Epicyclic oscillations of non-slender fluid tori around Kerr black holes

Considering epicyclic oscillations of pressure-supported perfect fluid tori orbiting Kerr black holes we examine non-geodesic (pressure) effects on the epicyclic modes properties. Using a perturbation method we derive fully general relativistic formulas for eigenfunctions and eigenfrequencies of the radial and vertical epicyclic modes of a slightly non-slender, constant specific angular momentum torus up to second-order accuracy with respect to the torus thickness. The behaviour of the axisymmetric and lowest-order ($m=\pm 1$) non-axisymmetric epicyclic modes is investigated. For an arbitrary black hole spin we find that, in comparison with the (axisymmetric) epicyclic frequencies of free test particles, non-slender tori receive negative pressure corrections and exhibit thus lower frequencies. Our findings are in qualitative agreement with the results of a recent pseudo-Newtonian study of analogous problem defined within the Paczy{\'n}ski-Wiita potential. Implications of our results on the high-frequency QPO models dealing with epicyclic oscillations are addressed.Comment: 24 pages, 8 figure

Multiple star systems in the Orion nebula

This is the author accepted manuscript. The final fersion is available from EDP Sciences via the DOI in this record.This work presents an interferometric study of the massive-binary fraction in the Orion Trapezium cluster with the recently comissioned GRAVITY instrument. We observed a total of 16 stars of mainly OB spectral type. We find three previously unknown companions for θ1 Ori B, θ2 Ori B, and θ2 Ori C. We determined a separation for the previously suspected companion of NU Ori. We confirm four companions for θ1 Ori A, θ1 Ori C, θ1 Ori D, and θ2 Ori A, all with substantially improved astrometry and photometric mass estimates. We refined the orbit of the eccentric high-mass binary θ1 Ori C and we are able to derive a new orbit for θ1 Ori D. We find a system mass of 21.7 M⊙ and a period of 53 days. Together with other previously detected companions seen in spectroscopy or direct imaging, eleven of the 16 high-mass stars are multiple systems. We obtain a total number of 22 companions with separations up to 600 AU. The companion fraction of the early B and O stars in our sample is about two, significantly higher than in earlier studies of mostly OB associations. The separation distribution hints toward a bimodality. Such a bimodality has been previously found in A stars, but rarely in OB binaries, which up to this point have been assumed to be mostly compact with a tail of wider companions. We also do not find a substantial population of equal-mass binaries. The observed distribution of mass ratios declines steeply with mass, and like the direct star counts, indicates that our companions follow a standard power law initial mass function. Again, this is in contrast to earlier findings of flat mass ratio distributions in OB associations. We excluded collision as a dominant formation mechanism but find no clear preference for core accretion or competitive accretion.Marie Skłodowska-Curie Grant AgreementFCT-PortugalERC Starting Gran

Systematic design of an extractive distillation for maximum-boiling azeotropes with heavy entrainers

Extractive distillation is one of the most attractive approaches for separating azeotropic mixtures. Few contributions have been reported to design an extractive distillation for separating maximum-boiling azeotropes and no systematic approaches for entrainer screening have been presented. A systematic approach to design of two-column extractive distillation for separating azeotropes with heavy entrainers has been proposed. A thermodynamic feasibility analysis for azeotropes with potential heavy entrainers was first conducted. Then, five important properties are selected for entrainer evaluation. Fuzzy logic and develop membership functions to calculate attribute values of selected properties have been used. An overall indicator for entrainer evaluation is proposed and a ranking list is generated. Finally, the top five entrainers from the ranking list have been selected and use process optimization techniques to further evaluate selected entrainers and generate an optimal design. The capability of the proposed method is illustrated using the separation of acetone–chloroform azeotropes with five potential entrainers