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Register a new userCritically rotating stars in binaries - an unsolved problem -
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In close binaries mass and angular momentum can be transferred from one star to the other during Roche-lobe overflow. The efficiency of this process is not well understood and constitutes one of the largest uncertainties in binary evolution. One of the problems lies in the transfer of angular momentum, which will spin up the accreting star. In very tight systems tidal friction can prevent reaching critical rotation, by locking the spin period to the orbital period. Accreting stars in systems with orbital periods larger than a few days reach critical rotation after accreting only a fraction of their mass, unless there is an effective mechanism to get rid of angular momentum. In low mass stars magnetic field might help. In more massive stars angular momentum loss will be accompanied by strong mass loss. This would imply that most interacting binaries with initial orbital periods larger than a few days evolve very non-conservatively. In this contribution we wish to draw attention to the unsolved problems related to mass and angular momentum transfer in binary systems. We do this by presenting the first results of an implementation of spin up by accretion into the TWIN version of the Eggleton stellar evolution code.
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Wilfs Sixth Unsolved Problem asks for any interesting properties of the set of partitions of integers for which the (nonzero) multiplicities of the parts are all different. We refer to these as emph{Wilf partitions}. Using $f(n)$ to denote the number of Wilf partitions, we establish lead-order asymptotics for $ln{f(n)}$.
The work initially started as a test to retrace the Shen & Ho (2014) Quasar Main Sequence diagram where they claimed that the parameter RFeII, which defines the Eigenvector 1 (EV1) is driven by the Eddington ratio alone. We subsequently construct a refined (error and redshift limited) sample from the original Shen et al. 2011 QSO catalogue. Based on our hypothesis - the main driver of the Quasar Main Sequence is the maximum of the accretion disk temperature defined by the Big Blue Bump on the Spectral Energy Distribution. We select the four extreme sources that have RFeII $geq$ 4.0 and use the SED modelling code CIGALE to fit the multi-band photometric data for these sources. We also perform detailed spectral fitting including the FeII pseudo-continuum to estimate and compare the value of RFeII for them. We show the metallicity dependent FeII strength in the context of this study.
Context. The recent estimates of the 3D shape of the M/Xe-type triple asteroid system (216) Kleopatra indicated a density of 5 g.cm$^{-3}$. Such a high density implies a high metal content and a low porosity which is not easy to reconcile with its peculiar dumbbell shape. Aims. Given the unprecedented angular resolution of the VLT/SPHERE/ZIMPOL camera, we aim to constrain the mass and the shape of Kleopatra with high accuracy, hence its density. Methods. We combined our new VLT/SPHERE observations of Kleopatra recorded in 2017 and 2018 with archival data, as well as lightcurve, occultation, and delay-Doppler images, to derive its 3D shape model using two different algorithms (ADAM, MPCD). Furthermore, an N-body dynamical model allowed us to retrieve the orbital elements of the two moons as explained in the accompanying paper. Results. The shape of Kleopatra is very close to an equilibrium dumbbell figure with two lobes and a thick neck. Its volume equivalent diameter (118.75$pm$1.40) km and mass (2.97$pm$0.32) 10$^{18}$ kg imply a bulk density of (3.38$pm$0.50) g cm$^{-3}$. Such a low density for a supposedly metal-rich body indicates a substantial porosity within the primary. This porous structure along with its near-equilibrium shape is compatible with a formation scenario including a giant impact followed by reaccumulation. Kleopatras current rotation period and dumbbell shape imply that it is in a critically rotating state. The low effective gravity along the equator of the body, together with the equatorial orbits of the moons and possibly rubble-pile structure, opens the possibility that the moons formed via mass shedding. Conclusions. Kleopatra is a puzzling multiple system due to the unique characteristics of the primary. It deserves particular attention in the future, with the Extremely Large Telescopes and possibly a dedicated space mission.
The coalescence of a neutron star with a black hole is a primary science target of ground-based gravitational wave detectors. Constraining or measuring the neutron star spin directly from gravitational wave observations requires knowledge of the dependence of the emission properties of these systems on the neutron star spin. This paper lays foundations for this task, by developing a numerical method to construct initial data for black hole--neutron star binaries with arbitrary spin on the neutron star. We demonstrate the robustness of the code by constructing initial-data sets in large regions of the parameter space. In addition to varying the neutron star spin-magnitude and spin-direction, we also explore neutron star compactness, mass-ratio, black hole spin, and black hole spin-direction. Specifically, we are able to construct initial data sets with neutron stars spinning near centrifugal break-up, and with black hole spins as large as $S_{rm BH}/M_{rm BH}^2=0.99$.
Evolutionary models of fast-rotating stars show that the stellar rotational velocity may approach the critical speed. Critically rotating stars cannot spin up more, therefore they lose their excess angular momentum through an equatorial outflowing disk. The radial extension of such disks is unknown, partly because we lack information about the radial variations of the viscosity. We study the magnetorotational instability, which is considered to be the origin of anomalous viscosity in outflowing disks. We used analytic calculations to study the stability of outflowing disks submerged in the magnetic field. The magnetorotational instability develops close to the star if the plasma parameter is large enough. At large radii the instability disappears in the region where the disk orbital velocity is roughly equal to the sound speed. The magnetorotational instability is a plausible source of anomalous viscosity in outflowing disks. This is also true in the region where the disk radial velocity approaches the sound speed. The disk sonic radius can therefore be roughly considered as an effective outer disk radius, although disk material may escape from the star to the insterstellar medium. The radial profile of the angular momentum-loss rate already flattens there, consequently, the disk mass-loss rate can be calculated with the sonic radius as the effective disk outer radius. We discuss a possible observation determination of the outer disk radius by using Be and Be/X-ray binaries.
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