Implications of mean field accretion disc theory for vorticity and magnetic field growth

In addition to the scalar Shakura–Sunyaev α _ss turbulent viscosity transport term used in simple analytic accretion disc modelling, a pseudo-scalar transport term also arises. The essence of this term can be captured even in simple models for which vertical averaging is interpreted as integration over a half-thickness and each hemisphere is separately studied. The additional term highlights a complementarity between mean field magnetic dynamo theory and accretion disc theory treated as a mean field theory. Such pseudo-scalar terms have been studied, and can lead to large-scale magnetic field and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which mean quantities depend only on radius. The simplest vorticity growth solutions seem to have scales and vortex survival times consistent with those required for facilitating planet formation. In addition, it is shown that, when the magnetic back-reaction is included to lowest order, the pseudo-scalar driving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the former pseudo‐scalar can more easily reverse sign in the two cases.     

A search for the origin of very low electron temperatures

VLET's (Very Low Electron Temperature) are regions in the solar wind (lasting 12–30 h) in which the electron temperature is abnormally low. Because it is generally believed that the thermal conductivity parallel to the interplanetary magnetic field lines is high for electrons, i.e. the contact with the Sun should be ideal, VLET's are surprising observations. In this work a statistical analysis of many of these events is made with respect to the dependence of this phenomenon on interplanetary plasma and field parameters. In contrast with earlier work it was found that VLET's exist not only after a shock front. The statistical analysis showed further that a VLET is always associated with a VLPT (Very Low Proton Temperature) event and that, whilst on average the temperature of the electrons and protons outside the low temperature regions is about the same, the mean proton temperature inside is three times lower than that of the electrons.A particular model for VLET's is investigated in detail; the closed magnetic loop or “blob” model. By assuming: (a) pure adiabatic expansion in a radially streaming solar wind without pressure equalization across the “blob” boundary, and (b) rapid pressure equalization across the boundary, an attempt was made to quantitatively investigate the feasibility of the “blob” model in the light of plasma and field data. It can be shown that the closed magnetic loop model is unlikely to be the major cause of VLET's.     

Temperature fluctuations in the solar photosphere

In paper I of this series it was shown that Edmonds' center-limb rms intensity fluctuation data provided strong evidence for the existence of a maximum in the horizontal temperature fluctuation near 250 km (optical depth 0.7). The data also gave a much less reliable indication of a second temperature fluctuation maximum approximately 100 km below this level. Two models, model 1 exhibiting a single temperature fluctuation maximum and model 2 which has two temperature fluctuation maxima, were put forward as worthy of further investigation. In this paper the theoretical mean limb-darkening for these models is compared with the observed limb-darkening. Neither is satisfactory and several modifications are discussed. Models of the first type can be made to fit these data only by making adjustments which appear to be inconsistent with convection as an explanation of the temperature fluctuations. Further, the agreement with the fluctuation data is now less satisfactory. However, a modified model of the second type is developed which is consistent with the convection hypothesis, which is in good agreement with the mean limb-darkening and is in qualitative agreement with the fluctuation data. This is interpreted as providing some evidence that the photospheric granulation arises from a shallow convection layer at the base of the photosphere.     

Asymptotic expansions in the perturbed two-body problem with application to systems with variable mass

The main theorems of the theory of averaging are formulated for slowly varying standard systems and we show that it is possible to extend the class of perturbation problems where averaging might be used. The application of the averaging method to the perturbed two-body problem is possible but involves many technical difficulties which in the case of the two-body problem with variable mass are avoided by deriving new and more suitable equations for these perturbation problems. Application of the averaging method to these perturbation problems yields asymptotic approximations which are valid on a long time-scale. It is shown by comparison with results obtained earlier that in the case of the two-body problem with slow decrease of mass the averaging method cannot be applied if the initial conditions are nearly parabolic. In studying the two-body problem with quick decrease of mass it is shown that the new formulation of the perturbation problem can be used to obtain matched asymptotic approximations.     

Space and time variations of the solar Na D line profiles

Preliminary results are presented of observations of the solar Na D lines obtained with high space and time resolution (2.4″ × 2.4″), (6 s). The following conclusions may be drawn.

