Effects of Rotation and Relativistic Charge Flow on Pulsar Magnetospheric Structure

We propose an analytical 3-D model of the open field-line region of a neutron star (NS) magnetosphere. We construct an explicit analytic solution for arbitrary obliquity (angle between the rotation and magnetic axes) incorporating the effects of magnetospheric rotation, relativistic flow of charges (e.g. primary electron beam) along the open field lines, and E X B drift of these charges. Our solution employs the space-charge-limited longitudinal current calculated in the electrodynamic model of Muslimov & Tsygan (1992) and is valid up to very high altitudes nearly approaching the light cylinder. We assume that in the innermost magnetosphere, the NS magnetic field can be well represented by a static magnetic dipole configuration. At high altitudes the open magnetic field lines significantly deviate from those of a static dipole and tend to focus into a cylindrical bundle, swept back in the direction opposite to the rotation, and also bent towards the rotational equator. We briefly discuss some implications of our study to spin-powered pulsars.Comment: 24 pages, 3 figures, accepted for publication in Ap

Optimal battery charge/discharge strategies for prosumers and suppliers

We discuss the application of classical variational methods to optimal charging/discharging strategies for a prosumer or storage supplier, where the price of electrical power is known in advance. We outline how a classical calculus of variations approach can be applied to two related problems: (i) how can a prosumer minimise the cost of charging/discharging a battery, when the price of electrical power is known throughout the charging/discharging period? and (ii) how can an electricity supplier incentivise desired prosumer/storage supplier behaviour by adjusting the price

On the Ionisation of Warm Opaque Interstellar Clouds and the Intercloud Medium

In this paper we use a number of observations to construct an integrated picture of the ionisation in the interiors of quiescent warm opaque interstellar clouds and in the intercloud medium (ICM) outside dense HII regions and hot dilute bubbles. Our main conclusion is that within $\sim$ 1kpc of the sun the ionisation rate of hydrogen per unit volume in both the interiors of such clouds and in the ICM is independent of the local density of neutral hydrogen, and varies with position by less than $\sim$ 20 per cent. These conclusions strongly favour the decaying neutrino hypothesis for the ionisation of the interstellar medium in these regions. Our analysis is based on a variety of observations, of which the most remarkable is the discovery by Spitzer and Fitzpatrick (1993) that, in the four slowly moving clouds along the line of sight to the halo star HD93521, the column densities of both SII and CII$^*$, which individually range over a factor $\sim$4, are proportional to the column density of HI to within $\sim$20 per cent. This proportionality is used to show that the free electrons exciting the CII to CII$^*$ are located mainly in the interiors of the clouds, rather than in their skins, despite the large opacity of the clouds to Lyman continuum radiation. The same conclusion also follows more unambiguously from the low value of the H$\alpha$ flux in this direction which was found by Reynolds (1996) in unpublished observations. These results are then used, in conjunction with observations of three pulsar parallaxes and dispersion measures, and with data on HeI, NII and OI line emissions, to constrain the ionisation of H, He, N and O and the flux of Lyman continuum photons from O stars in the ICM.Comment: 16 pages, no figures, Latex fil

Constraints on Stirring and Dissipation of MHD Turbulence in Molecular Clouds

We discuss constraints on the rates of stirring and dissipation of MHD turbulence in molecular clouds. Recent MHD simulations suggest that turbulence in clouds decays rapidly, thus providing a significant source of energy input, particularly if driven at small scales by, for example, bipolar outflows. We quantify the heating rates by combining the linewidth-size relations, which describe global cloud properties, with numerically determined dissipation rates. We argue that, if cloud turbulence is driven on small internal scales, the $^{12}$CO flux (enhanced by emission from weakly supersonic shocks) will be much larger than observed; this, in turn, would imply excitation temperatures significantly above observed values. We reach two conclusions: (1) small-scale driving by bipolar outflows cannot possibly account for cloud support and yield long-lived clouds, unless the published MHD dissipation rates are seriously overestimated; (2) driving on large scales (comparable to the cloud size) is much more viable from an energetic standpoint, and if the actual net dissipation rate is only slightly lower than what current MHD simulations estimate, then the observationally inferred lifetimes and apparent virial equilibrium of molecular clouds can be explained.Comment: 5 pages, 1 figure. To appear in ApJ (2001 April 10

The Inability of Ambipolar Diffusion to set a Characteristic Mass Scale in Molecular Clouds

We investigate the question of whether ambipolar diffusion (ion-neutral drift) determines the smallest length and mass scale on which structure forms in a turbulent molecular cloud. We simulate magnetized turbulence in a mostly neutral, uniformly driven, turbulent medium, using a three-dimensional, two-fluid, magnetohydrodynamics (MHD) code modified from Zeus-MP. We find that substantial structure persists below the ambipolar diffusion scale because of the propagation of compressive slow MHD waves at smaller scales. Contrary to simple scaling arguments, ambipolar diffusion thus does not suppress structure below its characteristic dissipation scale as would be expected for a classical diffusive process. We have found this to be true for the magnetic energy, velocity, and density. Correspondingly, ambipolar diffusion leaves the clump mass spectrum unchanged. Ambipolar diffusion appears unable to set a characteristic scale for gravitational collapse and star formation in turbulent molecular clouds.Comment: 16 pages, 5 figures. ApJ accepte

Angular Momentum Transfer in Star-Discs Encounters: The Case of Low-Mass Discs

A prerequisite for the formation of stars and planetary systems is that angular momentum is transported in some way from the inner regions of the accretion disc. Tidal effects may play an important part in this angular momentum transport. Here the angular momentum transfer in an star-disc encounter is investigated numerically for a variety of encounter parameters in the case of low mass discs. Although good agreement is found with analytical results for the entire disc, the loss {\it inside} the disc can be up to an order of magnitude higher than previously assumed. The differences in angular momentum transport by secondaries on a hyperbolic, parabolic and elliptical path are shown, and it is found that a succession of distant encounters might be equally, if not more, successful in removing angular momentum than single close encounter.Comment: 11pages, 8 figures, 1 tabl

Do Proto-Jovian Planets Drive Outflows?

