Exploring Cosmic Origins with CORE : Extragalactic Sources in Cosmic Microwave Background Maps
We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, CORE , that has been submitted in response to ESA’s call for a Medium-size mission opportunity as the successor of the Planck satellite. Even though the effective telescope size will be somewhat smaller than that of Planck, CORE will have a considerably better angular resolution at its highest frequencies, since, in contrast with Planck, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e. substantially fainter detection limits. In particular, CORE will detect thousands of strongly lensed high- galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the CORE resolution matches the typical sizes of high- galaxy proto-clusters much better than the Planck resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, CORE will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, CORE will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively.
1]G. De Zotti,\noteCorresponding author.
14]A. J. Banday,
28] F. Bouchet,
58] F. Boulanger,
32]C. S. Carvalho,
77]M. G. Castellano,
17, 49, 74]A. Challinor,
35,36]P. de Bernardis,
31,85]G. de Gasperis,
28,38]E. Di Valentino,
5,81]S. M. Feeney,
55]A. Le Brun,
69]B. F. Roukema,
50]R. van de Weygaert,
72]B. Van Tent,
]for the CORE collaboration
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Although not specifically designed for the observation of extragalactic sources, space-borne experiments aimed at investigating the Cosmic Microwave Background (CMB) have the potential to bring breakthroughs also in this field. An investigation of the impact on studies of extragalactic sources of the project named the Cosmic Origins Explorer plus (COrE), submitted in response to ESA’s call for the 4th Medium-size mission (M4) opportunity, was carried out by Ref. . Various options were considered, with effective telescope sizes of m, m and 2 m, and a frequency range from 60 to 1200 GHz. A proposal for ESA’s 5th Medium-size mission (M5) is envisaging an instrument (named CORE ) with a baseline telescope size of 1.2 m and 19 frequency channels, distributed over the 60–600 GHz frequency range. A decrease or an increase of the telescope size to 1 m and to 1.5 m, respectively, were also considered. These options will be referred to as CORE 100 and CORE 150. For the CORE 150 configuration we will also consider the added value of an extension of the frequency range to 800 GHz.
Since the analysis by Ref. was completed, considerable relevant new data have become available and more detailed studies have been carried out, motivating an update for the 5th Medium-size mission (M5) proposal. In particular, most analyses of the Planck data have now been published, giving much clearer predictions for the capabilities of next generation CMB experiments.
The plan of the paper is the following. In Sect. 2 we present a new assessment of the expected counts of the various classes of extragalactic sources in total intensity. In Sect. 3 we highlight the CORE potential for detecting galaxy proto-clusters during their early evolutionary phase when they did not yet possess the hot intergalactic medium allowing detection via their X-ray emission and/or the Sunyaev-Zeldovich (SZ) effect. As shown in Sect. 4, CORE will also provide unique information on the evolution of the star-formation rate (SFR) in virialized clusters. Section 5 deals with the information provided by CORE surveys on the Cosmic Infrared Background (CIB), while the effect of bright sub-mm lines on the power spectra measured in different frequency intervals and the possibility of counts being estimated in lines are considered in Sect. 6. In Sect. 7 we discuss counts in polarized flux density and report the results of new simulations aimed at determining the CORE detection limits in polarization, showing that CORE will provide a real breakthrough in this field. Our main conclusions are summarized in Sect. 8.
Throughout this paper we adopt the fiducial CDM cosmology with the best-fit values of the parameters derived from Planck CMB power spectra, in combination with lensing reconstruction and external data: ; ; and .
This work is part of a series of papers that present the science achievable by the CORE space mission. The performance requirements and the mission concept are described in . The instrument is described in . Reference  explores systematic effects that may represent a threat to the measurement accuracy. Reference  discusses polarised foregrounds and the -mode component separation. The constraints on cosmological parameters and fundamental physics that can be derived from CORE measurements are discussed in  while the constraints on inflationary models are discussed in . References  and  deal large-scale structure and cluster science, respectively, while  addresses the effect on the CMB of the observer’s peculiar motion.
|(GHz)||1 m||1.2 m||1.5 m||2 m|
2 Counts of extragalactic sources in total intensity
As pointed out by Ref. , CORE surveys will be confusion limited. This was already the case for the Planck High Frequency Instrument (HFI) which however reached the diffraction limit only up to 217 GHz, while CORE will be diffraction limited over its full frequency range. Since the confusion limit scales roughly as the beam solid angle, i.e. as the square of the full width at half maximum (FWHM) of the instrument [?, see figure 3 of Ref.]]DeZotti2015, CORE will substantially improve over Planck-HFI, even in the case of a somewhat smaller telescope. For example, at 545 GHz (m) the Planck beam has an effective , while the diffraction limit for its 1.5-m telescope is . Realistic simulations  gave, at this frequency, completeness limits of 86 mJy for the CORE 1.5-m option and of 142 mJy for the 1-m option. For comparison the 90% completeness limit for the Second Planck Catalog of Compact Sources [?, PCCS 2;]]PCCS2_2015 at 545 GHz is 555 mJy.
At the lower frequencies covered by the Planck Low Frequency Instrument (LFI), whose resolution was also at the diffraction limit, CORE performs better thanks to its lower instrumental noise. For example at 70 GHz the PCCS 2 90% completeness limit is 501 mJy, while simulations give, for CORE , completeness limits of 95 mJy and 200 mJy for the 1.5-m and 1-m options, respectively .
Reference  found that the CORE detection limits, , derived from realistic simulations, are well approximated by the formula:
Here, and are the rms fluctuations at the instrument resolution due source confusion and to CMB anisotropies, respectively, computed using the formulae in Sect. 2.1 of Ref. . The source confusion term, due to sources below the detection limit, includes contributions of Poisson fluctuations due to radio sources, , and to dusty galaxies , as well as the contribution of clustering of dusty galaxies, (the contribution of clustering of radio sources was found to be negligibly small). The contribution of CORE instrumental noise, , turns out to be always almost negligible. A tabulation of CORE detection limits, , for the 19 frequency channels and four effective telescope sizes (1 m, 1.2 m, 1.5 m, and 2 m) is given in Table 1.
2.1 Local dusty galaxies
The Planck surveys offered the first opportunity to accurately determine the luminosity function of dusty galaxies in the very local universe at several (sub-)millimetre wavelengths, using blindly selected samples of low-redshift sources, unaffected by cosmological evolution . At 857, 545 and 353 GHz the local luminosity function could be determined over about three decades in luminosity. Remarkably, Planck reached luminosities almost one order of magnitude fainter than Herschel’s Spectral and Photometric Imaging REceiver (SPIRE) surveys at the common or nearby frequencies (857 and 545 GHz, corresponding to wavelengths of 350 and m) : Planck’s all-sky coverage has proven to be much more effective in detecting local low-luminosity sub-mm galaxies than Herschel-SPIRE, in spite of the much deeper flux density levels reached by the latter instrument, on small sky areas.
