TOI-257b (HD 19916b): a warm sub-saturn orbiting an evolved F-type star

ABSTRACT

1 INTRODUCTION

When Mayor & Queloz (1995) announced the discovery of the first hot Jupiter, 51 Pegasi b, astronomers were baffled by the existence of a Jovian planet orbiting its host star with such a short orbital period (about 4.2  days). That discovery revolutionized our understanding of the planet formation process, revealing the situation to be more complex than had been expected based on studies of the Solar System (e.g. Lissauer 1993). Radial velocity and transit surveys over the past two decades have uncovered numerous warm and hot giant exoplanets with orbital periods shorter than 100 days (see, e.g. Butler et al. 1997; Bayliss et al. 2013; Brahm et al. 2016; Van Eylen et al. 2018; Dawson et al. 2019; Kipping et al. 2019), and occurrence studies based on those discoveries suggest that such planets can be found orbiting |$\sim 1{{\ \rm per\ cent}}$| of all Sun-like stars (e.g. Howard et al. 2010, 2012; Santerne et al. 2012; Wright et al. 2012; Santerne et al. 2016; Zhou et al. 2019) (in comparison to an occurrence rate of at least |$7{{\ \rm per\ cent}}$| for more distant planets; see, e.g. Foreman-Mackey et al. 2016; Wittenmyer et al. 2020).

In addition to the Solar System lacking a hot Jupiter, it also lacks other broad classes of planets such as super-Earths and mini-Neptunes (∼1.5−3 R_⊕) as well as planets larger than Neptune and smaller than Saturn, known as sub-Saturns (which we have defined as planets with a radius between ∼5 and 8 R_⊕). Sub-Saturns are a key class of planets to study for understanding the formation, migration, and compositions of giant planets in general. Their large size requires a significant H/He envelope that comprises a majority of their planetary volume, yet their masses are sufficiently small that their cores are not degenerate (unlike for planets near the mass of Jupiter). This means that modelling the interiors of sub-Saturns can be simplified as a planet consisting of a high-density core surrounded by extended H/He envelope and where measurements of mass and radius enable a single family of solutions for the planet’s core and envelope mass fraction (e.g. Weiss & Marcy 2014; Petigura et al. 2016; Pepper et al. 2017; Petigura et al. 2017).

It is commonly thought that close-in giant planets, such as hot/warm Jupiters and sub-Saturns, do not form in situ, but instead originate beyond the protostellar ice line (typically located at several astronomical units from the host star) where there is sufficient solid material available to build up ∼5−20 M_⊕ cores (Pollack et al. 1996; Weidenschilling 2005; Rafikov 2006). In the case of Jovian planets, once their cores reach this critical mass regime, they begin to rapidly accrete gas from the protoplanetary disk to form their gaseous envelopes. This process continues until the disk is dispersed (Rafikov 2006; Tanigawa & Ikoma 2007), resulting in Jupiter-sized planets with masses of ∼100−10 000 M_⊕. For sub-Saturns, however, the runaway accretion of gas appears to either not have occurred at all or did occur but in a gas-depleted disk (Lee, Chiang & Ferguson 2018). As a result, sub-Saturns have masses that range from ∼10 to 100 M_⊕. The mass of a sub-Saturn is strongly correlated with the metallicity of its host star, but is uncorrelated with the resulting radial size (Petigura et al. 2017).

The sample of measurements for longer period (P ≥ 10 d) ‘warm’ giants and sub-Saturns thus far is small. The detection of more of these systems is then important to better constrain the formation and migration mechanisms of close-in planets.

One such source of warm giant planetary systems is NASA’s Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2015), launched on 2018 April 18. As of 2019 November 6, the TESS mission has delivered a total of 1361 planetary candidates – objects that require further observations from ground-based facilities to confirm the existence of the candidate exoplanets.¹ To date, such follow-up observations have resulted in a total of 34 confirmed planetary discoveries (e.g. Nielsen et al. 2019; Quinn et al. 2019; Vanderburg et al. 2019; Wang et al. 2019) – and it is likely that many more planets will be confirmed in the months to come.

During its initial 2-year primary mission, TESS is expected to discover several dozen warm Jupiters, Saturns, and sub-Saturns orbiting bright (V < 10 mag) stars (Sullivan et al. 2015; Barclay, Pepper & Quintana 2018; Huang et al. 2018). Those planets will be suitable targets for follow-up observations to measure their masses, through radial velocity measurements, to probe their atmospheric compositions, through transmission and emission spectroscopy, and to determine their spin-orbit angles through measurements of the Rossiter-McLaughlin effect.

