We present an analysis of the deepest Herschel images in four major extragalactic fields GOODS-North, GOODS-South, UDS, and COSMOS obtained within the GOODS-Herschel and CANDELS-Herschel key programs. The star formation picture provided by a total of 10 497 individual far-infrared detections is supplemented by the stacking analysis of a mass complete sample of 62 361 starforming galaxies from the Hubble Space Telescope (HST) H band-selected catalogs of the CANDELS survey and from two deep ground-based K s band-selected catalogs in the GOODS-North and the COSMOS-wide field to obtain one of the most accurate and unbiased understanding to date of the stellar mass growth over the cosmic history. We show, for the first time, that stacking also provides a powerful tool to determine the dispersion of a physical correlation and describe our method called "scatter stacking", which may be easily generalized to other experiments. The combination of direct UV and far-infrared UV-reprocessed light provides a complete census on the star formation rates (SFRs), allowing us to demonstrate that galaxies at z = 4 to 0 of all stellar masses (M * ) follow a universal scaling law, the so-called main sequence of star-forming galaxies. We find a universal close-to-linear slope of the log 10 (SFR)-log 10 (M * ) relation, with evidence for a flattening of the main sequence at high masses (log 10 (M * /M ) > 10.5) that becomes less prominent with increasing redshift and almost vanishes by z 2. This flattening may be due to the parallel stellar growth of quiescent bulges in star-forming galaxies, which mostly happens over the same redshift range. Within the main sequence, we measure a nonvarying SFR dispersion of 0.3 dex: at a fixed redshift and stellar mass, about 68% of star-forming galaxies form stars at a universal rate within a factor 2. The specific SFR (sSFR = SFR/M * ) of star-forming galaxies is found to continuously increase from z = 0 to 4. Finally we discuss the implications of our findings on the cosmic SFR history and on the origin of present-day stars: more than two-thirds of present-day stars must have formed in a regime dominated by the "main sequence" mode. As a consequence we conclude that, although omnipresent in the distant Universe, galaxy mergers had little impact in shaping the global star formation history over the last 12.5 billion years.

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We present the deepest 100 to 500 μm far-infrared observations obtained with the Herschel Space Observatory as part of the GOODS-Herschel key program, and examine the infrared (IR) 3-500 μm spectral energy distributions (SEDs) of galaxies at 0 < z < 2.5, supplemented by a local reference sample from IRAS, ISO, Spitzer, and AKARI data. We determine the projected star formation densities of local galaxies from their radio and mid-IR continuum sizes. We find that the ratio of total IR luminosity to rest-frame 8 μm luminosity, IR8 (≡L tot IR /L 8 ), follows a Gaussian distribution centered on IR8 = 4 (σ = 1.6) and defines an IR main sequence for star-forming galaxies independent of redshift and luminosity. Outliers from this main sequence produce a tail skewed toward higher values of IR8. This minority population (<20%) is shown to consist of starbursts with compact projected star formation densities. IR8 can be used to separate galaxies with normal and extended modes of star formation from compact starbursts with high-IR8, high projected IR surface brightness (Σ IR > 3 × 10 10 L kpc −2 ) and a high specific star formation rate (i.e., starbursts). The rest-frame, UV-2700 Å size of these distant starbursts is typically half that of main sequence galaxies, supporting the correlation between star formation density and starburst activity that is measured for the local sample. Locally, luminous and ultraluminous IR galaxies, (U)LIRGs (L tot IR ≥ 10 11 L ), are systematically in the starburst mode, whereas most distant (U)LIRGs form stars in the "normal" main sequence mode. This confusion between two modes of star formation is the cause of the so-called "mid-IR excess" population of galaxies found at z > 1.5 by previous studies. Main sequence galaxies have strong polycyclic aromatic hydrocarbon (PAH) emission line features, a broad far-IR bump resulting from a combination of dust temperatures (T dust ∼ 15-50 K), and an effective T dust ∼ 31 K, as derived from the peak wavelength of their infrared SED. Galaxies in the starburst regime instead exhibit weak PAH equivalent widths and a sharper far-IR bump with an effective T dust ∼ 40 K. Finally, we present evidence that the mid-to-far IR emission of X-ray active galactic nuclei (AGN) is predominantly produced by star formation and that candidate dusty AGNs with a power-law emission in the mid-IR systematically occur in compact, dusty starbursts. After correcting for the effect of starbursts on IR8, we identify new candidates for extremely obscured AGNs.

We analyze the dependence of galaxy structure (size and Sersic index) and mode of star formation (Σ SF R and SF R IR /SF R UV ) on the position of galaxies in the SFR versus Mass diagram. Our sample comprises roughly 640000 galaxies at z ∼ 0.1, 130000 galaxies at z ∼ 1, and 36000 galaxies at z ∼ 2. Structural measurements for all but the z ∼ 0.1 galaxies are based on HST imaging, and SFRs are derived using a Herschel-calibrated ladder of SFR indicators. We find that a correlation between the structure and stellar population of galaxies (i.e., a 'Hubble sequence') is already in place since at least z ∼ 2.5. At all epochs, typical star-forming galaxies on the main sequence are well approximated by exponential disks, while the profiles of quiescent galaxies are better described by de Vaucouleurs profiles. In the upper envelope of the main sequence, the relation between the SFR and Sersic index reverses, suggesting a rapid build-up of the central mass concentration in these starbursting outliers. We observe quiescent, moderately and highly star-forming systems to co-exist over an order of magnitude or more in stellar mass. At each mass and redshift, galaxies on the main sequence have the largest size. The rate of size growth correlates with specific SFR, and so does Σ SF R at each redshift. A simple model using an empirically determined SF law and metallicity scaling, in combination with an assumed geometry for dust and stars is able to relate the observed Σ SF R and SF R IR /SF R UV , provided a more patchy dust geometry is assumed for high-redshift galaxies.

