A family of lowered isothermal models

We present a family of self-consistent, spherical, lowered isothermal models, consisting of one or more mass components, with parameterised prescriptions for the energy truncation and for the amount of radially biased pressure anisotropy. The models are particularly suited to describe the phase-space density of stars in tidally limited, mass-segregated star clusters in all stages of their life-cycle. The models extend a family of isotropic, single-mass models by Gomez-Leyton and Velazquez, of which the well-known Woolley, King and Wilson (in the non-rotating and isotropic limit) models are members. We derive analytic expressions for the density and velocity dispersion components in terms of potential and radius, and introduce a fast model solver in PYTHON (LIMEPY), that can be used for data fitting or for generating discrete samples.Comment: 17 pages, 10 figures, 4 appendices, MNRAS, updated to match final journal styl

On the uniqueness of kinematical signatures of intermediate-mass black holes in globular clusters

Finding an intermediate-mass black hole (IMBH) in a globular cluster (GC), or proving its absence, is a crucial ingredient in our understanding of galaxy formation and evolution. The challenge is to identify a unique signature of an IMBH that cannot be accounted for by other processes. Observational claims of IMBH detection are often based on analyses of the kinematics of stars, such as a rise in the velocity dispersion profile towards the centre. In this contribution we discuss the degeneracy between this IMBH signal and pressure anisotropy in the GC. We show that that by considering anisotropic models it is possible to partially explain the innermost shape of the projected velocity dispersion profile, even though models that do not account for an IMBH do not exhibit a cusp in the centre.Comment: 4 pages, 2 figures. To be published in the Proceedings IAU Symposium No. 312, Star Clusters and Black Holes in Galaxies Across Cosmic Tim

Modulation of iron responsive gene expression and enzymatic activities in response to changes of the iron nutritional status in _Cucumis sativus_ L.

Regulation exerted by the iron status of the plant on the iron deficiency responses was investigated in cucumber roots (_Cucumis sativus_ L.) both at the biochemical and molecular level. Absence of iron induced the expression of the CsFRO1, CsIRT1, CsHA1 and the Cspepc1 transcripts that was followed by an increase in the corresponding enzymatic activities. Supply of iron repressed gene expression, in particular those of the Fe(III)-chelate reductase and for the high affinity iron transporter and reduce the enzymatic activities. Our results confirm and extend the hypothesis of a coordinate regulation of these responses. Besides these two activities strictly correlated with iron deficiency adaptation, we considered also the H+-ATPase and the phosphoenolpyruvate carboxylase, that have been shown to be involved in this response

A dynamical study of Galactic globular clusters under different relaxation conditions

We perform a systematic combined photometric and kinematic analysis of a sample of globular clusters under different relaxation conditions, based on their core relaxation time (as listed in available catalogs), by means of two well-known families of spherical stellar dynamical models. Systems characterized by shorter relaxation time scales are expected to be better described by isotropic King models, while less relaxed systems might be interpreted by means of non-truncated, radially-biased anisotropic f^(\nu) models, originally designed to represent stellar systems produced by a violent relaxation formation process and applied here for the first time to the study of globular clusters. The comparison between dynamical models and observations is performed by fitting simultaneously surface brightness and velocity dispersion profiles. For each globular cluster, the best-fit model in each family is identified, along with a full error analysis on the relevant parameters. Detailed structural properties and mass-to-light ratios are also explicitly derived. We find that King models usually offer a good representation of the observed photometric profiles, but often lead to less satisfactory fits to the kinematic profiles, independently of the relaxation condition of the systems. For some less relaxed clusters, f^(\nu) models provide a good description of both observed profiles. Some derived structural characteristics, such as the total mass or the half-mass radius, turn out to be significantly model-dependent. The analysis confirms that, to answer some important dynamical questions that bear on the formation and evolution of globular clusters, it would be highly desirable to acquire larger numbers of accurate kinematic data-points, well distributed over the cluster field.Comment: 18 pages, 7 figures. Accepted for publication in Astronomy & Astrophysic

The effect of stellar-mass black holes on the central kinematics of omega Cen: a cautionary tale for IMBH interpretations

