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We study the physical properties (size, stellar mass, luminosity, star formation rate) and scaling relations for a sample of 166 star-forming clumps with redshift $z \sim 2-6.2$. They are magnified by the Hubble Frontier Field galaxy cluster MACS~J0416 and have robust lensing magnification ($2\lesssim \mu \lesssim 82$) computed by using our high-precision lens model, based on 182 multiple images. Our sample extends by $\sim 3$ times the number of spectroscopically-confirmed lensed clumps at $z \gtrsim 2$. We identify clumps in ultraviolet continuum images and find that, whenever the effective spatial resolution (enhanced by gravitational lensing) increases, they fragment into smaller entities, likely reflecting the hierarchically-organized nature of star formation. Kpc-scale clumps, most commonly observed in field, are not found in our sample. The physical properties of our sample extend the parameter space typically probed by $z \gtrsim 1$ field observations and simulations, by populating the low mass (M$_\star \lesssim 10^7$ M$_\odot$), low star formation rate (SFR $\lesssim 0.5$ M$_\odot$ yr$^{-1}$), and small size (R$_\mathrm{eff} \lesssim 100$ pc) regime. The new domain probed by our study approaches the regime of compact stellar complexes and star clusters. In the mass-size plane, our sample spans the region between galaxies and globular clusters, with a few clumps in the region populated by young star clusters and globular-clusters. For the bulk of our sample, we measure star-formation rates which are higher than those observed locally in compact stellar systems, indicating different conditions for star formation at high redshift than in the local Universe.

In the nearby universe jets from AGN are observed to have a dramatic impact on their surrounding extragalactic environment. Their effect at the `cosmic noon' (z>1.5), the epoch when star formation and AGN activity peak, is instead much less constrained. Here we present a study of the giant (750 kpc) radio galaxy 103025+052430 located at the centre of a protocluster at redshift z=1.7, with a focus on its interaction with the external medium. We present new LOFAR observations at 144 MHz, which we combine with VLA 1.4 GHz and 0.5-7 keV Chandra archival data. The new map at 144 MHz confirms that the source has a complex morphology, possibly consistent with the `hybrid morphology' classification. The large size of the source gave us the possibility to perform a resolved radio spectral index analysis, a very unique opportunity for a source at such high redshift. This reveals a tentative flattening of the radio spectral index at the edge of the backflow in the Western lobe, which might be indicating plasma compression. The spatial coincidence between this region and the thermal X-ray bubble C suggests a causal connection between the two. Contrary to previous estimates for the bright X-ray component A, we find that inverse Compton scattering between the radio-emitting plasma of the Eastern lobe and the CMB photons can account for a large fraction (~45%-80%) of its total 0.5-7 keV measured flux. Finally, the X-ray bubble C, which is consistent with a thermal origin, is found to be significantly overpressurised with respect to the ambient medium. This suggests that it will tend to expand and release its energy in the surroundings, contributing to the overall intracluster medium heating. Overall, 103025+052430 gives us the chance to investigate the interaction between AGN jets and the surrounding gas in a system that is likely the predecessor of the rich galaxy clusters we all well know at z=0., 12 pages, 5 figures, 2 tables, accepted for publication in A&A

By means of three-dimensional hydrodynamical simulations, we investigate the formation of second generation (SG) stars in young globular clusters of different masses. We consider clusters with a first generation of asymptotic giant branch (AGB) stars with mass 10^5 and 10^6 Msun moving at constant velocity through a uniform gas with density 10^(-24) and 10^(-23) g cm^(-3). Our setup is designed to reproduce the encounter of a young cluster with a reservoir of dense gas, e. g. during its orbital motion in the host galaxy. In the low-density models, as a result of the cooling AGB ejecta which collect in the centre, weakly perturbed by the external ram pressure, a compact central He-rich SG stellar component is formed on a timescale which decreases with increasing initial cluster mass. Our high-density models are subject to stronger ram pressure, which prevents the accumulation of the most He-rich AGB ejecta in the cluster centre. As a result, the SG is more extended and less He-enhanced than in the low-density models. By combining our results with previous simulations, we are able to study relevant, cluster-related scaling relations across a dynamical range of two orders of magnitude in mass (from 10^5 Msun to 10^7 Msun). In agreement with current observationally-based estimates, we find positive correlations between the SG-to-total number ratio and maximum He enhancement in SG stars as a function of the initial cluster mass., 18 pages, 8 figures, MNRAS, accepted for publication

