Torus-based compression by factor 4 and 6

We extend the torus-based compression technique for cyclotomic subgroups and show how the elements of certain subgroups in characteristic two and three fields can be compressed by a factor of 4 and 6, respectively. Our compression and decompression functions can be computed at a negligible cost. In particular, our techniques lead to very efficient exponentiation algorithms that work with the compressed representations of elements and can be easily incorporated into pairing-based protocols that require exponentiations or products of pairings

The quenching of star formation in accretion-driven clumpy turbulent tori of active galactic nuclei

Galactic gas-gas collisions involving a turbulent multiphase ISM share common ISM properties: dense extraplanar gas visible in CO, large linewidths (>= 50 km/s), strong mid-infrared H_2 line emission, low star formation activity, and strong radio continuum emission. Gas-gas collisions can occur in the form of ICM ram pressure stripping, galaxy head-on collisions, compression of the intragroup gas and/or galaxy ISM by an intruder galaxy which flies through the galaxy group at a high velocity, or external gas accretion on an existing gas torus in a galactic center. We suggest that the common theme of all these gas-gas interactions is adiabatic compression of the ISM leading to an increase of the turbulent velocity dispersion of the gas. The turbulent gas clouds are then overpressured and star formation is quenched. Within this scenario we developed a model for turbulent clumpy gas disks where the energy to drive turbulence is supplied by external infall or the gain of potential energy by radial gas accretion within the disk. The cloud size is determined by the size of a C-type shock propagating in dense molecular clouds with a low ionization fraction at a given velocity dispersion. We give expressions for the expected volume and area filling factors, mass, density, column density, and velocity dispersion of the clouds. The latter is based on scaling relations of intermittent turbulence whose open parameters are estimated for the CND in the Galactic Center. The properties of the model gas clouds and the external mass accretion rate necessary for the quenching of the star formation rate due to adiabatic compression are consistent with those derived from high-resolution H_2 line observations. Based on these findings, a scenario for the evolution of gas tori in galactic centers is proposed and the implications for star formation in the Galactic Center are discussed.Comment: 13 pages, 1 figure, accepted for publication by A&

Radio Galaxy NGC 1265 unveils the Accretion Shock onto the Perseus Galaxy Cluster

We present a consistent 3D model for the head-tail radio galaxy NGC 1265 that explains the complex radio morphology and spectrum by a past passage of the galaxy and radio bubble through a shock wave. Using analytical solutions to the full Riemann problem and hydrodynamical simulations, we study how this passage transformed the plasma bubble into a toroidal vortex ring. Adiabatic compression of the aged electron population causes it to be energized and to emit low-surface brightness and steep-spectrum radio emission. The large infall velocity of NGC 1265 and the low Faraday rotation measure values and variance of the jet strongly argue that this transformation was due to the accretion shock onto Perseus situated roughly at R_200. Estimating the volume change of the radio bubble enables inferring a shock Mach number of M = 4.2_{-1.2}^{+0.8}, a density jump of 3.4_{-0.4}^{+0.2}, a temperature jump of 6.3_{-2.7}^{+2.5}, and a pressure jump of 21.5 +/- 10.5 while allowing for uncertainties in the equation of state of the radio plasma and volume of the torus. Extrapolating X-ray profiles, we obtain upper limits on the gas temperature and density in the infalling warm-hot intergalactic medium of kT < 0.4 keV and n < 5e-5 / cm^3. The orientation of the ellipsoidally shaped radio torus in combination with the direction of the galaxy's head and tail in the plane of the sky is impossible to reconcile with projection effects. Instead, this argues for post-shock shear flows that have been caused by curvature in the shock surface with a characteristic radius of 850 kpc. The energy density of the shear flow corresponds to a turbulent-to-thermal energy density of 14%. The shock-injected vorticity might be important in generating and amplifying magnetic fields in galaxy clusters. Future LOFAR observations of head-tail galaxies can be complementary probes of accretion shocks onto galaxy clusters.Comment: 14 pages, 4 figures, ApJ, in print; v3: typos corrected to match the published version; v2: improved presentation, added 2D numerical simulations and exact solution to the 1D Riemann problem of a shock overrunning a spherical bubble that gets transformed into a vortex rin

