Understanding the behavior of Prometheus and Pandora

We revisit the dynamics of Prometheus and Pandora, two small moons flanking Saturn's F ring. Departures of their orbits from freely precessing ellipses result from mutual interactions via their 121:118 mean motion resonance. Motions are chaotic because the resonance is split into four overlapping components. Orbital longitudes were observed to drift away from predictions based on Voyager ephemerides. A sudden jump in mean motions took place close to the time at which the orbits' apses were antialigned in 2000. Numerical integrations reproduce both the longitude drifts and the jumps. The latter have been attributed to the greater strength of interactions near apse antialignment (every 6.2 yr), and it has been assumed that this drift-jump behavior will continue indefinitely. We re-examine the dynamics of the Prometheus-Pandora system by analogy with that of a nearly adiabatic, parametric pendulum. In terms of this analogy, the current value of the action of the satellite system is close to its maximum in the chaotic zone. Consequently, at present, the two separatrix crossings per precessional cycle occur close to apse antialignment. In this state libration only occurs when the potential's amplitude is nearly maximal, and the “jumps” in mean motion arise during the short intervals of libration that separate long stretches of circulation. Because chaotic systems explore the entire region of phase space available to them, we expect that at other times the Prometheus-Pandora system would be found in states of medium or low action. In a low action state it would spend most of the time in libration, and separatrix crossings would occur near apse alignment. We predict that transitions between these different states can happen in as little as a decade. Therefore, it is incorrect to assume that sudden changes in the orbits only happen near apse antialignment.     

QUEST on DASI: a South Pole CMB polarization experiment

QUEST on DASI is a ground-based, high-sensitivity, high-resolution (ℓ_max2500) experiment designed to map CMB polarization at 100 and 150 GHz and to measure the power spectra from E-modes, B-modes from lensing of the CMB, and B-modes from primordial gravitational waves. The experiment comprises a 2.6 m Cassegrain optical system, equipped with an array of 62 polarization-sensitive bolometers (PSBs), located at the South Pole. The instrument is designed to minimize systematic effects; features include differencing of pairs of orthogonal PSBs within a single feed, a rotatable achromatic waveplate, and axisymmetric rotatable optics. In addition the South Pole location allows both repeatable and highly controlled observations. QUEST on DASI will commence operation in early 2005.     

Magnetic remanence in the Murchison meteorite

Abstract— The Murchison meteorite is a carbonaceous chondrite containing a small amount of chondrules, various inclusions, and matrix with occasional porphyroblasts of olivine and/or pyroxene. It also contains amino acids that may have served as the necessary components for the origin of life. Magnetic analyses of Murchison identify an ultrasoft magnetic component due to superparamagnetism as a significant part of the magnetic remanence. The rest of the remanence may be due to electric discharge in the form of lightning bolts that may have formed the amino acids. The level of magnetic remanence does not support this possibility and points to a minimum ambient field of the remanence acquisition. We support our observation by showing that normalized mineral magnetic acquisition properties establish a calibration curve suitable for rough paleofield determination. When using this approach, 1–2% of the natural remanence left in terrestrial rocks with TRM and/or CRM determines the geomagnetic field intensity irrespective of grain size or type of magnetic mineral (with the exception of hematite). The same method is applied to the Murchison meteorite where the measured meteorite remanence determines the paleofield minimum intensity of 200–2000 nT during and/or after the formation of the parent body.     

Origin of chaos in the Prometheus-Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr⁻¹, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr⁻¹ arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.     

Parameter information from non-linear cosmological fields

We develop a general formalism for analysing parameter information from non-Gaussian cosmic fields. The method can be adapted to include the non-linear effects in galaxy redshift surveys, weak lensing surveys and cosmic velocity field surveys as part of parameter estimation. It can also be used as a test of non-Gaussianity of the cosmic microwave background. Generalizing maximum-likelihood analysis to second order, we calculate the non-linear Fisher information matrix and likelihood surfaces in parameter space. To this order we find that the information content is always increased by including non-linearity. Our methods are applied to a realistic model of a galaxy redshift survey, including non-linear evolution, galaxy bias, shot-noise and redshift-space distortions to second order. We find that including non-linearities allows all of the degeneracies between parameters to be lifted. Marginalized parameter uncertainties of a few per cent will then be obtainable using forthcoming galaxy redshift surveys.