Issue |
A&A
Volume 667, November 2022
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Article Number | L14 | |
Number of page(s) | 10 | |
Section | Letters to the Editor | |
DOI | https://doi.org/10.1051/0004-6361/202244747 | |
Published online | 25 November 2022 |
Letter to the Editor
Radial velocity survey for planets around young stars (RVSPY)
A transiting warm super-Jovian planet around HD 114082, a young star with a debris disk⋆
1
Max Planck Institute for Astronomy – MPIA, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: zakhozhay@mpia.de
2
Main Astronomical Observatory, National Academy of Sciences of the Ukraine, 03143 Kyiv, Ukraine
3
Department of Astronomy, Sofia University “St Kliment Ohridski”, 5 James Bourchier Blvd, 1164 Sofia, Bulgaria
4
Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, 69117 Heidelberg, Germany
5
Facultad de Ingeniera y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile
6
Millennium Institute of Astrophysics (MAS), Nuncio Monseñor Sótero Sanz 100, Providencia, Santiago, Chile
7
Data Observatory Foundation, DO; Diagonal Las Torres N o2460, Building E, Peñalolén, Santiago, Chile
8
Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
9
Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany
10
Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
11
Physikalisches Institut, Universität Bern, Gesellschaftsstr. 6, 3012 Bern, Switzerland
12
Institutionen för Astronomi, AlbaNova Universitetscentrum, Stockholms Universitet, 106 91 Stockholm, Sweden
Received:
12
August
2022
Accepted:
19
October
2022
Aims. We aim to detect planetary companions to young stars with debris disks via the radial velocity method.
Methods. We observed HD 114082 during April 2018–August 2022 as one of the targets of our RVSPY program (Radial Velocity Survey for Planets around Young stars). We use the FEROS spectrograph, mounted to the MPG/ESO 2.2 m telescope in Chile, to obtain high signal-to-noise spectra and time series of precise radial velocities (RVs). Additionally, we analyze archival HARPS spectra and TESS photometric data. We use the CERES, CERES++ and SERVAL pipelines to derive RVs and activity indicators and ExoStriker for the independent and combined analysis of the RVs and TESS photometry.
Results. We report the discovery of a warm super-Jovian companion around HD 114082 based on a 109.8±0.4 day signal in the combined RV data from FEROS and HARPS, and on one transit event in the TESS photometry. The best-fit model indicates a 8.0±1.0 MJup companion with a radius of 1.00±0.03 RJup in an orbit with a semi-major axis of 0.51±0.01 au and an eccentricity of 0.4±0.04. The companions orbit is in agreement with the known near edge-on debris disk located at ∼28 au. HD 114082 b is possibly the youngest (15±6 Myr), and one of only three young (< 100 Myr) giant planetary companions for which both their mass and radius have been determined observationally. It is probably the first properly model-constraining giant planet that allows distinguishing between hot and cold-start models. It is significantly more compatible with the cold-start model.
Key words: methods: observational / techniques: radial velocities / techniques: photometric / planets and satellites: detection / planets and satellites: formation / stars: activity
© O. V. Zakhozhay et al. 2022
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This article is published in open access under the Subscribe-to-Open model.
Open Access funding provided by Max Planck Society.
1. Introduction
The search for exoplanets is one of the fastest-developing topics of modern astronomy: We learn more details about newly discovered planets, their properties, and their evolution nearly every day. More than five thousand planets were detected by mid-2022 (see exoplanet.eu1; Schneider et al. 2011). Only for ∼10% of these have the masses and radii been determined directly through observations, however. Only two systems, V 1298 Tau (Suárez Mascareño 2022) and AU Mic (Plavchan et al. 2020; Martioli et al. 2021; Zicher et al. 2022), are younger than 50 Myr and have known planetary companions with such determinations. To constrain evolutionary models, we therefore need to know both quantities not only for a larger number of planets, but also for planets that are significantly younger (≪100 Myr) than those for which we currently have both parameters.
In 2017, we started a large radial velocity (RV) survey for planets around young stars (RVSPY) with debris disks using the FEROS spectrograph at the 2.2 m telescope at the La Silla Observatory in Chile (Zakhozhay et al. 2022). This survey aims to supplement the large direct Imaging Survey for Planets around Young stars (NaCo-I SPY), which was carried out between 2015 and 2019 (Launhardt et al. 2020). The two surveys overlap for 54 targets. In addition to our own observational data, we also use complementary data from HARPS2, TESS3, and Gaia4.
In this Letter, we report the discovery of a super-Jovian companion to HD 114082, a young (15±6 Myr, Pecaut & Mamajek 2016) F3V star in the lower Centaurus Crux association Gagné et al. (2018; see Table 1). The star is surrounded by a spatially resolved debris disk that has the form of a narrow dust ring at r∼28 au and an inclination with respect to the line of sight of 83.3 deg (SPHERE; Wahhaj et al. 2016). HD 114082 was also observed in the RVSPY high-cadence survey, but no hot Jupiter with P < 10 d was detected down to a 3σ detection limit of 2–3 MJup (Zakhozhay et al. 2022). In addition, it was also observed in the L′-band high-contrast direct-imaging I SPY survey, but no wide-orbit companion was detected down to 3σ detection limits of 40 MJup at 10 au to 4 MJup at 100 au and beyond (Launhardt et al. 2020).
Basic stellar parameters of HD 114082.
2. Observations and data reduction
HD 114082 was observed with FEROS (Kaufer et al. 1999), a high-resolution, environmentally controlled Échelle spectrograph that is mounted at the 2.2 m telescope at La Silla Observatory in Chile. This instrument has a high spectral resolution (R = 48 000), high efficiency (∼20%), and large wavelength coverage (350–920 nm). The observations were carried out in the object-calibration mode, with one fiber on the star and the other fiber fed by a ThAr+Ne calibration lamp. The observations were carried out between April 17, 2018, and August 20, 2022. During this period, we obtained seven sets of high-cadence time series5 with 63 useful spectra in total. We did not include 3 archival6 spectra taken on the single night of May 30, 2009, that is, almost nine years before the RVSPY survey. These observations were obtained with a different calibration plan.
The spectra were reduced and the RVs and bisector spans (BS)7 were derived in a semi-automatic fashion with the CERES pipeline (Brahm et al. 2017a). The stellar activity indicators (full width at half maximum (FWHM), Hα, HeI, and NaI D1+D2 indices) were derived from the FEROS spectra using the CERES-plusplus Python package8.
In addition, we downloaded 18 HARPS spectra that are publicly available in the ESO archive (at the time of writing). We obtained precise RVs and stellar activity indicators from the HARPS-RVBank9 (Trifonov et al. 2020), which was updated for this purpose, to include the latest spectra that became public after 2020. All data (RV, Hα, NaI D, NaII D, differential line width dLW, and chromatic RV index CRX10) were computed using the SERVAL pipeline (Zechmeister et al. 2018).
Furthermore, we found that HD 114082 is scheduled for TESS observations in four sectors: sectors 11, 38, 64, and 6511. The data for the first two sectors are already public, but only for sector 38 the light curves are available in the MAST database12. They have a cadence of 2 min. We tried to reduce sector 11 using the available raw data, but were not able to extract a light curve. The reason most probably is that the star lies close to the edge of the CCD in this sector. To verify that the sector 38 TESS light curve is not blended by another (known) star, we inspected the TESS target pixel file image (TPF; Aller et al. 2020) of sector 38 and used the automatic tool tpfplotter13 to overlay the Gaia EDR3 catalog on the TESS TPF (see Fig. A.1). The observations in sectors 64 and 65 will be carried out only in April and May 2023, respectively.
