Operator pencil passing through a given operator

Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight \lo on a manifold $M$. One can consider a pencil of operators \hPi(\Delta)=\{\Delta_\l\} passing through the operator $\Delta$ such that any \Delta_\l is a linear differential operator acting on densities of weight \l. This pencil can be identified with a linear differential operator \hD acting on the algebra of densities of all weights. The existence of an invariant scalar product in the algebra of densities implies a natural decomposition of operators, i.e. pencils of self-adjoint and anti-self-adjoint operators. We study lifting maps that are on one hand equivariant with respect to divergenceless vector fields, and, on the other hand, with values in self-adjoint or anti-self-adjoint operators. In particular we analyze the relation between these two concepts, and apply it to the study of \diff(M)-equivariant liftings. Finally we briefly consider the case of liftings equivariant with respect to the algebra of projective transformations and describe all regular self-adjoint and anti-self-adjoint liftings.Comment: 32 pages, LaTeX fil

Design of optimal transfers between North and South Pole-sitter orbits

Recent studies have shown the feasibility of an Earth pole-sitter mission, where a spacecraft follows the Earth’s polar axis to have a continuous, hemispherical view of one of the Earth’s Poles. However, due to the tilt of the polar axis, the North and South Poles are alternately situated in darkness for long periods dur-ing the year. This significantly constrains observations and decreases mission scientific return. This paper therefore investigates transfers between north and south pole-sitter orbits before the start of the Arctic and Antarctic winters to maximize scientific return by observing the polar regions only when lit. Clearly, such a transfer can also be employed for the sole purpose of visiting both the North and South Poles with one single spacecraft during one single mission. To enable such a novel transfer, two types of propulsion are proposed, including so-lar electric propulsion (SEP) and a hybridization of SEP with solar sailing. A di-rect optimization method based on pseudospectral transcription is used to find both transfers that minimize the SEP propellant consumption and transfers that trade-off SEP propellant consumption and observation time of the Poles. Also, a feedback control is developed to account for non-ideal properties of the solar sail. It is shown that, for all cases considered, hybrid low-thrust propulsion out-performs the pure SEP case, while enabling a transfer that would not be feasible with current solar sail technology

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill–Clohessy–Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Δv requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology

Time-delayed feedback control in astrodynamics

In this paper we present time-delayed feedback control (TDFC) for the purpose of autonomously driving trajectories of nonlinear systems into periodic orbits. As the generation of periodic orbits is a major component of many problems in astodynamics we propose this method as a useful tool in such applications. To motivate the use of this method we apply it to a number of well known problems in the astrodynamics literature. Firstly, TDFC is applied to control in the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Secondly, we apply TDFC to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid) and finally, we apply TDFC to eliminate the drift between two satellites in low Earth orbits to ensure their relative motion is bounded

Parsec-scale HI absorption structure in a low-redshift galaxy seen against a Compact Symmetric Object

We present global VLBI observations of the 21-cm transition of atomic hydrogen seen in absorption against the radio source J0855+5751. The foreground absorber (SDSS~J085519.05+575140.7) is a dwarf galaxy at $z$ = 0.026. As the background source is heavily resolved by VLBI, the data allow us to map the properties of the foreground HI gas with a spatial resolution of 2pc. The absorbing gas corresponds to a single coherent structure with an extent $>$35pc, but we also detect significant and coherent variations, including a change in the HI optical depth by a factor of five across a distance of $\leq$6pc. The large size of the structure provides support for the Heiles & Troland model of the ISM, as well as its applicability to external galaxies. The large variations in HI optical depth also suggest that caution should be applied when interpreting $T_S$ measurements from radio-detected DLAs. In addition, the distorted appearance of the background radio source is indicative of a strong jet-cloud interaction in its host galaxy. We have measured its redshift ($z$ = 0.54186) using optical spectroscopy on the William Herschel Telescope and this confirms that J0855+5751 is a FRII radio source with a physical extent of $<$1kpc and supports the previous identification of this source as a Compact Symmetric Object. These sources often show absorption associated with the host galaxy and we suggest that both HI and OH should be searched for in J0855+5751.Comment: 14 pages and 10 figures. Accepted for publication in MNRA

Deep Radio Imaging of Globular Clusters and the Cluster Pulsar Population

We have obtained deep multifrequency radio observations of seven globular clusters using the Very Large Array and the Australia Telescope Compact Array. Five of these, NGC 6440, NGC 6539, NGC 6544, NGC 6624 and Terzan 5 had previously been detected in a shallower survey for steep spectrum radio sources in globular clusters (Fruchter and Goss 1990). The sixth, the rich globular cluster, Liller 1, had heretofore been undetected in the radio, and the seventh, 47 Tucanae, was not included in our original survey. High resolution 6 and 20 cm images of three of the clusters, NGC 6440, NGC 6539, NGC 6624 reveal only point sources coincident with pulsars which have been discovered subsequent to our first imaging survey. 21 and 18 cm images reveal several point sources within a few core-radii of the center of 47 Tuc. Two of these are identified pulsars, and a third, which is both variable and has a steep spectrum, is also most likely a pulsar previously identified by a pulsed survey. However, the 6, 20 and 90 cm images of NGC 6544, Liller 1 and Terzan 5 display strong steep-spectrum emission which cannot be associated with known pulsars. The image of the rich cluster Terzan 5 displays numerous point sources within $30''$, or 4 core radii of the cluster center. The density of these objects rises rapidly toward the core, where an elongated region of emission is found. The brightest individual sources, as well as the extended emission, possess the steep spectra expected of pulsars. Furthermore, the flux distribution of the sources agrees well with the standard pulsar luminosity function. The total luminosity and number of objects observed suggest that Terzan 5 contains more pulsars than any other Galactic globular cluster.Comment: 33 pages, 6 Postscript figures; Accepted for publication in the Astrophysical Journal; abstract abridged. PDF version also available at http://nemesis.stsci.edu/~fruchter/fg99/fg99.pd