The search for intermediate-mass black holes (IMBHs) in the centre of globular clusters is often based on the observation of a central cusp in the surface brightness profile and a rise towards the centre in the velocity dispersion profiles. Similar signatures, however, could result from other effects, that need to be taken into account in order to determine the presence (or the absence) of an IMBH in these stellar systems. Following our previous exploration of the role of radial anisotropy in shaping these observational signatures, we analyse here the effects produced by the presence of a population of centrally concentrated stellar-mass black holes. We fit dynamical models to omega Cen data, and we show that models with ~5% of their mass in black holes (consistent with ~100% retention fraction after natal kicks) can reproduce the data. When simultaneously considering both radial anisotropy and mass segregation, the best-fit model includes a smaller population of remnants, and a less extreme degree of anisotropy with respect to the models that include only one of these features. These results underline that before conclusions about putative IMBHs can be made, the effects of stellar-mass black holes and radial anisotropy need to be properly accounted for.Comment: 13 pages, 5 figures. Accepted for publication in MNRA

Testing lowered isothermal models with direct N-body simulations of globular clusters - II: Multimass models

Lowered isothermal models, such as the multimass Michie-King models, have been successful in describing observational data of globular clusters. In this study we assess whether such models are able to describe the phase space properties of evolutionary $N$-body models. We compare the multimass models as implemented in (Gieles \& Zocchi) to $N$-body models of star clusters with different retention fractions for the black holes and neutron stars evolving in a tidal field. We find that multimass models successfully reproduce the density and velocity dispersion profiles of the different mass components in all evolutionary phases and for different remnants retention. We further use these results to study the evolution of global model parameters. We find that over the lifetime of clusters, radial anisotropy gradually evolves from the low-mass to the high-mass components and we identify features in the properties of observable stars that are indicative of the presence of stellar-mass black holes. We find that the model velocity scale depends on mass as $m^{-\delta}$, with $\delta\simeq0.5$ for almost all models, but the dependence of central velocity dispersion on $m$ can be shallower, depending on the dark remnant content, and agrees well with that of the $N$-body models. The reported model parameters, and correlations amongst them, can be used as theoretical priors when fitting these types of mass models to observational data.Comment: 28 pages, 22 figures, published in MNRA

Statistical mechanics of warm and cold unfolding in proteins

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins.Comment: 5 pages, REVTex, 4 Postscript figure

Terrence Malick Beyond Nature and Grace: Song to Song and the Experience of Forgiveness

In The Tree of Life Terrence Malick poses the question of the relation between the order of grace and the order of nature in the cosmos and in human existence, a question presented through the relation of mother and father in the O\u27Brien family. The aim of this article is to analyze this issue and to present the role of glory in The Tree of Life as the transfiguration of nature operated by grace. Specifically, the example of forgiveness as one strand of this glory seems to be an helpful tool to understand the movie. Forgiveness, already present in The Tree of Life, becomes particularly important then in Song to Song. I will present this movie as an exemplar analysis of the human soul and of the capacity of forgiveness to draw the soul close to the eternal, as already happening in The Tree of Life. Underlining the relationship between forgiveness, sacrifice and glory will help to understand both the continuity between the two movies and the specificity of Song to Song

Rotating Globular Clusters

Internal rotation is considered to play a major role in the dynamics of some globular clusters. However, in only few cases it has been studied by quantitative application of realistic and physically justified global models. Here we present a dynamical analysis of the photometry and three-dimensional kinematics of omega Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models. The three clusters, characterized by different relaxation conditions, show evidence of differential rotation and deviations from sphericity. The combination of line-of-sight velocities and proper motions allows us to determine their internal dynamics, predict their morphology, and estimate their dynamical distance. The well-relaxed cluster 47 Tuc is very well interpreted by our model; internal rotation is found to explain the observed morphology. For M15, we provide a global model in good agreement with the data, including the central behavior of the rotation profile and the shape of the ellipticity profile. For the partially relaxed cluster omega Cen, the selected model reproduces the complex three-dimensional kinematics; in particular the observed anisotropy profile, characterized by a transition from isotropy, to weakly-radial anisotropy, and then to tangential anisotropy in the outer parts. The discrepancy found for the steep central gradient in the observed line-of-sight velocity dispersion profile and for the ellipticity profile is ascribed to the condition of only partial relaxation of this cluster and the interplay between rotation and radial anisotropy.Comment: 19 pages, 14 figures, accepted for publication in the Astrophysical Journa