Bodily tides near the 1:1 spin-orbit resonance: correction to Goldreich’s dynamical model

Spin-orbit coupling is often described in an approach known as ??the MacDonald torque??, which has long become the textbook standard due to its apparent simplicity. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (Rev Geophys 2:467?C541, 1994), is combined with a convenient assumption that the quality factor Q is frequency-independent (or, equivalently, that the geometric lag angle is constant in time). This makes the treatment unphysical because MacDonald??s derivation of the said formula was, very implicitly, based on keeping the time lag frequency-independent, which is equivalent to setting Q scale as the inverse tidal frequency. This contradiction requires the entire MacDonald treatment of both non-resonant and resonant rotation to be rewritten. The non-resonant case was reconsidered by Efroimsky and Williams (Cel Mech Dyn Astron 104:257?C289, 2009), in application to spin modes distant from the major commensurabilities. In the current paper, we continue this work by introducing the necessary alterations into the MacDonald-torque-based model of falling into a 1-to-1 resonance. (The original version of this model was offered by Goldreich (Astron J 71:1?C7, 1996). Although the MacDonald torque, both in its original formulation and in its corrected version, is incompatible with realistic rheologies of minerals and mantles, it remains a useful toy model, which enables one to obtain, in some situations, qualitatively meaningful results without resorting to the more rigorous (and complicated) theory of Darwin and Kaula. We first address this simplified model in application to an oblate primary body, with tides raised on it by an orbiting zero-inclination secondary. (Here the role of the tidally-perturbed primary can be played by a satellite, the perturbing secondary being its host planet. A planet may as well be the perturbed primary, its host star acting as the tide-raising secondary). We then extend the model to a triaxial primary body experiencing both a tidal and a permanent-figure torque exerted by an orbiting secondary. We consider the effect of the triaxiality on both circulating and librating rotation near the synchronous state. Circulating rotation may evolve toward the libration region or toward a spin faster than synchronous (the so-called pseudosynchronous spin). Which behaviour depends on the orbit eccentricity, the triaxial figure of the primary, and the mass ratio of the secondary and primary bodies. The spin evolution will always stall for the oblate case. For libration with a small amplitude, expressions are derived for the libration frequency, damping rate, and average orientation. Importantly, the stability of pseudosynchronous spin hinges upon the dissipation model. Makarove and Efroimsky (Astrophys J, 2012) have found that a more realistic tidal dissipation model than the corrected MacDonald torque makes pseudosynchronous spin unstable. Besides, for a sufficiently large triaxiality, pseudosynchronism is impossible, no matter what dissipation model is used.     

Babbling brook to thunderous torrent: Using sound to monitor river stage

The passive, ambient sound above the water from a river has previously untapped potential for determining flow characteristics such as stage. Measuring sub-aerial sound could provide a new, efficient way to continuously monitor river stage, without the need for in-stream infrastructure. Previous published work has suggested that there might be a relationship between sound and river stage, but the analysis has been restricted to a narrow range of flow conditions and river morphologies. We present a method to determine site suitability and the process of how to record and analyse sound. Data collected along a 500 m length of the River Washburn during July 2019 is used to determine what makes a site suitable for sound monitoring. We found that sound is controlled by roughness elements in the channel, such as a boulder or weir, which influences the sound produced. On the basis of these findings, we collect audio recordings from six sites around the northeast of England, covering a range of flow conditions and different roughness elements, since 2019. We use data from those sites collected during storms Ciara and Dennis to produce a relationship between this sound and river stage. Our analysis has shown a positive relationship between an R² of 0.73 and 0.99 in all rivers, but requires careful site selection and data processing to achieve the best results. We introduce a filter that is capable of isolating a river's sound from other environmental sound. Future work in examining the role of these roughness elements is required to understand the full extent of this technique. By demonstrating that sound can operate as a hydrometric tool, we suggest that sound monitoring could be used to provide cost-effective monitoring devices, either to detect relative change in a river or, after more research, a reliable stage measurement.     

