# Analysis of Tidal Accelerations in the Solar System and in Extrasolar Planetary Systems
## 4 Discussion
This can be explained by the fact that due to the large radius of Earth, accretion heat from the period of formation and radioactive heating contribute more to the occurrence of volcanism on Earth than tidal heating. This also illustrates the need for awareness and consideration of other influences not covered just by tidal acceleration or tidal heating. Nevertheless, this is not a contradiction to our approach. In Figures 6 and 7, one can easily distinguish two main domains (indicated approximately by the dashed line): big objects like our Earth appear at the far-right margin of the plots at large radii \(R\), implying large contributions from radioactive decay and stored accretion energy. The other domain is tidally interesting objects, appearing at the top in the center and the left margin of the plots with small to intermediate radii \(R\) but large tidal accelerations. Therefore, this domain is the interesting one for tidal heating as the main contribution. Accretion heat and radioactive heating should be minor. All the objects considered as interesting ones in our study for the solar system can be found in this domain. It can be divided into two sub-domains: The top center contains the already well-known objects in the context of (cryo-)volcanism and tidal heating. The top left corner contains the additional objects suggested in this study, which have not been subjects of research for tidal heating until now. When looking at Figures 6 and 7, generalized boundaries for where cryo- and siliceous volcanism might be expected for a celestial object based on our solar system may not easily be transferred to extrasolar planetary systems. The smaller the extrasolar objects are (small radii \(R\) below the size of Earth), the easier this is to perform, as then mainly tidal forces should dominate the potential volcanic activity on these worlds. Approximate boundaries based on our solar system might be given to estimate the tidal-dominated volcanic activity on small extrasolar objects in future studies: The before mentioned minimal values of \(10^{-15}\) (m\({}^{2}\)/s\({}^{4}\)d) for \(\{A_{total}\)-\((\Delta A_{total}\)/\(\Delta t)\}_{max}\) and 200 km for \(R\) should hint at possible cryovolcanic activity when found in an extrasolar planetary system. The lower bound for potential siliceous volcanism powered by tidal influences might be deduced by the order of magnitude of the value of \(\{A_{total}\)-\((\Delta A_{total}\)/\(\Delta t)\}_{max}\) for (J1) Io, roughly about \(10^{-4}\) (m\({}^{2}\)/s\({}^{4}\)d) (compare to Table 1). These boundaries may be transferable to sub-Earth-sized extrasolar objects, as potential volcanic processes in these small worlds might clearly be tidal-dominated. For larger extrasolar objects, the two other influences on the volcanic activity mentioned, radioactive decay and stored accretion energy, have to be considered. Both may not be easily modeled when transferring to extrasolar systems of Earth's size and larger. A main reason for that may be the decline of these influences over time. This can already be seen in our solar system, as, e.g., Mars shows signs of mostly extinct volcanism that may mainly be dominated by radioactive decay and stored accretion energy. The larger \(R\), the better internal models considering the remaining accretion energy stored from the object's formation have to be. Additionally, for radioactive heating, other parameters and events have to be considered. These are mainly the metallicity of the host star, uneven distributions of these (radioactive) metals during planetary formation, possible special external metal enrichment events, or other special events shortly after the planet's formation. Examples in the solar system are the potential enrichment of the radioactive aluminum isotope [26]Al in the solar nebula by external sources [46; 47] and the potential giant collision between the proto-Earth and a planetary embryo named Theia forming the Moon and having consequences for the composition of both the Earth and the Moon, see, e.g., [48].