arXiv subjects

R. Banerjee

Publications and source records attributed to R. Banerjee.

At least 73 records · Page 4Linked to original sources

arXiv2011

Magnetic fields during the early stages of massive star formation - I. Accretion and disk evolution

We present simulations of collapsing 100 M_\sun mass cores in the context of massive star formation. The effect of variable initial rotational and magnetic energies on the formation of massive stars is studied in detail. We focus on accretion rates and on the question under which conditions massive Keplerian disks can form in the very early evolutionary stage of massive protostars. For this purpose, we perform 12 simulations with different initial conditions extending over a wide range in parameter space. The equations of magnetohydrodynamics (MHD) are solved under the assumption of ideal MHD. We find that the formation of Keplerian disks in the very early stages is suppressed for a mass-to-flux ratio normalised to the critical value μbelow 10, in agreement with a series of low-mass star formation simulations. This is caused by very efficient magnetic braking resulting in a nearly instantaneous removal of angular momentum from the disk. For weak magnetic fields, corresponding to μ> 10, large-scale, centrifugally supported disks build up with radii exceeding 100 AU. A stability analysis reveals that the disks are supported against gravitationally induced perturbations by the magnetic field and tend to form single stars rather than multiple objects. We find protostellar accretion rates of the order of a few 10^-4 M_\sun yr^-1 which, considering the large range covered by the initial conditions, vary only by a factor of ~ 3 between the different simulations. We attribute this fact to two competing effects of magnetic fields. On the one hand, magnetic braking enhances accretion by removing angular momentum from the disk thus lowering the centrifugal support against gravity. On the other hand, the combined effect of magnetic pressure and magnetic tension counteracts gravity by exerting an outward directed force on the gas in the disk thus reducing the accretion onto the protostars.

astro-ph.SR↗

arXiv2011

Probing the evolution of molecular cloud structure II: From chaos to confinement

We present an analysis of the large-scale molecular cloud structure and of the stability of clumpy structures in nearby molecular clouds. In our recent work, we identified a structural transition in molecular clouds by studying the probability distributions of gas column densities in them. In this paper, we further examine the nature of this transition. The transition takes place at the visual extinction of A_V^tail = 2-4 mag, or equivalently, at Σ^tail = 40-80 Ms pc^{-2}. The clumps identified above this limit have wide ranges of masses and sizes, but a remarkably constant mean volume density of n = 10^3 cm^{-3}. This is 5-10 times larger than the density of the medium surrounding the clumps. By examining the stability of the clumps, we show that they are gravitationally unbound entities, and that the external pressure from the parental molecular cloud is a significant source of confining pressure for them. Then, the structural transition at A_V^tail may be linked to a transition between this population and the surrounding medium. The star formation rates in the clouds correlate strongly with the total mass in the clumps, i.e, with the mass above A_V^tail, dropping abruptly below that threshold. These results imply that the formation of pressure confined clumps introduces a prerequisite for star formation. Furthermore, they give a physically motivated explanation for the recently reported relation between the star formation rates and the amount of dense material in molecular clouds. Likewise, they give rise to a natural threshold for star formation at A_V^tail.

astro-ph.GA↗

arXiv2008

From the warm magnetized atomic medium to molecular clouds

{It has recently been proposed that giant molecular complexes form at the sites where streams of diffuse warm atomic gas collide at transonic velocities.} {We study the global statistics of molecular clouds formed by large scale colliding flows of warm neutral atomic interstellar gas under ideal MHD conditions. The flows deliver material as well as kinetic energy and trigger thermal instability leading eventually to gravitational collapse.} {We perform adaptive mesh refinement MHD simulations which, for the first time in this context, treat self-consistently cooling and self-gravity.} {The clouds formed in the simulations develop a highly inhomogeneous density and temperature structure, with cold dense filaments and clumps condensing from converging flows of warm atomic gas. In the clouds, the column density probability density distribution (PDF) peaks at $\sim 2 \times 10^{21} \psc$ and decays rapidly at higher values; the magnetic intensity correlates weakly with density from $n \sim 0.1$ to $10^4 \pcc$, and then varies roughly as $n^{1/2}$ for higher densities.} {The global statistical properties of such molecular clouds are reasonably consistent with observational determinations. Our numerical simulations suggest that molecular clouds formed by the moderately supersonic collision of warm atomic gas streams.}

astro-ph↗

arXiv2000

Canonical transformations and soldering

We show that the recently developed soldering formalism in the Lagrangian approach and canonical transformations in the Hamiltonian approach are complementary. The examples of gauged chiral bosons in two dimensions and self-dual models in three dimensions are discussed in details.

hep-th↗

arXiv2000

The commutativity principle and lagrangian symmetries

Using the commutativity of a general variation with the time differentiation we discuss both global and local (gauge) symmetries of a lagrangian from a unified point of view. The Noether considerations are thereby applicable for both cases. A complete equivalence between the hamiltonian and lagrangian formulations is established.

hep-th↗

arXiv1999

Recursive Construction of Generator for Lagrangian Gauge Symmetries

We obtain, for a subclass of structure functions characterizing a first class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge parameters. We apply this to a non-trivial Hamiltonian system involving two primary constraints, as well as two secondary constraints of the Nambu-Goto type.

