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We have considered polar ring galaxy candidates, the images of which can be found in the SDSS. The sample of 78 galaxies includes the most reliable candidates from the SPRC and PRC catalogs, some of which already have kinematic confirmations. We analyze the distributions of studied objects by the angle between the polar ring and the central disk, and by the optical diameter of the outer ring structures. In the vast majority of cases, the outer structures lie in the plane close to polar (within 10-20 deg) which indicates the stability of the corresponding orbits in the gravitational potential of the halo. Moderately inclined outer structures are observed only in about 6% of objects which probably indicates their short lifetime. In such an unstable configuration, the polar ring would often cross the disk of the galaxy, being smaller than it in the diameter. We show that the inner polar structures and outer large-scale polar rings form a single family in the distribution of diameters normalized to the optical size of the galaxy. At the same time, this distribution is bimodal, as the number of objects with d_ring= (0.4-0.7)*d_disk is negligible. Such a shape of size distribution is most likely due to the fact that the stability of polar orbits in the inner regions of galaxies is maintained by the bulge or the bar, while in the outer regions it is provided by the spheroidal (or triaxial) halo.
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Spectroscopic observations at the Russian 6-m telescope are used to study the two polar ring galaxies (PRGs) from the catalogue by Moiseev et al.: SPRC-7 and SPRC-260. We have analyzed the kinematics of the stellar component of the central galaxies as well as the ionized gas kinematics in the external ring structures. The disc-halo decomposition of rotation curves in two perpendicular directions are considered. The observed 2D velocity fields are compared with the model predictions for different dark halo shapes. Based on these data, we constrain that for potential of DM halo semiaxis ratios is $s=0.8$, $q=1$ for SPRC-7 and $s=0.95$, $q=1.1$ for SPRC-260. Using 3D hydrodynamic simulations we also study the dynamics and evolution of the polar component in the potential of the galactic disc and dark halo for these two galaxies. We show that the polar component is dynamically quasi-stable on the scale of $sim10$ dynamical times (about a few Gyr). This is demonstrate the possibility for the growth of a spiral structure, which then steadily transforms to a lopsided gaseous system in the polar pane.
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V.P.Reshetnikov
, V.A.Hagen-Thorn
, V.A.Yakovleva (Astronomicaln Institute of St.Petersburg State University
1996
We present the results of detailed surface photometry of NGC 3808B and NGC 6286 - two spiral galaxies with possibly forming ring-like structures rotating around major axes of the galaxies. The formation of rings in NGC 3808B and NGC 6286 being accompanied by accretion of matter on galactic disk results in some interesting gasdynamical and stellardynamical effects in these galaxies. One can note, for instance, peculiar rotation curve of NGC 3808B gaseous disk; strong infrared and H-alpha emission from the galaxies; bending and flaring stellar disks in both galaxies. Our observations clearly illustrate the possibility that polar-ring galaxies may be formed as a result of matter accretion from one galaxy to another.
We show that the functor of $p$-typical co-Witt vectors on commutative algebras over a perfect field $k$ of characteristic $p$ is defined on, and in fact only depends on, a weaker structure than that of a $k$-algebra. We call this structure a $p$-polar $k$-algebra. By extension, the functors of points for any $p$-adic affine commutative group scheme and for any formal group are defined on, and only depend on, $p$-polar structures. In terms of abelian Hopf algebras, we show that a cofree cocommutative Hopf algebra can be defined on any $p$-polar $k$-algebra $P$, and it agrees with the cofree commutative Hopf algebra on a commutative $k$-algebra $A$ if $P$ is the $p$-polar algebra underlying $A$; a dual result holds for free commutative Hopf algebras on finite $k$-coalgebras.
As an extension of previous ungraded work, we define a graded $p$-polar ring to be an analog of a graded commutative ring where multiplication is only allowed on $p$-tuples (instead of pairs) of elements of equal degree. We show that the free affine $p$-adic group scheme functor, as well as the free formal group functor, defined on $k$-algebras for a perfect field $k$ of characteristic $p$, factors through $p$-polar $k$-algebras. It follows that the same is true for any affine $p$-adic or formal group functor, in particular for the functor of $p$-typical Witt vectors. As an application, we show that the latter is free on the $p$-polar affine line.
In the first half year of operation the satellite borne POLAR instrument detected a total of 55 Gamma-Ray Bursts about 10 of which were bright enough to allow for detailed polarization studies, thereby forming the start of the first Gamma-Ray Burst polarization catalog. In this paper a brief overview of the previous GRB polarization studies will be presented followed by an overview of the POLAR detector along with the first result of the in-flight performance. The detected Gamma-Ray bursts will be presented and finally prospects for polarization measurements of these events will be discussed.
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