In this work, we report the discovery of one such planet, TOI-257b (HD 19916b), based on photometric data obtained by TESS, and follow-up observations using the Minerva-Australis facility at the University of Southern Queensland’s Mt. Kent Observatory (Wittenmyer et al. 2018; Addison et al. 2019), the FEROS instrument (R = 48 000, Kaufer et al. 1999) on the MPG 2.2 m telescope at La Silla Observatory, and the HARPS spectrograph (R = 120 000, Mayor et al. 2003) on the ESO 3.6 m telescope at La Silla Observatory. The details of the spectrographs and spectroscopic observations are provided in Section 2.3.

In Section 2, we describe the TESS photometric data, and the reduction of the Minerva-Australis spectroscopic data and the radial velocity pipeline, as well as radial velocities collected with other instruments. Section 3 presents the analysis of the data, including the characterization of the host star, the derived properties of the planet, and the limits on any additional planets in the system. In Section 4, we compare TOI-257b with the demographics of the known exoplanets, and discuss the significance of the system. We provide concluding remarks and suggestions for future work in Section 5.

2 OBSERVATIONS AND DATA REDUCTION

TOI-257 (HD 19916) is a bright (V = 7.612 mag) late F-type star, located at a distance of 77.1 ± 0.2 pc (parallax of 12.9746 ± 0.0327 mas from Gaia DR2, Gaia Collaboration 2018a). The star is slightly evolved with a radius of 1.888 ± 0.033|$\, R_{\odot}$|⁠, mass of 1.390 ± 0.046|$\, M_{\odot}$|⁠, and surface gravity of log g = 4.030 ± 0.011 dex, derived from the asteroseismic analysis of the TESS photometry in Section 3.2. The star has an effective temperature of 6075 ± 90 K and metallicity of [M/H] = 0.19 ± 0.10 derived from the analysis of Minerva-Australis spectra in Section 3.1 as well as a rotational velocity of vsin i = 11.3 ± 0.5  km s⁻¹ in Section 3.3. TOI-257 has rotational period of 8.07 ± 0.27 days based on analysis of the TESS photometry in Section 3.3.

2.1 TESS photometry

The star TOI-257 (HD 19916, TIC 200723869 Stassun et al. 2019) was observed in Sectors 3 and 4 by Camera 3 of the TESS spacecraft in 2-min cadence mode nearly continuously between 2018 September 22 and 2018 November 15. The photometric data were processed by the Science Processing Operations Center (SPOC) pipeline as described in Jenkins et al. (2016). Overall, three transits were detected with depth of ∼1500 parts per million (ppm) and duration of ∼6  h. Two transits are detected in Sector 3 (on BJD 2458386 and BJD 2458404), and one in Sector 4 (on BJD 2458422). The transit at the beginning of Sector 3 was observed during an experiment to improve the spacecraft pointing,² and the transit in Sector 4 was observed during the thermal ramp.

The TESS light curves were accessed from the NASA’s Mikulski Archive for Space Telescopes. The light curves had been processed by the TESS team using two different techniques: pre-search data conditioning (PDC, the usual way of light curve extraction and removal of systematics, see, Jenkins et al. 2016) and simple aperture photometry (SAP, see, Twicken et al. 2010). These raw SAP and PDC light curves are shown in Fig. 1, along with their detrended versions.

Figure 1.

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TESS light curves of TOI-257 from Sector 3 (left panel) and Sector 4 (right panel). The pre-search data conditioning (PDC, upper panels) and simple aperture photometry (SAP, lower panels) versions of the light curves before (shown in red) and after detrending (shown in black and shifted down arbitrarily to avoid overlap with the red points). The detrending function is blue and transits are grey. Top left: A single transit event was recovered by PDC in Sector 3. Top right: A single transit event was recovered by PDC in Sector 4. Bottom left: Two transit events were recovered by SAP from Sector 3. Bottom right: A single transit event was recovered by SAP in Sector 4.

To detrend the PDC light curves, we removed all quality-flagged data (except for stray light flag 2048), clipped 5σ outliers, removed stellar and instrumental variability, normalized with the mean of the out-of-transit flux, and merged together Sectors 3 and 4. To remove the photometric variability, we used a Savitzky-Golay (SG) filter with a kernel width of 501 data points and a polynomial of order 2 over 3 iterations. During detrending, the planetary transits were masked and then detrended by dividing out the interpolated SG-filtered flux values from the out-of-transit data points. The SG detrending removed any longer-period stellar variability and systematics, and retained any features that occurred on timescales comparable or shorter than the duration of planetary transits (Kinemuchi et al. 2012; Jenkins et al. 2016).

