The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: I. circular orbits

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits; and develop an analysis that is independent of and complements radiation reaction models. For a Schwarzschild black hole, the polar orbits represent the abutment between the prograde and retrograde orbits at which Q is at its maximum value for given values of latus rectum (l) and eccentricity (e). The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or abutment, to be moved towards greater orbital inclination; thus it no longer cleanly separates prograde and retrograde orbits. To characterise the abutment of a Kerr black hole (KBH), we first investigated the last stable orbit (LSO) of a test-particle about a KBH, and then extended this work to general orbits. To develop a better understanding of the evolution of Q we developed analytical formulae for Q in terms of l, e, and S to describe elliptical orbits at the abutment, polar orbits, and last stable orbits (LSO). By knowing the analytical form of dQ/dl at the abutment, we were able to test a 2PN flux equation for Q. We also used these formulae to numerically calculate the di/dl of hypothetical circular orbits that evolve along the abutment. From these values we have determined that di/dl = -(122.7S - 36S^3)l^-11/2 -(63/2 S + 35/4 S^3) l^-9/2 -15/2 S l^-7/2 -9/2 S l^-5/2. Thus the abutment becomes an important analytical and numerical laboratory for studying the evolution of Q and i in Kerr spacetime and for testing current and future radiation back-reaction models for near-polar retrograde orbits.Comment: 51 pages, 8 figures, accepted by Classical and Quantum Gravity on September 22nd, 201

Multilocus perspectives on the monophyly and phylogeny of the order Charadriiformes (Aves)

BACKGROUND: The phylogeny of shorebirds (Aves: Charadriiformes) and their putative sister groups was reconstructed using approximately 5 kilobases of data from three nuclear loci and two mitochondrial genes, and compared to that based on two other nuclear loci. RESULTS: Charadriiformes represent a monophyletic group that consists of three monophyletic suborders Lari (i.e., Laridae [including Sternidae and Rynchopidae], Stercorariidae, Alcidae, Glareolidae, Dromadidae, and Turnicidae), Scolopaci (i.e., Scolopacidae [including Phalaropidae], Jacanidae, Rostratulidae, Thinocoridae, Pedionomidae), and Charadrii (i.e., Burhinidae, Chionididae, Charadriidae, Haematopodidae, Recurvirostridae, and presumably Ibidorhynchidae). The position of purported "gruiform" buttonquails within Charadriiformes is confirmed. Skimmers are most likely sister to terns alone, and plovers may be paraphyletic with respect to oystercatchers and stilts. The Egyptian Plover is not a member of the Glareolidae, but is instead relatively basal among Charadrii. None of the putative sisters of Charadriiformes were recovered as such. CONCLUSION: Hypotheses of non-monophyly and sister relationships of shorebirds are tested by multilocus analysis. The monophyly of and interfamilial relationships among shorebirds are confirmed and refined. Lineage-specific differences in evolutionary rates are more consistent across loci in shorebirds than other birds and may contribute to the congruence of locus-specific phylogenetic estimates in shorebirds

The Alignment of the Magnetic Field and Collimated Outflows in Star-forming Regions: the Case of NGC 2071

The magnetic field is believed to play a crucial role in the process of star formation. From the support it provides during the initial collapse of molecular clouds to the creation of strong collimated jets responsible for large mass losses, current theories predict its importance in many different stages during the formation of stars. Here we report on observational evidence which tests one aspect that can be inferred from these theories: the alignment between the local magnetic field and collimated bipolar outflows in such environments. There is good evidence of an alignment in the case of NGC 2071.Comment: 11 pages, 4 figure

A Study of Elliptical Last Stable Orbits About a Massive Kerr Black Hole

The last stable orbit (LSO) of a compact object (CO) is an important boundary condition when performing numerical analysis of orbit evolution. Although the LSO is already well understood for the case where a test-particle is in an elliptical orbit around a Schwarzschild black hole (SBH) and for the case of a circular orbit about a Kerr black hole (KBH) of normalised spin, S (|J|/M^2, where J is the spin angular momentum of the KBH); it is worthwhile to extend our knowledge to include elliptical orbits about a KBH. This extension helps to lay the foundation for a better understanding of gravitational wave (GW) emission. The mathematical developments described in this work sprang from the use of an effective potential (V) derived from the Kerr metric, which encapsulates the Lense-Thirring precession. That allowed us to develop a new form of analytical expression to calculate the LSO Radius for circular orbits (R_LSO) of arbitrary KBH spin. We were then able to construct a numerical method to calculate the latus rectum (l_LSO) for an elliptical LSO. Abstract Formulae for E^2 (square of normalised orbital energy) and L^2 (square of normalised orbital angular momentum) in terms of eccentricity, e, and latus rectum, l, were previously developed by others for elliptical orbits around an SBH and then extended to the KBH case; we used these results to generalise our analytical l_LSO equations to elliptical orbits. LSO data calculated from our analytical equations and numerical procedures, and those previously published, are then compared and found to be in excellent agreement.Comment: 42 pages, 9 figures, accepted for publication in Classical and Quantum Gravit

