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Aims: We leverage the largest available Atacama Large Millimetre/submillimetre Array (ALMA) survey from the archive (A$^3$COSMOS) to study to study infrared luminosity function and dust-obscured star formation rate density of sub-millimeter/millimeter (sub-mm/mm) galaxies from $z=0.5\,-\,6$. Methods: The A$^3$COSMOS survey utilizes all publicly available ALMA data in the COSMOS field, therefore having inhomogeneous coverage in terms of observing wavelength and depth. In order to derive the luminosity functions and star formation rate densities, we apply a newly developed method that corrects the statistics of an inhomogeously sampled survey of individual pointings to those representing an unbiased blind survey. Results: We find our sample to mostly consist of massive ($M_{\star} \sim 10^{10} - 10^{12}$ $\rm M_{\odot}$), IR-bright ($L_* \sim 10^{11}-10^{13.5} \rm L_{\odot}$), highly star-forming (SFR $\sim 100-1000$ $\rm M_{\odot}$ $\rm yr^{-1}$) galaxies. We find an evolutionary trend in the typical density ($\Phi^*$) and luminosity ($L^*$) of the galaxy population, which decrease and increase with redshift, respectively. Our IR LF is in agreement with previous literature results and we are able to extend to high redshift ($z > 3$) the constraints on the knee and bright-end of the LF, derived by using the Herschel data. Finally, we obtain the SFRD up to $z\sim 6$ by integrating the IR LF, finding a broad peak from $z \sim 1$ to $z \sim 3$ and a decline towards higher redshifts, in agreement with recent IR/mm-based studies, within the uncertainties, thus implying the presence of larger quantities of dust than what is expected by optical/UV studies., Comment: 17 pages, 15 figures, 5 tables, accepted for publication on A&A

We report ALMA high-resolution observations of water emission lines $p-{\rm{H_2O}} (2_{02}-1_{11}$), $o-{\rm{H_2O}} (3_{21}-3_{12})$, $p-{\rm{H_2O}} (4_{22}-4_{13})$, in the strongly lensed galaxy HATLASJ113526.2-01460 at redshift z $\sim$ 3.1. From the lensing-reconstructed maps of water emission and line profiles, we infer the general physical properties of the ISM in the molecular clouds where the lines arise. We find that the water vapor lines $o-{\rm{H_2O}} (3_{21}-3_{12})$, $p-{\rm{H_2O}} (4_{22}-4_{13})$ are mainly excited by FIR pumping from dust radiation in a warm and dense environment, with dust temperatures ranging from 70 K to $\sim 100$ K, as suggested by the line ratios. The $p-{\rm{H_2O}} (2_{02}-1_{11})$ line instead, is excited by a complex interplay between FIR pumping and collisional excitation in the dense core of the star-forming region. This scenario is also supported by the detection of the medium-level excitation of CO resulting in the line emission CO (J=8-7). Thanks to the unprecedented high resolution offered by the combination of ALMA capabilities and gravitational lensing, we discern the different phases of the ISM and locate the hot molecular clouds into a physical scale of $\sim$ 500 pc. We discuss the possibility of J1135 hosting an AGN in its accretion phase. Finally, we determine the relation between the water emission lines and the total IR luminosity of J1135, as well as the SFR as a function of water emission intensities, comparing the outcomes to local and high-$z$ galactic samples from the literature., Comment: 22 pages, 10 figures, final version to be published in Astrophysical Journal

