Drag-driven instability of a dust layer in a magnetized protoplanetary disc

We study drag-driven instability in a protoplanetary disc consisting of a layer of single-sized dust particles which are coupled to the magnetized gas aerodynamically and the particle-to-gas feedback is included. We find a dispersion relation for axisymmetric linear disturbances and growth rate of the unstable modes are calculated numerically. While the secular gravitational instability in the absence of particle-to- gas feedback predicts the dust layer is unstable, magnetic fields significantly amplify the instability if the Toomre parameter for the gas component is fixed. We also show that even a weak magnetic field is able to amplify the instability more or less irrespective of the dust-gas coupling.

The Case against Dark Matter and Modified Gravity: Flat Rotation Curves Are a Rigorous Requirement in Rotating Self-Gravitating Newtonian Gaseous Discs

By solving analytically the various types of Lane-Emden equations with rotation, we have discovered two new coupled fundamental properties of rotating, self-gravitating, gaseous discs in equilibrium: isothermal discs must, on average, exhibit strict power-law density profiles in radius x on their equatorial planes of the form , where A and k-1 are the integration constants;and “flat” rotation curves precisely such as those observed in spiral galaxy discs. Polytropic discs must, on average, exhibit strict density profiles of the form , where n is the polytropic index;and “flat” rotation curves described by square roots of upper incomplete gamma functions. By “on average”, we mean that, irrespective of the chosen boundary conditions, the actual profiles must oscillate around and remain close to the strict mean profiles of the analytic singular equilibrium solutions. We call such singular solutions the “intrinsic” solutions of the differential equations because they are demanded by the second-order equations themselves with no regard to the Cauchy problem. The results are directly applicable to gaseous galaxy discs that have long been known to be isothermal and to protoplanetary discs during the extended isothermal and adiabatic phases of their evolution. In galactic gas dynamics, they have the potential to resolve the dark matter—modified gravity controversy in a sweeping manner, as they render both of these hypotheses unnecessary. In protoplanetary disc research, they provide observers with a powerful new probing tool, as they predict a clear and simple connection between the radial density profiles and the rotation curves of self-gravitating discs in their very early (pre-Class 0) phases of evolution.

The Interplay of Gravity and Lorentz Transformation Collaborating with ChatGPT

This paper presents a short exploration of the phenomena of mass and heat increase, shedding light on the remarkable notion of an expanding universe. Aimed at physicists and mathematicians, this investigation draws on an innovative collaboration with ChatGPT, an AI language model trained using scientific knowledge, to enrich our understanding of these fundamental concepts. By delving into the Gravitational Constant, we unveil compelling evidence for an increase in mass and heat for all celestial objects within an isotropic and homogenous universe as a result of the Lorentz Transformation of mass energy (LTME). Traditionally, LTME has been considered relevant primarily for subatomic particles at high velocities. However, this study posits that LTME is equally applicable to celestial bodies, even at relatively low velocities. The journey commences with an examination of the Gamma Factor in the LTME, illuminating its significance in comprehending the expansion of the cosmos. Ultimately, this paper offers a comprehensive validation of “Expanding Matter” with responses from ChatGPT, illuminating the ever-growing nature of our universe. As physicists, embarking on this journey will lead to new perspectives on the profound mysteries that shape cosmic reality. This pursuit contemplates the possibility of an infinitely energetic universe, where energy metamorphoses into mass through M = E/c2. This interpretation proposes the existence of a Process of Continuously Created Matter, manifesting as an ongoing accretion, augmentation, and expansion, harmonizing with the universe’s ever-expansive nature. The study further incorporates state-of-the-art observational technologies to substantiate its claims, thereby opening new avenues for future research in both theoretical physics and cosmology.