arXiv subjects

C. Gruppioni

Publications and source records attributed to C. Gruppioni.

At least 109 records · Page 6Linked to original sources

arXiv2013

The deepest Herschel-PACS far-infrared survey: number counts and infrared luminosity functions from combined PEP/GOODS-H observations

We present results from the deepest Herschel-PACS (Photodetector Array Camera and Spectrometer) far-infrared blank field extragalactic survey, obtained by combining observations of the GOODS (Great Observatories Origins Deep Survey) fields from the PACS Evolutionary Probe (PEP) and GOODS-Herschel key programmes. We describe data reduction and the construction of images and catalogues. In the deepest parts of the GOODS-S field, the catalogues reach 3-sigma depths of 0.9, 0.6 and 1.3 mJy at 70, 100 and 160 um, respectively, and resolve ~75% of the cosmic infrared background at 100um and 160um into individually detected sources. We use these data to estimate the PACS confusion noise, to derive the PACS number counts down to unprecedented depths and to determine the infrared luminosity function of galaxies down to LIR=10^11 Lsun at z~1 and LIR=10^12 Lsun at z~2, respectively. For the infrared luminosity function of galaxies, our deep Herschel far-infrared observations are fundamental because they provide more accurate infrared luminosity estimates than those previously obtained from mid-infrared observations. Maps and source catalogues (>3-sigma) are now publicly released. Combined with the large wealth of multi-wavelength data available for the GOODS fields, these data provide a powerful new tool for studying galaxy evolution over a broad range of redshifts.

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arXiv2013

Panchromatic spectral energy distributions of Herschel sources

(abridged) Far-infrared Herschel photometry from the PEP and HerMES programs is combined with ancillary datasets in the GOODS-N, GOODS-S, and COSMOS fields. Based on this rich dataset, we reproduce the restframe UV to FIR ten-colors distribution of galaxies using a superposition of multi-variate Gaussian modes. The median SED of each mode is then fitted with a modified version of the MAGPHYS code that combines stellar light, emission from dust heated by stars and a possible warm dust contribution heated by an AGN. The defined Gaussian grouping is also used to identify rare sources. The zoology of outliers includes Herschel-detected ellipticals, very blue z~1 Ly-break galaxies, quiescent spirals, and torus-dominated AGN with star formation. Out of these groups and outliers, a new template library is assembled, consisting of 32 SEDs describing the intrinsic scatter in the restframe UV-to-submm colors of infrared galaxies. This library is tested against L(IR) estimates with and without Herschel data included, and compared to eight other popular methods often adopted in the literature. When implementing Herschel photometry, these approaches produce L(IR) values consistent with each other within a median absolute deviation of 10-20%, the scatter being dominated more by fine tuning of the codes, rather than by the choice of SED templates. Finally, the library is used to classify 24 micron detected sources in PEP GOODS fields. AGN appear to be distributed in the stellar mass (M*) vs. star formation rate (SFR) space along with all other galaxies, regardless of the amount of infrared luminosity they are powering, with the tendency to lie on the high SFR side of the "main sequence". The incidence of warmer star-forming sources grows for objects with higher specific star formation rates (sSFR), and they tend to populate the "off-sequence" region of the M*-SFR-z space.

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arXiv2012

Comparison of star formation rates from Halpha and infrared luminosities as seen by Herschel

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 μm). 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 μm 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.

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arXiv2012

The AGN content in luminous IR galaxies at z\sim2 from a global SED analysis including Herschel data

