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Register a new userPlanets: Power Laws and Classification
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Added by
Hector Javier Durand-Manterola
Publication date
2011
fields
Physics
and research's language is
English
Authors
Hector Javier Durand-Manterola
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The study of the interior of the planets requires the knowledge of how certain parameters, as radius and mean density, vary according to the planet mass. The aim of this work is to use known data of the Solar System Planets and Transiting Exoplanets (specifically the radius and mass) to create empirical laws for the planetary radius, mean density, and surface gravity as a function of mass. The method used is to calculate with the available data, the mean density and surface gravity for the planets and adjusts, using the least squares method, a function with respect to the radius-mass, density-mass and surface gravity-mass relations. In the mass interval from 10E19 to 10E29 kg, the planets separate in a natural way into three groups or classes which I called class A, class B and class C. In all these classes and with all the functions (radius, median density and surface gravity) those best fits are power laws.
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A planetary mass scale and a system of composition codes are presented for describing the geophysical characteristics of exoplanets and Solar System planets, dwarf planets, and spherical moons. The composition classes characterize the rock, ice, and gas properties of planetary bodies. The planetary mass scale includes five mass classes with upper and lower mass limits derived from recent studies of the exoplanet mass radius and mass density relationships and the physical characteristics of planets, dwarf planets, and spherical moons in the Solar System. The combined mass and composition codes provide a geophysical classification that allows for comparison of the global mass and composition characteristics of exoplanets with the Solar Systems planets, dwarf planets, and spherical moons. The system is flexible and can be combined with additional codes characterizing other physical, dynamical, or biological characteristics of planets.
The mass and distance functions of free-floating planets (FFPs) would give major insights into the formation and evolution of planetary systems, including any systematic differences between those in the disk and bulge. We show that the only way to measure the mass and distance of individual FFPs over a broad range of distances is to observe them simultaneously from two observatories separated by $Dsim {cal O}(0.01,AU)$ (to measure their microlens parallax $pi_{rm E}$) and to focus on the finite-source point-lens (FSPL) events (which yield the Einstein radius $theta_{rm E}$). By combining the existing KMTNet 3-telescope observatory with a 0.3m $4,{rm deg}^2$ telescope at L2, of order 130 such measurements could be made over four years, down to about $Msim 6,M_oplus$ for bulge FFPs and $Msim 0.7,M_oplus$ for disk FFPs. The same experiment would return masses and distances for many bound planetary systems. A more ambitious experiment, with two 0.5m satellites (one at L2 and the other nearer Earth) and similar camera layout but in the infrared, could measure masses and distances of sub-Moon mass objects, and thereby probe (and distinguish between) genuine sub-Moon FFPs and sub-Moon ``dwarf planets in exo-Kuiper Belts and exo-Oort Clouds.
The rapidly developing theory of complex networks indicates that real networks are not random, but have a highly robust large-scale architecture, governed by strict organizational principles. Here, we focus on the properties of biological networks, discussing their scale-free and hierarchical features. We illustrate the major network characteristics using examples from the metabolic network of the bacterium Escherichia coli. We also discuss the principles of network utilization, acknowledging that the interactions in a real network have unequal strengths. We study the interplay between topology and reaction fluxes provided by flux-balance analysis. We find that the cellular utilization of the metabolic network is both globally and locally highly inhomogeneous, dominated by hot-spots, representing connected high-flux pathways.
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that is ubiquitous in the real world, and calculate its degree distributions. Our results show that the tails of its degree distributions exhibits a distinct power law feature, providing robust theoretical support for the ubiquity of the power law feature. Second, we suggest that in the real world two important factors, network size and node disappearance probability, point to the existence of the power law feature in the observed networks. As network size reduces, or as the probability of node disappearance increases, then the power law feature becomes increasingly difficult to observe. Finally, we suggest that an effective way of detecting the power law property is to observe the asymptotic (limiting) behaviour of the degree distribution within its effective intervals.
Two separate statistical tests are applied to the AGASA and preliminary Auger Cosmic Ray Energy spectra in an attempt to find deviation from a pure power-law. The first test is constructed from the probability distribution for the maximum event of a sample drawn from a power-law. The second employs the TP-statistic, a function defined to deviate from zero when the sample deviates from the power-law form, regardless of the value of the power index. The AGASA data show no significant deviation from a power-law when subjected to both tests. Applying these tests to the Auger spectrum suggests deviation from a power-law. However, potentially large systematics on the relative energy scale prevent us from drawing definite conclusions at this time.
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