Free Access
Issue
A&A
Volume 631, November 2019
Article Number A109
Number of page(s) 12
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201935913
Published online 01 November 2019

© ESO 2019

1. Introduction

The correlation between far-infrared (FIR) and radio luminosities in normal star-forming galaxies, i.e. without significant active galaxy nuclei (AGN) activity, was discovered by Helou et al. (1985) using data from the Infrared Astronomical Satellite (IRAS). It has been confirmed in many subsequent studies with facilities like the Spitzer Space Telescope, the Balloon-Borne Large Aperture Submillimeter Telescope (BLAST) and the Herschel Space Observatory (Condon 1992; Yun et al. 2001; Sargent et al. 2010; Bourne et al. 2011; Ivison et al. 2010a,b) and has continued to intrigue for its tightness and extent over many orders of magnitude in luminosity. This relationship between FIR and radio luminosity had been prefigured in earlier studies at 10 μm by van der Kruit (1971, 1973), at 100 μm by Rickard & Harvey (1984), and at 60 μm using early-release IRAS data by Dickey & Salpeter (1984) and de Jong et al. (1985). Moreover, the FIR to radio correlation (FIRC) also seems to be more or less independent of redshift (e.g. Garrett 2002; Appleton et al. 2004; Ibar et al. 2008; Jarvis et al. 2010; Sargent et al. 2010; Bourne et al. 2011), although this is still an issue of intense debate as some studies do show evidence for redshift evolution (e.g. Seymour et al. 2009; Ivison et al. 2010a; Michałowski et al. 2010a,b; Magnelli et al. 2015; Basu et al. 2015; Delhaize et al. 2017).

Harwit & Pacini (1975) had proposed that the radio emission from star-forming galaxies could arise from supernova remnants (SNR) but Helou et al. (1985) showed that SNR could account for less than 10% of the radio emission. Instead Helou et al. (1985) suggested that relativistic electrons must leak out from SNR into the general magnetic field of the galaxy. This picture was later refined by Helou & Bicay (1993). In an idealized calorimeter model first proposed by Voelk (1989), the cosmic ray electrons lose all of their energy before escaping the galaxy, which is optically thick to ultraviolet (UV) photons. Assuming calorimetry, the logarithmic slope of the FIRC is equal to one (i.e. the FIRC is linear) as both the non-thermal synchrotron radiation and IR radiation (due to dust heated by UV photons) depend on the same star-formation rate (SFR). The calorimeter model, which may hold for starburst galaxies, was able to reproduce the tightness of the FIRC but also had several shortcomings. Alternative, more complex non-calorimetric models have also been proposed to explain the tight FIRC for normal star-forming galaxies (e.g. Bell 2003; Murgia et al. 2005; Thompson et al. 2006; Lacki et al. 2010; Schleicher & Beck 2013). For example, the “equipartition model” by Niklas & Beck (1997) was the first to predict that the logarithmic slope of the FIRC is different from one (i.e. the FIRC is non-linear) for normal star-forming galaxies. Although a detailed picture of the physical origin of the FIRC is still lacking, the basic understanding is that massive star formation is the driver of this correlation as UV photons from young stars heat dust grains which then radiate in the IR, and the same short-lived massive stars explode as supernovae which accelerate cosmic rays thereby contributing to non-thermal synchrotron emission in the radio.

An important application of the FIRC is the use of the radio continuum (RC) emission as a SFR tracer which (like the FIR-based SFR tracer) is not affected by dust extinction, as opposed to the often heavily obscured emission at UV or optical wavelengths. Another advantage of using RC emission as a SFR tracer is that radio observations using interferometers from the ground can achieve much higher angular resolutions (arcsec or even sub-arcsec resolution) compared to single aperture IR telescopes in space. The Herschel space observatory was the largest IR telescope ever launched with a 3.5 m primary mirror. The full width at half maximum (FWHM) of the Herschel-PACS beams are (for the most common observing mode) 5.6″, 6.8″ and 10.7″ at 70, 100, and 160 μm, respectively1 and the FWHM of the Herschel-SPIRE beams are 18.1″, 25.2″ and 36.6″ at 250, 350, and 500 μm, respectively (Swinyard et al. 2010).

The FIRC has been investigated mostly at GHz frequencies in the past, particularly at 1.4 GHz. For example, Yun et al. (2001) studied the NRAO Very Large Array (VLA) Sky Survey (NVSS) 1.4 GHz radio counterparts of IR galaxies selected from the IRAS Redshift survey out to z ∼ 0.15 and found the FIRC is well described by a linear relation over five orders of magnitude with a scatter of only 0.26 dex. Using 24 and 70 μm IR data from Spitzer and 1.4 GHz radio data from VLA, Appleton et al. (2004) found strong evidence for the universality of the FIRC out to z ∼ 1. Ivison et al. (2010b) studied the FIRC over the redshift range 0 <  z <  2 using multi-band IR data including observations from Spitzer, Herschel, and SCUBA, and 1.4 GHz data from the VLA. They found no evidence for significant evolution of the FIRC with redshift. Using deep IR observations from Herschel and deep 1.4 GHz VLA observations and Giant Metre-wave Radio Telescope (GMRT) 610 MHz observations in some of the most studied blank extragalactic fields, Magnelli et al. (2015) reported a moderate but statistically significant redshift evolution of the FIRC out to z ∼ 2.3. Thus, the overall conclusions are that there is a tight correlation between the FIR and radio luminosity at 1.4 GHz in the local Universe out to at least redshift z ∼ 2, but there is still ongoing debate over whether this correlation evolves with redshift.

