Theory-Group

Annual Report 1998

Astrophysical Plasmas

The work was continued with investigations into the diffusion by collective processes, reconnection and instability analysis based upon realistic, observed particle distribution functions. Furthermore, the interaction of interstellar pickup ions with interplanetary shocks and the problem of particle diffusion perpendicular to magnetic fields has been investigated.

The numerical solution of the dispersion relation for arbitrary particle distribution functions is a great deal more demanding than the usual model calculations, but is an important, in fact indispensible tool for understanding the dynamics of instabilities. Aside from improvements of the numerical code, an application to the dynamics of collective auroral acceleration processes was made.

Interstellar pickup ions come from interstellar matter which penetrates into the solar system, is ionized in the inner heliosphere, and picked up by the radially outward moving solar wind. Spacecraft observations have demonstrated that pickup ions are accelerated very efficiently at the shocks bounding corotating interaction regions. Corotating shocks are quasi-perpendicular shocks, i. e., the magnetic field is almost perpendicular to the shock normal. However, many interplanetary travelling shocks and planetary bow shocks are quasi-parallel. Therefore, the behaviour of pickup protons and He ions at quasi-parallel shocks has been investigated by one-dimensional simulations. Pickup ions are rather effectively reflected at quasi-parallel shocks; the reflection coefficient measured as the ratio of incident to reflected ions is more than an order of magnitude larger than the reflection coefficient for solar wind ions. The pickup ions are trapped for many gyroperiods during their first encounter with the shock and are accelerated to energies exceeding hundred times the shock ram energy.

The problem of particle motion in electromagnetic fields is fundamental for space and astrophysical plasmas. While pitch angle diffusion leading to a finite mean free path parallel to the magnetic field is fairly well understood, this is not so in the case of transport normal to the average field. According to a general theorem, charged particles in electromagnetic fields with at least one ignorable spatial coordinate are effectively tied to the same magnetic line of force, except for motion along the ignorable coordinate. However, from this theorem it cannot be concluded that cross-field diffusion actually does occur when three-dimensional fluctuations of the magnetic field are allowed. As a first step cross-field diffusion has been studied in a three-dimensional simulation of the resonant electromagnetic ion/ion beam instability. From the average of the square of the displacement of the particles the diffusion coefficient perpendicular to the magnetic field has been determined.

The work on magnetic reconnection has been continued. It is expected that the reconnection layer is bounded by slow mode shocks. In a collisionless plasma, collective effects are responsible for the dissipation/heating mechanism in such shocks. Kinetic simulations of reconnection have been performed in order to understand the dissipation processes in such slow mode shocks.

Plasma Crystals

Colloidal plasmas, i. e. plasmas containing micron-sized particles (dust particles), are investigated. In this area experiments in the laboratory were constructed and modified, a rocket experiment was launched, and theoretical investigations were performed.

This year the plasma crystal laboratory was reassembled at the Institut fur Plasmaphysik (which kindly made laboratory space available) after its transfer from the Institute for Space Simulation, DLR Cologne. The experiments were considerably modified in order to be able to investigate larger (horizontal) plasma crystals and to study the interaction of plasma crystals with weak magnetic fields. The following experiments and experimental series were performed:

1. Single-particle experiments and central collisions of two particles in the plasma sheath (see highlight article).

2. Formation of 2-dimensional "molecules" through the stepwise increase of the particle number starting with one particle. The experiment shows an explicit difference of the observed Yukawa interaction - based structures compared to the hard-sphere models upward from four particle systems (see Fig. 2.47).

3. Interaction of the colloidal plasma with a weak, homogeneous and vertical magnetic field of about 150 Gauss. Due to the drift of the ions caused by Lorentz forces, an ion drag force acts on the particle cloud which leads to a rotation of the total system depending on the plasma parameters (see Fig. 2.48).

4. Wave propagation through large plasma crystals.

5. Formation of Mach-cones in the crystal by fast moving particles.

econd plasma crystal rocket experiment (TEXUS 36) was launched from ESRANin the north of Sweden. Compared to the first experiment a smaller particle size was chosen and the hardware was modified to achieve a better functionality. The existence of a void, a particle free region in the center between the electrodes, and the poloidal convection at the outer edge found in the first rocket experiment (see annual report 1997) could be verified. The central void results from the action of the two major forces on the dust particles under microgravity, the ion drag and the electrostatic force.

