Tidal disruptions: A continuum theory for solid bodies

Although the theory of Roche 1847 for the tidal disruption limits of orbiting satellites assumes a fluid body, a length to diameter of exactly 2.07:1, and a particular body orientation, the theory is commonly applied to the satellites of the Solar System and to small asteroids and comets passing nearby a planet. Clearly these bodies are neither fluid nor generally are that elongated, so a more appropriate theory is needed. Here we present exact analytical results for the distortion and disruption limits of solid spinning ellipsoidal bodies subjected to tidal forces, using the Drucker-Prager strength model with zero cohesion. It is the appropriate model for dry granular materials such as sands and rocks, for rubble-pile asteroids and comets, and for larger satellites, asteroids and comets where the cohesion can be ignored. This study uses the same approach as the studies of spin limits for solid ellipsoidal bodies given in [Holsapple, K.A., 2001. Icarus 154, 432-448; Holsapple, K.A., 2004. Icarus 172, 272-303]. It is a static theory that predicts conditions for breakup and predicts the nature of the deformations at the limit state, but does not track the dynamics of the body as it comes apart. The strength is characterized by a single material parameter associated with an angle of friction, which can range from zero to 90°. The case with zero friction angle has no shear strength whatsoever, so it is then the model of a fluid or gas. The case of 90° represents a material that cannot fail in shear, but still has zero tensile strength. Typical dry soils have angles of friction of 30°-40°. Since the static fluid case is included in the theory as a special case, the classical results of Roche [Roche, E.A., 1847. Acad. Sci. Lett. Montpelier. Mem. Section Sci. 1, 243-262] and Jeans [Jeans, J.H., 1917. Mem. R. Astron. Soc. London 62, 1-48] are included and re-derived in their entirety; but the general solid case has much more variety and applicability. We consider both the spin-locked case, appropriate for most satellites of the Solar System; and the zero spin case, a possible case for a passing stray body. Detailed plots of many special cases are presented, in terms of shape, orientation and mass densities. A very typical result gives a closest approach d=1.5(ρ/ρP)^1/3R in terms of the planet radius R, and the satellite and planet mass densities ρ and ρP. We also use the theory to distinguish between conditions allowing global shape changes leading to new equilibrium states, or those leading to complete disruption. We apply the theory to the potentially hazardous Asteroid 99942 Apophis due to pass very near the Earth in 2029, and conclude it is extremely unlikely to experience any tidal readjustments during its passage. The states of many of the satellites of the Solar System are compared to the theory, and we find that all are well within their tidal disruption limits for expected values of the internal friction.     

Evidence for ponding and catastrophic floods in central Valles Marineris, Mars

The Valles Marineris canyon system of Mars is closely related to large flood channels, some of which emerge full born from chaotic terrain in canyon floors. Coprates Chasma, one of the largest Valles Marineris canyons, is connected at its west end to Melas Chasma and on its east end to chaotic terrain-filled Capri and Eos Chasmata. The area from central Melas to Eos Chasmata contains a 1500 km long and about 1 km deep depression in its floor. Despite the large volumes of groundwater that likely discharged from chaotic terrain in this depression, no evidence of related fluvial activity has thus far been reported. We present an analysis of the regional topography which, together with photogeologic interpretation of available imagery, suggests that ponding due to late Hesperian discharge of water possibly produced a lake (mean depth 842 m) spanning parts of the Valles Marineris depression (VMD). Overflow of this lake at its eastern end resulted in delivery of water to downstream chaos regions and outflow channels. Our ponding hypothesis is motivated primarily by the identification of scarp and terrace features which, despite a lateral spread of about 1500 km, have similar elevations. Furthermore, these elevations correspond to the maximum ponding elevation of the region (−3560 m). Simulated ponding in the VMD yields an overflow point at its eastern extremity, in Eos Chasma. The neighborhood of this overflow point contains clear indicators of fluvial erosion in a consistent east-west orientation.     