With the advent of the LOw Frequency ARray (LOFAR; Röttgering et al. 2011; van Haarlem et al. 2013) which combines a large field of view with high sensitivity on both small and large angular scales, we can now study the FIRC at lower frequencies where the contribution from thermal free-free emission is even less important than at 1.4 GHz. Operating between 30 and 230 MHz, LOFAR offers complementary information to the wealth of data collected at higher frequencies. Using deep LOFAR 150 MHz observations in the 7 deg2 Boötes field (Williams et al. 2016), Calistro Rivera et al. (2017) studied the FIRC at 150 MHz from z ∼ 0.05 out to z ∼ 2.5. They found fairly mild redshift evolution in the logarithmic IR to radio luminosity ratio in the form of qIR ∼ (1 + z)−0.22 ± 0.05. However, if the FIRC is non-linear (i.e. the logarithmic slope is different from one), then it implies that the qIR parameter would depend on luminosity. Therefore the reported redshift dependence of qIR may simply be a consequence of the non-linearity of the FIRC (Basu et al. 2015) as the mean SFR of galaxies is generally larger at higher redshifts (e.g., Hopkins & Beacom 2006; Madau & Dickinson 2014; Pearson et al. 2018; Liu et al. 2018; Wang et al. 2019). Based on LOFAR observations of the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS; Eales et al. 2010) 142 deg2 North Galactic Pole (NGP) field (Hardcastle et al. 2016), Gürkan et al. (2018) found that a broken power-law (with a break around SFR ∼1 M yr−1) compared to a single power law is a better calibrator for the relationship between RC luminosity and SFR, possibly implying additional mechanisms for generating cosmic rays and/or magnetic fields. Also using LOFAR data in the NGP field, Read et al. (2018) found evidence for redshift evolution of the FIRC at 150 MHz. Heesen et al. (2019) studied the relation between radio emission and SFR surface density using spatially resolved LOFAR data of a few nearby spiral galaxies. They found a sublinear relation between the resolved RC emission and the SFR surface densities based on GALEX UV and Spitzer 24 μm data.

The LOFAR Two-metre Sky Survey (LoTSS) is currently conducting a survey of the whole northern sky with a nominal central frequency of 150 MHz. The LoTSS First Data Release (DR1; Shimwell et al. 2019) contains a catalogue of over 325 000 sources detected over 425 deg2 of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Spring Field, with a median sensitivity of 71 μJy beam−1 and a resolution of ∼6″. In this paper, we cross-match the LOFAR catalogue in the HETDEX Spring Field with the 60 μm selected Revised IRAS Faint Source Survey Redshift (RIFSCz; Wang & Rowan-Robinson 2009; Wang et al. 2014) Catalogue, which is constructed from the all-sky IRAS Faint Source Catalog (FSC), in order to study the FIRC in the local Universe and the use of the rest-frame 150 MHz luminosity, L150, as a SFR tracer.

There are several key differences between this study and the previous studies of Calistro Rivera et al. (2017), Gürkan et al. (2018) and Read et al. (2018) which were based solely on Herschel observations from either the Herschel Multi-tiered Extragalactic Survey (HerMES; Oliver et al. 2012) or H-ATLAS. First, the sky coverage of this study is at least three times larger than any previous studies, which means we can detect more rare sources such as ultra-luminous infrared galaxies (ULIRGs) with total IR luminosity (LIR) greater than 1012L and SFR more than several hundred solar masses per year. Secondly, the previous LOFAR studies relied on Herschel observations to determine LIR of the LOFAR sources. The intrinsic 90% completeness limit of the IRAS Faint Source Survey at 60 μm is S60 = 0.36 Jy (Wang & Rowan-Robinson 2010). At the median redshift of our main sample z ∼ 0.05 (see Sect. 3.3), this flux limit corresponds to a 60 μm luminosity of L60 ∼ 1010.27L, or equivalently LIR ∼ 1010.5L, based on the median ratio of L60 to LIR using the IR spectral energy distribution (SED) templates from Chary & Elbaz (2001). In comparison, the H-ATLAS 5σ limit, including both confusion and instrumental noise, is 37 mJy (Valiante et al. 2016) at 250 μm which is the most sensitive band. At z ∼ 0.05, this flux limit corresponds to a 250 μm luminosity of L250 ∼ 108.84L, or equivalently LIR ∼ 1010.2L, based on the median ratio of L250 to LIR using the Chary & Elbaz (2001) templates. Therefore, the IRAS observations are only a factor of ∼2 shallower than the H-ATLAS survey. Finally, the IRAS photometric bands sample the peak of the dust SED for the IR luminous galaxies in the local Universe. In comparison, the Herschel-SPIRE bands sample the Rayleigh-Jeans regime of the SED. Due to the lack of photometric bands covering the peak of the IR SED, both Gürkan et al. (2018) and Read et al. (2018) focused on the relation between the L250 and L150, rather than between LIR and L150. Most of the sources in the RIFSCz lie at redshift below 0.1 and thus provide an excellent local benchmark. The median redshift of our main sample is z ∼ 0.05. In comparison, the lowest redshift bin in the Calistro Rivera et al. (2017) study has a median redshift of 0.16. The sample used in Gürkan et al. (2018) and Read et al. (2018) covers the redshift range at z <  0.25, with a median redshift of 0.1.

The paper is structured as follows. In Sect. 2, we introduce the two main datasets (and their associated multi-wavelength data) in our analysis, namely the RIFSCz catalogue and the LOFAR value-added catalogue (VAC) in the HETDEX Spring Field. The construction of the LOFAR-RIFSCz cross-matched sample and its basic properties such as its wavelength coverage and redshift distribution are summarised in Sect. 3. In Sect. 4, we present the main results of our study, the FIRC at both 1.4 GHz and 150 MHz and the correlation between the rest-frame 150 MHz luminosity and various SFR tracers. Finally, we give our conclusions in Sect. 5. Throughout the paper, we assume a flat ΛCDM universe with Ωm = 0.3, ΩΛ = 0.7, and H0 = 70 km s−1 Mpc−1. We adopt a Kroupa (2001) initial mass function (IMF) unless stated otherwise.

2. Data

2.1. The RIFSCz catalogue

The Revised IRAS Faint Source Survey Redshift (RIFSCz) Catalogue (Wang & Rowan-Robinson 2009; Wang et al. 2014; Rowan-Robinson & Wang 2015) is composed of galaxies selected from the IRAS Faint Source Catalog (FSC) over the whole sky at Galactic latitude |b|> 20°. RIFSCz incorporates data from GALEX, the Sloan Digital Sky Survey (SDSS; York et al. 2000), the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006), the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010), and Planck all-sky surveys (Planck Collaboration I 2013) to give wavelength coverage from 0.36−1380 μm. At a 60 μm flux density of S60 >  0.36 Jy, which is the 90% completeness limit of the FSC, 93% of RIFSCz sources have optical or near-IR (NIR) counterparts with spectroscopic or photometric redshifts (Wang et al. 2014). Spectroscopic redshifts are compiled from the SDSS spectroscopic DR10 survey (Ahn et al. 2014), the 2MASS Redshift Survey (2MRS; Huchra et al. 2012), the NASA/IPAC Extragalactic Database (NED), the PSC Redshift Survey (PSCz; Saunders et al. 2000), the 6dF Galaxy Survey, and the FSS redshift survey (FSSz; Oliver, PhD thesis). Photometric redshifts are derived by applying the template-fitting method used to construct the SWIRE Photometric Redshift Catalogue (Rowan-Robinson et al. 2008, and references therein). Six galaxy templates and three QSO templates are used. For sources with at least 8 photometric bands and with reduced χ2 <  3, the percentage of catastrophic outliers, i.e. (1 + zphot) differs from (1 + zspec) by more than 15%, is 0.17% and the rms accuracy is 3.5% after exclusion of these outliers. IR SED templates are fitted to the mid- and far-IR data, following the methodology of Rowan-Robinson et al. (2005, 2008) and as in Wang & Rowan-Robinson (2009), with a combination of two cirrus templates, three starburst templates and an AGN dust torus template. The total IR luminosity LIR (integrated between 8 and 1000 μm) is estimated based on the fitted templates.

The methodology of Rowan-Robinson et al. (2008) is followed to calculate stellar masses and SFR. Briefly, the rest-frame 3.6 μm luminosity is estimated and converted to stellar mass using the mass-to-light ratio derived from stellar synthesis models. To estimate SFR, the conversion recipes of Rowan-Robinson et al. (1997) and Rowan-Robinson (2001) are used

(1)

where η is the fraction of UV light absorbed by dust, taken as 2/3. The SFRs are calculated for a Salpeter (1955) IMF between 0.1 and 100 M. To convert to Kroupa (2001) IMF, we divide the values by 1.5. We can also estimate SFR based on the total IR luminosity LIR following the widely used recipe of Kennicutt (1998) after converting to Kroupa IMF,

(2)

In principle, the formula of Eq. (2) is only suitable for dusty starburst galaxies in which all of the radiation from young stars is assumed to be absorbed by dust and subsequently re-emitted in the IR. In practice, Eq. (2) has been found to also apply to normal galaxies (e.g. Rosa-González et al. 2002; Charlot et al. 2002). The explanation is that there are two competing effects, which are overestimation in SFR caused by assuming all of the IR luminosity arises from recent star formation (as opposed to old stellar populations) and underestimation in SFR caused by neglecting the possibility that some of the young stellar radiation is not absorbed by dust. It is a coincidence that these two effects cancel out (e.g. Inoue 2002; Hirashita et al. 2003).

For sources in the RIFSCz which have been cross-matched to SDSS DR 10, we also have SFR estimates based on the Hα line luminosity, SFR, corrected for dust attenuation and aperture effects provided in the MPA-JPU database (Brinchmann et al. 2004).

2.2. The LOFAR survey

Exploiting the unique capabilities of LOFAR (van Haarlem et al. 2013), LoTSS is an ongoing sensitive, high-resolution, low-frequency (120−168 MHz) radio survey of the northern sky and is described in Shimwell et al. (2017). LoTSS provides the astrometric precision needed for accurate and robust identification of optical and NIR counterparts (e.g. McAlpine et al. 2012) and a sensitivity that, for typical radio sources, is superior to previous wide area surveys at higher frequencies such as the NRAO VLA Sky Survey (NVSS; Condon et al. 1998) and Faint Images of the Radio Sky at Twenty-Centimeters (FIRST; Becker et al. 1995) and is similar to forthcoming higher frequency surveys such as the Evolutionary Map of the Universe (EMU; Norris et al. 2011), and the APERture Tile In Focus survey (e.g. Röttgering et al. 2011). The primary observational objectives of LoTSS are to reach a sensitivity of less than 100 μJy beam−1 at an angular resolution, defined as the FWHM of the synthesised beam, of ∼6″ across the whole northern hemisphere.

The LoTSS First Data Release (DR1) presents 424 deg2 of RC observations over the HETDEX Spring Field (10h45m00s < right ascension < 15h30m00s and 45°00′00″ < declination < 57°00′00″) with a median sensitivity of 71 μJy beam−1 and a resolution of 6″, resulting in a catalogue with over 325 000 sources. Shimwell et al. (2019) estimated that the positional accuracy of the catalogued sources is better than 0.2″. The VAC includes optical cross matches and photometric redshifts for the LOFAR sources. The procedure of cross-matching to currently available optical and mid-IR photometric surveys is presented in Williams et al. (2019). Photometric redshifts (phot-z) are estimated using a combination of template fitting methods and empirical training based methods (Duncan et al. 2019). The overall scatter and outlier fraction in the phot-z is 3.9% and 7.9%, respectively. Following Read et al. (2018), we calculate the K-corrected 150 MHz luminosity assuming a spectral shape of Sν ∝ να, where the spectral index α = 0.71 (Condon 1992; Mauch et al. 2013).

3. The RIFSCz-LOFAR cross-matched sample

In order to cross-match the IRAS sources in the RIFSCz catalogue and LOFAR sources in the HETDEX Spring Field, we take a combined approach of the closest match method and the likelihood ratio (LR) method as detailed below.

3.1. The closest match method

For IRAS sources in the RIFSCz which are matched to sources detected at other wavelengths (e.g., the SDSS optical bands or the WISE IR bands), we choose the closest LOFAR match within a 5″ searching radius which results in a cross-matched sample of 771 sources2. The conservative choice of 5″ for the searching radius is mainly motivated by the FWHM of the LOFAR beam, although we note that the positional uncertainty is much smaller than that (Shimwell et al. 2019). Only one source has two possible matches (one located at 1.8″ away and the other at 4.4″ away). The top panel of Fig. 1 shows that the majority of the matches have positional differences well within 1″, consistent with what we expect from the positional accuracies of LOFAR, SDSS and WISE (York et al. 2000; Wright et al. 2010; Shimwell et al. 2019).

thumbnail Fig. 1.

Top: distribution of positional separations of sources matched between RIFSCz and LOFAR. Middle: comparison of WISE W1 flux for sources listed in RIFSCz and in LOFAR. Sources inside the two horizontal red lines have good WISE flux agreement (i.e., the difference is within a factor of 1.5). Bottom: comparison of redshifts compiled in the RIFSCz and LOFAR VAC.

The middle panel of Fig. 1 compares the WISE W1 fluxes at 3.4 μm provided by the cross-id in both the RIFSCz and LOFAR catalogues. The excellent agreement for the vast majority of sources demonstrates that we have the same id for most of the RIFSCz-LOFAR matched sources. Some sources have fairly different WISE fluxes which indicate potential problems with the cross-ids (between RIFSCz and LOFAR, between RIFSCz and WISE, or between LOFAR and WISE). Therefore, we exclude a total of 22 sources for which the WISE flux ratio from the two catalogues differs by more than a factor of 1.5.

The bottom panel of Fig. 1 compares redshifts provided for the RIFSCz-LOFAR matched sources from both catalogues, after excluding the 22 sources that could be erroneous matches. The spectroscopic redshifts (spec-z) show excellent agreement. 15 sources that have no spec-z in the RIFSCz now have a spec-z from LOFAR (based on the SDSS DR14). 71 sources that have no spec-z from LOFAR but have a spec-z from RIFSCz3. The origin for these new spec-z are NED (54 out of 71), SDSS (2 out of 71), PSCz (3 out of 71), FSSz (12 out of 71). A generally good agreement can be found between the phot-z estimates from both catalogues. In some cases, the LOFAR phot-z tend to be higher than the phot-z from the RIFSCz. We have studied 39 cases where the phot-z estimates differ by more than 0.2 and found that the higher LOFAR phot-z are likely to be erroneous because they would imply unrealistically high optical luminosity. Therefore, we adopt a priority order of redshift estimates as follows: spec-z from RIFSCz (652 sources), followed by spec-z from the LOFAR VAC (15 sources), followed by phot-z from RIFSCz (76 sources), and finally phot-z from LOFAR (6 sources).

To summarise, we select the sources with good WISE flux agreement (749 out of 771) and call this our “main sample”. All of the sources in the main sample have redshift estimates. Out of 749 sources, 581 sources (78%) have spec-z from both RIFSCz and the LOFAR VAC. As discussed in the paragraph above, the two spec-z values are in perfect agreement with each other. We refer to this subset of the main sample as the “main spec-z sample” which is our most robust sample with no ambiguity in the multi-wavelength cross-id. If we include the 15 new spec-z from LOFAR and the new 71 spec-z from RIFSCz, then we increase the sample size to 667 galaxies (89%) and we refer to this subset as the “main joint spec-z sample”. Finally, 82 sources (11%) have phot-z. We refer to this subset of the main sample as the “main phot-z sample”.

3.2. The likelihood ratio method (LR)

For IRAS sources in the RIFSCz which have not been matched to sources at other wavelengths and therefore only have IRAS positions4, we adopt an LR method (Sutherland & Saunders 1992; Brusa et al. 2007; Wang & Rowan-Robinson 2010; Chapin et al. 2011; Wang et al. 2014) in order to match them with LOFAR sources. The accurate LOFAR positions would then allow these IRAS only sources to be matched with optical or NIR sources. The LR technique compares the probability of a true counterpart with the probability of a chance association, as a function of 60 μm to 150 MHz flux ratio S60/S150 and radial offset r. Assuming the probability of true counterpart and random association is separable in log10(S60/S150) (or C60 − 150 as a shorthand) and r, we can write

(3)

where q(C60 − 150) and p(C60 − 150) are the colour distributions of the true counterparts and random matches respectively, and f(r) and b(r) are the positional distributions of the true counterparts and random associations respectively.

To derive the positional distribution of the true counterparts f(r), we assume a symmetric Gaussian distribution as a function of orthogonal positional coordinates. Therefore, f(r) can be written as a Rayleigh radial distribution,

(4)

where the scale parameter, σr, is where f(r) peaks and . The positional distribution of random associations can be written as,

(5)

assuming a constant surface density of background LOFAR sources uncorrelated with IRAS sources.

In Fig. 2, we plot the distribution of radial offsets between the IRAS-only RIFSCz sources and LOFAR sources by selecting all matches within 3′, which contains both the true counterparts and the random associations. We fit our model

(6)

thumbnail Fig. 2.

Distribution of radial offsets between the RIFSCz sources (which only have IRAS observations) and LOFAR sources by selecting all matches within 3′. The radial distribution of the random associations is plotted as the red dashed line, while the radial distribution of the true counterparts is shown as the green dot dashed line. The black solid line is the sum of the two.

to the observed histogram to determine the best-fit parameters to be E = 251.24 ± 34.28, σr = 40.92″ ± 3.59″ and ρ = 0.0111 ± 0.0005. This is consistent with what we expect based on the positional accuracy of IRAS sources. The angular resolution of IRAS varied between about 0.5′ at 12 μm to about 2′ at 100 μm. The positional accuracy of the IRAS sources depends on their size, brightness and SED but is usually better than 20″ (1-σ). A histogram of the angular separations between IRAS positions and the NED positions can be found in Wang & Rowan-Robinson (2009).

In Fig. 3, we plot the 60 μm−150 MHz colour distribution of all matches within 3′ between the RIFSCz sources (which only have IRAS observations) and LOFAR sources. These matches contain both true and random associations. We assume that this colour distribution can be fit by two Gaussian distributions. We also plot the colour distribution of the RIFSCz-LOFAR matches from the main sample discussed in Sect. 3.1. It is clear that there are systematic differences in median values and widths between the green dot-dashed line and the blue histogram. This is caused by the difference in the redshift ranges (see discussions in Sect. 3.3).

thumbnail Fig. 3.

60 μm−150 MHz colour distribution of all matches within 3′ between the RIFSCz sources (which only have IRAS observations) and LOFAR sources (yellow histogram). The dot-dashed Gaussian represents the inferred colour distribution of the true counterparts and the dashed Gaussian represents that of the random associations. The black solid line is the sum of the two. The colour distribution of the main sample is shown as the blue histogram.

Having derived the positional and colour probability distributions of the true and random associations, we can now calculate the LR for every possible match based on its positional separation and IR-to-radio colour. So, for every RIFSCz object with more than one LOFAR counterpart within 3′, we select the match with the highest LR5. We also impose a minimal LR threshold to ensure the false identification rate is no more than 10%. The LR threshold is derived as follows:

  • First, we calculate the LR distribution of matches between a randomised RIFSCz and a randomised LOFAR VAC. The randomised catalogues are generated by randomly re-arranging the flux measurements of the sources, while keeping the positions unchanged.

  • Then, we compare the LR distribution of the matches between the randomised catalogues with that of the matches between the original catalogues (i.e. before randomisation).

  • Finally, we set the minimal LR threshold to that above which the number of random matches is 10% of the number of matches between the original catalogues.

In total, 141 galaxies are matched between RIFSCz and LOFAR using the LR method. Out of the 141 galaxies, 112 galaxies have multi-wavelength optical and NIR data in the LOFAR VAC which are then used in the phot-z estimation procedure discussed in Sect. 2.1. We refer to this subset of 112 galaxies matched between RIFSCz and LOFAR using the LR method as the “second sample”. 79 galaxies in the second sample have spec-z from the VAC. We refer this as the second spec-z sample and the rest of the galaxies as the second phot-z sample.

3.3. Summary of the cross-matched sample

Figure 4 shows a schematic view of our RIFSCz-LOFAR matched sample. The combined sample of 861 sources is a combination of the main sample (generated using the closest match method) and the second sample (generated using the likelihood ratio method). Both samples are divided into subsamples depending on whether the sources have spec-z or phot-z. In the main sample, there are a total of 581 sources with spec-z from both RIFSCz and LOFAR which we refer to as the main spec-z sample. An additional 86 sources have spec-z from either LOFAR or RIFSCz which form the main joint spec-z sample after combining with the main spec-z sample. The top panel in Fig. 5 shows the redshift distribution of the cross-matched RIFSCz-LOFAR sample. Most galaxies have spec-z. The majority of our sources lie at z <  0.1. The bottom panel shows the normalised distribution to bring out the contrast in the redshift distribution. The median redshift of the main sample and the second sample is 0.05 and 0.12, respectively.

thumbnail Fig. 4.

Schematic view of our RIFSCz-LOFAR matched sample.

thumbnail Fig. 5.

Top: redshift distribution of the RIFSCz-LOFAR cross-matched sample. Bottom: normalised distributions (i.e. the integral of the distribution is 1). The median redshifts of the main sample and the second sample are 0.05 (indicated by the dashed line) and 0.12 (the dot-dashed line), respectively.

Table 1 shows the number of sources in the main sample by IR wavelength coverage (i.e. the number of sources detected at a given IR wavelength). Most sources have been matched to WISE. For the IRAS fluxes, the flux quality is classified as high (NQ = 3), moderate (NQ = 2) or upper limit (NQ = 1). We require flux quality flag NQ > 1 to avoid upper limits. The exception is the 60 μm band. All sources in the RIFSCz have high-quality flux measurement in the 60 μm band. A small fraction also have AKARI flux measurement out to 160 μm. A very small number of sources also have Planck measurements at 250, 550, 850 and 1380 μm. Table 2 shows the number of sources in the second sample by IR wavelength coverage. Again, most sources have been matched to WISE. As the second sample is generally at higher redshift than the main sample, the IR SED coverage is poorer especially at the longer wavelengths from AKARI and Planck.

Table 1.

Number of sources in the main sample of the cross-matched RIFSCz-LOFAR sample (749 sources in total) by wavelength coverage.

4. Results

Given that the FIRC has been very well studied at 1.4 GHz (see Sect. 1), in this section we first study the FIRC at 1.4 GHz and compare with previous studies. Then we focus on the FIRC at 150 MHz and possible variations with respect to redshift. After that, we investigate the use of the 150 MHz luminosity density as a SFR tracer.

4.1. The FIR-radio correlation at 1.4 GHz

We obtained the 1.4 GHz FIRST survey catalogue (14 Dec. 17 version) which contains 946 432 sources observed from the 1993 through 2011 observations6. The FIRST detection limit is 1 mJy over most of the survey area. The angular resolution of FIRST is ∼5″, similar to LOFAR. We cross-matched FIRST with LOFAR by selecting the closest match within 3″. 412 matches were found with the main sample and 79 matches were found with the second sample. We derive the radio spectral index by following

(7)

where ν1 = 150 MHz and ν2 = 1400 MHz. Figure 6 shows the histogram of the derived spectral index values. We do not find a significant difference between the main sample and the second sample. The median value of the spectral index and scatter for the main sample are 0.58 and 0.22, respectively. The median value and scatter for the second sample are 0.64 and 0.35, respectively. These values are very similar to the spectral index found in Sabater et al. (2019) using the galaxies overlapping between the SDSS DR7 and LoTSS. Sabater et al. (2019) also showed that their spectral index value (median value 0.63) is probably biased to lower values for low luminosity galaxies due to selection biases in the shallower 1.4 GHz sample compared to the low-frequency LOFAR data (which misses sources with steeper radio spectra). The spectral index values found in our samples are also likely to be biased to lower values compared to the canonical value of 0.71 (see Sect. 2.2) because of the shallower 1.4 GHz data.

thumbnail Fig. 6.

Normalised distribution of the radio spectral index between 150 MHz and 1.4 GHz.

In the top panel of Fig. 7, we plot the 1.4 GHz radio luminosity against the IRAS 60 μm luminosity. The vertical dashed line indicates the 90% completeness limit L60 ∼ 1010.27L at the median redshift z ∼ 0.05 of the main sample. The vertical dotted line indicates the 90% completeness limit L60 ∼ 1011.08L at the median redshift z ∼ 0.12 of the second sample. In comparison, the detection limit of FIRST of around 1 mJy corresponds to a 1.4 GHz luminosity L1.4 ∼ 104.34L at z ∼ 0.05 and L1.4 ∼ 105.14L at z ∼ 0.12. Yun et al. (2001) studied a sample of IRAS sources with S60 >  2 Jy and found that over 98% of their sample follow a linear FIRC over five orders of magnitude in luminosity with a scatter of only 0.26 dex. We overplot their best-fit relation (with a slope of 0.99) in the top panel in Fig. 7. Most of our sources seem to follow the Yun et al. (2001) relation. Some sources in our second sample show deviations from the Yun et al. (2001) relation. However, the second sample is much smaller and less reliable.

thumbnail Fig. 7.

Top: 1.4 GHz radio luminosity plotted against the IRAS 60 μm luminosity. The vertical dashed line indicates the 90% completeness limit at the median redshift of the main sample. The vertical dotted line indicates the 90% completeness limit of the second sample. The solid line is the Yun et al. (2001) relation. Bottom: histogram of q (1.4 GHz) values, derived using Eq. (8), using only sources with NQ > 1 at 100 μm. The dashed line is a Gaussian distribution with mean and standard deviation set to 2.34 and 0.26 respectively, which are values found by Yun et al. (2001).

Because the FIRC has a slope of unity, it can also be examined with the “q” parameter, which is the logarithmic FIR to radio flux ratio and is commonly defined as (e.g., Helou et al. 1985; Condon et al. 1991; Yun et al. 2001),

(8)

where S1.4 is the observed 1.4 GHz flux density in units of W m−2 Hz−1 and

(9)

where S60 and S100 are the IRAS 60 and 100 μm flux densities in Jy (Helou et al. 1988). In the bottom panel Fig. 7, we plot the q (1.4 GHz) values derived for our sample, using only sources for which NQ > 1 at 100 μm. This requirement on moderate- or high-quality flux measurement at 100 μm reduces the sizes of the main and second sample to 452 and 51, respectively (see Tables 1 and 2). We do not see a significant difference between the main sample and the second sample. The median q (1.4 GHz) value and rms scatter for the main sample are 2.35 and 0.25 respectively, while the median q (1.4 GHz) value and scatter for the second sample are 2.34 and 0.35 respectively, using sources for which NQ > 1 at 100 μm. This indicates that there is no significant redshift evolution in the q (1.4 GHz) value although the redshift range probed by our sample is probably too small to detect this. We over-plot a Gaussian distribution with mean and standard deviation set to the values in Yun et al. (2001). The distributions of q (1.4 GHz) of our samples agree well with the Yun et al. (2001) distribution.

Table 2.

Number of sources in the second sample of the cross-matched RIFSCz-LOFAR sample (112 sources in total) by wavelength coverage.

Bell (2003) proposed an alternative definition of q using the total IR to radio luminosity ratio,

(10)

where L1.4 is the 1.4 GHz luminosity. In Fig. 8, we plot the distribution of the qIR (1.4 GHz) values of our sample. Bell (2003) found a median value of 2.64 and a scatter of 0.26 which are over-plotted in Fig. 8. Again, the distribution of our qIR (1.4 GHz) values (with median = 2.61 and scatter = 0.30 for the main sample) has excellent agreement with that of Bell (2003). It is also worth noting that Bell (2003) found perfect agreement with the Yun et al. (2001) study, after correcting for the difference in the definitions of q and qIR. Our results for the FIRC at 1.4 GHz are fully consistent with Yun et al. (2001) and Bell (2003). In the subsequent analysis, we adopt the Bell (2003) definition of qIR given in Eq. (10), based on the total IR to radio luminosity ratio. To calculate qIR at 150 MHz, qIR (150 MHz), we can simply replace the 1.4 GHz luminosity L1.4 with the 150 MHz luminosity L150.

thumbnail Fig. 8.

Histogram of qIR values at 1.4 GHz, derived using Eq. (10). The dashed line is a Gaussian with its mean and standard deviation set to 2.64 and 0.26 respectively, which are values found by Bell (2003).

4.2. The FIR-radio correlation at 150 MHz

Now we have shown that our results of the FIRC at 1.4 GHz are consistent with previous measurements, we can study the FIRC at 150 MHz. First, to identify AGNs from our sample, we use the AGN classifications from the LOFAR VAC. As detailed in Duncan et al. (2018a,b), AGN candidates have been identified using a variety of selection methods. Optical AGN are identified primarily through cross-matching with the Million Quasar Catalogue compilation of optical AGN, primarily based on SDSS (Alam et al. 2015) and other literature catalogues (Flesch 2015). Sources which have been spectroscopically classified as AGN are also flagged. Bright X-ray sources were identified based on the Second ROSAT all-sky survey (Boller et al. 2016) and the XMM-Newton slew survey. Finally, IR AGNs are selected using the Assef et al. (2013) criteria based on magnitude and colour at the WISE W1 and W2 bands. We select sources with IRClass > 4 from the VAC which corresponds to the “75% reliability” selection criteria. Table 3 lists the number of identified AGNs in our samples.

Table 3.

Numbers of AGNs identified by various methods in our main sample and second sample.

The top panel in Fig. 9 shows the correlation between log LIR and the rest-frame 150 MHz luminosity log L150 for the main spec-z sample and AGNs (predominantly luminous systems) identified using X-ray, optical and IR data. The vertical dashed line indicates the 90% completeness limit at the median redshift (z  ∼  0.05) of the main sample, at LIR  ∼  1010.5L. This value is derived from multiplying the 90% completeness limit at 60 μm, L60  ∼  1010.27L, by the median ratio of LIR to L60 using the IR SED templates from Chary & Elbaz (2001). The Chary & Elbaz (2001) templates are shown to be able to reproduce the observed luminosity-luminosity correlations at various IR wavelengths for local galaxies. In comparison, the selection effect due to the median sensitivity (71 μJy beam−1) of the LOFAR 150 MHz observations is negligible (i.e., LOFAR is much deeper than IRAS for typical galaxy SEDs). At z  ∼  0.05, this median sensitivity corresponds to L150 = 102.92L at 5σ. We perform a linear regression which is based on a fitting method called the bivariate correlated errors and intrinsic scatter (BCES) described in Akritas & Bershady (1996). We use the public code developed in Nemmen et al. (2012). The red solid line shows our best-fit linear relation using galaxies above the 90% completeness limit,

(11)

thumbnail Fig. 9.

Top: correlation between the IR luminosity and the rest-frame 150 MHz luminosity for the main spec-z sample, including AGNs identified in the X-ray, IR, the Million Quasar Catalog and in optical spectroscopy. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.05) of the main sample. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.12) of the second sample.

while the red dashed line shows the best-fit relation using all galaxies. While some optically-identified AGNs clearly show an excess radio emission and therefore do not lie on the FIRC, most of the optical AGNs still obey the FIRC. Most of the IR and X-ray identified AGN also lie on the FIRC.

The bottom panel in Fig. 9 shows the correlation between log LIR and log L150 for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.12) of the second sample, at LIR ∼ 1011.3L. By comparison, the LOFAR sensitivity limit at z ∼ 0.12 is at around L150 = 103.71L at 5σ. We do not attempt to fit the second sample (due to the small sample size) but simply over-plot the best-fit linear relation for the main sample which seems to describe the second sample reasonably well.

The top panel in Fig. 10 shows the correlation between log L150 and log LIR for our star-forming galaxies from the main sample, after removing AGNs. Using the BCES method, our best-fit linear relation between the log of L150 and the log of LIR for galaxies above the 90% completeness limit (plotted as the red solid line) is,

(12)

thumbnail Fig. 10.

Top: correlation between the IR luminosity and the 150 MHz luminosity for the main sample, after excluding AGNs. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.05) of the main sample. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.12) of the second sample.

The best-fit relation derived for all galaxies is plotted as the red dashed line. We also test the significance of the correlation by calculating the Pearson correlation coefficient ρ which is found to be 0.79 and the p-value which is 1.40 × 10−69. The bottom panel in Fig. 10 shows the correlation between log LIR and log L150 for star-forming galaxies in the second sample. Again we do not fit the second sample but simply over-plot the best-fit linear relation for the main sample. The Pearson correlation coefficient ρ and p-value for galaxies above the 90% completeness limit in the second sample are 0.36 and 0.05, respectively.

