The Impact of Nonlinear Structure Formation on the Power Spectrum of Transverse Momentum Fluctuations and the Kinetic Sunyaev-Zel'dovich Effect

Cosmological transverse momentum fields, whose directions are perpendicular to Fourier wave vectors, induce temperature anisotropies in the cosmic microwave background via the kinetic Sunyaev-Zeldovich (kSZ) effect. The transverse momentum power spectrum contains the four-point function of density and velocity fields, $\langle\delta\delta v v\rangle$. In the post-reionization epoch, nonlinear effects dominate in the power spectrum. We use perturbation theory and cosmological $N$-body simulations to calculate this nonlinearity. We derive the next-to-leading order expression for the power spectrum with a particular emphasis on the connected term that has been ignored in the literature. While the contribution from the connected term on small scales ($k>0.1\,h\,\rm{Mpc}^{-1}$) is subdominant relative to the unconnected term, we find that its contribution to the kSZ power spectrum at $\ell = 3000$ at $z<6$ can be as large as ten percent of the unconnected term, which would reduce the allowed contribution from the reionization epoch ($z>6$) by twenty percent. The power spectrum of transverse momentum on large scales is expected to scale as $k^2$ as a consequence of momentum conservation. We show that both the leading and the next-to-leading order terms satisfy this scaling. In particular, we find that both of the unconnected and connected terms are necessary to reproduce $k^2$.Comment: 13 pages, 5 figures, Accepted to Ap

The Cluster-Merger Shock in 1E 0657-56: Faster than the Speeding Bullet?

Shock waves driven in the intergalactic medium during the merging of galaxy clusters have been observed in X-ray imaging and spectroscopy. Fluid motions inferred from the shock strength and morphology can be compared to the cold dark matter (CDM) distribution inferred from gravitational lensing. A detailed reconstruction of the CDM kinematics, however, must take into account the nontrivial response of the fluid intracluster medium to the collisionless CDM motions. We have carried out two-dimensional simulations of gas dynamics in cluster collisions. We analyze the relative motion of the clusters, the bow shock wave, and the contact discontinuity and relate these to X-ray data. We focus on the "bullet cluster," 1E 0657-56, a near head-on collision of unequal-mass clusters, for which the gas density and temperature jumps across the prominent bow shock imply a high shock velocity 4,700 km/s. The velocity of the fluid shock has been widely interpreted as the relative velocity of the CDM components. This need not be the case, however. An illustrative simulation finds that the present relative velocity of the CDM halos is 16% lower than that of the shock. While this conclusion is sensitive to the detailed initial mass and gas density profile of the colliding clusters, such a decrease of the inferred halo relative velocity would increase the likelihood of finding 1E 0657-56 in a LambdaCDM universe.Comment: 4 pages, 4 figure

Acceleration Method of Neighbor Search with GRAPE and Morton-ordering

We describe a new method to accelerate neighbor searches on GRAPE, i.e. a special purpose hardware that efficiently calculates gravitational forces and potentials in $N$-body simulations. In addition to the gravitational calculations, GRAPE simultaneously constructs the lists of neighbor particles that are necessary for Smoothed Particle Hydrodynamics (SPH). However, data transfer of the neighbor lists from GRAPE to the host computer is time consuming, and can be a bottleneck. In fact, the data transfer can take about the same time as the calculations of forces themselves. Making use of GRAPE's special treatment of neighbor lists, we can reduce the amount of data transfer if we search neighbors in the order that the neighbor lists, constructed in a single GRAPE run, overlap each other. We find that the Morton-ordering requires very low additional calculation and programming costs, and results in successful speed-up on data transfer. We show some benchmark results in the case of GRAPE-5. Typical reduction in transferred data becomes as much as 90%. This method is suitable not only for GRAPE-5, but also GRAPE-3 and the other versions of GRAPE.Comment: 9 pages, 6 figures, accepted for publication in PAS

Equation of State for Parallel Rigid Spherocylinders

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto's method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto's original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto's original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2

Magnetic ground state of pyrochlore oxides close to metal-insulator boundary probed by muon spin rotation

Magnetism of ruthernium pyrochlore oxides A2Ru2O7 (A = Hg, Cd, Ca), whose electronic properties within a localized ion picture are characterized by non-degenerate t2g orbitals (Ru5+, 4d3) and thereby subject to geometrical frustration, has been investigated by muon spin rotation/relaxation (muSR) technique. The A cation (mostly divalent) was varied to examine the effect of covalency (Hg > Cd > Ca) on their electronic property. In a sample with A = Hg that exhibits a clear metal-insulator (MI) transition below >> 100 K (which is associated with a weak structural transition), a nearly commensurate magnetic order is observed to develop in accordance with the MI transition. Meanwhile, in the case of A = Cd where the MI transition is suppressed to the level of small anomaly in the resistivity, the local field distribution probed by muon indicates emergence of a certain magnetic inhomogeneity below {\guillemotright} 30 K. Moreover, in Ca2Ru2O7 that remains metallic, we find a highly inhomogeneous local magnetism below >>25 K that comes from randomly oriented Ru moments and thus described as a "frozen spin liquid" state. The systematic trend of increasing randomness and itinerant character with decreasing covalency suggests close relationship between these two characters. As a reference for the effect of orbital degeneracy and associated Jahn-Teller instability, we examine a tetravalent ruthernium pyrochlore, Tl2Ru2O7 (Ru4+, 4d4), where the result of muSR indicates a non-magnetic ground state that is consistent with the formation of the Haldane chains suggested by neutron diffraction experiment.Comment: 12 pages, 13 figure

Will Nonlinear Peculiar Velocity and Inhomogeneous Reionization Spoil 21cm Cosmology from the Epoch of Reionization?

The 21cm background from the epoch of reionization is a promising cosmological probe: line-of-sight velocity fluctuations distort redshift, so brightness fluctuations in Fourier space depend upon angle, which linear theory shows can separate cosmological from astrophysical information. Nonlinear fluctuations in ionization, density and velocity change this, however. The validity and accuracy of the separation scheme are tested here for the first time, by detailed reionization simulations. The scheme works reasonably well early in reionization ( 80% ionized).Comment: 2 figures, matches published PRL versio