# The host galaxies of radio-loud AGN: colour structure

E. J. A. Mannering1, D. M. Worrall1, M. Birkinshaw1
1H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol
BS8 1TL, UK E-mail<EMAIL_ADDRESS>
###### Abstract

We construct a sample of 3,516 radio-loud host galaxies of active galactic
nuclei (AGN) from the optical Sloan Digital Sky Survey (SDSS) and Faint Images
of the Radio Sky at Twenty cm (FIRST). These have 1.4 GHz luminosities in the
range $10^{23}-10^{25}$ WHz-1, span redshifts $0.02<z<0.18$, are brighter than
$r^{*}_{petro}<17.77$ mag and are constrained to ‘early-type’ morphology in
colour space ($u^{*}-r^{*}>2.22$ mag). Optical emission line ratios (at
$>3\sigma$) are used to remove type 1 AGN and star-forming galaxies from the
radio sample using BPT diagnostics. For comparison, we select a sample of
35,160 radio-quiet galaxies with the same $r^{*}$-band magnitude-redshift
distribution as the radio sample. We also create comparison radio and control
samples derived by adding the NRAO VLA Sky Survey (NVSS) to quantify the
effect of completeness on our results.

We investigate the effective radii of the surface brightness profiles in the
SDSS $r$ and $u$ bands in order to quantify any excess of blue colour in the
inner region of radio galaxies. We define a ratio $R=r_{e}(r)/r_{e}(u)$ and
use maximum likelihood analysis to compare the average value of $R$ and its
intrinsic dispersion between both samples. $R$ is larger for the radio-loud
AGN sample as compared to its control counterpart, and we conclude that the
two samples are not drawn from the same population at $>99\%$ significance.
Given that star formation proceeds over a longer time than radio activity, the
difference suggests that a subset of galaxies has the predisposition to become
radio loud. We discuss host galaxy features that cause the presence of a
radio-loud AGN to increase the scale size of a galaxy in red relative to blue
light, including excess central blue emission, point-like blue emission from
the AGN itself, and/or diffuse red emission. We favour an explanation that
arises from the stellar rather than the AGN light.

##  1 Introduction

Considerable uncertainties remain as to what controls the apparent link
between the activity of active galactic nuclei (AGN) during the time that a
black hole is fed and star formation. The accretion disk surrounding a super-
massive black hole (SMBH) emits highly energetic radiation and particles, and
can form powerful winds and/or collimated, relativistic jets (e.g., van
Breugel et al., 2004). The radiation and outflows might then affect the
interstellar medium, triggering star formation which might be detectable as an
excess of blue light from the central regions of galaxies. Alternatively, the
activity of the AGN may be sparked by specific events in the galaxy’s past.
For example, there is morphological evidence that activity in radio galaxies
might be triggered by mergers and galaxy interactions (e.g., González Delgado
et al., 2006), which in turn could contribute to central blue light through
enhanced star formation. In either case, we might expect an observable
association between AGN activity, for which in this work we use radio loudness
as a tracer, with bluer stellar continuum in the central regions of the
galaxy.

Previous work has hinted at such a relationship. For example, Mahabal et al.
(1999) examined the central light of 30 radio galaxies as compared to 30
normal galaxies from the Molongo Reference Catalogue and found excess blue
light in the inner regions of the radio galaxies as compared with the control
sample. This central excess is unrelated to the conventional colour gradient
of the broader distribution of stars. Gonzalez-Perez et al. (2010) studied
colour variations within galaxies from the Sloan Digital Sky Survey (SDSS;
York et al., 2000) DR7, finding marginally steeper colour gradients in massive
galaxies with nuclear activity and concluded that this is due to a higher
fraction of young stars in their central regions.

In the present paper we expand the work of Mahabal et al. (1999), by combining
optical information from SDSS with the FIRST and NVSS radio surveys (Becker et
al., 1995; Condon et al., 1998) to construct a local ($0.02<z<0.18$) sample of
powerful radio-loud AGN host galaxies (R-AGN), and a control sample of
‘normal’ early-type ellipticals. We define $R$ as the ratio of SDSS $r^{*}$ to
$u^{*}$ band de Vaucouleurs effective radii and compare its value between the
samples.

The paper is structured as follows. In Section 2 we briefly describe the
surveys used to construct our samples. Separation into the radio-loud and
control samples is discussed in Section 3. Section 4 outlines the maximum
likelihood analysis used to compare the average values of $R$ for the two
samples. In Section 5 we present a discussion of our findings in the context
of radio-AGN fuelling mechanisms and the properties of the host galaxies.
Throughout, we use a flat $\Lambda$CDM cosmology with $\Omega_{m_{0}}=0.3$ and
$\Omega_{\Lambda 0}=0.7$. We adopt $H_{0}=70$ km s-1 Mpc-1.

##  2 Data Sources

###  2.1 SDSS

SDSS is an imaging and spectroscopic survey covering $\sim$10,000 deg2,
primarily in the northern hemisphere. Its 7th data release (SDSS-DR7;
Abazajian et al., 2009) contains over 350 million entries, of which about one
million are confirmed galaxies with spectroscopic follow up.

In the photometric sample, flux densities are measured simultaneously in five
broadband filters ($u,g,r,i,z$), with effective wavelengths $3551$, $4686$,
$6165$, $7481$ and $8931$Å (Fukugita et al., 1996). All magnitudes are given
on the ABv system (Oke & Gunn, 1983), and are determined using Petrosian
apertures (see Blanton et al., 2001; Graham et al., 2005, for a complete
definition of the Petrosian system). In common with Ivezić et al. (2002), we
refer to SDSS measured magnitudes as $u^{*},g^{*},r^{*},i^{*}$ and $z^{*}$ due
to the uncertainty in the absolute calibration of the SDSS photometric system,
which has been assessed at $\lesssim$0.03 mag (Stoughton & Lupton, 2002). For
a complete guide to the photometric system, see Fukugita et al. (1996), Gunn
et al. (2001) and Stoughton & Lupton (2002).

####  2.1.1 Main galaxy sample (MGS)

We use the main galaxy survey spectroscopic sample (MGS, Strauss et al.,
2002). The MGS algorithm selected extended sources brighter than
$r^{*}_{petro}=17.77$ mag with Petrosian half-light surface brightness
$\mu_{50}\leq 24.5$ mag arcsec-2, providing $\sim$ 90 galaxies deg-2 (Blanton
et al., 2001). Candidate galaxies were then observed spectroscopically.
$99.9\%$ of the resulting redshifts have velocity errors $<$ 30 km s-1. The
survey is unbiased, except for galaxies with close companions. Around $6\%$ of
galaxies satisfying the photometric target criteria were not included for
spectroscopic follow up due to a companion galaxy within the 55″ minimum fibre
separation, although some of these galaxies have been subsequently observed.
The MGS contains $\sim$680,000 spectroscopically confirmed galaxies. The full
target selection is described in Strauss et al. (2002).

We corrected for Galactic extinction using the SDSS ‘reddening’ parameter,
which was derived from maps of the infrared emission from dust across the sky
in accordance with Schlegel, Finkbeiner & Davis (1998). We applied
$k$-corrections using the SDSS-derived ‘kcorr’ parameter as detailed in
Blanton & Roweis (2007). Typical corrections $k_{u},k_{g},k_{r}$ were
$(0-0.4)$, $(0-0.3)$, and $(0-0.1)$ mag.