Shock waves from non-spherical cavitation bubbles

We present detailed observations of the shock waves emitted at the collapse of single cavitation bubbles using simultaneous time-resolved shadowgraphy and hydrophone pressure measurements. The geometry of the bubbles is systematically varied from spherical to very non-spherical by decreasing their distance to a free or rigid surface or by modulating the gravity-induced pressure gradient aboard parabolic flights. The non-spherical collapse produces multiple shocks that are clearly associated with different processes, such as the jet impact and the individual collapses of the distinct bubble segments. For bubbles collapsing near a free surface, the energy and timing of each shock are measured separately as a function of the anisotropy parameter $\zeta$, which represents the dimensionless equivalent of the Kelvin impulse. For a given source of bubble deformation (free surface, rigid surface or gravity), the normalized shock energy depends only on $\zeta$, irrespective of the bubble radius $R_{0}$ and driving pressure $\Delta p$. Based on this finding, we develop a predictive framework for the peak pressure and energy of shock waves from non-spherical bubble collapses. Combining statistical analysis of the experimental data with theoretical derivations, we find that the shock peak pressures can be estimated as jet impact-induced hammer pressures, expressed as $p_{h} = 0.45\left(\rho c^{2}\Delta p\right)^{1/2} \zeta^{-1}$ at $\zeta > 10^{-3}$. The same approach is found to explain the shock energy quenching as a function of $\zeta^{-2/3}$.Comment: Accepted for publication in Physical Review Fluid

On the Formation of Cluster Radio Relics

(abridged) We present detailed 3-dimensional magneto-hydrodynamical simulations of the passage of a radio plasma cocoon filled with turbulent magnetic fields through a shock wave. Taking into account synchrotron, inverse Compton and adiabatic energy losses and gains we evolved the relativistic electron population to produce synthetic polarisation radio maps. On contact with the shock wave the radio cocoons are first compressed and finally torn into filamentary structures, as is observed in several cluster radio relics. In the synthetic radio maps the electric polarisation vectors are mostly perpendicular to the filamentary radio structures. If the magnetic field inside the cocoon is not too strong, the initially spherical radio cocoon is transformed into a torus after the passage of the shock wave. Very recent, high-resolution radio maps of cluster radio relics seem to exhibit such toroidal geometries in some cases. This supports the hypothesis that cluster radio relics are fossil radio cocoons that have been revived by a shock wave. For a late-stage relic the ratio of its global diameter to the filament diameter should correlate with the shock strength. Finally, we argue that the total radio polarisation of radio relic should be well correlated with the 3-dimensional orientation of the shock wave that produced the relic.Comment: accepted by MNRAS, 10 pages, 13 figures, some modifications due to comments of a refere

The length of unknotting tunnels

We show there exist tunnel number one hyperbolic 3-manifolds with arbitrarily long unknotting tunnel. This provides a negative answer to an old question of Colin Adams.Comment: 20 pages, 6 figures. 20 pages, 6 figures. Daryl Cooper added as author. V2 contains two new sections, including a second proof of the main result, and a proof that the result holds for knots in homology sphere

MHD models of Pulsar Wind Nebulae

Pulsar Wind Nebulae (PWNe) are bubbles or relativistic plasma that form when the pulsar wind is confined by the SNR or the ISM. Recent observations have shown a richness of emission features that has driven a renewed interest in the theoretical modeling of these objects. In recent years a MHD paradigm has been developed, capable of reproducing almost all of the observed properties of PWNe, shedding new light on many old issues. Given that PWNe are perhaps the nearest systems where processes related to relativistic dynamics can be investigated with high accuracy, a reliable model of their behavior is paramount for a correct understanding of high energy astrophysics in general. I will review the present status of MHD models: what are the key ingredients, their successes, and open questions that still need further investigation.Comment: 18 pages, 5 figures, Invited Review, Proceedings of the "ICREA Workshop on The High-Energy Emission from Pulsars and their Systems", Sant Cugat, Spain, April 12-16, 201

Theory of Pulsar Wind Nebulae

Our understanding of Pulsar Wind Nebulae (PWNe), has greatly improved in the last years thanks to unprecedented high resolution images taken from the HUBBLE, CHANDRA and XMM satellites. The discovery of complex but similar inner features, with the presence of unexpected axisymmetric rings and jets, has prompted a new investigation into the dynamics of the interaction of the pulsar winds with the surrounding SNR, which, thanks to the improvement in the computational resources, has let to a better understanding of the properties of these objects. On the other hand the discovery of non-thermal emission from bow shock PWNe, and of systems with a complex interaction between pulsar and SNR, has led to the development of more reliable evolutionary models. I will review the standard theory of PWNe, their evolution, and the current status in the modeling of their emission properties, in particular I will show that our evolutionary models are able to describe the observations, and that the X-ray emission can now be reproduced with sufficient accuracy, to the point that we can use these nebulae to investigate fundamental issues as the properties of relativistic outflows and particle acceleration.Comment: 9 page, 5 figures, Proceeding of the conference "40 Years of Pulsars", 12-17 August 2007, Montreal, Canada. (figures are not properly displayed in .ps or .pdf version please download archive for them