3. Results
We inspected the RV time series of both the FEROS and the HARPS data and performed a combined analysis using the exoplanet toolbox Exo-Striker14 (Trifonov 2019). For the period search, we computed the maximum likelihood periodogram (MLP; Baluev 2008, 2009), which is equal to fitting sine waves. This allows the determination of RV jitter for both instruments as well as the RV offset between the instruments. Visual examination of the data indicates evidence for a linear trend. We therefore computed the MLP for the detrended data. Figure 1 shows the resulting MLP power spectrum. Four significant peaks are seen around 23 d, 24 d, 28 d, and 109 d. These peaks mostly come from the FEROS data sample, which is more numerous and has a larger baseline. The 28 d signal is close to the fourth harmonic of the most significant peak at 109 d and possibly caused by an eccentric orbit. The peaks near 1 d are related to the data sampling and are daily aliases of the mentioned significant signals. The two peaks at 23 and 24 d cannot be explained by aliases and are explored in Sect. 3.1.
Fig. 1. MLP power of the combined RV data (FEROS and HARPS) for HD 114082. Horizontal lines reflect the 0.1%, 1%, and 10% false-alarm probabilities (from top to bottom). |
The sector 38 TESS light curve includes a single transit event, suggesting the presence of an ≈1 RJup-sized companion with a mass between 0.3 MJup and the brown dwarf mass regime, and with a minimum orbital period of d. Details of these analyses and estimates are described in Appendix A.2. Both the orbital period range and the mass range of the transiting companion overlap with the corresponding values inferred directly from modeling the RV data alone, which yields P = 109.3 d and Mpl = 8.6 MJup (model not shown here). Consequently, we have reason to assume that both signals are caused by the same companion. We therefore attempt a combined analysis of both data sets.
3.1. Combined analysis of RV data and TESS photometry
For the joint-fit analysis of transit and RV data, we used Exo-Striker, adopted a Keplerian model, and allowed a linear trend in the RV data. The fit parameters for the planet are orbital period P, eccentricity e, semi-amplitude K, argument of periastron ω, and the mid-transit time t0. Additional free parameters were RV and transit photometry data offsets (RVoff, FEROS, RVoff, HARPS, and transitoff, TESS), jitter values (RVjitt, FEROS, RVjitt, HARPS, and transit jitt, TESS), and the quadratic limb-darkening coefficients (u1 and u2). Details of the fitting procedure and the parameter priors can be found in Appendix A.3.
Figures 2–4 show the results. The RVs derived from the FEROS and HARPS spectra are shown in Fig. 2 together with the best-fit model. Figure 3 shows the phase-folded data and model, and Fig. 4 shows part of the TESS data around the transit event. The vertical blue line in Figs. 2 and 3 indicates the mid-transit time.
Fig. 2. RV time series data for HD 114082. FEROS data from RVSPY are shown as black circles. The RVs computed from the publicly available HARPS spectra are shown as gray circles. Error bars account for the suspected activity jitter (see text for details). The solid gray line shows the best-fit model (see parameters in Table 2), and the vertical blue line indicates the time of the observed transit. The lower panel shows the residuals of the fit. |
Fig. 4. Baseline-corrected sector 38 TESS data (relative flux) for HD 114082 around the transit event with the best-fit model of the transit overlaid (black line). The bottom panel shows the residuals of the fit. |
From the best-fit model we derived a companion mass Mpl = 8.0 ± 1.0 MJup, a radius Rpl = 1.0 ± 0.03 RJup, a semi-major axis a = 0.51±0.01 au, and an orbital period P = 109.75 d15. All key physical parameters are listed in Table 2. The MLP periodogram of the residuals from the best-fit model (see Fig. A.2) shows that all the signals of unknown origin are no longer significant. The reason probably is that the best-fit model is much more complex than the sinusoidal fit used to compute the initial MLP power spectrum of Fig. 1.
Basic planetary parameters of HD 114082 b.
