Astronomy & Astrophysics manuscript no. output c ESO 2016 November 25, 2016

Direct imaging of a substellar companion to the host HD 4113 A ?

A. Cheetham1, D. Ségransan1, S. Peretti1, J.-B. Delisle1, J. Hagelberg2, 3, J-L. Beuzit2, T. Forveille2, M. Marmier1, S. Udry1, and F. Wildi1

1 Département d’Astronomie, Université de Genève, 51 chemin des Maillettes, 1290, Versoix, Switzerland e-mail: [email protected] 2 Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France 3 Institute for Astronomy, University of Hawai’i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA November 2016

ABSTRACT

Using high-contrast imaging with the SPHERE instrument at the VLT, we report the first images of the companion to the exoplanet host star HD 4113A, to date the coolest directly imaged companion orbiting a solar-type star. Its separation of 530 mas and H-band contrast of 13.00 mag correspond to a projected separation of 22 AU and an isochronal estimate of 46 7 MJ. The companion shows strong methane absorption, and through atmospheric model fitting we estimate a of log± g=5 and an effective temperature of 400 K. A comparison of its spectrum with observed T dwarfs indicates a late-T or Y spectral type. By combining the observed from the imaging data with 27 of radial velocities, we use orbital fitting to constrain its +2 orbital and physical parameters, as well as update those of the planet HD 4113A b. The data suggest a dynamical mass of 69 4MJand +0.05 − moderate eccentricity of 0.38 0.05 for the brown dwarf. Through dynamical simulations we show that the planet may undergo strong Lidov-Kozai cycles, raising the− possibility that it formed on a quasi-circular orbit, and gained its currently observed high eccentricity (e 0.9) through interactions with the brown dwarf. Follow-up observations combining radial velocities, direct imaging and Gaia astrometry∼ will be crucial to precisely constrain the dynamical mass of the brown dwarf and allow for in-depth comparison with evolutionary and atmospheric models. Key words. Planets and satellites: detection, Planet-star interactions, : brown dwarfs

1. Introduction In addition, a comoving stellar companion to HD 4113A was discovered by Mugrauer et al. (2014) at a much larger separation HD 4113A is a nearby G5 dwarf that hosts a giant planet with (49 arcsec, 2000 AU) and was identified as an early M dwarf = one of the highest known orbital eccentricities (e 0.9). The plan- using near-IR photometry. The low mass of HD 4113B and its etary companion, HD 4113A b, was first detected via radial ve- extremely long period cannot explain the observed RV drift. locity (RV) measurements by Tamuz et al. (2008) using the The authors also excluded the presence of any additional stellar CORALIE spectrograph on the 1.2 m Swiss telescope at La Silla companions between 190 and 6500 AU down to the hydrogen- Observatory, as part of an ambitious planet search survey of a burning mass limit. well-defined sample of solar-type stars (Udry et al. 2000). While these previous imaging observations significantly nar- One common explanation for the presence of such a high ec- rowed down the parameter space to detect the unseen compan- centricity is through Lidov-Kozai (Kozai 1962; Lidov 1962) in- ion, the most recent generation of extreme adaptive optics instru- teractions with a companion on a wider orbit. The RV measure- ments such as SPHERE (Beuzit et al. 2008) and GPI (Macintosh ments presented by Tamuz et al. (2008) also revealed a long-term et al. 2008) are able to obtain higher contrasts at smaller angular trend, indicative of such a companion with a much longer or- separations, opening the search to even lower . bital period. These data suggested a of 10 MJand In this paper we report the first direct images of the sus- minimum semi-major axis of 8 AU. Using this knowledge, we pected companion HD 4113C, confirming its presumed nature made several unsuccessful attempts to image this companion, as a brown dwarf. In addition we present 6 additional years of first, with the NACO instrument at the VLT, using H-band SDI observations that when combined with the imag- in 2006 and 2007 (Montagnier 2008), coronagraphy in 2008 and ing data, allow constraints to be placed on the mass and orbital non-coronagraphic L-band ADI in 2013 (Hagelberg 2014). A parameters of the brown dwarf and planetary companion. summary of the L-band ADI results is presented in Appendix The paper is organized as follows: In Section 2 we revisit A. These observations ruled out stellar companions between 0.2- the stellar parameters of HD 4113A+B, using the most recent 2.5 arcsec (8-100 AU), suggesting that the outer companion was available data to better constrain their mass and age. In Section likely a brown dwarf. 3 we summarize the observations and data analysis procedures ? Based on observations collected at the European Organisation for the radial velocity and high contrast imaging data. In Sec- for Astronomical Research in the Southern Hemisphere under ESO tion 4, we present the results of the imaging data analysis and programmes 097.C-0893(A), 077.C-0293(A), 279.C-5052(A), 081.C- derived companion properties, an overview of the results from 0653(A) and 091.C-0721(B) the combined orbital fitting, as well as the results of dynamical

Article number, page 1 of 16 A&A proofs: manuscript no. output simulations showing the interactions between the brown dwarf Table 1: Stellar Parameters of HD 4113 A & B and giant planet. We conclude in Section 5 with a summary of the results presented and their implications. Param units HD 4113A HD 4113B SpType G5V M0-1V 2. Stellar parameters V 7.880 0.013 12.70 0.02 J 6.672 ± 0.023 9.447 ±0.024 ± ± Following the recent Gaia Data Release 1 (Gaia Collaboration H 6.345 0.021 8.74 0.02 ± ± et al. 2016), we are able to refine the stellar parameters of K 6.289 0.021 8.539 0.021 ± ± HD 4113A+B. This data gives an improved parallax of π = B-V 0.716 0.003 - ± 24.0 0.2 mas, setting the star at a slightly closer distance to π [mas] 23.986 0.237 0.4312(syst) ± ± the Sun± than previously thought (d= 41.7 0.7 pc1). d [pc] 41.70 0.86 ± ± For HD 4113A, we combined the Gaia parallaxes with the MV 4.780 0.046 9.600 0.049 ± ± Hipparcos and 2MASS photometry (Skrutskie et al. 2006) to MJ 3.572 0.050 6.347 0.051 ± ± derive the absolute magnitudes listed in Table 1. T , log g and MH 3.274 0.045 5.631 0.045 eff ± ± [Fe/H] are taken from the spectroscopic analysis done in Tamuz MK 3.234 0.045 5.445 0.045 ± ± et al. (2008) while the v sini and the log R0 are derived from Teff [K] 5688 26 50(syst) 3833 HK ± ± the CORALIE-07 spectra following the approach of Santos et al. [Fe/H] [dex] +0.20 0.04 - ± (2002) and Lovis et al. (2011) and implemented in CORALIE by log g 4.40 0.05 4.76 0 ± Marmier (2014). The fundamental parameters of this metal rich log RHK -5.104 0.003 - star ([Fe/H]= 0.20 0.04) were derived using the Geneva stellar v sin i [km/s] 2.324± - ± +1.3 evolution models (Mowlavi et al. 2012). The interpolation in the Age [Gyr] 5.0 1.7 5(fixed) −+0.04 model grid was done through a Bayesian formalism using obser- MA [M ] 1.05 0.55 0.02 vational Gaussian priors on Teff, MV , log g and [Fe/H] (Marmier − +0.04 2014). We derived a mass of M = 1.05 0.02 M and an age of +1.3 − We also include 4 measurements from the CORAVEL spec- 5.0 1.7 Gyr. −While HD 4113B is likely to have similar metal enrichment trograph taken between May 1989 and July 1994. While these as HD 4113A, Delfosse et al. (2000) showed that the Mass- measurements have large uncertainties, the significant increase relation for M dwarfs in the near-infrared is only in time baseline helps to constrain the possible amplitude and marginally affected by . For this reason we use the period of the signal introduced by the long period companion Solar metallicity model grids of Baraffe et al. (2015) combined responsible for the RV drift. with the 2MASS and Sofi/ESO NTT near-infrared photometry (Mugrauer et al. 2014) to derive its stellar parameters. The in- 3.2. SPHERE high-contrast imaging terpolation in the model grid was done through a Bayesian for- malism using observational Gaussian priors on MJ, MH, MK HD 4113A was observed with SPHERE, the extreme adaptive and the H K . Through this approach we obtain optics system at the VLT (Beuzit et al. 2008) on 2016-07-20. − a of MB = 0.55M and an effective temperature of Observations were taken in IRDIFS mode, which allows the In-