Estimates of the CORE detection limits  show that it will reach, at 500–600 GHz, flux densities a factor of 5 (1-m option) or 8.6 (1.5-m option) fainter than the PCCS2. CORE will thus explore a volume larger by a factor of or , respectively, thus improving the source statistics by similar factors. As a result, CORE will detect, at 600 GHz and with significance, from (1-m option) to (1.5-m option) star-forming galaxies out to in the “extragalactic zone” () defined by Ref. .
Within the timescales of the CORE launch, there will be several wide-angle redshift and photometric surveys available that should provide distance information for the majority, if not all, of the galaxies detected by the satellite. Of most interest of course are data sets covering the entire sky. In the near future spectroscopic data for all the Two Micron All Sky Survey (2MASS) galaxies (1 million over most of sky, median ) are expected from the TAIPAN survey  and the Low Redshift survey at Calar Alto (LoRCA) project . On a longer timescale, the Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer (SPHEREx) mission  aims at providing a low-resolution spectroscopic survey of the entire sky in the near-IR, including millions of galaxies up to .
Another avenue towards all-sky 3D catalogues is through combing imaging data-sets and deriving photometric redshifts. This was successfully completed first for 2MASS galaxies [?, 2MPZ;]]Bilicki2014 and recently also for a combination of WISE and SuperCOSMOS scans of photographic plates . The WISE/SuperCOSMOS catalogue maps the large scale structure (LSS) at for 70% of sky.
The deeper CORE surveys, compared to Planck, coupled with redshift information, will make it possible to extend the determination of the luminosity function of dusty galaxies down to fainter luminosities and to higher redshifts. The information from blind detections on CORE maps can be expanded by exploiting the prior knowledge of galaxy positions from optical/IR surveys to push the detection limits to fainter levels, a technique successfully tested in Ref. . Stacking analyses on positions of known galaxies will allow us to reach still fainter flux densities.
A variety of photometric data will also be available across the electromagnetic spectrum (radio, IRAS, AKARI, WISE, Euclid, GALEX, ROSAT, eROSITA) in addition to multi-band optical/near-IR imaging. Combining them with CORE data, it will be possible to carry out an extensive characterization of the properties of galaxies in the nearby Universe [?, e.g.]]Malek2014. CORE data will be crucial in particular to achieve progress towards understanding how dust mass and emission vary with galaxy type and stellar mass. The combination of the CORE data with data in different wavebands will allow us to determine, for each galaxy type and as a function of stellar mass, the distribution of dust temperatures, as well as the dust mass function, the SFR function, the relationship between star formation and nuclear activity, the relative contributions of newborn and evolved stars to dust heating, and more.
The next step will be to relate the properties of galaxies detected by CORE to the underlying dark matter field and to the properties of their host dark matter haloes. Local dusty star-forming galaxies are found to be more clustered and to reside in more massive haloes than galaxies with unobscured star formation [22, 23]. CORE will provide an unprecedented sample to investigate the link between local dusty galaxies of different types and their local environments.
At mm wavelengths we can exploit the synergy with the Stage-IV CMB (CMB-S4) surveys . This next generation ground-based program aims to deploy O(500,000) detectors spanning the 30–300 GHz frequency range. It will use multiple telescopes and sites to map most of the sky and is expected to be operational between about and . Thanks to its higher sensitivity, the CMB-S4 experiment will extend to longer wavelengths the spectral coverage of dusty galaxies detected by CORE at sub-mm wavelengths. Among other things, this will allow us to test the hints from Planck that some fraction of local galaxies have a significant very cold dust component [?, 10–13 K;]]RowanRobinsonClements2015 which the mm bands of CMB-S4 will be especially powerful in detecting.
2.2 High- dusty galaxies
At sub-mm wavelengths CORE will reach faint enough flux densities to see the transition from the Euclidean portion of the counts contributed by low- galaxies to the steeply rising portion caused by cosmological evolution. The precise shape of the counts in this transition region provides critical constraints to evolutionary models . There are in fact two main scenarios discussed in the literature for the evolution of galaxies as viewed at far-IR/sub-mm wavelengths. One scenario envisages a direct evolutionary link between local and high- galaxies, with no new populations. According to the other scenario, a major component of the dusty galaxy population at high-, is made, for example, by massive proto-spheroidal galaxies in the process of forming the bulk of their stars. These galaxies have no low- counterparts at far-IR/sub-mm wavelengths because they have been essentially passively evolving since –1.5. Clearly the first scenario implies a more gradual steepening of the slope of the counts than the second one.
CORE will provide a complete census of the brightest sub-mm galaxies in the Universe, including those with extreme amplification by gravitational lensing. Planck has already offered an exciting foretaste of that: “Planck’s dusty GEMS” [?, Gravitationally Enhanced subMillimetre Sources;]]Canameras2015. As discussed in Ref. , follow-up CO spectroscopy and multi-frequency photometry of 11 such sources have shown that they are at –3.6 and have apparent (uncorrected for gravitational amplification) far-IR luminosities of up to , making them among the brightest sources in the Universe. They are so rare that only very large area surveys can find them.
Ref.  have found 77 candidate strongly lensed galaxies brighter than 100 mJy at m from Herschel surveys covering , corresponding to a surface density of . A somewhat lower surface density at the same flux density limit has been derived in Ref.  from the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS); they found 79 candidates over an area of . Averaging the two estimates we obtain a surface density of . The CORE detection limits at m are mJy and mJy for the 1-m and the 1.5-m telescope, respectively. The average surface density of strongly lensed galaxies with mJy is implying that the 1-m option will allow the discovery of about one thousand strongly lensed galaxies in the “extragalactic zone”. A slight extrapolation to 90 mJy using the model shown in Fig. 1 leads to an estimate of about 3,000 strongly lensed galaxies detectable by CORE 150 in the “extragalactic zone”.
At these flux densities the selection of strongly lensed galaxies can be easily done with close to 100% efficiency [34, 35]. In fact, as illustrated by Fig. 1, in the relevant flux density range, i.e. above mJy, the dominant populations of extragalactic sources are low- galaxies and high- strongly lensed galaxies (see the right-hand panel of the figure). The former are easily recognisable in all-sky optical/near-IR surveys, such as the UK Schmidt Telescope and Second Palomar Observatory survey [?, see the recent SuperCOSMOS all-sky galaxy catalogue;]]Peacock2016, the Two-Micron All-Sky Survey [?, 2MASS;]]Skrutskie2006 and the Wide-field Infrared Survey Explorer [?, WISE;]]Wright2010. In addition there is a small fraction of radio sources, mostly blazars, also easily identifiable by cross-matching with all-sky radio surveys, such as the NRAO VLA Sky Survey [?, NVSS;]]Condon1998 plus the Sydney University Molonglo Sky Survey [?, SUMSS;]]Mauch2003.
