Disk Planet Interactions And Early Evolution in Young Planetary Systems

We study and review disk protoplanet interactions using local shearing box simulations. These suffer the disadvantage of having potential artefacts arising from periodic boundary conditions but the advantage, when compared to global simulations, of being able to capture much of the dynamics close to the protoplanet at high resolution for low computational cost. Cases with and without self sustained MHD turbulence are considered. The conditions for gap formation and the transition from type I migration are investigated and found to depend on whether the single parameter M _p R ³/(M_* H ³), with M _p, M_*, R, and H being the protoplanet mass, the central mass, the orbital radius and the disk semi-thickness, respectively, exceeds a number of order unity. We also investigate the coorbital torques experienced by a moving protoplanet in an inviscid disk. This is done by demonstrating the equivalence of the problem for a moving protoplanet to one where the protoplanet is in a fixed orbit which the disk material flows through radially as a result of the action of an appropriate external torque. For sustainable coorbital torques to be realized a quasi steady state must be realized in which the planet migrates through the disk without accreting significant mass. In that case, although there is sensitivity to computational parameters, in agreement with earlier work by Masset and Papaloizou [2003, ApJ, 588, 494] based on global simulations, the coorbital torques are proportional to the migration speed and result in a positive feedback on the migration, enhancing it and potentially leading to a runaway. This could lead to fast migration for protoplanets in the Saturn mass range in massive disks and may be relevant to the mass period correlation for extrasolar planets which gives a preponderance of sub Jovian masses at short orbital periods.     

On a Property of Gravitational Systems

If one attributes to each component i of a gravitational system a dimensionless parameter ψ _i equal to the ratio of its relative mass (with respect to the mass of the system) to its relative position (with respect to a generally defined radius) and sums up the ψ _i values of all components outside the central core, one obtains a mass distribution index Σψ of the order of unity irrespective of the size or the type of the system. In the case of spiral galaxies (and probable other galactic systems) this property applies not only to the whole galaxy, but also to the matter inside any radius larger than the core radius. The mass distribution index in these systems has a maximum Σψ_* at a certain radius r _*, which strongly correlates with the surface brightness at r _* in galaxies with similar mass to light ratio. The gravitational acceleration of all galaxies at r _* divided by (Σψ_*)² is constant and approximately equal to MOND acceleration parameter. Also, at this radius all galaxies have a surface temperature of the order of the temperature of the cosmic microwave background radiation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Collapse of primordial clouds and the formation of a central core

The collapse of rotating clouds is investigated using three-dimensional self-gravitating hydrodynamical simulations. We take into account the detailed non-equilibrium chemical reactions for primordial gas that consists of pure hydrogen. The parameters of the collapse and the condition of the fragmentation are compared with those of isothermal clouds. It is shown that the geometrical flatness of the central region of the disc is a good indicator for predicting whether the clouds fragment or not. If the flatness is greater than the critical value, ∼ 4π, a cloud fragments into filaments and blobs. On the other hand, if the flatness is smaller than the critical value, fragmentation is not expected before the central core formation even if the cooling is efficient and the total mass becomes much greater than the local Jeans mass at the centre. The critical mass is found to be 3 × 10⁶ M_⊙ for a typical initial condition. If the initial cloud mass is smaller than this critical value, fragmentation before the central core formation is not expected. For a typically estimated first collapsing cosmological baryonic object, M ≲ 10⁶ M_⊙, central core formation is expected and will have a significant effect on the later evolution of the whole system. This revised version was published online in July 2006 with corrections to the Cover Date.     

A calculation of structural parameters of spherical stellar systems by means of characteristic functions method. I. Theory

To calculate structural parameters of stellar systems such as an effective radius and central space (or surface) density, the method of characteristic functions is suggested. The characteristic function of the system is a Fourier image of their normalized space density profile f₃(r). In the case of spherical symmetry the probability distribution of r (Q₃(r) = (3/a³)r²f₃(r)) and its orthogonal projections have the same characteristic functions. This fact is used to calculate the effective radii of a few star cluster models (King law, Plummer model and Gausian profile). It is shown, that the characteristic function for King law clusters tends to a finite generalised function if the concentration parameter c is large. The expression for the effective radius (at c ≫ 1) is given. The formula of the effective radius in the Plummer model as well as the relation between the one-dimensional central velocity dispersion and the root mean square velocity are obtained. It is shown, that in the Gaussian model and for King law clusters the effective radius (half-mass visual radius) can differ from the effective (harmonic) radius a few times. This fact should be taken into account in estimating the mass-to-light ratio from the virial mass of such systems using the King radius.     

