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

Physics of ULIRGs with MUSE and ALMA: The PUMA project: III. Incidence and properties of ionised gas disks in ULIRGs, associated velocity dispersion, and its dependence on starburstiness

CONTEXT: A classical scenario suggests that ultra-luminous infrared galaxies (ULIRGs) transform colliding spiral galaxies into a spheroid-dominated early-type galaxy. Recent high-resolution simulations have instead shown that, under some circumstances, rotation disks can be preserved during the merging process or rapidly regrown after coalescence. Our goal is to analyse in detail the ionised gas kinematics in a sample of ULIRGs to infer the incidence of gas rotational dynamics in late-stage interacting galaxies and merger remnants. AIMS: We analysed integral field spectrograph MUSE data of a sample of 20 nearby (z < 0.165) ULIRGs (with 29 individual nuclei) as part of the Physics of ULIRGs with MUSE and ALMA (PUMA) project. We used multi-Gaussian fitting techniques to identify gaseous disk motions and the 3D-Barolo tool to model them. METHODS: We found that 27% (8 out of 29) individual nuclei are associated with kiloparsec-scale disk-like gas motions. The rest of the sample displays a plethora of gas kinematics, dominated by winds and merger-induced flows, which makes the detection of rotation signatures difficult. On the other hand, the incidence of stellar disk-like motions is ∼2 times larger than gaseous disks, as the former are probably less affected by winds and streams. The eight galaxies with a gaseous disk present relatively high intrinsic gas velocity dispersion (σ0 ∈ [30 − 85] km s−1), rotationally supported motions (with gas rotation velocity over velocity dispersion vrot/σ0 ∼ 1 − 8), and dynamical masses in the range (2 − 7)×1010 M⊙. By combining our results with those of local and high-z disk galaxies (up to z ∼ 2) from the literature, we found a significant correlation between σ0 and the offset from the main sequence (δMS), after correcting for their evolutionary trends. RESULTS: Our results confirm the presence of kiloparsec-scale rotating disks in interacting galaxies and merger remnants in the PUMA sample, with an incidence going from 27% (gas) to ≲50% (stars). Their gas σ0 is up to a factor of ∼4 higher than in local normal main sequence galaxies, similar to high-z starbursts as presented in the literature; this suggests that interactions and mergers enhance the star formation rate while simultaneously increasing the velocity dispersion in the interstellar medium

The PUMA project. III. Incidence and properties of ionised gas disks in ULIRGs, associated velocity dispersion and its dependence on starburstiness

A classical scenario suggests that ULIRGs transform colliding spiral galaxies into a spheroid dominated early-type galaxy. Recent high-resolution simulations have instead shown that, under some circumstances, rotation disks can be preserved during the merging process or rapidly regrown after coalescence. Our goal is to analyze in detail the ionised gas kinematics in a sample of ULIRGs to infer the incidence of gas rotational dynamics in late-stage interacting galaxies and merger remnants. We analysed MUSE data of a sample of 20 nearby (z<0.165) ULIRGs, as part of the "Physics of ULIRGs with MUSE and ALMA" (PUMA) project. We found that 27% individual nuclei are associated with kpc-scale disk-like gas motions. The rest of the sample displays a plethora of gas kinematics, dominated by winds and merger-induced flows, which make the detection of rotation signatures difficult. On the other hand, the incidence of stellar disk-like motions is ~2 times larger than gaseous disks, as the former are probably less affected by winds and streams. The eight galaxies with a gaseous disk present relatively high intrinsic gas velocity dispersion (sigma = 30-85 km/s), rotationally-supported motions (with gas rotation velocity over velocity dispersion vrot/sigma > 1-8), and dynamical masses in the range (2-7)x1e10 Msun. By combining our results with those of local and high-z disk galaxies from the literature, we found a significant correlation between sigma and the offset from the main sequence (MS), after correcting for their evolutionary trends. Our results confirm the presence of kpc-scale rotating disks in interacting galaxies and merger remnants, with an incidence going from 27% (gas) to ~50% (stars). The ULIRGs gas velocity dispersion is up to a factor of ~4 higher than in local normal MS galaxies, similar to high-z starbursts as presented in the literature

