On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier-Stokes equations

In our previous paper [12] (Rev. Math. Phys. 16, 383-420 (2004)), a general framework was outlined to treat the approximate solutions of semilinear evolution equations; more precisely, a scheme was presented to infer from an approximate solution the existence (local or global in time) of an exact solution, and to estimate their distance. In the first half of the present work the abstract framework of \cite{uno} is extended, so as to be applicable to evolutionary PDEs whose nonlinearities contain derivatives in the space variables. In the second half of the paper this extended framework is applied to theincompressible Navier-Stokes equations, on a torus T^d of any dimension. In this way a number of results are obtained in the setting of the Sobolev spaces H^n(T^d), choosing the approximate solutions in a number of different ways. With the simplest choices we recover local existence of the exact solution for arbitrary data and external forces, as well as global existence for small data and forces. With the supplementary assumption of exponential decay in time for the forces, the same decay law is derived for the exact solution with small (zero mean) data and forces. The interval of existence for arbitrary data, the upper bounds on data and forces for global existence, and all estimates on the exponential decay of the exact solution are derived in a fully quantitative way (i.e., giving the values of all the necessary constants; this makes a difference with most of the previous literature). Nextly, the Galerkin approximate solutions are considered and precise, still quantitative estimates are derived for their H^n distance from the exact solution; these are global in time for small data and forces (with exponential time decay of the above distance, if the forces decay similarly).Comment: LaTeX, 84 pages. The final version published in Reviews in Mathematical Physic

Observational hints of radial migration in disc galaxies from CALIFA

Context. According to numerical simulations, stars are not always kept at their birth galactocentric distances but they have a tendency to migrate. The importance of this radial migration in shaping galactic light distributions is still unclear. However, if radial migration is indeed important, galaxies with different surface brightness (SB) profiles must display differences in their stellar population properties. Aims: We investigate the role of radial migration in the light distribution and radial stellar content by comparing the inner colour, age, and metallicity gradients for galaxies with different SB profiles. We define these inner parts, avoiding the bulge and bar regions and up to around three disc scale lengths (type I, pure exponential) or the break radius (type II, downbending; type III, upbending). Methods: We analysed 214 spiral galaxies from the CALIFA survey covering different SB profiles. We made use of GASP2D and SDSS data to characterise the light distribution and obtain colour profiles of these spiral galaxies. The stellar age and metallicity profiles were computed using a methodology based on full-spectrum fitting techniques (pPXF, GANDALF, and STECKMAP) to the Integral Field Spectroscopic CALIFA data. Results: The distributions of the colour, stellar age, and stellar metallicity gradients in the inner parts for galaxies displaying different SB profiles are unalike as suggested by Kolmogorov-Smirnov and Anderson-Darling tests. We find a trend in which type II galaxies show the steepest profiles of all, type III show the shallowest, and type I display an intermediate behaviour. Conclusions: These results are consistent with a scenario in which radial migration is more efficient for type III galaxies than for type I systems, where type II galaxies present the lowest radial migration efficiency. In such a scenario, radial migration mixes the stellar content, thereby flattening the radial stellar properties and shaping different SB profiles. However, in light of these results we cannot further quantify the importance of radial migration in shaping spiral galaxies, and other processes, such as recent star formation or satellite accretion, might play a role

Stellar metallicity from optical and UV spectral indices: test case for WEAVE-StePS

