Modeling the Formation of Giant Planet Cores I: Evaluating Key Processes

One of the most challenging problems we face in our understanding of planet formation is how Jupiter and Saturn could have formed before the the solar nebula dispersed. The most popular model of giant planet formation is the so-called 'core accretion' model. In this model a large planetary embryo formed first, mainly by two-body accretion. This is then followed by a period of inflow of nebular gas directly onto the growing planet. The core accretion model has an Achilles heel, namely the very first step. We have undertaken the most comprehensive study of this process to date. In this study we numerically integrate the orbits of a number of planetary embryos embedded in a swarm of planetesimals. In these experiments we have included: 1) aerodynamic gas drag, 2) collisional damping between planetesimals, 3) enhanced embryo cross-sections due to their atmospheres, 4) planetesimal fragmentation, and 5) planetesimal driven migration. We find that the gravitational interaction between the embryos and the planetesimals lead to the wholesale redistribution of material - regions are cleared of material and gaps open near the embryos. Indeed, in 90% of our simulations without fragmentation, the region near that embryos is cleared of planetesimals before much growth can occur. The remaining 10%, however, the embryos undergo a burst of outward migration that significantly increases growth. On timescales of ~100,000 years, the outer embryo can migrate ~6 AU and grow to roughly 30 Earth-masses. We also find that the inclusion of planetesimal fragmentation tends to inhibit growth.Comment: Accepted to AJ, 62 pages 11 figure

Gravitational lens magnification by Abell 1689: Distortion of the background galaxy luminosity function

Gravitational lensing magnifies the luminosity of galaxies behind the lens. We use this effect to constrain the total mass in the cluster Abell 1689 by comparing the lensed luminosities of background galaxies with the luminosity function of an undistorted field. Since galaxies are assumed to be a random sampling of luminosity space, this method is not limited by clustering noise. We use photometric redshift information to estimate galaxy distance and intrinsic luminosity. Knowing the redshift distribution of the background population allows us to lift the mass/background degeneracy common to lensing analysis. In this paper we use 9 filters observed over 12 hours with the Calar Alto 3.5m telescope to determine the redshifts of 1000 galaxies in the field of Abell 1689. Using a complete sample of 151 background galaxies we measure the cluster mass profile. We find that the total projected mass interior to 0.25h^(-1)Mpc is (0.48 +/- 0.16) * 10^(15)h^(-1) solar masses, where our error budget includes uncertainties from the photometric redshift determination, the uncertainty in the off-set calibration and finite sampling. This result is in good agreement with that found by number count and shear-based methods and provides a new and independent method to determine cluster masses.Comment: 13 pages, 10 figures. Submitted to MNRAS (10/99); Replacement with 1 page extra text inc. new section, accepted by MNRA

Saturated torque formula for planetary migration in viscous disks with thermal diffusion: recipe for protoplanet population synthesis

We provide torque formulae for low mass planets undergoing type I migration in gaseous disks. These torque formulae put special emphasis on the horseshoe drag, which is prone to saturation: the asymptotic value reached by the horseshoe drag depends on a balance between coorbital dynamics (which tends to cancel out or saturate the torque) and diffusive processes (which tend to restore the unperturbed disk profiles, thereby desaturating the torque). We entertain here the question of this asymptotic value, and we derive torque formulae which give the total torque as a function of the disk's viscosity and thermal diffusivity. The horseshoe drag features two components: one which scales with the vortensity gradient, and one which scales with the entropy gradient, and which constitutes the most promising candidate for halting inward type I migration. Our analysis, which is complemented by numerical simulations, recovers characteristics already noted by numericists, namely that the viscous timescale across the horseshoe region must be shorter than the libration time in order to avoid saturation, and that, provided this condition is satisfied, the entropy related part of the horseshoe drag remains large if the thermal timescale is shorter than the libration time. Side results include a study of the Lindblad torque as a function of thermal diffusivity, and a contribution to the corotation torque arising from vortensity viscously created at the contact discontinuities that appear at the horseshoe separatrices. For the convenience of the reader mostly interested in the torque formulae, section 8 is self-contained.Comment: Affiliation details changed. Fixed equation numbering issue. Biblio info adde

Oligarchic and giant impact growth of terrestrial planets in the presence of gas giant planet migration

We present the results of N--body simulations which examine the effect that gas giant planet migration has on the formation of terrestrial planets. The models incorporate a 0.5 Jupiter mass planet undergoing type II migration through an inner protoplanet--planetesimal disk, with gas drag included. Each model is initiated with the inner disk being at successively increased levels of maturity, so that it is undergoing either oligarchic or giant impact style growth as the gas giant migrates. In all cases, a large fraction of the disk mass survives the passage of the giant, either by accreting into massive terrestrial planets shepherded inward of the giant, or by being scattered into external orbits. Shepherding is favored in younger disks where there is strong dynamical friction from planetesimals and gas drag is more influential, whereas scattering dominates in more mature disks where dissipation is weaker. In each scenario, sufficient mass is scattered outward to provide for the eventual accretion of a set of terrestrial planets in external orbits, including within the system's habitable zone. An interesting result is the generation of massive, short period, terrestrial planets from compacted material pushed ahead of the giant. These planets are reminiscent of the short period Neptune mass planets discovered recently, suggesting that such `hot Neptunes' could form locally as a by-product of giant planet migration.Comment: 17 pages, 11 figures, to be published in A&A. Higher resolution pdf available at: http://www.users.globalnet.co.uk/~mfogg/3453fogg.pd

