Confinement and diffusion time-scales of CR hadrons in AGN-inflated bubbles

While rich clusters are powerful sources of X-rays, gamma-ray emission from these large cosmic structures has not been detected yet. X-ray radiative energy losses in the central regions of relaxed galaxy clusters are so strong that one needs to consider special sources of energy, likely AGN feedback, to suppress catastrophic cooling of the gas. We consider a model of AGN feedback that postulates that the AGN supplies the energy to the gas by inflating bubbles of relativistic plasma, whose energy content is dominated by cosmic-ray (CR) hadrons. If most of these hadrons can quickly escape the bubbles, then collisions of CRs with thermal protons in the intracluster medium (ICM) should lead to strong gamma-ray emission, unless fast diffusion of CRs removes them from the cluster. Therefore, the lack of detections with modern gamma-ray telescopes sets limits on the confinement time of CR hadrons in bubbles and CR diffusive propagation in the ICM.Comment: 8 pages, 2 figures, accepted for publication in MNRA

The first measurement of temperature standard deviation along the line-of-sight in galaxy clusters

Clusters of galaxies are mainly formed by merging of smaller structures, according to the standard cosmological scenario. If the mass of a substructure is >10% of that of a galaxy cluster, the temperature distribution of the intracluster medium (ICM) in a merging cluster becomes inhomogeneous. Various methods have been used to derive the two-dimensional projected temperature distribution of the ICM. However, methods for studying temperature distribution along the line-of-sight through the cluster were absent. In this paper, we present the first measurement of the temperature standard deviation along the line-of-sight, using as a reference case the multifrequency SZ measurements of the Bullet Cluster. We find that the value of the temperature standard deviation is high and equals to (10.6+/-3.8) keV in the Bullet Cluster. This result shows that the temperature distribution in the Bullet Cluster is strongly inhomogeneous along the line-of-sight and provides a new method for studying galaxy clusters in depth.Comment: 5 pages, 1 figure, published in MNRAS Letter

YBCO microwave resonators for strong collective coupling with spin ensembles

Coplanar microwave resonators made of 330 nm-thick superconducting YBCO have been realized and characterized in a wide temperature ($T$, 2-100 K) and magnetic field ($B$, 0-7 T) range. The quality factor $Q_L$ exceeds 10$^4$ below 55 K and it slightly decreases for increasing fields, remaining 90$\%$ of $Q_L(B=0)$ for $B=7$ T and $T=2$ K. These features allow the coherent coupling of resonant photons with a spin ensemble at finite temperature and magnetic field. To demonstrate this, collective strong coupling was achieved by using DPPH organic radical placed at the magnetic antinode of the fundamental mode: the in-plane magnetic field is used to tune the spin frequency gap splitting across the single-mode cavity resonance at 7.75 GHz, where clear anticrossings are observed with a splitting as large as $\sim 82$ MHz at $T=2$ K. The spin-cavity collective coupling rate is shown to scale as the square root of the number of active spins in the ensemble.Comment: to appear in Appl. Phys. Let

Can electron distribution functions be derived through the Sunyaev-Zel'dovich effect?

Measurements of the Sunyaev-Zel'dovich (hereafter SZ) effect distortion of the cosmic microwave background provide methods to derive the gas pressure and temperature of galaxy clusters. Here we study the ability of SZ effect observations to derive the electron distribution function (DF) in massive galaxy clusters. Our calculations of the SZ effect include relativistic corrections considered within the framework of the Wright formalism and use a decomposition technique of electron DFs into Fourier series. Using multi-frequency measurements of the SZ effect, we find the solution of a linear system of equations that is used to derive the Fourier coefficients; we further analyze different frequency samples to decrease uncertainties in Fourier coefficient estimations. We propose a method to derive DFs of electrons using SZ multi-frequency observations of massive galaxy clusters. We found that the best frequency sample to derive an electron DF includes high frequencies $\nu$=375, 600, 700, 857 GHz. We show that it is possible to distinguish a Juttner DF from a Maxwell-Bolzman DF as well as from a Juttner DF with the second electron population by means of SZ observations for the best frequency sample if the precision of SZ intensity measurements is less than 0.1%. We demonstrate by means of 3D hydrodynamic numerical simulations of a hot merging galaxy cluster that the morphologies of SZ intensity maps are different for frequencies $\nu$=375, 600, 700, 857 GHz. We stress that measurements of SZ intensities at these frequencies are a promising tool for studying electron distribution functions in galaxy clusters.Comment: 11 pages, 12 figures, published in Astronomy and Astrophysic

Uncertainty relations in curved spaces

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde

Asymptotic formulas for integer partitions within the approach of microcanonical ensemble

The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary (one-dimensional) partitions, the correction to the leading asymptotic is obtained. The estimate for the number of two-dimensional (plane) partitions coincides with known asymptotic results.Розглянуто задачу про розбиття цiлих чисел у межах мiкроканонiчного пiдходу, який ґрунтується на аналогiї мiж цiєю задачею з теорiї чисел i обчисленням кiлькостi мiкростанiв багатобозонної системи. Для звичайних (одновимiрних) розбиттiв отримано поправку до головної асимптотики. Оцiнка кiлькостi двовимiрних (плоских) розбиттiв добре узгоджується з вiдомими асимптотичними результатами