Teff = 3833 K, in agreement with a M0-1V spectral type (Ra- tegral Field Spectrograph (IFS) and InfraRed Dual-band Imager jpurohit et al. 2013). All observed and derived stellar parameters and Spectrograph (IRDIS) modules to be used simultaneously. are given in Table 1. The IFS data cover a range of wavelengths from 0.96-1.34 µm with an average spectral resolution of 55.1. The IRDIS data were

taken in H2-H3 mode (λH2 = 1588.8µm, λH3 = 1667.1µm), de- 3. Observations and Data Reduction signed such that the H3 filter aligns with a methane absorption band. The conditions during the observations were good, with 3.1. Radial velocities stable wind and seeing, but with some intermittent clouds that may affect the photometry. Since the discovery of HD 4113A b by Tamuz et al. (2008), we The observing sequence consisted of 64 long (64 s) expo- have acquired more than 80 additional radial velocity measure- sure images taken with an apodized Lyot coronagraph (Soummer ments of HD 4113A, with the goal of better characterizing the et al. 2003) with a spot diameter of 185 mas. At the beginning long period and more massive companion responsible for the and end of the sequence, several exposures were taken with a observed radial velocity drift. The 210 measurements obtained waffle mode applied to the deformable mirror to measure the po- between October 1999 and September 2016 are shown in Fig. sition of the star behind the coronagraph. Several short exposure 1 with the corresponding Keplerian model for HD 4113A b and images were taken with an ND filter to estimate the stellar flux, the long term drift. During that period of time, CORALIE un- also at the beginning and end of the sequence. In addition, sev- derwent two upgrades that introduced small zero point RV off- eral long exposure sky frames were taken to estimate the back- sets (Ségransan et al. 2010). To account for these, we consider ground flux and help identify bad pixels on the detector. The the data as originating from three different instruments with un- total observing time was 100 mins, and included a maximum of known offsets: CORALIE-98, CORALIE-07 and CORALIE-14. 54 deg of field rotation between the coronagraphic frames. These values are then included in the orbital fit as additional pa- The SPHERE Data Reduction and Handling pipeline (Pavlov rameters. et al. 2008, v0.18.0) was used to perform the wavelength extrac- 1 A systematic error of 0.4312 mas - corresponding to the astromet- tion for the IFS data, turning the full-frame images of the lenslet ric excess noise measured by GAIA - was quadratically added to the spectra into image cubes. parallax error to absorb a suspected bias linked to the signature of The remainder of the data reduction and analysis procedure HD 4113A b in the GAIA data. was completed using the GRAPHIC pipeline (Hagelberg et al.

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ble throughout the observing sequence. Coronagraphic images were then centred to sub-pixel precision using an FFT-based al- gorithm. To reject frames with poor AO-correction, we used an algorithm that compares the flux in 4 annular quadrants close to the coronagraphic mask with the temporal mean. This was run independently for each IFS and IRDIS channel, resulting in a maximum of 2 rejected frames. An implementation of the Principal Component Analysis (PCA) based KLIP PSF subtraction algorithm (Soummer et al. 2012) was then run separately for images at each wavelength, and the resulting frames were derotated and median combined to produce a final PSF-subtracted image. The PCA algorithm was applied separately to annular sections of each image, and excluded images with small changes in parallactic angle to min- imize companion self-subtraction. The PCA-reduced IRDIS images are shown in Fig. 2. We clearly detect a companion, that we refer to as HD 4113C, and use its observed position to optimize and inform the remaining data analysis steps. An additional SDI reduction was performed for both the IFS and IRDIS datasets. For IRDIS, the images in the H2 filter were rescaled by the ratio of the wavelengths using an FFT-based ap- proach, and the H3 images taken simultaneously were then sub- tracted. Due to instrumental throughput and stellar flux differ- ences between the two channels, the values in the H3 images were scaled to have the same total flux in an annular region of the speckle halo centred on the edge of the AO-correction radius. The same PCA algorithm was then performed on the resulting Date [UTC] 19902000201020202030204020502060207020802090210021102120 images.

200 For each IFS image, the corresponding images in other

100 wavelength channels were rescaled by the ratio of the wave- lengths and flux-scaled using the same approach used for IRDIS. 0 A PSF reference was constructed from the median of these -100 rescaled images, and subtracted from the original image. Using ] s

/ -200

m the known position of the brown dwarf from the IRDIS reduc- [

V -300 tion, only wavelength channels where the companion position R ∆ -400 was shifted by 1 FWHM or more were considered to minimize

-500 self-subtraction. This was repeated for each image at each wave- length, before applying PCA. -600 An estimation of the noise as a function of radius from the -700 star was obtained from the standard deviation of the pixel values -800 50000 60000 70000 80000 90000 100000 measured in an annulus of width λ/D. The location of HD 4113C Date (BJD - 2,400,000.0) [d] was masked out for this calculation to avoid biasing the mea- surements. This was then converted to a contrast curve account- Fig. 1: Radial velocity measurements of HD 4113A taken with ing for the throughput of the PCA reduction and small sample CORALIE covering the time period from October 1999 to statistics (following the approach of Mawet et al. 2014). The 5σ September 2016. Four CORAVEL measurements from as early contrast curves obtained through this method are shown in Fig 3. as May 1989 are also included, extending the time baseline The position and relative flux of HD 4113C were mea- to 27 years. The top figure represents the observed CORALIE sured from the IRDIS data by subtracting a shifted and flux- RV time series with the eccentric orbit model of the giant scaled copy of the observed PSF from the final combined im- planet HD 4113A b as well as the long term drift correspond- age, and minimizing the residuals in a small (3λ/D) area. This ing to HD 4113 C. The middle figure shows a phase-folded was achieved using a nonlinear least-squares optimizer. A true representation of the RV orbit of HD 4113A b, while the bot- north offset of 1.75 0.08 deg and a plate scale of 12.255 tom figure shows the predicted and observed RVs for the or- 0.009 mas/pix were− used± to calculate the separation and position± bit of HD 4113C, after subtraction of the signal produced by angle of the companion, using the measurements presented in HD 4113A b Maire et al. (2016). To estimate the uncertainties on the fitted position and flux, a bootstrapping approach was taken where the fitting was per- formed to 500 images generated from the PCA-subtracted and 2016), with recent modifications to handle SPHERE data. The derotated frames through sampling with replacement. The scat- data were first sky subtracted, flat fielded and cleaned of bad ter of the best-fit values was taken as the uncertainty. In addi- pixels. The star position was measured from the mean of the tion, this approach was repeated for a range of PCA reductions images with the waffle mode applied, and assumed to be sta- by varying the number of modes, protection angle and annulus