###  2.2 FIRST

The FIRST survey (Becker et al., 1995) utilized the VLA (at 1.4 GHz in B
array) to map the radio sky over $\sim$9000 deg2 in the Northern hemisphere
and in a $2\overset{{}^{\circ}}{.}5$ wide strip along the celestial equator.
It has $\sim 8400$ deg2 overlap with SDSS, contains $\sim 97$ sources deg-2 at
the 1 mJy survey threshold and reaches an rms sensitivity of $\sim$0.15 mJy
beam-1. In this configuration, the VLA has a synthesized beam of 5.4″ FWHM,
providing accurate flux densities for small-scale radio structures, but
underestimating the flux densities of sources extended to several arcminutes.
At the 1 mJy survey threshold, individual sources have 90% confidence
astrometric errors $\lesssim 1\arcsec$. We adopted a mean spectral index of
$\alpha=0.7$ (where $S_{\nu}\propto\nu^{-\alpha}$) and obtained rest-frame 1.4
GHz power densities by applying k-corrections assuming the usual form

$L_{\nu,rest}=(1+z)^{(\alpha-1)}S_{\nu}\,4\pi D_{L}^{2}$ (1)

where $D_{L}$ is the luminosity distance.

###  2.3 NVSS

The NRAO VLA Sky Survey (NVSS, Condon et al., 1998) mapped the radio sky (at
1.4 GHz in D array) north of $-40\overset{{}^{\circ}}{}$ declination. The
survey is complete down to a point source flux density of $\sim$ 2.5 mJy. The
synthesized beam of 45″ is much larger than FIRST, providing more accurate
flux measurements for highly extended sources. Astrometric accuracy ranges
from 1″ for bright sources to 7″ for the faintest detections. The entire
survey contains over 1.8 million unique sources brighter than 2.5 mJy.
$k$-corrections are applied as in §2.2.

##  3 Sample selection

###  3.1 Cross-correlation: FIRST-SDSS

We initially derived a FIRST-SDSS sample of radio galaxies and a comparison
control sample with no nearby detectable radio counterpart. Figure
LABEL:fig:idlsep shows the distribution of angular separations between SDSS
objects and their nearest FIRST counterpart. We find that at $\sim$ 5″ the
distribution becomes dominated by random matches. Hence we adopt a match
criterion of 2″ angular separation to avoid such false matches. Our cross-
matched catalogue contains $25,931$ galaxies and we denote this as our
preliminary ‘radio’ sample. All unmatched sources are initial candidates for
our control sample of radio-quiet galaxies.

We define our efficiency as the fraction of matches in our radio sample which
are physically real (including contamination from line of sight false matches,
which cannot be accounted for here). In order to evaluate the number of random
false matches in our sample, we offset the RA and DEC of the FIRST sources by
$1^{\circ}$ and re-matched to our set of $680,056$ SDSS galaxies, selecting
objects within a 2″ radius. We found on average $58$ random matches,
corresponding to 0.3% contamination of the FIRST-SDSS match sample ($>$99%
efficiency, Figure LABEL:fig:idlsep, red dotted line).

We also need to know the completeness of our matching criteria - the fraction
of correct matches we recover. A factor affecting this is the possible
exclusion of large lobe-dominated radio sources (Kimball & Ivezić, 2008). Both
lobes will be included in FIRST but may be excluded in the cross-matched
subset for lobe-core distances $>$ 2″, if the core is weak. We estimated
$\sim$ 8$\%$ of real matches between the SDSS subset and FIRST that are
excluded from our radio sample, by assuming the radio lobes are outside a 2″
radius from the optical core, but within a 5″ radius (see Figure
LABEL:fig:idlsep). Our matching algorithm efficiency and completeness are
similar to Kimball & Ivezić (2008), who match FIRST to SDSS-DR6 positions
within a 2″ radius for sources with $z\leq$ 2 (95% efficiency and 98%
completeness111Kimball & Ivezić (2008) estimate their completeness and
efficiency by fitting a gaussian to the nearest-neighbour distribution
(representing physical matches) plus a rising linear function (representing
random matchings).).

However, we could not account for sources with FIRST lobes $>5$″ from the
optical core or the population of FIRST double-lobed sources with no
detectable radio core. Ivezić et al. (2002) cross-correlated all FIRST sources
with SDSS, then identified potential double-lobed radio sources with
undetected cores222Via comparing the mid-points of FIRST pairs to SDSS sources
within a separation $<\,90$″ and accepted all matches with offsets $<\,3$″.,
estimating these contribute less than $10\%$ of all radio sources (Best et
al., 2005a, estimate $\sim 5\%$ of their radio-loud AGN sample had no FIRST
detection).

Becker et al. (1995) estimated the FIRST catalogue to be $95\%$ complete at 2
mJy and $80\%$ complete down to the survey limit of 1 mJy. Figure 2 shows
integrated radio power against redshift for the preliminary radio sample
(25,931 sources). The solid black lines trace the 1 mJy and 2 mJy peak flux
density thresholds, the dotted and dashed lines show cuts we applied in
redshift and radio power (see §3.3 and §3.4), and the red points are the
resultant selection of radio sources. It is noted that for sources that are
not well-described by an elliptical Gaussian model, the integrated flux
density as derived by FIRST may be an inaccurate measure of the true value.
Such sources with radio powers corresponding to flux densities below the 1 mJy
threshold can be seen in Figure 2.

We note that although the two cuts improve the sample completeness (all red
points are above 1 mJy), many of our sources are below the 2 mJy line, and so
our sample completeness cannot be $>80\%$. Combining this with our estimation
of completeness in our selection criteria ($\sim 90\%$), we estimate the
actual completeness of our preliminary radio sample to be $\sim 72\%$ for
sources brighter than 1 mJy. The incompleteness is dominated by statistical
effects rather than the $10\%$ effect of sources missing due to weak cores.

Figure 2: Integrated FIRST radio power vs redshift for the preliminary ‘radio’
sample (see text). The solid black lines trace peak radio power at the 1 mJy
detection threshold and at 2 mJy, the dashed lines denote the redshift limits
imposed in §3.3 and the dotted line denotes the radio power cut imposed in
§3.4. The red points are the remaining radio sample after these cuts are
applied.

To produce a preliminary control sample, we select sources from the SDSS
subset which fall within the same spatial region as FIRST ($\sim 8000$ deg2).
We selected all objects from this subset which are not matched to a FIRST
source within 2″ of their optical core, providing $\sim$625,664 radio-quiet
galaxies. The efficiency of this sample, based on Figure LABEL:fig:idlsep is
$>99.9\%$ (i.e., $<1\%$ contamination by radio sources detectable at the FIRST
flux density limit) and the sample completeness is $>92\%$.

###  3.2 Cross-correlation: FIRST-NVSS-SDSS

For FIRST sources substantially larger than $5$″ some flux density is resolved
out, leading to an increase in the survey threshold for extended objects and
flux density underestimates for larger objects (Lu et al., 2007). Our FIRST-
SDSS radio sample is large due to the number of FIRST candidate sources near
the 1 mJy survey limit. Its limitations are potential flux density
underestimates, and incompleteness to extended radio sources, notably
extended, double-lobed sources with no detectable radio core within several
arcseconds of its optical counterpart.

To attempt to quantify these limitations, we created a complementary sample of
radio-loud AGN host galaxies using both NVSS and FIRST. Best et al. (2005a)
note that the 45″ resolution of NVSS is large enough that $\sim 99\%$ of all
radio sources are contained within a single component, allowing for a higher
sample completeness. However, NVSS is less deep than FIRST and consequently
the matched sample contains fewer galaxies. The NVSS-FIRST-SDSS matched sample
therefore does not benefit from such good statistics.

We used the Unified Radio Catalogue constructed by Kimball & Ivezić (2008)
(see sample ‘C’ in their table 8), selecting sources which are detected by
both FIRST and NVSS, matched to within 25″. This selection yields a radio flux
density limited ($S_{\mathrm{1.4GHz}}>2.5$ mJy) catalogue (hereafter FIRST-
NVSS) containing 141,881 sources. We cross-matched these to the $\sim 680,056$
MGS sources adopting the same 2″ match criterion used in §3.1. Our cross-
matched catalogue contains 5,719 galaxies and we denote this as the
preliminary ‘comparison radio’ (hereafter CR) sample. Integrated flux
densities as derived by Kimball & Ivezić (2008) are adopted in our analysis.

