Cocycle twisting of E(n)-module algebras and applications to the Brauer group

We classify the orbits of coquasi-triangular structures for the Hopf algebra E(n) under the action of lazy cocycles and the Hopf automorphism group. This is applied to detect subgroups of the Brauer group $BQ(k,E(n))$ of E(n) that are isomorphic. For a triangular structure $R$ on E(n) we prove that the subgroup $BM(k,E(n),R)$ of $BQ(k,E(n))$ arising from $R$ is isomorphic to a direct product of $BW(k)$, the Brauer-Wall group of the ground field $k$, and $Sym_n(k)$, the group of $n \times n$ symmetric matrices under addition. For a general quasi-triangular structure $R'$ on E(n) we construct a split short exact sequence having $BM(k,E(n), R')$ as a middle term and as a left term a central extension of the group of symmetric matrices of order $r<n$ ($r$ depending on $R'$). We finally describe how the image of the Hopf automorphism group inside $BQ(k,E(n))$ acts on $Sym_n(k)$.Comment: Accidentally an old version of the paper was posted. Main corrections are in Section 2 and in Section 4.

Feedback-limited Accretion: Luminous Signatures from Growing Planets

Planets form in discs of gas and dust around stars, and keep growing by accretion of disc material while available. Massive planets clear a gap in that protoplanetary disc, but still accrete through spiral wakes. On its way to the planet, the gas will settle on a \emph{circumplanetary} disc around the planet and slowly accrete on to it. The energy of the accreted gas will be released, heating the planet surroundings in a feedback process. For high enough accretion rates the planet should be detectable at infrared wavelengths. We aim to find whether detectable planet luminosities, $\gtrsim 10^{-3} \, \textrm{L}_\odot$, can occur when considering that the planet luminosity is coupled to the accretion, and also to study which other effects has the feedback on the dynamics of the circumplanetary and the gap regions. We model a planet with mass ratio $q=10^{-3}$, orbiting at 10 AU from a solar mass star, using a modified version of the 2D code FARGO-AD, which includes a prescription for the accretion and feedback luminosity of the planet. We find that the planetary feedback is able to partially deplete the circumplanetary disc, and to reduce the accretion rate onto the planet. However, detectable luminosities of $L_\textrm{p}\gtrsim 10^{-3}\, \textrm{L}_\odot$ are still produced. The feedback also contributes to partially refilling the gap, to heat up the coorbital region, and to perturb the orbital velocity of the gas.Comment: Submitted to MNRA

Galactic Centre stellar winds and Sgr A* accretion

(ABRIDGED) We present in detail our new 3D numerical models for the accretion of stellar winds on to Sgr A*. In our most sophisticated models, we put stars on realistic orbits around Sgr A*, include `slow' winds (300 km/s), and account for radiative cooling. We first model only one phase `fast' stellar winds (1000 km/s). For wind sources fixed in space, the accretion rate is Mdot ~ 1e-5 Msun/yr, fluctuates by < 10%, and is in a good agreement with previous models. In contrast, Mdot decreases by an order of magnitude for stars following circular orbits, and fluctuates by ~ 50%. Then we allow a fraction of stars to produce slow winds. Much of these winds cool radiatively, forming cold clumps immersed into the X-ray emitting gas. We test two orbital configurations for the stars in this scenario, an isotropic distribution and two rotating discs with perpendicular orientation. The morphology of cold gas is quite sensitive to the orbits. In both cases, however, most of the accreted gas is hot, with an almost constant Mdot ~ 3e-6 Msun/yr, consistent with Chandra observations. The cold gas accretes in intermittent, short but powerful episodes which may give rise to large amplitude variability in the luminosity of Sgr A* on time scales of 10s to 100s of years. The circularisation radii for the flows are ~ 1e3 and 1e4 Rsch, for the one and two-phase wind simulations, respectively, never forming the quasi-spherical accretion flows suggested in some previous work. Our work suggests that, averaged over time scales of 100s to 1000s of years, the radiative and mechanical luminosity of Sgr A* may be substantially higher than it is in its current state. Further improvements of the wind accretion modelling of Sgr A* will rely on improved observational constraints for the wind properties and stellar orbits.Comment: 16 pages, 18 colour figures. Accepted by MNRAS. Full resolution paper and movies available at http://www.mpa-garching.mpg.de/~jcuadra/Winds/ . (v2: minor changes

