On the ionization of interstellar magnesium

It has been shown that two concentric ionization zones of interstellar magnesium must exist around each star: internal, with a radius coinciding with that of the zone of hydrogen ionizationS _H; and external, with a radius greater thanS _H, by one order. Unlike interstellar hydrogen, interstellar magnesium is ionized throughout the Galaxy. It also transpires that the ionizing radiation of ordinary hot stars cannot provide for the observed high degree of ionization of interstellar magnesium. The discrepance can be eliminated by assuming the existence of circumstellar clouds or additional ionization sources of interstellar magnesium (X-ray background radiation, high-energy particles, etc.). Stars of the B5 and B0 class play the main role in the formation of ionization zones of interstellar magnesium; the contribution of O class stars is negligible (<1%).     

On the adjustment of outer solar layer models

Using the electron density n _e as an independent variable agreement between the models of the convective zone, photosphere, chromosphere, corona and solar wind is obtained. As a base the known data about the mean models of the individual layers of the quiet Sun are taken (i.e. without taking account of inhomogeneities and deviations from spherical symmetry). The chromospheric region is the exclusion. Here the run of T _e (n _e ) is revised anew to provide a smooth transition from temperature minimum to the corona and to satisfy the observed intensity distribution in the shortwave radio emission spectrum.A plot of the gas density versus n _e permits to get a clear representation about the rate of change of the degree of ionization x and to evaluate quickly the numerical values of x.     

Revised interstellar neutral helium/hydrogen density ratios and the interstellar UV-radiation field

The data deduced from the UV-spectroscope on theCopernicus satellite strongly suggest that the most important ionization source in interstellar space near the solar system is a UV radiation field originating from B-stars. Adopting this hypothesis, we have used the ionization state of several elements in the interstellar medium observed byCopernicus to determine the required radiation field. From this, the degree of ionization of elements that could not be observed byCopernicus is estimated.It is shown that this interpretation of thecopernicus data can be made consistent with neutral interstellar hydrogen densities inferred from extraterrestrial L observations and with electron densities deduced from pulsar dispersion measures. Furthermore, it is shown that the ratio of neutral interstellar helium to neutral interstellar hydrogen is likely to be 2 to 3 times as large as the cosmic abundance ratio of these elements. The possibility that this ratio is about 10 times as large, meaning equal interstellar neutral hydrogen and helium densities near the solar system, cannot be ruled out. It would, however, require an interstellar radiation temperature near 9000 K. A comparison of the intensity of the interplanetary back scattered He 584 Å and the H 1216 Å radiation would lead to a direct determination of this ratio provided the solar radiation at these lines is known.     

Substorm recovery phase

The recovery phase of the magnetospheric substorm is studied numerically by means of a two-dimensional time-dependent nonlinear resistive MHD code. The initial configuration was chosen from the earlier numerical model in which the magnetospheric substorm was driven by the solar wind plasmas. In order to study the recovery phase, the entering solar wind energy flux was reduced when the magnetospheric substorm was in its expansive phase. The system was found to respond instantly to this change and the result showed many characteristic features related to the recovery phase including the tailward motion of thex-point of the reconnected magnetic field lines and the restoration of a tail-like configuration of the magnetic field. Thex-point moved at almost the same speed of the plasma flow in the upstream region, which was considerably smaller than the speed of the plasma jetting or the speed of the plasmoid. As the recovery phase progressed, the plasma jetting across thex-point was reduced very much in the Earthside region. Although the plasma flow was generally in the Earthward direction in the Earthside region of thex-point, the tailward flow was also found near thex-point. The current density was reduced near thex-point and the neutral sheet was broadened in the recovered region. The plasma sheet also became thick in this region. During the recovery of the substorm, the energy conversion rate, both in the form of plasma acceleration and the Joule heating, was reduced. These results on the recovery phase together with the earlier simulation result on the expansive phase indicate that driven reconnection can be a viable mechanism for the magnetospheric substorm including the recovery phase.     

