On-off intermittency over an extended range of control parameter

We propose a simple phenomenological model exhibiting on-off intermittency over an extended range of control parameter. We find that the distribution of the 'off' periods has as a power-law tail with an exponent varying continuously between -1 and -2, at odds with standard on-off intermittency which occurs at a specific value of the control parameter, and leads to the exponent -3/2. This non-trivial behavior results from the competition between a strong slowing down of the dynamics at small values of the observable, and a systematic drift toward large values.Comment: 4 pages, 3 figure

On a conjecture by Boyd

The aim of this note is to prove the Mahler measure identity $m(x+x^{-1}+y+y^{-1}+5) = 6 m(x+x^{-1}+y+y^{-1}+1)$ which was conjectured by Boyd. The proof is achieved by proving relationships between regulators of both curves

Evolution of self-gravitating magnetized disks. I- Axisymmetric simulations

In this paper and a companion work, we report on the first global numerical simulations of self-gravitating magnetized tori, subject in particular to the influence of the magnetorotational instability (MRI). In this work, paper I, we restrict our calculations to the study of the axisymmetric evolution of such tori. Our goals are twofold: (1) to investigate how self-gravity influences the global structure and evolution of the disks; and (2) to determine whether turbulent density inhomogeneities can be enhanced by self-gravity in this regime. As in non self-gravitating models, the linear growth of the MRI is followed by a turbulent phase during which angular momentum is transported outward. As a result, self-gravitating tori quickly develop a dual structure composed of an inner thin Keplerian disk fed by a thicker self-gravitating disk, whose rotation profile is close to a Mestel disk. Our results show that the effects of self-gravity enhance density fluctuations much less than they smooth the disk, and giving it more coherence. We discuss the expected changes that will occur in 3D simulations, the results of which are presented in a companion paper.Comment: 20 pages, 7 figures, accepted for publication in Ap

Self-consistent nonspherical isothermal halos embedding zero-thickness disks

Disk-halo decompositions of galaxy rotation curves are generally performed in a parametric way. We construct self-consistent models of nonspherical isothermal halos embedding a zero-thickness disk, by assuming that the halo distribution function is a Maxwellian. The method developed here can be used to study other physically-based choices for the halo distribution function and the case of a disk accompanied by a bulge. In a preliminary investigation we note the existence of a fine tuning between the scalelengths R_{\Omega} and h, respectively characterizing the rise of the rotation curve and the luminosity profile of the disk, which surprisingly applies to both high surface brightness and low surface brightness galaxies. This empirical correlation identifies a much stronger conspiracy than the one required by the smoothness and flatness of the rotation curve (disk-halo conspiracy). The self-consistent models are characterized by smooth and flat rotation curves for very different disk-to-halo mass ratios, hence suggesting that conspiracy is not as dramatic as often imagined. For a typical rotation curve, with asymptotically flat rotation curve at V_{\infty} (the precise value of which can also be treated as a free parameter), and a typical density profile of the disk, self-consistent models are characterized by two dimensionless parameters, which correspond to the dimensional scales (the disk mass-to-light ratio M/L and the halo central density) of standard disk-halo decompositions. We show that if the rotation curve is decomposed by means of our self-consistent models, the disk-halo degeneracy is removed and typical rotation curves are fitted by models that are below the maximum-disk prescription. Similar results are obtained from a study of NGC 3198. Finally, we quantify the flattening of the spheroidal halo, which is significant, especially on the scale of the visible disk.Comment: accepted for publication in A&

Modelling elliptical galaxies: phase-space constraints on two-component (gamma1,gamma2) models

In the context of the study of the properties of the mutual mass distribution of the bright and dark matter in elliptical galaxies, present a family of two-component, spherical, self-consistent galaxy models, where one density distribution follows a gamma_1 profile, and the other a gamma_2 profile [(gamma_1,gamma_2) models], with different total masses and ``core'' radii. A variable amount of Osipkov-Merritt (radial) orbital anisotropy is allowed in both components. For these models, I derive analytically the necessary and sufficient conditions that the model parameters must satisfy in order to correspond to a physical system. Moreover, the possibility of adding a black hole at the center of radially anisotropic gamma models is discussed, determining analytically a lower limit of the anisotropy radius as a function of gamma. The analytical phase-space distribution function for (1,0) models is presented, together with the solution of the Jeans equations and the quantities entering the scalar virial theorem. It is proved that a globally isotropic gamma=1 component is consistent for any mass and core radius of the superimposed gamma=0 model; on the contrary, only a maximum value of the core radius is allowed for the gamma=0 model when a gamma=1 density distribution is added. The combined effects of mass concentration and orbital anisotropy are investigated, and an interesting behavior of the distribution function of the anisotropic gamma=0 component is found: there exists a region in the parameter space where a sufficient amount of anisotropy results in a consistent model, while the structurally identical but isotropic model would be inconsistent.Comment: 29 pages, LaTex, plus 5 .eps figures and macro aaspp4.sty - accepted by ApJ, main journa

Mahler measure of some n-variable polynomial families

The Mahler measures of some n-variable polynomial families are given in terms of special values of the Riemann zeta function and a Dirichlet L-series, generalizing the results of \cite{L}. The technique introduced in this work also motivates certain identities among Bernoulli numbers and symmetric functions

