# Compact Steep Spectrum Radio Sources with Enhanced Star Formation are
Smaller than $10\,$kpc

Yjan A. Gordon Department of Physics, University of Wisconsin-Madison, 1150
University Ave, Madison, WI 53706, USA  Christopher P. O’Dea Department of
Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
Stefi A. Baum Department of Physics and Astronomy, University of Manitoba,
Winnipeg, MB R3T 2N2, Canada  Keith Bechtol Department of Physics, University
of Wisconsin-Madison, 1150 University Ave, Madison, WI 53706, USA  Chetna
Duggal  Department of Physics and Astronomy, University of Manitoba, Winnipeg,
MB R3T 2N2, Canada  Peter S. Ferguson Department of Physics, University of
Wisconsin-Madison, 1150 University Ave, Madison, WI 53706, USA

(Received February 22, 2023; Revised April 12, 2023; Accepted April 20, 2023)

###### Abstract

Compact Steep Spectrum (CSS) radio sources are active galactic nuclei that
have radio jets propagating only on galactic scales, defined as having
projected linear sizes (LS) of up to $20\,$kpc. CSS sources are generally
hosted by massive early-type galaxies with little on-going star formation,
however a small fraction are known to have enhanced star formation. Using
archival data from the Faint Images of the Radio Sky at Twenty cm survey, the
Very Large Array Sky Survey and the Sloan Digital Sky Survey we identify a
volume-limited sample of $166$ CSS sources at $z<0.2$ with
$L_{1.4\,\text{GHz}}>10^{24}\,\text{W}\,\text{Hz}^{-1}$. Comparing the star
formation rates and linear sizes of these CSS sources, we find that the
$\approx 14\,\%$ of CSS sources with specific star formation rates above
$0.01\,\text{Gyr}^{-1}$ all have $\text{LS}<10\,$kpc. We discuss the possible
mechanisms driving this result, concluding that it is likely the excess star
formation in these sources occurred in multiple bursts and ceased prior to the
AGN jet being triggered.

Active galactic nuclei (16), AGN host galaxies (2017), Extragalactic radio
sources (508), Radio Galaxies (1343), Star formation (1569),

††journal: ApJL††facilities:  This work made use of observations from the Very
Large Array (VLA), SDSS and WISE.
The VLA is operated by The National Radio Astronomy Observatory, a facility of
the National Science Foundation operated under cooperative agreement by
Associated Universities, Inc.
Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan
Foundation, the Participating Institutions, the National Science Foundation,
the U.S. Department of Energy, the National Aeronautics and Space
Administration, the Japanese Monbukagakusho, the Max Planck Society, and the
Higher Education Funding Council for England. The SDSS Web Site is
http://www.sdss.org/.
The SDSS is managed by the Astrophysical Research Consortium for the
Participating Institutions. The Participating Institutions are the American
Museum of Natural History, Astrophysical Institute Potsdam, University of
Basel, University of Cambridge, Case Western Reserve University, University of
Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the
Japan Participation Group, Johns Hopkins University, the Joint Institute for
Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and
Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences
(LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for
Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico
State University, Ohio State University, University of Pittsburgh, University
of Portsmouth, Princeton University, the United States Naval Observatory, and
the University of Washington.
WISE is a joint project of the University of California, Los Angeles, and the
Jet Propulsion Laboratory/California Institute of Technology, and NEOWISE,
which is a project of the Jet Propulsion Laboratory/California Institute of
Technology. WISE and NEOWISE are funded by the National Aeronautics and Space
Administration.††software: We used the following software packages in the
preparation of this manuscript: AstroPy (Astropy Collaboration et al., 2013,
2018, 2022), Matplotlib (Hunter, 2007), NumPy (Harris et al., 2020), SAOImage
DS9 (Joye & Mandel, 2003), SciPy (Virtanen et al., 2020), Seaborn (Waskom,
2021) and TOPCAT (Taylor, 2005).

##  1 Introduction

Active Galactic Nuclei (AGN) are the phenomenon whereby matter is accreting
onto the central supermassive black hole of their host galaxies (Salpeter,
1964). A small fraction of AGN produce particle jets that result in radio
emission via mechanisms such as synchrotron radiation and inverse Compton
scattering (Padovani, 2017; Blandford et al., 2019). The jets produced by
these radio loud AGN (RLAGN) can sometimes propagate well beyond the host
galaxy, giving rise to large scale double-lobed structures such as Fanaroff
and Riley class I and II radio galaxies (FRIs and FRIIs, Fanaroff & Riley,
1974) that can span hundreds of kiloparsecs or more (e.g., Willis et al.,
1974; Ishwara-Chandra & Saikia, 1999; Dabhade et al., 2017). In contrast to
FRIs and FRIIs are compact RLAGN that have radio emission on scales similar to
or smaller than the host galaxy.

Compact Steep Spectrum (CSS) radio sources have radio extents smaller than
$\sim 20\,$kpc and radio spectral indices of $\alpha<-0.5$, where spectral
index, $\alpha$, is related to flux density, $S$, and frequency, $\nu$, by
$S\propto\nu^{\alpha}$ (Fanti et al., 1990; O’Dea, 1998; O’Dea & Saikia,
2021). It is thought that at least some CSS sources are young AGN that will
evolve into larger radio morphologies (Fanti et al., 1995; O’Dea, 1998; An &
Baan, 2012; O’Dea & Saikia, 2021). This hypothesis is based on very long
baseline interferometry (VLBI) observations of powerful CSS sources that show
double-lobed radio morphologies analogous to FRIs and FRIIs but on a much
smaller scale (Spencer et al., 1991; Dallacasa et al., 1995), and jet proper
motions indicative of a short travel time from the central engine (Owsianik &
Conway, 1998; Polatidis & Conway, 2003; An et al., 2012). The young AGN
scenario is further supported by CSS sources having host galaxies similar
those of larger radio galaxies.

An alternative to the young AGN scenario, is that the radio jets in CSS
sources are unable to travel as easily through the interstellar medium (ISM),
a phenomenon known as ‘frustration’ (van Breugel et al., 1984; Wilkinson et
al., 1984; O’Dea et al., 1991). Frustration can occur either as a result of
intrinsically weak jet power, the jet strongly interacting with a dense ISM,
or a combination of these factors. The jet frustration paradigm is supported
by high resolution images that show distinct asymmetry in some CSS radio
sources (Saikia et al., 1995; Saikia & Gupta, 2003; Orienti et al., 2007).

The galaxies that host CSS sources are generally massive early-type galaxies
with little star formation (SF), but a subset of the CSS population are known
to exhibit enhanced SF (de Vries et al., 1998, 2000; Drake et al., 2004;
Tadhunter et al., 2011; Dicken et al., 2012; O’Dea & Saikia, 2021). A
systematic study of SF in a large sample of CSS host galaxies may help shed
light on to why some CSS sources are star forming and constrain the
evolutionary path of these RLAGN. Such studies have previously been
problematic as most samples of CSS sources consisted of objects with high
radio luminosity that are rare in the local Universe. Consequently, the
relatively shallow wide-field multiwavelength surveys that can readily provide
star formation rates (SFRs) usually don’t cover the high luminosity radio
sources and expensive targeted observations are often necessary. The advent of
deep, wide-field radio continuum surveys with high angular resolution is now
making these types of systematic studies feasible (Sadler, 2016).

The Faint Images of the Radio Sky at Twenty cm survey (FIRST, Becker et al.,
1995) and the Very Large Array Sky Survey (VLASS, Lacy et al., 2020), which
have angular resolutions of $5.4^{\prime\prime}$ and $3^{\prime\prime}$
respectively, are well suited to identifying compact radio sources brighter
than $\approx 1\,$mJy. Furthermore, these surveys observe at different
frequencies; FIRST at $1.4\,$GHz and VLASS at $3\,$GHz. Using FIRST and VLASS
data together is a pragmatic approach to measuring the spectral indices of
large numbers of faint compact radio sources (Gordon et al., 2021). Both FIRST
and VLASS cover the $\approx 10,000\,\text{deg}^{2}$ footprint of the Sloan
Digital Sky Survey (SDSS, York et al., 2000) which provides optical
measurements and derived properties, including SFRs, for $\sim 10^{6}$
galaxies. Combining FIRST, VLASS and SDSS therefore has the potential to be an
effective method for studying SF in a large number of CSS sources in the local
Universe.

