11institutetext: Astronomisches Rechen-Institut, Zentrum für Astronomie der
Universität Heidelberg, Mönchhofstr. 12-14, 69120 Heidelberg,
Germany22institutetext: ASTRON, the Netherlands Institute for Radio Astronomy,
Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands 33institutetext:
Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AV
Groningen, The Netherlands

# Connecting the radio AGN life cycle to feedback

Ionised gas is more disturbed in young radio AGN

Pranav Kukreti and Raffaella Morganti 112233<EMAIL_ADDRESS>2233

(Received ** ** 2024 / Accepted ** ** 2024)

In the host galaxies of radio active galactic nuclei (AGN), kinematically
disturbed gas due to jet-driven feedback is a widely observed phenomenon.
Simulations predict that the impact of jets on the surrounding gas changes as
they grow. Useful insights into this phenomenon can be obtained by
characterising radio AGN into different evolutionary stages and studying their
impact on gas kinematics. We present a systematic study of the [OIII] gas
kinematics for a sample of 5 720 radio AGN up to $z$ $\sim$ 0.8 with a large
1.4 GHz luminosity range of $\approx 10^{22.5}-10^{28}$ W Hz-1, and 1 693
[OIII] detections. Our careful separation of radio emission from AGN and star
formation allows us to isolate the impact of radio jets. Taking advantage of
the wide frequency coverage of LOFAR and VLA surveys from $144-3000$ MHz, we
determine the radio spectral shapes, using them to characterise sources into
different stages of the radio AGN life cycle. We determine the [OIII]
kinematics from SDSS spectra and link it to the life cycle. Our main
conclusion is that the [OIII] gas is $\sim$ 3 times more likely to be
disturbed in the peaked spectrum (PS) sources (that represent a young phase of
activity) than non-peaked spectrum (NPS) sources (that represent more evolved
sources) at $z<0.4$. This changes to a factor of $\sim$ 2 at $z>0.4$. This
shows that on average, the strong impact of jets is limited to the initial
stages of the radio AGN life cycle. At later stages, the impact on gas is more
gentle. We also determine the dependence of this trend on 1.4 GHz and [OIII]
luminosities, and find that the difference between the two groups increases
with 1.4 GHz luminosity. Young radio AGN with $L_{\mathrm{1.4GHz}}>10^{25}$ W
Hz-1have the most extreme impact on [OIII] . Using a stacking analysis, we are
further able to trace the changing impact on [OIII] in the high frequency
peaked spectrum (i.e. youngest), low frequency peaked spectrum (?less young?),
and non-peaked spectrum (evolved) radio AGN.

###### Key Words.:

evolution - galaxies: interactions - galaxies: jets - ISM: jets and outflows -
galaxies: evolution - galaxies: active

##  1 Introduction

Active galactic nuclei (AGN) are now understood to be linked to the evolution
of massive galaxies in the Universe. This link manifests in the form of
feedback that can quench star formation, releasing energy that can prevent
cooling of the gas in hot halos, and even regulate the growth of the central
supermassive black hole itself (for example Silk & Rees 1998; Fabian 2012;
McNamara & Nulsen 2012). The mechanical energy released during a phase of
activity can shock the host galaxy’s gas, sometimes even sweeping it up in
high-velocity outflows. This mechanical energy can be propagated by accretion-
driven winds, radiation pressure, collimated jets of plasma, etc (see Fabian
2012; King & Pounds 2015; Harrison & Ramos Almeida 2024 for a review).
Observational evidence of this form of feedback has been found in both
radiatively efficient and inefficient AGN host galaxies.

Feedback driven by collimated jets has been widely observed in radio AGN host
galaxies. These are systems where radio emission is dominated by the AGN, and
cannot be entirely attributed to star formation. Although their energetic
output is often dominated by mechanical energy in relativistic plasma jets,
they can also release high levels of radiative energy. Over the years, many
observational studies have established the presence of jet-driven feedback in
radio AGN host galaxies (e.g. Morganti et al. 2021b; Murthy et al. 2022;
Nesvadba et al. 2021; Ruffa et al. 2022; Schulz et al. 2021 for some recent
results). A limited number of statistical studies have confirmed a positive
correlation between the presence of radio emission and disturbed ionised gas
kinematics, in particular Mullaney et al. (2013). An interesting aspect of
this study is that their AGN sample was selected using optical emission line
ratios, and these sources don’t necessarily harbour radio jets. But it
highlights the broader role that jets could play in feedback. Recently,
similar results have also been found for quasars and broad-line AGN by Escott
et al. 2024, who obtained a larger fraction of sources with outflows in radio-
detected than non-radio-detected sources. However, it is worth noting that
some studies have also found no significant relation between disturbed ionised
gas and radio luminosity or morphology (for example Woo et al. 2016; Ayubinia
et al. 2023).

Studies of radio AGN samples have also pointed towards a positive correlation
between young radio AGN and more disturbed gas kinematics (ionised and neutral
phase; e.g. Holt et al. 2008; Geréb et al. 2015; Roche et al. 2016; Molyneux
et al. 2019; Murthy et al. 2019; Kukreti et al. 2023), proposing a picture
where the impact of jet-driven feedback evolves throughout the active phase.
This picture is broadly supported by simulations of jet-ISM interaction, which
find a more extreme impact on the clumpy gas medium at early stages of jet
growth (Sutherland & Bicknell, 2007; Mukherjee et al., 2018).

For radio AGN, observational evidence for the link between different stages of
jet growth (young or evolved sources) and feedback, is still limited to
powerful systems ($>10^{26}$ W Hz-1) or small samples. Although some trends
have been found between radio emission and ionised gas kinematics for large
samples (e.g. Mullaney et al. 2013; Molyneux et al. 2019, they have been
focused on AGN selected using optical emission line ratios, and are not
necessarily radio AGN. To understand the relation between jet growth and
feedback using radio properties, selecting sources where the radio emission is
dominated by jets is crucial. Our approach is to select such a sample, split
it into different stages of life cycle and link it to its ionised gas
kinematics.

The radio AGN life cycle has been established over the years using their
spectral and morphological properties. In early stages of growth, young radio
AGN are found to have a peaked radio spectrum and morphologically compact
radio emission (for example Callingham et al. 2017, and see O’Dea 1998 and
O’Dea & Saikia 2021 for reviews). These properties have been observed in the
compact steep spectrum (CSS) and gigahertz peaked spectrum (GPS) sources, and
the period of this phase is found to be $\sim$ $0.001-1$ Myr from studies
based on radio spectral modelling (Murgia et al., 1999; Murgia, 2003) and hot
spot separation velocities (Polatidis & Conway, 2002; Giroletti et al., 2003;
Giroletti & Polatidis, 2009). The peaked radio spectrum is either due to
synchrotron self-absorption (Tingay & de Kool, 2003; Snellen et al., 2000; De
Vries et al., 2009; Artyukh et al., 2008) or free-free absorption from an
ionised medium (Kameno et al., 2000, 2005; Callingham et al., 2015; Mhaskey et
al., 2019; Keim et al., 2019). At later stages of the life cycle (a few tens
of Myr), the radio spectrum is observed to be optically thin, due to the peak
shifting to lower frequencies and eventually below the observing frequencies
of most radio telescopes.

A single phase of activity can last up to $\sim$ $10-100$ Myr (see Morganti
2017 for a review). After the activity stops and there is no more injection of
fresh electrons, radiative losses dominate the emission leading to steep
spectra and low surface brightness diffuse emission, called the remnant stage
of the life cycle (Parma et al., 2007; Saripalli et al., 2012; Brienza et al.,
2017). In some cases, remnant phase emission is found along with emission from
a young phase at the centre, suggesting that the new phase of activity has
started even before the radio plasma from the older phase has faded below
detection limits (13-15%; Jurlin et al. 2020). These are called restarted
radio AGN (for example, Brienza et al. 2018; Morganti et al. 2021c, a; Kukreti
et al. 2022). Therefore, the radio spectral properties change over the life
cycle and can be used to characterise a sample of radio AGN into different
stages of evolution.

This approach was used in Kukreti et al. (2023), hereafter K23, where we
already found some evidence for more disturbed ionised gas in young radio AGN
than their evolved counterparts. We characterised the evolutionary stage using
their radio spectral shape, and their ionised gas kinematics using the [OIII]
spectra. The main result of K23 was that on average, peaked radio spectrum
sources had a broader [OIII] profile than sources without a peak. Since peaked
sources represent a younger phase of activity, as discussed above, this
suggested a link between the life cycle and feedback on ionised gas.

Although interesting, this study only used a small sample of $\sim$ 130
sources up to $z\sim 0.2$ covering a radio luminosity range of $\sim$
$10^{23}-10^{25}$ W Hz-1. The small sample size also made it impossible to
control for important AGN parameters like radio and optical luminosity, source
sizes, etc. The purpose of the present paper is to investigate the link
between radio AGN life cycle and feedback for a sample of 5 720 radio AGN up
to $z\sim 0.8$ that cover a radio luminosity range from $\sim$
$10^{22.5}-10^{28}$ W Hz-1. The large size and range of luminosities allow us
to control for source properties and disentangle their role.

The paper is structured in the following manner: Section 2 describes the
approach for sample construction, Section 3 describes the modelling of the
stellar continuum and emission line profiles of the sources, Section 4
describes the diagnostics used to select the radio AGN sample and Section 5
describes the radio properties of this radio AGN sample. We then present the
results for different source groups in Section 6 and discuss them in Section
7. Throughout the paper, we have used the $\Lambda$CDM cosmological model,
with H0 = 70 km s-1 Mpc-1, $\Omega_{\mathrm{M}}=0.3$ and
$\Omega_{\mathrm{vac}}=0.7$.

##  2 Sample construction

This section outlines the approach used to construct the radio AGN sample. The
sample was constructed using the Faint Images of the Radio Sky at Twenty-cm
survey at 1400 MHz with $\sim$ 5.4′′ resolution (FIRST; Becker et al. 1995),
the LOFAR Two-metre Sky Survey at 144 MHz with 6′′ resolution (LoTSS; Shimwell
et al. 2017, 2022), the Very Large Array Sky Survey at 3000 MHz with $\sim$
$2.5-3$′′ resolution (VLASS; Lacy et al. 2016, 2020; Gordon et al. 2021) and
the Sloan Digital Sky Survey (SDSS) which provides spectra with a 3′′ size
fibre. These surveys were chosen as they provide radio and optical data over
similar resolutions, allowing comparison of these properties over similar
physical scales.

The parent sample was the 2014 December 17 version of the FIRST survey
catalogue (Helfand et al., 2015) which was cross-matched with the SDSS DR17
spectroscopic catalogue (Abdurro’uf et al., 2022) using a search radius of
3′′(approximately half the FIRST beam size). The cross-matching was done down
to a peak flux density of 5 mJy in FIRST, which corresponds to
$L_{\mathrm{1.4GHz}}\approx 5\times 10^{23}$ W Hz-1at $z=0.2$. This provided a
sample of 29 921 sources.

