Simulated Dataset of Io's Love Numbers (k2, h2, l2) and Libration Amplitudes for Self-Consistent Rheology-Melt Models

Abstract: This repository contains a simulated dataset of tidal parameters (Love numbers $k_2$, $h_2$, $l_2$) and libration amplitudes for the Jovian satellite Io. The data investigate the coupling between material rheology and melt fraction under different internal structure assumptions. Methodology: The results were obtained using a modified version of the California Planetary Geophysics Code (CPGC) (Ermakov & Akiba, 2024), adapted to implement a self-consistent feedback loop between material rheology and melt fraction (Bierson & Nimmo, 2016). Calculations were performed considering both incompressible and compressible internal structures. Model Scenarios: The dataset explores various physical parameters, including the radial position of the onset of melting $R_{\phi0}$, the latent heat of fusion $L$, and the Andrade rheological parameter $\beta$. In this dataset are analyzed two limiting parameterizations for $\beta$: We analyze two limiting parameterizations for $\beta$: a spatially uniform profile (constant), serving as a controlled reference configuration that isolates the effects of structural weakening from variations in transient anelasticity, and a melt-dependent profile (depth-dependent), which provides a physically realistic framework as it allows the rheology to respond to the local melt structure. Our analysis reveals that although deep-mantle heating dominates both configurations, the depth-dependent $\beta$ case captures an emerging shallow-mantle enhancement. In the latter case, the modeled presence of melt decreases the effective viscosity, increasing the anelasticity, and driving up local tidal dissipation. 1. Spatially Uniform Profile (Constant $\beta$): in this limiting case, a uniform value is assumed throughout the mantle. This configuration represents a simplified, "effective" rheological medium where the thermal enhancement of dissipation may be partially buffered by grain growth via Ostwald ripening. The constant-$\beta$ case is intended as a controlled reference configuration, which allows us to isolate the effect of structural weakening (reduction in shear modulus due to melt) from intrinsic variations in transient anelasticity. 2. Melt-Dependent Profile (Depth-Dependent $\beta$ case): the parameter evolves dynamically as a function of the local melt fraction ($\phi(r)$). This parameterization provides a physically realistic framework as it allows the rheology to respond to the local melt structure by enhancing anelastic dissipation in regions of higher melt fraction. Structural Assumptions: Each model assumes a liquid core, an Andrade viscoelastic mantle discretized into 67 sublayers, and a Maxwell viscoelastic crust.