On the Interaction Between Cosmic Rays and Dark Matter Molecular Clouds - II. The Age Distribution of Cosmic Ray Electrons

We explore further the proposal in paper I of this series that the confinement time of cosmic ray nuclei in the Milky Way is determined by their interaction with dark matter molecular clouds rather than by their escape from the halo, as is assumed in conventional models of cosmic ray propagation. The same proposal can be made for cosmic ray electrons. This proposal leads to a specific age distribution for the electrons which is in agreement with Tang's (1984) observations of the electron spectrum at high energies but not with Nishimura et al's (1980) earlier data, which lead to a flatter spectrum. However, the simplest leaky box and diffusion models disagree with both sets of data so that our trapping model is supported if Tang's data are correct.Comment: 7 pages, no figures, using MNRAS latex styl

Quasi-geometrical Optics Approximation in Gravitational Lensing

The gravitational lensing of gravitational waves should be treated in the wave optics instead of the geometrical optics when the wave length $\lambda$ of the gravitational waves is larger than the Schwarzschild radius of the lens mass $M$. The wave optics is based on the diffraction integral which represents the amplification of the wave amplitude by lensing. We study the asymptotic expansion of the diffraction integral in the powers of the wave length $\lambda$. The first term, arising from the short wavelength limit $\lambda \to 0$, corresponds to the geometrical optics limit. The second term, being of the order of $\lambda/M$, is the leading correction term arising from the diffraction effect. By analyzing this correction term, we find that (1) the lensing magnification $\mu$ is modified to $\mu ~(1+\delta)$, where $\delta$ is of the order of $(\lambda/M)^2$, and (2) if the lens has cuspy (or singular) density profile at the center $\rho(r) \propto r^{-\alpha}$ ($0 < \alpha \leq 2$), the diffracted image is formed at the lens center with the magnification $\mu \sim (\lambda/M)^{3-\alpha}$.Comment: 9 pages, 4 figures. Revised version accepted for publication in A&

High-energy γ\gamma-ray emission from GRBs

GRBs are nowadays a rather well understood phenomenon in the soft (KeV-MeV) $\gamma$-ray energy band, while only a few GRBs have been observed at high photon energies (E_{\gamma} \ut > 1 GeV). It is also widely recognized that GRBs accelerate protons to relativistic energies and that dense media are often present nearby the sources. Within this framework we compute in detail the high-energy $\gamma$-ray flux from the decay of neutral pions produced through the interaction of accelerate protons with nucleons in the surrounding medium. We also take into account the local and intergalactic $\gamma$-ray absorption. The presence of magnetic fields around the GRB sources causes the deflection of the accelerated protons and so a temporal spread of the produced high-energy $\gamma$-rays with respect to the signal in the soft $\gamma$-ray band. Moreover, we analyze the possibility to detect the $\gamma$-ray signal in the GeV-TeV energy range by the ARGO detector under construction in Tibet.Comment: 9 pages, 7 figures, abstract shortened, to appear in Astronomy and Astrophysic

Gamma ray emission from a baryonic dark halo

A recent re-analysis of EGRET data by Dixon et al. has led to the discovery of a statistically significant diffuse $\gamma$-ray emission from the galactic halo. We show that this emission can naturally be accounted for within a previously-proposed model for baryonic dark matter, according to which dark clusters of brown dwarfs and cold self-gravitating $H_2$ clouds populate the outer galactic halo and can show up in microlensing observations. Basically, cosmic-ray protons in the galactic halo scatter on the clouds clumped into dark clusters, giving rise to the observed $\gamma$-ray flux. We derive maps for the corresponding intensity distribution, which turn out to be in remarkably good agreement with those obtained by Dixon et al. We also address future prospects to test our predictions.Comment: 22 pages, 2 figures, slightly shortened version. to appear in New Journal of Physic

Microlensing by Compact Objects associated to Gas Clouds

We investigate gravitational microlensing of point-like lenses surrounded by diffuse gas clouds. Besides gravitational bending, one must also consider refraction and absorption phenomena. According to the cloud density, the light curves may suffer small to large deviations from Paczynski curves, up to complete eclipses. Moreover, the presence of the cloud endows this type of microlensing events with a high chromaticity and absorption lines recognizable by spectral analysis. It is possible that these objects populate the halo of our galaxy, giving a conspicuous contribution to the fraction of the baryonic dark matter. The required features for the extension and the mass of the cloud to provide appreciable signatures are also met by several astrophysical objects.Comment: 11 pages with 4 figures. Accepted by A&

