Embryo impacts and gas giant mergers II: Diversity of Hot Jupiters' internal structure

We consider the origin of compact, short-period, Jupiter-mass planets. We propose that their diverse structure is caused by giant impacts of embryos and super-Earths or mergers with other gas giants during the formation and evolution of these hot Jupiters. Through a series of numerical simulations, we show that typical head-on collisions generally lead to total coalescence of impinging gas giants. Although extremely energetic collisions can disintegrate the envelope of gas giants, these events seldom occur. During oblique and moderately energetic collisions, the merger products retain higher fraction of the colliders' cores than their envelopes. They can also deposit considerable amount of spin angular momentum to the gas giants and desynchronize their spins from their orbital mean motion. We find that the oblateness of gas giants can be used to infer the impact history. Subsequent dissipation of stellar tide inside the planets' envelope can lead to runaway inflation and potentially a substantial loss of gas through Roche-lobe overflow. The impact of super-Earths on parabolic orbits can also enlarge gas giant planets' envelope and elevates their tidal dissipation rate over $\sim$ 100 Myr time scale. Since giant impacts occur stochastically with a range of impactor sizes and energies, their diverse outcomes may account for the dispersion in the mass-radius relationship of hot Jupiters.Comment: 19 pages, 7 figures, 7 tables. Accepted for publication in MNRA

Green's function for the Relativistic Coulomb System via Sum Over Perturbation Series

We evaluate the Green's function of the D-dimensional relativistic Coulomb system via sum over perturbation series which is obtained by expanding the exponential containing the potential term $V({\bf x)}$ in the path integral into a power series. The energy spectra and wave functions are extracted from the resulting amplitude.Comment: 13 pages, ReVTeX, no figure

Remark on approximation in the calculation of the primordial spectrum generated during inflation

We re-examine approximations in the analytical calculation of the primordial spectrum of cosmological perturbation produced during inflation. Taking two inflation models (chaotic inflation and natural inflation) as examples, we numerically verify the accuracy of these approximations.Comment: 10 pages, 6 figures, to appear in PR

Entanglement creation between two causally-disconnected objects

We study the full entanglement dynamics of two uniformly accelerated Unruh-DeWitt detectors with no direct interaction in between but each coupled to a common quantum field and moving back-to-back in the field vacuum. For two detectors initially prepared in a separable state our exact results show that quantum entanglement between the detectors can be created by the quantum field under some specific circumstances, though each detector never enters the other's light cone in this setup. In the weak coupling limit, this entanglement creation can occur only if the initial moment is placed early enough and the proper acceleration of the detectors is not too large or too small compared to the natural frequency of the detectors. Once entanglement is created it lasts only a finite duration, and always disappears at late times. Prior result by Reznik derived using the time-dependent perturbation theory with extended integration domain is shown to be a limiting case of our exact solutions at some specific moment. In the strong coupling and high acceleration regime, vacuum fluctuations experienced by each detector locally always dominate over the cross correlations between the detectors, so entanglement between the detectors will never be generated.Comment: 16 pages, 8 figures; added Ref.[7] and related discussion

Path integral for a relativistic Aharonov-Bohm-Coulomb system

The path integral for the relativistic spinless Aharonov-Bohm-Coulomb system is solved, and the energy spectra are extracted from the resulting amplitude.Comment: 6 pages, Revte

The structure of the central disk of NGC 1068: a clumpy disk model

NGC 1068 is one of the best studied Seyfert II galaxies, for which the blackhole mass has been determined from the Doppler velocities of water maser. We show that the standard $\alpha$-disk model of NGC 1068 gives disk mass between the radii of 0.65 pc and 1.1 pc (the region from which water maser emission is detected) to be about 7x10$^7$ M$_\odot$ (for $\alpha=0.1$), more than four times the blackhole mass, and a Toomre Q-parameter for the disk is $\sim$0.001. This disk is therefore highly self-gravitating and is subject to large-amplitude density fluctuations. We conclude that the standard $\alpha$-viscosity description for the structure of the accretion disk is invalid for NGC 1068. In this paper we develop a new model for the accretion disk. The disk is considered to be composed of gravitationally bound clumps; accretion in this clumped disk model arises because of gravitational interaction of clumps with each other and the dynamical frictional drag exerted on clumps from the stars in the central region of the galaxy. The clumped disk model provides a self-consistent description of the observations of NGC 1068. The computed temperature and density are within the allowed parameter range for water maser emission, and the rotational velocity in the disk falls off as $r^{-0.35}$.Comment: To appear in Ap

