On the Fractal Distribution of HII Regions in Disk Galaxies

In this work we quantify the degree to which star-forming events are clumped. We apply a precise and accurate technique to calculate the correlation dimension Dc of the distribution of HII regions in a sample of disk galaxies. Our reliable results are distributed in the range 1.5<Dc<2.0. We get significant variations in the fractal dimension among galaxies, contrary to a universal picture sometimes claimed in literature. The faintest galaxies tend to distribute their HII regions in more clustered (less uniform) patterns. Moreover, the fractal dimension for the brightest HII regions within the same galaxy seems to be smaller than for the faintest ones suggesting some kind of evolutionary effect.Comment: 6 pages including 4 figures. To appear in Highlights of Spanish Astrophysics V: Proceedings of the VIII Scientific Meeting of the Spanish Astronomical Society held in Santander, July 7-11, 200

NGC 2548: clumpy spatial and kinematic structure in an intermediate-age galactic cluster

NGC 2548 is a 400-500 Myr old open cluster with evidence of spatial substructures likely caused by its interaction with the Galactic disk. In this work we use precise astrometric data from the Carte du Ciel - San Fernando (CdC-SF) catalogue to study the clumpy structure in this cluster. We confirm the fragmented structure of NGC 2548 but, additionally, the relatively high precision of our kinematic data lead us to the first detection of substructures in the proper motion space of a stellar cluster. There are three spatially separated cores each of which has its own counterpart in the proper motion distribution. The two main cores lie nearly parallel to the Galactic plane whereas the third one is significantly fainter than the others and it moves toward the Galactic plane separating from the rest of the cluster. We derive core positions and proper motions, as well as the stars belonging to each core.Comment: 9 pages, 8 figures, 4 tables. Accepted for publication in MNRA

A method for determining the radius of an open cluster from stellar proper motions

We propose a method for calculating the radius of an open cluster in an objective way from an astrometric catalogue containing, at least, positions and proper motions. It uses the minimum spanning tree (hereinafter MST) in the proper motion space to discriminate cluster stars from field stars and it quantifies the strength of the cluster-field separation by means of a statistical parameter defined for the first time in this paper. This is done for a range of different sampling radii from where the cluster radius is obtained as the size at which the best cluster-field separation is achieved. The novelty of this strategy is that the cluster radius is obtained independently of how its stars are spatially distributed. We test the reliability and robustness of the method with both simulated and real data from a well-studied open cluster (NGC 188), and apply it to UCAC4 data for five other open clusters with different catalogued radius values. NGC 188, NGC 1647, NGC 6603 and Ruprecht 155 yielded unambiguous radius values of 15.2+/-1.8, 29.4+/-3.4, 4.2+/-1.7 and 7.0+/-0.3 arcmin, respectively. ASCC 19 and Collinder 471 showed more than one possible solution but it is not possible to know whether this is due to the involved uncertainties or to the presence of complex patterns in their proper motion distributions, something that could be inherent to the physical object or due to the way in which the catalogue was sampled.Comment: 12 pages including 14 figures and 1 table. Accepted for publication in MNRA

A Decision Tree and S-Transform Based Approach for Power Quality Disturbances Classification

In this paper, it is presented an automated classification based on S-transform as feature extraction tool and Decision Tree as algorithm classifier. The signals generated according to mathematical models, including complex disturbances, have been used to design and test this approach, where noise is added to the signals from 40dB to 20dB. Finally, several disturbances, simple and complex, have been considered to test the implemented system. Evaluation results verifying the accuracy of the proposed method are presented.IEE

