Землеподобные модели внутреннего строения Венеры

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Abstract

На основе модели Земли PREM построены более тысячи моделей внутреннего строения Венеры, отличающихся радиусом и плотностью ядра, плотностью мантии, распределением вязкости и реологией. Радиус ядра варьируется в интервале от 2800 км до 3600 км, плотность в мантии и в ядре меняется в пределах нескольких процентов от значений модели PREM. При расчете приливных чисел Лява для учета неупругости мантии применяется реология Андраде. Используются именно те значения параметров реологической модели Андраде, которые наилучшим образом описывают приливную деформацию Земли. Это заметно снижает погрешность при вычислении чисел Лява. Показано, что у Венеры может быть внутреннее твердое ядро только в том случае, если состав планеты сильно отличается от земного. Сравнение наблюдаемых значений момента инерции и приливного числа Лява k2 с модельными величинами позволило заключить, что радиус ядра Венеры с большой вероятностью находится в интервале 3288±167 км.

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About the authors

D. O. Amorim

Московский физико-технический университет

Author for correspondence.
Email: amorim.dargilan@gmail.com
Russian Federation, Москва

Т. В. Гудкова

Институт физики Земли им. О.Ю. Шмидта РАН

Email: gudkova@ifz.ru
Russian Federation, Москва

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Supplementary files

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2. Fig. 1. For three models of Venus the following dependences are given: (a) – density on depth; (b) – density on pressure; (c) – shear modulus on depth; (d) – compression modulus on depth. The following models of Venus are considered: with an Earth-like structure (Rc = 3200 km, B = 1), with a small and light core (Rc = 2800 km, B = 0.98), with a large and dense core (Rc = 3600 km, B = 1.02).

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3. Fig. 2. Values ​​of the parameter A for a set of models of the internal structure of Venus. Dashed lines highlight Earth-like models with A in the range from 0.98 to 1.02. Models with A = 1 correspond to a planet with a mantle density as in PREM.

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4. Fig. 3. Pressure values ​​at the center of Venus for a set of models of the internal structure. The dashed line shows the pressure value at the boundary of the inner core of the Earth (the EIB boundary).

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5. Fig. 4. Values ​​of the moment of inertia for the constructed models of the internal structure of Venus. Dashed lines highlight the interval 0.337 ± 0.024 (Margot et al., 2021), the blue solid line is the moment of inertia of the Earth.

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6. Fig. 5. Values ​​of the real part of the tidal Love number k2 for Venus models depending on the core radius for the limiting viscosity models: (a) – MNV; (b) – MWV. Dashed lines highlight the interval of the observed value 0.295 ± 0.066 (2σ) from (Konopliv, Yoder, 1996). Colored triangles show the values ​​of k2 for some models with specific combinations of B, ζ and α.

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7. Fig. 6. Values ​​of the real part of the tidal Love number k2 of the constructed Venus models depending on the radius of the core. For each value of Rc, there is an interval of k2, which is obtained by varying the viscosity, B, α and ζ in the limits discussed in the text. Dashed lines highlight the interval of the observed value 0.295 ± 0.066 (2σ) from (Konopliv, Yoder, 1996). Colored dots show the values ​​of k2 of specific models.

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8. Fig. 7. All calculated models of the internal structure of Venus on the I × k2 plane. The intersection of the dashed lines indicates the central values ​​of I = 0.337 and k2 = 0.295. The colored lines are the level lines of the probability function according to formula (10).

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9. Fig. 8. Models with specific values ​​of the core radius on the I × k2 plane. The intersection of the dashed lines indicates the central values ​​I = 0.337 and k2 = 0.295. The level lines of the probability function are shown, as in Fig. 7.

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10. Fig. 9. Probability of each value of the radius of the core of Venus. The highest probability is for models with Rc = 3300 km. If we approximate the points with P > 0.3 with a normal distribution (dashed line), Rc = 3288 ± 167 km.

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11. Fig. 10. Values ​​of the tidal phase shift ε for all calculated models. Models with low viscosity have large values ​​of the phase shift, and models with high viscosity have small ε.

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12. Fig. 11. Values ​​of the tidal Love number h2 for all calculated models.

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