The impact of tidal friction evolution on the orbital decay of ultra-short period planets

Unveiling the fate of ultra-short period (USP) planets may help us understand the qualitative agreement between tidal theory and the observed exoplanet distribution. Nevertheless, due to the time-varying interchange of spin-orbit angular momentum in star-planet systems, the expected amount of tidal friction is unknown and depends on the dissipative properties of stellar and planetary interiors. In this work, we couple structural changes in the star and the planet resulting from the energy released per tidal cycle and simulate the orbital evolution of USP planets and the spin-up produced on their host star. For the first time, we allow the strength of magnetic braking to vary within a model that includes photo-evaporation, drag caused by the stellar wind, stellar mass loss, and stellar wind enhancement due to the in-falling USP planet. We apply our model to the two exoplanets with the shortest periods known to date, NGTS-10b and WASP-19b. We predict they will undergo orbital decay in time-scales that depend on the evolution of the tidal dissipation reservoir inside the star, as well as the contribution of the stellar convective envelope to the transfer of angular momentum. Contrary to previous work, which predicted mid-transit time shifts of ∼30 − 190 s over 10 years, we found that such changes would be smaller than 10 s. We note this is sensitive to the assumptions about the dissipative properties of the system. Our results have important implications for the search for observational evidence of orbital decay in USP planets, using present and future observational campaigns.

Modelling moving force of tectonic plates with the use of length of day variation

<p>The nature, the age and probably first of all the magnitude of driving forces of plate motion since long are a subject of scientific debates and it cannot be regarded as clarified even today.</p><p>The physical basis of recent plate tectonics is characterized by interaction between plates by viscous coupling to a convecting mantle.  Authors are going to demonstrate that changes in the Earth's axial rotation can affect the movement of tectonic plates, and the phenomenon of tidal friction is able to shift the lithospheric plates.</p><p>The tidal friction regulates the length of day (LOD)and consequently also the rotational energy of the Earth. It can be investigated with the use of total tidal energy<sub>, </sub>which can be determined as a sum of three energies (energy of axial rotation of the Earth, Moon’s orbital energy around the common centre of mass and the mutual potential energy). It was found that during the last 3 Ga the Earth lost 33% of its rotational energy. The LOD 0.5Ga BP (before present) was ~21 h. This means that the rotational energy loss rate was 4.1 times higher during the Pz (Phanerozoic, from 560 Ma BP to our age) than earlier in the Arch (Archean, 4 to 2.5 Ga BP) and Ptz (Proterozoic 2.5 to0.56 Ga BP). The low-velocity zone (LVZ) at 100-200 km depth interval, close to the boundary between the lithosphere and the asthenosphere characterized by a negative anomaly of shear wave velocities. Consequently, the LVZ can result in a decoupling effect. Tidal friction brakes the lithosphere and the part of the Earth below the asthenosphere with different forces. By model calculation, we show that this force difference is sufficient to move the tectonic plates along the Earth’s surface.  </p><p>Reference: Varga P., Fodor Cs., 2021. About the energy and age of the plate tectonics, Terra Nova. (in print) https://doi.org/10.1111/ter.12518</p>

High-eccentricity migration of planetesimals around polluted white dwarfs

ABSTRACT Several white dwarfs (WDs) with atmospheric metal pollution have been found to host small planetary bodies (planetesimals) orbiting near the tidal disruption radius. We study the physical properties and dynamical origin of these bodies under the hypothesis that they underwent high-eccentricity migration from initial distances of several astronomical units. We examine two plausible mechanisms for orbital migration and circularization: tidal friction and ram-pressure drag in a compact disc. For each mechanism, we derive general analytical expressions for the evolution of the orbit that can be rescaled for various situations. We identify the physical parameters that determine whether a planetesimal’s orbit can circularize within the appropriate time-scale and constrain these parameters based on the properties of the observed systems. For tidal migration to work, an internal viscosity similar to that of molten rock is required, and this may be naturally produced by tidal heating. For disc migration to operate, a minimal column density of the disc is implied; the inferred total disc mass is consistent with estimates of the total mass of metals accreted by polluted WDs.

Tidal evolution of eccentric binaries driven by convective turbulent viscosity

ABSTRACT Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main-sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency ωtide; when ωtide is larger than the turnover frequency of convective eddies, the viscosity is reduced. Previous works have focused on binaries in nearly circular orbits. However, for eccentric orbits, the tidal potential has many forcing frequencies. In this paper, we develop a formalism for computing tidal dissipation that captures the effect of frequency-dependent turbulent viscosity and is valid for arbitrary binary eccentricities. We also present an alternative simpler formulation that is suitable for very high eccentricities. We apply our formalisms to a giant branch (GB) star model and a solar-type star model. We find that a range of pseudo-synchronous rotation rates are possible for both stellar models, and the pseudo-synchronous rate can differ from the prediction of the commonly used weak tidal friction theory by up to a factor of a few. We also find that tidal decay and circularization due to turbulent viscosity can be a few orders of magnitude faster than predicted by weak tidal friction in GB stars on eccentric, small pericentre orbits, but is suppressed by a few orders of magnitude in solar-type stars due to viscosity reduction.

Development of the Distance Earth-Moon

The expansion of the universe has a much larger dimension than previously thought. Because of entropy constancy, all masses must fall and all distances must increase. This is investigated using the example of the development of the distance Earth-Moon. The influence of tidal friction on the increase in distance is investigated and quantified. It was found that tidal friction exerts less influence than is currently assumed. If the influence of expansion and tidal friction is taken into account, a very good agreement between the calculations made here and the measured distance is achieved.

6. Tides and the Earth

‘Tides and the Earth’ explains that the energy in tides comes, ultimately, from the Earth’s spin. Tidal streams, rubbing against the seabed, lose energy through friction and, to make up for this loss, energy is transferred into the tide from the Earth’s spin. As a result, Earth’s rotation is gradually slowing and the day is lengthening. Most tidal friction happens in shelf seas, where the currents are strongest and the water is shallow, but there is an additional loss of energy in the body of the deep ocean, through the creation of waves called internal tides, which mix the interior of the deep ocean.

Eclipses and the Earth’s Rotation

Analysis of historical records of eclipses of the Sun and Moon between 720 BC and AD 1600 gives a measure of the time difference, TT − UT = ΔT. The first derivative in time along a smooth curve fitted to the values of Δ T measures the changes in the length of the day (lod). The average rate of change of the lod is found to be significantly less than that expected on the basis of tidal friction. Fluctuations on a time-scale of centuries to millennia are mainly attributed to the effects of post-glacial uplift and core-mantle coupling.

Measurement of the Earth's rotation: 720 BC to AD 2015

New compilations of records of ancient and medieval eclipses in the period 720 BC to AD 1600, and of lunar occultations of stars in AD 1600–2015, are analysed to investigate variations in the Earth’s rate of rotation. It is found that the rate of rotation departs from uniformity, such that the change in the length of the mean solar day (lod) increases at an average rate of +1.8 ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3 ms per century. Besides this linear change in the lod, there are fluctuations about this trend on time scales of decades to centuries. A power spectral density analysis of fluctuations in the range 2–30 years follows a power law with exponent −1.3, and there is evidence of increased power at a period of 6 years. There is some indication of an oscillation in the lod with a period of roughly 1500 years. Our measurements of the Earth’s rotation for the period 720 BC to AD 2015 set firm boundaries for future work on post-glacial rebound and core–mantle coupling which are invoked to explain the departures from tidal friction.