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 self-gravitating 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 gravito-magneto-sonic waves and transverse non gravitational Alfven waves exhibiting larger effective wavespeeds, 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.
Highlights
The Jeans instability of sound modes in self-gravitating interstellar clouds is a well known phenomenon which plays a strategic role in understanding stars and galaxies formation, and 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 [1,2,3,4,5,6,7,8,9]
As already suggested in earlier papers [4, 10,11,12,13], an interesting research issue may be just given by a different structure for the standard Poisson-type gravity, leading to modified gravitational (MOG) frameworks accounting for the Universe Expansion, via the introduction of Einstein’s cosmological constant K
In order to overcome the well-known Jeans swindle and predict dark energy properties, and thinking of the recently detected gravitational waves [14], we here propose a non-stationary and non-relativistic Einstein’s equation, which includes K and a gravitational relaxation time. To this aim we introduce a reaction–diffusion equation for the gravitational potential and firstly test its stabilizing role on selfgravitating interstellar matter (ISM) clouds, described as polytropic Euler-Darcy fluids
Summary
The Jeans instability of sound modes in self-gravitating interstellar clouds is a well known phenomenon which plays a strategic role in understanding stars and galaxies formation, and as a possible justification for the existence of large amount of dark energy and dark matter (DM) in the Universe. We revisit the previous Jeans-Einstein instability criteria for the compressible resisto-elastic MHD (REMHD) scenario proposed in [15], through a non-ideal Ohm’s Law accounting for anomalous resistive features, due to the presence of a magnetic relaxation time. The Ohm number plays a key role in the theory: it leads to a modified Reynolds number RME 1⁄4 RMORF (RM being the standard magnetic Reynolds number) for the valuation of the interlacements between the resistive and elastic behavior towards the microphysics of cosmic plasmas In this way, the cosmological constant K, interpreted as a new critical wavenumber ascribable to DM, together with the classical plasma-beta (b), Meccanica (2020) 55:2199–2214 which is the ratio between the thermal and magnetic pressures, allow us to highlight an interesting relationship among the most significant parameters of our model (K, ORF, b, RME and the gravitational constant G), against collapse formation.
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