987 $\pm$ 0.011 R⊙*, making this host star a slightly metal-rich solar analogue.

Comparing the two results (iSpec and ZASPE), a very similar effective temperature was measured. However, the iSpec routine detected a smaller log g and higher metallicity. We attribute this discrepancy to the HARPS data having a significantly better signal-to-noise ratio than the reconnaissance spectroscopy which was measured from CORALIE. For further analysis, the results from ZASPE using HARPS data were used.

We measured the rotation period of EPIC 228735255  using an auto-correlation function of the K2 light curve (with the transit omitted) as described in (Giles et al., 2017). This determined a rotation period of $16.3\pm 0.1$  days (Fig. 7). Given R∗ = $0.987^{+0.011}_{-0.011}$, this rotation should result in a v\sin{i}$$\sim 3.1 km s*-1*assuming stellar spin axis is perpendicular to the orbital plane of the planet. The spectroscopically derived $v\sin{i}$  is slightly larger than this value ($v\sin{i}$=$3.8\pm 0.2$), which may be due to non-equatorial spots and solar-like differential rotation. Such an effect has been seen in other K2 transiting systems, e.g. HATS-36b (Bayliss et al., 2017a).

3.2 Joint Fit

We fit the photometry data from § 2.1 and § 2.3 jointly with the radial velocities from § 2.2 using the exonailer555https://github.com/nespinoza/exonailer algorithm (Espinoza et al., 2016). The exonailer fitting was conducted with loose priors on the period, P, time of first transit, T0, and planet-to-stellar-radii ratio, $p$ (see Table 4 for priors used). These were determined directly from the K2 light curve. In addition, extra (Gaussian) noise terms were added to the errors of the LCO and K2 photometry (in order to empirically estimate extra photometric jitter), with a prior of $\mathcal{N}(1,1000)$ for each. Extra Gaussian noise terms were also added to the CORALIE and HARPS radial velocities (in order to model radial-velocity jitter either instrumental or from stellar origin due to, e.g., activity).

Special care was taken in the modelling of the limb-darkening effect, as it is known that this can have a direct impact on the retrieved fitted transit parameters (Espinoza & Jordán, 2015). In order to select the best limb-darkening law, we followed Espinoza & Jordán (2016) and ran the ld-exosim algorithm666https://github.com/nespinoza/ld-exosim, which gives the mean-square error on each of the retrieved transit parameters for a given limb-darkening law (given the noise, sampling and geometry of the transit). The quadratic law was chosen as it was the law that gave the minimum mean-square error on the planet-to-star radius ratio. For this case, this was the most important transit parameter because it defines the exoplanet’s density. Additionally, the limb-darkening coefficients were individually fitted for the K2 and LCO light curves, as they have different response functions and span different wavelength ranges. An initial fit assuming different planet-to-star radius ratios for each dataset was also made, but both independently gave consistent parameters with no wavelength dependence. The final fit was made by using a common planet-to-star radius ratio for both datasets. Priors for the limb-darkening coefficients were set to be $\mathcal{N}(0,1)$, an uninformative transformation of the quadratic limb-darkening parameters (see Kipping, 2013b).

We tried fits assuming circular and non-circular orbits and the results favour the non-circular orbit, which gave an eccentricity of $0.120^{+0.056}_{-0.046}$  and an argument of periapsis of $98.88^{+3.85}_{-4.16}$  degrees.

The final fits for the K2 and LCO lightcurves are shown in red in Figures 1 and 4, and for the radial-velocities in Figure 2. The priors and posterior values of the fitted parameters with exonailer are listed in Table 4. As can be seen, the photometric jitter is significant only for the K2 lightcurve; the LCO photometric jitter is consistent with zero. This is due to the fact that we decided to estimate the errors directly from the K2 photometry, while the extra jitter was added in quadrature to the LCO errorbars given by the photometric pipeline. For the radial-velocity jitter, it can be seen that the extra term for both instruments is also consistent with zero.

3.3 Planet Parameters

exonailer was able to determine various system parameters from the light curve transit shape: $a/R_{*}$, the semi-major axis-to-stellar radius ratio; $R_{p}/R_{*}$, the ratio of planetary to stellar radius; $t_{0}$, the time of the first observed transit; P, the orbital period of the planet; and i, the inclination of the planet’s orbit. Additionally, from the radial velocity curves: e, the eccentricity; $\omega$, the periapsis argument; and K, the radial velocity semi-amplitude of the star. Through a combination of these parameters and the already determined stellar mass and radius from § 3.1, further properties of the planet can be determined using the equations as described in Seager & Mallén-Ornelas (2003). We measured the planetary mass to be $1.019\pm 0.070$MJup  with a radius of $1.095\pm 0.018$RJup. This indicates a bulk density which is slightly less than that of Jupiter, 0.726\pm 0.062$$\rho_{\rm Jup}. The planet has an incident flux of 2.565\pm 0.105$$\times 10^{8} erg s-1 cm-2. The predicted equilibrium temperature is $1114\pm 34$K, with the assumption of a blackbody and an efficient transfer of energy from the day- to night-side. These are all listed in Tab. 4.

4 Discussion

In this section we compare the properties of EPIC 228735255b to the population of known hot Jupiters, and for this purpose we use the NASA Exoplanet Archive 777exoplanetarchive.ipac.caltech.edu (Akeson et al., 2013) as accessed on 2017 June 6.

Of the known warm and hot Jupiters discovered from K2, EPIC 228735255b  currently has the third longest orbital period (see Tab. 5). This further demonstrates the ability of K2 to find longer period planets as was done by Kepler.

