Kiloparsec-scale radio emission in Seyfert and LINER galaxies Free

Abstract

Seyfert and LINER galaxies are known to exhibit compact radio emission on ∼10–100 pc scales, but larger Kiloparsec-Scale Radio structures (KSRs) often remain undetected in sub-arcsec high-resolution observations. We investigate the prevalence and nature of KSRs in Seyfert and LINER galaxies using the 1.4 GHz VLA FIRST and NVSS observations. Our sample consists of 2651 sources detected in FIRST and of these 1737 sources also have NVSS counterparts. Considering the ratio of total to peak flux density (θ = (S_int/S_peak)^1/2) as a parameter to infer the presence of extended radio emission we show that ≥30 per cent of FIRST-detected sources possess extended radio structures on scales larger than 1.0 kpc. The use of low-resolution NVSS observations help us to recover faint extended KSRs that are resolved out in FIRST observations and results in ≥42.5 per cent KSR sources in FIRST–NVSS sub-sample. This fraction is only a lower limit owing to the combination of projection, resolution and sensitivity effects. Our study demonstrates that KSRs may be more common than previously thought and are found across all redshifts, luminosities and radio loudness. The extranuclear radio luminosity of KSR sources is found to be positively correlated with the core radio luminosity as well as the [O iii] λ5007 Å line luminosity and this can be interpreted as KSRs being powered by AGN rather than star formation. The distributions of the FIR-to-radio ratios and mid-IR colours of KSR sources are also consistent with their AGN origin. However, contribution from star formation cannot be ruled out particularly in sources with low radio luminosities.

1 INTRODUCTION

Active Galactic Nuclei (AGN) are classified into radio-loud and radio-quiet sub-classes based on the ratio of 5 GHz radio flux density to 4400 Å optical continuum flux (R = |$\frac{{{\nu }_{\rm 5\, GHz}}{\rm {\it S}_{\rm 5\, GHz}}}{{\nu }_{\rm 4400\ {\mathring A}}{\rm {\it S}_{\rm 4400\, \mathring A}}}$|⁠) with R ≥ 10 for radio-loud AGN and R < 10 for radio-quiet AGN (Kellermann et al. 1989). This dichotomy may also be manifested in radio morphologies as radio-loud AGN exhibit bipolar jets terminating into radio lobes with total end-to-end size spanning up to few hundred kiloparsec to even few Megaparsec. While, radio-quiet AGN often display compact nuclear radio emission with occasional presence of extended radio emission limited to ≤10 kpc scale. Seyfert and Low-Ionization Nuclear Emission Region (LINER) galaxies are classified as radio-quiet AGN with low optical luminosity (M_B-band > −22.25 assuming H₀ = 71 km s⁻¹ Mpc⁻¹; Schmidt & Green 1983). High-resolution radio observations show that most of the Seyfert galaxies possess compact sub-parsec scale nuclear emission with brightness temperature ≥10⁷ K (Thean et al. 2000; Lal, Shastri & Gabuzda 2004; Middelberg et al. 2004). However, radio observations of arcsec resolution have revealed resolved structures, with hints of jets and extended emission in several Seyfert galaxies (Baum et al. 1993; Colbert et al. 1996; Morganti et al. 1999; Gallimore et al. 2006). This is further supported by the examples of few individual Seyfert galaxies that exhibit radio morphology consisting of a core, collimated jets and lobes similar to those found in radio-loud AGN (e.g. NGC 1052 – Wrobel 1984; NGC 1068 – Ulvestad, Neff & Wilson 1987; NGC 7674 – Momjian et al. 2003; MRK 3 – Kukula et al. 1999; MRK 6 – Kharb et al. 2006), although unlike radio-loud AGN the linear radio structures in Seyfert galaxies span only up to few kiloparsec. Also, Kpc-Scale Radio structures (KSRs) in Seyfert galaxies are not always found to be aligned with the pc-scale jet-like structures (Colbert et al. 1996; Kharb et al. 2006, 2010). It is believed that the low-power radio jets seen in Seyfert galaxies are analogous to the larger jets seen in radio galaxies but perhaps distorted or stunted by the interaction with the surrounding interstellar medium (ISM) of the host galaxy (Whittle & Wilson 2004; Gallimore et al. 2006). Overall it appears that the radio structures in Seyfert galaxies are much more complex than in powerful radio-loud AGN.

It is important to note that most of the radio studies of Seyfert/LINER samples have been carried out mainly at higher frequencies with long-baseline interferometers (e.g. VLA A-array, multi-element radio-linked interferometer network, very large baseline array) that filter out low-surface-brightness emission distributed over larger angular scales (e.g. Ulvestad & Wilson 1989; Kukula et al. 1995; Thean et al. 2000; Ho & Ulvestad 2001; Lal et al. 2004; Nagar, Falcke & Wilson 2005; Panessa & Giroletti 2013). Therefore, high-resolution observations are likely to miss the detection of KSRs. Indeed, in some Seyfert galaxies, the radio flux density arising from their parsec-scale structure is found to be much lower than that derived from observations with lower resolution, even if the nucleus appears unresolved. The missing flux has been interpreted as due to the presence of KSRs of low surface brightness (Sadler et al. 1995; Orienti & Prieto 2010). In fact, sensitive radio observations of arcsec resolution have suggested that there may be a large fraction of Seyferts with KSRs (e.g. Baum et al. 1993; Kukula et al. 1996; Gallimore et al. 2006). Using deep VLA (Very Large Array) ‘D’ array observations (∼15–20 arcsec resolution at 5 GHz with average rms ∼50 μJy) Gallimore et al. (2006) showed that ≥44 per cent sources in their sample of 43 Seyfert and LINER galaxies exhibit extended radio structures at least 1 kpc in total extent that do not match the morphology of the disc or its associated star-forming regions. This favours a scenario in which KSRs are likely to be an extension of the nuclear radio jet and therefore related to AGN activity. However, starburst galaxies (e.g. M82 – Seaquist & Odegard 1991; NGC 253 – Carilli et al. 1992) are also known to display KSRs probably originating from a superwind generated by the cumulative effects of stellar winds. These results raise questions whether KSRs are truly so common in Seyfert and LINER galaxies and whether they are related to the AGN or starburst. We note that all the previous studies on KSRs are limited to targeted observations of fairly small samples despite the availability of large Seyfert/LINER samples. In order to detect and examine the prevalence and nature of KSRs in Seyfert and LINER galaxies, we study radio emission properties in a large sample of ∼2651 sources using 1.4 GHz VLA FIRST (‘Faint Images of the Radio Sky at Twenty-cm’) and NVSS (‘NRAO VLA Sky Survey’) radio surveys. Our sample of Seyfert and LINER galaxies is derived from the 13th edition AGN catalogue of Véron-Cetty & Véron (2010) and is the largest sample of Seyfert and LINER galaxies hitherto used for KSRs studies.