Two transits were recovered using the PDC technique, one in Sector 3 and one in Sector 4. The transit at the beginning of Sector 3 was missed by the PDC procedure since it falls on the part of the light curve that was quality-flagged for manual exclusion during a spacecraft pointing improvement experiment. To recover the first transit in Sector 3, we performed the exact same detrending procedure on the SAP version of the light curve as on the PDC light curve, the only difference being that the manual exclusion (flag 128) data points were not removed. The resulting detrended SAP light curve was used for recovering the first transit observed by TESS in Sector 3 but this version of the light curve was not used in the global fit analysis as systematics were not removable as seen in Fig. 1. Indeed the noise level is higher (by ∼200 ppm) in the detrended SAP light curve just prior to this transit event.

To include the first transit from Sector 3 in the global fit analysis, we created a custom light curve following the procedures of Vanderburg et al. (2019) to obtain a cleaner light curve relatively free from systematics and stellar variability. We started by using a larger 4.5 pixel radius aperture to extract the Sector 3 photometry, which reduced the amplitude of the systematics observed in the early part of the light curve compared to the TESS pipeline’s SAP light curve. We then removed systematics from a small segment of the light curve surrounding the first transit (BJD 2458383.7 < t < 2458388.0) by decorrelating against the median background flux value from outside the aperture for each 2-min image and the standard deviation of the Q1, Q2, and Q3 quaternions within each 2-min exposure. We excluded points during the planet transit in our decorrelation to prevent the systematics correction from biasing or distorting the shape of the transit. Next, we simultaneously fit the low-frequency variability (which we modeled as a basis spline) with a transit model in a similar manner to Vanderburg et al. (2016a), except that we did not also simultaneously fit for the systematics and we introduced a discontinuity at BJD 2458385.95 where we switch from the custom light curve to the PDC light curve. The combination of our custom light curve and the PDC light curve are what we use in the final global fitting analysis with EXOFASTv2 (Eastman, Gaudi & Agol 2013; Eastman 2017; Eastman et al. 2019). Fig. 2 is the resulting 30-min binned and phase folded custom light curve along with the PDC light curve and the individual transits colour coded.

Figure 2.

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Phase folded TESS light curve of TOI-257 binned at a cadence of 30 min with the individual transits colour coded showing that they are of similar depth. The first transit comes from the custom light curve where we removed systematics that are the result of a spacecraft pointing anomaly. The second and third transit are from the pre-search data conditioning light curve. The red curve is the best-fitting transit model.

2.2 Direct imaging follow-up

If a target star has a close companion, the additional flux from the second source can cause photometric contamination, resulting in an underestimated planetary radius, or be the source of an astrophysical false positive. To rule out the presence of close companions, speckle imaging observations were taken of TOI-257 with the SOAR and Zorro instruments.

2.2.1 SOAR speckle imaging

TOI-257 was observed with SOAR speckle imaging (Tokovinin 2018) on 2019 February 18 UT, observing in a similar visible bandpass as TESS. The 5σ detection sensitivity and the speckle auto-correlation function from the SOAR observation are plotted in Fig. 3. Further details of the observations are available in Ziegler et al. (2020). No nearby stars were detected within 3^″ of TOI-257.

Figure 3.

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The 5σ detection sensitivity and inset speckle auto-correlation function from SOAR speckle observing of TOI-257 on 2019 February 18 UT in I-band, which is similar to the TESS bandpass. The orientation of the inset image has North pointed up and East to the left. No stars were detected within 3^″ of TOI-257.

2.2.2 Gemini-South high-resolution speckle imaging using Zorro

Direct imaging observations of TOI-257 was also carried out on 2019 September 12 UT using the Zorro speckle instrument on Gemini-South.³ Zorro simultaneously provides speckle imaging in two bands, 562 and 832 nm, with output data products including a reconstructed image, and robust limits on companion detections (Howell et al. 2011). Fig. 4 shows our 562 nm result and reconstructed speckle image and we find that TOI-257 is indeed a single star with no companion brighter than about 6 magnitudes detected within 1.75 ^″. This limit corresponds to approximately an M3V star at the inner working angle of ∼0.25 ^″and M5V at the outer working angle of ∼1.75 ^″.

Figure 4.

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Zorro speckle observation of TOI-257 taken at 562 nm. Our simultaneous 832 nm observation provides a similar result. The red line fit and blue points represent the 5σ fit to the sky level (black points) revealing that no companion star is detected from the diffraction limit (17 mas) out to 1.75 ^″within a Δ mag of 6 to 8. The inset reconstructed speckle image has north up and East to the left and is 2.5 ^″across.