There will be a large overlap between the strongly lensed galaxies detected by the CMB-S4 surveys and those detected by CORE . The two sets of observations will allow a better definition of the SEDs, hence a better photometric redshift estimate, and an improved determination of the source positions, essential for follow-up observation. Due to the shape of the dust emission SED, CORE will be more efficient at detecting objects at , while the longer wavelength observations by the CMB-S4 will be more effective at detecting those at . Note however that the sub-mm CORE measurements will be essential to characterize the emission peak, hence to derive basic quantities like the total IR luminosity, hence the SFR.
These large samples of strongly gravitationally lensed galaxies will be trivially easy targets for ALMA, NOEMA, etc., and the foreground lenses will almost certainly be detectable in, e.g., Euclid imaging. Follow-up observations will allow us to determine the total (visible and dark) mass of the lensing galaxies, to investigate their density profiles, and to measure cosmological parameters and especially the Hubble constant using gravitational time delays [?, e.g.]and references therein]Eales2015, Meng2015. The time delay distance measurement are estimated to reach an uncertainty of 5–7% and are independent of the local distance ladder; they thus provide a crucial test of any potential systematic uncertainties. Although the Planck determination of from CMB anisotropies has a much higher precision, it should be noted that time delay distances are completely independent of the properties of the early Universe and may thus allow one to break some of the main degeneracies in the interpretation of CMB data.
While other facilities (e.g., Euclid, Gaia, SKA) will also be generating large gravitational lens catalogues on a comparable timescale [?, see, e.g.,]for a recent review]Serjeant2016 the critical advantage of CORE and of CMB-S4 will be in extending the sources and lenses to much higher redshifts and in detecting the most extreme amplifications. This has been demonstrated by Planck: the magnification factors, , of “Planck’s dusty GEMS” are estimated to be up to 50 .
The flux boosting is accompanied by a stretching of images. In general, the image size scales approximately as in one direction (tangentially) while being unchanged in the perpendicular direction (radially). The geometric mean is an overall scaling of as demanded by the conservation of surface brightness. The extreme apparent luminosities and the stretching of images allow us to study the properties and internal structure of these high- sources in extraordinary detail, much greater than would be possible otherwise. The evolution of dark matter halo substructure and the stellar initial mass function (IMF) can thus be probed to much higher redshifts, providing key tests for galaxy evolution theory.
Another important advantage compared to optical/near-IR searches is that foreground lenses and background magnified galaxies stand out in different wavebands. The background lensed galaxies CORE will detect are heavily dust obscured, hence are bright at far-IR/(sub-)mm wavelengths but are almost invisible in the optical/near-IR. On the contrary, most foreground lenses are passive spheroidal galaxies, hence bright in the optical/near-IR but almost invisible at far-IR/(sub-)mm wavelengths. Therefore the mutual contamination of their images is small or negligible. This is obviously a major advantage for detailed modelling.
For the unlensed population, the CORE survey will also probe essentially the entire Hubble volume for the most intense hyperluminous starbursts, testing whether there are physical limits to the star-formation rates of galaxies [?, e.g. Eddington-limited star formation;]]vanderWerf2011.
3 Protoclusters of dusty galaxies
As shown in Ref. , at sub-mm wavelengths fluctuations in Planck maps are dominated by the clustering of dusty galaxies at high . This implies that low-resolution surveys in this spectral range are optimally suited for detecting overdensities of star-forming galaxies that may evolve into present day rich clusters .
A blind search on Planck maps for candidate high- proto-clusters was carried out in Ref. , looking for intensity peaks with “cold” sub-mm colours, i.e. with continuum spectra peaking between 353 and 857 GHz at resolution, consistent with redshifts for typical dust emission spectra. Their selection required detections at in all three highest frequency Planck bands and applied a flux density threshold of mJy. A total of 2151 high- source candidates satisfying these criteria were selected in the cleanest 26% of the sky, corresponding to a surface density of . Apart from a tiny fraction (around 3%) of extreme strongly lensed high- galaxies, these intensity peaks appear to be associated with excess surface densities of high- dusty star-forming galaxies. This conclusion was substantiated by Herschel/SPIRE follow-up of 234 Planck “cold” targets , finding that about 94% of them indeed show a significant excess of red 350 and m sources in comparison to reference SPIRE fields.
The detected sources have a flux density distribution peaking at Jy and extending up to Jy. If they are indeed proto-clusters at , they have extraordinarily high total (8–m) infrared luminosities, , peaking around for a reference dust temperature of 35 K . The corresponding star formation rate (SFR) is . The associated halo mass, , obtained from the SFR– relation at derived exploiting the abundance matching technique, is . But the surface density of halos that massive at is only , well below that of Planck over-densities.
On the other hand, the halo surface density increases steeply with decreasing : already at it reaches . This suggests that the candidate proto-clusters detected in Ref.  may not be individual objects but fluctuations in the number of somewhat smaller, physically unrelated clumps of dusty galaxies along the line of sight. Extensive simulations by Negrello et al. (in preparation) showed that indeed the results of Ref.  can be understood in these terms. Support for this view comes from the fact that the only Planck overdensity for which spectroscopic or photometric redshifts of member galaxies have been obtained was found to consist of two structures at and . Despite the fact that many of these clumps of emission selected with Planck are not single proto-clusters, they are nevertheless signposts of proto-cluster regions along the line of sight.
An alternative search for candidate high- proto-clusters has been carried out by Ref. [?]see also Greenslade et al. 2016, in preparation]Clements2014, by cross matching the 857 GHz Planck Catalogue of Compact Sources with over 1000 of Herschel survey fields (primarily H-ATLAS  and HerMES ) to search for evidence of compact emission from cold clumps of high- galaxies. Selected at 857 GHz, these sources are still “cold”, but “warmer” than those selected at 545 GHz by Planck , and thus corresponding to a higher dust temperature or redshifts for typical dust SEDs. A visual inspection of the Herschel maps at the positions of the Planck compact sources for excesses of red sources identifies a total of 59 proto-cluster candidates. As noted in Ref. , few of the Planck high- sources correspond to a PCCS2 source, so these two alternative methods likely probe different populations of proto-clusters.
Simulations of the distributions of the sub-mm flux from proto-clusters seen by Planck [?]see their figure 7]Granato2015 suggest that the typical 350-m flux density from a proto-cluster is on the order of 100 mJy, below Planck’s sensitivity. The detection of such sources in the PCCS2 however indicates a typical 350 m flux density of mJy, 5–10 times greater than predicted from the simulations. Since the typical highest proto-cluster SFR reached in the simulations was , this implies an observed SFR on the order of , consistent with the observations from blind searches on the Planck maps for cooler proto-clusters.
