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Mark Wardle

Publications and source records attributed to Mark Wardle.

69 records · Page 4Linked to original sources
arXiv2003

Magnetorotational instability in weakly ionised, stratified accretion discs

The magnetorotational instability (MRI) (Balbus and Hawley 1991, Hawley and Balbus 1991) transports angular momentum radially outwards in accretion discs through the distortion of the magnetic field lines that connect fluid elements. In protostellar discs, low conductivity is important, especially in the inner regions (Gammie 1996, Wardle 1997). As a result, low k modes are relevant and vertical stratification is a key factor of the analysis. However, most models of the MRI in these environments have adopted either the ambipolar diffusion or resistive approximations and have not simultaneously treated stratification and Hall conductivity. We present here a linear analysis of the MRI, including the Hall effect, in a stratified disc.

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arXiv2003

Star Formation and the Hall Effect

The breakdown of flux-freezing in molecular clouds and protostellar discs is usually approximated by ambipolar diffusion at low densities or by resistive diffusion at high densities. Here I discuss an intermediate regime in which the Hall term in the conductivity tensor is significant, and the vector evolution of the magnetic field -- and therefore the evolution of the system under consideration -- is dramatically altered. Calculations of charged particle abundances in dense gas in molecular clouds and protostellar discs demonstrate that Hall diffusion is important over a surprisingly broad range of conditions.

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arXiv2000

Radio continuum emission from the central stars of M20 and the detection of a new supernova remnant near M20

The Trifid nebula (M20) is a well-known prominent optical HII region trisected by obscuring dust lanes. Radio continuum VLA observations of this Nebula show free-free emission at lambda 3.6 and 6cm from three stellar sources lying close to the O7V star at the center of the nebula. We argue that neutral material associated with these stars are photoionized externally by the UV radiation from the hot central star. We also report the discovery of a barrel-shaped SNR G7.06--0.12 at the northwest rim of the nebula and two shell-like features G6.67--0.42 and G6.83--0.21 adjacent to W28 and M20. We discuss the nature of these features and their possible relationship to the pulsar PSR 1801-2306 and W28 OH (1720 MHz) masers.

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arXiv1999

Thermal stability of cold clouds in galaxy halos

We consider the thermal properties of cold, dense clouds of molecular hydrogen and atomic helium. For cloud masses below 10^-1.7 Msun, the internal pressure is sufficient to permit the existence of particles of solid or liquid hydrogen at temperatures above the microwave background temperature. Optically thin thermal continuum emission by these particles can balance cosmic-ray heating of the cloud, leading to equilibria which are thermally stable even though the heating rate is independent of cloud temperature. For the Galaxy, the known heating rate in the disk sets a minimum mass of order 10^-6 Msun necessary for survival. Clouds of this type may in principle comprise most of the dark matter in the Galactic halo. However, we caution that the equilibria do not exist at redshifts z > 1 when the temperature of the microwave background was substantially larger than its current value; the formation and survival of such clouds to the present epoch therefore remain open questions.

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arXiv1999

Enhanced OH in C-type shock waves in molecular clouds

Cosmic-ray and X-ray ionisations in molecular gas produce a weak far-ultraviolet flux through the radiative decay of H2 molecules that have been excited by collisions with energetic electrons (the Prasad-Tarafdar mechanism). I consider the effect of this dissociating flux on the oxygen chemistry in C-type shocks. Typically a few percent of the water molecules produced within the shock front are dissociated before the gas has cooled to 50K. The resulting column density of warm OH rises from 10^15 to 10^16 cm^-2 as the ionisation rate is increased from 10^-17 (typical of dark clouds) to 10^-15 s^-1 (adjacent to supernova remnants). These column densities produce substantial emission in the far-infrared rotational transitions of OH, and are consistent with the OH/H2O ratios inferred from ISO observations of emission from molecular shocks. For high ionisation rates the column of warm OH is sufficient to explain the OH(1720 MHz) masers that occur where molecular clouds are being shocked by supernova remnants. The predicted abundance of OH throughout the shock front will enable C-type shocks to be examined with high spectral resolution through radio observations of the four hyperfine ground state transitions of OH at 18cm and heterodyne measurements of emission in the FIR (e.g. from SOFIA)