We then restricted the sample to $z=0.8$, after which the [OIII]
$\mathrm{\lambdaup\lambdaup}$4958,5007Å doublet moves outside the SDSS
wavelength coverage. We removed sources below $z=0.02$, since below this
redshift the SDSS fibres probe too small a region in a galaxy to determine
reliable parameters. To obtain accurate redshifts, we only selected sources
with a fractional error in redshift less than 0.01. This narrowed the sample
down to 17 405 sources.

Next, we cross-matched this sample with the LoTSS DR2 (Shimwell et al., 2022)
and VLASS Quick Look epoch 2111https://cirada.ca/vlasscatalogueql0 (Lacy et
al., 2016) catalogues. We used the recommendations provided in the VLASS
catalogue user guide available online, to select sources with reliable
detections. Cross-matching was done using TOPCAT (Taylor, 2005), with a radius
of 6′′, which is comparable to the FIRST and LoTSS resolution. This gave us a
sample of 6 556 sources, all of which have a LoTSS cross-match and out of
which 6 400 have a VLASS cross-match.

(a) $L_{\mathrm{1.4GHz}}$ vs $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}}$ for radio AGN

(b) Properties of peaked and non-peaked sources in low redshift sample
($z<0.4$).

Figure 1: Properties of the radio AGN sample. (a) $L_{\mathrm{1.4GHz}}$ vs
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ for the full radio AGN
sample, with [OIII] detections and non-detections shown separately. In the
case of [OIII] non-detections, the contour plot shows the upper limits for
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$. The green hatched region
marks the luminosity space occupied by the control sample selected from
Mullaney et al. (2013), described in Sect. B. The dashed and dotted lines show
the radio luminosity expected from the interaction of AGN-driven winds with
the ISM from the model of Nims et al. (2015), for 1% and 10% of the shock
energy going into relativistic electrons. (b) Distributions of host galaxy
properties for the peaked and non-peaked radio AGN in the low redshift sample.
Only the [OIII] detections are shown. Vertical lines show the mean values of
the distributions. The same plot for the high redshift sample is shown in Fig.
LABEL:sampleproperties_highz

One of the diagnostics used for selecting radio AGN in this paper involves the
Wide-field Infrared Survey Explorer (WISE) mid-infrared colours, which trace
dust heated by AGN and stars. We added WISE data using the allWISE IPAC
release from November 2013 (Cutri et al., 2021). We used three bands of the
WISE catalogue - W1 at 3.4$\mu$m, W2 at 4.6$\mu$m and W3 at 12$\mu$m, that
have an angular resolution of $6.1-6.5$′′. We applied a signal-to-noise ratio
(S/N) cut of 5 for bands W1 and W2, and 3 for band W3 due to its poorer
sensitivity. However, we also kept sources with S/N less than 3 in W3 and used
them to determine upper limits. We selected only sources with cc_flag=000 as
suggested in the online user manual. To avoid performing $k$-corrections, we
only cross-matched the 2 310 sources up to $z=0.3$, and obtained a cross-match
for 2 308 sources.

Radio luminosity at 1.4 GHz is commonly used in literature for radio AGN. To
allow for comparison with other studies, we also estimated the total 1.4 GHz
luminosity of our sources. The low sensitivity of FIRST to extended emission
means that it could underestimate the total luminosity. The $\sim$
$5.4\text{${}^{\mathrm{\prime\prime}}$}$ resolution also means that a large
source can be split up into several individual components, further
underestimating the total luminosity. We therefore used the combined radio
catalogue from Mingo et al. (2016), who performed a detailed and accurate
cross-match between FIRST and the NRAO VLA Sky Survey (NVSS; Condon et al.
1998) sources at 1.4 GHz. The lower resolution ($\sim$ 45′′) of NVSS makes it
more reliable for estimating total radio luminosities. We used the combined
flux densities from this catalogue to estimate the $k$ corrected 1.4 GHz
luminosities.

We aim to use the [OIII] $\mathrm{\lambdaup\lambdaup}$4958,5007Å doublet to
trace the ionised gas kinematics, and other emission line ratios to measure
the ionisation properties. For this, we used the SDSS spectra. The details of
the stellar continuum and emission line modelling, [OIII] profile
characterisation, and stacking analysis are described in Sect. A. We remove 52
sources from this sample where either the spectra are corrupted at [OIII]
wavelength or an accurate characterisation of the [OIII] profile is not
possible. This gives a final sample of 6 504 sources. A summary of the number
of sources with different emission line detections is shown in Table. 2.

Table 1: Emission line detections summary

3 | Total |  [OIII] | H$\beta$ | H$\alpha$ | [Nii] | [Sii]
---|---|---|---|---|---|---
3 Full sample | 6504 | 2333 | 1469 | 1574 | 1574 | 1111
Radio AGN | 5720 | 1693 | 879 | 973 | 973 | 566 |
3 |  |  |  |  |  |  |

Note. Summary of emission line detections in the full sample and selected
radio AGN sample, discussed in Sect. A and B.

Finally, we identify 5 720 radio AGN from this final sample, using a
combination of diagnostics described in Best et al. (2005); Best & Heckman
(2012) and Sabater et al. (2019). These diagnostics help us construct a clean
sample of radio AGN, where the radio emission is dominated by the AGN and not
star formation. The procedure is described in Sect. B in the appendix. Our
radio AGN sample spans a wide range in total 1.4 GHz luminosity from $\sim$
$10^{22.5}-10^{27}$ W Hz-1, and has 1 693 [OIII] detections with an observed
[OIII] luminosity range of $\sim$ $10^{39}-10^{44}$ erg s-1. This is shown in
Fig. 1(a). The host galaxies have stellar masses from $\sim$ $10^{10}$ to
$10^{12.4}$ M⊙. The host galaxies also span a wide range in $g-r$ colour,
containing both red ($g-r>0.7$) and blue ($g-r<0.7$) objects, with a median
$g-r=1.5$.

Radio emission in the so-called radio-loud AGN is attributed to jets, however,
the origin is not completely clear for radio-quiet AGN. For these sources,
radio emission can have multiple origins: star formation, innermost accretion
disk coronal activity, low power jets and shocks due to interaction between
AGN-driven winds and the ISM (Panessa et al., 2019; Zakamska & Greene, 2014;
Zakamska et al., 2016). Since we aim to study jet-driven feedback down to
$L_{\mathrm{1.4GHz}}\sim 10^{23}$ W Hz-1, it is important to confirm that the
radio emission in our sample is dominated by jets even at low luminosities. We
have selected our sources to have radio emission significantly more than
expected from star formation, using the diagnostics mentioned before. Further,
most of our sources also have radio luminosities $>$ $10^{23}$ W Hz-1, which
is more than expected from the corona (Raginski & Laor, 2016). In Fig. 1(a) we
also plot the expected radio luminosity from AGN wind shocks, using the
fiducial models of Nims et al. (2015). An overwhelming majority of the sources
lie much above this model, confirming that the radio emission is dominated by
jets in our sample.

Our radio AGN sample spans a wide range in redshift from $z=0.02$ to $z=0.8$,
leading to a large range of 1.4 GHz luminosities. Figure 2 shows
$L_{\mathrm{1.4GHz}}$ as a function of redshift. It can be seen that the
typical radio luminosities being probed increase with redshift, as expected
for a flux-limited sample. This means we are probing jets of intrinsically
very different powers at the high and low redshift end. Therefore, we split
the sample into two groups about $z=0.4$ (see source numbers in Table 4). This
allows a reasonable comparison, while also keeping enough sources in each sub-
sample for a statistically significant analysis. The low redshift sample
($z<0.4$) probes a wide range of luminosities ($\sim$ $10^{22.5}-10^{26}$ W
Hz-1), while still being comparable to the sample used in K23. We discuss the
results for the low and high redshift samples separately in Sect. 4.

To determine the role of jets in driving feedback, it is also crucial to
compare the [OIII] kinematics of our radio AGN with a control sample of
optical AGN sources that do not host radio jets. The diagnostics we use allow
us to select a clean radio AGN sample, but the 743 sources classified as
SF/radio-quiet AGN could still have low luminosity radio AGN. Thus they do not
provide a clean control sample. Instead, we select a control sample from the
$\approx$ 24 000 type 1 and 2 AGN from Mullaney et al. (2013) up to $z=0.4$.
This sample overlaps with the redshift range of our low redshift sample. These
sources were classified as AGN using their optical emission line widths and
ratios from SDSS. To select as ‘clean’ a control sample as possible without
radio jets, we only use sources with no radio detections in NVSS or FIRST. But
at the sensitivity of NVSS and FIRST, a non-detection does not necessarily
imply a lack of radio jets in the source. Therefore we restrict the sources to
an upper limit of $L_{\mathrm{1.4GHz}}<10^{23}$ W Hz-1. Since LoTSS has higher
sensitivity than FIRST and NVSS, we also removed any source with a LoTSS
cross-match within a 6′′ radius. This ensures that our control sample has no
radio counterpart, and minimises any contamination from even low-luminosity
radio jets. We further restrict the sample to
$10^{39.5}<L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}<10^{42}$
$\mathrm{ergs^{-1}}$, $10^{11}<M_{\star}<10^{11.6}$ M⊙, and
$180<\sigma_{\star}<300$ km s-1to match it to the low redshift sample. This
gives us a control sample of 514 sources. The parameter space occupied by
these sources is shown in Fig. 1(a).

Figure 2: Redshift vs total $L_{\mathrm{1.4GHz}}$ for the selected from the
sample in Sect. B. Peaked and non-peaked sources are marked with different
colours. The sample is split about the dashed line at $z=0.4$ into low and
high redshift sources.

##  3 Radio properties

This section discusses the radio spectra and morphology of the sample. We
first estimate the spectral indices using a combination of LoTSS, FIRST and
VLASS data. We then divide the sources into different spectral shape groups
and link them to their evolutionary stage. Finally, we also characterise the
source sizes using LoTSS and FIRST data. These properties are then linked to
the [OIII] kinematics further in the paper.

###  3.1 Characterising spectral shape

Using the high resolution of LoTSS, FIRST and VLASS we can probe the central
$\sim$ 6′′ region of the radio sources, over spatial scales similar to that
covered by the SDSS fibre. This allows a direct comparison of the radio and
optical properties. To do that, we estimate the spectral indices using the
peak flux densities. For unresolved sources and sources with very weak
extended emission, the peak and total flux densities are similar. However, for
sources with bright extended emission, peak flux density can be significantly
smaller than the total flux density. If the extended emission is optically
thin and dominates the total flux density, using the total flux density to
estimate the spectral index would lead to a source being classified as
optically thin, even if there is a peaked spectrum source at the centre. This
motivated our choice to use the peak flux density for estimating spectral
indices of the radio AGN, to maximise the number of peaked spectrum sources
and detect them even at the centre of large extended sources.