In any case, the samples of “cold” intensity peaks detected by Planck (and in much greater abundance by CORE ) are of great interest for the investigation of the evolution of large-scale structure. Follow-up observations of galaxies within them, providing redshift estimates, would be a powerful tool to investigate the early phases of cluster formation, inaccessible by other means. In fact, these overdensities can be detected in the pre-virialization phase, when their intergalactic medium might not have been shock-heated yet, and hence they may not be detectable via X-ray emission or the Sunyaev-Zeldovich (SZ) effect.
The higher resolution of CORE will facilitate a much easier selection of true proto-clusters. The search described in Ref.  was carried out adopting an angular resolution of , corresponding to a physical size of about 2.5 Mpc at –2. This resolution is not optimal for detecting proto-clusters. The study by Ref.  of 274 clusters with from the Spitzer InfraRed Array Camera (IRAC) Shallow Cluster Survey, using Herschel/SPIRE 250-m imaging, showed that the density of IR-emitting cluster members dominates over the background field level only within Mpc of the cluster centre, while at Mpc the corrected source density of cluster members is only a small enhancement over the field source density.
A linear scale of 0.5 Mpc corresponds to an angular scale of about at redshifts in the range 1.5–2.5, i.e. to the angular radius of the CORE beam at GHz for the 1-m telescope option. The 1.5-m option, with its FWHM of at 600 GHz and of at 800 GHz, corresponding, in that redshift range, to linear radii of or kpc, respectively, will be much better suited to detect the bright cluster cores of the kind discovered in Ref.  at and in Ref.  at on scales of kpc (see Fig. 2).
A visual indication of the appearance of such proto-clusters at different resolutions is given in Fig. 3. Though only a single source is identifiable in the Planck maps, both CORE 100 and CORE 150 show that the nature of this source is a clear overdensity of fainter sources, as also seen in the Herschel maps. The all-sky nature of CORE would enable us to search for such overdensities over roughly 20 times the area surveyed by Herschel.
The CMB-S4 surveys also have a resolution well suited for proto-cluster detection. However, since most of detectable proto-clusters should be at relatively low redshifts (), their signal is much lower at the longer CMB-S4 wavelengths. Thus these objects are considerably easier to detect at the highest CORE frequencies. As in the case of strongly lensed galaxies, the CMB-S4 data will contribute to determining the SED, hence the photometric redshift (for an assumed dust temperature), the IR luminosity and the SFR of each source.
A complete, unbiased census of these proto-clusters is fundamental to our understanding of the full path of galaxy cluster formation and of the effect of dense environments on galaxy formation and evolution. Such structures, however, are rare and therefore difficult to find. The surface density of proto-clusters serendipitously detectable by CORE (and by CMB-S4) is estimated to be of a few to [?]see also Negrello et al. 2016, in preparation]Ivison2013; hence we may expect the detection by CORE of several hundreds to a few thousand violently starbursting proto-cluster cores.
4 Evolution of the IR emission of galaxy clusters
The serendipitously detected proto-clusters are likely in different evolutionary stages, from early agglomeration towards the collapse to virial equilibrium. There is, however, also clear evidence of strong evolution in the star-formation activity in virialized clusters \citep[and references therein]Wagner2016. The specific SFR increases rapidly from to , mostly driven by the activation of star formation in early-type galaxies at . CORE will allow us to investigate the evolution of galaxy populations in such clusters, detected via their X-ray emission [60, 61, 62] or via the thermal SZ (tSZ) effect [63, 64, 65].
The South Pole Telescope (SPT) tSZ survey sample contains clusters with median mass of
At dense cluster cores are preferentially populated by massive, passively evolving, early-type galaxies. Star-forming galaxies are generally found in the cluster outskirts and in the field. Ref.  showed that the star-formation activity in cluster core (Mpc) galaxies from to 1.5 is at the field level at but is suppressed faster at lower redshifts. A similar conclusion was reached by studying a sample of 57 groups and clusters in the range using the deepest surveys with Spitzer MIPS (Multi-Band Imaging Photometer for Spitzer) and Herschel Photoconductor Array Camera and Spectrometer (PACS) and SPIRE, on blank and cluster fields .
The ratio of the mean IR luminosity of galaxies in clusters (within Mpc from the cluster centre) to that of galaxies in the field, for , was found to be 
with large uncertainties; here is the cosmic time in Gyr. The cluster IR luminosity then can be written
where is the IR comoving luminosity density, is the cluster density contrast, , is the mean matter density whose present day value is , is the cluster volume and is the cluster mass.
According to figure 17 of Ref. , and for the standard CDM cosmology we have, approximately, for , so that the cluster IR luminosity at fixed mass evolves very strongly [, up to ].
Ref.  presented a detailed study of star formation in 11 near-IR selected, spectroscopically confirmed, massive () clusters at . They found that the star formation in cluster galaxies at is largely consistent with field galaxies at similar epochs, confirming earlier results from the Spitzer/IRAC Shallow Cluster Survey . Although the samples were uniformly selected there are quite strong variations in star formation from cluster to cluster.
We have used these results to make tentative predictions of expected flux densities of clusters as a whole. Figure 4 shows the expected flux densities due to dust emission from a cluster with mass as a function of redshift. The cluster luminosities were obtained using eq. (4), and the contributions of late-type, starburst and proto-spheroidal galaxies were computed using the model from Ref. .
As shown in Fig. 4 we expect that at 800 GHz the CORE 150 version will detect the dust emission of the brightest clusters and of typical clusters at . More massive clusters will be detected over broader redshift ranges. Stacking will allow us to carry out a statistical investigation of the evolution of the cluster IR emission over a much broader redshift baseline than has been possible so far. Targets for stacking will abound. By the time CORE will fly, eROSITA (extended ROentgen Survey with an Imaging Telescope Array), expected to be launched in 2017, should have provided an all-sky deep X-ray survey detecting galaxy clusters out to . About 38,000 cluster detections out to are expected, via the tSZ effect, from the baseline CORE mission, and about with CORE 150; combining CORE 150 and CMB-S4 data it will be possible to detect around 200,000 clusters in the sky visible from the South Pole (Melin et al., in preparation).
For comparison, Herschel has allowed the study of the IR emission from clusters up to , but the sample comprises only 11 clusters. The Herschel data have shown large variations in cluster properties, highlighting the need for evolutionary studies of large, uniform cluster samples over a broad redshift range. CORE will fulfill this need.