In this Letter we use data from FIRST, VLASS and SDSS to investigate the
relationship between radio source size and SF in CSS sources. The selection of
CSS sources is described in Section 2. In Section 3 we compare the radio sizes
and SFRs of our CSS sources. We discuss our results in Section 4 and state our
conclusions in Section 5. Throughout this work we assume a flat $\Lambda$CDM
cosmology with $h=0.7$,
$H_{0}=100h\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$, $\Omega_{m}=0.3$ and
$\Omega_{\Lambda}=0.7$.

##  2 Sample Selection

To identify likely CSS sources we start with the Best & Heckman (2012) catalog
of radio galaxies in the SDSS 7th Data Release (DR7, Abazajian et al., 2009)
spectroscopic sample. This catalog contains the host IDs of the radio sources,
identifies sources where the radio emission is likely due to SF rather than an
AGN, and where possible classifies RLAGN as either low- or high-excitation
radio galaxies (LERGs or HERGs). As we are interested in compact radio AGN in
this work, we select objects from the Best & Heckman (2012) catalog that are
associated with a single detection in FIRST, excluding multi-FIRST-component
sources from consideration.

High frequency ($\nu\sim 3\,$GHz) information on our sources is obtained by
cross matching with the VLASS Epoch 1 component catalog (Gordon et al., 2021).
We only search for VLASS components brighter than $3\,$mJy/beam, as fainter
components have less reliable flux density measurements (See section 3 of
Gordon et al., 2021). A search radius of $5^{\prime\prime}$ is used which,
given the on-sky component density of VLASS at $S>3\,$mJy ($\sim
18\,\text{deg}^{-2}$), has an expected contamination level from false-positive
matches of less than $0.05\,\%$. The $3\,$GHz flux density of our sources is
then scaled by $1/0.87$ to account for the systematic underestimation of flux
density measurements in the VLASS catalog reported in Gordon et al. (2021).
With flux densities at two different frequencies in hand, we determine the
spectral index, $\alpha$, between $1.4\,$GHz and $3\,$GHz for our sources.

The projected radio extents of CSS sources are smaller than $20\,$kpc (e.g.
Fanti et al., 1985; O’Dea & Baum, 1997; O’Dea & Saikia, 2021). The VLASS
catalog of Gordon et al. (2021) includes measurements of the source angular
size after after deconvolution from the beam111These measurements are produced
by the source-finder PyBDSF (Mohan & Rafferty, 2015).. Where the deconvolved
angular size is non-zero, this is used to calculate the projected linear size
(LS) of the source. If the source is so compact that it has a deconvolved
angular size of zero in VLASS, then we use the uncertainty in the angular size
to estimate an upper limit on the LS.

We select our likely CSS sources as having $\text{LS}<20\,$kpc and
$\alpha+\sigma_{\alpha}<-0.5$, identifying $1,109$ objects. In Figure 1 we
compare the redshifts and $1.4\,$GHz luminosities of this sample. By using
only sources at $z<0.2$ we select a volume-limited sample complete down radio
luminosities of $L_{1.4\,\text{GHZ}}>10^{24}\,\text{W}\,\text{Hz}^{-1}$. This
sample contains $259$ CSS candidates, all but $38$ ($15\,\%$) of which are
classified as LERGs. The radiatively efficient central engines in HERGs can
impact the observed properties of the host galaxy, including spectral line
measurements used in determining SFRs. Conversely, the radiatively inefficient
central engines of LERGs don’t produce the high energy photons necessary to
bias spectral line measurements (Hardcastle et al., 2006). We therefore
exclude the $38$ sources not classified as LERGs. Finally, $\approx 20\,\%$ of
single-FIRST-component RLAGN are expected to be multi-component sources in
VLASS (Gordon et al., 2019). To ensure we are only using sources with reliable
sizes and spectral indices, we visually inspect the VLASS maps using SAOImage
DS9 (Joye & Mandel, 2003) with the catalog components overlaid. As a result we
remove $55$ multi-VLASS-component sources from our sample, leaving $166$ CSS
sources that we use for the analysis presented in this Letter.

Figure 1: Redshift and $1.4\,$GHz luminosity distributions for our selection
of CSS sources. Our volume limited sample (red circles) is defined as having
$z<0.2$ and $L_{1.4\,\text{GHZ}}>10^{24}\,\text{W}\,\text{Hz}^{-1}$.

##  3 Comparing Star Formation and Linear Size in CSS Sources

All of our CSS sources have host galaxies with spectral line measurements,
stellar masses ($M_{*}$) and SFRs in the Max Plank institut für
Astrophysik/Johns Hopkins University (MPA/JHU) value added catalog for SDSS
DR7222https://wwwmpa.mpa-garching.mpg.de/SDSS/DR7/ (Kauffmann et al., 2003;
Brinchmann et al., 2004; Tremonti et al., 2004). In Figure 2 we plot the
stellar masses and SFRs of our CSS sources. For reference we also show the
distribution of all galaxies at $z<0.2$ in SDSS DR7 as grey shaded contours.
Galaxies in SDSS are split into two populations of ‘star-forming’ and
‘passive’ at a specific star formation rate ($\text{sSFR}=\text{SFR}/M_{*}$)
of approximately $0.01\,\text{Gyr}^{-1}$ (shown by the black dashed line in
Figure 2). The majority of our CSS sources are hosted by passive high-mass
galaxies, with only $24\ (14\,\%)$ having $\text{sSFR}>0.01\,\text{Gyr}^{-1}$.
We confirm these have a similar redshift distribution to the passive CSS hosts
in our sample by performing a Kolmogorov-Smirnov (KS) test, which returns a
$p-$value of $0.75$.

Figure 2: The stellar masses and star formation rates of our CSS sources (red
circles). The grey shaded contours show the distributions for SDSS DR7. The
black dashed line shows a fixed specific star formation rate of
$0.01\,\text{Gyr}^{-1}$.

Figure 3:  Comparisons of star-forming indicators and linear size (LS) for our
CSS sources. Panel a shows the SDSS sSFR measurements for our CSS sources with
a black dashed line indicating $\text{sSFR}=0.01\,\text{Gyr}^{-1}$. Panel b
shows the equivalent width of H$\alpha$ ($\text{EW}_{\text{H}\alpha}$) for our
CSS sources where this line is detected at $S/N>3$, while panel c shows the
strength of the $4,000\,$Å break. In Panel d the WISE colors are shown for
galaxies where the AGN does not dominate the IR color
($\text{W1}-\text{W2}<0.5$). Here the dot-dashed lines separate colors
associated with passive galaxies, star-forming galaxies and (U)LIRGs. In all
panels orange triangles denote CSS sources where the LS is an upper limit, and
the black cross shows the median uncertainty for the data points.

With SF being rare in CSS sources, one might ask whether there are differences
between CSS sources with SF and CSS sources hosted by passive galaxies? One of
the most fundamental properties of RLAGN is their size, i.e., how far the jets
have travelled from the central engine. To assess if the sizes of CSS sources
with SF and passive hosts differ we plot the LS of our CSS sources versus
their host sSFR in Figure 3a. CSS sources with
$\text{sSFR}<0.01\,\text{Gyr}^{-1}$ are seen at all sizes in our sample
($0<\text{LS}<20\,$kpc). However, higher sSFRs
($\text{sSFR}>0.01\,\text{Gyr}^{-1}$) are only seen in CSS sources with
$\text{LS}\lesssim 8\,$kpc. If we divide the CSS population at
$\text{LS}=10\,$kpc, $17.9_{-2.8}^{+3.8}\,\%$ of sources with
$\text{LS}<10\,$kpc have $\text{sSFR}>0.01\,\text{Gyr}^{-1}$, compared to
$0.0_{-0.0}^{+0.5}\,\%$ at $\text{LS}\geq 10\,$kpc. The uncertainties in these
population fractions are estimated using the binomial approach outlined in
Cameron (2011), and suggest a $\approx 2.9\sigma$ excess of star-forming hosts
in the smaller CSS sources.