We investigate the blue and optical rest-frame sizes (lambda~2300A-4000A) of three compact star-forming regions in a galaxy at z=4 strongly lensed (x30, x45, x100) by the Hubble Frontier Field galaxy cluster A2744 using GLASS-ERS JWST/NIRISS imaging at 1.15um, 1.50mu and 2.0mu with PSF < 0.1". In particular, the Balmer break is probed in detail for all multiply-imaged sources of the system. With ages of a few tens of Myr, stellar masses in the range (0.7-4.0) x 10^6 Msun and optical/ultraviolet effective radii spanning the interval 3 < R_eff < 20 pc, such objects are currently the highest redshift (spectroscopically-confirmed) gravitationally-bound young massive star clusters (YMCs), with stellar mass surface densities resembling those of local globular clusters. Optical (4000A, JWST-based) and ultraviolet (1600A, HST-based) sizes are fully compatible. The contribution to the ultraviolet underlying continuum emission (1600A) is ~30%, which decreases by a factor of two in the optical for two of the YMCs (~4000A rest-frame), reflecting the young ages (, 10 pages, 4 figures, 1 table. Submitted to ApJL

Using 3D radiation-hydrodynamical simulations, we study the effects of ionising radiation on the formation of second-generation (SG) stars in Globular Clusters (GCs) with multiple stellar populations. In particular, we focus on massive ($10^7 \mathrm{M}_{\odot}$) and young (40-Myr old) GCs. We consider stellar winds from asymptotic giant branch (AGB) stars, ram pressure, gas accretion onto the cluster, and photoionisation feedback of binary stars. We find that the stellar luminosity is strong enough to warm and ionise the intracluster medium, but it does not lead to a significant gas expulsion. The cluster can thus retain the ejecta of AGB stars and the accreted pristine gas. In addition, efficient cooling occurs in the central region of the cluster within $50 \mathrm{Myr}$ from the formation of first generation stars, leading to the formation of SG stars. Our results indicate that the inclusion of photoionisation does not suppress SG formation, but rather delays it by about $\sim10 \mathrm{Myr}$. The time delay depends on the density of the pristine gas, so that a denser medium exhibits a shorter delay in star formation. Moreover, photoionisation leads to a modest decrease in the total SG mass, compared to a model without it., 13 pages, 8 figures, 2 table. Accepted for publication in MNRAS

We present a new prediction of the luminosity functions of the [CII] line at 158 $\mu$m, of the CO lines from J=0 to J=24, and of the molecular gas mass density up to z=10, using the Spectro-Photometric Realisations of Infrared-selected Targets at all-z (SPRITZ) simulation (Bisigello et al. 2021). We update the state-of-the-art phenomenological simulation SPRITZ to include both the CO ($J\leq24$) and [CII] line luminosities. This has been performed using different empirical and theoretical relations to convert the total infrared luminosity (or star formation rate) to [CII] or CO luminosity. The resulting line luminosity functions have been compared for validation with a large set of observations available in the literature. We then used the derived CO and [CII] line luminosities to estimate the molecular gas mass density and compare it with available observations. The CO and [CII] luminosity functions presented here are well in agreement with all the available observations. In particular, the best results for [CII] are obtained deriving the [CII] luminosity directly from the star formation rate, but considering a dependence of this relation on the gas metallicity. For all the CO luminosity functions, the estimates favoured by the data are derived considering different relations, depending on the ionisation mechanism dominating each galaxy, i.e. star formation or active galactic nuclei, and, moreover, deriving the $J\geq4$ CO lines directly from the [CII] luminosity. However, further data are necessary to fully discriminate between models. Finally, the best agreement with observations of the molecular gas mass density are derived by converting the [CII] luminosity to H2 mass, using a [CII]-to-H2 conversion ~130 $\rm M_{\odot}/{\rm L}_{\odot}$. All the line luminosity functions, useful for planning and interpreting future observations, are made publicly available., Comment: 18 pages, 16 figures, 8 tables, accepted for publication in A&A