We present high-resolution ($\lesssim0.1$arcsec) ALMA observations of the strongly-lensed galaxy HATLASJ113526.2-01460 at redshift $z\sim3.1$ discovered in the Gama 12$^{\rm th}$ field of the Herschel-ATLAS survey. The gravitationally lensed system is remarkably peculiar in that neither the background source nor the foreground lens show a clearly detected optical/NIR emission. We perform accurate lens modeling and source morphology reconstruction in three different (sub-)mm continuum bands, and in the C[II] and CO(8-7) spectral lines. The modeling indicates a foreground lensing (likely elliptical) galaxy with mass $\gtrsim10^{11}\, M_\odot$ at $z\gtrsim1.5$, while the source (sub-)mm continuum and line emissions are amplified by factors $\mu\sim6-13$. We estimate extremely compact sizes $\lesssim0.5$ kpc for the star-forming region and $\lesssim 1$ kpc for the gas component, with no clear evidence of rotation or of ongoing merging events. We perform broadband SED-fitting and retrieve the intrinsic de-magnified physical properties of the source, which is found to feature a very high star-formation rate $\gtrsim10^3\, M_\odot$ yr$^{-1}$, that given the compact sizes is on the verge of the Eddington limit for starbursts; the radio luminosity at 6 cm from available EVLA observations is consistent with the star-formation activity. The galaxy is found to be extremely rich in gas $\sim10^{11}\, M_\odot$ and dust $\gtrsim10^9\, M_\odot$. The stellar content $\lesssim10^{11}\, M_\odot$ places the source well above the main sequence of starforming galaxies, indicating that the starburst is rather young with estimated age $\sim10^8$ yr. Our results indicate that the overall properties of HATLASJ113526.2-01460 are consistently explained by in-situ galaxy formation and evolution scenarios., Comment: 17 Pages, 12 Figures, 7 Tables. Submitted to ApJ

The Star Formation Rate Density (SFRD) history of the Universe is well constrained up to redshift $z \sim 2$. At earlier cosmic epochs, the picture has been largely inferred from UV-selected galaxies (e.g. Lyman-break galaxies, LBGs). However, LBGs' inferred SFRs strongly depend on the assumed dust extinction correction, which is not well-constrained at high-$z$, while observations in the radio domain are not affected by this issue. In this work we measure the SFRD from a 1.4 GHz-selected sample of $\sim$600 galaxies in the GOODS-N field up to redshift $\sim 3.5$. We take into account the contribution of Active Galactic Nuclei from the Infrared-Radio correlation. We measure the radio luminosity function, fitted with a modified Schechter function, and derive the SFRD. The cosmic SFRD shows a rise up to $z \sim 2$ and then an almost flat plateau up to $z \sim 3.5$. Our SFRD is in agreement with the ones from other FIR/radio surveys and a factor 2 higher than those from LBG samples. We also estimate that galaxies lacking a counterpart in the HST/WFC3 H-band ($H$-dark) make up $\sim 25\%$ of the $\phi$-integrated SFRD relative to the full sample at z $\sim 3.2$, and up to $58\%$ relative to LBG samples., Comment: 20 pages, 11 figures. Accepted for publication in ApJ

We investigate the radio-far infrared (FIR) correlation for a sample of $28$ bright high-redshift ($1 \lesssim z \lesssim 4$) star-forming galaxies selected in the FIR from the Herschel-ATLAS fields as candidates to be strongly gravitationally lensed. The radio information comes either from high sensitivity dedicated ATCA observations at $2.1$ GHz or from cross-matches with the FIRST survey at $1.4$ GHz. By taking advantage of source brightness possibly enhanced by lensing magnification, we identify a weak evolution with redshift out to $z\lesssim 4$ of the FIR-to-radio luminosity ratio $q_{\rm FIR}$. We also find that the $q_{\rm FIR}$ parameter as a function of the radio power $L_{1.4\,\rm GHz}$ displays a clear decreasing trend, similarly to what is observed for optically/radio selected lensed quasars found in literature, yet covering a complementary region in the $q_{\rm FIR}-L_{1.4\,\rm GHz}$ diagram. We interpret such a behavior in the framework of an in-situ galaxy formation scenario, as a result of the transition from an early dust-obscured star-forming phase (mainly pinpointed by our FIR selection) to a late radio-loud quasar phase (preferentially sampled by the optical/radio selection)., Comment: 12 pages, 6 figures. Minor changes and references updated to match the published version