Inferring the interior of Venus from the tides

Hi there! Today’s post presents you the study Tidal constraints on the interior of Venus, by Caroline Dumoulin, Gabriel Tobie, Olivier Verhoeven, Pascal Rosenblatt, and Nicolas Rambaux. This study has recently been accepted for publication in Journal of Geophysical Research: Planets. The idea is: because of its varying distance to the Sun, Venus experiences periodic variations. What could their measurements tell us on the interior?

Venus vs. the Earth

Venus is sometimes called the twin sister of the Earth, because of its proximity and its size. However, their physical properties show crucial differences, the most crucial one being the atmosphere.

Venus Earth
Semimajor axis (AU) 0.723332 1.000001
Eccentricity 0.0068 0.0167
Inclination 3.86° 7.155°
Obliquity 177.36° 23.439°
Orbital period 224.701 d 365.256 d
Spin period 243.025 d 0.997 d
Surface pressure 92 bar 1.01 bar
Magnetic field (none) 25-65 μT
Mean density 5,243 kg/m3 5,514 kg/m3

As you can see:

  • Venus has a retrograde and very slow rotation,
  • it has a very thick and dense atmosphere,
  • it has no magnetic field.

For a magnetic field to exist, you need a rotating solid core, a global conductive fluid layer, and convection, which is triggered by heat transfers from the core to the mantle. The absence of magnetic field means that at least one of these conditions is not fulfilled. Given the size of Venus and its measured k2 by the spacecraft Magellan (explanations in the next section), it has probably a fluid global layer. However, it seems plausible that the heat transfer is missing. Has the core cooled enough? Is the surface hot enough so that the temperature has reached an equilibrium? Possible.

Probing the interior of Venus is not an easy task; an idea is to measure the time variations of its gravity field.

Tidal deformations

The orbital eccentricity of Venus induces variations of its distance to the Sun, and variations of the gravitational torque exerted by it. Since Venus is not strictly rigid, it experiences periodic deformations, which frequencies are known as tidal frequencies. These deformations can be expressed with the potential Love number k2, which gives you the amplitude of the variations of the gravity field. Since the gravity field can be measured from deviations of the spacecraft orbiting the planet, we dispose of a measurement, i.e. k2 = 0.295 ± 0.066. It has been published in 1996 from Magellan data (see here a review on the past exploration of Venus). You can note the significant uncertainty on this number. Actually k2 should be decorrelated from the other parameters affecting the trajectory of the spacecraft, e.g. the flattening of the planet, the atmosphere, which is very dense, motor impulses of the spacecraft… This is why it was impossible to be more accurate.

Other parameters can be used to quantify the tides. Among them are

  • the topographic Love number h2, which quantified the deformations of the surface. Observing the surface of Venus is a task strongly complicated by the atmosphere. Magellan provided a detailed map thanks to a laser altimeter. Mountains have been detected. But these data do not permit to measure h2.
  • The dissipation function Q. If I consider that the deformations of the gravity field are periodic and represented by k2 only, I mean that Venus is elastic. That mean that it does not dissipate any energy, it has an instantaneous response to the tidal solicitations, and the resulting tidal bulge always points exactly to the Sun. Actually there is some dissipation, which results as a phase lag between the tidal bulge and the Venus – Sun direction. Measuring this phase lag would give k2/Q, and that information would help to constrain the interior.

A 3-layer-Venus

Such a large body is expected to be denser in the core than at the surface, and is usually modeled with 3 layers: a core, a mantle, and a crust. Venus also have an atmosphere, but this is not a very big deal in this specific case. These are not necessarily homogeneous layers, the mantle and the core are sometimes assumed to have a global outer fluid layer. If this would happen for the core, then we would have a solid (rigid) inner core, and a fluid (molten) outer core. This interior must be modeled to estimate the tidal quantities. More precisely, you need to know the radial evolution of the density, and of the velocities of the longitudinal (P) and transverse (S) seismic waves. These two velocities tell us about the viscosity of the material.

Possible interior of Venus (not to scale). Copyright: The Planetary Mechanics Blog

Modeling the core from PREM

PREM is the Preliminary Reference Earth Model. It was published in 1981, and elaborated from thousands of seismic observations. Their inversions gave the radial distribution of the density, dissipation function, and elastic properties for the Earth. It is now used as a standard Earth model.

The lack of data regarding the core of Venus prompted the authors, and many of their predecessors, to rescale PREM from the Earth to Venus.

Modeling the mantle from Perple_X

The properties of the mantle of Venus depend on its composition and the radial distribution of its temperature, its composition itself depending on the formation of the planet. The authors identified 5 different models of formation of Venus in the literature, which affect 5 variables: mass of the core, abundance of uranium (U), K/U ratio (K: potassium), Tl/U ratio (Tl: thallium), and FeO/(FeO+MgO) ratio (FeO: iron oxide, MgO: magnesium oxide). Only 3 of these 5 models were kept, two being end-members, and the third one being pretty close to the Earth. These 3 models were associated with two end-members for temperature profiles, which can be found in the scientific literature. This then resulted in 6 models, and their properties, i.e. density and velocities of the P- and S-waves, were obtained thanks to the Perple_X code. This code gives phase diagrams in a geodynamic context, i.e. under which conditions (pressure and temperature) you can have a solid, liquid, and / or gaseous phase(s) (they sometimes coexist) in a planetary body.

Numerical modeling of the tidal parameters

Once the core and the mantle have been modeled, a 60-km-thick crust have been added on the top, and then the tidal quantities have been calculated. For that, the authors used a numerical algorithm elaborated in Japan in 1974, using 6 radial functions y. y1 and y3 are associated with the radial and tangential displacements, y2 and y4 are related to the radial and tangential stresses, y5 is associated with the gravitational potential, while y6 guarantees a property of the continuity of the gravitational force in the structure. These functions will then give the tidal quantities.


The results essentially consist of a description of the possible interiors and elastic properties of Venus for different values of k2, which are consistent with the Magellan measurements. But the main information is this: Venus may have a solid inner core. Previous studied had discarded this possibility, arguing that k2 should have been 0.17 at the most. However, the authors show that considering viscoelastic properties of the mantle, i.e. dissipation, would result in a smaller pressure in the core, i.e. <300 GPa, for a k2 consistent with Magellan. This does not mean that Venus has a solid inner core, this just means that it is possible. Actually, the authors also get interior models with a fully fluid core.
The atmosphere would alter k2 by only 3 to 4%.

The authors claim that the uncertainty on k2 is too large to have an accurate knowledge on the interior, and they hope that future measurements of k2 and of k2/Q, which has never been measured yet, would give better constraints.

The forthcoming and proposed missions to Venus

For this hope to be fulfilled, we should send spacecrafts to Venus in the future. The authors mention EnVision, which applies to the ESA M5 call (M for middle-class). This is a very competitive call, and we should know the finalists very soon. If selected, EnVision would consist of an orbiter on a low and circular orbit, which would focus on geology and geochimical cycles. It should also measure k2 with an accuracy of 3%, and give us a first measurement of k2/Q.

In America, two missions to Venus have been proposed for the Discovery program of NASA: VERITAS (Venus Emissivity, Radio Science, InSAR, Topography, and Spectroscopy) and DAVINCI (Deep Atmosphere Venus Investigation of Noble gases, Chemistry, and Imaging). They have both been rejected.

To know more

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