Cold and eccentric: a high-spectral resolution view of 51 Eri b with VLT/HiRISE

TL;DR

This study uses four $R\approx140000$ HiRISE spectra of the directly imaged planet 51 Eri b to measure its radial velocity and break the line-of-sight degeneracy in its orbit. RVs are derived via forward modeling with ForMoSA employing cloud-free Exo-REM/$Exo_k$ atmospheres and by cross-correlating with H$_2$O, CH$_4$, and CO templates, yielding $v\sin i = 9.9 \pm 2.3\ \mathrm{km\,s^{-1}}$ and an upper limit on the rotation period $P_{rot} \lesssim 24$ h (with the 4th epoch affected by fringes). A joint fit of RVs with existing astrometry in a universal Keplerian-variables framework yields $a\approx9.1$ au, $e\approx0.55$, $i\approx159^\circ$, $\omega\approx55^\circ$, $\Omega\approx58^\circ$, and $P\approx23.5$ yr, breaking LOS degeneracy and enabling a phase-curve interpretation. The results support a dynamically excited history and constrain the parameter space for unseen outer perturbers, while highlighting the need for future RV and astrometric monitoring to tighten eccentricity and phase-curve measurements for potential reflected-light observations; Kozai–Lidov scenarios with known or unknown perturbers are discussed but not definitively required.

Abstract

Discovered almost 10 years ago, the giant planet 51 Eridani b is one of the least separated (0.2 arcsec) and faintest (J = 19.74 mag) directly imaged exoplanets known to date. Its atmospheric properties have been thoroughly investigated through low- and medium-resolution spectroscopic observations, enabling robust characterization of the planet's bulk parameters. However, the planet's intrinsically high contrast renders high-resolution spectroscopic observations difficult, despite their potential to yield key measurements essential for a more comprehensive characterization. This study seeks to constrain the planet's radial velocity, enabling a full 3D orbital solution when integrated with previous measurements. We have obtained 4 high-contrast high-resolution (R = 140000) spectroscopic datasets of the planet, collected over a two-year interval with the HiRISE visitor instrument at the VLT to derive the planet's radial velocity. Using self-consistent models of atmosphere, we were able to derive the radial velocity of the planet at each of the 4 epochs. These radial velocity measurements were then used in combination with all existing relative astrometry in order to constrain the orbit of the planet. Our radial velocity measurements allow us to break the degeneracy along the line of sight, making it now possible the unambiguous interpretation of the phase curve of the companion. We further constrain the orbital parameters, particularly the eccentricity, for which we derive e = 0.55 (-0.07, +0.03). The relatively high eccentricity indicates that the system has experienced dynamical interactions induced by an external perturber. We place constraints on the mass and semi-major axis of a hypothetical, unseen outer planet capable of producing the observed high eccentricities.

Figures (8)

• Figure 1: Combined CCF from the 4 nights. The combined CCF has been computed by shifting the each individual CCF to a RV of 0 $\mathrm{km}\,\mathrm{s}^{-1}\xspace$ in order to account for the variations of the RV of the companion across the different epochs.
• Figure 2: Orbit of 51 Eri b. The left panel shows the predicted RV of the planet as a function of time. The HiRISE RV measurements are overplotted as red dots, along with the rejected orbits in grey from the addition of the RV measurements. The middle panel is a zoomed-in version of the left panel around our RV measurements. In particular, we see that a future RV measurement at the end of 2026 should enable us to reject the last low-eccentric orbital populations. This is illustrated by the dashed vertical line overplotted at the end of 2026. The right panel displays the astrometric orbit of the planet inferred, including the line of nodes and the phase of the planet. The red crosses represent the estimate of the position of the planet during the HiRISE observations.
• Figure 3: Power-spectral density (PSD) of the data filtered from the stellar speckles estimate of our four epochs. The PSD was lowpass filtered in order to focus on its low-frequency content. A secondary axis is displayed at the top, which corresponds to an equivalent velocity. A peak is visible around a resolution of 25 000 for each epoch, which corresponds to $\sim$12 $\mathrm{km}\,\mathrm{s}^{-1}$. This peak is particularly prominent in the data from the last epoch, when the planet was closer to the host star.
• Figure 4: Normalized Autocorrelation Functions (ACF) of the individual CCFs. The first three epochs show highly consistent ACFs, whereas the last epoch shows deeply correlated structures in the CCF at multiples of 11 km/s. The vertical dashed lines are plotted at multiples of $\pm$ 11 $\mathrm{km}\,\mathrm{s}^{-1}$ to highlight the correlated structures.
• Figure 5: Individual CCF for the 4 epochs.