The SFR measurements in SDSS are based on either the H$\alpha$ luminosity or
the strength of the $4,000\,\text{\AA}$ break, $D_{4000}$, depending on the
spectral line properties of the galaxy (Brinchmann et al., 2004). In panels b
and c of Figure 3 we show both of these observable properties complement our
findings with respect to the derived sSFRs shown in Figure 3a. Where H$\alpha$
is detected ($S/N>3$), the strongest H$\alpha$ emission lines are found nearly
exclusively in CSS sources with $\text{LS}<6\,$kpc (Figure 3b). When
considering $D_{4000}$, the weakest breaks–indicating young stellar
populations–are found only in CSS sources with $\text{LS}\lesssim 10\,$kpc
(Figure 3c).

A further test of the relative compactness of CSS sources with enhanced SF is
to investigate how the infrared (IR) colors of the host change with LS. To
this end we obtain IR information from the Wide-field Infrared Survey Explorer
telescope (WISE, Wright et al., 2010) AllWISE catalog (Cutri et al., 2012,
2013). The WISE W2 ($4.3\mu$m) and W3 ($12\mu$m) filters can be used to
identify star-forming galaxies. Additionally, the W1 ($3.4\mu$m) and W2
filters can identify galaxies where the IR colors are contaminated by AGN
emission. From our sample of CSS sources, $102$ ($61\,$%) are detected
($S/N>2$) in the W1, W2 and W3 bands. Of these $102$ galaxies, $6$ have
$\text{W1}-\text{W2}>0.5$ indicating that their IR colors are dominated by the
AGN (Mingo et al., 2016). For the remaining $96$ CSS sources, we plot their
$\text{W2}-\text{W3}$ color against LS in Figure 3d. Adopting the criteria of
Mingo et al. (2016), galaxies with

  * •

$\text{W2}-\text{W3}<1.6$ are passive,

  * •

$1.6<\text{W2}-\text{W3}<3.4$ are star-forming,

  * •

and $\text{W2}-\text{W3}>3.4$ are (Ultra) Luminous Infrared Galaxies
([U]LIRGs).

Panel d of Figure 3 is consistent with panels a-c, showing that nearly all CSS
sources with IR colors indicative of SF have $\text{LS}<8\,$kpc. For CSS
sources with $\text{LS}<10\,$kpc, $40.0_{-5.0}^{+5.5}\,\%$ have star-forming
WISE colors. On the other hand, only $5.9_{-1.9}^{+11.3}\,\%$ of CSS sources
with $\text{LS}\geq 10\,$kpc have WISE colors associated with star-forming
galaxies–a deficit relative to the sub $10\,$kpc population at $\approx
2.8\sigma$ confidence.

##  4 Discussion

###  4.1 Physical Interpretation

Our data shows that where excess SF is present in CSS sources, those sources
are limited to scales smaller than $\approx 10\,$kpc. At first glance, there
are three likely possibilities that might explain this observation.

  1. 1.

The jet itself has triggered a brief period of SF (e.g. Rees, 1989; Labiano et
al., 2008; Duggal et al., 2021).

  2. 2.

A dense ISM is inhibiting the propagation of the radio jet resulting in its
confinement to scales $\lesssim 10\,$kpc.

  3. 3.

The AGN is younger than the SF, limiting the time available for the radio jets
to propagate away from the central engine.

Figure 4: Three toy model jets simulated using the semi-analytical code of
Hardcastle (2018) with powers $Q=10^{35}\,$W (circles), $Q=10^{36}\,$W
(squares) and $Q=10^{37}\,$W (stars). Panel a shows the evolution of
$1.4\,$GHz luminosity with linear size colored by the jet age. Panel b shows
the linear size growth as a function jet age, with the points colored by
$L_{1.4\,\text{GHz}}$. The red dashed line in panel b shows the $20\,$Myr
typical lifetime of O-type stars.

To explore these scenarios we compare the expected evolution of radio jets in
these sources to the timescale on which the SF is detectable. In order to
estimate the typical age of the jets in our CSS sources with enhanced SF, we
simulate three ‘toy model’ jets using the semi-analytical radio jet evolution
code of Hardcastle (2018). The median $1.4\,$GHz luminosity of our sample is
$10^{24.3}\,\text{W}\,\text{Hz}^{-1}$. For this simulation we assume a
universal pressure profile (Arnaud et al., 2010) for galaxies in a halo of
mass $M_{500}=10^{13.5}\,\text{M}_{\odot}$. In this scenario, a radio source
with $\text{LS}=10\,$kpc and
$L_{1.4\,\text{GHz}}=10^{24.3}\,\text{W}\,\text{Hz}^{-1}$ is expected to have
a jet power, $Q$, of $\sim 10^{36}\,\text{W}$ (see Figure 4a). Such a jet will
have taken $\approx 8\,$Myr to reach its current size, and would reach a
linear size of $\approx 19\,$kpc within $20\,$Myr of being switched on (see
Figure 4b).

Figure 5: Normalised distributions of $L_{1.4\,\text{GHz}}$ for subsamples of
our CSS sources. Both panels show the full CSS sample as a solid grey
histogram, and the CSS sources with $\text{LS}<10\,\text{kpc}$ as blue solid
line. Panel a shows a comparison with sources having $\text{LS}\geq
10\,\text{kpc}$ (red dashed line), while Panel b shows the radio luminosities
of CSS sources with $\text{sSFR}>0.01\,\text{Gyr}^{-1}$ (orange dot-dashed
line).

The increase in radio luminosity shown for our toy model jets as the radio
source grows is consistent with our data. In Figure 5a we show the
distributions of $L_{1.4\,\text{GHz}}$ for small ($\text{LS}<10\,\text{kpc}$)
and larger ($\text{LS}\geq 10\,\text{kpc}$) CSS sources in our sample.
Performing a KS test returns a $p$-value of $8\times 10^{-3}$, showing these
distributions to be statistically different. The smaller CSS sources have a
median radio luminosity of $10^{24.26}\,\text{W}\,\text{Hz}^{-1}$, while the
larger sources have a median value of $10^{24.49}\,\text{W}\,\text{Hz}^{-1}$.
Such a change in luminosity for a $10^{36}\,$W jet would be expected as it
grows from a linear size of $\approx 6\,$kpc to $\approx 12\,$kpc (see Figure
4a). The $L_{1.4\,\text{GHz}}\,$ distribution of the CSS sources with
$\text{sSFR}>0.01\,\text{Gyr}^{-1}$ (Figure 5b) is consistent with the
luminosity distribution of the smaller CSS sources, having a KS derived
$p$-value of $0.26$.

The SF indicators shown in Figure 3 are visible for different time periods
after SF ends. H$\alpha$ emission is the result of ionisation of the ISM by
massive O-type stars, limiting its visibility to $\approx 20\,$Myr after the
cessation of SF (Kennicutt, 1998). Conversely, $D_{4000}$ is affected by the
entire stellar population and evolves slowly following a starburst, taking
several hundred Myr for a strong break to develop (Goto et al., 2008). IR
colors resulting from SF evolve on a timescale between the two extremes of
H$\alpha$ and $D_{4000}$. The WISE W3 band traces SF through the polycyclic
aromatic hydrocarbons associated with B-type stars that live for $\approx
100\,$Myr following a starburst (Peeters et al., 2004; Jarrett et al., 2011).

Assuming a jet age on the order of $\sim 10\,$Myr, the absence of low
$D_{4000}$ values in CSS sources with $\text{LS}\gtrsim 10\,$kpc suggests that
the bulk of SF ceased hundreds of Myr prior to the jet being triggered. Our
results are thus inconsistent with the AGN jet triggering the SF unless jet
propagation is frustrated for hundreds of Myr. On the other hand, the presence
of strong H$\alpha$ emission in CSS sources with $\text{LS}\lesssim 10\,$kpc
is indicative of active SF as recently as $10\,$Myr prior to the jet being
triggered. Future observations that measure the jet (a)symmetry and hotspot
proper motions are necessary to test if these sources are indeed frustrated.

