Available Energy for Life on a Planet, with or without Stellar Radiation

The quest for life in the Universe is often affected by the free use of extrapolations of our phenomenological geocentric knowledge. We point out that the existence of a living organism, and a population of organisms, requires the existence of available energy or, more precisely, available power per unit volume (Sect. 1). This is not a geocentric concept, but a principle that belongs to the foundations of thermodynamics. A quest about availability in the Universe is justified. We discuss the case in which power comes from mining (Sect. 2), and from thermal disequilibrium (Sect. 3). Thermal disequilibrium may show up in two ways: on planets without a star (Sect. 4), and on planets where the surface thermal disequilibrium is dominated by the incoming photon flux from the nearest star (Sect. 6). In the first case we study the availability by simulating the structure of the planet with a simple model that contains the general features of the problem. For the first case we show that the availability is in general very small (Sect. 5). In the second case we show that the availability is in general large; the order of magnitude depends first of all on the star's temperature and the planet's orbit, but is also controlled by the greenhouse gases present on the planet.Comment: 30 pages, 10 figures, to be published in Nuovo Cimento

Prey-predator dynamics driven by the solar radiation. Part I

We study a model ecosystem represented by two components: prey and predator. The predator feeds only on the prey, the prey, in turn, feeds on the solar radiation. In this scheme the two-species dynamics is no longer independent of the external physical conditions. Such independence was instead postulated in the Lotka-Volterra scheme. In this paper we consider the growth of the prey not unbounded (exponential), but logistic, where the saturation factor is governed by the available solar flux, more precisely by the percent of the solar flux that contains the photon frequencies which can drive the photosynthesis. In this way the solar flux represents the driving term of the dynamics, as we expect in general for a realistic ecosystem. The system is asymptotically stable. The equilibrium values of the prey and predator numbers depend on several parameters. The system contains two nonlinear coupling terms and two coupling parameters. The dependence of the equilibrium point on the coupling parameters is studied in detail. According to this model, we can define a predator efficiency and a global solar efficiency. We discuss the relationship between these two functions of the coupling parameters and the maximum value that the predator population can reach

Constraints in the coupling Star-Life

If life is sustained by a process of photosynthesis, not necessarily the same existing on Earth, the surface temperature of the star and the orbit of the host planet cannot be whatsoever. In fact the global life cycle, no matter how complicated, must contain in general an upper photochemical branch and a lower dark branch, characterized by a higher and a lower temperature. These two temperatures are star-orbit related. The velocity along the cycle or, in other words, the power of the life machine, depends in general on several other parameters. First of all the Gibbs photon availability, which is a star-orbit parameter and is the input for the upper branch. Then follows the energy cascade that develops along the organic web with a large number of interactions and typical times that must match the typical times generated by the combination of spin value and orientation, eccentricity and precession. Finally, the capacity of the web to keep the global life cycle running along the life span of the star, comes from some inner form of self-endurance and self-balance. The property of not being transient could be the right way of introducing the concept of intelligent life.Comment: 56 pages, 21 figures. In order to reduce size, the version on the archive has low-resolution figures. A version of the paper with full resolution may be requested to [email protected]

Prey-predator dynamics with periodic solar input. Part II

We study a two-component model ecosystem driven by a sinusoidal solar radiation. The governing dynamical system is expressed by two nonlinear differential equations, where the driving term appears factorized to one of the two unknown functions. We show that the solution is asymptotically periodic, with the period of the driving term. Moreover, we find that the asymptotic solution, with the variation of the frequency of the input, shows a resonant-like behaviour. We discuss the interesting similarity between the response of the ecosystem to the external driving term and the response of a genuine resonant system

Eigenphases of the S-matrix at high energy

In the spirit of a statistical approach to the S-matrix, the authors discuss the concept of resonant state and are led to generalize the eigenphase formalism to many-particle processes. They show that the object to be considered is the connected part of the S-matrix at fixed total four-momentum and they give strong arguments in favour of the conjecture that this operator is compact. This enables them to write a generalized eigenfunction expansion. They define a 'structure function' which describes the distribution of the eigenvalues and study some of its general properties. They consider also some consequences of the assumption that the amplitude is dominated by resonances. (15 refs)