EDP Sciences
Free Access
Issue
A&A
Volume 617, September 2018
Article Number L2
Number of page(s) 11
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/201833584
Published online 12 September 2018

© ESO 2018

1. Introduction

Our knowledge of the formation mechanism and evolution of planets has developed by leaps and bounds since the first detection of an exoplanet by Mayor & Queloz (1995) around the main-sequence star 51 Peg. However, constraining the formation timescales, the location of planet formation, and the physical properties of such objects remains a challenge and to date has mostly been based on indirect arguments using measured properties of protoplanetary disks. What is really needed is a detection of planets around young stars still surrounded by a disk. Modern coronagraphic angular differential imaging surveys that utilize extreme adaptive optics, such as the SpHere INfrared survey for Exoplanets (SHINE; Chauvin et al. 2017), provide the necessary spatial resolution and sensitivity to find such young planetary systems.

In Keppler et al. (2018) we reported the first bona fide detection of a giant planet inside the gap of the transition disk around the star PDS 70 together with the characterization of its protoplanetary disk. PDS 70 is a K7-type 5.4 Myr young premain sequence member of the Upper Centaurus-Lupus group (Riaud et al. 2006; Pecaut & Mamajek 2016) at a distance of distance of 113.43 ± 0.52 pc (Gaia Collaboration 2016, 2018). Our determination of the stellar parameters are explained in detail in Appendix A. The planet was detected in five epochs with VLT/SPHERE (Beuzit et al. 2008), VLT/NaCo (Lenzen et al. 2003; Rousset et al. 2003), and Gemini/NICI (Chun et al. 2008) covering a wavelength range from H to L′ band. In this paper we present new deep K-band imaging and first YH spectroscopic data with SPHERE with the goal of putting constraints on the orbital parameters and properties of PDS 70 b.

2. Observations and data reduction

2.1. Observations

We observed PDS 70 during the SPHERE/SHINE GTO program on the night of February 24, 2018. The data were taken in the IRDIFS-EXT pupil tracking mode using the N_ALC_YJH_S (185 mas in diameter) apodized-Lyot coronagraph (Martinez et al. 2009; Carbillet et al. 2011). We used the IRDIS (Dohlen et al. 2008) dual-band imaging camera (Vigan et al. 2010) with the K1K2 narrow-band filter pair (λK1 = 2.110 ± 0.102 μm, λK2 = 2.251 ± 0.109 μm). A spectrum covering the spectral range from Y to H band (0.96–1.64 μm, Rλ = 30) was acquired simultaneously with the IFS integral field spectrograph (Claudi et al. 2008). We set the integration time for both detectors to 96 s and acquired a total time on target of almost 2.5 h. The total field rotation is 95.7°. During the course of observation the average coherence time was 7.7 ms and a Strehl ratio of 73% was measured at 1.6 μm, providing excellent observing conditions.

2.2. Data reduction

The IRDIS data were reduced as described in Keppler et al. (2018). The basic reduction steps consisted of bad-pixel correction, flat fielding, sky subtraction, distortion correction (Maire et al. 2016), and frame registration.

