HD 76920b pinned down: a detailed analysis of the most eccentric planetary system around an evolved star
C. Bergmann, M. I. Jones, J. Zhao, A. J. Mustill, R. Brahm, P. Torres, R. A. Wittenmyer, F. Gunn, K. R. Pollard, A. Zapata, L. Vanzi, Songhu Wang
PPublications of the Astronomical Society of Australia (PASA)doi: 10.1017/pas.2021.xxx.
HD 76920 b pinned down: a detailed analysis of themost eccentric planetary system around an evolved star
C. Bergmann ,
2∗ † , M. I. Jones , , J. Zhao , , A. J. Mustill , R. Brahm , , P. Torres , R. A.Wittenmyer , F. Gunn , K. R. Pollard , A. Zapata , L. Vanzi , S. Wang Exoplanetary Science at UNSW, School of Physics, UNSW Sydney, NSW 2052, Australia Deutsches Zentrum für Luft- und Raumfahrt, Münchener Str. 20, 82234 Weßling, Germany European Southern Observatory, Alonso de Córdova 3107, Casilla 19001, Santiago, Chile Instituto de Astronomía, Universidad Católica del Norte, Angamos 0610, 1270709, Antofagasta, Chile Penn State University, Department of Astronomy and Astrophysics, University Park, PA 16802, USA Lund Observatory, Department of Astronomy & Theoretical Physics, Lund University, Box 43, 221 00 Lund, Sweden Millennium Institute for Astrophysics, Chile Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile Department of Electrical Engineering and Center of Astro Engineering, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna4860, Santiago, Chile University of Southern Queensland, Centre for Astrophysics, Toowoomba, Queensland 4350, Australia School of Physical and Chemical Sciences, Te Kura Mat¯u, University of Canterbury, Christchurch 8020, New Zealand Department of Astronomy, Indiana University, Bloomington, IN 47405, USA
Abstract
We present 63 new multi-site radial velocity measurements of the K1III giant HD 76920, which wasrecently reported to host the most eccentric planet known to orbit an evolved star. We focussedour observational efforts on the time around the predicted periastron passage and achieved near-continuous phase coverage of the corresponding radial velocity peak. By combining our radial velocitymeasurements from four different instruments with previously published ones, we confirm the highlyeccentric nature of the system, and find an even higher eccentricity of e = 0 . ± . . +0 . − . d, and a minimum mass of 3 . +0 . − . M J for the planet. The uncertainties inthe orbital elements are greatly reduced, especially for the period and eccentricity. We also performeda detailed spectroscopic analysis to derive atmospheric stellar parameters, and thus the fundamentalstellar parameters ( M ∗ , R ∗ , L ∗ ), taking into account the parallax from Gaia DR2, and independentlydetermined the stellar mass and radius using asteroseismology. Intriguingly, at periastron the planetcomes to within 2.4 stellar radii of its host star’s surface. However, we find that the planet is notcurrently experiencing any significant orbital decay and will not be engulfed by the stellar envelope forat least another 50 −
80 Myr. Finally, while we calculate a relatively high transit probability of 16%, wedid not detect a transit in the TESS photometry.
Keywords: planetary systems – stars: individual: HD 76920 – techniques: radial velocities
Since the first detection of a planet around a main-sequence star more than two decades ago (Mayor &Queloz, 1995), thousands of planetary systems have beenfound with astonishing diversity. The transit methodhas produced the most planet discoveries to date, mostlydue to the overwhelming success of NASA’s
Kepler mis-sion (Borucki et al., 2010). Yet, a significant fractionof all planets has been found using the radial velocity ∗ Visiting Astronomer, University of Canterbury Mt John Ob-servatory † E-mail: [email protected] (RV) technique, including many longer-period planets,for which ground-based Doppler searches have a natu-ral advantage over short-lived space missions. The RVmethod also remains a valuable tool for the detectionand characterization of planets, as it yields the mini-mum mass of a planet and therefore nicely complementsthe transit method, which yields the size of a planet.Space-based transit searches such as
Kepler (Boruckiet al., 2010) or TESS (Ricker et al., 2015) also rely onground-based RV follow-up observations to confirm theirplanet candidates, to determine their masses and hencedensities, and to search for additional planets in these1 a r X i v : . [ a s t r o - ph . E P ] F e b C. Bergmann et al. systems.Slowly rotating solar-type and late-type stars are idealtargets for Doppler planet searches, as their spectra ex-hibit numerous sharp absorption lines. However, main-sequence stars more massive than about 1 . (cid:12) are gen-erally not suitable for precise RV measurements, due totheir high temperatures and fast rotation rates (e.g. Gal-land et al., 2005). Consequently, the occurrence rate anddistribution of planets as a function of stellar mass andmetallicity for intermediate-mass stars are not as well-established compared to planets around lower-mass stars(e.g. Johnson et al., 2010; Reffert et al., 2015; Jones et al.,2016; Wittenmyer et al., 2017a). In order to learn moreabout planetary systems around these intermediate-massstars, several planet search programmes have been specif-ically targeting evolved stars of the same mass (oftendubbed ’retired A-stars’), as they do not suffer fromthese effects (e.g. Frink et al., 2002; Sato et al., 2003;Johnson et al., 2007; Niedzielski et al., 2007; Wittenmyeret al., 2011; Jones et al., 2011).More than 100 planets have now been discovered orbit-ing giant stars, and except for the very few such systemsdiscovered by Kepler (e.g. Quinn et al., 2015), all of thesehave been discovered via the RV technique. Notably thefirst planet found to orbit a giant star, ι Dra b, also hap-pens to be on a very eccentric orbit with e = 0 .