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Fig. 3: The 5σ contrast obtained for the two IRDIS filters (H2, Fig. 5: A color-magnitude diagram showing the predicted H2- H3). The measured separation and contrast of the detection in H3 colors and H2 fluxes (relative to HD 4113C) for objects in the H2 band is marked with a cross. the SpeX Prism Library. The flux of HD 4113C and the 2σ upper limit on its H2-H3 color are shown with a red arrow. Its position is compatible with objects at the end of the T sequence, showing deep methane absorption indicative of T and Y dwarfs. width, and the scatter of these values was included in the final uncertainties. For the IFS data, a different approach was taken to mea- 4.2. Companion Properties sure the stellar flux, due to the low signal-to-noise ratio or non- detection of HD 4113C in many spectral channels. Aperture pho- To estimate the mass of HD 4113C, we can use stellar and plan- tometry was performed at the location measured from the IRDIS etary evolutionary models with the measured photometry. We data, using a circular aperture of size equal to the FWHM of the combined the BHAC15 (Baraffe et al. 2015) stellar isochrones PSF. The flux uncertainty for each IFS channel was estimated with the COND (Baraffe et al. 2003) substellar isochrones to from the scatter of similar measurements performed both in a predict the companion contrast as a function of age, temperature ring with a radius of 2 FWHM around HD 4113C, and at a range and mass in the IRDIS H2 and H3 filters. of position angles at the same separation. Using the predicted age and mass for the primary, the mea- sured H2 contrast of 13.00 mag suggests a mass of 46 7MJ. However, the isochrones predict a temperature of 840 90K± and ± 4. Results an H3 contrast of 14.1 mag, which is inconsistent with the strong methane absorption observed with IRDIS and our lower limit of 4.1. High-contrast imaging 14.6 mag. By compiling the H2-H3 colors and effective temper- atures from the isochrones at all ages, we find instead that the HD 4113C was detected at high significance in both IRDIS H2 upper limit on the H2-H3 color is consistent with a temperature and IRDIS SDI reductions, but was not recovered in the H3 filter, upper limit of 700 K. suggesting the presence of strong methane absorption. The mea- In order to estimate the spectral type of HD 4113C, we used sured relative photometry and astrometry are given in Table 2, the SpeX Prism library of near-IR spectra of brown dwarfs (Bur- while the IRDIS PSF-subtracted images are shown in Fig. 2. We gasser 2014) using the splat python package (Burgasser et al. adopt a lower limit on the contrast of 14.6 mag for the H3 filter, 2016). Each spectrum was flux calibrated to the distance of using the 2σ contrast curve at the location of the H2 detection. HD 4113. To compare the goodness of fit of each spectrum (Fk) In the IFS data utilizing PCA only, no significant detection to the observed spectrum ( f ), we use the Gk statistic used by was found in any individual wavelength channel or in the mean Cushing et al. (2008) and others, where each measurement is taken over wavelength. weighted by its spectral FWHM: After applying SDI to the IFS data, the companion is clearly n ! detected, with 13 of the wavelength channels showing an excess X fi CkFk,i Gk = wi − (1) of flux above 1.5σ significance at the location of the IRDIS de- σi tection. A weighted mean image is shown in Fig. 2. The data re- i=1 µ µ ff Pn duction for wavelengths below 1.02 m and above 1.33 m su er with the weights given by wi = ∆λi/ j=1 ∆λ j. Ck is a constant from considerably more residual noise in the SDI+PCA reduc- used to scale the flux of each spectrum, chosen to minimize Gk. tion, and are not included in the subsequent analysis. Each SpeX Prism spectrum was converted to the appropriate The measured contrast ratios from IFS and IRDIS were spectral resolution of each IFS measurement by convolution with converted to apparent flux measurements through multiplica- a Gaussian. The FWHM used for the convolution was assumed tion by a BT-NextGen spectral model (Allard et al. 2012) with to be 1.5 the separation between each wavelength channel. To × Teff=5700 K, [Fe/H]=0.3 dex and log g=4.5, close to the values predict the IRDIS fluxes, we used the transmission curves for the determined in Section 2. The model spectrum was flux-scaled H2 and H3 filters. using the distance and radius of HD 4113A. The extracted spec- Comparison with all objects with known distances in the trum is shown in Fig. 4. SpeX Prism library shows that HD 4113C is most compatible

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Fig. 2: The PSF-subtracted images from the IRDIS H2, H3 and SDI reductions, and a weighted combination of the IFS SDI images. Each IFS wavelength channel was weighted by the average flux predicted by the best fitting Morley et al. (2012) and Tremblin et al. (2015) models. The strong detection of the companion in H2 and the lack of a H3 counterpart indicates the presence of strong methane absorption. All images have the same scale and orientation.

Table 2: The measured astrometry and photometry of HD 4113C from the SPHERE observations.

Instrument Filter ρ (arcsec) θ (deg) Contrast (mag) IRDIS H2 0.5316 0.0015 39.22 0.20 13.00 0.14 IRDIS H3 ± ± >14.6± IRDIS H2-H3 0.5309 0.0016 39.06 0.18 13.28 0.10 ± ± ± with the coldest objects in the library, with spectral types of T8- dwarfs from Morley et al. (2012) and Tremblin et al. (2015) us- T9 providing the best fit. The absence of any Y dwarfs in the ing the same method. library prevents us from establishing a firm spectral type deter- The Morley et al. (2012) models include the effects of sul- mination, and we suggest only a conservative upper limit of T8. fide clouds at low temperatures and cover a range of effective Without including the Ck factor to scale the flux of the SpeX temperatures Teff = 400-1300 K and surface gravities log g = 4- Prism spectra, the individual flux values are marginally lower 5.5, with condensate sedimentation efficiency coefficients fSED than any object in the library, suggesting that it may be at the = 2-5. The Tremblin et al. (2015) models include the effects of T/Y transition. convection and non-equilibrium chemistry and cover a range of The best fits to the observed spectrum are given by the effective temperatures Teff = 200-1000 K and surface gravities objects UGPS J072227.51-054031.2 (Lucas et al. 2010) and log g = 4-5, with vertical mixing parameters log Kzz = 6-8. WISEP J045853.90+643452.6 Mainzer et al. (2011), a field For the Morley et al. (2012) models, lower temperature spec- dwarf of type T9 and a T8.5+T9 field binary respectively. These tra fit the observed values more closely, with the best fitting are the only objects in the SpeX Prism Library with spectral model being Teff=400 K, log g = 5.0, fSED=4. This effective tem- types later than T8. However, several objects with type T8 pro- perature is at the edge of the model grid, and so we interpret vide a similar fit to the data. the models as suggesting an upper limit T 400 K. The model eff ≤ Using the predicted H2 and H3 fluxes from the SpeX Prism spectra are not strongly affected by changes in fSED in this regime Library, we produced a color-magnitude diagram in Fig. 5. The of temperature and log g, and for all fSED values in the grid, the observed H2 flux is lower than that of any object in the Library, same effective temperature and surface gravity provide the best adding additional weight to the idea that it is at the T/Y transi- fit. tion. The 2σ upper limit on the H2-H3 color is consistent with When comparing the data with the Tremblin et al. (2015) spectral types T7 and later. model spectra, we find best fit parameters of Teff = 400 K, log g To further constrain the physical properties of HD 4113C, we = 4.8 and log Kzz = 6. With a lower minimum temperature for compared the observed SED to synthetic spectra for cool brown the grid, a clear Gk minimum is seen at 350-450 K. This suggests

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(a) The measured spectrum of HD 4113C extracted from the IFS and IRDIS images. While the companion is not detected with high significance in any individual IFS wavelength channels, the two significant peaks at 1.07 µm and 1.27 µm correspond well with the expected spectral features. The two best-fitting spectra from the SpeX Prism library are overplotted, with flux scaled to match HD 4113C. The predicted flux values for each datapoint are shown with crosses. The FWHM of the IRDIS filters are shown with grey bars.

