Spectrum of Relativistic and Subrelativistic Cosmic Rays in the 100 pc Central Region

From the rate of hydrogen ionization and the gamma ray flux, we derived the spectrum of relativistic and subrelativistic cosmic rays (CRs) nearby and inside the molecular cloud Sgr B2 near the Galactic Center (GC). We studied two cases of CR propagation in molecular clouds: free propagation and scattering of particles by magnetic fluctuations excited by the neutral gas turbulence. We showed that in the latter case CR propagation inside the cloud can be described as diffusion with the coefficient $sim 3times 10^{27}$ cm$^2$ s$^{-1}$. For the case of hydrogen ionization by subrelativistic protons, we showed that their spectrum outside the cloud is quite hard with the spectral index $delta>-1$. The energy density of subrelativistic protons ($>50$ eV cm$^{-3}$) is one order of magnitude higher than that of relativistic CRs. These protons generate the 6.4 keV emission from Sgr B2, which was about 30% of the flux observed by Suzaku in 2013. Future observations for the period after 2013 may discover the background flux generated by subrelativistic CRs in Sgr B2. Alternatively hydrogen ionization of the molecular gas in Sgr B2 may be caused by high energy electrons. We showed that the spectrum of electron bremsstrahlung is harder than the observed continuum from Sgr B2, and in principle this X-ray component provided by electrons could be seen from the INTEGRAL data as a stationary high energy excess above the observed spectrum $E_x^{-2}$.

Analysis of the magneto-rotational instability with the effect of cosmic-ray diffusion

We present the results obtained from linear stability analysis and 2.5-dimensional magnetohydrodynamic (MHD) simulations of the magnetorotational instability (MRI), including the effects of cosmic rays (CRs). We took into account of the CR diffusion along the magnetic field but neglect the cross-field-line diffusion. Two models are considered in this paper: shearing box model and differentially rotating cylinder model. We studied how MRI is affected by the initial CR pressure (i.e., energy) distribution. In the shearing box model, the initial state is uniform distribution. Linear analysis shows that the growth rate of MRI does not depend on the value of CR diffusion coefficient. In the differentially rotating cylinder model, the initial state is a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both results are confirmed by MHD simulations. The MHD simulation results show that the outward movement of matter by the growth of MRI is not impeded by the CR pressure gradient, and the centrifugal force which acts to the concentrated matter becomes larger. Consequently, the growth rate of MRI is increased. On the other hand, if the initial CR pressure is uniform, then the growth rate of the MRI barely depends on the value of the CR diffusion coefficient.

Multi-wavelength Emission from the Fermi Bubble III. Stochastic (Fermi) Re-Acceleration of Relativistic Electrons Emitted by SNRs

We analyse the model of stochastic re-acceleration of electrons, which are emitted by supernova remnants (SNRs) in the Galactic Disk and propagate then into the Galactic halo, in order to explain the origin on nonthermal (radio and gamma-ray) emission from the Fermi Bubbles (FB). We assume that the energy for re-acceleration in the halo is supplied by shocks generated by processes of star accretion onto the central black hole. Numerical simulations show that regions with strong turbulence (places for electron re-acceleration) are located high up in the Galactic Halo about several kpc above the disk. The energy of SNR electrons that reach these regions does not exceed several GeV because of synchrotron and inverse Compton energy losses. At appropriate parameters of re-acceleration these electrons can be re-accelerated up to the energy 10E12 eV which explains in this model the origin of the observed radio and gamma-ray emission from the FB. However although the model gamma-ray spectrum is consistent with the Fermi results, the model radio spectrum is steeper than the observed by WMAP and Planck. If adiabatic losses due to plasma outflow from the Galactic central regions are taken into account, then the re-acceleration model nicely reproduces the Planck datapoints.