We combine molecular gas masses inferred from CO emission in 500 star forming galaxies (SFGs) between z=0 and 3, from the IRAM-COLDGASS, PHIBSS1/2 and other surveys, with gas masses derived from Herschel far-IR dust measurements in 512 galaxy stacks over the same stellar mass/redshift range. We constrain the scaling relations of molecular gas depletion time scale (t depl ) and gas to stellar mass ratio (M molgas /M * ) of SFGs near the star formation 'main-sequence' with redshift, specific star formation rate (sSFR) and stellar mass (M * ). The CO-and dust-based scaling relations agree remarkably well. This suggests that the CO  H 2 mass conversion factor varies little within ±0.6dex of the main sequence (sSFR(ms,z,M * )), and less than 0.3dex throughout this redshift range. This study builds on and strengthens the results of earlier work. We find that t depl scales as (1+z) -0.3  (sSFR/sSFR(ms,z,M * )) -0.5 , with little dependence on M * . The resulting steep redshift dependence of M molgas /M *  (1+z) 3 mirrors that of the sSFR and probably reflects the gas supply rate. The decreasing gas fractions at high M * are driven by the flattening of the SFR-M * relation. Throughout the redshift range probed a larger sSFR at constant M * is due to a combination of an increasing gas fraction and a decreasing depletion time scale. As a result galaxy integrated samples of the M molgas -SFR rate relation exhibit a super-linear slope, which increases with the range of sSFR. With these new relations it is now possible to determine M molgas with an accuracy of ±0.1dex in relative terms, and ±0.2dex including systematic uncertainties.

We compare multi-wavelength star formation rate (SFR) indicators out to z ∼ 3 in the GOODS-South field. Our analysis uniquely combines U -to-8µm photometry from FIREWORKS, MIPS 24 µm and PACS 70, 100, and 160 µm photometry from the PEP survey, and Hα spectroscopy from the SINS survey. We describe a set of conversions that lead to a continuity across SFR indicators. A luminosityindependent conversion from 24 µm to total infrared luminosity yields estimates of L IR that are in the median consistent with the L IR derived from PACS photometry, albeit with significant scatter. Dust correction methods perform well at low to intermediate levels of star formation. They fail to recover the total amount of star formation in systems with large SF R IR /SF R UV ratios, typically occuring at the highest SFRs (SF R UV +IR 100 M ⊙ /yr) and redshifts (z 2.5) probed. Finally, we confirm that Hα-based SFRs at 1.5 < z < 2.6 are consistent with SF R SED and SF R UV +IR provided extra attenuation towards HII regions is taken into account (A V,neb = A V,continuum /0.44). With the cross-calibrated SFR indicators in hand, we perform a consistency check on the star formation histories inferred from SED modeling. We compare the observed SFR-M relations and mass functions at a range of redshifts to equivalents that are computed by evolving lower redshift galaxies backwards in time. We find evidence for underestimated stellar ages when no stringent constraints on formation epoch are applied in SED modeling. We demonstrate how resolved SED modeling, or alternatively deep UV data, may help to overcome this bias. The age bias is most severe for galaxies with young stellar populations, and reduces towards older systems. Finally, our analysis suggests that SFHs typically vary on timescales that are long (at least several 100 Myr) compared to the galaxies' dynamical time.

Aims. We use the deepest existing mid-and far-infrared observations (reaching ∼3 mJy at 70 μm) obtained with Spitzer in the Great Observatories Origins Deep Survey (GOODS) and Far Infrared Deep Extragalactic Legacy survey (FIDEL) fields to derive the evolution of the rest-frame 15 μm, 35 μm, and total infrared luminosity functions of galaxies spanning z < 1.3. We thereby quantify the fractional contribution of infrared luminous galaxies to the comoving star formation rate density over this redshift range. In comparison with previous studies, the present one takes advantage of deep 70 μm observations that provide a more robust infrared luminosity indicator than 24 μm affected by the emission of PAHs at high redshift (z ∼ 1), and we use several independent fields to control cosmic variance. Methods. We used a new extraction technique based on the well-determined positions of galaxies at shorter wavelengths to extract the 24 and 70 μm flux densities of galaxies. It is found that sources separated by a minimum of 0.5 × FWHM are deblended by this technique, which facilitates multi-wavelength associations of counterparts. Using a combination of photometric and spectroscopic redshifts that exist for ∼80% of the sources in our sample, we are able to estimate the rest-frame luminosities of galaxies at 15 μm and 35 μm. By complementing direct detections with a careful stacking analysis, we measured the mid-and far-infrared luminosity functions of galaxies over a factor ∼100 in luminosity (10 11 L <∼ L IR <∼ 10 13 L ) at z < 1.3. A stacking analysis was performed to validate the bolometric corrections and to compute comoving star-formation rate densities in three redshift bins 0.4 < z < 0.7, 0.7 < z < 1.0 and, 1.0 < z < 1.3. Results. We find that the average infrared spectral energy distribution of galaxies over the last 2/3 of the cosmic time is consistent with that of local galaxies, although individual sources do present significant scatter. We also measured both the bright and faint ends of the infrared luminosity functions and find no evidence for a change in the slope of the double power law used to characterize the luminosity function. The redshift evolution of infrared luminous galaxies is consistent with pure luminosity evolution proportional to (1 + z) 3.6±0.4 up to z ∼ 1.3. We do not find evidence of differential evolution between LIRGs and ULIRGs up to z ∼ 1.3, in contrast with previous claims. The comoving number density of infrared luminous galaxies has increased by a factor of ∼100 between 0 < z < 1. By z ∼ 1.0, LIRGs produce half of the total comoving infrared luminosity density.

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