3.2. Stellar activity analysis
We derived the activity indicators for all spectra available for our analysis using the tools described in Sect. 2. We analyzed the generalized Lomb–Scargle periodograms (GLS; Zechmeister & Kürster 2009) of the FEROS and HARPS activity indicators looking for correlations between these indicators and the RVs of the corresponding instrument (see Figs. A.4 and A.3 and Table A.2 for more details). Only two of all the activity indicators are significantly correlated with the RVs: the BS measured by FEROS, and the CRX measured by HARPS. These correlations have Pearson’s correlation coefficients and two-tailed p-values of 0.69, 4.21 × 10−10 and 0.81, 5.48 × 10−5, respectively. These correlations may indicate that the linear trend, for which we have strong evidence in the RV data (see Appendix A.3), is most probably related to long-term activity, perhaps an activity cycle, but not to the presence of a larger companion on an outer orbit. One way to create a positive BS(RV) correlation would be blending by the line system of a sufficiently bright companion, which is not supported by our mass determination. We exclude that the RV signal at the 109.8 d period is related to activity because the activity indices from FEROS and HARPS do not show any significant signals near this period (see Figs. A.4 and A.3). We also conclude that the 109.8 d period cannot be related to stellar rotation, which we estimated to be Prot ≤ 1.924 d (see Table 1).
4. Discussion
4.1. Uncertainties introduced by activity
Except for stellar activity, which manifests itself in significant correlations between the FEROS BS and RVs as well as the HARPS CRX and RVs and a linear trend that we associate with the long-term activity, no other strong activity effects are seen in more than one single indicator. Therefore, the HARPS and FEROS spectra do not support the presence of pronounced activity on HD 114082. Early-F dwarfs have shallow convection zones and are therefore not very active in general. However, the considerably large vsin(i) of this star may support a certain level of activity.
HD 114082 is a rapidly rotating F star (vsin(i) = 39.2±0.5 km s−1) that has far fever lines than later-type stars. It also shows substantial rotational broadening. Therefore, the instrumental RV precision is rather poor. Additionally, the star exhibits a large RV scatter, which we modeled as RV jitter quadratically added to the error budget in our fitting. The RV jitter amplitudes determined for both the FEROS and HARPS data individually are high, 146 m s−1 and 283 m s−1, respectively. This excess uncertainty may also indicate some short-term variability, such as rapid pulsations that are not well-sampled by our data. The star is located near the edge of the instability strip of the Hertzsprung–Russell diagram. Because of its young age, it has not yet fully arrived on the main sequence. This places it in the range of δ Scuti variables (Breger 1972, 2000; Murphy 2015), which display multiperiodic p- and g-mode pulsations with typical periods of the fundamental mode of a few hours (and more rapid pulsations of some of the harmonics). Although no such periodic pulsations are immediately evident in the GLS periodogram of the TESS data down to periods of ∼5 min, they might still be present but be much weaker than in HD 115820, for instance, where clearly visible δ-Scuti pulsations between 42 and 68 min cause a large (6.3 km s−1) RV jitter (Zakhozhay et al. 2022). This is well in line with the report by Grandjean et al. (2021) and the analysis of Lagrange et al. (2009), who described that the RV jitter in young A–F5 stars is dominated by pulsations.
4.2. Astrometry
HIPPARCOS (ESA 1997; van Leeuwen 2010) lists an uncritical goodness-of-fit parameter and no multiplicity flag for HD 114082. Gaia (DR3, Gaia Collaboration 2016; Vallenari et al. 2022) lists a renormalized unit weight error (RUWE) of 0.94, which is fully consistent with the hypothesis that none of the individual measurements deviates significantly from the single-body solution and with an astrometric excess noise of 149 μarcsec. While the value of the latter is considered uncritical for the validity of the single-body astrometric solution, it is significantly higher than the expected maximum astrometric signal of HD 114082 due to its companion (∼25 μarcsec), which thus remains completely hidden in the excess noise. Furthermore, no significant proper motion anomaly is detected between the long-term HIP-Gaia proper motion and the Gaia-only proper motion vector (PMaG2) according to the formalism described by Kervella et al. (2019), most likely also owing to the smallness and short period of the expected astrometric amplitude. Hence, the available astrometric data do not reveal the existence of this companion, nor do they contradict its existence.