71 (Frinket al., 2002; Kane et al., 2010). More recently, planets oneven more eccentric orbits were found around the K3IIIgiant BD+48 740 (HIP 12684) with e = 0 .
76 (Adamówet al., 2012, 2018), and around the K1III giant HD 76920with e = 0 .
86 (Wittenmyer et al., 2017b). The lattercurrently claims the title of being the most eccentricplanet orbiting an evolved star, and is the subject ofthis work.Orbits with certain combinations of high eccentricitiesand longitudes of periastron produce RV curves thatare essentially flat for the majority of the orbital periodand only exhibit a narrow peak near periastron passage.However, because nearly all the information needed todetermine the orbital parameters, including the RV semi-amplitude and thus the minimum mass of the planet, iscontained in this short phase of the orbit, it is ratherdifficult from an observational point of view to obtain agood orbital solution for such systems. In their discoverypaper, Wittenmyer et al. (2017b) pointed out that theperiastron passage of HD 76920 b still needed betterobservational sampling in order to sufficiently constrainthe orbital elements and minimum mass of the planet.We therefore planned a multi-site observing run andsuccessfully filled in the gap in the phase coverage nearperiastron passage with RV measurements.In this paper we present the results of our observa-tional campaign. We describe our multi-site observationsand RV measurements in Sections 2 and 3, respectively.We then present newly computed stellar parameters inSection 4. In Section 5 we describe the orbit fitting pro- cess and present our improved orbital solution. We alsopresent an upper mass limit for HD 76920 b in Section 6,followed by a discussion of our findings in Section 7.
Between January and March 2018, we acquired 63 ob-servations of HD 76920 using four different instruments.Firstly, 39 were taken at the University of CanterburyMt John Observatory (UCMJO) in Lake Tekapo, NewZealand, using the 1-m McLellan telescope in conjunc-tion with the HERCULES spectrograph (Hearnshawet al., 2002). Of these, 19 were taken with a 100- µ mcore-diameter fibre (’fibre 1’), corresponding to a resolv-ing power of R ∼
41 000, and another 20 were takenwith a different 100- µ m core-diameter fibre with a 50- µ mmicro-slit attached to its end (’fibre 3’), correspondingto a resolving power of R ∼
70 000. These observationsare referred to below as MJ1 and MJ3, respectively.A further 8 observations were obtained with the CH-IRON spectrograph (Tokovinin et al., 2013) attachedto the 1.5-m telescope at Cerro Tololo Inter-AmericanObservatory (CTIO) in Chile. These new spectra wereobtained using the ’slit mode’, which delivers a resolvingpower of R ∼
95 000 and a total system efficiency of ∼ . ± . ◦ C) is placed in the light path for wavelengthcalibration and for modelling of the instrumental profile.Finally, we also obtained 15 spectra using FIDEOS(Vanzi et al., 2018) and one new spectrum using FEROS(Kaufer et al., 1999). These two high-resolution ( R ∼
43 000 and R ∼
48 000, respectively) spectrographs arelocated at La Silla Observatory in Chile, and are at-tached to the ESO 1-m and 2.2-m telescopes, respec-tively. In addition, they are both fed by multiple opticalfibres, allowing a simultaneous ThAr wavelength cali-bration during the science exposure for precision radialvelocities.
Raw-reduction of the HERCULES observations was per-formed with the latest version (v5.2.9) of the HER-CULES Reduction Software Package (
HRSP ; Skuljan,2004) and the pipeline described in Bergmann (2015).From the reduced spectra we derived radial velocitiesusing our version of the
AUSTRAL
Doppler code describedby Endl et al. (2000). We used a high-S/N, iodine-freespectrum of the K1III star ν Octantis as a template(Ramm et al., 2016). While this setup has proven todeliver long-term RV precisions of about 4 . − (withshort-term precision of (cid:46) − ) for bright solar-typestars (Bergmann, 2015; Bergmann et al., 2015), the etailed analysis of HD 76920 betailed analysis of HD 76920 b
Doppler code describedby Endl et al. (2000). We used a high-S/N, iodine-freespectrum of the K1III star ν Octantis as a template(Ramm et al., 2016). While this setup has proven todeliver long-term RV precisions of about 4 . − (withshort-term precision of (cid:46) − ) for bright solar-typestars (Bergmann, 2015; Bergmann et al., 2015), the etailed analysis of HD 76920 betailed analysis of HD 76920 b V = 7 .
8) combined withpoor seeing conditions for a majority of the nights re-sulted in single-shot uncertainties of typically 14 . − for the higher-resolution fibre, and 16 . − for thelower-resolution fibre, which was preferred if the seeingwas worse than about 3 arcsec.The CHIRON spectra were reduced with the obser-vatory customized pipeline, which provides order byorder extracted and wavelength calibrated spectra forCHIRON users. The RVs were computed following themethod described in Jones et al. (2017). We note thatthe new CHIRON velocities have larger uncertaintiescompared to those in Wittenmyer et al. (2017b), as thenew spectra were obtained in ’slit mode’, rather thanin ’fibre-slicer mode’ ( R ∼
80 000). As a consequence,although the new data were taken at a slightly higherresolving power, the efficiency is drastically reduced (bya factor of ∼ CERES code (Brahm et al., 2017a), in-cluding a re-reduction of the 8 FEROS observations pub-lished in Wittenmyer et al. (2017b).
