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Orbital misalignment of the Neptune-mass exoplanet GJ 436b with the spin of its cool star



The angle between the spin of a star and the orbital planes of its planets traces the history of the planetary system. Exoplanets orbiting close to cool stars are expected to be on circular, aligned orbits because of strong tidal interactions with the stellar convective envelope1. Spin–orbit alignment can be measured when the planet transits its star, but such ground-based spectroscopic measurements are challenging for cool, slowly rotating stars2. Here we report the three-dimensional characterization of the trajectory of an exoplanet around an M dwarf star, derived by mapping the spectrum of the stellar photosphere along the chord transited by the planet3. We find that the eccentric orbit of the Neptune-mass exoplanet GJ 436b is nearly perpendicular to the stellar equator. Both eccentricity and misalignment, surprising around a cool star, can result from dynamical interactions (via Kozai migration4) with a yet-undetected outer companion. This inward migration of GJ 436b could have triggered the atmospheric escape that now sustains its giant exosphere5.

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Figure 1: Properties of the stellar photosphere along the transit chord of GJ 436b.
Figure 2: Architecture of the GJ 436 system, projected on the plane of the sky.
Figure 3: Secular evolution of GJ 436b.
Figure 4: Constraints on the mass and period of a putative perturber GJ 436c.

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This work is based on observations made with the HARPS spectrograph on the 3.6 m ESO telescope at the ESO La Silla Observatory, Chile, under GTO program ID 072.C-0488, and with the Italian Telescopio Nazionale Galileo operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias under OPTICON program 16A/049, ‘Sensing Planetary Atmospheres with Differential Echelle Spectroscopy’ (SPADES). OPTICON has received funding from the European Community’s Seventh Framework Programme (FP7/2013-2016) under grant agreement number 312430. This project has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement number 724427 (FOUR ACES). This work was carried out in the framework of the National Centre for Competence in Research ‘PlanetS’ supported by the Swiss National Science Foundation (SNSF). R.A., N.A.-D., V.B., D.E., C.L. and A.W. acknowledge the financial support of the SNSF. H.M.C. gratefully acknowledges support as a CHEOPS Fellow from the SNSF National Centre of Competence in Research ‘PlanetS’. G.W.H. acknowledges long-term support from Tennessee State University and the State of Tennessee through its Centers of Excellence programme. X.B. and X.D. acknowledge the support of CNRS/PNP (Programme national de planétologie). X.B. acknowledges funding from the European Research Council under the ERC Grant Agreement number 337591-ExTrA. We thank C. A. Watson for calculating the convective mass of GJ 436, H. Knutson for facilitating the determination of the stellar rotation period, J.-B. Delisle for discussing the system geometry, and the Telescopio Nazionale Galileo staff for the service observation.

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Authors and Affiliations



V.B. coordinated the study of the GJ 436 system, performed the reduction and analysis of the transit data, interpreted the results, and wrote the paper. V.B. and D.E. proposed the original idea. D.E. developed the HARPS-N transit observation programme (led by D.E. and A.W.). V.B., H.M.C. and C.L. developed and refined the reloaded Rossiter–McLaughlin technique. H.B. performed the Kozai simulations and contributed to the interpretation. G.W.H. derived the stellar rotation period from analysis of photometry. N.A.-D. and X.D. derived the stellar rotation period from analysis of activity indices. X.B. and N.A.-D. analysed radial velocity values, and D.S. analysed direct imaging data used to constrain GJ 436c. R.A., H.C., C.L. and A.W. contributed to the analysis and interpretation of the transit data. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Vincent Bourrier.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks A. C. Cameron and A. Mann for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Observed and modelled CCF of GJ 436.

a, Typical HARPS-N CCF of GJ 436 (blue points), fitted with a double-Gaussian model (solid black line). This model is the combination of a Gaussian profile for the CCF continuum and lobes plus an inverted Gaussian profile for the CCF core (individual components are plotted as dashed black lines). b, Residuals between the observed CCF and its best fit.

Extended Data Figure 2 Comparison between the properties of the lobe and core Gaussian components of the CCF model.

