Type-2 Fuzzy Entropy-Sets

The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with Type-2 Fuzzy Sets. We denote this concept Type-2 Fuzzy Entropy-Set. However, the construction of the notion of entropy measure on an infinite set, such us [0, 1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a Fuzzy Set on the universe [0, 1]. Furthermore, whenever the membership function of the considered Fuzzy Set in the universe [0, 1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca y Termini. Finally, we present an illustrative example where we use Type-2 Fuzzy Entropy-Sets instead of fuzzy entropies in a classical fuzzy algorithm

The globular cluster system of NGC 1316. II - The extraordinary object SH2

SH2 has been described as an isolated HII-region, located about 6.5 arcmin south of the nucleus of NGC 1316 (Fornax A), a merger remnant in the the outskirts of the Fornax cluster of galaxies. We give a first, preliminary description of the stellar content and environment of this remarkable object. We used photometric data in the Washington system and HST photometry from the Hubble Legacy Archive for a morphological description and preliminary aperture photometry. Low-resolution spectroscopy provides radial velocities of the brightest star cluster in SH2 and a nearby intermediate-age cluster. SH2 is not a normal HII-region, ionized by very young stars. It contains a multitude of star clusters with ages of approximately 0.1 Gyr. A ring-like morphology is striking. SH2 seems to be connected to an intermediate-age massive globular cluster with a similar radial velocity, which itself is the main object of a group of fainter clusters. Metallicity estimates from emission lines remain ambiguous. The present data do not yet allow firm conclusions about the nature or origin of SH2. It might be a dwarf galaxy that has experienced a burst of extremely clustered star formation. We may witness how globular clusters are donated to a parent galaxy.Comment: 5 pages, to appear in A&A, format slightly different from the printed versio

The role of quenching time in the evolution of the mass-size relation of passive galaxies from the WISP survey

We analyze how passive galaxies at z $\sim$ 1.5 populate the mass-size plane as a function of their stellar age, to understand if the observed size growth with time can be explained with the appearance of larger quenched galaxies at lower redshift. We use a sample of 32 passive galaxies extracted from the Wide Field Camera 3 Infrared Spectroscopic Parallel (WISP) survey with spectroscopic redshift 1.3 $\lesssim$ z $\lesssim$ 2.05, specific star-formation rates lower than 0.01 Gyr$^{-1}$, and stellar masses above 4.5 $\times$ 10$^{10}$ M$_\odot$. All galaxies have spectrally determined stellar ages from fitting of their rest-frame optical spectra and photometry with stellar population models. When dividing our sample into young (age $\leq$ 2.1 Gyr) and old (age $>$ 2.1 Gyr) galaxies we do not find a significant trend in the distributions of the difference between the observed radius and the one predicted by the mass-size relation. This result indicates that the relation between the galaxy age and its distance from the mass-size relation, if it exists, is rather shallow, with a slope alpha $\gtrsim$ -0.6. At face value, this finding suggests that multiple dry and/or wet minor mergers, rather than the appearance of newly quenched galaxies, are mainly responsible for the observed time evolution of the mass-size relation in passive galaxies.Comment: Accepted for publication in ApJ Letters; 6 pages, 3 figures, 1 tabl

The link between the masses and central stellar populations of S0 galaxies

Using high signal-to-noise ratio VLT/FORS2 long-slit spectroscopy, we have studied the properties of the central stellar populations and dynamics of a sample of S0 galaxies in the Fornax Cluster. The central absorption-line indices in these galaxies correlate well with the central velocity dispersions (Sigma0) in accordance with what previous studies found for elliptical galaxies. However, contrary to what it is usually assumed for cluster ellipticals, the observed correlations seem to be driven by systematic age and alpha-element abundance variations, and not changes in overall metallicity. We also found that the observed scatter in the Index-Sigma0 relations can be partially explained by the rotationally-supported nature of these systems. Indeed, even tighter correlations exist between the line indices and the maximum circular velocity of the galaxies. This study suggests that the dynamical mass is the physical property driving these correlations, and for S0 galaxies such masses have to be estimated assuming a large degree of rotational support. The observed trends imply that the most massive S0s have the shortest star-formation timescales and the oldest stellar populations.Comment: 21 pages, 17 figures, 9 tables, accepted for publication in MNRA

The globular cluster system of NGC1316. I. Wide-field photometry in the Washington system