We use Herschel-PACS far-infrared data, combined with previous multi-band information and mid-IR spectra, to properly account for the presence of an active nucleus and constrain its energetic contribution in luminous infrared (IR) sources at z\sim2. The sample is composed of 24 sources in the GOODS-South field, with typical IR luminosity of 10^{12} Lo. Data from the 4 Ms Chandra X-ray imaging in this field are also used to identify and characterize AGN emission. We reproduce the observed spectral energy distribution (SED), decomposed into a host-galaxy and an AGN component. A smooth-torus model for circum-nuclear dust is used to account for the direct and re-processed contribution from the AGN. We confirm that galaxies with typical L_{8-1000um}\sim10^{12}Lo at z\sim2 are powered predominantly by star-formation. An AGN component is present in nine objects (\sim35% of the sample) at the 3sigma confidence level, but its contribution to the 8-1000 um emission accounts for only \sim5% of the energy budget. The AGN contribution rises to \sim23% over the 5-30 um range (in agreement with Spitzer IRS results) and to \sim60% over the narrow 2-6 um range. The presence of an AGN is confirmed by X-ray data for 3 (out of nine) sources, with X-ray spectral analysis indicating the presence of significant absorption, i.e. NH\sim10^{23}-10^{24} cm^{-2}. An additional source shows indications of obscured AGN emission from X-ray data. The comparison between the mid-IR--derived X-ray luminosities and those obtained from X-ray data suggests that obscuration is likely present also in the remaining six sources that harbour an AGN according to the SED-fitting analysis.

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arXiv2011

The evolution of the star formation activity per halo mass up to redshift ~ 1.6 as seen by Herschel

Star formation in massive galaxies is quenched at some point during hierarchical mass assembly. To understand where and when the quenching processes takes place, we study the evolution of the total star formation rate per unit total halo mass (Σ(SFR/M)) in three different mass scales: low mass halos (field galaxies), groups, and clusters, up to a redshift ~1.6. We use deep far-infrared PACS data at 100 and 160 um to accurately estimate the total star formation rate of the Luminous Infrared Galaxy population of 9 clusters with mass ~10^{15} M_{\odot}, and 9 groups/poor clusters with mass ~ 5 x 10^{13} M_{\odot}. Estimates of the field Σ(SFR/M) are derived from the literature, by dividing the star formation rate density by the mean comoving matter density of the universe. The field Σ(SFR/M) increases with redshift up to z~1 and it is constant thereafter. The evolution of the Σ(SFR/M)-z relation in galaxy systems is much faster than in the field. Up to redshift z~0.2, the field has a higher Σ(SFR/M) than galaxy groups and galaxy clusters. At higher redshifts, galaxy groups and the field have similar Σ(SFR/M), while massive clusters have significantly lower Σ(SFR/M) than both groups and the field. There is a hint of a reversal of the SFR activity vs. environment at z~1.6, where the group Σ(SFR/M) lies above the field Σ(SFR/M)-z relation. We discuss possible interpretations of our results in terms of the processes of downsizing, and star-formation quenching.

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arXiv2011

The lesser role of starbursts for star formation at z=2

Two main modes of star formation are know to control the growth of galaxies: a relatively steady one in disk-like galaxies, defining a tight star formation rate (SFR)-stellar mass sequence, and a starburst mode in outliers to such a sequence which is generally interpreted as driven by merging. Such starburst galaxies are rare but have much higher SFRs, and it is of interest to establish the relative importance of these two modes. PACS/Herschel observations over the whole COSMOS and GOODS-South fields, in conjunction with previous optical/near-IR data, have allowed us to accurately quantify for the first time the relative contribution of the two modes to the global SFR density in the redshift interval 1.5 1000M(sun)/yr, off-sequence sources significantly contribute to the SFR density (46+/-20%). We conclude that merger-driven starbursts play a relatively minor role for the formation of stars in galaxies, whereas they may represent a critical phase towards the quenching of star formation and morphological transformation in galaxies.

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arXiv2011

The evolution of quiescent galaxies at high redshift (z > 1.4)

