# The Interactions of Social Norms about Climate Change: Science, Institutions
and Economics††thanks: We gratefully acknowledge the financial help of the
European Union’s Horizon 2020 research and innovation programme under the
Marie Sklodowska-Curie grant agreement No 891124.

Antonio Cabrales, Manu García, David Ramos Muñoz & Angel Sánchez Universidad
Carlos III de Madrid. E-mail<EMAIL_ADDRESS>University in
St. Louis. E-mail<EMAIL_ADDRESS>Carlos III de Madrid. E-mal:
<EMAIL_ADDRESS>Carlos III de Madrid. E-mail:
<EMAIL_ADDRESS>
(. )

###### Abstract

We study the evolution of interest about climate change between different
actors of the population, and how the interest of those actors affect one
another. We first document the evolution individually, and then provide a
model of cross influences between them, that we then estimate with a VAR. We
find large swings over time of said interest for the general public by
creating a Climate Change Index for Europe and the US (CCI) using news media
mentions, and little interest among economists (measured by publications in
top journals of the discipline). The general interest science journals and
policymakers have a more steady interest, although policymakers get interested
much later.

JEL Classification: Q54, Q58, D85, A13.
Keywords: Climate Change, Social Norms, Text Analysis, Social Networks.

##  1 Introduction

_”The furnaces of the world are now burning about 2,000,000,000 tons of coal a
year. When this is burned, uniting with oxygen, it adds about 7,000,000,000
tons of carbon dioxide to the atmosphere yearly. This tends to make the air a
more effective blanket for the earth and to raise its temperature. The effect
may be considerable in a few centuries.”_. August 14, 1912, Rodney & Otamatea
Times “Science Notes and News”.

As the quote above shows, the knowledge about anthropogenic climate change is
not exactly new. Nor is the knowledge that it can create problems for
humanity. Huntington (1917) in the _Quarterly Journal of Economics_ already
claimed that climate change (not necessarily anthropogenic in this case)
partially explained the fall of Rome.

Tackling this problem requires that regulators of different sorts take
decisions that provide incentives for abatement. But as the references above
show they are being very slow in doing this. The science about climate change
has been there for a long time. So why does it seem that action is not
happening sufficiently quickly?

A first answer is that there is already some action. Many regulators are aware
of the problem. The European Commission has a Technical Expert Group on
sustainable finance (TEG) which has produced several reports, for example, an
EU taxonomy – to determine whether an economic activity is environmentally
sustainable; an EU Green Bond Standard; methodologies for EU climate
benchmarks and disclosures for benchmarks; and guidance to improve corporate
disclosure of climate-related information. All of this suggests that perhaps
in the future we will have a stronger reaction by regulators to climate
change. But there is still the question why has this not happened much earlier
and how long will it take until there are significant effects.

Our hypothesis is that the evolution of social norms is a slow process, and
their transmission between different social groups is also complicated. We
start from a situation in which, as Carney (2015) pointed out “The horizon for
monetary policy extends out to 2-3 years. For financial stability it is a bit
longer, but typically only to the outer boundaries of the credit cycle – about
a decade.” If that is the status quo (social norm) about appropriate actions
by central banks, it is difficult to expect the regulators to start taking a
view that goes perhaps to half a century or more.

But even if norms are slow in changing, they do change. A recent study shows
that women are now seen as equal or more competent than men, something that
didn’t happen half a century ago. A similar thing happens with same-sex
marriage. These changes in attitudes are now encoded in regulations fostering
gender equality in corporate boards, or laws allowing same-gender marriage.
But it gets even better. For environmental protection both farmers, and
businesses in general, often go beyond legal mandates. And as Gunningham et
al. (2004) say: “the increasing incidence of “beyond compliance” corporate
behavior can be better explained in terms of the interplay between social
pressures and economic constraints.”

Our project approach to answering the question for how norms change and
diffuse between groups starts by proposing a model of norms transmission in
social networks. We assume that individuals take actions that have an
(idiosyncratic) benefit and a cost. In addition, there is a complementarity
between the actions of the individual and those of others in her group and in
other groups that are “close” to them or whose opinions are important. The
model has a simple linear quadratic structure (as in Ballester et al. (2006))
and delivers a unique equilibrium where the actions of group members depend on
their idiosyncratic preferences and those of others in close groups. Given its
structure, the model’s parameters can be easily identified through an
econometric model.

We complement the analytical framework for the problem with its empirical
analysis. The aim of this part of the project is to ascertain the web of
influences between different actors in climate change policy. We have
collected information (using advanced web-scraping methods) about mentions to
climate change in mainstream news media (from the US, UK, Germany, France, and
Spain), general interest scientific journals (Nature, Science), top Economics
journals,111 The so-called top 5: _Quarterly Journal of Economics_ , _American
Economic Review_ , _Journal of Political Economy_ , _Econometrica_ and _Review
of Economic Studies_. European Parliament questions, and European Central Bank
presidential speeches, since the 1990s. We then build a Vector Auto Regressive
model (VAR) to estimate how the mentions in one of these actors in one period
are correlated with lagged mentions by other actors.

In terms of descriptive evidence, we have found that natural scientists had
been concerned with the problem since more than 30 years ago, academic
economists are generally unconcerned even now, the mainstream media and the
European Parliament started worrying seriously about the problem about the
turn of the century, and the ECB increased their concern in very recent years.

In terms of the analytical results from the VAR, we study the data at
quarterly frequency. Three of our variables are mentions about climate change
in different outlets: the news media, Euro parliament, and general interest
scientific journals. We also use GDP as a control variable. We find that media
and the parliament are mutually affected. Other than that, we also find strong
interactions with GDP fluctuations. This is a concern. A long term problem
like climate change should not ebb and flow with relatively small (in the
grand scheme of things) output fluctuations. But the finding can be a tool for
concerned organizations to focus the resources at times of social inattention.

We cannot find influences of science on media or parliament. It is tempting to
think scientific efforts are useless in this domain, particularly given the
slow motion of regulatory responses. But we need to be cautious, it could also
be that the influences are more subtle than the statistical model can capture.

###  1.1 Related literature

This paper contribute to several strands of the literature. One of them is the
one related to social norms. Fehr and Schurtenberger (2018) have argued that
many regularities regarding cooperation can be explained if individuals hold a
social norm of conditional cooperation (Kimbrough and Vostroknutov (2016) and
Kölle et al. (2020), Szekely et al. (2021) provide evidence of norm-following
that leads to cooperation). In fact, social norms have been proposed as a key
instrument to solve social dilemmas (Ostrom (2000); Bicchieri (2005); Biel and
Thøgersen (2007)) in general, and climate change in particular Riehm et al.
(2020). We contribute to this literature by providing a model and evidence
showing how those norms spread in the population.

We also contribute to a large literature about the media communication of
climate change (Wilson (2013), Gavin (2009)). To this literature we provide a
comprehensive view of the evolution of the coverage and its interaction with
other domains. A similar contribution is provided to the literature on
scientific journals coverage of climate change (including the surprisingly low
coverage in top economics journals) as in Nielsen and Schmidt Kjærgaard
(2011), Ladle et al. (2005), Oswald and Stern (2019), or in political circles
Willis (2017), Willis (2018), and central banks Olovsson (2018), Skinner
(2021).

Our method for creating indices is taken from Baker et al. (2016) and Ghirelli
et al. (2021) applied to a different field. Our theoretical model is inspired
by the work in social networks pioneered by Ballester et al. (2006)

##  2 Evolution of mentions to climate change

In this section we provide a visual description of the evolution of climate
change mentions in different sectors: the news media, the Euro parliament,
scientific journals, and ECB speeches. This is our proxy for the preoccupation
about climate change in those sectors.

###  2.1 Developing a Climate Change Index of Public Interest

We analyze the presence of Climate Change and their evolution over time for
the main American and European newspapers. Baker et al. (2016) manages to
measure an unobservable variable, such as uncertainty in Economic Policy, with
an idea as simple as it is powerful: the level of impact that this variable
has is reflected in the repetition of terms related to economic uncertainty in
the different newspapers over time. The more these terms are used, the more
impact/interest the variable is having in that period. In a similar way, we
develop a Climate Change Index (CCI) using the universe of news in top
European and United States newspapers using the keywords ”climate change”. It
is trivial to observe, due to the nature of these words, that any text that
uses them will be alluding to this problem, making identification very simple.

Following Baker et al. (2016), we standardize the monthly shares newspaper-
level series to unit standard deviation from 1995 to 2021 and then average
across the 12 European papers by month. Finally, we divide this average by the
mean and multiply by 100 for the same period to obtain the normalized series.

Figure 1: Monthly Climate Change Index for Europe and the USA

Figure 1 shows the Climate Change Index for Europe and the US, which have a
correlation of 0.947. As we can see media does not show interest until around
2003, but it is not until 2015 that it becomes part of the relevant topics. It
is interesting to notice how the media seems to respond to trends; there are
peaks in which it pays attention to climate change, and other periods in which
the intensity drops even though the problem has not been solved, but on the
contrary seems that the problem has become worse.

In the appendix we include the shares that climate change news occupy for the
different newspapers that make up the index, in addition to an index for each
country.

###  2.2 Climate Change and Top 5 journals in Economics

We count the number of papers published in Top 5 journals in Economics that
use ”Global Warming” or ”Climate Change” in their abstract for the period
1999-2021. The results speak for themselves about economists’ interest in the
topic. Since the data is about published papers, it is difficult to know to
which extent referees and editors are responsible for this, as we do not have
data on submissions. It could be that climate change related papers have a
higher proportion relative to total submissions.

Table 1: Count of words in the Top-5 Journals in Economics | 99 | 00 | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Climate Change | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 2 | 2 | 0 | 0 | 1 | 1 | 0
Global Warming | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0
Systemic Risk | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0
Environmental | 2 | 3 | 3 | 0 | 0 | 4 | 1 | 3 | 1 | 2 | 2 | 1 | 2 | 7 | 2 | 2 | 2 | 3 | 1 | 4 | 3 | 4 | 5
Pollution | 0 | 0 | 1 | 1 | 1 | 0 | 2 | 1 | 0 | 2 | 3 | 1 | 2 | 2 | 1 | 1 | 1 | 4 | 2 | 4 | 2 | 2 | 3
Carbon Tax | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 2 | 1 | 1 | 1 | 1 | 0
Optimal Taxation | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 2 | 1 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 2 | 2 | 0
Countercyclical | 2 | 2 | 0 | 1 | 1 | 4 | 2 | 1 | 3 | 0 | 2 | 1 | 0 | 8 | 2 | 3 | 1 | 2 | 5 | 5 | 1 | 2 | 1
Gold Standard | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0
Corruption | 1 | 1 | 0 | 2 | 2 | 0 | 2 | 1 | 3 | 1 | 1 | 0 | 1 | 0 | 1 | 2 | 3 | 2 | 0 | 2 | 0 | 2 | 2
Unemployment | 3 | 2 | 5 | 2 | 4 | 7 | 5 | 5 | 8 | 7 | 6 | 9 | 7 | 5 | 7 | 6 | 7 | 11 | 13 | 12 | 6 | 9 | 7
Marketing | 0 | 0 | 2 | 0 | 2 | 1 | 0 | 2 | 0 | 0 | 1 | 2 | 2 | 3 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1
Monetary Policy | 2 | 4 | 3 | 5 | 10 | 4 | 10 | 4 | 3 | 4 | 4 | 5 | 6 | 7 | 4 | 3 | 3 | 10 | 7 | 8 | 8 | 15 | 7
Game Theory | 1 | 2 | 0 | 3 | 2 | 1 | 1 | 1 | 3 | 0 | 0 | 1 | 2 | 1 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 0 | 1
Optimal Policy | 3 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 4 | 2 | 4 | 2 | 5 | 2 | 1 | 1 | 4 | 0 | 2 | 3 | 2 | 1
Inflation | 1 | 6 | 8 | 7 | 12 | 3 | 12 | 7 | 7 | 7 | 9 | 2 | 10 | 3 | 3 | 2 | 5 | 4 | 7 | 8 | 12 | 6 | 7
Tax | 9 | 4 | 7 | 9 | 10 | 4 | 13 | 10 | 5 | 11 | 13 | 8 | 9 | 11 | 21 | 11 | 16 | 20 | 19 | 14 | 28 | 16 | 21
Inequality | 10 | 11 | 6 | 11 | 10 | 12 | 7 | 10 | 5 | 5 | 9 | 10 | 7 | 4 | 11 | 7 | 8 | 14 | 15 | 15 | 10 | 17 | 9
Transportation | 0 | 0 | 1 | 0 | 0 | 2 | 1 | 0 | 1 | 1 | 2 | 0 | 2 | 1 | 0 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 0
Institutions | 5 | 3 | 2 | 7 | 5 | 3 | 7 | 6 | 6 | 7 | 7 | 7 | 10 | 8 | 7 | 8 | 7 | 8 | 7 | 3 | 9 | 6 | 3
WWII | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0

###  2.3 Climate Change and General Interest Scientific Journals

Following the methodology of the CCI for media, we construct an index using
the main General Interest Scientific Journals, Nature and Science between
1995-2021. As we can see, interest in climate change is clearly growing with
an stable trend over time, unlike what happens with the media, which seems to
respond to behavioral criteria.

Figure 2: Quarterly Climate Change Index for the General Interest Science
Journals.

###  2.4 European Parliament

We create a new source of information from the share of questions made in the
European Parliament for the period 1995-2021 containing the words ”climate
change”, normalized to have standard deviation and mean 100.

Figure 3: Quarterly Climate Change Index for the European Parliament

###  2.5 Central Bank Speeches

Figure 4: Share of Speeches containing the words ”Climate Change”

We count the share of ECB presidential speeches222Available at ECB site. in
English mentioning the words ”Climate Change” for the period since its
creation in 1997, also, from the Central bankers’ speeches available at the
BIS repository333The BIS site contains more then 17,000 speeches in English
from the Federal Reserve, ECB, and many Central Banks..

Until 2018, these keywords were practically not used, demonstrating the lack
of interest in the subject. However, since 2019, more than 50% of the ECB
speeches and around a 25% of the total Central Bankers speeches already
included these words, showing that although it cannot be analyzed in this
paper due to the scarcity of data, climate change has become a crucial issue
for the Central Banks.

In the Appendix we show the results of comparing mentions of climate change in
ECB speeches with mentions of other relevant terms, like “taxes” or
“inequality”. Taxation is mentioned very frequently from the beginning,
inequality is less frequent, but it starts earlier than climate change.
Strikingly, climate change is now more frequently mentioned than either taxes
or inequality.

###  2.6 The Federal Open Market Committee - FOMC

As a counterpoint to the ECB speeches we count the number of questions made in
the transcripts from the FOMC for ”Climate Change” for the period 1975-2015
(the transcripts are available only 5 years after). ”Climate Change” appear
only once (related to climate) here. Nevertheless, in the minutes published by
the FOMC from 1993 to present, it only appear twice, in 2019 and 2020.

##  3 A simple theoretical framework

In order to understand the relationship between the different institutions and
social group whose preoccupation with climate we characterize with their
public utterances, we first describe a tractable model which we later estimate
using a vector auto-regression (VAR).

Every individual $j$ belongs to some group $G_{j}$ where $|G_{j}|\in R$. A
parameter $\lambda_{G_{i}G_{j}}$ measures how a group $i$ person cares about a
group $j$ person. Every individual experiences an idiosyncratic amount of
intrinsic interest in the policy $b_{i}$. There is a costly action $a_{i_{t}}$
that each individual takes in every period $t$. This action has a cost per
unit $c_{i}$. With these elements in place, we can write the utility function
as:

$U\,_{i}\left(a_{i_{t}},\mathbf{a}_{t-1}\right)=a_{i_{t}}\left(b_{i}+\sum_{j\in
R}\lambda_{G_{i}G_{j}}a_{j_{t-1}}\right)-\frac{c_{i}}{2}a_{i_{t}}^{2}$

Then, the optimal action for each individual can be written as:

$a_{it}=\frac{1}{c_{i}}\left(b_{i}+\sum_{j\in
R}\lambda_{G_{i}G_{j}}a_{j_{t-1}}\right)$

And since the individual actions are linear in others’ previous actions, we
can aggregate to an institutional level (a key assumption in this case is that
the interaction parameters $\lambda_{G_{i}G_{j}}$ are common within groups).
Given this, the VAR constant in the equation for each group’s ”action” (the
number of messages) is $b_{i}/c_{i}$, i.e. the intrinsic interest in the
policy (relative to the cost of messaging) and a coefficient of the action of
other groups is $\lambda_{G_{i}G_{j}}/c_{i}$ i.e. the impact on the marginal
benefit of group $G_{i}$ of an increase in $G_{j}$ action (relative to the
cost). We have introduced just one lag in this description but, of course, we
can write as many as we want. Also we have written lagged actions in the
utility function, but we can also write expectations and say that the
expectations are formed naively so that

$E\left(\mathbf{a}_{t}\right)=\mathbf{a}_{t-1}.$

##  4 VAR model estimation

To understand the interconnection between the different actors we estimate a
VAR micro-founded from the model in Section 3. It can be written as
$X_{t}=\Pi(L)X_{t}+\epsilon_{t}$, where $X_{t}$ is a set of endogenous
variables, $\Pi$ is a matrix of VAR coefficients capturing the dynamics of the
system, and $\epsilon_{t}:N(0,\Sigma)$ is a vector of shocks having zero mean
and variance–covariance matrix $\Sigma$. The variables in $X_{t}$ are the
following: $x_{1}$ is mentions of climate change in the media (CCI), $x_{2}$
is mentions in the European parliament questions (normalized), $x_{3}$ is
mentions in science journals (CCI), and $x_{4}$ is GDP for the Euro Area
(normalized).

