Data analysis of continuous gravitational wave: Fourier transform – II

In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) a 1-yr observation time and (ii) an arbitrary observation time, for an arbitrary location of detector and source, taking into account the effects arising due to the rotational as well as orbital motion of the Earth. As an application of the transform we considered spin-down and N -component signal analysis.     

Dark matter in dwarf spheroidals – II. Observations and modelling of Draco

We present stellar radial velocity data for the Draco dwarf spheroidal (dSph) galaxy obtained using the AF2/WYFFOS instrument combination on the William Herschel Telescope. Our data set consists of 186 member stars, 159 of which have good quality velocities, extending to a magnitude   V ≈19.5  with a mean velocity precision of ≈2 km s⁻¹. As this survey is based on a high-precision photometric target list, it contains many more Draco members at large radii. For the first time, this allows a robust determination of the radial behaviour of the velocity dispersion in a dSph.
We find statistically strong evidence of a rising velocity dispersion consistent with a dark matter halo that has a gently rising rotation curve. There is a <2 σ signature of rotation about the long axis, inconsistent with tidal disruption as the source of the rising dispersion. By comparing our data set with earlier velocities, we find that Draco probably has a binary distribution and fraction comparable to those in the solar neighbourhood.
We apply a novel maximum likelihood algorithm and fit the velocity data to a two parameter spherical model with an adjustable dark matter content and velocity anisotropy. Draco is best fit by a weakly tangentially anisotropic distribution of stellar orbits in a dark matter halo with a very slowly rising rotation law  ( v _circ∝ r ^0.17)  . We are able to rule out both a mass-follows-light distribution and an extended halo with a harmonic core at the 2.5 to 3 σ significance level, depending on the details of our assumptions about Draco's stellar binary population. Our modelling lends support to the idea that the dark matter in dwarf spheroidals is distributed in the form of massive, nearly isothermal haloes.     

The Near-Earth Asteroid Size-Frequency Distribution: A Snapshot of the Lunar Impactor Size-Frequency Distribution

It is shown that the size-frequency distribution (SFD) of a time-averaged projectile population derived from the lunar crater SFD of Neukum and Ivanov (in Hazards Due to Comets and Asteroids (T. Gehrels, Ed.), 1994, pp. 359-416, Univ. of Arizona Press, Tucson) provides a convincing fit to the SFD of the current near-Earth asteroid (NEA) population, as deduced from the results of asteroid search programs. Our results suggest that the shape of the SFD of the impactor flux has remained in a steady state since the late heavy bombardment, so that the current NEA population can be viewed as a snapshot of the flux of impactors on the Moon. The number of bodies in the projectile population with diameters of 1 km or more is 700±130, which is in good agreement with recent estimates of the total number of NEAs in this size range. Our results imply that the contribution to the projectile flux from comets is small for diameters below 10 km.     

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.     

The 1.95-2.50 μm Spectrum of J6 Himalia

The reflectance spectrum of Jupiter's sixth satellite, Himalia, is featureless in the wavelength region 1.95-2.50 μm as seen at a spectral resolution of 0.005 μm, with no absorptions deeper than a few percent. From model calculations we establish an upper limit of 10% by weight of H₂O (30-μm grains) mixed intimately in the soil of Himalia, or alternatively 0.3% of the surface covered by exposures of H₂O ice spatially segregated from the darker soil. For CH₄ and CO₂ ices the upper limits in spatially segregated models are both 0.3%.     

Comparison between the Shkuratov and Hapke Scattering Theories for Solid Planetary Surfaces: Application to the Surface Composition of Two Centaurs

This project examines the different approaches which deal with the theory of radiative transfer on atmosphereless bodies. We present the relative merits of two scattering theories based on the equivalent slab model: the extensively used Hapke theory (Hapke 1981, J. Geophys. Res.86, 3039-3054) and the Shkuratov theory (Shkuratov et al. 1999, Icarus141, 132-155). We found that their main difference is the role of the phase function of individual particles of regolith, which is predicted (and generally forward directed) in the case of the Shkuratov model instead of being a free parameter as formulated in the Hapke model. We also emphasize that different assumptions as to the manner in which different constituents are physically mixed in either model have a substantial effect on the synthetic spectra inferred. This leads to a significant extension of the validity of Hapke's or similar practical approaches to areas where these approaches are valid.We used two objects (the Centaurs 5145 Pholus and 8405 Asbolus) as examples. Previous modeling of the spectra of these two bodies with the Hapke approach gave suspect results in terms of the derived grain sizes, which were smaller than the wavelength, violating key assumptions of the model (Cruikshank et al. 1998, Icarus135, 389-407 for Pholus; Barucci et al. 2000, Astron. Astrophys.357, L53-56 for Asbolus). We considered several different types of powdered surfaces to interpret the surface composition of these two Centaurs. The effect of fine-scale contamination of water ice grains by small amounts of carbon and/or tholins is also explored. We can explain the strong red color and the rich near-infrared spectral signatures of Pholus using a five-component surface (contaminated water ice, amorphous carbon, Titan tholin, olivine, and methanol ice) where the grain sizes are consistent with the model assumptions. These components are similar to those inferred by Cruikshank et al. (1998), but we obtain very different grain sizes and relative abundances. For example, we obtain a relative abundance of water ice on the surface of Pholus of about 40% instead of 6% found with the Hapke model. Organic and carbonaceous components change by similar amounts. In the case of Asbolus, a tholin and amorphous carbon areal mixture can reproduce the spectrum, with water remaining at 9% or less. Using the albedo published by Fernandez et al. (2002, Astron. J.123, 1050-1055) which is higher than most workers assume for Centaurs and Kuiper belt objects, a surface composition similar to that of Pholus is found. It appears that model-based uncertainties in relative compositions must be regarded with more attention.