CERES performs astandard échelle spectra reduction including bias subtrac-tion, order tracing, optimal extraction, and wavelengthcalibration. The RVs for the two instruments were ob-tained from the cross-correlation function (CCF; Tonry& Davis, 1979). In the case of FIDEOS, the templateused for the CCF corresponds to a numerical binarymask as explained in Brahm et al. (2017a), while in thecase of FEROS data we use a high S/N template, whichis built by stacking all of the individual observed spectra(Jones et al., 2017). The final velocities are obtainedafter correcting for the night drift (from the simultane-ous calibration fibre) and barycentric velocity. Note thatthe newly computed FEROS RVs are superior to thosepresented in Wittenmyer et al. (2017b), where a muchlower S/N template was used. All radial velocities usedin this work and their corresponding uncertainties aresummarized in Table 5.
We computed the atmospheric parameters of HD 76920using the
ZASPE code (Brahm et al., 2017b). For thispurpose, we first combined all of the individual FEROSspectra. The co-added master spectrum is then com-pared to the ATLAS9 grid of stellar models (Castelli &Kurucz, 2004), in carefully selected regions that are moresensitive to changes in the atmospheric parameters. This
Figure 1.
HR diagram showing the position of HD 76920. Thesolid and dashed lines correspond to
PARSEC models with M ? =1 . (cid:12) , for [Fe / H] = − .
24 and − .
14 dex, respectively. procedure is performed iteratively until we obtain theeffective temperature ( T eff ), the surface gravity (log g ),the stellar metallicity ([Fe / H]), and the projected rota-tional velocity ( v sin i ). Using these derived parameters,we then computed the corresponding spectral energy dis-tribution (SED). For this we used the BT-Settl-CIFIST models (Baraffe et al., 2015). From the SED we com-puted synthetic magnitudes and we compared them tothe observed ones, which are listed in Table 1. Duringthis process the stellar radius ( R ? ) and the visual extinc-tion ( A V ) are derived, and thus the stellar luminosity( L ? ).Finally, to obtain the stellar mass and evolutionarystatus of HD 76920, we compared the derived atmo-spheric parameters to the PARSEC evolutionary models(Bressan et al., 2012). We found that HD 76920 has amass of M ? = 1 . ± . (cid:12) , and that it is ascendingthe red giant branch (RGB) phase. Figure 1 shows theposition of HD 76920 in the HR diagram. For compar-ison, two different PARSEC isomass evolutionary tracksare overplotted. As can be seen, HD 76920 is locatedmidway on its RGB ascent, and is reaching the lumi-nosity bump region. We note that no horizontal branchtrack (i.e. Helium burning core) crosses its position inthe HR diagram. All derived atmospheric and physicalparameters are listed in Table 1.
As an independent method, we used asteroseismologyto derive the stellar mass from the TESS (Ricker et al.,2015) photometric data. The TESS mission observedHD 76920 in the long cadence mode (30 min) in sec-tors 9, 10, and 11, adding up to a total of 3492 indi-vidual photometric measurements. To obtain the lightcurve we used the python tool tesseract (Rojas etal. in prep) using the autoap aperture. We removedthe most deviant outliers using the clean.py tool and
C. Bergmann et al.
Figure 2.
Normalized and detrended TESS photometry ofHD 76920. normalized each sector data independently by its me-dian value. We also detrended the light curve usinga linear fit, achieving a dispersion of 494.6 ppm. Fig-ure 2 shows the resulting normalized TESS photometryof HD 76920. Then we ran a generalized Lomb-Scargle(GLS, Zechmeister & Kürster (2009)) routine to ob-tain the power spectral density (PSD) and search forasteroseismic power excess in order to measure ν max and ∆ ν . We also corrected the background using a verywide gaussian profile kernel. After this correction wefollowed the method presented in Jones et al. (2018),which consists of convolving a gaussian profile with a σ = 12 µ Hz kernel around the power excess in orderto find the peak that corresponds to ν max . To obtain∆ ν we convolved a gaussian profile with a σ = 1 µ Hzkernel and we ran an autocorrelation routine. Using thisprocedure, we obtained ν max = 54 . ± . µ Hz and∆ ν = 5 . ± . µ Hz. From these values, and followingthe scaling relations presented in Kjeldsen & Bedding(1995), we obtained a mass of M ? = 1 . ± .
17 M (cid:12) anda radius R ? = 9 . ± .
63 R (cid:12) . The corresponding 1- σ error bars were obtained from a bootstrap analysis. Theasteroseismic mass and radius are in reasonably goodagreement with the spectroscopic values. Wittenmyer et al. (2017b) published 37 RVs of HD 76920obtained with three different spectrographs. Of these, 17were taken with UCLES (Diego et al., 1990) installed atthe 3.9-m Anglo-Australian Telescope (AAT), 12 weretaken with CHIRON at the 1.5-m telescope at CTIO,and 8 were taken with FEROS installed at the 2.2-mtelescope at La Silla.We combined our 63 new RV measurements withthe 12 re-reduced CHIRON RVs, the 8 newly reducedFEROS RVs, and the remaining 17 UCLES RVs fromWittenmyer et al. (2017b), and fitted a single Keplerianmodel to the combined data set consisting of a total of100 RVs. We used the emcee
Table 1
Stellar parameters of HD 76920
Parameter Value Method/SourceB [mag] 8.83 ± ± ± ± ± ± ± ± ± T eff [K] 4664 ± ZASPE log g [cm s − ] 2.71 ± ZASPE + Gaia[Fe / H] [dex] -0.19 ± ZASPE v sin i [km s − ] 2.5 ± ZASPE R ? [R (cid:12) ] 8 . ± . ZASPE + Gaia9 . ± .
