How the three arches of the foot intercorrelate

Background: The foot is composed of medial, lateral and transverse arches which, particularly the medial arch, provide it with the ability to function both as a flexible and rigid structure for proper locomotion. Arches of the foot, as well as their effect on lower extremity function, have been studied. However, quantitative data on the relationship between these arches still remain scanty. The purpose of this study was, therefore, to examine how the three arches of the foot intercorrelate. Materials and methods: Seventy-six participants (58 males, 18 females) were recruited to participate in the study. Bilateral weight-bearing lateral radiographs of the right foot were taken from each participant. Navicular heights (NH), medial cuneiform height (MCH), calcaneal inclination angle (CIA) and calcaneal-first metatarsal angle (C1MA) were measured to represent the medial arch. The lateral arch was represented by cuboid height (CH) and calcaneal-fifth metatarsal angle (C5MA) whereas; MCH and CH represented the transverse arch. Mean difference of variables between males and females was compared using independent t-test while the correlation between the variables was determined using Pearson correlation. Results: All the variables were not significantly related to gender. Significant moderate to excellent linear correlations were observed between the variables. CIA showed the strongest correlation with C1MA (r = –0.90) and C5MA (r = –0.84) whereas, CH had the least correlation with other variables. Conclusions: The moderate to excellent correlations between the variables indicate that deformation or elevation of the medial arch may consequently result in similar movements of the lateral and transverse arches and vice versa

The spatially resolved star formation history of CALIFA galaxies: Cosmic time scales

This paper presents the mass assembly time scales of nearby galaxies observed by CALIFA at the 3.5m telescope in Calar Alto. We apply the fossil record method of the stellar populations to the complete sample of the 3rd CALIFA data release, with a total of 661 galaxies, covering stellar masses from 10$^{8.4}$ to 10$^{12}$ M$_{\odot}$ and a wide range of Hubble types. We apply spectral synthesis techniques to the datacubes and process the results to produce the mass growth time scales and mass weighted ages, from which we obtain temporal and spatially resolved information in seven bins of galaxy morphology and six bins of stellar mass (M$_{\star}$) and stellar mass surface density ($\Sigma_{\star}$). We use three different tracers of the spatially resolved star formation history (mass assembly curves, ratio of half mass to half light radii, and mass-weighted age gradients) to test if galaxies grow inside-out, and its dependence with galaxy stellar mass, $\Sigma_{\star}$, and morphology. Our main results are as follows: (a) The innermost regions of galaxies assemble their mass at an earlier time than regions located in the outer parts; this happens at any given M$_{\star}$, $\Sigma_{\star}$, or Hubble type, including the lowest mass systems. (b) Galaxies present a significant diversity in their characteristic formation epochs for lower-mass systems. This diversity shows a strong dependence of the mass assembly time scales on $\Sigma_{\star}$ and Hubble type in the lower-mass range (10$^{8.4}$ to 10$^{10.4}$), but a very mild dependence in higher-mass bins. (c) All galaxies show negative $\langle$log age$\rangle_{M}$ gradients in the inner 1 HLR. The profile flattens with increasing values of $\Sigma_{\star}$. There is no significant dependence on M$_{\star}$ within a particular $\Sigma_{\star}$ bin, except for the lowest bin, where the gradients becomes steeper.Comment: 15 pages, 13 figures, 3 tables, accepted for publication in Astronomy & Astrophysics. *Abridged abstract

The cosmic evolution of the spatially-resolved star formation rate and stellar mass of the CALIFA survey

We investigate the cosmic evolution of the absolute and specific star formation rate (SFR, sSFR) of galaxies as derived from a spatially-resolved study of the stellar populations in a set of 366 nearby galaxies from the CALIFA survey. The analysis combines GALEX and SDSS images with the 4000 break, H_beta, and [MgFe] indices measured from the datacubes, to constrain parametric models for the SFH, which are then used to study the cosmic evolution of the star formation rate density (SFRD), the sSFR, the main sequence of star formation (MSSF), and the stellar mass density (SMD). A delayed-tau model, provides the best results, in good agreement with those obtained from cosmological surveys. Our main results from this model are: a) The time since the onset of the star formation is larger in the inner regions than in the outer ones, while tau is similar or smaller in the inner than in the outer regions. b) The sSFR declines rapidly as the Universe evolves, and faster for early than for late type galaxies, and for the inner than for the outer regions of galaxies. c) SFRD and SMD agree well with results from cosmological surveys. At z< 0.5, most star formation takes place in the outer regions of late spiral galaxies, while at z>2 the inner regions of the progenitors of the current E and S0 are the major contributors to SFRD. d) The inner regions of galaxies are the major contributor to SMD at z> 0.5, growing their mass faster than the outer regions, with a lookback time at 50% SMD of 9 and 6 Gyr for the inner and outer regions. e) The MSSF follows a power-law at high redshift, with the slope evolving with time, but always being sub-linear. f) In agreement with galaxy surveys at different redshifts, the average SFH of CALIFA galaxies indicates that galaxies grow their mass mainly in a mode that is well represented by a delayed-tau model, with the peak at z~2 and an e-folding time of 3.9 Gyr.Comment: 23 pages, 16 figures, 6 tables, accepted for publication in Astronomy & Astrophysics. *Abridged abstract

The spatially-resolved star formation histories of CALIFA galaxies: Implications for galaxy formation

