Motion of test particles in parabolic density distributions

A detailed study of the motion of test-particles [either having a nonzero rest-mass or zero rest-mass] has been carried out for Tolman's type VII solution with vanishing surface density, which is one of the few physically relevant exact solutions of Einstein's field equations for static and spherically symmetric mass distributions.The trapping angles, 0, at which the test-particles escape these configurations are calculated and the trajectories of test-particles are studied in detail. The types of trajectories found for this spacetime geometry are: (1) arc-like trajectories, (2) spiral-like trajectories ending into a circle of constant radius, (3) trajectories with a cusp at the minimum distance, (4) double-bounded trajectories, and (5) double-bounded trajectories with a cusp at the minimum distance. The test-particles following the trajectories of type (1) and type (3) escape the configuration while others are trapped within the structure. Besides the advancement of periastron of the orbits the retrogradation of periastrons are also observed.The stability of the structures is considered by using the variational method (Chandrasekhar, 1964a,b), and its is seen that the structures remain stable at least for a central redshift,z0, as large as 5.09.These studies may distinguish relativistic cluster from a Newtonian one and may find application to the local models of quasi-stellar objects (QSOs).     

A model of an exploding,radiating star in general relativity

In a previous paper Adams, Cary and Cohen (1994) presented a model of a supernova. In that paper the equations of General Relativity describing the evolution of a spherically symmetric, radiating star were solved analytically. The evolution of the star was determined by the application of boundary conditions at the center and at the edge. Due to lmitations in the presupernova model, only the very slow inward motion of an unstable, degenerate core could be considered. The solution was also limited by the need to exclude a runaway term, one that increased exponentially with time. Without the exclusion of the runaway, the luminosity would have increased without bound and the mass would have become negative.This paper presents a completely analytic solution to the equations of General Relativity describing the evolution of a Type II supernova. Professor S.E. Woosley kindly gave us data on the physical variables of a 12M ₀ presupernova star. In our model the core collapses within 1 s, leaving a 1.3M ₀ remnant. Shortly afterward 10.6M ₀ is ejected to infinity, and 0.17M ₀ is radiated away in the form of neutrinos. The distance of the edge from the center increases proportionally to the two-thirds power of the time. The luminosity decreases proportionally to the inverse four-thirds power.Although the runaway solution was modified by the exploding rather than a static envelope, it must still be excluded by adjusting initial conditions. Its character is changed from an exponential to a very large power (55) of time. The removal of a degree of freedom by this exclusion leads to physically non-sensical results such as negative luminosity. The inclusion of a term describing motion of the mantle due to neutrino interactions provides the additional degree of freedom necessary for physically reasonable results.     

Propagation of MHD body and surface waves in magnetically structured regions of the solar atmosphere

The fact that magnetically structured regions exist in the solar atmosphere has been known for a number of years. It has been suggested that different kinds of magnetohydrodynamic (MHD) waves can be efficiently damped in these regions and that the dissipated wave energy may be responsible for the observed enhancement in radiative losses. From a theoretical point of view, an important task would be to investigate the propagation and dissipation of MHD waves in these highly structured regions of the solar atmosphere. In this paper, we study the behavior of MHD body and surface waves in a medium with either a single or double (slab) magnetic interface by use of a nonlinear, two-dimensional, time-dependent, ideal MHD numerical model constructed on the basis of a Lagrangean grid and semi-implicit scheme. The processes of wave confinement and wave energy leakage are discussed in detail. It is shown that the obtained results depend strongly on the type of perturbations imposed on the interface or slab and on the plasma parameter, . The relevance of the obtained results to the heating problem of the upper parts of the solar atmosphere is also discussed.     

Coronal magnetic fields from microwave polarization observations

The solar active region (AR) 7530 was observed at 6 cm on July 3 and 4, 1993 with the Westerbork Synthesis Radio Telescope, using a multi-channel receiver with very narrow bandwidth. We compare the radio data with Yohkoh SXT observations and with the magnetic field extrapolated from the Marshall vector magnetograms in the force-free and current-free approximations. The comparison with soft X-rays shows that, although a general agreement exists between the shape of the radio intensity map and the X-ray loops, the brightness temperature, T _b, obtained using the parameters derived from the SXT is much lower than that observed. The comparison with the extrapolated photospheric fields shows instead that they account very well for the observed T _b above the main sunspots, if gyroresonance emission is assumed. In the observation of July 4 an inversion and strong suppression of the circular polarization was clearly present above different portions of the AR, which indicates that particular relationships exist between the electron density and the magnetic field in the region where the corresponding lines of sight cross the field quasi-perpendicularly. The extrapolated magnetic field at a much higher level ( 10¹⁰ cm), satisfies the constraints required by the wave propagation theory all over the AR. However, a rather low electron density is derived.     

