Tidal and rotational effects in the perturbations of hierarchical triple stellar systems. II. Eccentric systems - the case of AS Camelopardalis

We study the perturbations of a relatively close third star on a tidally distorted eccentric eclipsing binary. We consider both the observational consequences of the variations of the orbital elements and the interactions of the stellar rotation with the orbital revolution in the presence of dissipation. We concentrate mainly on the effect of a hypothetical third companion on both the real, and the observed apsidal motion period. We investigate how the observed period derived mainly from some variants of the O-C relates to the real apsidal motion period. We carried out both analytical and numerical investigations and give the time variations of the orbital elements of the binary both in the dynamical and the observational reference frames. We give the direct analytical form of an eclipsing O-C affected simultaneously by the mutual tidal forces and the gravitational interactions with a tertiary. We also integrated numerically simultaneously the orbital and rotational equations for the possible hierarchical triple stellar system AS Camelopardalis. We find that there is a significant domain of the possible hierarchical triple system configurations, where both the dynamical and the observational effects tend to measure longer apsidal advance rate than is expected theoretically. This happens when the mutual inclination of the close and the wide orbits is large, and the orbital plane of the tertiary almost coincides with the plane of the sky. We also obtain new numerical results on the interaction of the orbital evolution and stellar rotation in such triplets. The most important fact is that resonances might occur as the stellar rotational rate varies during the dissipation-driven synchronization process...Comment: 33 pages, 12 figures (reduced quality!), accepted for publication for Astronomy and Astrophysic

Hierarchical progressive surveys. Multi-resolution HEALPix data structures for astronomical images, catalogues, and 3-dimensional data cubes

Scientific exploitation of the ever increasing volumes of astronomical data requires efficient and practical methods for data access, visualisation, and analysis. Hierarchical sky tessellation techniques enable a multi-resolution approach to organising data on angular scales from the full sky down to the individual image pixels. Aims. We aim to show that the Hierarchical progressive survey (HiPS) scheme for describing astronomical images, source catalogues, and three-dimensional data cubes is a practical solution to managing large volumes of heterogeneous data and that it enables a new level of scientific interoperability across large collections of data of these different data types. Methods. HiPS uses the HEALPix tessellation of the sphere to define a hierarchical tile and pixel structure to describe and organise astronomical data. HiPS is designed to conserve the scientific properties of the data alongside both visualisation considerations and emphasis on the ease of implementation. We describe the development of HiPS to manage a large number of diverse image surveys, as well as the extension of hierarchical image systems to cube and catalogue data. We demonstrate the interoperability of HiPS and Multi-Order Coverage (MOC) maps and highlight the HiPS mechanism to provide links to the original data. Results. Hierarchical progressive surveys have been generated by various data centres and groups for ~200 data collections including many wide area sky surveys, and archives of pointed observations. These can be accessed and visualised in Aladin, Aladin Lite, and other applications. HiPS provides a basis for further innovations in the use of hierarchical data structures to facilitate the description and statistical analysis of large astronomical data sets.Comment: 21 pages, 6 figures. Accepted for publication in Astronomy & Astrophysic

MS‾\overline{\rm MS}-on-shell quark mass relation up to four loops in QCD and a general SU(N)(N) gauge group

In this paper we compute the relation between heavy quark masses defined in the modified minimal subtraction and on-shell scheme. Detailed results are presented for all coefficients of the SU$(N_c)$ colour factors. The reduction of the four-loop on-shell integrals is performed for a general QCD gauge parameter. Some of the about 380 master integrals are computed analytically, others with high numerical precision based on Mellin-Barnes representations, and the rest numerically with the help of {\tt FIESTA}. We discuss in detail the precise numerical evaluation of the four-loop master integrals. Updated relations between various short-distance masses and the $\overline{\rm MS}$ quark mass to next-to-next-to-next-to-leading order accuracy are provided for the charm, bottom and top quark. We discuss the dependence on the renormalization and factorization scale.Comment: 53 pages, 11 figures, v2: minor changes, references added, corresponds to published versio

Angular power spectrum of galaxies in the 2MASS Redshift Survey

We present the measurement and interpretation of the angular power spectrum of nearby galaxies in the 2MASS Redshift Survey catalog with spectroscopic redshifts up to $z\approx 0.1$. We detect the angular power spectrum up to a multipole of $\ell\approx 1000$. We find that the measured power spectrum is dominated by galaxies living inside nearby galaxy clusters and groups. We use the halo occupation distribution (HOD) formalism to model the power spectrum, obtaining a fit with reasonable parameters. These HOD parameters are in agreement with the 2MASS galaxy distribution we measure toward the known nearby galaxy clusters, confirming validity of our analysis.Comment: 8 pages, 6 figure