Fig. 2.47: The experimentally determined positions of the plasma-crystal "molecules" are shown in the first column, their triangulation in the second and the comparable hard-sphere configurations for the same number of particles in the molecule are shown in the third column for particle numbers of 1 - 19. In the second column the cells are color coded when the geometry deviates from the usual hexagon (blue for pentagon geometry and red for septagon)

These act in opposite directions, the ion drag pushes the particles away from the center, the electric field towards the center. As expected from theoretical considerations, the void could be filled and the velocity of the poloidal convection decreased due to the change to smaller particles and by using very low rf-power. However, a new phenomenon occurred while the void was filled with particles - a colloid-plasma instability. The particle cloud shows pulsed motion of the particles, symmetrically towards the center and away from it, with a frequency of about 1.5 Hz.

Fig. 2.48: Particle trajectories are shown for a rotating 2-dimensional plasma crystal in a magnetic field. The arrows show the direction of rotation. In this case the plasma crystal rotates basically as a rigid rotator.
 

Along with the experiments theoretical considerations on colloidal plasmas were carried out, too:

1. A charged dust particle in a plasma absorbing ions and electrons is surrounded by an electrostatic potential which is not completely screened exponentially by the plasma particles. Using linearized fluid equations the influence of a magnetic field of the order of 1 Tesla on this electrostatic potential has been investigated.

2. Using linearized fluid equations the electric potential around a charged dust particle exerting an oscillating motion in response to an external oscillating electric field in a weakly ionized plasma was investigated. Analytical approximations indicate that the potential around the oscillating dust particle does not deviate significantly from the potential around a dust particle being at rest if the oscillation frequency is small compared to the ratio between the square of the ion plasma frequency and the ion-collision frequency.

3. The dust ion acoustic and dust acoustic modes in a collisional dusty plasma were studied taking into account the influence of ion-neutral collisions, ion drag and neutral friction as well as ionization. It was shown that in the long-wavelength limit the branches of the modes join and form the hybrid branch. In the presence of ionization the long-wavelength modes become unstable when the wavelength exceeds a threshold. There exist two types of instability. The first one is the instability of the dust ion acoustic mode. The second type is the instability of the dust acoustic mode when ion drag is added to ionization. The latter type is proposed to be responsible for the instability observed in experiments with growing particles.

4. It was shown that the charge distribution on the surface of a dielectric particle immersed in a supersonic plasma flow is strongly inhomogeneous, which results in appearance of a large dipole moment. The dependences of both the charge and dipole moment of the particle on the drift velocity of the ambient plasma were calculated. It was found that under equal conditions the charge of a dielectric particle considerably exceeds the charge of a metal one. Taking into account the charge fluctuations on the dust particles in a low-pressure gas discharge, the stochastic differential equation for the one-dimensional dust lattice wave is derived. The analysis of the equation shows that for sufficiently small gas pressure the charge fluctuations can result in the exponential growth of the average energy of the lattice oscillations.

Star Formation

Numerical calculations for the dynamical evolution of few-body clusters, detailed observations of a T-Tauri star, and studies for the modulation of X-ray flares by star rotation were performed.

With optical follow-up observations of previously unidentified ROSAT X-ray sources, several hundred new T-Tauri stars were discovered in the last few years, many of which are located outside the star-forming dark clouds. These isolated stars might have been ejected from their birth places by few-body encounters. Therefore, a numerical study of few-body cluster decay has been undertaken. The results show that the decay of systems consisting of 3 to 5 protostars produce binary separation distributions, secondary mass distributions, and remnant escape speeds which compare well with observations of star-forming regions.

As a good example of such an ejected run-away T-Tauri star, the object Par 1724 has been studied observationally in great detail. It is located 15 arcminutes north of the Trapazium cluster in Orion. Extensive photometric measurements show a rotational period of 5.7 days. Repeated high-resolution spectra show variability in the radial velocity with the same period. A Doppler imaging analysis based on high-resolution spectra yields an image showing a pronounced dark feature, a dark spot, at relatively low latitude, which is responsible for most or all of the observed variability. The high-resolution spectra yield a mean heliocentric radial velocity of 23 km/s, consistent with membership to the Orion association. Deep infrared imaging at high spatial resolution reveals no physically bound visual companions down to 1 arcsecond separation. According to its present location and 3D space motion, Par 1724 may have been ejected from the Trapezium about 100 000 years ago.

