We measure the stellar mass function (SMF) and stellar mass density of galaxies in the COSMOS field up to z ∼ 6. We select them in the near-IR bands of the COSMOS2015 catalogue, which includes ultra-deep photometry from UltraVISTA-DR2, SPLASH, and Subaru/Hyper SuprimeCam. At z > 2.5 we use new precise photometric redshifts with error σ z = 0.03(1 + z) and an outlier fraction of 12%, estimated by means of the unique spectroscopic sample of COSMOS (∼100 000 spectroscopic measurements in total, more than one thousand having robust z spec > 2.5). The increased exposure time in the DR2, along with our panchromatic detection strategy, allow us to improve the completeness at high z with respect to previous UltraVISTA catalogues (e.g. our sample is >75% complete at 10 10 M and z = 5). We also identify passive galaxies through a robust colour-colour selection, extending their SMF estimate up to z = 4. Our work provides a comprehensive view of galaxy-stellar-mass assembly between z = 0.1 and 6, for the first time using consistent estimates across the entire redshift range. We fit these measurements with a Schechter function, correcting for Eddington bias. We compare the SMF fit with the halo mass function predicted from ΛCDM simulations, finding that at z > 3 both functions decline with a similar slope in the high-mass end. This feature could be explained assuming that mechanisms quenching star formation in massive haloes become less effective at high redshifts; however further work needs to be done to confirm this scenario. Concerning the SMF low-mass end, it shows a progressive steepening as it moves towards higher redshifts, with α decreasing from −1.47 +0.02 −0.02 at z 0.1 to −2.11 +0.30 −0.13 at z 5. This slope depends on the characterisation of the observational uncertainties, which is crucial to properly remove the Eddington bias. We show that there is currently no consensus on the method to quantify such errors: different error models result in different best-fit Schechter parameters.

Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

Based on a sample of over 1, 800 radio AGN at redshifts out to z ∼ 5, which have typical stellar masses within ∼ 3 × (10 10 − 10 11 ) M ⊙ , and 3 GHz radio data in the COSMOS field, we derived the 1.4 GHz radio luminosity functions for radio AGN (L 1.4GHz ∼ 10 22 − 10 27 W Hz −1 ) out to z ∼ 5. We constrained the evolution of this population via continuous models of pure density and pure luminosity evolutions, and we found best-fit parametrizations of Φ * ∝ (1 + z) (2.00±0.18)−(0.60±0.14)z , and L * ∝ (1 + z) (2.88±0.82)−(0.84±0.34)z , respectively, with a turnover in number and luminosity densities of the population at z ≈ 1.5. We converted 1.4 GHz luminosity to kinetic luminosity taking uncertainties of the scaling relation used into account. We thereby derived the cosmic evolution of the kinetic luminosity density provided by the AGN and compared this luminosity density to the radio-mode AGN feedback assumed in the Semi-Analytic Galaxy Evolution (SAGE) model, i.e., to the redshift evolution of the central supermassive black hole accretion luminosity taken in the model as the source of heating that offsets the energy losses of the cooling, hot halo gas, and thereby limits further stellar mass growth of massive galaxies. We find that the kinetic luminosity exerted by our radio AGN may be high enough to balance the radiative cooling of the hot gas at each cosmic epoch since z ∼ 5. However, although our findings support the idea of radio-mode AGN feedback as a cosmologically relevant process in massive galaxy formation, many simplifications in both the observational and semi-analytic approaches still remain and need to be resolved before robust conclusions can be reached.

We present the VLA-COSMOS 3 GHz Large Project based on 384 h of observations with the Karl G. Jansky Very Large Array (VLA) at 3 GHz (10 cm) toward the two square degree Cosmic Evolution Survey (COSMOS) field. The final mosaic reaches a median rms of 2.3 µJy beam −1 over the two square degrees at an angular resolution of 0.75 . To fully account for the spectral shape and resolution variations across the broad (2 GHz) band, we image all data with a multiscale, multifrequency synthesis algorithm. We present a catalog of 10 830 radio sources down to 5σ, out of which 67 are combined from multiple components. Comparing the positions of our 3 GHz sources with those from the Very Long Baseline Array (VLBA)-COSMOS survey, we estimate that the astrometry is accurate to 0.01 at the bright end (signal-to-noise ratio, S /N 3 GHz > 20). Survival analysis on our data combined with the VLA-COSMOS 1.4 GHz Joint Project catalog yields an expected median radio spectral index of α = −0.7. We compute completeness corrections via Monte Carlo simulations to derive the corrected 3 GHz source counts. Our counts are in agreement with previously derived 3 GHz counts based on single-pointing (0.087 square degrees) VLA data. In summary, the VLA-COSMOS 3 GHz Large Project simultaneously provides the largest and deepest radio continuum survey at high (0.75 ) angular resolution to date, bridging the gap between last-generation and next-generation surveys.

We make use of the deep Karl G. Jansky Very Large Array (VLA) COSMOS radio observations at 3 GHz to infer radio luminosity functions of star-forming galaxies up to redshifts of z ∼ 5 based on approximately 6 000 detections with reliable optical counterparts. This is currently the largest radio-selected sample available out to z ∼ 5 across an area of 2 square degrees with a sensitivity of rms ≈ 2.3 µJy beam −1 . By fixing the faint and bright end shape of the radio luminosity function to the local values, we find a strong redshift trend that can be fitted with a pure luminosity evolution L 1.4 GHz ∝ (1 + z) (3.16±0.2)−(0.32±0.07)z . We estimate star formation rates (SFRs) from our radio luminosities using an infrared (IR)-radio correlation that is redshift dependent. By integrating the parametric fits of the evolved luminosity function we calculate the cosmic SFR density (SFRD) history since z ∼ 5. Our data suggest that the SFRD history peaks between 2 < z < 3 and that the ultraluminous infrared galaxies (ULIRGs; 100 M ⊙ yr −1 < SFR < 1000 M ⊙ yr −1 ) contribute up to ∼25% to the total SFRD in the same redshift range. Hyperluminous infrared galaxies (HyLIRGs; SFR > 1000 M ⊙ yr −1 ) contribute an additional 2% in the entire observed redshift range. We find evidence of a potential underestimation of SFRD based on ultraviolet (UV) rest-frame observations of Lyman break galaxies (LBGs) at high redshifts (z 4) on the order of 15-20%, owing to appreciable star formation in highly dust-obscured galaxies, which might remain undetected in such UV observations.