We introduce a new set of zoom-in cosmological simulations with sub-pc resolution, intended to model extremely faint, highly magnified star-forming stellar clumps, detected at z=6.14 thanks to gravitational lensing. The simulations include feedback from individual massive stars (in both the pre-supernova and supernova phases), generated via stochastic, direct sampling of the stellar initial mass function. We adopt a modified 'delayed cooling' feedback scheme, specifically created to prevent artificial radiative loss of the energy injected by individual stars in very dense gas (n~10^3-10^5 cm^{-3}). The sites where star formation ignites are characterised by maximum densities of the order of 10^5 cm^{-3} and gravitational pressures P/k>10^7 K/cm^3, corresponding to the values of the local, turbulent regions where the densest stellar aggregates form. The total stellar mass at z=6.14 is 3.4x10^7 M_sun, in satisfactory agreement with the observed stellar mass of the observed systems. The most massive clumps have masses of ~10^6 M_sun and half-mass sizes of ~100 pc. These sizes are larger than the observed ones, including also other samples of lensed high-redshift clumps, and imply an average density one order of magnitude lower than the observed one. In the size-mass plane, our clumps populate a sequence that is intermediate between the ones of observed high-redshift clumps and local dSph galaxies., MNRAS, accepted for publication. 24 pages, 17 figures

We investigate the abundance and distribution of metals in the high-redshift intergalactic medium and circum-galactic medium through the analysis of a sample of almost 600 SiIV absorption lines detected in high and intermediate resolution spectra of 147 quasars. The evolution of the number density of SiIV lines, the column density distribution function and the cosmic mass density are studied in the redshift interval 1.7 = 12.5. All quantities show a rapid increase between z~6 and z< 5 and then an almost constant behaviour to z~2 in very good agreement with what is already observed for CIV absorption lines. The present results are challenging for numerical simulations: when simulations reproduce our SiIV results, they tend to underpredict the properties of CIV, and when the properties of CIV are reproduced, the number of strong SiIV lines (log N(SiIV) > 14) is overpredicted., 14 pages, 8 figures, accepted for publication in MNRAS

We combine results from deep ALMA observations of massive (M* > 1010 M⊙) galaxies at different redshifts to show that the column density of their interstellar medium (ISM) rapidly increases toward early cosmic epochs. Our analysis includes objects from the ASPECS and ALPINE large programs, as well as individual observations of z ∼ 6 quasar hosts. When accounting for non-detections and correcting for selection effects, we find that the median surface density of the ISM of the massive galaxy population evolves as ∼(1 + z)3.3. This means that the ISM column density toward the nucleus of a z > 3 galaxy is typically > 100 times larger than locally, and it may reach values as high as Compton-thick at z ≳ 6. Remarkably, the median ISM column density is on the same order of what is measured from X-ray observations of large active galactic nucleus (AGN) samples already at z ≳ 2. We have developed a simple analytic model for the spatial distribution of ISM clouds within galaxies, and estimate the total covering factor toward active nuclei when obscuration by ISM clouds on the host scale is added to that of parsec-scale circumnuclear material (the so-called torus). The model includes clouds with a distribution of sizes, masses, and surface densities, and also allows for an evolution of the characteristic cloud surface density with redshift, Σc, * ∝ (1 + z)γ. We show that, for γ = 2, such a model successfully reproduces the increase in the obscured AGN fraction with redshift that is commonly observed in deep X-ray surveys, both when different absorption thresholds and AGN luminosities are considered. Our results suggest that 80–90% of supermassive black holes in the early Universe (z > 6 − 8) are hidden to our view, primarily by the ISM in their hosts. We finally discuss the implications of our results and how they can be tested observationally with current and forthcoming facilities (e.g., VLT, E-ELT, ALMA, and JWST) and with next-generation X-ray imaging satellites. By extrapolating the observed X-ray nebulae around local AGN to the environments of supermassive black holes at high redshifts, we find ≲1″ nebulae impose stringent design constraints on the spatial resolution of any future X-ray imaging Great Observatory in the coming decades., We acknowledge financial contribution from the agreement ASI-INAF n. 2017-14-H.O. KI acknowledges support by the Spanish MCINN under grant PID2019-105510GB-C33/AEI/10.13039/501100011033 and “Unit of excellence María de Maeztu 2020–2023” awarded to ICCUB (CEX2019-000918-M). SM acknowledges funding from the INAF “Progetti di Ricerca di Rilevante Interesse Nazionale” (PRIN), Bando 2019 (project: “Piercing through the clouds: a multiwavelength study of obscured accretion in nearby supermassive black holes”).

