Metallicity, planetary formation and migration

Recent observations show a clear correlation between the probability of hosting a planet and the metallicity of the parent star. As radial velocity surveys are biased, however, towards detecting planets with short orbital periods, the probability–metallicity correlation could merely reflect a dependence of migration rates on metallicity. We investigated the possibility, but find no basis to suggest that the migration process is sensitive to the metallicity. The indication is, therefore, that a higher metallicity results in a higher probability for planet  formation .     

A supposed new law for planetary distances

In this paper it is remarked that the so called Basano-Hughes law of planetary distances coincides with a formula suggested by G. Armellini in 1921. Besides some additional remarks are made on the laws of planetary distances.

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Riassunto In quest' articolo viene mostrato che la cosiddetta legge di Basano-Hughes sulle distanze planetarie coincide con la formula di G. Armellini (1921). Inoltre vengono fatte alcune considerazioni sulle leggi relative alle distanze planetarie.

     

Evolution of cometary perihelion distances in oort cloud: Another statistical approach

The evolution of the perihelion distance distribution in the Oort cloud was studied over the age of the solar system, under the gravitational perturbations of random passing stars, using a statistical approach. These perturbations are accounted for through an empirical relation relating the change in cometary perihelion distance to the closest-approach comet-star distance; this relation is deduced from a previous study [H. Scholl, A. Cazenave, and A. Brahic, Astron. Astrophys.112, 157–166 (1982)]. Two kinds of initial perihelion distances are considered: (a) perihelion distances <2500 AU, associated with an origin of comets as icy planetesimals in the region of the giant planets, and (b) larger perihelion distances (up to 5 × 10⁴ AU), possibly representative of comet formation as satellite fragments in the accretion disk of the primitive solar nebula. Distant star-comet encounters, as well as rare close encounters, are considered. Several quantities are estimated: (i) number of “new” comets entering into the planetary region, (ii) number of comets escaping the Sun sphere of influence or lost by hyperbolic ejection and (iii) percentage of total comet loss over the age of the solar system. From these quantities, the current and original cloud populations are deduced, as well as the corresponding cloud mass, for the two types of formation scenarios.     

Circumstellar disks and planetary formation

The role of circumstellar disks in star and planetary formation is briefly reviewed. The observed disk around MWC 349 is used as an example and a table of evolutionary time scales and parameters is presented. The disk about MWC 349 is characteristic of that expected about a massive star. Disk structure about solar mass stars is more completely reviewed by Cameron (1978). The parameters for the disk indicate that there is a deduced region where conditions are appropriate for dust condensation and possible aggregation of material to planetary masses. For the purposes of the discussion we are assuming that the infrared as well as optical radiation arises from the disk which extends the known extent of the disk to 10¹⁴cm. It is not yet certain that this is the case.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Orbital resonances and planetary formation sites

Orbital resonances may have played an important role in determining the locations where the planetesimal swarm eventually accreted into full-size planets. Several pairs of planets do indeed have commensurable orbital periods at present, but the case for control of planet formation by resonances is weakened by the fact that many pairs are not commensurable and that those which are do not necessarily exist at the strongest resonances. However, the mass loss and redistribution that occurred in the early solar system evolution can substantially alter the positions of planets and planetary embryos within the swarm. A cascaded resonance structure is hypothesized where planetesimal growth was accelerated at 2:1 interior and 1:2 exterior resonances with an early-formed Jupiter producing runaway growth of planetary embryos. These embryos produce their own resonances which, in turn, lead to additional embryos in a process that successively propagates inward and outward to generate a resonant configuration of embryos. In this manner, the early presence of Jupiter imposed a harmonic structure on the accumulating planetesimal swarm. For an accretion disk with surface density obeying a power law of index ?1.2 the positions of the planetary embryos can be moved into a reasonably good agreement with most of the present planetary positions that is as good as that given by the Titius-Bode law.     

