We investigated how spatial variations in tidal heating affect Io's isostatic topography at long wavelengths. The long-wavelength relief is less than the 0.3 km uncertainty in Io's global shape. Assuming Airy isostasy, degree-2 topography <0.3 km amplitude is only possible if surface heat flux varies spatially by <19% of the mean value. This is consistent with Io's volcano distribution and is possible if tidal heat is generated within and redistributed by a convecting layer underneath the lithosphere. However, that layer would require a viscosity <10¹⁰ Pa s. A magma ocean would have low enough viscosity but would not generate enough tidal heat internally. Conversely, assuming Pratt isostasy, we found ∼0.15 km degree-2 topography is easily achievable. If a magma ocean was present, Airy isostasy would dominate; we therefore conclude that Io is unlikely to possess a magma ocean.

中文翻译：

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艾奥的长波长地形作为地下岩浆海洋的探测器

我们研究了潮汐加热的空间变化如何影响木卫一在长波长下的均衡地形。长波长起伏小于木卫一全球形状的 0.3 公里不确定性。假设艾里均衡，只有当表面热通量在空间上变化<平均值的19％时，才有可能出现<0.3公里幅度的2级地形。这与木卫一的火山分布一致，如果潮汐热在岩石圈下方的对流层内产生并通过其重新分布，则这是可能的。然而，该层需要的粘度<10 ¹⁰  Pa s。岩浆海洋的粘度足够低，但内部不会产生足够的潮汐热。相反，假设普拉特均衡，我们发现~0.15公里2度地形是很容易实现的。如果存在岩浆海洋，艾里均衡将占主导地位；因此，我们得出结论，木卫一不太可能拥有岩浆海洋。