The IFS data were reduced with the SPHERE Data Center pipeline (Delorme et al. 2017), which uses the Data Reduction and Handling software (v0.15.0, Pavlov et al. 2008) and additional IDL routines for the IFS data reduction (Mesa et al. 2015). The modeling and subtraction of the stellar speckle pattern for both the IRDIS and IFS data set were performed with a smart Principal Component Analysis (sPCA) algorithm based on Absil et al. (2013) using the same setup as described in Keppler et al. (2018). Figure 1 shows the high-quality IRDIS combined K1K2 image of PDS 70. The outer disk and the planetary companion inside the gap are clearly visible. In addition, there are several disk related features present, which are described in Appendix B. For this image the data were processed with a classical ADI reduction technique (Marois et al. 2006) to minimize self-subtraction of the disk. The extraction of astrometric and contrast values was performed by injecting negative point source signals into the raw data (using the unsaturated flux measurements of PDS 70) which were varied in contrast and position based on a predefined grid created from a first initial estimate of the planet’s contrast and position. For every parameter combination of the inserted negative planet the data were reduced with the same sPCA setup (maximum of 20 modes, protection angle of 0.75 × FWHM) and a χ2 value within a segment of 2 × FWHM and 4 × FWHM around the planet’s position was computed. Following Olofsson et al. (2016), the marginalized posterior probability distributions for each parameter was computed to derive final contrast and astrometric values and their corresponding uncertainties (the uncertainties correspond to the 68% confidence interval). For an independent confirmation of the extracted astrometry and photometry we used SpeCal (Galicher et al. 2018) and find the values in good agreement with each other within 1σ uncertainty.

thumbnail Fig. 1

IRDIS combined K1K2 image of PDS 70 using classical ADI reduction technique showing the planet inside the gap of the disk around PDS 70. The central part of the image is masked out for better display. North is up, East is to the left.

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2.3. Conversion of the planet contrasts to physical fluxes

The measured contrasts of PDS 70 b from all data sets (SPHERE, NaCo, and NICI) were converted to physical fluxes following the approach used in Vigan et al. (2016) and Samland et al. (2017), who used a synthetic spectrum calibrated by the stellar SED to convert the measured planet contrasts at specific wavelengths to physical fluxes. In our case, instead of a synthetic spectrum, which does not account for any (near-)infrared excess, we made use of the flux calibrated spectrum of PDS 70 from the SpeX spectrograph (Rayner et al. 2003), which is presented in Long et al. (2018). The spectrum Long et al. (2018). The spectrum covers a wavelength the entire IFS and IRDIS data set. To obtain flux values for our data sets taken in L′ band at 3.8 μm, we modeled the stellar SED with simple blackbodies to account for the observed infrared excess (Hashimoto et al. 2012; Dong et al. 2012). The final SED of the planet is shown in Fig. 2. The IFS SED of the planet is shown in Fig. 2. The IFS spectrum has a steep slope and displays a few features only, mainly water values are listed in Table C.1.

thumbnail Fig. 2

Spectral energy distribution of PDS 70 b as a function of wavelength constructed from Y- to H-band IFS spectra (orange points), IRDIS H2H3 (first epoch in dark blue, second epoch in light blue), and K1K2 (first epoch in dark green, second epoch in light green), NaCo (red), and NICI (orange) L′-band images. Plotted are the best fits for the seven model grids smoothed to the resolution of IFS.

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3. Results

3.1. Atmospheric modeling

We performed atmospheric simulations for PDS 70 b with the self-consistent 1D radiative-convective equilibrium tool petitCODE (Mollière et al. 2015, 2017), which resulted in three different grids of self-luminous cloudy planetary model atmospheres (see Table 1). These grids mainly differ in the treatment of clouds: petitCODE(1) does not consider scattering and includes only Mg2SiO4 cloud opacities; petitCODE(2) adds scattering; petit-CODE(3) contains four more cloud species including iron (Na2S, KCl, Mg2SiO4, Fe). Additionally, we also use the publicly available cloud-free petitCODE model grid (here called petitCODE(0); see Samland et al. 2017 for a detailed description of this grid) and the public PHOENIX BT-Settl grid (Allard 2014; Baraffe et al. 2015).

