Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: I. Effects of interaction with planetesimals and other protoplanets

We have performed N-body simulations on the stage of protoplanet formation from planetesimals, taking into account so-called “type-I migration,” and damping of orbital eccentricities and inclinations, as a result of tidal interaction with a gas disk without gap formation. One of the most serious problems in formation of terrestrial planets and jovian planet cores is that the migration time scale predicted by the linear theory is shorter than the disk lifetime (10⁶-10⁷ years). In this paper, we investigate retardation of type-I migration of a protoplanet due to a torque from a planetesimal disk in which a gap is opened up by the protoplanet, and torques from other protoplanets which are formed in inner and outer regions. In the first series of runs, we carried out N-body simulations of the planetesimal disk, which ranges from 0.9 to 1.1 AU, with a protoplanet seed in order to clarify how much retardation can be induced by the planetesimal disk and how long such retardation can last. We simulated six cases with different migration speeds. We found that in all of our simulations, a clear gap is not maintained for more than 10⁵ years in the planetesimal disk. For very fast migration, a gap cannot be created in the planetesimal disk. For migration slower than some critical speed, a gap does form. However, because of the growth of the surrounding planetesimals, gravitational perturbation of the planetesimals eventually becomes so strong that the planetesimals diffuse into the vicinity of the protoplanets, resulting in destruction of the gap. After the gap is destroyed, close encounters with the planetesimals rather accelerate the protoplanet migration. In this way, the migration cannot be retarded by the torque from the planetesimal disk, regardless of the migration speed. In the second series of runs, we simulated accretion of planetesimals in wide range of semimajor axis, 0.5 to 2-5 AU, starting with equal mass planetesimals without a protoplanet seed. Since formation of comparable-mass multiple protoplanets (“oligarchic growth”) is expected, the interactions with other protoplanets have a potential to alter the migration speed. However, inner protoplanets migrate before outer ones are formed, so that the migration and the accretion process of a runaway protoplanet are not affected by the other protoplanets placed inner and outer regions of its orbit. From the results of these two series of simulations, we conclude that the existence of planetesimals and multiple protoplanets do not affect type-I migration and therefore the migration shall proceed as the linear theory has suggested.     

Relative velocities among accreting planetesimals in binary systems: The circumprimary case

We investigate classical planetesimal accretion in a binary star system of separation ab?50 AU by numerical simulations, with particular focus on the region at a distance of 1 AU from the primary. The planetesimals orbit the primary, are perturbed by the companion and are in addition subjected to a gas drag force. We concentrate on the problem of relative velocities Δv among planetesimals of different sizes. For various stellar mass ratios and binary orbital parameters we determine regions where Δv exceed planetesimal escape velocities vesc (thus preventing runaway accretion) or even the threshold velocity vero for which erosion dominates accretion. Gaseous friction has two crucial effects on the velocity distribution: it damps secular perturbations by forcing periastron alignment of orbits, but at the same time the size-dependence of this orbital alignment induces a significant Δv increase between bodies of different sizes. This differential phasing effect proves very efficient and almost always increases Δv to values preventing runaway accretion, except in a narrow eb?0 domain. The erosion threshold Δv>vero is reached in a wide (ab,eb) space for small <10-km planetesimals, but in a much more limited region for bigger ?50-km objects. In the intermediate vesc<Δv<vero domain, a possible growth mode would be the type II runaway growth identified by Kortenkamp et al. [Kortenkamp, S., Wetherill, G., Inaba, S., 2001. Science 293, 1127-1129].     

Anomalous X-ray pulsars: persistent states with fallback disks

The anomalous X-ray pulsar 4U 0142+61 was recently detected in the mid infrared bands with the SPITZER Observatory (Wang, Chakrabarty and Kaplan: Nature 440, 772 (2006)). This observation is the first instance for a disk around an AXP. From a reanalysis of optical and infrared data, we show that the observations indicate that the disk is likely to be an active disk rather than a passive dust disk beyond the light cylinder, as proposed in the discovering paper. Furthermore, we show that the irradiated accretion disk model can also account for all the optical and infrared observations of the anomalous X-ray pulsars in the persistent state.     

