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Szymon Sikora

Publications and source records attributed to Szymon Sikora.

14 recordsLinked to original sources
arXiv2024

The model of the local Universe in the framework of the second-order perturbation theory

Recently, we constructed the specific solution to the second-order cosmological perturbation theory, around any Friedmann-Lemaitre-Robertson-Walker (FLRW) background filled with dust matter and a positive cosmological constant. In this paper, we use the Cosmicflows-4 (CF4) sample of galaxies from the Extragalactic Distance Database to constrain this metric tensor. We obtain an approximation to the local matter distribution and geometry. We numerically solve for null geodesics for randomly distributed mock sources and compare this model with the Lemaitre-Hubble constant inferred from the observations under the assumption of perfect isotropy and homogeneity. We conclude on effects of realistic inhomogeneities on the luminosity distance in the context of the Hubble tension and discuss limitations of our approach.

astro-ph.CO↗
arXiv2022

Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant

In this paper, a specific solution to the second-order cosmological perturbation theory is given. Perturbations are performed around any FLRW spacetime filled with dust and with a positive cosmological constant. In particular, with a possibly non-vanishing spatial curvature. The adopted symmetry condition allows us to simplify the equations, leaving us with a great deal of freedom to choose the density distribution. In the result, we get a relatively simple metric of an inhomogeneous cosmological model, which will give a perfect tool for studying the influence of the local inhomogeneities onto the cosmological observables.

gr-qc↗
arXiv2020

Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude

We construct an approximate solution to the cosmological perturbation theory around Einstein-de Sitter background up to the fourth-order perturbations. This could be done with the help of the specific symmetry condition imposed on the metric, from which follows, that the model density forms an infinite, cubic lattice. We show that the perturbative solution obtained this way can be interpreted as the exact solution to the Einstein equations for a dust-like energy-momentum tensor. In our model, it seems that physical quantities averaged over a large scales overlap with the respective Einstein-de Sitter prediction, while local observables could differ significantly from their background counterparts. As an example, we analyze in details a behaviour of the local and the global measurements of the Hubble constant, which is important in the context of a current Hubble tension problem.

gr-qc↗
arXiv2018

Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities

We constructed a simple cosmological model which approximates the Einstein-de Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter $λ$, we are able to achieve large values of the density contrast. With a metric explicitly given, many model properties can be calculated in a straightforward way which is interesting in the context of the current discussion concerning the averaging of the inhomogeneities and their backreaction in cosmology. Although the Einstein-de Sitter model can be thought as the model \emph{average}, the light propagation differs from that of the Einstein-de Sitter. The angular diameter distance-redshift relation is affected by the presence of inhomogeneities and depends on the observer's position. The model construction scheme enables some generalizations in the future, so the present work is a step towards more realistic cosmological model described by a relatively simple analytical metric.

gr-qc↗
arXiv2016

Example of an inhomogeneous cosmological model in the context of backreaction

In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein-de Sitter background with a periodically distributed dust overdensities. The model construction enables application of the Green-Wald averaging scheme and the Buchert averaging technique simultaneously. We compare the angular diameter distance function of the considered model to the angular diameter distances corresponding to the average space-times given by the Green-Wald and the Buchert frameworks respectively.

gr-qc↗
arXiv2016

Magnetic flux density from the relative circular motion of stars and partially ionized gas in the Galaxy mid-plane vicinity

Observations suggest a slower stellar rotation relative to gas rotation in the outer part of the Milky Way Galaxy. This difference could be attributed to an interaction with the interstellar magnetic field. In a simple model, fields of order 10 micro Gauss are then required, consistently with the observed values. This coincidence suggests a tool for estimating magnetic fields in spiral galaxies. A North-South asymmetry in the rotation of gas in the Galaxy could be of magnetic origin too.

astro-ph.GA↗
arXiv2015

Velocity dispersion as a factor modifying the distribution of mass in disk-like galaxies -- an example of galaxy UGC 6446

Within the disk model framework used to approximately describe flattened galaxies, we develop an iterative method of determining column mass density from rotation curve supplemented with isotropic velocity dispersion profile. This generalizes our previous iterative method to the case when the velocity dispersion becomes important. We show on the example of UGC 6446 galaxy, that taking the velocity dispersion into account results in some observational signatures in the behavior of the local mass-to-light ratio. Along with galactic magnetic fields, this is another factor allowing to substantially reduce the local mass-to-light ratio at galactic outskirts. Taking the velocity dispersion into account may also have some consequences for the division of mass distribution between various mass components in modeling rotation curves.

astro-ph.GA↗
arXiv2015

Modeling vertical structure in circular velocity of spiral galaxy NGC 4244

We study the vertical gradient in azimuthal velocity of spiral galaxy NGC 4244 in a thin disk model. With surface density accounting for the rotation curve, we model the gradient properties in the approximation of quasi-circular orbits and find the predictions to be consistent with the gradient properties inferred from measurements. This consistency may suggest that the mass distribution in this galaxy is flattened.

astro-ph.GA↗
arXiv2015

Velocity-density twin transforms in thin disk model

Ring mass density and the corresponding circular velocity in thin disk model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to one-fold integrals with identical weight functions. It may be of practical value that the integral for the surface density does not involve the velocity derivative, unlike the equivalent and widely known Toomre's formula.

astro-ph.GA↗
arXiv2015

Motion of halo compact objects in the gravitational potential of a low-mass model of the Galaxy

Recently, we determined a lower bound for the Milky Way mass in a point mass approximation. This result was obtained for most general spherically symmetric phase-space distribution functions consistent with a measured radial velocity dispersion. As a stability test of these predictions against a perturbation of the point mass potential, in this paper we make use of a representative of these functions to set the initial conditions for a simulation in a more realistic potential of similar mass and accounting for other observations. The predicted radial velocity dispersion profile evolves to forms still consistent with the measured profile, proving structural stability of the point mass approximation and the reliability of the resulting mass estimate of $2.1\times10^{11}\mathrm{M}_{\odot}$ within $150\,\mathrm{kpc}$. We also find an interesting coincidence with the recent estimates based on the kinematics of the extended Orphan Stream. As a byproduct, we obtain the equations of motion in axial symmetry from a nonstandard Hamiltonian, and derive a formula in the spherical symmetry relating the radial velocity dispersion profile to a directly measured kinematical observable.

astro-ph.GA↗
arXiv2014

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

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

astro-ph.GA↗
arXiv2014

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

We model the phase-space 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 construct a family of phase-spaces with the resulting radial velocity dispersion overlapping with that of distant kinematic tracers, while making no assumptions about the density of the tracers and the radial profile of the velocity anisotropy (beta). 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 $2.4 \times 10^{11}$ of solar masses, 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.

astro-ph.GA↗
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↗