Figure 11 shows the distribution of qIR (150 MHz) values of our sample derived using Eq. (10) and replacing the 1.4 GHz luminosity with the 150 MHz luminosity. The median value and scatter of qIR (150 MHz) are 2.14 and 0.34, respectively, for the main sample. The median value and scatter are 1.93 and 0.61, respectively, for the second sample. Calistro Rivera et al. (2017) found a median qIR (150 MHz) value of 1.544. This is inconsistent with our result. The main cause of this inconsistency is the large difference in the distributions of LIR in the two studies. The mean LIR of the galaxy sample in Calistro Rivera et al. (2017) is roughly 1.3 dex higher than this study. Using Eq. (12), we can derive that an increase in LIR by 1.3 dex would reduce qIR (150 MHz) by ∼0.5.

thumbnail Fig. 11.

Histogram of the qIR values at 150 MHz using the definition in Eq. (10) and replacing the 1.4 GHz luminosity with the 150 MHz luminosity.

In Fig. 12, we plot the qIR (150 MHz) values against redshift. A mild redshift evolution has been report by Calistro Rivera et al. (2017) and Read et al. (2018). We do not see significant evidence for any redshift evolution although our sample is perhaps too low redshift to see any evolutionary effects. When LoTSS is completed, the areal overlap between IRAS and LoTSS will reach ∼20 000 deg2. By then, we will have a much larger cross-matched sample which will be more adequate for detecting mild redshift evolution effect, if it exists.

thumbnail Fig. 12.

qIR (150 MHz) values as a function of redshift for the RIFSCz-LOFAR matched sources.

4.3. The rest-frame 150 MHz luminosity as a SFR tracer

In the top panel in Fig. 13, we compare the rest-frame 150 MHz luminosity L150 with several SFR tracers for star-forming galaxies from the main sample. The blue symbols correspond to SFRs derived based on the total IR luminosity LIR. The red symbols correspond to SFRs provided in the RIFSCz based on L60 (see Sect. 2.1). The green symbols correspond to SFR derived from the Hα line luminosity. Good agreement between the various SFR estimates are found. Our best-fit linear relation between log L150 and the logarithmic value of SFR based on L60 for galaxies above the 90% completeness limit is,

(13)

thumbnail Fig. 13.

Top: correlation between the rest-frame 150 MHz luminosity and various SFR tracers for the main sample, after excluding AGNs. The vertical dashed line indicates the 90% completeness limit at the median redshift (z  ∼  0.05) of the main sample. The solid lines are best-fit relations derived using only galaxies above the completeness limit. The dashed lines are best-fit relations derived using all galaxies. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z  ∼  0.12) of the second sample.

The Pearson correlation coefficient ρ is equal to 0.68 and the p-value is 2.38 × 10−43. Our best-fit linear relation between log L150 and the logarithm of SFR based on LIR for galaxies above the 90% completeness limit is,

(14)

The Pearson correlation coefficient ρ is equal to 0.79 and the p-value is 1.40 × 10−69. Our best-fit linear relation between log L150 and the logarithm of SFR based on Hα line luminosity for galaxies above the 90% completeness limit is,

(15)

The Pearson correlation coefficient ρ is equal to 0.67 and the p-value is 2.99 × 10−32. Thus, the relation between the logarithm of the 150 MHz luminosity and the logarithm of SFR is linear with a slope of 1.3 over a dynamic range of four orders of magnitude in SFR. We also show the best-fit relations derived using all galaxies, i.e., including the fainter galaxies below the completeness limit. These relations (plotted as dashed lines) show shallower slopes.

The bottom panel in Fig. 13 compares L150 with several SFR tracers for star-forming galaxies from the second sample. Due to the small sample size, we do not attempt to fit the second sample but simply over-plot the best-fit linear relations for the main sample. In the plot, we also show the Pearson correlation coefficient ρ and p-value derived for the galaxies above the 90% completeness limit in the second sample.

5. Conclusions

In this paper, we set out to study the FIRC in both the 1.4 GHz and the 150 MHz bands in the local Universe as the median redshift of our main sample is at z  ∼  0.05, with the aim of testing the use of the rest-frame 150 MHz luminosity L150 as a SFR tracer. We cross-match the 60 μm selected RIFSCz catalogue and the 150 MHz selected LOFAR VAC in the HETDEX spring field, using a combination of the closest match method and the likelihood ratio technique. We also cross-match our sample with the 1.4 GHz selected FIRST survey catalogue. We estimate L150 for the LOFAR sources and compare it with the IR luminosity, LIR, and several SFR tracers, after removing AGNs. Our main conclusions are:

  • A linear and tight correlation with a slope of unity between log LIR and log L1.4 holds. Our median q value and scatter at 1.4 GHz for the main sample, which are 2.37 and 0.26, respectively, are consistent with previous studies such as Yun et al. (2001).

  • A linear and tight correlation between log LIR and log L150 holds with a slope of 1.37. Our median qIR value is higher than the number reported in Calistro Rivera et al. (2017). This is mainly due to a large difference in the distributions of LIR of our samples.

  • The logarithm of L150 correlates tightly with the logarithm of SFR derived from three tracers, including SFR derived from Hα line luminosity, the rest-frame 60 μm luminosity and LIR. Best-fit formulae for the correlation between L150 and the three SFR tracers are provided, which are in excellent agreement with each other. The logarithmic slope (∼1.3) of the correlation between L150 and SFR suggests that the correlation is non-linear.

The LoTSS Second Data Release will include images and catalogues for 2500 deg2 of the northern sky and will be released by 2020. The all-sky IRAS survey allows the maximum areal overlap with LOFAR. At the eventual completion of LoTSS, the areal overlap between IRAS and LoTSS will reach ∼20 000 deg2. Therefore, we will be able to not only repeat the same analysis with a much larger sample but also to study in detail the FIRC at 150 MHz and its variation with galaxy physical properties such as stellar mass, SED type and morphology.


1

These values are taken from HERSCHEL-HSC-DOC-2151, version 1.0, February 28, 2017.

2

The positions given in the RIFSCz catalogue correspond to the positions of the multi-wavelength cross-id matched to the IRAS sources, prioritised in the order of SDSS, 2MASS, WISE, NED and IRAS FSC.

3

In the RIFSCz, the recommended spec-z and flags are 1 = SDSS DR10, 2 = PSCz, 3 = FSSz, 4 = 6dF, 5 = NED and 6 = 2MRS, prioritised as NED > SDSS > 2MRS > PSCz > FSSz > 6dF. These spectroscopic surveys (except SDSS) are not used in the construction of the LOFAR VAC.