A tantalising explanation for our results is that of galaxy mergers–a known
trigger for both SF and AGN (e.g. Ellison et al., 2013; Pearson et al., 2019;
Gao et al., 2020; Pierce et al., 2022, 2023). In galaxy mergers SF is episodic
and the time required for gas to fall into the central engine means that RLAGN
are not expected to be triggered until a few hundred Myr after the first
starburst (Tadhunter et al., 2005; Peirani et al., 2010; Shabala et al.,
2017). A final starburst in the merger sequence that ceases $\approx 10\,$Myr
prior to the jet being triggered, and has a much smaller burst fraction than
the initial starburst several hundred Myr earlier, might produce the observed
H$\alpha$ with a limited impact on $D_{4000}$. It is therefore prudent to ask
if our sample of CSS sources with enhanced SF are associated with mergers? To
this end we visually inspect optical images obtained from the 9th data release
of the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys (Dey et
al., 2019) for the $24$ CSS sources with $\text{sSFR}>0.01\,\text{Gyr}^{-1}$.
We find that $11\ (46\,\%)$ show clear evidence of tidal features indicative
of a recent major galaxy-galaxy interaction. This is a higher incidence than
the $28\,\%$ of the LERG population shown to have tidal features in Gordon et
al. (2019). The relatively high fraction of our sample with tidal features
suggests that mergers likely explain at least some CSS sources with enhanced
SF, and this warrants further study.

###  4.2 Are our CSS Sources Really Variable Sources?

We have selected our CSS sources using legacy data from two different radio
surveys. Because these observations were not made simultaneously–two decades
separate FIRST and VLASS–it is possible the difference in flux density
measurements may be an effect of radio source variability rather than the
shape of spectral energy distribution. Variable radio sources typically have
very compact morphologies. Nyland et al. (2020) show that sources showing
variability between FIRST and VLASS have $\text{LS}<1\,$kpc, while Wołowska et
al. (2021) use VLBI imaging to show such sources typically have sizes of just
a few tens of parsecs.

Of the $24$ CSS sources with $\text{sSFR}>0.01\,\text{Gyr}^{-1}$, only $3$ are
completely unresolved by VLASS (shown as upper limits in Figure 3). A further
$9$ of these $24$ sources have measured linear sizes below $2\,$kpc, notably
all of which are greater than $1\,$kpc. The other half of our CSS sample with
enhanced SF have $2\,\text{kpc}<\text{LS}<8\,\text{kpc}$ and are therefore
larger than variable sources are expected to be. If we were to cautiously
assume that the $12$ sources within our sample with enhanced SF and
$\text{LS}<2\,$kpc are all variable sources then our conclusion would still be
valid: CSS sources with enhanced SF are smaller than $\approx 10\,$kpc.

##  5 Conclusions

In this Letter we have systematically investigated the relationship between
star formation and radio source size in CSS sources. We find that where
enhanced SF is present the radio source has $\text{LS}\lesssim 10\,$kpc, while
passive hosts are seen in CSS sources with $0\leq\text{LS}<20\,$kpc. Based on
simulated jet propagation times, the absence of CSS hosts with weak $4,000\,$Å
break strengths at $\text{LS}\gtrsim 10\,$kpc suggests the bulk of SF ceased
several hundred Myr before the AGN jet was triggered. The presence of
H$\alpha$ emission in CSS sources with $\text{LS}<10\,$kpc indicates that some
SF occurred $\approx 10\,$ Myr prior to the jet triggering. We interpret this
apparent ambiguity as being the result of episodic SF in these CSS sources
where the later starbursts have a lower ‘burst fraction’, potentially
resulting from galaxy-galaxy interactions.

##

We thank the anonymous referee for their helpful report that has improved the
quality of this work. Y.A.G. is supported by U.S. National Science Foundation
grant AST 20-09441. C.P.O., S.A.B. and C.D. are supported by NSERC, the
National Sciences and Engineering Research Council of Canada.

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# Using convolutional neural networks for the classification of breast cancer
images.

Eric Bonnet
Centre National de Recherche en Génomique Humaine
Institut de Biologie François Jacob
Commissariat à l’Energie Atomique
Université Paris–Saclay, Evry, France
<EMAIL_ADDRESS>
(June 2021)

###### Abstract

In this study I compare different architectures of convolutional neural
networks and different hardware acceleration devices for the detection of
breast cancer metastasis tissue from microscopic images of sentinel lymph
nodes. Convolutional models with increasing depth are trained and tested on a
public data set of more than 300,000 images of lymph node tissue, on three
different hardware acceleration cards, using an off–the–shelf deep learning
framework. The impact of transfer learning, data augmentation and
hyperparameters fine-tuning are also tested. Hardware acceleration device
performance can improve training time by a factor of five to seven, depending
on the model used. On the other hand, increasing convolutional depth will
augment the training time by a factor of four to six times, depending on the
acceleration device used. Increasing the depth of the model, as could be
expected, clearly improves performance, while data augmentation and transfer
learning do not. Fine-tuning the hyperparameters of the model notably improves
the results, with the best model showing a performance comparable to
state–of–the–art models.

## Introduction

Pathologists have been making diagnoses using digital images of glass
microscope slides for many decades. In recent years, advances in slide
scanning techniques has allowed the full digitization of microscopic stained
tissue sections. There are many advantages to the digitalization of such
images, including standardization, reproducibility, the ability to create
workflows, remote diagnostics, immediate access to archive, easier sharing
among expert pathologists [1]. Breast cancer is the leading cancer type in
women worldwide, with an estimated 2 million new cases and 627,000 deaths in
2018. Breast cancer staging refers to the process of describing the tumor
growth or spread. Accurate staging by pathologists is an essential task that
will determine the patient’s treatment and his chances of recovery
(prognosis). An important part of breast cancer staging is the assessment of
the sentinel axillary node, a tissue commonly used for the detection of early
signs of tumor spreading (metastasis). However, sentinel lymph nodes
assessment by pathologists is not always easy and optimal. For instance, a
retrospective survey performed in 2012 by expert pathologists requalified the
status of a high proportion of sentinel nodes [2]. Deep learning algorithms
have made major advances relatively recently in solving problems that have
resisted the machine learning and artificial intelligence community such as
speech recognition, the activity of potential drug molecules, brain circuits
reconstruction and the prediction of the effects of non-coding RNA mutation on
gene expression and disease [3]. Convolutional neural networks (CNNs) are a
class of deep neural networks characterized by a shared-weight architecture of
convolution kernels (or filters) that slide along input features and provide
translation equivariant features known as feature maps. One of the main
advantages of CNNs is that the network learns to optimize the filters through
automated learning, requiring very little pre-processing compared to other
machine learning techniques. Since their introduction in the 1990’s [4], CNNs
have shown excellent performances in the most challenging visual
classification tasks and are currently dominating this research field [5].
When applied to medical imaging, CNNs demonstrated excellent performance and
have been successfully used for the identification of retinal diseases from
fundus images [6, 7, 8], tuberculosis from chest radiography images [9, 10]
and malignant melanoma from skin images [11]. CNNs have also been used for the
detection of lymph node metastases in women with breast cancer in an algorithm
competition known as CAMELYON16 (Cancer Metastases in Lymph Nodes Challenge),
with the best models showing equal or slightly better performances than a
panel of pathologists [12]. In this study, I use a data set of more than
300,000 lymph node images derived from CAMELYON, known as the PCam (Patch
CAMELYON) data set [13] to characterize and analyze the performance of
different CNNs network architectures and GPU accelerators, using a standard,
off–the–shelf, deep learning computational library.

## Material and methods

The PCam data set was downloaded from the original website
(https://github.com/basveeling/pcam). All images have a size of 96 x 96
pixels, in three colors. The training set has 262,144 images (80 % of the
total), the validation set has 32,768 images (10 %) and the test set has also
32,768 images (10 %). All data sets have a 50/50 balance between positive
(tumor present) and negative (tumor absent) samples.

All models were coded in Python (v3.7.5) using the TensorFlow (v2.4.1) and
integrated Keras API (v2.4.0). Some additional statistics and performance
indicators were calculated with the Sci-Kit Learn Python package [14]. The
model performance was tested on three different GPU architectures: Nvidia
Tesla K80 with 32 Gb of RAM, Nvidia Tesla P100 with 16 Gb of RAM and Nvidia
Tesla V100 with 32 Gb of RAM. All the models tested in this study, including
the code for tuning some of the models, are available on GitHub
(https://github.com/erbon7/pcam_analysis).

For each network architecture tested in this study, the same procedure is
used: the model is trained on the training set for 15 epochs, with an
evaluation on the validation set after each epoch. Depending on the accurracy
value of the model, the weights are saved after each epoch to keep the best
model, which is then evaluated on the test set. For some models, I used the
KerasTuner framework with the Hyperband algorithm to optimize some
hyperparameters [15]. For the CNN-2L and CNN-6L models, the batch size, the
size of the dense layer and the learning rate were optimized. For the IV3-F
model, only the learning rate and batch size were optimized.

