New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation

We discuss a numerical method to compute the homogeneous solutions of the Teukolsky equation which is the basic equation of the black hole perturbation method. We use the formalism developed by Mano, Suzuki and Takasugi, in which the homogeneous solutions of the radial Teukolsky equation are expressed in terms of two kinds of series of special functions, and the formulas for the asymptotic amplitudes are derived explicitly.Although the application of this method was previously limited to the analytical evaluation of the homogeneous solutions, we find that it is also useful for numerical computation. We also find that so-called "renormalized angular momentum parameter", $\nu$, can be found only in the limited region of $\omega$ for each $l,m$ if we assume $\nu$ is real (here, $\omega$ is the angular frequency, and $l$ and $m$ are degree and order of the spin-weighted spheroidal harmonics respectively). We also compute the flux of the gravitational waves induced by a compact star in a circular orbit on the equatorial plane around a rotating black hole. We find that the relative error of the energy flux is about $10^{-14}$ which is much smaller than the one obtained by usual numerical integration methods.Comment: 36 pages,7 figure

Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol

Recent breakthroughs in numerical relativity enable one to examine the validity of the post-Newtonian expansion in the late stages of inspiral. For the comparison between post-Newtonian (PN) expansion and numerical simulations, the waveforms in terms of the spin-weighted spherical harmonics are more useful than the plus and cross polarizations, which are used for data analysis of gravitational waves. Factorized resummed waveforms achieve better agreement with numerical results than the conventional Taylor expanded post-Newtonian waveforms. In this paper, we revisit the post-Newtonian expansion of gravitational waves for a test-particle of mass \m in circular orbit of radius $r_0$ around a Schwarzschild black hole of mass $M$ and derive the spherical harmonic components associated with the gravitational wave polarizations up to order $v^{11}$ beyond Newtonian. Using the more accurate $h_{\ell m}$'s computed in this work, we provide the more complete set of associated $\rho_{\ell m}$'s and $\delta_{\ell m}$'s that form important bricks in the factorized resummation of waveforms with potential applications for the construction of further improved waveforms for prototypical compact binary sources in the future. We also provide ready-to-use expressions of the 5.5PN gravitational waves polarizations $h_+$ and $h_\times$ in the test-particle limit for gravitational wave data analysis applications. Additionally, we provide closed analytical expressions for 2.5PN $h_{\ell m}$, 2PN $\rho_{\ell m}$ and 3PN $\delta_{\ell m}$, for general multipolar orders $\ell$ and $m$ in the test-particle limit. Finally, we also examine the implications of the present analysis for compact binary sources in Laser Interferometer Space Antenna.Comment: 42 pages, 2 figures, match with accepted version by PR

Holographic entanglement entropy of a 1+11+1 dimensional pp-wave superconductor

We examine the behavior of entanglement entropy of a subsystem $A$ in a fully backreacted holographic model of a $1+1$ dimensional $p$ wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size $l$ smaller than a critical size $l_{c1}$, entanglement entropy continues to increase as a function of the charge density as we cross the phase transition. When $l$ lies between $l_{c1}$ and another critical size $l_{c2}$ the entanglement entropy displays a non-monotonic behavior, while for $l > l_{c2}$ it decreases monotonically. At large charge densities entanglement entropy appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.Comment: 16 pages, 17 figures, v2: references added, section 3.1 added, JHEP styl

Chandra Observations of A2670 and A2107: A Comet Galaxy and cDs with Large Peculiar Velocities

We present an analysis of Chandra observations of the galaxy clusters A2670 and A2107. Their cD galaxies have large peculiar velocities (>200km/s) and thus the clusters appear to be undergoing mergers. In A2670, we find a comet-like structure around one of the brightest galaxies. At the leading edge of the structure, there is a cold front. The mass of the X-ray gas in the comet-like structure suggests that the galaxy was in a small cluster or group, and its intracluster medium (ICM) is being stripped by ram-pressure. The regions of cool interstellar medium (ISM) of the cD galaxies in A2670 and A2107 are very compact. This is similar to the brightest galaxies in the Coma cluster, which is also a merging cluster. In each galaxy, the short cooling time of the ISM requires a heating source; the compact nature of the ISM makes it unlikely that the heating source is a central active galactic nucleus (AGN).Comment: PASJ in pres

Delta Effects in Pion-Nucleon Scattering and the Strength of the Two-Pion-Exchange Three-Nucleon Interaction

We consider the relationship between P-wave pi-N scattering and the strength of the P-wave two-pion-exchange three-nucleon interaction (TPE3NI). We explain why effective theories that do not contain the delta resonance as an explicit degree of freedom tend to overestimate the strength of the TPE3NI. The overestimation can be remedied by higher-order terms in these ``delta-less'' theories, but such terms are not yet included in state-of-the-art chiral EFT calculations of the nuclear force. This suggests that these calculations can only predict the strength of the TPE3NI to an accuracy of +/-25%.Comment: 13 pages, 2 figures, uses eps

