Topic

# Radius

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

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TL;DR: In this paper, exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening are presented for the HST observations of HD 209458, showing that the ratio of the planetary to stellar radii is 0.1207+-0.0003.

Abstract: We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we show that the exact lightcurve can be well approximated by assuming the region of the star blocked by the planet has constant surface brightness. We apply these results to the HST observations of HD 209458, showing that the ratio of the planetary to stellar radii is 0.1207+-0.0003. These formulae give a fast and accurate means of computing lightcurves using limb-darkening coefficients from model atmospheres which should aid in the detection, simulation, and parameter fitting of planetary transits.

2,370 citations

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TL;DR: In this paper, the exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening were presented, and the authors applied these results to the Hubble Space Telescope observations of HD 209458, showing that the ratio of the planetary to stellar radii is 0.1207 ± 0.0003.

Abstract: We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we show that the exact light curve can be well approximated by assuming the region of the star blocked by the planet has constant surface brightness. We apply these results to the Hubble Space Telescope observations of HD 209458, showing that the ratio of the planetary to stellar radii is 0.1207 ± 0.0003. These formulae give a fast and accurate means of computing light curves using limb-darkening coefficients from model atmospheres that should aid in the detection, simulation, and parameter fitting of planetary transits.

2,253 citations

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TL;DR: In this paper, the authors defined the distance from wall pipe radius pipe diameter mean local velocity parallel to wall velocity fluctuations parallel and normal to flow mass density coefficient of viscosity shear stress velocity correlation coefficient mixing length universal constant in I = Ky modified universal constant eddy viscosities size of roughness friction factor = 8rw/p V 2

Abstract: y* h k* a* A* = = = = = = = = = = = = = = = = = = = = = = = = = = = = distance from wall pipe radius pipe diameter mean local velocity parallel to wall velocity fluctuations parallel and normal to flow mass density coefficient of viscosity shear stress velocity correlation coefficient mixing length universal constant in I = Ky modified universal constant eddy viscosity size of roughness friction factor = 8rw/p V 2

1,710 citations

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TL;DR: In this paper, a model of radiative transfer through subthermally excited CO in the molecular disks was proposed, which yields gas masses of ~5 × 109 M and a ratio M/L ≈ 0.8 M

