arXiv subjects

Manasvi Lingam

Publications and source records attributed to Manasvi Lingam.

96 records · Page 6Linked to original sources

arXiv2016

Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics

The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie-dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, which is widely utilized in Chern-Simons theory. The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.

physics.plasm-ph↗

arXiv2015

Modeling astrophysical outflows via the unified Dynamo-Reverse Dynamo mechanism

The unified Dynamo-Reverse Dynamo (Dy-RDy) mechanism, capable of simultaneously generating large scale outflows and magnetic fields from an ambient microscopic reservoir, is explored in a broad astrophysical context. The Dy-RDy mechanism is derived via Hall magnetohydrodynamics, which unifies the evolution of magnetic field and fluid vorticity. It also introduces an intrinsic length scale, the ion skin depth, allowing for the proper normalization and categorization of microscopic and macroscopic scales. The large scale Alfvén Mach number $\mathcal{M}_{A}$, defining the relative "abundance" of the flow field to the magnetic field is shown to be tied to a microscopic scale length that reflects the characteristics of the ambient short scale reservoir. The dynamo (Dy), preferentially producing the large scale magnetic field, is the dominant mode when the ambient turbulence is mostly kinetic, while the outflow producing reverse dynamo (RDy) is the principal manifestation of a magnetically dominated turbulent reservoir. It is conjectured that an efficient RDy may be the source of many observed astrophysical outflows that have $\mathcal{M}_{A} \gg 1$.

astro-ph.HE↗

arXiv2014

Analytical solutions for weak black hole kicks

The black hole is modeled by a combined gravitational potential of the bulge, disk and halo and is subjected to an initial weak kick. The resulting differential equations are set up, and shown to possess analytical solutions. The effects of black hole accretion and dynamical friction are also incorporated into this analytical framework. The resultant frequencies and amplitudes are computed, and are compared with the ones obtained from numerical simulations. Within the valid range of parameters of the analytical model, the two sets of results are shown to be in reasonable agreement. It is shown that this model reproduces the linear dependence of the amplitude on the initial kick velocity, and the constant of proportionality is close to that obtained from the simulations. The analytical treatment presented is quite general, and its applications to other areas are also indicated.

astro-ph.GA↗

arXiv2014

The effects of a non-zero cosmological constant on the Veltmann models

The Veltmann models, which include the Plummer and Hernquist models as special cases, are studied in the presence of a cosmological constant. Physically relevant quantities such as the velocity dispersion profiles and the anisotropy parameter are computed through the use of the self-consistent approach. The cutoff radii for these models and the mass contained within this volume are also calculated. It is shown that the inclusion of a cosmological constant leads to many observable quantities such as the surface density, dispersion profiles and the anisotropy parameter becoming increasingly modified. In some scenarios, they are easily distinguished from the case where the cosmological constant is absent, as a result of their non-monotonic behaviour. The effects of neighbouring gravitational systems on the central system are also studied, and compared against the effects arising from the cosmological constant. Consequently, it is suggested that the effects of a cosmological constant can prove to be quite important when modelling dilute collisionless systems.

astro-ph.GA↗

arXiv2014

The double-power approach to spherically symmetric astrophysical systems

In this paper, we present two simple approaches for deriving anisotropic distribution functions for a wide range of spherical models. The first method involves multiplying and dividing a basic augmented density with polynomials in $r$ and constructing more complex augmented densities in the process, from which we obtain the double-power distribution functions. This procedure is applied to a specific case of the Veltmann models that is known to closely approximate the Navarro-Frenk-White (NFW) profile, and also to the Plummer and Hernquist profiles (in the appendix). The second part of the paper is concerned with obtaining hypervirial distribution functions, i.e. distribution functions that satisfy the local virial theorem, for several well-known models. In order to construct the hypervirial augmented densities and the corresponding distribution functions, we start with an appropriate ansatz for the former and proceed to determine the coefficients appearing in that ansatz by expanding the potential--density pair as a series, around $r=0$ and $r=\infty$. By doing so, we obtain hypervirial distribution functions, valid in these two limits, that can generate the potential--density pairs of these models to an arbitrarily high degree of accuracy. This procedure is explicitly carried out for the Hénon isochrone, Jaffe, Dehnen and NFW models and the accuracy of this procedure is established. Finally, we derive some universal properties for these hypervirial distribution functions, involving the asymptotic behaviour of the anisotropy parameter and its relation to the density slope in this regime. In particular, we show that the cusp slope--central anisotropy inequality is saturated.

astro-ph.GA↗

arXiv2013

Analytical families of 2-component anisotropic polytropes and their relativistic extensions

In this paper, we study a family of two-component anisotropic polytropes which model a wide range of spherically symmetric astrophysical systems such as early-type baryonic galaxies. This family is found to contain a large class of models such as the hypervirial family (which satisfy the virial theorem locally), the Plummer and Hernquist models and Navarro-Frenk-White (NFW)-like models. The potential--density pair for these models are derived, as well as their velocity dispersions and anisotropy parameters. The projected quantities are computed and found to reduce to analytical expressions in some cases. The first section of this paper presents an extension of the two-term anisotropic polytropes to encompass a very wide range of potential-density pairs. In the next section, we present the general relativistic extension of the potential-density pair, and calculate the stress-energy tensor, the relativistic anisotropy parameter, the velocity of circular orbits and the angular momentum. Remarkably, for the case of the hypervirial family, the relativistic pressure in the Newtonian limit and the relativistic anisotropy parameter are found to coincide with the corresponding Newtonian expressions. The weak, dominant and strong energy conditions are found to be satisfied only for a certain range of the free parameters. We show that the relativistic hypervirial family also has a finite total mass like its Newtonian counterpart. In the first appendix, a relativistic extension of a different hypervirial family of models is studied, and the relativistic anisotropy parameter is found to coincide with the Newtonian one. Finally, we present a family of models obtained from our distribution function that are similar to the Ossipkov-Merritt models; by computing their anisotropy parameters, we show that they model systems with isotropic cores and radially anisotropic exteriors.

gr-qc↗