arXiv subjects

Łukasz Bratek

Publications and source records attributed to Łukasz Bratek.

32 records · Page 2Linked to original sources

arXiv2012

Gravitational microlensing as a test of a finite-width disk model of the Galaxy

The aim of this work is to show, in the framework of a simple finite-width disk model, that the amount of mass seen through gravitational microlensing measurements in the region $0<R<R0$ is consistent with the dynamical mass ascertained from Galaxy rotation after subtracting gas contribution. Since microlensing only detects compact objects, this result suggests that a non-baryonic mass component may be negligible in this region.

astro-ph.GA↗

arXiv2012

The role of large-scale magnetic fields in galaxy NGC 891. Can magnetic fields help to reduce the local mass-to-light ratio in the galactic outskirts?

We address the problem of the influence of large-scale magnetic fields on galactic rotation for the example of the spiral galaxy NGC 891. Based on its rotation curve and the surface density of HI we determine, in the framework of the global disc model, the surface density of matter. Then, based on the surface brightness, we determine the corresponding profile of the local mass-to-light ratio. We also model the vertical gradient of azimuthal velocity in the quasi-circular-orbit approximation, and compare it with measurements. We discuss what factors may influence the rotation of matter in NGC 891 and how this can translate to changes in the profile of the local mass-to-light ratio. In particular, we discuss the possible effect of magnetic fields on the motion of ionized gas, and, consequently, on the determination of the profile of the local mass-to-light ratio. Finally, we put forward the hypothesis that the asymmetry in magnetic fields observed in NGC 891 might be responsible for the observed anomalous behaviour of the vertical gradient.

astro-ph.GA↗

arXiv2012

Can rapidity become a gauge variable? Dirac Hamiltonian method and Relativistic Rotators

The minimal Hamiltonian for a family of relativistic rotators is constructed by a direct application of the Dirac procedure for constrained systems. The Hamiltonian equations can be easily solved. It is found that the resulting motion is unique and qualitatively the same for all phenomenological rotators, only the relation between mass and spin is different. There is a critical point in the construction when such a relation cannot be established, implying that the number of primary constraints is greater. In that case the mass and the spin become unrelated, separately fixed parameters, and the corresponding Hamiltonian changes qualitatively. Furthermore, a genuine physical observable becomes a gauge variable. This paradoxical result is consistent with the fact already known at the Lagrangian level that the Hessian rank is lower than expected, and the equations of motion indeterminate on $\mathbb{R}^3\times\mathbb{S}^2$.

math-ph↗

arXiv2011

Spinor particle. An indeterminacy in the motion of relativistic dynamical systems with separately fixed mass and spin

We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite worldline). This paradox suggests that for a consistent description of spinning particles something more general than a worldline concept should be used. As a particular case, we study at the Lagrangian level the Cauchy problem for a spinor particle and then, at the constrained Hamiltonian level, we generalize our result to other particles.

math-ph↗

arXiv2011

Transverse gradients of azimuthal velocity in a global disk model of the Milky Way

In this paper, we aim to estimate the vertical gradients in the rotational velocity of the Galaxy. This is carried out in the framework of a global thin disc model approximation. The predicted gradient values coincide with the observed vertical fall-off in the rotation curve of the Galaxy. The gradient is estimated based on a statistical analysis of trajectories of test bodies in the gravitational field of the disc and in an analytical way using a quasi-circular orbit approximation. The agreement of the results with the gradient measurements is remarkable in view of other more complicated, non-gravitational mechanisms used for explaining the observed gradient values. Finally, we find that models with a significant spheroidal component give worse vertical gradient estimates than the simple disc model. In view of these results, we can surmise that, apart from the central spherical bulge and Galactic halo, the gross mass distribution in the Galaxy forms a flattened rather than spheroidal figure.

astro-ph.GA↗

arXiv2011

Vertical gradients of azimuthal velocity in a global thin disk model of spiral galaxies NGC 2403, NGC 4559, NGC 4302 and NGC 5775

We estimate the vertical gradient of rotational velocity for several spiral galaxies in the framework of a global thin-disc model, using the approximation of quasi-circular orbits. We obtain gradients having a broad range of values, in agreement with measurements, for galaxies with both low and high gradients. To model the gradient, it suffices to know the rotation curve only. We illustrate, using the example of galaxy NGC 4302 with particularly high gradients, that mass models of galactic rotation curves that assume a significant spheroidal mass component reduce the predicted gradient value, which may suggest that the mass distribution is dominated by a flattened disc-like component. We conclude that the value and behaviour of the vertical gradient in rotational velocity can be used to study the mass distribution in spiral galaxies.

astro-ph.GA↗

arXiv2011

Global disk model for galaxies NGC 1365, NGC 6946, NGC 7793, UGC 6446

Spiral galaxies are studied using a simple global disc model as a means for approximate determination of mass profiles. Based on rotation curves and the amount of gas (HI+He), we find global surface mass densities consistent with measurements and compare them with B-band surface brightness profiles. As a result we obtain mass-to-light ratio profiles. We give some arguments for why our approach is reliable and sometimes better than those assuming ad hoc the presence of a massive non-baryonic dark matter halo. Using this model, we study galaxies NGC 7793, 1365, 6946 and UGC 6446. Based on a rotation curve from The HI Nearby Galaxy Survey (THINGS) we also study galaxy NGC 4536 and compare the results with those we published elsewhere for the same galaxy.

astro-ph.GA↗

arXiv2011

Fundamental Relativistic Rotator. Hessian singularity and the issue of the minimal interaction with electromagnetic field