The situation is somewhat less favourable at GHz, where, however, CORE will nevertheless substantially improve over Planck. At this frequency a direct source detection by CORE will be possible only for cluster masses . But again, the stacking approach will allow substantial progress in the exploration of the evolution of the IR emission as a function of cluster mass and redshift. This will shed light on the mechanisms which drive the evolution of massive spheroidal galaxies in clusters, from actively star forming to passively evolving in dense environments, and on the role of nuclear activity in this process.
Figure 4 shows that, according to the model in Ref. , different galaxy populations are expected to dominate the cluster sub-mm emission at different redshifts. At the main contribution comes from late-type galaxies with relatively cold dust temperatures. This is consistent with the dust temperature, K, estimated in Ref.  for their sample of clusters detected by Planck, with an estimated mean redshift . This study also found a slight increase of dust temperature with redshift, comparing clusters at larger and smaller than 0.25. Such an increase is indeed predicted by the model, due to the increasing contribution of the warmer starburst population that takes over above and out to . At still higher redshifts the dominant population is the proto-spheroidal galaxies in the process of forming most of their stars.
Once more, we will take advantage of the synergies with CMB-S4, as pointed out in the previous sections. The characterization of the IR emission in individual clusters, obtained combining CORE and CMB-S4 data, is essential to extract the relativistic correction in the hottest clusters and the contribution from non-thermal electrons to the SZ effect [71, 72]. Relativistic corrections would allow us to estimate in an independent way the plasma temperature while non-thermal contributions provide information on outflows from star formation and/or from nuclear activity.
5 The Cosmic Infrared Background (CIB)
Progress in our understanding of the power spectrum of the CIB that will be made possible by CORE has been discussed in Ref. . Briefly, the better CORE angular resolution, compared to Planck, will allow us to measure, in a uniform way, the CIB power spectrum over an unprecedented range of frequencies and of angular scales (from arcmin to tens of degrees), thus breaking the degeneracy between the Poisson contribution and that of non-linear effects (one-halo term), that complicates the interpretation of Planck measurements without resorting to external data. Accurate determinations of the CIB power spectrum at different frequencies provide, on the one hand constraints on the evolution of the cosmic star-formation density and, on the other hand, on halo masses associated with sources of the CIB [73, 74, 75].
The exploitation of CIB anisotropies as a probe of star-formation history in the Universe and also as a dark matter tracer requires a careful removal of foreground radiations, the most important of which, at sub-mm wavelengths, is the Galactic thermal dust emission. The separation of dust and CIB components is challenging since both have frequency spectra scaling approximately as modified black-bodies with similar emissivity indices. An approach successfully applied to Planck temperature maps combines the frequency information, to reconstruct the Galactic thermal dust model, with spatial information, taking advantage of different power spectra of the components . In fact, the CIB power spectrum scales approximately as , while the Galactic dust power spectrum scales approximately as or for . With its much more numerous frequency channels, higher sensitivity and better angular resolution, CORE will substantially improve over Planck both in the spectral and spatial characterization, thus enabling a much easier and more robust separation of the two components. Obviously, a better Galactic thermal dust model will also allow an improved cleaning of CMB maps.
Moreover, the large number of CORE channels will make it possible to investigate in detail the decorrelation of power spectra measured in different frequency bands. A decorrelation is expected because the redshift distribution of CIB sources shifts to higher and higher redshifts with decreasing frequency. Accurate measurements of the CIB cross-spectra for different frequency channels set strong constraints on the frequency dependence of redshift distributions, hence on the evolution of the cosmic SFR. Ref.  found that the CORE design is very close to the optimal design for improving the SFR constraints at all redshifts.
As pointed out by Ref. , the angular power spectrum of the CIB is a sensitive probe of primordial non-Gaussianity. It potentially outperforms the forthcoming large-scale galaxy redshift surveys because the CIB traces the large-scale structure over a much larger comoving volume. Again, the key factor is an accurate subtraction of the Galactic thermal dust emission, achievable with the numerous sub-mm channels of CORE . This will make possible to constrain the “local type” primordial non-Gaussianity parameter called down to an amplitude .
Another interesting issue is the possibility of exploiting the multi-frequency measurements of the dipole spectrum to constrain the CIB intensity spectrum [79, 80, 81, 82]. This arises from the fact that the dipole amplitude is directly proportional to the first derivative of the photon occupation number. High accuracy measurements of the CIB dipole amplitude at sub-mm wavelengths will provide important constraints on the CIB intensity, currently known with a uncertainty \citepFixsen1998. Such a large uncertainty constitutes a major limitation to our understanding of the dust-obscured star formation phase of galaxy evolution. The exploitation of this possibility requires a very accurate inter-channel cross-calibration and a careful control of the systematics from the foreground Galaxy subtraction . A detailed discussion of this topic will be presented in a companion paper (Burigana et al., in preparation).
6 Resonant scattering on metals and ions at high redshifts
The multi-frequency CORE observations will not only allow us to separate the usual foreground signals, such as the diffuse Galactic emission and point sources, but might also enable the identification of subtler astrophysical signals. In particular, metals and ions in the intergalactic medium (IGM) leave signatures in the anisotropy pattern of the CMB intensity and polarization.
As shown in Refs.  and , in low over-density regions the dominant mechanism coupling the CMB photons with metals and ions is resonant scattering. On large angular scales such scattering blurs the intrinsic anisotropy pattern and induces a frequency dependent variation of the observed angular power spectrum given by
where is the intrinsic CMB angular power spectrum and is the increment of the optical depth associated with resonant transitions of one or several species corresponding to two different observing frequencies and .
Low frequency channels are affected by resonant lines produced at high redshifts. But at high enough redshifts the abundance of metals and ions is negligible; hence the CMB power spectrum measured at low frequencies is the intrinsic one, so that low frequency channels can be used as a reference, against which to compare observations at higher frequencies that correspond to lower redshift lines. This comparison allows us to set constraints on the abundance of different species of metals and ions at different cosmological epochs \citep[see ][for more details]Basu04,CHMetal07.
However, real life is significantly more complicated. Besides foregrounds there are other issues, the most important being inter-channel calibration and beam characterization \citepCHMetal06. In the future, the proposed PIXIE experiment  could provide absolutely calibrated low-resolution maps of the sky to improve the channel inter-calibration and mitigate this problem. If we assume that foregrounds can be projected out down to negligible levels and that we can achieve an inter-channel calibration at the 0.001% level (approximately times better than for the Planck-HFI cosmological channels), then a comparison of the power spectrum measured by CORE at 80 GHz with those measured at higher frequencies would yield the constraints (at 3 or % confidence level) on different species shown in Fig. 5. These limits are obtained assuming that only one transition contributes to the signal, and that the beams can be characterized with arbitrary precision. For a given species, constraints are tighter at higher redshifts/lower frequencies, where the control of free-free and synchrotron emission is more demanding.