We have studied the evolution of high redshift quiescent galaxies over an effective area of ~1.7 deg^2 in the COSMOS field. Galaxies have been divided according to their star-formation activity and the evolution of the different populations has been investigated in detail. We have studied an IRAC (mag_3.6 < 22.0) selected sample of ~18000 galaxies at z > 1.4 with multi-wavelength coverage. We have derived accurate photometric redshifts (sigma=0.06) and other important physical parameters through a SED-fitting procedure. We have divided our sample into actively star-forming, intermediate and quiescent galaxies depending on their specific star formation rate. We have computed the galaxy stellar mass function of the total sample and the different populations at z=1.4-3.0. We have studied the properties of high redshift quiescent galaxies finding that they are old (1-4 Gyr), massive (log(M/M_sun)~10.65), weakly star forming stellar populations with low dust extinction (E(B-V) < 0.15) and small e-folding time scales (tau ~ 0.1-0.3 Gyr). We observe a significant evolution of the quiescent stellar mass function from 2.5 < z < 3.0 to 1.4 < z < 1.6, increasing by ~ 1 dex in this redshift interval. We find that z ~ 1.5 is an epoch of transition of the GSMF. The fraction of star-forming galaxies decreases from 60% to 20% from z ~ 2.5-3.0 to z ~ 1.4-1.6 for log(M/M_sun) > 11, while the quiescent population increases from 10% to 50% at the same redshift and mass intervals. We compare the fraction of quiescent galaxies derived with that predicted by theoretical models and find that the Kitzbichler & White (2007) model is the one that better reproduces the data. Finally, we calculate the stellar mass density of the star-forming and quiescent populations finding that there is already a significant number of quiescent galaxies at z > 2.5 (rho~6.0 MsunMpc^-3).

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arXiv2011

PACS Evolutionary Probe (PEP) - A Herschel Key Program

Deep far-infrared photometric surveys studying galaxy evolution and the nature of the cosmic infrared background are a key strength of the Herschel mission. We describe the scientific motivation for the PACS Evolutionary Probe (PEP) guaranteed time key program and its role in the complement of Herschel surveys, and the field selection which includes popular multiwavelength fields such as GOODS, COSMOS, Lockman Hole, ECDFS, EGS. We provide an account of the observing strategies and data reduction methods used. An overview of first science results illustrates the potential of PEP in providing calorimetric star formation rates for high redshift galaxy populations, thus testing and superseeding previous extrapolations from other wavelengths, and enabling a wide range of galaxy evolution studies.

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arXiv2011

The PEP survey: clustering of infrared-selected galaxies and structure formation at z~2 in the GOODS South

ABRIDGED-This paper presents the first direct estimate of the 3D clustering properties of far-infrared sources up to z~3. This has been possible thanks to the Pacs Evolutionary Probe (PEP) survey of the GOODS South field performed with the PACS instrument onboard the Herschel Satellite. An analysis of the two-point correlation function over the whole redshift range spanned by the data reports for the correlation length, r_0~6.3 Mpc and r_0~6.7 Mpc, respectively at 100um and 160um, corresponding to dark matter halo masses M>~10^{12.4} M_sun. Objects at z~2 instead seem to be more strongly clustered, with r_0~19 Mpc and r_0~17 Mpc in the two considered PACS channels. This dramatic increase of the correlation length between z~1 and z~2 is connected with the presence of a wide, M>~10^{14} M_sun, filamentary structure which includes more than 50% of the sources detected at z~2. An investigation of the properties of such sources indicates the possibility for boosted star-forming activity in those which reside within the overdense environment with respect of more isolated galaxies found in the same redshift range. Lastly, we also present our results on the evolution of the relationship between luminous and dark matter in star-forming galaxies between z~1 and z~2. We find that the increase of (average) stellar mass in galaxies between z~1 and z~2 is about a factor 10 lower than that of the dark matter haloes hosting such objects ( [z~1]/ [z~2] ~ 0.4 vs M_{halo}[z~1]/M_{halo}[z~2] ~ 0.04). Our findings agree with the evolutionary picture of downsizing whereby massive galaxies at z~2 were more actively forming stars than their z~1 counterparts, while at the same time contained a lower fraction of their mass in the form of luminous matter.