(b) Same as Fig. 4a, this time showing the comparison between the observed spectrum and the best-fit spectra from the Morley et al. (2012) and Tremblin et al. (2015) models.

Fig. 4: Comparison of the observed spectrum of HD 4113C with similar ultracool dwarfs and brown dwarf atmospheric models.

that while the Morley et al. (2012) models could provide only an Center for (DACE)2 which performs a multiple Kep- upper limit on the effective temperature, the most likely value lerian adjustment to the data as described in Delisle et al. (2016). may be close to 400 K. It allows us to derive initial conditions for a combined analysis The best-fitting spectrum from each model grid is shown in of the direct imaging and RV data, performed within a Bayesian Fig. 4b. Both reproduce well the H2-H3 color from the IRDIS formalism. The observed signal is modeled with two Kepleri- data, as well as the relative flux between the H-band and J band ans and four RV offsets (one offset for each RV instrument). We peaks. However, the two models show significant differences at model the noise using a nuisance parameter for each RV instru- shorter wavelengths. This region is not well constrained by the ment (Gregory 2005). These nuisance parameters are quadrati- IFS data, and more accurate Y band photometry will be useful to cally added to the individual measurement errors. We combine gain insight into the physical processes that dominate the spec- the signal and the noise model into a likelihood function that is trum at short wavelengths. probed using emcee - a python implementation of the Affine In- variant Markov chain Monte Carlo (MCMC) Ensemble sampler (Foreman-Mackey et al. 2013; Goodman & Weare 2010). The 4.3. Orbit determination and dynamical masses 2 The DACE platform is available at http://dace.unige.ch while the on- The initial RV data analysis presented in this paper was accom- line tools to analyse radial velocity data can be found in the section plished using a set of online tools hosted by the Data & Analysis Observations=>Radial Velocities

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2020 400 2010 2030 2110

2040

200 ] s 2050 a m [

δ 2100 ∆ 0

2060 21/09/1992 02/02/2097

-200 2070 2090 2080

-400 800 600 400 200 0 -200 -400 ∆α∗ [mas]

Fig. 6: Observed and predicted orbital motion of HD 4113 AC, shown as the relative projected position of HD 4113C. A series of orbits are plotted, drawn from the posterior distribution of the combined RV+imaging analysis.

full technical description of the combined data analysis is given Fig. 7: Marginalized 1-D and 2-D posterior distributions of in Appendix B and we focus here on the data analysis results. the Mass vs. Semi-Major axis corresponding to the global fit of the RV and direct imaging models. Confidence intervals at Despite the single direct imaging measurement and the par- 2.275%, 15.85%, 50.0%, 84.15%, 97.725% are over-plotted on tial RV coverage of the orbit, we are able to bring significant the 1-D posterior distributions while the median 1 σ value constraints on the geometry of the orbit and mass of HD 4113 C. are given on top of each 1-D distribution. 1, 2 and± 3 σ contour Indeed, the observed RV drift displays a large peak-to-peak value 1 levels are over-plotted on the 2-D posterior distribution. of 300 ms− over the 17 yrs of CORALIE observations, setting a clear minimum mass boundary for the brown dwarf. In addi- tion, the observed RV signal departs from the pure sine function planetary orbits. In the case of HD 4113A b, this idea was raised which betrays the presence of a significant eccentricity. To fur- at the time of its discovery by Tamuz et al. (2008). The observed ther constrain the geometry of the system, we set an upper mass radial velocity drift was evidence of a high mass, long-period limit for HD 4113 C of M < 72 M . This conservative upper C J companion that would naturally interact gravitationally with the limit corresponds to the stellar/brown dwarf boundary, since the planet. presence of strong methane absorption is incompatible with a stellar-mass companion. Using the orbital parameters derived from the new radial ve- locity and direct imaging measurements, we are able to test the Within this framework and based on the MCMC posterior Lidov-Kozai scenario in more detail. We adopt the best-fitting distribution, we are able to set confidence intervals for the orbital parameters for the planet and brown dwarf (see Table 3) in or- elements and physical parameters of HD 4113 C. At the 1σ level, der to have a coherent set of orbital elements. The only parame- the period ranges between 85 yr and 121 yr, its semi-major axis, ters that are unconstrained by the observations are the inclination between 20.0 AU and 25.4 AU while its mass is in the range (i ) and the longitude of the ascending node (Ω ) of the planet. 65.3-71.1 M . The eccentricity is well constrained with a value Ab Ab J We thus let these parameters vary. We also let the mass of the of e=0.38 0.05. ± planet (MAb) vary accordingly with its inclination, since the ra- The results of the MCMC analysis are summarized in Ta- dial velocity data constrain only its minimum mass (MAb sin iAb). ble 3 and the corresponding orbits are shown in Fig. 6. A mass- We run a set of 1681 (41 41) simulations of the system us- separation diagram based on the marginalized 2D posterior dis- ing the GENGA integrator× (see Grimm & Stadel 2014), with tribution is represented in Fig 7. iAb varying in the range [5◦, 175◦](MAb [1.55 17.84]), and With only a single imaging , we are unable to distin- ∈ − ∆Ω = ΩAb ΩC varying in the range [ 180◦, 180◦]. The time guish between two families of physically equivalent solutions step is set to− 0.001 yr and the orbits are− integrated for 1 Myr, for the inclination i and longitude of ascending node Ω, which including the effects of General Relativity. correspond to the orbit and its reflection about the line between Figure 8 shows the initial mutual inclination between the or- HD 4113A and HD 4113C. One group is shown in Fig. 6 and Ta- bits of the planet and brown dwarf (iAb C), plotted as a function ble 3, but solutions with 180 i and Ω + 180 are equally valid − − of the two unknown parameters. Figure 9 shows the minimum given the available data. value reached by the planet’s eccentricity during the whole sim- ulation. Unstable integrations are stopped and drawn in white 4.4. Dynamics and formation in Fig. 9. In particular, the simulations in which the planet ap- proaches the star by less than 0.005 AU (close to one stellar As seen in Table 3, the eccentricity of HD 4113Ab is particularly radius) are stopped. Depending on the initial parameters (iAb, high (eAb 0.9). The Lidov-Kozai mechanism (see Lidov 1962; ΩAb), strong Lidov-Kozai cycles are observed and the eccentric- Kozai 1962)≈ has often been proposed to explain highly eccentric ity of the planet can reach very low values (blue points in Fig. 9).

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Table 3: Orbital elements and companion properties derived from the posterior distribution. The mean longitude, λ0 = M0 + ω + Ω, is given at the reference epoch of BJD=55500.0 d.