The panels show the difference between the radial velocity (RV) centroids of the lobe and core components (a), the ratio between their FWHMs (b), and the ratio between their amplitudes (c), as a function of GJ 436b’s orbital phase for each exposure in visit 1 (red), visit 2 (blue) and visit 3 (orange). There is little dispersion of these values around their average in each visit, shown as dashed horizontal lines. Vertical dotted lines are the transit contacts.

Extended Data Figure 3 Correction for the effects of Earth’s atmosphere.

Properties derived from the double-Gaussian fits to the CCFDI are shown before correction (ac) and after correction of the flux distribution (df), as a function of GJ 436b’s orbital phase. The contrast of the CCFDI is shown in a and d, their FWHMs in b and e, and their radial velocities in c and f. Radial velocities are relative to the systemic velocity in each visit, and have been offset by 25 m s−1. They are overplotted with the expected Keplerian radial velocity curve. Visits 1, 2 and 3 are coloured in red, blue and orange, respectively. Vertical dotted lines are the transit contacts; horizontal dashed lines show the average values in each visit.

Extended Data Figure 4 Maps of the residuals between the scaled CCFDI and the .

Residuals are coloured as a function of their flux, and plotted as a function of radial velocity in the stellar rest frame (in abscissa) and orbital phase (in ordinate) for visit 1 (a), visit 2 (b) and visit 3 (c). The vertical and horizontal dashed black lines indicate the mid-transit time and stellar rest velocity, respectively. In-transit residuals correspond to the CCFPO, and show the average stellar line profile (recognizable by a lower flux in the CCFPO cores) from the regions occulted by GJ 436b across the stellar disk. Out-of-transit residuals show little dispersion in all visits, consistent with the low activity of the host star.

Extended Data Figure 5 Properties of the CCFPO as a function of GJ 436b orbital phase.

The contrast (a), FWHM (b), and radial velocity values (c) are derived from the double-Gaussian best fits to the CCFPO, and show similar values over the three nights. ac, Visits 1, 2 and 3 are coloured in red, blue and orange, respectively. All error bars are 1σ. Horizontal error bars correspond to the exposure time. Vertical dashed lines are the transit contacts. a, b, The width and contrast of the (horizontal dashed lines) are similar over the three visits. c, The dashed black line is the reloaded Rossiter–McLaughlin model corresponding to the best fit for the planet trajectory and the velocity field of the star.

Extended Data Figure 6 Correlation diagram for the posterior probability distributions of the solid-body rotation model parameters.

Green and blue lines show the two-dimensional confidence regions that contain 39.3% and 86.5% of the accepted steps, respectively. One-dimensional histograms correspond to the distribution projected on the space of each line parameter, with the orange dashed line limiting the 68.3% confidence interval. The red line and white point show median values.

Extended Data Figure 7 Ground-based photometry of GJ 436.

a, Time series of GJ 436 nightly magnitude with transit points removed and normalized to the same seasonal mean. utc, Coordinated Universal time; hjd, heliocentric Julian date. b, Frequency spectrum of the normalized observations with strongest peak at a photometric period of 44.09 days, and secondary peaks corresponding to yearly aliases caused by the temporal sampling. c, Normalized data and best-fit sine curve (blue line) phased to Prot = 44.09 days. The binned data (red squares) highlight the low-level brightness modulation of GJ 436 (peak-to-peak amplitude of 0.0032 mag).

Extended Data Figure 8 Conditions on GJ 436b and GJ 436c orbital planes.

For a given mutual inclination im (vertical axis), the acceptable properties for the orbital planes describe an oval ring in the (Ω, ic) plane. Ω is the difference between the longitudes of the ascending nodes and ic is the orbital inclination of GJ 436c.

Extended Data Table 1 Log of GJ 436b transit observations
Extended Data Table 2 Properties of the GJ 436 system

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Bourrier, V., Lovis, C., Beust, H. et al. Orbital misalignment of the Neptune-mass exoplanet GJ 436b with the spin of its cool star. Nature 553, 477–480 (2018).

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