1. The line profiles vary strongly with space and time implying that time averaging over a long period and large area will not produce the ‘true’ profile.
2. The centre-limb increase in apparent Doppler width in the D lines is intrinsic. It is not due to space or time averaging.
3. The amplitude of the 300-s oscillation may range up to 1.5 km/s in the region of formation of the D lines. Large line asymmetries are associated with this motion. Observations which do not resolve this motion can not be considered adequate.
4. The variation of the D line profile caused by the 300-s oscillation may be described as follows: (a) The core is raised and lowered without change of shape, (b) The wings broaden as the central intensity rises and narrow as it falls. These variations are qualitatively explained by the scanning of the line formation region through the solar atmosphere.
5. Doppler width values derived from pairs of D line profiles are strongly correlated with the motion of the element observed. Hotter elements move upward, cooler downward.
6. Indications of running waves have been found in the time variation of the core line bisectors.

The profile variations observed provide a framework in which various properties of the centre limb variation of these lines may be considered. In particular they show that any expectation of accuracy in profile coincidence above a certain value must be doomed by the intrinsic variability of the solar atmosphere.     

Geo-informational simulation of possible changes in Central Asian water resources

This study simulates water resources in the Tien Shan alpine basins to forecast how global and regional climate changes would affect river runoff. The model employed annual mean values for the major characteristics of the water cycle: annual air temperature, precipitation, evapotranspiration and river runoff. The simulation was based on 304 hydro-meteorological stations, 23 precipitation sites, 328 high altitudinal points with glaciological measurements, 123 stream-gauges, and 54 evaporation sites, and it took into account topography. The findings were simulated over Tien Shan relief using a 1:500,000 scale 100 m grid resolution Digital Elevation Model. An applicable GIS-based distributed River Runoff Model was implemented in regional conditions and tested in the Tien Shan basins. The annual evapotranspiration exceeds the river runoff in the Tien Shan watersheds particularly up to 3700 m. Hypothetical climate-change scenarios in the Tien Shan predict that by 2100 river runoff will increase by 1.047 times with an increase in air temperature averaging 3 °C and an increase in precipitation averaging 1.2 times the current levels. Change in precipitation, rather than temperature, is the main parameter determining river runoff in the Tien Shan. The maximum ratio for predicted river runoff could reach up to 2.2 and the minimum is predicted to be 0.55 times current levels. This possibly dramatic change in river runoff indicates on non-linear system response caused mainly by the non-linear response of evapotranspiration from air temperature and precipitation changes. In the frame of forecasted possible climate change scenarios the probability of river runoff growth amounts 83–87% and probability of this decline is 17–13% by 2100 in the Tien Shan River basins.     

Key Properties of Solar Chromospheric Line Formation Process

The distribution or wavelength-dependence of the formation regions of frequently used solar lines, Hα，Hβ，CaIIH and CaII8542,in quiet Sun,faint and bright flares is explored in the unpolarized case.We stress four aspects characterising the property of line formation process:1) width of line formation core;2) line formation region;3)influence of the temperature minimum region; and 4) wavelength ranges within which one can obtain pure chromospheric and photospheric filtergrams.It is shown that the above four aspects depend strongly on the atmospheric physical condition and the lines used. The formation regions of all the wavelength points within a line may be continuously distributed over one depth domain or discretely distributed because of no contribution coming from the temperature minimum region, an important domain in the solar atmosphere that determines the distribution pattern of escape photons. On the other hand, the formation region of one wavelength point may cover only one height range or spread over two domains which are separated again by the temperature minimum region. Different lines may form in different regions in the quiet Sun. However, these line formation regions become closer in solar flaring regions. Finally, though the stratification of line-of-sight velocity can alter the position of the line formation core within the line band and result in the asymmetry of the line formation core about the shifted line center, it can only lead to negligible changes in the line formation region or the line formation core width. All these results can be instructive to solar filtering observations.     

Some investigations into the atmospheric drag problem

This paper calls into question the validity of the well-known formulae for the perturbations in the Keplerian elements, over one revolution of an orbit, for the motion of a drag-perturbed artificial satellite. These formulae are derived from Gauss's form of the planetary equations, by averaging over a single revolution of the orbit, and using the eccentric anomaly as the independent variable.It is shown that for light balloon-type satellites in near-circular orbits neither the eccentric anomaly nor the true longitude is a suitable choice of independent variable for the averaging procedure. Under these circumstances, it would seem that simple formulae for the variations in the elements cannot be derived from Gauss's equations.     