2.3 Spectroscopy

We obtained high-resolution spectroscopic observations of TOI-257 with Minerva-Australis, FEROS, and HARPS to confirm and measure the mass of the TESS transiting planet candidate. Here we describe the observations from each spectrograph and list the derived radial velocities in Table 2.

2.3.1 High-resolution spectroscopy with Minerva-Australis

The Minerva-Australis facility is an array of five independently operated 0.7 m CDK700 telescopes located at the Mount Kent Observatory in Queensland, Australia (see, Addison et al. 2019, for a detailed description of the facility). Designed as a robotic observatory, instruments are remotely accessible and can be operated both in manual or automatic configurations. Four of the telescopes in the array (T2, T3, T4, T6) simultaneously feed stellar light to a single KiwiSpec R4-100 high-resolution spectrograph via fiber optic cables. Only three out of the four telescopes, T3, T4, and T6, were used for spectroscopic observations of TOI-257.

A total of 53 spectra (observations taken simultaneously from multiple telescopes in the array are counted as one observation) of TOI-257 were obtained at 28 epochs between 2019 July 12 and October 15. Each of the telescopes in the Minerva-Australis array simultaneously feed via 50 μm circular fiber cables a single KiwiSpec R4-100 high-resolution (R = 80 000) spectrograph (Barnes et al. 2012) with wavelength coverage from 480 to 630 nm.

Radial velocities are derived for each telescope using the least-squares technique of Anglada-Escudé & Butler (2012) and corrected for spectrograph drifts with simultaneous Thorium-Argon (ThAr) arc lamp observations. We observed TOI-257 with up to three telescopes simultaneously with one or two 20 to 30-minute exposures per epoch, resulting in a signal-to-noise ratio between 30 and 80 per resolution element at ∼550 nm.

The radial velocities from each telescope are given in Table 2 labeled by their fiber number. Each telescope (fiber) has its own velocity zero-point which is modeled as a free parameter, and the mean internal uncertainty estimate of the Minerva-Australis observations is 4.6 m s⁻¹. The radial velocities collected by Minerva-Australis show a ∼10  m s⁻¹ sinusoidal variation (RMS uncertainty of 13.9 m s⁻¹ based on the residuals from the EXOFASTv2 one-planet fit) that is in phase with the photometric ephemeris with an amplitude compatible with a sub-Saturn-sized planet on a circular orbit as shown in Figs 9 and 10. Additionally, we measured the bisector velocity span (BVS) values using the cross-correlation functions as a check to ensure that the radial velocity variation observed is not from stellar activity or a background eclipsing binary system. As shown in Fig. 11, no correlations are apparent in the BVS values.

2.3.2 High-resolution spectroscopy with the fiber-fed extended range optical spectrograph

TOI-257 was observed with the fiber-fed extended range optical spectrograph (FEROS) instrument (R = 48 000, Kaufer et al. 1999) on the MPG 2.2 m telescope at La Silla Observatory between 2018 December 15 and 2019 January 22. We collected a total of eight spectra and the observations were performed in simultaneous calibration mode, utilizing the ThAr arc lamp on the secondary fiber to track and remove instrumental variations due to changes in the temperature and pressure during the science exposures. The exposure times were set to 300 s, resulting in signal-to-noise ratio between 270 and 370 per resolution element at ∼510 nm. We produced radial velocities by cross-correlation with a G2-type binary mask template using the CERES pipeline (Brahm, Jordán & Espinoza 2017a), which also corrects the radial velocities for instrumental systematics and the Earth’s motion.

2.3.3 High-resolution spectroscopy with the high accuracy radial velocity planet searcher

We monitored TOI-257 with the high accuracy radial velocity planet searcher (HARPS) spectrograph (R = 120 000, Mayor et al. 2003) on the ESO 3.6 m telescope at La Silla Observatory between December 2018 and November 2019. A total of 33 observations were obtained and the data was processed using the CERES pipeline (Brahm, Jordán & Espinoza 2017a). The exposure times were set to 300 s and taken using the high-precision radial velocity mode with simultaneous ThAr, providing a signal-to-noise ratio between 90 and 180 per resolution element at ∼510 nm. We produced radial velocities by cross-correlation with a G2-type binary mask template and derived the stellar properties as T_eff = 6178 ± 80 K, log g = 4.06 ± 0.11 dex, [Fe/H] = 0.32 ± 0.05 dex, and vsin i = 10.2 ± 0.5 km s⁻¹ for the host star with the HARPS spectra using ZASPE (Brahm et al. 2017b). The metallicity results from the HARPS spectra indicate that the star is definitively metal rich.

