Compelled to do the right thing

We use a model of opinion formation to study the consequences of some mechanisms attempting to enforce the right behaviour in a society. We start from a model where the possible choices are not equivalent (such is the case when the agents decide to comply or not with a law) and where an imitation mechanism allow the agents to change their behaviour based on the influence of a group of partners. In addition, we consider the existence of two social constraints: a) an external authority, called monitor, that imposes the correct behaviour with infinite persuasion and b) an educated group of agents that act upon their fellows but never change their own opinion, i.e., they exhibit infinite adamancy. We determine the minimum number of monitors to induce an effective change in the behaviour of the social group, and the size of the educated group that produces the same effect. Also, we compare the results for the cases of random social interactions and agents placed on a network. We have verified that a small number of monitors are enough to change the behaviour of the society. This also happens with a relatively small educated group in the case of random interactions.Comment: 8 pages, 9 figures, submitted to EPJ

The extended HeII4686-emitting region in IZw18 unveiled: clues for peculiar ionizing sources

New integral field spectroscopy has been obtained for IZw18, the nearby lowest-metallicity galaxy considered our best local analog of systems forming at high-z. Here we report the spatially resolved spectral map of the nebular HeII4686 emission in IZw18, from which we derived for the first time its total HeII-ionizing flux. Nebular HeII emission implies the existence of a hard radiation field. HeII-emitters are observed to be more frequent among high-z galaxies than for local objects. So investigating the HeII-ionizing source(s) in IZw18 may reveal the ionization processes at high-z. HeII emission in star-forming galaxies, has been suggested to be mainly associated with Wolf-Rayet stars (WRs), but WRs cannot satisfactorily explain the HeII-ionization at all times, in particular at lowest metallicities. Shocks from supernova remnants, or X-ray binaries, have been proposed as additional potential sources of HeII-ionizing photons. Our data indicate that conventional HeII-ionizing sources (WRs, shocks, X-ray binaries) are not sufficient to explain the observed nebular HeII4686 emission in IZw18. We find that the HeII-ionizing radiation expected from models for either low-metallicity super-massive O stars or rotating metal-free stars could account for the HeII-ionization budget measured, while only the latter models could explain the highest values of HeII4686/Hbeta observed. The presence of such peculiar stars in IZw18 is suggestive and further investigation in this regard is needed. This letter highlights that some of the clues of the early Universe can be found here in our cosmic backyard.Comment: 6 pages, 3 figures. Accepted for publication in ApJ Letter

Aperture-free star formation rate of SDSS star-forming galaxies

Large area surveys with a high number of galaxies observed have undoubtedly marked a milestone in the understanding of several properties of galaxies, such as star-formation history, morphology, and metallicity. However, in many cases, these surveys provide fluxes from fixed small apertures (e.g. fibre), which cover a scant fraction of the galaxy, compelling us to use aperture corrections to study the global properties of galaxies. In this work, we derive the current total star formation rate (SFR) of Sloan Digital Sky Survey (SDSS) star-forming galaxies, using an empirically based aperture correction of the measured $\rm H\alpha$ flux for the first time, thus minimising the uncertainties associated with reduced apertures. All the $\rm H\alpha$ fluxes have been extinction-corrected using the $\rm H\alpha/H\beta$ ratio free from aperture effects. The total SFR for $\sim$210,000 SDSS star-forming galaxies has been derived applying pure empirical $\rm H\alpha$ and $\rm H\alpha/H\beta$ aperture corrections based on the Calar Alto Legacy Integral Field Area (CALIFA) survey. We find that, on average, the aperture-corrected SFR is $\sim$0.65dex higher than the SDSS fibre-based SFR. The relation between the SFR and stellar mass for SDSS star-forming galaxies (SFR--$\rm M_\star$) has been obtained, together with its dependence on extinction and $\rm H\alpha$ equivalent width. We compare our results with those obtained in previous works and examine the behaviour of the derived SFR in six redshift bins, over the redshift range $\rm 0.005 \leq z\leq 0.22$. The SFR--$\rm M_\star$ sequence derived here is in agreement with selected observational studies based on integral field spectroscopy of individual galaxies as well as with the predictions of recent theoretical models of disc galaxies

Entropy and equilibrium state of free market models

Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange between molecules during collisions. In physical systems, the energy exchange among molecules leads to a state of equipartition of the energy and to an equilibrium situation where the entropy is a maximum. On the other hand, in the majority of exchange models, the system converges to a very unequal condensed state, where one or a few agents concentrate all the wealth of the society while the wide majority of agents shares zero or almost zero fraction of the wealth. So, in those economic systems a minimum entropy state is attained. We propose here an analytical model where we investigate the effects of a particular class of economic exchanges that minimize the entropy. By solving the model we discuss the conditions that can drive the system to a state of minimum entropy, as well as the mechanisms to recover a kind of equipartition of wealth