## Results

Figure 1: Normal and tumor example images from the PCam data set. The red
rectangle corresponds to the 32 x 32 pixels center. The presence of at least
one pixel of tumor tissue in this region dictates a positive label (1),
otherwise the image is labeled as negative(0).

In the CAMELYON16 challenge [12], hundreds of whole-slide images of sentinel
lymph nodes sections with or without nodal metastases verified by standard
immunohistochemical staining by expert pathologists are provided to the
participants to build algorithms. The PCam data set is composed of patches of
96 x 96 pixels images automatically extracted from the CAMELYON data set [13].
For each image, a positive label indicates that the 32 x 32 pixel center of
the image contains at least one pixel annotated as tumor tissue (Figure 1).

Figure 2: Simplified architecture of the CNN-2L (a, two convolutional layers)
and CNN-6L (b, six convolutional layers) models.

Three different CNN models were used in this study, with different depth
levels (Table 1). The first model (CNN-2L) is very simple with only two
convolutional layers (Figure 2a). This model was trained with a batch size of
32, the Adam gradient optimizer [16] with default rate 1e-3, a final dense
layer of 256 nodes and a training epoch number of 15. The second model
(CNN-6L) is more deep and complex with six convolutional layers (Figure 2b).
It is trained with the same parameter values as the CNN-2L. The architecture
for the CNN-6L model was inspired by the Kaggle models of F. Marazzi
(https://bit.ly/35wINGv) and H. Mello (https://bit.ly/3xwI6cl). Note that the
CNN-6L model include batch normalization [17] and dropout steps to improve
performance.

Table 1: CNN models. Model name | Description
---|---
CNN-2L | Simple model with 2 convolutional layers
CNN-6L | Deep model with 6 convolutional layers
IV3 | InceptionV3 [18] very deep convolutional model,
| with (IV3-TL) or without (IV3-F) transfer learning.

The last model is InceptionV3, a model created in 2015 with a very deep
architecture (94 convolutional layers) that performs very well on various
computer vision tasks [18], such as the the ImageNet challenge (https://image-
net.org/challenges/LSVRC/), a competition with hundreds of object categories
and millions of images [19]. The InceptionV3 model is available in the
TensorFlow Keras as part of some ”standard” deep learning models included in
this library. Furthermore, it is possible to load the model pre-weighted with
ImageNet training weights, thus enabling transfer learning (TF). TF is a
popular approach in deep learning where pre-trained models are used as the
starting point on computer vision and natural language processing tasks in
order to save computing and time resources. Here I have used the InceptionV3
model both pre-trained with imagenet weights (IV3-TL) and fully re-trained
(IV3-F) with the PCam data sets. For the pre-trained version, only the last
layers of the model are re-trained with the PCam data set (global average
pooling layer, dense layer and final output). Of course, given that the number
of training parameters is much greater in the case of the fully re-trained
InceptionV3 model, the computation time needed for training the model is also
expected to be much longer. Table 2 is detailing the architecture and
parameters for each of the models used in this study.

Table 2: CNN models architecture and parameters. | CNN-2L | CNN-6L | IV3-TL | IV3-F
---|---|---|---|---
Number of convolutional layers | 2 | 6 | 94 | 94
Total number of parameters | 9.5M | 2.4M | 22M | 22M
Number of training parameters | 9.5M | 2.4M | 524K | 22M
Batch size | 32 | 32 | 32 | 32
Dense layer size | 256 | 256 | 256 | 256

The computational running time for the different models is detailed in Table
3. Note that the time corresponds to the average time observed for one epoch.
We can compare the model architecture and the hardware GPUs acceleration for
the PCam data set analysis. As expected, the running time is increasing with
the complexity and depth of the model. The IV3-F model is taking 4 to 6 times
longer to train than the simple 2 convolutional layers CNN-2L model, depending
on the GPU card model. The 6 layers CNN model is taking 1.7 times longer than
the 2 layers CNN to train. With the InceptionV3 model, using transfer learning
is obviously saving a lot of training time, as a full model training is taking
$\sim$3 times longer to train on all GPU models. In fact, even though the IVF-
TL model (transfer learning) is much more complex, the running time is
comparable to the 2 and 6-layers models. Regarding the different GPU cards
tested here, more recent and powerful GPU cards decrease the computing time
quite drastically, with an acceleration factor between 5 and 7 times for the
most recent architecture tested here (V100) on all the CNN models compared to
the oldest model tested here (K80). It is worth noticing that the deepest
model tested here can be fully trained in about one hour with a V100 GPU card.

Table 3: Run time in seconds for one epoch on different GPU architectures. NbCU: number of CUDA cores. Pp: processing power in GFlops. GPU card | NbCU | Pp | CNN-2L | CNN-6L | IV3-TL | IV3-F
---|---|---|---|---|---|---
K80 (2014) | 4992 | 2400 | 325 | 562 | 468 | 1333
P100 (2016) | 3584 | 5000 | 70 | 121 | 143 | 393
V100 (2017) | 5120 | 7000 | 47 | 78 | 98 | 279

The performance of all the models on the PCam data set is described in Table
4. All the indicators are measured on the test set. A global improvement of
the performances is quite clearly associated with an increased depth of the
models. For instance the AUC of the simple 2-layers convolutional model is
0.85, increasing to 0.91 with the 6-layers convolutional model. The
InceptionV3 model, which has 94 convolutional layers, also has an AUC of 0.91.
Transfer learning does not work very well, since the AUC of the InceptionV3
model trained with the ImageNet weights is only 0.88, better than the 2
convolutional layers model but worse than the 6 convolutional layers (0.91)
and the InceptionV3 fully re-trained (0.91). It might be that the visual
structures (i.e. the filters) learned with the ImageNet data set are not
adapted to the PCam images. Object categories in the ImageNet data set (such
as ”ballon”, ”strawberry”, etc.) are indeed very different from the type and
structures seen on lymph node tissue microscopy images. Image data
augmentation is a technique that can be used to artificially expand the size
of a training data set by creating modified versions of the images. This
technique was used for the CNN-6L model, but with no obvious positive result
on the performance (test loss 0.70, test accuracy 0.73, AUC 0.90). We can see
in the table that fine-tuning models is improving performance for both the 6
convolutional layers model (AUC 0.92) and the InceptionV3 fully re-trained
model (AUC 0.954). The performance of the fined-tuned InceptionV3 model fully
re-trained (IV3-F) is comparable to current state–of–the–art models for
computational pathology analysis. It is within the top 5 best algorithms of
the CAMELYON16 challenge [12] and is within the top 10 best models for the
PCam dataset (https://paperswithcode.com/sota/breast-tumour-classification-on-
pcam). The current best PCam models have an AUC around 0.97 and implement
rotation equivariant strategies [20, 21, 22]. Indeed, histology images are
typically symmetric under rotation, meaning that each orientation is equally
as likely to appear. Rotation–equivariance removes the necessity lo learn this
type of transformation from the data, thus allowing more discriminative
features to be learned and also reducing the number of parameters of the
model.

Table 4: Performance of the models on the PCam test set. Tn CNN-6L: fine-tuned version of the CNN-6L model. Tn IV3-F: fine-tuned version of the IV3-F model. AUC: area under the ROC curve. Metric | CNN-2L | CNN-6L | IV3-TL | IV3-F | Tn CNN-6L | Tn IV3-F
---|---|---|---|---|---|---
Loss | 0.47 | 0.44 | 0.46 | 0.42 | 0.45 | 0.32
Accuracy | 0.78 | 0.84 | 0.78 | 0.84 | 0.85 | 0.89
AUC | 0.85 | 0.91 | 0.88 | 0.91 | 0.92 | 0.95

## Acknowledgements

I wish to thank Claude Scarpelli and Jean-François Deleuze for their general
support and discussions. I would also like to thank Christine Ménaché and
Xavier Delaruelle for giving me access to the new FENIX infrastucture of the
CEA cluster computer at the Très Grand Centre de Calcul (TGCC). Last, I would
like to thank the TGCC support team for their patient and competent answers to
my multiple questions and requests.