We discuss the possibility that gaseous giant planets drive strong outflows during early phases of their formation. We consider the range of parameters appropriate for magneto-centrifugally driven stellar and disk outflow models and find that if the proto-Jovian planet or accretion disk had a magnetic field of >~ 10 Gauss and moderate mass inflow rates through the disk of less than 10^-7 M_J/yr that it is possible to drive an outflow. Estimates based both on scaling from empirical laws observed in proto-stellar outflows and the magneto-centrigugal disk and stellar+disk wind models suggest that winds with mass outflow rates of 10^-8 M_J/yr and velocities of order ~ 20 km/s could be driven from proto-Jovian planets. Prospects for detection and some implications for the formation of the solar system are briefly discussed.Comment: AAS Latex, accepted for Ap

On the Timescale for the Formation of Protostellar Cores in Magnetic Interstellar Clouds

We revisit the problem of the formation of dense protostellar cores due to ambipolar diffusion within magnetically supported molecular clouds, and derive an analytical expression for the core formation timescale. The resulting expression is similar to the canonical expression = t_{ff}^2/t_{ni} ~ 10 t_{ni} (where t_{ff} is the free-fall time and t_{ni} is the neutral-ion collision time), except that it is multiplied by a numerical factor C(\mu_{c0}), where \mu_{c0} is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. C(\mu_{c0}) is typically ~ 1 in highly subcritical clouds (\mu_{c0} << 1), although certain conditions allow C(\mu_{c0}) >> 1. For clouds that are not highly subcritical, C(\mu_{c0}) can be much less than unity, with C(\mu_{c0}) --> 0 for \mu_{c0} --> 1, significantly reducing the time required to form a supercritical core. This, along with recent observations of clouds with mass-to-flux ratios close to the critical value, may reconcile the results of ambipolar diffusion models with statistical analyses of cores and YSO's which suggest an evolutionary timescale \~ 1 Myr for objects of mean density ~ 10^4 cm^{-3}. We compare our analytical relation to the results of numerical simulations, and also discuss the effects of dust grains on the core formation timescale.Comment: 11 pages, 2 figures, accepted for publication in the Astrophysical Journa

Unstable Disk Galaxies. I. Modal Properties

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear eigenvalue problem which is solved using standard numerical methods. I apply the method to the dynamics of a model stellar disk which is embedded in the field of a soft-centered logarithmic potential. The outcome is the full spectrum of eigenfrequencies and their conjugate normal modes for prescribed azimuthal wavenumbers. The results show that the fundamental bar mode is isolated in the frequency space while spiral modes belong to discrete families that bifurcate from the continuous family of van Kampen modes. The population of spiral modes in the bifurcating family increases by cooling the disk and declines by increasing the fraction of dark to luminous matter. It is shown that the variety of unstable modes is controlled by the shape of the dark matter density profile.Comment: Accepted for publication in The Astrophysical Journa

Gravitational Instability in Radiation Pressure Dominated Backgrounds

I consider the physics of gravitational instabilities in the presence of dynamically important radiation pressure and gray radiative diffusion, governed by a constant opacity, kappa. For any non-zero radiation diffusion rate on an optically-thick scale, the medium is unstable unless the classical gas-only isothermal Jeans criterion is satisfied. When diffusion is "slow," although the dynamical Jeans instability is stabilized by radiation pressure on scales smaller than the adiabatic Jeans length, on these same spatial scales the medium is unstable to a diffusive mode. In this regime, neglecting gas pressure, the characteristic timescale for growth is independent of spatial scale and given by (3 kappa c_s^2)/(4 pi G c), where c_s is the adiabatic sound speed. This timescale is that required for a fluid parcel to radiate away its thermal energy content at the Eddington limit, the Kelvin-Helmholz timescale for a radiation pressure supported self-gravitating object. In the limit of "rapid" diffusion, radiation does nothing to suppress the Jeans instability and the medium is dynamically unstable unless the gas-only Jeans criterion is satisfied. I connect with treatments of Silk damping in the early universe. I discuss several applications, including photons diffusing in regions of extreme star formation (starburst galaxies & pc-scale AGN disks), and the diffusion of cosmic rays in normal galaxies and galaxy clusters. The former (particularly, starbursts) are "rapidly" diffusing and thus cannot be supported against dynamical instability in the linear regime by radiation pressure alone. The latter are more nearly "slowly" diffusing. I speculate that the turbulence in starbursts may be driven by the dynamical coupling between the radiation field and the self-gravitating gas, perhaps mediated by magnetic fields. (Abridged)Comment: 15 pages; accepted to Ap