In order to compare the data to the petitCODE models we use the same tools as described in Samland et al. (2017), using the python MCMC code emcee (Foreman-Mackey et al. 2013) on N-dimensional model grids linearly interpolated at each evaluation. We assume a Gaussian likelihood function and take into account the spectral correlation of the IFS spectra (Greco & Brandt 2016). For an additional independent confirmation of the results obtained using petitCODE, we also used cloudy models from the Exo-REM code. The models and corresponding simulations are described in Charnay et al. (2018). Exo-REM assumes non-equilibrium chemistry, and silicate and iron clouds. For the model grid Exo-REM(1) the cloud particles are fixed at 20 μm and the vertical distribution takes into account vertical mixing (with a parametrized Kzz) and sedimentation. The Exo-REM(2) model uses a cloud distribution with a fixed sedimentation parameter fsed = 1 as in the model by Ackerman & Marley (2001) and petitCODE. Table 2 provides a compilation of the best-fit values and Fig. 2 shows the respective spectra. The values quoted correspond to the peak of the respective marginalized posterior probability distribution. The cloud-free models fail to represent the data and result in unphysical parameters. In contrast, the cloudy models provide a much better representation of the data. The results obtained by the petitCODE and Exo-REM models are consistent with each other. However, because of higher cloud opacities in the Exo-REM(2) models the log g values are less constrained and the water feature at 1.4 μm is less pronounced. Therefore, the resulting spectrum is closer to a blackbody and the resulting mass is less constrained. All these models indicate a relatively low temperature and surface gravity, but in some cases unrealistically high radii. Evolutionary models predict radii smaller than 2 RJ for planetary-mass objects (Mordasini et al. 2017). The radius can be pushed toward lower values if cloud opacities are removed, for example by removing iron (petitCODE(2)). However, a direct comparison for the same model parameters shows that this effect is very small. In petitCODE(1) this is shown in an exaggerated way by artificially removing scattering from the models, which leads to a significant reduction in radius. In general, we find a wide range of models that are compatible with the current data. The parts of the spectrum most suitable for ruling out models are the possible water absorption feature at 1.4 μm, and the spectral behavior at longer wavelengths (K to L′ band). Given the low signal-to-noise ratio in the water absorption feature and the large uncertainties in the L′ flux, it is very challenging to draw detailed physical conclusions about the nature of the object. We emphasize that other possible explanations for the larger than expected radii from evolutionary models include the recent accretion of material, additional reddening by circumplanetary material, and significant flux contributions from a potential circumplanetary disk. The third possibility is especially interesting in the light of possible features in our reduced images that could present spiral arm structures close to the planet (Fig. 1). There also appears to be an increase in HCO+ velocity dispersion close to the location of the planet in the ALMA data presented by Long et al. (2018).

Table 1.

Model grids used as input for MCMC exploration.

Table 2.

Parameters of best-fit models based on the grids listed in Table 1.

3.2. Orbital properties of PDS 70 b

The detailed results of the relative astrometry and photometry extracted from our observation from February 2018 are listed in Table C.1 together with the earlier epochs presented in Keppler et al. (2018). A first verification of the relative position of PDS 70 b with what we could expect for a stationary background contaminant is shown in Fig. 3. The latest SPHERE observations of February 24, 2018, confirms that the companion is comoving with the central star.

thumbnail Fig. 3

Multi-epoch astrometric measurements of PDS 70 b relative to PDS 70 (in blue). The plot also shows the predictions of the relative position under the hypothesis of a stationary background star for the same observing dates (in red). The gray dotted line shows one of the most likely orbital solutions based on our MCMC analysis (see text for details).