Context. The upcoming generation of optical spectrographs on four meter-class telescopes, with their huge multiplexing capabilities, excellent spectral resolution, and unprecedented wavelength coverage, will provide high-quality spectra for thousands of galaxies. These data will allow us to examine of the stellar population properties at intermediate redshift, an epoch that remains unexplored by large and deep surveys. Aims. We assess our capability to retrieve the mean stellar metallicity in galaxies at different redshifts and signal-to-noise ratios (S/N), while simultaneously exploiting the ultraviolet (UV) and optical rest-frame wavelength coverage. Methods. The work is based on a comprehensive library of spectral templates of stellar populations, covering a wide range of age and metallicity values and built assuming various star formation histories (SFHs), to cover an observable parameter space with diverse chemical enrichment histories and dust attenuation. We took into account possible observational errors, simulating realistic observations of a large sample of galaxies carried out with WEAVE at the William Herschel Telescope at different redshifts and S/N values. We measured all the available and reliable indices on the simulated spectra and on the comparison library. We then adopted a Bayesian approach to compare the two sets of measurements in order to obtain the probability distribution of stellar metallicity with an accurate estimate of the uncertainties. Results. The analysis of the spectral indices has shown how some mid-UV indices, such as BL3580 and Fe3619, can provide reliable constraints on stellar metallicity, along with optical indicators. The analysis of the mock observations has shown that even at S/N = 10, the metallicity can be derived within 0.3 dex, in particular, for stellar populations older than 2 Gyr. The S/N value plays a crucial role in the uncertainty of the estimated metallicity and so, the differences between S/N = 10 and S/N = 30 are quite large, with uncertainties of ∼ 0.15 dex in the latter case. On the contrary, moving from S/N = 30 to S/N = 50, the improvement on the uncertainty of the metallicity measurements is almost negligible. Our results are in good agreement with other theoretical and observational works in the literature and show how the UV indicators, coupled with classic optical ones, can be advantageous in constraining metallicities. Conclusions. We demonstrate that a good accuracy can be reached on the spectroscopic measurements of the stellar metallicity of galaxies at intermediate redshift, even at low S/N, when a large number of indices can be employed, including some UV indices. This is very promising for the upcoming surveys carried out with new, highly multiplexed, large-field spectrographs, such as StePS at the WEAVE and 4MOST, which will provide spectra of thousands of galaxies covering large spectral ranges (between 3600 and 9000 Å in the observed frame) at relatively high S/N (> 10 Å−1 )

Delving deep: a population of extremely dusty dwarfs observed by JWST

We take advantage of the NIRCam photometric observations available as part of the Cosmic Evolution Early Release Science survey (CEERS) to identify and analyse very red sources in an effort to discover very dusty star forming galaxies. We select red galaxies as objects with a S/N>3 at 4.4 $\mu$m and a S/N<2 in all JWST and HST filters at $\lambda\leq2\mu$m, which corresponds to [F200W]-[F444W]>1.2 considering CEERS depths. This selection is ideal to identify very dusty (Av>1 mag) galaxies with stellar masses between $10^6$ to $10^{10}\, \rm M_{\odot}$ at z<5, more massive dusty galaxies at z=5-18 and galaxies at z>18 due to the Lyman absorption, independently of their dust extinction. Our sample of F200W-dropouts contains no strong candidates at z>6.5, instead it consists almost completely (~81%) of z<2 low-mass galaxies, with a median stellar mass of $10^{7.3} \rm M_{\odot}$. These galaxies show an exceptional dust extinction with median value of Av=4.9 mag, completely unexpected given their low stellar mass. The remaining galaxies, which are at z1), but they are generally more massive $>10^{7.5}\rm M_{\odot}$.Comment: 30 pages, 1 table, 19 figures, accepted for publication in A&

Two-dimensional multi-component photometric decomposition of CALIFA galaxies

We present a two-dimensional multi-component photometric decomposition of 404 galaxies from the Calar Alto Legacy Integral Field Area Data Release 3 (CALIFA-DR3). They represent all possible galaxies with no clear signs of interaction and not strongly inclined in the final CALIFA data release. Galaxies are modelled in the g, r, and i Sloan Digital Sky Survey (SDSS) images including, when appropriate, a nuclear point source, bulge, bar, and an exponential or broken disc component. We use a human-supervised approach to determine the optimal number of structures to be included in the fit. The dataset, including the photometric parameters of the CALIFA sample, is released together with statistical errors and a visual analysis of the quality of each fit. The analysis of the photometric components reveals a clear segregation of the structural composition of galaxies with stellar mass. At high masses (log(M⋆/M⊙) > 11), the galaxy population is dominated by galaxies modelled with a single Sérsic or a bulge+disc with a bulge-to-total (B/T) luminosity ratio B/T > 0.2. At intermediate masses (9.5 < log(M⋆/M⊙) < 11), galaxies described with bulge+disc but B/T < 0.2 are preponderant, whereas, at the low mass end (log(M⋆/M⊙)< 9.5), the prevailing population is constituted by galaxies modelled with either pure discs or nuclear point sources+discs (i.e., no discernible bulge). We obtain that 57% of the volume corrected sample of disc galaxies in the CALIFA sample host a bar. This bar fraction shows a significant drop with increasing galaxy mass in the range 9.5 < log(M⋆/M⊙) < 11.5. The analyses of the extended multi-component radial profile result in a volume-corrected distribution of 62%, 28%, and 10% for the so-called Type I (pure exponential), Type II (down-bending), and Type III (up-bending) disc profiles, respectively. These fractions are in discordance with previous findings. We argue that the different methodologies used to detect the breaks are the main cause for these differences.PostprintPeer reviewe