4.3. HD 114082 b in mass–radius space
Figure 5 shows the distribution of all 562 known companions to stars with radii derived from primary transits and masses derived from RVs, excluding planets with only upper-limit mass estimates, together with HD 114082 b and color-coded ages. Of these, 408 planets have host stars with ages listed on exoplanet.eu. While all values are initially retrieved from Exoplanet.eu, ages, masses, and radii of the few systems that are younger than 100 Myr were verified from the respective latest original papers and the values from these papers were used. HD 114082 b, with 15±6 Myr, might be the youngest, and one of only five known exoplanets with ages younger than 30 Myr for which we know both mass and radius. The four other planets are V 1298 Tau b and e with 20±10 Myr (Suárez Mascareño 2022) and AU Mic b and c with 22±3 Myr (Plavchan et al. 2020; Martioli et al. 2021; Zicher et al. 2022). The next-youngest system with known mass and radius is CoroT-20 b with 100±40 Myr (Raetz et al. 2019).
Fig. 5. Mass–radius distribution of known exoplanets (and brown dwarfs) with radii derived from primary transits and masses derived from RVs (562 planets and companions, excluding upper mass limits). Stellar ages are taken from Exoplanet.eu and are color-coded. Stars with ages < 50 Myr (all green) are shown as larger circles. Stars without known ages are marked as empty circles. The bright green triangle denotes HD 114082 b. Error bars, where known, are smaller than the symbol sizes. Thick colored lines mark isochrones for ages of 10–20 Myr from Fortney et al. (2008) for hot-start models (blue) and cold-start models (green). The dashed black line shows the isochrone from the combined COND (Baraffe et al. 2003) and DUSTY (Chabrier et al. 2000) models. |
Figure 5 shows that the measured radius of HD 114082 b is close to what cold-start evolutionary models (Fortney et al. 2008) predict for a 7–10 MJup mass planet at age 10–20 Myr. It is less consistent with the prediction of hot-start models, both from Fortney et al. (2008) and from the combined COND (Baraffe et al. 2003) and DUSTY (Chabrier et al. 2000) models. Together with the two other young (< 30 Myr) giant planets (GPs) with known mass and radius (V 1298 Tau b and e; the two AU Mic planets have a lower mass and are rocky and thus probe different physics), we have now three young GPs with measured radii that are significantly smaller than what is predicted by most commonly adopted hot-start models, and not yet a single young GP that agrees with these models.
4.4. Comparison with similar planetary systems
HD 114082 b is not the only massive planet found orbiting an F star. Similar systems include 30 Ari B b, a massive planet in a hierarchical stellar triple system (Guenther et al. 2009; Kane et al. 2015), and the single-star planets HD 23596 b (Perrier et al. 2003; Wittenmyer et al. 2009), HD 89744 b (Korzennik et al. 2000; Valenti & Fischer 2005; Wittenmyer et al. 2019), HD 86264 b (Fischer et al. 2009), and HD 1666 b (Harakawa et al. 2015). HD 114082 is much younger, and its companion also has the shortest orbital period of the other similar planets mentioned, which range from about 250 days to just over four years. Otherwise, these systems are similar, however.
Furthermore, a similar population of planets has been found orbiting stars in a more evolved evolutionary stage, mostly K giants. Almost one-third of all planets and brown dwarfs found around G and K giants (44 out of 14116) have masses in excess of 6 MJup, and the period distribution is also similar, ranging from about 100 days to 11 years, with a maximum of about 500 days.
HD 114082 is again at the lower end of the period range, but is otherwise similar to the planets around more evolved stars with comparable masses. The most similar system to HD 114082 with an evolved host star is TYC 4282-605-1 (González-Álvarez et al. 2017), which hosts a 10 MJup planet on a mildly eccentric 102-day orbit. We conclude that the planet orbiting HD 114082 is not an exception, although no system with such a young age was known so far.