Estimating accurate spectral indices requires reliable flux density values and
comparison over the same spatial scales. The flux densities in the VLASS epoch
1 quick look catalogue were found to be underestimated by a factor of $\sim$
0.87 by Gordon et al. (2021). They compared the VLASS flux densities with TGSS
at 150 MHz, WENSS at 330 MHz, SUMSS at 840 MHz, and FIRST at 1400 MHz to
estimate the systematic flux scale offset. Assuming their corrected flux scale
to be the true flux scale, we have re-scaled our VLASS epoch 2 values to match
the corrected VLASS epoch 1 flux scale. For this, we first compared the flux
densities of epoch 2 to epoch 1 for our sources. The comparison was done only
for point sources with a deconvolved major axis size less than 2′′ in both
epoch data. We found a mean ratio of 0.95 for peak flux densities from epoch 1
to epoch 2, showing that the uncorrected epoch 2 flux densities were larger
than the uncorrected epoch 1 values. Finally, to match the corrected scale
from Gordon et al. (2021), we divided our epoch 2 values by $\approx$
0.87/0.95 = 0.92. We scaled all our VLASS peak flux density values by this
factor. Although this is a large correction factor and a more accurate flux
scale correction probably requires a deeper analysis, this correction is
sufficient for our purpose. Changes in this factor do not affect our results
significantly as we discuss later.

Figure 3: Colour-colour plot of spectral indices for the radio AGN sample. The
different quadrants are labelled with the spectral shapes of the sources lying
in that region. The spectral shapes are also shown above the labels. The red
square marks the region where flat-spectrum (FS) sources lie. A 1:1 line is
shown in blue. While studying the link of spectral shape with gas kinematics,
only HFPS, LFPS and NPS sources are considered.

The next step was to match the resolution of VLASS ($\sim$
$2.5-3\text{${}^{\mathrm{\prime\prime}}$}$) images to FIRST ($\sim$ 5.4′′). We
smoothed the VLASS cutouts around our sources to match the FIRST resolution,
using the same approach as in K23. We used the task IMSMOOTH in CASA to smooth
all VLASS cutouts to the resolution of FIRST. We re-extracted the flux
densities from these images using pyBDSF (Mohan et al., 2015). Finally, the
spectral indices were estimated using the formula
$\alpha=\textrm{log}(F_{\textrm{1,peak}}/F_{\textrm{2,peak}})/\textrm{log}(\nu_{1}/\nu_{2})$.
We plot all the sources on a colour-colour diagram of spectral indices from
144 to 3000 MHz, shown in Fig. 3. Spectral classification of the sources was
then done using this diagram.

As discussed in the introduction, the radio spectrum is absorbed during the
young phase in the radio AGN life cycle. If the observed spectral shape is
fully inverted in our frequency range
($\alpha^{144}_{1400}>0,\alpha^{1400}_{3000}>0$), we classify the source as
high frequency peaked spectrum (HFPS), except for a source in the FS region,
as discussed below. They lie in the top right quadrant of the colour-colour
plot in Fig. 3. These sources likely have a peak frequency larger than 3000
MHz. Some HFPS sources may have a peak frequency between our frequency range,
however, we expect this group to be dominated by the inverted spectrum
sources. If the observed spectral shape has a turnover within our frequency
range ($\alpha^{144}_{1400}>0,\alpha^{1400}_{3000}<0$), we label the source as
low-frequency peaked spectrum (LFPS), shown in the bottom right quadrant of
the colour-colour plot. These sources likely have a peak frequency within our
frequency range. Again, sources lying in the FS region are not included, as
discussed below. In the radio AGN life cycle, HFPS sources represent a younger
phase than LFPS sources, since the peak moves to lower frequencies as the
source evolves. We first combine these two groups and call them peaked
spectrum (PS) sources, to study their [OIII] properties. But we also study
these two groups separately in more detail. Thanks to the low-frequency point
provided by LoTSS, we can detect PS sources down to 144 MHz.

As radio AGN evolve, the peak in their spectrum shifts to lower frequencies,
and eventually the spectrum becomes fully optically thin
($\alpha^{144}_{1400}<0,\alpha^{1400}_{3000}<0$). We label these as non-peaked
spectrum (NPS) sources, and they lie in the bottom left quadrant of Fig. 3,
except for the sources in the FS region. The host galaxy properties of PS and
NPS sources are compared in Fig.1(b), 2 and LABEL:sampleproperties_highz. It
can be clearly seen that they have similar $L_{\mathrm{1.4GHz}}$,
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$, $M_{\star}$,
$D_{\mathrm{{n}}}(4000)$ and $\sigma_{\star}$ distributions. The
$\sigma_{\star}$ values used throughout the paper have been corrected for the
SDSS instrumental resolution ($\approx$ 70 km s-1) and the resolution of the
base spectra used for stellar continuum modelling ($\approx$ 150 km s-1). The
distributions show that there are no intrinsic differences between the host
galaxies of PS and NPS sources. A similar conclusion for the optical
properties of GPS/CSS and Megahertz-Peaked spectrum sources was also reached
by Nascimento et al. (2022).

Sources where free-free emission from the core dominates the radio emission,
or where the emission is relativistically beamed due to a small jet viewing
angle, can have a flat radio spectrum. These flat spectrum sources are usually
defined to have a spectral index $\alpha>-0.5$ (O’Dea, 1998) and are marked
with the red box in Fig. 3. We classify sources with
$-0.55<\alpha^{144}_{1400}<0.05$ and $-0.65<\alpha^{1400}_{3000}<0.15$ as flat
spectrum (FS) sources. The spectral index and radio luminosities of these
sources could affected by relativistic beaming, leading to ’false’ high
luminosity sources. Therefore we do not use them in our analysis of the [OIII]
kinematics. Some sources also have a convex-shaped spectrum, which is
optically thin at lower frequencies and optically thick at higher frequencies.
Although their nature is uncertain, such spectra could be a result of multiple
epochs of jet activity. We label these as convex spectrum (CS) sources and
they lie in the top left quadrant of Fig. 3.

Out of the 5 720 radio AGN, flux densities with a signal-to-noise ratio
greater than 5 were available for 5 686 sources in LoTSS and 5 569 sources in
VLASS. The spectral shape classifications and number of sources in each group
are summarised in Table 4. We note that the flux scale correction of VLASS
data could overestimate the flux densities at 3000 MHz, artificially
flattening the spectral index between $1400-3000$ MHz. This could cause some
NPS sources to move into the FS and CS region of Fig. 3, and lower the number
of NPS sources. However, this will not affect our results since we are still
able to select a clean sample of NPS sources.

Although we use only the peak flux densities in the central region to
calculate the spectral indices, the physical scale covered by a telescope beam
increases with redshift. This leads to a larger contribution from any steep
spectrum diffuse emission around the PS source, if present, to the observed
peak flux density. This resolution effect means that genuine PS sources could
be classified as NPS. Therefore the fraction of PS sources should decrease and
the fraction of NPS sources should increase with redshift, as can be seen in
Fig. 4. This contamination by PS sources makes it harder to select a clean
sample of NPS sources at high redshifts. We discuss this in the context of our
results in Sect. 5.1.

Errors in the spectral indices were estimated using a quadrature combination
of the RMS noise and the flux scale errors of the surveys. We used a flux
scale error of 10% for LoTSS and 5% for FIRST. Since we have also performed
scaling of the VLASS flux scale, we used a conservative value of 10% for VLASS
data. The median error for the spectral index from $144-1400$ MHz was 0.05,
and for $1400-3000$ MHz was 0.15. To test the impact of these errors on the
spectral shape classification, we took the following approach. We added a
random value $\Delta\alpha_{i}$, to each spectral index $\alpha_{i}$, to
obtain a spectral index with an offset, given by
$\alpha^{\textrm{{offset}}}_{i}=\alpha_{i}+\Delta\alpha_{i}$. This
$\Delta\alpha_{i}$ was drawn randomly from a Gaussian distribution with unit
area, zero mean and standard deviation equal to the error in $\alpha_{i}$. The
spectral indices with offsets are shown in Fig. LABEL:lowspecindex_offset and
LABEL:highspecindex_offset. We then reclassified all the sources using the
colour-colour plot with the new offset spectral indices. All results presented
in this paper were then tested with the classifications obtained with these
spectral index offsets.

Figure 4: Fraction of PS and NPS sources in redshift ($z$) bins for the full
radio AGN sample. The fraction is the number of PS (or NPS) sources divided by
the total number of sources in the bin (of all spectral shapes). The
horizontal error bars show widths of the redshift bins used to estimate the
fraction and the vertical error bars show uncertainties on the fraction of PS
and NPS sources in the bin.

###  3.2 Radio source sizes

Morphologically compact radio AGN are considered to be young sources in the
radio AGN life cycle. Therefore the presence of more disturbed ionised and
neutral gas in these sources has been used to suggest a link between the radio
AGN life cycle and feedback (e.g. Geréb et al. 2015; Maccagni et al. 2017;
Molyneux et al. 2019; Murthy et al. 2019; Santoro et al. 2020). However, in
this study, we aim to go further and use the radio spectral properties to
characterise young radio AGN. Indeed, it can be seen in Fig. 5 that compact
sizes are not always the most reliable indicator for a young source. We find
that PS sources span a wide range of sizes in LoTSS, but are almost all
smaller than 3′′ in FIRST 222Although VLASS images have a higher angular
resolution ($\sim$ $3\text{${}^{\mathrm{\prime\prime}}$}$) than LoTSS and
FIRST, their lower image fidelity makes it harder to determine reliable source
sizes.. This difference is due to the significantly higher sensitivity of
LoTSS to extended emission than FIRST. This can also be seen in the fact that
LoTSS sizes for our sources are consistently greater than FIRST sizes. NPS
sources on the other hand span a wide range of sizes in both surveys. Most
importantly, this shows that using only a size threshold in a single frequency
continuum survey does not guarantee the selection of a clean sample of young
radio AGN.

As mentioned before, studies have found evidence for more disturbed ionised
gas in compact sources. However, there is no universal definition of a compact
radio AGN. For comparison with the literature, we also explore this link in
our sample. Different studies use either a ratio of major and minor axis
sizes, total and peak flux densities or a combination of the two to classify a
source as compact or extended. Using angular sizes for this can lead to
sources of very different physical sizes being classified as compact (or
extended) at low and high redshifts. To avoid this, we use the deconvolved
major axis sizes from LoTSS as a proxy for the radio sizes of our sources and
convert them to physical sizes using the source redshifts. Although the
majority of our sample is unresolved ($\sim$ $75\%$) in LoTSS according to the
criteria of Shimwell et al. (2022), at $z<0.4$ these sizes can still give
reasonable upper limits. We explore the relation between [OIII] kinematics and
source sizes in Sect. 4.6 and discuss them in Sect. 5.4. To quantify the link
between the two, we use the fraction of disturbed [OIII] sources above and
below 20 kpc. We choose this limit because GPS and CSS sources, which are
young radio AGN, typically have sizes varying between $1-20$ kpc (e.g. O’Dea
1998; O’Dea & Saikia 2021; Fanti et al. 1990; Dallacasa et al. 2002).