Galactic dynamo with helicity fluxes

We construct an approximation for the magnetic field of galaxies that takes into account the magnetic helicity conservation law. In our calculations, we use the fact that the galactic disk is fairly thin and, therefore, the magnetic field component perpendicular to the galactic disk can be neglected (the so-called no-z approximation). However, an averaging of the magnetic field over the entire galaxy, as was done in previous works, is not performed. Our results are compared both with the approximation that disregards the helicity flux and with the results obtained in models with helicity fluxes but without averaging. We show that, compared to the classical model, there are a number of new effects (for example, magnetic field oscillations) and, compared to the model with averaging, the behavior of the magnetic field “softens”: its stationary value is reached more slowly and the oscillation amplitude decreases. This is because the dissipative processes changing the magnetic field growth rate are taken into account in our model. In contrast to the model with averaging, here it becomes possible to construct the dependence of the magnetic field and helicity on the distance from the galactic center.     

The evershed effect as a wave phenomenon

It is suggested that longitudinal compression waves are propagating parallel to the solar surface from the umbra towards the photosphere. It is shown that the line-absorption coefficient is asymmetrical, when integrated over a wavelength of the compression wave. The effect of the waves on the line profile is discussed, and it is shown that asymmetrical line profiles of the type observed in sunspot penumbrae will be produced.With the Evershed effect interpreted as an acoustical wave phenomenon the propagation (of the waves) may also be perpendicular to the magnetic lines of force, whereas material motion is likely to be restricted to the direction along the lines of force.     

Maximum and minimum temperatures at armagh observatory, 1844–1992, and the length of the sunspot cycle

The question of whether or not the Earth's climate is influenced by solar activity has received considerable attention since the mid-nineteenth century. Most investigations have adopted the sunspot number as the parameter of solar activity. Recently, however, it has been shown by Friis-Christensen and Lassen (1991) that the mean northern hemisphere temperature, from 1861–1990, follows a strikingly similar trend to thelength of the sunspot cycle, suggesting that the recent global warming could, at least in part, arise from changes in solar activity. In view of the importance of this result, we have examined a set of continuous meteorological records, maintained at Armagh Observatory since 1844, to assess, first, whether data from a single site can give meaningful information on global trends, and second, whether the data from this particular site for the period 1844–1866 can be used to extend the baseline of the comparison with solar activity. We find that both are indeed the case and that there is a strong correlation between the solar cycle length and the mean temperature at Armagh over the past 149 years.     

High‐fidelity spectroscopy at the highest resolutions

High‐fidelity spectroscopy presents challenges for both observations and in designing instruments. High‐resolution and high‐accuracy spectra are required for verifying hydrodynamic stellar atmospheres and for resolving intergalactic absorption‐line structures in quasars. Even with great photon fluxes from large telescopes with matching spectrometers, precise measurements of line profiles and wavelength positions encounter various physical, observational, and instrumental limits. The analysis may be limited by astrophysical and telluric blends, lack of suitable lines, imprecise laboratory wavelengths, or instrumental imperfections. To some extent, such limits can be pushed by forming averages over many similar spectral lines, thus averaging away small random blends and wavelength errors. In situations where theoretical predictions of lineshapes and shifts can be accurately made (e.g., hydrodynamic models of solar‐type stars), the consistency between noisy observations and theoretical predictions may be verified; however this is not feasible for, e.g., the complex of intergalactic metal lines in spectra of distant quasars, where the primary data must come from observations. To more fully resolve lineshapes and interpret wavelength shifts in stars and quasars alike, spectral resolutions on order R = 300 000 or more are required; a level that is becoming (but is not yet) available. A grand challenge remains to design efficient spectrometers with resolutions approaching R = 1 000 000 for the forthcoming generation of extremely large telescopes (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On temperature in line-gap regions

The small regions in the photosphere where many absorption lines weaken have been investigated by several authors. Sheeley attempted to explain the weakening of neutral lines in terms of a temperature increase on the basis of a simple theoretical model. It is shown that this model is not applicable but that a modified theory is able to interpret the observed behaviour of both neutral and ionized lines in terms of a temperature increase of a few percent.Mitteilungen aus dem Fraunhofer Institut, Nr. 98.     