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To explore the possible orbital solutions of PDS 70 b, we applied the Markov chain Monte Carlo (MCMC) Bayesian analysis technique (Ford 2005, 2006) developed for β Pictoris (Chauvin et al. 2012), which is well suited for observations covering a small part of the whole orbit (for large orbital periods), as in the case of PDS 70 b. We did not initially consider any prior information on the inclination or longitude of ascending node to explore the full orbital parameter space of bound orbits. As described in Appendix A of Chauvin et al. (2012), we assume the prior distribution p0(x) to be uniform in x = (log P, e, cos i, Ω + ω, ωΩ, tp) and work on a modified parameter vector u(x) to avoid singularities in inclination and eccentricities and to improve the convergence of the Markov chains. The results of the MCMC analysis are shown in Fig. D.1, together with the results of a classical least-squares linear method (LSLM) flagged by the red line. It shows the standard statistical distribution matrix of the orbital elements a, e, i, Ω, ω, and tp, where a stands for the semi-major axis, e for the eccentricity, i for the inclination, Ω the longitude of the ascending node (measured from north), ω the argument of periastron, and tp the time for periastron passage. The results of our MCMC fit (Table D.1) indicate orbital distributions that peak at (the uncertainties correspond to the 68% confidence interval) for the semi-major axis, ° for the inclination, and eccentricities compatible with low-eccentric solutions as shown by the (a, e) correlation diagram. The elements Ω and ω are poorly constrained as low-eccentric solutions are favored and as pole-on solutions are also likely possible. Time at periastron is poorly constrained. The inclination distribution clearly favors retrograde orbits (i > 90°), which is compatible with the observed clockwise orbital motion resolved with SPHERE, NaCo, and NICI. To consider the disk geometry described by Keppler et al. (2018), we decided to explore the MCMC solutions compatible with a planet-disk coplanar configuration. We restrained the PDS 70 b solution set given by the MCMC to those solutions with orbital plane making a tilt angle less than 5° with respect to the disk midplane described by Keppler et al. (2018), i.e., i = 180° − 49.8° and PA = 158.6°. The results are shown in Fig. D.2 and Table D.1 together with the relative astrometry of PDS 70 b reported with 200 orbital solutions randomly drawn from our MCMC distributions in Fig. D.4. Figure D.3 shows the posterior distribution (out of Fig. D.1) of the tilt angle with the disk plane assuming idisk = 130.2° and PA = 158.6°. The distribution peaks around 50°, which remains consistent with a likely coplanar planet-disk configuration (or a moderate tilt angle) given the uncertainties. Given the small fraction of orbit covered by our observations, a broad range of orbital configurations are possible including coplanar solutions that could explain the formation of the broad disk cavity carved by PDS 70 b.

4. Summary and conclusions

We presented new deep SPHERE/IRDIS imaging data and, for the first time, SPHERE/IFS spectroscopy of the planetary mass companion orbiting inside the gap of the transition disk around PDS 70. With the accurate distance provided by Gaia DR2 we derived new estimates for the stellar mass (0.76 ± 0.02 M) and age (5.4 ± 1.0 Myr). Taking into account the data sets presented in Keppler et al. (2018) we achieve an orbital coverage of 6 yr. Our MCMC Bayesian analysis favors a circular ~22 au wide and a disk coplanar orbit, which translates to an orbital period of 118 yr. The new imaging data show rich details in the structure of the circumstellar disk. Several arcs and potential spirals can be identified (see Fig. B.1). Determining the way these features are connected to the presence of the planet is beyond the scope of this study. With the new IFS spectroscopic data and photometric measurements from previous IRDIS, NaCo, and NICI observations we were able to construct a SED of the planet covering a wavelength range of 0.96–3.8 μm. We computed three sets of cloudy model grids with the petitCODE and two models with Exo-REM with different treatment of clouds. These model grids and the BT-Settl grid were fitted to the planet’s SED. The atmospheric analysis clearly demonstrates that cloud-free models do not provide a good fit to the data. In contrast, we find a range of cloudy models that can describe the spectrophotometric data reasonably well, and result in a temperature range of 1000–1600 K and log g no larger than 3.5 dex. The radius varies significantly between 1.4 and 3.7 RJ based on the model assumptions and is in some cases higher than what we expect from evolutionary models. The planet’s mass derived from the best-fit values ranges from 2 to 17 MJ, which is similar to the masses derived from evolutionary models by Keppler et al. (2018). This paper provides the first step toward a comprehensive characterization of the orbit and atmospheric parameters of an embedded young planet. Observations with JWST and ALMA will provide additional constraints on the nature of this object, especially in the presence of a circumplanetary disk.