Map making in small field modulated CMB polarization experiments: approximating the maximum likelihood method

Map making presents a significant computational challenge to the next generation of kilopixel cosmic microwave background polarization experiments. Years worth of time ordered data (TOD) from thousands of detectors will need to be compressed into maps of the T , Q and U Stokes parameters. Fundamental to the science goal of these experiments, the observation of B modes, is the ability to control noise and systematics. In this paper, we consider an alternative to the maximum likelihood method, called destriping , where the noise is modelled as a set of discrete offset functions and then subtracted from the time stream. We compare our destriping code (Descart: the DEStriping CARTographer) to a full maximum likelihood mapmaker, applying them to 200 Monte Carlo simulations of TOD from a ground-based, partial-sky polarization modulation experiment. In these simulations, the noise is dominated by either detector or atmospheric  1/ f   noise. Using prior information of the power spectrum of this noise, we produce destriped maps of T , Q and U which are negligibly different from optimal. The method does not filter the signal or bias the E- or B-mode power spectra. Depending on the length of the destriping baseline, the method delivers between five and 22 times improvement in computation time over the maximum likelihood algorithm. We find that, for the specific case of single detector maps, it is essential to destripe the atmospheric  1/ f   in order to detect B modes, even though the Q and U signals are modulated by a half-wave plate spinning at 5 Hz.     

Bayesian modelling of clusters of galaxies from multifrequency-pointed Sunyaev–Zel'dovich observations

We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev–Zel'dovich effect. We use the recently developed multinest technique to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the presence of primary CMB signal, radio point sources (detected as well as an unresolved background) and receiver noise, show that our algorithm is able to analyse jointly the data from six frequency channels, sample the posterior space of the model and calculate the Bayesian evidence very efficiently on a single processor. We also illustrate the robustness of our detection process by applying it to a field with radio sources and primordial CMB but no cluster, and show that indeed no cluster is identified. The extension of our methodology to the detection and modelling of multiple clusters in multi-frequency SZ survey data will be described in a future work.     

Sources of insoluble inclusions in stratospheric sulfate particles

Abstract– Properties of aerosol collected in the stratosphere from altitudes of 20–45 km are reviewed. Removal of the soluble material from predominantly sulfate particles collected at 20 km revealed the presence of insoluble individual particles, or small groups of them, typically 40–50 nm in diameter. The size distribution of components of chain aggregates found above 35 km was almost identical, suggesting that rupture of the chains by condensing sulfuric acid, as they fell into the sulfate layer from above, was the source of the inclusions. Particles collected above 35 km on thin films of metal all showed the presence of a partially volatile liquid. On a copper surface, the liquid was stabilized, and of greater extent than the solid component. Three observations suggest that the upper stratospheric particles and their associated liquid were partly or wholly organic and derived from cometary dust too small to be heated on entering the atmosphere. These are: (1) the presence of a liquid that reacts with copper and the similarity to the behavior of particles collected on copper during a manned space flight, (2) their morphological similarity to published photographs of particles collected in the mesosphere from rockets, (3) the consistency with recent spacecraft observations of the size distribution of components sub‐10 μm aggregates in cometary dust and the presence within them of carbon compounds.     

地下开采块状硫化物矿的一种简化经济滤波器

隐伏矿产资源评价和勘查早期，以及计划阶段，需要建立预可行成本模式。勘查过程中，区分经济与非经济矿床的这些成本模式有助于勘查企业集中在能获益的靶区勘查。资源评价过程中，这些模式用来排除那些即便发现但没有经济价值的矿床。美国矿业局（USBM）先前建立的简化成本模式就是为了解决这一问题的（Camm，1991）。这些成本模式采用矿床储量、品位和埋深参数评估运行成本和固定成本，也是USBM预可行分析软件的一部分（Smith，1991）。     

Generalized limits to the number of light particle degrees of freedom from big bang nucleosynthesis