A mechanism is studied numerically which leads to the formation and subsequent ejection of a substellar companion via the collision of circumstellar accretion disks in a binary system. The calculations show that in cases of a prograde and flat encounter which disrupts the disks, the fragmentation of the debris disk material leads to the formation of a stable spherical low-mass object (with approximately two Jupiter masses). The kinematics of this object is mainly influenced by the gravitational potential of the binary and the configuration can therefore be treated as a three-body system. The calculations show also that such triple systems decay very quickly, within a few orbital periods of the binary, which means that the substellar object is ejected. Astrophysical examples of colliding circumstellar disks or even ejected substellar companions can be found in HD 98800 and TMR-1C.

Rotational modulation of X-ray flares have been analysed for four outbursts on late-type stars, namely on Algol, and three T-Tauri stars. The structure of their X-ray light curves is untypical in that the maximum emission extends over several hours, producing a round hump in the light curve instead of a sharp peak. This deviation can be explained as the result of a flare erupting on the back side of the star and gradually moving into the line of sight due to the star's rotation. Making use of the known rotational periods of the stars, this model allows the determination of the decay timescale of the flares and the size of the X-ray emitting volume according to the standard magnetic-loop model.

Astrophysical and Cosmological Studies of Galaxy Clusters

The properties of galaxy clusters and groups of galaxies were investigated, a survey of southern X-ray clusters of galaxies was performed, a mathematical filter for cluster detection was developed, and theoretical investigations on the nature of the dark matter in clusters of galaxies were continued.

1. General Properties of Galaxy Clusters: Clusters of galaxies are ideal probes to study the large-scale matter distribution in the Universe. Hot intergalactic gas within clusters emits X-rays, providing information on the size, mass, and morphology of the clusters. Using the ROSAT All-Sky Survey an X-ray flux-limited sample of 63 clusters (flux limit F_x (0.5-2.0 keV) ³ 2 x 10^-11 erg cm^-2s^-1) has been selected and the total mass (including the dark matter) has been determined using deeper pointed observations. Integration of the resulting mass function (clusters density per mass interval) shows among other results that only a small fraction (~1%) of the total mass in the Universe is bound in galaxy clusters with masses M³ 3 x 10¹³ solar masses.

For a sample of 106 clusters the relation between several physical parameters of galaxy clusters, e. g. X-ray luminosity, gas temperature, gas mass and total mass, have been studied. The relation found between the relatively easily measureable X-ray luminosity and the harder to determine total mass can be utilized in the future in connection with larger cluster surveys (see below), where only the luminosity is known, to study the mass distribution in wider parts of the Universe (Fig. 2.49).

Fig. 2.49: Correlation of the X-ray luminosity and the gravitational mass for a sample of 106 ROSAT clusters of galaxies, with masses determined from the X-ray data.

2. Survey of Southern X-ray Clusters of Galaxies: Although the presently available samples of clusters of galaxies are not very reliable, in principle they could give strong constraints on the global structure of spacetime and on structure-formation scenarios. An important step towards a higher statistical quality of the samples can be achieved when the clusters are selected using their X-ray properties because this effectively selects clusters of galaxies within a well-defined mass range (see above).
The ROSAT ESO Flux-Limited X-Ray (REFLEX) survey tries to provide a very homogeneously selected sample of X-ray clusters of galaxies of the southern hemisphere. Based on the ROSAT All-Sky Survey, the actual catalogue of 460 clusters down to the flux limit Fn = 3.0 x 10^-12 erg/(cm² s) (0.1-2.4 keV) and with redshifts smaller than z = 0.3 - corresponding to a spatial depth of about 1h^-1 Gpc (h = H₀/[100 km s^-1 Mpc^-1] with Hubble constant H₀) - is presently one of the largest cluster catalogues of this quality. The final catalogue will have about 700 galaxy clusters.

Preliminary analyses of the REFLEX sample indicate a high completeness of the catalogue. The figure shows a cone diagrame of a part of the spatial distribution of the REFLEX clusters around the South Galactic Pole (Fig. 2.50). The radial coordinate gives a measure of the distance, the transverse coordinate gives the Right Ascension of the clusters. The clearly visible inhomogeneities have scales larger than 100 h^-1 Mpc and are thus the largest coherent structures of the universe. With samples of this quality we can measure for the first time the distribution of matter and its fluctuations on scales up to 0.5h^-1 Gpc and compare them with cosmological structure formation scenarios.