63 Asteroseis. + TESS L ? [L (cid:12) ] 29 . +1 . − . ZASPE + Gaia M ? [M (cid:12) ] 1 . ± . PARSEC . ± .
17 Asteroseis. + TESSEnsemble sampler (Goodman & Weare, 2010), to obtainthe best-fit parameters. We used logarithmic priors for P , T , and K , i.e. we fit in terms of log P , log T , andlog K , and used uniform priors for all other parameters .We deployed 32 walkers and ran 3 000 steps for the firstburn-in phase until the walkers had explored the param-eter space sufficiently. At the end of the first burn-inphase, walkers are re-sampled around the most probableposition to reject bad samplings. We then continuedwith a second burn-in phase for another 3 000 steps. Allparameters have clearly converged after the second burn-in phase. Finally, we collected the samples from the last10 000 steps to calculate the maximum-likelihood set ofparameters and estimate the uncertainties. The randomzero-point offsets between the different instrumental se-tups were included as additional free parameters in thefitting process. For consistency with the work of Wit-tenmyer et al. (2017b), we also added 7 m s − of stellarjitter in quadrature to the error bars, as is appropri-ate for this type of star (Kjeldsen & Bedding, 1995), For T , which is technically allowed to assume negative values,this choice of parameterization introduces an unintentional, butweak informative prior on the parameter. However, as the occur-rence of T is periodic in uniform space, if fitted with a uniformprior, the posterior distribution may look bi-modal if the initialvalue is not optimal. Having a logarithmic prior makes the walkersconverge to the optimal value quickly, as a linear change in log( T )results in an exponential change in T . Because T is periodic, onepositive solution is enough to derive all other solutions. etailed analysis of HD 76920 betailed analysis of HD 76920 b
17 Asteroseis. + TESSEnsemble sampler (Goodman & Weare, 2010), to obtainthe best-fit parameters. We used logarithmic priors for P , T , and K , i.e. we fit in terms of log P , log T , andlog K , and used uniform priors for all other parameters .We deployed 32 walkers and ran 3 000 steps for the firstburn-in phase until the walkers had explored the param-eter space sufficiently. At the end of the first burn-inphase, walkers are re-sampled around the most probableposition to reject bad samplings. We then continuedwith a second burn-in phase for another 3 000 steps. Allparameters have clearly converged after the second burn-in phase. Finally, we collected the samples from the last10 000 steps to calculate the maximum-likelihood set ofparameters and estimate the uncertainties. The randomzero-point offsets between the different instrumental se-tups were included as additional free parameters in thefitting process. For consistency with the work of Wit-tenmyer et al. (2017b), we also added 7 m s − of stellarjitter in quadrature to the error bars, as is appropri-ate for this type of star (Kjeldsen & Bedding, 1995), For T , which is technically allowed to assume negative values,this choice of parameterization introduces an unintentional, butweak informative prior on the parameter. However, as the occur-rence of T is periodic in uniform space, if fitted with a uniformprior, the posterior distribution may look bi-modal if the initialvalue is not optimal. Having a logarithmic prior makes the walkersconverge to the optimal value quickly, as a linear change in log( T )results in an exponential change in T . Because T is periodic, onepositive solution is enough to derive all other solutions. etailed analysis of HD 76920 betailed analysis of HD 76920 b σ = q σ + σ . jitt . + σ . jitt . , (1)where σ int is the internal error as reported in Table 5, σ st . jitt . is the stellar jitter, and σ inst . jitt . is the instrumen-tal jitter. The RMS around the combined fit is 14 . − ,and the weighted RMS is 11 . − . Figure 3 shows alldata points together with our best-fit orbital solution,Fig. 4 shows a phase-folded version of that plot, andFig. 5 shows a close-up view of the RV peak near pe-riastron passage (again phase-folded with the orbitalperiod). A corner plot of the posterior probability dis-tributions of the parameters, generated from the last10 000 steps and demonstrating that all parameters arewell constrained, is shown in Fig. 12 in the appendix.In order to confirm our MCMC results, we also fitteda single Keplerian orbit using the IDL package RVLIN (Wright & Howard, 2009). Here we estimated the cor-responding uncertainties in the orbital parameters viathe bootstrapping algorithm from the
BOOTTRAN pack-age (Wang et al., 2012) using 100 000 steps. Becausethe extra instrumental jitter term cannot be set as afree parameter, we used the modified error bars givenby Eq. 1 as input to the fitting. While the uncertaintyestimates derived with the bootstrapping method aresomewhat larger, the two sets of best-fit parameters arein good agreement. Both best-fit single-Keplerian orbitalsolutions and the corresponding parameter uncertaintyestimates are summarized in Table 2.For the calculation of the semi-major axis and mini-mum mass of the planet we give the values using boththe spectroscopic stellar mass of M ∗ = 1 . ± . (cid:12) (see Sect. 4.1), as well as the asteroseismic mass of1 . ± .
17 M (cid:12) (see Sect. 4.2). For the rest of this workwe will adopt the spectroscopically derived stellar massand radius unless otherwise mentioned. Note that theuncertainty in the semi-major axis is completely dom-inated by the uncertainty in stellar mass, which to alesser extent also affects the uncertainty in the minimummass of the planet. Note that Wittenmyer et al. (2017b)used a mass of 1 . ± .
20 M (cid:12) , which has a comparable
Figure 3.