This paper is organized as follows. In Section 2, we discuss our sample selection and its merits. The details on the radio data are given in Section 3 and the identification of FIRST and NVSS radio counterparts is discussed in Section 4. The methods of using flux densities to ascertain the presence of extended emission are discussed in Section 5. A brief discussion on the sources with multicomponent radio structures is presented in Section 6. Section 7 is devoted to the discussion on the origin of KSRs. The conclusions of our study are given in Section 8.

In this paper we have assumed H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_M = 0.27, Ω_Λ = 0.73.

2 THE SAMPLE

Our sample of Seyfert and LINER galaxies is derived from the 13th edition AGN catalogue of Véron-Cetty & Véron (2010, hereafter VV10) which is the most updated complete survey of the literature and lists all the quasars, BL Lacs, active galaxies known to the catalogue authors prior to 2009 July 1. The VV10 catalogue follows conventional definition of Seyfert and LINER galaxies that are defined as AGN of low optical luminosity with absolute B-band magnitude fainter than −22.25 (i.e. M_B > −22.25; Schmidt & Green 1983). The use of Hubble parameter H₀ = 71 km s⁻¹ Mpc⁻¹ instead of 50 km s⁻¹ Mpc⁻¹ has changed the optical luminosity limit to M_B = −22.25 rather than M_B = −23.0 considered in some early studies. The VV10 catalogue contains total 34 231 Low-Luminosity AGN (LLAGN) with M_B > −22.25. To select our sample of Seyfert and LINER galaxies, we have taken only those sources that have confirmed Seyfert or LINER classification in the VV10 catalogue and excluded sources without classification or with uncertain classification. We refer Seyfert and LINER galaxies collectively as ‘LLAGN’. We obtain a sample of 23 448 LLAGN that contains 16 517 Seyfert 1s (designated as ‘S1’), 6024 Seyfert 2s (designated as ‘S2’) and 907 LINERs (designated as ‘S3’). In our sample, we have grouped intermediate Seyferts (i.e. types 1.0, 1.2, 1.5, 1.8 and 1.9) into Seyfert type 1s noting the fact that intermediate Seyferts are classified based on the appearance of broad permitted Balmer lines which are characteristics of type 1s (Osterbrock 1981). Narrow line Seyfert galaxies (designated as ‘S1n’) and Seyfert galaxies with broad permitted lines detected in infrared wavelengths (designated as ‘S1i’) or in polarized light (designated as ‘S1h’) are also included in Seyfert type 1s.

Table 1 lists the number of Seyferts and LINERs extracted from the VV10 catalogue and their detections in FIRST and NVSS radio surveys. Fig. 1 shows the redshift distributions of all Seyfert and LINER galaxies detected in FIRST survey. The FIRST-detected LLAGN have median redshift (z_median) ∼0.15, with 98.7 per cent at z ≤ 1.0. In comparison to Seyfert galaxies, LINERs are seen at lower redshifts with median redshift (z_median) ∼0.048. The FIRST-detected Seyfert type 1s and type 2s have similar redshift distributions with median redshifts ∼0.158 and ∼0.162, respectively. Two sample Kolmogorov–Smirnov test shows that the redshift distributions of Seyfert 1s and Seyfert 2s are similar (D ∼ 0.05) with probability of null hypothesis that the two samples are drawn from two different parent population is only 0.095. Since our final sample consists of FIRST-detected sources (i.e. radio selected) and radio emission is optically thin to dust obscuration, therefore, our sample is unaffected by the biases introduced by obscuration caused by dusty torus present around AGN. This is evident from the comparison of redshift distributions of Seyfert type 1s and type 2s. In general, optically selected Seyfert samples are known to be biased against Seyfert type 2s as AGN view is intercepted by the circumnuclear obscuring torus (Ho & Ulvestad 2001).

3 RADIO DATA

We use the FIRST¹ survey carried out at 1.4 GHz by VLA in its ‘B’ configuration and it covers sky region over 10 000 deg² of the North and South Galactic Caps (Becker, White & Helfand 1995). The FIRST radio maps have resolution of ∼5 arcsec and typical rms down to ∼0.15 mJy. We have used most recent version of FIRST source catalogue (released on March 2014) that lists peak as well as integrated flux densities and radio sizes derived by fitting a two-dimensional Gaussian to a source detected at a flux limit of ∼1.0 mJy (SNR ≥ 5.0). The astrometric reference frame of FIRST maps is accurate to ∼0.05 arcsec and individual sources have ∼90 per cent confidence error circles of radius < 0.5 arcsec at the 3 mJy level and ∼1 arcsec at the survey threshold.

In order to detect faint kpc-scale extend radio emission, we also use the NVSS² which is a 1.4 GHz continuum survey carried out by VLA in its ‘D’ configuration. NVSS covers the entire sky north of −40 deg declination and produces radio images with resolution of ∼45 arcsec and sensitivity of ∼2.4 mJy at 5σ level (Condon et al. 1998). NVSS observations of low resolution are advantageous in detecting low-surface-brightness KSRs that are resolved out, and therefore, missed by higher resolution FIRST observations. We use the NVSS catalogue which contains over 1.8 million unique detections brighter than 2.5 mJy and give total integrated 1.4 GHz flux densities of all the radio sources. The astrometric accuracy ranges from ∼1.0 arcsec for the brightest NVSS detections to about ∼7.0 arcsec for the faintest detections.

4 FIRST AND NVSS RADIO COUNTERPARTS

4.1 FIRST counterparts of Seyfert and LINER galaxies

To find the radio counterparts of Seyfert and LINER galaxies in FIRST survey, we searched for FIRST detection around the optical positions of sources. The accurate astrometry of FIRST and optical positions of LLAGN allows us to use a simple positional matching with high completeness and low contamination. The source positions in the FIRST as well as in the VV10 catalogue are measured with an accuracy better than one arcsec (Becker et al. 1995; VV10). The choice of matching radius between the optical and radio positions is a trade-off between the completeness and contamination, i.e. a smaller matching radius greatly reduces the contamination at the expense of completeness. In order to choose an optimum matching radius, we cross-matched our LLAGN to the FIRST sources using a large matching radius of 30 arcsec and plotted the histogram of the separation between the LLAGN optical position and FIRST radio position for all the cross-match sources. We find that the histogram follows nearly a Gaussian distribution between 0 and 3.0 arcsec and a flat tail onwards (see Fig. 2). Therefore, based on the histogram of the separation between LLAGN optical positions and FIRST radio positions, we choose matching radius to be 3.0 arcsec. Previous studies on the cross-matching between Seyfert galaxies and the FIRST sources have also reported 3.0 arcsec as a reliable limit with negligible probability (<0.05 per cent) of being merely a chance match (see Wadadekar 2004).