1

The parallax of PDS 70 is treated as an unknown parameter in our fit to the host star’s properties, together with mass, age and AV. However we imposed a parallax prior, using Gaia DR2, which strongly constrains the allowed distance values. As a result, the best-fit distance value reported here from the MCMC posterior draws is identical to the value provided by the Gaia collaboration.

Acknowledgments

SPHERE is an instrument designed and built by a consortium consisting of IPAG (Grenoble, France), MPIA (Heidelberg, Germany), LAM (Marseille, France), LESIA (Paris, France), Laboratoire Lagrange (Nice, France), INAF–Osservatorio di Padova (Italy), Observatoire de Genève (Switzerland), ETH Zurich (Switzerland), NOVA (Netherlands), ONERA (France) and ASTRON (Netherlands) in collaboration with ESO. SPHERE was funded by ESO, with additional contributions from CNRS (France), MPIA (Germany), INAF (Italy), FINES (Switzerland) and NOVA (Netherlands). SPHERE also received funding from the European Commission Sixth and Seventh Framework Programmes as part of the Optical Infrared Coordination Network for Astronomy (OPTICON) under grant number RII3-Ct-2004-001566 for FP6 (2004– 2008), grant number 226604 for FP7 (2009–2012) and grant number 312430 for FP7 (2013–2016). We also acknowledge financial support from the Programme National de Planétologie (PNP) and the Programme National de Physique Stellaire (PNPS) of CNRS-INSU in France. This work has also been supported by a grant from the French Labex OSUG@2020 (Investissements d’avenir–ANR10 LABX56). The project is supported by CNRS, by the Agence Nationale de la Recherche (ANR-14-CE33-0018). It has also been carried out within the frame of the National Centre for Competence in Research PlanetS supported by the Swiss National Science Foundation (SNSF). M.R.M., H.M.S., and S.D. are pleased to acknowledge the financial support of the SNSF. Finally, this work has made use of the the SPHERE Data Centre, jointly operated by OSUG/IPAG (Grenoble), PYTHEAS/LAM/CESAM (Marseille), OCA/Lagrange (Nice), and Observtoire de Paris/LESIA (Paris). We thank P. Delorme and E. Lagadec (SPHERE Data Centre) for their efficient help during the data reduction process. This work has made use of the SPHERE Data Centre, jointly operated by OSUG/IPAG (Grenoble), PYTHEAS/LAM/CeSAM (Marseille), OCA/Lagrange (Nice) and Observatoire de Paris/LESIA (Paris) and supported by a grant from Labex OSUG@2020 (Investissements d’avenir–ANR10 LABX56). A.M. acknowledges the support of the DFG priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets” (MU 4172/1-1). F.Me. and M.B. acknowledge funding from ANR of France under contract number ANR-16-CE31-0013. D.M. acknowledges support from the ESO-Government of Chile Joint Comittee program “Direct imaging and characterization of exoplanets”. J.L.B. acknowledges the support of the UK Science and Technology Facilities Council. A.Z. acknowledges support from the CONICYT+PAI/Convocatoria nacional subvención a la instalación en la academia, convocatoria 2017+Folio PAI77170087. We thank the anonymous referee for the constructive report on the manuscript. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has made use of NASA’s Astrophysics Data System Bibliographic Services of the SIMBAD database, operated at CDS, Strasbourg. Based on observations obtained at the Gemini Observatory (acquired through the Gemini Observatory Archive), which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil).

References

Appendix A: Determination of host star properties

We used a Markov chain Monte Carlo approach to find the posterior distribution for the PDS 70 host star parameters, adopting the emcee code (Foreman-Mackey et al. 2013). The unknown parameters are the stellar mass, age, extinction, and parallax1, and we assumed solar metallicity. The photometric measurements used for the fit, and the independently determined effective temperature Teff and radius are listed in Table A.1. We perform a simultaneous fit of all these observables. The uncertainties are treated as Gaussians and we assume no covariance between them.

