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Rajaram Nityananda

Publications and source records attributed to Rajaram Nityananda.

12 recordsLinked to original sources
arXiv2026

Exactly solved model of a one dimensional self gravitating system

A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles orbiting in their own self consistent potential are given exactly, in terms of time, by the truncations of sine and cosine functions to the first two terms in their respective Taylor series. The potential and density also have simple analytic expressions in terms of time as parameter. It is not being claimed that this system has any direct astronomical application. However, it does motivate a conjecture about the behaviour of the density, potential, and orbits near caustics in simulations of cold collisionless dark matter. It is a rather surprising result which might interest practitioners of stellar dynamics and serve as an elementary example in teaching the subject.

astro-ph.GA↗
arXiv2024

Closure invariants for polarised radio interferometric observations: a graph theoretical approach

Aperture synthesis observations with full polarisation have long been used to study the magnetic fields of synchrotron emitting sources. Recently proposed closure invariants give us a powerful method for extracting information from measured visibilities which are corrupted by antenna and polarisation dependent gains. In this paper, a formalism developed earlier for complete graphs (where all visibilities are available) is extended to incomplete graphs. The formalism provides a complete and independent set of closure invariants from the measured visibilities in a general situation where not all visibilities are available. We then show in a simulated, quasi-realistic case that the invariants developed here contain usable information even in the presence of noise.

astro-ph.IM↗
arXiv2022

Invariants in Co-polar Interferometry: an Abelian Gauge Theory

An $N$-element interferometer measures correlations among pairs of array elements. Closure invariants associated with closed loops among array elements are immune to multiplicative, element-based ("local") corruptions that occur in these measurements. Till recently, it has been unclear how a complete set of independent invariants can be analytically determined. We view the local, element-based corruptions in co-polar correlations as gauge tranformations belonging to the gauge group $\textrm{GL}(1,\mathbb{C})$. Closure quantities are then naturally gauge invariant. We use this to provide a simple and effective formalism, and identify the complete set of independent closure invariants from co-polar interferometric correlations using only quantities defined on $(N-1)(N-2)/2$ elementary and independent triangular loops. The $(N-1)(N-2)/2$ closure phases and $N(N-3)/2$ closure amplitudes (totaling $N^2-3N+1$ real invariants), familiar in astronomical interferometry, naturally emerge from this formalism, which unifies what has required separate treatments until now. We do not require auto-correlations, but can easily include them if reliably measured. This unified view clarifies issues relating to noise and inference of object model parameters. It also allows us to extend the rule of parallel transport associated with Pancharatnam phase in optics to apply to amplitudes as well. The framework presented here extends to $\textrm{GL}(2,\mathbb{C}$) for full polarimetric interferometry as presented in a companion paper, which generalizes and clarifies earlier work. Our findings are relevant to state of the art co-polar and full polarimetric very long baseline interferometry measurements to determine features very near the event horizons of blackholes at the centers of M87, Centaurus~A, and the Milky Way.

astro-ph.IM↗
arXiv2022

Invariants in Polarimetric Interferometry: a non-Abelian Gauge Theory

The discovery of magnetic fields close to the M87 black hole using Very Long Baseline Interferometry (VLBI) by the Event Horizon Telescope collaboration utilized the novel concept of "closure traces", that are immune to element-based aberrations. We take a fundamentally new approach to this promising tool of polarimetric VLBI, using ideas from the geometric phase and gauge theories. The multiplicative distortion of polarized signals at the individual elements are represented as gauge transformations by general $2\times 2$ complex matrices, so the closure traces now appear as gauge-invariant quantities. We apply this formalism to polarimetric interferometry and generalize it to any number of interferometer elements. Our approach goes beyond existing studies in the following respects: (1) we use triangular combinations of correlations as basic building blocks of invariants, (2) we use well-known symmetry properties of the Lorentz group to transparently identify a complete and independent set of invariants, and (3) we do not need auto-correlations, which are susceptible to large systematic biases, and therefore unreliable. This set contains all the information, immune to corruption, available in the interferometer measurements, thus providing important robust constraints for interferometric studies.

gr-qc↗
arXiv2015

Comment on "Spin-Gradient-Driven Light Amplification in a Quantum Plasma"

A comment on the Letter by S. Braun, F. A. Asenjo and S. M. Mahajan, Phys. Rev. Lett., 109, 175003 (2012). We show that recent arguments for light amplification driven by inhomogeneous quantum spin fields in low temperature electron plasmas in metals are invalid. In essence, a neglect of Pauli `blocking' led the authors to over-estimate the effects of intrinsic spin.

