The mass function and dynamical mass of young star clusters: Why their initial crossing-time matters crucially

We highlight the impact of cluster-mass-dependent evolutionary rates upon the evolution of the cluster mass function during violent relaxation, that is, while clusters dynamically respond to the expulsion of their residual star-forming gas. Mass-dependent evolutionary rates arise when the mean volume density of cluster-forming regions is mass-dependent. In that case, even if the initial conditions are such that the cluster mass function at the end of violent relaxation has the same shape as the embedded-cluster mass function (i.e. infant weight-loss is mass-independent), the shape of the cluster mass function does change transiently {\it during} violent relaxation. In contrast, for cluster-forming regions of constant mean volume density, the cluster mass function shape is preserved all through violent relaxation since all clusters then evolve at the same mass-independent rate. On the scale of individual clusters, we model the evolution of the ratio between the dynamical mass and luminous mass of a cluster after gas expulsion. Specifically, we map the radial dependence of the time-scale for a star cluster to return to equilibrium. We stress that fields-of-view a few pc in size only, typical of compact clusters with rapid evolutionary rates, are likely to reveal cluster regions which have returned to equilibrium even if the cluster experienced a major gas expulsion episode a few Myr earlier. We provide models with the aperture and time expressed in units of the initial half-mass radius and initial crossing-time, respectively, so that our results can be applied to clusters with initial densities, sizes, and apertures different from ours.Comment: 14 pages, 10 figures, accepted for publication in MNRA

The puzzle of the cluster-forming core mass-radius relation and why it matters

We highlight how the mass-radius relation of cluster-forming cores combined with an external tidal field can influence infant weight-loss and disruption likelihood of clusters after gas expulsion. Specifically, we study how the relation between the bound fraction of stars staying in clusters at the end of violent relaxation and the cluster-forming core mass is affected by the slope and normalization of the core mass-radius relation. Assuming mass-independent star formation efficiency and gas-expulsion time-scale $\tau_{GExp}/\tau_{cross}$ and a given external tidal field, it is found that constant surface density cores and constant radius cores have the potential to lead to the preferential removal of high- and low-mass clusters, respectively. In contrast, constant volume density cores result in mass-independent cluster infant weight-loss, as suggested by observations. Our modelling includes predictions about the evolution of high-mass cluster-forming cores, a regime not yet covered by the observations. An overview of various issues directly affected by the nature of the core mass-radius relation is presented (e.g. cluster mass function, galaxy star formation histories, globular cluster self-enrichment). Finally, we emphasize that observational mass-radius data-sets of dense gas regions must be handled with caution as they may be the imprint of the molecular tracer used to map them, rather than reflecting cluster formation conditions. [Abridged]Comment: 14 pages, 7 figures, accepted to MNRA

Research Diary Visual Mapping : a reflective methodological tool for process and strategy-as-practice studies

Balogun, Huff and Johnson (2003) highlight the growing paradox for researchers who must focus on context and details while favouring general lines of research. These authors focus their reflection around the collection of qualitative data, particularly those of discussion groups, collaborative research and of research journal redaction techniques. We propose, in the context of collaborative research, a new utilisation of the personal diary, fuelled by our doctoral experiences in collaborative research. While the personal diary in its usual form increases the level of reflectivity on an intervening process, it is nevertheless difficult to exploit for the work of interpreting and legitimizing research. We therefore propose personal diary mapping. In addition to the advantages of personal diary mapping as a methodological tool for viewing the phenomenon, it allows a process to be described by highlighting specifics that are not obvious in reading a text. Moreover, the process of personal diary mapping provides a contribution to the epistemic work in a constructivist reference because it helps make the relationship between knowledge and empirical information explicit (Martinet 2007). After a summary bringing process studies closer to SaP and a review of the modalities of action research and their implications in terms of ethics and researcher responsibility, we present the origins, principles and benefits of visual mapping as regards the researcher's responsibility. In a second step, we illustrate the normative elements of this approach through a case study on strategic competence development based on personal diary mapping.Research Diary ; Visual Mapping ; methodological tool ; process ; strategy-as-practice

Normative Power, EU Preferences and Russia. Lessons from the Russian-Georgian War

The Russian-Georgian conflict of August 2008 proves to be a useful case in order to understand the functioning of the EU as a normative power in times of crisis. The core of the article is focused on the six EU major countries – Germany, France, Great-Britain, Italy, Poland and Spain – which embody different sets of preferences, and the way they want to deal with Russia. In the end, it tries to understand how preferences are linked with norms in that geopolitical context.Normative power, Georgian-Russian war, Mediation, Sanctions

The European Neighbourhood Policy as a Process of Democratic Norms Diffusion in Ukraine. The Case of the EU Act Beyond Conditionality?