Programmed motion in the presence of homogeneity

In the framework of the inverse problem of dynamics, we face the following question with reference to the motion of one material point: Given a region T_orb of the xy plane, described by the inequality g (x, y) ≤ c₀, are there potentials V = V (x, y) which can produce monoparametric families of orbits f (x, y) = c (also to be found) lying exclusively in the region T_orb? As the relevant PDEs are nonlinear, an answer to this question (generally affirmative, but not with assurance) can be given by the procedure of the determination of certain constants specifying the pertinent functions. In this paper we ease the mathematics involved by making certain simplifying assumptions referring to the homogeneity of both the function g (x, y) (describing the boundary of T_orb) and of the slope function γ(x, y) = f_y/f_x (representing the required family f (x, y) = c). We develop the method to treat the so formulated problem and we show that, even under these restrictive assumptions, an affirmative answer is guaranteed provided that two algebraic equations have in common at least one solution (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrogen and helium ionization structure of gaseous nebulae

In this paper we discuss the ionization equilibrium of hydrogen and helium in a nebula with an arbitrary gas density distribution. If we consider the spectral characteristics of hot stars, a power law is found to provide a good approximation to the Lyman continuum spectrum for stars withT _eff≤100 000 K. With this simplification the ionization equilibrium equation is analytically solved first for a pure hydrogen nebula, then for the general case of a nebula containing H, He, and heavy elements. A simple and quite general formula for the determination of the size and the emission of the He⁺ zone is obtained. Finally, the ionization equilibrium He⁺⁺?He⁺ is considered. This problem can be decoupled from that of the ionization of H⁰ and He⁰ if the stellar spectrum is steeper thanv ^?0.9 or, equivalently, if the star effective temperature is lower than 200 000 K. Within this limit, which surely includes all classicalHii regions and the low-medium excitation planetary nebulae, an analytical solution of the problem can be used.     

Radial HI profiles at the periphery of galactic disks: The role of ionizing background radiation

Observations of neutral hydrogen in spiral galaxies reveal a sharp cutoff in the radial density profile at some distance from the center. Using 22 galaxies with known HI distributions as an example, we discuss the question of whether this effect can be associated exclusively with external ionizing radiation, as is commonly assumed. We show that before the surface density reaches δ _HI ≤ 0.5 M _⊙ pc⁻² (the same for galaxies of different types), it is hard to expect the gas to be fully ionized by background radiation. For two of 13 galaxies with a sharp drop in the HI profile, the “steepening” can actually be caused by ionization. At the same time, for the remaining galaxies, the observed cutoff in the radial HI profile is closer to the center than if it was a consequence of ionization by background radiation and, therefore, it should be caused by other factors.     

Structure of X-ray irradiated stellar wind

The effect of X-ray irradiation on the line-driven stellar wind in X-ray binary systems is studied. The product of the X-ray luminosityL _x and the densityn in the wind is a measure to distinguish between the optically thin and thick wind regimes. For an X-ray source of the radiation temperature of 10 keV, the critical value(L _x n) _c , is of the order of 10³⁷ erg s^–1 cm^–3; hence, most of wind-fed X-ray sources lie in the optically thick wind regime because ofL _x n>(L _x n) _c . Then the wind structure is determined not only by the parameter =(L _x /nR ²),R the distance from the X-ray source, but also by the optical thickness due to helium. The formation of fully ionized helium region depends onL _x andn in a way different from that of the Strömgren sphere. In such an optically thick wind, the region behind the He II ionization boundary is little affected by X-ray irradiation and the trace elements remain to be responsible for wind acceleration. Thus, its location is important for the structure of the wind and the interpretation of various phenomena in objects such as wind-fed X-ray pulsars.     

Experimental investigation of the critical ionization velocity in gas mixtures

The critical ionization velocity which is of cosmogonic and astrophysical interest has hitherto mainly been investigated for pure gases. Since in space we always have gas mixtures, it is of interest also to study gas mixtures. The present report, which is a summary of a more detailed report (Axnäs, 1976), summarizes the results of systematic experiments on the critical ionization velocity as a function of the mixing ratio for binary gas mixtures of H₂, He, N₂, O₂, Ne and Ar. The apparatus used is a coaxial plasma gun with an azimuthal magnetic field. The discharge parameters are chosen so that the plasma is weakly ionized. In some of the mixtures it is found that one of the components tends to dominate in the sense that only a small amount (regarding volume) of that component is needed for the discharge to adopt a limiting velocity close to that for the pure component. Thus in a mixture between a heavy and a light component having nearly equal ionization potentials, the heavy component dominates. Also, if there is a considerable difference in ionization potential between the components, the component with the lowest ionization potential tends to dominate.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Families of orbits in planar anisotropic fields