High sensitivity, multi-frequency CMB observations are also sensitive to other signals involving atoms and molecules, such as the collisional/rotational emission of CO and the Cm line [?]]righi08,DeZotti2016,Mashian2016 or the Field-Wouthuysen effect on OI atoms \citepchmOI07,chmOI08. The poor spectral resolution of CMB experiments implies a strong dilution of the lines, making them undetectable in individual sources. But an improvement of the spectral resolution, , by a factor of several, at least for some high frequency channels, would make possible the detection of thousands of sources in these lines. Examples are shown in Fig. 6 for a modest .
The integral counts shown in this figure were worked out exploiting the model in Ref.  for the cosmological evolution of the IR luminosity function, coupled with relations between line intensities and IR luminosities. For the CO lines we have used the relations of Ref.  and for the Cm line that by Ref. . More details on the calculations can be found in Ref. . As illustrated by Fig. 6, an all-sky survey with is expected to detect line emission brighter than 30 mJy (a flux density limit achievable by CORE 150) of galaxies in the “extragalactic zone”. The Cm line becomes increasingly important with increasing frequency.
6.1 Radio sources
The overwhelming majority of extragalactic radio sources detectable by CORE are blazars, i.e. sources whose radio emission is dominated by Doppler-boosted emission from relativistic jets closely aligned with the line of sight . These objects, with their extreme properties, are of special interest since they are also strong –ray sources. About 90% of the firmly identified extragalactic sources and about 94% of the “associated” sources (i.e. of sources having a counterpart with a probability of being the real identification) in the Third Fermi Large Area Telescope (LAT) catalogue  are blazars.
Accurate source counts over large flux density intervals provide key constraints on blazar evolutionary models. Because high frequency surveys are still far less extensive than those at low frequencies, evolutionary models for blazar populations, flat spectrum radio quasars (FSRQs) and BL Lacertae sources (BL Lacs), are less developed than those for steep-spectrum radio sources [97, 98]. For example, while clear evidence for downsizing
Furthermore, source counts constrain the compactness of the synchrotron-emitting regions in the jets. Already the counts at mm wavelengths available in 2011 allowed Ref.  to rule out simple power-law spectra for these sources and to constrain models for spectral breaks of the synchrotron emission in blazar jets. Furthermore, the assumption of uniform spectral properties for the whole blazar population was found to be, at best, only marginally consistent with the data. A clearly better match with the observed counts was obtained by assuming that BL Lacs have, on average, substantially higher break frequencies than FSRQs, suggesting that the synchrotron emission comes from more compact regions. This led to the prediction of a substantial increase of the BL Lac fraction at still higher frequencies and at bright flux densities. To test this prediction surveys at sub-mm wavelengths, such as those carried out by CORE , are paramount.
In order to characterize the blazar synchrotron peak it is crucial to push the photometry to sub-mm wavelengths, which will be provided by CORE . Ref.  investigated the global spectral energy distributions (SEDs) of a sample of 104 extragalactic radio sources drawn from the Planck Early Release Compact Source Catalogue (ERCSC), combining Planck data with simultaneous observations ranging from radio to –rays. They have shown that Planck data provide key information on the energy spectrum of relativistic electrons responsible for the synchrotron emission, with implications for the acceleration mechanisms provided by shocks along the relativistic jets.
The further analysis in Ref.  has confirmed that the flattest high-frequency radio spectral indices are close to zero, indicating that the original energy spectrum of accelerated electrons is much harder than commonly thought, with power-law index around 1.5 instead of the canonical 2.5. The radio spectra of these sources peak at remarkably high frequencies, tens of GHz, and there are significant statistical differences between subclasses of Active Galactic Nuclei (AGN) at high frequencies, particularly between highly-polarized quasars and BL Lac objects.
An interesting open question is the geometry of the emitting region. The data analysed in Ref.  are consistent with a single synchrotron emission zone, but their analysis was limited to frequencies up to 217 GHz. However, simultaneous SED data, including Planck photometry, for some particularly bright sources suggest double emission zones peaking at different frequencies with a transition occurring at sub-mm/far-IR wavelengths [?]and references therein]Cutini2014. As illustrated by Fig. 7 and by Table 2, the deeper sub-mm surveys by CORE will increase by about two orders of magnitude the number of sources detected up to 600 GHz. The improved constraints on the spectral energy distributions at sub-mm wavelengths entail correspondingly better constraints on the geometry of the emitting regions.
Key information on the flow of the plasma within the relativistic jets is provided by variability. Signatures of evolving shocks in the strongest radio flares were seen in a study of Planck sources , although much of the high frequency variability may be better approximated by achromatic variations. These results are compatible with the standard shocked jet model, but other interpretations are also possible. CORE will shed light on this by providing much larger samples and a broader spectral coverage.
Definite conclusions on all the above issues are currently hampered by the limited statistics. To illustrate the improvement made possible by CORE with respect to Planck we have considered the complete Planck-ATCA Co-eval Observations (PACO) “bright” sample . The sample comprises the 189 sources with AT20G flux densities mJy, only a few of which were detected by Planck beyond 217 GHz (see Table 2). Figure 7 shows the continuum spectra of the subset of 145 sources for which we could obtain good fits with smooth functions that can be used to extrapolate the spectra to higher frequencies.
|PCCS2||103 (71%)||132 (91%)||135 (93%)||91 (63%)||3 (2%)||1 (0.7%)|
|CORE 100||143 (99%)||142 (98%)||141 (97%)||141 (97%)||137 (95%)||91 (63%)|
|CORE 150||145 (100%)||145 (100%)||145 (100%)||145 (100%)||142 (98%)||120 (83%)|
Together with CORE , CMB-S4 will extend by a factor of 30 the frequency range over which accurate number counts of radio sources down to tens to hundred mJy will be determined. At the moment, counts down to at least these levels are available only at GHz [?, see Ref.]for a review]DeZotti2010, and between 95 and 220 GHz, where the Planck counts are supplemented at fainter flux densities by those from the South Pole Telescope [?, SPT;]]Mocanu2013 and from the Atacama Cosmology Telescope [?, ACT;]]Marsden2014. At other frequencies GHz the best current information on radio source counts comes from Planck  and is limited to flux densities not much below 1 Jy.