Table A.1.

Stellar parameters of PDS 70.

We used a Gaussian prior from Gaia for the distance and a Gaussian prior with mean 0.01 mag and sigma 0.07 mag, truncated at AV = 0 mag, for the extinction (Pecaut & Mamajek 2016). Given AV, we computed the extinction in all the adopted bands by assuming a Cardelli et al. (1989) extinction law. We used a Chabrier (2003) initial mass function (IMF) prior on the mass and a uniform prior on the age. The stellar models adopted to compute the expected observables, given the fit parameters, are from the MIST project (Paxton et al. 2011, 2013, 2015; Dotter 2016; Choi et al. 2016). These models were extensively tested against young cluster data, and against pre-main sequence stars in multiple systems, with measured dynamical masses, and compared to other stellar evolutionary models (see Choi et al. 2016 for details). The result of the fit constrains the age of PDS 70 to 5.4 ± 1.0 Myr and its mass to 0.76 ± 0.02 M. The best-fit parameter values are given by the 50% quantile (the median) and their uncertainties are based on the 16% and 84% quantile of the marginalized posterior probability distribution. The stellar parameters are identical to the values used by Keppler et al. (2018). We note that the derived stellar age of PDS 70 is significantly younger than the median age derived for UCL with 16 ± 2 Myr and an age spread of 7 Myr by Pecaut & Mamajek (2016). For the computation of the median age Pecaut & Mamajek (2016) excluded K- and M-type stars for the reason of stellar activity which might bias the derived age. When the entire sample of stars is considered a median age of 9 ± 1 Myr is derived. The authors provide an age of 8 Myr for PDS 70 based on evolutionary models. Furthermore, the kinematic parallax for PDS 70 therein is larger by ~15% compared to the new Gaia parallax. Thus, the luminosity on which the age determination is based is underestimated and, subsequently, the age is overestimated.

Appendix B: Disk seen with IRDIS

Figure B.1 shows the IRDIS combined K1K2 image using classical ADI. The image shows the outer disk ring, with a radius of approximately 54 au, with the western (near) side being brighter than the eastern (far) side, as in Hashimoto et al. (2012) and Keppler et al. (2018). The image reveals a highly structured disk with several features: 1) a double ring structure along the west side, which is clearly pronounced along the northwest arc, and which is less clear but still visible along the southwest side; 2) a possible connection from the outer disk to the central region; 3,4) a possible spiral-shaped feature close to the coronagraph; and 5) two arc-like features in the gap on the southeast side of the central region. Whereas features 1 and 2 have already been tentatively seen in previous observations (see Figs. 5 and 9 in Keppler et al. 2018), our new and unprecedentedly deep data set allows us to identify extended structures well within the gap (features 3–5). Future observations at high resolution, i.e., with interferometry, will be needed to prove the existence and to investigate the nature of these features, which, if real, would provide an excellent laboratory for probing theoretical predictions of planetdisk interactions.

thumbnail Fig. B.1.

IRDIS combined K1K2 image of PDS 70 using classical ADI. To increase the dynamic range of the faint disk structures, the companion’s full intensity range is not shown. The black lines indicate the structures discussed in the above text. North is up, east is to the left.

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Appendix C: Astrometric and photometric detailed results

Table C.1.

Relative astrometry and photometry of PDS 70 b as derived from the sPCA reduction.

Appendix D: Markov chain Monte Carlo results

Table D.1.

MCMC solutions for the orbital parameters of PDS 70 b.

thumbnail Fig. D.1.

Results of the MCMC fit of the SPHERE, NaCo, and NICI combined astrometric data of PDS 70 b reported in terms of statistical distribution matrix of the orbital elements a, e, i, Ω, ω, and tp. The red line in the histograms and the black star in the correlation plots indicate the position of the best LSLM model obtained for comparison.

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thumbnail Fig. D.2.