Stability of strange dwarfs. I. Static criterion for stability. Statement of the problem

This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M _0core /M _⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons, and radius of strange dwarfs are uniquely determined by the central energy density ρ _c and the energy density ρ _tr of the crust at the surface of the quark core. Thus, the entire range of variation of ρ _c and ρ _tr must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations with a fixed rest mass M ₀ (total baryon number) of the quark core and different masses of the crust. In each series, ρ _tr ranges from the value for white dwarfs to ρ _drip = 4.3∙10¹¹ g/cm³, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an individual series when the mass of the strange dwarf reaches a maximum as a function of ρ _tr . Translated from Astrofizika, Vol. 52, No. 2, pp. 325–332 (May 2009).     

On the onset of thermal metastabilities in the solar core

For infinitesimal, homologous perturbations, stability analysis has found the solar radiative interior thermally stable. It is considered for the first time here whether stability is preserved when finite amplitude nonhomologous perturbations are present. We argue that local heated regions may develop in the solar core due to magnetic instabilities. Simple numerical estimations are derived for the timescales of the decay of these events and, when heated bubbles are generated that rise towards the surface, of their rising motion. These estimations suggest that the solar core is in a metastable state. For more detailed analysis, we developed a numerical code to solve the differential equation system. Our calculations determined the conditions of metastability and the evolution of timescales. We obtained two principal results. One of them shows that small amplitude heating events (with energy surplus Q_o < 10²⁶ ergs) contribute to subtle but long-lifetime heat waves and give the solar interior a persistently oscillating character. Interestingly, the slow decay of heat waves may make their accumulation possible and so their overlapping may contribute to the development of an intermittent, individual, local process of bubble generation, which may also be generated directly by stronger (Q_o > 10²⁶ ergs) heating events. Our second principal result is that for heated regions with ΔT/T ≥ 10⁻⁴ and radius 10⁵–10⁶cm, the generated bubbles may travel distances larger than their linear size. We point out to some possible observable consequences of the obtained results.     

An improved lunar moment of inertia determination: a proposed strategy

The current error of 0.0025 on the lunar homogeneity parameterI/MR ² is dominated by the uncertainties in theC ₂₀ andC ₂₂ gravity harmonics. This error level is equivalent to a 4.20 gm cm^–3 density uncertainty for a lunar interior model having a core 300 km in radius. Covariance analyses are performed using Doppler data from the relay satellite of the proposed Lunar Polar Orbiter mission to determine an optimum reduction strategy which obtains an order of magnitude improvement in the gravity estimates. Error studies show the long-arc reduction method obtains results which are an order of magnitude more accurate than the short-arc technique. The nominal 4000 km circular orbit of the relay satellite is very sensitive to the unmodeled effects of gravity harmonics of degree 5 through 9. Results from this orbital geometry indicate that it may not be possible to achieve the desired order of magnitude accuracy improvement. A modified orbit having the identical orbital conditions as the nominal one, but with a larger semi-major axis of 7000 km is studied. Results show the desired order of magnitude improvement can be achieved when a complete fourth degree and order model and some fifth and sixth degree terms are estimated while considering the unmodeled effects of the remaining harmonics through degree and order eight. Studies also show a 50% additional improvement inC ₂₂ can be achieved if differential differenced Doppler is also processed with the direct Doppler. The improved uncertainty inI/MR ² reduces the core density error from 4.20 gm cm^–3 to 0.1 gm cm^–3 for the case of a lunar density model having a 300 km core radius.Contribution #2885 of the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, U.S.A.     

Radiative cooling flows of self-gravitating filamentary clouds

We study the dynamics of a self-gravitating cooling filamentary cloud using a simplified model. We concentrate on the radial distribution and restrict ourselves to quasi-hydrostatic, cylindrically symmetric cooling flows. For a power-law dependence of cooling function on the temperature, self-similar solutions which describe quasi-hydrostatic cooling flows are derived. We consider obtically thin filaments with a constant mass per unit length and the solutions are parameterized by their line masses. There is no polytropic relation between the density and the pressure. The filament experiences radiative condensation, irrespective of the γ,the gas specific heat ratio. So, the filament becomes denser due to the quasi-hydrostatic flows and the density at the center (ρ_c) increases in proportion to (t ₀-t)^-1, where t denotes the time. The term,t ₀, denotes an epoch at which the central density increases infinitely. We also found that the radius of the filament (r _c) decreases in proportion to (t ₀-t)^1/2. This revised version was published online in July 2006 with corrections to the Cover Date.     

