III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet, Incubator Lifescape

B. Our Whole Scale EcosmoVerse Description Project

Pranav, Pratyush, et al. The Topology of the Cosmic Web in Terms of Betti Numbers. arXiv:1608.04519. In 2016, a seven person astronomer team from the Netherlands and Austria can describe is mathematical detail how interstellar and intergalactic reaches are formed and distinguished by vast network “connectivities” which stretch across megaparsecs. Notable phrases are algebraic topology, persistent homology, computational formalism, and fractal, multiscale hierarchies. Search Coutinho for a similar posting in April as The Network Behind the Cosmic Web (1604.03236). But our further interest is a concurrent neuroscience entry Algebraic-Topological Tools for Understanding Higher-Order Structure in Neural Data (1601.01704, search Giusti), which uses the same technical phrases to describe the human connectome. In our midst, largely unbeknownst, are an appearance of inherent congruences between such widely separate realms. Might in turn we imagine a cosmic connectome, whereof our phenomenal purpose is to learn to decode, sequence, read, and continue?

We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure, and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles.

The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different weblike morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of weblike configurations, and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys. (Abstract)

In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes, after Enrico Betti (1823-1892), an Italian mathematician. In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane, after Georgy Vorony (1868-1908), a Russian mathematician.

Pratt, Gabriel, et al. The Galaxy Cluster Mass Scale. Space Science Reviews. 215/25, 2019. In a topical collection, Clusters of Galaxies: Physics and Cosmology, we cite this entry by eight European astrophysicists for its discussion of how it might be possible to weigh the “total mass of a galactic cluster.” This value is said to be important because it will impact other “cosmological constraints.” We also wish to reflect on how fantastic it is that our worldwise collaborative sentient species can in a few decades be able to consider and achieve such quantifications of universal significance. Surely we peoples must possess some heretofore unrealized purpose and futurity.

Regev, Oded. Chaos and Complexity in Astrophysics. Cambridge: Cambridge University Press, 2006. A comprehensive text in two parts – a 250 page primer on complex systems theory, followed by 200 pages of cosmological applications. By these advances, a ‘hierarchical spatial clustering’ in both the interstellar medium and the distribution of galaxies is found to have a fractal self-similar geometry up to the largest cosmic scales.

The most striking quality of this modern approach to dynamical systems theory is, in my view, its extremely diverse range of applicability. Mechanics, fluid dynamics, chemical kinetics, electronic circuits, biology and even economics, as well as astrophysics, are among the subjects in which chaotic behavior occurs. At the heart of the theory lies the quest for the universal and the generic, from which an understanding of complicated and seemingly heterogeneous phenomena can emerge. The ideas of bifurcations, strange attractors, fractal sets and so on, seem to provide the tools for such an unexpected conceptual unification. (ix)

NOVA Universe Revealed: Age of Stars. kpbs.org/news/2021/10/21/universe-revealed-on-nova-age-of-stars. A home website for this autumn 2021, four part Universe Revealed series. The other three were about the Milky Way, the Big Bang, and Black Holes. By way of authoritative speakers and graphic imagery, this lead program achieved a latest epochal vista. As not possible earlier, a grand scenario was traced from an original point some 13.8 billion years ago all the wild way to our planetary sapience. A philoSophia view can then wonder how fantastic it is that a habitable speciesphere can altogether look back reconstruct from whence they came. We note also for its outlines of a second singularity cited at the close of our 2022 Introduction. But as still set in the old scheme of no greater reality, especially no purpose for peoples who incredibly can achieve this, we remain mere spectators.

The sun is a constant presence in our lives and has been a lifegiving source of light, heat, and energy for 4.6 billion years. Yet we’ve only begun to learn about its past and its place among an even grander cycle of birth, death, and renewal that makes this the age of stars. Here we view a trail of evidence leads back to the first star nurseries, forging the elements that would make up planets and our own bodies. And for a final act, we glimpse billions of years into the future, when our sun and the age of stars will fade to darkness.

