Diffusion of Elements in the Interstellar Medium in Early-Type Galaxies

We consider the role of diffusion in the redistribution of elements in the hot interstellar medium (ISM) of early-type galaxies. It is well known that gravitational sedimentation can affect significantly the abundances of helium and heavy elements in the intracluster gas of massive galaxy clusters. The self-similarity of the temperature profiles and tight mass--temperature relation of relaxed cool-core clusters suggest that the maximum effect of sedimentation take place in the most massive virialized objects in the Universe. However, Chandra and XMM-Newton observations demonstrate more complex scaling relations between the masses of early-type galaxies and other parameters, such as the ISM temperature and gas mass fraction. An important fact is that early-type galaxies can show both decreasing and increasing radial temperature profiles. We have calculated the diffusion based on the observed gas density and temperature distributions for 13 early-type galaxies that belonging to the different environments and cover a wide range of X-ray luminosities. To estimate the maximum effect of sedimentation and thermal diffusion, we have solved the full set of Burgers' equations for a non-magnetized ISM plasma. The results obtained demonstrate a considerable increase of the He/H ratio within one effective radius for all galaxies of our sample. For galaxies with a flat or declining radial temperature profile the average increase of the helium abundance is 60\% in one billion years of diffusion. The revealed effect can introduce a significant bias in the metal abundance measurements based on X-ray spectroscopy and can affect the evolution of stars that could be formed from a gas with a high helium abundance.Comment: 15 pages, 9 figures, 3 tables, published in Astronomy Letters, 2017, Volume 43, Issue 5, pp.285-30

Impact of thermal diffusion and other abundance anomalies on cosmological uses of galaxy clusters

Depending on the topology of the magnetic field and characteristics of turbulent motions, diffusion can significantly affect the distribution of elements, in particular helium, in the intracluster medium (ICM). As has been noted previously, an incorrect assumption about the helium abundance will lead to an error in the iron abundance determined from X-ray spectroscopy. The corresponding effect on the temperature measurement is negligibly small. An incorrectly assumed helium abundance will also lead to a systematic error in angular distance measurements based on X-ray and Sunyaev-Zeldovich (SZ) observations of clusters of galaxies. Its magnitude is further amplified by the associated error in the metal abundance determination, the impact being larger at lower ICM temperatures. Overall, a factor of 2-5 error in the helium abundance will lead to an ~ 10-25 % error in the angular distance. We solve the full set of Burgers equations for a multi-component intracluster plasma to determine the maximal effect of diffusion on the interpretation of X-ray and microwave observations of clusters of galaxies. For an isothermal cluster, gravitational sedimentation can lead to up to a factor of ~ 5-10 enhancements of helium and metal abundances in the cluster center on a ~ 3-7 Gyr timescale. In cool-core clusters on the contrary, thermal diffusion can counteract gravitational sedimentation and effectively remove helium and metals from the cluster inner core. In either case, a significant, up to ~ 40 %, error in the metal abundances determined by means of X-ray spectroscopy is possible. The angular distance determined from X-ray and SZ data can be underestimated by up to ~ 10-25 %.Comment: 11 pages, 10 figure

An upper limit on nickel overabundance in the supercritical accretion disk wind of SS 433 from X-ray spectroscopy

We take advantage of a long (with a total exposure time of 120 ks) X-ray observation of the unique Galactic microquasar SS 433, carried out with the XMM-Newton space observatory, to search for a fluorescent line of neutral (or weakly ionized) nickel at the energy 7.5 keV. We consider two models of the formation of fluorescent lines in the spectrum of SS 433: 1) due to reflection of hard X-ray radiation from a putative central source on the optically thick walls of the accretion disk "funnel"; and 2) due to scattering of the radiation coming from the hottest parts of the jets in the optically thin wind of the system. It is shown, that for these cases, the photon flux of Ni I K$_{\alpha}$ fluorescent line is expected to be 0.45 of the flux of Fe I K$_{\alpha}$ fluorescent line at 6.4 keV, for the relative nickel overabundance $Z_{Ni}/Z = 10$, as observed in the jets of SS 433. For the continuum model without the absorption edge of neutral iron, we set a 90 per cent upper limit on the flux of the narrow Ni I K$_{\alpha}$ line at the level of $0.9 \times 10^{-5}$ ph s$^{-1}$ cm$^{-2}$. For the continuum model with the absorption edge, the corresponding upper limit is $2.5 \times 10^{-5}$ ph s$^{-1}$ cm$^{-2}$. At the same time, for the Fe I K$_{\alpha}$ line, we measure the flux of $9.9_{8.4}^{11.2} \times 10^{-5}$ ph s$^{-1}$ cm$^{-2}$. Taken at the face value, the results imply that the relative overabundance of nickel in the wind of the accretion disc should be at least 1.5 times less than the corresponding excess of nickel observed in the jets of SS 433.Comment: 17 pages, 12 figures, 4 tables, Astronomy Letters, in press, 2018, Volume 44, Issue