3 ANALYSIS

3.1 Host star properties from spectroscopy

We used the Minerva-Australis spectra to determine TOI-257’s atmospheric stellar parameters. Through the python package iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019), we stacked the stellar spectra to derive the effective temperature, surface gravity, and overall metallicity ([M/H]) of the star. We configured the iSpec synthetic grid to incorporate an MARCS atmospheric model (Gustafsson et al. 2008) and utilized the spectrum (Gray & Corbally 1994) radiative transfer code. [M/H] was derived using version 5.0 of Gaia-ESO Survey’s (GES) line-list (Heiter et al. 2015) normalized by solar values obtained by Asplund et al. (2009). Our synthetic spectra fit was constructed by setting initial values for T_eff, log g and [M/H] of 6050 K, 4.44 dex, and 0.00 dex, respectively, based on the parameters from a broadband spectral energy distribution (SED) analysis with EXOFASTv2. Fig. 5 depicts our observed spectra and synthetic model produced by iSpec. Our derived T_eff, log g and [M/H] values were then fed into the Bayesian isochrone modeler isochrones (Morton 2015; Montet et al. 2015) that uses the Dartmouth Stellar Evolution Database (Dotter et al. 2008).

Figure 5.

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The best-fitting synthetic model spectrum from iSpec (the red dashed line) of TOI-257 to that of the combined stellar spectrum obtained from the Minerva-Australis spectroscopic observations (the blue solid line) for the wavelength region between 624.0 and 625.5 nm. The residuals of the fit are shown as the green solid line.

isochrones uses nested sampling scheme called multinest (Feroz, Hobson & Bridges 2009) to determine the stellar mass, radius, and age, which was then used to derive the stellar density and luminosity of TOI-257. For this particular analysis, we used the stellar parameter results from iSpec as well as the parallax value from Gaia DR2 with G, H, J, K, V, and W1 magnitudes⁴ as priors in the global fit. The spectroscopic stellar iSpec and isochrones values can be found in Table 1 and are in good agreement with the SED analysis performed using EXOFASTv2 and the asteroseismology. We then incorporated the T_eff and [M/H] values derived from the iSpec analysis of the Minerva-Australis spectra as priors in the final EXOFASTv2 global fit of the data in Section 3.4 and stellar luminosity of L = 4.57 ± 0.16 |$\, L_{\odot}$| derived from SED fitting as a prior in the asteroseismology analysis in Section 3.2. We also note that stellar atmospheric parameters derived from the HARPS spectra are in general agreement with the ones derived with the Minerva-Australis spectra, though the HARPS spectra suggest that the star is definitely metal rich ([Fe/H] = 0.32 ± 0.05 dex) while the Minerva-Australis spectra is compatible with solar metallicity to within 2σ ([M/H] = 0.19 ± 0.10 dex). Given that the SED analysis is in better agreement with the derived stellar parameter from the Minerva-Australis spectra and the strong degeneracies in the model atmospheres with parameters such as T_eff, metallicity, and log g (e.g. see, Hinkel et al. 2016), we have chosen to use the stellar atmospheric parameters from Minerva-Australis in the global analysis.

3.2 Asteroseismology

3.2.1 Global asteroseismic parameters

To perform asteroseismic analysis on TOI-257, we produced a custom light curve using the TESS Asteroseismic Science Operations Center (TASOC, Lund et al. 2017) photometry pipeline⁵ (Handberg et al., in prep.), which is based on software originally developed to generate light curves for data collected by the K2 Mission (Lund et al. 2015). The TASOC pipeline implements a series of corrections to optimize light curves for an asteroseismic analysis (Handberg & Lund 2014), including the removal of instrumental artefacts and of the transit events using a combination of filters utilizing the estimated planetary period. The photometric performance of the TASOC light curve was comparable to the light curve produced by the SPOC pipeline.

Solar-like oscillations are broadly described by a frequency of maximum oscillation power (ν_max) and a large frequency separation (Δν), which approximately scale with log g and the mean stellar density, respectively (see, García & Ballot 2019). The power spectrum of the Sector 3 light curve of TOI-257 displays a power excess near ∼ 1200 μHz (Fig. 6), consistent with the spectroscopic log g and the expected frequency range from the TESS asteroseismic target list (ATL, Schofield et al. 2019). An autocorrelation of the power spectrum reveals a peak at a frequency spacing consistent with the location of the excess power (e.g. Stello et al. 2009). Furthermore, the amplitude of the power excess (∼ 9 ppm) is consistent with the expected value from observations by Kepler (Huber et al. 2011). The addition of the Sector 4 light curve reduced the significance of the asteroseismic detection due to the slightly elevated noise level, and was thus discarded for the remainder of our analysis.

