Why are there so few hot Jupiters?

We use numerical simulations to model the migration of massive planets at small radii and compare the results with the known properties of 'hot Jupiters' (extrasolar planets with semimajor axes   a < 0.1  au). For planet masses   M _pl sin  i > 0.5 M _J  , the evidence for any 'pile-up' at small radii is weak (statistically insignificant), and although the mass function of hot Jupiters is deficient in high-mass planets as compared to a reference sample located further out, the small sample size precludes definitive conclusions. We suggest that these properties are consistent with disc migration followed by entry into a magnetospheric cavity close to the star. Entry into the cavity results in a slowing of migration, accompanied by a growth in orbital eccentricity. For planet masses in excess of 1 Jupiter mass we find eccentricity growth time-scales of a few ×10⁵ yr, suggesting that these planets may often be rapidly destroyed. Eccentricity growth appears to be faster for more massive planets which may explain changes in the planetary mass function at small radii and may also predict a pile-up of lower mass planets, the sample of which is still incomplete.     

Gravitationally unstable protoplanetary discs

The possibility that protoplanetary gaseous discs are dynamically unstable to axisymmetric and non-axisymmetric gravity perturbations (e.g. those produced by spontaneous disturbances) with characteristic scales larger than the vertical scale height is discussed analytically, using a local Wentzel–Kramers–Brillouin (WKB) approach. It is shown that such discs might be clumpy, and these gravitationally bound clumps may later collapse to become giant planets ('hot Jupiters'). The chief aim in this paper is to underscore a fact of vital importance for application in the planetary formation process: gravitationally unstable non-axisymmetric (spiral) perturbations can effectively transport both the angular momentum and the mass in a spatially inhomogeneous disc.     

Lunar-forming collisions with pre-impact rotation

Prior models of lunar-forming impacts assume that both the impactor and the target protoearth were not rotating prior to the Moon-forming event. However, planet formation models suggest that such objects would have been rotating rapidly during the late stages of terrestrial accretion. In this paper I explore the effects of pre-impact rotation on impact outcomes through more than 100 hydrodynamical simulations that consider a range of impactor masses, impact angles and impact speeds. Pre-impact rotation, particularly in the target protoearth, can substantially alter collisional outcomes and leads to a more diverse set of final planet-disk systems than seen previously. However, the subset of these impacts that are also lunar-forming candidates—i.e. that produce a sufficiently massive and iron-depleted protolunar disk—have properties similar to those determined for collisions of non-rotating objects [Canup, R.M., Asphaug, E., 2001. Nature 412, 708-712; Canup, R.M., 2004a. Icarus 168, 433-456]. With or without pre-impact rotation, a lunar-forming impact requires an impact angle near 45 degrees, together with a low impact velocity that is not more than 10% larger than the Earth's escape velocity, and produces a disk containing up to about two lunar masses that is composed predominantly of material originating from the impactor. The most significant differences in the successful cases involving pre-impact spin occur for impacts into a retrograde rotating protoearth, which allow for larger impactors (containing up to 20% of Earth's mass) and provide an improved match with the current Earth-Moon system angular momentum compared to prior results. The most difficult state to reconcile with the Moon is that of a rapidly spinning, low-obliquity protoearth before the giant impact, as these cases produce disks that are not massive enough to yield the Moon.     

On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration

We study the torque on low-mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit. We consider a wide range of surface density distributions including cases where the surface density increases smoothly outwards. We perform both linear disc response calculations and non-linear numerical simulations. We consider a large range of viscosities, including the inviscid limit, as well as a range of protoplanet mass ratios, with special emphasis on the co-orbital region and the corotation torque acting between disc and protoplanet.
For low-mass protoplanets and large viscosity, the corotation torque behaves as expected from linear theory. However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward. This happens after a time that is equal to the horseshoe libration period reduced by a factor amounting to about twice the disc aspect ratio. This torque scales with the radial gradient of specific vorticity, as does the linear torque, but we find it to be many times larger. If the viscosity is large enough for viscous diffusion across the co-orbital region to occur within a libration period, we find that the horseshoe drag may be sustained. If not, the corotation torque saturates leaving only the linear Lindblad torques. As the magnitude of the non-linear co-orbital torque (horseshoe drag) is always found to be larger than the linear torque, we find that the sign of the total torque may change even for mildly positive surface density gradients. In combination with a kinematic viscosity large enough to keep the torque from saturating, strong sustained deviations from linear theory and outward or stalled migration may occur in such cases.     