NGC 1316 (Fornax A) is a prominent merger remnant in the outskirts of the Fornax cluster. The cluster system has not yet been studied in its entirety. We therefore present a wide-field study of the globular cluster system of NGC 1316, investigating its properties in relation to the global morphology of NGC 1316. We used the MOSAIC II camera at the 4-m Blanco telescope at CTIO in the filters Washington C and Harris R. We identify globular cluster candidates and study their color distribution and the structural properties of the system. In an appendix, we also make morphological remarks, present color maps, and present new models for the brightness and color profiles of the galaxy. The cluster system is well confined to the optically visible outer contours of NGC 1316. The color distribution of the entire sample is unimodal, but the color distribution of bright subsamples in the bulge shows two peaks that, by comparison with theoretical Washington colors with solar metallicity, correspond to ages of about 2 Gyr and 0.8 Gyr, respectively. We also find a significant population of clusters in the color range 0.8 < C-R < 1.1 which must be populated by clusters younger than 0.8 Gyr, unless they are very metal-poor. The color interval 1.3 < C-R < 1.6 hosts the bulk of intermediate-age clusters which show a surface density profile with a sharp decline at about 4 arcmin. The outer cluster population shows an unimodal color distribution with a peak at C-R=1.1, indicating a larger contribution of old, metal-poor clusters. Their luminosity function does not show the expected turn-over, so the fraction of younger clusters is still significant. Cluster formation in NGC 1316 has continued after an initial burst, presumably related to the main merger. A toy model with two bursts of ages 2 Gyr and 0.8 Gyr is consistent with photometric properties and dynamical M/L-values.Comment: 19 pages, to appear in Astronomy and Astrophysics, abstract abridged, format slightly different from the printed versio

Dust extinction from Balmer decrements of star-forming galaxies at 0.75<z<1.5 with HST/WFC3 spectroscopy from the WISP survey

Spectroscopic observations of Halpha and Hbeta emission lines of 128 star-forming galaxies in the redshift range 0.75<z<1.5 are presented. These data were taken with slitless spectroscopy using the G102 and G141 grisms of the Wide-Field-Camera 3 (WFC3) on board the Hubble Space Telescope as part of the WFC3 Infrared Spectroscopic Parallel (WISP) survey. Interstellar dust extinction is measured from stacked spectra that cover the Balmer decrement (Halpha/Hbeta). We present dust extinction as a function of Halpha luminosity (down to 3 x 10^{41} erg/s), galaxy stellar mass (reaching 4 x 10^{8} Msun), and rest-frame Halpha equivalent width. The faintest galaxies are two times fainter in Halpha luminosity than galaxies previously studied at z~1.5. An evolution is observed where galaxies of the same Halpha luminosity have lower extinction at higher redshifts, whereas no evolution is found within our error bars with stellar mass. The lower Halpha luminosity galaxies in our sample are found to be consistent with no dust extinction. We find an anti-correlation of the [OIII]5007/Halpha flux ratio as a function of luminosity where galaxies with L_{Halpha}<5 x 10^{41} erg/s are brighter in [OIII]5007 than Halpha. This trend is evident even after extinction correction, suggesting that the increased [OIII]5007/Halpha ratio in low luminosity galaxies is likely due to lower metallicity and/or higher ionization parameters.Comment: 11 pages, 9 figures, 2 tables; version addressing the referee comment

HST-WFC3 Near-Infrared Spectroscopy of Quenched Galaxies at zeta approx 1.5 from the WISP Survey: Stellar Populations Properties

We combine Hubble Space Telescope (HST) G102 and G141 near-IR (NIR) grism spectroscopy with HST/WFC3- UVIS, HST/WFC3-IR, and Spitzer/IRAC [3.6 microns] photometry to assemble a sample of massive (log(Mstar/M solar mass) at approx 11.0) and quenched (specific star formation rate 2 and the zeta approx 1.5 RS. According to their estimated ages, the time required for quenched galaxies off the RS to join their counterparts on the z approx. 1.5 RS is of the order of approx. 1G/yr

Tetrahedral mesh improvement by shell transformation

Existing flips for tetrahedral meshes simply make a selection from a few possible configurations within a single shell (i.e., a polyhedron that can be filled up with a mesh composed of a set of elements that meet each other at one edge), and their effectiveness is usually confined. A new topological operation for tetrahedral meshes named shell transformation is proposed. Its recursive callings execute a sequence of shell transformations on neighboring shells, acting like composite edge removal transformations. Such topological transformations are able to perform on a much larger element set than that of a single flip, thereby leading the way towards a better local optimum solution. Hence, a new mesh improvement algorithm is developed by combining this recursive scheme with other schemes, including smoothing, point insertion and point suppression. Numerical experiments reveal that the proposed algorithm can well balance some stringent and yet sometimes even conflict requirements of mesh improvement, i.e., resulting in high-quality meshes and reducing computing time at the same time. Therefore, it can be used for mesh quality improvement tasks involving millions of elements, in which it is essential not only to generate high-quality meshes, but also to reduce total computational time for mesh improvement