We investigate the strongly lensed (\mu x10-100) Lyman continuum (LyC) galaxy, dubbed Sunburst, at z=2.37, taking advantage of a new accurate model of the lens. A characterization of the intrinsic (delensed) properties of the galaxy yields a size of ~3 sq.kpc, a luminosity Muv=-20.3,and a stellar mass M~10^9 Msun;16% of the ultraviolet light is located in a 3 Myr old gravitationally-bound young massive star cluster (YMC) with an effective radius of Re~8 pc and a dynamical mass of ~10^7 Msun (similar to the stellar mass), from which LyC radiation is detected (\lambda < 912A). The inferred outflowing gas velocity (>300 km/s) exceeds the escape velocity of the star cluster. The resulting escape fraction of the ionizing radiation emerging from the Sunburst galaxy is >6-12%, whilst it is >46-93% if inferred from the YMC. 12 additional likely star clusters with 3~30%, which is consistent with the high \Gamma derived in local galaxies experiencing extreme gas physical conditions. The presence of the YMC influences the morphology (nucleation), photometry (photometric jumps) and spectroscopic output (nebular emission) of the entire galaxy. The de-lensed LyC and UV (1600A) magnitudes of the YMC are ~30.6 and ~26.9, whilst the galaxy has m1600~24.8. A relatively large rest-frame equivalent width of EWrest(Hb+[OIII]4959-5007)~450A emerges from the galaxy with the YMC contributing to ~30%. If O-type stars are mainly forged in star clusters, then such engines were the key ionizing agents during reionization and the increasing occurrence of high EW lines (Hb+[OIII]) observed at z>6.5 might be an indirect signature of a high \Gamma at reionization.Future facilities (like VLT/MAVIS or ELT), will probe bound clusters on moderately magnified (\mu, Comment: 17 pages (12 main body), 10 Figures and 1 Table. Accepted for publication in Astronomy & Astrophysics. Figure 6 shows the stellar cluster formation efficiency of the Sunburst galaxy; Figure C.1 shows the MUSE narrow field mode image of the counter-arc

By means of 3D hydrodynamic simulations, we explore the effects of rotation in the formation of second-generation (SG) stars in globular clusters (GC). Our simulations follow the SG formation in a first-generation (FG) internally rotating GC; SG stars form out of FG asymptotic giant branch (AGB) ejecta and external pristine gas accreted by the system. We have explored two different initial rotational velocity profiles for the FG cluster and two different inclinations of the rotational axis with respect to the direction of motion of the external infalling gas, whose density has also been varied. For a low (10^-24 g cm^-3) external gas density, a disk of SG helium-enhanced stars is formed. The SG is characterized by distinct chemo-dynamical phase space patterns: it shows a more rapid rotation than the FG with the helium-enhanced SG subsystem rotating more rapidly than the moderate helium-enhanced one. In models with high external gas density (10^-23 g cm^-3), the inner SG disc is disrupted by the early arrival of external gas and only a small fraction of highly enhanced helium stars preserves the rotation acquired at birth. Variations in the inclination angle between the rotation axis and the direction of the infalling gas and the velocity profile can slightly alter the extent of the stellar disc and the rotational amplitude. No significant variation has been found in the timespan of our simulations when changing the inclination angle between the rotation axis and the direction of the infalling gas, while different velocity profiles can slightly alter the extent of the stellar disc and the rotational amplitude. The results of our simulations illustrate the complex link between dynamical and chemical properties of multiple populations and provide new elements for the interpretation of observational studies and future investigations of the dynamics of multiple-population GCs., Comment: 16 pages, 13 figures, accepted for publication in MNRAS

