A CLOSER VIEW OF THE RADIO–FIR CORRELATION: DISENTANGLING THE CONTRIBUTIONS OF STAR FORMATION AND ACTIVE GALACTIC NUCLEUS ACTIVITY^*

Kimball & Ivezić (2008) have constructed a catalog of radio sources detected by the GB6 (6 cm), FIRST (Becker et al. 1995), NVSS (Condon et al. 1998; 20 cm), and WENSS (92 cm) radio surveys, as well as the SDSS (DR6) optical survey (York et al. 2000). This "Unified Radio Catalog" has been generated in such a way that it allows a broad range of 20 cm based sample selections and source analysis (see Kimball & Ivezić 2008 for details). The 2.7 million entries are comprised of the closest three FIRST to NVSS matches (within 30'') and vice versa, as well as unmatched sources from each survey. All entries have been supplemented by data from the other radio and optical surveys, where available. Here we select from the Unified Radio Catalog (version 1.1) all 20 cm sources that have been detected by the NVSS radio survey (using matchflag\_nvss = −1 and matchflag\_first ⩽ 1; see Kimball & Ivezić 2008 for details). This selection yields a radio flux limited (F_1.4 GHz ≳ 2.5 mJy) sample that contains 1,814,748 galaxies. In the following section, we expand this catalog to IR wavelengths, and augment it with additional (spectroscopic and SED-based) information.

2.2.1. IRAS

For the purpose of this paper, we have expanded the Unified Radio Catalog to IR wavelengths by cross-correlating it with the IRAS point-source and faint-source catalogs (hereafter PSC and FSC, respectively). The IRAS PSC contains 245,889 confirmed point sources detected at 12, 25, 60 and 100 μm, respectively (Strauss et al. 1990). The completeness of the catalog at these wavelengths reaches down to 0.4, 0.5, 0.6, and 1.0 Jy, respectively. The FSC was tuned to fainter levels based on the same IR data by point-source filtering the individual detector data streams and then co-adding those using a trimmed-average algorithm (see Moshir et al. 1992). The reliability of the FSC is slightly lower than that of the PSC (≳94% compared to 99.997%); however its sensitivity is higher by a factor of ∼2.5. The FSC contains 173,044 point sources with flux densities typically greater than 0.2 Jy at 12, 25, and 60 μm and 0.5 Jy at 100 μm.

We used matching radius of 30'', as optimized by Obrić et al. (2006), in cross-correlating the Unified Radio Catalog with the IR IRAS data. In Figure 1, we show the distribution of the distances between the IR and radio detections. The cumulative distribution displayed in Figure 1 shows that ∼70% of the positional matches are within an angular distance of 15''.

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Our NVSS-selected radio sample contains 18,313 galaxies with high quality IR photometry⁹ (see Table 1). As the FSC and PSC have been generated based on the same data, most of the PSC sources are included in the FSC. In our entire NVSS-IRAS sample, 26% of the sources have a PSC detection but are not included in the FSC. This fraction, however, reduces to only 3% after an optical (SDSS) cross-match is performed.

Table 1. Sample Summary

	IRAS (FSC + PSC)	SDSS (MAIN + QUASAR)	IRAS–SDSS
Total radio sample	18313	9591	524
Quasars	⋅⋅⋅	4490	21
Absorption	⋅⋅⋅	3072	16
Composite	⋅⋅⋅	654	203
SF unambiguous	⋅⋅⋅	621	216
SF ambiguous	⋅⋅⋅	9	0
AGN unambiguous	⋅⋅⋅	454	43
AGN ambiguous	⋅⋅⋅	291	25
Seyfert unambiguous	⋅⋅⋅	200	37
LINER unambiguous	⋅⋅⋅	254	6

Notes. The first column denotes the number of radio—IRAS (Point Source, PS, and Faint Source, FS) catalog with high quality IR photometry. The second column shows the number of sources in the radio—SDSS ("main" and quasar) catalog, and the third column is the matched radio–SDSS ("main" and quasar)–IRAS catalog. The rows indicate the various galaxy types we separate the objects into. The unambiguous/ambiguous selection is based on various spectroscopic diagnostic tools (see Figure 5 and the text for details). The shown numbers are limited to the 0.04 < z < 0.3 redshift range.

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The 60 and 100 μm magnitudes reported in the PSC and FSC are in agreement for the union of the two IR samples. The biweighted mean of the flux difference (for a subsample with SDSS detections) is 0.02 and 0.03 Jy at 60 and 100 μm, respectively. The root mean scatter of the 60 μm flux difference distribution is 0.06 Jy, while that of the 100 μm distribution is significantly larger, i.e., 0.16 Jy. Therefore, in order to access the highest quality IR photometry, hereafter we use the values reported in either the FSC or PSC catalog corresponding to the higher photometric quality flag quoted in the catalogs. The distribution of the 60 μm and 20 cm flux densities is shown in Figure 2.

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2.2.2. SDSS Quasar and Main Galaxy Sample Catalogs

We have further matched the NVSS-selected sample from the Unified Radio Catalog with data drawn from (1) the SDSS DR5 quasar sample (Schneider et al. 2007), and (2) the DR4 "main" spectroscopic sample for which derivations of emission-line fluxes from the SDSS spectra are available (see Smolčić et al. 2009 and references therein; note that the DR5 quasar and DR4 main galaxy catalogs were the most up-to-date versions available at the time). The latter was complemented with stellar masses, SFRs, dust attenuations, ages, metallicities, and a variety of other parameters based on spectral energy distribution (SED) fitting of the SDSS (ugriz) photometry using the Bruzual et al. (2003) stellar population synthesis models. The SED fitting was performed as described in detail in Smolčić et al. (2008).

During the inspection of the validity of the final catalog, we have found about 1% of objects with different spectroscopic redshifts in various SDSS data releases (Δz > 5 × 10⁻⁴). We have excluded those from the sample. Furthermore, a small number (∼0.2%) of duplicate objects was present in both the SDSS "main" galaxy sample and the SDSS Quasar Catalog. Visually inspecting their spectra yielded that most of these objects are better matched to the properties of the "main" galaxy sample (as no power-law continuum nor broad emission lines were present in the spectrum), and we have excluded these from our quasar sample. A summary of the various radio–IR–optical samples is given in Table 1, and in Figure 3 and Figure 4 we show the radio (20 cm), optical (r band), and far-IR luminosities as a function of redshift for the final NVSS–SDSS and NVSS–SDSS–IRAS samples (see Equations (3) and (4)). Note that the shallow IRAS sensitivity (compared to the NVSS and SDSS data) significantly reduces the number of objects, and biases the sample toward lower redshifts.

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2.3.1. Star-forming and AGN Galaxy Subsamples

We have used the optical spectroscopic information added to the NVSS selected sample to spectroscopically separate the galaxies present in the SDSS (DR4) "main" galaxy sample as absorption line, AGN (LINER/Seyfert), star-forming, or composite galaxies.

We define emission-line galaxies as those where the relevant emission lines (Hα, Hβ, O[III,λ5007], N[II,λ6584], S[II,λλ6717,6731]) have been detected at S/N ⩾ 3, and consider all galaxies with S/N < 3 in any of these lines as absorption line systems (see e.g., Best et al. 2005; Kewley et al. 2006; Smolčić et al. 2009). As strong emission lines are not present in the spectra of the latter, yet they are luminous at 20 cm, they can be considered to be (low excitation) AGNs (see e.g., Best et al. 2005; Smolčić et al. 2008 for a more detailed discussion). Furthermore as illustrated in Figure 5, using standard optical spectroscopic diagnostics (Baldwin et al. 1981; Kauffmann et al. 2003; Kewley et al. 2001, 2006) we sort the emission-line galaxies into (1) star-forming, (2) composite, (3) Seyfert, and (4) LINER galaxies. The last two classes have been selected "unambiguously" by requiring combined criteria using three emission-line flux ratios (see the middle and right panels in Figure 5). A summary of the number of objects in each class is given in Table 1. It is noteworthy that the IR detection fraction is a strong function of spectral class. It is the lowest for absorption line (0.6%) and LINER (6.5%) galaxies, intermediate for Seyferts (22%) and the highest for composite (40%) and star-forming (46%) galaxies. These results suggest lower amounts of dust (and gas; Solomon & Vanden Bout 2005) in the former or alternatively dominantly very cold dust that peaks at longer wavelengths.

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The redshift distribution of the various galaxy types with 20 cm NVSS and NVSS-IRAS detections is shown in the two top panels in Figure 6. Note that the redshift distribution of 20 cm detected absorption line galaxies is biased toward higher redshifts, compared to all other galaxy types (see the top panel in Figure 6). However, this is not the case when an IRAS IR detection is required, as illustrated in the middle panel in Figure 6. The IR detection fraction of the different galaxy classes is shown as a function of redshift in the bottom panel in Figure 6. Except for the overall trend that absorption and LINER galaxies are detected less efficiently in the IR, there is no substantial difference between the detection fractions as a function of redshift for different types of spectroscopically selected galaxies.

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Hereafter, we apply redshift range limits of 0.04 < z < 0.3 to our sample. The lower redshift limit is adopted from Kewley et al. (2005). Kewley et al. explored effects of fixed-size aperture of the SDSS spectroscopic fibers on the spectral characteristics such as metallicity, SFR, and reddening. They concluded that a minimum aperture size covering ≈20% of spectral light was required to properly approximate global values. The SDSS fiber aperture of 3'' diameter collects such a fraction of light for galaxies of average size, type, and luminosity at z ≳ 0.04. The upper redshift limit of z = 0.3 is equivalent to that of the SDSS "main" spectroscopic sample (note however that the majority of IR-detected galaxies are at z < 0.2, see Figure 4). It is worth noting that, because of lower spectral signal to noise for fixed-luminosity galaxies at greater distances, galaxies with weak emission lines, such as LINERs, can get confused with absorption line galaxies at z > 0.1 (Kewley et al. 2005). However, as LINER and absorption galaxies have similar physical properties (e.g., Smolčić et al. 2009), we simply combine these two types of galaxies, and treat them hereafter as a single class.

2.3.2. Quasar Subsample

The radio–FIR correlation is usually quantified by its slope via the q parameter (Helou et al. 1985), defined as the logarithmic ratio of the far-infrared flux to radio flux density:

$$\begin{equation} q = \log \left\lbrace \frac{F_{\rm FIR}/(3.75 \times 10^{12} \,\mathrm{Hz})}{F_{\rm 1.4\;GHz}}\right\rbrace, \end{equation} \tag{ 1 }$$

where F_1.4 GHz is the 1.4 GHz radio flux density in units of Wm^-2Hz⁻¹ and F_FIR is the far-infrared flux in units of Wm^-2. Following Sanders & Mirabel (1996), we define the latter as

$$\begin{equation} F_{\rm FIR} = 1.26 \times 10^{-14}\,(2.58 S_{60\;\mbox{$\mu $m}} + S_{100\;\mbox{$\mu $m}}), \end{equation} \tag{ 2 }$$

where S_60 μm and S_100 μm are observed flux densities at 60 and 100 μm (in Jy), respectively.

We compute the far-infrared luminosity as

$$\begin{equation} L_{{\rm FIR}} = 4\pi D_{L}^{2} C F_{{\rm FIR}}\left[L_\odot \right], \end{equation} \tag{ 3 }$$

where D_L is the luminosity distance (in units of m) and C is a scale factor used to correct for the extrapolated flux longward of the IRAS 100 μm filter. We use C = 1.6 (see Table 1 in Sanders & Mirabel 1996). Note that this expression can also be utilized to compute the FIR luminosities for our IR-detected quasars, given their relatively low redshifts.

The radio luminosity density is computed as

$$\begin{equation} L_{\rm 1.4\;GHz} = \frac{4\pi D_{L}^{2}}{(1+z)^{1-\alpha }}F_{\rm 1.4\;GHz}, \end{equation} \tag{ 4 }$$

where z is the redshift of the source, F_1.4 GHz is its integrated flux density, and α is the radio spectral index (assuming F_ν ∝ ν^−α). To compute the radio luminosities, we assumed a spectral index of α = 0.7.

The radio–FIR correlation for the NVSS–SDSS–IRAS sample is summarized in Figure 7. The radio and FIR flux densities (top left panel) and luminosities (top right panel) clearly show a tight correlation that holds over many orders of magnitude. In the middle panels we show the q parameter, that characterizes the slope of the radio–FIR correlation (see Equation (1)), as a function of FIR and radio luminosities. The average q is constant as a function of FIR luminosity (middle left panel), and it is decreasing with increasing radio power (middle right panel; see also below). In the bottom panels of Figure 7, we show the q parameter as a function of redshift, as well as its distribution for all our NVSS–SDSS–IRAS sources (galaxies and quasars). We find that the average (biweighted mean) q-value for the entire NVSS–SDSS–IRAS sample is q = 2.273 ± 0.008, with a root-mean-square scatter of σ = 0.18. This is in very good agreement with previous findings (Condon 1992; Yun et al. 2001; Condon et al. 2002; Bell 2003; Mauch & Sadler 2007), and will be discussed in more detail in Section 5.

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The quasars in our sample comprise the high-luminosity end at both IR and radio wavelengths (they are also located at higher redshifts, compared to the IR- and radio-detected "main" galaxy sample). It is also obvious that there is a larger fraction of quasars that do not lie on the radio–IR correlation, compared to that for the "main" sample galaxies.

In Figure 8, we present the radio–FIR correlation for the SDSS "main" galaxy sample subdivided into different, spectroscopically selected galaxy types (absorption, LINER, Seyfert, composite, and star-forming galaxies; see Section 2.3.1 and Figure 5 for details on the selection). The decrease in q with increasing radio power for all types of galaxies (middle right panel) is consistent with various other observations (e.g., Smolčić et al. 2008; Kartaltepe et al. 2010; Sargent et al. 2010; Ivison et al. 2010). Note that, given the definition of the FIR/radio ratio, for any sample in which q does not vary with FIR luminosity, and has a non-zero dispersion, it is expected to decrease with increasing radio luminosity (see, e.g., Condon 1984). To test whether the magnitude of the decrease is as expected from statistics or, e.g., higher due to an additional effect (such as AGN contribution) we have computed the radio luminosity for each source based on its observed FIR luminosity and an FIR/radio ratio drawn from a Gaussian distribution with a dispersion of 0.18 and a mean of 2.27. We find that the decrease of q with radio luminosity in the observed data is consistent with that in the simulated data, thus not requiring additional effects (such as increasing AGN contribution with increasing radio power) to explain this trend (at least in the radio luminosity range probed here).

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A quantitative analysis of the radio–FIR correlation for different galaxy types is presented in Figure 9. The spectroscopic selection of pure star-forming galaxies allows us to quantify the radio–IR correlation in a rather unbiased manner. For our star-forming galaxies we find an average q value of 〈q〉 = 2.27 ±  0.05, with a small rms scatter of σ = 0.13. It is interesting to note that as the AGN contribution rises in galaxies (as inferred based on optical spectroscopic diagnostics) the scatter in q increases by ∼50% to ∼150%. Interestingly, the scatter is the highest for Seyfert types of galaxies, for which we also find the lowest average q-value, 〈q〉 = 2.14 ±  0.05. These differences will be further discussed in Section 5.

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In Figure 10, we quantify the radio–FIR correlation for the 21 IR-detected quasars in our sample. The distribution of the FIR/radio ratio cannot be well fit with a Gaussian distribution. The median q-value of the sample is 2.04, comparable to the average q value we have found for Seyfert galaxies (2.14), and lower than that for star-forming galaxies (2.27; see Figure 9). It is worth noting that the higher redshift quasars (0.2 ≲ z ≲ 0.4) appear to be biased toward more radio-loud AGNs.

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Extensive studies of the radio–FIR correlation (e.g., Helou et al. 1985; Condon 1992; Yun et al. 2001; Condon et al. 2002; Obrić et al. 2006; Mauch & Sadler 2007) have led to an average FIR/radio ratio in the local (z < 0.3) universe of q ∼ 2.3, and lower for AGN-bearing galaxies (see Table 2 in Sargent et al. 2010 for a summary). For example, using the IRAS 2 Jy galaxy sample (F_60 μm ⩾ 2 Jy; 1809 sources with optical counterparts and well determined redshifts) combined with NVSS data, Yun et al. (2001) have found 〈q〉 = 2.34 ± 0.01. A lower average q-value is generally inferred when using radio-selected samples, and reaching fainter in the IR (see Sargent et al. 2010 for a detailed discussion of selection effects). Combining NVSS data with the optical Uppsala Galaxy Catalog (UGC) and the IRAS FSC and PSC, Condon et al. (2002) have found 〈q〉 = 2.3 and rms width σ = 0.18. Furthermore, matching NVSS and 6dFGS survey data only with the IRAS FSC, Mauch & Sadler (2007) inferred a mean q-value of 2.28 with a rms scatter of 0.22 for their entire sample. For a subset of the radio-loud AGN (that would correspond to our Seyfert, LINER, absorption, and quasar classes combined), they found an even lower average value, 〈q〉 = 2.0, and a significantly higher scatter in the FIR/radio ratio (σ = 0.5).

In Figure 9, we have presented the distribution of q for various types of our spectroscopically selected NVSS–SDSS-IRAS (PSC+FSC) galaxies. Our results yield that the dispersion is the tightest for star-forming galaxies (σ = 0.13), and rises by a factor of 1.5, 2.5, and 2.2 for composite, Seyfert, and absorption/LINER galaxies, respectively. We find that the average FIR/radio ratio for all objects in our radio–optical-IR sample is 2.27 ± 0.01 with a dispersion of 0.2. This is in very good agreement with the results from Mauch & Sadler (2007). Furthermore, if we limit the 60 μm fluxes of our full sample to ⩾2 Jy we obtain an average value of 2.34, consistent with that inferred by Yun et al. (2001).

Our results yield a lower FIR/radio ratio (〈q〉 = 2.14 ± 0.05) for Seyfert galaxies, and a significantly higher rms scatter (σ = 0.3), compared to that found for SF galaxies. It is interesting that the mean q-value for our IR-detected LINER and absorption line galaxies is comparable to that for star-forming galaxies. However, the spread in q for the former is significantly larger than for the latter (0.28 compared to 0.13, respectively). The average FIR/radio ratio for the 21 quasars in our sample is q = 2.04, comparable to that inferred for Seyferts and lower than that for star-forming galaxies. If we combine our AGN-bearing galaxies (quasars, Seyferts, LINERs, absorption galaxies) into one class in order to match the AGN sample of Mauch & Sadler (2007), we infer an average q of 2.16 ±  0.03 (with an rms scatter of σ = 0.24). This is in relatively good agreement with their results. In the next sections we will discuss the variation of q with radio luminosity and the AGN contribution to the radio–FIR correlation.

A low q-value is often used to discriminate between star-forming galaxies and AGNs. For example, Condon et al. (2002) have classified radio-loud AGNs as those having q ⩽ 1.8. Assuming that the FIR emission arises solely from star formation, this criterion selects galaxies with more than three times the radio emission from galaxies on the FIR–radio correlation. Yun et al. (2001) have used q = 1.64 as a star formation/AGN separator, identifying galaxies that emit in radio more than five times that predicted by the correlation. It is important to point out that these discriminating values are tuned to select only the most radio-loud AGN. Having (1) separated our NVSS–SDSS–IRAS sample into various classes of AGNs, and (2) independently estimated SFRs in their host galaxies, we can now analyze the physical source of FIR and radio emission in galaxies both following and offset from the radio–FIR correlation.

Assuming that the additional source of FIR and radio emission (relative to that expected from star formation) observed in our composite, Seyfert, absorption, and LINER galaxies (see Figure 12) arises from the central supermassive black hole, the distribution of our luminosity excess, Δlog L defined in Equation (5), allows us to constrain the average contribution of star formation and AGN activity to the total power output for a given galaxy population. Taking that star formation and AGN activity are the two dominant FIR/radio emission generators, i.e., L_tot = L_SF + L_AGN, the average fractional contributions of these two sources (〈f_SF〉 and 〈f_AGN〉) to the total power output can then be computed as 〈f_SF〉 = 10^{−〈Δlog L〉} and 〈f_AGN〉 = 1 − 〈f_SF〉, where 〈Δlog L〉 denotes the average (median) of the Δlog L distribution (see Figure 12).

The median Δlog L values and the fractional star formation/AGN contributions are summarized in Table 2. As expected, for star-forming galaxies we infer that the average contribution to FIR and radio emission due to star formation is 100%. We find that composite objects are dominated by star formation at the ∼80%–90% level. Further, the FIR emission from Seyfert galaxies arises predominantly from star formation (∼75%), while the AGN contribution to radio luminosity in Seyfert galaxies is about a factor of 2 higher in the radio than in the FIR (see Table 2). The latter explains the lower average q-value (compared to the nominal value) for Seyfert galaxies inferred here, as well as in, e.g., Obrić et al. (2006) and Mauch & Sadler (2007). Lastly, based on the above calculation, IR-detected absorption and LINER galaxies are on average strongly dominated by AGN activity (∼90%) in both their FIR and radio emission although their average FIR/radio ratio is consistent with that expected for star-forming galaxies (see Figure 12).

One of the main results of this work is that, for the large majority of galaxies with radio and/or IR emission excess, we infer q-values consistent with the average FIR/radio ratio found for star-forming galaxies (see Figure 12). Thus, although a significant AGN contribution is likely present in these galaxies (adding to both the FIR and radio emission), they would not be identified with a simple low-q discriminator value, as is commonly used to select a radio-loud AGN. Our results indicate that the FIR/radio ratio is not particularly sensitive to AGN contribution and that the radio–FIR correlation is a poor discriminant of AGN activity, except for the most powerful AGN. This is consistent with observations of several AGN-bearing galaxies in the high-redshift universe.

Based on an SED analysis, Riechers et al. (2009) find that both the radio and FIR luminosity in the z = 3.9 quasar APM08279+5255 are dominated by the central AGN, but that it has a q-value consistent with the local radio–FIR correlation. Furthermore, Murphy et al. (2009) have analyzed Spitzer-IRS spectra of a sample of 22 0.6 ≲ z ≲ 2.6 galaxies, composed of submillimeter galaxies, as well as X-ray and optically selected AGNs in GOODS-N. Making use of their Infrared Spectrograph (IRS) spectra, they have performed a thorough starburst-AGN decomposition for each object which allowed them to estimate the fractional AGN contribution to the total IR luminosity output of each source. They demonstrate that the four galaxies having the largest mid-IR AGN fractions (>60%) in their sample have q-values consistent with the canonical value. Furthermore, they find that the FIR/radio ratio shows no trend with the fractional contribution of AGN activity in the galaxies in the IR, consistent with our results.