Atmospheric odd oxygen production due to the photodissociation of ordinary and isotopic molecular oxygen

Through a line by line calculation, the contributions of the Schumann-Runge bands of the ordinary and isotopic oxygen to the photodissociation of these molecules at different altitudes have been calculated. The photodissociation rates are expressed analytically. Contribution of the satellite lines has been taken into account. Due to the broadening of the SR lines, this contribution is insignificant. Similarly, it is shown that the first and higher vibrational states of the initial molecular states contribute insignificantly to the dissociation rates. It is also shown that the main contribution to the odd oxygen production in the important ozone producing altitudes is from the low vibrational and high rotational quantum numbers. The effect of the temperature on dissociation rates has similarly been studied.Due to its selective absorption, the isotopic oxygen ¹⁶O¹⁸O produces at 70 km 10 times as much odd oxygen as would be produced if the isotope did not have selective absorption. At this altitude 6% of the odd oxygen produced is due to this isotope. Also, 1.45% of the odd oxygen produced per second in an atmospheric column is due to ¹⁶O¹⁸O. However, the excess odd oxygen produced is not enough to explain the excess amount of ozone observed in the atmosphere which cannot be accounted for in the photochemical models.The calculated dissociation rates for the isotope are in moderate agreement with similar rates obtained by Blake et al. (1984, J. geophys. Res.89, 7277), but are by an order of magnitude smaller than similar rates given by Cicerone and McCrumb (1980, Geophys. Res. Lett.7, 251).     

The angular momenta of solar system bodies: Implications for asteroid strengths

The angular momentum H is plotted versus mass M for the planets and for all asteroids with known rotation rates and shapes, primarily taken from D. C. McAdoo and J. A. Burns [Icarus18, 285–293 (1973)]. An asteroid's angular momentum is derived from its rotation rate as determined by the period of its lightcurve, its shape as indicated by the lightcurve amplitude, and where possible its size as given by polarimetry or radiometry. The asteroid is assumed to be rotating about its axis of maximum moment of inertia. As previously found by F. F. Fish [Icarus7, 251–256 (1967]) and W. K. Hartmann and S. M. Larson [Icarus7, 257–260 (1967)], H is approximately proportional to $\text{M}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$, which shows that the asteroids and most planets spin with nearly the same rate. The very smallest asteroids on the plot deviate from the above reaction, usually containing excess angular momentum. This suggests that collisions have transferred substantial angular momentum to the smallest asteroids, perhaps causing their internal stress states to be substantially modified by centrifugal effects.The forces produced by gravitation are then compared to centrifugal effects for a rotating, triaxial ellipsoid of density 3 g cm^?3. For all asteroids with known properties the gravitational attraction is shown to be larger than the centrifugal acceleration of a particle on the surface: thus the observed asteroid regoliths are gravitationally bound. Poisson's equation for the gravitational potential is investigated and it is shown by mathematical and physical arguments that any arbitrarily shaped ellipsoid with the attractive surface force boundary condition found above will have only attractive internal forces. Thus the internal stress states in asteroids are always compressive so that asteroids could be internally fractured without losing their integrity.     

Rotation rate and velocity dispersion of planetary ring particles with size distribution II. Numerical simulation for gravitating particles

We examine rotation rates of gravitating particles in low optical depth rings, on the basis of the evolution equation of particle rotational energy derived by Ohtsuki [Ohtsuki, K., 2006. Rotation rate and velocity dispersion of planetary ring particles with size distribution. I. Formulation and analytic calculation. Icarus 183, 373-383]. We obtain the rates of evolution of particle rotation rate and velocity dispersion, using three-body orbital integration that takes into account distribution of random velocities and rotation rates. The obtained stirring and friction rates are used to calculate the evolution of velocity dispersion and rotation rate for particles in one- and two-size component rings as well as those with a narrow size distribution, and agreement with N-body simulation is confirmed. Then, we perform calculations to examine equilibrium rotation rates and velocity dispersion of gravitating ring particles with a broad size distribution, from 1 cm up to 10 m. We find that small particles spin rapidly with 〈ω²〉^1/2/Ω?¹⁰²-¹⁰³, where ω and Ω are the particle rotation rate and its orbital angular frequency, respectively, while the largest particles spin slowly, with 〈ω²〉^1/2/Ω?1. The vertical scale height of rapidly rotating small particles is much larger than that of slowly rotating large particles. Thus, rotational states of ring particles have vertical heterogeneity, which should be taken into account in modeling thermal infrared emission from Saturn's rings.     

