Łukasz Bratek

Is Dark Matter Present in NGC 4736? An Iterative Spectral Method for Finding Mass Distribution in Spiral Galaxies

An iterative method for reconstructing mass distribution in spiral galaxies using a thin disk approximation is developed. As an example, the method is applied to galaxy NGC 4736; its rotation curve does not allow one to employ a model with a massive spherical halo. We find a global mass distribution in this galaxy (without nonbaryonic dark matter) that agrees perfectly with the high-resolution rotation curve of the galaxy. This mass distribution is consistent with the I-band luminosity profile with the mean mass-to-light ratio M/LI = 1.2, and it also agrees with the amount of hydrogen observed in the outermost regions of the galaxy. We predict the total mass of the galaxy to be only 3.43 × 1010 M☉. It is very close to the value predicted by the modified gravity models and much less than the currently accepted value of 5.0 × 1010 M☉ (with ≈70% of the mass in a dark matter halo).

On the axisymmetric thin disc model of flattened galaxies

Non-monotonic features of rotation curves, and also the related gravitational effects typical of thin discs – like backward-reaction or amplification of rotation by negative surface density gradients – which are characteristic imprints of disc-like mass distributions, are discussed in the axisymmetric thin disc model. The influence of the data cut-off 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 disc approximation, accounts for the rotation curve of the galaxy. To obtain these results, the iteration method developed recently by the authors has been applied.

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 < R◦ 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.

Transverse gradients of azimuthal velocity in a global disc 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.

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.

Global disc models for galaxies NGC 1365, 6946, 7793 and 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.

Constraining the vertical structure of the Milky Way rotation by microlensing in a finite-width global disk model

We model the vertical structure of mass distribution of the Milky Way galaxy in the framework of a finite-width global disk model. Assuming only the Galactic rotation curve, we tested the predictions of the model inside the solar orbit for two measurable processes that are unrelated to each other: the gravitational microlensing that allows one to fix the disk width-scale by the best fit to measurements, and the vertical gradient of rotation modeled in the quasi-circular orbits approximation. The former is sensitive to the gravitating mass in compact objects, the latter to all kinds of gravitating matter. The analysis points to a small width-scale of the considered disks and an at-most insignificant contribution of non-baryonic dark matter in the solar circle. The predicted high vertical gradient values in the rotation are consistent with the gradient measurements.

A possible influence of magnetic fields on the rotation of gas in NGC 253

The magnetic fields that are present in the galaxy NGC 253 are exceptionally strong. This means that they can influence the rotation of matter and hence the mass-to-light ratio. In this context, we address the issue of the presence of a non-baryonic dark matter halo in this galaxy.

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 Poincare 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.

A lower bound on the Milky Way mass from general phase-space distribution function models

We model the phase-space distribution of the kinematic tracers using general, smooth distribution functions to derive a conservative lower bound on the total mass within ≈150−200 kpc. By approximating the potential as Keplerian, the phase-space distribution can be simplified to that of a smooth distribution of energies and eccentricities. Our approach naturally allows for calculating moments of the distribution function, such as the radial profile of the orbital anisotropy. We systematically construct a family of phase-space functions with the resulting radial velocity dispersion overlapping with the one obtained using data on radial motions of distant kinematic tracers, while making no assumptions about the density of the tracers and the velocity anisotropy parameter β regarded as a function of the radial variable. While there is no apparent upper bound for the Milky Way mass, at least as long as only the radial motions are concerned, we find a sharp lower bound for the mass that is small. In particular, a mass value of 2.4 × 10 11 M� , obtained in the past for lower and intermediate radii, is still consistent with the dispersion profile at larger radii. Compared with much greater mass values in the literature, this result shows that determining the Milky Way mass is strongly model-dependent. We expect a similar reduction of mass estimates in models assuming more realistic mass profiles.