An ultra-short-period super-Earth with an extremely high density and an outer companion

Abstract

We present the discovery and characterization of a new multi-planetary system around the Sun-like star K2-360 (EPIC 201595106). K2-360 was first identified in K2 photometry as the host of an ultra-short-period (USP) planet candidate with a period of 0.88 d. We obtained follow-up transit photometry, confirming the star as the host of the signal. High precision radial velocity measurements from HARPS and HARPS-N confirm the transiting USP planet and reveal the existence of an outer (non-transiting) planet with an orbital period of $\sim$ 10 d. We measure a mass of $7.67\pm 0.75$ $M_{\oplus }$ and a radius of $1.57\pm 0.08$ $R_{\oplus }$ for the transiting planet, yielding a high mean density of $11\pm 2$ g ${\text{cm}}^{-3}$ , making it the densest well-characterized USP super-Earth discovered to date. We measure a minimum mass of $15.2\pm 1.8$ $M_{\oplus }$ for the outer planet, and explore a migration formation pathway via the von Zeipel-Kozai-Lidov (ZKL) mechanism and tidal dissipation.

Fig. 1

K2 light curve (gray points) with GP variability model (top); time series residuals with marginal histogram and the total noise estimate from the model (bottom). Note the transits are not easily discernible by eye, but can be seen as a heavy tail in the marginal histogram.

Fig. 2

Flattened and phase-folded K2 light curve with best-fitting transit model overplotted in blue (top), and residuals (bottom).

Fig. 3

Upper panels—RV and $S_{\text{HK}}$ time series. Each plot shows (from top to bottom): RV data together with full (stellar plus planetary signal inferred models); RV data with stellar signal model subtracted; RV residuals; $S_{\text{HK}}$ data together with inferred stellar model, and $S_{\text{HK}}$ residuals. All time series are shown after been corrected by inferred offsets. For the RV time series we also show the inferred stellar (red line) and planetary (green line) recovered signals with an offset to make them clearly visible. HARPS (blue) and HARPS-N (orange) RV and $S_{\text{HK}}$ are shown in the corresponding panels. Measurements are shown with filled symbols with error bars with a semi-transparent error bar extension accounting for the inferred jitter. The solid (black) lines show the inferred full model coming from our multi-GP, light grey shaded areas showing the one and two sigma credible intervals of the corresponding GP model. Lower panels—Phase-folded RV data for planets b (left) and c (right) with best-fit Keplerian model, after subtracting the RV signal of the other planet and stellar activity.

Fig. 4

Left panel: Distribution of the final period of the inner planet, at the end of the secular simulations. The red line indicates the period of K2-360  b. Right panel: Distribution of mutual inclinations between the two planets, only for the realizations that end up with a USP (defined as any planet at less than one day orbit).

Fig. 5

Visualization of the radial density variation from our interior composition model for K2-360 b.

Fig. 6

Density (left) and temperature (right) profiles of K2-360 b based on the observed chemical abundances of the host star.

Fig. 7

Mass-radius diagram showing the position of K2-360  b (red), as well as all known planets with masses and radii measured to better than 15% precision (black), with USP planets shown in orange. The known planet parameters are from the NASA Exoplanet Archive confirmed planets table, as queried on February 15, 2024, and a KDE of the population is shown in gray. The light blue shaded rectangle indicates the 1$\sigma$ range for the mass and radius of the non-transiting planet, K2-360  c, where the mass corresponds to the measured minimum mass (i.e. assuming $i{=\mathbf{90}}^{\circ }$) and the radius is estimated from a mass-radius relation.

Fig. 8

Period-radius (left) and period-mass (right) diagrams showing the positions of K2-360  b (red) and K2-360  c (blue), each showing the distribution of known planets, with a KDE of the distribution shown in gray. Note the radius of K2-360  c shown in the left panel was estimated from a mass-radius relation assuming $i={90}^{\circ }$. As in Fig. 7, the known planet parameters were obtained from the NASA Exoplanet Archive, and only those planets with both radii and masses measured to better than 15% are considered. The dotted line shows the location of the radius valley, and the planets below the radius valley are highlighted in orange in both panels. The KDEs were computed using only the data within the limits shown.

Fig. 9

K2-360 11$\times$11 pixel K2 “postage stamp” (left) and archival Palomar Observatory Sky Survey II (POSS II) image (right) centered on K2-360, with the EVEREST photometric aperture overplotted in blue. The nearby star EPIC 201595004 can be seen 13.6” away from K2-360 in the POSS II image, just outside the aperture.

Fig. 10

WIYN/NESSI reconstructed images and contrast curves. The inset images are 4.6”$\times$4.6”.

Fig. 11

Lomb-Scargle periodograms of the WASP-South, Camera-225 photometry of K2-360, showing a periodicity of $28.0\pm 1.4$ d. The top panel combines the data from the lower two panels. The horizontal line is the estimated 1% false-alarm probability. At right are folds of the data on the best period.

Fig. 12

Joint posterior distribution of stellar parameters sampled with MultiNest via the isochrones interface to the MIST stellar evolution models. Note the gray shading of the marginal distributions show the 68% credible regions, and the values reported are centered on the mode.

Fig. 13

Left: BLS periodogram showing the orbital period of the transiting planet (shaded blue) and its harmonics (dashed blue lines). Right: K2 photometry folded on the peak BLS period (black), and binned by a factor of 50 (blue).

Fig. 14

GLS periodograms of the BIS (left) and S-Index (right) activity indicator time series. The vertical gray and gray-dashed lines denote the rotation period and its first harmonic, respectively.

Fig. 15

${\ell }_1$ periodogram of the RVs.

Fig. 16

S-Index vs RV, with the color of the error bars corresponding to the instrument, and the color of the data point corresponding to the time of observation. The data from 2017 exhibit distinctly lower S-Index values than the subsequent observing seasons, possibly due to magnetic activity cycles.

Fig. 17

Stacked Bayesian Generalized Lomb Scargle periodograms near the periods of the USP planet (left), the non-transiting planet (middle), and the stellar activity signal (right).

Fig. 18

The FCO periodogram of the RV data. The reduced ${\chi }^2$ is minimized for the transit period (dashed vertical line).

Fig. 19

The phase-folded RV curve of K2-360 b from the FCO method; RVs for individual time chunks are shown with the same symbol and color (left). The orbital fit to the 10 d RV variations (right).

Fig. 20

Simulations of the output K-amplitude derived using the FCO method as a function of the input amplitude. The line indicates a slope of unity.

Fig. 21

Critical angular momentum deficit as a function of mutual inclination, for different values of the period of K2-360  b. The red line is the threshold above which the system is unstable. The shaded region indicates the uncertainty in the AMD due to the uncertainty in the eccentricity of K2-360  c.

Fig. 22

The density, gravity, pressure and temperature (Y-axis) profiles against planetary radius (X-axis) for different interior conditions of K2-360  b. The top two panels show the gravity and pressure profiles at the observed stellar abundances. The bottom four panels show the density, gravity, pressure and temperature profiles for K2-360  b if the Fe and Mg abundances are higher than what was measured.