All available RV data together with our best-fit Kep-lerian orbital solution for HD 76920 b. The black points are theAAT data from Wittenmyer et al. (2017b), the red points are there-reduced CHIRON and FEROS data, and the blue points arethe CHIRON, FEROS, FIDEOS, and HERCULES data takenfor this work. Error bars represent the total uncertainty given byEq. 1. The RMS about this fit is 14 . − . relative error. This leads us to believe that their uncer-tainty estimate for m P sin i is underestimated and maynot include the uncertainty in stellar mass.We also searched for periodic signals in the residuals(Fig. 6), but did not find any significant power, as canbe seen in the GLS periodogram shown in Fig. 7. To better constrain the mass of HD 76920 b we appliedthe method presented in Jones et al. (2017) (which isbased on Sahlmann et al. 2011), to derive the orbitalinclination angle, and thus its dynamical mass. To dothis, we combined the orbital elements derived here withthe Hipparcos intermediate astrometric data (HIAD) ob-tained in van Leeuwen (2007b). This dataset comprisesa total of 106 one-dimensional abscissa measurements(see section 2.2.2 in van Leeuwen (2007a)), with a meanuncertainty of 1 . i and the lon-gitude of the ascending node Ω, while keeping fixed thefive parameters derived from the Keplerian fit ( P , e , ω , K , T ), and correcting for the 5 single-star param-eters solution ( α ? , δ , µ α ? , µ δ , $ ). Unfortunately, dueto the small astrometric signal, in part due to the rel-atively small parallax (correspondingly large distance)of HD 76920 ( $ = 5.41 ± C. Bergmann et al.
Table 2
Best-fit orbital solution and derived quantities for HD 76920 b. † A negative value for the square of the instrumental jitter indicates that the formal internal errors are overestimated andthat the fitted instrumental jitter needs to be subtracted in quadrature in Eq. 1.
Element emcee RVLIN
W17 P [d] 415 . +0 . − . . ± .
047 415 . ± . T [BJD − .
0] 4812 . +0 . − . . ± .
36 4813 . ± . e . ± . . ± . . ± . ω [ ◦ ] 1 . ± . . ± . . +1 . − . K [m s − ] 178 . +2 . − . . ± . . ± . a [AU] (spec) 1 . +0 . − . . ± .
103 1 . ± . m P sin i [M J ] (spec) 3 . +0 . − . . ± .
42 3 . +0 . − . a [AU] (seis) 1 . +0 . − . . ± .
074 — m P sin i [M J ] (seis) 3 . +0 . − . . ± .
33 —RMS about fit [m s − ] 14 .
11 13 .
79 9 . − ] 11 .
71 11 .
26 —zero point (AAT) [m s − ] 3 . +2 . − . . ± . − zero point (CHIRON) [m s − ] − . +1 . − . − . ± . − zero point (FEROS) [m s − ] − . ± . − . ± . − zero point (FIDEOS) [m s − ] − . +4 . − . − . ± . − zero point (MJ1) [m s − ] − . +6 . − . − . ± . − zero point (MJ3) [m s − ] − . +4 . − . − . ± . − σ inst.jitt. (AAT) [ m s − ] 324 . +128 . − . — — σ inst.jitt. (CHIRON) [ m s − ] 56 . +36 . − . — — σ inst.jitt. (FEROS) [ m s − ] 14 . +43 . − . — — σ inst.jitt. (FIDEOS) [ m s − ] 473 . +186 . − . — — σ inst.jitt. (MJ1) [ m s − ] † − . +34 . − . — — σ inst.jitt. (MJ3) [ m s − ] 153 . +110 . − . — — etailed analysis of HD 76920 betailed analysis of HD 76920 b
26 —zero point (AAT) [m s − ] 3 . +2 . − . . ± . − zero point (CHIRON) [m s − ] − . +1 . − . − . ± . − zero point (FEROS) [m s − ] − . ± . − . ± . − zero point (FIDEOS) [m s − ] − . +4 . − . − . ± . − zero point (MJ1) [m s − ] − . +6 . − . − . ± . − zero point (MJ3) [m s − ] − . +4 . − . − . ± . − σ inst.jitt. (AAT) [ m s − ] 324 . +128 . − . — — σ inst.jitt. (CHIRON) [ m s − ] 56 . +36 . − . — — σ inst.jitt. (FEROS) [ m s − ] 14 . +43 . − . — — σ inst.jitt. (FIDEOS) [ m s − ] 473 . +186 . − . — — σ inst.jitt. (MJ1) [ m s − ] † − . +34 . − . — — σ inst.jitt. (MJ3) [ m s − ] 153 . +110 . − . — — etailed analysis of HD 76920 betailed analysis of HD 76920 b Figure 4.
Same as Fig. 3, but phase-folded on the orbital pe-riod. Data from different instruments/setups are shown in dif-ferent colours: AAT — black, CHIRON — cyan, FEROS — green,FIDEOS — orange, MJ1 — red, MJ3 — blue.
Figure 5.
Close-up view of the RV peak near periastron passage.Colour-coding is the same as in Fig. 4.
Figure 6.
Residuals from the best-fit orbital solution. Error barsrepresent the total uncertainty given by Eq. 1. Colour-coding isthe same as in Fig. 4 and Fig. 5.
Figure 7.
GLS periodogram of the residuals from the best-fitorbital solution shown in Fig. 6.