Rosa, A. C. P., et al. Nonextensivity and Entropy of Astrophysical Sources. Physica A. Online July, 2013. We select this paper by Programa de Modelagem Computacional - SENAI - Cimatec, and Departamento de Fsica – UEFS, Brazil, physicists from a growing number that seek to describe such cosmic phenomena by way of the same complex, self-similar systems found everywhere in nature from biochemicals to civilizations. The work is based on the “nonextensive statistics” theory from Constantine Tsallis over the past two decades, see his Introduction to Nonextensive Statistical Mechanics (Springer, 2009). While equilibrium thermodynamics applies to closed, short-range cases with an “extensive” entropy, in open natural realms as this, a far-from-equilibrium, “non-extensive” entropic version is rightfully required. Compare, for example, with Figueiredo, P. H., et al for proteins, Pittman-Polletta, Benjamin, et al for physiology, and Hu, Kun, et al for cerebral activities.

We study the x-ray intensities of 142 light curves of cataclysmic variables, galaxies, pulsars, supernovae remnants and other x-ray sources present in the public data collected by the instrument All Sky Monitor on board of the satellite Rossi x-ray timing explorer. We show that the x-ray light curves coming from astrophysical systems obey Tsallis’s q-gaussian distribution as probability density. This fact strongly suggests that these astrophysical systems behave in a non-extensive manner. Furthermore, the q entropic index for these systems were obtained and they provide an indication of the nonextensivity degree of each one of these astrophysical systems. (Abstract)

X-rays arising from astrophysical systems are due to the diffusive processes that atomic particles are submitted on their gravitation field. Cataclysmic variables, x-ray binary systems, pulsars and quasars have their own characteristics, but a similarity shows up when we observe the power-law and scale invariant correlations in their x-ray light curves. In this sense, in recent years, there has been growing evidence indicating that astrophysical systems have self-affinity characterized by long range power-law correlations. In astrophysics, these long-range correlations have been applied to the study of simulations in self-gravitating systems - non-equilibrium structures that feature characteristic of long-range correlations - in the analysis of galaxy distribution and in the characterization of self-similarity in solar active regions. (1)

Rowan-Robinson, Michael. The Nine Numbers of the Cosmos. Oxford, UK: Oxford University Press, 1999. The density of baryonic matter, anisotropy, rate of expansion, age, microwave background temperature, density of both cold and hot dark matter, cosmological constant, and star formation history altogether make the universe comprehensible.

Scharf, Caleb. Is Physical Law an Alien Intelligence? Nautilus. Issue 42, 2016. The Columbia University astrobiologist (search) muses over trending evidence with regard to universal, and multiversal properties which inspire inklings that maybe lively systems equations and systems are actually an intrinsic essence which suffuse our reality. Our interest is to say that such an epochal revolution might imply, akin to Gaian self-regulation on Earth, that animate forces might similarly begin to influence the entire ecosmos.

The universe began to expand at an accelerated rate about 5 billion years ago. This acceleration is conventionally chalked up to dark energy. In fact, one explanation is that the timing has to do with life—an anthropic argument. The dark energy didn’t become significant until enough time had gone by for life to take hold on Earth. For many cosmologists, that means our universe must be part of a vast multiverse where the strength of dark energy varies from place to place. We live in one of the places suitable for life like us. Elsewhere, dark energy is stronger and blows the universe apart too quickly for cosmic structures to form and life to take root. But perhaps there is another reason for the timing coincidence: that dark energy is related to the activities of living things. After all, any very early life in the universe would have already experienced 8 billion years of evolutionary time by the time expansion began to accelerate. It’s a stretch, but maybe there’s something about life itself that affects the cosmos.

Schrijuver, Karel, et al. Principles of Heliophysics: A Textbook on the Universal Processes behind Planetary Habitability. arXiv:1910.14022. This is a 426 page edition by 60 authors which begins with Foundations from matter and energy to the wide array of stellar suns, exoplanetary systems, radiative forces, torques and tides, and more. A next section Comparative Eco-Astrophysics adds evolutionary trajectories for myriad stars, worlds, atmospheres, relative habitability, magnetospheres, and indeed everything under the sun and cosmos.