This paper presents the spatially resolved star formation history (SFH) of nearby galaxies with the aim of furthering our understanding of the different processes involved in the formation and evolution of galaxies. To this end, we apply the fossil record method of stellar population synthesis to a rich and diverse data set of 436 galaxies observed with integral field spectroscopy in the CALIFA survey. The sample covers a wide range of Hubble types, with stellar masses ranging from $M_\star \sim 10^9$ to $7 \times 10^{11} M_\odot$. Spectral synthesis techniques are applied to the datacubes to retrieve the spatially resolved time evolution of the star formation rate (SFR), its intensity ($\Sigma_{\rm SFR}$), and other descriptors of the 2D-SFH in seven bins of galaxy morphology (E, S0, Sa, Sb, Sbc, Sc, and Sd), and five bins of stellar mass. Our main results are: a) Galaxies form very fast independently of their current stellar mass, with the peak of star formation at high redshift ($z > 2$). Subsequent star formation is driven by $M_\star$ and morphology, with less massive and later type spirals showing more prolonged periods of star formation. b) At any epoch in the past the SFR is proportional to $M_\star$, with most massive galaxies having the highest absolute (but lowest specific) SFRs. c) While nowadays $\Sigma_{\rm SFR}$ is similar for all spirals, and significantly lower in early type galaxies (ETG), in the past $\Sigma_{\rm SFR}$ scales well with morphology. The central regions of today's ETGs are where $\Sigma_{\rm SFR}$ reached the highest values ($> 10^3 \,M_\odot\,$Gyr$^{-1}\,$pc$^{-2}$), similar to those measured in high redshift star forming galaxies. d) The evolution of $\Sigma_{\rm SFR}$ in Sbc systems matches that of models for Milky-Way-like galaxies, suggesting that the formation of a thick disk may be a common phase in spirals at early epochs.Comment: 21 pages, 11 figures, 1 table, accepted for publication in Astronomy & Astrophysics, abstract abridged for arXiv submissio

Resolving galaxies in time and space: II: Uncertainties in the spectral synthesis of datacubes

In a companion paper we have presented many products derived from the application of the spectral synthesis code STARLIGHT to datacubes from the CALIFA survey, including 2D maps of stellar population properties and 1D averages in the temporal and spatial dimensions. Here we evaluate the uncertainties in these products. Uncertainties due to noise and spectral shape calibration errors and to the synthesis method are investigated by means of a suite of simulations based on 1638 CALIFA spectra for NGC 2916, with perturbations amplitudes gauged in terms of the expected errors. A separate study was conducted to assess uncertainties related to the choice of evolutionary synthesis models. We compare results obtained with the Bruzual & Charlot models, a preliminary update of them, and a combination of spectra derived from the Granada and MILES models. About 100k CALIFA spectra are used in this comparison. Noise and shape-related errors at the level expected for CALIFA propagate to 0.10-0.15 dex uncertainties in stellar masses, mean ages and metallicities. Uncertainties in A_V increase from 0.06 mag in the case of random noise to 0.16 mag for shape errors. Higher order products such as SFHs are more uncertain, but still relatively stable. Due to the large number statistics of datacubes, spatial averaging reduces uncertainties while preserving information on the history and structure of stellar populations. Radial profiles of global properties, as well as SFHs averaged over different regions are much more stable than for individual spaxels. Uncertainties related to the choice of base models are larger than those associated with data and method. Differences in mean age, mass and metallicity are ~ 0.15 to 0.25 dex, and 0.1 mag in A_V. Spectral residuals are ~ 1% on average, but with systematic features of up to 4%. The origin of these features is discussed. (Abridged)Comment: A&A, accepte

The redshift evolution of oxygen and nitrogen abundances in emission-line SDSS galaxies

The oxygen and nitrogen abundance evolutions with redshift and galaxy stellar mass in emission-line SDSS galaxies are investigated. This is the first such study for nitrogen abundances, and it provides an additional constraint for the study of the chemical evolution of galaxies. We have devised a criterion to recognize and exclude from consideration AGNs and star-forming galaxies with large errors in the line flux measurements. To select star-forming galaxies with accurate line fluxes measurements, we require that, for each galaxy, the nitrogen abundances derived with various calibrations based on different emission lines agree. Using this selection criterion, subsamples of star-forming galaxies have been extracted from catalogs of the MPA/JHU group. We found that the galaxies of highest masses, those with masses > 10^11.2 M_sun, have not been enriched in both oxygen and nitrogen over the last 3 Gyr: they have formed their stars in the so distant past that these have returned their nucleosynthesis products to the interstellar medium before z=0.25. The galaxies in the mass range from 10^11.0 M_sun to 10^11.2 M_sun do not show an appreciable enrichment in oxygen, but do show some enrichment in nitrogen: they also formed their stars before z=0.25 but later in comparison to the galaxies of highest masses; these stars have not returned nitrogen to the interstellar medium before z=0.25 because they have not had enough time to evolve. This suggests that stars with lifetimes of 2-3 Gyr contribute to the nitrogen production. Finally, galaxies with masses < 10^11 M_sun show enrichment in both oxygen and nitrogen during the last 3 Gyr: they have undergone appreciable star formation and have converted up to 20% of their mass into stars over this period.Comment: 43 pages, 15 figures, accepted for publication in the Astrophysical Journa