The economic diplomacy of geoengineering

Geoengineering is a new term, still seeking a definition. It seems to imply something global, intentional, and unnatural. For the radiation balance, geoengineering may be fifty years in the future; today's means may be out of date then, and the future means are not yet known. It might immensely simplify greenhouse policy, transforming it from an exceedingly complicated regulatory regime to a problem in international cost sharing, a problem that we are familiar with. Putting things in the stratosphere or in orbit can probably be done by exo-national programs, not depending on the behavior of populations, not requiring national regulations or incentives, not dependent on universal participation. It will involve merely deciding what to do, how much to do, and who is to pay for it.     

Imaging coronal emission lines under high sky-background conditions

We have obtained images in solar coronal emission lines under high sky-background conditions by making precise differential measurements between the coronal emission line and the near-by continuum, which is primarily due to scattered light from the solar disk. Chopping between the two wavelengths was performed at 100 kHz to avoid artifacts from fast-flying dust particles and other aerosols, and also from seeing effects. The differential signal was detected with a novel CCD camera that demodulates signals up to 100 kHz. These preliminary observations show coronal emission at the 0.2% level of the scattered-light background and pave the way to efficient and precise imaging of coronal emission features under less than ideal coronal-sky conditions.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.     

Pb−Sr−Nd−O isotopic constraints on the origin of rhyolites from the Taupo Volcanic Zone of New Zealand: evidence for assimilation followed by fractionation from basalt

A comprehensive Sr–Nd–Pb–O isotopic study is reported for rhyolites from the Maroa Volcanic Centre in the Taupo Volcanic Zone (TVZ) of New Zealand. The Sr–Nd isotopic compositions of the rhyolites (⁸⁷Sr/⁸⁶Sr=0.705236 to 0.705660 and _Nd = 2.0 to 0.2) are intermediate between those of primitive basalts (⁸⁷Sr/⁸⁶Sr=0.70387 and _Nd = 5.3) and the Torlesse basement (⁸⁷Sr/⁸⁶Sr=0.709 and _Nd = -4.5). The relatively low mantle-like oxygen isotopic compositions of ¹⁸ O = 7 ± 0.5 are consistent with the Nd-Sr isotopic constraints in that they can be accounted for by 15% to 25% crustal contamination of a basaltic parent by relatively ¹⁸ O-rich Torlesse metasediment. High precision Pb isotopic analyses of plagioclase separates from the Maroa rhyolites show that they have essentially the same compositions as the Torlesse metasedimentary terrane which is itself distinctive from the Western or Waipapa metasediments. Due to the high concentration of Pb in the Torlesse metasediments (>20 ppm) compared to the basalts (<2 ppm), the Pb isotopic composition of the volcanics may be controlled by relatively small amounts (>10%) of crustal contamination. All these results are shown to be consistent with derivation of the rhyolites by 15% to 25% contamination of relatively primitive basaltic magmas with Torlesse metasedimentary crust, followed by extensive, essentially closed system fractionation of the basalt to a magma of rhyolite composition. It is argued that the processes of assimilation and fractionation are separated in both space and time. The voluminous high silica rhyolites, which make up >97% of the exposed volcanism in the continental margin back-are basin environment of the TVZ, therefore appear to be a product of predominantly new additions to the crust with assimilation-recycling of pre-existing crust being of secondary importance.     

Rosat wide field camera data and the temperature of the interstellar medium

The shadowing effects of the molecular clouds in the nearby interstellar medium on the soft x-ray background has been investigated, using ROSAT WFC data in conjunction with previous rocket B and C band surveys. Shadowing over a 5° extent occurs only for a few percent of the sky, but the mixed model of the ISM is supported.Detailed modelling of the Draco shadowing region shows little evidence for a multi-temperature, hot ISM component.     

Strategy of DENIS observations

Doing a homogenious and fast survey requires an intelligent model for the observing-strategy. This contribution shows a model simulating the parameters for the survey of the southern hemisphere. Input parameters are weather statistics and requirements of the photometry and of the technical equipment. It does not include priorities for special zones of the sky or deeper observations, even if the program is already able to consider such parameters.     

Reservoir timescales for anthropogenic CO2 in the atmosphere

Non-steady state timescales are complicated and their application to specific geophysical systems requires a common theoretical foundation. We first extend reservoir theory by quantifying the difference between turnover time and transit time (or residence time) for time-dependent systems under any mixing conditions. We explicitly demonstrate the errors which result from assuming these timescales are equal, which is only true at steady state. We also derive a new response function which allows the calculation of age distributions and timescales for well-mixed reservoirs away from steady state, and differentiate between timescales based on gross and net fluxes. These theoretical results are particularly important to tracer-calibrated "box models" currently used to study the carbon cycle, which usually approximate reservoirs as well-mixed. We then apply the results to the important case of anthropogenic CO2 in the atmosphere, since timescales describing its behavior are commonly used but ambiguously defined. All relevant timescales, including lifetime, transit time, and adjustment time, are precisely defined and calculated from data and models. Apparent discrepancies between the current, empirically determined turnover time of 30-60 years and longer model-derived estimates of expected lifetime and adjustment time are explained within this theoretical framework. We also discuss the results in light of policy issues related to global warming, in particular since any comparisons of the "lifetimes" of different greenhouse gases (CO2, CH4, N2O, CFC's etc.) must use a consistent definition to be meaningful.