Morphology of HCN and CN in Comet Hale-Bopp (1995 O1)

We compare images of Comet Hale-Bopp (1995 O1) in HCN and CN taken near perihelion (April 1, 1997) to determine the origin of CN in comets. We imaged the J=1→0 transition of HCN at λ=3 mm with the BIMA Array. Data from two weeks around perihelion were summed within four phase bins based on the rotational period of the comet. This increases both the signal-to-noise ratio and the u-v coverage while decreasing the smearing of the spatial features. The similarly phased narrowband CN images were taken at Lowell Observatory within the same range of dates as the HCN images. We find that there is a better correlation between HCN and CN than between HCN and the optically dominant dust. If the CN in jets does have a dust source it would have to have a very low albedo and/or small particle size. The production rates are consistent with HCN being a primary parent of CN, although there are discrepancies between the HCN destruction scalelength and the CN production scalelength which we discuss.     

Methane Abundance on Titan, Measured by the Space Telescope Imaging Spectrograph

Although methane is the dominant absorber in Titan's reflection spectrum, the amount of methane in the atmosphere has only been determined to an order of magnitude. We analyzed spectra from the Space Telescope Imaging Spectrograph, looking at both a bright surface region (700-km radius) and a dark surface region. The difference between the spectra of the two regions is attributed to light that has scattered off the surface, and therefore made a round-trip through all of Titan's methane. Considering only absorption, the shape of the difference spectrum provides an upper limit on methane abundance of 3.5 km-am. Modeling the multiple scattering in the atmosphere further constrains the methane abundance to 2.63±0.17 km-am. In the absence of supersaturation and with a simplified methane vertical profile, this corresponds to a surface methane-mole fraction near 3.8% and a relative humidity of 0.32. With supersaturation near the tropopause, the surface methane mole fraction could be as low as 3%.     

RHESSI Observation of Atmospheric Gamma Rays from Impact of Solar Energetic Particles on 21 April 2002

The RHESSI high-resolution spectrometer detected γ-ray lines and continuum emitted by the Earth's atmosphere during impact of solar energetic particles in the south polar region from 16:00–17:00 UT on 21 April 2002. The particle intensity at the time of the observation was a factor of 10–100 weaker than previous events when gamma-rays were detected by other instruments. This is the first high-resolution observation of atmospheric gamma-ray lines produced by solar energetic particles. De-excitation lines were resolved that, in part, come from ¹⁴N at 728, 1635, 2313, 3890, and 5106 keV, and the ¹²C spallation product at ∼ 4439 keV. Other unresolved lines were also detected. We provide best-fit line energies and widths and compare these with moderate resolution measurements by SMM of lines from an SEP event and with high-resolution measurements made by HEAO 3 of lines excited by cosmic rays. We use line ratios to estimate the spectrum of solar energetic particles that impacted the atmosphere. The 21 April spectrum was significantly harder than that measured by SMM during the 20 October 1989 shock event; it is comparable to that measured by Yohkoh on 15 July 2000. This is consistent with measurements of 10–50 MeV protons made in space at the time of the γ-ray observations.     

The X-ray spectrum of Cyg X-2

The spectra of disc accreting neutron stars generally show complex curvature, and individual components from the disc, boundary layer and neutron star surface cannot be uniquely identified. Here we show that much of the confusion over the spectral form derives from inadequate approximations for Comptonization and for the iron line. There is an intrinsic low-energy cut-off in Comptonized spectra at the seed photon energy. It is very important to model this correctly in neutron star systems as these have expected seed photon temperatures (from either the neutron star surface, inner disc or self-absorbed cyclotron) of ≈1 keV, clearly within the observed X-ray energy band. There is also reflected continuum emission which must accompany the observed iron line, which distorts the higher energy spectrum. We illustrate these points by a reanalysis of the Ginga spectra of Cyg X-2 at all points along its Z track, and show that the spectrum can be well fitted by models in which the low-energy spectrum is dominated by the disc, while the higher energy spectrum is dominated by Comptonized emission from the boundary layer, together with its reflected spectrum from a relativistically smeared, ionized disc.     

An extension of Newton's apsidal precession theorem

Newton's apsidal precession theorem in Proposition 45 of Book I of the 'Principia' has great mathematical, physical, astronomical and historical interest. The lunar theory and the precession of the perihelion of the planet Mercury are but two examples of the applications of this theorem. We have examined the precession of orbits under varying force laws as measured by the apsidal angle θ( N , e ), where N is the index for the centripetal force law, for varying eccentricity e . The paper derives a general function for the apsidal angle, dependent only on e and N as the potential is spherically symmetric. Further, we explore approximate ways of the solution of this equation, in the neighbourhood of   N = 2  which happens to be the case of greatest historical interest. Exact solutions are derived where they are possible. The first derivatives  ∂θ/∂ N   and  ∂θ/∂ h   [where h ( N , e ) is the angular momentum] are analytically expressed in the neighbourhood of   N = 2  (case of the inverse square law). The value of  ∂θ/∂ N   is computed numerically as well for  1 ≤ N < 3  . The resulting integrals are interesting improper integrals with singularities at both limits. Some of the integrals, especially for   N = 2  , can be given in closed form in terms of generalized hypergeometric functions which are reducible in terms of algebraic and logarithmic functions. No evidence was found for isolated cases of zero precession as e was increased. The   N = 1  case of the logarithmic potential is also briefly discussed in view of its interest for the dynamics of eccentric orbits and its relevance to realistic galaxy models. The possibility of apsidal precession was also examined for a few cases of high-eccentricity asteroids and extrasolar planets. We find that these systems may provide interesting new laboratories for studies of gravity.