Abstract

We have cross-matched the 1.4-GHz NRAO VLA Sky Survey (NVSS) with the first 210 fields observed in the 2dF Galaxy Redshift Survey (2dFGRS), covering an effective area of 325deg2 (about 20 per cent of the final 2dFGRS area). This yields a set of optical spectra of 912 candidate NVSS counterparts, of which we identify 757 as genuine radio identifications – the largest and most homogeneous set of radio source spectra ever obtained. The 2dFGRS radio sources span the redshift range graphic to 0.438, and are a mixture of active galaxies (60 per cent) and star-forming galaxies (40 per cent). About 25 per cent of the 2dFGRS radio sources are spatially resolved by NVSS, and the sample includes three giant radio galaxies with projected linear size greater than 1Mpc. The high quality of the 2dF spectra means we can usually distinguish unambiguously between AGN and star-forming galaxies. We make a new determination of the local radio luminosity function at 1.4GHz for both active and star-forming galaxies, and derive a local star formation density of graphicgraphic.

Introduction

Radio source surveys are ideal tools for studying the distant Universe, since they are unaffected by dust obscuration and detect large numbers of galaxies over a wide span of cosmic epochs (the median redshift of galaxies detected in radio surveys is typically graphicCondon 1989).

At 1.4-GHz flux densities above about 50mJy, more than 95 per cent of radio sources are classical radio galaxies and quasars powered by active galactic nuclei (AGN). Below 50mJy, the AGN proportion declines and an increasing fraction of the faint radio source population is identified with star-forming galaxies (e.g. Condon 1989, 1992). These are usually disc galaxies, sometimes interacting with neighbours, in which the radio emission arises mainly through synchrotron emission from relativistic electrons accelerated by supernova explosions. Thus radio surveys to levels of a few mJy probe both the AGN population and a population of star-forming galaxies. It is important to be able to separate these, in order to determine the local space density and redshift evolution of each population.

A new generation of radio imaging surveys (NVSS, Condon et al. 1998; FIRST, Becker, White & Helfand 1995; WENSS, Rengelink et al. 1997; SUMSS, Bock, Large & Sadler 1999) is now covering the whole sky to sensitivities of a few mJy. Radio source counts from such surveys potentially yield important information on the cosmological evolution of active and star-forming galaxies (e.g. Longair 1966; Jauncey 1975; Wall, Pearson & Longair 1980), but their interpretation is strongly model-dependent. The scientific return from large radio surveys is enormously increased if the optical counterparts of the radio sources can be identified, their optical spectra classified (as AGN, starburst galaxy, etc.), and their redshift distribution measured. In the past, however, this was a slow and tedious process which could only be carried out for relatively small samples.

Now, fibre-fed optical spectrographs make it possible to carry out spectroscopy of complete samples of hundreds of thousands of galaxies in the local Universe. The Anglo-Australian Observatory's Two-degree Field (2dF) spectrograph can observe up to 400 galaxies simultaneously over a 2°-diameter region of sky (Lewis et al., in preparation; see also). A Six-degree Field (6dF) spectrograph will be commissioned on the AAO's Schmidt Telescope in 2001, with 150 fibres over a 6°-diameter field, and in the northern hemisphere the Sloan Digital Sky Survey (SDSS) (York et al. 2000) has begun a programme of spectroscopy of 106 galaxies. Cross-matching radio continuum surveys with these new optical redshift surveys will provide redshifts and spectroscopic data for tens of thousands of local radio-emitting galaxies, rather than the few hundred available at present.

Two recent studies show the potential of these new redshift surveys. Machalski & Condon (1999, hereafter MC99) identified 1157 galaxies in the Las Campanas Redshift Survey (LCRS) with NVSS radio sources above 2.5mJy at 1.4GHz. They attempted to determine the radio and infrared properties of galaxies in the LCRS redshift range of graphic, but had difficulties because the LCRS was sparsely sampled, with optical spectra being taken for only about one galaxy in three. Nevertheless, Machalski & Godlowski (2000, hereafter MG) used the LCRS to derive the local radio luminosity function (RLF) for both AGN and star-forming galaxies, and to test for evolution over the LCRS redshift range.

Sadler et al. (1999, hereafter Paper I) cross-matched the NVSS radio catalogue with the first 30 fields observed in the 2dFGRS, and found that it was usually straightforward to tell from the optical spectra whether the radio emission arose from star formation or an AGN (unlike LCRS, the 2dFGRS has a spectroscopic completeness of 95 per cent).

The present paper is the second in a series analysing the properties of NVSS radio sources which are identified with galaxies in the 2dF Galaxy Redshift Survey (2dFGRS) (Colless 1999; Colless et al. 2001; see also). When complete, the 2dFGRS will yield good-quality optical spectra for up to 4000 radio-emitting galaxies in the redshift range graphic to 0.4. Such a large sample should allow us to disentangle the effects of age, orientation and luminosity in the local AGN population, as well as providing a definitive measurement of the local RLF for active and star-forming galaxies. Our Paper I was a preliminary investigation of a small sample of the early 2dFGRS data, and showed that the 2dFGRS radio source population is composed of roughly similar numbers of AGN and star-forming galaxies. In this paper we analyse a 2dFGRS data set which is almost an order of magnitude larger than that in Paper I, and use it to derive the local RLF for active and star-forming galaxies at 1.4GHz.

The spectra analysed in this paper are included in the first public release of 2dFGRS data, which took place in 2001 June.

Throughout this paper, we use graphic and graphic.

Sample selection

In this paper we analyse 2dFGRS spectra from the first two years of the survey, i.e., up to 1999 May. Observations made before 1997 October were excluded, because the instrument was still in a commissioning phase and the data are of variable quality. The data set analysed here comprises 210 fields, or about 20 per cent of the total 2dFGRS area. The original selection of 2dFGRS optical targets included all non-stellar objects brighter than graphic from the photographic UKST Southern Sky Survey, and should involve no explicit biases so far as radio properties are concerned.

Area covered

The 2dFGRS uses a tiling algorithm with variable overlap depending on the underlying galaxy density. Some 2dFGRS fields are also shared with a parallel QSO redshift survey, so calculating the exact area of sky observed is not straightforward until the whole survey is complete.

We therefore use the method described by Folkes et al. (1999), and estimate the area of sky covered by dividing the number of galaxies observed by the mean surface density of galaxies in the target list. The data set observed in the period from 1997 October to 1999 May inclusive contains 58 454 2dFGRS targets. Taking the Folkes et al. surface density of 180galaxiesdeg−2 to the survey limit of graphic gives an effective area of 325deg2 for the data set we will analyse here.

Radio source identifications

We cross-matched the 2dFGRS catalogue positions with the NVSS radio catalogue, and took all matches with position offsets of 15arcsec or less as candidate radio detections. This yielded a total of 927 observations of 903 targets. Not all these will be true identifications – as discussed in Paper I, we expect most unresolved radio sources with offsets of 10arcsec or less to be true associations with 2dFGRS galaxies, along with a smaller (and quantifiable) fraction of sources with offsets of graphic.

There are also three classes of objects for which the situation is more complex: (i) extended (resolved) NVSS radio sources, (ii) radio sources which are resolved by NVSS into two or more distinct components, and (iii) radio sources associated with nearby bright galaxies graphic. As we discuss in Section 4, these received extra attention to determine whether to accept a candidate identification (ID) as a correct one.

For completeness, and because others may wish to use our data with different selection criteria for radio source IDs, we have tabulated 2dFGRS spectral types and redshifts for all 912 candidate radio source IDs with radio–optical offsets of 15.0arcsec or less. We showed in Paper I that, with the exception of a small number of double NVSS radio sources (see Section 4.2), there should be very few correct IDs with radio–optical offsets larger than 15arcsec. This is confirmed in Fig. 1, which shows that by 15arcsec from the 2dF position the number of candidate detections falls to the level expected from chance coincidences alone.

Figure 1.

Number of candidate NVSS detections of 2dFGRS galaxies plotted against the offset Δ between radio and optical positions. The solid line shows the number of matches expected by chance from a sample of 58454 2dFGRS galaxies, assuming that NVSS radio sources are randomly distributed on the sky with a surface density of 60deg−2. Note that at a separation of 15arcsec or more, the number of matches declines to that which would be expected by chance, so we adopted a separation cut-off of 15arcsec for candidate 2dFGRS radio sources.

Figure 1.

Number of candidate NVSS detections of 2dFGRS galaxies plotted against the offset Δ between radio and optical positions. The solid line shows the number of matches expected by chance from a sample of 58454 2dFGRS galaxies, assuming that NVSS radio sources are randomly distributed on the sky with a surface density of 60deg−2. Note that at a separation of 15arcsec or more, the number of matches declines to that which would be expected by chance, so we adopted a separation cut-off of 15arcsec for candidate 2dFGRS radio sources.