Energy distribution function of translationally hot O(3P) atoms in the atmosphere of Earth

Translationally hot O(³P) atoms are produced in the atmosphere of Earth by photolysis of O₂ and O₃ and quenching of O(¹D). A rigorous kinetic theory analysis of this problem is developed and compared with the approach previously employed by Logan and McElroy [Planet. Space Sci.25, 117 (1977)]. It is shown that the kinetic theory employed by the previous workers is somewhat deficient. With the line-of-centers cross-section, the rates of reactions of the translationally hot O(³P) atoms with other atmospheric gases are calculated and found to be in some instances many orders of magnitude larger than the equilibrium rates. Though the non-equilibrium reaction rates with O(³P) are substantially increased, they are still not competitive with the corresponding reaction rates with O(¹D).     

Long-Term Variations of Solar Differential Rotation and Sunspot Activity: Revisited

Long-term variations of solar differential rotation and sunspot activity are investigated through re-analyzing the data on parameters of the differential-rotation law obtained by Makarov, Tlatov, and Callebaut (Solar Phys. 170, 373, 1997), Javaraiah, Bertello, and Ulrich (Astrophys. J. 626, 579, 2005a; Solar Phys. 232, 25, 2005b), and Javaraiah et al. (Solar Phys. 257, 61, 2009). Our results indicate that the solar-surface-rotation rate at the Equator (indicated by the A-parameter of the standard solar-rotation law) shows a secular decrease since Cycle 12 onwards, given by about 1?–?1.5×10^?3 (deg?day^?1?year^?1). The B-parameter of the standard differential-rotation law seems to also show a secular decrease since Cycle 12 onwards, but of weak statistical significance. The rotation rate averaged over latitudes 0^°?–?40^° does not show a secular trend of statistical significance. Moreover, the average sunspot area shows a secular increase of statistical significance since Cycle 12 onwards, while a negative correlation is found between the level of sunspot activity (indicated by the average sunspot area) and the solar equatorial rotation on long-term scales.     

Asteroid rotation rates: II. A theory for the collisional evolution of rotation rates

A model for the evolution of the mean rotation rate of asteroids arising from mutual collisions yields reasonable agreement with observed rotation rates. The mean rotation rate of large asteroids for which gravitational binding energy exceeds material strength should be constant with respect to size. Since collisional erosion of small asteroids is more rapid than collisional spin-up, the onset of increased mean rotation rate occurs at a considerably smaller radius than the size at which material strength begins to dominate gravitational binding energy. For strong igneous rock, increased rotation rates are not expected among bodies larger than a few kilometers. If there is a real trend toward more rapid rotation among asteroids of ≈1?km radius (Degewij and Gehrels, (1976). Bull. Amer. Astron. Soc.8, 459), then a substantial population of strong asteroids in that size range is implied by this model. The slower mean rotation rate of C-type asteroids than other types (paper I) implies a ratio of densities of ≈2:3 between those types, in the context of this model.     