Contribution of tidal dissipation to lunar thermal history

The possible contributions of tidal heating to lunar thermal history are investigated. Analytic determinations of tidal dissipation in a homogeneous, incompressible Moon and in a two-layer Moon with a soft core and rigid mantle are given as a function of position in the Moon and as a function of Earth-Moon separation. The most recent information on the historical values of the lunar obliquity is employed, and we present results for the constant values of orbital eccentricity of e = 0.0 and e = 0.055. For a simplified orbital evolution and a dissipation factor Q = 100, the total increase in the mean lunar temperature for the homogeneous case does not exceed several tens of degrees. For the two-layer models the local dissipation may be enhanced over that of the homogeneous Moon by a factor of 5 for a core radius of 0.5 lunar radii and by a factor of 100 for a core radius of 0.95 lunar radii. The corresponding factors for the total dissipation are 3 and 15 for the two values of core radii, respectively. We conclude that tidal contributions to lunar thermal history are probably not important. But under special circumstances the enhanced dissipation in a two-layer Moon could have led to a spectacular thermal event.     

On the detectability of turbulence and bulk flows in X-ray clusters

Coolingflows, cluster mergers, and the motions of galaxies through cluster gas with supersonic and sonic velocities must lead to large scale motions of the intracluster medium (ICM). A high-resolution numerical simulation of X-ray cluster formation by Norman and Bryan (1999) predicts cluster-wide turbulence with ν_turb ≈300–600 km s^?1 and eddy scales l_outer ≈100–500 kpc, the larger numbers being characteristic of turbulence near the virial radius, while the smaller numbers pertain to the core. The simulation also predicts the existence of ordered bulk flows in the core with v≈400 km s^?1 on scales of several hundred kpc. In this paper, we consider the observability of such fluid motions via the distortions they induce in the CMB via the kinematic SZ effect, as well as via Doppler broadening and shifting of metal lines in the X-ray spectrum. We estimate |ΔT/T|_kinematic?6—at or below current limits of detectability. However, we find that an energy resolution of a few eV is sufficient to detect several Doppler shifted components in the 6.7 keV Fe line in the cluster core.     

Low‐temperature primordial gas in merging halos

The thermal regime of the baryons behind shock waves arising in the process of virialization of dark matter halos is governed at certain conditions by radiation of HD lines. A small fraction of the shocked gas can cool down to the temperature of the cosmic microwave background (CMB). We estimate an upper limit for this fraction: at z = 10 it increases sharply from about q_T ∼ 10^–3 for dark halos of M = 5 × 10⁷ M_⊙ to ∼ 0.1 for halos with M = 10⁸ M_⊙. Further increase of the halo mass does not lead however to a significant growth of q_T – the asymptotic value for M ≫ 10⁸ M_⊙ is 0.3. We estimate the star formation rate associated with such shock waves, and show that they can provide a small but not negligible fraction of the star formation. We argue that extremely metal‐poor low‐mass stars in the Milky Way may have been formed from primordial gas behind such shocks. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The environment of Hercules A

We have made VLA radio total intensity and polarisation observations in the A, B and C configurations at 1665, 1435, 1365 and 1295 MHz and in the B, C and D configurations at 8465 and 8415 MHz to study the environment of the powerful radio galaxy Hercules A. We have also made ROSAT PSPC and HRI X-ray observations to study the intracluster gas in the Hercules A cluster. We have mapped the Faraday rotation field with high resolution (1.′′42.5 h⁻¹₁₀₀ kpc for q₀=0), and combined this with the X-ray data on the gas distribution in order to map the magnetic field of the cluster. We have found that Hercules A exhibits a strong Laing-Garrington effect: the western side of the radio emission is more depolarised than the eastern side. The X-ray observations have revealed an extended X-ray emission elongated along the radio galaxy axis and a weak nuclear component. The Hercules A cluster is a cooling flow cluster, which appears isothermal at large radii. Comparing the Faraday dispersion profile with the X-ray estimated density profile, we found that the magnetic field is decreasing with radius and we have estimated a central value of 3B₀ (μG) 9. The estimated core electron density of n₀6.6×10³ m⁻³ reveals a dense environment in which Hercules A is situated.     