HD 4113A b HD 4113C Parameter Units Mode (Err-Err+) Median (Err-Err+) CI(2.275) CI(97.725) P 526.573 d (-0.016,+0.03) 101 yr ( -16,+20) 73 140 1 K [ms− ] 91.3 (-1.3,+2.2) 370 (-40, +40) 290 450 e 0.897 (-0.003,+0.004) 0.38 (-0.05, 0.05) 0.28 0.47 ω [deg] -47.0 ( -1.2, 1.1) 194 ( -14, 13) 169 218 T0 [d] 55642.59 ( -0.09, 0.15) 48200 ( -800, 800) 46800 49800 Ω [deg] -- 55 ( -6, 9) 45 71 λ0 [deg] 50.5 ( -1.2, 1.1) -37 ( -7, 8) -50 -22 i [deg] -- 64 ( -10, 10) 45 79 m. sin (i) [MJ] 1.66 ( -0.08, 0.08) 61 ( -6, 5) 48 69 m [MJ] -- 69 ( -4, 2) 61 72 ar [AU] 1.30 ( -0.03, 0.03) 23 ( -3, 3) 18 28

iAb C (deg) eAb,min − 0 20 40 60 80 100 120 140 160 180 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

17.84 17.84 160 160 3.52 3.52 140 140 2.11 2.11

120 ) 120 ) 1.67 1.67 Jup 100 Jup 100 M M ( ( (deg) (deg) 1.55 1.55 Ab

Ab 80

80 Ab Ab i i M 1.67 M 1.67 60 60 2.11 2.11 40 40 3.52 3.52 20 20 17.84 17.84 150 100 50 0 50 100 150 150 100 50 0 50 100 150 − − − − − − ∆Ω (deg) ∆Ω (deg)

Fig. 8: Initial mutual inclination between the planet and brown Fig. 9: Minimum value reached by the planet eccentricity during dwarf orbits (iAb C), as a function of the planet’s inclination the 1 Myr of integration (eAb,min), as a function of the planet’s (i ), and longitude− of the ascending node (∆Ω = Ω Ω ). initial inclination (i ), and longitude of the ascending node Ab Ab − C Ab (∆Ω = ΩAb ΩC). White points correspond to unstable simu- lations, that stopped− before 1 Myr. Figure 10 shows an example of a simulation where strong Lidov- Kozai cycles are observed. Thus, it is possible that the planet formed on a quasi-circular orbit and that the observed eccentric- ity (0.9) is the result of Lidov-Kozai oscillations with the ob- served brown dwarf. tion of the planet (see Wu & Murray 2003; Fabrycky & Tremaine From Fig. 9 we could derive constraints on the missing or- 2007; Correia et al. 2011). In this scenario, the planet initially bital elements of the planet (iAb, ΩAb) for the system to be stable forms at a larger distance to the star and with a quasi-circular (i.e. not located in a white region), and for the planet to have orbit. It then undergoes strong Lidov-Kozai oscillations, which formed with a low eccentricity (blue parts). We note that sev- brings the planet very close to the star at periastron. In addi- eral effects could modify the results shown in Fig. 9. Consider- tion to shrinking the planet orbit (decreasing semi-major axis), able uncertainties remain on several of the orbital parameters for tides (and general relativity) tend to damp the amplitude of the the brown dwarf, and changes in these orbital parameters would Kozai oscillations. The maximum eccentricity reached during a reflect on Fig. 9. Moreover, in some of the simulations shown Lidov-Kozai cycle does not change much, but the minimum ec- here, the eccentricity of the planet reaches very high values. In centricity increases. When the Lidov-Kozai amplitude is vanish- this case, the time step we use (0.001 yr) is not sufficiently small ing, the eccentricity is simply damped from a very high value, to correctly model the periastron passage, and some orbits that down to zero. If HD 4113A b is following this path, the ampli- are detected as unstable (white parts in Fig. 9) might be stable tude of the Lidov-Kozai cycles could have already been signifi- (and vice versa). In addition, in the very high eccentricity cases, cantly damped. Therefore, the minimum eccentricity reached by tides may play an important role. Indeed the combination of the the planet during a Lidov-Kozai cycle could be high, even if the Lidov-Kozai mechanism and tides can induce an inward migra- planet initially formed on a quasi-circular orbit.

Article number, page 8 of 16 A. Cheetham et al.: Direct imaging of a substellar companion to HD 4113 A

1.0 of brown dwarf spectra, we find that it is most consistent with the coldest objects in the library, indicating a spectral type of Ab T8 or later, with the best match coming from a T9 field dwarf. 0.8 However, the lack of Y-dwarf spectra for comparison prevents us C from establishing a firm spectral type, and we can suggest only a lower limit of >T8 based on available data. 0.6 Using the atmospheric models of Morley et al. (2012) and Tremblin et al. (2015), we find the observed spectrum is most e consistent with Teff = 400 K and a log g = 5. Such a low effective 0.4 temperature would make HD 4113C the coldest imaged compan- ion to a solar-type star. However, due to the large uncertainties on the spectrum obtained with IFS, more accurate photometry 0.2 covering a wider range of wavelengths is needed to further char- acterize HD 4113C, and to confirm the spectral type, effective temperature and surface gravity estimate. 0.0 We place constraints on the orbital and physical parameters of HD 4113C through orbital fitting to the radial velocity and 75 +2 imaging data. This suggests a mass of 69 4 MJ, and a moder- +0.05 − 70 ate eccentricity of 0.38 0.05. With longer time baselines for both the imaging and radial− velocity data, orbital fitting will provide 65 tighter constraints on the mass, and this system could act as a useful mass-luminosity benchmark for T/Y dwarfs. 60 While some parameters are strongly constrained by the MCMC, the observed posterior for the mass of HD 4113C shows (deg) 55 C an apparent underlying inconsistency between the input data. − / Ab As seen in Fig. 7, the predicted mass is at the stellar substellar i 50 boundary, while the spectrum obtained through direct imag- 45 ing shows an extremely cool temperature that would suggest a much lower mass. Performing the MCMC without the strong 40 prior on the mass of HD 4113C results in a maximum likeli- hood value slightly above 72 MJ. However, the observed spec- 35 trum clearly rules out high effective temperatures associated with 0.0 0.2 0.4 0.6 0.8 1.0 stellar masses. t (yr) 106 Several possible scenarios could have led to an overestimate × of the mass in the MCMC. The GAIA parallax may be system- Fig. 10: Example of temporal evolution of the eccentricities of atically biased by the signal introduced by HD 4113A b, espe- the planet and the brown dwarf (top) as well as their mutual in- cially if it had a low inclination and thus higher mass than might clination (bottom). The initial conditions are set using the best- be expected by its m sin i. Indeed the high reported excess noise in the GAIA Data Release 1 hints that this may be a contribut- fitting parameters (see Table 3), and i = 73◦ (M = 1.75 M ), Ab Ab J ing factor. An overestimate of the separation from the SPHERE and ∆Ω = 36◦. This corresponds to an initial mutual inclination imaging data (or an underestimate of its uncertainty) may also of about 39◦. The minimum value of the planet’s eccentricity is about 0.05, and is reached when the mutual inclination reaches have led to an overestimate of the inclination and thus the mass of HD 4113C. Alternatively, the presence of an additional com- about 71◦. panion could have biased the RV data to a higher m sin i value. For example, the long-term RV signal may be caused by an un- 5. Discussion and Conclusion seen planetary-mass companion at a smaller separation, while the imaged companion may be a longer period intermediate mass The HD 4113 system is a unique laboratory for studying a range brown dwarf that contributes only a linear drift to the observed of issues in stellar and substellar physics. The primary star, radial velocities. These scenarios could be tested through ad- HD 4113A, hosts a planetary companion on a highly eccentric ditional imaging epochs and radial velocity data, as well as a orbit. By fitting to 27 years of radial velocity data, we update the multiple-component fit to the GAIA data. orbital parameters from those presented at the time of its discov- Through dynamical simulations we show that the observed ery by Tamuz et al. (2008). In addition, we present high-contrast high eccentricity (e 0.9) of the giant planet HD 4113A b could imaging data that reveals the nature of a long period RV signal be the result of strong∼ Lidov-Kozai cycles caused by interac- as originating from a cool brown dwarf companion. tions with the orbit of the brown dwarf. For certain ranges of The imaging data shows that the brown dwarf has a con- the unknown orbital parameters iAb and ∆Ω, eccentricity oscilla- trast in the SPHERE H2 filter of 13.00 mag, and a deep methane tions of >0.8 are observed, typically with an oscillation period of absorption feature that causes it to have a H2-H3 color of > 104 105 yr. This raises the possibility that HD 4113A b formed 1.6 mag. Using the BHAC15 and COND isochrones, the ob- on an− initially quasi-circular orbit and subsequently underwent served contrast suggests a mass of 46 7 MJ. eccentricity excitation through interaction with HD 4113C. Fitting to the observed spectrum from± IFS and IRDIS allows However, further questions about the formation of us to place more stringent constraints on the effective temper- HD 4113A b remain. The brown dwarf companion would ature and spectral type, and to estimate the surface gravity of be expected to truncate the circumstellar disk of HD 4113A at HD 4113C. Through comparison with the SpeX Prism Library 1/2 - 1/3 of its semi-major axis (Artymowicz & Lubow 1994),