Joule heating of Io's ionosphere by unipolar induction currents

The unexpectedly large scale height of Io's ionosphere (Kliore, A., et al., 1975, Icarus24, 407–410) together with the relatively large molecular weight of the likely principal constituent, SO₂ (Pearl, J., et al., 1979, Nature280, 755–758), suggest a high ionospheric temperature. Electrical induction in Io's ionosphere due to the corotating plasma bound to the Jovian magnetosphere is one possible source for attainment of such high temperatures. Accordingly, unipolar induction models were constructed to calculate ionospheric joule heating numerically. Heating rates produced by highly simplified models lie in the range 10^?9 to 10^?8 W/m³. These heating rates are lower than those determined from uv photodissociative heating models (Kumar, S., 1980, Geophys. Res. Lett.7, 9–12) at low levels in the ionosphere but are comparable in the upper ionosphere. The low electrical heating rate throughout most of the ionosphere is due to the power limitation imposed by the Alfvén wings which complete the electrical circuit (Neubauer, F.M., 1980, J. Geophys. Res.85, 1171–1178). Contrary to the pre-Voyager calculations of Cloutier, P. A., et al. (1978, Astrophys. Space Sci.55, 93–112), our numerical results show that the J × B force density due to unipolar induction currents in the ionosphere is much less than the gravitational force density when the combined mass of the neutral species is included. The binding and coupling of the ionosphere is principally due to the relatively dense (possibly localized) neutral SO₂ atmosphere. In regions where the ions and neutrals are collisionally coupled the ionosphere will not be stripped off by the J × B forces. However at a level above that (to which the ions move by diffusion only) the charged species would be removed. Thus there appears to be no need to postulate the existence of an intrinsic Ionian magnetic field as suggested by Kivelson, M. G., et al. (79, Science 205, 491–493) and Southwood, S. J., et al. (1980, J. Geophys. Res., in press) in order to retain the observed ionosphere.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

Ion momentum and energy transfer rates for charge exchange collisions

The rates of momentum and energy transfer have been obtained for charge exchange collisions between ion and neutral gases having arbitrary Maxwellian temperatures T_i and T_n and bulk transport velocities c_i and c_n. The results are directly applicable to the F-region of the ionosphere where O⁺ - O charge is the dominant mechanism affecting ion momentum and energy transfer.     

Numerical Evaluation of the General Yarkovsky Effect: Effects on Eccentricity and Longitude of Periapse

J. N. Spitale and R. Greenberg (2001, Icarus149, 222-234) developed a nonlinearized, finite-difference solution to the heat equation that yields orbital rates of change due to the Yarkovsky effect for small, spherical, bare-rock asteroids and used it to investigate changes in semimajor axis caused by the Yarkovsky effect. Here, we present results for changes in eccentricity and longitude of periapse. These results may be useful as benchmarks for simplified analytical solutions. Moreover, we explore a range of parameters, some of which are inaccessible to most other approaches. Instantaneous rates can be quite fast: For a 1-m scale body rotating with a 5-h period, de/dt can be as fast as 0.1 per million years (da/dt rates for similar test bodies were reported in J. N. Spitale and R. Greenberg (2001, Icarus149, 222-234)). For more typical rotation periods, these rates would be considerably slower. Output from our calculation method could be used in simulations of asteroid population evolution such as that by W. F. Bottke, D. P. Rubincam, and J. A. Burns (2000, Icarus145, 301-331). On long time scales, impacts would randomize the spin axis before significant orbital evolution could occur. Nevertheless, occasional favorable rotation states might persist long enough for substantial eccentricity changes to accumulate (1) if the body is decoupled from the main belt (e.g., many near-Earth asteroids), (2) if the population of very small (mm-scale) main-belt impactors is less than expected, or (3) if our numerical results are scaled up to km-size bodies.     

Empirical models of pressure and density in Saturn's interior: Implications for the helium concentration, its depth dependence, and Saturn's precession rate

We present ‘empirical’ models (pressure vs. density) of Saturn's interior constrained by the gravitational coefficients J₂, J₄, and J₆ for different assumed rotation rates of the planet. The empirical pressure-density profile is interpreted in terms of a hydrogen and helium physical equation of state to deduce the hydrogen to helium ratio in Saturn and to constrain the depth dependence of helium and heavy element abundances. The planet's internal structure (pressure vs. density) and composition are found to be insensitive to the assumed rotation rate for periods between 10h:32m:35s and 10h:41m:35s. We find that helium is depleted in the upper envelope, while in the high pressure region (P?1 Mbar) either the helium abundance or the concentration of heavier elements is significantly enhanced. Taking the ratio of hydrogen to helium in Saturn to be solar, we find that the maximum mass of heavy elements in Saturn's interior ranges from ∼6 to 20 M_⊕. The empirical models of Saturn's interior yield a moment of inertia factor varying from 0.22271 to 0.22599 for rotation periods between 10h:32m:35s and 10h:41m:35s, respectively. A long-term precession rate of about ^0.754″ yr⁻¹ is found to be consistent with the derived moment of inertia values and assumed rotation rates over the entire range of investigated rotation rates. This suggests that the long-term precession period of Saturn is somewhat shorter than the generally assumed value of 1.77×¹⁰⁶ years inferred from modeling and observations.     

