Magmatic intrusions control Io's crustal thickness

Io, the most volcanically active body in the solar system, loses heat through eruptions of hot lava. Heat is supplied by tidal heating and is thought to be transferred through the mantle by magmatic segregation, a mode of transport that sets it apart from convecting terrestrial planets. We present a model that couples magmatic transport of tidal heat to the volcanic system in the crust, in order to determine the controls on crustal thickness, magmatic intrusions, and eruption rates. We demonstrate that magmatic intrusions are a key component of Io's crustal heat balance; around 80% of the magma delivered to the base of the crust must be emplaced and frozen as plutons to match rough estimates of crustal thickness. As magma ascends from a partially molten mantle into the crust, a decompacting boundary layer forms, which can explain inferred observations of a high-melt-fraction region.Comment: Accepted to JGR:Planets. 24 pages inc appendices and references. 7 figure

Integrability and explicit solutions in some Bianchi cosmological dynamical systems

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G_2 cosmologies. By using Darboux's theory in order to study ordinary differential equations in the complex projective plane CP^2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases

The Sensitivity of First Generation Epoch of Reionization Observatories and Their Potential for Differentiating Theoretical Power Spectra

Statistical observations of the epoch of reionization (EOR) power spectrum provide a rich data set for understanding the transition from the cosmic "dark ages" to the ionized universe we see today. EOR observations have become an active area of experimental cosmology, and three first generation observatories--MWA, PAST, and LOFAR--are currently under development. In this paper we provide the first quantitative calculation of the three dimensional power spectrum sensitivity, incorporating the design parameters of a planned array. This calculation is then used to explore the constraints these first generation observations can place on the EOR power spectrum. The results demonstrate the potential of upcoming power spectrum observations to constrain theories of structure formation and reionization.Comment: 7 pages with 5 figures. Submitted to Ap

Space-times admitting a three-dimensional conformal group

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dimensional conformal Lie group and the nature of their corresponding orbits (that are assumed to be non-null). Each metric is then explicitly displayed in coordinates adapted to the symmetry vectors. Attention is then restricted to the diagonal case, and exact perfect fluid solutions are obtained in both the cases in which the fluid four-velocity is tangential or orthogonal to the conformal orbits, as well as in the more general "tilting" case.Comment: Latex 34 page

The Asymptotic Behaviour of Tilted Bianchi type VI0_0 Universes

We study the asymptotic behaviour of the Bianchi type VI$_0$ universes with a tilted $\gamma$-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, $\gamma=6/5$, there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point to an extremely tilted equilibrium point. The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for $\gamma<2$.Comment: 22 pages, 4 figures, to appear in CQ

Self-similar Bianchi models: II. Class B models

In a companion article (referred hearafter as paper I) a detailed study of the simply transitive Spatially Homogeneous (SH) models of class A concerning the existence of a simply transitive similarity group has been given. The present work (paper II) continues and completes the above study by considering the remaining set of class B models. Following the procedure of paper I we find all SH models of class B subjected only to the minimal geometric assumption to admit a proper Homothetic Vector Field (HVF). The physical implications of the obtained geometric results are studied by specialising our considerations to the case of vacuum and $\gamma -$law perfect fluid models. As a result we regain all the known exact solutions regarding vacuum and non-tilted perfect fluid models. In the case of tilted fluids we find the \emph{general }self-similar solution for the exceptional type VI$_{-1/9}$ model and we identify it as equilibrium point in the corresponding dynamical state space. It is found that this \emph{new} exact solution belongs to the subclass of models $n_\alpha ^\alpha =0$, is defined for $\gamma \in (\frac 43,\frac 32)$ and although has a five dimensional stable manifold there exist always two unstable modes in the restricted state space. Furthermore the analysis of the remaining types, guarantees that tilted perfect fluid models of types III, IV, V and VII$_h$ cannot admit a proper HVF strongly suggesting that these models either may not be asymptotically self-similar (type V) or may be extreme tilted at late times. Finally for each Bianchi type, we give the extreme tilted equilibrium points of their state space.Comment: Latex, 15 pages, no figures; to appear in Classical Quantum Gravity (uses iopart style/class files); (v2) minor corrections to match published versio

A dynamical systems approach to the tilted Bianchi models of solvable type

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$) with a perfect fluid and a linear barotropic $\gamma$-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi VII$_0$ models. We prove the important result that for non-inflationary Bianchi type VII$_h$ models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VII$_h$ invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exists closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VII$_h$ models there is a bifurcation in which a set of equilibrium points turn into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VII$_h$ models in this region the solution curves approach a compact surface which is topologically a torus.Comment: 29 page

On the 590cm-1 B1g feature in underdoped Bi2Sr2CaCu2O8+delta

Raman scattering studies have been performed on underdoped Bi2Sr2CaCu2O8+delta. In single crystals underdoped by oxygen removal, a 590 cm-1 peak is observed in the B1g spectrum. The feature is observed to soften in frequency by 3.8% with isotopic exchange for 16-O by 18-O. In contrast, the 590cm-1 peak is not observed in crystals underdoped by Y substitution which suggests that it correspond to a disorder induced vibrational mode. We have also found that underdoping leads to a depletion of low energy spectral weight from regions of the Fermi surface located near the Brillouin zone axes.Comment: 4 pages Latex, 4 eps figures, submitted to PRB Rapid Communication - Feb. 16, 199

Relative entropy as a measure of inhomogeneity in general relativity

We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike slices. The resulting quantity gives a lower bound on the number of bits which are necessary to describe one metric given the other. For illustration, we study some examples, in particular gravitational waves, and conclude that the relative volume entropy is a suitable device for quantitative comparison of the inhomogeneity of two spacetimes.Comment: 15 pages, 7 figure

Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh

Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the important result that the only future attracting equilibrium points for non-inflationary fluids are the plane-wave solutions in Bianchi type VII$_h$ models is discussed. A tiny region of parameter space (the loophole) in the Bianchi type IV model is shown to contain a closed orbit which is found to act as an attractor (the Mussel attractor). From an extensive numerical analysis it is found that at late times the normalised energy-density tends to zero and the normalised variables 'freeze' into their asymptotic values. A detailed numerical analysis of the type VII$_h$ models then shows that there is an open set of parameter space in which solution curves approach a compact surface that is topologically a torus.Comment: 30 pages, many postscript figure