Article number, page 9 of 16 A&A proofs: manuscript no. output which corresponds to 7-11 AU on its present orbit. Forming a This research has benefitted from the SpeX Prism Spectral Libraries, maintained planetary companion in such an active dynamical system within by Adam Burgasser at http://pono.ucsd.edu/ adam/browndwarfs/spexprism a truncated disk may prove challenging. One open possibility is that HD 4113A b is on a highly in- clined orbit, with a much higher mass consistent with a stellar References formation pathway. From Fig. 9, we can see that such a configu- Allard, F., Homeier, D., & Freytag, B. 2012, Philosophical Transactions of the ration could be stable, with several high MAb regions lasting for Royal Society of London Series A, 370, 2765 the duration of the 1 Myr long simulation. Artymowicz, P. & Lubow, S. H. 1994, ApJ, 421, 651 Baraffe, I., Chabrier, G., Barman, T. S., Allard, F., & Hauschildt, P. H. 2003, An exciting prospect for further characterization of this sys- A&A, 402, 701 tem are the future Gaia data releases. The astrometric signal of Baraffe, I., Homeier, D., Allard, F., & Chabrier, G. 2015, A&A, 577, A42 the giant planet HD 4113A b should be detectable with Gaia, and Beuzit, J.-L., Feldt, M., Dohlen, K., et al. 2008, in Proc. SPIE, Vol. 7014 will give an accurate inclination measurement. The planet will Burgasser, A. J. 2014, in Astronomical Society of India Conference Series, introduce astrometric motion with a peak-to-peak amplitude of Vol. 11, Astronomical Society of India Conference Series Burgasser, A. J., Aganze, C., Escala, I., et al. 2016, in American Astronomical at least 0.05 mas. In addition, a long term drift corresponding to Society Meeting Abstracts, Vol. 227, American Astronomical Society Meet- the HD 4113A-C orbit should also be visible. Over the 5 ing Abstracts, 434.08 lifetime of Gaia, this will introduce a 6 mas drift in the position Correia, A. C. M., Laskar, J., Farago, F., & Boué, G. 2011, Celestial Mechanics of HD 4113A, with a maximum deviation of 0.13 mas from lin- and Dynamical Astronomy, 111, 105–130 Cushing, M. C., Marley, M. S., Saumon, D., et al. 2008, ApJ, 678, 1372 earity. Delfosse, X., Forveille, T., Ségransan, D., et al. 2000, A&A, 364, 217 The combination of Gaia astrometry with future RV and Delisle, J.-B., Ségransan, D., Buchschacher, N., & Alesina, F. 2016, A&A, 590, imaging datasets will allow for much tighter constraints on the A134 Fabrycky, D. & Tremaine, S. 2007, ApJ, 669, 1298–1315 orbits and physical parameters of each component. Most criti- Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, cally, Gaia astrometry will give a first measurement of the un- 306 known orbital parameters of the planet. This will be crucial Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2016, ArXiv e-prints for studying the Lidov-Kozai interactions and stability of the [arXiv:1609.04172] system, by significantly reducing the parameter range to ex- Goodman, J. & Weare, J. 2010, COMM. APP. MATH. AND COMP. SCI., 5, 65 Gregory, P. C. 2005, Bayesian Logical Data Analysis for the Physical Sciences: plore and by resolving the degeneracy with the unknown planet A Comparative Approach with ‘Mathematica’ Support (Cambridge Univer- mass. Moreover, the combination of more accurate mass mea- sity Press) surements of the brown dwarf with improved spectroscopy and Grimm, S. L. & Stadel, J. G. 2014, ApJ, 796, 23 photometry will be useful for comparison with atmospheric and Hagelberg, J. 2014, Theses, Université Genève Hagelberg, J., Ségransan, D., Udry, S., & Wildi, F. 2016, MNRAS, 455, 2178 evolutionary models. Kozai, Y. 1962, AJ, 67, 591 Lidov, M. L. 1962, Planet. Space Sci., 9, 719 Acknowledgements. This work has been carried out within the frame of the Na- Lovis, C., Dumusque, X., Santos, N. C., et al. 2011, ArXiv e-prints tional Centre for Competence in Research “PlanetS” supported by the Swiss Na- [arXiv:1107.5325] tional Science Foundation (SNSF). Lucas, P. W., Tinney, C. G., Burningham, B., et al. 2010, MNRAS, 408, L56 This publication makes use of The Data & Analysis Center for Exoplanets Macintosh, B. A., Graham, J. R., Palmer, D. W., et al. 2008, in Proc. SPIE, Vol. (DACE), which is a facility based at the University of Geneva (CH) dedicated 7015 to extrasolar planets data visualisation, exchange and analysis. DACE is a plat- Mainzer, A., Cushing, M. C., Skrutskie, M., et al. 2011, ApJ, 726, 30 form of the Swiss National Centre of Competence in Research (NCCR) Plan- Maire, A.-L., Langlois, M., Dohlen, K., et al. 2016, Proc. SPIE etS, federating the Swiss expertise in Exoplanet research. The DACE platform is Marmier, M. 2014, PhD thesis, Geneva Observatory, University of Geneva available at https://dace.unige.ch. Mawet, D., Milli, J., Wahhaj, Z., et al. 2014, ApJ, 792, 97 SPHERE is an instrument designed and built by a consortium consisting of Montagnier, G. 2008, Theses, Université Joseph-Fourier - Grenoble I IPAG (Grenoble, France), MPIA (Heidelberg, Germany), LAM (Marseille, Morley, C. V., Fortney, J. J., Marley, M. S., et al. 2012, ApJ, 756, 172 France), LESIA (Paris, France), Laboratoire Lagrange (Nice, France), INAF - Mowlavi, N., Eggenberger, P., Meynet, G., et al. 2012, A&A, 541, A41 Osservatorio di Padova (Italy), Observatoire Astronomique de l’Université de Genève (Switzerland), ETH Zurich (Switzerland), NOVA (Netherlands), ON- Mugrauer, M., Ginski, C., & Seeliger, M. 2014, MNRAS, 439, 1063 ERA (France) and ASTRON (Netherlands) in collaboration with ESO. SPHERE Pavlov, A., Möller-Nilsson, O., Feldt, M., et al. 2008, in Proc. SPIE, Vol. 7019, was funded by ESO, with additional contributions from CNRS (France), Advanced Software and Control for Astronomy II, 701939 MPIA (Germany), INAF (Italy), FINES (Switzerland) and NOVA (Netherlands). Rajpurohit, A. S., Reylé, C., Allard, F., et al. 2013, A&A, 556, A15 SPHERE also received funding from the European Commission Sixth and Sev- Santos, N. C., Mayor, M., Naef, D., et al. 2002, A&A, 392, 215 enth Framework Programmes as part of the Optical Infrared Coordination Net- Ségransan, D., Udry, S., Mayor, M., et al. 2010, A&A, 511, A45 work for Astronomy (OPTICON) under grant number RII3-Ct-2004-001566 for Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 FP6 (2004-2008), grant number 226604 for FP7 (2009-2012) and grant number Sokal, A. 1997, in Functional integration: basics and applications. Proceedings 312430 for FP7 (2013-2016). of a NATO Advanced Study Institute, Cargèse, France, September 1–14, 1996 We acknowledge financial support from the Programme National de Planétolo- (New York, NY: Plenum Press), 131–192 gie (PNP) and the Programme National de Physique Stellaire (PNPS) of CNRS- Soummer, R., Aime, C., & Falloon, P. E. 2003, A&A, 397, 1161 INSU. This work has also been supported by a grant from the French Labex Soummer, R., Pueyo, L., & Larkin, J. 2012, ApJ, 755, L28 OSUG@2020 (Investissements d’avenir – ANR10 LABX56). Tamuz, O., Ségransan, D., Udry, S., et al. 2008, A&A, 480, L33 This work has made use of data from the European Space Agency (ESA) mis- Tremblin, P., Amundsen, D. S., Mourier, P., et al. 2015, ApJ, 804, L17 sion Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Udry, S., Mayor, M., Naef, D., et al. 2000, A&A, 356, 590 Processing and Analysis Consortium (DPAC, http://www.cosmos.esa.int/ Wu, Y. & Murray, N. 2003, ApJ, 589, 605–614 web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Mul- tilateral Agreement. This publication makes use of data products from the Two Micron All Sky Sur- vey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. J.H. is supported by the Swiss National Science Foundation (SNSF), and the French National Research agency through the GIPSE grant ANR-14-CE33- 0018.