Santiago Ibarra: Historia de un inmigrante vasco = euskal etorkin baten historia

Reseña bibliográfica de la obra "Santiago Ibarra: Historia de un inmigrante vasco = euskal etorkin baten historia" de Ángeles de Dios de Martina. El libro es el resultado del análisis detallado de una extensa carta escrita por Santiago Ibarra desde Argentina a su hermana Leoncia de Bilbao en 1954. Este estudio incluye ilustraciones de la época y análisis del contexto histórico de los eventos que narra en la carta

General Relativistic Flux Modulations from Disk Instabilities in Sagittarius A*

Near-IR and X-ray flares have been detected from the supermassive black hole Sgr A* at the center of our Galaxy with a (quasi)-period of ~17-20 minutes, suggesting an emission region only a few Schwarzschild radii above the event horizon. The latest X-ray flare, detected with XMM-Newton, is notable for its detailed lightcurve, yielding not only the highest quality period thus far, but also important structure reflecting the geometry of the emitting region. Recent MHD simulations of Sgr A*'s disk have demonstrated the growth of a Rossby wave instability, that enhances the accretion rate for several hours, possibly accounting for the observed flares. In this Letter, we carry out ray-tracing calculations in a Schwarzschild metric to determine as accurately as possible the lightcurve produced by general relativistic effects during such a disruption. We find that the Rossby wave induced spiral pattern in the disk is an excellent fit to the data, implying a disk inclination angle of ~77 deg. Note, however, that if this association is correct, the observed period is not due to the underlying Keplerian motion but, rather, to the pattern speed. The favorable comparison between the observed and simulated lightcurves provides important additional evidence that the flares are produced in Sgr A*'s inner disk.Comment: 5 Pages, 3 Figures, accepted for publication in ApJ Lette

The X-ray Ridge Surrounding Sgr A* at the Galactic Center

We present the first detailed simulation of the interaction between the supernova explosion that produced Sgr A East and the wind-swept inner ~ 2-pc region at the Galactic center. The passage of the supernova ejecta through this medium produces an X-ray ridge ~ 9'' to 15'' to the NE of the supermassive black hole Sagittarius A* (Sgr A*). We show that the morphology and X-ray intensity of this feature match very well with recently obtained Chandra images, and we infer a supernova remnant age of less than 2,000 years. This young age--a factor 3--4 lower than previous estimates--arises from our inclusion of stellar wind effects in the initial (pre-explosion) conditions in the medium. The supernova does not clear out the central ~ 0.2-pc region around Sgr~A* and does not significantly alter the accretion rate onto the central black hole upon passage through the Galactic center.Comment: 10 pages, 3 figures, submitted to ApJ

Binary formation and mass function variations in fragmenting discs with short cooling times

Accretion discs at sub-pc distances around supermassive black holes are likely to cool rapidly enough that self-gravity results in fragmentation. Here, we use high-resolution hydrodynamic simulations of a simplified disc model to study how the outcome of fragmentation depends upon numerical resolution and cooling time, and to investigate the incidence of binary formation within fragmenting discs. We investigate a range of cooling times, from the relatively long cooling time-scales that are marginally unstable to fragmentation down to highly unstable cooling on a time-scale that is shorter than the local dynamical time. The characteristic mass of fragments decreases with reduced cooling time, though the effect is modest and dependent upon details of how rapidly bound clumps radiate. We observe a high incidence of capture binaries, though we are unable to determine their final orbits or probability of survival. The results suggest that faster cooling in the parent disc results in an increased binary fraction, and that a high primordial binary fraction may result from disc fragmentation. We discuss our results in terms of the young massive stars close to the Galactic Centre, and suggest that observations of some stellar binaries close to the Galactic Centre remain consistent with formation in a fragmenting accretion disc.Comment: 10 pages, 5 figures. Accepted for publication in MNRAS. Figures 1 and 3 degraded to meet arXiv size limits - version with high resolution figures available at http://www.strw.leidenuniv.nl/~rda/publications.htm

Picard groups and strongly graded coalgebras

AbstractIn this paper we study strongly graded coalgebras and its relation to the Picard group. A classification theorem for this kind of coalgebras is given via the second Doi's cohomology group. The strong Picard group of a coalgebra is introduced in order to characterize those graded coalgebras with strongly graded dual ring. Finally, for a Hopf algebra H we also characterize the H∗-Galois coextensions with dual H-Galois extension solving the question proposed in Dăscălescu et al., J. Algebra 178 (1995) 400–413