Comparison of post-Newtonian templates for extreme mass ratio inspirals

Extreme mass ratio inspirals (EMRIs), the inspirals of compact objects into supermassive black holes, are important gravitational wave sources for the Laser Interferometer Space Antenna (LISA). We study the performance of various post-Newtonian (PN) template families relative to the high precision numerical waveforms in the context of EMRI parameter estimation with LISA. Expressions for the time domain waveforms TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt are derived up to 22PN order, i.e $\mathcal{O}(v^{44})$ ($v$ is the characteristic velocity of the binary) beyond the Newtonian term, for a test particle in a circular orbit around a Schwarzschild black hole. The phase difference between the above 22PN waveform families and numerical waveforms are evaluated during two-year inspirals for two prototypical EMRI systems with mass ratios $10^{-4}$ and $10^{-5}$. We find that the dephases (in radians) for TaylorT1 and TaylorT2, respectively, are about $10^{-9}$ ($10^{-2}$) and $10^{-9}$ ($10^{-3}$) for mass ratio $10^{-4}$ ($10^{-5}$). This suggests that using 22PN TaylorT1 or TaylorT2 waveforms for parameter estimation of EMRIs will result in accuracies comparable to numerical waveform accuracy for most of the LISA parameter space. On the other hand, from the dephase results, we find that TaylorT3, TaylorT4 and TaylorEt fare relatively poorly as one approaches the last stable orbit. This implies that, as for comparable mass binaries using the 3.5PN phase of waveforms, the 22PN TaylorT3 and TaylorEt approximants do not perform well enough for the EMRIs. The reason underlying the poor performance of TaylorT3, TaylorT4 and TaylorEt relative to TaylorT1 and TaylorT2 is finally examined.Comment: 10 page

Review of solar fuel-producing quantum conversion processes

The status and potential of fuel-producing solar photochemical processes are discussed. Research focused on splitting water to produce dihydrogen and is at a relatively early stage of development. Current emphasis is primarily directed toward understanding the basic chemistry underlying such quantum conversion processes. Theoretical analyses by various investigators predict a limiting thermodynamic efficiency of 31% for devices with a single photosystem operating with unfocused sunlight at 300 K. When non-idealities are included, it appears unlikely that actual devices will have efficiencies greater than 12 to 15%. Observed efficiencies are well below theoretical limits. Cyclic homogeneous photochemical processes for splitting water have efficiencies considerably less than 1%. Efficiency can be significantly increased by addition of a sacrificial reagent; however, such systems are no longer cyclic and it is doubtful that they would be economical on a commercial scale. The observed efficiencies for photoelectrochemical processes are also low but such systems appear more promising than homogeneous photochemical systems. Operating and systems options, including operation at elevated temperature and hybrid and coupled quantum-thermal conversion processes, are also considered

Solar photochemical process engineering for production of fuels and chemicals

The engineering costs and performance of a nominal 25,000 scmd (883,000 scfd) photochemical plant to produce dihydrogen from water were studied. Two systems were considered, one based on flat-plate collector/reactors and the other on linear parabolic troughs. Engineering subsystems were specified including the collector/reactor, support hardware, field transport piping, gas compression equipment, and balance-of-plant (BOP) items. Overall plant efficiencies of 10.3 and 11.6% are estimated for the flat-plate and trough systems, respectively, based on assumed solar photochemical efficiencies of 12.9 and 14.6%. Because of the opposing effects of concentration ratio and operating temperature on efficiency, it was concluded that reactor cooling would be necessary with the trough system. Both active and passive cooling methods were considered. Capital costs and energy costs, for both concentrating and non-concentrating systems, were determined and their sensitivity to efficiency and economic parameters were analyzed. The overall plant efficiency is the single most important factor in determining the cost of the fuel

Electronic and Magnetic Properties of Nanographite Ribbons

Electronic and magnetic properties of ribbon-shaped nanographite systems with zigzag and armchair edges in a magnetic field are investigated by using a tight binding model. One of the most remarkable features of these systems is the appearance of edge states, strongly localized near zigzag edges. The edge state in magnetic field, generating a rational fraction of the magnetic flux (\phi= p/q) in each hexagonal plaquette of the graphite plane, behaves like a zero-field edge state with q internal degrees of freedom. The orbital diamagnetic susceptibility strongly depends on the edge shapes. The reason is found in the analysis of the ring currents, which are very sensitive to the lattice topology near the edge. Moreover, the orbital diamagnetic susceptibility is scaled as a function of the temperature, Fermi energy and ribbon width. Because the edge states lead to a sharp peak in the density of states at the Fermi level, the graphite ribbons with zigzag edges show Curie-like temperature dependence of the Pauli paramagnetic susceptibility. Hence, it is shown that the crossover from high-temperature diamagnetic to low-temperature paramagnetic behavior of the magnetic susceptibility of nanographite ribbons with zigzag edges.Comment: 13 pages including 19 figures, submitted to Physical Rev