Afterslip Moment Scaling and Variability from a Global Compilation of Estimates

Aseismic afterslip is postseismic fault sliding that may significantly redistribute crustal stresses and drive aftershock sequences. Afterslip is typically modeled through geodetic observations of surface deformation on a case-by-case basis, thus questions of how and why the afterslip moment varies between earthquakes remain largely unaddressed. We compile 148 afterslip studies following 53 Mw6.0–9.1 earthquakes, and formally analyze a subset of 88 well-constrained kinematic models. Afterslip and coseismic moments scale near-linearly, with a median Spearman's rank correlation coefficient (CC) of 0.91 after bootstrapping (95% range: 0.89–0.93). We infer that afterslip area and average slip scale with coseismic moment as urn:x-wiley:21699313:media:jgrb55593:jgrb55593-math-0001 and urn:x-wiley:21699313:media:jgrb55593:jgrb55593-math-0002, respectively. The ratio of afterslip to coseismic moment (Mrel) varies from 300% (interquartile range: 9%–32%). Mrel weakly correlates with Mo (CC: −0.21, attributed to a publication bias), rupture aspect ratio (CC: −0.31), and fault slip rate (CC: 0.26, treated as a proxy for fault maturity), indicating that these factors affect afterslip. Mrel does not correlate with mainshock dip, rake, or depth. Given the power-law decay of afterslip, we expected studies that started earlier and spanned longer timescales to capture more afterslip, but Mrel does not correlate with observation start time or duration. Because Mrel estimates for a single earthquake can vary by an order of magnitude, we propose that modeling uncertainty currently presents a challenge for systematic afterslip analysis. Standardizing modeling practices may improve model comparability, and eventually allow for predictive afterslip models that account for mainshock and fault zone factors to be incorporated into aftershock hazard models

Redshifted formaldehyde from the gravitational lens B0218+357

The gravitational lens toward B0218+357 offers the unique possibility to study cool moderately dense gas with high sensitivity and angular resolution in a cloud that existed half a Hubble time ago. Observations of the radio continuum and six formaldehyde (H2CO) lines were carried out with the VLA, the Plateau de Bure interferometer, and the Effelsberg 100-m telescope. Three radio continuum maps indicate a flux density ratio between the two main images, A and B, of ~ 3.4 +/- 0.2. Within the errors the ratio is the same at 8.6, 14.1, and 43 GHz. The 1_{01}-0_{00} line of para-H2CO is shown to absorb the continuum of image A. Large Velocity Gradient radiative transfer calculations are performed to reproduce the optical depths of the observed two cm-wave "K-doublet" and four mm-wave rotational lines. These calculations also account for a likely frequency-dependent continuum cloud coverage. Confirming the diffuse nature of the cloud, an n(H2) density of < 1000 cm^{-3} is derived, with the best fit suggesting n(H2) ~ 200 cm^{-3}. The H2CO column density of the main velocity component is ~5 * 10^{13} cm^{-2}, to which about 7.5 * 10^{12} cm^{-2} has to be added to also account for a weaker feature on the blue side, 13 km/s apart. N(H2CO)/N(NH3) ~ 0.6, which is four times less than the average ratio obtained from a small number of local diffuse (galactic) clouds seen in absorption. The ortho-to-para H2CO abundance ratio is 2.0 - 3.0, which is consistent with the kinetic temperature of the molecular gas associated with the lens of B0218+357. With the gas kinetic temperature and density known, it is found that optically thin transitions of CS, HCN, HNC, HCO+, and N2H+ (but not CO) will provide excellent probes of the cosmic microwave background at redshift z=0.68.Comment: Accepted for A&A, 8 Pages, 3 Figures, 5 Table

Pulsar Radio Emission Altitude from Curvature Radiation

We assume that the relativistic sources moving along the dipolar magnetic field lines emit curvature radiation. The beamed emission occurs in the direction of tangents to the field lines, and to receive it, the sight line must align with the tangent within the beaming angle 1/gamma, where gamma is the particle Lorentz factor. By solving the viewing geometry in an inclined and rotating dipole magnetic field, we show that, at any given pulse phase, observer tends to receive radiation only from the specific heights allowed by the geometry. We find outer conal components are emitted at higher altitudes compared to inner components including the core. At any pulse phase, low frequency emission comes from higher altitudes than high frequency emission. We have modeled the emission heights of pulse components of PSR B0329+54, and estimated field line curvature radii and particle Lorentz factors in the emission regions.Comment: 14 pages, 3 figures. Accepted for Astrophysical Journal, 200

Chemical Raman Enhancement of Organic Adsorbates on Metal Surfaces

Using a combination of first-principles theory and experiments, we provide a quantitative explanation for chemical contributions to surface-enhanced Raman spectroscopy for a well-studied organic molecule, benzene thiol, chemisorbed on planar Au(111) surfaces. With density functional theory calculations of the static Raman tensor, we demonstrate and quantify a strong mode-dependent modification of benzene thiol Raman spectra by Au substrates. Raman active modes with the largest enhancements result from stronger contributions from Au to their electron-vibron coupling, as quantified through a deformation potential, a well-defined property of each vibrational mode. A straightforward and general analysis is introduced that allows extraction of chemical enhancement from experiments for specific vibrational modes; measured values are in excellent agreement with our calculations.Comment: 5 pages, 4 figures and Supplementary material included as ancillary fil