Gaseous drag and planetary formation by accretion

We have made numerical experiments of the collisional and gravitational interaction of a planetesimal swarm in the early Solar System. In particular we study the dynamical evolution of an initial population of kilometer-size planetesimals subject to collisions (accretion, rebound, cratering, and catastrophic fragmentation). This study is based on a Monte-Carlo statistical method and provides the mass and velocity distributions of the planetesimal swarm as a function of time as well as their distribution in heliocentric distance. Several experiments have been performed and three of them are presented here. They simulate the accretional growth of numerous planetesimals in the absence (or presence) of gaseous drag, with (or without) one larger embryo among them, and with (or without) a size gradient. The results show that (i) for a population of planetesimals submitted to a negative gradient in size as the heliocentric distance increases, the outer planetesimals spiral toward the Sun faster than inner ones, leading after some time to an accumulation of bodies inside the cloud which allows the formation of an embryo; (ii) the growth of one embryo among a population of planetesimals is accelerated by the presence of gas and is warranted as long as its feeding zone is fed by the inward flow of planetesimals due to gas drag. These results offer some complementary new insights in the understanding of the accretional formation of 4–5 terrestrial planets instead of the numerous Moon-size planets generally found in numerical experiments.     

The floccule theory for planetary formation

The accumulation of floccules into protoplanets is discussed, and it is pointed out that the simplifications which have been introduced into recent numerical models may result in the incorrect conclusion being reached.     

Radiation forces and the formation of planetary systems

We briefly support on some new results about the influence of the rotation and finite size of a stellar radiation source on dust particle orbits, emphasizing the possibility of stable orbits, in the equatorial plane, for dust sizes near the radiation pressure limit.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

The magnitude distribution, perihelion distribution and flux of long-period comets

The mass distribution and perihelion distribution of long-period comets are re-assessed. The mass distribution index is found to be 1.598±0.016 , indicating that the distribution is somewhat steeper than was obtained by previous analyses of an amalgam of all the available historical data. The number of long-period comets that have orbital perihelion distances, q , that fall in a specific q to q +d q range is found to be independent of q . It is also noted that the flux of long-period comets to the inner Solar system has remained constant throughout recorded history.
The number of long-period comets, , per 1-au interval of perihelion distance, per year, brighter than H , entering the inner Solar system is found to be given by log₁₀ =−2.607+0.359 H . It is therefore estimated that, for example, about 0.5, 30 and 2000 long-period comets with absolute magnitudes brighter than 0, 5 and 10 respectively pass the Sun on orbits with perihelion distances less than 2.0 au, every century.     

Secular light curve of 2P/Encke, a comet active at aphelion

We present the secular light curve of Comet 2P/Encke in two phase spaces, the log plot, and the time plot. The main conclusions of this work are: (a) The comet shows activity at perihelion and aphelion, caused by two different active areas: Source 1, close to the south pole, active at perihelion, and Source 2, at the north pole, centered at aphelion. (b) More than 18 physical parameters are measured from the secular light curves, many of them new, and are listed in the individual plots of the comet. Specifically we find for Source 1 the location of the turn on and turn off points of activity, RON=−1.63±0.03 AU, ROFF=+1.49±0.20 AU, TON=−87±5 d, TOFF=+94±15 d, the time lag, LAG(q)=6±1 d, the total active time, TACTIVITY=181±16 d, and the amplitude of the secular light curve, ASEC(1,1)=4.8±0.1 mag. (c) From this information the photometric age and the time-age defined in Ferrín [2005a. Icarus 178, 493-516; 2006. Icarus 185, 523-543], can be calculated, and we find P-AGE = 97 ± 8 comet years and T-AGE = 103 ± 9 comet years (cy). Thus Comet 2P/Encke is an old comet entering the methuselah stage (100 cy < age). (d) The activity at aphelion (Source 2), extends for TACTIVITY=815±30 d and the amplitude of the secular light curve is ASEC(1,Q)=3.0±0.2 mag. (e) From a new phase diagram an absolute magnitude and phase coefficient for the nucleus are determined, and we find RNUC(1,1,0)=15.05±0.14, and β=0.066±0.003. From this data we find a nucleus effective diameter DEFFE=5.12(+2.5;−1.7) km. These values are not much different from previous determinations but exhibit smaller errors. (f) The activity of Source 1 is due to H₂O sublimation because it shows curvature. The activity of Source 2 might also be due to H₂O due to the circumstantial situation that the poles point to the Sun at perihelion and aphelion. (g) We found a photometric anomaly at aphelion, with minimum brightness between +393 and +413 days after perihelion that may be an indication of topography. (h) We have re-reduced the 1858 secular light curve of Kamel [1991. Icarus 93, 226-245]. There are secular changes in 7 physical parameters, and we achieve for the first time, an absolute age calibration. We find that the comet entered the inner Solar System and began sublimating in 1645±40 AD. (i) It is concluded that the secular light curve can place constraints on the pole orientation of the nucleus of some comets, and we measure the ecliptic longitude of the south pole of 2P/Encke equal to 213.2±4.5°, in excellent agreement with other determinations of this parameter, but with smaller error. (j) Using the observed absolute magnitude of 1858 and 2003 and a suitable theoretical model, the extinction date of the comet is determined. We obtain ED=2056±3 AD, implying that the comet's lifetime is 125±12 revolutions about the Sun after entering the inner Solar System.     

