Application of the Titius-Bode Rule to the 55 Cancri System: Tentative Prediction of a Possibly Habitable Planet

Following the notion that the Titius-Bode rule (TBR) may also be applicable to some extra-solar planetary systems, although this number could be relatively small, it is applied to 55 Cancri, which is a G-type main-sequence star currently known to host five planets. Following a concise computational process, we tentatively identify four new hypothetical planetary positions given as 0.081, 0.41, 1.51 and 2.95 AU from the star. The likelihood that these positions are occupied by real existing planets is significantly enhanced for the positions of 1.51 and 2.95 AU in the view of previous simulations on planet formation and planetary orbital stability. For example, Raymond et al. (2008) [ApJ 689, 478] argued that additional planets would be possible between 55 Cnc f and 55 Cnc d, which would include planets situated at 1.51 and 2.95 AU. If two additional planets are assumed to exist between 55 Cnc f and 55 Cnc d, the deduced domains of stability would be given as 1.3-1.6 and 2.2-3.3 AU. The possible planet near 1.5 AU appears to be located at the outskirts of the stellar habitable zone, which is however notably affected by the stellar parameters as well as the adopted model of circumstellar habitability. We also compute the distance of the next possible outer planet in the 55 Cnc system, which if existing is predicted to be located between 10.9 and 12.2 AU, which is consistent with orbital stability constraints. The inherent statistical significance of the TBR is evaluated following the method by Lynch (2003) [MNRAS 341, 1174]. Yet it is up to future planetary search missions to verify or falsify the applicability of the TBR to the 55 Cnc system, and to attain information on additional planets, if existing.Comment: 9 pages, 3 figures, 9 tables; accepted by Publications of the Astronomical Society of Japan; to be published on 2012 August 25; Ref.: PASJ 64 (4

C*-algebras associated with endomorphisms and polymorphisms of compact abelian groups

A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of continuous functions $C(H)$ which acts as multiplication operators on $L^2(H)$. Under a natural condition on the endo- or polymorphism, this algebra is simple and can be described by generators and relations. In the case of an endomorphism it is always purely infinite, while for a polymorphism in the class we consider, it is either purely infinite or has a unique trace. We prove a formula allowing to determine the $K$-theory of these algebras and use it to compute the $K$-groups in a number of interesting examples.Comment: 25 page

Generation of Longitudinal Flux Tube Waves in Theoretical Main-Sequence Stars: Effects of Model Parameters

Context. Continued investigation of the linkage between magneto-acoustic energy generation in stellar convective zones and the energy dissipation and radiative emission in outer stellar atmospheres in stars of different activity levels. Aims. We compute the wave energy fluxes carried by longitudinal tube waves along vertically oriented thin magnetic fluxes tubes embedded in the atmospheres of theoretical main-sequence stars based on stellar parameters deduced by R. L. Kurucz and D. F. Gray. Additionally, we present a fitting formula for the wave energy flux based on the governing stellar and magnetic parameters. Methods. A modified theory of turbulence generation based on the mixing-length concept is combined with the magneto-hydrodynamic equations to numerically account for the wave energies generated at the base of magnetic flux tubes. Results. The results indicate a stiff dependence of the generated wave energy on the stellar and magnetic parameters in principal agreement with previous studies. The wave energy flux F_LTW decreases by about a factor of 1.7 between G0V and K0V stars, but drops by almost two orders of magnitude between K0V and M0V stars. In addition, the values for F_LTW are significantly higher for lower in-tube magnetic field strengths. Both results are consistent with the findings from previous studies. Conclusions. Our study will add to the description of magnetic energy generation in late-type main-sequence stars. Our results will be helpful for calculating theoretical atmospheric models for stars of different levels of magnetic activity.Comment: 9 pages, 5 figures, 6 tables; submitted to Astronomy & Astrophysic

Habitability of Super-Earth Planets around Main-Sequence Stars including Red Giant Branch Evolution: Models based on the Integrated System Approach

In a previous study published in Astrobiology, we focused on the evolution of habitability of a 10 M_E super-Earth planet orbiting a star akin to the Sun. This study was based on a concept of planetary habitability in accordance to the integrated system approach that describes the photosynthetic biomass production taking into account a variety of climatological, biogeochemical, and geodynamical processes. In the present study, we pursue a significant augmentation of our previous work by considering stars with zero-age main sequence masses between 0.5 and 2.0 M_sun with special emphasis on models of 0.8, 0.9, 1.2 and 1.5 M_sun. Our models of habitability consider again geodynamical processes during the main-sequence stage of these stars as well as during their red giant branch evolution. Pertaining to the different types of stars, we identify so-called photosynthesis-sustaining habitable zones (pHZ) determined by the limits of biological productivity on the planetary surface. We obtain various sets of solutions consistent with the principal possibility of life. Considering that stars of relatively high masses depart from the main-sequence much earlier than low-mass stars, it is found that the biospheric life-span of super-Earth planets of stars with masses above approximately 1.5 M_sun is always limited by the increase in stellar luminosity. However, for stars with masses below 0.9 M_sun, the life-span of super-Earths is solely determined by the geodynamic time-scale. For central star masses between 0.9 and 1.5 M_sun, the possibility of life in the framework of our models depends on the relative continental area of the super-Earth planet.Comment: 25 pages, 6 figures, 2 tables; submitted to: International Journal of Astrobiolog