We estimated our matching criterion of 2″ to be $>99\%$ complete, and $>99\%$
efficient (8 random matches were found when the FIRST-NVSS RA and DEC were
offset by $1^{\circ}$). The FIRST-NVSS catalogue used to create the CR sample
is 99$\%$ complete and matched with $96\%$ efficiency (see table 2 of Kimball
& Ivezić, 2008). We therefore estimated the comparison radio sample to be
$>99\%$ complete and $>95\%$ efficient (see Table 1). 5 of the 5,719 galaxies
in the CR sample reside in the control sample derived in §3.1 and these were
removed. 4,935 of the CR sample (86$\%$) are also in the FIRST-SDSS sample.

Matched |  $S_{\mathrm{lim}}$(mJy) |  Objects |  Completeness |  Efficiency
---|---|---|---|---
surveys |  |  |  |
FIRST-SDSS |  1.0 |  25,931 |  $72\%$ |  $>99\%$
FIRST-NVSS-SDSS |  2.5 |  5,719 |  $99\%$ |  $>95\%$
Table 1: Radio flux density limits, $S_{\mathrm{lim}}$, of both the radio
sample (FIRST-SDSS) and the candidate CR sample (FIRST-NVSS-SDSS), the number
of objects in each and the estimated completeness and efficiency.

###  3.3 Redshift range

In the following sections (§3.3-3.8) we discuss the secondary selection
criteria applied to the FIRST-SDSS sample. The CR sample follows the same
path, and a summary of the final CR sample properties are presented alongside
those of the final radio sample in §3.9.

We imposed a redshift cut of $0.02<z<$ 0.18 to ensure that the galaxy spatial
structure could be well examined. For $z<0.02$, redshift is not a reliable
distance indicator. Figure LABEL:fig:lumredradio shows less than 2% of matched
sources have redshift $<0.02$. The MGS magnitude limit of
$r^{*}_{petro}<$17.77 corresponds to L${}_{r^{*}}>2.6\times 10^{23}$ W Hz-1 at
$z=0.18$, and our sample should be complete to this optical luminosity
density.

We restricted the SDSS-derived redshift confidence (zconfidence) to be greater
than $95\%$, which cuts out 12% of objects from the preliminary radio sample
and 10% of objects from the preliminary control sample. After redshift
selection, $499,418$ radio-quiet galaxies remained in the control sample,
$\sim$70% of the parent MGS, whilst the radio sample contained $17,024$
galaxies. The average error in redshift for both samples is $<0.002$ and the
redshift distributions of these two samples were indistinguishable at the 1%
level on the basis of a two-tailed K-S test.

###  3.4 Radio Power

Best et al. (2005a) suggested that typical radio-loud AGN have powers above
$10^{23}$ W Hz-1 at 1.4 GHz and Condon (1989) shows that
P${}_{\mathrm{1.4\,GHz}}=10^{23}$ W Hz-1 separates the spiral starburst
population from the AGN - E/S0 population in local galaxy fields. We therefore
restrict the radio sample to galaxies harbouring radio sources with
P${}_{\mathrm{1.4\,GHz}}>10^{23}$ W Hz-1, which selects 5,119 galaxies (30%)
from the radio sample. Figure LABEL:fig:lumredradio shows that this threshold
in radio power is well matched to our redshift selection. We name this set of
5,119 galaxies the ‘radio-loud’ sample. The mean redshift of the radio sample
increased from $\sim 0.095$ to $\sim 0.136$ when the radio power cut was
applied.

AGN can be split on the basis of large-scale radio structure into FRI type,
where radio brightness decreases outwards from the centre and FRII type, with
edge-brightened lobes and hot spots (Fanaroff & Riley, 1974). FRIIs are more
luminous P${}_{178\mathrm{\,MHz}}\geq 1.3\times 10^{26}$ W Hz-1 and are rare
in a low-redshift sample such as ours (Figure LABEL:fig:lumredradio), since
this 178 MHz power corresponds to P${}_{\mathrm{1.4\,GHz}}\approx 3.1\times
10^{25}$ WHz-1 for a typical spectral index of $\alpha=0.7$.

###  3.5 Removing type 1 AGN

In unified AGN models (e.g, Antonucci, 1993) the appearance of the central
black hole and associated continuum of an AGN differ only in the viewing angle
at which it is observed. Sources viewed face on (type 1) show broad emission
lines that are absent in those observed edge on and where the broad emission
line region is obscured by a dusty torus (type 2). Type 1 AGN are excluded
from this study, as the optical continuum can be dominated by relativistically
boosted non-thermal emission, which may overwhelm measurements of the host
galaxy’s properties.

The SDSS spectral classification pipeline automatically flags and excludes
quasars from the MGS, but we chose to verify its reliability and the relative
numbers of type 1 AGN remaining in our sample. We followed the method outlined
by Masci et al. (2010) to identify broad line emission. H$\alpha$ or H$\beta$
emission lines exceeding 1000 km s-1 (FWHM) with a $S/N>3$ and
H$\alpha$/H$\beta$ EW $>5$Å were classified as broad line. Galaxies with both
broad H$\alpha$ and H$\beta$ emission were classified as type 1 AGN. 3
galaxies of the 5,119 radio-loud sample have broad H$\alpha$ and H$\beta$
emission lines and were removed from the sample.

184 galaxies (4$\%$) of the remaining 5,116 radio-loud sample have broad
H$\alpha$ emission, but do not have broad $H\beta$ emission.

Osterbrock (1989) classified these objects as type ‘1.9’ AGN, which have
substantial but not complete obscuration of the central continuum source.
Kauffmann et al. (2003) determine that the contribution to the observed
continuum is not significant in these sources, so we retain these within our
sample. The control sample contained 10 type 1 AGN and 1835 type ‘1.9’ AGN. We
removed the type 1 AGN to leave 499,408 galaxies within the control sample.

###  3.6 Removing star-forming galaxies

Type 2 AGN have narrow permitted and forbidden lines and their stellar
continuum is often similar to normal starforming galaxies. Yun et al. (2001)
show a tight correlation between far infra-red luminosity (indicative of star
formation) and P${}_{\mathrm{1.4\,GHz}}$. This will cause a level of
contamination by star-forming galaxies if P1.4GHz is used as the sole tracer
of galaxies hosting a radio-loud AGN. We should therefore remove the small
subset of radio-loud galaxies in which the radio power arises from star
formation (SF) and not from an AGN.

AGN separation from SF galaxies in the local Universe can be achieved via
optical emission line ratio diagnostics (Baldwin, Phillips & Terlevich, 1981,
herein BPT). Emission-line ratios probe the ionizing source: for AGN, non-
thermal continuum from the accretion disc around a black hole and in star-
forming galaxies (SFGs), photoionization via hot massive stars. However, Best
et al. (2005b) find no correlation between a galaxy being radio-loud and
whether it is optically classified as an AGN. In agreement with this, we found
no correlation333Spearman’s rank correlation result is $\pm$0.06 or less
between the radio-flux and optical emission-line flux ratios for our radio
galaxy sample. between radio flux at 1.4 GHz and the optical line ratios
[NII]/H$\alpha$ or [OIII]/H$\beta$ in our sample. Hence, a substantial
fraction of radio-loud AGN would not be selected using BPT diagnostics, and
were we to apply them to the radio sample it would be biased towards radio
galaxies with particularly strong optical emission lines.

We instead remove galaxies which are strongly identified as non-AGN, i.e.
star-forming. Despite this method leaving a small fraction of star-forming
galaxies which are faint in optical line emission, all radio-loud AGN, whether
optically bright or otherwise, will remain in the sample. This decrease in
efficiency of the sample is preferential to a drastic decrease in
completeness. A similar problem was identified by Sadler et al. (2002), who
defined a sample of radio-loud AGN from the 2dFGRS catalogue. They found
approximately half of the sample have absorption spectra similar to those of
inactive giant ellipticals, and therefore would be mostly missed by optical
AGN emission-line selection.

