Constraining the interior structure of Venus based on its moment of inertia and k2 values

Models of Venus's interior structure were developed based on PREM. These models are derived by solving the differential equations for mass and hydrostatic equilibrium throughout the planet and are fully characterized by the core radius Rc and two parameters denoted as A and B. The pressure dependence of the density in Venus’ mantle ρ(P) is modeled by scaling PREM’s ρ(P) with a factor A. Differences in density between these planets can arise from differences in composition and temperature. For instance, models with A<1 may correspond to a mantle with higher temperatures and/or lower iron content compared to Earth's mantle. Similarly, the density in Venus’ liquid core is obtained by scaling PREM’s ρ(P) with a factor B. We investigate Rc values ranging from 3000 to 3500 km and B values from 0.98 to 1.02. For each combination of Rc and B, we calculate the exact value of A required for our Venus model to satisfy the mass constraint. The A values range from as low as 0.92 when the core is large and dense, to as high as 1.04, associated with a smaller, less dense core. Shear and bulk moduli profiles were also obtained based on PREM.

In all models the pressure at the very center of the planet is considerably lower than the pressure at Earth’s ICB. This suggests that Venus could only have a solid inner core if the composition and temperature values in its core differ substantially from Earth’s.

Margot et al. (2021) estimated Venus's moment of inertia (MoI) to be 0.337 ± 0.024. The MoI values of all our models fall within this range, with Rc values between 3050 km and 3225 km yielding the closest match to 0.337. However, the uncertainty in this MoI estimate is too large, necessitating the use of additional constraints to study Venus's interior structure.

Venus’ tidal Love number k2 was estimated to be 0.295 +- 0.033 in Konopliv and Yoder (1996). In order to compute the Love numbers of our Venus models, we have developed a series of realistic viscosity profiles based on estimates available in literature. The anelasticity of Venus’ interior is modeled with an Andrade rheology, which depends on two parameters (α and ζ). In Amorim and Gudkova (2025) estimates of these parameters were obtained for Earth’s mantle, and similar but wider ranges are applied to Venus in this work.

The Love numbers of each of Venus's interior structure models were calculated using different viscosity profiles and Andrade parameter values. A statistical analysis of all models was conducted based on the available estimates of Venus's MoI and k2. The core radius is most likely within the range of 3125 km to 3400 km. For low-viscosity models, Rc is expected to be closer to 3125 km, while for high-viscosity models, it must be closer to 3400 km.

The tidal phase lag and the h2 Love number were also computed for all our models as a prospective for future missions to Venus that might measure them.