We also note that the 2dFGRS input catalogue is incomplete for galaxies brighter than graphic, and so some bright, nearby galaxies are missing from the 2dFGRS. Almost all these missing galaxies should already have redshift measurements, and can be added back into the sample once the entire 2dFGRS is complete. In calculating luminosity functions (see Section 8), we correct for the absence of these bright galaxies.

Optical spectra

As noted earlier, the spectra analysed in this paper were collected as the 2dFGRS progressed, and cover the period to 1999 May. Most of these spectra are included in the first (mid-2001) public release of 2dFGRS data (see Colless et al. 2001 for details of the public-release data base). In a few cases, a new spectrum taken after 1999 May may be better than the one used here and will replace it in the final data base.

Although in most cases the public-release data are identical to those analysed here, some values of bJ, z and Q listed in Table 1 may change. This is because there have been revisions of the bJ magnitude scale, and a re-reduction of all the early 2dFGRS redshifts, since we began our analysis. In the great majority of cases, the data base revisions produced no significant difference, especially for spectra with graphic. Small changes in the values of bJ or z for individual galaxies will not affect the overall results of the analysis which follows.

Table 1.

Candidate 2dFGRS/NVSS radio sources. This is a sample – the full available in the on-line version of the journal on .

Table 1.

Candidate 2dFGRS/NVSS radio sources. This is a sample – the full available in the on-line version of the journal on .

Spectral classification

2dFGRS spectra of each of the 912 candidate radio source IDs were examined and classified visually by one of us (EMS). As in Paper I, each spectrum was classified as either ‘AGN’ or ‘star-forming’ (SF) based on its 2dF spectrum. AGN galaxies have either an absorption-line spectrum like that of a giant elliptical galaxy (these we classed ‘Aa’); an absorption-line spectrum with weak LINER-like emission lines (class ‘Aae’), or a stellar continuum dominated by nebular emission lines such as [Oii] and [Oiii] which are strong compared with any Balmer-line emission (class ‘Ae’). ‘SF’ galaxies are those where strong, narrow emission lines of Hα and (usually) Hβ dominate the spectrum. Objects where the spectra were too noisy for reliable classification are classed as ‘??’.

There are several independent tests of the reliability of our visual classification of the spectra: (a) the visual classifications generally agree well with the results of principal components analysis (PCA) methods, as we will show in Section 3.3, (b) for galaxies with optical emission lines, our Ae/SF classifications agree well with those derived by Jackson & Londish (2000) from diagnostic emission-line ratios, and (c) most galaxies that we classify as SF are detected by IRAS and fall on the radio–FIR correlation (see Section 6), whereas none of the galaxies we classified as Aa are detected by IRAS. Thus we are confident that our visual classification of the 2dFGRS spectra allows us to distinguish AGN and SF galaxies in a consistent and reliable way.

Data table

Table 1 lists the entire sample of 912 candidate radio IDs, i.e., the 903 2dFGRS targets whose catalogued position is within 15arcsec of the catalogued position of an NVSS radio source, together with a further nine extended and double radio sources which were identified separately as described in Section 4.2. The full table is only available electronically in the on-line version of the journal on Synergy; a small subsample is reproduced in the printed journal for reference. The table columns are as follows.

  • (1)

    2dFGRS galaxy name (this is the name used in the 2dFGRS data base). An asterisk following the name indicates that this galaxy appears in the notes at the end of Table 1.

  • (2)

    Other name – we have cross-identified with other galaxy catalogues where possible.

  • (3)

    The optical position (J2000.0) at which the 2dFGRS fibre was placed.

  • (4)

    The offset between 2dFGRS (optical) and NVSS (radio) positions, in arcsec.

  • (5)

    Total blue (bJ) magnitude, from the 2dFGRS data base. The magnitudes listed here are taken from the 2000 May version of the data base.

  • (6)

    Total radio flux density at 1.4GHz, from the NVSS catalogue (Condon et al. 1998). Where a source is split into more than one component in the NVSS catalogue, this is indicated in the notes at the end of the table, and the value quoted here is the sum of all the components.

  • (7)

    IRAS 60-μm flux density (in Jy), where listed in the NASA Extragalactic Database (NED). Although IRAS surveyed 97 per cent of the sky, the incompleteness near the Galactic poles is larger than in other areas. Based on the IRAS sky coverage plots given by Beichman et al. (1988), about 10 per cent of the 2dFGRS survey area had either one or no IRAS scans and so was not catalogued. The main 2dFGRS areas missed by IRAS lie in the region between 10h and 11h RA in the northern zone and 23h and 0h RA in the southern zone, but there are also smaller gaps elsewhere.

  • (8)

    Heliocentric redshift, from 2dFGRS observations unless otherwise indicated in the notes.

  • (9)

    2dFGRS spectrum quality code Q, where graphic or 5 are excellent-quality spectra, graphic acceptable, and graphic, 1 or 2 poor-quality. Galaxies with graphic are excluded from further analysis because their redshifts are highly uncertain. Checks against repeat observations and published redshifts show that 2dFGRS redshifts with graphic are about 90 per cent reliable, and those with graphic or 5 are 99 per cent reliable (Colless et al. 2001).

  • (10)

    Spectral class, based on our visual classification.

Comparison of visual and PCA spectral classifications

We would eventually like to compare the 2dFGRS radio-emitting galaxies with the parent sample from which they are drawn (in order to answer questions like ‘what fraction of Seyfert 1 and 2 galaxies are radio-loud, and how does this vary with redshift?’), so we compared our simple visual classification of the spectra (as Aa, Ae or SF) with the PCA methods developed for use with the 2dFGRS by Folkes et al. (1999) and Madgwick et al. (2001). PCA is an automatic method of classifying spectra which has the great advantages of being objective, quantitative and easily applied to very large samples. A series of principal components (PCs) or eigenspectra (PC1, PC2, …) are determined from the distribution of all the spectra in a very large multidimensional space; most of the information in the spectra is included in the first few PCs. This means that each spectrum can be well represented by a set of just three or four numbers, corresponding to the relative power in the dominant PCs.

We find good agreement between the visual and automatic methods of classifying galaxy spectra. For example, in a plot of PC3 against PC1 (Fig. 2) there is a clear separation between the different visual spectral types. By combining similar plots involving PC2, it looks as if it will be possible to define an almost unique mapping between the two classification methods, making it easy to compare the properties of the 1.5 per cent of the galaxies which are radio sources with the full 2dFGRS sample of up to 250000 optical galaxies.

Figure 2.

Plots of the first and third PCA components from 2dF spectra of radio-emitting galaxies. The three spectral classes from our visual classification are reasonably well separated in this plot, although some Ae galaxies overlap the region populated by SF galaxies. The PCA data used in this preliminary analysis were taken from an early version of the data base, and there have been some significant revisions of the PCA scheme since then (Madgwick et al. 2001).

Figure 2.

Plots of the first and third PCA components from 2dF spectra of radio-emitting galaxies. The three spectral classes from our visual classification are reasonably well separated in this plot, although some Ae galaxies overlap the region populated by SF galaxies. The PCA data used in this preliminary analysis were taken from an early version of the data base, and there have been some significant revisions of the PCA scheme since then (Madgwick et al. 2001).

Spectral class and redshift

Fig. 3 shows how the composition of the 2dFGRS radio sources changes with redshift. As we showed in Paper I, star-forming galaxies dominate the population at low redshift, while active galaxies dominate above graphic. This is because star-forming galaxies are low-luminosity radio sources graphic, which drop out of the sample when they fall below the NVSS radio detection limit. Conversely, most AGN have higher radio luminosities and remain in the sample out to graphic, where they finally drop below the 2dFGRS optical magnitude limit.

Figure 3.

Change in spectral mix with redshift for 2dFGRS/NVSS galaxies. SF indicates star-forming galaxies with Hii-region optical spectra, and AGN (em) and AGN (abs) indicate active galaxies with and without strong optical emission lines.

Figure 3.

Change in spectral mix with redshift for 2dFGRS/NVSS galaxies. SF indicates star-forming galaxies with Hii-region optical spectra, and AGN (em) and AGN (abs) indicate active galaxies with and without strong optical emission lines.

Interestingly, the fraction of emission-line AGN (Ae) galaxies remains roughly constant (at graphic per cent) throughout the sample volume, even though the overall AGN fraction increases dramatically with redshift. We need to keep in mind, however, that the 2-arcsec diameter 2dF fibres include an increasing fraction of the total galaxy light for more distant galaxies (see Fig. 4). As a result, galaxies with emission-line nuclei will be easier to recognize at lower redshift, where there is less dilution from the surrounding stellar galaxy, than at higher redshift. We therefore assume that the probability of recognizing a galaxy as Ae rather than Aa varies with redshift, and so we combine the Aa and Ae classes in most of our later analysis.