On the width and shape of the corotation region for low-mass planets

We study the coorbital flow for embedded, low-mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high-resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, x _s, which in the limit of zero softening is given by   x _s/ r _p= 1.68( q / h )^1/2  , where q is the planet to central star mass ratio, h is the disc aspect ratio and   r _p  is the orbital radius. This is in very good agreement with the same quantity measured from simulations. This result is used to show that horseshoe drag is about an order of magnitude larger than the linear corotation torque in the zero-softening limit. Thus, the horseshoe drag, the sign of which depends on the gradient of specific vorticity, is important for estimates of the total torque acting on the planet. We further show that phenomena, such as the Lindblad wakes, with a radial separation from corotation of approximately a pressure scaleheight H can affect x _s, even though for low-mass planets   x _s≪ H   . The effect is to distort streamlines and reduce x _s through the action of a back pressure. This effect is reduced for smaller gravitational softening parameters and planets of higher mass, for which x _s becomes comparable to H .     

Simulations of a late lunar-forming impact

Results of about 100 hydrodynamic simulations of potential Moon-forming impacts are presented, focusing on the “late impact” scenario in which the lunar forming impact occurs near the very end of Earth's accretion (Canup and Asphaug, 2001, Nature 412, 708-712). A new equation of state is utilized that includes a treatment of molecular vapor (“M-ANEOS”; Melosh, 2000, in: Proc. Lunar Planet. Sci. Conf. 31st, p. 1903). The sensitivity of impact outcome to collision conditions is assessed, in particular how the mass, angular momentum, composition and origin (target vs. impactor) of the material placed into circumterrestrial orbit vary with impact angle, speed, impactor-to-target mass ratio, and initial thermal state of the colliding objects. The most favorable conditions for producing a sufficiently massive and iron-depleted protolunar disk involve collisions with an impact angle near 45 degrees and an impactor velocity at infinity <4 km/sec. For a total mass and angular momentum near to that of the current Earth-Moon system, such impacts typically place about a lunar mass of material into orbits exterior to the Roche limit, with the orbiting material composed of 10 to 30% vapor by mass. In all cases, the vast majority of the orbiting material originates from the impactor, consistent with previous findings. By mapping the end fate (escaping, orbiting, or in the planet) of each particle and the peak temperature it experiences during the impact onto the figure of the initial objects, it is shown that in the successful collisions, the impactor material that ends up in orbit is primarily that portion of the object that was heated the least, having avoided direct collision with the Earth. Using these and previous results as a guide, a continuous suite of impact conditions intermediate to the “late impact” (Canup and Asphaug, 2001, Nature 412, 708-712) and “early Earth” (Cameron, 2000, in: Canup, R.M., Righter, K. (Eds.), Origin of the Earth and Moon, pp. 133-144; 2001, Meteorit. Planet. Sci. 36, 9-22) scenarios is identified that should also produce iron-poor, ∼lunar-sized satellites and a system angular momentum similar to that of the Earth-Moon system. Among these, those that leave the Earth >95% accreted after the Moon-forming impact are favored here, implying a giant impactor mass between 0.11 and 0.14 Earth masses.     

A new view of proto-planetary disks with ALMA

The dynamical, physical and chemical processes which lead to planet formation constitute an astrophysical domain which will strongly benefit from ALMA in terms of frequency coverage, sensitivity and angular resolution. Recent results from current mm/submm interferometers obtained on molecules and dust in proto-planetary disks are presented. The observational coupling between gas and dust is discussed and it is shown that dust disks must be analyzed with the knowledge provided by gas disks, and respectively, both from the chemical and physical points. For these purposes, the methods of analysis of mm/submm interferometric data specific to disks are summarized. Emphasis is given on recent, unexpected, findings obtained in the highest sensitivity and resolution observations obtained so far, as they provide a hint of what ALMA could discover. A comparison with the expected sensitivities for ALMA illustrates how ALMA can enhance our knowledge of the disk physics, either by providing statistics or by allowing much more detailed studies of representative objects.     