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arXiv2011

Modelling Galaxy and AGN Evolution in the IR: Black Hole Accretion versus Star-Formation Activity

We present a new backward evolution model for galaxies and AGNs in the infrared (IR). What is new in this model is the separate study of the evolutionary properties of the different IR populations (i.e. spiral galaxies, starburst galaxies, low-luminosity AGNs, "unobscured" type 1 AGNs and "obscured" type 2 AGNs) defined through a detailed analysis of the spectral energy distributions (SEDs) of large samples of IR selected sources. The evolutionary parameters have been constrained by means of all the available observables from surveys in the mid- and far-IR (source counts, redshift and luminosity distributions, luminosity functions). By decomposing the SEDs representative of the three AGN classes into three distinct components (a stellar component emitting most of its power in the optical/near-IR, an AGN component due to hot dust heated by the central black hole peaking in the mid-IR, and a starburst component dominating the far-IR spectrum) we have disentangled the AGN contribution to the monochromatic and total IR luminosity emitted by the different populations considered in our model from that due to star-formation activity. We have then obtained an estimate of the total IR luminosity density (and star-formation density - SFD - produced by IR galaxies) and the first ever estimate of the black hole mass accretion density (BHAR) from the IR. The derived evolution of the BHAR is in agreement with estimates from X-rays, though the BHAR values we derive from IR are slightly higher than the X-ray ones. Finally, we have simulated source counts, redshift distributions and SFD and BHAR that we expect to obtain with the future cosmological Surveys in the mid-/far-IR that will be performed with JWST-MIRI and SPICA-SAFARI.

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arXiv2010

Evolution of Dust Temperature of Galaxies through Cosmic Time as seen by Herschel

We study the dust properties of galaxies in the redshift range 0.1 0.5 with L_IR>5x10^{10} L_\odot, appears to be 2-5 K colder than that of AKARI-selected local galaxies with similar luminosities; and the dispersion in T_dust for high-z galaxies increases with L_IR due to the existence of cold galaxies that are not seen among local galaxies. We show that this large dispersion of the L_IR-T_dust relation can bridge the gap between local star-forming galaxies and high-z submillimeter galaxies (SMGs). We also find that three SMGs with very low T_dust (<20 K) covered in this study have close neighbouring sources with similar 24-\mum brightness, which could lead to an overestimation of FIR/(sub)millimeter fluxes of the SMGs.

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arXiv2010

Herschel FIR counterparts of selected Ly-alpha emitters at z~2.2. Fast evolution since z~3 or missed obscured AGNs?

Ly-alpha emitters (LAEs) are seen everywhere in the redshift domain from local to z~7. Far-infrared (FIR) counterparts of LAEs at different epochs could provide direct clues on dust content, extinction, and spectral energy distribution (SED) for these galaxies. We search for FIR counterparts of LAEs that are optically detected in the GOODS-North field at redshift z~2.2 using data from the Herschel Space Telescope with the Photodetector Array Camera and Spectrometer (PACS). The LAE candidates were isolated via color-magnitude diagram using the medium-band photometry from the ALHAMBRA Survey, ancillary data on GOODS-North, and stellar population models. According to the fitting of these spectral synthesis models and FIR/optical diagnostics, most of them seem to be obscured galaxies whose spectra are AGN-dominated. From the analysis of the optical data, we have observed a fraction of AGN or composite over source total number of ~0.75 in the LAE population at z~2.2, which is marginally consistent with the fraction previously observed at z=2.25 and even at low redshift (0.2<z<0.45), but significantly different from the one observed at redshift ~3, which could be compatible either with a scenario of rapid change in the AGN fraction between the epochs involved or with a non detection of obscured AGN in other z=2-3 LAE samples due to lack of deep FIR observations. We found three robust FIR (PACS) counterparts at z~2.2 in GOODS-North. This demonstrates the possibility of finding dust emission in LAEs even at higher redshifts.