The aim of the planar inverse problem of dynamics is: given a monoparametric family of curves f(x, y) = c, find the potential V (x, y) under whose action a material point of unit mass can describe the curves of the family. In this study we look for V in the class of the anisotropic potentials V(x, y) = v(a²x² + y²), (a=constant). These potentials have been used lately in the search of connections between classical, quantum, and relativistic mechanics. We establish a general condition which must be satisfied by all the families produced by an anisotropic potential. We treat special cases regarding the families (e. g. families traced isoenergetically) and we present certain pertinent examples of compatible pairs of families of curves and anisotropic potentials. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The interpretation of XUV rocket measurements of intensity ratios of solar spectral lines of the lithiumlike ions O vi,Ne viii,and Mg x

A rocket borne spectrometer was flown to measure absolute intensities of extreme ultraviolet spectral lines from the three ions O vi, Ne viii, and Mg x present in the Sun. From these measurements, intensity ratios of lines from O vi, ratios of lines from Ne viii, and ratios of lines from Mg x were formed. These experimental ratios were compared with ratios calculated by using specific theoretical values of the ionization equilibrium in which dielectronic recombination was included in the processes establishing ionization balance. The effects of the electron density and temperature gradient on the temperature distribution of the flux of the spectral lines in the solar atmosphere have been taken into account in the calculations of the ratios. The agreement between the experimental and calculated ratios is good for the ions Ne viii and Mg x and satisfactory for the ion O vi for which the calculated ratio is subject to large uncertainties. A reliable measurement of the electron temperature in the lower corona was obtained from the experimental ratios for Mg x. This experimental temperature is in good agreement with the emission temperature of the spectral lines of Mg x predicted from the theoretical values of the ionization equilibrium. The design and photometric calibration of a new rocket spectrometer developed to measure the intensity ratios over the broad spectral region 50 to 1250 Å are also described.     

Effects of turbulence on the electron cyclotron-maser mechanism for solar microwave spike bursts

It is shown that small magnetic perturbations can significantly alter the rates of cyclotron growth, absorption, mode conversion, and refraction because of the sensitive dependence of these processes on the field strength in narrow layers. In particular, growth lengths are increased, absorption depths decreased, mode conversion becomes more effective, and turbulent refraction leads to isotropization of the emission. The criteria for significant effects to occur are derived and it is shown that they can be met by the few-percent field perturbations observed in coronal loops. Relative to the theory of cyclotron-maser emission in smoothly varying plasmas, perturbations enable fundamental o-mode (o1) and second-harmonic x-mode (x2) radiation to saturate more effectively, increase the chance of x1, o1, and x2 radiation escaping to infinity through absorption and mode-coupling windows, and partially isotropize radiation emitted near the x-mode cutoff. It is concluded that o1 and x1 emission are both likely to be present, and that x2 emission is possible under some circumstances. However, x1 radiation can escape only at near-parallel propagation ( 0) or via mode conversion to the o-mode at 90°, whereas o1 and x2 emission can escape for a wide range of angles around = 0 and, under many circumstances, near = 90°.     

Lukewarm models of the intergalactic medium

The physical state of a moderately dense, uniform, pure hydrogen medium, pervading the metagalaxy and partaking in the general cosmic expansion, is considered. The cosmic X-ray photon spectrum, which is now observed down to about 0.25 keV, together with various plausible extrapolations down to the Lyman limit, is invoked as the source of ionization and heating of this medium. Isothermal and adiabatic modes of expansion of the intergalactic medium are studied as limiting cases of the present mode of expansion. The isothermal mode generates highly ionized but lukewarm (7700 KT25000 K) models of the medium, with the, so far unknown, turnover point in the cosmic X-ray spectrum as the parameter required to fix the temperature and degree of ionization uniquely, for any assumed value of the present density. The adiabatic mode, while giving rise to high degrees of ionization, also produces significantly higher temperatures which are independent of density and always greater than about 28000 K. In conclusion, a possible explanation for the anomalous 3C 9 result is adduced.     

