True spin-orbit obliquities distribution: data-driven confirmation of no clustering of misaligned planets

TL;DR

This work expands the catalog of exoplanet true spin-orbit obliquities Ψ by applying a homogeneous rotation-period deprojection to λ across 116 planets (plus 4 literature values) to assemble a 120-planet Ψ sample, the largest to date. Using an MCMC framework with priors on $R_{\star}$, $P_{\mathrm{rot}}$, and $v\sin i_{\star}$ and an isotropic $i_{\star}$ prior, the authors derive Ψ via $\cos\Psi$ and show that the distribution features a single peak at alignment with an isotropic tail for misaligned systems, rather than the previously claimed dichotomy. They demonstrate that biases in stellar inclination can artificially induce apparent bimodalities, reinforcing the importance of accounting for $i_{\star}$ when interpreting obliquity statistics. A focused analysis of Neptune-sized planets suggests a tentative two-component structure in Ψ but remains premature due to small numbers, underscoring the need for larger Neptunian samples to confirm potential dichotomies and to clarify the role of companions and formation pathways in shaping obliquities.

Abstract

Context. True spin-orbit obliquities Ψ offer valuable insights into the evolutionary history of exoplanetary systems. Previous studies have suggested that exoplanets tend to occupy either aligned or perpendicular orbits. However, recent research has indicated potential biases caused by the low sample, questioning whether this dichotomy would persist with a larger dataset. Simultaneously, a similar dichotomous behavior has been suggested for Neptune-sized planets. Aims. We aim to investigate the distribution of true spin-orbit obliquities Ψ with an enlarged sample, looking for confirmation of the disputed dichotomy previously found, with a focus also on the obliquities of Neptunes. Methods. Starting from a sample of 264 projected obliquities λ, we homogeneously compute true obliquities Ψ for 116 planets using the rotation period method. We combine them with 4 further values gathered from literature and we then study their distribution, also as a function of various star-planet system parameters. Results. Our data-driven work based on 120 true obliquities Ψ - the largest sample to date - strongly confirms the presence of a single cluster of aligned planets, followed by an isotropic distribution of misaligned planets with no preferred misalignment. This result is based on a uniform distribution of stellar inclinations {i_\star} , for which non-uniformity could have biased previous interpretations of the arrangement of true obliquities. We confirm that Neptunians show a tentative dichotomous distribution with data available today, but its veracity needs confirmation with an enlarged sample, also because an anisotropic distribution of stellar inclination may be one of the factors hindering the real distribution.

Figures (13)

• Figure 1: Comparison between our stellar inclinations $i_{\star}$ and the ones computed by Morgan_2024, starting from the same dataset. The gray dashed lines represent the $y=x$ relation, whereas the solid red line represents the linear fit, and the shaded red region represents the $68\%$ confidence interval. Residuals are computed with respect to the fit relation. Uncertainties in the residuals panel are omitted to ensure a better readability.
• Figure 2: Comparison between our true obliquities and the ones computed by Albrecht_2021. Starting from the same dataset, we achieve an excellent agreement within the $68\%$ confidence interval of the linear fit. The light gray dashed line represents the $y=x$ relation. The linear correlation is guaranteed by a $\chi^2$ test yielding $p=1.0$, allowing the rejection of the null hypothesis that the data are not linearly correlated. Residuals are computed with respect to the fit line. Uncertainties in the residuals panel are omitted to ensure a better readability. The presence of outliers is due to our inability to recover the $i_\mathrm{orb}$ values used by Albrecht_2021, but also highlights their importance for a correct inference.
• Figure 3: Comparison between the true obliquities computed in this work and correspondent literature values, aside from Albrecht_2021, where available. Aesthetics follow the style of \ref{['fig:simVSalbrecht+21']}. The plot is made assuming the conventional stellar inclination ($i_{\star} \leq 90^\circ$).
• Figure 4: Distribution of the 120 true obliquities present in our sample. In the top panel, $\Psi$ values are shown as a superposition of their normalized posteriors, fitted with a Kernel Density Estimation (KDE) with Gaussian kernel and Silverman's bandwidth (other bandwidth selections yielded either similar results or overfitted graphs). The shaded blue and light blue regions represent $68\%$ and $95\%$ highest density intervals (HDI), respectively. The middle panel displays a simple histogram of true obliquities. The lower panel addresses two key issues: (i) the arbitrariness of binning; (ii) the apparent valley around $90^\circ - 100^\circ$. To account for these, 100 histograms with 20 bins were generated, with $20\%$ variability on their boundaries. The average histogram is represented by the solid blue line, while the dashed blue line represents the KDE.
• Figure 5: Comparison between the dataset of $\Psi$ from Albrecht_2021 and that of this work. An A-D test provided evidence that the two distributions significantly differ, along with a dip-test for uni-modality proving that Albrecht_2021 true obliquities distribution is consistent with a multi-modal distribution while our sample of true obliquities is consistent with a uni-modal distribution. KDEs are plotted for ease of visualization.