The gravitational instability in the dust layer of a protoplanetary disk:: axisymmetric solutions for nonuniform dust density distributions in the direction vertical to the midplane

The gravitational instability in the dust layer of a protoplanetary disk with nonuniform dust density distributions in the direction vertical to the midplane is investigated. The linear analysis of the gravitational instability is performed. The following assumptions are used: (1) One fluid model is adopted, that is, difference of velocities between dust and gas are neglected. (2) The gas is incompressible. (3) Models are axisymmetric with respect to the rotation axis of the disk. Numerical results show that the critical density at the midplane is higher than the one for the uniform dust density distribution by Sekiya (1983, Prog. Theor. Phys. 69, 1116-1130). For the Gaussian dust density distribution, the critical density is 1.3 times higher, although we do not consider this dust density distribution to be realistic because of the shear instability in the dust layer. For the dust density distribution with a constant Richardson number, which is considered to be realized due to the shear instability, the critical density is 2.85 times higher and is independent of the value of the Richardson number. Further, if a constant Richardson number could decrease to the order of 0.001, the gravitational instability would be realized even for the dust to gas surface density ratio with the solar abundance. Our results give a new restriction on planetesimal formation by the gravitational instability.     

On the photodissociation of H2 by the first stars

The first star formation in the Universe is expected to take place within small protogalaxies, in which the gas is cooled by molecular hydrogen. However, if massive stars form within these protogalaxies, they may suppress further star formation by photodissociating the H₂. We examine the importance of this effect by estimating the time-scale on which significant H₂ is destroyed. We show that photodissociation is significant in the least massive protogalaxies, but becomes less so as the protogalactic mass increases. We also examine the effects of photodissociation on dense clumps of gas within the protogalaxy. We find that while collapse will be inhibited in low-density clumps, denser ones may survive to form stars.     

球状星团的金属丰度特征与其恒星形成史

本文根据球状星团所特有的金属丰度特征,利用星族综合方法,探讨了球状星团诸恒星的形成史。研究表明,这些恒星不可能通过恒星形成率和初始质量函数均不随时间变化的单一恒星形成模式产生。原初云通过恒星演化而得到金属丰度污染的过程和多数恒星的形成过程必须分为两个不同的阶段。 球状星团得到金属丰度污染的过程中,若恒星形成具有通常的初始质量函数,则其恒星形成率必须较低,且初始质量函数不能太陡,从而使污染过程中只形成数量较少的低质量恒星,以保证单个球状星团内金属丰度的均匀性。另一种可能性是污染阶段有非常特殊的初始质量函数,只形成大质量的恒星,从而除提供适量污染外不留下任何痕迹。 多数恒星应是在原初云不同部位得到适当污染后通过局域的短暂的爆发性恒星形成(星暴过程)产生。本文进一步探讨了在Fan和Rees球状星团形成模型的框架下,两相介质中温云块相互碰撞造成星暴过程的可能性。     

Order and Chaos in Self-Consistent Galactic Models

We construct and compare two different self-consistent N-body equilibrium configurations of galactic models. The two systems have their origin in cosmological initial conditions selected so that the radial orbit instability appears in one model and gives an E5 type elliptical galaxy, but not in the other that gives an E1 type. We examine their phase spaces using uniformly distributed orbits of test particles in the resulting potential and compare with the distribution of the orbits of the real particles in the two systems. The main types of orbits in both cases are box, tube and chaotic orbits. One main conclusion is that the orbits of the test particles in the 3-dimensional potential are foliated in a way quite close to the foliation of invariant tori in a 2-dimensional potential. The real particles describe orbits having similar foliation. However, their distribution is far from being uniform. The difference between the two models of equilibrium is realized mainly by different balances of the populations of real particles in box and tube orbits.     