To compare the ability to find longer period warm and hot Jupiters from the ground, a subset of all confirmed planets with masses greater than 0.2MJup  (and with other significant parameters – such as eccentricity, planet density, and planet radius – also measured) were split by their discovery ‘location’ (i.e. Kepler, K2, other space missions and missions from the ground). Currently, K2 has only found 8 planets within this subset.

The number of planets discovered by Kepler and K2 over the period range strongly reveals that, as expected, K2 is less sensitive to long-period planets than Kepler, equally sensitive to short-period planets (Fig.  8). Kepler observed 156,000 stars and, to date, K2 has observed a total of 171,610 (all stars observed by K2 in long cadence from Campaigns 1–10). However, there will be a natural cut off at $\sim$30-40d orbital period planets for K2 as campaigns typically do not last longer than 80 days, whereas Kepler had almost 4 years of continuous observation of its stars. Additionally, due to the necessary follow-up time required per planet (radial velocity, imaging etc.) the community has had much longer to confirm Kepler candidates compared with K2 candidates – there are still regular announcements of discoveries from older K2 campaigns as well as discoveries from the current campaign. Given more time, the distribution for K2 may well fill out similarly to Kepler. By the conclusion of the K2 mission (assuming 19 full campaigns), we may expect K2 will produce more than double the number of transiting giant planets with periods <10 d compared to Kepler.

In Fig. 9 we plot the measured eccentricities for transiting hot Jupiters with periods between 1–10 d. Below $\sim 5.5$ d, approximately 70% of hot Jupiters have measured eccentricity consistent with 0. However for systems with period greater than 5.5,̣ this fraction drops below 50%. It is therefore not surprising that we find a non-zero eccentricity for EPIC 228735255b (e=$0.120^{+0.056}_{-0.046}$). If we assume a Q-factor of $10^{6}$ (Wu, 2005) we calculate (Goldreich & Soter, 1966) a tidal circularisation timescale of \tau_{e}=$$2.577 Gyr. Given our best estimate for the age of the system ($4.22\pm 0.95$Gyr), this means that the timescale is of the same order of the age of the star.

A common avenue of investigation associated with warm and hot Jupiters is determining whether they are inflated or not. Based on the mass and radius of EPIC 228735255b, it is slightly inflated compared with Jupiter, but not inflated with respect to other exoplanets with similar incident flux (see Fig. 10). The planet receives an incident flux of 2.565\pm 0.105$$\times 10^{8} erg s-1 cm-2, which is very close to the empirical limit for inflation (2$\times 10^{8}$ erg s-1 cm-2 Demory & Seager, 2011). Discovering exoplanet in this incident flux regime is important for studying the onset of the mechanism by which hot Jupiters are inflated.

5 Conclusions

We found a hot-Jupiter planet in data from K2 Campaign 10 and followed it up with radial velocity measurements and high angular resolution imaging. EPIC 228735255b  orbits a V=$12.624\pm 0.030$, $4.22\pm 0.95$ Gyr star with a [Fe/H] of $0.12\pm 0.045$. The planet has an non-circular orbit with an eccentricity of $0.120^{+0.056}_{-0.046}$and period of $\rm 6.57$  days and a mass and radius of $1.019\pm 0.070$MJup  and $1.095\pm 0.018$RJup  respectively. It is the third longest period giant exoplanet discovered from K2 and has a period longer period than 94% of giant planets discovered from ground-based transit surveys.

Acknowledgements

We thank the Swiss National Science Foundation (SNSF) and the Geneva University for their continuous support to our planet search programs. This work has been in particular carried out in the frame of the National Centre for Competence in Research ‘PlanetS’ supported by the Swiss National Science Foundation (SNSF).

N.E. acknowledges support from Financiamiento Basal PFB06. R.B., N.E., and A.J. acknowledge support from the Ministry for the Economy, Development and Tourism Programa Iniciativa Científica Milenio through grant IC 120009, awarded to the Millenium Institute of Astrophysics. A.J. acknowledges support by Fondecyt grant 1171208 and partial support by CATA-Basal (PB06, CONICYT). J.S.J. acknowledges support by Fondecyt grant 1161218 and partial support by CATA-Basal (PB06, CONICYT).

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

This research was made possible through the use of the AAVSO Photometric All-Sky Survey (APASS), funded by the Robert Martin Ayers Sciences Fund.

This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

Some/all of the data presented in this paper 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 paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate.

This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

This work makes use of observations from the LCO network.

The Robo-AO team thanks NSF and NOAO for making the Kitt Peak 2.1-m telescope available. We thank the observatory staff at Kitt Peak for their efforts to assist Robo-AO KP operations. Robo-AO KP is a partnership between the California Institute of Technology, the University of Hawai‘i, the University of North Carolina at Chapel Hill, the Inter-University Centre for Astronomy and Astrophysics (IUCAA) at Pune, India, and the National Central University, Taiwan. The Murty family feels very happy to have added a small value to this important project. Robo-AO KP is also supported by grants from the John Templeton Foundation and the Mt. Cuba Astronomical Foundation. The Robo-AO instrument was developed with support from the National Science Foundation under grants AST-0906060, AST-0960343, and AST-1207891, IUCAA, the Mt. Cuba Astronomical Foundation, and by a gift from Samuel Oschin. These data are based on observations at Kitt Peak National Observatory, National Optical Astronomy Observatory (NOAO Prop. ID: 15B-3001), which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation. C.B. acknowledges support from the Alfred P. Sloan Foundation. A.C.C. acknowledges support from STFC consolidated grant number ST/M001296/1. DJA acknowledges support from STFC consolidated grant reference ST/P000495/1.

This research has made use of the SIMBAD database and of the VizieR catalogue access tool operated at CDS, France, and used the DACE platform developed in the frame of PlanetS (https://dace.unige.ch).