Prominence plasma diagnostics through EUV absorption

In this paper we introduce a new diagnostic technique that uses prominence EUV and UV absorption to determine the prominence plasma electron temperature and column emission measure, as well as He/H relative abundance; if a realistic assumption on the geometry of the absorbing plasma can be made, this technique can also yield the absorbing plasma electron density. This technique capitalizes on the absorption properties of Hydrogen and Helium at different wavelength ranges and temperature regimes. Several cases where this technique can be successfully applied are described. This technique works best when prominence plasmas are hotter than 15,000 K and thus it is ideally suited for rapidly heating erupting prominences observed during the initial phases of coronal mass ejections. An example is made using simulated intensities of 4 channels of the SDO/AIA instrument. This technique can be easily applied to existing observations from almost all space missions devoted to the study of the solar atmosphere, which we list.Comment: 17 pages, 4 figures, submitted to Ap

String Geometry and the Noncommutative Torus

We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra A and the noncommutative torus. We show that the (truncated) tachyon subalgebra of A is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus. We construct the corresponding even real spectral triples and determine their Morita equivalence classes using string duality arguments. These constructions yield simple proofs of the O(d,d;Z) Morita equivalences between $d$-dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duality group of toroidally compactified string theory. We classify the automorphisms of the twisted modules and construct the most general gauge theory which is invariant under the automorphism group. We compute bosonic and fermionic actions associated with these gauge theories and show that they are explicitly duality-symmetric. The duality-invariant gauge theory is manifestly covariant but contains highly non-local interactions. We show that it also admits a new sort of particle-antiparticle duality which enables the construction of instanton field configurations in any dimension. The duality non-symmetric on-shell projection of the field theory is shown to coincide with the standard non-abelian Yang-Mills gauge theory minimally coupled to massive Dirac fermion fields.Comment: 37 pages, LaTeX. Major revisions in section 3. Other minor revisions in the rest of the paper, references adde

Bright hot impacts by erupted fragments falling back on the Sun: UV redshifts in stellar accretion

A solar eruption after a flare on 7 Jun 2011 produced EUV-bright impacts of fallbacks far from the eruption site, observed with the Solar Dynamics Observatory. These impacts can be taken as a template for the impact of stellar accretion flows. Broad red-shifted UV lines have been commonly observed in young accreting stars. Here we study the emission from the impacts in the Atmospheric Imaging Assembly's UV channels and compare the inferred velocity distribution to stellar observations. We model the impacts with 2D hydrodynamic simulations. We find that the localised UV 1600A emission and its timing with respect to the EUV emission can be explained by the impact of a cloud of fragments. The first impacts produce strong initial upflows. The following fragments are hit and shocked by these upflows. The UV emission comes mostly from the shocked front shell of the fragments while they are still falling, and is therefore redshifted when observed from above. The EUV emission instead continues from the hot surface layer that is fed by the impacts. Fragmented accretion can therefore explain broad redshifted UV lines (e.g. C IV 1550A) to speeds around 400 km/s observed in accreting young stellar objects.Comment: 12 pages, 4 figures (movies available upon request), accepted for publicatio

Acceleration of weakly collisional solar-type winds

One of the basic properties of the solar wind, that is the high speed of the fast wind, is still not satisfactorily explained. This is mainly due to the theoretical difficulty of treating weakly collisional plasmas. The fluid approach implies that the medium is collision dominated and that the particle velocity distributions are close to Maxwellians. However the electron velocity distributions observed in the solar wind depart significantly from Maxwellians. Recent kinetic collisionless models (called exospheric) using velocity distributions with a suprathermal tail have been able to reproduce the high speeds of the fast solar wind. In this letter we present new developments of these models by generalizing them over a large range of corona conditions. We also present new results obtained by numerical simulations that include collisions. Both approaches calculate the heat flux self-consistently without any assumption on the energy transport. We show that both approaches - the exospheric and the collisional one - yield a similar variation of the wind speed with the basic parameters of the problem; both produce a fast wind speed if the coronal electron distribution has a suprathermal tail. This suggests that exospheric models contain the necessary ingredients for the powering of a transonic stellar wind, including the fast solar one.Comment: Accepted for publication in The Astrophysical Journal Letters (accepted: 13 May 2005

Activation of MHD reconnection on ideal timescales

Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number $S$, up to $10^7$. Results confirm that when the critical aspect ratio of $S^{1/3}$ is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfv\'enic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be robust, as the predicted scaling is measured both in inviscid simulations and when using a Prandtl number $P=1$ in the viscous regime.Comment: Accepted for publication in Plasma Physics and Controlled Fusio

Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration $S^7 \to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equations on $S^4_q$, for which we find an `instanton' solution coming from the natural projection defining the tautological bundle over $S^4_q$.Comment: v2: 38 pages; completely rewritten. The crucial difference with respect to the first version is that in the present one the quantum four-sphere, the base space of the fibration, is NOT a quantum homogeneous space. This has important consequences and led to very drastic changes to the paper. To appear in CM

The social diversification of fashion

We propose a model to investigate the dynamics of fashion traits purely driven by social interactions. We assume that people adapt their style to maximize social success, and we describe the interaction as a repeated group game in which the payoffs reflect the social norms dictated by fashion. On one hand, the tendency to imitate the trendy stereotypes opposed to the tendency to diverge from them to proclaim identity; on the other hand, the exploitation of sex appeal for dating success opposed to the moral principles of the society. These opposing forces promote diversity in fashion traits, as predicted by the modeling framework of adaptive dynamics. Our results link the so-called horizontal dynamics—the primary driver of fashion evolution, compared with the vertical dynamics accounting for interclass and economic drivers—to style variety

Dia t\=on gramm\=on: Euclidean geometry to solve trigonometric problems

Ancient astronomers faced the problem of dealing with arcs and angles in their observations and predictions without the help of modern trigonometry. The usual method to deal with such problems was the Menelaus Theorem, explicitly discussed and extensively used by Ptolemy. It is generally assumed that Hipparchus, who in his Exegesis explicitly states that he developed a method to calculate Simultaneous Risings and Settings, used either the Menelaus' Theorem, or stereographic projections, even if both methods are only attested for later periods and their availability to Hipparchus is debated. In this paper we argue that simultaneous risings and settings could be calculated using less advanced mathematical tools unquestionably available to Hipparchus: the theorem of Pythagoras, the theory of proportions, and the table of chords. Without claiming that this was indeed the method that Hipparchus used, we argue that there is no need to postulate the availability of more sophisticated tools to carry out the calculations which Hipparchus mentions in the Exegesis