Showing papers by "Scott Tremaine published in 2008"

Dynamical Origin of Extrasolar Planet Eccentricity Distribution

Abstract: We explore the possibility that the observed eccentricity distribution of extrasolar planets arose through planet-planet interactions, after the initial stage of planet formation was complete. Our results are based on ~3250 numerical integrations of ensembles of randomly constructed planetary systems, each lasting 100 Myr. We find that for a remarkably wide range of initial conditions the eccentricity distributions of dynamically active planetary systems relax toward a common final equilibrium distribution, well described by the fitting formula $dn p eexp [ − f{1}{2}(e/0.3)2] de$ -->. This distribution agrees well with the observed eccentricity distribution for -->e 0.2 but predicts too few planets at lower eccentricities, even when we exclude planets subject to tidal circularization. These findings suggest that a period of large-scale dynamical instability has occurred in a significant fraction of newly formed planetary systems, lasting 1-2 orders of magnitude longer than the ~1 Myr interval in which gas giant planets are assembled. This mechanism predicts no (or weak) correlations between semimajor axis, eccentricity, inclination, and mass in dynamically relaxed planetary systems. An additional observational consequence of dynamical relaxation is a significant population of planets (10%) that are highly inclined (25?) with respect to the initial symmetry plane of the protoplanetary disk; this population may be detectable in transiting planets through the Rossiter-McLaughlin effect.

Measuring the non-thermal pressure in early-type galaxy atmospheres: a comparison of X-ray and optical potential profiles in M87 and NGC 1399

Abstract: We compare the gravitational potential profiles of the elliptical galaxies NGC 4486 (M87) and NGC 1399 (the central galaxy in the Fornax cluster) derived from X-ray and optical data. This comparison suggests that the combined contribution of cosmic rays, magnetic fields and microturbulence to the pressure is ∼10 per cent of the gas thermal pressure in the cores of NGC 1399 and M87, although the uncertainties in our model assumptions (e.g. spherical symmetry) are sufficiently large that the contribution could be consistent with zero. In the absence of any other form of non-thermal pressure support, these upper bounds translate into upper limits on the magnetic field of ∼10–20 μG at a distance of 1–2 arcmin from the centers of NGC 1399 and M87. We show that these results are consistent with the current paradigm of cool cluster cores, based on the assumption that active galactic nuclei regulate the thermal state of the gas by injecting energy into the intracluster medium. The limit of ∼10–20 per cent on the energy density in the form of relativistic protons applies not only to the current state of the gas, but also essentially to the entire history of the intracluster medium, provided that cosmic ray protons evolve adiabatically and that their spatial diffusion is suppressed.

Stability of the distant satellites of the giant planets in the solar system

Abstract: We conduct a systematic survey of the regions in which distant satellites can orbit stably around the four giant planets in the solar system, using orbital integrations of up to 109 yr. In contrast to previous investigations, we use a grid of initial conditions on a surface of section to explore phase space uniformly inside and outside the planet's Hill sphere (radius r H; satellites outside the Hill sphere sometimes are also known as quasi-satellites). Our confirmations and extensions of old results and new findings include the following: (1) many prograde and retrograde satellites can survive out to radii ~0.5r H and ~0.7r H, respectively, while some coplanar retrograde satellites of Jupiter and Neptune can survive out to ~r H; (2) stable orbits do not exist within the Hill sphere at high ecliptic inclinations when the semimajor axis is large enough that the solar tide is the dominant non-Keplerian perturbation; (3) there is a gap between ~r H and 2r H in which no stable orbits exist; (4) at distances 2r H stable satellite orbits exist around Jupiter, Uranus, and Neptune (but not Saturn). For Uranus and Neptune, in particular, stable orbits are found at distances as large as ~10r H; (5) the differences in the stable zones beyond the Hill sphere arise mainly from differences in the planet/Sun mass ratio and perturbations from other planets; in particular, the absence of stable satellites around Saturn is mainly due to perturbations from Jupiter. It is, therefore, likely that satellites at distances 2r H could survive for the lifetime of the solar system around Uranus, Neptune, and, perhaps, Jupiter.