arXiv:2111.11453v1, Mid- and far-infrared (IR) photometric and spectroscopic observations are fundamental to a full understanding of the dust-obscured Universe and the evolution of both star formation and black hole accretion in galaxies. In this work, using the specifications of the SPace Infrared telescope for Cosmology and Astrophysics (SPICA) as a baseline, we investigate the capability to study the dust-obscured Universe of mid- and far-IR photometry at 34 and 70 µm and low-resolution spectroscopy at 17−36 µm using the state-of-the-art SpectroPhotometric Realisations of Infrared-selected Targets at all-z (SPRITZ) simulation. This investigation is also compared to the expected performance of the Origins Space Telescope and the Galaxy Evolution Probe. The photometric view of the Universe of a SPICA-like mission could cover not only bright objects (e.g. LIR > 1012 L) up to z = 10, but also normal galaxies (LIR < 1011 L) up to z ∼ 4. At the same time, the spectroscopic observations of such mission could also allow us to estimate the redshifts and study the physical properties for thousands of star-forming galaxies and active galactic nuclei by observing the polycyclic aromatic hydrocarbons and a large set of IR nebular emission lines. In this way, a cold, 2.5-m size space telescope with spectro-photometric capability analogous to SPICA, could provide us with a complete three-dimensional (i.e. images and integrated spectra) view of the dust-obscured Universe and the physics governing galaxy evolution up to z ∼ 4., We acknowledge the whole SPICA Collaboration Team. LB, CG, LS and JAFO acknowledge financial support by the Agenzia Spaziale Italiana (ASI) under the research contract 2018-31-HH.0. AF and FC acknowledges the support from grant PRIN MIUR2017-20173ML3WW_001. MPS acknowledges support from the Comunidad de Madrid through the Atracción de Talento Investigador Grant 2018-T1/TIC11035 and PID2019-105423GA-I00 (MCIU/AEI/FEDER,UE). FJC acknowledges financial support from the Spanish Ministry MCIU under project RTI2018-096686-B-C21 (MCIU/AEI/FEDER/UE), cofunded by FEDER funds and from the Agencia Estatal de Investigación, Unidad de Excelencia Maria de Maeztu, ref. MDM-2017-0765.

We publicly release the spectroscopic and photometric redshift catalog of the sources detected with Chandra in the field of the $z$=6.3 quasar SDSS J1030+0525. This is currently the fifth deepest X-ray field, and reaches a 0.5-2 keV flux limit $f_{\rm 0.5-2}$=6$\times$10$^{-17}$ erg s$^{-1}$ cm$^{-2}$. By using two independent methods, we measure a photometric redshift for 243 objects, while 123 (51%) sources also have a spectroscopic redshift, 110 of which coming from an INAF-Large Binocular Telescope (LBT) Strategic Program. We use the spectroscopic redshifts to determine the quality of the photometric ones, and find it in agreement with that of other X-ray surveys which used a similar number of photometric data-points. In particular, we measure a sample normalized median absolute deviation $\sigma_{NMAD}$=1.48||$z_{phot}$-$z_{spec}$||/(1+$z_{spec}$)=0.065. We use these new spectroscopic and photometric redshifts to study the properties of the Chandra J1030 field. We observe several peaks in our spectroscopic redshift distribution between $z$=0.15 and $z$=1.5, and find that the sources in each peak are often distributed across the whole Chandra field of view. This evidence confirms that X-ray selected AGN can efficiently track large-scale structures over physical scales of several Mpc. Finally, we computed the Chandra J1030 $z>$3 number counts: while the spectroscopic completeness at high-redshift of our sample is limited, our results point towards a potential source excess at $z\geq$4, which we plan to either confirm or reject in the near future with dedicated spectroscopic campaigns., Comment: 21 pages, 15 figures. Accepted for publication in Astronomy and Astrophysics