Mass flow and the validity of ionization equilibrium on the Sun

Ionization equilibrium is a useful assumption which allows temperatures and other plasma properties to be deduced from spectral observations. Inherent to this assumption is the premise that the ion stage densities are determined solely by atomic processes which are local functions of the plasma temperature and electron density. However, if the time scale of plasma flow through a temperature gradient is less than the characteristic time scale for an important atomic process, deviations from the ionization stage densities expected for equilibrium will occur which could introduce serious errors into subsequent analyses. In the past few years, significant flow velocities in the upper solar atmosphere have been inferred from observations of emission lines originaing in the transition region (about 10⁴–10⁶ K) and corona. In this paper, three models of the solar atmosphere (quiet Sun, coronal hole, and a network model) are examined to determine if the emission expected from these model atmospheres could be produced from equilibrium ion populations when steady flows of several kilometers per second are assumed. If the flows are quasi-periodic instead of steady, spatial and temporal averaging inherent in the observations may allow for the construction of satisfactory models based on the assumption of ionization equilibrium. Representative emission lines are analysed for the following ions: C iii, iv, O iv, v, vi, Ne vii, viii, Mg ix, x, Si xii, and Fe ix–xiv. Two principle conclusions are drawn. First, only the iron ions are generally in equilibrium for steady flows of 20 km s^–1. For carbon and oxygen, ionization equilibrium is not a valid assumption for steady flows as small as 1 km s^–1. Second, the three models representing different solar conditions behave in a qualitatively similar manner, implying that these results are not particularly model dependent over the range of temperature gradients and electron densities thus far inferred for the Sun. In view of the flow velocities which have been reported for the Sun, our results strongly suggest caution in using the assumption of ionization equilibrium for interpreting spectral lines produced in the transition region.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Simulation of ionosphere-plasmasphere coupling taking into account ion inertia and temperature anisotropy

In this paper we offer a model for the Earth's ionosphere and plasmasphere, allowing for the inertia and anisotropic energy distribution of thermal plasma. A procedure for simultaneous solution of equations of continuity and motion for the O⁺ and H⁺ ions, subject to inertia terms, is described. The model also includes transfer equations for longitudinal and transversal thermal energies. The system of simulating equations and the kinetic equation for superthermal electron spectra are concordantly solved along geomagnetic field lines. Within the framework of the model we developed a study is made of the dynamics of filling of the evacuated plasmaspheric reservoir after a magnetospheric disturbance. It is shown that the filling of the tubes offorce with L ? 3.5 proceeds with supersonic speeds during the first several days and the character of filling differs very much from a diffusion-equilibrium one. The spatio-temporal behavior of electron and ion temperature anisotropy that is formed in the process of filling, is considered. It is found that the value of electron anisotropy can be large. A brief analysis is made of the causes of electron and ion temperature anisotropy.     

Annihilation model of quasi-stellar objects

The possibility that annihilation is a major source of energy in cosmic physics is discussed. Since Klein suggested that the Universe might be matter-antimatter symmetric over two decades ago, there have been a significant number of papers developing the consequences of this view. These, however, have been largely ignored in the general literature. There have also been a number of papers claiming to prove that there cannot be antimatter anywhere in the observable Universe. In the first part of this paper an assessment of the differing views is given, and it is shown that none of the arguments against antimatter is convincing. The existence of antimatter is not in conflict with any observational fact. The reason for the negative attitude towards the existence of antimatter seems to be that this view is in conflict with a number of speculative but generally accepted theories. However, recent magnetospheric and heliospheric research, includingin situ measurements of cosmic plasmas, is now drastically changing cosmic plasma physics in a way that leads to growing scepticism about quite a few of the speculative theories.An attempt is made to develop a simple phenomenological model of QSOs based on star-antistar collisions. This model can account for such basic observational properties as the acceleration to very large (non-cosmological) velocities, the existence of broad emission lines, and at the same time narrow absorption lines with different redshifts. The absence of blueshifts is also explained. The model predicts that relatively young QSOs should be at cosmological distances whereas the old ones may very well be much closer to us than indicated by their redshift.     