Further evidence for collisions among asteroids

The 64 asteroids with reliably known rotational properties [rotation period P, magnitude B(1, 0) and maximum change of magnitude Δm] are studied. A plot of B(1,0) vs P illustrates that smaller asteroids tend to rotate faster than larger asteroids. The mean P for all 64 asteroids is 8.8 hr. The class of irregular asteroids (taken to be those with Δm >0.38, i.e., those whose axes differ by more than 40%) called group C are studied separately; they are shown to rotate much faster (mean P = 7.7 hr) than the remaining more regular asteroids (mean P = 9.2 hr). The smaller bodies are more irregular on the average. These results are interpreted in terms of a model in which collisions break asteroids into irregular fragments. Since angular momentum is transmitted in such collisions, significant increases in the mean can occur in the angular velocity of the largest fragment. The effect of interasteroid collisions on the mean orbital parameters is briefly discussed and is shown to be masked by selection effects.     

Impact cratering and spall failure of gabbro

Both hypervelocity impact and dynamic spall experiments were carried out on a series of well-indurated samples of gabbro to examine the relation between spall strength and maximum spall ejecta thickness. The impact experiments carried out with 0.04- to 0.2-g, 5- to 6-km/sec projectiles produced decimeter- to centimeter-sized craters and demonstrated crater efficiencies of 6 × 10^?9 g/erg, an order of magnitude greater than in metal and some two to three times that of previous experiments on less strong igneous rocks. Most of the crater volume (some 60 to 80%) is due to spall failure. Distribution of cumulative fragment number, as a function of mass of fragments with masses greater than 0.1 g yield values of b = d(log N_f)/d log(m) ?0.5 ?0.6, where N is the cumulative number of fragments and m is the mass of fragments. These values are in agreement or slightly higher than those obtained for less strong rocks and indicate that a large fraction of the ejecta resides in a few large fragments. The large fragments are plate-like with mean values of B/A and C/A 0.8 0.2, respectively (A = long, B = _termediate, and C = short fragment axes). The small equant-dimensioned fragments (with mass < 0.1 g and B ～ 0.1 mm) represent material which has been subjected to shear failure. The dynamic tensile strenght of San Marcos gabbro was determined at strain rates of 10⁴ to 10⁵ sec^?1 to be 147 ± 9 MPa. This is 3 to 10 times greater than inferred from quasi-static (strain rate 10⁰ sec^?1) loading experiments. Utilizing these parameters in a continuum fracture model predicts a tensile strenght of $\text{σ}{}_{\mathrm{<mtext>m</mtext>}}\text{∝}\text{ε}\text{?}{}^{\mathrm{[0.25–0.3]}}$, where ε is strain rate. It is suggested that the high spall strenght of basic igneous rocks gives rise to enhanced cratering efficiencies due to spall in the <10²-m crater diamter strength-dominated regime. Although the impact spall mechanism can enhance cratering efficiencies it is unclear that resulting spall fragments achieve sufficient velocities such that fragments of basic rocks can escape from the surfaces of planets such as the Moon or Mars.     

Hyperion: Collisional disruption of a resonant satellite

Hyperion is an irregularly shaped object of about 285 km in mean diameter, which appears as the likely remmant of a catastrophic collisional evolution. Since the peculiar orbit of this satellite (in $\text{4}\text{3}$ resonance locking with Titan) provides an effective mechanism to prevent any reaccretion of secondary fragments originated in a breakup event, the present Hyperion is probably the “core” of a disrupted precursor. This contrasts with the other, regularly shaped small satellites of Saturn, which, according to B.A. Smith et al. [Science215, 504–537 (1982)], were disrupted several times but could reaccrete from narrow rings of collisional fragments. The numerical experiments performed to explore the region of the phase space surrounding the present orbit show that most fragments ejected with a relative velocity $\text{?0.1}\text{km}\text{/}\text{sec}$ rapidly attain chaotic-type orbits, having repeated close encounters with Titan. Ejection velocities of this order of magnitude are indeed expected for a collision at a velocity of ～ 10 km/sec with a projectile-to-target mass ratio of the order of 10^?3; similar effects could be produced by less energetic but nearly grazing collisions. Such events are not likely to displace the largest remnant (i.e., the present Hyperion) outside the stable region of the phase space associated with the resonance, but could be responsible for the large amplitude of the observed orbital libration.     