New insight on the nature of cosmic reionizers from the CEERS survey

The Epoch of Reionization (EoR) began when galaxies grew in abundance and luminosity, so their escaping Lyman continuum (LyC) radiation started ionizing the surrounding neutral intergalactic medium (IGM). Despite significant recent progress, the nature and role of cosmic reionizers are still unclear: in order to define them, it would be necessary to directly measure their LyC escape fraction ($f_{esc}$). However, this is impossible during the EoR due to the opacity of the IGM. Consequently, many efforts at low and intermediate redshift have been made to determine measurable indirect indicators in high-redshift galaxies so that their $f_{esc}$ can be predicted. This work presents the analysis of the indirect indicators of 62 spectroscopically confirmed star-forming galaxies at $6 \leq z \leq 9$ from the Cosmic Evolution Early Release Science (CEERS) survey, combined with 12 sources with public data from other JWST-ERS campaigns. From the NIRCam and NIRSpec observations, we measured their physical and spectroscopic properties. We discovered that on average $6<z<9$ star-forming galaxies are compact in the rest-frame UV ($r_e \sim$ 0.4 kpc), are blue sources (UV-$\beta$ slope $\sim$ -2.17), and have a predicted $f_{esc}$ of about 0.13. A comparison of our results to models and predictions as well as an estimation of the ionizing budget suggests that low-mass galaxies with UV magnitudes fainter than $M_{1500} = -18$ that we currently do not characterize with JWST observations probably played a key role in the process of reionization.Comment: 14 pages, 11 figures, submitted to A&

Galaxy morphology from z ~ 6 through the lens of JWST

Context: The James Webb Space Telescope's (JWST's) unprecedented combination of sensitivity, spatial resolution, and infrared coverage has enabled a new era of galaxy morphology exploration across most of cosmic history. Aims: We analyze the near-infrared (NIR ~ 0.8 -1 μm) rest-frame morphologies of galaxies with log M∗/M⊙ &gt; 9 in the redshift range of 0 &lt; z &lt; 6, compare with previous HST-based results and release the first JWST-based morphological catalog of ~20 000 galaxies in the CEERS survey. Methods: We classified the galaxies in our sample into four main broad classes: spheroid, disk+spheroid, disk, and disturbed, based on imaging with four filters: F150W, F200W, F356W, and F444W. We used convolutional neural networks (CNNs) trained on HST/WFC3 labeled images and domain-adapted to JWST/NIRCam. Results: We find that ~90% and ~75% of galaxies at z &lt; 3 have the same early and late and regular and irregular classification, respectively, in JWST and HST imaging when considering similar wavelengths. For small (large) and faint objects, JWST-based classifications tend to systematically present less bulge-dominated systems (peculiar galaxies) than HST-based ones, but the impact on the reported evolution of morphological fractions is less than ~10%. Using JWST-based morphologies at the same rest-frame wavelength ( ~0.8 -1 μm), we confirm an increase in peculiar galaxies and a decrease in bulge-dominated galaxies with redshift, as reported in previous HST-based works, suggesting that the stellar mass distribution, in addition to light distribution, is more disturbed in the early Universe. However, we find that undisturbed disk-like systems already dominate the high-mass end of the late-type galaxy population (log M∗/M⊙ &gt; 10.5) at z ~ 5, and bulge-dominated galaxies also exist at these early epochs, confirming a rich and evolved morphological diversity of galaxies ~1 Gyr after the Big Bang. Finally, we find that the morphology-quenching relation is already in place for massive galaxies at z &gt; 3, with massive quiescent galaxies (log M∗/M⊙ &gt; 10.5) being predominantly bulge-dominated.</p