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arXiv1999

The Cloudy Universe

Modelling of Extreme Scattering Events suggests that the Galaxy's dark matter is an undetected population of cold, AU-sized, planetary-mass gas clouds. None of the direct observational constraints on this picture -- thermal/non-thermal emission, extinction and lensing -- are problematic. The theoretical situation is less comfortable, but still satisfactory. Galactic clouds can survive in their current condition for billions of years, but we do not have a firm description for either their origin or their evolution to the present epoch. We hypothesise that the proto-clouds formed during the quark-hadron phase transition, thereby introducing the inhomogeneity necessary for compatibility with light element nucleosynthesis in a purely baryonic universe. We outline the prospects for directly detecting the inferred cloud population. The most promising signatures are cosmic-ray-induced H-alpha emission from clouds in the solar neighbourhood, optical flashes arising from cloud-cloud collisions, ultraviolet extinction, and three varieties of lensing phenomena.

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arXiv1999

The Balbus-Hawley instability in weakly ionised discs

MHD in protostellar discs is modified by the Hall current when the ambipolar diffusion approximation breaks down. Here I examine the Balbus-Hawley (magnetorotational) instability of a weak, vertical magnetic field within a weakly-ionized disc. Vertical stratification is neglected, and a linear analysis is undertaken for the case that the wave vector of the perturbation is parallel to the magnetic field. The growth rate depends on whether the initial magnetic field is parallel or antiparallel to the angular momentum of the disc. The parallel case is less (more) unstable than the antiparallel case if the Hall current is dominated by negative (positive) species. The less-unstable orientation is stable for chi less than about 0.5, where chi is the ratio of a generalised neutral-ion collision frequency to the Keplerian frequency. The other orientation has a formal growth rate of order the Keplerian angular frequency even in the limit that chi tends to zero! In this limit the wavelength of the fastest growing mode tends to infinity, so the minimum level of ionization for instability is determined by the requirement that a wavelength fit within a disc scale height. In the ambipolar diffusion case, this requires chi > v_A/c_s; in the Hall case this imposes a potentially much weaker limit, chi > v_A^2 / c_s^2.

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arXiv1998

High velocity gas from the Galactic dark halo

We present the germ of a new model for High Velocity Clouds, derived from the idea that the dark matter halo of our Galaxy is in the form of cold, planetary-mass gas clouds. In this picture HVCs arise as a result of disruptive collisions between dark matter clouds: high velocity atomic gas is a natural consequence of the dark halo kinematics, and is intimately associated with assembly of the visible Galaxy. Quasi-spherical halo models predict a broad 21 cm line background, together with a number of individually detectable, low-mass HVCs conforming to a particular velocity field. A halo model which incorporates satellite substructure -- after the fashion of the current paradigm of hierarchical structure formation -- includes both these components and, in addition, some massive HVCs. These latter HVCs are simply the wakes of the orbiting satellite halos, and each may have a mass up to 0.3% of the mass of the satellite.

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arXiv1998

OH(1720 MHz) Masers at the Galactic Centre

OH(1720 MHz) masers permit direct measurements of the magnetic field strength at the Galactic Centre, and their angular broadening constrains models for the medium that scatters radio waves in the central 100 pc of the Galaxy. As the 1720 MHz masers are unaccompanied by the main-line masers at 1665 and 1667 MHz, they must be pumped by collisions in molecular gas that is cooling after being overrun by a non-dissociative (i.e. C-type) shock wave. In particular, this confirms that the ``SNR'' Sgr A East is driving a shock into the M-0.02-0.07 molecular cloud. The intensity of the v=1--0 S(1) line of H_2 is consistent with the shock strength expected to be driven into the molecular gas by the pressure within Sgr A East.

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arXiv1998

The conductivity of dense molecular gas

We evaluate the conductivity tensor for molecular gas at densities ranging from 10^4 to 10^15 cm^-3 for a variety of grain models. The Hall contribution to the conductivity has generally been neglected in treatments of the dynamics of molecular gas. We find that it is not important if only 0.1 micron grains are considered, but for a Mathis-Rumpl-Nordsieck grain-size distribution (with or without PAHs) it becomes important for densities between 10^7 and 10^11 cm^-3. If PAHs are included, this range is reduced to 10^9 -- 10^10 cm^-3. The consequences for the magnetic field evolution and dynamics of dense molecular gas are profound. To illustrate this, we consider the propagation of Alfven waves under these conditions. A linear analysis yields a dispersion relation valid for frequencies below the neutral collision frequencies of the charged species. The dispersion relation shows that there is a pair of circularly polarised modes with distinct propagation speeds and damping rates. We note that the gravitational collapse of dense cloud cores may be substantially modified by the Hall term.