This basically means that the orbital solution does notimprove the standard Hipparcos 5-parameter solution.However, we could still compute an upper mass limitfor the companion by injecting synthetic astrometric sig-nals induced by the companion at different inclinationangles (the smaller the value of i , the larger the astro-metric signal). Briefly, we generated synthetic datasets,keeping fixed the time of the individual epochs of theHIAD and computing the expected astrometric signalinduced by the companion by propagating the orbitalsolution to the epoch of the HIAD observations. Thiswas performed at decreasing inclination angles, whilerandomly selecting Ω in the range between 0–360 ◦ . Foreach synthetic dataset we added Gaussian distributeduncertainties with standard deviation equal to the me-dian abscissa error (1 . i , Ω) pairs. Figure 8 showsthe resulting ( i, Ω) values for a total of 100 syntheticdatasets, with an input inclination angle of 0 . ◦ , whichcorresponds to an angular semi-major axis of 1 . i -value we are capable ofrecovering most of the synthetic signals with relativelygood accuracy. We obtained a median of i = 0 . ◦ witha standard deviation of 0 . ◦ . We also note that only ineight cases we obtained a reduced χ -value larger thanfor the Hipparcos 5-parameter solution. For comparison,we repeated this analysis for an inclination angle of 0 . ◦ (corresponding to a = 1 . . ◦ , and already in 17% of the simulationsthe reduced χ of the synthetic solution is larger than forthe Hipparcos 5-parameter solution, showing how rapidlythe detectability drops with the astrometric amplitude.In fact, only at inclination values of i < . ◦ we obtainedreduced χ -values of the synthetic solution lower thanfor the Hipparcos 5-parameter model in >
99% of thecases. Based on this analysis, we might adopt a lower
C. Bergmann et al.
Figure 8.
Upper panel : Inclination angles recovered from the 100simulations, as a function of synthetic Ω values. The horizontaldashed line corresponds to the input value of i = 0.6 deg. Lowerpanel : Same as the upper panel, but this time for the Ω values.The dashed line corresponds to the one-to-one correlation. i -value of ∼ . . ◦ , which corresponds to an uppermass limit for HD 76920 b of ∼ . . (cid:12) . Finally, wenote that by considering an orbital inclination angle of90 ◦ (edge-on orbit), the astrometric semi-major axis isonly 20 µ as, which is comparable to the Gaia precision(Gaia Collaboration et al., 2016). It would thus be verychallenging to significantly detect such a small signaleven in the Gaia data. The method described in Section 6.1 does not place verystringent upper limits on the mass of the planet. It istherefore interesting to note that we can put a muchlower limit on the planet’s mass from simple geometry.While the inclination is unknown, we know that there isno preferred orientation of the orbital plane with respectto the line of sight, in other words the inclination hasan isotropic probability density function (pdf). Thiscorresponds to a pdf that is flat in cos i , which makes iteasy to draw from for a Monte Carlo simulation usingrandom inclination angles. We used a sample size of 10 and found a 3- σ (99.73% confidence) upper mass limit of42 . J , corresponding to an inclination of 4 . ◦ . Resultsfor a number of confidence levels are summarized inTable 3. We obtained 63 new radial velocity measurements ofHD 76920 from four different instruments around thetime of the predicted periastron passage. The unusuallyhigh eccentricity of HD 76920 b means that ∼
90% of thepeak-to-peak RV is traversed up and down in only ∼
14% of the orbital period, and the RV curve is approximatelyflat for the remaining ∼
360 days of the orbital period,making it difficult to determine precise orbital elementsfrom an observational point of view. However, in orderto constrain the orbital elements, it is essential to havegood sampling of the non-flat parts of the orbit where theRV changes rapidly over time. As the orbital phase nearperiastron passage was not very well covered in theirinitial work, Wittenmyer et al. (2017b) suggested follow-up observations be carried out during the next periastronpassage. Flexible scheduling of observing time duringperiastron passage on telescopes with high-resolutionspectrographs is an effective way of confirming the natureof highly eccentric planets and determining their orbitalproperties and minimum mass to high precision. Forexample, HD 37605 b with an eccentricity of e = 0 .
74, orHD 45350 b with an eccentricity of e = 0 .
76 have beenconfirmed in this way (Cochran et al., 2004; Endl et al.,2006).We were fortunate enough to be granted access to theHERCULES, CHIRON, FEROS, and FIDEOS spectro-graphs during that period, and hence managed to obtainnear-continuous coverage of the corresponding RV peak.In hindsight, getting enough telescope time either side ofthe predicted periastron passage was particularly impor-tant because the periastron passage actually happenedabout 3 days later than predicted, or about 3 . e = 0 .
88 and an orbital period of 415 . − , and asemi-major axis of 1 .
09 AU. The new orbital solution cor-responds to minimum mass of 3 . J for the planet thatis about 20% lower than that reported by Wittenmyeret al. (2017b), mainly owing to our new lower stellarmass estimate. Formally, the RMS of the residuals fromour fit is larger than in Wittenmyer et al. (2017b), partlybecause the individual uncertainties in and the scatterof the HERCULES data are about three times largercompared to the other instruments, and partly becausewe have effectively given different weights to the RVmeasurements during the fitting via the error treatmentdescribed in section 5. In particular, note that the RMSof the AAT residuals from our best fit is now 17 . − ,which is of course expected as they now carry less weightcompared to (Wittenmyer et al., 2017b). More impor- etailed analysis of HD 76920 betailed analysis of HD 76920 b
09 AU. The new orbital solution cor-responds to minimum mass of 3 . J for the planet thatis about 20% lower than that reported by Wittenmyeret al. (2017b), mainly owing to our new lower stellarmass estimate. Formally, the RMS of the residuals fromour fit is larger than in Wittenmyer et al. (2017b), partlybecause the individual uncertainties in and the scatterof the HERCULES data are about three times largercompared to the other instruments, and partly becausewe have effectively given different weights to the RVmeasurements during the fitting via the error treatmentdescribed in section 5. In particular, note that the RMSof the AAT residuals from our best fit is now 17 . − ,which is of course expected as they now carry less weightcompared to (Wittenmyer et al., 2017b). More impor- etailed analysis of HD 76920 betailed analysis of HD 76920 b Table 3
Geometric upper mass limits and corresponding inclinations for HD 76920 b for different confidence levels. confidence level upper mass limit [M J ] inclination [ ◦ ]99.73% 42.6 4.299% 22.2 8.195% 10.0 18.290% 7.2 25.8 Figure 9.
