Operator Splitting for Quasi-Linear Abstract Hyperbolic Equation

We consider an abstract hyperbolic equation with a Lipschitz continuous operator, where the main operator is self-adjoint and positive definite and represents a sum of two similar operators. For this equation, we construct a decomposition scheme of high order of accuracy. This scheme is based on rational splitting of cosine-operator function

Review article: MHD wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfven speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfven wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfven-speed profile. In a $\beta=0$ plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfven wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfven wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfven wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.Comment: 34 pages, 5 figures, invited review in Space Science Reviews => Note this is a 2011 paper, not a 2010 pape

Gravitational phase transition of heavy neutrino matter

In the framework of the Thomas-Fermi model at finite temperature, we show that a cooling nondegenerate gas of massive neutrinos will undergo a phase transition in which quasi-degenerate supermassive neutrino stars are formed through gravitational collapse. For neutrinos in the mass range of 10 to 25 keV these compact dark objects could mimic the role of supermassive black holes that are usually assumed to exist at the centres galaxies. Astrophysical implications and constraints on the neutrino mass are discussed for this scenario.Comment: 10 pages, LaTex, 4 postscript figure

The motion of stars near the Galactic center: A comparison of the black hole and fermion ball scenarios

After a discussion of the properties of degenerate fermion balls, we analyze the orbits of the stars S0-1 and S0-2, which have the smallest projected distances to Sgr A*, in the supermassive black hole as well as in the fermion ball scenarios of the Galactic center. It is shown that both scenarios are consistent with the data, as measured during the last six years by Genzel et al. and Ghez et al. The free parameters of the projected orbit of a star are the unknown components of its velocity v_z and distance z to Sgr A* in 1995.4, with the z-axis being in the line of sight. We show, in the case of S0-1 and S0-2, that the z-v_z phase-space which fits the data, is much larger for the fermion ball than for the black hole scenario. Future measurements of the positions or radial velocities of S0-1 and S0-2 could reduce this allowed phase-space and eventually rule out one of the currently acceptable scenarios. This may shed some light into the nature of the supermassive compact dark object, or dark matter in general at the center of our Galaxy.Comment: 30 pages, 12 figures, Latex, aasms4 styl

Star Formation and Dynamics in the Galactic Centre

The centre of our Galaxy is one of the most studied and yet enigmatic places in the Universe. At a distance of about 8 kpc from our Sun, the Galactic centre (GC) is the ideal environment to study the extreme processes that take place in the vicinity of a supermassive black hole (SMBH). Despite the hostile environment, several tens of early-type stars populate the central parsec of our Galaxy. A fraction of them lie in a thin ring with mild eccentricity and inner radius ~0.04 pc, while the S-stars, i.e. the ~30 stars closest to the SMBH (<0.04 pc), have randomly oriented and highly eccentric orbits. The formation of such early-type stars has been a puzzle for a long time: molecular clouds should be tidally disrupted by the SMBH before they can fragment into stars. We review the main scenarios proposed to explain the formation and the dynamical evolution of the early-type stars in the GC. In particular, we discuss the most popular in situ scenarios (accretion disc fragmentation and molecular cloud disruption) and migration scenarios (star cluster inspiral and Hills mechanism). We focus on the most pressing challenges that must be faced to shed light on the process of star formation in the vicinity of a SMBH.Comment: 68 pages, 35 figures; invited review chapter, to be published in expanded form in Haardt, F., Gorini, V., Moschella, U. and Treves, A., 'Astrophysical Black Holes'. Lecture Notes in Physics. Springer 201

Kpp and KKp Clusters

The three-body kaonic Kpp and KKp clusters are studied using the method of hyperspherical harmonics (HH) in momentum representation and differential Faddeev equations (DFE). We use different NN and KN interactions. Results obtained by the methods of HH and DFE are in reasonable agreement. The binding energy and the width show very strong dependence on the KN potential. We have two different classes of results: the results based on phenomenological strong KN potential, and the results obtained with much weaker chiral SU(3)-based KN potential

Closest Star Seen Orbiting the Supermassive Black Hole at the Centre of the Milky Way

Measurements of stellar velocities and variable X-ray emission near the centre of the Milky Way have provided the strongest evidence so far that the dark mass concentrations seen in many galactic nuclei are likely supermassive black holes, but have not yet excluded several alternative configurations. Here we report ten years of high resolution astrometric imaging that allow us to trace two thirds of the orbit of the star currently closest to the compact radio source and massive black hole candidate SgrA*. In particular, we have observed both peri- and apocentre passages. Our observations show that the star is on a bound, highly elliptical Keplerian orbit around SgrA*, with an orbital period of 15.2 years and a peri-centre distance of only 17 light hours. The orbital elements require an enclosed point mass of 3.7+-1.5x10^6 solar masses. The data exclude with high confidence that the central dark mass consists of a cluster of astrophysical objects or massive, degenerate fermions, and strongly constrain the central density structure.Comment: 13 pages, 3 figures, scheduled for publication in Nature on 17 Oct 200

Propagating Disturbances in Coronal Loops: A Detailed Analysis of Propagation Speeds

Quasi-periodic disturbances have been observed in the outer solar atmosphere for many years now. Although first interpreted as upflows (Schrijver et al. (1999)), they have been widely regarded as slow magnetoacoustic waves, due to observed velocities and periods. However, recent observations have questioned this interpretation, as periodic disturbances in Doppler velocity, line width and profile asymmetry were found to be in phase with the intensity oscillations (De Pontieu et al. (2010),Tian1 et al. (2011))}, suggesting the disturbances could be quasi-periodic upflows. Here we conduct a detailed analysis of the velocities of these disturbances across several wavelengths using the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). We analysed 41 examples, including both sunspot and non sunspot regions of the Sun. We found that the velocities of propagating disturbances (PDs) located at sunspots are more likely to be temperature dependent, whereas the velocities of PDs at non sunspot locations do not show a clear temperature dependence. We also considered on what scale the underlying driver is affecting the properties of the PDs. Finally, we found that removing the contribution due to the cooler ions in the 193 A wavelength suggests that a substantial part of the 193 emission of sunspot PDs can be contributed to the cool component of 193\AA.Comment: 26 Papges, 15 Figure

Excess all-cause mortality and COVID-19-related mortality: a temporal analysis in 22 countries, from January until August 2020

Background This study aimed to investigate overall and sex-specific excess all-cause mortality since the inception of the COVID-19 pandemic until August 2020 among 22 countries. Methods Countries reported weekly or monthly all-cause mortality from January 2015 until the end of June or August 2020. Weekly or monthly COVID-19 deaths were reported for 2020. Excess mortality for 2020 was calculated by comparing weekly or monthly 2020 mortality (observed deaths) against a baseline mortality obtained from 2015–2019 data for the same week or month using two methods: (i) difference in observed mortality rates between 2020 and the 2015–2019 average and (ii) difference between observed and expected 2020 deaths. Results Brazil, France, Italy, Spain, Sweden, the UK (England, Wales, Northern Ireland and Scotland) and the USA demonstrated excess all-cause mortality, whereas Australia, Denmark and Georgia experienced a decrease in all-cause mortality. Israel, Ukraine and Ireland demonstrated sex-specific changes in all-cause mortality. Conclusions All-cause mortality up to August 2020 was higher than in previous years in some, but not all, participating countries. Geographical location and seasonality of each country, as well as the prompt application of high-stringency control measures, may explain the observed variability in mortality changes