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# Scaling relation between Sunyaev–Zel’dovich effect and X-ray luminosity and scale-free evolution of cosmic baryon field

Department of Astronomy, Beijing Normal University, Beijing 100875, PR China; Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918-3, Beijing 100049, PR China; Kavli Institute for Theoretical Physics China, Institute of Theoretical Physics, Chinese Academy of Sciences (KITPC/ITP-CAS), P.O. Box 2735, Beijing 100080, PR China; Department of Physics, University of Arizona, Tucson AZ 85721, United States; Purple Mountain Observatory, Nanjing 210008, PR China; National Astronomical Observatories, Chinese Academy of Science, Chao-Yang District, Beijing 100012, PR China; Beijing Planetarium, Beijing 100044, PR China

New Astronomy (Impact Factor: 1.85). 07/2008; DOI: 10.1016/j.newast.2008.07.004 Source: arXiv

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**ABSTRACT:**We investigate the dynamical effect of the turbulence in baryonic intergalactic medium (IGM) on the baryon fraction distribution. In the fully developed nonlinear regime, the IGM will evolve into the state of turbulence, containing strong and curved shocks, vorticity and complex structures. Turbulence would lead to the density and velocity fields of the IGM to be different from those of underlying collisionless dark matter. Consequently, the baryon fraction f_b will deviate from its cosmic mean . We study these phenomena with simulation samples produced by the weighted essentially non-oscillatory (WENO) hybrid cosmological hydrodynamic/N-body code, which is effective of capturing shocks and complex structures. We find that the distribution of baryon fraction is highly nonuniform on scales from hundreds kpc to a few of Mpc, and f_b varies from as low as 1% to a few times of the cosmic mean. We further show that the turbulence pressure in the IGM is weakly scale-dependent and comparable to the gravitational energy density of halos with mass around 10^11 h-1 M\odot . The baryon fraction in halos with mass equal to or smaller than 10^11 h^-1 M\odot should be substantially lower than f_b^cosmic. Numerical results show that f_b is decreasing from 0.8 f_b^cosmic at halo mass scales around 10^12 h^-1 M\odot to 0.3f_b^cosmic at 10^11 h^-1 M\odot and shows further decrease when halo mass is less than 10^11 h^-1 M\odot. The strong mass dependence of f_b is similar to the observed results. Although the simulated f_b in halos are higher than the observed value by a factor of 2, the turbulence of the IGM should be an important dynamical reason leading to the remarkable missing of baryonic matter in halos with mass \leq 10^12 h^-1 M\odot.03/2011; - [Show abstract] [Hide abstract]

**ABSTRACT:**We develop an analytic framework to understand fragmentation in turbulent, self-gravitating media. Previously, we showed some properties of turbulence can be predicted with the excursion-set formalism. Here, we generalize to fully time-dependent gravo-turbulent fragmentation & collapse. We show that turbulent systems are always gravitationally unstable (in a probabilistic sense). The fragmentation mass spectra, size/mass relations, correlation functions, range of scales over which fragmentation occurs, & time-dependent rates of fragmentation are predictable. We show how this depends on bulk turbulent properties (Mach numbers & power spectra). We also generalize to include rotation, complicated equations of state, collapsing/expanding backgrounds, magnetic fields, intermittency, & non-normal statistics. We derive how fragmentation is suppressed with 'stiffer' equations of state or different driving mechanisms. Suppression appears at an 'effective sonic scale' where Mach(R,rho)~1. Gas becomes stable below this scale for polytropic gamma>4/3, but fragmentation still occurs on larger scales. The scale-free nature of turbulence and gravity generically drives mass spectra and correlation functions towards universal shapes, with weak dependence on many properties of the media. Correlated fluctuation structures, non-Gaussian density distributions, & intermittency have surprisingly small effects on the fragmentation process. This is because fragmentation cascades on small scales are 'frozen in' when large-scale modes push the 'parent' region above the collapse threshold; though they collapse, their statistics are only weakly modified by the collapse process. With thermal support, structure develops 'top-down' in time via fragmentation cascades; but strong rotational support reverses this to 'bottom-up' growth via mergers & introduces a maximal instability scale distinct from the Toomre scale.Monthly Notices of the Royal Astronomical Society 10/2012; 430(3). · 5.52 Impact Factor -
##### Article: Dynamical effect of the turbulence of the intergalactic medium on the baryon fraction distribution

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**ABSTRACT:**We investigate the dynamical effect of turbulence in the baryonic intergalactic medium (IGM) on the baryon fraction distribution. In the fully developed non-linear regime, the IGM will evolve into a state of turbulence, containing strong and curved shocks, vorticity and complex structures. Turbulence would mean that the density and velocity fields of the IGM would be different from those of the underlying collisionless dark matter. Consequently, the baryon fraction fb will deviate from its cosmic mean fcosmicb. We study these phenomena with simulation samples produced by the weighted essentially non-oscillatory (weno) hybrid cosmological hydrodynamic/N-body code, which is effective for capturing shocks and complex structures. We find that the distribution of the baryon fraction is highly non-uniform on scales from hundreds of kpc to a few Mpc, and fb varies from as low as 1 per cent to a few times the cosmic mean. We further show that the turbulence pressure in the IGM is weakly scale-dependent and comparable to the gravitational energy density of haloes with mass around 1011 h−1 M⊙. The baryon fraction in haloes with mass equal to or smaller than 1011 h−1 M⊙ should be substantially lower than fcosmicb. Numerical results show that fb is decreasing from 0.8fcosmicb at halo mass scales around 1012 h−1 M⊙ to 0.3fcosmicb at 1011 h−1 M⊙ and shows further decrease when halo mass is less than 1011 h−1 M⊙. The strong mass dependence of fb is similar to the observed results. Although the simulated fb in haloes are higher than the observed value by a factor of 2, the turbulence of the IGM should be an important dynamical reason for the remarkable lack of baryonic matter in haloes with mass ≤1012 h−1 M⊙.Monthly Notices of the Royal Astronomical Society 06/2011; 415(2):1093 - 1104. · 5.52 Impact Factor

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