The cross-matching of our LLAGN sample sources and the FIRST sources using a matching radius of 3.0 arcsec results in 2651 sources. Table 1 lists the number of Seyfert type 1s, Seyfert type 2s and LINER galaxies detected in FIRST. Before cross-matching LLAGN and FIRST sources we corrected for systematic offset between optical and radio catalogues (i.e. ΔRA = RA_LLAGN − RA_FIRST = −0.025 arcsec and ΔDec = Dec_LLAGN − Dec_FIRST = −0.31 arcsec). Also, in cross-matching we considered only those FIRST sources that have sidelobe probability ≤0.1 (i.e. there is 90 per cent probability that the FIRST source is real). To check the level of contamination by chance matching in our cross-matched sample, we shifted the optical positions of our LLAGN by 30–45 arcsec in random directions and find only 0.3 per cent cross-matched sources. This shows that the contamination due to chance matching in our cross-matched sample is negligible.

To find extended radio sources with multicomponents, we searched for radio components around all the 2651 FIRST-detected LLAGN using a large search radius of 120 arcsec. We made visual inspection of the FIRST cut-out images of all the sources that show one or more radio components within 120 arcsec around the central core radio component. We exclude radio components that are completely unrelated to the source. This exercise resulted is a total of 180 out of 2651 LLAGN that having multicomponents detected in the FIRST survey. To get the total flux density of a source with multicomponents, we add up integrated flux densities of all the components. We note that, in general, extended radio morphologies of Seyfert and LINER galaxies are more complex and diverse than core-jet-lobe morphology seen in radio galaxies. Therefore, to search for extended sources with multicomponents, it is not possible to opt for a single criterion that are often being used for quasars, i.e. two radio sources are located nearly symmetrically around the quasar position and the ratio of their distances to the quasar is ‘1/3 < d1/d2 < 3’ (de Vries, Becker & White 2006). In fact, even for quasars with more complex radio morphologies (i.e. sources with distorted asymmetric lobes and a compact core, or for cases in which extended lobes are resolved into complex structure), the visual inspection needs to be used (see Lu et al. 2007).

4.2 NVSS counterparts of FIRST-detected Seyfert and LINER galaxies

To find the NVSS counterparts of FIRST-detected LLAGN, we use a search radius of 20 arcsec for all the sources that show only a single component in the FIRST. The histogram of the separation between FIRST and NVSS positions of cross-matched sources tails off beyond 20 arcsec (see Fig. 3). Using a matching radius larger than 20 arcsec (e.g. 30–45 arcsec) gives only 1–2 per cent increase in the number of cross-matched sources which is comparable to the level of chance matching. Thus, we chose optimum matching radius to 20 arcsec at which chance matching is only 0.9 per cent (i.e. with FIRST source density ∼90 deg⁻²). For extended sources with multicomponents in FIRST, we use matching radius equal to the separation between two farthest components and obtain NVSS counterparts of all such sources. We made visual inspection of FIRST and NVSS image cut-outs to ensure reliable cross-matching. The cross-matching between our FIRST-detected LLAGN and NVSS catalogue yields NVSS counterparts for 1737 out of 2651 sources (i.e. 65.5 per cent). Most of FIRST-detected LLAGN that remained undetected in NVSS fall below the NVSS flux limit, i.e. 2.5 mJy. Table in the appendix lists the FIRST and NVSS parameters of our sample sources.

5 FLUX DENSITY RATIO DIAGNOSTIC TO IDENTIFY EXTENDED RADIO EMISSION

We can classify a radio source as unresolved or resolved by defining a dimensionless concentration parameter θ = |${\rm (\it {S}_{\rm int}/{\it S}_{\rm peak})^{1/2}}$| (Ivezic et al. 2002). Using the distribution of radio sources in the two-dimensional plot of θ versus extended flux density, Kimball & Ivezić (2008) proposed that FIRST radio sources can be categorized as ‘unresolved’ and ‘resolved’ by defining θ = |${\rm ({\it S}_{\rm int, FIRST}/{\it S}_{\rm peak, FIRST})^{1/2}}$| ≃ 1.06 as a separating value. Therefore, we use the parameter θ = |${\rm (\it {S}_{\rm int}/{\it S}_{\rm peak})^{1/2}}$| (square root of the ratio of integrated to peak flux density of FIRST) to infer the presence of extended radio emission at scale larger than the FIRST beam-size of ∼5 arcsec.

Furthermore, FIRST is a relatively high-resolution radio survey, and therefore, underestimates the flux of extended and lobe-dominated sources (Becker et al. 1995; Lu et al. 2007). Also, multiple-component radio sources with core and lobes are often detected as separate objects by FIRST but as only a single object in the lower resolution NVSS observations at same wavelength. Therefore, the ratio between the NVSS and FIRST flux densities can be used as a diagnostic measure of the presence of faint extended radio emission that is missed by FIRST. Kimball & Ivezić (2008) showed that the distribution of the difference of FIRST and NVSS radio magnitudes Δt = t_FIRST − t_NVSS is bimodal with two peaks centred at Δt = 0 and 0.7, where radio magnitude is defined as t = −2.5 log(⁠|$\frac{\rm \it {S}_{\rm int}}{\rm 3631\,Jy}$|⁠). The visual inspection of thousand of FIRST images confirmed that sources at the Δt = 0 locus are single component sources, while those in the Δt = 0.7 locus are multiple-component or extended. By fitting the bimodal distribution of Δt with two Gaussians Kimball & Ivezić (2008) proposed that Δt = t_FIRST − t_NVSS ≃ 0.35 can be used as a separating value between ‘simple’ (Δt < 0.35) and ‘complex’ (Δt > 0.35) radio morphologies. In terms of flux density ratio, the difference in FIRST and NVSS radio magnitude Δt = 0.35 corresponds to |$\frac{ S_{\rm int, NVSS}}{ {\it S}_{\rm int, FIRST}}$| ≃ 1.38. Hence, we define a parameter |${\theta }_{\rm NVSS\text{--}FIRST}$| = |${\rm ({\it S}_{\rm NVSS, int}/{\it S}_{\rm FIRST, int})^{1/2}}$| with separating value |${\theta }_{\rm NVSS\text{--}FIRST}$| = 1.175 (i.e. corresponding Δt = 0.35) to classify radio sources into ‘simple’ (⁠|${\theta }_{\rm NVSS\text{--}FIRST}$| ≤ 1.175) and ‘complex’ (⁠|${\theta }_{\rm NVSS\text{--}FIRST}$| > 1.175) radio morphology categories.

Therefore, using FIRST and NVSS flux densities we can divide radio sources into following classes.

• ‘Unresolved’ point sources in FIRST with ‘simple’ radio morphology inferred from FIRST–NVSS flux density comparison. These sources can be characterized with θ_FIRST ≤ 1.06 and |${\theta }_{\rm NVSS\text{--}FIRST}$| ≤ 1.175.

• ‘Unresolved’ sources in FIRST but with ‘complex’ radio morphology inferred from FIRST–NVSS flux density comparison. These sources can be characterized with θ_FIRST ≤ 1.06 and |${\theta }_{\rm NVSS\text{--}FIRST}$| > 1.175. These sources possess extended low-surface-brightness radio emission that is resolved out in FIRST but detected in NVSS due to larger beam-size.

• ‘Resolved’ sources in FIRST but ‘simple’ radio morphology inferred from FIRST–NVSS flux density comparison. These sources can be characterized with θ_FIRST > 1.06 and |${\theta }_{\rm NVSS\text{--}FIRST}$| ≤ 1.175. These sources do have extended radio emission detected in FIRST but there is no significant additional flux detected by NVSS.

• ‘Resolved’ sources in FIRST and ‘complex’ radio morphology inferred from FIRST–NVSS comparison. These sources can be characterized with θ_FIRST > 1.06 and |${\theta }_{\rm NVSS\text{--}FIRST}$| > 1.175. These sources do have extended radio emission detected in FIRST and also have additional faint low-surface-brightness radio emission component detected in NVSS.

In interpreting the results based on the flux density ratios, we should keep the caveat in mind that FIRST has higher sensitivity than NVSS. Table 2 lists the number and fraction of Seyferts/LINER galaxies with unresolved/resolved and simple/complex radio morphologies.

5.1 Comparison of total to peak flux densities in FIRST

Fig. 4 (left-hand panel) shows the distribution of FIRST total flux density (S_int,FIRST) versus θ_FIRST = (S_int,FIRST/S_peak,FIRST)^1/2. It is evident that resolved sources with extended radio emission larger than 5 arcsec (i.e. θ_FIRST > 1.06) are present across all flux densities. Although, sources with high ratios of total-to-peak flux densities are found only in radio-bright LLAGN. For example, sources with θ_FIRST > 2.0 (i.e. S_int higher than 4 times of S_peak) are found only at S_int ≥ 5.0 mJy. The comparison of FIRST total to peak density (θ_FIRST) shows that 827/2615 ∼31.2 per cent sources possess extended radio emission on scales larger than 5 arcsec (see Table 2). We note that the resolved sources with extended radio emission (θ_FIRST > 1.06) are distributed across all redshifts spanning over 0.002–2.26 with median redshift ∼0.136 (Fig. 4, right-hand panel). There are 794/2651 ∼30 per cent sources with redshift (z) ≥ 0.01, where 5 arcsec angular size corresponds to ≥1.0 kpc. Therefore, we infer that 30 per cent FIRST-detected LLAGN possess KSRs, i.e. radio emitting structures larger than 1.0 kpc. This is only a lower limit as sources with radio structures of ≥1.0 kpc would appear unresolved at higher redshifts (z ≥ 0.01). Also, LLAGN with AGN jet lying close to the line of sight (in type 1s) would have much smaller projected size and therefore, would appear as unresolved despite possessing extended radio emission.

5.2 Comparison of NVSS and FIRST flux densities

The faint extended low-surface-brightness radio emission that is resolved out in FIRST observations can be detected in NVSS due to its much larger 45 arcsec beam. Therefore, we also compare NVSS and FIRST total flux densities by defining a parameter |${\theta }_{\rm NVSS\text{--}FIRST}$| = |${\rm ({\it S}_{\rm int, NVSS}/{\it S}_{\rm int, FIRST})^{1/2}}$| which is used to infer the radio morphologies of our sample sources. Fig. 5 (left-hand panel) shows the distribution of FIRST total flux density (S_int,FIRST) versus |${\theta }_{\rm NVSS\text{--}FIRST}$| = |${\rm ({\it S}_{\rm int, NVSS}/{\it S}_{\rm int, FIRST})^{1/2}}$|⁠. It is clear that sources characterized with complex morphology (i.e. |${\theta }_{\rm NVSS\text{--}FIRST}$| > 1.75) are present in radio-faint as well as in radio-bright LLAGN. However, there is no additional NVSS flux density detected in very bright radio sources, i.e. S_int,FIRST ≥ 100 mJy. Table 2 lists the number and fraction of LLAGN that possess additional flux density detected in NVSS but missed out in FIRST. We note that the extra flux detected in NVSS is present in resolved as well as unresolved FIRST sources. The comparison of NVSS and FIRST flux densities reveals the presence of complex radio morphology (i.e. |${\theta }_{\rm NVSS\text{--}FIRST}$| > 1.75) in ∼17 per cent of FIRST–NVSS-detected sources. Interestingly, there are ∼11 per cent FIRST–NVSS-detected LLAGN in which FIRST detects only unresolved compact emission (θ_FIRST < 1.06) while NVSS picks up additional flux density (θ_FIRST > 1.175). Thus, in ∼11 per cent of sources, the comparison of NVSS and FIRST flux densities helps to recover low-surface-brightness extended radio emission that is missed in FIRST observations. Total fraction of sources with extended radio emission identified either via FIRST (θ_FIRST) or via NVSS (⁠|${\theta }_{\rm NVSS\text{--}FIRST}$|⁠) flux diagnostics is as high as ∼45 per cent among the FIRST–NVSS-detected LLAGN (see Table 2). The |${\theta }_{\rm NVSS\text{--}FIRST}$| versus redshift (z) plot (see Fig. 5; right-hand panel) shows that complex sources are present across all redshifts. Among the FIRST–NVSS-detected LLAGN there are 911/1737 ∼42 per cent resolved/complex sources lying at redshift z ≥ 0.01 and thus possess KSRs (i.e. 5 arcsec angular scale corresponds to 1.0 kpc at z ≥ 0.01). We note that this fraction is only a lower limit as it is possible that in sources of bright compact component with very faint extended emission, the total flux is primarily due to the brighter compact component, thus, resulting |${\theta }_{\rm NVSS\text{--}FIRST}$| = |${\rm ({\it S}_{\rm int, NVSS}/{\it S}_{\rm int, FIRST})^{1/2}}$| ≤ 1.06 with source being classified as compact.

Fig. 6 shows θ_FIRST versus |${\theta }_{\rm NVSS\text{--}FIRST}$| plot. This plot does not show any systematic trend suggesting that there are wide variety of radio sources, i.e. (i) unresolved sources in both FIRST and NVSS, (ii) unresolved sources in FIRST but extended emission detected in NVSS, (iii) resolved sources in FIRST with no extra flux density in NVSS and (iv) resolved sources in FIRST with additional flux density detected in NVSS. Indeed, this is also evident from Table 2 that lists the fraction of sources with different radio morphologies.

Table 3 shows the comparison of the fraction of KSR sources in our sample and previous studies. It evident that high-resolution radio observations carried out at higher frequencies miss the detection of KSRs. While low-frequency observations with relatively lower resolution can efficiently detect kpc-scale radio emission of low surface brightness. Noting the importance of low-frequency observations with relatively low resolution in detecting KSRs, we have carried out 325 and 610 MHz Giant Metrewave Radio Telescope (GMRT) observations of a carefully chosen sample of Seyfert galaxies (e.g. Kharb et al. 2014b). Our investigation on faint KSRs using low-frequency GMRT observations is expected to conclude soon (Singh et al., in preparation).

6 LLAGN WITH MULTICOMPONENT RADIO EMISSION DETECTED IN FIRST

There are a total of 180 Seyfert and LINER galaxies in our sample that display multicomponent radio emission in FIRST observations. These sources have more than one component wherein each component is fitted with an elliptical Gaussian. In Fig. 7, we show FIRST and NVSS contours overplotted on the DSS optical images for three sources (i.e. NGC 4636, NGC 5033 and NGC 7479) that display extended multicomponent radio emission.

• FIRST observations of NGC 4636, a LINER galaxy at redshift (z) ∼0.003, show an S-shaped radio structure with projected size of ∼2.48 kpc (∼40 arcsec) along Position Angle (PA) ∼40° (see Fig. 7, left-hand panel). There is another radio component located at the distance of ∼34 arcsec to the west of the central component. The jet-like radio structure accompanied by a strong ridge of radio emission displaying an S-shaped structure of ∼5.0 kpc has been reported in previous observations (see Birkinshaw & Davies 1985). The linear jet-like radio structure lies nearly along the minor axis of host galaxy (Stanger & Warwick 1986).

• The FIRST image of NGC 5033, a Seyfert type 1.8 galaxy at redshift (z) ∼0.003, shows a central radio component accompanied by a diffuse extended radio structures with projected size of ∼3.6 kpc (∼60 arcsec) along PA ∼135° (see Fig. 7, middle panel). The diffuse extended radio emission appears to align with the host galaxy major axis. This source possesses a complex radio structure with a slightly resolved core surrounded by a diffuse envelope of radio structure of ∼10 arcsec (0.9 kpc), roughly along the east–west direction (Nagar et al. 2002). The tapered maps have shown the ridge of emission spanning over ∼3.6 kpc in north–south direction along the galaxy major axis.

• NGC 7479, a Seyfert 1.9 galaxy at redshift (z) 0.0079, exhibits a curve-shaped extended emission along the north direction and a weaker southern component. The total extension of north–south component is ∼9.2 kpc (56 arcsec). Beck et al. (2002) reported that NGC 7479 has strong polarized radio emission, mainly due to the nuclear jet.

The detailed study of the radio structures in all our sample LLAGN with multicomponent radio emission will be presented in our next paper. The FIRST images of three sources presented here show that KSRs in Seyferts and LINERs exhibit varying morphologies e.g. linear, S-shaped, diffuse. This is consistent with previous studies based on more sensitive targeted radio observations of small Seyfert samples (e.g. Ulvestad & Wilson 1989; Baum et al. 1993; Kukula et al. 1993; Colbert et al. 1996; Gallimore et al. 2006).

7 NATURE OF KPC-SCALE RADIO EMISSION

We attempt to investigate the nature and origin of KSRs detected in Seyfert and LINER galaxies of our sample. We study radio-luminosity distributions, radio-loudness parameters, the dependence of KSRs radio power on the AGN power, ratios of radio-to-FIR fluxes and mid-IR colours to derive the statistical inferences about the origin of KSRs.

7.1 Radio luminosities

Fig. 8 shows the radio-luminosity distributions of unresolved and resolved sample sources detected in FIRST. It is evident that the luminosity distribution for unresolved sources can be represented by a normal distribution, while radio-luminosity distribution of resolved sources is skewed towards higher radio luminosity. Although, both unresolved sources (θ_FIRST ≤ 1.06) and resolved sources (θ_FIRST > 1.06) have similar median radio-luminosity values ∼2.25 × 10²³ and ∼1.98 × 10²³ W Hz⁻¹, respectively. The skewed distribution of resolved sources indicates that the resolved source population is relatively more dominant at higher radio luminosities.

To examine if the occurrence of KSRs is related to the total radio luminosity of a source, we plot extended emission parameters θ_FIRST and |${\theta }_{\rm NVSS\text{--}FIRST}$| versus 1.4 GHz FIRST total radio luminosity (L_int,FIRST). Fig. 9 shows the plots of θ_FIRST versus L_int,FIRST (left-hand panel), and |${\theta }_{\rm NVSS\text{--}FIRST}$| versus L_int,FIRST (right-hand panel). We note that resolved and complex sources (i.e. sources with θ_FIRST > 1.06 and |${\theta }_{\rm NVSS\text{--}FIRST}$| > 1.175) are present across all luminosities ranging from ∼10¹⁹ to ∼10²⁹ W Hz⁻¹. This shows that KSRs are found in sources of low as well as high radio luminosities. We further note that a small fraction (90/827 ∼11 per cent) of KSR sources characterized with high θ_FIRST (>2) are preferentially found at high radio luminosities, i.e. L_1.4 GHz > 10²⁴ W Hz⁻¹. The high radio luminosities (L_1.4 GHz) ∼10²⁴–10²⁸ W Hz⁻¹ of these sources imply that they are radio-loud AGN wherein L_1.4 GHz ∼10^24.5 W Hz⁻¹ can be considered as the dividing line between FR I and FR II radio galaxies (Fanaroff & Riley 1974; Rafter, Crenshaw & Wiita 2011). Sources with θ_FIRST > 2 means that extranuclear flux density is three times of the peak flux density which in turn makes them extended-emission-dominated radio sources. Indeed, several optically classified Seyfert galaxies are known to be radio-loud AGN with lobe-dominated KSRs (see Doi et al. 2012). Moreover, we note that the sources of high radio luminosities (L_1.4 GHz > 10²⁴ W Hz⁻¹) may have radio galaxy contaminants that are either incorrectly classified as Seyfert galaxies or there seems to be a population of sources that can be classified as radio galaxies based on its radio properties but optical properties are similar to Seyfert galaxies. In general, Seyfert galaxies are found to be hosted in late-type disc or lenticular galaxies (Schawinski et al. 2011), while radio-loud AGN are mainly hosted in early-type galaxies (Best et al. 2005). However, in recent times a few examples of radio galaxies hosted in disc galaxies have also been reported (e.g. NGC 612 – Emonts et al. 2008; Speca – Hota et al. 2011; PKS 1814-637 – Morganti et al. 2011; J2345-0449 – Bagchi et al. 2014). The optical and mid-IR properties of host galaxy ISM of these sources often show more in common with Seyfert galaxies than they do with radio galaxies (Morganti et al. 2011). Therefore, a detailed investigation on the properties of host galaxies and ISM of radio-powerful Seyfert galaxies is required to confirm their nature.

Furthermore, unlike sources with high θ_FIRST, several sources with high NVSS-to-FIRST flux density ratios (say |${\theta }_{\rm NVSS\text{--}FIRST}$| > 1.5) are found at lower radio luminosities. A comparison of radio-luminosity distributions of simple (⁠|${\theta }_{\rm NVSS\text{--}FIRST}$| ≤ 1.175) and complex radio sources (⁠|${\theta }_{\rm NVSS\text{--}FIRST}$| ≥ 1.175) shows that the complex sources indeed have systematically lower radio luminosities (with median radio luminosity L_{1.4 GHz,FIRST,median} ∼5.1 × 10²² W Hz⁻¹) than simple sources (with median radio luminosity L_{1.4 GHz,FIRST,median} ∼4.4 × 10²³ W Hz⁻¹). This implies that low-surface-brightness extended radio emission detected by NVSS is more often present in low-luminosity sources. Thus, the additional radio emission detected in NVSS may have significant contribution from star formation as AGN are relatively weaker.

7.2 Radio loudness

In general, radio source population is known to exhibit bimodal distribution of radio-loudness parameter (R) with dividing line at R = 10 that categories radio sources into radio quiet (R < 10) and radio loud (R ≥ 10), where R is defined as the ratio of monochromatic 5 GHz radio luminosity to the 4400 Å optical luminosity (R = |$\frac{{{\nu }_{\rm 5\, GHz}}{\rm {\it L}_{\rm 5\, GHz}}}{{\nu }_{\rm 4400\ {\mathring A}}{\rm {\it L}_{\rm 4400\, {\mathring A}}}}$|⁠) (Visnovsky et al. 1992; Kellermann et al. 1994). The physical origin of the bimodality is generally attributed to the differences in the fundamental parameters of AGN–galaxy system such as the mass and spin of black hole, accretion rate and the Hubble type of host galaxy (Laor 2000; McLure & Jarvis 2004; Sikora, Stawarz & Lasota 2007; Rafter, Crenshaw & Wiita 2011). Therefore, the degree of radio loudness can be used to characterize the nature of AGN. We study radio loudness of our sample sources to investigate if the presence of KSRs is related to radio loudness. We derive 5 GHz radio luminosity (L_5 GHz) for our sample sources from 1.4 GHz radio luminosity (L_1.4 GHz) using a typical radio spectral index of −0.7 for Seyfert galaxies (Morganti et al. 1999; Singh et al. 2013). The optical continuum luminosity at 4400 Å (L_λ4400 Å) is derived from 5100 Å luminosity (L_λ5100 Å) using a typical optical spectral index of −0.5 (Sikora et al. 2007). The 5100 Å luminosity (L_λ5100 Å) is empirically estimated from H_{αλ6563 Å} luminosity as both are found to be related to bolometric luminosity (McLure & Jarvis 2004; Greene & Ho 2005). Thus, 4400 Å luminosity (L_λ4400 Å) can be estimated from H_{αλ6563 Å} as : L_λ4400 Å = L_λ5100 Å |$({\frac{4400\, \rm {\mathring A}}{5100\, \rm {\mathring A}}})^{-0.5}$| = (2.59 × 10⁴³) |$({\frac{\rm {L_{H{\alpha }}}}{10^{42}})}^{0.86}$| erg s⁻¹ (see Rafter, Crenshaw & Wiita 2009). The H_{αλ6563 Å} flux for our sample sources is obtained from SDSS DR10. There are only ∼749/2651 sources with Hα_λ6563 Å flux available from SDSS DR10 and therefore our analysis on radio loudness is limited only to this sub-sample. Fig. 10 shows the distribution of radio-loudness parameter for extended (KSRs) and compact (non-KSRs) radio sources of our sample. We find that both extended and compact radio sources show similar distributions of radio-loudness parameter. As expected, majority (∼85 per cent) of our Seyfert/LINER sample sources are radio quiet (R < 10), while ∼15 per cent sources fall into the radio-loud (R ≥ 10) category. We find that radio-loudness parameter is correlated with total radio luminosity for both compact (unresolved) and extended (resolved) sources (see Fig. 10, right-hand panel). Spearman rank correlation coefficients for unresolved and resolved sources are ∼0.70 and 0.78, respectively. The observed correlation is consistent with previous studies characterizing radio loudness in terms of radio luminosity (e.g. Rafter et al. 2009). It is evident that most of the radio-powerful sources (L_1.4 GHz ≥ 10^24.5 W Hz⁻¹) are radio loud, while radio weak (L_1.4 GHz ≤ 10²³ W Hz⁻¹) are found to be radio quiet. Moreover, a small fraction (∼10 per cent) of our sample sources with 1.4 GHz radio luminosity (L_1.4 GHz) ∼10²³–10^24.5 W Hz⁻¹ can be classified as radio-intermediate with radio-loudness parameter (R) ∼10–100. The presence of powerful radio-loud sources (R > 100 and L_1.4 GHz ≥ 10^24.5 W Hz⁻¹), although only a very small fraction (∼3.0 per cent), is apparently unexpected as these sources can simply be categorized as FR II radio galaxies. As discussed in the previous section, these sources are either radio galaxy contaminants or there is a population of sources in which radio and optical properties give different classification. The radio-loudness versus radio-luminosity plot for our sample sources suggests that radio-loudness parameter in Seyfert, LINER galaxies is distributed in a continuous fashion and overlaps with that of FR I/FR II radio galaxies. This is consistent with Kharb et al. (2014a) results showing the overlap in the radio loudness of Seyfert galaxies and FR I radio galaxies with ∼11 per cent of Seyfert galaxies in their sample classified as radio loud. Using a sample of broad line AGN, Rafter et al. (2009) also found no clear demarcation between the radio-loud (R ≥ 10) and radio-quiet (R < 10) sources but instead fill in a more radio-intermediate population in a continuous fashion. Finally, we note that the presence of KSRs in Seyfert and LINER galaxies does not seem to have any dependence on the radio loudness as both extended (KSRs) and compact (non-KSRs) sources show similar distribution of radio-loudness parameter.

7.3 KSR radio power versus AGN power

A test on the correlation between the strength of kpc-scale radio emission and the AGN power may provide clues about the origin of KSRs. A positive correlation between the radio power of KSRs and AGN power can be expected if KSRs are powered by AGN. We use core radio power, O[III] λ 5007 Å luminosity as the proxies for AGN power. We derive extended emission from total emission subtracted by peak emission (S_ext = S_int,FIRST − S_peak,FIRST) and FIRST peak flux density is considered as core radio emission. However, we caution that our estimates of core and extended radio emission (L_core) using FIRST peak emission are fairly crude as the FIRST peak flux density may contain extended emission in high-z sources and in type 1 sources where AGN jets are oriented towards observer. High-resolution observations detecting core radio emission at parsec-scale would give more robust estimates of core radio emission, but high-resolution radio data are not available for our sample sources. To get more accurate estimate of core and extended radio emission, we create a sub-sample of low-redshift sources (z ≤ 0.01) for which FIRST beam of 5 arcsec corresponds to ≤1.0 kpc and thus give better segregation of core and extended emission. However, number of such sources is too small with limited span in luminosity space to give a robust statistical result.

7.3.1 KSR radio power versus core radio power

The nuclear radio emission is optically thin to torus dust obscuration and also jets in Seyfert and LINER galaxies are not relativistically beamed (Middelberg et al. 2004; Ulvestad et al. 2005). Therefore, AGN core radio emission can be considered an isotropic property in Seyfert galaxies that provides an orientation-independent measurement of AGN power (Kukula et al. 1995; Xu, Livio & Baum 1999; Thean et al. 2001). To check if extended KSRs emission is related to the AGN core radio power, we plot radio luminosity of extended emission versus core radio luminosity; Fig. 11 (left-hand panel) shows that the core radio luminosity is positively correlated with the radio luminosity of extended emission component. Spearman rank correlation test gives correlation coefficient (ρ) = 0.94 with the probability of two parameters being uncorrelated (p) < 2.2 × 10⁻¹⁶. We also performed statistical test on the correlation between core radio flux density (S_core = S_peak,FIRST) and extended radio flux density (S_ext = S_int,FIRST − S_peak,FIRST). Spearman rank correlation test results correlation coefficient (ρ) = 0.69 with the probability of two parameters being uncorrelated (p) < 1.0 × 10⁻¹⁶. This demonstrates that correlation between core radio luminosity and extended radio emission luminosity is not driven by distance effect. The correlation between core radio luminosity and extended radio emission luminosity can be interpreted as more powerful AGN tend to show more powerful KSRs and therefore, inferring that KSRs are likely to be powered by AGN. Sources with L_core > L_ext can be considered as core-dominated sources while sources with L_core < L_ext are extended-emission-dominated sources. From Fig. 11 it is evident that extended-emission-dominated sources are preferentially found at higher radio luminosities (L_core > 10²³ W Hz⁻¹), which is also inferred from the θ_FIRST versus L_1.4GHz,FIRST plot (see Fig. 9).

7.3.2 KSR radio power versus [O iii] λ 5007 Å line luminosity

[O iii] λ 5007 Å line emission is believed to originate from narrow line region and is found to be correlated with nuclear ionizing continuum, as well as nuclear X-ray luminosity, and therefore is considered as the proxy for intrinsic AGN power (Nelson & Whittle 1995; Heckman et al. 2005). Also, it is unaffected by the torus obscuration as it originates outside the torus. Fig. 11 (right-hand panel) shows an increasing trend of KSRs extended emission radio luminosity (L_ext) with [O iii] luminosity, however with a large scatter. Spearman rank correlation test yields correlation coefficient (ρ) = 0.59 with the probability of two parameters being uncorrelated (p) < 1.0 × 10⁻¹⁶. The apparent correlations between extended emission (KSRs) radio luminosity (L_ext) and [O iii] λ 5007 Å line emission luminosity (⁠|$L_{\rm [O\,\small {iii}] 5007\, {\mathring A}}$|⁠) can be interpreted if extended radio emission is related to AGN power. If [O iii] λ 5007 Å line luminosity is considered as the accurate measure of AGN power then the large scatter can be understood if KSRs emission is influenced by other factors such as the contamination from star formation, presence of circumnuclear starburst and the variation in the type of host galaxy.

7.4 Ratio of FIR-to-radio flux

Star-forming galaxies are known to display a tight correlation between far-infrared and radio continuum emission as both FIR and radio emission are believed to be linked to star formation activity (Condon 1992; Kovács et al. 2006; Sargent et al. 2010). However, AGN exhibit radio excess due to additional radio emission from AGN core and jets, and tend to deviate from typical radio–FIR correlation (Yun, Reddy & Condon 2001; Morić et al. 2010). AGN galaxies can be expected to show tighter radio–FIR correlation if radio emission component from AGN is subtracted out. Using a sample of Seyfert galaxies, Baum et al. (1993) reported that extranuclear radio power derived by subtracting nuclear radio power from the total radio power exhibit tighter correlation with the total FIR luminosity. Following a similar approach, we use radio–FIR correlation to examine whether KSRs are powered by AGN or star formation. In Seyfert and LINER galaxies, if extranuclear KSR emission is attributed to star formation and nuclear emission is solely from AGN core then extranuclear radio emission is expected to show tighter correlation with total FIR emission. We derive extranuclear KSRs radio emission (S_ext) by subtracting FIRST peak emission (S_peak) from the NVSS total radio emission (S_total) and assume that the FIRST peak radio emission is primarily from AGN core.

We investigate the ratio of FIR to radio continuum (q parameter) for our KSR sample sources using both total and extranuclear radio emission. The ratio of FIR to radio continuum is defined as q = log[(FIR/3.75 × 10¹² Hz)/S_1.4 GHz], where FIR = 1.26 × 10⁻¹⁴[2.58S_60 μm + S_100 μm] W m⁻² (Helou, Soifer & Rowan-Robinson 1985). The FIR fluxes at 60 and 100 μm are obtained from InfraRed Astronomical Survey (IRAS³) and are in Jy units. Using IRAS observations, we find FIR counterparts of only 217/776 ∼28 per cent KSR sources and therefore our investigation on radio–FIR correlation is limited to FIR-detected sub-sample. Fig. 12 shows the distributions of the ratio of FIR to radio (q parameter) for resolved (θ_FIRST > 1.06) and complex (⁠|${\theta }_{\rm FIRST\text{--}NVSS}$| > 1.175) KSR sources. We find that both resolved and complex sources exhibit wide range of q values over 0.5–4.0 with median values ∼2.27 and 2.21, respectively, with standard deviations 0.56 and ∼0.37, respectively. The average value of q parameter for star-forming galaxies in the local universe is found to be (q) ∼2.3, and it decreases for AGN-bearing galaxies (Sargent et al. 2010). The lower median value and wide distribution of q parameter for our (resolved and complex) KSR sources is indicative of the presence of AGN.