Sea-level rise and shoreline retreat of the Nile Delta promontories, Egypt

Studies of the Nile Delta coast have indicated wide values of local subsidence, ranging from 0.4 to 5 mm/yr. Trend analysis of sea-level rise and shoreline retreat at two Nile Delta promontories have been studied. Records from tide gauges at Alexandria (1944–1989) and Port Said (1926–1987), north of the Nile delta coast, indicate a submergence of the land and/or a rise of the sea-level of 2 and 2.4 mm/yr, respectively.Dramatic erosion has occurred on some beaches of the Nile Delta. This is greatest at the tips of the Rosetta and Damietta promontories, with shoreline retreat up to 58 m/yr. Relationship between the shoreline retreat and sea level trends in terms of correlation analysis and application of the Bruun Rule indicates that the sea level rise has, by itself, a relatively minor effect on coastal erosion. The sea-level trend at the Nile delta coast is found to be only one of several effects on shoreline retreat. Major recent effects include a combination of cut-off of sediment supply to the coast by damming the River Nile and local hydrodynamic forces of waves and currents. Estimates of local future sea-level rise by the year 2100 at Alexandria and Port Said, respectively, is expected to be 37.9 and 44.2 cm. These expectations, combined with other factors, could accelerate coastal erosion, inundate wetlands and lowlands, and increase the salinity of lakes and aquifers.     

Archean greenstone-tonalite duality: Thermochemical mantle convection models or plate tectonics in the early Earth global dynamics?

Mantle convection and plate tectonics are one system, because oceanic plates are cold upper thermal boundary layers of the convection cells. As a corollary, Phanerozoic-style of plate tectonics or more likely a different version of it (i.e. a larger number of slowly moving plates, or similar number of faster plates) is expected to have operated in the hotter, vigorously convecting early Earth. Despite the recent advances in understanding the origin of Archean greenstone–granitoid terranes, the question regarding the operation of plate tectonics in the early Earth remains still controversial. Numerical model outputs for the Archean Earth range from predominantly shallow to flat subduction between 4.0 and 2.5 Ga and well-established steep subduction since 2.5 Ga [Abbott, D., Drury, R., Smith, W.H.F., 1994. Flat to steep transition in subduction style. Geology 22, 937–940], to no plate tectonics but rather foundering of 1000 km sectors of basaltic crust, then “resurfaced” by upper asthenospheric mantle basaltic melts that generate the observed duality of basalts and tonalities [van Thienen, P., van den Berg, A.P., Vlaar, N.J., 2004a. Production and recycling of oceanic crust in the early earth. Tectonophysics 386, 41–65; van Thienen, P., Van den Berg, A.P., Vlaar, N.J., 2004b. On the formation of continental silicic melts in thermochemical mantle convection models: implications for early Earth. Tectonophysics 394, 111–124]. These model outputs can be tested against the geological record. Greenstone belt volcanics are composites of komatiite–basalt plateau sequences erupted from deep mantle plumes and bimodal basalt–dacite sequences having the geochemical signatures of convergent margins; i.e. horizontally imbricated plateau and island arc crust. Greenstone belts from 3.8 to 2.5 Ga include volcanic types reported from Cenozoic convergent margins including: boninites; arc picrites; and the association of adakites–Mg andesites- and Nb-enriched basalts.Archean cratons were intruded by voluminous norites from the Neoarchean through Proterozoic; norites are accounted for by melting of subduction metasomatized Archean continental lithospheric mantle (CLM). Deep CLM defines Archean cratons; it extends to  350 km, includes the diamond facies, and xenoliths signify a composition of the buoyant, refractory, residue of plume melting, a natural consequence of imbricated plateau-arc crust. Voluminous tonalites of Archean greenstone–granitoid terranes show a secular trend of increasing Mg#, Cr, Ni consistent with slab melts hybridizing with thicker mantle wedge as subduction angle steepens. Strike-slip faults of 1000 km scale; diachronous accretion of distinct tectonostratigraphic terranes; and broad Cordilleran-type orogens featuring multiple sutures, and oceanward migration of arcs, in the Archean Superior and Yilgarn cratons, are in common with the Altaid and Phanerozoic Cordilleran orogens. There is increasing geological evidence of the supercontinent cycle operating back to  2.7 Ga: Kenorland or Ur  2.7–2.4 Ga; Columbia  1.6–1.4 Ga; Rodinia  1100–750 Ma; and Pangea  230 Ma. High-resolution seismic reflection profiling of Archean terranes reveals a prevalence of low angle structures, and evidence for paleo-subduction zones. Collectively, the geological–geochemical–seismic records endorse the operation of plate tectonics since the early Archean.     