Global Models for the Evolution of Embedded, Accreting Protostellar Disks

Most analytic work to date on protostellar disks has focused on those in isolation from their environments. However, observations are now beginning to probe the earliest, most embedded phases of star formation, during which disks are rapidly accreting from their parent cores and cannot be modeled in isolation. We present a simple, one-zone model of protostellar accretion disks with high mass infall rates. Our model combines a self-consistent calculation of disk temperatures with an approximate treatment of angular momentum transport via two mechanisms. We use this model to survey the properties of protostellar disks across a wide range of stellar masses and evolutionary times, and make predictions for disks' masses, sizes, spiral structure, and fragmentation that will be directly testable by future large-scale surveys of deeply embedded disks. We define a dimensionless accretion-rotation parameter which, in conjunction with the disk's temperature, controls the disk evolution. We track the dominant mode of angular momentum transport, and demonstrate that for stars with final masses greater than roughly one solar mass, gravitational instabilities are the most important mechanism as most of the mass accumulates. We predict that binary formation through disk fission, fragmentation of the disk into small objects, and spiral arm strength all increase in importance to higher stellar masses.Comment: 17 pages, 9 figures, accepted for publication in ApJ. Model updated to better reflect simulations in the literature; discussion of key assumptions and strategy clarifie

The Seven Sisters DANCe III: Projected spatial distribution

Methods. We compute Bayesian evidences and Bayes Factors for a set of variations of the classical radial models by King (1962), Elson et al. (1987) and Lauer et al. (1995). The variations incorporate different degrees of model freedom and complexity, amongst which we include biaxial (elliptical) symmetry, and luminosity segregation. As a by-product of the model comparison, we obtain posterior distributions and maximum a posteriori estimates for each set of model parameters. Results. We find that the model comparison results depend on the spatial extent of the region used for the analysis. For a circle of 11.5 parsecs around the cluster centre (the most homogeneous and complete region), we find no compelling reason to abandon Kings model, although the Generalised King model, introduced in this work, has slightly better fitting properties. Furthermore, we find strong evidence against radially symmetric models when compared to the elliptic extensions. Finally, we find that including mass segregation in the form of luminosity segregation in the J band, is strongly supported in all our models. Conclusions. We have put the question of the projected spatial distribution of the Pleiades cluster on a solid probabilistic framework, and inferred its properties using the most exhaustive and least contaminated list of Pleiades candidate members available to date. Our results suggest however that this sample may still lack about 20% of the expected number of cluster members. Therefore, this study should be revised when the completeness and homogeneity of the data can be extended beyond the 11.5 parsecs limit. Such study will allow a more precise determination of the Pleiades spatial distribution, its tidal radius, ellipticity, number of objects and total mass.Comment: 39 pages, 31 figure

Comparison of the properties of two fossil groups of galaxies with the normal group NGC 6034 based on multiband imaging and optical spectroscopy

We collected multiband imaging and spectroscopy for two fossil groups (RX J1119.7+2126 and 1RXS J235814.4+150524) and one normal group (NGC 6034). We computed photometric redshifts in the central zones of each group, combining previous data with the SDSS five-band data. For each group we investigated the red sequence (RS) of the color-magnitude relation and computed the luminosity functions, stellar population ages and distributions of the group members. Spectroscopy allowed us to investigate the large-scale surroundings of these groups and the substructure levels in 1RXS J235814.4+150524 and NGC 6034. The large-scale environment of 1RXS J235814.4+150524 is poor, though its galaxy density map shows a clear signature of the surrounding cosmic web. RX J1119.7+2126 appears to be very isolated, while the cosmic environment of NGC 6034 is very rich. At the group scale, 1RXS J235814.4+150524 shows no substructure. Galaxies with recent stellar populations seem preferentially located in the group outskirts. A RS is discernable for all three groups in a color-magnitude diagram. The luminosity functions based on photometric redshift selection and on statistical background subtraction have comparable shapes, and agree with the few points obtained from spectroscopic redshifts. These luminosity functions show the expected dip between first and second brightest galaxies for the fossil groups only. Their shape is also regular and relatively flat at faint magnitudes down to the completeness level for RX J1119.7+2126 and NGC 6034, while there is a clear lack of faint galaxies for 1RXS J235814.4+150524. RX J1119.7+2126 is definitely classified as a fossil group; 1RXS J235814.4+150524 also has properties very close to those of a fossil group, while we confirm that NGC 6034 is a normal group.Comment: Accepted in A&A, english-improved, 5 jpeg figures, and shortened abstrac

A difference boosting neural network for automated star-galaxy classification

In this paper we describe the use of a new artificial neural network, called the difference boosting neural network (DBNN), for automated classification problems in astronomical data analysis. We illustrate the capabilities of the network by applying it to star galaxy classification using recently released, deep imaging data. We have compared our results with classification made by the widely used Source Extractor (SExtractor) package. We show that while the performance of the DBNN in star-galaxy classification is comparable to that of SExtractor, it has the advantage of significantly higher speed and flexibility during training as well as classification.Comment: 9 pages, 1figure, 7 tables, accepted for publication in Astronomy and Astrophysic