Figure 6.

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Power spectrum of the Sector 3 TASOC light curve of TOI-257 (grey line). The black and red lines show the power spectrum smoothed with a boxcar width of 2 μHz and Gaussian with a full width at half max of Δν = 61.4, respectively. The inset shows the autocorrelation of the power spectrum, with a red line marking the expected value of Δν based on the location of the power excess.

To test the significance of the detection and measure ν_max and Δν we used 15 independent analysis methods within working group 1 of the TESS Asteroseismic Science Consortium (e.g. Huber et al. 2009; Mathur et al. 2010; Benomar et al. 2012; Kallinger et al. 2012; Mosser et al. 2012; Corsaro & De Ridder 2014; Davies & Miglio 2016; Campante 2018). All but one pipeline reported a significant detection of solar-like oscillations. The final parameters are ν_max = 1188 ± 40 μHz and Δν = 61.4 ± 1.5 μHz, with the central value taken from the solution closest to the median of all solutions, and uncertainties calculated from the median formal uncertainty returned by individual pipelines added in quadrature to the scatter over individual methods.

3.2.2 Grid-based modelling

We used a number of independent approaches to model the observed global asteroseismic parameters, including different stellar evolution codes (ASTEC, GARSTEC, MESA, and YREC, Christensen-Dalsgaard 2008; Weiss, Moffat & Kudelka 2008; Paxton et al. 2011, 2013, 2015; Choi et al. 2016a; Demarque et al. 2008) and modelling methods (BeSPP, BASTA, PARAM, isoclassify, Silva Aguirre et al. 2015; Serenelli et al. 2017; Rodrigues et al. 2014, 2017; Huber et al. 2017; García Saravia Ortiz de Montellano, Hekker & Themeßl 2018). Model inputs included the spectroscopic temperature and metallicity (see Section 3.1), ν_max, Δν, and the luminosity derived from the Gaia parallax and SED fitting. To investigate the effects of different input parameters, modelers were asked to provide solutions with and without taking into account the luminosity constraint.

The modelling results showed a bi-modality in mass (and thus age) at ∼1.2 and ∼1.4|$\, M_{\odot}$|⁠, with all pipelines favoring the higher mass solution once the luminosity constraint was included. We adopted the solution closest to the median of all returned values, with uncertainties calculated by adding the median uncertainty for a given stellar parameter in quadrature to the standard deviation of the parameter for all methods. This method has been commonly adopted for Kepler (e.g. Chaplin et al. 2014) and captures both random and systematic errors estimated from the spread among different methods. The final estimates of the stellar parameters, taking into account the luminosity constraint, are summarized in Table 3, constraining the radius, mass, density, and age of TOI-257 to ∼ 2  per cent, ∼ 3  per cent, ∼ 3  per cent, and ∼ 13  per cent. We emphasize that these uncertainties in stellar parameters are robust against systematic errors from different stellar model grids, which are frequently neglected when characterizing exoplanets. The stellar mass and radius derived from this analysis is used as priors in the final EXOFASTv2 global fit of the data in Section 3.4.

3.3 Stellar rotation period estimates

The rotation period of TOI-257 was derived from the estimated stellar radius and by performing Lomb-Scargle (Scargle 1982) periodogram and auto-correlation function analysis (e.g. McQuillan, Aigrain & Mazeh 2013) on the TESS light curve, and measuring the projected stellar rotation velocity (vsin i) from Minerva-Australis spectra, assuming the axis of stellar rotation is perpendicular to the line of sight.

We calculated the Lomb-Scargle periodograms for the raw TESS light curves from Sectors 3 and 4 individually and from the combined light curve of the two sectors, after masking the transit events. For Sector 3, the periodogram shows that the variability has a period of P = 5.01 ± 0.46 days and amplitude of A = 114 ± 2 ppm. Sector 4 light curve has a variability with a period of P = 4.13 ± 0.22 days and amplitude of A = 144 ± 2 ppm. The period and amplitude from the two sectors is reasonably consistent. Performing this analysis on the combined light curves reveals that the variability has a period of P = 4.04 ± 0.13 d, amplitude of A = 88 ± 1 ppm, and false alarm probability (FAP)<<0.01. A second very strong peak is observed at ∼2.69 days (or 2P/3) in the Lomb-Scargle periodograms. The FAP was computed from Monte Carlo simulations (e.g. Messina et al. 2010) and the uncertainty in the period of variability was calculated following the procedure of Lamm et al. (2004). The variability from both sectors combined phases-up well at a period of 4.036 days as shown in Fig. 7, which indicates that the variability is likely to be astrophysical in nature (from stellar rotation and star spots) and not systematics. We therefore have adopted the period of variability as 4.04 ± 0.13 d.