The product of the globular cluster collapse

In this paper we calculate the number of close binaries formed during the evolution process of a globular cluster core. The globular cluster core is assumed to contain a massive black hole at its center. We show that the central black hole can drive binaries formation in the core and the rate of binaries formation depends on the mass of the black hole at its center. When the massM of the black hole is between 10² M and 3×10³ M , there will be a few binaries formed. When the mass of the black hole is 4×10³ M M6×10³ M , the number of binary star formation will suddenly increase with a jump to the maximum value 58. When the mass of the black hole is 7×10³ M M9×10³ M , the number of binary star will immediately decrease. Whether cluster X-ray is produced mainly by the central black hole or by binaries in the core depends on the mass of the central black hole. Therefore, two cases arise: namely, black hole accretion domination and binaries radiation domination. We do think that we cannot exclude the possibility of the existence of a central black hole even when binary radiation characteristics have been observed in globular cluster X-ray sources.     

The collapse of primordial stars: importance of radiation

We simulate the collapse of a primordial protostellar cloud by means of a 1D hydrodynamics code accounting for chemical evolution, radiative transfer and radiation pressure. We find that the role of radiation pressure is negligible throughout the whole simulations, i.e. Until shortly after the formation of a central hydrostatic core. We also estimate the luminosity and the spectrum of such collapsing clouds. The luminosity is initially due to a number of H₂ lines and is of the order of 10^33-34 erg s^-1. It then grows to values ≳10³⁶ erg s^-1 by the time the core forms, and results from both HH lines and continuum radiation. This revised version was published online in September 2006 with corrections to the Cover Date.     

Growth and evolution of small porous icy bodies with an adaptive-grid thermal evolution code: I. Application to Kuiper belt objects and Enceladus

We present a new 1-dimensional thermal evolution code suited for small icy bodies of the Solar System, based on modern adaptive grid numerical techniques, and suited for multiphase flow through a porous medium. The code is used for evolutionary calculations spanning 4.6×¹⁰⁹ yr of a growing body made of ice and rock, starting with a 10 km radius seed and ending with an object 250 km in radius. Initial conditions are chosen to match two different classes of objects: a Kuiper belt object, and Saturn's moon Enceladus. Heating by the decay of ²⁶Al, as well as long-lived radionuclides is taken into account. Several values of the thermal conductivity and accretion laws are tested. We find that in all cases the melting point of ice is reached in a central core. Evaporation and flow of water and vapor gradually remove the water from the core and the final (present) structure is differentiated, with a rocky, highly porous core of 80 km radius (and up to 160 km for very low conductivities). Outside the core, due to refreezing of water and vapor, a compact, ice-rich layer forms, a few tens of km thick (except in the case of very high conductivity). If the ice is initially amorphous, as expected in the Kuiper belt, the amorphous ice is preserved in an outer layer about 20 km thick. We conclude by suggesting various ways in which the code may be extended.     

A simple way to classify supermassive black holes

We propose a classification of supermassive black holes (SMBHs) based on their efficiency in the conversion of infalling mass in emitted radiation. We use a theoretical model that assumes a conservation of angular momentum between the gas falling inside the hole and the photons emitted outwards, and suggests the existence of the scaling relation M_•‐R_eσ³, where M_• is the mass of the central SMBH, whereas R_e and σ are the effective radius and velocity dispersion of the host galaxies (bulges), respectively. We apply our model on a data set of 57 galaxies of different morphological types and with M_• measurements, obtained through the analysis of Spitzer /IRAC 3.6‐µ m images. In order to find the best fit of the corresponding scaling law, we use the FITEXY routine to perform a least‐squares regression of M_• on R_eσ³ for the considered sample of galaxies. Our analysis shows that the relation is tight and our theoretical model allows to easily estimate the efficiency of mass conversion into radiation of the central SMBHs. Finally we propose a new appealing way to classify the SMBHs in terms of this parameter. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The maximum limit of the density variation parameter λ for a stable neutron star

A static spherically-symmetric model, based on an exact solution of Einstein's equation, gives the permissible matter density 2×10¹⁴ g cm^–3. If we use the change in the ratio of central density to the radiusr=a (i.e., central density per unit radius (₀/a), we call it radius density) minimum, we have estimated the upper limit of the density variation parameter () and minimum mass limit of a superdense star like a neutron star. This limit gives an idea of the domain where the neutron abundance with negligible number of electrons and protons (may be treated as pure neutrons) and equilibrium in neutrons begins.     