Constraints on Cold H_2 Clouds from Gravitational Microlensing Searches

It has been proposed that the Galaxy might contain a population of cold clouds in numbers sufficient to account for a substantial fraction of the total mass of the Galaxy. These clouds would have masses of the order of 10^{-3} Solar mass and sizes of the order of 10 AU. We consider here the lensing effects of such clouds on the light from background stars. A semianalytical formalism for calculation of the magnification event rate produced by such gaseous lensing is developed, taking into account the spatial distribution of the dark matter in the Galaxy, the velocity distribution of the lensing clouds and source stars, and motion of the observer. Event rates are calculated for the case of gaseous lensing of stars in the Large Magellanic Cloud and results are directly compared with the results of the search for gravitational microlensing events undertaken by the MACHO collaboration. The MACHO experiment strongly constrains the properties of the proposed molecular clouds, but does not completely rule them out. Future monitoring programs will either detect or more strongly constrain this proposed population.Comment: 36 pages, 9 figures, 1 table, typos corrected, minor change

Starspot induced effects in microlensing events with rotating source star

We consider the effects induced by the presence of hot and cold spots on the source star in the light curves of simulated microlensing events due to either single or binary lenses taking into account the rotation of the source star and the orbital motion of the lens system. Our goal is to study the anomalies induced by these effects on simulated microlensing light curves.Comment: 5 pages, 2 figures, accepted for publication in MNRA

The Effects of Globalization on the Location of Industries in the OECD and European Union

Most international trade theory, whether classical or "new," predictst that increased globalization will be associated with increased locational concentration of particular economic activities, and hence increased specialization of national and regional economies, due to the greater freedom for industries to locate according to comparative advantage and economies of scale, and to integrate production systems based on an internationalization of intermediate goods sourcing. Relatively little empirical evidence exists on whether these predictions are correct. This paper presents the results of a statistical investigation of the trade-location relationship, using the OECD-STAN database, from 1970 to 1995. This investigation shows that in spite of rapidly rising trade, only in a very few industries has the spatial distribution changed substantially over the period studied. While intra-industry trade has risen across-the-board, locational concentration and specialization have increased little, if at all, in the European Union countries, and European economies remain much less specialized than equivalent regions of the USA. The paper then tries to speculate as to why this might be the case. Much of the intra-industry trade observed in Europe is probably not intermediate divisions of labor (production sharing), but head-to-head competition of largely national industries competing around similar products, through cross-market penetration. The question is how they manage to survive as such in an age of globalization. One hypothesis is that there are evolutionary dynamics involved: mature national firms and production clusters have capacities to adapt to changing circumstances which permit them to survive in more open markets. One major technique for adaptation is product differentiation, both horizontal (making the same products as competitors, through uptake of global state-ofthe- art knowledge) and vertical (quality differentiation, based on superior local knowledge). In this sense, the response of the European economies to globalization may reflect fundamentally different evolutionary dynamics from their American counterpart, whose regions integrated early on before they had mature industrial complexes, and where new industries tend to assume highly localized patterns, that serve as locational cores for the entire national industry. Most importantly, all of this implies that we need to develop non-deterministic theories of the relationship between trade and location, which take into account much more than the standard factors of comparative advantage and scale and integrate a dynamic evolutionary perspective.Globalization, locational specialization, product differentiation

Signatures of rotating binaries in micro-lensing experiments

Gravitational microlensing offers a powerful method with which to probe a variety of binary-lens systems, as the binarity of the lens introduces deviations from the typical (single-lens) Paczy\'nski behaviour in the event light curves. Generally, a static binary lens is considered to fit the observed light curve and, when the orbital motion is taken into account, an oversimplified model is usually employed. In this paper, we treat the binary-lens motion in a realistic way and focus on simulated events that are fitted well by a Paczy\'nski curve. We show that an accurate timing analysis of the residuals (calculated with respect to the best-fitting Paczy\'nski model) is usually sufficient to infer the orbital period of the binary lens. It goes without saying that the independently estimated period may be used to further constrain the orbital parameters obtained by the best-fitting procedure, which often gives degenerate solutions. We also present a preliminary analysis of the event OGLE-2011-BLG-1127 / MOA-2011-BLG-322, which has been recognized to be the result of a binary lens. The period analysis results in a periodicity of \simeq 12 days, which confirms the oscillation of the observed data around the best-fitting model. The estimated periodicity is probably associated with an intrinsic variability of the source star, and therefore there is an opportunity to use this technique to investigate either the intrinsic variability of the source or the effects induced by the binary-lens orbital motion.Comment: In press on MNRAS, 2014. 8 pages, 4 figures. On-line material available on the Journal web-pag