Pre-enriched, not primordial ellipticals

We follow the chemical evolution of a galaxy through star formation and its feedback into the inter-stellar medium, starting from primordial gas and allowing for gas to inflow into the region being modelled. We attempt to reproduce observed spectral line-strengths for early-type galaxies to constrain their star formation histories. The efficiencies and times of star formation are varied as well as the amount and duration of inflow. We evaluate the chemical enrichment and the mass of stars made with time. Single stellar population (SSP) data are then used to predict line-strengths for composite stellar populations. The results are compared with observed line-strengths in ten ellipticals, including some features which help to break the problem of age-metallicity degeneracy in old stellar populations. We find that the elliptical galaxies modelled require high metallicity SSPs (>3 x solar) at later times. In addition the strong lines observed cannot be produced by an initial starburst in primordial gas, even if a large amount of inflow is allowed for during the first few x 10E+8 years. This is because some pre-enrichment is required for lines in the bulk of the stars to approach the observed line-strengths in ellipticals.Comment: 18 pages, 8 figures, Latex, accepted for publication in MNRA

Random Field XY Model in Three Dimensions: The Role of Vortices

We study vortex states in a 3d random-field XY model of up to one billion lattice spins. Starting with random spin orientations, the sample freezes into the vortex-glass state with a stretched-exponential decay of spin correlations, having short correlation length and a low susceptibility, compared to vortex-free states. In a field opposite to the initial magnetization, peculiar topological objects -- walls of spins still opposite to the field -- emerge along the hysteresis curve. On increasing the field strength, the walls develop cracks bounded by vortex loops. The loops then grow in size and eat the walls away. Applications to magnets and superconductors are discussed.Comment: 5 pages, 8 figure

Constraining the Star Formation Histories of Spiral Bulges

Long-slit spectroscopic observations of line-strengths and kinematics made along the minor axes of four spiral bulges are reported. Comparisons are made between central line-strengths in spiral bulges and those in other morphological types. The bulges are found to have central line-strengths comparable with those of single stellar populations (SSPs) of approximately solar abundance or above. Negative radial gradients are observed in line-strengths, similar to those in elliptical galaxies. The bulge data are consistent with correlations between Mg2, and central velocity dispersion observed in elliptical galaxiess. In contrast to elliptical galaxies, central line-strengths lie within the loci defining the range of and Mg2 achieved by Worthey's (1994) solar abundance ratio, SSPs. The implication of solar abundance ratios indicates differences in the star formation histories of spiral bulges and elliptical galaxies. A ``single zone with in- fall'' model of galactic chemical evolution, using Worthey's (1994) SSPs, is used to constrain possible star formation histories in our sample. We show that , Mg2 and Hbeta line-strengths observed in these bulges cannot be reproduced using primordial collapse models of formation but can be reproduced by models with extended in-fall of gas and star formation (2-17 Gyr) in the region modelled. One galaxy (NGC 5689) shows a central population with luminosity weighted average age of ~5 Gyr, supporting the idea of extended star formation. Kinematic substructure, possibly associated with a central spike in metallicity, is observed at the centre of the Sa galaxy NGC 3623.Comment: 14 pages. MNRAS latex file. Accepted for publication in MNRA

Mean flow instabilities of two-dimensional convection in strong magnetic fields

The interaction of magnetic fields with convection is of great importance in astrophysics. Two well-known aspects of the interaction are the tendency of convection cells to become narrow in the perpendicular direction when the imposed field is strong, and the occurrence of streaming instabilities involving horizontal shears. Previous studies have found that the latter instability mechanism operates only when the cells are narrow, and so we investigate the occurrence of the streaming instability for large imposed fields, when the cells are naturally narrow near onset. The basic cellular solution can be treated in the asymptotic limit as a nonlinear eigenvalue problem. In the limit of large imposed field, the instability occurs for asymptotically small Prandtl number. The determination of the stability boundary turns out to be surprisingly complicated. At leading order, the linear stability problem is the linearisation of the same nonlinear eigenvalue problem, and as a result, it is necessary to go to higher order to obtain a stability criterion. We establish that the flow can only be unstable to a horizontal mean flow if the Prandtl number is smaller than order , where B0 is the imposed magnetic field, and that the mean flow is concentrated in a horizontal jet of width in the middle of the layer. The result applies to stress-free or no-slip boundary conditions at the top and bottom of the layer

Magnetic buoyancy instabilities in the presence of magnetic flux pumping at the base of the solar convection zone

We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer (‘the convection zone’) on magnetic buoyancy instabilities in a lower layer (‘the upper parts of the radiative interior – including the tachocline’), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfvén speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer. In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior

Oscillations and secondary bifurcations in nonlinear magnetoconvection

Complicated bifurcation structures that appear in nonlinear systems governed by partial differential equations (PDEs) can be explained by studying appropriate low-order amplitude equations. We demonstrate the power of this approach by considering compressible magnetoconvection. Numerical experiments reveal a transition from a regime with a subcritical Hopf bifurcation from the static solution, to one where finite-amplitude oscillations persist although there is no Hopf bifurcation from the static solution. This transition is associated with a codimension-two bifurcation with a pair of zero eigenvalues. We show that the bifurcation pattern found for the PDEs is indeed predicted by the second-order normal form equation (with cubic nonlinearities) for a Takens-Bogdanov bifurcation with Z2 symmetry. We then extend this equation by adding quintic nonlinearities and analyse the resulting system. Its predictions provide a qualitatively accurate description of solutions of the full PDEs over a wider range of parameter values. Replacing the reflecting (Z2) lateral boundary conditions with periodic [O(2)] boundaries allows stable travelling wave and modulated wave solutions to appear; they could be described by a third-order system

Simultaneous Iliacus and Psoas Muscle Variations

Dissection of a 98-year-old female cadaver identified three previously unrecorded simultaneous variations in the iliac region. A variant iliacus muscle originated in the iliac fossa and then split at the insertion point of the lesser trochanter to blend with the psoas major and vastus medialis muscles. Two variant psoas muscles were found located medial and lateral to the psoas major muscle. The position of the psoas muscle variations resulted in an altered course of the typical path of both the femoral and obturator nerves. The current findings and clinical significance are discussed

Analysis of the shearing instability in nonlinear convection and magnetoconvection

Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced