Radius

About: Radius is a research topic. Over the lifetime, 20599 publications have been published within this topic receiving 413557 citations.

Characteristics of planetary candidates observed by Kepler, II: Analysis of the first four months of data

Abstract: On 1 February 2011 the Kepler Mission released data for 156,453 stars observed from the beginning of the science observations on 2 May through 16 September 2009. There are 1235 planetary candidates with transit like signatures detected in this period. These are associated with 997 host stars. Distributions of the characteristics of the planetary candidates are separated into five class-sizes; 68 candidates of approximately Earth-size (radius < 1.25 Earth radii), 288 super-Earth size (1.25 Earth radii < radius < 2 Earth radii), 662 Neptune-size (2 Earth radii < radius < 6 Earth radii), 165 Jupiter-size (6 Earth radii < radius < 15 Earth radii), and 19 up to twice the size of Jupiter (15 Earth radii < radius < 22 Earth radii). In the temperature range appropriate for the habitable zone, 54 candidates are found with sizes ranging from Earth-size to larger than that of Jupiter. Five are less than twice the size of the Earth. Over 74% of the planetary candidates are smaller than Neptune. The observed number versus size distribution of planetary candidates increases to a peak at two to three times Earth-size and then declines inversely proportional to area of the candidate. Our current best estimates of the intrinsic frequencies of planetary candidates, after correcting for geometric and sensitivity biases, are 6% for Earth-size candidates, 7% for super-Earth size candidates, 17% for Neptune-size candidates, and 4% for Jupiter-size candidates. Multi-candidate, transiting systems are frequent; 17% of the host stars have multi-candidate systems, and 33.9% of all the candidates are part of multi-candidate systems.

On Continued Gravitational Contraction

Abstract: When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

The inner structure of ΛCDM haloes – III. Universality and asymptotic slopes

Abstract: We investigate the mass profile of cold dark matter (ΛCDM) haloes using a suite of numerical simulations spanning five decades in halo mass, from dwarf galaxies to rich galaxy clusters. These haloes typically have a few million particles within the virial radius (r200), allowing robust mass profile estimates down to radii <1 per cent of r200. Our analysis confirms the proposal of Navarro, Frenk & White (NFW) that the shape of the ΛCDM halo mass profiles differs strongly from a power law and depends little on mass. The logarithmic slope of the spherically averaged density profile, as measured by β=−d ln ρ/d ln r, decreases monotonically towards the centre and becomes shallower than isothermal (β< 2) inside a characteristic radius, r2. The fitting formula proposed by NFW provides a reasonably good approximation to the density and circular velocity profiles of individual haloes; circular velocities typically deviate from NFW best fits by <10 per cent over the radial range that is numerically well resolved. Alternatively, systematic deviations from the NFW best fits are also noticeable. Inside r2, the profile of simulated haloes becomes shallower with radius more gradually than predicted and, as a result, NFW fits tend to underestimate the dark matter density in these regions. This discrepancy has been interpreted as indicating a steeply divergent cusp with asymptotic inner slope, β0≡β(r = 0) 1.5. Our results suggest a different interpretation. We use the density and enclosed mass at our innermost resolved radii to place strong constraints on β0: density cusps as steep as r1.5 are inconsistent with most of our simulations, although β0= 1 is still consistent with our data. Our density profiles show no sign of converging to a well-defined asymptotic inner power law. We propose a simple formula that reproduces the radial dependence of the slope better than the NFW profile, and so may minimize errors when extrapolating our results inward to radii not yet reliably probed by numerical simulations.

The mechanics of large bubbles rising through extended liquids and through liquids in tubes

Abstract: Part I describes measurements of the shape and rate of rise of air bubbles varying in volume from 1·5 to 200 cm. 3 when they rise through nitrobenzene or water. Measurements of photographs of bubbles formed in nitrobenzene show that the greater part of the upper surface is always spherical. A theoretical discussion, based on the assumption that the pressure over the front of the bubble is the same as that in ideal hydrodynamic flow round a sphere, shows that the velocity of rise, U , should be related to the radius of curvature, R , in the region of the vertex, by the equation U = 2/3√( gR ); the agreement between this relationship and the experimental results is excellent. For geometrically similar bubbles of such large diameter that the drag coefficient would be independent of Reynolds’s number, it would be expected that U would be proportional to the sixth root of the volume, V ; measurements of eighty-eight bubbles show considerable scatter in the values of U/V 1/6 , although there is no systematic variation in the value of this ratio with the volume. Part II. Though the characteristics of a large bubble are associated with the observed fact that the hydrodynamic pressure on the front of a spherical cap moving through a fluid is nearly the same as that on a complete sphere, the mechanics of a rising bubble cannot be completely understood till the observed pressure distribution on a spherical cap is understood. Failing this, the case of a large bubble running up a circular tube filled with water and emptying at the bottom is capable of being analyzed completely because the bubble is not then followed by a wake. An approxim ate calculation shows that the velocity U of rise is U = 0·46 √( ga ), where a is the radius of the tube. Experiments with a tube 7·9 cm. diameter gave values of U from 29·1 to 30·6 cm./sec., corresponding with values of U /√( ga ) from 0·466 to 0·490.