Three-dimensional Separator Reconnection – How Does It Occur?

In two dimensions magnetic energy release takes place at locations where the magnetic field strength becomes zero and has an x-point topology. The x-point topology can collapse into two y-points connected by a current sheet when the advection of magnetic flux into the x-point is larger than the dissipation of magnetic flux at the x-point. In three dimensions magnetic fields may also contain singularities in the form of three-dimensional null points. Three-dimensional nulls are created in pairs and are therefore, at least in the initial stages, always connected by at least one field line – the separator. The separator line is defined by the intersection of the fan planes of the two nulls. In the plane perpendicular to a single separator the field line topology locally has a two dimensional x-point structure. Using a numerical approach we find that the collapse of the separator can be initiated at the two nulls by a velocity shear across the fan plane. It is found that for a current concentration to connect the two nulls along the separator, the current sheet can only obtain two different orientations relative to the field line structure of the nulls. The sheet has to have an orientation midway between the fan plane and the spine axis of each null. As part of this process the spine axes are found to lose their identity by transforming into an integrated part of the separator surfaces that divide space into four magnetically independent regions around the current sheet.     

Some Features of the X-Ray and Radio Emission from OH Megamaser Galaxies

The properties of OH megamaser galaxies in the x-ray and radio ranges are discussed. Based on a sample of OH megamaser galaxies it is shown that the x-ray emission and the width of the OH radio line are closely related. The line width is also related to the radio emission from megamasers, but it depends only weakly on the infrared emission and this relationship is statistically less significant. The OH line width and the radio and x-ray emissions depend on the central mass of megamasers. There is a weak correlation between the radio and x-ray emissions owing to multiple scattering of synchrotron photons and bursts from the galactic nucleus. These results indicate that an active nucleus can be dominant in OH megamaser galaxies.__________Translated from Astrofizika, Vol. 48, No. 3, pp. 421–430 (August 2005).     

An X-ray hubble diagram for quasi-stellar objects

To form the Hubble diagram for quasi-stellar objects (QSOs),we have made use of the recently published data on X-ray fluxes of 159 QSOs observed from the Einstein Observatory. The scatter in the Hubble diagram and the lack of an obvious redshift-flux density correlation for these QSOs have been attributed to the observational selection effect that the intrinsically less luminous QSOs can be detected only in the nearby region of space. When the optical, radio and X-ray selection effects are removed, keeping only the intrinsically brighter sources, we obtain a sample of 16 QSOs having a small dispersion in X-ray luminosities (〈 logL _x〉) = 46.12 ± 0.28), a statistically significant linear correlation between (logf _x, logcz) pairs and a slopeA =-1.906 ± 0.061 of the linear regression oflog f _x on logcz. This slope is consistent, at a confidence level of 95 per cent or greater, with the slope of-2.0 expected theoretically based on the assumption that the redshifts of QSOs are cosmological in nature.     