Non-Thermal Production of WIMPs and the Sub-Galactic Structure of the Universe

There is increasing evidence that conventional cold dark matter (CDM) models lead to conflicts between observations and numerical simulations of dark matter halos on sub-galactic scales. Spergel and Steinhardt showed that if the CDM is strongly self-interacting, then the conflicts disappear. However, the assumption of strong self-interaction would rule out the favored candidates for CDM, namely weakly interacting massive particles (WIMPs), such as the neutralino. In this paper we propose a mechanism of non-thermal production of WIMPs and study its implications on the power spectrum. We find that the non-vanishing velocity of the WIMPs suppresses the power spectrum on small scales compared to what it obtained in the conventional CDM model. Our results show that, in this context, WIMPs as candidates for dark matter can work well both on large scales and on sub-galactic scales.Comment: 6 pages, 2 figures; typo corrected; to appear in PR

Internal Gravity Waves Modulate the Apparent Misalignment of Exoplanets around Hot Stars

We propose that the observed misalignment between extra-solar planets and their hot host stars can be explained by angular momentum transport within the host star. Observations have shown that this misalignment is preferentially around hot stars, which have convective cores and extended radiative envelopes. This situation is amenable to substantial angular momentum transport by internal gravity waves (IGW) generated at the convective-radiative interface. Here we present numerical simulations of this process and show that IGW can modulate the surface rotation of the star. With these two- dimensional simulations we show that IGW could explain the retrograde orbits observed in systems such as HAT-P-6 and HAT-P-7, however, extension to high obliquity objects will await future three- dimensional simulations. We note that these results also imply that individual massive stars should show temporal variations in their v sini measurements.Comment: 6 pages, 2 figures, Accepted for publication in ApJ

#Bigbirds never die: Understanding social dynamics of emergent hashtag

We examine the growth, survival, and context of 256 novel hashtags during the 2012 U.S. presidential debates. Our analysis reveals the trajectories of hashtag use fall into two distinct classes: “winners” that emerge more quickly and are sustained for longer periods of time than other “also-rans” hashtags. We propose a “conversational vibrancy” framework to capture dynamics of hashtags based on their topicality, interactivity, diversity, and prominence. Statistical analyses of the growth and persistence of hashtags reveal novel relationships between features of this framework and the relative success of hashtags. Specifically, retweets always contribute to faster hashtag adoption, replies extend the life of “winners” while having no effect on “also-rans.” This is the first study on the lifecycle of hashtag adoption and use in response to purely exogenous shocks. We draw on theories of uses and gratification, organizational ecology, and language evolution to discuss these findings and their implications for understanding social influence and collective action in social media more generally

Critical Protoplanetary Core Masses in Protoplanetary Disks and the Formation of Short-Period Giant Planets

We study a solid protoplanetary core of 1-10 earth masses migrating through a disk. We suppose the core luminosity is generated as a result of planetesimal accretion and calculate the structure of the gaseous envelope assuming equilibrium. This is a good approximation when the core mass is less than the critical value, M_{crit}, above which rapid gas accretion begins. We model the structure of the protoplanetary nebula as an accretion disk with constant \alpha. We present analytic fits for the steady state relation between disk surface density and mass accretion rate as a function of radius r. We calculate M_{crit} as a function of r, gas accretion rate through the disk, and planetesimal accretion rate onto the core \dot{M}. For a fixed \dot{M}, M_{crit} increases inwards, and it decreases with \dot{M}. We find that \dot{M} onto cores migrating inwards in a time 10^3-10^5 yr at 1 AU is sufficient to prevent the attainment of M_{crit} during the migration process. Only at small radii where planetesimals no longer exist can M_{crit} be attained. At small radii, the runaway gas accretion phase may become longer than the disk lifetime if the core mass is too small. However, massive cores can be built-up through the merger of additional incoming cores on a timescale shorter than for in situ formation. Therefore, feeding zone depletion in the neighborhood of a fixed orbit may be avoided. Accordingly, we suggest that giant planets may begin to form early in the life of the protostellar disk at small radii, on a timescale that may be significantly shorter than for in situ formation. (abridged)Comment: 24 pages (including 9 figures), LaTeX, uses emulateapj.sty, to be published in ApJ, also available at http://www.ucolick.org/~ct/home.htm