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# Feasible climate policies in a democracy with a climate-denying party

Andrea Di Benedetto
Institute for Marine and Atmospheric Research (IMAU)
Centre for Complex Systems Studies (CCSS)
Utrecht University
Princetonplein 5, 3584 CC Utrecht, The Netherlands
<EMAIL_ADDRESS>
& Claudia E. Wieners
Institute for Marine and Atmospheric Research (IMAU)
Centre for Complex Systems Studies (CCSS)
Utrecht University
Princetonplein 5, 3584 CC Utrecht, The Netherlands
& Anna S. von der Heydt
Institute for Marine and Atmospheric Research (IMAU)
Centre for Complex Systems Studies (CCSS)
Utrecht University
Princetonplein 5, 3584 CC Utrecht, The Netherlands

###### Abstract

Climate policy has become increasingly politicized in many countries including
the US, with some political parties unwilling to pursue strong measures.
Therefore, to be successful in mitigation, climate policies must be
politically feasible. Currently, climate mitigation pathways are explored in
so-called Integrated Assessment Models (IAMs) which evaluate climate policies
from an economic perspective, typically focusing on cost-effectiveness and
overlooking transition costs. However, the economy is intertwined with the
political system, in which policymakers impose economic policies, but are (in
democracies) dependent on public opinion, which in turn can be influenced by
economic performance. In cases where some parties are much less ambitious in
climate mitigation than others, climate policy can be abruptly disrupted,
influencing voting behaviour. In this study, we analyze the political
feasibility of a set of green policies in case some parties are strongly
unwilling to protect the climate. We show that this simple additional social
layer of complexity largely affects the outcome of the abatement measures. In
particular, we conclude that a (high) pure carbon tax is particularly
vulnerable to abrupt interruptions and its economic side effects discourage
votes for green parties. Nevertheless, a strategically selected combination of
policies can reduce political uncertainty, resulting in a more feasible and
effective mitigation measure.

_Keywords_ Integrated Assessment Models $\cdot$ Agent-Based Models $\cdot$
Climate change

##  1 Introduction

Climate mitigation pathways are currently explored in so-called Integrated
Assessment Models (IAMs) Hadi Dowlatabadi (1995); Weyant, J. (2017). IAMs are
elaborate tools but generally have two weaknesses: they have difficulties
modelling abrupt changes, and they focus only on specific subsystems, namely
the economy (especially the energy and land-use sector) and the climate while
ignoring social and political processes Keppo, I., Butnar, I., Bauer, N.,
Caspani, M., Edelenbosch, O., Emmerling, J., Fragkos, P., Guivarch, C.,
Harmsen, M., Lefèvre, J., Le Gallic, T., Leimbach, M., McDowall, W., Mercure,
J.-F., Schaeffer, R., Trutnevyte, E., Wagner, F. (2021); van Soest, H. L., van
Vuuren, D. P., Hilaire, J., Minx, J. C., Harmsen, M. J.H.M., Krey, V., Popp,
A., Riahi, K., Luderer, G. (2019). These models evaluate climate policies from
an economic perspective, typically focusing on cost-effectiveness Volker., K.
(2014); Fisher-Vanden, K. and Weyant, J. (2020).
However, the economy is not an isolated system. Rather, it is intertwined with
the political system, in which policymakers impose economic policies, but are
(in democracies) dependent on public opinion, which in turn can be influenced
by economic performance Peng, W., Iyer, G.,Bosetti, V., Chaturvedi, V.,
Edmonds, J., Fawcett, A. A. , Hallegatte, S., Victor, D., van Vuuren, D.,
Weyant, J. (2021); Meng, K. C., Rode, A. (2019). Changing governments can lead
to disruptions in climate policy if some parties are much more ambitious in
climate protection than others. On the other hand, climate policy will also
influence voting behaviour. In light of these considerations, previous
research has emphasized that the primary source of uncertainty in curbing
global temperature rise is less about scientific or technological issues and
more about political decisions that postpone mitigation efforts Rogelj, J. ,
McCollum, D. L., Reisinger,A. , Meinshausen, M., Riahi, K. (2013). Therefore,
a truly integrated assessment of climate policy must take into account socio-
political processes, including a political system as well as human and
collective behaviour Beck, M. and Krueger, T. (2016). Decision-makers with
climate ambitions need to find policies that are feasible and robust against
political instability and interruptions. A recent example of a politics-
induced failure is the fuel tax proposed by the French government in 2018
which caused a large series of protests around the country and subsequently a
big step backwards by the policymakers.
In this study, we assess the effect of party politics on the green transition
by implementing a two-party election model in an agent-based IAM to analyze
the effectiveness of a set of green policies in case of one party is unwilling
to protect the climate.
Three election scenarios are compared: No elections (“green” party always
rules), Coinflip (the ruling party is selected with 50% chance every 4 years)
and Coupled (chance of re-election depends on economic performance and global
warming). We model public discontent with (economically costly) climate
policies by assuming that voters punish parties during whose government
unemployment rises. This is based on empirical evidence from various countries
that suggests that experiencing job loss often precipitates a shift in the
political spectrum Sipma, T. and Lubbers, M. and Spierings, N. (2023); Wright,
J. (2012); Wiertz, D. and Rodon, T. (2021).

Figure 1: In black the processes of the previous version of the model Wieners,
C. E., Lamperti, F., Roventini, A. (2022); Lamperti, F., Bosetti, V.,
Roventini, A., Tavoni, M. (2019). In red, are the newly introduced socio-
political feedbacks. Climate policies, which were present also in the previous
model version, are now implemented by parties whose probability of being
elected depends on the state of the economy and climate.

As the Integrated Assessment Model, we use the Dystopian Schumpeter-Keynes
(DSK) model, the first agent-based IAM Lamperti, F., Bosetti, V., Roventini,
A., Tavoni, M. (2019). The DSK model simulates the industrial sector of one
country. Its agent-based nature allows for a detailed analysis of the
macroeconomic transition costs, which are often overlooked by models based on
General Equilibrium (GE) assumptions. In DSK, complete decarbonisation
requires a transition to green energy in the electricity sector and full
electrification in the heavy industry (“capital goods”) sector. Here, we test
several policy mixes (see Table 1 and Methods), combining carbon tax,
subsidies and regulations, for their political feasibility under elections. To
this end, we define the difference in temperature outcomes between the No-
election and the Coupled case as _political uncertainty_ Rogelj, J. ,
McCollum, D. L., Reisinger,A. , Meinshausen, M., Riahi, K. (2013); Vaughan, N.
E. and Lenton, T. M. and Shepherd, J. G. (2009); Bosetti, V. and Carraro, C.
and Sgobbi, A. and others (2009); Sanderson, B. M. and O’Neill, B. C. (2020);
Beck, M. and Krueger, T. (2016) and consider policies which minimise political
uncertainty to be _politically feasible_.
Throughout this study, our aim is to explore the overall system behaviour
resulting from the complex interactions among economics, climate and society,
rather than to provide exact quantitative predictions.

## Main

### Pure carbon tax

In the absence of elections, a moderate carbon tax (Tc, see Table 1) ensures a
green transition in the electricity sector. However, to keep warming well
below 2°C, a much higher tax (T2) is needed Wieners, C. E., Lamperti, F.,
Roventini, A. (2022), because of inertia in the electricity sector Grubb, M.,
Wieners, C.E., Yang, P. (2021) and because the tax increases both fuel and
electricity price; thereby being slow in enforcing electrification in the
capital-good firms. The T2 carbon tax leads to a strong rise in fuel and
electricity prices and higher production costs for the capital goods sector.
Machine sales and production hence drop, leading to unemployment. Higher
production costs and lower employment (and hence, lower consumption) also lead
to slight reductions in consumption good production, exacerbating
unemployment. This causes a decade-long unemployment rise (17.6% for
2024-2028; baseline: 4.4%; Fig. 3).
In the Coinflip model, both green technologies in the electricity sector and
electrification are significantly delayed (Fig. 3), leading to 3 degrees
warming, compared to 1.8 in the No-election case (Fig. 5). This is because in
years when the Brown party is in power, no carbon tax is in place to prevent
the construction of brown plants (Fig. 4). In fact, in such years the economy
recovers from the stagnation induced by the tax, boosting the energy demand
and hence (brown) plant construction.

Figure 2: Timeseries of the electrification fraction in the capital good
sector, the number of brown plants, the fraction of unemployed workers and the
share of green energy for the three election cases and policy T2 (See Table
1). The shaded region represents the range from the 20th to the 80th
percentile, providing a view of the variability in outcomes. The thick lines
describe the means across 50 Monte Carlo runs. The simulation starts in 2000.
The number of plants normalized by the 2020 mean value.