Figure 5:  Deconvolved major axis sizes from LoTSS vs FIRST for the full radio
AGN sample up to $z\sim 0.8$. The red, blue and grey points mark the PS, NPS
and the rest of the sources in the sample. The horizontal and vertical dashed
lines mark the 3′′size. A 1:1 ratio is marked by the dashdotted line.

##  4 Results

Table 2: Number of sources in each spectral shape group (c) Peaked spectrum
$0.4<z<0.8$ (d) Non-peaked spectrum $0.4<z<0.8$

Figure 8: Same plot as Fig. LABEL:radoptlum. The top row shows the plots for
(a) peaked spectrum and (b) non-peaked spectrum sources in the low redshift
sample. The bottom row shows the plots for (c) peaked spectrum and (d) non-
peaked spectrum sources in the high redshift sample.

We construct a similar plot for the high redshift PS and NPS sources, in Fig.
2. Here we find only marginal differences in the widths of the [OIII] profiles
of PS and NPS sources in any bin. The fraction of disturbed sources, is almost
always larger for PS than NPS sources, at any $L_{\mathrm{1.4GHz}}$ or
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ bin. This suggests that in
comparison to NPS sources, more disturbed [OIII] in PS sources can also be
found at $0.4<z<0.8$, however the difference is only marginal. Similar to the
low redshift sample, our results are consistent with the classification after
spectral index offsets, shown in Fig. 15(g) and 15(h). We do not present a
stacking analysis below for the high redshift sample, since we did not find
any significant difference between the profiles. But discuss this result
further in Sect. 5.

###  4.4 Stacking analysis of PS and NPS sources

(a) $L_{\mathrm{1.4GHz}}=10^{23}-10^{24}$ W Hz-1

(b) $L_{\mathrm{1.4GHz}}=10^{24}-10^{25}$ W Hz-1

(d) $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}=10^{39}-10^{40}$
$\mathrm{ergs^{-1}}$ (e) $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}}=10^{40}-10^{41}$ $\mathrm{ergs^{-1}}$ (f)
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}=10^{41}-10^{42}$
$\mathrm{ergs^{-1}}$

Figure 9: Stacked [OIII] profiles for the peaked and non-peaked spectrum
sources in the low redshift sample, while controlling for
$L_{\mathrm{1.4GHz}}$ and $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$.
The shaded regions show the $1\sigma$ errors on the stacked profiles,
estimated by stacking 1000 bootstrapped samples. The best-fit model parameters
for each profile are summarised in Table LABEL:model_fit. (a)$-$(c) Stacked
profiles for PS and NPS sources while controlling for $L_{\mathrm{1.4GHz}}$.
(d)$-$(f) Stacked profiles for PS and NPS sources while controlling for
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$.

In the section above, we find that the difference in the widths of [OIII]
profiles of low redshift PS and NPS sources is related to
$L_{\mathrm{1.4GHz}}$ and $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$.
But this is hard to judge from Fig. 2 alone. We also want to observe these
differences in the widths of average [OIII] profiles of PS and NPS sources and
quantify them. For this purpose, we use a stacking analysis. We stack the
[OIII] profiles for low redshift PS and NPS sources while controlling for
$L_{\mathrm{1.4GHz}}$ and $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$
individually.

To cover most of the source luminosity range discussed in Sect.
LABEL:radiolumvsoiii while keeping a significant number of sources in each
group, we decided to split the sample into three groups of
$L_{\mathrm{1.4GHz}}$ from $10^{23}$ to $10^{26}$ W Hz-1and
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ from $10^{39}$ to
$10^{42}$ $\mathrm{ergs^{-1}}$. For consistency with Sect.
LABEL:radiolumvsoiii and LABEL:specshape_and_lum, we keep the width of each
luminosity group the same, that is 1 dex on the log scale. Since we want to
study the average [OIII] profiles of these sources and have a small number of
objects in the highest luminosity groups, we have carefully tested whether the
results are reliable for the stacked profile. We have removed three sources
with high S/N spectra and extremely disturbed and broad [OIII] profiles
($v_{\textrm{broad}}$ up to $-600$ km s-1and FWHM${}_{\textrm{broad}}$ up to
1450 km s-1) that dominate the stacked profile in the $10^{25}-10^{26}$ W
Hz-1group. We do this to avoid the results being driven by a few individual
extremely disturbed sources, and to get a stacked profile more representative
of the true average.

The stacked [OIII] profiles are now shown in Fig. 2. For the groups in
$L_{\mathrm{1.4GHz}}$, we find that the differences in the widths of stacked
profiles become more prominent with increasing $L_{\mathrm{1.4GHz}}$. In the
$10^{23}-10^{24}$ W Hz-1group, the stacked profile of PS sources is marginally
broader than the NPS sources. Although in Fig. 2 we see that PS sources in
this $L_{\mathrm{1.4GHz}}$ range have wider profiles and more disturbed [OIII]
than NPS sources. The difference is much more significant at $10^{24}-10^{25}$
W Hz-1and the most at $10^{25}-10^{26}$ W Hz-1. We measure the widths of the
profiles by fitting models made up of Gaussian components as discussed in
Sect. A. Although the figures only show the 5007 Å component of the [OIII]
doublet line, while fitting the models we also use the 4958 Å component for
accurate characterisation of the stacked profile. The best-fit model
parameters are summarised in Table LABEL:model_fit. Here, we focus on the
widths of the low-level broad components. In the
$L_{\mathrm{1.4GHz}}=10^{24}-10^{25}$ W Hz-1group, FWHM of the broad component
is 1338 km s-1for PS and 1179 km s-1for NPS sources. At
$L_{\mathrm{1.4GHz}}=10^{25}-10^{26}$ W Hz-1, the FWHM of the broad component
is 1639 km s-1for PS and 1091 km s-1for NPS sources. Therefore, the difference
between the FWHMs of PS and NPS sources increases from $\approx$ 160 km s-1to
$\approx$ 550 km s-1with $L_{\mathrm{1.4GHz}}$. This suggests that the
‘difference’ in the impact of young and evolved radio AGN on [OIII] gas also
increases with $L_{\mathrm{1.4GHz}}$.

Next, we investigate the role of
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$, shown in the bottom panel
of Fig. 2. Similar to $L_{\mathrm{1.4GHz}}$, we find no difference in the
stacked profiles of the lowest luminosity group from $10^{39}-10^{40}$
$\mathrm{ergs^{-1}}$. At higher luminosities, the difference in the broad
component widths decreases marginally with increasing
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$. In the stacked profiles
of $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}=10^{40}-10^{41}$
$\mathrm{ergs^{-1}}$group, FWHM of broad component is 1353 km s-1for PS and
981 km s-1for NPS sources. However in the highest luminosity group of
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}=10^{41}-10^{42}$
$\mathrm{ergs^{-1}}$, FWHM of the broad component is 1434 km s-1for PS and
1202 km s-1for NPS sources. The difference between the FWHMs decreases from
$\approx$ 370 km s-1to $\approx$ 230 km s-1with
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$. Therefore, we find no
significant change in the average profiles of PS and NPS sources with
increasing $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ beyond
$10^{40}$ $\mathrm{ergs^{-1}}$. Including the [OIII] non-detections while
stacking did not affect any results.

Figure 10: Stacked profile for HFPS, LFPS and NPS sources in the low redshift
sample covering a $L_{\mathrm{1.4GHz}}$ range of $10^{24}-10^{26}$ W Hz-1. The
shaded regions show the $1\sigma$ errors estimated using the bootstrapped
samples. The best-fit model parameters and group sizes are summarised in
Table. LABEL:model_fit.

###  4.5 Stacking analysis of HFPS, LFPS and NPS sources

(a) $0.02<z<0.4$

(b) $0.4<z<0.8$

Figure 11: LoTSS major axis physical sizes (deconvolved) vs
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ for the
(a) low redshift and (b) high redshift sample. The different colours show the
peaked and non-peaked spectrum sources. Sources that are unresolved in LoTSS
are marked with a horizontal arrow since the sizes are upper limits in these
cases. Dashed and dashdotted lines show the median values for the peaked and
non-peaked sources respectively, in bins of major axis sizes. The dotted
horizontal line marks the
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ threshold
for classifying the [OIII] in a source as disturbed.

In the sections so far, we have found significant evidence to show that [OIII]
gas in PS sources is more disturbed than NPS sources in the low redshift
sample, even while controlling for $L_{\mathrm{1.4GHz}}$ and
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$. This supports the picture
of young radio AGN having a stronger impact on the surrounding [OIII] gas than
their evolved counterparts. However, as discussed in Sect. 3.1, PS sources are
made up of HFPS sources, which would be the youngest in the sample, and LFPS
sources which would be ”less” young. Although we make a sharp distinction
between HFPS and LFPS sources here, it is worth noting that the peaked sources
have a continuous distribution in the colour-colour plot of Fig. 3. The
distinction used here is only to make bins for stacking. If the impact on
[OIII] kinematics in radio AGN is linked to their evolutionary stage, in
principle we should be able to trace the differences in the [OIII] profiles of
HFPS, LFPS and NPS sources in our low redshift sample. Since the number of
HFPS and LFPS sources is small, 105 and 112 respectively, we have used a
stacking analysis to test whether we can recover the difference in the average
[OIII] profiles of these groups.

In the stacking analysis of the previous section, we find that the profiles
show significant differences in the $L_{\mathrm{1.4GHz}}$ range of
$10^{24}-10^{26}$ W Hz-1. Therefore, we have restricted the sample to this
luminosity range. We also exclude the four strong PS sources mentioned in the
section above, out of which one is HFPS and three are LFPS sources. The
stacked profiles are shown in Fig. 10 and the best-fit parameters and bin
sizes are summarised in Table LABEL:model_fit. We observe a clear difference
in the stacked profiles of the three groups. HFPS sources show the broadest
profile at the base, on both blue and red sides, and a broad component FWHM of
1642 km s-1. The profiles then get narrower gradually as we move to LFPS and
NPS sources, which have a broad component FWHM of 1333 km s-1and 1145 km s-1,
respectively. This shows that the average [OIII] profile of our sources gets
narrower as we go from the youngest to the most evolved sources, showing the
changing impact on [OIII] gas. It also shows that it is possible to trace the
changing impact on the average [OIII] profiles, using a radio spectral shape
classification. Similar to the stacking analysis in the section above,
including the [OIII] non-detections while stacking did not affect our results.

