Inferring Venus interior structure based on present geophysical constraints

Introduction: The upcoming decade of Venus exploration, supported by unprecedented measurement accuracies, is expected to yield tight constraints on the planet’s interior structure. Key geophysical properties that enable inference of Venus’ interior include the Moment of Inertia (MoI), mass, and tidal Love number k2. Although current estimates and their associated uncertainties limit a detailed characterization of the deep interior, the combination of these parameters is essential for deriving consistent interior structure models. By using present observational accuracies, we investigate Venus’ interior through a Bayesian inference approach based on the Markov Chain Monte Carlo (MCMC) method [1]. In our study we account for an accurate modeling of the possible composition of the core and the mantle and retrieve pressure, temperature and density profiles that are consistent with the probability distributions of the observations. Geophysical Constraints: Venus’ high surface temperature and pressure of about 730 K and 92 bar [2], resulting from its dense atmosphere, along with its lack of plate tectonics [3] and magnetic field, suggest significant differences in internal dynamics compared to Earth. If an Earth-like dynamo [4] were active on Venus, it would have implied convection mechanisms in an outer fluid core surrounding a solid inner core. The absence of a global magnetic field, instead, could be explained by an insufficient cooling of Venus’ core [5], or by limited convection in the mantle, insufficient to start the dynamo process [6]. While the existence of a solid inner core, thus, cannot be excluded, the lack of seismic data prevents better constraints on the mantle-core boundary. Venus’ slow rotation and consequent small oblateness hinder the determination of its MoI based solely on gravity data. Margot et al., 2021 [7] determined Venus’ MoI of 0.337± 0.024 (1-σ) through Earth-based radar observations of Venus’ spin vector. The tidal Love number k2 = 0.295±0.033 (1-σ) [8] is the only direct constraint on Venus’ interior structure, although the current uncertainty doesn’t allow definitive conclusions regarding the state of the core [9]. Interior Model Inversion: A multi-layered configuration is assumed for the internal structure of Venus, including a crust, upper and lower mantle and an iron-rich core (Figure 1) [10]. The model accounts for both fully molten and partially solidified core scenarios, including a fluid outer core and a solid inner core. To obtain an accurate modeling of the structure of Venus, variations in mantle and core compositions are included in this study. The first step of the proposed approach is to identify a set of free parameters that can be explored to generate internal structure models. The crust is assumed to have uniform density. The upper mantle, whose constituents are assumed to be MgO, FeO and SiO2, extends to 25 GPa, which is the phase transition pressure of the Olivine to Perovskite. The lower mantle is assumed to have a homogeneous chemical composition with respect to the upper mantle. The model also considers a fluid core composed of FeSi, FeS, and FeO mixed with pure iron, as well as the potential presence of a solid core of pure iron, provided the required pressure and temperature conditions for solidification are satisfied. Further assumptions governing the generation of interior structure models include a single-stage core segregation at a certain segregation pressure, with mantle composition derived via a metal-silicate partitioning model [11]. The temperature at the crust-mantle interface is sampled within a range compatible with basaltic magma generation. A temperature drop at the core-mantle interface is also accounted for. Our MCMC method explores the parameter space using the Metropolis Hastings algorithm, and convergence is checked through the Gelman-Rubin criterion. The posterior distribution of the properties of Venus’ interior provides models that match the observed values of mass, MoI and k2. The planet’s tidal response is computed using PyALMA [12], assuming Andrade rheological model and constant viscosities. Our preliminary results based on current geophysical measurements show a distribution of models with a core radius between 3250 and 3650 km (1-σ) (Figure 2), consistent with previous estimates [7,9]. A subset of models highlighted in orange (~6%) supports the existence of a solid inner core, while those highlighted in green indicate a Perovskite to post-Perovskite phase transition in the lower mantle. The method's convergence is validated by the 2D histograms of the target values for mass, MoI, and k2 (Figure 3), which align with the observed constraints. It should be noted that the adopted compositional assumptions, combined with the observed uncertainty in k2, impose tighter constraints on the MoI than current geophysical estimates, ensuring consistency with the measured mass. Summary: We present here a robust Bayesian inference approach to evaluate the likely interior structure of Venus based on multidisciplinary geophysical constraints. Current estimates of the tidal Love number k2 are key to inferring Venus’ interior providing more stringent constraints than the moment of inertia. The proposed methodology offers a flexible framework that can be extended to incorporate more precise data from upcoming missions enabling deeper insights into Venus’s core and mantle. References: [1] Genova A. et al (2019) GRL 46(7), 3625–3633 [2] Lebonnois S. et al., (2010) JGR, 115(E6). [3] Kaula, W. M. (1994). Philos.Trans.R.Soc. A, 349 (1690). [4] Elsasser W. M. (1956) Rev.Mod.Phys 28(2), 135–163. [5] Stevenson, D. J (1983) Icarus, 54(3), 466–489 [6] Nimmo, F. (2002) Geology, 30(11), 987. [7] Margot J.L. et al (2021) Nat.Astron. 5(7), 676–683. [8] Yoder C. F. and Ahrens, T. (1995) AGU, 1. [9] Dumoulin C. et al. (2017) JGR 22(6), 1338–1352. [10] Shah O. et al (2022) ApJ, 926, 2. [11] Fischer R.A. et al (2015). Geochim.Cosmochim.Acta., 167, 177–194. [12] Petricca F. et al. (2024) Icarus, 417, 116120.