Figure 3: Timeseries of the electrification fraction in the capital good
sector, the number of brown plants, the fraction of unemployed workers and the
share of green energy for the three election cases and policy T2eB (See Table
1). The shaded region represents the range from the 20th to the 80th
percentile, providing a view of the variability in outcomes. The thick lines
describe the means across 50 Monte Carlo runs. The simulation starts in 2000.
The number of plants normalized by the 2020 mean value.

In the Coupled case, mitigation results are further worsened because high
peaks in unemployment during the Green party’s mandate reduce the probability
of the Green party being elected (Fig. 4). These unemployment spikes stem from
the implementation of a tax policy during the Green Party’s mandates, which
lower $P_{U}$ and $P_{dU}$ (See Methods, Eq. 1), thus the probability of being
elected $P_{g}$ (See Fig. 4). On average, the Green Party has a <50% chance of
being in power in 2020-2100 (See Fig. 3, 4). This leads to a poor performance
in limiting global warming, with 3.5 degrees warming by 2100 (See Fig. 5).

### Pure carbon tax with subsidy

By redistributing the tax revenue, the negative impact of the carbon tax on
the unemployment rate can be significantly reduced. A possible approach could
be redistributing the money as a wage subsidy to firms (T2f). This measure
substantially lowers the unemployment peak to approach baseline levels, with a
slower green transition which results in similar maximum levels of global
warming (around 3 degrees) and political uncertainty for both the election
cases (See Fig. 5). This removes the punishment faced by the Green Party and
narrows the gap in temperature projections between the Coinflip and Coupled
scenarios (See Fig. 5). Another possibility is subsidizing the construction of
green plants (T2C). This measure does not directly reduce unemployment in the
short term (20% peak, See Fig. 5) but promotes a faster green transition. This
leads to reduced maximum temperatures for all election cases, improving its
effectiveness but not its political feasibility.

Figure 4: Overview of the processes arising in the coupled case when a carbon
tax T2 or a combination of sectoral tax and brown investment ban (T2eB) are
implemented by the green party. The vertical yellow line marks the start of
the implementation of climate policies. The left plots show the evolution of
meaningful macro-variables in a single run. The number of plants normalized by
the 2120 baseline mean value. On the right plots, the evolution of the terms
involved in the election model (See Eq. 1) from the same simulation. $P_{g}$
is the probability for the Green Party of being elected. Blue (red) shaded
means Green (Brown) party in power. For example, with T2, the Green Party is
in power during the 2022-2025 mandate (right plot), introducing a carbon tax
causing unemployment to grow until 2025 (left plot). This leads to a drop in
‘$P_{U}$ and $P_{dU}$ (See Eq. 1) for the mandate 2026-2029 (right plot),
lowering the chance of Green being elected to 0.3. Indeed, the brown party is
elected in 2026. Unemployment is a 4-year moving average.

### No-tax policies

Another possible strategy is the implementation of investment restrictions or
incentives to trigger the construction of new green plants together with
regulations to enforce the electrification of the capital good sector. Within
this model, electrification can be enforced by a sector-specific carbon tax on
the "hard-to-abate" capital good industry. We consider two different
intensities, T2e and Tce. For the high tax, T2e, 80% electrification is
reached after a decade, while for the weaker tax, Tce, it takes a decade. In
the electricity sector, we consider a “brown ban” which prohibits further
investments in brown plants (B). In the absence of elections, the brown ban
becomes active 16 years after its announcement in 2020. Within this grace
period, the electricity firm can “prepare” by investing in green RnD and
already building up a stock of green plants Wieners, C. E., Lamperti, F.,
Roventini, A. (2022). When the brown party takes power, it revokes the
announcement of the ban, and the electricity firm stops preparations.
Therefore, the actual enforcement of the ban is postponed by the number of
years that the brown party holds power during this 16-year grace period. After
the enforcement starts, the ban is only enacted when the Green Party rules,
while under the Brown Party, the construction of brown plants remains
possible.
With the sectoral tax only addressing electrification and the brown ban only
green electricity production, a combination is needed to decarbonise. Under
No-elections, the combination T2eB achieves similar mitigation to T2 (See Fig.
5), but when elections are present, it outperforms T2. Unemployment rates are
likewise lower under T2eB.
The combination T2eB achieves similar mitigation to T2 alone, while lowering
the unemployment rate peaks (See Fig. 3). In the electricity sector, two
factors contribute. First, during the years when the electricity form
“prepares” for the ban, large green investments are made, which directly
increase green electricity and also help to drive down the price of green
plants. Second, T2eB does not cause strong economic stagnation when the Green
party rules, and therefore does not strongly reduce the incentive to build new
plants precisely while policies are in place to ensure green investments (See
Fig. 4). By combining T2eB with a modest carbon tax (Tc) that is used to
subsidise further green plant construction (policy mix TcT2eBC), we obtain the
fastest green transition with the lowest political uncertainty and
comparatively low unemployment (See 5).
The result by Wieners et al. Wieners, C. E., Lamperti, F., Roventini, A.
(2022) that a strategically selected combination of policies leads to the best
outcomes thus also holds in the presence of elections. In particular, a well-
chosen policy mix can strongly reduce political uncertainty w.r.t. a pure
carbon tax.

### Discussion and conclusion

We illustrated the complex dynamics which arise by encapsulating political
dynamics into IAMs. More specifically, we describe an idealized two-party
scenario in which the Green party introduces ambitious climate policy while
the Brown party blocks them all. In our model, either party can
instantaneously fully revert the other’s policy, which is of course a
simplification Basseches, J. A., Bromley-Trujillo, R., Boykoff, M. T.,
Culhane, T., Hall, G., Healy, N., Hess, D. J., Hsu, D., Krause, R. M.,
Prechel, H., Roberts, J. Timmons, Stephens, J. C. (2022).
In our framework, the success of incumbents hinges on their handling of
unemployment and climate change mitigation. However, real-life elections are
influenced by a wider range of factors, including candidate likability,
campaign strategies, regional dynamics, and exogenous events like wars,
terrorist attacks, or pandemics. In addition, our current model version
assumes bulk probabilities for re-election rather than modelling opinion
dynamics explicitly. Future work could integrate a more advanced agent-based
framework that accounts for the diverse (voting) behaviours of heterogeneous
households Di Benedetto, A. and Wieners, C. E. and Dijkstra, H. A. and Stoof,
H. T.C. (2023); Lackner, T., Fierro, L., E., Mellacher, P. (2024). Another
possible limitation is the fact that policy costs borne by the state - such as
refinancing the electricity firm in case it goes bankrupt under a brown ban -
have little effect on the wider economy, as the state is not cash-constrained
and no adverse consequences follow from increased spending on climate policy.
However, in real life, a modest carbon tax could be levied to fund climate
policy spending.
In conclusion, we have presented a modelling framework for incorporating
political dynamics into integrated assessment models. Our results suggest that
a high pure carbon tax, which could seem effective in reducing emissions, is
particularly susceptible to abrupt interruptions caused by democratic
alternation. These "Brown" periods coincide with increased energy demand which
causes boom phases of brown plants construction delaying the green transition.
On top of this, when coupling elections to parties’ performances, results get
even worse with the Green Party punished by its strongly unemployment-
affecting policies, demonstrating that a carbon tax does not represent a
feasible policy. This high political uncertainty poses a significant challenge
to the implementation of high carbon taxes in democracies and necessarily asks
for the implementation of other additional policy tools. We show that a viable
solution to this final complication is the redistribution of the tax revenue.
Another promising approach is combining strategies aimed at both pushing for
the electrification of the capital good sector and subsidising the
construction of new renewable green power plants. In this scenario, the
electricity sector is forced to build green plants and the negative impact of
the elections is mitigated.
These findings underscore that politics plays a crucial role in policy
assessment. A more nuanced and politically aware policy design for climate
change mitigation strategies is necessary, with policies that must be robust
to disruptions and publicly acceptable Hammerle, M. and Best, R. and Crosby,
P. (2021); Kallbekken (2013): their objectives, mechanisms, and impacts,
should be readily available and comprehensible to voters. Only in this way,
the public can engage with, understand, and support them, contributing to
their long-term endurance and effectiveness with their votes. We aim to spark
the interest of fellow researchers, encouraging them to build on our findings
in more intricate and expansive models. This effort marks a step toward
enriching the understanding of complex interactions within climate policy
assessments.