Study of accretion disk dynamics in presence of cooling

We examine the behaviour of accretion flow around a rotating black hole in presence of cooling. We obtain global flow solutions for various accretion parameters that govern the accreting flow. We show that standing isothermal shock wave may develop in such an advective accretion flow in presence of cooling. This shocked solution has observational consequences as it successfully provides the possible explanations of energy spectra as well as generation of outflows/jets of various galactic and extra-galactic black hole candidates. We study the properties of isothermal shock wave and find that it strongly depends on the cooling efficiency. We identify the region in the parameter space spanned by the specific energy and specific angular momentum of the flow for standing isothermal shock as a function of cooling efficiencies and find that parameter space gradually shrinks with the increase of cooling rates. Our results imply that accretion flow ceases to contain isothermal shocks when cooling is beyond its critical value.     

The photometric period of the cataclysmic variable HV Andromedae

We present four nights of time-resolved photometry of the cataclysmic variable star HV And. Our time series analysis has revealed a prominent period at 3.368 ± 0.060 h, as well as some low frequency power. We interpret this signal, from saw-tooth waves in the light curve, as evidence of superhumps in HV And.     

Thin accretion disc with a corona in a central magnetic field

We study the steady-state structure of an accretion disc with a corona surrounding a central, rotating, magnetized star. We assume that the magneto-rotational instability is the dominant mechanism of angular momentum transport inside the disc and is responsible for producing magnetic tubes above the disc. In our model, a fraction of the dissipated energy inside the disc is transported to the corona via these magnetic tubes. This energy exchange from the disc to the corona which depends on the disc physical properties is modified because of the magnetic interaction between the stellar magnetic field and the accretion disc. According to our fully analytical solutions for such a system, the existence of a corona not only increases the surface density but reduces the temperature of the accretion disc. Also, the presence of a corona enhances the ratio of gas pressure to the total pressure. Our solutions show that when the strength of the magnetic field of the central neutron star is large or the star is rotating fast enough, profiles of the physical variables of the disc significantly modify due to the existence of a corona.     

Moonlets and clumps in Saturn's F ring

Cassini UVIS star occultations by the F ring detect 13 events ranging from 27 m to 9 km in width. We interpret these structures as likely temporary aggregations of multiple smaller objects, which result from the balance between fragmentation and accretion processes. One of these features was simultaneously observed by VIMS. There is evidence that this feature is elongated in azimuth. Some features show sharp edges. At least one F ring object is opaque and may be a “moonlet.” This possible moonlet provides evidence for larger objects embedded in Saturn's F ring, which were predicted as the sources of the F ring material by Cuzzi and Burns [Cuzzi, J.N., Burns, J.A., 1988. Icarus 74, 284-324], and as an outcome of tidally modified accretion by Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171]. We see too few events to confirm the bi-modal distribution which Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171] predict. These F ring structures and other youthful features detected by Cassini may result from ongoing destruction of small parent bodies in the rings and subsequent aggregation of the fragments. If so, the temporary aggregates are 10 times more abundant than the solid objects. If recycling by re-accretion is significant, the rings could be quite ancient, and likely to persist far into the future.