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arXiv1998

Dust grains and the structure of steady C-type magnetohydrodynamic shock waves in molecular clouds

I examine the role of dust grains in determining the structure of steady, cold, oblique C-type shocks in dense molecular gas. Gas pressure, the inertia of the charged components, and changes in ionisation are neglected. The grain charge and rate coefficients for electron-neutral and grain-neutral elastic scattering are assumed constant at values appropriate to the shock interior. An MRN size distribution is accounted for by estimating an effective grain abundance and Hall parameter for single-size grains. A one-parameter family of intermediate shocks exists for each shock speed v_s between the intermediate signal speed v_A cos theta and sqrt{2} v_A cot theta, where v_A is the preshock Alfven speed and theta is the angle between the preshock magnetic field and the normal to the shock front. In addition, there is a unique fast shock for each v_s > v_A. If the preshock density n_H is greater than about 10^5 cm^-3 and the preshock magnetic field satisfies B(mG) less than about n_H(10^5 cm^-3) grains are partially decoupled from the magnetic field and the field and velocity components within fast shocks do not lie in the plane containing the preshock field and the shock normal. The resulting shock structure is significantly thinner than in models that do not take this into account. Existing models systematically underestimate the grain-neutral drift speed and the heating rate within the shock front. At densities in excess of 10^8 cm^-3 these effects may be reduced by the nearly-equal abundances of positive and negative grains.

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arXiv1998

A model for OH(1720 MHz) masers associated with supernova remnants, and an application to Sgr A East

OH(1720 MHz) masers unaccompanied by 1665/7 MHz line masers have recently been proposed as indicators of the interaction of supernova remnants (SNRs) and molecular clouds. We present a model for the masing region in which water produced in a C-type shock wave driven into the molecular cloud is dissociated as a result of the X-ray flux from the SNR. We note that the magnetic field strengths inferred from Zeeman splitting of the 1720 MHz line measure the internal pressure of the supernova remnant. In addition, we discuss the interaction of Sgr A East, a SNR candidate, with the 50 km/s cloud at the Galactic Centre and present near-infrared observations of H_2 emission towards the regions where OH(1720 MHz) maser emission is concentrated. The magnetic field strength obtained from earlier Zeeman measurements is consistent with rough pressure equilibrium between the postshock gas and the X-ray gas filling Sgr A East detected by ASCA. Further, the intensity of the v=1-0 S(1) line of H_2 is consistent with the shock strength expected to be driven into the molecular gas by this pressure. The relative intensities of the H_2 lines in Sgr A East imply mainly collisional excitation.

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arXiv1998

Extreme scattering events and Galactic dark matter

Extreme Scattering Events (ESEs) are attributed to radio-wave refraction by a cloud of free-electrons crossing the line-of-sight. We present a new model in which these electrons form the photo-ionized 'skin' of an underlying cool, self-gravitating cloud in the Galactic halo. In this way we avoid the severe over-pressure problem which afflicts other models. The UV flux in the Galactic halo naturally generates electron densities of the right order. We demonstrate, for the first time, a good reproduction of the prototypical ESE in the quasar 0954+658. The neutral clouds are a few AU in radius and have masses less than about 10^{-3} solar. The observed rate of ESEs implies that a large fraction of the mass of the Galaxy is in this form.

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arXiv1997

Magnetically-Driven Winds from Protostellar Disks

Angular momentum transport in protostellar disks can be achieved by the action of a large scale magnetic field that runs vertically through the disk. The magnetic field centrifugally drives material from the disk surfaces into a wind, initiating a bipolar outflow. One apparent difficulty for this model is that the conductivity of the disk is extremely low in the inner 0.1--10 AU of the disk, where grains are the dominant charge carriers. Near the midplane, charged grains are unable to drift through the neutral gas and there is negligible coupling between the magnetic field and the disk material. However, the removal of angular momentum and acceleration of a wind by a magnetic field can still take place in the surface layers of the disk where the gas conductivity increases dramatically. Solutions to the multifluid MHD equations for the vertical structure of a disk at a particular radius are presented. Most of the disk material sits in hydrostatic equilibrium and does not interact with the magnetic field running vertically through it. Near the disk surfaces, the coupling between the magnetic field and disk material is sufficient to initiate an outflow from the disk surface.

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