In classifying galaxies as AGN or star-forming, we utilized the demarcation
criterion of Kauffmann et al. (2003)

$\mathrm{log}(\mathrm{[OIII]}/\mathrm{H}\beta)>0.61/\\{\mathrm{log}([\mathrm{NII}]/\mathrm{H}\alpha)-0.05\\}+1.3$
(2)

plotted as the dashed line on Figure 4.

Figure 4: BPT diagram for galaxies within the radio-loud sample with emission
line ratios. 1,069 galaxies from the 5,116 radio-loud sample have emission
line ratios and are plotted as grey crosses where the size of the symbol does
not indicate the sizes of the error bars, which vary widely. The dashed curve
(eq. 2) indicates the demarcation given by Kauffmann et al. (2003) between
optical AGN (above the line) and SF galaxies (below the line). 766 galaxies
plotted have emission line ratios with $>3\sigma$ significance. The density of
these galaxies is shown by contours, 85% of the 766 galaxies lie above the
line as optically classified AGN. The remaining 15% (118 galaxies) lie below
the curve (red circles) and we classified these as star-forming. We also show
the maximum uncertainty for a point on the Kauffmann separator with S/N of 3
(dotted lines). 69 objects detected at S/N $>3$ (black crosses) lie between
the Kauffmann separator and the upper maximum uncertainty line.

Figure 4 shows the standard line ratio diagnostics for galaxies from the
radio-loud sample with all four emission lines catalogued in the SDSS (grey
crosses, 1,069 objects of the 5,116). 766 of these 1,069 galaxies have both
optical emission-line ratios at S/N $\geq 3$ and their density on the BPT
diagram is shown as contours. 118 (11%) lie below the demarcation line and are
marked with red circles (112 out of these 118 have all four emission-lines
with S/N $\geq 5$). We removed these 118 optically selected SF galaxies from
the radio-loud sample, to leave a sample of 4,998 predominantly radio-loud AGN
hosts.

We then estimated the residual contamination expected in the radio AGN sample
from star-forming galaxies by plotting the maximum uncertainty for a point on
the Kauffmann separator with S/N of 3 (Fig 4, dotted lines). 69 objects
detected at S/N $>3$ (black crosses) lie between the Kauffmann separator and
the upper maximum uncertainty line. Therefore the contamination expected in
the radio AGN sample from star-forming galaxies is $\sim 11\%$.

Our radio sample contains predominantly FRI galaxies, which are usually hosted
by giant elliptical galaxies and on average have weak or no optical nuclear
emission lines (Lin et al., 2010, and references therein). Within our sample
of radio-loud AGN, 79% of objects do not have optical emission line fluxes. We
estimate $\approx 11\%$ contamination of non-AGN (e.g. SFG) if galaxies
without SDSS emission lines are similar to galaxies with bright line emission.
5 galaxies without emission line fluxes $>$ 3$\sigma$ lie below the
demarcation line in Figure 4 and are potentially star forming, but without
reliable line information we retain these within our sample.

As discussed by Best et al. (2005b), a potential shortfall of spectral
classification of emission-line radio-loud AGN is that emission-line AGN
activity is often accompanied by star formation (e.g., Kauffmann et al.,
2003). This star formation will give rise to radio emission, even if the AGN
itself is radio quiet. For these sources, the optical spectrum could still be
dominated by a (radio-quiet) AGN leading to classification as an emission-line
radio-loud AGN.

Morić et al. (2010) (hereafter M10) derive a population of sources matched
from all NVSS galaxies in the Unified Radio Catalog (Kimball & Ivezić, 2008),
the SDSS-MGS and IRAS data. The matched sources are divided into star-forming,
composite and AGN using standard BPT diagnostics. Star formation rates are
derived via broad-band spectral fitting to the NUV-NIR SDSS photometry, and
the _average_ fractional star formation/AGN contribution to the radio power is
estimated (see their table 2). They find that in 203 composite galaxies,
81.3$\%$ of the total radio power is due to star formation. The variation of
this fraction with radio power is not specified.

Following M10, we defined 206 composite galaxies in our own radio sample
(27$\%$ of the emission-line galaxies confirmed at S/N $\geq 3$), using the
diagnostics of Kewley et al. (2001) and Kauffmann et al. (2003). If the
average fractional contribution is independent of total radio luminosity, then
we estimated an upper limit of $\sim 27\%$ of our radio sample may have radio
power boosted by star formation but possess a radio-quiet AGN. However,
$\lesssim 14\%$ of the composite sample defined by Morić have log[P1.4(W
Hz-1)] $>23$. Mauch & Sadler (2007) find SF galaxies tend to have median
log[P1.4(W Hz-1)] = 22.13, whereas AGN have a median log[P1.4(W Hz-1)] =
23.04. Therefore, our luminosity cut will have significantly reduced the
numbers of galaxies where star-formation is the principal contributer to the
total radio power, and we expect far less than $27\%$ contamination from
radio-quiet, optically-loud AGN.

We also cannot account for the population of ‘composite’ radio-loud host
galaxies with ongoing star formation that have been lost from our sample
through this selection technique. Mauch & Sadler (2007) estimate that $\sim
10\%$ of local radio sources may have a starforming spectrum but have radio
flux densities dominated by a radio-loud AGN.

###  3.7 Colour bimodality

As low-redshift radio-loud AGN are hosted predominantly by elliptical
galaxies, we attempted to constrain the control sample to contain only early-
type galaxies. The colour distributions of galaxies have been shown to be
highly bimodal (Yan et al., 2006; Yan et al., 2010; Strateva et al., 2001).
Figure 5 shows a colour-colour plot in $g$*-$r$* against $u$*-$g$* as explored
by Strateva et al. (2001) who define an optimal colour separator444On a
spectroscopically classified galaxy sample, early-types are recovered at
$\gtrsim$98% completeness and $\gtrsim$83% reliability. between early and late
types of $u^{*}-r^{*}\geq 2.22$ mag. Early-types (E, S0, Sa) populate the
upper right region, and late types (Sb, Sc, Irr) occupy the lower left.

Figure 5: Colour-colour plot for the entire control sample (grey) and 34606
visually classified ellipticals from Galaxy Zoo-control sample match (log10
contours). The dashed line is $u^{*}-r^{*}\geq 2.22$ mag from Strateva et al.
(2001) and defines a morphological colour separator. 80% of the Galaxy Zoo-MGS
sample lie above the line. The $u^{*}$, $g^{*}$ and $r^{*}$ magnitudes are
derived from SDSS columns: petrocounts $-$ reddening $-$ kcorr.

In order to test the completeness of this demarcation, we used the 62,190
galaxies visually classified as ellipticals in Galaxy Zoo data (Lintott et
al., 2010). We cross-matched these to the control sample, selecting objects
within 1″ radius. 34,606 matches were found, and 27,569 of these lie above
$u$*-$r$*$>$2.22 mag. Therefore, this demarcation gives $\sim 80\%$
reliability (Fig 5, contours), suggesting $\sim 20\%$ of the early-type galaxy
population may be excluded through applying this criterion. 147,275 visually
classified ‘spiral’ galaxies from the Galaxy Zoo data are also present in our
control sample. 22% of these lie above $u$*-$r$*$>$2.22, i.e. we expect $\sim
22\%$ contamination in the early-type sample. Of the 499,408 galaxies in the
control sample, $\sim 40\%$ were classified as early-types, using the Strateva
et al. colour selection, to leave 199,391 early-type galaxies in the control
sample, morphologically selected in colour space at $\sim 80\%$ completeness
and $\sim 78\%$ efficiency based on Galaxy Zoo visual analysis.

We explore the 4,998 radio-loud AGN selected galaxies in colour space. Figure
6 shows the radio-loud AGN are predominately early types, with $>70\%$ lying
above $u$*-$r$*$>$2.22, i.e. the radio-loud AGN sources are predominantly
hosted by ellipticals as defined in colour space. The distribution in colour
space is similar to that of the control sample, despite the AGN colours
possibly influencing the light. In agreement with this result, Griffith &
Stern (2010) found radio-selected AGN have a high incidence of being hosted by
early-type galaxies.