We empirically test the relation between the SFR(LIR) derived from the infrared luminosity, LIR, and the SFR(Ha) derived from the Ha emission line luminosity using simple conversion relations. We use a sample of 474 galaxies at z = 0.06 - 0.46 with both Ha detection (from 20k zCOSMOS survey) and new far-IR Herschel data (100 and 160 {\mu}m). We derive SFR(Ha) from the Ha extinction corrected emission line luminosity. We find a very clear trend between E(B - V) and LIR that allows to estimate extinction values for each galaxy even if the Ha emission line measurement is not reliable. We calculate the LIR by integrating from 8 up to 1000 {\mu}m the SED that is best fitting our data. We compare SFR(Ha) with the SFR(LIR). We find a very good agreement between the two SFR estimates, with a slope of m = 1.01 \pm 0.03 in the SFR(LIR) vs SFR(Ha) diagram, a normalization constant of a = -0.08 \pm 0.03 and a dispersion of sigma = 0.28 dex.We study the effect of some intrinsic properties of the galaxies in the SFR(LIR)-SFR(Ha) relation, such as the redshift, the mass, the SSFR or the metallicity. The metallicity is the parameter that affects most the SFR comparison. The mean ratio of the two SFR estimators log[SFR(LIR)/SFR(Ha)] varies by approx. 0.6 dex from metal-poor to metal-rich galaxies (8.1 < log(O/H) + 12 < 9.2). This effect is consistent with the prediction of a theoretical model for the dust evolution in spiral galaxies. Considering different morphological types, we find a very good agreement between the two SFR indicators for the Sa, Sb and Sc morphologically classified galaxies, both in slope and normalization. For the Sd, irregular sample (Sd/Irr), the formal best-fit slope becomes much steeper (m = 1.62 \pm 0.43), but it is still consistent with 1 at the 1.5 sigma level, because of the reduced statistics of this sub-sample.

Aims: We examine radial and vertical metallicity gradients using a suite of disk galaxy hydrodynamical simulations, supplemented with two classic chemical evolution approaches. We determine the rate of change of gradient slope and reconcile the differences existing between extant models and observations within the canonical "inside-out" disk growth paradigm. Methods: A suite of 25 cosmological disks is used to examine the evolution of metallicity gradients; this consists of 19 galaxies selected from the RaDES (Ramses Disk Environment Study) sample, realised with the adaptive mesh refinement code ramses, including eight drawn from the "field" and six from "loose group" environments. Four disks are selected from the MUGS (McMaster Unbiased Galaxy Simulations) sample, generated with the smoothed particle hydrodynamics (SPH) code gasoline. Two chemical evolution models of inside-out disk growth were employed to contrast the temporal evolution of their radial gradients with those of the simulations. Results: We first show that generically flatter gradients are observed at redshift zero when comparing older stars with those forming today, consistent with expectations of kinematically hot simulations, but counter to that observed in the Milky Way. The vertical abundance gradients at ~1-3 disk scalelengths are comparable to those observed in the thick disk of the Milky Way, but significantly shallower than those seen in the thin disk. Most importantly, we find that systematic differences exist between the predicted evolution of radial abundance gradients in the RaDES and chemical evolution models, compared with the MUGS sample; specifically, the MUGS simulations are systematically steeper at high-redshift, and present much more rapid evolution in their gradients. Conclusions: We find that the majority of the models predict radial gradients today which are consistent with those observed in late-type disks, but they evolve to this self-similarity in different fashions, despite each adhering to classical "inside-out" growth. We find that radial dependence of the efficiency with which stars form as a function of time drives the differences seen in the gradients; systematic differences in the sub-grid physics between the various codes are responsible for setting these gradients. Recent, albeit limited, data at redshift z ~ 1.5 are consistent with the steeper gradients seen in our SPH sample, suggesting a modest revision of the classical chemical evolution models may be required.

