Heating plasma loops in the solar corona

We find a new heat source term for hot coronal loops and include it in the energy equation. This term requires the loop to be hotter than the ambient corona and depends on the combined effect of electron fluid shear and the temperature gradient. Under certain circumstances, the shear drives the heat up the radial temperature gradient into a cross section of the magnetic flux tube from which it leaves by radiation and by conduction down the axial temperature gradient in the usual manner. The heat source is thus a surface term applied over the whole of the loop rather than a volume-distributed term, and its strength is proportional to the cube of the temperature. We apply it to the usual scaling law and obtain an expression for the radius of the flux tube for thermal equilibrium to hold. The temperature distribution around the plasma loop is determined and compared with recent observations and is found to be in satisfactory agreement with them

On the magnetic structure of the solar transition region

We examine the hypothesis that ``cool loops'' dominate emission from solar transition region plasma below temperatures of $2\times10^5$K. We compare published VAULT images of H L$\alpha$, a lower transition region line, with near-contemporaneous magnetograms from Kitt Peak, obtained during the second flight (VAULT-2) on 14 June 2002. The measured surface fields and potential extrapolations suggest that there are too few short loops, and that L$\alpha$ emission is associated with the base regions of longer, coronal loops. VAULT-2 data of network boundaries have an asymmetry on scales larger than supergranules, also indicating an association with long loops. We complement the Kitt Peak data with very sensitive vector polarimetric data from the Spectro-Polarimeter on board Hinode, to determine the influence of very small magnetic concentrations on our analysis. From these data two classes of behavior are found: within the cores of strong magnetic flux concentrations ($> 5\times10^{18}$ Mx) associated with active network and plage, small-scale mixed fields are absent and any short loops can connect just the peripheries of the flux to cell interiors. Core fields return to the surface via longer, most likely coronal, loops. In weaker concentrations, short loops can connect between concentrations and produce mixed fields within network boundaries as suggested by Dowdy and colleagues. The VAULT-2 data which we examined are associated with strong concentrations. We conclude that the cool loop model applies only to a small fraction of the VAULT-2 emission, but we cannot discount a significant role for cool loops in quieter regions. We suggest a physical picture for how network L$\alpha$ emission may occur through the cross-field diffusion of neutral atoms from chromospheric into coronal plasma.Comment: Accepted by ApJ, 9 May 200

Black hole pairs and supergravity domain walls

We examine the pair creation of black holes in the presence of supergravity domain walls with broken and unbroken supersymmetry. We show that black holes will be nucleated in the presence of non- extreme, repulsive walls which break the supersymmetry, but that as one allows the parameter measuring deviation from extremality to approach zero the rate of creation will be suppressed. In particular, we show that the probability for creation of black holes in the presence of an extreme domain wall is identically zero, even though an extreme vacuum domain wall still has repulsive gravitational energy. This is consistent with the fact that the supersymmetric, extreme domain wall configurations are BPS states and should be stable against quantum corrections. We discuss how these walls arise in string theory, and speculate about what string theory might tell us about such objects.Comment: 21 pages LaTeX, special style files (psfrag.sty, efsf_psfrag.sty, a4local.sty, epsf.tex), minor revisions and amended reference

Abelian Higgs hair for extreme black holes and selection rules for snapping strings

It has been argued that a black hole horizon can support the long range fields of a Nielsen-Olesen string, and that one can think of such a vortex as black hole ``hair''. We show that the fields inside the vortex are completely expelled from a charged black hole in the extreme limit (but not in the near extreme limit). This would seem to imply that a vortex cannot be attached to an extreme black hole. Furthermore, we provide evidence that it is energetically unfavourable for a thin vortex to interact with a large extreme black hole. This dispels the notion that a black hole can support `long' Abelian Higgs hair in the extreme limit. We discuss the implications for strings that end at black holes, as in processes where a string snaps by nucleating black holes.Comment: 4 pages REVTeX plus 3 figures. Additional figures and mpeg movies available at http://www.damtp.cam.ac.uk/user/ats25/strhole.html This paper is a condensed version of gr-qc/9706004, and is essentially the talk presented at The Eighth Marcel Grossmann Meeting on General Relativity, 22-27 June 1997, The Hebrew University, Jerusalem, Israe

Can extreme black holes have (long) Abelian Higgs hair?