Effective depth of spectral line formation in planetary atmospheres

The effective level of line formation for spectroscopic absorption lines has long been regarded as a useful parameter for determining average atmospheric values of the quantities involved in line formation. The identity of this parameter has recently been disputed. Here we reestablish the dependence of this parameter on the average depth at which photons are absorbed in a semi-infinite atmosphere and show that the mean depths derived by others are similar in nature and behavior.     

The influence of stellar evolution on planetary nebula formation

A discussion of how the fact that the central star evolves while the planetary nebula is forming affects the formation of the nebula. Numerical models point to a number of effects, such as more efficient shaping in the early phases and the formation of a surrounding shell. It is also found that for identical initial density distributions, quickly evolving (more massive) stars will form bipolar PNs and more slowly evolving stars will form elliptical PNs.Physics Dept. UMIST Manchester UK     

Possible patterns in the distribution of planetary formation regions

Eris, an object larger than Pluto, is known to reside in the transneptunian region further away than Pluto. One can wonder whether its semimajor orbital axis fits in a generalized Titius–Bode law, in the same way as Pluto does. We performed a new least-squares fit to a generalized Titius–Bode law including Eris and found that not only does Eris fit in the trend, but also the correlation coefficient improves. In addition, there is a remarkable symmetry of the location of the planetary formation regions with respect to Jupiter when the natural logarithm of the heliocentric distance is used as the metric. The issue of whether the observed patterns have some physical meaning or are due to mere chance is addressed using a Monte Carlo approach identical to that of Lynch. Although the probability of chance occurrence is highly dependent on the way in which the random configurations of synthetic planetary systems are selected, we find that in all reasonable scenarios of random planetary systems the probability of chance occurrence of the observed patterns is small (below 1 per cent in most cases). If the trend were used as a prediction tool, one might expect another planet or dwarf planet or a swarm of bodies with semimajor orbital axis of 120 ± 20 au. Simple calculations show that the protoplanetary nebula most likely had enough mass to allow the accretion of at least a dwarf planet at that distance. We also found that if the surface density of the nebula decayed with heliocentric distance ( r ) as a power of −2, the regular spacing in ln  r in the Solar system could be a natural consequence of the existence of a threshold mass for planetary formation.     

The physicochemical mechanism of the formation of planetary systems

The planets and their satellites are formed in accordance with similar mechanisms as a result of spatially periodic condensation of gaseous matter during the formation of the central body.Using the diffusion theory one can calculate the age of the planets and explain the nature of the Titius-Bode law.     

The formation of planetary disks and winds: an ultraviolet view

Planetary systems are angular momentum reservoirs generated during star formation. This accretion process produces very powerful engines able to drive the optical jets and the molecular outflows. A fraction of the engine energy is released into heating thus the temperature of the engine ranges from the 3000 K of the inner disk material to the 10 MK in the areas where magnetic reconnection occurs. There are important unsolved problems concerning the nature of the engine, its evolution and the impact of the engine in the chemical evolution of the inner disk. Of special relevance is the understanding of the shear layer between the stellar photosphere and the disk; this layer controls a significant fraction of the magnetic field building up and the subsequent dissipative processes ougth to be studied in the UV. This contribution focus on describing the connections between 1 Myr old suns and the Sun and the requirements for new UV instrumentation to address their evolution during this period. Two types of observations are shown to be needed: monitoring programmes and high resolution imaging down to, at least, milliarsecond scales.     

On the formation of the planetary system the titius-bode law

The linear density and velocity perturbations are analyzed in a differentially rotating thin gravitating disc consisting of gas and dust. For the radial behaviour of the equilibrium density and the velocity of sound we assume a power law. The zeros of these perturbations have a distance behaviour like the distances of the planets and their satellites known as the Titius-Bode rule. It is suggested, that the knots of the velocity disturbances are the places where ring like dust accumulations occur. The mechanism is the same as in the Kundt's tube, where collisions between the dust and the oscillating gas are responsible for this effect.