###  4.6 Radio sizes

In this section, we investigate the relation between
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ and the
total radio sizes (physical) from LoTSS, plotted in Fig. 11 for the low and
high redshift samples. We do not observe any clear trend between the two
quantities. In the low redshift sample, 30 out of the 256 sources
(11.7${}^{+2.3}_{-1.7}$ %) smaller than 20 kpc and 19 out of the 167 sources
(11.4${}^{+3.0}_{-2.0}$ %) larger than 20 kpc are disturbed. Similarly in the
high redshift sample, 5 out of the 50 sources (10.0${}^{+6.0}_{-2.9}$ %)
smaller than 20 kpc and 54 out of the 472 sources (11.4${}^{+1.7}_{-1.3}$ %)
larger than 20 kpc are disturbed. However, it is interesting that the median
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ at
different sizes is consistently larger for PS sources than NPS sources in the
low redshift sample, as shown by the dashed and dashdotted lines in Fig. 11.
This shows that irrespective of the radio size, a PS source at the centre
typically has more disturbed [OIII] gas than an NPS source. We discuss the
role of radio sizes and morphology further in Sect. 5.4.

At this stage, we remind the reader that the radio spectral shape is
determined using only the peak flux densities in the central region of the
sources, therefore PS or NPS does not classify the spectrum over the entire
extent of the radio source. This method allows us to identify a PS at the
centre of large sources, which could be candidates for restarted radio AGN. We
identify 138 out of 850 PS sources up to $z=0.8$ that have extended emission
in their LoTSS images on scales ¿ 50 kpc. This is done by visual inspection of
the LoTSS images and also includes the [OIII] non-detections. Since the young
source is likely $\sim$ $0.1-1$ Myr old, this phase of activity could not have
formed the extended emission observed on ¿ 50 kpc scales. This suggests that
the PS source and the extended emission represent two distinct phases of
activity, and these sources are good restarted candidates. This sample could
be useful to study the cumulative impact of AGN feedback on the host galaxies
over multiple epochs of activity and will be followed up in detail in a future
project.

###  4.7 Ionised gas densities of PS and NPS sources

Although the PS and NPS host galaxies are similarly massive, the difference in
the [OIII] kinematics of these sources could also be due to a richer medium
available for interaction with the young jets in PS sources. To test this, we
estimated the electron densities for these sources using the
[Sii]$\mathrm{\lambdaup\lambdaup}$6717,30 Å doublet method. For sources that
have a $\geq$3 $\sigma$ [Sii] detection, the 6717 to 6730 Å line ratio is
related to the electron density as (Sanders et al., 2016):

$\displaystyle n_{e}(R)=\frac{cR-ab}{a-R},$ (1)

where $n_{e}$ is the electron density, $R$ is the flux ratio of the 6717 to
6730 Å [Sii] line, $a=0.4315$, $b=2,107$ and $c=627.1$. These values are
estimated for a gas with an electron temperature of 10 000 K. Since this
relation saturates at electron densities below $\sim$ 10 cm-3 ($R<1.3$) and
above $\sim$ 10 000 cm-3 ($R>0.45$), we only used sources with $0.45<R<1.3$,
to stay within the theoretical line ratio limits of this relation. We note
that this method has several limitations as it assumes a fully ionised medium
whereas the gas could be partially ionised. It is also not sensitive to high-
density gas (see a discussion in Davies et al. 2020). Studies using auroral
and transauroral lines have found significantly higher densities of the
ionised gas than those estimated using the
[Sii]$\mathrm{\lambda\lambda}$6716,6731 Å ratio (Holt et al., 2011; Santoro et
al., 2020; Rose et al., 2018; Davies et al., 2020).

Out of the 566 [Sii] detections in the radio AGN sample, electron densities
can be estimated for 301 sources using this method, out of which 66 are PS and
90 are NPS sources up to $z\approx 0.5$. In Fig. 12, we plot distributions of
the estimated electron densities. We find no significant difference in the PS
and NPS distributions, confirmed by a 2-sample KS test (statistic=0.14, p
value=0.40). Although the densities could only be estimated for a subset of
the PS and NPS sources, it gives some insight into the ionised gas medium. The
lack of any difference between the two suggests that the ionised medium is
similarly dense in both groups. We discuss this in the context of jet-driven
feedback in the next section.

Figure 12: Electron density distributions for PS and NPS sources, that have
$\geq$ 3 $\sigma$ [Sii]detections.

##  5 Discussion

In this paper, we have investigated the [OIII] gas kinematics for a large
sample of 5 720 radio AGN, over a $L_{\mathrm{1.4GHz}}$ range of
$10^{22.5}-10^{28}$ W Hz-1, out to redshift $z=0.8$. Our careful selection of
radio AGN allows us to probe the feedback from jets on the [OIII] gas
kinematics. Using the spectral shape over a wide frequency range ($144-3000$
MHz) we have separated young and evolved radio AGN, making it possible to
study their impact in detail. Below, we discuss our results from Sect. 4 in
the context of jet-driven feedback in radio AGN host galaxies.

###  5.1 Impact of jets over the radio AGN life cycle

In our analysis, we have been able to disentangle the effects of radio jets
and radiation on disturbing the ionised gas. Comparison between the widths of
[OIII] profiles of our radio AGN sample and the control sample in Fig.
LABEL:cumdist_lowz_all shows that the presence of jets in AGN host galaxies
causes significantly more disturbed [OIII] gas. Evidence for a positive
correlation between the presence of radio emission and disturbed [OIII]
kinematics has been found before, for instance, by Mullaney et al. (2013) and
recently by Escott et al. 2024. However, the radio emission in their sources
could have different origins: star formation, shocks, or low-power jets. On
the other hand, our sample is selected to have radio emission dominated by
jets since we study jet-driven feedback on [OIII] .

With the spectral shape classification, we were able to go one step further
and study the changes in the impact on [OIII] at different evolutionary stages
of radio AGN. This link between the radio spectral shape and the [OIII]
kinematics is the most important result of this paper. In Sect.
LABEL:specshape, we found that [OIII] in PS sources is $\sim$ 3 times more
likely to be disturbed than NPS sources in the low redshift sample, even
though both groups cover similar ranges of host galaxy properties. Since the
radio emission in our sample is dominated by jets, this gives insight into the
link between jets and [OIII] kinematics. Our results show that the impact of
radio jets on surrounding [OIII] gas changes as they grow, with the strongest
impact on the gas kinematics occurring when they are young. At evolved stages,
[OIII] is less disturbed. These trends support previous evidence in this
context by K23, now confirmed with a sample that is $\sim$ 44 times larger.
Since the young phase of activity typically lasts for $\sim$ $0.001-1$ Myr
(see Sect. 1), this suggests that the impact of radio AGN on the warm ionised
gas is most extreme in the initial stages, which are a small fraction of their
total lifetime ($\sim$ $10-100$ Myr). At later stages of evolution, the impact
on the ionised gas is more ‘gentle’.

In the high redshift ($z>0.4$) sample, we find only marginal evidence for more
disturbed [OIII] in PS sources ($\sim$ 2 times more likely). Although less
significant ($2\sigma$), the observed trend is still in agreement with the low
redshift sample. We propose that this is likely due to contamination of the
NPS sources by PS sources in the high redshift sample, as mentioned in Sect.
3.1. This contamination would lead to broader [OIII] in NPS sources at high
redshift. This can be seen in Fig. LABEL:cmldist_specshape, where see that the
fraction of sources with
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}>350$ km
s-1is larger for NPS sources in the high redshift than the low redshift
sample.

Radio and [OIII] luminosity of an AGN are crucial parameters to determine the
energy output of the system which couples with the gas in the host galaxy.
Although PS and NPS sources in our sample cover a wide range in
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ and $L_{\mathrm{1.4GHz}}$
(see Fig. 1), we find that controlling for these parameters does not affect
our results. At any $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ or
$L_{\mathrm{1.4GHz}}$, PS sources show wider and larger fraction of disturbed
[OIII] profiles than NPS sources. This is most evident in the low redshift
sample. This shows that the difference we find in [OIII] profiles of PS and
NPS sources is not driven by source luminosities, but is indeed a result of
the changing impact of jets in radio AGN along their life cycle.

Controlling for $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ in the
stacking analysis provides insight into the role of radiation in our sample
(Fig. 2). We find that above $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}}=10^{40}$ $\mathrm{ergs^{-1}}$, [OIII] luminosity does not play a
significant role in determining the difference between widths of stacked
profiles of PS and NPS sources. PS sources are consistently broader than NPS
in different $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ groups.
However, below $10^{40}$ $\mathrm{ergs^{-1}}$, we do not observe any
difference between PS and NPS stacked profiles, likely due to the low S/N of
the spectra. The strength of radiation is likely not significant for
determining the difference in the impact of PS and NPS sources.

Similarly, from the stacked profiles in Fig. 2, we find that the ’difference’
between the profile widths of PS and NPS sources, increases with
$L_{\mathrm{1.4GHz}}$. That is, there is a positive link between the varying
impact of radio AGN and the 1.4 GHz luminosity. Since $L_{\mathrm{1.4GHz}}$ is
a proxy for jet power (Cavagnolo et al., 2010; McNamara & Nulsen, 2012;
Hardcastle, 2018), this points towards young and powerful jets being more
effective at pushing the ionised gas clouds in their path to faster
velocities. This is broadly in agreement with the results of some jet-ISM
interaction simulations which predict that powerful jets would drill through
the surrounding medium with ease while driving fast outflows (Mukherjee et
al., 2016, 2018). These simulations also indicate that low-power jets, on the
other hand, would struggle to break through the ISM and dissipate their energy
by inducing turbulence in the ambient medium. It is not possible to make a
direct comparison of these simulations with our results, and that requires
spatially resolved optical spectra. However, the trends we observe for the
sample appear to agree with these predictions.

The larger sample in this study compared to K23 means that we can also trace
the changing impact in different regions of the colour-colour plot in Fig. 3.
Our stacked profiles of HFPS, LFPS and NPS sources (see Fig. 10) show a
gradual narrowing as we move from the youngest to the ”less” young and the
most evolved source. This can also be observed by tracking the change in the
broad component FWHM of the stacked profiles. On average, within the PS source
group, the impact of HFPS sources on [OIII] is stronger than LFPS sources.
This further supports our results on the varying impact on [OIII] over the
radio AGN life cycle. Such a detailed tracing of the impact at different
stages of the life cycle has been possible due to the addition of low-
frequency data (144 MHz) with LoTSS, which allowed the detection of a large
number of PS sources. Although evidence for disturbed ionised gas has been
found in powerful young AGN before ($L_{\mathrm{1.4GHz}}\gtrsim$ $10^{26}$ W
Hz-1, e.g. Gelderman & Whittle 1994; Holt et al. 2008, 2011; de Vries et al.
2009; Santoro et al. 2020), our study expands this to a much larger sample of
typical radio AGN, down to $L_{\mathrm{1.4GHz}}\sim$ $10^{23}$ W Hz-1. We find
that the impact on ionised gas and the difference between young and evolved
radio AGN is significant even down to $L_{\mathrm{1.4GHz}}=10^{24}$ W Hz-1
(confirming the findings for single objects like Murthy et al. 2022; Oosterloo
et al. 2017; Audibert et al. 2019; Ruffa et al. 2022).