Kinematic control of the inertiality of the system of Tycho-2 and UCAC2 stellar proper motions

Based on the Ogorodnikov-Milne model, we analyze the proper motions of Tycho-2 and UCAC2 stars. We have established that the model component that describes the rotation of all stars under consideration around the Galactic y axis differs significantly from zero at various magnitudes. We interpret this rotation found using the most distant stars as a residual rotation of the ICRS/Tycho-2 system relative to the inertial reference frame. For the most distant (d≈900 pc) Tycho-2 and UCAC2 stars, the mean rotation around the Galactic y axis has been found to be M ₁₃ ^? =?0.37±0.04 mas yr^?1. The proper motions of UCAC2 stars with magnitudes in the range 12–15^m are shown to be distorted appreciably by the magnitude equation in μ_α cos δ, which has the strongest effect for northern-sky stars with a coefficient of ?0.60±0.05 mas yr^?1 mag^?1. We have detected no significant effect of the magnitude equation in the proper motions of UCAC2 stars brighter than ≈11^m.     

Lightcurves and phase relations of the asteroids 82 alkmene and 444 Gyptis

The asteroids 82 Alkmene and 444 Gyptis were observed photoelectrically at Table Mountain Observatory and at Torino Observatory during their 1979 oppositions. The rotation periods and amplitudes of variation observed were, for 82: P_syn = 12.^h999, Δm = 0.55; and for 444: P_syn = 6.^h214, Δm = 0.15. The phase relation of 82 Alkmene can be well fit to the theory of K. Lumme and E. Bowell (Astron. J. (1981), 86, 1705). It showed a probable decrease in brightness of ～0.04 mag from 1 month before opposition to 2 months after opposition, which can be attributed to the changing viewing aspect coupled with polar flattering of the asteroid. The phase relation of 444 Gyptis is poorly fit by the Lumme and Bowell theory when only Q and V(0η) are treated as variables. A good fit can be obtained by adjusting some of the other parameters of their theory, but the physical interpretation is ambiguous.     

Discrete source counts and the rotation of the local Universe in hierarchical cosmology

Attention is given to four reasons for believing that the upper limit on the rotation of the Universe ω set by isotropy of the 3K background may not be appropriate to the local system because of its hierarchical structure. In particular, recent work of Rubinet al. (1973) on the anisotropy of Hubble's parameter (H) as determined by certain galaxies is examined. The anisotropy inH is a 1st order harmonic effect, inconsistent with an origin in an acceleration of the expansion of the Universe (U _α;4≠0), but explicable as being due to a large peculiar velocity of the Local Group. This compromises limits set on ω by isotropy of the 3K field, as does the realization that only weak limits can be set if the last-scattering surface (z _*) is notz _*→∞ but is at smallz _* (as expected in a hierarchy). In a rotating Universe, the 3-spaces of constant density cannot be orthogonal on the world lines of matter: a number test of Gödell based on this is generalized and applied (after consideration of Galactic obscuration) to the local Universe, by taking data on clusters of galaxies from the Abell and Zwicky catalogues. Data from the former give only a marginally significant result for the component ω₁ of ω in one direction, but a bootstrap argument is applied which takes significance over from Abell's data (considered as a class of galaxies) to Zwicky's data (taken as a class of clusters), giving a statistically significant result on the hypothesis that clusters are the fundamental units of the Universe: it seems likely that ω₁r?(const)r^-n with 0?n?1 over the interval 500–1000 Mpc (H=60 km s^?1 Mpc^?1) with a total rotation of ω<2ω₁, and ω₁ = 1.2 (+0.25) x 10^-18 s^-1 evaluated on data out to 10³ Mpc. Strictly, the quoted value of the rotation only applies to a region of space that in some sense has an isotropic limit: if the actual hierarchy has a large density-dependence away from a local origin (i.e., large thinning factor), then the numerical value of the rotation is smaller than the quoted value but still finite and significant.