Expectations of the size evolution of massive galaxies at 3≤z≤63 \leq z \leq 6 from the TNG50 simulation: the CEERS/JWST view

We present a catalog of about 25,000 images of massive ($M_{\star} \ge 10^9 M_{\odot}$) galaxies at redshift $3 \leq z \leq 6$ from the TNG50 cosmological simulation, tailored for observations at multiple wavelengths carried out with JWST. The synthetic images were created with the SKIRT radiative transfer code, including the effects of dust attenuation and scattering. The noiseless images were processed with the mirage simulator to mimic the Near Infrared Camera (NIRCam) observational strategy (e.g., noise, dithering pattern, etc.) of the Cosmic Evolution Early Release Science (CEERS) survey. In this paper, we analyze the predictions of the TNG50 simulation for the size evolution of galaxies at $3 \leq z \leq 6$ and the expectations for CEERS to probe that evolution. In particular, we investigate how sizes depend on wavelength, redshift, mass, and angular resolution of the images. We find that the effective radius accurately describes the three-dimensional half-mass radius of TNG50 galaxies. Sizes observed at 2~$\mu$m are consistent with those measured at 3.56~$\mu$m at all redshifts and masses. At all masses, the population of higher-$z$ galaxies is more compact than their lower-$z$ counterparts. However, the intrinsic sizes are smaller than the mock observed sizes for the most massive galaxies, especially at $z \lesssim 4$. This discrepancy between the mass and light distribution may point to a transition in the galaxy morphology at $z$=4-5, where massive compact systems start to develop more extended stellar structures.Comment: Accepted for publication in ApJ (20 pages, 12 figures). Data publicly released at https://www.tng-project.org/costantin22 and at https://www.lucacostantin.com/OMEG

Probing the earliest phases in the formation of massive galaxies with simulated HST+JWST imaging data from Illustris

We use the Illustris-1 simulation to explore the capabilities of the $\textit{Hubble}$ and $\textit{James Webb Space Telescope}$ data to analyze the stellar populations in high-redshift galaxies, taking advantage of the combined depth, spatial resolution, and wavelength coverage. For that purpose, we use simulated broad-band ACS, WFC3 and NIRCam data and 2-dimensional stellar population synthesis (2D-SPS) to derive the integrated star formation history (SFH) of massive (M$_{\ast}>10^{10}\,$M$_{\odot}$) simulated galaxies at $110^{11}\,$M$_{\odot}$ galaxy. In particular, we explore the potential of HST and JWST datasets reaching a depth similar to those of the CANDELS and ongoing CEERS observations, respectively, and concentrate on determining the capabilities of this dataset for characterizing the first episodes in the SFH of local M$_{\ast}>10^{11}\,$M$_{\odot}$ galaxies by studying their progenitors at $z>1$. The 2D-SPS method presented in this paper has been calibrated to robustly recover the cosmic times when the first star formation episodes occurred in massive galaxies, i.e., the first stages in their integrated SFHs. In particular, we discuss the times when the first 1% to 50% of their total stellar mass formed in the simulation. We demonstrate that we can recover these ages with typical median systematic offset of less than 5% and scatter around 20%-30%. According to our measurements on Illustris data, we are able to recover that local M$_{\ast}>10^{11}\,$M$_{\odot}$ galaxies would have started their formation by $z=16$, forming the first 5% of their stellar mass present at $z \sim 1$ by $z=4.5$, 10% by $z=3.7$, and 25% by $z=2.7$.Comment: 28 pages, 13 figures, 4 tables. ApJ in press. Summary of changes from original submission: the major change is that we now include in Sec. 6 the comparison of the results obtained for our sample of massive 1 < z < 4 progenitors with those obtained by considering all massive galaxies at 1 < z < 4 in the simulated images. Several figures and sections have been update