We further check that the differences we observe in [OIII] profiles of PS and
NPS sources are not due to any selection effects. PS sources are selected
based on absorption in their radio spectra. Other than synchrotron self-
absorption, this could be caused by free-free absorption from a highly dense
ionised medium surrounding the radio jets. Therefore PS sources could also
have more high-density ionised gas. AGN with such a dense medium in the
central region would have a larger possibility of jet-ISM interactions. They
would be more likely to show prominent broad wings in their spectra than NPS
sources. However, as we show in Fig. 12 for a subset of sources, the ionised
gas densities for PS and NPS sources are similar. Therefore, the result of
[OIII] kinematics with radio spectral shape is not due to a selection effect,
but due to genuine differences in their interaction with the ionised gas.

###  5.2 Disturbed [OIII] gas in NPS sources

It is intriguing that NPS sources consistently show less disturbed [OIII] gas
than PS sources, even though the jets are still active. Since the disturbed
gas is likely driven by shocks due to jet-ISM interaction (Sutherland &
Bicknell, 2007; Mukherjee et al., 2018), one possibility is that by the time
jets have grown to larger scales, the shocked gas in the central region has
cooled down, and is not as disturbed as before. In this case, the strength of
the broad component could be reduced, leading to narrower observer profiles in
NPS sources. Indeed, using hydrodynamical simulations of jet-ISM interaction,
Meenakshi et al. (2022) found that as the jets start and propagate, they shock
ionise the clouds, pushing them to high velocities, and clear the region which
is then photoionised by the AGN radiation. In their scenario, once the jets
have evolved to larger scales and their direct interaction with the gas clouds
has stopped, the shocked gas clouds would cool down. Another possibility is
that on the time scale of the NPS sources (a few to tens of Myr), the
disturbed [OIII] gas clouds have been pushed by jet-ISM interaction to
distances beyond the coverage of the 3′′SDSS fibre. In that case, as well, the
gas within the SDSS fibre would appear less disturbed.

Determining the exact nature of the disturbed gas in NPS sources is beyond the
scope of this paper. Testing these possibilities would require high-resolution
spatially resolved optical spectra. Indeed, spatially resolved molecular gas
kinematics has provided evidence for changing effects of jet-ISM interaction
as the jets expand in radio-loud (for example PKS 0023-26 by Morganti et al.
2021b) and radio-quiet (for example Girdhar et al. 2024) AGN (see Morganti et
al. 2023 for an overview). We are currently performing a study with integral
field unit (IFU) data for a subset of these sources to examine the size and
shape of the disturbed [OIII] gas emission in more detail and understand its
nature.

(a) Peaked ($0.02<z<0.4$) (c) FIRST compact and extended (d) FIRST compact
PS+NPS sources

Figure 13: Distributions of
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}$ and
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$. (a) & (b)
Colour map showing the average
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}$ values
for peaked and non-peaked sources in the low redshift sample, in bins of
$L_{\mathrm{1.4GHz}}$ and $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$,
similar to Fig. LABEL:lowz_radoptlum. (c) Cumulative distributions of the
average [OIII] velocity dispersions. Comparison for compact
($<3\text{${}^{\mathrm{\prime\prime}}$}$) and extended
($>3\text{${}^{\mathrm{\prime\prime}}$}$) sources according to FIRST sizes in
the low redshift sample. We also plot the compact NPS sources for comparison.
The inset plot shows the asymmetry distributions for the [OIII] profiles with
multiple kinematic components. (d) Cumulative distributions for low redshift
PS and NPS sources that are compact in FIRST.

###  5.3 Role of $L_{\mathrm{1.4GHz}}$ and
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$

In Sect. LABEL:radiolumvsoiii, we find that the width and fraction of
disturbed [OIII] profiles increase with both $L_{\mathrm{1.4GHz}}$ and
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$. This trend is most
evident for the low redshift sample, as shown in Fig. LABEL:lowz_radoptlum.
With our approach of separating the PS and NPS sources, we can observe an even
stronger trend between $L_{\mathrm{1.4GHz}}$ and [OIII] profile widths. This
can be seen for the low redshift sample in Fig. 2. Therefore
$L_{\mathrm{1.4GHz}}$, and hence the radio jet power, plays an important role
in determining the impact on [OIII] kinematics. The highest luminosity radio
AGN have the most disturbed gas. However, this trend is not very clearly
observed in the high redshift sample.

It is worth noting that some studies of AGN samples have found slightly
different trends between $L_{\mathrm{1.4GHz}}$ and [OIII] profile widths. For
instance, Mullaney et al. (2013) found that the average widths of [OIII]
profiles were largest between $L_{\mathrm{1.4GHz}}=10^{23}-10^{25}$ W Hz-1,
and therefore [OIII] was less disturbed at luminosities below and above this
range. Our analysis differs in the sample selection criteria, as mentioned
before. Therefore, our sample is more suited for studying the role of radio
luminosity in jet-driven feedback. Our additional selection criteria of
spectral shape (PS and NPS sources) means that our sample is also not
contaminated by flat-spectrum sources, which could affect the results from
Mullaney et al. (2013) at $L_{\mathrm{1.4GHz}}>$ 1025 W Hz-1.

Previous studies have reported a correlation between the [OIII] and stellar
velocity dispersions ($\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$
vs $\sigma_{\star}$), suggesting that the [OIII] gas kinematics are determined
by the bulge gravitational potential (for example Nelson & Whittle 1996;
Boroson 2002; Sexton et al. 2020). Although there is a large scatter in this
correlation, it is still important to be cautious about the role of the bulge
in determining [OIII] kinematics (Bennert et al., 2018; Le et al., 2023).
Based on this correlation, some studies have used $\sigma_{\star}$ to account
for the gravitational kinematics component in
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$. For instance, Woo et
al. (2016) have used the quantity
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}$ to
study the impact of AGN feedback for a sample of 39 000 type 2 AGN out to $z$
$\sim$ 0.3. They find that the correlation between $L_{\mathrm{1.4GHz}}$ and
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ vanishes when
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ is normalised using
$\sigma_{\star}$. Using similar techniques for a sample of $\sim$ $6000$ AGN
out to $z$ $\sim$ 0.4, Ayubinia et al. (2023) have found the same result
between $L_{\mathrm{1.4GHz}}$ and
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}$. They
also do not find any dependence of
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}$ on the
radio-loud/radio-quiet, compact/extended groups of radio AGN. These results
have suggested that radio AGN have a limited impact on [OIII] kinematics, and
radio AGN-driven outflows are much weaker than accretion-driven outflows
(although radio AGN can provide an extra boost to the disturbed [OIII] gas).

For comparison, we test our results for PS and NPS sources in the low redshift
sample using $\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}}/\sigma_{\star}$, as shown in Fig. 12(a) and LABEL:nonpeaked_normalised. We
again find that PS sources have consistently more disturbed [OIII] kinematics.
In this case, we define [OIII] to be disturbed if
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}>1.5$,
however the specific value of this limit does not affect our broad result.
This shows that there is an intrinsic difference in the [OIII] kinematics of
PS and NPS sources. We also note that using this approach to select disturbed
[OIII] sources does not affect our results. The fraction of disturbed sources
at any source luminosity is in agreement with the result presented in Fig. 2.
Another important result is the dependence of this ratio on
$L_{\mathrm{1.4GHz}}$ and $L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$.
We find that PS (and to some extent NPS) sources with higher luminosities have
larger $\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}}/\sigma_{\star}$. This also supports our result for the dependence of [OIII]
kinematics on source luminosity. However, we did not use the
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}$
approach for the entire paper because the large scatter between
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ and $\sigma_{\star}$
makes it less reliable. The difference in the relation between
$\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}/\sigma_{\star}$ and
$L_{\mathrm{1.4GHz}}$ for our sample compared to Woo et al. (2016) can be
attributed to sample selection effects, as they study type 2 AGN. Although
Ayubinia et al. (2023) also study radio AGN, most of their sources lie below
$L_{\mathrm{1.4GHz}}=10^{24}$ W Hz-1whereas most of our sources lie above it.
Indeed, in Fig. 12(a) and LABEL:nonpeaked_normalised, we do not observe any
significant dependence on radio luminosity below this limit. Our separation of
PS and NPS sources also helps emphasise the role of $L_{\mathrm{1.4GHz}}$.

From Fig. LABEL:lowz_radoptlum, we also conclude that increasing only
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ (which is proxy for the
total radiative power of an AGN; Heckman et al. 2004) also increases the
[OIII] profile widths and fraction of disturbed sources. Most of the radio AGN
are low excitation radio galaxies (LERGs), i.e. systems with radiatively
inefficient accretion and low accretion rates (Best & Heckman, 2012). Our
results suggest that even in such systems, radiation strength plays an
important role in driving feedback on [OIII] gas kinematics. For a sample of
$\sim$ 800 LERGs up to $z$ $\sim$ 0.3, Singha et al. (2021) also found that
the majority of sources with an [OIII] outflow (only $\sim$ 1.5% of their
sample) had high accretion rates. They concluded that outflows in LERGs are
radiative pressure driven. We note a crucial difference between our studies
regarding the identification of disturbed [OIII] . Singha et al. (2021) focus
only on the outflow detections, which are the most extreme form of feedback,
whereas we study the average velocity dispersion for the entire radio AGN
sample. However, there seems to be a general agreement between the results on
the role of radiation pressure.

###  5.4 [OIII] and radio source sizes

Finally, we also studied the dependence of
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ on the
radio sizes from LoTSS in Sect. 4.6, and found no significant relation between
the two. We find that sources larger and smaller than 20 kpc in LoTSS are
equally likely to have disturbed [OIII] in both low and high redshift samples.
However, it is interesting that we find larger
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ values for
PS than NPS sources, at all sizes in the low redshift sample (Fig. 11). This
suggests that in radio AGN host galaxies, the impact on [OIII] is not
determined by the extent of the radio emission, but by the emission properties
in the central region.

Many studies in literature have found links between the radio morphology of
AGN and the multiphase gas kinematics. In neutral gas, Hi absorption studies
have found broader and more asymmetric line profiles in compact radio sources
compared to extended sources (for e.g. Geréb et al. 2014, 2015; Maccagni et
al. 2017). Since young radio AGN usually have a compact radio morphology, this
suggested the presence of more disturbed Hi gas in young radio AGN. In the
ionised phase, Mullaney et al. (2013) have found evidence for more disturbed
[OIII] in AGN with compact radio morphology. Molyneux et al. (2019) use the
type 1 and 2 AGN sample up to $z\sim 0.2$ from Mullaney et al. (2013), and
also find more disturbed [OIII] in compact radio emission sources. They
conclude that the SDSS spectra of their AGN are twice more likely to have
broad [OIII] profiles (FWHM ¿ 1000 km s-1) if the radio emission is confined
within 3′′in their FIRST images. It is worth noting that the typical radio
luminosity of their sources is lower by $\sim$ 2 orders of magnitude compared
to ours, as they do not select for radio AGN. The radio emission in their
sources can also be due to AGN-driven winds that drive outflows and shock the
ISM to produce radio emission. This could also explain the correlation between
radio size and the prevalence of outflows. Another major difference in our
study is the way we select young radio AGN, using a spectral shape
classification down to low frequencies of 144 MHz (thanks to the addition of
LoTSS data) instead of source extent. This allows us to identify young phases
of activity even at the centres of extended sources.

Still, it is worth comparing their results with our low redshift sample in the
context of radio morphology and spectral shape. For this, we split our low
redshift sample using the FIRST deconvolved major axis sizes into compact
($<3\text{${}^{\mathrm{\prime\prime}}$}$) and extended
($>3\text{${}^{\mathrm{\prime\prime}}$}$) sources. It is important to note
from Fig. 5 that all the PS sources in the low redshift sample are smaller
than $3\text{${}^{\mathrm{\prime\prime}}$}$ in FIRST. Therefore the compact
group consists of both PS and NPS sources but the extended group consists only
of NPS sources. We compare their
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$
distributions in Fig. 12(c) and find that they are significantly different (KS
statistic = 0.22, p-value = 4.8$\times$10-3). We also find that the fraction
of sources with FWHM ¿ 1000 km s-1is 4.5${}^{+1.4}_{-0.9}$ % for compact and
1.4${}^{+3.1}_{-0.4}$ % for extended FIRST sources. This is in agreement with
the results of Molyneux et al. (2019).

However, we propose that this result in our sample is driven by the PS sources
present in the compact group. We test for this by controlling for spectral
shape and only using the NPS sources for the compact group, shown in Fig.
12(c). We find that the distributions of compact and extended sources are now
not significantly different (KS statistic = 0.13, p-value = 0.35). The
fraction of sources with FWHM ¿ 1000 km s-1also comes down to
1.5${}^{+1.9}_{-0.5}$ % for compact sources. Therefore, controlling for
spectral shape removes the difference between the [OIII] profile widths of
compact and extended FIRST sources. This shows that the difference found
before is indeed driven by PS sources. Further, in Fig. 12(d) we even compare
the $\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$
distributions of only compact PS and NPS sources, and find that they are still
significantly different (KS statistic = 0.20, p-value = 1.6$\times$10-3). We
conclude that controlling for FIRST sizes does not affect our results on the
[OIII] profiles of PS and NPS sources.

Therefore, we find that the [OIII] kinematics in our radio AGN sample is not
significantly dependent on the FIRST or LoTSS sizes. Instead, we consistently
find that the [OIII] kinematics is most strongly related to the radio spectral
shape. We conclude that young radio AGN picked using their peaked radio
spectrum are more likely to show disturbed [OIII] profiles than evolved radio
AGN with a non-peaked spectrum.

##  6 Summary and conclusions

In this study, we have selected a sample of 5 720 radio AGN up to $z$ $\sim$
0.8 where the radio emission is dominated by jets. We have shown that the
presence of radio jets in AGN disturbs the [OIII] gas more compared to AGN
without jets. Using a wide-frequency radio spectral analysis, we have been
able to identify sources in different stages of their life cycle. We have then
established a link between the radio spectral shape (proxy for AGN
evolutionary stage), and the [OIII] kinematics. Our main findings are
summarised below:

  1. 1.

[OIII] in PS sources is $\sim$ 3 times more likely to be disturbed than in NPS
sources at $z<0.4$. This shows that jets in young radio AGN have a stronger
impact on the surrounding ionised gas. At $z>0.4$, we find marginal evidence
for PS sources having $\sim$ 2 times more disturbed [OIII] .

  2. 2.

The fraction of disturbed sources and the average [OIII] velocity dispersion
is consistently higher for PS sources, even when controlling for 1.4 GHz and
[OIII] luminosity. This shows that the feedback is indeed linked to the
evolutionary stage of radio AGN. The most extreme impact of radio AGN is
likely limited to the initial stages of evolution.

  3. 3.

The difference between the widths of stacked [OIII] profiles of PS and NPS
sources increases with 1.4 GHz luminosity. This shows that young and powerful
jets have the strongest impact on [OIII] gas.

  4. 4.

A lower fraction of disturbed [OIII] sources in the NPS group suggests that
the shocked gas has cooled down by the time jets evolve to large scales.
Although the shocked gas may have been pushed out to distances beyond the
coverage of the SDSS fibre. Testing this hypothesis would require studying the
spatially resolved gas kinematics.

  5. 5.

Using a stacking analysis, we find that the average [OIII] profile becomes
narrower as the source spectral shape changes from completely inverted, to
peaked and finally to non-peaked. We propose that this traces, in detail, the
changes in the impact of jets along the radio AGN life cycle.

  6. 6.

We find that the fraction of disturbed [OIII] sources and average velocity
dispersion increases with both 1.4 GHz and [OIII] luminosity, even while
controlling for one of the two. This highlights the role of the total
energetic output in driving feedback and shows that in radio AGN, radiation
pressure can also add to the effect of jets on ionised gas.

  7. 7.

We do not find any strong dependence of [OIII] kinematics on the source sizes.
We find that any dependence is driven by PS and NPS sources, and controlling
for spectral shape removes it. We suggest that the trends observed between
disturbed [OIII] and compact radio AGN are driven by PS sources.

Our study shows that the impact of jets on the host galaxy’s gas could change
as the jets evolve. Understanding the exact changes in the ionised gas
kinematics and morphology over galaxy scales, and the eventual impact on star
formation, requires detailed studies of the spatially resolved gas and stellar
properties. We plan to perform such studies using IFU data from MaNGA (Bundy
et al., 2015) and the GMOS-N spectrograph on the GEMINI telescope, for a
subset of sources from this sample.

###### Acknowledgements.

P.K. acknowledges support through an Emmy Noether Grant (German Research
Foundation) of Dominika Wylezalek (WY 179/1-1). LOFAR (van Haarlem et al.,
2013) is the Low Frequency Array designed and constructed by ASTRON. It has
observing, data processing, and data storage facilities in several countries,
which are owned by various parties (each with their own funding sources), and
are collectively operated by the ILT foundation under a joint scientific
policy. The ILT resources have benefited from the following recent major
funding sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans,
France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI),
Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The
Netherlands; The Science and Technology Facilities Council, UK; Ministry of
Science and Higher Education, Poland; The Istituto Nazionale di Astrofisica
(INAF), Italy. Funding for the Sloan Digital Sky Survey IV has been provided
by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of
Science, and the Participating Institutions. The National Radio Astronomy
Observatory is a facility of the National Science Foundation operated under a
cooperative agreement by Associated Universities, Inc. CIRADA is funded by a
grant from the Canada Foundation for Innovation 2017 Innovation Fund (Project
35999), as well as by the Provinces of Ontario, British Columbia, Alberta,
Manitoba and Quebec.

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##  Appendix A Modelling the stellar continuum and emission line
characterisation

To obtain the emission line spectra, we first modelled the stellar continuum
and removed it from the observed SDSS spectra. Modelling was done using the
STARLIGHT spectral synthesis code444http://www.starlight.ufsc.br/ (Cid
Fernandes et al., 2005, 2009). Single stellar population models of Bruzual &
Charlot (2003) with young (1, 3.2, 5, 10, 25, 40 and 100 Myr), intermediate
(0.29, 0.64, 0.9, 1.43, 2.5 and 5 Gyr) and old (11 and 13 Gyr) age populations
were used. We assumed a Chabrier initial mass function, and three different
metallicities: 0.004, 0.02 and 0.05 in mass-fraction notation. Before
modelling the stellar continuum, the spectra were shifted to rest-frame
wavelength, and the following emission lines were masked: [OII]
$\mathrm{\lambdaup\lambdaup}$3726,28Å, H$\delta$, H$\gamma$, H$\beta$, [OIII]
$\mathrm{\lambdaup\lambdaup}$4958,5007Å, [OI] $\mathrm{\lambdaup}$6300 Å,
[Nii]$\mathrm{\lambdaup\lambdaup}$6548,84Å, H$\alpha$ and
[Sii]$\mathrm{\lambdaup\lambdaup}$6717,30 Å. A visual inspection revealed that
this procedure could reproduce the stellar continuum emission of the sources
well, and can be used for subtraction to obtain the emission line spectra.

After obtaining the continuum subtracted spectra, modelling of the line
profiles was done using Gaussian functions. For reference, we used the [OIII]
doublet which is usually the strongest emission line. We used kinematic
components made up of two Gaussian functions, with a fixed amplitude ratio
($A_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }4958}=\frac{1}{3}\times
A_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }5007}$) and equal widths
($\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}4958}=\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }5007}$) according
to atomic physics. We started with a single kinematic component and added up
to two components depending on whether adding an extra component significantly
improved the fit. We judged this using an F-test, and considered an extra
component to significantly improve the fit, if it improved the $\chi^{2}$ at
¿99% confidence level. We considered a source as an [OIII] detection if its
amplitude was $\geq 3\sigma$, where $\sigma$ is the standard deviation of the
residuals after subtracting the best-fit model. We obtained 2 363 [OIII]
detections, out of which 410 required double and 120 required triple
components.

For sources with [OIII] detections, we then fit the H$\beta$ line. We used the
[OIII] best-fit model and allowed one more component to account for any
possible broad line region (BLR) emission in the H$\beta$ line from type 1
AGN. Out of all the H$\beta$ detections, 173 sources required an extra BLR
component in the H$\beta$ line. Similarly using the best-fit [OIII] model, we
then fit the [Nii]$\mathrm{\lambdaup\lambdaup}$6548,84Å and the H$\alpha$
lines. The separation between the [Nii] and H$\alpha$ lines, and the relative
amplitudes of the two components of the [Nii] line
($A_{\mathrm{\text{[N{ii}]}5648}}=\frac{1}{3}\times
A_{\mathrm{\text{[N{ii}]}5684}}$) were fixed. We again allowed for an extra
broad component in the H$\alpha$ line, whenever one was needed for the
H$\beta$ line. Lastly, we fit the [Sii]$\mathrm{\lambdaup\lambdaup}$6717,30 Å
doublet, with a fixed velocity separation and the same velocity dispersion and
number of components as the best fit [OIII] model. The number of different
emission line detections in the full sample and the radio AGN sample selected
in the next section, are summarised in Table 2.

Next, we estimated the emission line fluxes by adding up fluxes of the
Gaussian components in the best-fit model. In the case of H$\beta$ and
H$\alpha$ line fits that required an extra BLR component, we neglected the
flux of the BLR component as we did not want the light from the BLR region to
affect our fluxes. For non-detections, we used a $3\sigma$ value to estimate
an upper limit on the fluxes.

