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On Nearly Circular Orbits in Stellar Dynamics

Ninković A.

Acta Astronomica

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2021

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Vol. 71, No. 1

73--88

EN

We analyze the motion of a test particle in a stationary and axially symmetric potential along a nearly circular orbit. The dependence of the distance on time is studied. The solution is obtained by applying energy conservation, which requires to find approximate relations valid for nearly circular motion between the pair energy and angular momentum and the one consisting of the mean distance and eccentricity. The results obtained in this way are then subjected to a more general approximation which includes a power law dependence of the circular speed on distance, but without assuming a priori a low eccentricity. The sinusoidal dependence of distance on time, though confirmed as the first approximation, is not sufficient. Therefore, in the present paper an amendment is proposed. The difference of the squares of angular momenta which concern a purely circular orbit and the corresponding (same mean distance) nearly circular orbit is approximately proportional to the eccentricity square. The difference of the speed square at the mean distance divided by the circular speed from unity is, in the case of increasing circular speed, in the vicinity of the mean distance, approximately proportional to the eccentricity square. Otherwise it is negligible. The influence of the local circular speed slope on the period with respect to distance is much more significant than that of eccentricity. This conclusion is rather confirmed also after studying realistic galactocentric orbits, even of not too low eccentricity. The basic drawback of the sinusoidal dependence of distance is that it predicts equal time intervals between the moments of pericentric distance and mean distance and between those of the mean and apocentric distances, which is incorrect even for very low eccentricities.

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High-Velocity Moving Groups in the Solar Neighborhood in Gaia DR2

Baluev R. V., Shaidulin V. Sh., Veselova A. V.

Acta Astronomica

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2020

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Vol. 70, No. 2

141--168

EN

We use an improved wavelet analysis technique to reconstruct the (U,V,W) velocity distribution for ≈250 000 stars from Gaia DR2, located in the solar neighborhood of 200 pc. The 2D wavelet transforms for three bivariate distributions (U,V), (U,W), and (V,W) were investigated. Though most of currently known (low-velocity) stellar moving groups are densely overlapped in these diagrams, our analysis allowed us to detect and disentangle about twenty statistically significant 3D groups of stars with high velocities. Most of them appear to be new discoverirs. We also discuss the issue of correct noise thresholding in the wavelet transform and highlight the importance of using a global rather than local statistic for that. Using of a local significance measure may lead to an overstated statistical confidence for individual patterns due to the effect of multiple testing.

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Mapping the Northern Galactic Disk Warp with Classical Cepheids

Skowron D. M., Skowron J., Mróz P., Udalski A., Pietrukowicz P., Soszyński I., Szymański M. K., Poleski R., Kozłowski S., Ulaczyk K., Rybicki K., Iwanek P., Wrona M., Gromadzki M.

Acta Astronomica

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2019

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Vol. 69, No. 4

305--320

EN

We present an updated three dimensional map of the Milky Way based on a sample of 2431 classical Cepheid variable stars, supplemented with about 200 newly detected classical Cepheids from the OGLE survey. The new objects were discovered as a result of a dedicated observing campaign of the ≈280 square degree extension of the OGLE footprint of the Galactic disk during 2018-2019 observing seasons. These regions cover the main part of the northern Galactic warp that has been deficient in Cepheids so far. We use direct distances to the sample of over 2390 classical Cepheids to model the distribution of the young stellar population in the Milky Way and recalculate the parameters of the Galactic disk warp. Our data show that its northern part is very prominent and its amplitude is ≈10% larger than that of the southern part. By combining Gaia astrometric data with the Galactic rotation curve and distances to Cepheids from our sample, we construct a map of the vertical component of the velocity vector for all Cepheids in the Milky Way disk. We find large-scale vertical motions with amplitudes of 10-20 km/s, such that Cepheids located in the northern warp exhibit large positive vertical velocity (toward the north Galactic pole), whereas those in the southern warp - negative vertical velocity (toward the south Galactic pole).

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Ratio of the Mean Random Velocity Squares Revisited

Ninković S.

Acta Astronomica

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2018

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Vol. 68, No. 3

301--313

EN

The paper aims at obtaining a new formula for the ratio of the mean squares of random velocity in the Galactic plane valid for nearly circular orbits. The formula is obtained by considering a more general case and then reducing it to that concerning low eccentricities. The formula usually referred to as "epicyclic one" is its special case. In addition to the ratio of the Oort constants moduli the ratio of the mean velocity squares depends on the distribution of stars in orbital phases which is presented by means of two parameters, including the asymmetry as well. Inclusion of asymmetry contributes to the increase of moduli of both parameters.