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arXiv2010

Unveiling Far-Infrared Counterparts of Bright Submillimeter Galaxies Using PACS Imaging

We present a search for Herschel-PACS counterparts of dust-obscured, high-redshift objects previously selected at submillimeter and millimeter wavelengths in the Great Observatories Origins Deep Survey North field. We detect 22 of 56 submillimeter galaxies (39%) with a SNR of >=3 at 100 micron down to 3.0 mJy, and/or at 160 micron down to 5.7 mJy. The fraction of SMGs seen at 160 micron is higher than that at 100 micron. About 50% of radio-identified SMGs are associated with PACS sources. We find a trend between the SCUBA/PACS flux ratio and redshift, suggesting that these flux ratios could be used as a coarse redshift indicator. PACS undetected submm/mm selected sources tend to lie at higher redshifts than the PACS detected ones. A total of 12 sources (21% of our SMG sample) remain unidentified and the fact that they are blank fields at Herschel-PACS and VLA 20 cm wavelength may imply higher redshifts for them than for the average SMG population (e.g., z>3-4). The Herschel-PACS imaging of these dust-obscured starbursts at high-redshifts suggests that their far-infrared spectral energy distributions have significantly different shapes than template libraries of local infrared galaxies.

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arXiv2010

The dust content of high-z submillimeter galaxies revealed by Herschel

We use deep observations taken with the Photodetector Array Camera and Spectrometer (PACS), on board the Herschel satellite as part of the PACS evolutionary probe (PEP) guaranteed project along with submm ground-based observations to measure the dust mass of a sample of high-z submillimeter galaxies (SMGs). We investigate their dust content relative to their stellar and gas masses, and compare them with local star-forming galaxies. High-z SMGs are dust rich, i.e. they have higher dust-to-stellar mass ratios compared to local spiral galaxies (by a factor of 30) and also compared to local ultraluminous infrared galaxies (ULIRGs, by a factor of 6). This indicates that the large masses of gas typically hosted in SMGs have already been highly enriched with metals and dust. Indeed, for those SMGs whose gas mass is measured, we infer dust-to-gas ratios similar or higher than local spirals and ULIRGs. However, similarly to other strongly star-forming galaxies in the local Universe and at high-z, SMGs are characterized by gas metalicities lower (by a factor of a few) than local spirals, as inferred from their optical nebular lines, which are generally ascribed to infall of metal-poor gas. This is in contrast with the large dust content inferred from the far-IR and submm data. In short, the metalicity inferred from the dust mass is much higher (by more than an order of magnitude) than that inferred from the optical nebular lines. We discuss the possible explanations of this discrepancy and the possible implications for the investigation of the metalicity evolution at high-z.

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arXiv2010

Herschel deep far-infrared counts through the Abell 2218 cluster-lens

Gravitational lensing by massive galaxy clusters allows study of the population of intrinsically faint infrared galaxies that lie below the sensitivity and confusion limits of current infrared and submillimeter telescopes. We present ultra-deep PACS 100 and 160 microns observations toward the cluster lens Abell 2218, to penetrate the Herschel confusion limit. We derive source counts down to a flux density of 1 mJy at 100 microns and 2 mJy at 160 microns, aided by strong gravitational lensing. At these levels, source densities are 20 and 10 beams/source in the two bands, approaching source density confusion at 160 microns. The slope of the counts below the turnover of the Euclidean-normalized differential curve is constrained in both bands and is consistent with most of the recent backwards evolutionary models. By integrating number counts over the flux range accessed by Abell 2218 lensing (0.94-35 mJy at 100 microns and 1.47-35 mJy at 160 microns, we retrieve a cosmic infrared background (CIB) surface brightness of ~8.0 and ~9.9 nW m^-2 sr^-1, in the respective bands. These values correspond to 55% (+/- 24%) and 77% (+/- 31%) of DIRBE direct measurements. Combining Abell 2218 results with wider/shallower fields, these figures increase to 62% (+/- 25%) and 88% (+/- 32%) CIB total fractions, resolved at 100 and 160 microns, disregarding the high uncertainties of DIRBE absolute values.