Superbroad Component in Emission Lines of SS 433

We have detected new components in stationary emission lines of SS 433; these are the superbroad components that are low-contrast substrates with a width of 2000--2500 km s-1 in He I $\lambda4922$ and H$\beta$ and 4000--5000 km s-1 in He II $\lambda4686$. Based on 44 spectra taken during four years of observations from 2003 to 2007, we have found that these components in the He II and He I lines are eclipsed by the donor star; their behavior with precessional and orbital phases is regular and similar to the behavior of the optical brightness of SS 433. The same component in H$\beta$ shows neither eclipses nor precessional variability. We conclude that the superbroad components in the helium and hydrogen lines are different in origin. Electron scattering is shown to reproduce well the superbroad component of H$\beta$ at a gas temperature of 20--35 kK and an optical depth for Thomson scattering $\tau \approx$ 0.25--0.35. The superbroad components of the helium lines are probably formed in the wind from the supercritical accretion disk. We have computed a wind model based on the concept of Shakura-Sunyaev supercritical disk accretion. The main patterns of the He II line profiles are well reproduced in this model: not only the appearance of the superbroad component but also the evolution of the central two-component part of the profile of this line during its eclipse by the donor star can be explained.Comment: 17 pages, 13 figures, 2 tables, published in Astronomy Letters, 2013, vol. 39, N 12, pp. 826 - 84

The shape evolution of cometary nuclei via anisotropic mass loss

Context. Breathtaking imagery recorded during the European Space Agency's Rosetta mission confirmed the bilobate nature of comet 67P/Churyumov-Gerasimenko's nucleus. Its peculiar appearance is not unique among comets. The majority of cometary cores imaged at high resolution exhibit a similar build. Various theories have been brought forward as to how cometary nuclei attain such peculiar shapes. Aims. We illustrate that anisotropic mass loss and local collapse of subsurface structures caused by non-uniform exposure of the nucleus to solar irradiation can transform initially spherical comet cores into bilobed ones. Methods. A mathematical framework to describe the changes in morphology resulting from non-uniform insolation during a nucleus' spin-orbit evolution is derived. The resulting partial differential equations that govern the change in the shape of a nucleus subject to mass loss and consequent collapse of depleted subsurface structures are solved analytically for simple insolation configurations and numerically for more realistic scenarios. Results. The here proposed mechanism is capable of explaining why a large fraction of periodic comets appear to have peanut-shaped cores and why light-curve amplitudes of comet nuclei are on average larger than those of typical main belt asteroids of the same size.Comment: 4 pages of the main text, 2 pages of appendix, 4 figure

Chaos-Order Transition in Matrix Theory

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.Comment: 14 pages, Latex, 10 figure

Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, ``comma'' and matrix representations of vertices.Comment: 160 pages, LaTeX, 29 EPS figures. Lectures given by I.Ya.Aref'eva at the Swieca Summer School, Brazil, January 2001; Summer School in Modern Mathematical Physics, Sokobanja, Yugoslavia, August 2001; Max Born Symposium, Karpacz, Poland, September, 2001; Workshop "Noncommutative Geometry, Strings and Renormalization", Leipzig, Germany, September 2001. Typos corrected, references adde

The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

Fermi-liquid and Fermi surface geometry effects in propagation of low frequency electromagnetic waves through thin metal films

In the present work we theoretically analyze the contribution from a transverse Fermi-liquid collective mode to the transmission of electromagnetic waves through a thin film of a clean metal in the presence of a strong external magnetic field. We show that at the appropriate Fermi surface geometry the transverse Fermi-liquid wave may appear in conduction electrons liquid at frequencies $\omega$ significantly smaller than the cyclotron frequency of charge carriers $\Omega$ provided that the mean collision frequency $\tau^{-1}$ is smaller than $\omega.$ Also, we show that in realistic metals size oscillations in the transmission coefficient associated with the Firmi-liquid mode may be observable in experiments. Under certain conditions these oscillations may predominate over the remaining size effects in the transmission coefficient.Comment: 9 pages, 5 figures, text adde