Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous work on gravi
tational billiards has been concerned with two dimensional boundaries. In particular the case of linear boundaries, also known as the wedge billiard, has been widely studied. In this work, we introduce a three dimensional version of the wedge; that is, we study the nonlinear dynamics of a billiard in a constant gravitational field colliding elastically with a linear cone of half angle $theta$. We derive a two-dimensional Poincar{e} map with two parameters, the half angle of the cone and $ell$, the $z$-component of the billiards angular momentum. Although this map is sufficient to determine the future motion of the billiard, the three-dimensional nature of the physical trajectory means that a periodic orbit of the mapping does not always correspond to a periodic trajectory in coordinate space. We demonstrate several integrable cases of the parameter values, and analytically compute the systems fixed point, analyzing the stability of this orbit as a function of the parameters as well as its relation to the physical trajectory of the billiard. Next, we explore the phase space of the system numerically. We find that for small values of $ell$ the conic billiard exhibits behavior characteristic of two-degree-of-freedom Hamiltonian systems with a discontinuity, and the dynamics is qualitatively similar to that of the wedge billiard, although the correspondence is not exact. As we increase $ell$ the dynamics becomes on the whole less chaotic, and the correspondence with the wedge billiard is lost.
We present our very recent results on the sub-mJy radio source populations at 1.4 GHz based on the Extended Chandra Deep Field South VLA survey, which reaches ~ 30 {mu}Jy, with details on their number counts, evolution, and luminosity functions. The
sub-mJy radio sky turns out to be a complex mix of star-forming galaxies and radio-quiet AGN evolving at a similar, strong rate and declining radio-loud AGN. While the well-known flattening of the radio number counts below 1 mJy is mostly due to star-forming galaxies, these sources and AGN make up an approximately equal fraction of the sub-mJy sky. Our results shed also light on a fifty-year-old issue, namely radio emission from radio-quiet AGN, and suggest that it is closely related to star formation, at least at z ~ 1.5 - 2. The implications of our findings for future, deeper radio surveys, including those with the Square Kilometre Array, are also discussed. One of the main messages, especially to non-radio astronomers, is that radio surveys are reaching such faint limits that, while previously they were mainly useful for radio quasars and radio galaxies, they are now detecting mostly star-forming galaxies and radio-quiet AGN, i.e., the bulk of the extragalactic sources studied in the infrared, optical, and X-ray bands.
We present the evolutionary properties and luminosity functions of the radio sources belonging to the Chandra Deep Field South VLA survey, which reaches a flux density limit at 1.4 GHz of 43 microJy at the field center and redshift ~5, and which incl
udes the first radio-selected complete sample of radio-quiet active galactic nuclei (AGN). We use a new, comprehensive classification scheme based on radio, far- and near-IR, optical, and X-ray data to disentangle star-forming galaxies from AGN and radio-quiet from radio-loud AGN. We confirm our previous result that star-forming galaxies become dominant only below 0.1 mJy. The sub-mJy radio sky turns out to be a complex mix of star-forming galaxies and radio-quiet AGN evolving at a similar, strong rate; non-evolving low-luminosity radio galaxies; and declining radio powerful (P > 3 10^24 W/Hz) AGN. Our results suggest that radio emission from radio-quiet AGN is closely related to star formation. The detection of compact, high brightness temperature cores in several nearby radio-quiet AGN can be explained by the co-existence of two components, one non-evolving and AGN-related and one evolving and star-formation-related. Radio-quiet AGN are an important class of sub-mJy sources, accounting for ~30% of the sample and ~60% of all AGN, and outnumbering radio-loud AGN at < 0.1 mJy. This implies that future, large area sub-mJy surveys, given the appropriate ancillary multi-wavelength data, have the potential of being able to assemble vast samples of radio-quiet AGN by-passing the problems of obscuration, which plague the optical and soft X-ray bands.
We examine the radius evolution of close-in giant planets with a planet evolution model that couples the orbital-tidal and thermal evolution. For 45 transiting systems, we compute a large grid of cooling/contraction paths forward in time, starting fr
om a large phase space of initial semi-major axes and eccentricities. Given observational constraints at the current time for a given planet (semi-major axis, eccentricity, and system age) we find possible evolutionary paths that match these constraints, and compare the calculated radii to observations. We find that tidal evolution has two effects. First, planets start their evolution at larger semi-major axis, allowing them to contract more efficiently at earlier times. Second, tidal heating can significantly inflate the radius when the orbit is being circularized, but this effect on the radius is short-lived thereafter. Often circularization of the orbit is proceeded by a long period while the semi-major axis slowly decreases. Some systems with previously unexplained large radii that we can reproduce with our coupled model are HAT-P-7, HAT-P-9, WASP-10, and XO-4. This increases the number of planets for which we can match the radius from 24 (of 45) to as many as 35 for our standard case, but for some of these systems we are required to be viewing them at a special time around the era of current radius inflation. This is a concern for the viability of tidal inflation as a general mechanism to explain most inflated radii. Also, large initial eccentricities would have to be common. We also investigate the evolution of models that have a floor on the eccentricity, as may be due to a perturber. In this scenario we match the extremely large radius of WASP-12b. (Abridged)
