The dynamics of spiral arms in pure stellar disks

It has been believed that spirals in pure stellar disks, especially the ones spontaneously formed, decay in several galactic rotations due to the increase of stellar velocity dispersions. Therefore, some cooling mechanism, for example dissipational effects of the interstellar medium, was assumed to be necessary to keep the spiral arms. Here we show that stellar disks can maintain spiral features for several tens of rotations without the help of cooling, using a series of high-resolution three-dimensional $N$-body simulations of pure stellar disks. We found that if the number of particles is sufficiently large, e.g., $3\times 10^6$, multi-arm spirals developed in an isolated disk can survive for more than 10 Gyrs. We confirmed that there is a self-regulating mechanism that maintains the amplitude of the spiral arms. Spiral arms increase Toomre's $Q$ of the disk, and the heating rate correlates with the squared amplitude of the spirals. Since the amplitude itself is limited by the value of $Q$, this makes the dynamical heating less effective in the later phase of evolution. A simple analytical argument suggests that the heating is caused by gravitational scattering of stars by spiral arms, and that the self-regulating mechanism in pure-stellar disks can effectively maintain spiral arms on a cosmological timescale. In the case of a smaller number of particles, e.g., $3\times 10^5$, spiral arms grow faster in the beginning of the simulation (while $Q$ is small) and they cause a rapid increase of $Q$. As a result, the spiral arms become faint in several Gyrs.Comment: 18 pages, 19 figures, accepted for Ap

Functionalization of different polymers with sulfonic groups as a way to coat them with a biomimetic apatite layer

Covalent coupling of sulfonic group (–SO3H) was attempted on different polymers to evaluate efficacy of this functional group in inducing nucleation of apatite in body environment, and thereupon to design a simple biomimetic process for preparing bonelike apatite-polymer composites. Substrates of polyethylene terephthalate (PET), polycaprolactam (Nylon 6), high molecular weight polyethylene (HMWPE) and ethylene-vinyl alcohol copolymer (EVOH) were subjected to sulfonation by being soaked in sulfuric acid (H2SO4) or chlorosulfonic acid (ClSO3H) with different concentrations. In order to incorporate calcium ions, the sulfonated substrates were soaked in saturated solution of calcium hydroxide (Ca(OH)2). The treated substrates were soaked in a simulated body fluid (SBF). Fourier transformed infrared spectroscopy, thin-film X-ray diffraction, and scanning electron microscopy showed that the sulfonation and subsequent Ca(OH)2 treatments allowed formation of –SO3H groups binding Ca2+ ions on the surface of HMWPE and EVOH, but not on PET and Nylon 6. The HMWPE and EVOH could thus form bonelike apatite layer on their surfaces in SBF within 7 d. These results indicate that the –SO3H groups are effective for inducing apatite nucleation, and thereby that surface sulfonation of polymers are effective pre-treatment method for preparing biomimetic apatite on their surfaces

Consequences of the simultaneous formation of giant planets by the core accretion mechanism

The core accretion mechanism is presently the most widely accepted cause of the formation of giant planets. For simplicity, most models presently assume that the growth of planetary embryos occurs in isolation. We explore how the simultaneous growth of two embryos at the present locations of Jupiter and Saturn affects the outcome of planetary formation. We model planet formation on the basis of the core accretion scenario and include several key physical ingredients. We consider a protoplanetary gas disk that exponentially decays with time. For planetesimals, we allow for a distribution of sizes from 100~m to 100~km with most of the mass in the smaller objects. We include planetesimal migration as well as different profiles for the surface density $\Sigma$ of the disk. The core growth is computed in the framework of the oligarchic growth regime and includes the viscous enhancement of the planetesimal capture cross-section. Planet migration is ignored. By comparing calculations assuming formation of embryos in isolation to calculations with simultaneous embryo growth, we find that the growth of one embryo generally significantly affects the other. This occurs in spite of the feeding zones of each planet never overlapping. The results may be classified as a function of the gas surface density profile $\Sigma$: if $\Sigma \propto r^{-3/2}$ and the protoplanetary disk is rather massive, Jupiter's formation inhibits the growth of Saturn. If $\Sigma \propto r^{-1}$ isolated and simultaneous formation lead to very similar outcomes; in the the case of $\Sigma \propto r^{-1/2}$ Saturn grows faster and induces a density wave that later acclerates the formation of Jupiter. Our results indicate that the simultaneous growth of several embryos impacts the final outcome and should be taken into account by planet formation models.Comment: Accepted for publication in Astronomy and Astrophysic

Accretion among preplanetary bodies: the many faces of runaway growth

(abridged) When preplanetary bodies reach proportions of ~1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R_0. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion.Comment: Accepted for publication in Icaru

Formation of terrestrial planets in close binary systems: the case of Alpha Centauri A

At present the possible existence of planets around the stars of a close binary system is still matter of debate. Can planetary bodies form in spite of the strong gravitational perturbations of the companion star? We study in this paper via numerical simulation the last stage of planetary formation, from embryos to terrestrial planets in the Alpha Cen system, the prototype of close binary systems. We find that Earth class planets can grow around Alpha Cen A on a time-scale of 50 Myr. In some of our numerical models the planets form directly in the habitable zone of the star in low eccentric orbits. In one simulation two of the final planets are in a 2:1 mean motion resonance that, however, becomes unstable after 200 Myr. During the formation process some planetary embryos fall into the stars possibly altering their metallicity.Comment: accepted for pubblication in A&A, 13 pages, 9 figure

Migration then assembly: Formation of Neptune mass planets inside 1 AU

We demonstrate that the observed distribution of `Hot Neptune'/`Super-Earth' systems is well reproduced by a model in which planet assembly occurs in situ, with no significant migration post-assembly. This is achieved only if the amount of mass in rocky material is $\sim 50$--$100 M_{\oplus}$ interior to 1 AU. Such a reservoir of material implies that significant radial migration of solid material takes place, and that it occur before the stage of final planet assembly. The model not only reproduces the general distribution of mass versus period, but also the detailed statistics of multiple planet systems in the sample. We furthermore demonstrate that cores of this size are also likely to meet the criterion to gravitationally capture gas from the nebula, although accretion is rapidly limited by the opening of gaps in the gas disk. If the mass growth is limited by this tidal truncation, then the scenario sketched here naturally produces Neptune-mass objects with substantial components of both rock and gas, as is observed. The quantitative expectations of this scenario are that most planets in the `Hot Neptune/Super-Earth' class inhabit multiple-planet systems, with characteristic orbital spacings. The model also provides a natural division into gas-rich (Hot Neptune) and gas-poor (Super-Earth) classes at fixed period. The dividing mass ranges from $\sim 3 M_{\oplus}$ at 10 day orbital periods to $\sim 10 M_{\oplus}$ at 100 day orbital periods. For orbital periods $< 10$ days, the division is less clear because a gas atmosphere may be significantly eroded by stellar radiation.Comment: 41 pages in preprint style, 15 figures, final version accepted to Ap

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

Surface potential change in bioactive polymer during the process of biomimetic apatite formation in a simulated body fluid

A bioactive polyethylene substrate can be produced by incorporation of sulfonic functional groups (-SO3H) on its surface and by soaking in a calcium hydroxide saturated solution. Variation of the surface potential of the polyethylene modified with -SO3H groups with soaking in a simulated body fluid (SBF) was investigated using a laser electrophoresis zeta-potential analyzer. To complement the study using laser electrophoresis, the surface was examined by X-ray photoelectron spectroscopy (XPS), thin film X-ray diffraction (TF-XRD), field-emission scanning electron microscopy (FE-SEM) and energy-dispersive electron X-ray spectroscopy (EDS). Comparing the zeta potential of sulfonated and Ca(OH)2-treated polyethylene with its surface structure at each interval of these soaking times in SBF, it is apparent that the polymer has a negative surface potential when it forms -SO3H groups on its surface. The surface potential of the polymer increases when it forms amorphous calcium sulfate. The potential decreases when it forms amorphous calcium phosphate, revealing a constant negative value after forming apatite. The XPS and zeta potential analysis demonstrated that the surface potential of the polyethylene was highly negatively charged after soaking in SBF for 0.5 h, increased for higher soaking times (up to 48 h), and then decreased. The negative charge of the polymer at a soaking time of 0.5 h is attributed to the presence of -SO3H groups on the surface. The initial increase in the surface potential was attributed to the incorporation of positively charged calcium ions to form calcium sulfate, and then the subsequent decrease was assigned to the incorporation of negatively charged phosphate ions to form amorphous calcium phosphate, which eventually transformed into apatite. These results indicate that the formation of apatite on bioactive polyethylene in SBF is due to electrostatic interaction of the polymer surface and ions in the fluid

Biomimetic apatite formation on different polymeric microspheres modified with calcium silicate solutions

Proceedings of the 18th International Symposium on Ceramics in Medicine, The Annual Meeting of the International Society for Ceramics in Medicine (ISCM), Kyoto, Japan, 5-8 December 2005. Published in : Key Enggineering Materials, vol. 309 - 311Bioactive polymeric microspheres can be produced by pre-coating them with a calcium silicate solution and the subsequent soaking in a simulated body fluid (SBF). Such combination should allow for the development of bioactive microspheres for several applications in the medical field including tissue engineering. In this work, three types of polymeric microspheres with different sizes were used: (i) ethylene-vinyl alcohol co-polymer (20-30 'm), (ii) polyamide 12 (10-30 'm) and (iii) polyamide 12 (300 'm). These microspheres were soaked in a calcium silicate solution at 36.5ºC for different periods of time under several conditions. Afterwards, they were dried in air at 100ºC for 24 hrs. Then, the samples were soaked in SBF for 1, 3 and 7 days. Fourier transformed infrared spectroscopy, thin-film X-ray diffraction, and scanning electron microscopy showed that after the calcium silicate treatment and the subsequent soaking in SBF, the microspheres successfully formed a bonelike apatite layer on their surfaces in SBF within 7 days due to the formation of silanol (Si-OH) groups that are quite effective for apatite formation.I. B. Leonor thanks the Portuguese Foundation for Science and Technology (FCT) for providing her a PhD scholarship (SFRH/BD/9031/2002) and the European Union funded STREP Project HIPPOCRATES (NMP3-CT-2003-505758) and the European NoE EXPERTISSUES (NMP3-CT-2004-500283)