Figure 7.

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The left-hand panel shows the TESS light curve of TOI-257 from Sectors 3 and 4 with the best-fitting variability. The middle panel is the Lomb-Scargle periodogram for raw light curves from Sectors 3 and 4 combined. The right-hand panel is the phase-folded light curve at the peak period found from the Lomb-Scargle periodogram.

We also performed an auto-correlation function analysis on the light curves from the individual sectors and combined sectors, and find that the period of variability as P = 5.03 ± 0.61 days and P = 4.12 ± 0.32 days for Sectors 3 and 4, respectively, and a period of P = 4.14 ± 0.22 days for the combined light curves. We also find a strong secondary period in the combined light curves of ∼2.7 days. These results are consistent with the periods found from the Lomb-Scargle periodograms.

To determine whether the period of variability is the true rotation period of the star or one of its harmonics, we calculate an upper limit on the rotation period from the star’s vsin i and estimated radius. We measured the vsin i of TOI-257 by fitting a rotationally broadened Gaussian (Gray 2005) to a least-squares deconvolution profile (Donati & Collier Cameron 1997) obtained from the sum of all the spectral orders from the combined highest S/N Minerva-Australis spectra of TOI-257. The resulting vsin i is 11.3 ± 0.5  km s⁻¹ and combined with the stellar radius from asteroseismology of R_⋆ = 1.888 ± 0.033 |$\, R_{\odot}$|⁠, sets the upper limit on the rotation period for the star of ∼8.5 days, assuming that the inclination of the stellar rotation axis is near |$90\deg$| to the line of sight.

Given the above analyses, we attribute the 4.04 day period of variability observed in the combined TESS light curve to be half the true rotation period of 8.08 ± 0.26 days (which gives a v_rot = 2*π*R_⋆/P_rot = 11.8  km s⁻¹, consistent with the value of vsin i). The very strong secondary peak observed at ∼2.7 days in both the Lomb-Scargle periodograms and the auto-correlation function analysis provides further evidence in support of the 8.08 ± 0.26 days being the true rotation period since the secondary peak corresponds nicely with the P_rot/3 harmonic. It is common for the observed rotational modulation to be at one or more of the harmonics, in particular at half and one-third the true rotation period (Vanderburg et al. 2016b). If the rotation period is 4.04 days, we would have expected to find a strong secondary peak at ∼2.02 days instead of ∼2.7 days. Given that the rotational period and stellar radius gives a rotational velocity consistent with the measured vsin i, this suggests that the stellar obliquity is low (i.e. |$i_{\star }\sim 90\deg$|⁠).

3.4 Planetary system parameters from global analysis

To determine the system parameters for TOI-257 and its planet, we used EXOFASTv2 (Eastman, Gaudi & Agol 2013; Eastman 2017; Eastman et al. 2019) to perform a joint analysis of the TESS photometry and the radial velocity data. We placed Gaussian priors on T_eff and [Fe/H] from the Minerva-Australis high-resolution spectroscopy and Gaussian priors on R_⋆ and M_⋆ from asteroseismology. We applied an upper limit on the V-band extinction from the Finkbeiner (2011) dust maps at the location of TOI-257. We also performed a separate SED analysis (so as not to double count information used from the asteroseismic priors) as an independent check on the stellar parameters using catalog photometry from Tycho (Høg et al. 2000), 2MASS (Cutri et al. 2003), WISE (Cutri et al. 2013), and Gaia (Gaia Collaboration 2018b) as well as MIST stellar evolutionary models (Dotter 2016; Choi et al. 2016b). Gaussian priors were placed on the parallax from Gaia DR2, adding 82 μas to correct for the systematic offset found by Stassun & Torres (2018) and adding the 33 μas uncertainty in their offset in quadrature to the Gaia-reported uncertainty. For the quadratic stellar limb darkening coefficients u₁ and u₂, EXOFASTv2 applied weakly informative Gaussian priors drawn from the interpolation of the Claret & Bloemen (2011) limb darkening models at each step in log g, T_eff, and [Fe/H] taken in the global model to help guide the coefficients. Table 1 lists the broadband magnitudes used in the SED analysis and the stellar parameters including the ones used as priors in the global analysis.