The 118 galaxies we flagged as star forming and removed from the radio-loud
sample in §3.6 are shown as crosses in Figure 6, and 98% of these sit below
the line. We select the radio-loud AGN above the colour cut, to give 3,516
‘early-type’ radio-loud AGN hosts.

Figure 6: Colour-colour plot of radio-loud AGN (contoured, binsize =
$0.1\times 0.1\,$mag, 4 equally spaced levels, max density contour = 400/bin),
and SF galaxies as defined in §3.6 (crosses) The dashed line is
$u^{*}-r^{*}\geq 2.22$ from Strateva et al. (2001) and defines a morphological
colour separator.

###  3.8 Redshift distributions

(a) Redshift distributions

(b) Absolute $r^{*}$ magnitude distributions

Figure 7: The fractional distributions of (a) redshift and (b) $r^{*}$ band
luminosity. The solid black line shows the radio-loud AGN distributions. The
red dashed line shows the control sample distribution prior to nearest
neighbour matching in redshift-magnitude space. The blue dotted line shows the
resultant sample randomly selected to match the redshift-magnitude
distributions of the radio sample.

At this stage we re-examined the redshift distributions of the samples, using
the KS test. The probability of the control sample and the radio-loud AGN
being drawn from the same parent sample in redshift was $<0.1\%$: the
distributions in redshift differ (Figure 7(a)). Evolutionary differences in
host galaxy properties should be small over this entire redshift range,
however we chose to re-sample the control sample redshift distribution to
match that of the radio-loud AGN sample.

We also examined the intrinsic $r^{*}$ band luminosity of the two samples.
Figure 7(b) shows the radio sample is globally brighter in $r^{*}$ than the
control sample. It has been well established that radio-loud AGN are hosted
preferentially in the brightest and most massive elliptical galaxies (Best et
al., 2005b; Mauch & Sadler, 2007). Since we wanted to test whether radio-loud
AGN harbour an excess of blue emission in their centres, we chose to re-sample
the control sample to have the same $r^{*}$ band optical properties so as to
avoid any possible correlation of colour gradient with galaxy luminosity.

We generated a matched control sample by selecting the 10 galaxies from the
whole sample that lie closest to each radio-loud AGN in magnitude-redshift
space. The final control sample contains 35,160 galaxies, whose magnitude and
redshift distributions are shown as dotted lines in Figure 7. This final
selection should allow the distribution of observables in the radio and
control samples to be compared directly.

###  3.9 Comparison radio sample (CR)

The criteria applied to the ‘radio’ sample in §3.3-3.8 were also applied to
the 5,719 objects in the CR sample (see §3.2).

We imposed a redshift cut of $0.02<z<0.18$ and restricted the redshift
confidence parameter given by SDSS to $>95\%$, leaving 3,727 sources. We
examined the CR sample radio powers based on NVSS and FIRST. Figure 8 shows
the NVSS and FIRST luminosities for the 3,727 CR sources (grey crosses). Those
with P${}_{\mathrm{1.4\,GHz}}^{\mathrm{NVSS}}>10^{23}$ W Hz-1 are highlighted
by blue squares (50$\%$). We restricted the CR sample to galaxies harbouring
radio sources with P${}_{\mathrm{1.4\,GHz}}^{\mathrm{NVSS}}>10^{23}$ W Hz-1,
which selects 1,847 (50$\%$) of the sample.

Of those 1,847 sources, 251 have FIRST derived powers $<10^{23}$ W Hz-1, and
were therefore excluded in the radio sample selection in §3.4.

Figure 8: FIRST vs NVSS derived luminosities for the 3,737 sources in the
candidate CR sample (grey crosses). Those with
P${}_{\mathrm{1.4\,GHz}}^{\mathrm{NVSS}}>10^{23}$ W Hz-1 are highlighted by
blue squares (1,847). Of those, 251 sources with
P${}_{\mathrm{1.4\,GHz}}^{\mathrm{FIRST}}<10^{23}$ W Hz-1 are shown as red
crosses. These are the sources excluded in the radio sample’s luminosity cut
(§3.4).

We removed 2 type 1 AGN and 48 star-forming galaxies confirmed at S/N $>3$
from the CR sample, leaving 1,797 radio-loud narrow-line AGN hosts. 4$\%$ of
the sample are classified as type ‘1.9’ AGN, with substaintial but not full
obscuration of the central source. We applied the Strateva et al. colour cut
($u$*-$r$*$>$2.22 mag) detailed in §3.7 to select 1,295 early-type galaxies
from the CR sample.

The control sample was cross-matched with the FIRST-NVSS catalogue to within
2″and the 5 galaxies found were removed to ensure the comparison control
sample is comprised solely of ‘radio-quiet’ AGN elliptical hosts. 199,386
galaxies remain in the CR-control sample.

We selected the 10 galaxies from the control sample that lie closest to each
CR radio-loud AGN in magnitude-redshift space. The final CR-control sample
contains 12,950 sources, matched to the CR sample in $r^{*}$-band magnitude
and redshift distributions.

###  3.10 Summary of Final Samples

Radio-loud ‘early type’ AGN (R-AGN) - 3,516 sources
After matching FIRST to the MGS ($r^{*}_{petro}<17.77$ mag, $0.02<z<0.18$)
within 2″, we classified as radio-loud AGN hosts with
P${}_{\mathrm{1.4\,GHz}}>10^{23}$ W Hz-1. Type 1 AGN exhibiting both broad
H$\alpha$ and H$\beta$ emission lines were removed from the sample. Optical
emission line ratios (if confirmed at 3$\sigma$) were used to remove star-
forming galaxies using the demarcation of Kauffmann et al. (2003). We then
created a subset with $u^{*}$-$r^{*}>2.22$ mag i.e. ‘early-types’ to remain
consistent with the colour cut applied to the control sample.

Control sample - 35,160 sources
We removed all galaxies from SDSS-MGS ($r^{*}_{petro}<17.77$ mag,
$0.02<z<0.18$) with FIRST and NVSS counterparts. Type 1 AGN exhibiting both
broad H$\alpha$ and H$\beta$ emission lines were removed from the sample.
Galaxies were constrained in colour to bias towards early-type morphology
where a comparison with results of the Galaxy Zoo program suggests we have
$\gtrsim 80\%$ completeness and $78\%$ efficiency. The resultant sample
comprises radio-quiet, ‘normal’, predominantly elliptical galaxies. We then
selected a subsample to match the redshift and optical $r^{*}$-band magnitude
distributions of the R-AGN sample, thus removing any redshift bias and
potential correlation of colour gradient with galaxy luminosity.

Comparison radio (CR) - 1,295 sources
We cross-matched the FIRST-NVSS catalogue derived by Kimball & Ivezić (2008)
with the MGS ($r^{*}_{petro}<17.77$ mag, $0.02<z<0.18$) to within 2″, and
classified radio-loud AGN hosts as those sources exhibiting
P${}_{\mathrm{1.4\,GHz}}^{\mathrm{NVSS}}>10^{23}$ W Hz-1. Type 1 AGN
exhibiting both broad H$\alpha$ and H$\beta$ emission lines were removed from
the sample. Optical emission line ratios (if confirmed at 3$\sigma$) were used
to remove star-forming galaxies using the demarcation of Kauffmann et al.
(2003). We then created a subset with $u^{*}$-$r^{*}>$2.22 mag i.e. ‘early-
types’ to remain consistent with the colour cut applied to the control sample.

CR-control sample - 12,950 sources
All selection criteria as above for the control sample, we also removed 5
galaxies within the control sample that were also present in the CR sample. We
then selected a subsample to match the redshift and optical $r^{*}$-band
magnitude distributions of the CR sample.

We therefore have two radio-loud AGN samples, both with a comparison control
sample. The CR sample is derived using both radio catalogues, and is a
brighter radio sample (the NVSS flux density completeness limit is $2.5$ mJy)
for comparison with our deeper ($>1$ mJy), larger but more incomplete R-AGN
sample derived solely from the FIRST catalogue.

##  4 analysis

The surface brightness profile of an early-type galaxy can be described by the
Sérsic equation

$I(r)=I(r_{e})e^{-b[(r/r_{e})^{1/n}-1]}$ (3)

where $r_{e}$ is the effective radius (scale length) and $I(r_{e})$ is the
corresponding effective surface brightness. $b\approx 2n-1/3$ is chosen so
$r_{e}$ contains half the light in the galaxy. n $\approx$ 4 for bright
ellipticals decreasing to n $\approx$ 2 as luminosity decreases (Caon et al.,
1993). SDSS chooses to fix $n=4$, fitting the ‘de Vaucouleurs profile’,
truncating the profile beyond 7 $r_{e}$. The model fitted by SDSS has an
arbitrary axis ratio and position angle and is convolved with a double-
Gaussian representation of the PSF. The fitting then yields, among other
properties; the effective radius, $r_{e}$ and error, $\Delta r_{e}$. In
general, the error for the $u$ model is greater than other bands. It is noted
that SDSS’s fitting algorithm generates some weak discretization of model
parameters, especially in $r_{e}(r)$ and $r_{e}(u)$. Objects with scale
lengths lying in discrete bands in $r_{e}$ tend to have poorer goodness of
fit. This is not included in the error estimates, $\Delta r_{e}$, which were
derived from count statistics on the image. In our work with the $r_{e}$
values, we consider $\Delta r_{e}$ rather than DeV_l (the likelihood of the
model fit) due to our reluctance to remove data with poor de Vaucouleurs $u$
band fitting. A poor goodness of fit to the deVaucouleurs profile may be
indicative of a cuspy $u$ band and removing such objects could bias results.

SDSS denotes the fracDeV parameter as the fraction of the total flux
contributed by the de Vaucouleurs component in a linear combination of a de
Vaucouleurs and an exponential model to find the best fit. It is noted that
the likelihood values in the $r^{*}$-band are intrinsically poor (all samples
have mean values $\sim\,0.01$), but the likelihood ratios still pick out
reliable best-fit parameters. The fracDeV parameter ($f$ hereafter) is
correlated with the Sérsic index; n = 1 corresponds to $f$ = 0, n = 4
corresponds to $f$ = 1 (Kuehn & Ryden, 2005, and references therein).
Following Vincent & Ryden (2005), galaxies with $0.5\leq f\leq 0.9$
($2.0\lesssim$ n $\lesssim 3.3$) are labeled “de/ex” galaxies and galaxies
with $f$ $\geq 0.9$ (n $\gtrsim 3.3$) are labeled “de” galaxies. We chose not
to remove objects with $f$ $<\,0.5$, but instead created subsets of each
sample with $f$ $>\,0.5$ for comparison.

We investigate the colour structure of AGN host galaxies principally through
the distribution of $R$, which we define as $R=r_{e}(r)/r_{e}(u)$, which is
the ratio of $r$ to $u$ de Vaucouleurs effective radii. This should avoid any
intrinsic scale differences in $r$ and $u$ between individual galaxies.

###  4.1 Diversity of intrinsic distributions.

The distributions of $R$ for the R-AGN and control sample are shown in Figure
9. Both samples have a few ($<0.001\%$) strong outliers ($R>100$) which
significantly disturb the mean. The medians of the R-AGN and control
distributions are 0.837 and 0.793 respectively. Using a two-tailed Kolmogorov-
Smirnov test we find the probability of the control and the R-AGN sample being
drawn from the same distribution to be small ($<0.1\%$).

Similarly, the CR sample’s $R$ distribution also shows a higher median
compared to the CR-control sample (0.851 and 0.797 respectively). The KS test
also finds the probability of the CR and CR-control sample being drawn from
the same distribution in $R$ is vanishingly small ($<0.1\%$).

Figure 9: Normalised distributions of $R$ for the radio-loud AGN (R-AGN)
sample (solid) and the control sample (red dashed).

###  4.2 Maximum likelihood analysis

The fractional errors in individual values of $r_{e}(u)$ are relatively large,
which makes proving an intrinsic difference between the radio-loud AGN samples
and their respective control sample distributions challenging. We used a
maximum likelihood analysis to compare the average values of $R$ for the AGN
and control samples, taking into account measurement errors according to
Maccacaro et al. (1988) and Worrall (1989), in order to quantify the
difference between the distributions of $R$.

Under the assumption that both the AGN and control samples have normally-
distributed intrinsic values of $R$, then the population mean, $\overline{R}$,
and intrinsic dispersion, $\sigma$, of either can be determined from
individual values $R_{i}\pm\sigma_{i}$ by minimizing the function

$\centering{{\large
S}={\displaystyle\sum\limits_{i}}\left[\dfrac{(R_{i}-\overline{R})^{2}}{(\sigma^{2}+\sigma_{i}^{2})}+\mathrm{ln}(\sigma^{2}+\sigma_{i}^{2})\right]}.\@add@centering$
(4)

(a) R-AGN and control (b) CR and CR-control

Figure 10: 90% (solid line) and 99% (dashed/dotted line) confidence contours
of the mean ratio of scale lengths ($R=r_{e}(r)$/$r_{e}(u)$) and intrinsic
dispersion for radio-loud AGN galaxies and ‘normal’ early types. The control
and radio-loud ‘early-type’ AGN are distinct populations, as are the CR and
CR-control samples.

Figure 10 shows the results of minimization of Eq 4 across $\overline{R}$ and
$\sigma$ parameter space, for the two samples. The 90% and 99% joint-
confidence contours for $\overline{R}$ and $\sigma$ are given by
S${}_{min}+\Delta$S for $\Delta$S$=4.61$ and 9.21 respectively. Table 2 shows
the best fit $\overline{R},\sigma$ planes for both distributions. A clear
separation between radio-loud ‘early type’ AGN and ‘normal’ control galaxies
can be seen for both the R-AGN and CR samples, and we conclude the two are not
drawn from the same population at $\gg 99\%$ confidence.

We applied the cut $f>0.5$ in the $r^{*}$-band, and re-examine the results for
both radio-AGN samples. This cut will ensure the reliability of the de
Vaucouleur’s scale lengths used to derive $R$, and this subset is used as a
comparison to the full samples to verify whether galaxies with shapes that
differ significantly from the de Vaucouleurs profile perturb our main result.
Table 2 also shows the fraction of each sample with ‘good’ de Vaucouleurs
$r^{*}$-band fits and their $\overline{R}$ values (see Figure 11). Although
the values do not significantly differ from the full sample, the confidence
contours now overlap in the smaller, but more complete, CR sample. However,
the R-AGN and control samples are still seen to come from distinct
populations.

Sample | $\overline{R}$ | $\sigma$ | $f>0.5$ | $\overline{R}_{f}$ | $\sigma_{f}$
---|---|---|---|---|---
R-AGN | 0.76$\pm$0.02 | 0.23$\pm$0.01 | 53$\%$ | 0.77$\pm$0.02 | 0.25$\pm$0.02
Control | 0.719$\pm$0.005 | 0.206$\pm$0.003 | 49$\%$ | 0.722$\pm$0.006 | 0.208$\pm$0.005
CR | 0.78$\pm$0.02 | 0.20$\pm$0.02 | 44$\%$ | 0.77$\pm$0.03 | 0.19$\pm$0.03
CR-Control | 0.731$\pm$0.007 | 0.204$\pm$0.006 | 49$\%$ | 0.730$\pm$0.010 | 0.206$\pm$0.007
Table 2: Best fit $\overline{R}$ and $\sigma$ corresponding to $90\%$ error,
for the R-AGN and CR sample, and their relative control samples. The fraction
of each sample with $r^{*}$-band $f>0.5$ is shown, and the resultant mean and
standard deviation, $\overline{R}_{f}$ and $\sigma_{f}$.