Stochastic particle acceleration and the problem of backgroud plasma overheating

The origin of hard X-ray (HXR) excess emission from clusters of galaxies is still an enigma, whose nature is debated. One of the possible mechanism to produce this emission is the bremsstrahlung model. However, previous analytical and numerical calculations showed that in this case the intracluster plasma had to be overheated very fast because suprathermal electrons emitting the HXR excess lose their energy mainly by Coulomb losses, i.e., they heat the background plasma. It was concluded also from these investigations that it is problematic to produce emitting electrons from a background plasma by stochastic (Fermi) acceleration because the energy supplied by external sources in the form of Fermi acceleration is quickly absorbed by the background plasma. In other words the Fermi acceleration is ineffective for particle acceleration. We revisited this problem and found that at some parameter of acceleration the rate of plasma heating is rather low and the acceleration tails of non-thermal particles can be generated and exist for a long time while the plasma temperature is almost constant. We showed also that for some regime of acceleration the plasma cools down instead of being heated up, even though external sources (in the form of external acceleration) supply energy to the system. The reason is that the acceleration withdraws effectively high energy particles from the thermal pool (analogue of Maxwell demon).

The Fermi Bubble as a Source of Cosmic Rays in the Energy Range > 10E15 eV

The {it Fermi} Large Area Telescope has recently discovered two giant gamma-ray bubbles which extend north and south of the Galactic center with diameters and heights of the order of $Hsim 10$ kpc. We suggest that the periodic star capture processes by the Galactic supermassive black hole Sgr A$^*$, with a capture rate of $tau_{rm cap}^{-1}sim 3times 10^{-5}$ yr$^{-1}$ and an energy release of $Wsim 3times 10^{52}$ erg per capture, can result in hot plasma injecting into the Galactic halo at a wind velocity of $usim 10^8$ cm s$^{-1}$. The periodic injection of hot plasma can produce a series of shocks. Energetic protons in the bubble are re-accelerated when they interact with these shocks. We show that for energy larger than $E> 10^{15}$ eV, the acceleration process can be better described by the stochastic second-order Fermi acceleration. We propose that hadronic cosmic rays (CRs) within the ``knee of the observed CR spectrum are produced by Galactic supernova remnants distributed in the Galactic disk. Re-acceleration of these particles in the Fermi Bubble produces CRs beyond the knee. With a mean CR diffusion coefficient in this energy range in the bubble $D_Bsim 3times 10^{30}$ cm$^2$ s$^{-1}$, we can reproduce the spectral index of the spectrum beyond the knee and within. The conversion efficiency from shock energy of the bubble into CR energy is about 10%. This model provides a natural explanation of the observed CR flux, spectral indices, and matching of spectra at the knee.

Nuclear Interaction Gamma-Ray Lines from the Galactic Center Region

Aims. The accretion of stars onto the central supermassive black hole at the center of the Milky Way is predicted to generate large fluxes of subrelativistic ions in the Galactic center region. We analyze the intensity, shape and spatial distribution of de-excitation gamma-ray lines produced by nuclear interactions of these energetic particles with the ambient medium. Methods. We first estimate the amount and mean kinetic energy of particles released from the central black hole during star disruption. We then calculate from a kinetic equation the energy and spatial distributions of these particles in the Galactic center region. These particle distributions are then used to derive the characteristics of the main nuclear interaction gamma-ray lines. Results. Because the time period of star capture by the supermassive black hole is expected to be shorter than the lifetime of the ejected fast particles against Coulomb losses, the gamma-ray emission is predicted to be stationary. We find that the nuclear de-excitation lines should be emitted from a region of maximum 5$^circ$ angular radius. The total gamma-ray line flux below 8 MeV is calculated to be $approx10^{-4}$ photons cm$^{-2}$ s$^{-1}$. The most promising lines for detection are those at 4.44 and $sim$6.2 MeV, with a predicted flux in each line of $approx$$10^{-5}$ photons cm$^{-2}$ s$^{-1}$. Unfortunately, it is unlikely that this emission can be detected with the INTEGRAL observatory. But the predicted line intensities appear to be within reach of future gamma-ray space instruments. A future detection of de-excitation gamma-ray lines from the Galactic center region would provide unique information on the high-energy processes induced by the central supermassive black hole and the physical conditions of the emitting region.