Article number, page 10 of 16 A. Cheetham et al.: Direct imaging of a substellar companion to HD 4113 A

yi represents both the measured radial velocities and the direct imaging data ( i.e. ρ, PA).

yi = fi(X) + ei (B.1)

The likelihood function is given in Eq. B.2 where σi is the estimated error on each data point yi and σ0 is an additional white noise parameter (see Gregory 2005) added to each RV in- strument. These nuisance parameters account for any additional noise sources that were not included in the measurement’s error bars.

1 XN 1 XN (y f (X))2 log = log (σ2 + σ2) i − i (B.2) L −2 0 i − 2 σ2 + σ2 i=1 i=1 0 i

Appendix B.2: Choice of parameters Our model for the RV measurements is composed of 4 lin- ear terms: the systematic RV of CORALIE-07 (γC07), the off- set between CORALIE-98 and CORALIE-07 (∆V(C98 C07)), the offset between CORALIE-14 and CORALIE-07 (∆V−(C14 C07)) and the offset between CORAVEL and CORALIE-07− (∆V(CORA C07)). The CORALIE offsets originate from the different instrument− upgrades performed over the 17 years of ob- servations. We model the Keplerian corresponding to HD 4113A b with the parameters log P, log K, √e cos ω, √e sin ω and λ0, using the period P, radial velocity semi-amplitude K, eccentricity e, argument of periastron ω and the mean longitude λ0 given at a given reference epoch. We use a different set of variables to model HD 4113C to reduce correlations between them. We use log P, √e cos ω, σ Fig. A.1: The 5 contrast obtained from the NACO L’ data √e sin ω, mC sin i, TMAX(rv), sin i and Ω. The last four variables taken in 2013. The location of the SPHERE detection is marked correspond to the minimum mass of the brown dwarf, the date at with a dashed line. At this separation, the corresponding limit is which the maximum RV occurs, the sine of the orbital inclina- 9.3 mag and was insufficient to detect the brown dwarf compan- tion and the longitude of the ascending node. ion. The final reduced image is also shown, with the expected position of the brown dwarf labelled with a yellow circle. Appendix B.3: Choice of priors All adjusted parameters have uniform priors with the exception Appendix A: NACO L-band direct imaging data of the RV offset ∆(C98 C07) and ∆(CORA C07). ∆(C98 C07) has been calibrated using− RV standard stars− that were observed− We present here the results of the 2013-08-21 data taken with with both C98 and C07, allowing us to adopt a Gaussian prior 1 NACO. This dataset was processed with the GRAPHIC pipeline centered on zero with a standard deviation of 5 ms− . The prior (Hagelberg et al. 2016), using a similar reduction sequence as the on the offset between CORAVEL and CORALIE is a truncated SPHERE data described in Section 3, without the application of normal distribution which parameters are given in Table B.1. SDI. The detection limits and final reduced image are presented We also include a set of priors for the parallax and masses in Fig. A.1. The companion was not detected in this data, with of the system HD 4113AC based on our external knowledge. We the 5σ contrast limit at the location of the SPHERE detection adopted a Gaussian prior for the parallax based on the latest Gaia being 9.3 mag. measurements and we choose a uniform prior for the mass of HD 4113C with an upper bound at the hydrogen-burning limit, i.e. 72 MJ. For the mass of HD 4113 A, we used a split normal Appendix B: MCMC Details distribution with asymmetric standard deviation taken from Ta- ble 1. Appendix B.1: Likelihood function

Throughout this section we assume that the observed signals are Appendix B.4: MCMC runs modeled with two independent Keplerians and four RV offsets corresponding to the number of RV instruments. The noise as- We probed the model parameter space using emcee, a python im- sociated with each measurement is assumed to be independently plementation of the Affine Invariant Markov chain Monte Carlo drawn from a Normal distribution with zero mean N(0, σi). The (MCMC) Ensemble sampler (Foreman-Mackey et al. 2013; observed signal yi is written in Eq. B.1 as a sum between the Goodman & Weare 2010) and the likelihood function described model fi(X) for parameters X and a realization of the noise ei. in the above subsections.

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We ran several MCMC simulations. For the first MCMC run, we performed 4 500 iterations using 50 walkers with initial con- ditions drawn from the solution obtained using DACE. A first set of parameter posterior distributions were derived using a burn-in phase of 1 500 iterations. In order to obtain a statistically robust sample, we ran a second MCMC simulation with 100 walkers drawn from the posterior of our first simulation with a total of 45 000 iterations which guarantees a fast convergence to equi- librium. We derive our final sample by first computing the cor- relation time scale (τ) of the samples, which in this case was always less than 100 iterations. We eliminate the initialization bias by discarding the first 2 500 elements (> 20τ, see Sokal 1997). We are left with 4 250 000 MCMC samples among which at least 42 500 data points are independent. We are therefore able to retrieve and characterize the underlying parameter distribu- tions with a 0.5% accuracy (Sokal 1997) which corresponds to 3σ confidence intervals. Figures B.1 and B.2 shows the marginalized 1-D and 2- D posterior distributions of the Keplerian model parameters of the giant planet HD 4113 A b. As illustrated, the distributions are close to Gaussian, with small linear correlations. The corre- sponding parameters and confidence intervals are listed in Table B.1. The case of HD 4113 C is less straightforward due to the presence of strong correlations in the 2-D posterior distributions (see Fig. B.3 and B.4). Furthermore, most of the 1-D distri- butions are non-Gaussian, which makes the use of mean value and error bars potentially misleading. Instead, we prefer to list the values corresponding to the maximum likelihood, the sam- ple median as well as the mode of the distribution in Table B.1. Confidence intervals corresponding to 1σ and 2σ are also given for each parameter as well as the prior distribution used.