5. Summary
We presented the results of four years of observations of HD 114082 with the FEROS spectrograph. The combined analysis of our own FEROS data together with the archival HARPS spectra and TESS photometric data indicates the presence of a GP with a mass of M2 = 8.0 ± 1.0 MJup on a 109.8±0.4 d orbit with a = 0.51±0.01 au and e = 0.4±0.04. The orbit of HD 114082 b is thus comparable to the Mercury orbit in our own Solar System, but it is more eccentric. Based on one transit event in the TESS photometry, we were able to constrain the planetary radius to 1.0 ± 0.03 RJup, which compares well to the very few other exoplanets in this mass range with known masses and radii.
HD 114082 b might be the youngest such massive GP for which both its mass and radius have been determined observationally. It is also one out of only three young GPs in the 10–30 Myr age range for which both its mass and radius are known. It is therefore probably the first real model-constraining GP in mass–radius space based on which we can distinguish between hot- and cold-start models. It is significantly more consistent with the latter. Together with the two other young (< 30 Myr) GPs with known mass and radius (V 1298 Tau b and e), we have now three young giant planets with measured radii that are significantly smaller than what is predicted by most of the commonly adopted hot-start models. Although certainly more such young and massive objects with both observationally constrained mass and radius are needed, this accumulating observational evidence should start triggering an adaption of the evolutionary models. HD 114082 b is also one of the rare cases in which a planetary companion to a star was first discovered in RVs and was then confirmed through a TESS transit.
HARPS is the High Accuracy Radial velocity Planet Searcher, mounted at the 3.6 m telescope at ESO’s La Silla observatory in Chile (Mayor et al. 2003).
TESS is the Transiting Exoplanet Survey Satellite (Ricker et al. 2015).
Gaia is the Global Astrometric Interferometer for Astrophysics (Gaia Collaboration 2016).
The bisector span is a measure of the asymmetry of absorption lines (Queloz et al. 2001).
Chromatic index is RV gradient as a function of wavelength with the RVs measured in the echelle orders of the spectrograph (Zechmeister et al. 2018).
Acknowledgments
The authors thank Coryn Bailer-Jones, Christoph Mordasini and Remo Burn for helpful discussions and feedback. O.Z. acknowledges support within the framework of the Ukraine aid package for individual grants of the Max-Planck Society 2022. T.T. acknowledges support by the BNSF program “VIHREN-2021” project No. КП-06-ДВ/5. Th.H. acknowledges support from the European Research Council under the European Union’s Horizon 2020 research and innovation program under grant agreement No. 832428-Origins. S.R. and G.-D.M. acknowledge support of the DFG (German Science Foundation) priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets” (RE 2694/7-1 and MA 9185/1-1). R.B. acknowledges support from FONDECYT Project 11200751 and from project IC120009 “Millennium Institute of Astrophysics (MAS)” of the Millenium Science Initiative. J.I.V. acknowledges support of CONICYT-PFCHA/Doctorado Nacional-21191829. This research made use of the SIMBAD database, operated at the CDS, Strasbourg, France. G.-D.M. also acknowledges the support from the Swiss National Science Foundation under grant 200021_204847 “PlanetsInTime”. This work presents results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). Parts of this work have been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation. This research has made use of data obtained from or tools provided by the portal exoplanet.eu (http://exoplanet.eu/) of The Extrasolar Planets Encyclopaedia. This work made use of tpfplotter by J. Lillo-Box (publicly available in www.github.com/jlillo/tpfplotter, which also made use of the python packages astropy, lightkurve, matplotlib and numpy. We also wish to thank the anonymous referee for constructive criticism that helped to improve the clarity of the paper.