Comparison of the best-fit model RV curve from thiswork (solid grey line) with the one from Wittenmyer et al. (2017b)(dashed grey line). The periastron passage happened about 3 dayslater than predicted by the orbital elements from Wittenmyeret al. (2017b). tantly though, due to the much improved phase coveragenear periastron passage the uncertainties in the orbitalelements are now significantly reduced. Notably, the un-certainty in the orbital period was reduced by a factor of5, and the uncertainty in the eccentricity was reduced bymore than a factor of 3. In addition, we also estimatedan upper mass limit of 0 . . (cid:12) for the companionfrom HIPPARCOS astrometry, and a 3- σ upper masslimit of 42 . J from geometric considerations. Note that our value of the semi-major axis is slightlysmaller the one given by Wittenmyer et al. (2017b),while our eccentricity is slightly larger. However, thisseemingly small difference means that the planet actuallycomes to within 2 . ± . SSE stellarmodels (Hurley et al., 2000) with the asteroseismic massof 1 . (cid:12) and a Solar metallicity. We furthermore con-sider two values for the Reimers η mass loss parameter(Reimers, 1975): a standard value of η = 0 .
6, and anextreme case of η = 0 . η = 0 . η = 0 .
0, the orbitaleccentricity decays by only about 0 .
002 before the starengulfs the planet. With no stellar mass loss ( η = 0 . .
01 AU, while with massloss ( η = 0 .
6) the semi-major axis increases by 0 .
003 AU.The planet enters the stellar envelope when the star hasgrown to a little over 3 times its present radius, some50 Myr hence. Adopting the spectroscopic stellar mass of1 . (cid:12) does not qualitatively change the future evolution:the eccentricity decay is a little larger (0 . − . ∼
80 Myr),but there are still no large changes to the orbit expected.
Our updated orbital solution also leads to an even highertransit probability than the 10 .
3% reported in Witten-myer et al. (2017b). From the emcee best-fit orbitalelements listed in Table 2, it follows that at inferiorconjunction, which happens at a true anomaly of 88 . ◦ and 5 .
06 d after periastron passage, the star-planet sep-aration is 0 .
245 AU, and the azimuthal component ofthe orbital velocity is 60 . − . In order to calcu-late the probability, depth, and duration of a potentialtransit, we must first have an estimate of the planetaryradius. We used the mass-radius relationship for theJovian regime in form of the power law R pl ∝ m − . P C. Bergmann et al. as given by (Chen & Kipping, 2017), with which we cal-culated the planet’s radius to be 0 . R J . With that inhand, we calculated a relatively high transit probabilityof 16 . . .
013 %or 130 ppm, assuming an inclination of i = 90 ◦ andignoring limb darkening effects. While the large stellarradius increases the transit probability, unfortunatelyit also decreases the transit depth, requiring a levelof photometric precision that is extremely challengingfor ground-based transit searches, albeit perhaps notimpossible (e.g. Tregloan-Reed & Southworth, 2013).However, TESS can technically achieve the required pre-cision for a star of this magnitude (Ricker et al., 2015).HD 76920 has ecliptic coordinates of about λ = 202 . ◦ and β = − . ◦ , and therefore lies about five degreesoutside the southern TESS continuous viewing zone.However, by pure coincidence, this placed HD 76920 in-side the sector that TESS was observing at the time ofthe next potential transit (sector 9), which we predictedto occur approximately between JD2458559.43 ± ± . − .
16 March 2019).We list predicted mid-transit times, as well as ingressand egress times for potential future transits in Table 4.Unfortunately, due to it being an evolved star,HD 76920 presents a photometric variability at the 500ppm level, which is significantly larger than the expectedtransit depth. However, before searching for a potentialtransit signal, we corrected the light curve using a Gaus-sian process (GP), following a similar procedure to thatdescribed in Jones et al. (2019). The fit was performedwith the
Juliet code (Espinoza et al., 2019) using aMatérn kernel. To model the asteroseismic signal weused a Gaussian prior with mean equal to the periodcorresponding to ν max , as derived in section 4.2. Figure10 shows the TESS light curve and the GP model.Finally, to determine if the planet transits on the pre-dicted date, we compared the Bayesian evidence betweena transit model and a non-transit model. As we foundno significant difference, we assumed the simpler model,i.e. the non-transit model. The GP corrected light curvearound the expected transit time is shown in Figure 11. The origin of Hot Jupiters and/or highly eccentric plan-ets is usually explained via the Kozai-Lidov mecha-nism, whereby perturbations caused by a massive thirdbody (i.e. a stellar companion) can cause oscillationsbetween the planet’s eccentricity and inclination as longas its angular momentum component parallel to theorbital angular momentum of the two stars remains con-stant (Lidov, 1962; Kozai, 1962). However, as alreadynoted by Wittenmyer et al. (2017b), there are no indi-cations for additional massive companions in the RVdata. Also, while the Gaia DR2 catalogue (Gaia Collab-
Figure 10.
TESS light curve around the expected transit time,which is highlighted in light blue. The yellow line represents theGaussian process fit.
Figure 11.
