Tidal Barrier and the Asymptotic Mass of Proto Gas-Giant Planets

Extrasolar planets found with radial velocity surveys have masses ranging from several Earth to several Jupiter masses. While mass accretion onto protoplanetary cores in weak-line T-Tauri disks may eventually be quenched by a global depletion of gas, such a mechanism is unlikely to have stalled the growth of some known planetary systems which contain relatively low-mass and close-in planets along with more massive and longer period companions. Here, we suggest a potential solution for this conundrum. In general, supersonic infall of surrounding gas onto a protoplanet is only possible interior to both of its Bondi and Roche radii. At a critical mass, a protoplanet's Bondi and Roche radii are equal to the disk thickness. Above this mass, the protoplanets' tidal perturbation induces the formation of a gap. Although the disk gas may continue to diffuse into the gap, the azimuthal flux across the protoplanets' Roche lobe is quenched. Using two different schemes, we present the results of numerical simulations and analysis to show that the accretion rate increases rapidly with the ratio of the protoplanet's Roche to Bondi radii or equivalently to the disk thickness. In regions with low geometric aspect ratios, gas accretion is quenched with relatively low protoplanetary masses. This effect is important for determining the gas-giant planets' mass function, the distribution of their masses within multiple planet systems around solar type stars, and for suppressing the emergence of gas-giants around low mass stars

Crumpling wires in two dimensions

An energy-minimal simulation is proposed to study the patterns and mechanical properties of elastically crumpled wires in two dimensions. We varied the bending rigidity and stretching modulus to measure the energy allocation, size-mass exponent, and the stiffness exponent. The mass exponent is shown to be universal at value $D_{M}=1.33$. We also found that the stiffness exponent $\alpha =-0.25$ is universal, but varies with the plasticity parameters $s$ and $\theta_{p}$. These numerical findings agree excellently with the experimental results

Analytical Solutions of Singular Isothermal Quadrupole Lens

Using analytical method, we study the Singular Isothermal Quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the Singular Isothermal Sphere (SIS) lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this paper, including deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. As have been found, naked cusps will appear when the relative intensity $k$ of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity \citep{dal98}. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations that a point source infinitely approaches a cusp or a fold. The sum of magnifications of cusp image triplet is usually not equal to 0, and it is usually positive for major cusp while negative for minor cusp. Similarly, the sum of magnifications of fold image pair is usually neither equal to 0. Nevertheless, the cusp and fold relations are still equal to 0, in that the sum values are divided by infinite absolute magnifications by definition.Comment: 12 pages, 2 figures, accepted for publication in ApJ

Formation time distribution of dark matter haloes: theories versus N-body simulations

This paper uses numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytic excursion set approaches. The formation time distribution is closely linked to the conditional mass function and this test is therefore an indirect probe of this distribution. The excursion set models tested are the extended Press-Schechter (EPS) model, the ellipsoidal collapse (EC) model, and the non-spherical collapse boundary (NCB) model. Three sets of simulations (6 realizations) have been used to investigate the halo formation time distribution for halo masses ranging from dwarf-galaxy like haloes ($M=10^{-3} M_*$, where $M_*$ is the characteristic non-linear mass scale) to massive haloes of $M=8.7 M_*$. None of the models can match the simulation results at both high and low redshift. In particular, dark matter haloes formed generally earlier in our simulations than predicted by the EPS model. This discrepancy might help explain why semi-analytic models of galaxy formation, based on EPS merger trees, under-predict the number of high redshift galaxies compared with recent observations.Comment: 7 pages, 5 figures, accepted for publication in MNRA

Intrinsic Josephson Effects in the Magnetic Superconductor RuSr2GdCu2O8

We have measured interlayer current transport in small sized RuSr2GdCu2O8 single crystals. We find a clear intrinsic Josephson effect showing that the material acts as a natural superconductor-insulator-ferromagnet-insulator-superconductor superlattice. So far, we detected no unconventional behavior due to the magnetism of the RuO2 layers.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

Magnification relations of quad lenses and applications on Einstein crosses

In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It can also explain that for many observed fold image pairs, the fluxes of the Fermat minimum images are apt to be larger than those of the saddle images. We define a new quantity cross relation which describes the magnification discrepancy between two minimum images and two saddle images. Distance ratio is also defined as the ratio of the distance of two saddle images to that of two minimum images. We calculate the cross relations and distance ratios for nine observed Einstein crosses. In theory, for most of the quad lens models, the cross relations decrease as the distance ratios increase. In observation, the cross relations of the nine samples do not agree with the quad lens models very well, nevertheless, the cross relations of the nine samples do not give obvious evidence for anomalous flux ratio as the cusp and fold types do. Then, we discuss several reasons for the disagreement, and expect good consistencies for more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA