Teaming up Radio and Sub-mm/FIR Observations to Probe Dusty Star-Forming Galaxies
The radio spectra of DSFGs are a combination of a flat free-free component from HII regions containing massive ionizing stars and a steep synchrotron component resulting from relativistic electrons accelerated by supernova remnants. An additional synchrotron emission from a small-scale jet or winds/outflows associated with the nuclear activity may be present with various (and variable) spectral behaviours (see [26]). As the frequency increases, the radio emission is progressively overwhelmed by the rising, grey-body component due to dust emission associated with star formation. On average, the frequency of this transition falls in the range ∼30–100 GHz, but it depends on redshift, galaxy age, and the relative role of nuclear activity and star formation. In fact, although X-ray follow-up observations of FIR-selected DSFGs at high redshift have clearly pinpointed the presence of heavily obscured, accreting central supermassive black holes (see [27]), their capability for driving appreciable radio emission is still to be assessed, especially in connection with galaxy properties (e.g., age, specific star-formation rate, obscuration, etc.).
Hence, a comprehensive description of this galactic population necessitates the combination of both the radio and FIR information by selecting samples in one electromagnetic regime and performing follow-ups in the other or by merging statistically significant population properties obtained from large-area surveys. However, the large number of parameters and processes involved makes extrapolations between different frequency domains extremely tough and at the limit of instrumental sensitivities, so that follow-ups in other bands of selected samples typically have low success rates.
2.1. DSFG in Radio Observations
Despite DSFGs constituting the bulk of sub-mJy radio source populations [13], they remain substantially unexplored because of limits in sensitivity and resolution of the current facilities and of the positive k-correction that hampers the possibility of reaching extremely high redshifts in the radio bands.
The expected contribution to the 1.4 GHz source counts of the different populations of extragalactic sources has been estimated by [28] (see their Figure 8). In particular, at sub-mJy fluxes, the counts are dominated by star-forming galaxies (radio-loud AGNs are largely subdominant), of which DSFGs constitute a relevant fraction; this is even more true focusing on progressively high-redshift sources. For example, a star-forming galaxy at redshift (≈3) with 1.4 GHz radio flux of ≈100 μJy would feature a 1.4 GHz radio luminosity of ≈1030 (≈1031) erg s−1 Hz−1; assuming a standard FIR-radio correlation, this would correspond to a FIR luminosity of ≈1045 (≈1046) erg s−1, which in turn would represent an appreciable SFR of ≈30 (≈300) yr−1. Such high SFRs imply a rapid metal and dust enrichment that make these objects heavily obscured and, thus, proper DSFGs. Their bright FIR/submm emission can be exploited, via cross-matching with radio surveys, to distinguish them from low-redshift , less star-forming, and less obscured systems.
For reference, based on the source counts by [28], we estimated the observing time requested by the Australia Telescope Compact Array (ATCA1) to detect star-forming galaxies at 2.1 GHz, reporting it as a function of the flux density limit and survey area in Figure 1: the estimates consider the mosaicing conditions (Nyquist sampling) for areas larger than 1 field-of-view (FOV) but does not consider overheads, which could be as high as 40% because of RFI typically affecting this frequency band. For the same conditions, we estimated the number of expected sources in a given area as a function of the flux density limit (see Figure 2). It is clear that the shape of the differential source counts implies that to achieve a statistically significant number of SFGs, it is more efficient to reach deep sensitivities even if over small areas. Nevertheless, high redshift sources remain rare, and only deep large area surveys can collect significant samples.
At frequencies GHz (≳10 cm in wavelength), the DSFG signal is dominated by the synchrotron emission associated with star formation [19,20]. The minimum, generated by the combination of fading synchrotron and rising dust signals, is expected to be located in the 30–100 GHz frequency (∼3–7 mm wavelength) range. Therefore, radio observations targeted to DSFGs are preferentially performed across ∼1–3 GHz frequency range.
On the one hand, the FOV size scales as , where λ is the observational wavelength and A is the antenna(s) diameter size. Therefore, in the cm-wavelength domain, the larger FOV allows for a faster coverage of large areas of the sky, with respect to what can be achieved at mm-wavelength bands. On the other hand, the resolution scales as , where λ is the observational wavelength and B is the maximum distance (i.e., the maximum baseline length), by taking into account all the couples of antennas in the array. Therefore, for a given telescope, the resolution gets worse in the cm-domain with respect to the mm-domain, with the consequence of possible effects of confusion and blending going to the deepest flux densities (i.e., Malmquist and Eddington biases).
Furthermore, the lowest frequencies are the most seriously affected by radio frequency interference (RFI) and human activities, raising dramatically the confusion level and the level of flagging that is needed to reach reliable detections when the observation requires high sensitivity, as for radio-faint DSFGs.
Other effects that must be accounted for are those introduced as a consequence of the imaging process for radio interferometers. Images are the result of an inverse Fourier transformation of the observed data (visibilities, edited to remove RFI and misbehaviours, if needed). The noise is non-Gaussian, with a pattern that is determined by the antenna configuration and the observing time allocation. The non-Gaussianity and the presence of noise features increase as the array is sparser or the observing time shorter or limited to small chunks. This issue implies that the reliability of a source might change depending on its position across the FOV and with respect to other brighter sources that may be present in the vicinity (e.g., within a few degrees). Techniques like self-calibration or source subtractions/peeling in the visibility domain can significantly improve the dynamic range in the image domain but are not always possible (e.g., not enough signal-to-noise ratio for self-calibration solutions to converge or poor sky/bright sources modelling). Continuum observation imaging combines visibilities over the whole bandwidth (i.e., multi-frequency synthesis) to achieve deeper sensitivities, but the telescope response may be significantly different across a wide bandwidth, as it scales linearly with the wavelength (as mentioned above for the overall FOV size). This fact can be significant at low frequencies, producing a chromatic aberration called “bandwidth smearing”, which blurs images radially, altering source positions and flux density measurements.
For all these reasons, deep radio surveys have been typically limited to small areas, and uncertainty due to the confusing effects significantly hampers a comprehensive description of the sub-mJy population at cm-wavelengths. Most of the issues in modern surveys have been addressed by data processing software refinements, which for larger and larger facilities introduce computational complexity that make surveys critically resource demanding.
This situation is improving in the cm-domain thanks to the profusion of surveys already in progress or planned for the next years with SKA pathfinders and precursors (e.g., EMU, MIGHTEE, RACS, and VLASS), which will combine homogeneous low noise patterns, fast survey speed due to a large number of observing elements with high resolution over long baselines, and advanced processing techniques. Nevertheless, an issue concerning cross-matching with the FIR observations will remain, as explained in the next section.
In the mm-domain, the expected WSU for ALMA will dramatically increase the survey speed, allowing for relatively large areas of the sky to be covered in reasonable time, as we demonstrate later in this paper. The ALMA telescope frequency coverage from 30 to 950 GHz permits the combination of observations across the synchrotron- to dust-dominated regimes and the proper reconstruction of the spectral energy distribution (SED) of the observed DSFGs.
2.2. Cross-Matches of Radio and FIR Surveys
The Herschel surveys have depicted a general statistical description of the DSFG population in the FIR regime. Specifically, the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) [29] is the largest, covering 600 deg2 in five photometric bands (100, 160, 250, 350, and 500 μm). A plethora of follow-ups of many small samples each selected with different criteria, for different purposes, have been observed in different settings with sub-mm telescopes (e.g., ALMA, PdB, and SPT). High-resolution and sensitivity follow-up helped tremendously to achieve a robust characterization of the dust emission profiles and contributed to improving the redshift measurements for a currently consistent albeit inhomogeneous collection of DSFGs.
Furthermore, high-resolution follow-up pointed out that FIR surveys suffer from source blending due to the high density of sources occasionally enhanced by clustering. This is particularly relevant in the SPIRE 500 μm maps where the PSF is 35.2 arcsec2: in several cases, the flux densities of multiple objects are mixed and associated to a single detection, confusing the determination of its dust properties and photometric redshift. This issue might limit the identification of counterparts in very densely populated surveys, like those reaching very deep levels at IR and optical wavelengths (e.g., Spitzer; see also [4,30]). ALMA high-resolution follow-ups at similar frequencies, VLA in the radio bands and Spitzer in the MIR, have helped in de-blending many sources (e.g., [31,32,33]). However, as the frequency gap between observations and follow-up increases, the cross-matches become more uncertain and biased.
On the one hand, radio follow-ups of FIR- or sub-mm-selected sources tend to be biased toward the silent radio objects, making it difficult to probe the overall faint population and quite often producing radio non-detections. On the other hand, the lack of sub-mm or FIR information for radio surveys results in poor classification and redshift determination of the detected sources via SED reconstruction (e.g., [13,34,35,36]). Therefore, an unbiased overview of the sub-mJy radio source population could be obtained by combining deep blind radio surveys with Herschel catalogues (e.g., [37]).