Influence of temperature fluctuations on continuum spectra of cosmic objects

The presence of convective and turbulent motions, and the evolution of magnetic fields give rise to existence of temperature fluctuations in stellar atmospheres, active galactic nuclei and other cosmic objects. We observe the time and surface averaged radiation fluxes from these objects. These fluxes depend on both the mean temperature and averaged temperature fluctuations. The usual photosphere models do not take into account the temperature fluctuations and use only the distribution of the mean temperature into surface layers of stars. We investigate how the temperature fluctuations change the spectra in continuum assuming that the degree of fluctuations (the ratio of mean temperature fluctuation to the mean temperature) is small. We suggest the procedure of calculation of continuum spectra, which takes into account the temperature fluctuations. As a first step one uses the usual model of a photosphere without fluctuations. The observed spectrum is presented as a part depending on mean temperature and the additional part proportional to quadratic value of fluctuation degree. It is shown that for some forms of absorption factor the additional part in Wien’s region of spectrum can be evaluated directly from observed spectrum. This part depends on the first and second wavelength derivatives, which can be calculated numerically from the observed spectrum. Our estimates show that the temperature dependence of absorption factors is very important by calculation of continuum spectra corrections. As the examples we present the estimates for a few stars from Pulkovo spectrophotometric catalog and for the Sun. The influence of temperature fluctuations on color indices of observed cosmic objects is also investigated.     

A paradox in measuring the magnetic field of the Sun

Significant discrepancies are often observed among the values of the mean magnetic field (MMF) of the Sun as a star observed by various instruments using various spectral lines. This is conventionally attributed to the measurement errors and “saturation” of a solar magnetograph in fine-structure photospheric elements with a strong magnetic field. Measurements of the longitudinal MMF performed in 1968–2006 at six observatories are compared in this paper. It is shown that the degree of discrepancy (slopes b of linear regression lines) varies significantly over the phase of the 11-year cycle. This gives rise to a paradox: the magnetograph calibration is affected by the state of the Sun itself. The proposed explanation is based on quantum properties of light, namely, nonlocality and “coupling” of photons whose polarization at the telescope-spectrograph output is determined by spacious parts of the solar disk. In this case, the degree of coupling, or “identity,” of photons depends on the field distribution in the photosphere and the instrument design (as Bohr said, “the instrument inevitably affects the result”). The “puzzling” values of slope b are readily explained by the dependence of the coupling on the solar-cycle phase. The very statistical nature of light makes discrepancies unavoidable and requires the simple averaging of data to obtain the best approximation of the actual MMF. A 39-year time series of the MMF absolute value is presented, which is indicative of significant variations in the magnitude of the solar magnetic field with a cycle period of 10.5(7) yr.     

Dynamics of the solar tachocline – I. An incompressible study

Gough & McIntyre have suggested that the dynamics of the solar tachocline are dominated by the advection–diffusion balance between the differential rotation, a large-scale primordial field and baroclinicly driven meridional motions. This paper presents the first part of a study of the tachocline, in which a model of the rotation profile below the convection zone is constructed along the lines suggested by Gough & McIntyre and solved numerically. In this first part, a reduced model of the tachocline is derived in which the effects of compressibility and energy transport on the system are neglected; the meridional motions are driven instead by Ekman–Hartmann pumping. Through this simplification, the interaction of the fluid flow and the magnetic field can be isolated and is studied through non-linear numerical analysis for various field strengths and diffusivities. It is shown that there exists only a narrow range of magnetic field strengths for which the system can achieve a nearly uniform rotation. The results are discussed with respect to observations and to the limitations of this initial approach. A following paper combines the effects of realistic baroclinic driving and stratification with a model that closely follows the lines of work of Gough & McIntyre.     

Spectral averaging of the point spread function for Yohkoh's SXT

The point spread function of the soft X-ray telescope (SXT) aboard the Yohkoh spacecraft is a Moffat function with elliptical characteristics. This function has two parameters, a and b, that are wavelength dependent in the X-ray region of interest. Since most SXT data analysis is performed with respect to plasma temperature rather than wavelength, it is useful to spectrally average these two parameters over wavelength with temperature as the free variable. The results of this spectral averaging are given here for users of SXT data.