Results of the MCMC fit of the SPHERE, NaCo, and NICI combined astrometric data of PDS 70 b reported in terms of statistical distribution matrix of the orbital elements a, e, i, Ω, ω, and tp. We restrained the PDS70 b solution set given by the MCMC to solutions with orbital plane making a tilt angle of less than 5° with respect to the disk midplane described by Keppler et al. (2018), i.e., i = 180°−49.8° and PA = 158.6°.

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thumbnail Fig. D.3.

Posterior distribution (from Fig. D.1) of the tilt angle. The distribution peaks around 50°, which remains consistent with a likely coplanar planet-disk configuration. The red line indicates the position of the best LSLM model obtained for comparison.

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thumbnail Fig. D.4.

Relative astrometry of PDS 70 b solutions drawn from the MCMC distribution for the coplanar planet-disk configuration. One of the most likely solutions from our MCMC analysis is shown as an illustration (in red).

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All Tables

Table 1.

Model grids used as input for MCMC exploration.

Table 2.

Parameters of best-fit models based on the grids listed in Table 1.

Table A.1.

Stellar parameters of PDS 70.

Table C.1.

Relative astrometry and photometry of PDS 70 b as derived from the sPCA reduction.

Table D.1.

MCMC solutions for the orbital parameters of PDS 70 b.

All Figures

thumbnail Fig. 1

IRDIS combined K1K2 image of PDS 70 using classical ADI reduction technique showing the planet inside the gap of the disk around PDS 70. The central part of the image is masked out for better display. North is up, East is to the left.

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In the text
thumbnail Fig. 2

Spectral energy distribution of PDS 70 b as a function of wavelength constructed from Y- to H-band IFS spectra (orange points), IRDIS H2H3 (first epoch in dark blue, second epoch in light blue), and K1K2 (first epoch in dark green, second epoch in light green), NaCo (red), and NICI (orange) L′-band images. Plotted are the best fits for the seven model grids smoothed to the resolution of IFS.

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In the text
thumbnail Fig. 3

Multi-epoch astrometric measurements of PDS 70 b relative to PDS 70 (in blue). The plot also shows the predictions of the relative position under the hypothesis of a stationary background star for the same observing dates (in red). The gray dotted line shows one of the most likely orbital solutions based on our MCMC analysis (see text for details).

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In the text
thumbnail Fig. B.1.

IRDIS combined K1K2 image of PDS 70 using classical ADI. To increase the dynamic range of the faint disk structures, the companion’s full intensity range is not shown. The black lines indicate the structures discussed in the above text. North is up, east is to the left.

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In the text
thumbnail Fig. D.1.

Results of the MCMC fit of the SPHERE, NaCo, and NICI combined astrometric data of PDS 70 b reported in terms of statistical distribution matrix of the orbital elements a, e, i, Ω, ω, and tp. The red line in the histograms and the black star in the correlation plots indicate the position of the best LSLM model obtained for comparison.

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In the text
thumbnail Fig. D.2.

Results of the MCMC fit of the SPHERE, NaCo, and NICI combined astrometric data of PDS 70 b reported in terms of statistical distribution matrix of the orbital elements a, e, i, Ω, ω, and tp. We restrained the PDS70 b solution set given by the MCMC to solutions with orbital plane making a tilt angle of less than 5° with respect to the disk midplane described by Keppler et al. (2018), i.e., i = 180°−49.8° and PA = 158.6°.

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In the text
thumbnail Fig. D.3.

Posterior distribution (from Fig. D.1) of the tilt angle. The distribution peaks around 50°, which remains consistent with a likely coplanar planet-disk configuration. The red line indicates the position of the best LSLM model obtained for comparison.

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In the text
thumbnail Fig. D.4.

Relative astrometry of PDS 70 b solutions drawn from the MCMC distribution for the coplanar planet-disk configuration. One of the most likely solutions from our MCMC analysis is shown as an illustration (in red).

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In the text

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