Viscoelastic type magnetic effects and self-gravity on the propagation of MHD waves
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ORIGINAL PAPERS
Viscoelastic type magnetic effects and self-gravity on the propagation of MHD waves Franca Franchi . Barbara Lazzari . Roberta Nibbi
Received: 19 July 2020 / Accepted: 23 September 2020 Ó The Author(s) 2020
Abstract We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional shear-like Alfven waves in triggering the formation of network patterns, by proposing new mathematical models for selfgravitating interstellar non ideal MHD plasmas. The diffusion of the gravitational field is included via a parabolic Einstein’s equation with the cosmological constant, whereas anomalous resistive features are described through non ideal Ohm’s laws incorporating inertia terms, to account of relaxation and retardation magnetic responses. We perform a spectral analysis to test the stability properties of the novel constitutive settings where dissipative and elastic devices act together, by emphasizing the differences with previous models. As a main result, we highlight the definition of a lower critical threshold, here called the Jeans-Einstein wavenumber, against collapse formation towards the formation of longitudinal gravitomagneto-sonic waves and transverse non gravitational Alfven waves exhibiting larger effective wavespeeds, F. Franchi B. Lazzari R. Nibbi (&) Department of Mathematics, University of Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy e-mail: [email protected] F. Franchi e-mail: [email protected] B. Lazzari e-mail: [email protected]
due to the hyperbolic-parabolic diffusion of the magnetic field. Consequently shorter collisional times are allowable so, beyond the plasma-beta, another interesting key point is the definition of the Ohm number to revisit the timescale topic, towards reviewed Reynolds and Lundquist numbers able to better capture the microphysical phenomena of Magnetic Reconnection in narrow diffusion regimes. Keywords Diffusion-reaction gravity equation Viscoelastic type resistive MHD models Jeans instability analysis MHD dispersive waves Complex structures
1 Introduction The Jeans instability of sound modes in self-gravitating interstellar clouds is a well known phenomenon which plays a strategic role in understanding not only stars and galaxies formation, but also as a possible justification for the existence of large amount of dark energy and dark matter (DM) in the Universe. Thereby such a topic represents a long standing problem whose newness is strictly related to the development of several new mathematical models to better fit the interstellar matter [1–9]. In particular, as already suggested in earlier papers [4, 10–13], an interesting research issue may be just given by a
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Meccanica
different structure for the standard Poisson-type gravity, leading to modified gravitational (MOG) frameworks accounting for the Universe Expansion, via the introduction of Eins
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