Comparison of central pit craters on Mars,Mercury, Ganymede,and the Saturnian satellites

We report on the first results of a large‐scale comparison study of central pit craters throughout the solar system, focused on Mars, Mercury, Ganymede, Rhea, Dione, and Tethys. We have identified 10 more central pit craters on Rhea, Dione, and Tethys than have previously been reported. We see a general trend that the median ratio of the pit to crater diameter (D_p/D_c) decreases with increasing gravity and decreasing volatile content of the crust. Floor pits are more common on volatile‐rich bodies while summit pits become more common as crustal volatile content decreases. Uplifted bedrock from below the crater floor occurs in the central peak upon which summit pits are found and in rims around floor pits, which may or may not break the surface. Peaks on which summit pits are found on Mars and Mercury share similar characteristics to those of nonpitted central peaks, indicating that some normal central peaks undergo an additional process to create summit pits. Martian floor pits do not appear to be the result of a central peak collapse as the median ratio of the peak to crater diameter (D_pk/D_c) is about twice as high for central peaks/summit pits than D_p/D_c values for floor pits. Median D_pk/D_c is twice as high for Mars as for Mercury, reflecting differing crustal strength between the two bodies. Results indicate that a complicated interplay of crustal volatiles, target strength, surface gravity, and impactor energy along with both uplift and collapse are involved in central pit formation. Multiple formation models may be required to explain the range of central pits seen throughout the solar system.     

A Nonequilibrium Figure of Saturn’s Satellite Iapetus and the Origin of the Equatorial Ridge on Its Surface

The structure, dynamical equilibrium, and evolution of Saturn’s moon Iapetus are studied. It has been shown that, in the current epoch, the oblateness of the satellite ε₂ ≈ 0.046 does not correspond to its angular velocity of rotation, which causes the secular spherization behavior of the ice shell of Iapetus. To study this evolution, we apply a spheroidal model, containing a rock core and an ice shell with an external surface ε₂, to Iapetus. The model is based on the equilibrium finite-difference equation of the Clairaut theory, while the model parameters are taken from observations. The mean radius of the rock core and the oblateness of its level surface, ε₁ ≈ 0.028, were determined. It was found that Iapetus is covered with a thick ice shell, which is 56.6% of the mean radius of the figure. We analyze a role of the core in the evolution of the shape of a gravitating figure. It was determined that the rock core plays a key part in the settling of the ice masses of the equatorial bulge, which finally results in the formation of a large circular equatorial ridge on the surface of the satellite. From the known mean altitude of this ice ridge, it was found that, in the epoch of its formation, the rotation period of Iapetus was 166 times shorter than that at present, as little as T ≈ 11^h27^m. This is consistent with the fact that a driving force of the evolution of the satellite in our model was its substantial despinning. The model also predicts that the ice ridge should be formed more intensively in the leading (dark and, consequently, warmer) hemisphere of the satellite, where the ice is softer. This inference agrees with the observations: in the leading hemisphere of Iapetus, the ridge is actually high and continuous everywhere, while it degenerates into individual ice peaks in the opposite colder hemisphere.     

Direct GRB fireball Lorentz factor measurements through REM early afterglow observations

The huge energies involved in gamma-ray bursts (GRBs) coupled with the short emission time scales unavoidably imply that the emitting source is moving relativistically, with a speed close to that of light. Here we present the REM telescope observations of the early-time near-infrared light curves of the GRB 060418 and GRB 060607A afterglows. The detection of the afterglow peak provides for the first time a direct measurement of the initial Lorentz factor Γ₀ of the radiating material. We find that the emitting region was indeed highly relativistic in the first seconds after the explosions, with Γ₀∼400. Comparison with the Lorentz factor as determined at later epochs provides direct evidence that the emitting shell is decelerating and confirms that the afterglow emission is powered by the dissipation of bulk kinetic energy. The deceleration radius was inferred to be R _dec≈10¹⁷ cm. This is much larger than the internal shocks radius (believed to power the prompt emission), thus providing further evidence for a different origin of the prompt and afterglow stages of the GRB. Susanna D. Vergani on behalf of the REM collaboration.