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&

RIOJA. Complex Dusty Starbursts in a Major Merger B14-65666 at z=7.15

We present JWST NIRCam imaging of B14-65666 ("Big Three Dragons"), a bright Lyman-break galaxy system ($M_\text{UV}=-22.5$ mag) at $z=7.15$. The high angular resolution of NIRCam reveals the complex morphology of two galaxy components: galaxy E has a compact core (E-core), surrounded by diffuse, extended, rest-frame optical emission, which is likely to be tidal tails; and galaxy W has a clumpy and elongated morphology with a blue UV slope ($\beta_\text{UV}=-2.2\pm0.1$). The flux excess, F356W$-$F444W, peaks at the E-core ($1.05^{+0.08}_{-0.09}$ mag), tracing the presence of strong [OIII] 4960,5008 \r{A} emission. ALMA archival data show that the bluer galaxy W is brighter in dust continua than the redder galaxy E, while the tails are bright in [OIII] 88 $\mathrm{\mu m}$. The UV/optical and sub-mm SED fitting confirms that B14-65666 is a major merger in a starburst phase as derived from the stellar mass ratio (3:1 to 2:1) and the star-formation rate, $\simeq1$ dex higher than the star-formation main sequence at the same redshift. The galaxy E is a dusty ($A_\text{V}=1.2\pm0.1$ mag) starburst with a possible high dust temperature ($\ge63$-$68$ K). The galaxy W would have a low dust temperature ($\le27$-$33$ K) or patchy stellar-and-dust geometry, as suggested from the infrared excess (IRX) and $\beta_\text{UV}$ diagram. The high optical-to-FIR [OIII] line ratio of the E-core shows its lower gas-phase metallicity ($\simeq0.2$ Z$_{\odot}$) than the galaxy W. These results agree with a scenario where major mergers disturb morphology and induce nuclear dusty starbursts triggered by less-enriched inflows. B14-65666 shows a picture of complex stellar buildup processes during major mergers in the epoch of reionization.Comment: 18 pages, 6 figures, 4 tables. Submitted to Ap

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

A few StePS forward in unveiling the complexity of galaxy evolution: Light-weighted stellar ages of intermediate-redshift galaxies with WEAVE

The upcoming new generation of optical spectrographs on four-meter-class telescopes will provide invaluable information for reconstructing the history of star formation in individual galaxies up to redshifts of about 0.7. We aim at defining simple but robust and meaningful physical parameters that can be used to trace the coexistence of widely diverse stellar components: younger stellar populations superimposed on the bulk of older ones. We produce spectra of galaxies closely mimicking data from the forthcoming Stellar Populations at intermediate redshifts Survey (StePS), a survey that uses the WEAVE spectrograph on the William Herschel Telescope. First, we assess our ability to reliably measure both ultraviolet and optical spectral indices in galaxies of different spectral types for typically expected signal-to-noise levels. Then, we analyze such mock spectra with a Bayesian approach, deriving the probability density function of r- and u-band light-weighted ages as well as of their difference. We find that the ultraviolet indices significantly narrow the uncertainties in estimating the r- and u-band light-weighted ages and their difference in individual galaxies. These diagnostics, robustly retrievable for large galaxy samples even when observed at moderate signal-to-noise ratios, allow us to identify secondary episodes of star formation up to an age of ~0.1 Gyr for stellar populations older than ~1.5 Gyr, pushing up to an age of ~1 Gyr for stellar populations older than ~5 Gyr. The difference between r-band and u-band light-weighted ages is shown to be a powerful diagnostic to characterize and constrain extended star-formation histories and the presence of young stellar populations on top of older ones. This parameter can be used to explore the interplay between different galaxy star-formation histories and physical parameters such as galaxy mass, size, morphology, and environment