We also estimate the ratio of FIR-to-radio (q_ext) using extranuclear flux density for resolved and complex KSR sources. The extranuclear radio emission for KSR sources is derived by subtracting FIRST peak flux density from total FIRST and NVSS flux density, respectively (i.e. S_ext FIRST = S_int,FIRST − S_peak,FIRST and S_ext NVSS = S_int,NVSS − S_peak,FIRST). We note that both resolved and complex KSR sources show an even wider distribution of q_ext spanning over 0.5–4.5 with median values ∼2.77 and 2.46, respectively, and standard deviation ∼0.58 and 0.41, respectively. The wider distribution of q_ext compared to q suggests that extranuclear KSR radio emission is likely to be powered by AGN (e.g. Roy et al. 1998). The higher median values of q_ext can be understood if extranuclear total radio emission is underestimated as the FIRST peak emission can have significant contribution from star formation. The dusty torus around AGN may also contribute significantly to total FIR emission and can result in a higher value of q_ext parameter.

7.5 Mid-IR colours

IR colours can be used to measure the relative contribution of a starburst or AGN to the total bolometric luminosity, with redder (cooler) colours characterizing the dominance of starburst (Rush, Malkan & Spinoglio 1993; Dopita et al. 1998; Lacy et al. 2004; Stern et al. 2012). We use mid-IR colour–colour diagram to check if KSR sources are dominated by starburst or AGN using Wide-field Infrared Survey Explorer (WISE)⁴ data. WISE covers all sky in four mid-IR bands, i.e. W1 [3.4 μm], W2 [4.6 μm], W3 [12 μm] and W4 [22 μm]) with an angular resolution of 6.1, 6.4, 6.5 and 12 arcsec, respectively. WISE counterparts of our sources are found using a search radius of 2.0 arcsec around the optical positions. Only 752/827 sources (91 per cent) with extended radio emission have WISE counterparts.

In the literature, several mid-IR colour–colour diagnostics have been developed for separating AGN and star-forming normal galaxies (e.g. Lacy et al. 2004; Stern et al. 2005) and WISE colours have been used to identify AGN (e.g. Mateos et al. 2012; Stern et al. 2012). We use WISE colour–colour diagrams of our sample sources, where the AGN selection wedge is defined as : W1 − W2 ≥ 0.315 × (W2 W3) − 0.222 and W1 − W2 ≥ 0.315 × (W2 W3) + 0.796 and W1 − W2 = −3.172 × (W2 W3) + 7.624 (see Mateos et al. 2012). Using 22 μm WISE band is not much useful due to its significantly shallower depth in comparison to the first three bands and also star formation contribution is likely to increase at 22 μm (Mateos et al. 2012). Fig. 13 shows that KSR sources have a wide range of IR colours with majority of them falling into AGN wedge. We note that, in general, sources within the AGN selection wedge are radio-powerful sources while sources falling outside the AGN wedge are of relatively lower radio luminosities. This can be understood if mid-IR emission is dominated by AGN in radio-powerful sources (L_1.4 GHz ≥ 10²⁴ W Hz⁻¹), while in sources with relatively lower radio luminosity mid-IR emission apparently has greater contribution from dust heated by stars. Therefore, KSRs in radio luminous sources are likely to be powered by AGN. On the other hand, in sources of relatively low radio luminosities, KSRs can have contribution from star formation. Moreover, we caution that the WISE mid-IR colour cuts should be used with care as these colour cuts may be biased against heavily obscured type 2 AGN. Also, there are suggestions that radio-selected AGN may have a different accretion mode, i.e. radiatively inefficient (radio mode), and may not strictly follow the mid-IR colour selection criteria (Hardcastle, Evans & Croston 2007; Griffith & Stern 2010).

8 CONCLUSIONS

We have studied the prevalence and nature of KSRs in Seyfert and LINER galaxies using 1.4 GHz VLA FIRST and NVSS observations. Our sample is the largest sample hitherto used for KSR studies and consists of 2651 sources detected in FIRST. Of these, 1737 sources also have NVSS counterparts. Similar redshift distributions of Seyfert type 1s and type 2s suggest that our sample is not affected by biases introduced by dust obscuration. Conclusions of our study are outlined below.

• Using a concentration parameter based on the ratio of total-to-peak flux density θ_FIRST = |${\rm ({\it S}_{\rm int,\,FIRST}/{\it S}_{\rm peak,\,FIRST})^{1/2}}$|⁠, we find ≥30 per cent KSR sources (i.e. sources with radio structures larger than 1.0 kpc) in the FIRST-detected sample. The comparison of NVSS to FIRST flux densities helps us in detecting faint extended radio emission that is resolved out in FIRST observations and we obtain ≥42 per cent KSR sources in FIRST–NVSS sub-sample. This fraction of KSR sources is only a lower limit owing to the combined effects of projection, resolution and sensitivity. The comparison of the fraction of KSRs detected in our sample with the previous studies demonstrates the importance of low-frequency observations with relatively lower resolution in detecting KSRs efficiently.

• There are a total of 180 Seyfert and LINER galaxies in our sample that exhibit multicomponent KSRs in FIRST observations. We find that these sources display varying morphologies e.g. linear, S-shaped and diffuse, which is consistent with the previous studies based on sensitive targeted observations of small samples.

• We find that KSR sources are distributed across all redshifts, luminosities and radio loudness. We show that the presence of KSRs in Seyfert and LINER galaxies does not seem to have any dependence on the radio luminosity and radio loudness. A small fraction (∼10–15 per cent) of KSR sources characterized with high total-to-peak flux density ratio and high radio luminosity (L_1.4 GHz > 10²⁴ W Hz⁻¹) are radio loud. These sources may constitute a population of radio-powerful Seyfert and LINER galaxies with radio properties overlapping with radio galaxies.

• We find that the extranuclear radio power in KSR sources is positively correlated with the core radio power and [O iii] λ 5007 Å line luminosity. This can be interpreted as KSRs are powered by AGN rather than star formation.

• The ratio of FIR-to-radio continuum (q parameter) for KSR sources shows a wide distribution spanning over 0.5–4.0 with median value lower than that for typical star-forming galaxies and thus indicating the dominance of AGN radio emission. The ratio of FIR-to-radio continuum (q_ext) using extranuclear radio flux density (derived by subtracting FIRST peak flux density from NVSS total flux density) shows an even wider distribution suggesting that the extranuclear KSR radio emission is likely to be originated from AGN.

• The mid-IR colour–colour diagram for KSR sources shows that the mid-IR emission in radio-powerful sources tends to be dominated by AGN, while in sources with lower radio luminosities mid-IR emission apparently have greater contribution from dust heated by stars. This can be understood if KSRs in radio luminous sources are primarily powered by AGN, while in sources with relatively low radio luminosities KSRs may have substantial contribution from star formation.

We acknowledge support from the Indo-French Center for the Promotion of Advanced Research (Centre Franco-Indien pour la Promotion de la Recherche Avance) under programme no. 4404-3. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This publication makes use of data products from WISE, which is a joint project of the University of California, Los Angeles and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington and Yale University.

REFERENCES

APPENDIX A: FIRST AND NVSS OBSERVED PARAMETERS FOR OUR SAMPLE LLAGN