The characterization of the blazar emission at both mm and sub-mm wavelengths is an essential ingredient for understanding the physics of these sources [101, 109, 110]. There is an obvious synergy, in this respect, between CMB-S4 and CORE surveys. The synergy extends also to the study of variability properties. Multi-epoch (sub-)millimetre observations can serendipitously detect variable objects and flares in BL Lacs and FSRQs, particularly in regions with high scan coverage, as seen by Planck in the blazar S . Planck/HFI carried out five full surveys of the sky, while CORE is expected to make six to ten full surveys. In combination with CMB-S4 observations, CORE will enable a multifrequency study of variability on scales from months to several years.
|CORE 100 (1-m telescope)||CORE 150 (1.5-m telescope)|
|Freq.||FWHM||Noise||Pix. size||Pixel no.||FWHM||Noise||Pix. size||Pixel no.|
7 Detecting sources in polarization
The preliminary estimates  suggested that CORE will allow a real breakthrough in the characterization of the polarization properties of extragalactic sources. However, those estimates were only tentative, being based on simplifying assumptions that allowed analytical calculations. We have now re-assessed them by means of realistic simulations in polarization (the simulations described in Ref.  were only in total intensity), carried out for the two options for the telescope size.
The relevant technical details of the simulations are summarized in Table 3. The size of the simulated patch varies with frequency, on account of the varying angular resolution of the survey, quantified by the FWHM of the telescope beam. In the 1-m telescope case, the patch size decreases from at 60 GHz to at 600 GHz; in the 1.5-m case it decreases from at 60 GHz to at 800 GHz. Given the smallness of the patches, a flat-sky approximation was used.
Our simulations include both radio sources and star-forming galaxies. The latter comprise two sub-populations, late-type galaxies and what we are referring to as proto-spheroids, which have different clustering properties [?, e.g.]]Xia2012, Cai2013. We started from source counts using models that accurately reproduce observational data, specifically the model in Ref.  for radio sources and the model in Ref.  for star-forming galaxies.
We have selected the sets of frequencies, specified in Table 3, in the range covered by CORE and for each frequency we populated sky patches with sources in the flux density range 0.01 mJy–100 Jy, assigning to each source a flux density drawn at random from the number counts. For each simulation we checked the consistency, within Poisson errors, of the counts of simulated sources with those given by the model. Then we associated with each source a polarization degree randomly extracted from probability distributions appropriate for each source population, as detailed below. The polarization angles were drawn at random from a uniform probability distribution.
The most extensive study of the polarization properties of extragalactic radio sources at high radio frequencies was carried out in Ref. . These authors obtained polarization data for 180 extragalactic sources extracted from the Australia Telescope 20-GHz (AT20G) survey catalogue and observed with the Australia Telescope Compact Array (ATCA) during a dedicated, high-sensitivity run (mJy). Complementing their data with polarization information for seven extended sources from the 9–yr Wilkinson Microwave Anisotropy Probe (WMAP) co-added maps at 23 GHz, they obtained a roughly complete sample of extragalactic sources brighter than mJy at the selection epoch.
The sample has a 91.4% detection rate in polarization at 20 GHz. The results are in general agreement with those of other polarization surveys at high radio frequencies, carefully reviewed in Ref.  and, most recently, in Ref. . The distribution of polarization degrees was found to be well described by a log-normal function with mean and dispersion of and , respectively. We have assumed that this distribution holds at all the frequencies considered, consistent with the results of Ref. .
Most recently, Ref.  applied the stacking technique to estimate the average fractional polarization from 30 to 353 GHz of a sample of 1560 compact sources - essentially all radio sources - detected in the 30 GHz Planck all-sky map. The average and median polarization fractions for the 881 sources, presumably extragalactic, outside the Galactic mask were found to be and , approximately independent of frequency.
In the case of star-forming galaxies, the polarized emission in the CORE frequency range is dominated by dust, except perhaps at the lowest frequencies, where the polarization due to synchrotron emission may take over, at least for low- galaxies. But at low frequencies the polarized emission of these galaxies is undetectable by CORE in any case.
Polarization properties of dusty galaxies as a whole are almost completely unexplored. The only available information has come from SCUPOL, the polarimeter for SCUBA on the James Clerk Maxwell Telescope, that has provided polarization measurements at m for only two galaxies, M 82  and M 87 . However the global polarization degree has been published only for M 82 and is . This low value is in keeping with the notion that the polarized dust emission integrated over the whole galaxy is reduced because of the complex structure of galactic magnetic fields, with reversals along the line of sight, and also of the disordered alignment of dust grains. For our simulations we adopted a log-normal probability distribution of with mean of 0.5% and dispersion of .
Integrating the Planck dust polarization maps over a wide band centred on the Galactic plane we find an average value of the Stokes parameter of about 2.7%. We may then expect a similar value for spiral galaxies seen edge-on. For a galaxy seen with an inclination angle we expect that the polarization degree is reduced by a factor . If all galaxies are about as polarized as ours, the average polarization fraction for unresolved galaxies, averaged over all possible orientations, should be about half of 2.7%, i.e. around 1.4%. If so our choice of the mean polarisation degree would be quite conservative and the number of detections in polarisation of dusty galaxies would be underestimated by a factor of around .
The angular clustering of the radio sources is strongly diluted by the broadness of their luminosity functions, implying that objects distributed over distance ranges much larger than the clustering radius contribute to the counts at any flux density. This effect makes their clustering essentially irrelevant in the present context.
Analyses of clustering properties of star-forming galaxies [112, 28] have demonstrated a strong difference between late-types and proto-spheroids. The clustering of the former objects adds a minor contribution to the intensity fluctuations due to point sources, which, in the CORE frequency range, are dominated by the latter population. Ignoring the clustering properties of late-type galaxies is thus a good approximation, since we are only interested in characterizing the fluctuation field; these galaxies have therefore been distributed at random inside the simulated sky area.
In contrast, for proto-spheroidal galaxies we used the method elaborated in Ref. , which allowed us to distribute the sources consistently with their clustering properties, as described by the angular power spectrum, . At each frequency we adopted the given by the model of Ref.  that fits the available clustering data on dusty galaxies.
We have used the latest version of the Planck Sky Model [?, PSM;]]Delabrouille2013 to check that, in “clean” regions at high Galactic latitudes (), the contribution of Galactic emission to fluctuations at the CORE resolution is small compared to noise and, except at the highest CORE frequencies, to CMB fluctuations. The PSM currently incorporates all the available information on the various emission components, thus providing a realistic representation of the sky. We have therefore neglected the Galactic emissions. This implies that the detection limits derived below are lower limits for regions with substantial Galactic emission.
As for the CMB, we made use of the PSM software package to generate all-sky intensity and polarization maps in the HEALPix pixelization with high resolution, i.e. with , corresponding to a pixel size of 25.65 arcsec. Regions of the chosen size and angular resolution were projected onto the plane and added to the source maps (that were built on a planar surface). Each map was then filtered with a Gaussian beam function with the appropriated FWHM, and the instrumental noise was added; the adopted values for the FWHM and the noise are specified in Table 3.
We have applied the Mexican-hat wavelet 2 as described in Ref.  and . This filtering approach allows an efficient point-source detection and extraction, since it effectively removes CMB structures or extended emission. This cleaning was carried out before attempting any detection. The rms of the final filtered patch was computed after masking all sources detected with signal-to-noise ratio .
