A conserved local cross helicity for non-barotropic MHD

Cross helicity is not conserved in non-barotropic magnetohydro-dynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of local cross helicity which is conserved in the non-barotropic case. This local cross helicity can be integrated to a global non-barotropic cross helicity which was suggested in the work of Webb et al. (2014a,b). The non-barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new local cross helicity is conserved even for topologies for which the variational principle does not apply.     

Near-Earth object velocity distributions and consequences for the Chicxulub impactor

An Öpik-based geometric algorithm is used to compute impact probabilities and velocity distributions for various near-Earth object (NEO) populations. The resulting crater size distributions for the Earth and Moon are calculated by combining these distributions with assumed NEO size distributions and a selection of crater scaling laws. This crater probability distribution indicates that the largest craters on both the Earth and the Moon are dominated by comets. However, from a calculation of the fractional probabilities of iridium deposition, and the velocity distributions at impact of each NEO population, the only realistic possibilities for the Chicxulub impactor are a short-period comet (possibly inactive) or a near-Earth asteroid. For these classes of object, sufficiently large impacts have mean intervals of 100 and 300 Myr respectively, slightly favouring the cometary hypothesis.     

The origin of the June Bootid outburst in 1998 and determination of cometary ejection velocities

Numerical integrations are used to show that the main contribution to the outburst observed in the June Bootid meteor shower in 1998 was a subset of meteoroids released from the parent comet, 7P/Pons–Winnecke, at its 1825 return. A substantial part of the June Bootid stream is in 2:1 resonance with Jupiter. This inhibits chaotic motion, allowing structures in the stream to remain compact enough over centuries that meteor outbursts can still be produced. Circumstances of ejection in 1825 are calculated that exactly result in orbits capable of producing meteors at the observed time in 1998. Required ejection velocities are  10–20 m s^-1  .     

Towards a Dynamical History of ‘Proto-Encke‘

There are too few active comets to account for the observed zodiacal dust. Rather we look to the collisional fragmentation and erosion of sub-kilometre meteoroids in orbit close to the ecliptic. Since 1975 we have also been aware of an apparently massive meteoroidal swarm in probable 7:2 mean motion resonance with Jupiter, seemingly at the heart of the Taurid Complex and connecting therefore with the near-ecliptic system through the so-called Štohl Stream. The notable absence of pre-1786 apparitions of 2P/Encke took on a new significance with the 1983 detection by IRAS of its asymmetric trail inside this resonance. Thus it was possible all these meteoroidal components were ultimately derived from a continuously eroded, substantially dormant, librating progenitor within the trail whose more volatile inclusions are exposed from time to time and expelled either singly or severally as independent comets. A Taurid progenitor of this kind (proto-Encke) dominating the inner Solar System environment probably then accounts for most of the recorded enhancements of the larger meteoroid flux to Earth, including ‘Tunguska’ bodies as well. Terrestrial dust insertions which control mean temperature and hence climate are also inferred based upon the libration and nodal precession half-periods of proto-Encke (∼0.2 kyr, ∼2.5 kyr respectively) albeit the longer of these cycles was not at first evident in the terrestrial record (Asher & Clube 1993). Recently however this cycle appears to have been confirmed as a significant (long term) global warming/meridional atmospheric circulation / iceberg calving cycle with the correct phase producing the so-called mini-Heinrich and Heinrich events of the Holocene and late Upper Pleistocene respectively, i.e., during the past ∼60 kyr BP. The comparative stability of this terrestrial cycle, in contrast with the weakness of the observed resonance, suggests a fairly recent diversion therefore from a much stronger sungrazing 7:2 Jovian resonance in which proto-Encke's and Jupiter's longitudes of perihelion are related by ϖ pE ≈ ϖ J or ϖ J + π. Thus both the Hephaistos Stream and the Taurid Complex could have formed together during a recent close planetary encounter, say with Mercury ∼5 kyr BP. It follows that we envisage a single large progenitor in 7:2 Jovian sungrazing resonance for 50 kyr or so which undergoes repeated tidal stress: a continuous dust-induced major glaciation is thus sustained on Earth for most of this dynamical timescale before a disruptive planetgrazing event finally brings its sungrazing status to an end and produces the present meteoroidal complex. This evolutionary sequence almost certainly requires that the original sungrazing stream still exists (without its source): a potentially significant fact because it may have a direct bearing on both the observed zodiacal bands and the original progenitor orbit as well as the known periodic variation of solar radiance and convected magnetic field, of possible relevance to the solar cycle. While these aspects have to be further explored, the purpose of the present investigation is to describe some preliminary modelling with a view to inferring the likely dynamical history of proto-Encke. This revised version was published online in July 2006 with corrections to the Cover Date.