Fig. 2.50: Spatial distribution of X-ray clusters of galaxies around the South Galactic Pole. Radial coordinate: cz [km/s] (z redshift, c vacuum velocity of light); transverse angular coordinate: Right Ascension a [h]; Declination: d [deg]; survey area: 13924 square degrees. At larger distances the number of clusters degrades due to the flux limit Fn = 3.0 x 10^-12 erg cm^-2s^-1 (0.1-2.4 keV) of the sample.

3. Groups of Galaxies: The NGC 383 group is a rich group of galaxies, located in the Perseus Pisces filament. Deep ROSAT X-ray observations allowed to study the emission from the intra-group medium and the optically brightest member galaxies. Widely extended hot X-ray emitting gas is detected implying that the group of galaxies is bound by a deep `dark matter' potential. An analysis of luminosity distribution and temperature of the hot gas allows to derive the gas density distribution and "dark matter" content. For the NGC 383 group we find a 20% contribution of the X-ray emitting gas to the total mass (inside a radius of ~ 3 million lightyears), showing that the bulk of the mass is contributed by "dark matter".

Located near the center of the group is the well-studied radio galaxy 3C 31. Its X-ray spectrum can be best explained by a contribution from two different spectral components: thermal emission from hot gas within the galaxy and a second component likely related to the presence of an "active nucleus" in the center of the galaxy.

4. Likelihood-Filter for Cluster Detection: To get a more objective identification and characterization of optical clusters of galaxies, a mathematical filter for cluster detection was developed. The method can, however, also be used for the identification of X-ray clusters of galaxies. In a statistical sense, the average physical properties of clusters of galaxies do not strongly depend on redshift. This helps in constructing digital filters for cluster detection, redshift and richness estimation. The theory of inhomogeneous point processes provides a mathematically exact handling of this problem. The probability generating functional of an inhomogeneous Poisson process is used to determine the so-called Janossy density which determines uniquely the likelihood function. The new method provides a generalization of hitherto known algorithms and is less sensitive to systematic errors in the estimation of cluster redshift and richness. The method gives information on important optical parameters of clusters and will be applied to studies concerning the correlations between optical and X-ray properties of galaxy clusters.

5. Theoretical investigations on the nature of the dark matter in clusters of galaxies: In continuation of the activities of the last year (1997) the statistical violent relaxation model of clusters has been further investigated. The progress consists in the mass-independent formulation of the model assuming phase space elements of different sizes for different populations. With the help of this model the fit of the X-ray emission of the coma cluster could be improved. It turns out that the mixed matter model including massive (though light) neutrinos is not unrealistic. However, nothing is changed with respect to the conclusion that the model yields too high a fraction of baryonic matter - incompatible with a homogeneous flat universe.

Astrophysical Compact Sources

This research area concentrated on the investigation of quasars, galactic micro-quasars and a progenitor of micro-quasars.

Quasars are active galaxies with extremely high emission from a compact nucleus. For about 15% of all known quasars strong absorption structures were found on the blue side of prominent UV lines, indicating matter outflows with velocities of a few times 10⁴ km/s. None of these BAL (Broad Absorption Line) quasars has been detected in the soft X-ray band by ROSAT and even ASCA with its wider energy range (E < 10 keV) showed only marginal detections. The data are compatible with the idea that the emission from the "central machine" is similar for all quasars, but in BAL objects the radiation is absorbed by cold matter with high column density (10²³ hydrogen atoms per cm²).

There might be a substantial number of yet unknown BAL quasars amongst the catalogued quasar population. Therefore, it could be possible that a large fraction of the radio-quiet quasars not detected in the ROSAT All-Sky Survey are BAL objects. In a statistical analysis of the ROSAT data it could be shown that there is no substantial fraction of unidentified BAL quasars in current catalogs, if the the BAL phenomenon can be related to absorption.

