q-Deformed quaternions and su(2) instantons

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion language we have formulated and found solutions of the (anti)selfduality equation [instantons and multi-instantons] of a would-be deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on some noncommuting parameters, indicating that the moduli space of a complete theory should be a noncommutative manifold. We summarize these results and add an explicit comparison between the two SO_q(4)-covariant differential calculi on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi- (resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially coincide.Comment: Latex file, 18 page

q-Quaternions and q-deformed su(2) instantons

We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.Comment: Latex file, 39 pages. Final version appeared in JM

Realization of Uq(so(N))U_q(so(N)) within the differntial algebra on RqN{\bf R}_q^N

We realize the Hopf algebra $U_{q^{-1}}(so(N))$ as an algebra of differential operators on the quantum Euclidean space ${\bf R}_q^N$. The generators are suitable q-deformed analogs of the angular momentum components on ordinary ${\bf R}^N$. The algebra $Fun({\bf R}_q^N)$ of functions on ${\bf R}_q^N$ splits into a direct sum of irreducible vector representations of $U_{q^{-1}}(so(N))$; the latter are explicitly constructed as highest weight representations.Comment: 26 pages, 1 figur

Multiphase gas flows in the nearby Seyfert galaxy ESO428-G14

We present ALMA rest-frame 230 GHz continuum and CO(2-1) line observations of the nearby Compton-thick Seyfert galaxy ESO428-G14, with angular resolution 0.7 arcsec (78 pc). We detect CO(2-1) emission from spiral arms and a circum-nuclear ring with 200 pc radius, and from a transverse gas lane with size of $\sim100$ pc, which crosses the nucleus and connects the two portions the circumnuclear ring. The molecular gas in the host galaxy is distributed in a rotating disk with intrinsic circular velocity $v_{rot}=135$ km/s, inclination $i=57$ deg, and dynamical mass $M_{dyn }=5\times 10^9~\rm M_{\odot}$ within a radius of $\sim 1$ kpc. In the inner 100 pc region CO is distributed in a equatorial bar, whose kinematics is highly perturbed and consistent with an inflow of gas towards the AGN. This inner CO bar overlaps with the most obscured, Compton-thick region seen in X-rays. We derive a column density of $\rm N(H_2) \approx 2\times10^{23}~ cm^{-2}$ in this region, suggesting that molecular gas may contribute significantly to the AGN obscuration. We detect a molecular outflow with a total outflow rate $\rm \dot M_{of}\approx 0.8~M_{\odot}/yr$, distributed along a bi-conical structure with size of $700$ pc on both sides of the AGN. The bi-conical outflow is also detected in the $\rm H_2$ emission line at 2.12 $\mu$m, which traces a warmer nuclear outflow located within 170 pc from the AGN. This suggests that the outflow cools with increasing distance from the AGN. We find that the hard X-ray emitting nuclear region mapped with Chandra is CO-deprived, but filled with warm molecular gas traced by $\rm H_2$ - thus confirming that the hard (3-6 keV) continuum and Fe K$\alpha$ emission are due to scattering from dense neutral clouds in the ISM.Comment: Submitted to Ap

Determining efficient temperature sets for the simulated tempering method

In statistical physics, the efficiency of tempering approaches strongly depends on ingredients such as the number of replicas $R$, reliable determination of weight factors and the set of used temperatures, ${\mathcal T}_R = \{T_1, T_2, \ldots, T_R\}$. For the simulated tempering (SP) in particular -- useful due to its generality and conceptual simplicity -- the latter aspect (closely related to the actual $R$) may be a key issue in problems displaying metastability and trapping in certain regions of the phase space. To determine ${\mathcal T}_R$'s leading to accurate thermodynamics estimates and still trying to minimize the simulation computational time, here it is considered a fixed exchange frequency scheme for the ST. From the temperature of interest $T_1$, successive $T$'s are chosen so that the exchange frequency between any adjacent pair $T_r$ and $T_{r+1}$ has a same value $f$. By varying the $f$'s and analyzing the ${\mathcal T}_R$'s through relatively inexpensive tests (e.g., time decay toward the steady regime), an optimal situation in which the simulations visit much faster and more uniformly the relevant portions of the phase space is determined. As illustrations, the proposal is applied to three lattice models, BEG, Bell-Lavis, and Potts, in the hard case of extreme first-order phase transitions, always giving very good results, even for $R=3$. Also, comparisons with other protocols (constant entropy and arithmetic progression) to choose the set ${\mathcal T}_R$ are undertaken. The fixed exchange frequency method is found to be consistently superior, specially for small $R$'s. Finally, distinct instances where the prescription could be helpful (in second-order transitions and for the parallel tempering approach) are briefly discussed.Comment: 10 pages, 14 figure

Iron line emission in X-ray afterglows

Recent observations of X-ray afterglows reveal the presence of a redshifted Kalpha iron line in emission in four bursts. In GRB 991216, the line was detected by the low energy grating of Chandra, which showed the line to be broad, with a full width of ~15,000 km/s. These observations indicate the presence of a >1 solar mass of iron rich material in the close vicinity of the burst, most likely a supernova remnant. The fact that such strong lines are observed less than a day after the trigger strongly limits the size of the remnant, which must be very compact. If the remnant had the observed velocity since the supernova explosion, its age would be less than a month. In this case nickel and cobalt have not yet decayed into iron. We show how to solve this paradox.Comment: 3 pages, to appear in the proceedings of the the 2nd Workshop on Gamma-Ray Bursts in the Afterglow Era, Rome, Oct. 200