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.     

The orientations of molecular clouds in the outer Galaxy: evidence for the scale of the turbulence driver?

Supernova (SN) explosions inject a considerable amount of energy into the interstellar medium (ISM) in regions with high-to-moderate star formation rates. In order to assess whether the driving of turbulence by supernovae is also important in the outer Galactic disc, where the star formation rates are lower, we study the spatial distribution of molecular cloud (MC) inclinations with respect to the Galactic plane. The latter contains important information on the nature of the mechanism of energy injection into the ISM. We analyse the spatial correlations between the position angles (PAs) of a selected sample of MCs (the largest clouds in the catalogue of the outer Galaxy published by Heyer et al). Our results show that when the PAs of the clouds are all mapped to values into the  [0°, 90°]  interval, there is a significant degree of spatial correlation between the PAs on spatial scales in the range of 100–800 pc. These scales are of the order of the sizes of individual SN shells in low-density environments such as those prevailing in the outer Galaxy and where the metallicity of the ambient gas is of the order of the solar value or smaller. These findings suggest that individual SN explosions, occurring in the outer regions of the Galaxy and in likewise spiral galaxies, albeit at lower rates, continue to play an important role in shaping the structure and dynamics of the ISM in those regions. The SN explosions we postulate here are likely associated with the existence of young stellar clusters in the far outer regions of the Galaxy and the ultraviolet emission and low levels of star formation observed with the Galaxy Evolution Explorer (GALEX) satellite in the outer regions of local galaxies.     

‘Crossing’ method for studying the turbulence in solar and stellar atmospheres

A new crossing method for the study of turbulent velocities in solar and stellar photospheres is considered. The method does not need knowledge of the abundance and oscillator strengths for determining the microturbulent velocity, if the macroturbulent velocity is adopted; or it allows investigation of the micro- and macro-velocities simultaneously, if the abundance and oscillator strengths are known. Using the crossing method for 200 lines of neutral iron we obtain microturbulent velocities for a large range of depths in the solar photosphere. The distribution of macroturbulent velocities with depth is also investigated. The total velocity field calculated from the obtained micro- and macro-velocities agrees with previous results from independent methods. This demonstrates the reliability of using the crossing method for separate determination of the micro- and macroturbulent velocities in solar and stellar atmospheres.     

A unified model for the 3.28 μ emission and the λ2200 å interstellar extinction feature

The 3.28 m feature observed in the diffuse galactic emission and the 2200 Å interstellar extinction feature must have a common source. This requirement rules out graphitic-type PAH molecules such as coronone and tends to favour naturally occurring bi-cyclic ring structures typified by quinoline and its derivatives.     

Improved nutation series for the non–rigid earth with a precise adjustment of parameters with nonlinear dependence

In this paper, the previous nutation series corresponding to the rotation of a non‐rigid earth composed of a rigid mantle and a liquid core obtained by Getino and Ferrándiz in 1997 are notably improved by using a high performance data fitting method. This method can be applied to many other problems presenting a non‐linear dependence on the free parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Tides in a body librating about a spin–orbit resonance: generalisation of the Darwin–Kaula theory

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.     

Black holes in the Einstein–Gauss–Bonnet theory and the geometry of their thermodynamics—II

In the present work we study (i) the charged black hole in Einstein–Gauss–Bonnet (EGB) theory, known as the Einstein–Maxwell–Gauss–Bonnet (EMGB) black hole and (ii) the black hole in EGB gravity with a Yang–Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss–Bonnet theory.     

Application of a coupled approach for the solution of nonlinear singular initial value problems of Lane–Emden type

Lane–Emden type equations have been interesting since long time due to their wide applications in mathematical physics and astrophysics. In this paper, a coupled approach has been proposed for the solution of nonlinear singular value problems of Lane–Emden type.     

Analytic forms of the perpendicular cosmic ray diffusion coefficient for an arbitrary turbulence spectrum and applications on transport of Galactic protons and acceleration at interplanetary shocks

We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.     

Erratum to “Juno,the angular momentum of Jupiter and the Lense–Thirring effect” [New Astronomy 15 (2010) 554–560]

I correct some errors, disclosed in the aforementioned paper, concerning the long-term precessions due to the multipolar expansion of the gravitational potential of Jupiter. The conclusions of the paper turn out to be even enforced since the systematic uncertainties on the Lense–Thirring signature due to the zonals are slightly reduced.     

Estimates of the number of sunspot groups: Application to the activity cycle 1960–1970

It was verified that the total number of sunspot groups at certain region on the solar surface for a certain activity cycle can be estimated quite accurately by using the Markov chain approximation method on the total number of spot groups observed on the same region at an earlier activity cycle. Application has been carried out on the observed sunspots on three northern longitude intervals (40–50, 80–90, and 130–140) during the activity cycle 1950–1960 and 1960–1970. The total number of spot groups in these regions for the activity cycle 1960–1970 has been estimated from the observational data of the cycle 1950–1960. A good correlation between the observed and estimated number of spot groups for the activity cycle 1960–1970 has been noted.     

E–ELT: Expected Applications to Asteroid Observations in the Thermal Infrared

Applications of the 42m European Extremely Large Telescope (E–ELT) for the physical characterization of asteroids is presented. In particular, this work focuses on the determination of sizes and other physical properties of asteroids from measurements of their heat emission in the thermal infrared (>5 μm). Here we show that E–ELT will be best suited for the physical characterization of some selected asteroids of particular interest, as for instance: (i) targets of sample return missions to near-Earth Asteroids (NEAs); (ii) km and sub-km binary asteroids for which size information will allow their bulk density to be derived; (iii) sizes and values of the thermal inertia of potentially hazardous asteroids (PHAs). These two parameters both affect the Yarkovsky effect, which plays a role in the orbital evolution of km sized asteroids and represents a large source of uncertainty in the Earth impact probability prediction of some PHAs. Thermal inertia is also a sensitive indicator for the presence or absence of thermal insulating regolith on the surface of atmosphere-less bodies. Knowledge of this parameter is thus important for the design and the development of lander- and sample return-missions to asteroids. The E–ELT will also be able to spatially resolve asteroids and detect binaries in a range of sizes that are at present not accessible to present day adaptive optics.     

Multicomponent theory of buoyancy instabilities in magnetized plasmas: the case of magnetic field parallel to gravity

We investigate electromagnetic buoyancy instabilities of the electron-ion plasma with the heat flux based on not the magnetohydrodynamic (MHD) equations, but using the multicomponent plasma approach when the momentum equations are solved for each species. We consider a geometry in which the background magnetic field, gravity, and stratification are directed along one axis. The nonzero background electron thermal flux is taken into account. Collisions between electrons and ions are included in the momentum equations. No simplifications usual for the one-fluid MHD-approach in studying these instabilities are used. We derive a simple dispersion relation, which shows that the thermal flux perturbation generally stabilizes an instability for the geometry under consideration. This result contradicts to conclusion obtained in the MHD-approach. We show that the reason of this contradiction is the simplified assumptions used in the MHD analysis of buoyancy instabilities and the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. Our dispersion relation also shows that the medium with the electron thermal flux can be unstable, if the temperature gradients of ions and electrons have the opposite signs. The results obtained can be applied to the weakly collisional magnetized plasma objects in laboratory and astrophysics.