Limits of stability for an area-preserving polynomial mapping

The Henon-Heiles mappingx=x+a(y–y ³), y=y–a(x–x³) has been studied, with the aim of finding where the unstable regions of the (x, y) plane are. When this mapping is put into the normal form, it is found to be a typical twist mapping. The criteria of Moser (1971) are used to obtain an upper limit to the size of a stable region around the origin, and this limit decreases to zero as the value of the parameter a increases toward 2.0. However, direct calculation fora=1.99 shows that there is a fairly large region insidex=0.412,y=0, from which escape from near the outer boundary requires at least 160 mappings. The region of high stability thus appears to be much larger than any region of absolute stability predicted by the KAM theorem.A general survey has been made of instability regions for the parameter valuea=1.0, this survey having been carried out to the extent which is allowed by a computer with 18-decimal-place accuracy. First, for all thex-axis fixed points (of the above mapping) deemed to be representative and significant, both the locations and variational matrix traces have been calculated. (The latter show whether the fixed point is elliptic or hyperbolic.) Ifn is the number of mappings andk is the number of circuits around the origin, then the listing (Table IV) is for fractionsk/n between 1/6 and 1/22, inclusive. (This covers the range 0x<0.96, withx=0 the fixed point forn=6,k=1).Escape toward infinity can be rapid, with less than 200 mappings necessary to reach the vicinity of then=1 fixed points (atx=±1,y=0 andx=0,y=±1) from outer regions of the (x, y) plane, such as for |x|>0.93,y=0. In this case, the unstable regions may be tongues encircling the origin. However, as the distance from the origin is decreased, the tongues can be replaced by exceedingly fine threads rapidly becoming less than say 10^–16 in thickness. Such a thread issues fromx=0.905468199,y=0 and requires of the order of 40 000 mappings to escape. It does so by spiralling about the origin and penetrating through several series of loops associated with various fixed points at successively greater (absolute) values ofx(y=0). The region between this thread and the origin is therefore highly stable. Practical stability of a region may be regarded as attained when the region is interior to a series of loops for which the trace of the variational matrix is close to 2.0. This occurs forn=53,k=4, with fixed point atx=0.819786,y=0 and Trace=2.0000 0004.If an invariant curve does in fact exist, then one must be able to show that the outward spiralling from a given series of loops is brought to a halt at some stage. This does not occur in the region where direct computation is possible, as we show in this article, and it remains to be seen under what conditions it can take place.     

Evidence for a disaggregation of the universe

Combining the kinematical definitions of the two dimensionless parameters, the deceleration q(x) and the Hubble t ₀ H(x), we get a differential equation (where x=t/t ₀ is the age of the universe relative to its present value t ₀). First integration gives the function H(x). The present values of the Hubble parameter H(1) [approximately t ₀ H(1)≈1], and the deceleration parameter [approximately q(1)≈−0.5], determine the function H(x). A second integration gives the cosmological scale factor a(x). Differentiation of a(x) gives the speed of expansion of the universe. The evolution of the universe that results from our approach is: an initial extremely fast exponential expansion (inflation), followed by an almost linear expansion (first decelerated, and later accelerated). For the future, at approximately t≈3t ₀ there is a final exponential expansion, a second inflation that produces a disaggregation of the universe to infinity. We find the necessary and sufficient conditions for this disaggregation to occur. The precise value of the final age is given only with one parameter: the present value of the deceleration parameter [q(1)≈−0.5]. This emerging picture of the history of the universe represents an important challenge, an opportunity for the immediate research on the Universe. These conclusions have been elaborated without the use of any particular cosmological model of the universe.     

Special Families of Orbits in the Direct Problem of Dynamics

The direct problem of dynamics in two dimensions is modeled by a nonlinear second-order partial differential equation, which is therefore difficult to be solved. The task may be made easier by adding some constraints on the unknown function = f _y /f _x , where f(x, y) = c is the monoparametric family of orbits traced in the xy Cartesian plane by a material point of unit mass, under the action of a given potential V(x, y). If the function is supposed to verify a linear first-order partial differential equation, for potentials V satisfying a differential condition, can be found as a common solution of certain polynomial equations.The various situations which can appear are discussed and are then illustrated by some examples, for which the energy on the members of the family, as well as the region where the motion takes place, are determined. One example is dedicated to a Hénon—Heiles type potential, while another one gives rise to families of isothermal curves (a special case of orthogonal families). The connection between the inverse/direct problem of dynamics and the possibility of detecting integrability of a given potential is briefly discussed.This revised version was published online in October 2005 with corrections to the Cover Date.     

Two‐dimension potentials which generate spatial families of orbits

We consider the following case of the 3D inverse problem of dynamics: Given a spatial two‐parametric family of curves f (x, y, z) = c₁, g (x, y, z) = c₂, find possibly existing two‐dimension potentials under whose action the curves of the family are trajectories for a unit mass particle. First we establish the conditions which must be fulfilled by the family so that potentials of the form w (y, z) give rise to the curves of the family, and we present some applications. Then we examine briefly the existence of potentials depending on (x, z), respectively (x, y), which are compatible with the given family (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)