The Nature of the Gould Belt from a Fractal Analysis of its Stellar Population

The Gould Belt (GB) is a system of gas and young, bright stars distributed along a plane that is inclined with respect to the main plane of the Milky Way. Observational evidence suggests that the GB is our closest star formation complex, but its true nature and origin remain rather controversial. In this work we analyze the fractal structure of the stellar component of the GB. In order to do this, we tailor and apply an algorithm that estimates the fractal dimension in a precise and accurate way, avoiding both boundary and small data set problems. We find that early OB stars (of spectral types earlier than B4) in the GB have a fractal dimension very similar to that of the gas clouds in our Galaxy. On the contrary, stars in the GB of later spectral types show a larger fractal dimension, similar to that found for OB stars of both age groups in the local Galactic disk (LGD). This result seems to indicate that while the younger OB stars in the GB preserve the memory of the spatial structure of the cloud where they were born, older stars are distributed following a similar morphology as that found for the LGD stars. The possible causes for these differences are discussed.Comment: 20 pages including 7 figures and 1 table. ApJ (in press

The Fractal Dimension of Projected Clouds

The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a tri-dimensional fractal distorts its measured properties. Here we use simulated fractal clouds to study the relationship between the tri-dimensional fractal dimension (D_f) of modeled clouds and the dimension resulting from their projected images. We analyze different fractal dimension estimators: the correlation and mass dimensions of the clouds, and the perimeter-based dimension of their boundaries (D_per). We find the functional forms relating D_f with the projected fractal dimensions, as well as the dependence on the image resolution, which allow to estimatethe "real" D_f value of a cloud from its projection. The application of these results to Orion A indicates in a self-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a value higher than the result D_per+1 = 2.3 some times assumed in literature for interstellar clouds.Comment: 27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor change

On the properties of fractal cloud complexes

We study the physical properties derived from interstellar cloud complexes having a fractal structure. We first generate fractal clouds with a given fractal dimension and associate each clump with a maximum in the resulting density field. Then, we discuss the effect that different criteria for clump selection has on the derived global properties. We calculate the masses, sizes and average densities of the clumps as a function of the fractal dimension (D_f) and the fraction of the total mass in the form of clumps (epsilon). In general, clump mass does not fulfill a simple power law with size of the type M_cl ~ (R_cl)**(gamma), instead the power changes, from gamma ~ 3 at small sizes to gamma<3 at larger sizes. The number of clumps per logarithmic mass interval can be fitted to a power law N_cl ~ (M_cl)**(-alpha_M) in the range of relatively large masses, and the corresponding size distribution is N_cl ~ (R_cl)**(-alpha_R) at large sizes. When all the mass is forming clumps (epsilon=1) we obtain that as D_f increases from 2 to 3 alpha_M increases from ~0.3 to ~0.6 and alpha_R increases from ~1.0 to ~2.1. Comparison with observations suggests that D_f ~ 2.6 is roughly consistent with the average properties of the ISM. On the other hand, as the fraction of mass in clumps decreases (epsilon<1) alpha_M increases and alpha_R decreases. When only ~10% of the complex mass is in the form of dense clumps we obtain alpha_M ~ 1.2 for D_f=2.6 (not very different from the Salpeter value 1.35), suggesting this a likely link between the stellar initial mass function and the internal structure of molecular cloud complexes.Comment: 32 pages, 13 figures, 1 table. Accepted for publication in Ap

Fractal dimension of interstellar clouds: opacity and noise effects

There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. The measurement of the fractal dimension (Df) of interstellar clouds is a simple way to characterize this fractal structure, but several factors, both intrinsic to the clouds and to the observations, may contribute to affect the values obtained. In this work we study the effects that opacity and noise have on the determination of Df. We focus on two different fractal dimension estimators: the perimeter-area based dimension (Dper) and the mass-size dimension (Dm). We first use simulated fractal clouds to show that opacity does not affect the estimation of Dper. However, Dm tends to increase as opacity increases and this estimator fails when applied to optically thick regions. In addition, very noisy maps can seriously affect the estimation of both Dper and Dm, decreasing the final estimation of Df. We apply these methods to emission maps of Ophiuchus, Perseus and Orion molecular clouds in different molecular lines and we obtain that the fractal dimension is always in the range 2.6 < Df < 2.8 for these regions. These results support the idea of a relatively high (> 2.3) average fractal dimension for the interstellar medium, as traced by different chemical species.Comment: 17 pages including 6 figures and 1 table. Accepted for publication in Ap