Constituents of the soft X-ray background

The X-ray background is generated by various classes of objects and variety of emission mechanisms. Relative contribution of individual components depends on energy. The goal is to assess the integral emission of the major components of the soft X-ray background (extragalactic discrete sources dominated by AGNs, galactic plasma, and the Warm/Hot Intergalactic Medium), investigating the angular structure of the background. Fluctuations of the background are measured using the auto-correlation function of the XRB determined in 5 energy bands between 0.3 and 4.5 keV. The investigation is based on the extensive observational data set selected from the XMM-Newton archives. Amplitudes of the auto-correlation functions calculated in three energy bands above ~1 keV are consistent with the conjecture that the background fluctuations result solely from clustering of sources which produce the background. At energies below 1 keV the relative fluctuation amplitude decreases indicating that a fraction of the soft XRB is associated with a smooth plasma emission in the Galaxy. It is shown, however, that the mean spectrum of extragalactic discrete sources steepens in the soft X-rays and is not well represented by a single power law in the energy range 0.3-4.5 keV. The WHIM contribution to the total background fluctuations is small and consistent with the WHIM properties derived from the cross-correlation of the XRB with galaxies.Comment: 7 pages, 2 figure

Missing baryons and the soft X-ray background

The X-ray background intensity around Lick count galaxies and rich clusters of galaxies is investigated in three ROSAT energy bands. It is found that the X-ray enhancements surrounding concentrations of galaxies exhibit significantly softer spectrum than the standard cluster emission and the average extragalactic background. The diffuse soft emission accompanying the galaxies is consistent with the thermal emission of the hot gas postulated first by the Cen & Ostriker hydrodynamic simulations. Our estimates of the gas temperature - although subject to large uncertainties - averaged over several Mpc scales are below 1 keV, which is substantially below the temperature of the intra-cluster gas, but consistent with temperatures predicted for the local intergalactic medium. It is pointed out that the planned ROSITA mission would be essential for our understanding of the diffuse thermal component of the background.Comment: AA accepted, 6 pages, incl. 4 figure

The diffuse X-ray background

The deepest observations of the X-ray background approach the surface brightness of the truly diffuse component generated by Thomson scattering of cosmic X-ray photons. Available estimates of the electron density and the X-ray luminosity density of AGNs as a function of cosmological epoch are used to calculate the integral scattered X-ray background component. It is shown that the scattered component constitutes 1.0 - 1.7 % of the total background, depending on the AGN cosmic evolution. Albeit this is a minute fragment of the total flux, it becomes a perceptible fraction of the still unresolved part of the background and should be taken into account in the future rigorous assessments of the X-ray background structure. This diffuse component at energies < 1 keV sums up with the emission by WHIM to 3 - 4 %. Consequently, one should expect that integrated counts of discrete sources account for just 96 - 97 % for soft background and ~99 % at higher energies.Comment: 5 pages, 2 figures, AA in prin

The harmonic power spectrum of the soft X-ray background I. The data analysis

Fluctuations of the soft X-ray background are investigated using harmonic analysis. A section of the ROSAT All-Sky Survey around the north galactic pole is used. The flux distribution is expanded into a set of harmonic functions and the power spectrum is determined. Several subsamples of the RASS have been used and the spectra for different regions and energies are presented. The effects of the data binning in pixels are assessed and taken into account. The spectra of the analyzed samples reflect both small scale effects generated by strong discrete sources and the large scale gradients of the XRB distribution. Our results show that the power spectrum technique can be effectively used to investigate anisotropy of the XRB at various scales. This statistics will become a useful tool in the investigation of various XRB components.Comment: 12 pages, A&A accepte

Compactifications of discrete quantum groups

Given a discrete quantum group A we construct a certain Hopf *-algebra AP which is a unital *-subalgebra of the multiplier algebra of A. The structure maps for AP are inherited from M(A) and thus the construction yields a compactification of A which is analogous to the Bohr compactification of a locally compact group. This algebra has the expected universal property with respect to homomorphisms from multiplier Hopf algebras of compact type (and is therefore unique). This provides an easy proof of the fact that for a discrete quantum group with an infinite dimensional algebra the multiplier algebra is never a Hopf algebra

Infinite-dimensional Compact Quantum Semigroup

In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra $\mathcal{T}$. The existence of a subalgebra, isomorphic to the algebra of regular Borel's measures on a circle with convolution product, in the dual algebra $\mathcal{T}^*$ is shown. The existence of Haar functionals in the dual algebra and in the above-mentioned subalgebra is proved. Also we show the connection between $\mathcal{T}$ and the structure of weak Hopf algebra.Comment: 17 page

Constraining the thermal history of the Warm-Hot Intergalactic Medium

We have identified a large-scale structure traced by galaxies at z=0.8, within the Lockman Hole, by means of multi-object spectroscopic observations. By using deep XMM images we have investigated the soft X-ray emission from the Warm-Hot Intergalactic Medium (WHIM) expected to be associated with this large-scale structure and we set a tight upper limit to its flux in the very soft 0.2-0.4 keV band. The non-detection requires the WHIM at these redshifts to be cooler than 0.1 keV. Combined with the WHIM emission detections at lower redshift, our result indicates that the WHIM temperature is rapidly decreasing with redshift, as expected in popular cosmological models.Comment: 10 pages, 5 figures, 1 appendix. A&A accepte

Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration $S^7 \to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equations on $S^4_q$, for which we find an `instanton' solution coming from the natural projection defining the tautological bundle over $S^4_q$.Comment: v2: 38 pages; completely rewritten. The crucial difference with respect to the first version is that in the present one the quantum four-sphere, the base space of the fibration, is NOT a quantum homogeneous space. This has important consequences and led to very drastic changes to the paper. To appear in CM

A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries

Let $G$ be a co-amenable compact quantum group. We show that a right coideal of $G$ is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of the dual discrete quantum group. We apply this result to theory of Poisson boundaries introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on $SU_q(N)$ for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral is an isomorphism between the Poisson boundary and the right coideal of quotient type by maximal quantum subgroup of Kac type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group.Comment: 28 pages, Remark 4.9 adde