Galaxy morphology from z ~ 6 through the lens of JWST

Context: The James Webb Space Telescope's (JWST's) unprecedented combination of sensitivity, spatial resolution, and infrared coverage has enabled a new era of galaxy morphology exploration across most of cosmic history. Aims: We analyze the near-infrared (NIR ~ 0.8 -1 μm) rest-frame morphologies of galaxies with log M∗/M⊙ &gt; 9 in the redshift range of 0 &lt; z &lt; 6, compare with previous HST-based results and release the first JWST-based morphological catalog of ~20 000 galaxies in the CEERS survey. Methods: We classified the galaxies in our sample into four main broad classes: spheroid, disk+spheroid, disk, and disturbed, based on imaging with four filters: F150W, F200W, F356W, and F444W. We used convolutional neural networks (CNNs) trained on HST/WFC3 labeled images and domain-adapted to JWST/NIRCam. Results: We find that ~90% and ~75% of galaxies at z &lt; 3 have the same early and late and regular and irregular classification, respectively, in JWST and HST imaging when considering similar wavelengths. For small (large) and faint objects, JWST-based classifications tend to systematically present less bulge-dominated systems (peculiar galaxies) than HST-based ones, but the impact on the reported evolution of morphological fractions is less than ~10%. Using JWST-based morphologies at the same rest-frame wavelength ( ~0.8 -1 μm), we confirm an increase in peculiar galaxies and a decrease in bulge-dominated galaxies with redshift, as reported in previous HST-based works, suggesting that the stellar mass distribution, in addition to light distribution, is more disturbed in the early Universe. However, we find that undisturbed disk-like systems already dominate the high-mass end of the late-type galaxy population (log M∗/M⊙ &gt; 10.5) at z ~ 5, and bulge-dominated galaxies also exist at these early epochs, confirming a rich and evolved morphological diversity of galaxies ~1 Gyr after the Big Bang. Finally, we find that the morphology-quenching relation is already in place for massive galaxies at z &gt; 3, with massive quiescent galaxies (log M∗/M⊙ &gt; 10.5) being predominantly bulge-dominated.</p

Uncovering the stellar structure of the dusty star-forming galaxy GN20 at z=4.055 with MIRI/JWST

Luminous infrared galaxies at high redshifts ($z$>4) include extreme starbursts that build their stellar mass over short periods of time (>100 Myr). These galaxies are considered to be the progenitors of massive quiescent galaxies at intermediate redshifts ($z\sim$2) but their stellar structure and buildup is unknown. Here, we present the first spatially resolved near-infrared imaging of GN20, one of the most luminous dusty star-forming galaxies known to date, observed at an epoch when the Universe was only 1.5 Gyr old. The 5.6$\mu$m image taken with the JWST Mid-Infrared Instrument (MIRI/JWST) shows that GN20 is a very luminous galaxy (M$_\mathrm{1.1\mu m,AB}$=$-$25.01), with a stellar structure composed of a conspicuous central source and an extended envelope. The central source is an unresolved nucleus that carries 9% of the total flux. The nucleus is co-aligned with the peak of the cold dust emission, and offset by 3.9 kpc from the ultraviolet stellar emission. The diffuse stellar envelope is similar in size to the clumpy CO molecular gas distribution. The centroid of the stellar envelope is offset by 1 kpc from the unresolved nucleus, suggesting GN20 is involved in an interaction or merger event supported by its location as the brightest galaxy in a proto-cluster. The stellar size of GN20 is larger by a factor of about 3-5 than known spheroids, disks, and irregulars at $z\sim$4, while its size and low S\'ersic index are similar to those measured in dusty, infrared luminous galaxies at $z\sim$2 of the same mass. GN20 has all the ingredients necessary for evolving into a massive spheroidal quiescent galaxy at intermediate $z$: it is a large, luminous galaxy at $z$=4.05 involved in a short and massive starburst centred in the stellar nucleus and extended over the entire galaxy, out to radii of 4 kpc, and likely induced by the interaction or merger with a member of the proto-cluster.Comment: 7 pages, 4 figure