(a) R-AGN and control (b) CR and CR-control

Figure 11: 90% (solid line) and 99% (dashed/dotted line) confidence contours
of the mean ratio of scale lengths ($R=r_{e}(r)$/$r_{e}(u)$) and intrinsic
dispersion for the subset of galaxies with $f>0.5$. The 1,851 radio-loud AGN
galaxies and 17,338 ‘normal’ early types are shown in panel (a), the 575 CR
galaxies and 6,364 CR-control galaxies are shown in panel (b). The control and
radio-loud ‘early-type’ AGN remain distinct populations. The smaller CR and
CR-control sample lead to larger confidence contours that overlap, but these
remain distinct at $89\%$ confidence.

##  5 Discussion

Our results confirm that radio-loud AGN are hosted by brighter, bigger
galaxies on average (see Figure 7). Our technique has shown the presence of an
AGN is associated with an increase of the scale size of a galaxy in red light
relative to blue light. This suggests that radio galaxies have a bluer central
bulge and/or more diffusely distributed red light compared to their radio-
quiet counterparts. With the analysis so far, we cannot tell whether this
difference is from AGN driven or diffuse star-like light within the bulge, or
more distributed red light.

The CR sample is also significantly different in $\overline{R}$ relative to
the CR-control sample, so that our R-AGN sample’s lower completeness in
extended sources does not significantly affect the result. The CR sample
dispersion is smaller than that of the R-AGN sample, whereas all four control
samples have values of $\sigma$ that are similar. We applied a flux cut of
$>4$ mJy to the R-AGN sample (61$\%$), and found $\overline{R}=0.80\pm 0.02$
and $\sigma=0.21\pm 0.01$. The increased scatter about $R$ is caused by
fainter radio sources, which tend to be more heterogenous, and/or have
underestimates of errors on $r_{e}$ values in more distant objects.

The subset of CR galaxies constrained to have good $r^{*}$-band de Vaucouleurs
fits ($f>0.5$) does not contain enough radio galaxies to show strongly a
significant separation from the CR-control sample (see Figure 11(b)). We
present discussion predominantly on the R-AGN and control sample, which
display a clear separation in both Figure 10(a) and 11(a). We concluded the
two are not drawn from the same population at $\gg 99\%$ confidence. This
sample is incomplete to radio sources with lobes $>5.4$″ and the population of
galaxies with a weak radio AGN core but powerful lobes. However it is large
due to the depth of the FIRST survey. The CR results for all Figures in the
discussion are similar to the results presented for the R-AGN sample. We find
no significant deviation between the two in any subsequent parameter examined,
except in $\sigma$, as discussed above.

Figure 12: Radio luminosity density vs $R$ for the CR sample. We found no
correlation ($>99\%$ certainty) between the two.

Mahabal et al. (1999, hereafter MKM99) used a complementary
ratio555$r_{e}(B)/r_{e}(R)$ to demonstrate the ubiquity of inner blue
components in a sample of only 30 radio galaxies and 30 control galaxies, and
argued that the blue light is due to star formation associated with the
presence of a radio source (e.g. Antón et al., 2008). Figure 4 of MKM99 (power
at 408 MHz vs log [$r_{e}(B)/r_{e}(R)$]) shows a trend for more powerful radio
galaxies to have steeper colour gradients as indicated by the ratio of scale
lengths. In contrast to this, when considering only the brightest
(P${}_{\mathrm{1.4\,GHz}}>10^{25}$ WHz-1) radio sources in the CR sample (for
which the powers are more accurate) we find no correlation between radio power
and $R$. We also find no correlation over the full range of radio powers and
$R$ as shown in Figure 12: the Spearman’s rank correlation result is $\pm
0.07$ or less between P${}_{\mathrm{1.4\,GHz}}$ and $R$. We infer that a high
value of $R$ (and possible blue central bulge) is not associated with the
power of the radio source.

There are several possible scenarios to be considered to explain the larger
$R$ in the R-AGN sample.

###  5.1 AGN light

Central point-like $u^{*}$ light may be indicative of a blue AGN. We
investigated the nature of the R-AGN excess $R$, using the goodness of the
deVaucouleurs fit. The SDSS deVaucouleurs fitting procedure returns the
likelihood (between $0$ and $1$) associated with the model from the $\chi^{2}$
fit. If the $u^{*}$-band goodness of fit for the R-AGN sample approaches 1 for
low $R$ and 0 for high $R$ then this is indicative of an AGN/core component
(as the AGN point-like component would perturb a deVaucouleurs fit) driving a
blue excess and high $R$. If no structure is seen in $R$ vs deVaucouleurs
$u^{*}$-band goodness of fit in either sample, then any blue excess is more
likely driven by some sort of diffuse starlight in the central bulge.

The $u^{*}$-band data for both the R-AGN and control samples are generally
well fit by a deVaucouleurs profile (the R-AGN/control median likelihood
values are 0.86 and 0.83 respectively), and there is no trend for the
$u^{*}$-band or $r^{*}$-band fits to be worse at large $R$ in the R-AGN than
the control sample. We can conclude that the high $R$ in the R-AGN sample is
not due to any point-like AGN component.

###  5.2 Radio AGN triggering star formation

It is generally agreed that AGN feedback regulates the supply of cold gas for
star formation by supplying energy to the ISM and IGM. Some radio-loud star-
forming AGN show a connection between the suppression of star formation and
the strength of the radio jets, by heating and expelling the surrounding gas
(Nesvadba et al., 2008). Schawinski et al. (2009) looked at a sample of low
redshift SDSS early-type galaxies for which late-time star formation is being
quenched. They found that molecular gas disappears less than 100 Myr after the
onset of accretion onto the central black hole. These galaxies were not
associated with radio jets, but show that low-luminosity AGN episodes are
sufficient to suppress residual star-formation in early-type galaxies.

Figure 13: Residual fractional number density distributions (R-AGN - control),
in 2 kpc bins, for the $u^{*}$-band and $r^{*}$-band scale radii. There is a
higher fraction of blue cores in the R-AGN sample as compared to the control
sample at $r_{e}\sim 10$ kpc. This plot does not demonstrate the correlation
between the red and blue scale radii (see Figure 14). The measurement errors
are larger in the $u^{*}$ band which may account for the higher variability in
the residuals.

The residual fractional number density distribution of scale lengths are shown
in Figure 13, for the control sample subtracted from the R-AGN sample. There
is a clear excess of blue cores ($0.1-10$ kpc) in the R-AGN sample as compared
to the control sample. There are also more small $r_{e}(r^{*})$ in the R-AGN
sample, ranging from $4-10$ kpc. This plot does not demonstrate the
correlation between the red and blue emission, which is shown in Figure 14,
but it does demonstrate that the presence of a radio AGN seems not to have
suppressed star-formation in the central regions of its host galaxy.

Figure 14: Normalised number densities of $r_{e}(u^{*})$ and $r_{e}(r^{*})$
for the R-AGN (solid) and control sample (red dashed). The dotted - dashed
line is the locus $r_{e}(r^{*})=0.719r_{e}(u^{*})$, galaxies above this line
become bluer inward. Contours show the fractional number densities of each
sample with levels at 0.004, 0.008 and 0.011. There is a larger fraction of
the R-AGN sample above the line, possibly denoting a tendency to become bluer
inward more often than the control sample.

Figure 14 plots $r_{e}(u^{*})$ against $r_{e}(r^{*})$ for the R-AGN sample
(black) and the control sample (red dashed). The dotted - dashed line denotes
the locus $r_{e}(r^{*})=0.719r_{e}(u^{*})$ as defined by the control sample
(see Table 2).