Formation of spectral lines in a dynamically active stochastic and multicomponent atmosphere

This paper is devoted to a determination of the statistical mean quantities describing spectral line radiation of dynamically active stochastic and multicomponent atmospheres. The lines in LTE are considered so that the effects of multiple scattering can be neglected. Two types of problem are discussed. In the first it is assumed that the realization of one or another type of nonthermal motion depends on the type of structural element and in the other this type of dependence is absent, i.e., it is supposed that the assumed random values of the velocity are distributed according to a law that is common to all the components. Particular attention is paid to a determination of the relative mean square deviation of the intensity of the observed radiation. It appears that the distinctive feature of the relative mean square deviation of the radiation in a line formed in a dynamically active stochastic atmosphere is local “spikes” (maxima) in the wings of the line. The theoretical results in this paper are compared with spectral observations of quiescent solar prominences obtained in framework of the SOHO space mission. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 121–134 (February 2007).     

Predicting spectral features in galaxy spectra from broad-band photometry

We explore the prospects of predicting emission-line features present in galaxy spectra given broad-band photometry alone. There is a general consent that colours, and spectral features, most notably the 4000 Å break, can predict many properties of galaxies, including star formation rates and hence they could infer some of the line properties. We argue that these techniques have great prospects in helping us understand line emission in extragalactic objects and might speed up future galaxy redshift surveys if they are to target emission-line objects only. We use two independent methods, Artificial Neural Networks (based on the ANNz code) and Locally Weighted Regression (LWR), to retrieve correlations present in the colour N -dimensional space and to predict the equivalent widths present in the corresponding spectra. We also investigate how well it is possible to separate galaxies with and without lines from broad-band photometry only. We find, unsurprisingly, that recombination lines can be well predicted by galaxy colours. However, among collisional lines some can and some cannot be predicted well from galaxy colours alone, without any further redshift information. We also use our techniques to estimate how much information contained in spectral diagnostic diagrams can be recovered from broad-band photometry alone. We find that it is possible to classify active galactic nuclei and star formation objects relatively well using colours only. We suggest that this technique could be used to considerably improve redshift surveys such as the upcoming Fibre Multi Object Spectrograph (FMOS) survey and the planned Wide Field Multi Object Spectrograph (WFMOS) survey.     

Core instability models of giant planet accretion – II. Forming planetary systems

We develop a simple model for computing planetary formation based on the core instability model for the gas accretion and the oligarchic growth regime for the accretion of the solid core. In this model several planets can form simultaneously in the disc, a fact that has important implications especially for the changes in the dynamic of the planetesimals and the growth of the cores since we consider the collision between them as a source of potential growth. The type I and type II migration of the embryos and the migration of the planetesimals due to the interaction with the disc of gas are also taken into account. With this model we consider different initial conditions to generate a variety of planetary systems and analyse them statistically. We explore the effects of using different type I migration rates on the final number of planets formed per planetary system such as on the distribution of masses and semimajor axis of extrasolar planets, where we also analyse the implications of considering different gas accretion rates. A particularly interesting result is the generation of a larger population of habitable planets when the gas accretion rate and type I migration are slower.     

Numerical modeling of protocore destabilization during planetary accretion: Methodology and results

We developed and tested an efficient 2D numerical methodology for modeling gravitational redistribution processes in a quasi spherical planetary body based on a simple Cartesian grid. This methodology allows one to implement large viscosity contrasts and to handle properly a free surface and self-gravitation. With this novel method we investigated in a simplified way the evolution of gravitationally unstable global three-layer structures in the interiors of large metal-silicate planetary bodies like those suggested by previous models of cold accretion [Sasaki, S., Nakazawa, K., 1986. J. Geophys. Res. 91, 9231-9238; Karato, S., Murthy, V.R., 1997. Phys. Earth Planet Interios 100, 61-79; Senshu, H., Kuramoto, K., Matsui, T., 2002. J. Geophys. Res. 107 (E12), 5118. 10.1029/2001JE001819]: an innermost solid protocore (either undifferentiated or partly differentiated), an intermediate metal-rich layer (either continuous or disrupted), and an outermost silicate-rich layer. Long-wavelength (degree-one) instability of this three-layer structure may strongly contribute to core formation dynamics by triggering planetary-scale gravitational redistribution processes. We studied possible geometrical modes of the resulting planetary reshaping using scaled 2D numerical experiments for self-gravitating planetary bodies with Mercury-, Mars- and Earth-size. In our simplified model the viscosity of each material remains constant during the experiment and rheological effects of gravitational energy dissipation are not taken into account. However, in contrast to a previously conducted numerical study [Honda, R., Mizutani, H., Yamamoto, T., 1993. J. Geophys. Res. 98, 2075-2089] we explored a freely deformable planetary surface and a broad range of viscosity ratios between the metallic layer and the protocore (0.001-1000) as well as between the silicate layer and the protocore (0.001-1000). An important new prediction from our study is that realistic modes of planetary reshaping characterized by a high viscosity protocore and low viscosity molten silicate and metal [Senshu, H., Kuramoto, K., Matsui, T., 2002. J. Geophys. Res. 107 (E12), 5118. 10.1029/2001JE001819] may result in the transient exposure of the protocore to the planetary surface and a strongly (up to 8% of the planetary diameter) aspherical deviation of the planetary shape during the early stages of core formation. Exposure of the protocore might happen in the early stages of iron core formation. This process may conceivably convert a large amount of potential energy into temperature increase and a transient strongly non-uniform depth of the magma ocean around the protoplanet. Our simplified model also predicts that the time for metallic core formation out of the metal-rich layer depends mainly on the dynamics of the deformation of the solid strong protocore. In nature this dynamics will be strongly dependent on the effective viscosity of the protocore, which should generally have non-Newtonian pressure-, temperature-, and stress-dependent rheology with strong thermomechanical feedbacks from gravitational energy dissipation.     