physics.plasm-ph↗
arXiv2015

Strong constraints on magnetized white dwarfs surpassing the Chandrasekhar mass limit

We show that recently proposed white dwarf models with masses well in excess of the Chandrasekhar limit, based on modifying the equation of state by a super-strong magnetic field in the centre, are very far from equilibrium because of the neglect of Lorentz forces. An upper bound on the central magnetic fields, from a spherically averaged hydrostatic equation, is much smaller than the values assumed. Robust estimates of the Lorentz forces are also made without assuming spherical averaging. These again bear out the results obtained from a spherically averaged model. In our assessment, these estimates rule out the possibility that magnetic tension could change the situation in favor of larger magnetic fields. We conclude that such super-Chandrasekhar models are unphysical and exploration of their astrophysical consequences is premature. Erratum : We correct certain numerical estimates made in our paper. This correction however does not alter the conclusion that when Lorentz forces are taken into account the super-massive white dwarf models, obtained simply by modifying the equation of state in presence of a super-strong magnetic field in the centre, fail to be in equilibrium.

astro-ph.SR↗
arXiv2014

A critique of recent semi-classical spin-half quantum plasma theories

Certain recent semi-classical theories of spin-half quantum plasmas are examined with regard to their internal consistency, physical applicability and relevance to fusion, astrophysical and condensed matter plasmas. It is shown that the derivations and some of the results obtained in these theories are internally inconsistent and contradict well-established principles of quantum and statistical mechanics, especially in their treatment of fermions and spin. Claims of large semi-classical effects of spin magnetic moments that could dominate the plasma dynamics are found to be invalid both for single-particles and collectively. Larmor moments dominate at high temperature while spin moments cancel due to Pauli blocking at low temperatures. Explicit numerical estimates from a variety of plasmas are provided to demonstrate that spin effects are indeed much smaller than many neglected classical effects. The analysis presented suggests that the aforementioned `Spin Quantum Hydrodynamic' theories are not relevant to conventional laboratory or astrophysical plasmas.

physics.plasm-ph↗
arXiv2013

A critique of recent theories of spin half quantum plasmas

In this Letter certain fundamental physics issues relating to recent theories of so-called `spin quantum plasmas' are examined. It is shown that the derivations and some of the results obtained in these theories contradict well-established principles of quantum mechanics, especially in their treatment of fermions and spin. The analysis presented suggests that the aforementioned theories do not apply for any range of temperatures at the stated densities and furthermore fail to make any experimentally accessible and testable predictions.

physics.plasm-ph↗
arXiv2008

Determination of the orbital parameters of binary pulsars

We present a simple method for determination of the orbital parameters of binary pulsars, using data on the pulsar period at multiple observing epochs. This method uses the circular nature of the velocity space orbit of Keplerian motion and produces preliminary values based on two one dimensional searches. Preliminary orbital parameter values are then refined using a computationally efficient linear least square fit. This method works for random and sparse sampling of the binary orbit. We demonstrate the technique on (a) the highly eccentric binary pulsar PSR J0514-4002 (the first known pulsar in the globular cluster NGC 1851) and (b) 47 Tuc T, a binary pulsar with a nearly circular orbit.

astro-ph↗
arXiv2001

Solving for closure errors due to polarization leakage in radio interferometry of unpolarized sources

Mechanical and electronic imperfections can result into polarization leakage in individual antennas of a radio interferometer. Such leakages manifest themselves as closure errors even in co-polar visibility measurements of unpolarized sources. This paper describes and tests a method for the study of polarization leakage for radio interferometric telescopes using {\it only} the nominally co-polar visibilities for unpolarized calibrators. Interpretation of the resulting closure phases on the Poincaré sphere is presented. Since unpolarized sources are used, the actual solutions for leakage parameters is subject to a degeneracy which is discussed. This however, does not affect the correction of closure errors in our scheme.

astro-ph↗
arXiv2000

Transport along Null Curves

Fermi Transport is useful for describing the behaviour of spins or gyroscopes following non-geodesic, timelike world lines. However, Fermi Transport breaks down for null world lines. We introduce a transport law for polarisation vectors along non-geodesic null curves. We show how this law emerges naturally from the geometry of null directions by comparing polarisation vectors associated with two distinct null directions. We then give a spinorial treatment of this topic and make contact with the geometric phase of quantum mechanics. There are two significant differences between the null and timelike cases. In the null case (i) The transport law does not approach a unique smooth limit as the null curve approaches a null geodesic. (ii) The transport law for vectors is integrable, i.e the result depends only on the local properties of the curve and not on the entire path taken. However, the transport of spinors is not integrable: there is a global sign of topological origin.

gr-qc↗