It has been argued that a black hole horizon can support the long range fields of a Nielsen-Olesen string, and that one can think of such a vortex as black hole ``hair''. In this paper, we examine the properties of an Abelian Higgs vortex in the presence of a charged black hole as we allow the hole to approach extremality. Using both analytical and numerical techniques, we show that the magnetic field lines (as well as the scalar field) of the vortex are completely expelled from the black hole in the extreme limit. This was to be expected, since extreme black holes in Einstein-Maxwell theory are known to exhibit such a ``Meissner effect'' in general. This would seem to imply that a vortex does not want to be attached to an extreme black hole. We calculate the total energy of the vortex fields in the presence of an extreme black hole. When the hole is small relative to the size of the vortex, it is energetically favoured for the hole to remain inside the vortex region, contrary to the intuition that the hole should be expelled. However, as we allow the extreme horizon radius to become very large compared to the radius of the vortex, we do find evidence of an instability. This proves that it is energetically unfavourable for a thin vortex to interact with a large extreme black hole. This would seem to dispel the notion that a black hole can support `long' abelian Higgs hair in the extreme limit. We show that these considerations do not go through in the near extreme limit. Finally, we discuss whether this has implications for strings that end at black holes.Comment: 21 pages REVTeX plus 9 figures. Additional figures and mpeg movies available at http://www.damtp.cam.ac.uk/user/ats25/strhole.html We have made several cosmetic changes, and we have revised and extended the discussion of strings which end on extreme horizon

Heating the solar corona by plasma loops

We investigate the heating of the corona via plasma loops. It is shown that it may be possible to maintain the high corona temperatures using plasma loops as conduits. Under certain conditions heat can flow across magnetic fields up temperature gradients, a mechanism that has been previously applied to the heating of plasma loops. A typical conduit loop is hotter than the ambient plasma in the upper chromosphere and transition layer, and is cooler than the ambient plasma in the background corona. Hence, heat enters the loop at the bottom, is transported by a combination of conduction (if there is a negative temperature gradient), convection and shock waves up the loop into the corona. Typical values show that this type of heating is sufficient to maintain both the quiet and active corona and that it also has the non-homogeneous temperature distribution observed in the lower corona. The behaviour of some brightening events seen in TRACE data support the proposed convective and shock wave mechanisms. The model offers a possible explanation of a long-standing problem, namely why the corona is so hot.

Pickover biomorphs and non-standard complex numbers

In this study Pickover biomorphs are analysed as being dependent on the chosen complex number system in which iterations of analytic functions are performed. Moran’s spatial autocorrelation function and two forms of entropy, the Shannon entropy and the sample entropy, are chosen in order to find correlations and measure complexity in Pickover biomorphs. These turn out to be strongly correlated and low-entropy objects with a fractal dimension between 1.4 and 2. It is shown that there is a strong maximum in correlation and a strong minimum in entropy for the case of Galilean complex numbers corresponding to the square of the generalised imaginary unit being equal to zero

Numerical simulation of two-dimensional and three-dimensional axisymmetric advection-diffusion systems with complex geometries using finite-volume methods

A finite-volume method has been developed that can deal accurately with complicated, curved boundaries for both two-dimensional and three-dimensional axisymmetric advection-diffusion systems. The motivation behind this is threefold. Firstly, the ability to model the correct geometry of a situation yields more accurate results. Secondly, smooth geometries eliminate corner singularities in the calculation of, for example, mechanical variables and thirdly, different geometries can be tested for experimental applications. An example illustrating each of these is given: fluid carrying a dye and rotating in an annulus, bone fracture healing in mice, and using vessels of different geometry in an ultracentrifuge

Blinkers in the solar transition region

In this paper it is shown that the small flare-like patches known as ‘blinkers’ may be explained as the result of an instability in transition layer magnetic flux tubes, which are represented by a set of isolated, high-aspect ratio vertical cylinders as the legs of coronal plasma loops. An essential prerequisite for the instability is that the heating, which is assumed to be only due to ohmic dissipation, closely balances the radiation losses. The instability occurs in the plasma pressure and could be triggered by a random shock wave; it rapidly increases the local pressure and results in a minor ‘explosion’. By dissipating energy away from the region, this reduces the local pressure and restores stability on a timescale of a few minutes, which is in agreement with observations of blinkers. The theory is an extension of Ashbourn and Woods’ previous treatment of the transition layer differential emission measure