The effect of magnetic fields on the formation of circumstellar discs around young stars

We present first results of our simulations of magnetic fields in the formation of single and binary stars using a recently developed method for incorporating Magnetohydrodynamics (MHD) into the Smoothed Particle Hydrodynamics (SPH) method. An overview of the method is presented before discussing the effect of magnetic fields on the formation of circumstellar discs around young stars. We find that the presence of magnetic fields during the disc formation process can lead to significantly smaller and less massive discs which are much less prone to gravitational instability. Similarly in the case of binary star formation we find that magnetic fields, overall, suppress fragmentation. However these effects are found to be largely driven by magnetic pressure. The relative importance of magnetic tension is dependent on the orientation of the field with respect to the rotation axis, but can, with the right orientation, lead to a dilution of the magnetic pressure-driven suppression of fragmentation.     

Expanding,homogeneous, ellipsoidal density perturbations. III. A simple theory for the acquisition of angular momentum by tidal torques with the effects of the spin growth on the expansion included

The effects of the acquisition of angular momentum on the expansion of homogeneous, ellipsoidal density perturbations is investigated by generalizing the theory of previous papers of this series, where spin grows to the first order in overdensity. A small difference is found to be between the two cases, except for the fact that the body under consideration becomes unbound earlier in the current approach. A comparison is also made with the results of a different theory, where spin grows to the second order in overdensity. Quasi-oblate triaxial configurations turn out to gain less angular momentum in respect to both oblate and more elongated configurations with same minor to major axis ratio. In all cases of physical interest, the spin growth from the beginning to the maximum ellipsoidal volume exceeds the spin growth from the maximum ellipsoidal volume to the turnaround of the major axis, by a factor of at least 3. It is also inferred that the spin growth from the turnaround of the major axis on, probably does not exceed about one third the angular momentum previously gained.     

Galaxy Evolution in the Northern HDF

The history of star formation in the Northern Hubble Deep Field is probed using a combination of optical and near infrared images taken with WFPC2 and NICMOS on the Hubble Space Telescope. These images cover more than a factor of five in wavelength. This broad wavelength coverage allows accurate photometric determinations of redshift, extinction and intrinsic spectral energy distribution for each galaxy. From these parameters the star formation rate for each galaxy is determined by relating the 1500 angstrom flux to the net star formation rate. We then correct the rates at high redshift for the effects of surface brightness dimming by using a standard form of the star formation intensity distribution. Our measurements show that the star formation rate in the Northern HDF is roughly constant from a redshift of 1 through 6. This revised version was published online in September 2006 with corrections to the Cover Date.     

Cosmological Evolution of Supergiant Star-Forming Clouds

We present the results of very high resolution CDM simulations of galaxy formation designed to follow the formation and evolution of self-gravitating, supergiant star-forming clouds. We find that the mass spectrum of these clouds is identical to that of globular clusters and GMCs; dN/dM ∝ M ^-1.7 ± 0.1. This revised version was published online in September 2006 with corrections to the Cover Date.