This paper is then focused on the European Neighbourhood Policy and democracypromotion in its Eastern neighbours. Can the EU act beyond ‘hard conditionality’ experiencedduring the enlargement process in order to succeed in democratizing its neighbourhood? Whatare the obstacles to democratisation and political change within the neighbours? At the heart of the analysis lies the question of efficiency of the ENP without hardconditionality linked with adhesion. Conditionality, i.e. linking the granting of benefits to thefulfilment of some conditions, has been at the core of the EU policy when dealing withaccession candidate countries. During the enlargement process, ‘hard conditionality’(describing measures a country must meet in order to access any money or politicalretribution) was the key means for democratic norms diffusion. By contrast, neighbourhoodpolicy uses conditionality in a more flexible way, which is tantamount to ‘soft conditionality’,destined to influence policies but not to propose a one-fits-for-all policy. It is often arguedthat because of the lack of an effective or ‘hard’ conditionality, the EU cannot pretend to amajor role as a promoter of democratic norms.enlargement

The effects of the marginal tax rate in a matching model with endogenous labor supply

This paper analyzes the effects of the marginal tax rate on unemployment and economic efficiency in a matching model with homogenous agents when wages and working hours are bargained over. I show that the theoretical impact of a higher marginal tax rate on unemployment is ambiguous whatever the instantaneous utility in unemployment i.e. for an utility in unemployment that is either fixed or perfectly indexed on net wages. These results are in sharp contrast with the literature. Numerical simulations applied to France suggest that a higher marginal tax rate generally reduces the unemployment rate but at the expense of lower economic efficiency. The simulations point also out that the relation between the optimal marginal tax rate and the elasticity of labor supply is not monotonic.Matching model; Marginal Tax Rate; Labor supply; Utility in unemployment

The Origin of the Gaussian Initial Mass Function of Old Globular Cluster Systems

[Abridged] Evidence favouring a Gaussian initial globular cluster mass function has accumulated over recent years. We show that an approximately Gaussian mass function is naturally generated from a power-law mass distribution of protoglobular clouds by expulsion from the protocluster of star forming gas due to supernova activity, provided that the power-law mass distribution shows a lower-mass limit. As a result of gas loss, the gravitational potential of the protocluster gets weaker and only a fraction of the newly formed stars is retained. The mass fraction of bound stars ranges from zero to unity, depending on the local star formation efficiency $\epsilon$. Assuming that $\epsilon$ is independent of the protoglobular cloud mass, we investigate how such variations affect the mapping of a protoglobular cloud mass function to the resulting globular cluster initial mass function. A truncated power-law cloud mass spectrum generates bell-shaped cluster initial mass functions, with a turnover location mostly sensitive to the lower limit of the cloud mass range. We also show that a Gaussian mass function for the protoglobular clouds with a mean ${\rm log}m_G \simeq 6.1-6.2$ and a standard deviation $\sigma \lesssim 0.4$ provides results very similar to those resulting from a truncated power-law cloud mass spectrum, that is, the distribution function of masses of protoglobular clouds influences only weakly the shape of the resulting globular star cluster initial mass function. The gas removal process and the protoglobular cloud mass-scale dominate the relevant physics. Moreover, gas removal during star formation in massive clouds is likely the prime cause of the predominance of field stars in the Galactic halo.Comment: 24 pages, accepted for publication in MNRA

A non-grey analytical model for irradiated atmospheres. I: Derivation

Context. Semi-grey atmospheric models (with one opacity for the visible and one opacity for the infrared) are useful to understand the global structure of irradiated atmospheres, their dynamics and the interior structure and evolution of planets, brown dwarfs and stars. But when compared to direct numerical radiative transfer calculations for irradiated exoplanets, these models systematically overestimate the temperatures at low optical depth, independently of the opacity parameters. We wish to understand why semi-grey models fail at low optical depths, and provide a more accurate approximation to the atmospheric structure by accounting for the variable opacity in the infrared. Our analytical irradiated non-grey model is found to provide a range of temperatures that is consistent with that obtained by numerical calculations. We find that even for slightly non-grey thermal opacities the temperature structure differs significantly from previous semi-grey models. For small values of beta (expected when lines are dominant), we find that the non-grey effects are confined to low-optical depths. However, for beta larger than 0.5 (appropriate in the presence of bands with a wavelength-dependence smaller or comparable with the width of the Planck function), we find that the temperature structure is affected even down to infrared optical depths unity and deeper as a result of the so-called blanketing effect. The expressions that we derive may be used to provide a proper functional form for algorithms that invert the atmospheric properties from spectral information. Because a full atmospheric structure can be calculated directly, these expressions should be useful for simulations of the dynamics of these atmospheres and of the thermal evolution of the planets. Finally, they should be used to test full radiative transfer models and improve their convergence.Comment: Accepted by A&A, model available at http://www.oca.eu/parmentier/nongre