Theoretical foundations of the Schrödinger method for LSS formation [CL]

It has been shown that the formation of large scale structures (LSS) in the universe can be described in terms of a Schr$\ddot{o}$dinger-Poisson system. This procedure, known as Schr$\ddot{o}$dinger method, has no theoretical basis, but it is intended as a mere tool to model the N-body dynamics of dark matter halos which form LSS. Furthermore, in this approach the “Planck constant” $\hbar$ in the Schr$\ddot{o}$dinger equation is just a free parameter. In this paper we give a theoretical foundation of the Schr$\ddot{o}$dinger method based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. The order of magnitude of the effective Planck constant is estimated as $\hbar \sim m^{5/3} G^{1/2} (N/<\rho>)^{1/6}$, where $N$ and $m$ are the number and the mass of the dark matter halos, $<\rho_0>$ is their average density, and $G$ the gravitational constant. The relevance of this finding for the study of LSS is discussed.

F. Briscese
Thu, 15 Dec 16
30/59

Constraints on Bounded Motion and Mutual Escape for the Full 3-Body Problem [EPA]

When gravitational aggregates are spun to fission they can undergo complex dynamical evolution, including escape and reconfiguration. Previous work has shown that a simple analysis of the full 2-body problem provides physically relevant insights for whether a fissioned system can lead to escape of the components and the creation of asteroid pairs. In this paper we extend the analysis to the full 3-body problem, utilizing recent advances in the understanding of fission mechanics of these systems. Specifically, we find that the full 3-body problem can eject a body with as much as 0.31 of the total system mass, significantly larger than the 0.17 mass limit previously calculated for the full 2-body problem. This paper derives rigorous limits on a fissioned 3-body system with regards to whether fissioned system components can physically escape from each other and what other stable relative equilibria they could settle in. We explore this question with a narrow focus on the Spherical Full Three Body Problem studied in detail earlier.

D. Scheeres
Thu, 1 Dec 16
4/75

Comments: Accepted for publication in Celestial Mechanics and Dynamical Astronomy

On the complexity and the information content of cosmic structures [CEA]

The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to measure the information content of cosmic structure and to quantify the complexity that emerges from it, based on Information Theory. The emergence of complex evolutionary patterns is studied with a statistical symbolic analysis of the datastream produced by state-of-the-art cosmological simulations of forming galaxy clusters. This powerful approach allows us to measure how many bits of information are necessary to predict the evolution of energy fields in a statistical way, and it offers a simple way to quantify when, where and how the cosmic gas behaves in complex ways. The most complex behaviors are found in the peripheral regions of galaxy clusters, where supersonic flows drive shocks and large energy fluctuations over a few tens of million years. Describing the evolution of magnetic energy requires at least a twice as large amount of bits than for the other energy fields. When radiative cooling and feedback from galaxy formation are considered, the cosmic gas is overall found to double its degree of complexity. In the future, Cosmic Information Theory can significantly increase our understanding of the emergence of cosmic structure as it represents an innovative framework to design and analyze complex simulations of the Universe in a simple, yet powerful way.

F. Vazza
Tue, 29 Nov 16
21/77

Comments: 15 pages, 14 figures. MNRAS accepted, in press

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Revisiting Evidence of Chaos in X-ray Light Curves: The Case of GRS 1915+105 [HEAP]

Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer (RXTE). With a view to building simpler models of X-ray variability, attempts have been made to classify the light curves of GRS 1915+105 as chaotic or stochastic. Contrary to some of the earlier suggestions, after careful analysis, we find no evidence for chaos or determinism in any of the GRS 1915+105 classes. The dearth of long and stationary data sets representing all the different variability classes of GRS 1915+105 make it a poor candidate for analysis using nonlinear time series techniques. We conclude that either very exhaustive data analysis with sufficiently long and stationary light curves should be performed keeping all the pitfalls of nonlinear time series analysis in mind, or alternative schemes of classifying the light curves should be adopted. The generic limitations of the techniques that we point out in the context of GRS 1915+105 affect all similar investigations of light curves from other astrophysical sources.

M. Mannattil, H. Gupta and S. Chakraborty
Tue, 8 Nov 16
8/75

Comments: Accepted in The Astrophysical Journal

Distributed chaos and Rayleigh-Benard turbulence at very high Ra [CL]

It is shown, by the means of distributed chaos approach and using the experimental data, that at very large Rayleigh number $Ra > 10^{14}$ and Prandtl number $Pr \sim 1$ the Rayleigh-B\'{e}nard turbulence can undergo a transition related to spontaneous breaking of the fundamental Lagrangian relabeling symmetry. Due to the Noether’s theorem helicity plays central role in this process. After the transition the temperature spectrum has a stretched exponential form $E (k) \propto \exp(-k/k_{\beta})^{\beta}$ with $\beta =2/5$ both at the cell midplain and at the near-wall (low boundary) regions. There is a similarity between this phenomenon and the effects of polymer additives.

Wed, 2 Nov 16
13/55

Strong turbulent convection: distributed chaos and large-scale circulation [CL]

Two types of spontaneous breaking of the space translational symmetry in distributed chaos have been considered for turbulent thermal convection at large values of Rayleigh number. First type is related to boundaries and second type is related to appearance of inertial range of scales. The first type is dominated by vorticity correlation integral: $\int_{V} \langle {\boldsymbol \omega} ({\bf x},t) \cdot {\boldsymbol \omega} ({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by stretched exponential spectrum $\exp-(k/k_{\beta})^{\beta }$ with $\beta =1/2$. The second type is dominated by energy correlation integral: $\int_{V} \langle {\bf u}^2 ({\bf x},t) ~ {\bf u}^2({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by $\beta =3/5$. Good agreement has been established with laboratory experimental data obtained at large values of Rayleigh number $Ra \sim 10^{11}-10^{14}$ (the range relevant to solar photosphere) in upright cylinder cells. Taylor hypothesis transforms the wavenumber spectrum into frequency spectrum $\exp-(f/f_{\beta})^{1/2}$. It is shown that turnover frequency of large-scale circulation (wind): $f_w = f_{\beta}/2$. Results of an experiment in horizontal cylinder are also briefly discussed. The analysis suggests that in this case the large-scale circulation can be considered as a natural (harmonic) part of the distributed chaos.

Wed, 19 Oct 16
27/87

Comments: extended version (a discussion and some data have been added)

Vertical stability of circular orbits in relativistic razor-thin disks [CL]

During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these systems is not yet so developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits which deviate slightly from the equatorial plane. Such new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant by the geodesic flow.

R. Vieira, J. Ramos-Caro and A. Saa
Mon, 10 Oct 16
27/51

Comments: 13 pages, 4 figures; Accepted for publication in Physical Review D