Figure 4.

Projected diameter of the 2dF fibres (in kpc) for galaxies over the redshift range graphic to 0.35.

Figure 4.

Projected diameter of the 2dF fibres (in kpc) for galaxies over the redshift range graphic to 0.35.

In star-forming galaxies, the line emission is expected to come mainly from an extended disc, and dilution of the emission-line flux with redshift is less likely. Indeed, we might expect star-forming galaxies to be easier to recognize at higher redshift, since the 2dF aperture includes a larger fraction of the total disc light.

Radio–optical identifications

We now need to determine which of the candidate radio source identifications in Table 1 are real associations between a 2dFGRS galaxy and an NVSS radio source. This is not always straightforward – as noted in Paper I, we expect some chance coincidences even at the smallest radio–optical separations. In Paper I we used a simple 10-arcsec cut-off as the criterion for association. Although this will include a few objects that are not real associations and exclude some that are, the number of such objects can be quantified statistically and taken into account when calculating the luminosity function.

We use a similar 10-arcsec cut-off here, but also recognize that a simple cut-off may exclude some extended sources with complex radio structure. Thus we also inspected radio–optical overlays of all the extended sources in the candidate list, and accepted some of these as genuine IDs even though the radio–optical offset was larger than 10arcsec.

Extended radio sources

About 25 per cent of the candidate NVSS/2dFGRS radio sources are resolved by the 45-arcsec NVSS beam, giving us an estimate of their linear size. In most such cases we still see a single radio source, but with an apparent size larger than 45arcsec in at least one dimension. For these galaxies, the NVSS radio position is calculated by fitting a two-dimensional Gaussian to the radio image. If the fit is not perfect, the quoted position may have a much larger uncertainly than that of an unresolved radio source of similar flux density.

For all extended NVSS sources with radio–optical offsets in the range graphic, we inspected overlays of the radio contours on to DSS images (see Fig. 5 for examples). If the optical galaxy lay along the major axis of the extended radio source, or the radio emission appeared to be symmetric about the optical galaxy, we accepted this as a correct ID.

Figure 5.

Overlays of NVSS radio contours on DSS optical images of some of the extended radio sources identified with 2dFGRS galaxies. Each frame shows a region 6.4arcmin across. Contours are at 1, 2, 4, 8, 16, 32, … mJybeam−1, except for (h) TGS398Z220 and (i) TGS190Z105, where the lowest contour is at 4mJybeam−1. For TGS190Z105, two dark lines mark the position of the faint galaxy identified as the radio source.

Figure 5.

Overlays of NVSS radio contours on DSS optical images of some of the extended radio sources identified with 2dFGRS galaxies. Each frame shows a region 6.4arcmin across. Contours are at 1, 2, 4, 8, 16, 32, … mJybeam−1, except for (h) TGS398Z220 and (i) TGS190Z105, where the lowest contour is at 4mJybeam−1. For TGS190Z105, two dark lines mark the position of the faint galaxy identified as the radio source.

Double radio sources

A few NVSS radio sources are resolved into two or more distinct components, so we need to be able to recognize these, and to search for an optical ID near the radio centroid rather than at the position of each individual component.

We first identified all the candidate double radio sources in the NVSS catalogue by using the semi-empirical link-length measure defined by Magliocchetti et al. (1998). A pair of radio sources are defined to be associated if

  • (i)

    the ratio of their flux densities S1 and S2 lies in the range graphic, and

  • (ii)

    the projected separation of the two radio components is smaller than their link length r, which is calculated from the total flux density in mJy and defined as  

    (1)
    formula

  • This yielded a total of 525 candidate NVSS doubles in the 1700deg2 region of sky covered by the 2dFGRS. Of these, 59 had a 2dFGRS galaxy within 30arcsec of the radio centroid, and 17 of these galaxies had spectra taken up to 1999 May. These objects were then inspected to see whether the optical galaxy lay on or near the radio axis of the NVSS double. As a result, eight new 2dFGRS galaxies were added to the sample as optical hosts of NVSS doubles. These are listed at the end of Table 1, along with an unusual diffuse source, tentatively identified with TGN307Z092, which is discussed in Section 5.2. These nine extra galaxies bring the total number of candidate NVSS/2dFGRS matches to 912 (of these, 56 per cent are AGN and 35 per cent SF galaxies).

Optically bright galaxies

We paid special attention to the brightest 2dFGRS galaxies graphic. For these bright galaxies, the radio–optical offset alone is not always a reliable indicator of whether the galaxy is associated with an NVSS radio source. There are three reasons for this: (i) it can be difficult to measure an accurate optical position for these galaxies from Schmidt plates, since the central regions are often overexposed, (ii) we found that the 2dFGRS fibre positions used for bright galaxies were sometimes offset from what appeared to be the optical nucleus, and (iii) much of the radio emission in these galaxies arises from star formation-related processes in a resolved disc (see Section 5 for more details), so that the centroid of the radio emission can be offset by several arcsec from the galaxy nucleus. We therefore inspected radio overlays on DSS images of all galaxies brighter than mag 17.0, and accepted those with graphic offsets as correct IDs if the radio emission appeared to be roughly centred on the optical galaxy. When this was done, it is noted in the final column of Table 1.

The final sample

Our final sample of accepted NVSS/2dFGRS IDs comprises all sources with radio–optical offsets of 10.0arcsec or less, along with the nine additional double galaxies described above and 47 additional galaxies with radio–optical offsets of graphic (28 of them are radio sources associated with optically bright galaxies, and 19 are extended radio sources). This gives a final sample of 757 ‘accepted’ NVSS/2dFGRS IDs, which we use in further analysis.

Table 2 summarizes the spectral properties of the final sample. The 2dFGRS spectra are generally of excellent quality, allowing both the redshift and spectral class to be determined accurately. Of the 912 targets analysed here only 30 had spectra of quality class 1 or 2, i.e., were too noisy for a reliable redshift measurement. 18 targets turned out to be misclassified Galactic stars (i.e., had absorption-line spectra with graphic, and two of the AGN were quasars (at redshifts graphic and 3.0).

Table 2.

Summary of spectral classifications for the galaxies listed in Table 1

Table 2.

Summary of spectral classifications for the galaxies listed in Table 1

We can use the data presented in Fig. 1 to place some quantitative limits on the reliability and completeness of the final sample. We consider three zones in radio–optical offset Δ: (a) offsets below 10arcsec, where all matches (other than Galactic stars) are accepted as correct IDs, (b) offsets of graphic, where we accept only a subset of matches (those associated with bright optical galaxies or extended radio sources, where an eye inspection suggests that the match is a correct one), and (c) offsets greater than 15arcsec, which are rejected as correct IDs.

In the first zone graphic there are 712 matches, and we include 702 of these in the final sample. However, integrating under the line in Fig. 1 implies that ∼75 of these are likely to be chance coincidences. In the second zone graphic there are 191 matches, of which 47 are included in the final sample. We expect 106 chance coincidences, suggesting that the final sample should contain ∼85 objects in this zone, rather than the 47 which are actually included. Thus our selection criteria have probably excluded some genuine IDs in this zone. In the third zone graphic there are 590 matches, all of which we reject (we do, however, include eight NVSS extended double radio sources, which were selected separately as described in Section 4.2). Integrating under the line in Fig. 1 implies that we expect ∼575 chance coincidences in this zone, suggesting that there are few or no ‘missing’ sample members in this zone.

In summary, we estimate that our final sample of 757 radio source IDs includes ∼75 objects which are chance coincidences of an 2dFGRs galaxy and a background radio source, and is missing ∼40 genuine radio-emitting galaxies which should have been included. Thus the sample is currently about 95 per cent complete and 90 per cent reliable (and the overall sample size is within 5 per cent of the correct value). In principle, both the completeness and the reliability could be raised to almost 100 per cent by measuring more accurate radio positions for the weaker graphic radio sources in Table 1, and this will be done in the future.

Radio stars?

As noted above, our final sample of radio source IDs rejected all the NVSS–2dFGRS matches which had spectra characteristic of Galactic stars (with redshifts graphic. As can be seen from Table 2, 18 of the 155 rejected IDs graphic per cent) are Galactic stars. This is roughly twice the number expected for objects drawn at random from the 2dFGRS data set (6 per cent of the 2dFGRS objects observed up to 2001 March were Galactic stars; Colless et al. 2001), posing the question of whether we have detected any Galactic radio stars.

At first glance, this seems unlikely. Searches for radio stars in the NVSS and FIRST radio surveys (Condon, Kaplan & Yin 1997; Helfand et al. 1999) find a very low detection rate at high Galactic latitudes (both studies find less than one radio-detected star per 200deg2 for graphic, and Helfand et al. note that the detection probability drops steeply at fainter magnitudes).

