An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole

We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can be evaluated by solving the Teukolsky equation with a point like source term, which is computed from the stress-energy tensor of a test particle moving on generic bound geodesic orbits. In our previous papers, we computed the homogeneous solutions of the Teukolsky equation using a formalism developed by Mano, Suzuki and Takasugi and showed that we could compute gravitational waves efficiently and very accurately in the case of circular orbits on the equatorial plane. Here, we apply this method to eccentric inclined orbits. The geodesics around a Kerr black hole have three constants of motion: energy, angular momentum and the Carter constant. We compute the rates of change of the Carter constant as well as those of energy and angular momentum. This is the first time that the rate of change of the Carter constant has been evaluated accurately. We also treat the case of highly eccentric orbits with $e=0.9$. To confirm the accuracy of our codes, several tests are performed. We find that the accuracy is only limited by the truncation of $\ell$-, $k$- and $n$-modes, where $\ell$ is the index of the spin-weighted spheroidal harmonics, and $n$ and $k$ are the harmonics of the radial and polar motion, respectively. When we set the maximum of $\ell$ to 20, we obtain a relative accuracy of $10^{-5}$ even in the highly eccentric case of $e=0.9$. The accuracy is better for lower eccentricity. Our numerical code is expected to be useful for computing templates of the extreme mass ratio inspirals, which is one of the main targets of the Laser Interferometer Space Antenna (LISA).Comment: Reference added in section

Pressure-Induced Ferromagnetic to Nonmagnetic Transition and the Enhancement of Ferromagnetic Interaction in the Thiazyl-Based Organic Ferromagnet γ-BBDTA·GaCl4

A thiazyl-based ferromagnet, the γ-phase of BBDTA (i.e., benzo[1,2- d :4,5- d \u27]bis[1,3,2]dithiazole)·GaCl 4 , has a high ferromagnetic ordering temperature of 7.0 K in organic radical ferromagnets. In this system, pressurization generated more compact molecular packing, resulting in that the ferromagnetic state at P = 16.2 kbar is stabilized over a temperature range of more than twice of the initial range. However, the saturation magnetic moment was reduced with increasing pressure, decreasing to about 12% of the initial value even at the low pressure level of P = 1.0 kbar. This suggests that the ferromagnetic molecular packing of the monoclinic γ-phase is easily transformed into that of the diamagnetic phase. Powder X-ray diffraction experiments revealed that the diamagnetic non-monoclinic (α- or β-) phase became stable instead of the monoclinic γ-phase across the pressure of 2.5–5.8 kbar. The increase in the temperature of onset of ferromagnetic state occurs in the surviving ferromagnetic domain surrounded by the diamagnetic domains

Analytical solutions of bound timelike geodesic orbits in Kerr spacetime

We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $\lambda$ as the independent variable. Mino time decouples the radial and polar motion of a particle and hence leads to forms more useful to estimate three fundamental frequencies, radial, polar and azimuthal motion, for the bound timelike geodesics in Kerr spacetime. This paper gives the first derivation of the analytical expressions of the fundamental frequencies. This paper also gives the first derivation of the analytical expressions of all coordinates for the bound timelike geodesics using Mino time. These analytical expressions should be useful not only to investigate physical properties of Kerr geodesics but more importantly to applications related to the estimation of gravitational waves from the extreme mass ratio inspirals.Comment: A typo in the first expression in equation 21 was fixe

Effects of Hydrostatic Pressure and Uniaxial Strain on Spin-Peierls Transition in an Organic Radical Magnet, BBDTA·InCl4

We investigated the effects of hydrostatic pressure and uniaxial strain on the spin-Peierls (SP) transition of an organic radical magnet, benzo[1,2-d:4,5-d\u27]bis[1,3,2]dithiazole(BBDTA)·InCl 4 . It has a one-dimensional coordination polymer structure along its c -axis and its SP transition occurs at 108 K. The SP transition temperature T SP decreased to 99 K at a hydrostatic pressure of 10 kbar, while it increased to 132 K at a uniaxial strain along the c -axis of 8 kbar. The pressure dependences of T SP under these two conditions were discussed by evaluating two parameters, namely, the intrachain interaction 2 J / k B and the effective spin–lattice coupling parameter η, that are related to T SP by the equation T SP =1.6η J / k B . Under ambient pressure, the a - and c -axes of this material shortened monotonically with decreasing temperature, while the b -axis elongated below T SP . In this study, we found the correlation between η and the change in the lattice constant b . 2 J / k B increased with increasing hydrostatic pressure and uniaxial strain, suggesting that the contraction along the c -axis does not depend on the manner of pressurization. From the evaluation of η, the observed variation in T SP is explained by the difference between the changes in b under the two pressurization conditions

Crystal structure, Hirshfeld surface analysis, and physicochemical studies of a new Cu(II) complex with 2-amino-4-methylpyrimidine

International audienceThe chemical preparation, crystal structure, magnetic study and spectroscopic characterization of the new Cu(II) complex with the monodentate ligand 2-amino-4-methylpyrimidine [Cu2(CH3COO)4(C5N3H7)2] are reported. The copper atoms are surrounded by one nitrogen atom from one 2-amino-4-methylpyrimidine ligand and four oxygen atoms of CH3COO − groups yielding to a penta-coordination of the metal ion. In the structural arrangement, the amino group and the pyrimidine nitrogen atom of neighboring molecules are linked together through a pair of N-H…N hydrogen bonds forming a 1-D corrugated chain running along the [111] direction wherein the complex molecules are located parallel to the (a, c) plane at z = ½. Intermolecular interactions were investigated by Hirshfeld surfaces and contact enrichment tools. Mulliken charge distribution, molecular electrostatic potential (MEP) maps and HOMO and LUMO energy gaps have been computed. The vibrational absorption bands were identified by infrared spectroscopy. Magnetic properties were also studied to characterize the complex

Narrowing Down the Mapping of Plant Sex-Determination Regions Using New Y-Chromosome-Specific Markers and Heavy-Ion Beam Irradiation-Induced Y-Deletion Mutants in Silene latifolia

Silene latifolia is a well-studied model system for plant XY sex determination. Three maleness factors are thought to function on the Y chromosome, gynoecium suppression factor (GSF), stamen-promoting factor (SPF), and male fertility factor (MFF), and their deletions result in hermaphrodites, anther defects, and pollen defects, respectively. Although a framework map of the Y chromosome exists, the sex determination genes have not been identified, and no markers close enough to potentially be used for BAC library screening are yet available. The analysis of Y deletion mutants by Y-chromosome-specific STS markers is an efficient way to isolate sex determination regions, but more Y-specific STS markers are needed to accelerate the exploration of sex determination factors. Herein, we report a marker design method that uses simple sequence repeats, which is especially effective on the Y chromosome of S. latifolia because it contains many simple sequence repeats. Six new Y-chromosome-specific STS markers were obtained, SmicSy1–6. These were used to detect relatively small Y deletion sites in heavy-ion beam irradiation-induced mutants. The mapping of male sex determination regions was narrowed down by using more markers and smaller-sized Y deletion mutants. One new marker, SmicSy6, is a proximal marker to SPF and, thus, a second index for SPF. The region including SPF is thought to be located between two SPF proximal markers. The flower phenotype correlates with the deletion size of SPF using SPF proximal markers. These findings represent new progress in isolating the sex determination factor, which has been studied for more than 50 years