4

These IRAS only sources can be selected by applying FLAG position = 5 in the RIFSCz catalogue. Around 19% of the sources in the RIFSCz catalogue have only IRAS observations.

5

A total of 9 IRAS sources only have one LOFAR match within 3′. For these sources, we simply select the only LOFAR match.

Acknowledgments

We thank the anonymous referee for a through and constructive report. We thank Rainer Beck for helpful discussions on the far-infrared to radio correlation. SCR acknowledges support from the UK Science and Technology Facilities Council [ST/N504105/1]. MB and IP acknowledge support from INAF under PRIN SKA/CTA FORECaST. MJH acknowledges support from the UK Science and Technology Facilities Council [ST/R000905/1]. JS is grateful for support from the UK Science and Technology Facilities Council (STFC) via grant ST/M001229/1 and ST/R000972/1. GG acknowledges the postdoctoral research fellowship from CSIRO. HJAR, WLW and KJD acknowledge support from the ERC Advanced Investigator programme NewClusters 321271. WLW also acknowledges support from the CAS-NWO programme for radio astronomy with project number 629.001.024, which is financed by the Netherlands Organisation for Scientific Research (NWO). Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, Uni- versity of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. LOFAR is the Low Frequency Array designed and constructed by ASTRON. It has observing, data processing, and data storage facilities in several countries, which are owned by various parties (each with their own funding sources), and which are collectively operated by the ILT foundation under a joint scientific policy. The ILT resources have benefitted from the following recent major funding sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; The Science and Technology Facilities Council, UK; Ministry of Science and Higher Education, Poland. This research made use of the Dutch national e-infrastructure with support of the SURF Cooperative (e-infra 180169) and the LOFAR e-infra group. The Jülich LOFAR Long Term Archive and the German LOFAR network are both coordinated and operated by the Jülich Supercomputing Centre (JSC), and computing resources on the Supercomputer JUWELS at JSC were provided by the Gauss Centre for Supercomputing e.V. (grant CHTB00) through the John von Neumann Institute for Computing (NIC). This research made use of the University of Hertfordshire high-performance computing facility and the LOFAR-UK computing facility located at the University of Hertfordshire and supported by STFC [ST/P000096/1].

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All Tables

Table 1.

Number of sources in the main sample of the cross-matched RIFSCz-LOFAR sample (749 sources in total) by wavelength coverage.

Table 2.

Number of sources in the second sample of the cross-matched RIFSCz-LOFAR sample (112 sources in total) by wavelength coverage.

Table 3.

Numbers of AGNs identified by various methods in our main sample and second sample.

All Figures

thumbnail Fig. 1.

Top: distribution of positional separations of sources matched between RIFSCz and LOFAR. Middle: comparison of WISE W1 flux for sources listed in RIFSCz and in LOFAR. Sources inside the two horizontal red lines have good WISE flux agreement (i.e., the difference is within a factor of 1.5). Bottom: comparison of redshifts compiled in the RIFSCz and LOFAR VAC.

In the text
thumbnail Fig. 2.

Distribution of radial offsets between the RIFSCz sources (which only have IRAS observations) and LOFAR sources by selecting all matches within 3′. The radial distribution of the random associations is plotted as the red dashed line, while the radial distribution of the true counterparts is shown as the green dot dashed line. The black solid line is the sum of the two.

In the text
thumbnail Fig. 3.

60 μm−150 MHz colour distribution of all matches within 3′ between the RIFSCz sources (which only have IRAS observations) and LOFAR sources (yellow histogram). The dot-dashed Gaussian represents the inferred colour distribution of the true counterparts and the dashed Gaussian represents that of the random associations. The black solid line is the sum of the two. The colour distribution of the main sample is shown as the blue histogram.

In the text
thumbnail Fig. 4.

Schematic view of our RIFSCz-LOFAR matched sample.

In the text
thumbnail Fig. 5.

Top: redshift distribution of the RIFSCz-LOFAR cross-matched sample. Bottom: normalised distributions (i.e. the integral of the distribution is 1). The median redshifts of the main sample and the second sample are 0.05 (indicated by the dashed line) and 0.12 (the dot-dashed line), respectively.

In the text
thumbnail Fig. 6.

Normalised distribution of the radio spectral index between 150 MHz and 1.4 GHz.

In the text
thumbnail Fig. 7.

Top: 1.4 GHz radio luminosity plotted against the IRAS 60 μm luminosity. The vertical dashed line indicates the 90% completeness limit at the median redshift of the main sample. The vertical dotted line indicates the 90% completeness limit of the second sample. The solid line is the Yun et al. (2001) relation. Bottom: histogram of q (1.4 GHz) values, derived using Eq. (8), using only sources with NQ > 1 at 100 μm. The dashed line is a Gaussian distribution with mean and standard deviation set to 2.34 and 0.26 respectively, which are values found by Yun et al. (2001).

In the text
thumbnail Fig. 8.

Histogram of qIR values at 1.4 GHz, derived using Eq. (10). The dashed line is a Gaussian with its mean and standard deviation set to 2.64 and 0.26 respectively, which are values found by Bell (2003).

In the text
thumbnail Fig. 9.

Top: correlation between the IR luminosity and the rest-frame 150 MHz luminosity for the main spec-z sample, including AGNs identified in the X-ray, IR, the Million Quasar Catalog and in optical spectroscopy. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.05) of the main sample. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.12) of the second sample.

In the text
thumbnail Fig. 10.

Top: correlation between the IR luminosity and the 150 MHz luminosity for the main sample, after excluding AGNs. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.05) of the main sample. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z ∼ 0.12) of the second sample.

In the text
thumbnail Fig. 11.

Histogram of the qIR values at 150 MHz using the definition in Eq. (10) and replacing the 1.4 GHz luminosity with the 150 MHz luminosity.

In the text
thumbnail Fig. 12.

qIR (150 MHz) values as a function of redshift for the RIFSCz-LOFAR matched sources.

In the text
thumbnail Fig. 13.

Top: correlation between the rest-frame 150 MHz luminosity and various SFR tracers for the main sample, after excluding AGNs. The vertical dashed line indicates the 90% completeness limit at the median redshift (z  ∼  0.05) of the main sample. The solid lines are best-fit relations derived using only galaxies above the completeness limit. The dashed lines are best-fit relations derived using all galaxies. Bottom: same as top panel but for the second sample. The vertical dashed line indicates the 90% completeness limit at the median redshift (z  ∼  0.12) of the second sample.

In the text

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