Stability of Distant Satellites of Giant Planets in the Solar System

Abstract: We conduct a systematic survey of the regions in which distant satellites can orbit stably around the four giant planets in the solar system, using orbital integrations of up to $10^9$ yr. In contrast to previous investigations, we use a grid of initial conditions on a surface of section to explore phase space uniformly inside and outside the planet's Hill sphere (radius $r_{\rm H}$; satellites outside the Hill sphere sometimes are also known as quasi-satellites). Our confirmations and extensions of old results and new findings include the following: (i) many prograde and retrograde satellites can survive out to radii $\sim 0.5r_{\rm H}$ and $\sim 0.7r_{\rm H}$, respectively, while some coplanar retrograde satellites of Jupiter and Neptune can survive out to $\sim r_{\rm H}$; (ii) stable orbits do not exist within the Hill sphere at high ecliptic inclinations when the semi-major axis is large enough that the solar tide is the dominant non-Keplerian perturbation; (iii) there is a gap between $\sim r_{\rm H}$ and $2r_{\rm H}$ in which no stable orbits exist; (iv) at distances $\gtrsim 2r_{\rm H}$ stable satellite orbits exist around Jupiter, Uranus and Neptune (but not Saturn). For Uranus and Neptune, in particular, stable orbits are found at distances as large as $\sim 10r_{\rm H}$; (v) the differences in the stable zones beyond the Hill sphere arise mainly from differences in the planet/Sun mass ratio and perturbations from other planets; in particular, the absence of stable satellites around Saturn is mainly due to perturbations from Jupiter. It is therefore likely that satellites at distances $\gtrsim 2r_{\rm H}$ could survive for the lifetime of the solar system around Uranus, Neptune, and perhaps Jupiter.

Dynamics of WIMPs in the solar system and implications for detection

Abstract: Semi-analytic treatments of the evolution of orbits of weakly interacting massive particles (WIMPs) in the solar system suggest that the WIMPs bound to the solar system may enhance the direct detection rate relative to that of the unbound population by up to a factor of order unity, and boost the flux of neutrinos from WIMP annihilation in the Earth by up to two orders of magnitude. To test these important but uncertain results, we perform a suite of numerical orbit integrations to explore the properties of the bound WIMP population as a function of the WIMP mass and the scattering cross section with baryonic matter. For regions of WIMP parameter space presently allowed by experiments, we find that (i) the bound WIMP population enhances the direct detection rate by at most ~1% relative to the rate from unbound halo WIMPs; (ii) it is unlikely that planned km^3-scale neutrino telescopes will detect neutrinos from WIMP annihilation in the Earth; (iii) the event rate from neutrinos produced by WIMP annihilation in the Sun may be much smaller than implied by the usual calculations, which assume that WIMPs scattered onto bound orbits are rapidly thermalized in the Sun.

Dynamics of WIMPs in the solar system and implications for direct and indirect detection

Abstract: Semi-analytic treatments of the evolution of orbits of weakly interacting massive particles (WIMPs) in the solar system suggest that the WIMPs bound to the solar system may enhance the direct detection rate relative to that of the unbound population by up to a factor of order unity, and boost the flux of neutrinos from WIMP annihilation in the Earth by up to two orders of magnitude. To test these important but uncertain results, we perform a suite of numerical orbit integrations to explore the properties of the bound WIMP population as a function of the WIMP mass and the scattering cross section with baryonic matter. For regions of WIMP parameter space presently allowed by experiments, we find that (i) the bound WIMP population enhances the direct detection rate by at most ~1% relative to the rate from unbound halo WIMPs; (ii) it is unlikely that planned km^3-scale neutrino telescopes will detect neutrinos from WIMP annihilation in the Earth; (iii) the event rate from neutrinos produced by WIMP annihilation in the Sun may be much smaller than implied by the usual calculations, which assume that WIMPs scattered onto bound orbits are rapidly thermalized in the Sun.

Dynamics of WIMPs in the Solar System and Implications for Direct and Indirect Detection

Abstract: Semi-analytic treatments of the evolution of orbits of weakly interacting massive particles (WIMPs) in the solar system suggest that the WIMPs bound to the solar system may enhance the direct detection rate relative to that of the unbound pop ulation by up to a factor of order unity, and boost the flux of neutrinos from WIMP annihilation in the Earth by up to two orders of magnitude. To test these important but uncertain results, we perform a suite of numerical orbit integrations to explore the properties of the bound WIMP population as a function of the WIMP mass and the scattering cross section with baryonic matter. For regions of WIMP parameter space presently allowed by experiments, we find that (i) the bound W IMP population enhances the direct detection rate by at most ∼ 1% relative to the rate from unbound halo WIMPs; (ii) it is unlikely that planned km 3 -scale neutrino telescopes will detect neutrinos from WIMP annihilation in the Earth; (iii) the event rate from neutrinos produced by WIMP annihilation in the Sun may be much smaller than implied by the usual calculations, which assume that WIMPs scattered onto bound orbits are rapidly thermalized in the Sun.

Gauss's method for secular dynamics, softened

Abstract: We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular dynamical evolution of nearly Keplerian systems such as stellar clusters surrounding black holes in galactic nuclei, cometary clouds, or planetesimal discs. We illustrate its accuracy, efficiency and versatility on a variety of configurations. In particular, we examine a secularly unstable unstable system of counter-rotating disks, and follow the unfolding and saturation of the instability into a global, uniformly precessing, lopsided (m=1) mode.