The effect of type I migration on the formation of terrestrial planets in hot-Jupiter systems

Context: Our previous models of a giant planet migrating through an inner protoplanet/planetesimal disk find that the giant shepherds a portion of the material it encounters into interior orbits, whilst scattering the rest into external orbits. Scattering tends to dominate, leaving behind abundant material that can accrete into terrestrial planets. Aims: We add to the possible realism of our model by simulating type I migration forces which cause an inward drift, and strong eccentricity and inclination damping of protoplanetary bodies. This extra dissipation might be expected to enhance shepherding at the expense of scattering, possibly modifying our previous conclusions. Methods: We employ an N-body code that is linked to a viscous gas disk algorithm capable of simulating: gas accretion onto the central star; gap formation in the vicinity of the giant planet; type II migration of the giant planet; type I migration of protoplanets; and the effect of gas drag on planetesimals. We use the code to re-run three scenarios from a previous work where type I migration was not included. Results: The additional dissipation introduced by type I migration enhances the inward shepherding of material but does not severely reduce scattering. We find that > 50% of the solids disk material still survives the migration in scattered exterior orbits: most of it well placed to complete terrestrial planet formation at < 3 AU. The shepherded portion of the disk accretes into hot-Earths, which survive in interior orbits for the duration of our simulations. Conclusions: Water-rich terrestrial planets can form in the habitable zones of hot-Jupiter systems and hot-Earths and hot-Neptunes may also be present. These systems should be targets of future planet search missions.Comment: Accepted by A&A. 15 pages, 14 figures. Higher resolution pdf available at http://www.users.globalnet.co.uk/~mfogg/7950fogg.pd

Formation and Dynamical Evolution of the Neptune Trojans - the Influence of the Initial Solar System Architecture

In this work, we investigate the dynamical stability of pre-formed Neptune Trojans under the gravitational influence of the four giant planets in compact planetary architectures, over 10 Myr. In our modelling, the initial orbital locations of Uranus and Neptune (aN) were varied to produce systems in which those planets moved on non-resonant orbits, or in which they lay in their mutual 1:2, 2:3 and 3:4 mean-motion resonances (MMRs). In total, 420 simulations were carried out, examining 42 different architectures, with a total of 840000 particles across all runs. In the non-resonant cases, the Trojans suffered only moderate levels of dynamical erosion, with the most compact systems (those with aN less than or equal 18 AU) losing around 50% of their Trojans by the end of the integrations. In the 2:3 and 3:4 MMR scenarios, however, dynamical erosion was much higher with depletion rates typically greater than 66% and total depletion in the most compact systems. The 1:2 resonant scenarios featured disruption on levels intermediate between the non-resonant cases and other resonant scenarios, with depletion rates of the order of tens of percent. Overall, the great majority of plausible pre-migration planetary architectures resulted in severe levels of depletion of the Neptunian Trojan clouds. In particular, if Uranus and Neptune formed near their mutual 2:3 or 3:4 MMR and at heliocentric distances within 18 AU (as favoured by recent studies), we found that the great majority of pre-formed Trojans would have been lost prior to Neptune's migration. This strengthens the case for the great bulk of the current Neptunian Trojan population having been captured during that migration.Comment: 17 pages, 2 figures, MNRAS (in press). Abstract slightly reduced in size, but in original form in the PDF fil

Intermediate-mass Black Hole and stellar orbits in the Galactic Center

Many young stars reside within the central half-parsec from SgrA*, the supermassive black hole in the Galactic Center. The origin of these stars remains a puzzle. Recently, Hansen and Milosavljevic (2003, HM) have argued that an Intermediate-Mass Black Hole (IMBH) could have delivered the young stars to the immediate vicinity of SgrA*. Here we focus on the final stages of the HM scenario. Namely, we integrate numerically the orbits of stars which are initially bound to the IMBH, but are stripped from it by the tidal field of SgrA*. Our numerical algorithm is a symplectic integrator designed specifically for the problem at hand; however, we have checked our results with SYMBA, a version of the widely available SWIFT code. We find that the distribution of the post-inspiral orbital parameters is sensitive to the eccentricity of the inspiraling IMBH. If the IMBH is on a circular orbit, then the inclinations of numerically computed orbits relative to the inspiral plane are almost always smaller than 10 degrees, and therefore (a) the simulations are in good agreement with the observed motions of stars in a clockwise-moving stellar disc, (b) the simulations never reproduce the orbits of stars outside this disc, which include those in the second thick ring of stars and the randomly oriented unrelaxed orbits of some of the S-stars. If the IMBH's orbital eccentricity is e=0.6, then approximately half of the stars end up with orbital inclinations below 10 degrees, and another half have inclinations anywhere between 0 and 180 degrees; this is somewhat closer to what's observed. We also show that if IRS13 cluster is bound by an IMBH, as has been argued by Maillard et. al. 2004, then the same IMBH could not have delivered all of the young stars to their present location.Comment: 16 pages, 10 figure

Theory Challenges of the Accelerating Universe

The accelerating expansion of the universe presents an exciting, fundamental challenge to the standard models of particle physics and cosmology. I highlight some of the outstanding challenges in both developing theoretical models and interpreting without bias the observational results from precision cosmology experiments in the next decade that will return data to help reveal the nature of the new physics. Examples given focus on distinguishing a new component of energy from a new law of gravity, and the effect of early dark energy on baryon acoustic oscillations.Comment: 10 pages, 4 figures; minor changes to match J. Phys. A versio