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Appendix A: Supplementary material
A.1. Target pixel image of HD 11408 in TESS sector 38
Fig. A.1 shows the target pixel file (TPF) image of HD 114082 in TESS sector 38. There is one faint object at the edge of the TESS aperture (number 2 in Fig. A.1) that is very faint (Gmag = 12.56, as compared to 8.1 for HD 114082) and causes a dilution of 0.984 to the transit light curve of HD 114082. This contamination dilution was already corrected for in the pre-search data conditioning simple aperture photometry TESS data (PDC-SAP; Smith et al. 2012; Stumpe et al. 2012, see Sect. A.3) we used.
Fig. A.1. Target pixel file image of HD 114082 in TESS sector 38. |
A.2. Companion signature in TESS data
The only useful photometric TESS time-series data available (sector 38) show one single transit, which very likely indicates the presence of a bound companion with an orbital period > 27 d (the length of the TESS observing sector). The relative transit depth of ≈0.5% translates into a companion radius of ≈1 RJup, which is indicative of a companion mass between 0.3 MJup and the brown dwarf mass regime (Fig. 5). The transit duration of ≈0.53 ± 0.01 d translates into an upper limit to the instantaneous orbital speed (because of the unknown impact parameter) of ≲44 km s−1. Assuming MPl ≪ M* and allowing for a moderate eccentricity of up to e = 0.2, Kepler’s third law implies a minimum orbital period of d. Since both the orbital period range and the mass range of the transiting companion overlap with the values inferred directly from the RV data alone, we can reasonably assume that both signals are caused by the same companion. We therefore attempted a combined analysis of both data sets in Sect. 3.1.
A.3. Modeling procedure
For a combined fit of RVs (the reduced data are listed in Tables A.3 and A.4) and TESS photometry, we used the Exo-Striker toolbox, which allowed us to simultaneously fit both types of data. We used the publically available PDC-SAP TESS data (Smith et al. 2012; Stumpe et al. 2012), which were corrected for contamination from nearby stars and instrumental systematics. We further detrended and normalized the PDC-SAP light curves with a squared exponential Gaussian processing kernel using the Wotan Python package (Hippke et al. 2019), which is integrated into Exo-Striker. Some obvious photometry outliers were also removed, and the data were cut to ∼ ±1 d from the mid-transit to save computational time because the rest of the out-of-transit data do not contain useful information. The TESS data (Fig. 4) seem to show an asymmetry during the transit phase, which leads to a slightly inclined bottom of the light curve. So far, it is not clear whether this is a genuine stellar effect or if it arises because no detrending was applied to the transit phase.
Orbital posteriors were obtained with the Nested Sampling (NS) technique (Skilling et al. 2004) using the dynesty sampler (Speagle 2020). Our parameter priors are listed in Table A.1. Our NS setup consists of 50 live points per fitted parameter, which we sampled via a random walk focused on converging on the posterior probability distribution. We computed the Bayesian log-evidence ln(Z) to qualitatively compare a Keplerian fit to a Keplerian-and-linear-trend fit.
Our results show that the Bayesian evidence of the simpler model without a linear trend on the RVs has lnZ = 8686.25 ± 0.20, whereas the Keplerian model with trend has lnZ = 8711.54 ± 0.23. The inclusion of the linear trend leads to a significant improvement over the trend-free model (i.e., ΔlnZ > 25, see, Trotta 2008), which additionally justifies use of the model with the linear trend.
The weighted rms from the best fit are 158.8 and 290.2 m s−1 for FEROS and HARPS RVs, respectively. The MLP periodogram of the residuals (Fig. A.2) shows that all the signals of unknown origin are no longer significant. This is most probably explained by the fact that the best-fit Keplerian model is much more complex than the sinusoidal fit we used to compute the MLP power spectrum.