We compute the big bang nucleosynthesis limit on the number of light neutrino degrees of freedom in a model-independent likelihood analysis based on the abundances of ⁴He and ⁷Li. We use the two-dimensional likelihood functions to simultaneously constrain the baryon-to-photon ratio and the number of light neutrinos for a range of ⁴He abundances Y_p = 0.225–0.250, as well as a range in primordial ⁷Li abundances from (1.6 to 4.1) ×10⁻¹⁰. For (⁷Li/H)_p = 1.6 × 10⁻¹⁰, as can be inferred from the ⁷Li data from Population II halo stars, the upper limit to N_ν based on the current best estimate of the primordial ⁴He abundance of Y_p = 0.238 is N_ν < 4.3 and varies from N_ν < 3.3 (at 95% C.L.) when Y_p = 0.225 to N_ν < 5.3 when Y_p = 0.250. If ⁷Li is depleted in these stars the upper limit to N_ν is relaxed. Taking (⁷Li/H)_p = 4.1 × 10⁻¹⁰, the limit varies from N_ν < 3.9 when Y_p = 0.225 to N_ν 6 when Y_p = 0.250. We also consider the consequences on the upper limit to N_ν if recent observations of deuterium in high-redshift quasar absorption-line systems are confirmed.     

First XMM-Newton observations of strongly magnetic cataclysmic variables – II. Timing studies of DP Leo and WW Hor

XMM-Newton was used to observe two eclipsing, magnetic cataclysmic variables, DP Leo and WW Hor, continuously for three orbital cycles each. Both systems were in an intermediate state of accretion. For WW Hor we also obtained optical light curves with the XMM-Newton Optical Monitor and from ground-based observations. Our analysis of the X-ray and optical light curves allows us to constrain physical and geometrical parameters of the accretion regions and derive orbital parameters and eclipse ephemerides of the systems. For WW Hor we directly measure horizontal and vertical temperature variations in the accretion column. From comparisons with previous observations we find that changes in the accretion spot longitude are correlated with the accretion rate. For DP Leo the shape of the hard X-ray light curve is not as expected for optically thin emission, showing the importance of optical depth effects in the post-shock region. We find that the spin period of the white dwarf is slightly shorter than the orbital period and that the orbital period is decreasing faster than expected for energy loss by gravitational radiation alone.     

Solar limb darkening

The coefficients of several polynomial representations of the limb darkening at 62 wavelengths in the UV and visible portions of the solar spectrum obtained at the McMath Solar Telescope are presented in tabular form. Full corrections for scattered light and seeing have been included in the reductions.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Valences of Ti,Cr, and V in Apollo 17 high-Ti and very low-Ti basalts and implications for their formation

To assess the variability of redox states among mare basalt source regions, investigation of the valence of Ti, Cr, and V and the coordination environment of Ti in pyroxene and olivine in lunar rocks via XANES (X-ray absorption near-edge structure) spectroscopy has been extended to Apollo 17 basalts: two high-Ti (70017 and 74275) hand samples, and three very low-Ti (70006,371, 70007,289B, and 70007,296) basalt fragments from the Apollo 17 deep drill core. Valences of Ti in pyroxene of both suites range from 3.6 to 4, or from 40% to 0% Ti³⁺, averaging 15–20% Ti³⁺. Assuming Ti³⁺ is more compatible in pyroxene than Ti⁴⁺, then even lower Ti³⁺ proportions are indicated for the parental melts. The VLT pyroxene exhibits a slightly wider range of V valences (2.57–2.96) than the high-Ti pyroxene (2.65–2.86) and a much wider range of Cr valences (2.32–2.80 versus 2.68–2.86); Cr is generally reduced in VLT pyroxene compared to high-Ti pyroxene. Valences of Ti and Cr in VLT pyroxene become less reduced with increasing FeO contents, possibly indicating change in oxygen fugacity during crystallization. Olivine in all samples has very low (<20%) proportions of Ti³⁺, with no Ti³⁺ and higher proportions of Ti in tetrahedral coordination in the VLTs than in the high-Ti basalts. Olivine in 74275, including that in a dunite clast, has much higher proportions of Cr²⁺ than the pyroxene in that sample, consistent with previous studies indicating that the olivine grains in this sample are xenocrysts and possibly indicating oxidation just prior to pyroxene crystallization. Results for this sample, the VLTs, and previously studied Apollo 14 and 15 basalts all indicate that mare magmas were in reducing environments at depth, as recorded in early crystallization products, and that later, presumably shallower environments, were relatively oxidizing; single, characteristic fO₂s of formation cannot be assigned to these samples. A process likely to account for this feature seen in multiple samples is loss by degassing of a reducing, H-rich vapor (probably H₂) during ascent and/or eruption, causing oxidation of the residual melt, recorded in relatively late-crystallized pyroxene.