hep-th↗

arXiv1999

Master Equation for Lagrangian Gauge Symmetries

Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily reproduced from this equation. We also discuss the connection with the purely Lagrangian approach. The general considerations are applied to the Yang-Mills theory.

hep-th↗

arXiv1999

Hamiltonian Approach to Lagrangian Gauge Symmetries

We reconsider the problem of finding all local symmetries of a Lagrangian. Our approach is completely Hamiltonian without any reference to the associated action. We present a simple algorithm for obtaining the restrictions on the gauge parameters entering in the definition of the generator of gauge transformations.

hep-th↗

arXiv1999

Some Comments on the Spin of the Chern - Simons Vortices

We compute the spin of both the topological and nontopological solitons of the Chern - Simons - Higgs model by using our approach based on constrained analysis. We also propose an extension of our method to the non - relativistic Chern - Simons models. The spin formula for both the relativistic and nonrelativistic theories turn out to be structurally identical. This form invariance manifests the topological origin of the Chern - Simons term responsible for inducing fractional spin. Also, some comparisons with the existing results are done.

hep-th↗

arXiv1999

Self-duality and soldering in odd dimensions

Using the recently developed soldering formalism we highlight certain features of quantum mechanical models. The complete correspondence between these models and self dual field theoretical models in odd dimensions is established. The distinction between self duality and self dual factorisation in these dimensions is clarified.

hep-th↗

arXiv1998

On the constrained structure of duality symmetric Maxwell theory

The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more economical and elegant. Distinctions from the constrained analysis of the usual Maxwell theory are pointed out and their implications are also discussed.

hep-th↗

arXiv1998

Screening in three-dimensional QED with arbitrary fermion mass

We compute the quark--antiquark potential in three dimensional massive Quantum Electrodynamics for arbitrary fermion mass. The result indicates that screening prevails for any quark masses, contrary to the classical expectations, generalizing our previous result obtained for large masses. We also test the validity of several approximation schemes using a detailed numerical analysis. The classical result is still reproduced for small separation of the quarks.

hep-th↗

arXiv1998

Mode Analysis and Duality Symmetry in Different Dimensions

The problem of duality symmetry in free field models is examined in details by performing a mode expansion of these fields which provides a mapping with the purely quantum mechanical example of a harmonic oscillator. By analysing the duality symmetry in the harmonic oscillator, we show that the massless scalar theory in two dimensions display, along with the expected discrete $Z_2$ symmetry, the continuous SO(2) symmetry as well. The same holds for the free Maxwell theory in four dimensions, which is usually regarded to manifest only the SO(2) symmetry. This leads to the new result that, following a proper interpretation, the duality groups in two and four dimensions become identical. Incidentally, duality in quantum mechanics is generally not covered in the literature that considers only $D=4k$ or $D=4k+2$ spacetime dimensions, for integral $k$.

hep-th↗

arXiv1998

Bosonisation and Duality Symmetry in the Soldering Formalism

We develop a technique that solders the dual aspects of some symmetry. Using this technique it is possible to combine two theories with such symmetries to yield a new effective theory. Some applications in two and three dimensional bosonisation are discussed. In particular, it is shown that two apparently independent three dimensional massive Thirring models with same coupling but opposite mass signatures, in the long wavelegth limit, combine by the process of bosonisation and soldering to yield an effective massive Maxwell theory. Similar features also hold for quantum electrodynamics in three dimensions. We also provide a systematic derivation of duality symmetric actions and show that the soldering mechanism leads to a master action which is duality invariant under a bigger set of symmetries than is usually envisaged. The concept of duality swapping is introduced and its implications are analysed. The example of electromagnetic duality is discussed in details.

hep-th↗

arXiv1998

The Chiral Oscillator and its Applications in Quantum Theory

The fundamental importance of the chiral oscillator is elaborated. Its quantum invariants are computed. As an application the Zeeman effect is analysed. We also show that the chiral oscillator is the most basic example of a duality invariant model, simulating the effect of the familiar electric-magnetic duality.

quant-ph↗

arXiv1998

Quantization of the multidimensional rotor

We reconsider the problem of quantising a particle on the $D$-dimensional sphere. Adopting a Lagrangian method of reducing the degrees of freedom, the quantum Hamiltonian is found to be the usual Schrödinger operator without any boundary term. The equivalence with the Dirac Hamiltonian approach is demonstrated, either in the cartesian or in the curvilinear basis. We also briefly comment on the path integral approach.

quant-ph↗

arXiv1997

Reducible systems and embedding procedures in the canonical formalism

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not necessary, as in the Dirac approach, to isolate the independent subset of constraints or to introduce, as in the symplectic analysis, a series of lagrange multipliers-for-lagrange multipiers. This analysis illuminates the close connection between the Dirac and symplectic approaches of treating reducible theories, which is otherwise lacking. The example of p-form gauge fields (p=2,3) is analyzed in details.

hep-th↗

arXiv1997

Screening in three-dimensional QED

We compute the quark-antiquark potential in three dimensional massive Quantum Electrodynamics. The result indicates that screening prevails for large quark masses, contrary to the classical expectations. The classical result is reproduced for small separation of the quarks.

hep-th↗