Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence

Electron magnetohydrodynamic (EMHD) turbulence in two dimensions is studied via high-resolution numerical simulations with a normal diffusivity. The resulting energy spectra asymptotically approach a $k^{-5/2}$ law with increasing $R_B$, the ratio of the nonlinear to linear timescales in the governing equation. No evidence is found of a dissipative cutoff, consistent with non-local spectral energy transfer. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. Relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further, EMHD turbulence displays scale-dependent anisotropy with reduced energy transfer in the direction parallel to the uniform background field, consistent with previous studies. Finally, the governing equation is found to yield an inverse cascade, at least partially transferring magnetic energy from small to large scales.Comment: 16 pages, 6 figures, accepted by Physics of Plasmas. For high resolution figures, please visit the PoP website or contact C.Warein

It's a wonderful tail: the mass loss history of Mira

Recent observations of the Mira AB binary system have revealed a surrounding arc-like structure and a stream of material stretching 2 degrees away in opposition to the arc. The alignment of the proper motion vector and the arc-like structure shows the structures to be a bow shock and accompanying tail. We have successfully hydrodynamically modelled the bow shock and tail as the interaction between the asymptotic giant branch (AGB) wind launched from Mira A and the surrounding interstellar medium. Our simulations show that the wake behind the bow shock is turbulent: this forms periodic density variations in the tail similar to those observed. We investigate the possiblity of mass-loss variations, but find that these have limited effect on the tail structure. The tail is estimated to be approximately 450,000 years old, and is moving with a velocity close to that of Mira itself. We suggest that the duration of the high mass-loss phase on the AGB may have been underestimated. Finally, both the tail curvature and the rebrightening at large distance can be qualitatively understood if Mira recently entered the Local Bubble. This is estimated to have occured 17 pc downstream from its current location.Comment: 12 pages, 3 colour figures, accepted by ApJ Part II (Letters

Cascades in decaying three-dimensional electron magnetohydrodynamic turbulence

Decaying electron magnetohydrodynamic (EMHD) turbulence in three dimensions is studied via high-resolution numerical simulations. The resulting energy spectra asymptotically approach a k^{-2} law with increasing R_B, the ratio of the nonlinear to linear timescales in the governing equation, consistent with theoretical predictions. No evidence is found of a dissipative cutoff, consistent with non-local spectral energy transfer and recent studies of 2D EMHD turbulence. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. In another similarity to 2D EMHD turbulence, relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further, cascades of energy in 3D EMHD turbulence are found to be suppressed in all directions under the influence of a uniform background field. Energy transfer is further reduced in the direction parallel to the field, displaying scale dependent anisotropy. Finally, the governing equation is found to yield a weak inverse cascade, at least partially transferring magnetic energy from small to large scales.Comment: 16 pages, 7 figures, accepted to Journal of Plasma Physics. High resolution figures available from the autho

Vortices in the wakes of AGB stars

Vortices have been postulated at a range of size scales in the universe including at the stellar size-scale. Whilst hydrodynamically simulating the wind from an asymptotic giant branch (AGB) star moving through and sweeping up its surrounding interstellar medium (ISM), we have found vortices on the size scale of 10^-1 pc to 10^1 pc in the wake of the star. These vortices appear to be the result of instabilities at the head of the bow shock formed upstream of the AGB star. The instabilities peel off downstream and form vortices in the tail of AGB material behind the bow shock, mixing with the surrounding ISM. We suggest such structures are visible in the planetary nebula Sh 2-188.Comment: ApJL accepted, preprint form, 13 pages including 4 pages of figure

The interaction of planetary nebulae and their AGB progenitors with the interstellar medium

Interaction with the Interstellar Medium (ISM) cannot be ignored in understanding planetary nebula (PN) evolution and shaping. In an effort to understand the range of shapes observed in the outer envelopes of PNe, we have run a comprehensive set of three-dimensional hydrodynamic simulations, from the beginning of the asymptotic giant branch (AGB) superwind phase until the end of the post--AGB/PN phase. A 'triple-wind' model is used, including a slow AGB wind, fast post--AGB wind and third wind reflecting the linear movement through the ISM. A wide range of stellar velocities, mass-loss rates and ISM densities have been considered. We find ISM interaction strongly affects outer PN structures, with the dominant shaping occuring during the AGB phase. The simulations predict four stages of PN--ISM interaction whereby the PN is initially unaffected (1), then limb-brightened in the direction of motion (2), then distorted with the star moving away from the geometric centre (3) and finally so distorted that the object is no longer recognisable as a PN and may not be classed as such (4). Parsec-size shells around PN are predicted to be common. The structure and brightness of ancient PNe is largely determined by the ISM interaction, caused by rebrightening during the second stage; this effect may address the current discrepancies in Galactic PN abundance. The majority of PNe will have tail structures. Evidence for strong interaction is found for all known planetary nebulae in globular clusters.Comment: 22 pages, 16 figures, accepted by MNRAS (consists of 14 page journal paper and 8 page online-only appendix). Email C Wareing for high quality PDF versio

Sh2-188: a model for a speedy PN

Sh2-188 is thought to be an ancient planetary nebula in the galactic disk. It appears to be one-sided with recent observations revealing structure behind the filamentary limb. We postulate that Sh2-188 is interacting with the ISM and simulate it in terms of a ``triple-wind'' model comprising of the usual ``fast'' and ``slow'' interacting stellar winds plus the wind due to motion through the ISM. We have run simulations at various velocities of the central star relative to the ISM and find that a high velocity of 125 km/s best approximates the observed structure. We also suggest that Sh2-188 is younger than previously thought and that much of the mass lost on the AGB has been swept downstream.Comment: 5 pages, 3 figures, Proceedings of the "Stellar end products" workshop, 13-15 April 2005, Granada, Spain, ed. M.A. Perez-Torres. To appear in Vol. 77 (Jan 2006) of MmSAI. Reference corrected, start of 2nd paragraph in discussion corrected, image scaling correcte

Glutathione-s-transferase pi expression in leukaemia: a comparative analysis with mdr-1 data.

Drug resistance in haemopoietic cells may be partly related to the expression of the glutathione-s-transferase (GST) pi and mdr-1 genes. We have used RNA slot blotting techniques to investigate the expression of GST pi in peripheral blood and bone marrow of eleven normal subjects, nine patients with myelodysplastic syndrome (MDS), eighteen patients with acute myeloblastic leukaemia (AML), and thirty-two patients with chronic lymphocyte leukaemia (CLL). We found increased expression of GST pi in 8 of 9 MDS, (7 peripheral blood, 1 bone marrow) 12 of 18 AML (5 peripheral blood, 7 bone marrow; 4 of 5 untreated, 1 of 5 secondary, 7 of 11 relapse or refractory) and in the peripheral blood of 24 of 32 CLL (3 of 7 untreated, 21 of 25 treated) relative to normal controls. Increased expression of GST pi can occur at any stage of disease and shows no clear relation to mdr-1 expression except, possibly, in CLL. In 3 AML patients GST pi transcript levels were the same or lower on relapse compared to presentation. Upregulation of the GST pi gene could not be demonstrated in 2 CLL patients in response to treatment with intermittent chlorambucil