GP corrected TESS light curve of HD 76920. Theexpected transit time is highlighted in light blue. oration et al., 2016, 2018) lists two faint ( G ∼
21 mag)stellar objects (Gaia DR2 IDs 5224124753994137984and 5224127812011479808) with compatible parallaxeswithin 5 arcmins from HD 76920, corresponding to aphysical separation of (cid:46)
55 000 AU at a distance of d = 184 pc (Bailer-Jones et al., 2018), their respectiveproper motions and B − R colours are very differentfrom the corresponding values for HD 76920, which rulesthem out as physically close companions. Furthermore,as also noted by Wittenmyer et al. (2017b), in the Kozai-Lidov scenario planets like HD 76920 b are readily beingengulfed by their host stars as they move up the red gi-ant branch (Frewen & Hansen, 2016), and, according tosimulations by Parker et al. (2017), free-floating planetsare almost exclusively captured into much wider orbits( a >
100 AU). This leaves planet-planet scattering asthe most likely explanation for the highly eccentric or-bit of HD 76920 b (e.g. Chatterjee et al., 2008). In thisscenario, a second planet of comparable mass wouldhave either been ejected from the system as the resultof a close encounter with HD 76920 b, or at least pushed etailed analysis of HD 76920 betailed analysis of HD 76920 b
100 AU). This leaves planet-planet scattering asthe most likely explanation for the highly eccentric or-bit of HD 76920 b (e.g. Chatterjee et al., 2008). In thisscenario, a second planet of comparable mass wouldhave either been ejected from the system as the resultof a close encounter with HD 76920 b, or at least pushed etailed analysis of HD 76920 betailed analysis of HD 76920 b Table 4
Predicted windows for potential past and future transits of HD 76920 b. ingress mid-transit egress UT date (mid)[JD - 2400000.0]58559 . ± .
63 58560 . ± .
54 58561 . ± .
63 18 Mar 201958975 . ± .
66 58976 . ± .
58 58977 . ± .
66 06 May 202059391 . ± .
68 59392 . ± .
61 59393 . ± .
68 26 Jun 202159807 . ± .
71 59808 . ± .
64 59809 . ± .
71 16 Aug 202260222 . ± .
75 60224 . ± .
68 60225 . ± .
75 06 Oct 2023outwards into a long-period orbit that is beyond ourcurrent detection limits. A third option is that the sec-ond planet disappeared from the system because it wasthrown towards the star and engulfed by it.
The very high eccentricity of HD 76920 b not only makesit the most eccentric planet known to orbit an evolvedstar by some margin, but also puts it in fifth placeamongst all known exoplanets . Its eccentricity is onlysurpassed by HD 4113 A b ( e = 0 .
90) (Tamuz et al.,2008), HD 7449 A b ( e = 0 .
92) (Dumusque et al., 2011;Wittenmyer et al., 2019a), HD 80606 b ( e = 0 .
93) (Naefet al., 2001; Moutou et al., 2009), and HD 20782 b ( e =0 .
97) (Jones et al., 2006; O’Toole et al., 2009; Kane et al.,2016), all of which are gas giants orbiting solar-massmain-sequence stars.Several studies have highlighted the possibility thata RV curve produced by two low-eccentricity planetscan be misinterpreted as being caused by one planetwith medium to high eccentricity, especially for lowsignal-to-noise ratios
K/σ , poor sampling, and/or if thetwo planets are in resonant orbits (e.g. Shen & Turner,2008; Rodigas & Hinz, 2009; Anglada-Escudé et al.,2010; Wittenmyer et al., 2012, 2013, 2019a,b). However,given the large
K/σ ratio, the dense sampling we haveachieved around periastron passage, and the very higheccentricity (which is well outside the "danger zone" asidentified by Wittenmyer et al. (2019b), i.e. the rangeof eccentricities that can be most easily mimicked bytwo near-circular planets), we are very confident thatthe results presented in this paper remove any possiblyremaining doubts about the RV variations being causedby a single planetary companion in a highly eccentricorbit.
CB was supported by Australian Research Council DiscoveryGrant DP170103491. LV acknowledges support from http://exoplanet.eu (Schneider et al., 2011). Note that whenlast accessed on 31 January 2021, WASP-74 b was erroneouslylisted to have an eccentricity of 0.88, but it really is the limb-darkening coefficient (cid:15) that has this value (Luque et al., 2020). CONICYT through projects Fondecyt n. 1171364 and AnilloACT-1417. AZ is supported by CONICYT grant n. 2117053.SW thanks the Heising-Simons Foundation for their generoussupport. AJM acknowledges support from the Knut andAlice Wallenberg Foundation (project grant 2014.0017),the Swedish Research Council (starting grant 2017-04945),and the Walter Gyllenberg Foundation of the RoyalPhysiographic Society of Lund. RB acknowledges supportfrom FONDECYT Project 11200751, from CORFO projectN ◦ . This work has made useof data from the European Space Agency (ESA) mission Gaia ( ), processedby the Gaia
Data Processing and Analysis Consortium(DPAC, ). Funding for the DPAC has been provided bynational institutions, in particular the institutions participat-ing in the
Gaia
Multilateral Agreement. Finally, we wouldlike to thank the anonymous referee for their insightfulcomments that helped noticeably to improve this manuscript.
A RADIAL VELOCITY DATAB CORNER PLOT OF THE FITPARAMETERSREFERENCES
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Figure 12.
Corner plot of the posterior probability distributions of the 17 free parameters used in the emcee fitting. All numericalvalues shown are rounded to two decimal places. etailed analysis of HD 76920 betailed analysis of HD 76920 b
Corner plot of the posterior probability distributions of the 17 free parameters used in the emcee fitting. All numericalvalues shown are rounded to two decimal places. etailed analysis of HD 76920 betailed analysis of HD 76920 b Table 5
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