Fig. A.2. MLP power of residuals (bottom panel of Fig. 2). The horizontal lines reflect the 0.1%, 1%, and 10% false-alarm probabilities (from top to bottom). |
A.4. Activity analysis
Figs. A.3 and A.4 show the time series of the activity indicators that we analyzed in this work (for FEROS and HARPS instruments, respectively) in the left columns and their GLS periodograms in the middle panels. The correlations between the activity indicators and the RVs measured by corresponding instrument are shown in the left columns and are listed in Table A.2. More information about these parameters is presented in Sect. 2.
Fitting parameter priors. The adopted priors are 𝒰 for uniform and 𝒩 for Gaussian.
Pearson’s correlation coefficients and two-tailed p-values for correlations of the activity indicators with the respective RVs taken with the same instrument (FEROS or HARPS).
HARPS Doppler measurements of HD 114082.
FEROS Doppler measurements of HD 114082.
Fig. A.3. Time series and GLS of the RVs and activity indicators derived from the FEROS spectra (left and middle panels, respectively). The right panels show the correlation with respect to the FEROS RVs for the derived key activity indicators. The type of activity indicator is given in each of the panels of the middle column. The vertical red line shows the suspected planetary period (P = 109.8 d), from the model with linear trend of the combined RVs (FEROS+HARPS) and photometric (TESS) data. |
All Tables
Fitting parameter priors. The adopted priors are 𝒰 for uniform and 𝒩 for Gaussian.
Pearson’s correlation coefficients and two-tailed p-values for correlations of the activity indicators with the respective RVs taken with the same instrument (FEROS or HARPS).
All Figures
Fig. 1. MLP power of the combined RV data (FEROS and HARPS) for HD 114082. Horizontal lines reflect the 0.1%, 1%, and 10% false-alarm probabilities (from top to bottom). |
|
In the text |
Fig. 2. RV time series data for HD 114082. FEROS data from RVSPY are shown as black circles. The RVs computed from the publicly available HARPS spectra are shown as gray circles. Error bars account for the suspected activity jitter (see text for details). The solid gray line shows the best-fit model (see parameters in Table 2), and the vertical blue line indicates the time of the observed transit. The lower panel shows the residuals of the fit. |
|
In the text |
Fig. 3. Phase-folded version of Fig. 2, folded with the period of planet b, 109.8 days. |
|
In the text |
Fig. 4. Baseline-corrected sector 38 TESS data (relative flux) for HD 114082 around the transit event with the best-fit model of the transit overlaid (black line). The bottom panel shows the residuals of the fit. |
|
In the text |
Fig. 5. Mass–radius distribution of known exoplanets (and brown dwarfs) with radii derived from primary transits and masses derived from RVs (562 planets and companions, excluding upper mass limits). Stellar ages are taken from Exoplanet.eu and are color-coded. Stars with ages < 50 Myr (all green) are shown as larger circles. Stars without known ages are marked as empty circles. The bright green triangle denotes HD 114082 b. Error bars, where known, are smaller than the symbol sizes. Thick colored lines mark isochrones for ages of 10–20 Myr from Fortney et al. (2008) for hot-start models (blue) and cold-start models (green). The dashed black line shows the isochrone from the combined COND (Baraffe et al. 2003) and DUSTY (Chabrier et al. 2000) models. |
|
In the text |
Fig. A.1. Target pixel file image of HD 114082 in TESS sector 38. |
|
In the text |
Fig. A.2. MLP power of residuals (bottom panel of Fig. 2). The horizontal lines reflect the 0.1%, 1%, and 10% false-alarm probabilities (from top to bottom). |
|
In the text |
Fig. A.3. Time series and GLS of the RVs and activity indicators derived from the FEROS spectra (left and middle panels, respectively). The right panels show the correlation with respect to the FEROS RVs for the derived key activity indicators. The type of activity indicator is given in each of the panels of the middle column. The vertical red line shows the suspected planetary period (P = 109.8 d), from the model with linear trend of the combined RVs (FEROS+HARPS) and photometric (TESS) data. |
|
In the text |
Fig. A.4. Same as in Fig. A.3, but for RVs and activity indicators computed from the HARPS spectra. |
|
In the text |
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