We ran two global models with EXOFASTv2, an eccentric orbit model with ecos ω_* and esin ω_* as free parameters and a circular orbit model with eccentricity fixed to 0 to determine the significance of any potential eccentricity. We computed the small-sample Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC, see, Akaike 1974; Burnham & Anderson 2002) for each model. We find that the Δ AICc between the eccentric and circular model is 4.03, indicating that the circular model is moderately preferred over the eccentric model. Therefore, we have chosen the one-planet circular model as the preferred solution. The results for analysis of both models are reported in Table 4.

The resulting best-fitting models for the transit light curves are plotted in Fig. 8, and for the radial velocities in Figs 9 and 10. Fig. 11 is a plot of the bisector velocity span showing no correlation between the bisectors and the radial velocities for the Minerva-Australis observations, indicating that the measured radial velocity signal is likely planetary in nature and not due to stellar photospheric activity (Figueira et al. 2013).

Figure 8.

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Phase-folded TESS light curve of TOI-257 with the individual transits colour coded similar to Fig. 2. The red solid line is the best-fitting model.

Figure 9.

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Radial velocity measurements of TOI-257 as a function of time. The radial velocity measurements from each instrument have been binned by day for clarity, however, the analysis was performed using the unbinned data. Minerva-Australis radial velocities are represented by the purple filled-in circles. Radial velocities from FEROS and HARPS are the lime green and gold filled-in circles, respectively. The best-fitting model is plotted as the dashed grey line and the center-of-mass velocity has been subtracted. The bottom panel shows the residuals between the data and the best-fitting model.

Figure 10.

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Same as Fig. 9 but phased to one orbital period. The units of the horizontal axis were chosen so that the transit mid-time corresponds to an orbital phase of 0.25.

Figure 11.

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Bisector velocity span as a function of the radial velocities for the Minerva-Australis radial velocities. There is no significant correlation between the bisector velocity span and the radial velocities.

From the best-fitting Kurucz stellar atmosphere model from the SED and the best-fitting MIST stellar evolutionary model, we find that TOI-257 is a somewhat evolved late-F star with |$R_{\star }=1.951^{+0.066}_{-0.051}$| |$\, R_{\odot}$|⁠, |$M_{\star }=1.35^{+0.12}_{-0.38}$| |$\, M_{\odot}$|⁠, |$T_{\rm eff}=6066^{+86}_{-110}$| K, and |$\log {g}=3.986^{+0.047}_{-0.150}$| (where g is in units of cm s⁻²). These stellar parameters are in good agreement with the parameters derived from the Minerva-Australis and HARPS spectroscopy and asteroseismology. However, we choose not to adopt these stellar parameters since they are not as precise as the ones derived from spectroscopy and asteroseismology and list the stellar parameters derived from the joint analysis of the TESS photometry and the radial velocity data in Table 4. From the joint analysis, we find that TOI-257 hosts a sub-Saturn sized planet with a radius of R_P = 0.639 ± 0.013 |$\rm {R_J}$| (7.16 ± 0.15 |$\, R_{\rm \oplus}$|⁠) and mass of M_P = 0.138 ± 0.023 |$\rm {M_J}$| (43.9 ± 7.3 |$\, M_{\rm \oplus}$|⁠), on a circular ∼18.4 day orbit.

To ensure that our results are not potentially biased from the use of the Claret & Bloemen (2011) limb darkening interpolation tables in EXOFASTv2, we ran two additional transit only circular models, one with and one without the Claret and Bloemen tables (setting the NOCLARET flag in EXOFASTv2 such that u₁ and u₂ are completely free parameters). Both transit only models provided consistent results confirming the stellar and planetary parameters are not being biased by the EXOFASTv2 Claret and Bloemen interpolation tables.

Whilst we do find that the circular model provides a somewhat better fit to the TESS light curve and radial velocity data than compared with the eccentric model, the planet could still be on an eccentric orbit given the ∼3.7 σ eccentricity detection. As such, future transit observations to measure chromatic limb darkening as well as additional radial velocities can validate (or refute) any potential eccentricity in the orbit of TOI-257 b.

3.5 Complementary analysis, and limits on additional planets

We further analyse the radial velocity data set in Table 2 with RadVel (Fulton et al. 2018) to provide both an independent analysis for checking consistency in the mass and eccentricity of planet b, and to search for any additional planets. The search for additional planets is motivated by two reasons. First, moderately eccentric Keplerian signals can sometimes resolve into two near-circular resonant signals with additional radial velocity data (e.g. Wittenmyer et al. 2013; Trifonov et al. 2017; Boisvert, Nelson & Steffen 2018; Wittenmyer et al. 2019). Second, we wish to evaluate the multiplicity of systems like TOI-257 with warm sub-Saturns.