Recently, a class of galactic compact sources was discovered which is termed "micro-quasars", as they show similar phenomena seen in quasars albeit on smaller scales. These micro-quasars are solar-mass rotating black holes in binary systems, accreting mass from the companion (in contrast, the black hole of a quasar has typically ~10⁸ solar masses). As all astrophysically relevant time scales around black holes scale with the mass of the hole, the micro-quasars allow fast investigations and the study of effects which will otherwise take a few 100 million years in ordinary quasars.

The peculiar object SS433, known for nearly 20 years, can be regarded as a progenitor of such micro-quasars. It emits two oppositely directed jets with relativistic velocities. The detailed understanding of the emission from the jets can reveal important insights into the jet phenomenon found in quasars and micro-quasars. In numerical simulations we studied various physical effects affecting the X-ray emission from the jets. It could be shown that the inclusion of these effects into the interpretation of the data not only yields different results for the system's parameters (mass outflow rate, energetics, size of the jets) but also provides new diagnostic tools for the study of the jets with future sensitive instruments (AXAF, XMM).

For the superluminal jets of the micro-quasar GRS 1915+105 a new method to find a lower limit to the jet's kinetic power was discussed. The large value obtained favours the electromagnetic Pointing flux as the most likely energy carrier. Using a finite difference MHD code in two dimensions, the formation of such a jet from a magnetized accretion disk was studied. Detailed optical observations of the micro-quasar GRO J1655-40 revealed that the temporal variations of the polarimetric properties of the object are consistent with the orbital period of the sytem .

Complex Dynamics

In this field we focus on developing and testing quantitative methods for analysing temporally and/or spatially complex systems.

The method to quantify nonlinear predictability of time series described in the annual report 97 is a version of the correlation entropy. It has been extended in such a way that not only the delay time but arbitrary time steps can be taken into consideration. As an application we analyse high-resolution time series of the solar wind density and velocity obtained from the Proton Monitor onboard the SOHO spacecraft. Nonlinearities in the density time series on minute time scales have been established, and the possibility to make predictions up to 20 minutes was demonstrated for this type of time series.

The institute's "scaling-index-method" (SIM) was applied to ROSAT data. As one example, it was investigated whether radio-loud quasars "live" in an environment with higher X-ray background radiation than radio-quiet quasars do. To that end all ROSAT quasar observations with an exposure time of more than 10 ksec were analysed. By use of the SIM all point sources around the quasar were extracted and the remaining background radiation was determined. The result does not support the speculation that the two types of quasars are located in significantly different X-ray environments.

In a further case, a puzzle presented by the observation of some spatial structures in a deep HRI measurement of the supernova remnant Kes32, which do not fit with the ASCA measurements taken at much higher energies, was investigated. In both measurements the features hardly exceed the background noise. Although the statistical distribution of the measured photons gave a hint of "nonrandom" fluctuations, the confirmation of the features could be established only by a comparison of spectra of the real data with those of surrogates, employing SIM.

The application of the techniques developed in the MPE is by no means restricted to astropysical systems. In the field of medicine and physiology the methods were used for a refinement of medical diagnostics. Both, the methodical approach and the fields of application were extended. The basis of the analysis (apart from image analysis and characterisation - as employed for instance, in tumor diagnostics - see annual report 1997) is mostly the mapping of the one- or multi-dimensional time series into an artificial phase space. The further development deals in particular with the description of the trajectory or the pseudo flow of the system in this phase space. The derived measures serve as a description of the system state and/or are used for classification of the examined system. In that way it is possible, for instance, to determine the state of sleep with high precision using only ECG data or to perform a fetal monitoring and risk identification in the antepartual and intrapartual phase. Often the problem is to show nonlinear correlations between different physiological parameters (e. g. respiration-heartrate-capillary blood flow). In addition to these applications new investigations were started within the area of "decentralized diagnostics". Purpose of this work is, for example, the non-invasive determination of the glucose level of blood and the identification of disease patterns from blood samples. Although such investigations are still preliminary, the efforts are already quite successful in parts. These projects are realized in close cooperation with hospitals (gynaecological clinic TU Munich, paediatric clinics of the LMU and TUM) and industrial partners.

Our research has been supported by DLR (50.WM.9445.6, 50.TT.9527.9 and (50.TT.9731.0). Furthermore we have received support from the Verbundforschung (05.3ME82A(7), 05.3ME62.(0) and 50.OR.9306.5). The biosignal project have been supported by the B-W-Stiftung.