Article number, page 12 of 16 A. Cheetham et al.: Direct imaging of a substellar companion to HD 4113 A ) 2 07 . 0 + ) 2 2 43 04 . . 200) 0 0 , √ + 25) , , 2 2 200 100) 20) 500) 30) 30) 30) 10) 1) 1) 1) 25 − 10) 10) 10) + + + + + + + + + 80000) + 07 985) 985) 72) . , . . 237 , , , , , , , , , , , 360) 360) − 360) + + + . , 0 0 0 , , , 1 1 1 , , , , 0 , , 3 30 10 20 30 30 (0 − − − + (0 (0 (0 (0 (0 (0 , √ 200 ( ( ( 500 100 − − − − − (0 (0 , U 2 ( ( ( ( ( , U U U − − U U U (0 U U U ( ( U U U U U U U (45000 51 02 . U U − 986 U 0 TN . ( √ (23 − TN , N 05 . :truncated normal (1 SN TN :split normal, SN : normal, N : uniform, U sets ff RV o HD 4113C Likelihood HD 4113A b External priors Nuisance parameters -0.17 -0.16 -0.11 0.12 -0.29 -0.0094 -0.38 0.12 0.394 0.378 0.397 0.042 0.329 0.426 0.283 0.466 0.763 0.900 0.949 0.067 0.807 0.959 0.709 0.983 -0.604 -0.585 -0.605 0.044 -0.628 -0.530 -0.657 -0.458 0.8996 0.8977 0.8972 0.0028 0.8945 0.9008 0.8911 0.9036 ]) 1.9672 1.9626 1.9655 0.0072 1.9543 1.9707 1.9460 1.9788 1 − ] 4964 4919 4911 40 4876 4969 4828 5004 ] 34 190 180 110 59 330 8.4 390 ]] -250 6.0] -120]] 5.1 5.23 5.97 -200 2.11 5.81 6.16 5.0 2.24 90] 5.61 2.0 6.22 -210 2.25 0.67 92.7 2.8 0.55 -2.4 0.92 91.7 5.10 5.55 7.4 -250 1.16 6.61 91.3 6.79 100 0.5 3.26 4.45 4.99 1.5 0.21 9.7 7.51 90.0 7.56 4.34 93.5 88.3 95.2 - ] 13.9 13.9 13.5 1.7 12.0 15.9 10.1 17.9 1 ] 1.059 1.049 1.053 0.063 0.976 1.121 0.9102 1.193 ] 53.9 61.0 60.8 4.9 54.6 66.0 48.5 69.2 ] 1.674 1.658 1.657 0.070 1.580] 1.740 70.6 1.504 68.8 1.814 71.5 2.5 65.3 - 71.1 61.5 71.9 1 1 1 1 1 1 1 1 − s] 327 370 359 36 331 413 294 454 - J J J

− − − − − − − − / [yr] 104 101 91 16 85 121 73 140 - [M [M [M [M [AU] 1.301 1.297 1.300 0.026 1.267[AU] 1.327 23.1 1.237 22.5 1.354 22.7 2.3 20.0 - 25.4 18.3 28.0 - [deg] 97.485 97.503 97.502 0.074 97.421 97.590 97.339 97.680 [deg] -47.1 -47.0 -47.0 1.0 -48.2 -45.9 -49.4 -44.7 [deg] 50.35 50.49 50.51 0.98 49.35 51.59 48.24 52.73 - [deg] 196 195 191 11 181 207 169 218 - [deg][deg][deg] 62 -35.4 49.8 71 -36.9 64.1 -37.2 52 62.6 6.4 17 8.4 -44.0 53 53.8 -29.3 73.6 93 -50.3 45.1 -21.8 43 79.5 111 - - - [deg] 66.5 55.3 51.3 6.5 48.8 64.0 44.5 71.4 [] 38100 37000 33100 5800 30900 44300 26700 51300 - [day] 55642.59 55642.620 55642.59 0.11 55642.50 55642.74 55642.38 55642.88 - [mas] 23.89 24.17 24.17 0.36 23.76 24.60 23.39 25.01 [days] 526.581 526.579 526.574 0.020 526.557 526.602 526.535 526.627 - [days] 64500 63500 62300 1400 62100 65300 61100 66800 [days] 48890 48210 48060 700 47400 49000 46830 49750 - [ms Table B.1: Priors and parameters probed with the MCMC. Distributions: 07) [ms C − 07) [ms 07) [ms C C − − i ω ω ) [ms ) log10([ms i ) log10([days]) 2.721465 2.721463 2.721459 0.000016) 2.721445 2.721482 2.721427 2.721503 log10([days]) 4.581 4.568 4.584 0.067 4.490 4.647 4.427 4.710 98 14 sin P P K cos sin CORAV C C 07) [kms 98)07)14) [ms [ms [ms . i ( ( ( sin A 0 0 e e C C C Cora C C C . p V V V r r RVmax 0 ( 0 0 ( ( ( ( √ √ M s M s s s M M M P K P P A A Param.log Posteriorlog Likelihoodlog Priorπ Unitsγ Max(Like) Med -547.6 -546.1 -555.6 -553.8 Mod -1.47 -555.8 -553.3 Std -1.59log ( CI(15.85) 2.6 2.5 CI(84.15) -1.39 CI(2.275) -558.9 -557.0 CI(97.725) 0.85 -552.9 -551.3 -2.71 -562.9 -560.9 -550.9 -0.84 -549.4 log ( Prior -4.38 -0.39 ∆ ∆ log ( e ω e K [m m T λ ∆ T sin ω T i λ Ω

Article number, page 13 of 16 A&A proofs: manuscript no. output

Fig. B.1: Marginalized 1-D and 2-D posterior distributions of the model parameters corresponding to the global fit of the RV and direct imaging models for HD 4113 A b. Confidence intervals at 2.275%, 15.85%, 50.0%, 84.15%, 97.725% are over-plotted on the 1-D posterior distribution while the median 1 σ value are given on top of each 1-D posterior distributions. 1, 2 and 3 σ contour levels are over-plotted on the 2-D posterior distributions.± The model parameters adjusted during the MCMC run are shown (P, K, e, ω, M0)

Fig. B.2: Same as Fig. B.1, showing the additional parameters derived from the MCMC posterior samples (a, m sin i, T p, λ0) for HD 4113A b

Article number, page 14 of 16 A. Cheetham et al.: Direct imaging of a substellar companion to HD 4113 A

Fig. B.3: Same as Fig. B.1, for HD 4113C, showing the correlations and marginalized posterior distributions for the model parame- ters adjusted during the MCMC run (P, m sin i, √e cos ω, √e sin ω, TVmax, sin i, ω)

Article number, page 15 of 16 A&A proofs: manuscript no. output

Fig. B.4: Same as Fig. B.2, showing the additional parameters derived from the MCMC posterior samples for HD 4113C (a, m, K, e, ω, λ0, i).

Article number, page 16 of 16