Furthermore, the 2dFGRS stars are not randomly selected stars, but stars which have been misclassified as galaxies. Thus some of them are likely to be the chance superposition of a galaxy and a foreground star. At least one object in Table 1 (TGN156Z046) certainly falls into this class – it was originally classified as a star with graphic, but examination of the spectrum showed that although the blue end of the spectrum was dominated by light from a foreground star, a higher redshift system at graphic with emission lines of Hα, [Nii] and [Sii], and Mg and NaD absorption lines, could be seen clearly at the red end.

Nevertheless, the superposition of galaxies and foreground stars is unlikely to provide a complete explanation for a larger-than-expected number of NVSS sources matched with Galactic stars, because it is hard to understand why radio-emitting galaxies should be more likely than other 2dFGRS galaxies to be obscured by foreground stars. It will be interesting to see whether the ‘radio star’ excess persists as the 2dFGRS data set grows. If so, it is possible that there may be a rare and so-far unrecognized class of radio sources associated with faint graphic Galactic stars.

Other identification criteria

MC99 took a different approach to cross-identifying NVSS radio sources with optical galaxies, and calculated a probability of association based on the radio–optical offset and the quoted errors in radio and optical positions. They considered all NVSS radio sources within 30arcsec of an LCRS galaxy, and calculated a normalized offset

 

(2)
where Δ and Δ are the differences between radio and optical positions, and σ and σ are the combined errors in the quoted radio and optical positions. They accepted a candidate identification as a true ID if graphic. This method has the advantage that it allows a larger search radius for objects with larger position errors, but the disadvantage is that the probability of finding a spurious optical ID is larger for faint sources because of the larger error box.

We looked at the effect of applying the MC99 identification criterion to our own sample. Of the 695 unresolved sources in Table 1, 543 are identified as IDs by both criteria (i.e., MC99 and our own procedure as described above). 41 sources are rejected by both criteria, 38 are accepted by us but rejected by MC99, and 73 are accepted by MC99 but rejected by us. Thus the MC99 criterion produces about 6 per cent more IDs than our method for the same data set. This is probably not surprising – we know that our method excludes a few genuine IDs with large radio–optical separation in order to produce a sample which is as uncontaminated by chance coincidences as possible.

K-corrections

The galaxies in our sample have redshifts as high as graphic to 0.4, so when calculating galaxy luminosities we need to apply optical, radio and infrared k-corrections to take proper account of the effects of redshift on both the observed flux and the width of the passband.

In the optical, we follow Folkes et al. (1999) and adopt the B-magnitude k-corrections tabulated by Pence (1976), using Pence's E/S0 values for our Aa and Ae galaxies, and the Sbc values for our SF galaxies. We also convert Pence's k(B) values to k(bJ) using the relation

 

(3)
formula

In the radio, we assume a mean spectral index of graphic (where graphic and apply the usual k-correction of the form

 

(4)
formula
at redshift z.

In the far-infrared, the situation is more complex because of the wide range in IRAS‘spectral index’ (i.e., dust temperature) observed in these galaxies (see Section 6). Because the FIR k-correction can be either positive or negative depending on what assumptions are made about the spectral energy distribution, and because many of our galaxies are weak IRAS sources with detections in only one or two bands, we chose to apply no k-correction when calculating FIR luminosities. Since most of the FIR-detected galaxies we will study are at low redshift graphic, the k-correction has little or no effect in any case.

Radio structures of resolved galaxies

About 25 per cent of the radio sources associated with 2dFGRS galaxies are spatially resolved by NVSS, allowing us to measure their projected linear size. In a few cases we remeasured the angular size ourselves (usually because the NVSS source catalogue split a single source into several components), otherwise we used the NVSS catalogue value. Fig. 5 shows some of the extended NVSS sources identified with AGN and star-forming galaxies.

Fig. 6 plots radio power against projected linear size for the 182 extended NVSS radio sources with good-quality 2dFGRs spectra (i.e., with graphic in Table 1). As expected, most star-forming galaxies are associated with radio sources less than about 60kpc in diameter, i.e., no larger than a galaxy disc. The few star-forming galaxies whose radio extent is larger than this appear to be members of pairs or close groups in which more than one galaxy contributes to the radio emission. In contrast, many of the radio sources with AGN spectra are several hundred kpc in extent, consistent with classical (core plus jet) radio galaxies.

Figure 6.

Relationship between radio power and projected linear size for spatially resolved 2dFGRS/NVSS radio sources. The dashed line shows the locus of a source with an observed angular size of 20arcsec and flux density 2.5mJy over the redshift range graphic. Most of the upper limits for unresolved sources fall to the left of this line. Sources larger than about 100kpc will be resolved throughout the 2dFGRS sample volume.

Figure 6.

Relationship between radio power and projected linear size for spatially resolved 2dFGRS/NVSS radio sources. The dashed line shows the locus of a source with an observed angular size of 20arcsec and flux density 2.5mJy over the redshift range graphic. Most of the upper limits for unresolved sources fall to the left of this line. Sources larger than about 100kpc will be resolved throughout the 2dFGRS sample volume.

Giant radio galaxies

Our sample includes three giant radio galaxies with projected linear sizes greater than 1Mpc, which are shown in Fig. 7. Two are newly discovered GRGs – TGS223Z232 graphic and TGS190Z081 graphic. The third, TGS241Z299, corresponds to the radio galaxy MRCB0312–271 graphic, which has already been identified as a GRG by Kapahi et al. (1998).

Figure 7.

Radio contours overlaid on DSS optical images of the three giant radio galaxies (GRGs) detected in our sample: (a) TGS223Z232 (contours 1, 2, 3, 4, 5, 10, 20, 50mJybeam−1), (b) TGS190Z081 (contours 1, 2, 4, 8, 16, 32, 64, 128mJybeam−1), (c) TGS241Z299 (contours 1, 2, 5, 10, 20, 50mJybeam−1). Each frame is 12.8arcmin across.

Figure 7.

Radio contours overlaid on DSS optical images of the three giant radio galaxies (GRGs) detected in our sample: (a) TGS223Z232 (contours 1, 2, 3, 4, 5, 10, 20, 50mJybeam−1), (b) TGS190Z081 (contours 1, 2, 4, 8, 16, 32, 64, 128mJybeam−1), (c) TGS241Z299 (contours 1, 2, 5, 10, 20, 50mJybeam−1). Each frame is 12.8arcmin across.

About graphic GRGs are currently known (Ishwara-Chandra & Saikia 1999; Schoenmakers et al. 2000) – they are believed to represent the last stages of radio galaxy evolution, and to be unusually old or long-lived radio sources. The three GRGs in our sample represent just under 1 per cent of the 441 AGN accepted as radio source IDs, so they are clearly rare. It would be interesting to determine whether there is anything different about their environment (e.g., low density, lack of recent interactions with companions) which has allowed these radio sources to grow undisturbed to such a large size.

Unusual radio sources

Fig. 8 shows two unusual radio sources discovered in our data set. The diffuse radio source shown in Fig. 8(a) is resolved into four separate components in the NVSS catalogue, and one of these was originally picked up as a possible match for the 2dFGRS galaxy TGN307Z090. Inspection of the radio contours showed that this is a large (∼6.5arcmin diameter) source with very low radio surface brightness.

Figure 8.

Radio contours overlaid on DSS optical images of two unusual radio sources in our sample. Each frame is 8.6arcmin across. (a) Overlay of NVSS radio contours on a DSS image of TGN307Z092 and its fainter companion TGN307Z090 (contour levels 1, 2, 3, 4, 6, 8, 10, 12mJybeam−1), (b) NVSS contours overlaid on an image of TGS119Z122 graphic contour levels 1, 2, 4, 6, 8mJybeam−1).

Figure 8.

Radio contours overlaid on DSS optical images of two unusual radio sources in our sample. Each frame is 8.6arcmin across. (a) Overlay of NVSS radio contours on a DSS image of TGN307Z092 and its fainter companion TGN307Z090 (contour levels 1, 2, 3, 4, 6, 8, 10, 12mJybeam−1), (b) NVSS contours overlaid on an image of TGS119Z122 graphic contour levels 1, 2, 4, 6, 8mJybeam−1).

The source is clearly real, since it was independently detected at Green Bank (also at 1.4GHz) by White & Becker (1992). The single-dish flux density of 189mJy suggests that NVSS may have missed some flux. At present, nothing is known about the radio spectral index. While the identification is uncertain at this stage, the radio centroid is closer to the 2dFGRS galaxy TGN307Z092 than to its companion TGN307Z090, so we tentatively identify the source with TGN307Z092. At the redshift of TGN307Z092 graphic, the source has a projected linear size of 310kpc and a 1.4-GHz radio power of graphic. Its radio surface brightness is, however, unusually low. The nature of the source remains uncertain, although it may be a relic radio galaxy whose central engine has turned off (e.g. Komissarov & Gubanov 1994).