We removed 22 sources from the sample where the spectra were corrupted at the
[OIII] wavelengths. We further removed 30 sources where the H$\beta$ profile
required an extra broad component, and the emission was strong enough to leak
into the [OIII] profile. This contaminates the profile width and flux
estimates. Finally, we were left with a sample of 6 504 sources.

[OIII] profile characterisation and stacking: The multi-component fitting
routine makes it challenging to compare [OIII] profiles with different number
of kinematic components in their best-fit model. To overcome this, we
estimated a flux weighted average velocity dispersion
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$, similar
to Mullaney et al. (2013), given as

$\displaystyle\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}}=\left(\sum\limits_{i}(f(i)\times\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\
}}(i))^{2}\right)^{\frac{1}{2}},$ (2)

where $f(i)$ is the flux ratio of the $i$ th component to the total flux of
the line and $\sigma_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}(i)$ is
the velocity dispersion of the $i$ th component in the best-fit model. Using
this one parameter we can compare profiles with different numbers of
components. In addition, it is also useful to assess the shape of the line
profiles and determine any asymmetry, if present. The asymmetry helps trace
kinematically disturbed gas in the sources. We measured the asymmetry of the
lines using the definition from Liu et al. (2013), given as

$\displaystyle A=\frac{(v_{90}-v_{50})-(v_{50}-v_{10})}{v_{90}-v_{10}},$ (3)

where $v_{90}$, $v_{50}$, and $v_{10}$ are the velocities at 90, 50 and 10 per
cent of the cumulative flux. In this convention, a heavily blueshifted profile
has $A<0$ whereas a heavily redshifted profile has $A>0$ and a symmetric
profile has $A=0$.

In this paper, we also use a stacking analysis to measure the average
differences between [OIII] profiles of different source groups. Using a
stacking approach, we can control for various source properties and
disentangle their role in driving the [OIII] kinematics. It also suppresses
the noise (by 1/$\sqrt{N}$ for N samples) thus allowing the detection of low-
level broad components, which would be otherwise missed in individual fits.
Stacking requires accurate spectroscopic redshift measurements to align the
rest-frame spectra, which we have for the entire sample. We estimated the
stacked spectrum using the equation

$\displaystyle
S(\lambdaup)=\frac{\sum\limits_{i}\frac{1}{\sigma^{2}(i)}S(i,\lambdaup)}{\sum\limits_{i}\frac{1}{\sigma^{2}(i)}},$
(4)

where S$(i,\lambdaup)$ is the individual source spectrum, $\sigma(i)$ is the
noise in a line-free region of the source spectrum and S($\lambdaup$) is the
stacked spectrum. We estimate errors on the average stacked spectrum using a
bootstrapping approach. We randomly select sources in each bin to create a
bootstrapped sample and stack their spectra, repeating this process 1000
times. We use the standard deviation of the distribution at each wavelength as
the error for that wavelength point.

We also estimate the impact of errors in redshift on the stacked [OIII]
profiles. To do this, we add a random value to each redshift, to obtain a
redshift with an offset. This value is drawn randomly from a Gaussian
distribution with unit area, zero mean and standard deviation equal to the
error in reported in SDSS for that redshift. We then re-perform the stacking
analysis to test the impact of redshift errors. We find that it has a
negligible impact on the final stacked profiles.

##  Appendix B Selecting radio AGN

To study the relation between radio AGN life cycle and their impact on [OIII]
gas, we first need to select a clean sample of radio AGN. Radio emission from
a galaxy can originate either from the AGN itself or star formation (SF). In
the local universe, star-forming galaxies dominate a radio-selected sample up
to $L_{\mathrm{1.4GHz}}\approx 10^{23}$ W Hz-1 (e.g. Sadler et al. 2002; Best
et al. 2005). This makes it important to separate them from radio AGN. Even
AGN identified using optical emission line ratios can have radio emission
dominated by star formation in the host galaxy. In this section, we discuss
the approach used for selecting a clean sample of radio AGN from the 6 504
radio selected sources in Sect. 2. We followed the method outlined in Best et
al. (2005); Best & Heckman (2012) and Sabater et al. (2019), which combines
four diagnostic methods. The plot for each diagnostic is shown in Fig. 2.

First is the ‘$D_{\mathrm{{n}}}(4000)$ versus
$L_{\mathrm{1.4GHz}}$/$M_{\star}$’ method, shown in Fig. LABEL:d4pm and
developed by Best et al. (2005). $D_{\mathrm{{n}}}(4000)$ is the 4000 Å break
in the spectrum of the galaxy (sensitive to the presence of a young stellar
population), and $L_{\mathrm{1.4GHz}}$/$M_{\star}$ is the ratio of the radio
luminosity to the stellar mass. This method relies on the idea that star-
forming galaxies with various star formation histories, would lie in a similar
region on a plot of these two quantities. This is because both of these
quantities are dependent on the specific star formation rate. However, radio
AGN have jets that add to the radio emission ($L_{\mathrm{1.4GHz}}$), allowing
us to separate the two populations. Best et al. (2005) obtained the track of a
galaxy with an exponentially decreasing star formation rate on this diagram,
which can be used to separate the two sources of radio emission. They then
added 0.225 to the $D_{\mathrm{{n}}}(4000)$ values of this track to construct
a conservative division. This division was later modified by Kauffmann et al.
(2008), who used a straight line division at
$L_{\mathrm{1.4GHz}}$/$M_{\star}<12.2$. For our sample, we estimated
$D_{\mathrm{{n}}}(4000)$ as the flux ratio between 4000-4100 Å and 3850-3950
Å. We used the stellar masses from the ‘Portsmouth SED-fit’ catalogue by
Maraston et al. (2013), which were available for 5 535 sources. The stellar
masses were estimated from broad-band spectral energy distribution (SED)
fitting of stellar population models using $u$, $g$, $r$, $i$ and $z$ band
photometry and spectroscopic redshifts from SDSS. We classified the sources as
radio AGN if they lie above the criterion from Kauffmann et al. (2008)
555Provided by Philip Best (private communication), and as star-forming (i.e.
galaxies where the radio emission is dominated by star formation) if they lie
below it.

The second diagnostic uses $L_{\textrm{H}\alpha}$ versus $L_{\mathrm{1.4GHz}}$
to classify sources, shown in Fig. LABEL:harad. It is based on the idea that
for star-forming galaxies, both H$\alpha$ and radio luminosities are related
to the star formation rate of massive stars. Therefore sources with excess
radio emission (coming from jets) can be separated from sources where both
H$\alpha$ and radio luminosities come from star formation. We used the
division from Best & Heckman (2012), which is a conservative division designed
to produce clean radio AGN samples, and given as
log($L_{\textrm{H}\alpha}$/L${}_{\odot})=1.12\times$
(log($L_{\mathrm{1.4GHz}}$/ W Hz-1)$-17.5)$. We classify sources with larger
radio luminosity than predicted from this relation as radio AGN and the rest
as star-forming. We use upper limits on H$\alpha$ luminosities for non-
detections. Overall, we were able to classify 4 027 sources using this
diagnostic.

The third diagnostic is the BPT diagram (Baldwin et al., 1981) shown in Fig.
13(c), which uses the [Nii]/H$\alpha$ and [Oiii]/H$\beta$ emission line ratios
to separate AGN and star-forming sources of ionisation. We used the relation
from Kauffmann et al. (2003) to classify sources as AGN if they lie above the
relation, and star forming if they lie below it. Although we do not have
emission line detections for the majority of the sample, it can still provide
useful information for sources with upper limits. We classified 1 503 sources
using the BPT diagram.

The fourth diagnostic is the WISE colour-colour diagram, shown in Fig. 13(d).
Star-forming galaxies can be separated from radio AGN host galaxies (typically
ellipticals with low levels of star formation) in their $W2-W3$ colour (Yan et
al., 2013). Herpich et al. (2016) used a division of $W2-W3$ (AB) = 0.7 to
separate galaxies with and without star formation, however, the division is
not very clean. Sabater et al. (2019) modified it to $W2-W3$ (AB) = 0.8 for
LoTSS sources following a comparison with the radio AGN in the Herschel-ATLAS
North Galactic Plane field selected by Gürkan et al. (2018). For this work, we
used the same division as Sabater et al. (2019). Since this is a crude
division, it has less weight in the overall classification and we use it only
to resolve cases where other diagnostics give contradictory results. Since we
did not perform $k$-corrections to the WISE magnitudes, we use them only for
$z<0.3$ sources. We classified 2 019 sources using this method.

In each diagnostic, a source can be labelled as an AGN (or radio AGN),
SF/radio-quiet AGN or unclassified, leading to 81 different possible
combinations. A summary of the source classifications by each diagnostic is
given in Table B. We use these combinations to give a final classification to
each source, following the approach of Sabater et al. (2019) and Best &
Heckman (2012). We refer the reader to these papers for further details on the
classification. Sources that could not be classified with any diagnostic, or
were classified as SF using only one diagnostic, were assigned a final
classification of radio AGN if their 1.4 GHz luminosity was greater than
$10^{25}$ W Hz-1. The different combinations, number of sources in each, and
their final classification are summarised in Table LABEL:classification.
Overall, we classified 5 720 sources as radio AGN, 726 as SF/radio-quiet AGN
and 58 were unclassified.

Table 3: Number of sources classified by each diagnostic (c) BPT (d) WISE
colour-colour

Figure 14: Diagnostic plots for selecting radio AGN. Red points mark the
sources classified as radio AGN after combining all four diagnostics, and
black points show the star-forming/radio-quiet AGN (SF/RQAGN) sources. (a)
$D_{\mathrm{{n}}}(4000)$ vs $L_{\mathrm{1.4GHz}}$/$M_{\star}$ plot. The dashed
curve marks the division used for radio AGN and SF/RQAGN from Best & Heckman
(2012). (b) $L_{\textrm{H}\alpha}$ versus $L_{\mathrm{1.4GHz}}$ plot, with the
separation line from Best & Heckman (2012). (c) BPT diagram for the sources.
The dashed curve shows the semi-empirical relation from Kauffmann et al.
(2003). (d) WISE colour-colour plot for sources with the division line from
Sabater et al. (2019).

(e) PS sources offset ($z<0.4$)

(f) NPS sources offset ($z<0.4$)

(g) PS sources offset ($z>0.4$)

(h) NPS sources offset ($z>0.4$)

Figure 16:  Results for the radio AGN sample after adding offsets to spectral
indices. (a)$-$(b) Comparison of spectral indices before and after adding the
offsets described in Sect. 3.1. (c)$-$(d) Cumulative distributions of
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ after
reclassifying sources with the spectral index offset. (e)$-$(h) Colour maps
showing the average
$\overline{\sigma}_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$ values and
fraction of disturbed sources in bins of $L_{\mathrm{1.4GHz}}$ and
$L_{\textrm{\mbox{[}{OIII}]\leavevmode\nobreak\ }}$, again after reclassifying
sources with the spectral index offset.