Figure 5: Overview of the results for the policies discussed (See Table 1).
All values are averaged across 50 Monte Carlo runs and error bars reproduce
the spread between the 20th and 80th percentile of the ensemble. Global peak
warming in degrees Celsius. Netcosts in portion of GDP, averaged across the
time interval (2020-2100). The average $P_{g}$ is shown only for the coupled
case.

## Methods

### The original DSK model

We introduce a 2-party election model in the Dystopian-Schumpter-Keynes model
Lamperti, F., Dosi, G., Napoletano M., Roventini, A., Sapio, A. (2018);
Lamperti, F., Bosetti, V., Roventini, A., Tavoni, M. (2019) where one party
with strong climate policy ambitions competes with a party with low ambition
(see Fig. 1). The DSK model an agent-based IAM which describes the economy of
a country by modelling a set of heterogeneous, interacting firms and a climate
module. 50 Capital-good firms produce machines, using labour and energy. The
energy can be fuel, which is bought on an exogenous fuel market, or
electricity, which is provided by the electricity sector. 200 consumption-good
firms buy machines and use them, as well as labour and electricity (but not
fuel), to produce a homogenous consumption good that is sold to households.
Households are modelled as an aggregate labour and consumer force. They work,
buy consumption goods from the market and, if applicable, receive unemployment
benefits from the government. Electricity is produced by a profit-seeking
monopolist using “brown” (fuel-burning) and “green” (renewable) electricity
plants. Plants are scrapped after 60 years. New ones are built such that the
electricity demand by capital-good and consumption-good firms is always
fulfilled. Green plants initially have high fixed costs, brown ones have low
fixed costs but operational costs from fuel use. Without climate policy, green
plants never become cost-competitve. Research and Development (RnD) can reduce
fixed costs for both types of plants, and improve fuel efficiency in brown
plants. Innovation potential is greater for green plants, as brown ones are
already a mature technology, so green plants can eventually become cost-
competitive. The RnD budget is split between brown and green plants according
to their fraction in energy production; in particular, if green plants are not
used, they receive no RnD funding. Decarbonisation requires 1) full green
energy in the electricity sector and 2) electrification in the capital good
sector.
Climate dynamics follow the C-ROADS model Sterman, J., Fiddaman, T., Franck,
T., Jones, A., McCauley, S., Rice, P., Sawin, E., Siegel, L. (2012). When CO2
is emitted, part of it remains in the atmosphere and leads to global warming.
The equilibrium climate sensitivity (ECS) is 3 degrees (Kelvin) per doubling
CO2. We do not take climate damage into account, as DSK lacks many of the most
vulnerable sectors (e.g., agriculture), and our focus is on how to avoid
dangerous climate change, rather than studying its impact. In the no-policy
baseline, GDP growth is 3% (2020-2120) and global warming is 4.8 degrees in
2100 (see Fig. 5), in line with the SSP5 scenario Kriegler, E. et al. (2017).
The economic model is spun up for 60 years before the actual simulation. The
climate model is activated after spin-up and initialised to observed 2020
conditions. Climate policy starts in 2021. The model has been shown to
reproduce key emergent properties of the economy (“stylized facts”) Dosi, G. ,
Fagiolo, G., Roventini, A. (2010); Dosi, G. , Fagiolo, G. , Napoletano, M.,
Roventini, A. (2013); Lamperti, F., Dosi, G., Napoletano M., Roventini, A.,
Sapio, A. (2018) and allows to study of the dynamic impacts of a rich set of
climate policies Wieners, C. E., Lamperti, F., Roventini, A. (2022).

### Coupling DSK to a simple election model

In our simple election model, the “green” party implements an ambitious
climate policy, while the “brown” party implements no climate policy at all.
The electorate votes based on the parties’ handling of climate policy and the
economy.
To distinguish between the effects of (random) interruptions of policies and
actual election dynamics, we compare two election models. In the “coinflip”
model, the ruling party is elected randomly, with equal probabilities, every
four years. In the “coupled” model, the probability $P_{g}$ of the Green Party
to be elected for a mandate $M$ is given by

$P_{g}(M)=0.5+P_{T}+P_{U}+P_{dU}+P_{B},$ (1)

where

$\begin{split}&P_{T}=\alpha T,\\\ &P_{U}=-\sigma\beta[(U(M-1)-U_{0})],\\\
&P_{dU}=-\sigma\gamma[U(M-1)-U(M-2)],\\\ &P_{B}=-\sigma\epsilon N.\end{split}$
(2)

The term $P_{T}$ reproduces an inclination to vote green when global warming
($T$) is felt, with $\sigma=+1$ if the Green Party is incumbent and -1 else.
$\alpha>0$ is chosen such that a 3-degree warming results in an advantage of
$12\%$ for the Green party.
$P_{U}$ and $P_{dU}$ reproduce the influence of unemployment on the
probability of electoral success. $P_{U}$ depends on the difference between
the average unemployment rate from the previous election cycle $M-1$ and the
average unemployment in a no-policy baseline scenario $U_{0}$. Similarly,
$P_{dU}$ reflects the change in average unemployment rates across the two most
recent electoral terms, Voters thus punish the incumbent party if recently
unemployment was high ($P_{U}$) or got worse ($P_{dU}$). The parameter
$\beta>0$ is calibrated on historical data for presidential odds Sports Odds
History (2024) and the unemployment rate change in the U.S. Wik (2024) (see
SM, Fig. 1-2). For simplicity, we assume $\beta=\gamma$.
Several studies documented that unemployment adversely impacts both the
personal well-being and professional lives of individuals. This often
influences political leanings and voting patterns over time. Observations from
different countries indeed show that job loss often triggers an ideological
response towards the party historically considered more suitable for solving
the issue Sipma, T. and Lubbers, M. and Spierings, N. (2023); Wright, J.
(2012); Wiertz, D. and Rodon, T. (2021)). Similarly, we assume that
unemployment triggers a response favouring the party deemed most likely to
mitigate these issues, which, in our simulation, is the Brown one.
$P_{B}$ (“the boredom term”) describes voters gradually getting fed up with
the ruling party and is proportional to the number of consecutive mandates the
incumbent party has ruled before the elections. Empirical observations suggest
that more consecutive mandates mean a lower probability of being elected,
preventing the system from reaching a state where one party has a persistent
overwhelming majority Fair, R. C. (2009). However, the exact degree of
influence ($\epsilon$) of this pattern on electoral outcomes remains partially
uncertain, as these qualitative insights do not directly translate into
specific electoral odds (see SM, Fig. 3).
The probability of being elected for the Brown Party is given by
$P_{b}(M)=1-P_{g}(M)$. Throughout the study, we refer to this final modelling
setup as the "Coupled case". The calibration, along with sensitivity analysis,
is available in the Supplementary Material.

Policy |  Explanation
---|---
Baseline |  Baseline experiment without any climate policy.
Tc |  Critical tax: constant carbon tax, just sufficient to induce a green transition in all Monte Carlo members. It starts in 2022 and the revenue is added to the government budget.
T2 |  Tax high enough to keep global warming below 2 degrees until 2160 in all Monte Carlo members without any additional policy.
T2f |  As T2, but tax revenue is spent on subsidising firms to pay wages.
Tce |  Sector-dependent tax: As Tc, but the tax applies only to the capital good sector, to promote electrification.
T2e |  Sector-dependent tax: As T2, but the tax applies only to the capital good sector, to promote electrification.
B |  Brown investment ban. Brown plants cannot be built 16 years later than the announcement.
C |  The state invests the money obtained by the carbon tax in building green plants, even if not strictly needed to fulfil demands.
TcT2eBC |  Tc only applied to the electricity sector combined with T2e, B and C.
Table 1: Climate policies. Combinations are named by directly appending the
names of the individual policies it comprise.

## Acknowledgements

This publication is part of the project ‘Interacting climate tipping elements:
When does tipping cause tipping?’ (with project number VI.C.202.081 of the NWO
Talent programme) financed by the Dutch Research Council (NWO). The authors
are thankful to Teresa Lackner, Simon L. L. Michel, Luca Fierro and Patrick
Mellacher for helpful comments and discussions.

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## Author contributions statement

C. E. W. , A. D. and A. S. H. conceived the experiment; A. D. conducted the
experiment; all authors reviewed the manuscript.