At $r_{e}(r^{*})>0.719r_{e}(u^{*})$, the surface brightness in $u^{*}$
increases more rapidly toward the centre of a galaxy than in $r^{*}$ as
compared to the mean of the control sample, i.e. half the blue light from the
galaxy is contained in a smaller region than half the red light, implying the
galaxy becomes bluer inward.

The distribution of number densities in Figure 14 shows radio galaxies appear
to become bluer inwards more often than the control galaxies (66% of the R-AGN
sample are above the locus $r_{e}(r)=0.719\,r_{e}(u)$, compared to 60% of the
control sample).

There are fewer blue smaller cores in the control sample as compared with the
R-AGN sample (see also Figure 13), implying there may be a blue excess near
the AGN core for some of the radio galaxies. However, the higher $R$ values of
the R-AGN sample also seems to be driven by a higher scale length in $r^{*}$,
seen in the difference between the inner two contour levels of each sample
(see also §5.4), so we cannot definitively conclude that the increased $R$ in
the R-AGN sample is due to star formation within the central few kpc. Star-
formation within the central few kpc would contradict feedback models which
predict the suppression of star formation near an AGN.

###  5.3 Star formation in the bulge

Shabala et al. (2008) found that radio sources in massive hosts are re-
triggered more frequently than their less massive counterparts, suggesting
that the onset of an AGN quiescent phase is due to fuel depletion. AGN
activity is therefore promoted by an increase in gas in the centres of the
galaxies, which may imply a link between the AGN radio phase and star
formation in the bulge ($<10$kpc) of the host galaxy.

It has been suggested that AGN activity and a major episode of star formation
in radio-loud galaxies is triggered by the accretion of gas during major
mergers and/or tidal interactions. However AGN activity is initiated later in
the merger event than the starburst (e.g. Schawinski et al., 2007; Emonts et
al., 2006; Tadhunter et al., 2005). Our spectroscopic selection rules out
major merger events (see §2.1.1), but residual star formation may still be
present on global scales.

Observationally, there is a strong link between AGN and starbursts (Shin et
al., 2011, and references therein). Kauffmann et al. (2003) found powerful
optical AGN (as classified by the strength of the [OIII] emission
$L_{\mathrm{[OIII]}}>10^{7}L_{\odot}$) predominantly reside in ‘young bulges’.
Recent star formation can provide up to $25-40\%$ of the optical/UV continuum
in radio galaxies at low and intermediate z e.g. (e.g., Holt et al., 2007;
Tadhunter et al., 2005).

We found a higher fraction of R-AGN galaxies have $r_{e}(u^{*})<10$ kpc as
compared to the control sample (see Figure 13), perhaps indicative of star
formation in the outskirts of the bulge, fuelled by gas expelled from the
central regions by the AGN.

###  5.4 Diffuse red emission

An alternative interpretation of a larger $R$ is that the R-AGN sample has
more distributed red light. Radio-loud ‘early-type’ galaxies predominantly
reside in elliptical galaxies, which are well known to be redder than late-
types (e.g., Strateva et al., 2001). Diffuse red emission would cause a larger
deVaucouleurs scale radius in the $r^{*}$ band and an increased $R$.

Figure 14 suggests the increased $R$ in the R-AGN sample may also be
attributed to more diffuse red light; between $r_{e}(u^{*})\sim 4-10$ kpc,
$r_{e}(r^{*})$ is on average higher for the radio population. This is also
seen in the lower panel of Figure 13.

Our results show a difference in the distributions of red and blue light in
R-AGN and normal ‘early-type’ galaxy populations, though a high value of $R$
is not a property of every active galaxy. We found the higher $R$ in the R-AGN
sample is contributed to by a higher fraction of radio galaxies harbouring
small blue cores but also an increase in the numbers of radio galaxies with
more diffuse red light as compared to the control sample. Given that star
formation proceeds over a longer timescale than radio activity, this
disfavours the idea that all galaxies undergo short bursts of radio activity,
but rather implies that a subset have the predisposition to become radio-loud.

##  6 Conclusion

We cross-matched low-redshift ($0.02<z<0.18$) data from the SDSS MGS
($r^{*}_{petro}<17.77$ mag) and FIRST to within 2″, deriving a radio sample of
galaxies at $>99\%$ efficiency and $>72\%$ completeness. Radio luminosities
were in the range $10^{23}-10^{25}$ WHz-1. Type 1 AGN were removed from the
sample (identified via $H\alpha$ and $H\beta$ broad line characteristics),
4$\%$ of the sample are classified as type ‘1.9’ AGN, with substantial but not
full obscuration of the central source. Contamination from SFGs (identified
via optical emission line ratios) in the radio sample is expected at $\sim
11\%$. A control sample was defined from SDSS sources with no match to a FIRST
source within 2″ of their optical core, providing a sample of $>99\%$
efficiency and $>92\%$ completeness. At 80% reliability, the demarcation
$u^{*}-r^{*}>2.22$ mag selected ‘early-type’ galaxies in both samples. Samples
were matched in $r^{*}$-band magnitude and redshift distributions and final
sample sizes were 3,516 radio-loud AGN galaxies (R-AGN) and 35,160 control
galaxies.

We also created a complementary flux-limited sample through cross-matching
with NVSS (the CR sample). The same cuts were applied to derive a radio-loud
‘early-type’ AGN sample, except we used the more all-encompassing NVSS flux
estimates to cut in radio luminosity, thereby retaining the populations of
galaxies with weak/no core radio emission but bright, extended radio lobes.
This sample had higher completeness for comparison with the R-AGN sample. A
control sample was defined from the SDSS sources with no match to a NVSS-FIRST
source within 2″ of their optical cores. We further considered only sources
where fracDeV (f) $>0.5$ to restrict all four samples to having good
$r^{*}$-band deVaucouleurs fits.

We investigated the colour structure of AGN host galaxies through $R$, the
ratio of $r^{*}$ to $u^{*}$ de Vaucouleurs effective radii and used maximum
likelihood analysis to quantify the degree of difference in the distribution
of $R$ between samples. We concluded the radio (R-AGN/CR) samples are not
drawn from the same population as their radio-faint control samples at $\gg
99\%$ confidence: the presence of an AGN increases the scale size of a galaxy
in red light relative to blue light, on average.

Our result does not appear to be driven by the presence of blue AGN in the
radio-loud samples since the goodness of the de Vaucouleurs fits does not
become worse as $R$ increases. We found no structure in $R$ vs $u^{*}$-band
goodness of fit in either radio sample. We found an excess of blue cores in
radio-loud galaxies as compared to radio-quiet, ‘early-type’ galaxies,
implying the increased $R$ may be due to star formation in the central few
kpc, in contrast with feedback models which predict the suppression of star
formation near an AGN. Spectroscopic selection of our samples rules out major
merger events, as starbursts can be triggered by the accretion of gas/tidal
interactions. We also found radio AGN hosts to have larger red scale lengths
in relation to their blue light and note this to be a contributing factor in
an increased $R$. We cannot definitively discern whether a small blue core or
larger distribution of red light is the driving factor in this result.

Given the longer timescale for star formation than radio activity, our results
imply a subset of galaxies have the predisposition to become radio-loud,
rather than all galaxies undergoing bursts of radio activity at some stage in
their lifetimes.

## Acknowledgements

EM gratefully acknowledges support from the UK Science and Technology
Facilities Council and thanks Luke Davies and James Price for helpful
comments. We thank the anonymous referee for helpful and insightful comments
that have resulted in an improved analysis. In undertaking this research, we
made extensive use of the topcat software (Taylor, 2005). Funding for the SDSS
has been provided by the Alfred P. Sloan Foundation, the Participating
Institutions, the National Science Foundation, the U.S. Department of Energy,
the National Aeronautics and Space Administration, the Japanese
Monbukagakusho, the Max Planck Society, and the Higher Education Funding
Council for England. This research makes use of the NVSS and FIRST radio
surveys, carried out using the National Radio Astronomy Observatory Very Large
Array: NRAO is operated by Associated Universities Inc., under cooperative
agreement with the National Science Foundation.

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