A new portable in situ flume for measuring critical shear stress on river beds

A new portable in situ flume(PISF)for measuring critical bed shear stress(CBSS)was developed in this study.The PISF consists of an open bottom sediment erosion chamber and an electrically-driven pump.Unlike most existing in situ flumes with similar designs,the new PISF does not rely on monitoring the flow conditions or particle density in the sediment erosion chamber;instead,it is a pre-calibrated flume.The calibration was performed by first determining CBSS of various selected sediment samples of known particle size and density(using the law of the wall),based on flow velocity-depth profiles measured in a 6 m straight open-channel flume using a Particle Image Velocimetry(PIV)system.These same particles of known CBSS were then used in the new in-situ flume under controlled lab conditions to obtain a series of calibration curves of CBSS vs.pump electrical power.A wide variety of particle types and sizes(simulated sediments)were used in this two-step calibration procedure to widen CBSS measurement range and simulate cohesive force effects.The size of the PISF is much smaller and more practical than other similar devices as lamellar flow conditions are not required and it can be applied to a wide range of sediment types including cohesive sediments.     

Multi-wavelength observations of Asteroid 2100 Ra-Shalom

We observed near-Earth asteroid (NEA) 2100 Ra-Shalom over a six-year period, obtaining rotationally resolved spectra in the visible, near-infrared, thermal-infrared, and radar wavelengths. We find that Ra-Shalom has an effective diameter of Deff=2.3±0.2 km, rotation period P=19.793±0.001 h, visual albedo pv=0.13±0.03, radar albedo , and polarization ratio μc=0.25±0.04. We used our radar observations to generate a three-dimensional shape model which shows several structural features of interest. Based on our thermal observations, Ra-Shalom has a high thermal inertia of ∼10³ J m⁻² s^−0.5 K⁻¹, consistent with a coarse or rocky surface and the inferences of others [Harris, A.W., Davies, J.K., Green, S.F., 1998. Icarus 135, 441-450; Delbo, M., Harris, A.W., Binzel, R.P., Pravec, P., Davies, J.K., 2003. Icarus 166, 116-130]. Our spectral data indicate that Ra-Shalom is a K-class asteroid and we find excellent agreement between our spectra and laboratory spectra of the CV3 meteorite Grosnaja. Our spectra show rotation-dependent variations consistent with global variations in grain size. Our radar observations show rotation-dependent variations in radar albedo consistent with global variations in the thickness of a relatively thin regolith.     

Lensing, reddening and extinction effects of Mg ii absorbers from z= 0.4 to 2

Using a sample of almost 7000 strong Mg  ii absorbers with   W ₀ > 1 Å  and  0.4 < z < 2.2  detected in the SDSS DR4 data set, we investigate the gravitational lensing and dust extinction effects they induce on background quasars. After carefully quantifying several selection biases, we isolate the reddening effects as a function of redshift and absorber rest equivalent width, W ₀. We find the amount of dust to increase with cosmic time as  τ( z ) ∝ (1 + z )^−1.1±0.4  , following the evolution of cosmic star density or integrated star formation rate. We measure the reddening effects over a factor of 30 in E ( B − V ) and we find that  τ∝ ( W ₀)^1.9±0.1  , providing us with an important scaling for theoretical modelling of metal absorbers. We also measure the dust-to-metal ratio and find it similar to that of the Milky Way. In contrast to previous studies, we do not detect any gravitational magnification by Mg  ii systems. We measure the upper limit  μ < 1.10  and discuss the origin of the discrepancy. Finally, we estimate the fraction of absorbers missed due to extinction effects and show that it rises from 1 to 50 per cent in the range  1 < W ₀ < 6 Å  . We parametrize this effect and provide a correction for recovering the intrinsic  ∂ N /∂ W ₀  distribution.     

Dynamical friction in modified Newtonian dynamics

We have tested a previous analytical estimate of the dynamical friction time-scale in modified Newtonian dynamics (MOND) with fully non-linear N -body simulations. The simulations confirm that the dynamical friction time-scale is significantly shorter in MOND than in equivalent Newtonian systems, i.e. systems with the same phase-space distribution of baryons and additional dark matter. An apparent conflict between this result and the long time-scales determined for bars to slow and mergers to be completed in previous N -body simulations of MOND systems is explained. The confirmation of the short dynamical-friction time-scale in MOND underlines the challenge that the Fornax dwarf spheroidal poses to the viability of MOND.     

Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields

We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad – Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced “photospheric” and more force-free “chromospheric” vector magnetic field boundary data derived from the model. When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field’s free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though, like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. On 07/07/2007, the NLFFF team was saddened by the news that Tom Metcalf had died as the result of an accident. We remain grateful for having had the opportunity to benefit from his unwavering dedication to the problems encountered in attempting to understand the Sun’s magnetic field; Tom had completed this paper several months before his death, leading the team through the many steps described above.