There are two relativistic rotators with Casimir invariants of the Poincaré group being fixed parameters. The particular models of spinning particles were studied in the past both at the classical and quantum level. Recently, a minimal interaction with electromagnetic field has been considered. We show that the dynamical systems can be uniquely singled out from among other relativistic rotators by the unphysical requirement that the Hessian referring to the physical degrees of freedom should be singular. Closely related is the fact that the equations of free motion are not independent, making the evolution indeterminate. We show that the Hessian singularity cannot be removed by the minimal interaction with the electromagnetic field. By making use of a nontrivial Hessian null space, we show that a single constraint appears in the external field for consistency of the equations of motion with the Hessian singularity. The constraint imposes unphysical limitation on the initial conditions and admissible motions. We discuss the mechanism of appearance of unique solutions in external fields on an example of motion in the uniform magnetic field. We give a simple model to illustrate that similarly constrained evolution cannot be determinate in arbitrary fields.

math-ph↗

arXiv2010

False constraints. A toy model for studying dynamical systems with degenerate Hessian form

This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler setup, this enables one to gain an insight into the principal difference between mechanical systems with singular and non-singular Hessian, whilst avoiding the complications resulting from the more intricate form of the equations of motion in the fully relativistic regime. In particular, one can comprehend the apparent contradiction between Hessian singularity and simultaneous occurrence of unique solutions for the motion of the fundamental relativistic rotator minimally coupled to the electromagnetic field. With the aid of the toy model the author supports and illustrates his thesis put forward elsewhere that the Hessian singularity is a defect that makes physically unviable some geometric models of spinning particles considered in the literature.

math-ph↗

arXiv2010

SQM stars around pulsar PSR B1257+12

Following Wolszczan's landmark discovery of planets in orbit around pulsar PSR B1257+12 in 1991, over 300 planets in more than 200 planetary systems have been found. Therefore, the meaning of Wolszczan's discovery cannot be overestimated. In this paper we aim to convince the reader that the objects accompanying pulsar PSR B1257+12 are more exotic than thought so far. They might not be ordinary planets but dwarf strange quark stars, whereas the pulsar might be a quark star with standard mass, not a neutron star. If this was the case, it would indicate that strange quark matter is the ground state of matter.

astro-ph.EP↗

arXiv2009

Modified relativistic rotator. Toward classical Fundamental Dynamical Systems consisting of a worldline and a single spinor

The Author shows how to construct a class of Lagrangians for relativistic dynamical systems described by position and a single spinor. One arrives to it by imposing three requirements: 1) Hamilton action should be reparametrization invariant, 2) the number of dimensional parameters should be minimal, 3) the spinor phase should be a cyclic variable. In more detail are discussed those of the the Lagrangians which depend on the spinor's null vector and its worldline. An interesting relation between a Hessian determinant and Casimir invariants for such objects leads to the conclusion that no fundamental objects of this kind exist with worldlines uniquely determinable from the Hamilton action and the initial conditions. This unexpected result poses the general question about existence of classical fundamental dynamical systems with well posed Cauchy problem. [A relativistic dynamical system is said to be fundamental if its Casimir invariants are parameters, not constants of motion]

math-ph↗

arXiv2009

Breathing Relativistic Rotators and Fundamental Dynamical Systems

Recently, it was shown, that the mechanical model of a massive spinning particle proposed by Kuzenko, Lyakhovich and Segal in 1994, which is also the fundamental relativistic rotator rediscovered independently 15 years later by Staruszkiewicz in quite a different context, is defective as a dynamical system, that is, its Cauchy problem is not well posed. This dynamical system is fundamental, since its mass and spin are parameters, not arbitrary constants of motion, which is a classical counterpart of quantum irreducibility. It is therefore desirable to find other objects which, apart from being fundamental, would also have well posed Cauchy problem. For that purpose, a class of breathing rotators is considered. A breathing rotator consists of a single null vector associated with position and moves in accordance with some relativistic laws of motion. Surprisingly, breathing rotators which are fundamental, are also defective as dynamical systems. More generally, it has been shown, that the necessary condition for a breathing rotator to be similarly defective, is functional dependence of its Casimir invariants of the Poincar{é} group.

math-ph↗

arXiv2009

On the nonuniqueness of free motion of the fundamental relativistic rotator

Consider a class of relativistic rotators described by position and a single null direction. Such a rotator is called fundamental if both its Casimir invariants are intrinsic dimensional parameters independent of arbitrary constants of motion. As shown by Staruszkiewicz, only one rotator with this property exists (its partner with similar property can be excluded on physical grounds). We obtain a general solution to equations of free motion of the fundamental relativistic rotator in a covariant manner. Surprisingly, this motion is not entirely determined by initial conditions but depends on one arbitrary function of time, which specifies rotation of the null direction in the centre of momentum frame. This arbitrariness is in manifest contradiction with classical determinism. In this sense the isolated fundamental relativistic rotator is pathological as a dynamical system. To understand why this is so, we study the necessary condition for the uniqueness of the related Cauchy problem. It turns out that the fundamental relativistic rotator (together with its partner) can be uniquely characterized by violating this condition in the considered class of rotators.

math-ph↗

arXiv2008

On the axisymmetric thin disk model of flattened galaxies

Non-monotonic features of rotation curves, and also the related gravitational effects typical of thin disks -- like backward-reaction or amplification of rotation by negative surface density gradients -- which are characteristic imprints of disk-like mass distributions, are discussed in the axisymmetric thin disk model. The influence of the data cutoff in rotational velocity measurements on the determination of the mass distribution in flattened galaxies is studied. It has also been found that the baryonic matter distribution in the spiral galaxy NGC 5475, obtained in the axisymmetric thin disk approximation, accounts for the rotation curve of the galaxy. To obtain these results, the iteration method developed recently by the authors has been applied.

astro-ph↗