Probing the Magnetic Field with Molecular Ion Spectra

Observations of the effect of the magnetic field on its environment are usually achieved with techniques which rely on the interaction with the spin of the particles under study. Because of the relative weakness of this effect, extraction of the field characteristics proves to be a most challenging task. We take a totally different approach to the problem and show that the manifestation of the magnetic field can be directly observed by means of a comparison of the spectra of molecular ions with those of neutral molecules. This takes advantage of the strong cyclotron interaction between the ions and the field, but requires the presence of flows or turbulent motion in the gas. We compare our theory to data obtained on the OMC-1, OMC-2, OMC-3 and DR21(OH) molecular clouds.Comment: 16 pages, 3 figures, 2 table

Polarisation Observations of H2_{2}O JK−1K1=532−441J_{K_{-1}K_{1}} = 5_{32} - 4_{41} 620.701 GHz Maser Emission with Herschel/HIFI in Orion KL

Context. The high intensities and narrow bandwidths exhibited by some astronomical masers make them ideal tools for studying star-forming giant molecular clouds. The water maser transition $J_{K_{-1}K_{1}}=5_{32}-4_{41}$ at 620.701 GHz can only be observed from above Earth's strongly absorbing atmosphere; its emission has recently been detected from space. Aims. We sought to further characterize the star-forming environment of Orion KL by investigating the linear polarisation of a source emitting a narrow 620.701 GHz maser feature with the heterodyne spectrometer HIFI on board the Herschel Space Observatory. Methods. High-resolution spectral datasets were collected over a thirteen month period beginning in 2011 March, to establish not only the linear polarisation but also the temporal variability of the source. Results. Within a $3\sigma$ uncertainty, no polarisation was detected to an upper limit of approximately 2%. These results are compared with coeval linear polarisation measurements of the 22.235 GHz $J_{K_{-1}K_{1}}=6_{16}-5_{23}$ maser line from the Effelsberg 100-m radio telescope, typically a much stronger maser transition. Although strongly polarised emission is observed for one component of the 22.235 GHz maser at 7.2 km s$^{-1}$, a weaker component at the same velocity as the 620.701 GHz maser at 11.7 km s$^{-1}$ is much less polarised.Comment: Accepted for publication in A&

Phylogeny of ‘core Gruiformes’ (Aves: Grues) and resolution of the Limpkin–Sungrebe problem

Abstract Opinions on the systematic relationships of birds in the avian order Gruiformes have been as diverse as the families included within it. Despite ongoing debate over monophyly of the order and relationships among its various members, recent opinion has converged on the monophyly of a ''core'' group of five families classified as the suborder Grues: the rails (Rallidae), the cranes (Gruidae), the Limpkin (Aramidae), the trumpeters (Psophiidae), and the finfoots (Heliornithidae). We present DNA sequence data from four mitochondrial (cytochrome b, 12S rRNA, Valine tRNA, and 16S rRNA) and three nuclear loci (intron 7 of b-fibrinogen, intron 5 of alcohol dehydrogenase-I, and introns 3 through 5 of glyceraldehyde-3-phosphate dehydrogenase) to test previous hypotheses of interfamilial relationships within Grues, with particular attention to the enigmatic family Heliornithidae. Separate and combined analyses of these gene sequences confirm the monophyly of Grues as a whole, and of the five families individually, including all three species of Heliornithidae. The preferred topology unambiguously supports relationships among four of the five families, with only the position of Psophiidae remaining equivocal. Bayesian ''relaxed-clock'' dating methods suggest that the divergences of the three heliornithid species occurred in the mid-Tertiary, suggesting that their present disjunct pantropical distribution is a result of early-to mid-Tertiary dispersal

The Distribution of Ortho-H_2D+(1_1,0 - 1_1,1) in L1544: Tracing the Deuteration Factory in Prestellar Cores

Prestellar cores are unique laboratories for studies of the chemical and physical conditions preceding star formation. We observed the prestellar core L1544 in the fundamental transition of ortho-H2D+ (1_1,0-1_1,1) at different positions over 100", and found a strong correlation between its abundance and the CO depletion factor. We also present a tentative detection of the fundamental transition of para-D2H+ (1_1,0-1_0,1) at the dust emission peak. Maps in N2H+, N2D+, HCO+ and DCO+ are used, and interpreted with the aid of a spherically symmetric chemical model that predicts the column densities and abundances of these species as a function of radius. The correlation between the observed deuterium fractionation of H3+, N2H+ and HCO+ and the observed integrated CO depletion factor across the core can be reproduced by this chemical model. In addition a simpler model is used to study the H2D+ ortho-to-para ratio. We conclude that, in order to reproduce the observed ortho-H2D+ observations, the grain radius should be larger than 0.3 microns.Comment: 24 pages, 9 figures, accepted in ApJ (to be published in July 2006