Abstract: New CO interferometer data show that the molecular gas in infrared ultraluminous galaxies is in rotating nuclear disks or rings. The CO maps yield disk radii, kinematic major axes, rotation speeds, enclosed dynamical masses, and gas masses. The CO brightness temperatures, the double-peaked CO line profiles, the limits on thermal continuum flux from dust, and the constraint that the gas mass must be less than the dynamical mass all indicate that the CO lines are subthermally excited and moderately opaque (τ = 4 to 10). We fit kinematic models in which most of the CO flux comes from a moderate-density warm intercloud medium, rather than from self-gravitating clouds. Typical ring radii are 300 to 800 pc. We derive gas masses not from a standard CO-to-mass ratio, but from a model of radiative transfer through subthermally excited CO in the molecular disks. This model yields gas masses of ~5 × 109 M☉, ~5 times lower than the standard method, and a ratio M/L ≈ 0.8 M☉ (K km s-1 pc2)-1. In the nuclear disks, we derive a ratio of gas to dynamical mass of Mgas/Mdyn ≈ 1/6, and a maximum ratio of gas to total mass surface density, μ/μtot, of 1/3. For the galaxies VII Zw 31, Arp 193, and IRAS 10565+2448, the CO position-velocity diagrams provide good evidence for rotating molecular rings with a central gap. In addition to the rotating central rings or disks, a new class of star formation region is identified, which we call an extreme starburst. These have a characteristic sizes of only 100 pc, with about 109 M☉ of gas and an IR luminosity of ≈ 3 × 1011 L☉ from recently formed OB stars. Four extreme starbursts are identified in the 3 closest galaxies in the sample, including Arp 220, Arp 193, and Mrk 273. These are the most prodigious star formation events in the local universe, each representing about 1000 times as many OB stars as 30 Doradus. In Mrk 231, the CO (2-1) velocity diagram along the line of nodes shows a 12 diameter inner disk and a 3'' diameter outer disk. The narrow CO line width, the single-peak line profile, the equality of the major and minor axes, and the observed velocity gradients all imply that the molecular disk is nearly face-on, yielding low optical and UV extinction to the active galactic nucleus (AGN). Such a geometry means that the molecular disk cannot be heated by the AGN; the far-infrared (FIR) luminosity of Mrk 231 is powered by a starburst, not the AGN. In Mrk 273, the CO (1-0) maps show long streamers of radius 5 kpc (7'') with velocity gradients north-south, and a nuclear disk of radius 400 pc (06) with velocity gradients east-west. The nuclear disk contains a bright CO core of radius 120 pc (02). In Arp 220, the CO and 1.3 mm continuum maps show the two "nuclei" embedded in a central ring or disk at P.A. 50° and a fainter structure extending 7'' (3 kpc) to the east, normal to the nuclear disk. Models of the CO and dust flux indicate that the two K-band sources contain high-density gas, with n(H2) = 2 × 104 cm-3. There is no evidence that these sources really are the premerger nuclei. They are more likely to be compact extreme starburst regions, containing 109 M☉ of dense molecular gas and new stars, but no old stars. Most of the HCN emission arises in the two nuclei. The luminosity-to-mass ratios for the CO sources in Arp 220 are compatible with the early phases of compact starbursts. There is a large mass of molecular gas currently forming stars with plenty of ionizing photons, and no obvious AGN. The entire bolometric luminosity of Arp 220 comes from starbursts, not an AGN. The CO maps show that the gas in ultraluminous IR galaxies is in extended disks that cannot intercept all the power of central AGNs, even if they exist. We conclude that in ultraluminous IR galaxies—even in Mrk 231, which hosts a quasar—the FIR luminosity is powered by extreme starbursts in the molecular rings or disks, not by dust-enshrouded quasars.

1,528 citations

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TL;DR: In this paper, gas and total mass profiles for 13 low-redshift, relaxed clusters spanning a temperature range 0.7-9 keV were derived from all available Chandra data of sufficient quality.

Abstract: We present gas and total mass profiles for 13 low-redshift, relaxed clusters spanning a temperature range 0.7-9 keV, derived from all available Chandra data of sufficient quality. In all clusters, gas-temperature profiles are measured to large radii (Vikhlinin et al.) so that direct hydrostatic mass estimates are possible to nearly r500 or beyond. The gas density was accurately traced to larger radii; its profile is not described well by a beta model, showing continuous steepening with radius. The derived ρtot profiles and their scaling with mass generally follow the Navarro-Frenk-White model with concentration expected for dark matter halos in ΛCDM cosmology. However, in three cool clusters, we detect a central mass component in excess of the Navarro-Frenk-White profile, apparently associated with their cD galaxies. In the inner region (r < 0.1r500), the gas density and temperature profiles exhibit significant scatter and trends with mass, but they become nearly self-similar at larger radii. Correspondingly, we find that the slope of the mass-temperature relation for these relaxed clusters is in good agreement with the simple self-similar behavior, M500 Tα, where α = (1.5-1.6) ± 0.1, if the gas temperatures are measured excluding the central cool cores. The normalization of this M-T relation is significantly, by ≈30%, higher than most previous X-ray determinations. We derive accurate gas mass fraction profiles, which show an increase with both radius and cluster mass. The enclosed fgas profiles within r2500 0.4r500 have not yet reached any asymptotic value and are still far (by a factor of 1.5-2) from the universal baryon fraction according to the cosmic microwave background (CMB) observations. The fgas trends become weaker and its values closer to universal at larger radii, in particular, in spherical shells r2500 < r < r500.

1,448 citations