Schumacher, Jorg and Katepalli Sreenivasan. Colloquium: Unusual Dynamics of Convection in the Sun. Reviews of Modern Physics. 92/041001, 2020. Technical University of Ilmenau, Germany and NYU Tandon School mathematicians (search KS) proceed to analyze, model and describe the active turbulence that composes our home star. We note for its content, and also to record and reflect how incredible it is that we curious creaturely beings are able to achieve such deep and wide cosmic quantifications. One wonders what participant agency and function we peoples are, as yet unawares, carrying out.

The Sun is our nearest star; it is also the most important star that determines life on Earth. A large variety of phenomena observed on the Sun’s surface, with potential impact on Earth, is thought to arise from turbulent convection in Sun’s interior, this being the dominant mode of heat transport within the outer envelope at r≳0.715R⊙. However, convection in the Sun differs in most of its aspects from convection processes known on Earth, certainly those under controlled laboratory conditions, thus seriously challenging existing physical models of convective turbulence and boundary conditions in the Sun. Solar convection is a multiscale-multiphysics phenomenon including the transport of mass, momentum, and heat in the presence of rotation, dynamo action, radiation fluxes, and partial changes in chemical composition. (Abstract excerpt)

Stanway, Elizabeth. Applications of Stellar Population Synthesis in the Distant Universe. /galaxies. 8/1, 2020. A University of Warwick astrophysicist provides another example of the 21st century reach and depth of scientific explorations still in thier initial development via Earth and space sensory instrumentation, along with computational methods. By a natural philoSophia going forward, our collaborative humankinder, as able to instantly post, communicate, iterate and advance, seems poised to carry out a self-quantitative description of the whole animate ecosmos.

This review discusses both our current state of understanding of galaxies in the distant Universe, and how that understanding is informed by the stellar population synthesis models we use. Key examples and uncertainties are highlighted, and a holistic approach, in which all possible diagnostic indicators of a stellar population are considered, is advocated. (2)

Steinhardt, Charles and Josh Speagle. A Uniform History for Galaxy Evolution. arXiv:1409.2883. In a paper to appear in the Astrophysical Journal, California Institute of Technology and University of Tokyo researchers report a consensus observation result that developing galaxies of a common mass are remarkably similar to each other at any fixed redshift over a broad range. With such affinities, they are seen to have a predictable temporal course as a “morphological evolution.” But how amazing is it that human persons on a minute orb are yet able at all to quantify, describe, and comprehend such vast reaches. Surely there must be some reason of cosmic import unto discovery that we ought to ask about.

Recent observations indicate a remarkable similarity in the properties of evolving galaxies at fixed mass and redshift, prompting us to consider the possibility that most galaxies may evolve with a common history encompassing star formation, quasar accretion, and eventual quiescence. We quantify this by defining a "synchronization timescale" for galaxies as a function of mass and redshift that characterizes the extent to which different galaxies of a common mass are evolving in the same manner at various cosmic epochs. As a result, we propose a model in which the star-forming "main sequence", analogous quasar behavior, and other observations form a galactic evolution "main sequence", in which star formation occurs earliest, followed by supermassive black hole accretion, and feedback between the two are dominated by deterministic rather than stochastic processes. (Abstract)

Strigari, Louis, et al. A Common Mass Scale for Satellite Galaxies of the Milky Way. Nature. 454/1096, 2008. A collaboration from Irvine, Pasadena, New Haven, Cambridge, MA, and Cambridge, UK finds that some 23 mini-galaxies around the Milky Way, a notable discovery in themselves, in a realm attributed to dark matter, can be seen to take on a correlative hierarchical geometry. One then wonders what kind of universe evolves an Earthkind whom is lately able to gain such consciously perceived quantification.

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