Fig. 8(b) shows the radio emission associated with the 16th-magnitude star-forming galaxy TGS119Z122 at graphic. The NVSS flux density at 1.4GHz is 11.7mJy. However, the same object is listed in the Parkes catalogue as graphic, with flux densities of 230 and 130mJy at 2.7 and 5.0GHz respectively. The Parkes observations were made by Wall, Wright & Bolton (1976), and the observing dates are given by them as 1974.0 and 1974.8 for the 2.7- and 5.0-GHz observations respectively. Thus the source was detected at two different frequencies and on two different occasions separated by several months, and appears to have been real. The optical identification with a 16th-magnitude galaxy was first made by Savage & Wall (1976).

The radio luminosity of graphic has declined dramatically since the 1974 Parkes observations. One possibility, since TGS119Z122 is actively forming stars, is that the bulk of the Parkes emission came from a radio-loud supernova like SN1986J or SN1998Z (e.g. Weiler et al. 1998), which has since faded. However, the early Parkes observations imply a 5-GHz radio power around graphic, which is 3 times higher than the peak luminosity of any known radio supernova, including the gamma-ray burst object SN1998bw (Kulkarni et al. 1998). A transient Galactic radio source seems unlikely at graphic, and the nature of the catalogued Parkes source remains unclear.

IRAS detections and star-forming galaxies

IRAS detections of 2dFGRS galaxies

In the well-known correlation between far-infrared (FIR) and radio continuum emission in star-forming galaxies (e.g. de Jong et al. 1985; Helou, Soifer & Rowan-Robinson 1985), the FIR/radio ratio graphic has a mean value of ∼105 (Condon & Broderick 1988). By a happy coincidence, this is very close to the ratio between the 280-mJy limit of the IRAS Faint Source Catalogue (FSC) (Moshir et al. 1990) at 60μm and the 2.5-mJy detection limit of the NVSS at 1.4GHz. As a result, we expect most star-forming galaxies detected as radio sources by NVSS to be detected as 60-μm sources in the IRAS FSC, and vice versa.

In practice, as noted earlier in Section 3.2, about 10 per cent of the 2dFGRS survey region was either unobserved by IRAS or had only single-scan coverage. Thus the absence of an individual galaxy from the IRAS catalogue does not necessarily mean that it has a 60-μm flux below the FSC limit.

Table 3 summarizes the spectral properties of the 183 accepted radio source IDs from Table 1 that were also detected at 60μm by IRAS. Most galaxies detected at 60μm (83 per cent) were also detected by IRAS at 100μm.

Table 3.

Summary of spectral classifications for radio source IDs which were also detected by IRAS

Table 3.

Summary of spectral classifications for radio source IDs which were also detected by IRAS

All the 2dF spectra of galaxies detected as IRAS sources show optical emission lines, in agreement with earlier studies (e.g. Allen, Roche & Norris 1985; Lawrence et al. 1986). The great majority (89 per cent) are classified as SF, with the remainder (11 per cent) being emission-line AGN with Seyfert-like spectra.

Extrapolating from our current sample suggests that the full 2dFGRS data base, when complete, will contain spectra of ∼1000 IRAS galaxies. While this is smaller than targeted redshift surveys such as the IRAS PSCz (Saunders et al. 2000), which has more than 15000 redshifts, it reaches to lower IRAS flux densities (and a higher median redshift) than most earlier surveys, as can be seen from Fig. 9. Since the general properties of IRAS galaxies are already well explored by earlier studies, we focus here on the radio properties of star-forming galaxies in the 2dFGRS.

Figure 9.

Plot of IRAS 60-μm flux density versus redshift for IRAS-detected 2dFGRS radio sources. ULIRGs with graphic are shown by filled circles, and other galaxies by open circles. The vertical line at 0.6Jy corresponds to the flux limit of the PSCz survey (Saunders et al. 2000).

Figure 9.

Plot of IRAS 60-μm flux density versus redshift for IRAS-detected 2dFGRS radio sources. ULIRGs with graphic are shown by filled circles, and other galaxies by open circles. The vertical line at 0.6Jy corresponds to the flux limit of the PSCz survey (Saunders et al. 2000).

The FIR–radio correlation

We calculated the FIR luminosity for each galaxy detected by IRAS, using the FIR flux defined by Helou et al. (1985):

 

(5)
where S60 and S100 are the 60- and 100-μm flux densities in Jy graphic, and SFIR is in Wm−2.

Fig. 10 plots FIR luminosity versus 1.4-GHz radio power for the IRAS-detected galaxies in our sample. Most galaxies fall close to the FIR–radio correlation for normal galaxies derived by Devereux & Eales (1989),

Figure 10.

Relation between FIR and radio continuum luminosity for radio source IDs from Table 1. Galaxies with SF spectra are shown as open circles, and those with AGN spectra as stars. The solid line shows the FIR–radio correlation for normal galaxies derived by Devereux & Eales (1989). Note that because of the requirement that they lie above the 2.8-mJy NVSS detection limit, most of our 2dFGRS star-forming galaxies have star formation rates which are significantly higher than the majority of ‘normal’ galaxies.

Figure 10.

Relation between FIR and radio continuum luminosity for radio source IDs from Table 1. Galaxies with SF spectra are shown as open circles, and those with AGN spectra as stars. The solid line shows the FIR–radio correlation for normal galaxies derived by Devereux & Eales (1989). Note that because of the requirement that they lie above the 2.8-mJy NVSS detection limit, most of our 2dFGRS star-forming galaxies have star formation rates which are significantly higher than the majority of ‘normal’ galaxies.

 

(6)
formula
but the scatter increases strongly for the most luminous galaxies.

As can be seen from Table 4, the fraction of galaxies with AGN-like optical spectra increases with FIR luminosity, and so it seems likely that the increased scatter in the FIR–radio correlation results from an increasingly diverse mix of pure star-forming galaxies and AGN or composite objects at higher FIR luminosities.

Table 4.

Summary of spectral properties for three bins in FIR luminosity. Hot IRAS galaxies are those with (de Grijp et al. 1985)

Table 4.

Summary of spectral properties for three bins in FIR luminosity. Hot IRAS galaxies are those with (de Grijp et al. 1985)

IRAS colours and 2dF spectral types

As noted by de Grijp et al. (1985), galaxies with active nuclei tend to have hotter IRAS colours (as measured by the flux ratio graphic than ‘normal’ star-forming galaxies, and galaxies with Seyfert nuclei generally have graphic.

Fig. 11 shows a FIR ‘colour–magnitude diagram’ for galaxies in our sample. The IRAS flux densities for weaker sources have typical errors of graphic per cent, so the IRAS colours can have uncertainties of 30 per cent or more. However, there is still a general increase in the fraction of galaxies with ‘hot’IRAS colours at higher FIR luminosity (see also the summary in Table 4), consistent with an increasing contribution from active nuclei at higher FIR luminosity.

Figure 11.

Plot of IRAS‘colour’graphic versus FIR luminosity for galaxies in our sample. ‘Warm’ galaxies are defined by de Grijp et al. (1985) as those with graphic, and they find that most Seyfert galaxies have ‘warm’IRAS colours. The boundary between warm and cool galaxies as defined by de Grijp et al. is shown by the dotted horizontal line, and a typical error bar for the weakest IRAS sources graphic is shown in the lower right-hand corner. As in Fig. 10, open circles and stars denote galaxies classified spectroscopically as SF and AGN respectively.

Figure 11.

Plot of IRAS‘colour’graphic versus FIR luminosity for galaxies in our sample. ‘Warm’ galaxies are defined by de Grijp et al. (1985) as those with graphic, and they find that most Seyfert galaxies have ‘warm’IRAS colours. The boundary between warm and cool galaxies as defined by de Grijp et al. is shown by the dotted horizontal line, and a typical error bar for the weakest IRAS sources graphic is shown in the lower right-hand corner. As in Fig. 10, open circles and stars denote galaxies classified spectroscopically as SF and AGN respectively.

Ultraluminous IRAS galaxies

10 of the IRAS galaxies in our sample (listed in Table 5) have FIR luminosities above 1012L, and can be considered ‘ultraluminous IRAS galaxies’ (ULIRGS) (e.g. Sanders & Mirabel 1996). Most of these galaxies are already known as ULIRGs from other surveys, but there are two newly discovered ULIRGs, TGN152Z171 and TGN131Z280. Fig. 12 shows their spectra.

Table 5.

Ultraluminous IRAS Galaxies (ULIRGs) in the sample.

Table 5.

Ultraluminous IRAS Galaxies (ULIRGs) in the sample.

Figure 12.

2dFGRS spectra of the two newly discovered ULIRGs in our sample, TGN152Z171 graphic and TGN131Z280 graphic. Both spectra show residuals due to incomplete subtraction of the atmospheric airglow line at 6300Å.

Figure 12.

2dFGRS spectra of the two newly discovered ULIRGs in our sample, TGN152Z171 graphic and TGN131Z280 graphic. Both spectra show residuals due to incomplete subtraction of the atmospheric airglow line at 6300Å.

All the galaxies in Table 5 have unresolved radio sources in the NVSS, although because of the relatively large distances of these galaxies this only sets fairly unrestrictive limits (typically graphic on the linear size of the associated radio emission.

ROSAT detections

Bauer et al. (2000) have cross-matched the NVSS source catalogue with the ROSAT Bright Source Catalogue (RSBC) of X-ray sources (Voges et al. 1999). They showed that the relatively low surface density of NVSS sources allows reliable identification of the radio counterparts of RSBC sources, despite uncertainties of 10arcsec or more in the X-ray positions. The more accurate radio positions then allow a reliable optical identification to be attempted. Bauer et al. showed that the RSBC/NVSS radio sources were dominated by AGN with an average redshift of graphic.

We cross-matched the galaxies in Table 1 with the ROSAT All-Sky Survey (RASS) catalogue, taking a simple cut-off of 30arcsec as our matching radius rather than the more complex criteria prescribed by Bauer et al. (2000). This gave the six matches listed in Table 6, four of which are also in the Bauer et al. list (the other two fall below the 0.1counts−1 X-ray limit imposed by Bauer et al. for their sample).

Table 6.

Galaxies detected as X-ray sources in the ROSAT All-Sky Survey (RASS)

Table 6.

Galaxies detected as X-ray sources in the ROSAT All-Sky Survey (RASS)

All six galaxies in Table 6 have strong emission lines and spectra classed as Ae, but in other respects they are a diverse population, including three powerful, double-lobed radio galaxies, two Seyfert 1 galaxies with less powerful radio emission, and one ultraluminous IRAS galaxy (ULIRG) (see Table 5 and Fig. 13).

Bauer et al. (2000) identified 1512 extragalactic RSBC/NVSS sources with Galactic latitude graphic in the 10.3-sr NVSS survey area. This corresponds to a surface density of about 0.05 objects per square degree, or about 4 times higher than the corresponding surface density derived from the RSBC/NVSS/2dFGRS objects in Table 6 (0.012 objects per square degree).

Where are the missing RSBC/NVSS objects? We expect most of them to fall within the 2dFGRS volume, since Bauer et al. (2000) note that their objects are mostly local with a mean redshift of about 0.1. Closer examination of the Bauer et al. objects in the 2dFGRS area suggests that about half the missing objects are bright, nearby galaxies that were excluded from the 2dFGRS. Most of the remainder appear to be Seyfert galaxies excluded because of their compact, stellar appearance on sky survey plates, along with a few higher redshift QSOs.

The local radio luminosity function (RLF) at 1.4GHz

Calculation of the local RLF

We now calculate the radio luminosity function (RLF) for 2dFGRS–NVSS galaxies with graphic, both for the sample as a whole and for the AGN and SF subclasses. We assigned spectral types to the 19 unclassified galaxies with measured redshifts as follows: galaxies with bJ fainter than magnitude 17.0 and radio power above 1023WHz−1 were assigned to the Aa (absorption-line AGN) class, otherwise they were are assumed to be star-forming (SF). Using these criteria, we classify 18 of the low S/N galaxies as Aa and only one as SF.

To calculate the local RLF, we use the graphic method (Schmidt 1968), as discussed by Condon (1989). Vmax is calculated from the joint optical and radio limits of the sample, i.e., a radio cut-off of 2.8mJy and optical cut-offs at graphic (bright) and 19.4mag (faint). Table 7 lists the derived local RLF for the whole sample, and for the AGN and SF classes separately. At this stage, we make no corrections for incompleteness and the only normalization is the effective area of 325deg2 derived in Section 2.1.

Table 7.

The local radio luminosity function at 1.4GHz.

Table 7.

The local radio luminosity function at 1.4GHz.

Fig. 14 shows the derived RLF, together with earlier values derived by Condon (1989) and MG. An advantage of the 2dF/NVSS sample is that all the data are drawn from a single radio survey and a set of homogeneous optical spectra from a single instrument. Most previous determinations of the local RLF used data from several radio surveys to span the equivalent range in radio power. The good overall agreement with earlier derivations confirms our earlier calculation that the incompleteness in our final sample is small (<10 per cent).

Figure 14.

Local RLF derived from the 662 galaxies in Table 1 that are accepted as correct IDs and have radio flux density graphic, optical magnitude graphic and redshift graphic. Previous derivations by Condon (1989) and Machalski & Godlowski (2000) are shown for comparison. Between 1022 and 1024WHz−1, our values and those of Machalski & Godlowski are sometimes so close that they are indistinguishable in the diagram.

Figure 14.

Local RLF derived from the 662 galaxies in Table 1 that are accepted as correct IDs and have radio flux density graphic, optical magnitude graphic and redshift graphic. Previous derivations by Condon (1989) and Machalski & Godlowski (2000) are shown for comparison. Between 1022 and 1024WHz−1, our values and those of Machalski & Godlowski are sometimes so close that they are indistinguishable in the diagram.

Comparison with earlier work

Figs 14 and 15 shows a comparison between our values of the local RLF and those derived by MG for a sample of 1157 radio-identified galaxies from the LCRS. This is the only other determination which uses a comparably large data set of homogeneous optical spectra.

Figure 13.

2dFGRS spectra of four NVSS galaxies detected as X-ray sources in the ROSAT All-Sky Survey. All show optical emission lines with line ratios characteristic of active galaxies but, as noted in the text, they are otherwise a diverse class of objects.

Figure 13.

2dFGRS spectra of four NVSS galaxies detected as X-ray sources in the ROSAT All-Sky Survey. All show optical emission lines with line ratios characteristic of active galaxies but, as noted in the text, they are otherwise a diverse class of objects.

Figure 15.

Local RLFs derived for AGN and SF galaxies separately. Filled points connected by solid lines show our own data for AGN (squares) and SF galaxies (triangles). The local RLFs for AGN and SF galaxies derived by Machalski & Godlowski (2000) are plotted using open symbols connected by dotted lines.

Figure 15.

Local RLFs derived for AGN and SF galaxies separately. Filled points connected by solid lines show our own data for AGN (squares) and SF galaxies (triangles). The local RLFs for AGN and SF galaxies derived by Machalski & Godlowski (2000) are plotted using open symbols connected by dotted lines.

As can be seen from Fig. 14, the overall agreement between our total (i.e., AGN plus SF) RLF and that of MG is extremely good. This is remarkable, given the differences between the two samples.

  • (1)

    Our criteria for determining radio source IDs differ from those used by MC99, as noted in Section 4.6.

  • (2)

    All the 2dFGRS redshifts were determined spectroscopically, whereas most of the redshifts listed by MC99 were estimated from optical magnitudes (so that some individual values may have large errors).

Such good agreement between two independent samples chosen in different ways suggests that the RLF is a very robust indicator of the overall density of radio sources in the local Universe.

As can be seen from Fig. 15, however, the agreement between our results and those of MG breaks down when we split our sample into AGN and SF galaxies. We find that the space density of AGN radio sources continues to rise as we go to radio powers as low as 1022WHz−1, with no sign of a turnover (see Fig. 15). In contrast, MG find a decreasing density of radio AGN below 1024WHz−1, which is reflected in the divergence of the two AGN LFs in Fig. 15. This turnover in the MG LF for AGN has also been discussed by Brown, Webster & Boyle (2001), who ascribe it to incompleteness in the AGN data used by MG. The good agreement between the faint end of our local RLF for AGN and that derived by Sadler, Jenkins & Kotanyi (1989) for nearby galaxies can be seen in Fig. 18, and strongly supports the view that our values are correct and that the MG sample is incomplete for low-luminosity AGN.

Figure 18.

Local RLF for active galaxies, combining data from our sample (filled circles) with values from Sadler et al. (1989) for nearby E/S0 galaxies (open triangles). The Sadler et al. values have been converted to 1.4GHz, assuming a spectral index of graphic. As in Fig. 16, the NVSS/2dFGRS values of Φ have been increased by 5 per cent to take into account the 95 per cent redshift completeness of the 2dFGRS, and the solid line shows the best-fitting analytic function (see Table 8).

Figure 18.

Local RLF for active galaxies, combining data from our sample (filled circles) with values from Sadler et al. (1989) for nearby E/S0 galaxies (open triangles). The Sadler et al. values have been converted to 1.4GHz, assuming a spectral index of graphic. As in Fig. 16, the NVSS/2dFGRS values of Φ have been increased by 5 per cent to take into account the 95 per cent redshift completeness of the 2dFGRS, and the solid line shows the best-fitting analytic function (see Table 8).

Thus, although we and MG agree on the overall density of radio sources in the local Universe, we disagree on the relative fraction of AGN and SF galaxies below 1024WHz−1. There are two possible explanations for this, namely a selection difference (i.e., the different criteria for inclusion in the two samples select roughly the same number of galaxies, but do not necessarily select the same kind of galaxies), and a classification difference. Our AGN/SF classification is based on optical spectra, whereas MG used the classifications from MC99, which take into account several factors including the radio–optical flux ratio, angular extent of the radio emission, and IRAS data where available.

There are 92 galaxies in common between our set of radio source IDs in Table 1 and the LCRS data set used by MC99. Of these, we agree on the classification of 69 (40 AGN, 29 SF), i.e., 75 per cent of the galaxies in common. Of the 25 per cent of galaxies where there is disagreement, most are classified by us as AGN and by MC99 as SF (i.e., for a data set classified by both groups, we find more AGN, and fewer SF galaxies, than MC99).

A detailed comparison of the 2dFGRS and LCRS data sets is outside the scope of this paper, but it seems likely that both selection differences and misclassification of low-power AGN as SF galaxies contribute to the incompleteness of the MG AGN data at low radio powers. The identification criteria used by MC99 may exclude some genuine radio IDs with flux densities above 5mJy and radio–optical position offsets of less than 10arcsec (see Section 4.6), and the radio–optical flux ratio which they use in their classification may misclassify some low-power AGN as SF galaxies (especially since the radio sources in low-power AGN are rarely spatially resolved by NVSS, and so cannot be recognized by their radio morphology in the same way as many powerful radio AGN).

Star-forming galaxies and the local star formation density

As noted earlier, the 2dFGRS excluded most bright, nearby galaxies with graphic. To extend our sample to lower radio luminosity, we therefore combined our measured RLF with the local RLF derived by Condon (1989) for galaxies in the Revised Shapley–Ames Catalogue (RSA) (Sandage & Tammann 1981). In doing this, we also increased the values of Φ listed in Table 7 by 5 per cent to correct for the ∼5 per cent spectroscopic incompleteness of the 2dFGRS (i.e., the spectra in Table 1 with graphic for which no reliable redshift could be measured). As can be seen from Fig. 16, our results agree well with the Condon RSA values in the small region of overlap. We then fitted an analytic function of the type described by Saunders et al. (1990),

Figure 16.

Local RLF for star-forming galaxies, combining data from our sample (filled circles) with values from Condon (1989) for nearby star-forming galaxies from the Revised Shapley–Ames Catalogue (open squares). The NVSS/2dFGRS values of Φ have been increased by 5 per cent to take into account the 95 per cent redshift completeness of the 2dFGRS. The solid line shows the best-fitting analytic function as described in the text.

Figure 16.

Local RLF for star-forming galaxies, combining data from our sample (filled circles) with values from Condon (1989) for nearby star-forming galaxies from the Revised Shapley–Ames Catalogue (open squares). The NVSS/2dFGRS values of Φ have been increased by 5 per cent to take into account the 95 per cent redshift completeness of the 2dFGRS. The solid line shows the best-fitting analytic function as described in the text.

 

(7)
formula
to the combined data, and Table 8 summarizes the results.

Table 8.

Parametric fits to the local RLFs for AGN and SF galaxies, using the Saunders et al. (1990) fitting function as described in the text

Table 8.

Parametric fits to the local RLFs for AGN and SF galaxies, using the Saunders et al. (1990) fitting function as described in the text

We can now use the RLF for star-forming galaxies to estimate the local star formation density (i.e., the zero-point of the Madau diagram; Madau et al. 1996). Following Cram (1998) and Haarsma et al. (2000), we assume a Salpeter-like initial mass function

 

(8)
formula
over the range 0.1 to 100M, and convert from a radio luminosity to a star formation rate (SFR) via the relation

 

(9)
formula

(Sullivan et al. 2001). The local star formation density at any given SFR is then

 

(10)
formula
where Φ is the local RLF from Tables 7 and 8, multiplied by 1.05 to correct for incompleteness as noted above. Fig. 17 shows the results – our data imply that the greatest contribution to the local star formation density comes from galaxies with SFRs around 10Myr−1.

Figure 17.

Local star formation density (in Myr−1mag−1Mpc−3) for galaxies with star formation rates between 0.01 and 1000Myr−1. The solid line is derived from the fit to the local RLF for star-forming galaxies (Table 8) after correcting for spectroscopic incompleteness. Error bars from the individual data points used to derive the fit are also shown. Filled squares show the values of local star formation density derived from Hα measurements by Gallego et al. (1995).

Figure 17.

Local star formation density (in Myr−1mag−1Mpc−3) for galaxies with star formation rates between 0.01 and 1000Myr−1. The solid line is derived from the fit to the local RLF for star-forming galaxies (Table 8) after correcting for spectroscopic incompleteness. Error bars from the individual data points used to derive the fit are also shown. Filled squares show the values of local star formation density derived from Hα measurements by Gallego et al. (1995).

As can be seen from Fig. 17, our radio-derived values for the local star formation density are in excellent agreement with the values derived from Hα by Gallego et al. (1995, hereafter G95) for galaxies with star formation rates up to graphic.

For galaxies with the highest star formation rates (>30Myr−1), however, we find a significantly higher density than G95. The reasons for this are not completely clear – our SF galaxies with high derived SFRs appear to be genuine star-forming galaxies which follow the FIR–radio correlation (see Fig. 10). Where measurements of diagnostic emission-line ratios have been carried out on the 2dF spectra, these also confirm the SF classification (Jackson & Londish 2000).

Our sample volume for galaxies with a high SFR is larger than that surveyed by G95. Their survey covered 471deg2 to a depth of graphic (beyond which the graphic lines were shifted out of their passband), i.e., a maximum volume of about graphic. The equivalent volume for the SF galaxies in our current (325deg2) sample is set by the redshift at which the observed radio flux density falls below our 2.8mJy cut-off. For a galaxy with an SFR of ∼100Myr−1, this redshift is graphic, giving a volume of graphic, or 5 times the volume surveyed by G95.

Because of this increase in sample volume for stronger radio sources, the 2dFGRS/NVSS SF sample is dominated by galaxies with high star formation rates (well over half the SF galaxies we detect have derived star formation rates above 30Myr−1, compared to only 5 per cent of the G95 galaxies), so we would expect to have better statistics than G95 for galaxies with high SFRs, assuming that the radio luminosity continues to scale linearly with SFR.

It is possible that at high star formation rates the Hα emission line is increasingly obscured by dust, so that optical surveys underestimate the number of galaxies with very high star formation rates. Deep VLA studies of galaxy clusters at graphic (Smail et al. 1999) and local galaxies with ‘post-starburst’ optical spectra (Miller & Owen 2001) suggest that some galaxies may have star-forming regions which are largely hidden by dust. Follow-up observations of the galaxies in Table 1 for which the radio data imply high star formation rates would therefore be valuable.

Integrating under the curve in Fig. 17 gives a local star formation density of graphic, which is slightly higher than the value of graphic derived by G95 from Hα data. The difference arises mainly because our sample contains more galaxies with high star formation rates (>30Myr−1). For galaxies with star formation rates up to 50Myr−1, we derive a local density of graphic, in excellent agreement with the G95 value.

Active galaxies and radio galaxies

As in Section 8.3, we combined the NVSS/2dFGRS sample with published data for bright, nearby galaxies to extend our results to lower radio power. Fig. 18 shows the results – the NVSS/2dFGRS data points agree well with the RLF for nearby graphic elliptical and S0 galaxies from Sadler et al. (1989). Once again, we fitted an analytic function as described in Section 8.3, and the results are given in Table 8. However, it is remarkable that the space density of radio-emitting AGN is also well fitted by a single power law of the form

 

(11)
formula
over almost five decades in luminosity from 1020.5 to 1025WHz−1, before turning down above 1025WHz−1. As pointed out by Sadler et al. (1989), the AGN RLF must also turn down below 1020WHz−1 in order not to exceed the space density of luminous galaxies.

Black holes in radio AGN

Franceschini, Vercellone & Fabian (1998) examine the relation between galaxy luminosity, black hole mass and radio power in nearby active galaxies, and conclude that the radio power of an AGN is both a good tracer of supermassive black holes and an estimator of their mass (although Laor 2000 notes that the correlation between radio power and black hole mass shows considerable scatter).

Following the precepts of Franceschini et al. (1998), we can estimate the local mass density of black holes from our AGN RLF with the following conversion factors:

 

(12)
formula
and

 

(13)
formula

This yields the mass density distribution shown in Fig. 19. In contrast to the star formation density plot shown in Fig. 17, the total mass density of black holes does not converge, but continues to increase down to the lowest values (a few times 107M) so far probed by radio surveys. Integrating over the values in Fig. 19 gives a total mass density of massive black holes graphic in galactic nuclei of

Figure 19.

Local mass density (in Mmag−1Mpc−3) of black holes, derived from the local radio luminosity function for AGN (Tables 7 and 8), together with the mean relation between radio power and black hole mass from Franceschini et al. (1998). As in Fig. 17, error bars are shown for the individual points used to derive the fit in Table 8.

Figure 19.

Local mass density (in Mmag−1Mpc−3) of black holes, derived from the local radio luminosity function for AGN (Tables 7 and 8), together with the mean relation between radio power and black hole mass from Franceschini et al. (1998). As in Fig. 17, error bars are shown for the individual points used to derive the fit in Table 8.

 

(14)
which is within the range graphic derived by Chokshi & Turner (1992) from the optical luminosity function of QSOs. We note that the value derived here is actually a lower limit, since the derived black-hole mass density is still increasing at the lowest values of MBH we can measure. Thus a comparison of black-hole mass densities for radio galaxies in the local Universe and high-redshift QSOs suggests that local radio-emitting AGN are the direct descendants of most or all of the high-z QSOs.

Redshift evolution of the radio luminosity function

Although the 2dFGRS probes to redshifts of graphic to 0.4 where we might expect to see cosmic evolution of the radio source population, only the most luminous objects in our sample can be seen to these distances, and hence we can test for evolutionary effects only over a narrow range in luminosity. There are already hints that we are seeing evolution in the most powerful AGN in our sample –Table 9 shows the mean values of graphic for AGN and star-forming galaxies split into bins in radio luminosity. For AGN with graphic, graphic is significantly higher than the expected value of 0.50, implying that the space density of these objects is higher at higher redshift.

Table 9.

Values of from RLF calculations split into bins in radio power

Table 9.

Values of from RLF calculations split into bins in radio power

Because the number of objects which we can use to probe evolutionary effects is small, we defer discussion of the RLF evolution to a later paper in this series, which will analyse the full set of 2dFGRS data.

Discussion and conclusions

Main results

We have shown how combining data from large radio continuum and optical redshift surveys allows us to derive accurate local radio luminosity functions (RLFs) for AGN and star-forming (SF) galaxies. Both AGN and star-forming galaxies are significant contributors to the local RLF below 1024WHz−1 (at higher radio powers, almost all the sources are AGN), so good-quality optical spectra are needed to classify the radio sources correctly.

This paper establishes an accurate local benchmark for future studies of the cosmic evolution of both AGN and star-forming galaxies at higher redshift. The full data set of ∼4000 radio source spectra, which will become available when the 2dFGRS is completed, should be large enough to measure the evolution of radio galaxies to graphic and the most luminous star-forming galaxies to graphic.

2dFGRS radio-source populations needing further investigation

We showed in Section 6 that there may be a substantial local population of radio-luminous star-forming galaxies (with implied star formation rates of 50Myr−1 or more) which are not seen in Hα emission-line surveys. Determining whether these ‘high-SFR’ galaxies are dust-enshrouded starbursts or misclassified AGN is important if we are to have an accurate census of star formation in the local Universe (if they are indeed starbursts, the ‘high-SFR galaxies’ contribute about 20 per cent of the local star formation density). High-resolution radio imaging, together with infrared spectroscopy, should allow us to determine whether the radio emission seen by NVSS arises mainly from dusty star-forming regions.

Optical spectra of the remaining NVSS/ROSAT sources in the 2dFGRS area (see Section 7) would be valuable in determining whether some radio AGN have been excluded from the 2dFGRS because they have a bright nucleus which leads to them being classified as stars rather than galaxies on sky-survey plates. We estimate that no more than five or six potential members of the current sample have been excluded in this way, but it would be useful to confirm this.

Prospects for deeper radio and optical observations in the 2dFGRS area

Since the overlap between 2dFGRS galaxies and NVSS radio sources is relatively small – about 5 per cent of NVSS radio sources in the 2dFGRS area are associated with 2dFGRS galaxies, and graphic per cent of 2dFGRS galaxies are detected by NVSS – it is tempting to speculate on what could be achieved with deeper radio and optical observations in the 2dFGRS area.

Radio observations to sub-mJy sensitivities at 1.4GHz would increase the detection rate for galaxies in the 2dFGRS sample, particularly for star-forming galaxies since many of these lie close to the 2.8-mJy NVSS detection limit (see Section 3.4). For example, observations with a 3σ detection limit of 0.4mJy at 1.4GHz could detect galaxies with a star formation rate of ∼17Myr−1 at graphic, which is significantly lower than the limit of ∼120Myr−1 at the same redshift for galaxies near the NVSS detection limit of 2.8mJy.

About 30 per cent of all NVSS radio sources have an optical counterpart visible on the digitized sky survey (i.e., brighter than graphic. Deep 2dF spectroscopy should be possible to graphic (and even fainter for emission-line objects) with integration times of graphic rather than the graphic used by the 2dFGRS, and careful attention to sky-subtraction techniques (Cannon 2001). This would allow spectroscopy of the host galaxies of powerful AGN (and hence studies of their cosmic evolution) to redshifts of graphic rather than the graphic limit of the 2dFGRS.

Implications for deep radio surveys to μJy levels

Fig. 20 shows the local RLFs for SF galaxies and AGN over the whole range in radio power for which data are currently available. The two RLFs cross over (i.e., AGN and SF galaxies contribute equally to the local radio source population) at graphicgraphic. Both AGN and SF galaxies contribute at least 20 per cent of the radio source population over the range graphic.

Figure 20.

Local radio luminosity functions for AGN and star-forming galaxies, combining 2dFGRS data with nearby RSA spirals (SF) from Condon (1989) and nearby E/S0 galaxies (AGN) from Sadler et al. (1989). Note that both AGN and SF galaxies contribute significantly at all radio powers below ∼1025WHz−1 at 1.4GHz.

Figure 20.

Local radio luminosity functions for AGN and star-forming galaxies, combining 2dFGRS data with nearby RSA spirals (SF) from Condon (1989) and nearby E/S0 galaxies (AGN) from Sadler et al. (1989). Note that both AGN and SF galaxies contribute significantly at all radio powers below ∼1025WHz−1 at 1.4GHz.

Fig. 21 shows the radio luminosity range probed at different redshifts by 1.4-GHz surveys with flux density limits of 2.8mJy (NVSS), 100μJy (e.g. Gruppioni at al. 1997; Hopkins et al. 1998) and 20μJy (e.g. Haarsma et al. 2000). Extrapolating from the local RLF suggests that all μJy-level radio surveys should find a mixture of AGN and SF galaxies at all redshifts, i.e., there is no observational regime in which we can simply assume that a faint radio source arises from a starburst. Deep radio continuum surveys in the Hubble Deep Field (Richards et al. 1998; Garrett et al. 2000) suggest that the μJy radio source population is composed of a mixture of graphic per cent spiral and irregular/merging galaxies and graphic per cent ellipticals.

Figure 21.

Radio luminosity limits at high redshift for NVSS (2.8-mJy limit) and deeper 1.4GHz surveys (100- and 20-μJy limits). The vertical line at graphic marks the effective redshift limit of the 2dFGRS. Note that at graphic, the deepest surveys so far carried out detect galaxies with radio luminosities above about 1023WHz−1, i.e., in the regime where we expect a mixture of AGN and star-forming galaxies.

Figure 21.

Radio luminosity limits at high redshift for NVSS (2.8-mJy limit) and deeper 1.4GHz surveys (100- and 20-μJy limits). The vertical line at graphic marks the effective redshift limit of the 2dFGRS. Note that at graphic, the deepest surveys so far carried out detect galaxies with radio luminosities above about 1023WHz−1, i.e., in the regime where we expect a mixture of AGN and star-forming galaxies.

A mixture of SF galaxies and AGN is probably present even at flux densities below 1μJy –Hopkins et al. (2000) remark that in their simulations of the faint radio source population to a flux density limit of 0.1μJy, the proportion of AGN is still significant. If this is true, then optical/IR spectroscopy will play a key role in disentangling the faint radio source population probed by future deep radio surveys, and partnerships between radio and optical telescopes in mapping out the distant Universe will increase in importance in the years to come.

Acknowledgments

The 2dF Galaxy Redshift Survey was made possible through the dedicated efforts of the staff of the Anglo-Australian Observatory, both in creating the 2dF instrument and in supporting it on the telescope. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, Caltech, under contract with NASA. We thank Professor Lawrence Cram for helpful conversations about the derivation of star formation rates from radio data, and the referee, Dr I. Snellen, for several perceptive comments which improved the final version of this paper.

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