Collisional formation of massive exomoons of super-terrestrial exoplanets

Exomoons orbiting terrestrial or super-terrestrial exoplanets have not yet been discovered; their possible existence and properties are therefore still an unresolved question. Here we explore the collisional formation of exomoons through giant planetary impacts. We make use of smooth particle hydrodynamical (SPH) collision simulations and survey a large phase-space of terrestrial/super-terrestrial planetary collisions. We characterize the properties of such collisions, finding one rare case in which an exomoon forms through a graze&capture scenario, in addition to a few graze&merge or hit&run scenarios. Typically however, our collisions form massive circumplanetary discs, for which we use follow-up N-body simulations in order to derive lower-limit mass estimates for the ensuing exomoons. We investigate the mass, long-term tidal-stability, composition and origin of material in both the discs and the exomoons. Our giant-impact models often generate relatively iron-rich moons, that form beyond the synchronous radius of the planet, and would thus tidally evolve outward with stable orbits, rather than be destroyed. Our results suggest that it is extremely difficult to collisionally form currently-detectable exomoons orbiting super-terrestrial planets, through single giant impacts. It might be possible to form massive, detectable exomoons through several mergers of smaller exomoons, formed by multiple impacts, however more studies are required in order to reach a conclusion. Given the current observational initiatives, the search should focus primarily on more massive planet categories. However, about a quarter of the exomoons predicted by our models are approximately Mercury-mass or more, and are much more likely to be detectable given a factor 2 improvement in the detection capability of future instruments, providing further motivation for their development

Heavy-tailed distributions in fatal traffic accidents: role of human activities

Human activities can play a crucial role in the statistical properties of observables in many complex systems such as social, technological and economic systems. We demonstrate this by looking into the heavy-tailed distributions of observables in fatal plane and car accidents. Their origin is examined and can be understood as stochastic processes that are related to human activities. Simple mathematical models are proposed to illustrate such processes and compared with empirical results obtained from existing databanks.Comment: 10 pages, 5 figure

Multiplicative point process as a model of trading activity

Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of the frequency f. Furthermore, we analyze the relation between the power-law correlations and the origin of the power-law probability distribution of the signal intensity. We introduce a stochastic multiplicative model for the time intervals between point events and analyze the statistical properties of the signal analytically and numerically. Such model system exhibits power-law spectral density S(f)~1/f**beta for various values of beta, including beta=1/2, 1 and 3/2. Explicit expressions for the power spectra in the low frequency limit and for the distribution density of the interevent time are obtained. The counting statistics of the events is analyzed analytically and numerically, as well. The specific interest of our analysis is related with the financial markets, where long-range correlations of price fluctuations largely depend on the number of transactions. We analyze the spectral density and counting statistics of the number of transactions. The model reproduces spectral properties of the real markets and explains the mechanism of power-law distribution of trading activity. The study provides evidence that the statistical properties of the financial markets are enclosed in the statistics of the time interval between trades. A multiplicative point process serves as a consistent model generating this statistics.Comment: 10 pages, 3 figure

Scaling and correlations in the dynamics of forest-fire occurrence

Forest-fire waiting times, defined as the time between successive events above a certain size in a given region, are calculated for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact that the distribution of fire sizes is not a power law. The meaning of such behavior in terms of the possible self-similarity of the process in a nonstationary system is discussed. We find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a non-trivial ``instantaneous'' scaling law, sustained by the correlations of the process.Comment: Not a long paper, but many figures (but no large size in kb