Spectral Dynamics of the Velocity Gradient Field in Restricted Flows

We study the velocity gradients of the fundamental Eulerian equation, $\partial_t u +u\cdot \nabla u=F$, which shows up in different contexts dictated by the different modeling of $F$'s. To this end we utilize a basic description for the spectral dynamics of $\nabla u$, expressed in terms of the (possibly complex) eigenvalues, $\lambda=\lambda(\nabla u)$, which are shown to be governed by the Ricatti-like equation $\lambda_t+u\cdot \nabla\lambda+\lambda^2=$. We address the question of the time regularity of four prototype models associated with different forcing $F$. Using the spectral dynamics as our essential tool in these investigations, we obtain a simple form of a critical threshold for the linear damping model and we identify the 2D vanishing viscosity limit for the viscous irrotational dusty medium model. Moreover, for the $n$-dimensional restricted Euler equations we obtain $[n/2]+1$ global invariants, interesting for their own sake, which enable us to precisely characterize the local topology at breakdown time, extending previous studies in the $n=3$-dimensional case. Finally, as a forth model we introduce the $n$-dimensional restricted Euler-Poisson (REP)system, identifying a set of $[n/2]$ global invariants, which in turn yield (i) sufficient conditions for finite time breakdown, and (ii) characterization of a large class of 2-dimensional initial configurations leading to global smooth solutions. Consequently, the 2D restricted Euler-Poisson equations are shown to admit a critical threshold

A Quasi-Spherical Gravitational Wave Solution in Kaluza-Klein Theory

An exact solution of the source-free Kaluza-Klein field equations is presented. It is a 5D generalization of the Robinson-Trautman quasi-spherical gravitational wave with a cosmological constant. The properties of the 5D solution are briefly described.Comment: 10 pages Latex, Revtex, submitted to GR

Nucleus from String Theory

In generic holographic QCD, we find that baryons are bound to form a nucleus, and that its radius obeys the empirically-known mass number (A) dependence r A^{1/3} for large A. Our result is robust, since we use only a generic property of D-brane actions in string theory. We also show that nucleons are bound completely in a finite volume. Furthermore, employing a concrete holographic model (derived by Hashimoto, Iizuka, and Yi, describing a multi-baryon system in the Sakai-Sugimoto model), the nuclear radius is evaluated as O(1) x A^{1/3} [fm], which is consistent with experiments.Comment: 4 pages; Ver.2: terminology on nuclear density saturation modified, a reference adde

Observations of Feedback from Radio-Quiet Quasars: I. Extents and Morphologies of Ionized Gas Nebulae

Black hole feedback -- the strong interaction between the energy output of supermassive black holes and their surrounding environments -- is routinely invoked to explain the absence of overly luminous galaxies, the black hole vs. bulge correlations and the similarity of black hole accretion and star formation histories. Yet direct probes of this process in action are scarce and limited to small samples of active nuclei. We present Gemini IFU observations of the distribution of ionized gas around luminous, obscured, radio-quiet (RQ) quasars at z~0.5. We detect extended ionized gas nebulae via [O III]5007 emission in every case, with a mean diameter of 28 kpc. These nebulae are nearly perfectly round. The regular morphologies of nebulae around RQ quasars are in striking contrast with lumpy or elongated nebulae seen around radio galaxies at low and high redshifts. We present the uniformly measured size-luminosity relationship of [O III] nebulae around Seyfert 2 galaxies and type 2 quasars spanning 6 orders of magnitude in luminosity and confirm the flat slope of the correlation (R ~ L^{0.25+/-0.02}). We find a universal behavior of the [O III]/H-beta ratio in our entire RQ quasar sample: it persists at a constant value (~10) in the central regions, until reaching a "break" isophotal radius ranging from 4 to 11 kpc where it starts to decrease. We propose a model of clumpy nebulae in which clouds that produce line emission transition from being ionization-bounded at small distances from the quasar to being matter-bounded in the outer parts of the nebula, which qualitatively explains the observed line ratio and surface brightness profiles. It is striking that we see such smooth and round large-scale gas nebulosities in this sample, which are inconsistent with illuminated merger debris and which we suggest may be the signature of accretion energy from the nucleus reaching gas at large scales.Comment: 44 pages, 11 figures, 3 tables. Accepted for publication in MNRA

Observations of Feedback from Radio-Quiet Quasars - II. Kinematics of Ionized Gas Nebulae

The prevalence and energetics of quasar feedback is a major unresolved problem in galaxy formation theory. In this paper, we present Gemini Integral Field Unit observations of ionized gas around eleven luminous, obscured, radio-quiet quasars at z~0.5 out to ~15 kpc from the quasar; specifically, we measure the kinematics and morphology of [O III]5007 emission. The round morphologies of the nebulae and the large line-of-sight velocity widths (with velocities containing 80% of the emission as high as 1000 km/s combined with relatively small velocity difference across them (from 90 to 520 km/s) point toward wide-angle quasi-spherical outflows. We use the observed velocity widths to estimate a median outflow velocity of 760 km/s, similar to or above the escape velocities from the host galaxies. The line-of-sight velocity dispersion declines slightly toward outer parts of the nebulae (by 3% per kpc on average). The majority of nebulae show blueshifted excesses in their line profiles across most of their extents, signifying gas outflows. For the median outflow velocity, we find a kinetic energy flow between 4x10^{44} and 3x10^{45} erg/s and mass outflow rate between 2000 and 20000 Msun/yr. These values are large enough for the observed quasar winds to have a significant impact on their host galaxies. The median rate of converting bolometric luminosity to kinetic energy of ionized gas clouds is ~2%. We report four new candidates for "super-bubbles" -- outflows that may have broken out of the denser regions of the host galaxy.Comment: 23 pages, 10 figures, 2 tables, accepted for publication in MNRA

Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes

In this paper, we study the phase structure and equilibrium state space geometry of charged topological Gauss-Bonnet black holes in $d$-dimensional anti-de Sitter spacetime. Several critical points are obtained in the canonical ensemble, and the critical phenomena and critical exponents near them are examined. We find that the phase structures and critical phenomena drastically depend on the cosmological constant $\Lambda$ and dimensionality $d$. The result also shows that there exists an analogy between the black hole and the van der Waals liquid gas system. Moreover, we explore the phase transition and possible property of the microstructure using the state space geometry. It is found that the Ruppeiner curvature diverges exactly at the points where the heat capacity at constant charge of the black hole diverges. This black hole is also found to be a multiple system, i.e., it is similar to the ideal gas of fermions in some range of the parameters, while to the ideal gas of bosons in another range.Comment: 17 pages, 8 figures, 3 table