We compare predicted Type Ib/c supernova (SN) rates with the observed long-duration gamma-ray burst (GRB) rates both locally and as a function of redshift. To do that, we assume different star formation histories in galaxies of different morphological type: ellipticals, spirals and irregulars. In particular, the predicted Type Ib/c SN rate (SNRIb/c) is always higher than the GRB rate, as expected, suggesting that only a small fraction (0.1-1%) of them become GRBs. We predict a ratio between the cosmic GRB rate and the cosmic SNRIb/c in the range 10-2 - 10-3, in agreement with previous estimates. Finally, due to the high star formation in spheroids at high redshift, we predict more GRBs at high redshift than previous estimates, a prediction which awaits to be proven by future observations by GLAST. Based on our studies and on the current LAT performance, an estimate of the detection possibility of this high-redshift burst population is finally presented.

By means of chemical evolution models of different morphological types, we study the mass-metallicity (MZ) relation and its evolution with redshift. Our aim is to understand the role of galaxies of different morphological types in the MZ relation at various redshift. One major result is that at high redshift, the majority of the galaxies falling on the MZ plot are apparently proto-ellipticals. Finally, we show some preliminary results of a study of the MZ relation in a framework of hierarchical galaxy formation., Comment: 4 pages, 2 figures, talk presented at "Probing Stellar Populations out to the Distant Universe," September 2008, Cefalu, Italy

We report ALMA Cycle 0 observations at 1.3mm of LESS J033229.4-275619 (XID403), an Ultraluminous Infrared Galaxy at $z=4.75$ in the Chandra Deep Field South hosting a Compton-thick QSO. The source is not resolved in our data at a resolution of $\sim$0.75 arcsec, placing an upper-limit of 2.5 kpc to the half-light radius of the continuum emission from heated-dust. After deconvolving for the beam size, however, we found a $\sim3\sigma$ indication of an intrinsic source size of $0.27\pm0.08$ arcsec (Gaussian FWHM), which would correspond to $r_{half}\sim0.9\pm0.3$ kpc. We build the far-IR SED of XID403 by combining datapoints from both ALMA and Herschel and fit it with a modified blackbody spectrum. For the first time, we measure the dust temperature $T_d=58.5\pm5.3$ K in this system, which is comparable to what has been observed in other high-z submillimeter galaxies. The measured star formation rate is SFR=$1020\pm150$ $M_{\odot}$ yr$^{-1}$, in agreement with previous estimates at lower S/N. Based on the measured SFR and source size, we constrain the SFR surface density to be $\Sigma_{SFR}>26\;M_{\odot}$yr$^{-1}$kpc$^{-2}$ ($\sim200\;M_{\odot}$yr$^{-1}$kpc$^{-2}$ for $r_{half}\sim0.9$ kpc). The compactness of this starburst is comparable to what has been observed in other local and high-z starburst galaxies. If the gas mass measured from previous [CII] and CO(2-1) observations at low resolution is confined within the same dust region, assuming $r_{half}\sim0.9\pm0.3$ kpc, this would produce a column density of $N_H\sim0.3-1.1\times10^{24}$cm$^{-2}$ towards the central SMBH, similar to the column density of $\approx1.4\times10^{24}$cm$^{-2}$ measured from the X-rays. Then, in principle, if both gas and dust were confined on sub-kpc scales, this would be sufficient to produce the observed X-ray column density without any need of a pc-scale absorber [abridged]., Comment: 11 pages, 5 figures. Accepted for publication in A&A