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1. Szymon Sikora, Krzysztof Głód Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities Phys. Rev. D: Part. Fields , vol. 99, p. 083512 (2019). [abstract] [preprint] [journal]  Abstract: We constructed a simple cosmological model which approximates the Einsteinde 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 Einsteinde Sitter model can be thought of as the model average, the light propagation differs from that of Einsteinde Sitter. The angular diameter distanceredshift 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 toward more realistic cosmological model described by a relatively simple analytical metric.  2. Sikora S., Bratek Ł., Jałocha J., Kutschera M. The influence of the velocity dispersion on the velocitydensity relation in the disk model of the galaxy Acta Phys. Pol., B , vol. 48, p. 2071 (2017). [abstract] [journal]  Abstract: Taking the velocity dispersion term into account in the Jeans equation describing the disk model, counterintuitively allows to reduce the local masstolight ratio at the outskirts of flattened galaxies, and stop the unbound growth of mass function. This is possible thanks to a more intertwined relation between the gravitational potential and the rotation curve than for spheroidal systems. This effect is illustrated on the example of
galaxy UGC 6446 by finding iteratively the column mass density from the rotation curve supplemented with an isotropic velocity dispersion profile in the disk plane. Along with galactic magnetic fields, this effect would allow to reduce the local masstolight ratio at the galactic outskirts.  3. Szymon Sikora, Krzysztof Głód Example of an inhomogeneous cosmological model in the context of backreaction Phys. Rev. D: Part. Fields , vol. 95, p. 063517 (2017). [abstract] [preprint] [journal]  Abstract: 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 periodically distributed dust overdensities. The model construction enables application of the GreenWald 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 spacetimes given by the GreenWald and the Buchert frameworks respectively.  4. Jałocha J., Bratek Ł., Pękala J., Sikora S., Kutschera M. Magnetic flux density from the relative circular motion of stars and partially ionized gas in the Galaxy midplane vicinity Astrophys J. , vol. 833, p. 174 (2016). [abstract] [preprint] [journal]  Abstract: 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 NorthSouth asymmetry in the rotation of gas in the Galaxy could be of magnetic origin too.  5. Bratek Ł., Sikora S., Jałocha J., Kutschera M. Velocitydensity twin transforms in the thin disk model Mon. Not. R. Astron. Soc. , vol. 451, p. 4018 (2015). [abstract] [preprint] [journal]  Abstract: Ring mass density and the corresponding circular velocity in thin disc model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to onefold 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.  6. Jałocha J., Bratek Ł., Sikora S., Kutschera M. Modelling vertical structure in circular velocity of spiral galaxy NGC 4244 Mon. Not. R. Astron. Soc. , vol. 451, p. 3366 (2015). [abstract] [preprint] [journal]  Abstract: We study the vertical gradient in azimuthal velocity of spiral galaxy NGC 4244 in a thin disc model. With surface density accounting for the rotation curve, we model the gradient properties in the approximation of quasicircular orbits. It is worthy to note that the prediction of our model is consistent with the gradient properties inferred recently from a numerical model implementing the positionvelocity diagram of this galaxy. The confirmation of our prediction by the future measurement of the gradient would provide support for the expectation that the mass distribution in this galaxy is flattened.  
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