In fact the size of patches over which we simulated the source distribution were too small to contain a statistically significant number of sources with polarized flux densities detected with . To determine the detection limits we then injected, at each frequency, fake sources with gradually increasing polarized flux densities. At least five sources per polarized flux density bin were introduced in the maps, distributed with a separation at least three times larger than the beam size.
The source detection algorithm was then applied blindly to each of the simulated patches, producing a list of detections. Once the detection limits were determined at each frequency, the surface density of sources brighter than such limits were obtained from the model. The estimated detection limits and number of sources per steradian above them are given in Tables 4 and 5 and illustrated by Fig. 8; results are presented for a set of frequencies in the CORE range and for the 1-m and 1.5-m options.
Objects detected in polarization are essentially only radio sources for frequencies up to around GHz. The number of detected dusty galaxies increases with increasing frequency. For the adopted distribution of polarization fraction, CORE will detect similar numbers of radio sources and of dusty galaxies at GHz. At 600 GHz the latter population will dominate, reaching an integral count of for sources detected with . Of course these estimates are only guesses, since the distribution of the global polarization fraction of dusty galaxies is unknown. We will need the measurements of CORE to probe the polarization distribution.
The CORE 150 configuration will do much better, reaching thousands of detections per steradian in polarization of both proto-spheroidal and late-type galaxies at its highest frequency (800 GHz). As illustrated by Fig. 9 the progress with respect to Planck polarization results is spectacular. In fact, in the “extragalactic zone”, Planck detected only a few tens of extragalactic objects in polarisation, all of them radio sources.
Polarization surveys of extragalactic sources are essential to control the contamination of CMB polarimetry experiments with arcmin pixel sizes, and carry crucial information on the source physics. Polarimetric properties of radio-loud AGN at millimetric and sub-millimetric wavelengths tell us about magnetic fields and about the plasma in the inner, unresolved regions of their relativistic jets. Additionally, polarimetry of dusty galaxies as a function of their inclination is informative on the structure and on the ordering of large-scale magnetic fields.
Finally, we note that, like in the total intensity case, CMB-S4 will primarily detect radio sources, reaching deeper flux density levels than CORE . In turn, CORE will extend the frequency coverage and the time-span for variability studies. For studies of polarization properties of dusty galaxies, CORE data will be unique.
In spite of their sensitivities, now approaching fundamental limits, modern space-borne CMB experiments have provided only shallow surveys of extragalactic sources. The key limitation is source confusion, i.e. intensity peaks due to random positive fluctuations of faint sources that mimic real individual sources. The rms confusion noise scales approximately as the square of the FWHM (see figure 3 of ). Hence the substantially better resolution of the diffraction-limited CORE telescope, compared to Planck, especially at the highest frequencies, offers a large advantage in terms of detection limits. The advantage is further boosted in terms of the number of detected sources by the steepness of the source counts.
The power of all-sky surveys at mm and sub-mm wavelengths has already been vividly demonstrated by Planck, which has detected thousands of dusty galaxies as well as many hundreds of extragalactic radio sources in this spectral range, which is difficult or impossible to explore from the ground and only lightly surveyed by other space missions. Planck photometry proved to be crucially important to characterize the synchrotron peak of blazars. Surveys at mm wavelengths are the most effective way to select this class of sources, which, among other things, constitute the overwhelming majority of the identified extragalactic –ray sources detected by the Fermi-LAT. Planck data have also provided key information on the energy spectrum of relativistic electrons responsible for the synchrotron emission with interesting implications for their acceleration mechanisms.
Planck detected several of the most extreme, strongly-lensed, high- galaxies, with estimated gravitational amplifications, , of up to 50; CORE will detect thousands of strongly lensed galaxies. Strong lensing offers the opportunity of detailed follow-up studies of high- galaxies with otherwise unattainable sensitivity: the exposure time to reach a given flux density limit varies as and, since lensing conserves surface brightness, it stretches the image, thus effectively increasing the angular resolution by a substantial factor (at least in one dimension).
Moreover, Planck proved to be a powerful probe of the evolution of the large-scale structure of the Universe in the phase when early-type galaxies, the dominant population in rich clusters and groups of galaxies, were forming the bulk of their stars.
Beyond strongly expanding the samples of source populations detected by Planck, CORE will open new windows. In particular, it will: (i) provide unbiased, flux limited samples of dense proto-cluster cores of star-forming galaxies, some examples of which were detected by Herschel; (ii) allow a detailed investigation, via direct detections complemented with stacking analysis, of the evolution of the star-formation rate in virialized galaxy clusters detected by surveys of the SZ effect (including those carried out by CORE itself) or by X-ray surveys; (iii) provide the spectrum of the CIB dipole anisotropy, which contains important information on the average CIB intensity spectrum; and (iv) provide the first blind high frequency census of the polarization properties of radio sources and of star-forming galaxies.
Work supported in part by ASI/INAF agreement n. 2014-024-R.1 and by PRIN–INAF 2014 “Probing the AGN/galaxy co-evolution through ultra-deep and ultra-high resolution radio surveys”. JGN acknowledges financial support from the Spanish MINECO for a “Ramon y Cajal” fellowship (RYC-2013-13256) and the ID 2015 project AYA2015-65887-P (MINECO/FEDER). CH-M acknowledges the financial support of the Spanish MINECO through ID project AYA-2015-66211-C2-2-P. MB is supported by the Netherlands Organization for Scientific Research, NWO, through grant number 614.001.451, and by the Polish National Science Centre under contract UMO-2012/07/D/ST9/02785. CJM is supported by an FCT Research Professorship, contract reference IF/00064/2012, funded by FCT/MCTES (Portugal) and POPH/FSE (EC). GR acknowledges support from the National Research Foundation of Korea (NRF) through NRF-SGER 2014055950 funded by the Korean Ministry of Education, Science and Technology (MoEST), and from the faculty research fund of Sejong University in 2016.
- Note that table 13 of Ref.  lists the total number of Planck detections, not only those above the 90% completeness limit.
- We define as the total mass within the radius for which the mean overdensity is 500 times the mean matter density of the Universe. Note that frequently is defined to correspond to an overdensity 500 times the critical density.
- “Downsizing” refers to the very different evolutionary behaviour of high- and low-luminosity sources, in the sense that the redshift of the peak space density of sources decreases with luminosity .
- We have updated the analysis of Ref.  using the PCCS2 data. The number of sources with smooth spectra decreased from 147 to 145, with no significant change to the earlier conclusions.
- The PCCS2 lists hundreds of detections in polarization, mostly at low Galactic latitudes. The surface densities shown in Fig. 9 are our own estimates based on detections in the “extragalactic zone” above the 90% completeness limit.
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