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arXiv2010

Herschel unveils a puzzling uniformity of distant dusty galaxies

The Herschel Space Observatory enables us to accurately measure the bolometric output of starburst galaxies and active galactic nuclei (AGN) by directly sampling the peak of their far-infrared (IR) emission. Here we examine whether the spectral energy distribution (SED) and dust temperature of galaxies have strongly evolved since z~2.5. We use Herschel deep extragalactic surveys from 100 to 500um to compute total IR luminosities in galaxies down to the faintest levels, using PACS and SPIRE in the GOODS-North field (PEP and HerMES key programs). We show that measurements in the SPIRE bands can be used below the statistical confusion limit if information at higher spatial resolution is used to identify isolated galaxies whose flux is not boosted by bright neighbors. Below z~1.5, mid-IR extrapolations are correct for star-forming galaxies with a dispersion of only 40% (0.15dex), therefore similar to z~0 galaxies. This narrow distribution is puzzling when considering the range of physical processes that could have affected the SED of these galaxies. Extrapolations from only one of the 160um, 250um or 350um bands alone tend to overestimate the total IR luminosity. This may be explained by the lack of far-IR constraints around and above ~150um (rest-frame) on local templates. We also note that the dust temperature of luminous IR galaxies around z~1 is mildly colder by 10-15% than their local analogs and up to 20% for ULIRGs at z~1.6. Above z=1.5, distant galaxies are found to exhibit a substantially larger mid- over far-IR ratio, which could either result from stronger broad emission lines or warm dust continuum heated by a hidden AGN. Two thirds of the AGNs identified in the field with a measured redshift exhibit the same behavior as purely star-forming galaxies. Hence a large fraction of AGNs harbor star formation at very high SFR and in conditions similar to purely star-forming galaxies.

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arXiv2010

Star formation in AGN hosts in GOODS-N

Sensitive Herschel far-infrared observations can break degeneracies that were inherent to previous studies of star formation in high-z AGN hosts. Combining PACS 100 and 160um observations of the GOODS-N field with 2Msec Chandra data, we detect ~20% of X-ray AGN individually at >3sig. The host far-infrared luminosity of AGN with L2-10~10^43erg/s increases with redshift by an order of magnitude from z=0 to z~1. In contrast, there is little dependence of far-infrared luminosity on AGN luminosity, for L2-10<~10^44erg/s AGN at z>~1. We do not find a dependence of far-infrared luminosity on X-ray obscuring column, for our sample which is dominated by L2-10<10^44erg/s AGN. In conjunction with properties of local and luminous high-z AGN, we interpret these results as reflecting the interplay between two paths of AGN/host coevolution. A correlation of AGN luminosity and host star formation is traced locally over a wide range of luminosities and also extends to luminous high z AGN. This correlation reflects an evolutionary connection, likely via merging. For lower AGN luminosities, star formation is similar to that in non-active massive galaxies and shows little dependence on AGN luminosity. The level of this secular, non-merger driven star formation increasingly dominates over the correlation at increasing redshift.

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arXiv2010

PEP: first Herschel probe of dusty galaxy evolution up to z~3

We exploit the deepest existing far-infrared (FIR) data obtained so far by Herschel at 100 and 160 um in the GOODS-N, as part of the PACS Evolutionary Probe (PEP) survey, to derive for the first time the evolution of the rest-frame 60-um, 90-um, and total IR luminosity functions (LFs) of galaxies and AGNs from z=0 to unprecedented high redshifts (z~2-3). The PEP LFs were computed using the 1/Vmax method. The FIR sources were classified by means of a detailed broad- band SED-fitting analysis and spectral characterisation. Based on the best-fit model results, k-correction and total IR (8-1000 um) luminosity were obtained for each source. LFs (monochromatic and total) were then derived for various IR populations separately in different redshift bins and compared to backward evolution model predictions. We detect strong evolution in the LF to at least z~2. Objects with SEDs similar to local spiral galaxies are the major contributors to the star formation density (SFD) at z< 0.3, then, as redshift increases, moderate SF galaxies - most likely containing a low-luminosity AGN - start dominating up to z ~= 1.5. At >1.5 the SFD is dominated by the contributions of starburst galaxies. In agreement with previous findings, the comoving IR LD derived from our data evolves approximately as (1 + z)^(3.8+/-0.3) up to z~1, there being some evidence of flattening up to z~2.

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