Table 2 displays the results. The notation ARx(y,z) means that ”x” is the lag,
”y” the index of the variable whose effect we measure, and z is the index of
the variable affected by it.

The data is quarterly, and at one quarter all variables are affected by their
own lags. The Euro Parliament positively affects the media. This means that an
increase in the debate in the European Parliament on climate change translates
into an increase in the media interest in the following quarter.

At two quarters there are no own effects. We also find a negative effect of
Euro Parliament on media, which can be interpreted as the loss of media
interest on climate change after a quarter. There is also a reciprocal
negative effect of media on Euro parliament.

At three quarters the only own effects are given by scientific journals and
GDP. There is a negative effect of GDP in the Euro Parliament. Six months
after a boom they forget about climate change, but they mention it more during
a recession.

At four quarters the only own effect is given by GDP, and there is only one
positive effect from GDP to the Euro parliament. This can be interpreted as
the lack of persistence of the effect appeared at three quarters.

Generally speaking, we find that media is affected by the parliament, and
parliament is affected by the media. Other than that, we also find very strong
interactions with GDP fluctuations. This is worrying since attention in a long
term issue like climate change should not be driven by short time fluctuations
in economic activity. But it is an important finding as it suggests a time
when activists should concentrate their efforts. Science, on the other hand,
seems to have no discernible effect on either parliament or the media. This is
probably because the influences of Science are more subtle and long-term than
the statistical model can uncover.

Table 2: VAR: ARx(y,z) ”x” is the lag, ”y” is affecting variable, and ”z” is
affected variable
| Value | Standard Error | TStatistic | PValue
---|---|---|---|---
Constant(1) | -101.51 | 56.43 | -1.8 | 0.07
Constant(2) | -92.19 | 78.69 | -1.17 | 0.24
Constant(3) | -93.88* | 41.64 | -2.25 | 0.02
Constant(4) | 1.54 | 2.59 | 0.6 | 0.55
AR1(1,1) | 0.82*** | 0.12 | 6.91 | 0
AR1(2,1) | 0.61*** | 0.17 | 3.69 | 0
AR1(3,1) | 0.01 | 0.09 | 0.15 | 0.88
AR1(4,1) | 0 | 0.01 | -0.39 | 0.7
AR1(1,2) | -0.07 | 0.08 | -0.88 | 0.38
AR1(2,2) | 0.24** | 0.11 | 2.08 | 0.04
AR1(3,2) | 0 | 0.06 | 0.01 | 0.99
AR1(4,2) | -0.01 | 0 | -1.55 | 0.12
AR1(1,3) | 0.06 | 0.14 | 0.42 | 0.68
AR1(2,3) | -0.17 | 0.19 | -0.88 | 0.38
AR1(3,3) | 0.39*** | 0.1 | 3.88 | 0
AR1(4,3) | 0.01 | 0.01 | 1.48 | 0.14
AR1(1,4) | 3.23 | 2.23 | 1.45 | 0.15
AR1(2,4) | 0.3 | 3.11 | 0.1 | 0.92
AR1(3,4) | 0.91 | 1.65 | 0.55 | 0.58
AR1(4,4) | 0.79*** | 0.1 | 7.76 | 0
AR2(1,1) | 0.23 | 0.15 | 1.57 | 0.12
AR2(2,1) | -0.44* | 0.21 | -2.1 | 0.04
AR2(3,1) | 0.11 | 0.11 | 0.96 | 0.34
AR2(4,1) | 0 | 0.01 | -0.57 | 0.57
AR2(1,2) | -0.25 | 0.08 | -2.97 | 0
AR2(2,2) | 0.16 | 0.12 | 1.35 | 0.18
AR2(3,2) | -0.02 | 0.06 | -0.38 | 0.71
AR2(4,2) | 0 | 0 | -0.38 | 0.71
Table 3: VAR: ARx(y,z) ”x” is the lag, ”y” is affecting variable, and ”z” is
affected variable
| Value | Standard Error | TStatistic | PValue
---|---|---|---|---
AR2(1,3) | 0.2 | 0.14 | 1.43 | 0.15
AR2(2,3) | -0.1 | 0.2 | -0.48 | 0.63
AR2(3,3) | -0.12 | 0.11 | -1.12 | 0.26
AR2(4,3) | 0.01 | 0.01 | 1.28 | 0.2
AR2(1,4) | -4.44 | 2.55 | -1.74 | 0.08
AR2(2,4) | 1.21 | 3.56 | 0.34 | 0.73
AR2(3,4) | -2.39 | 1.88 | -1.27 | 0.2
AR2(4,4) | 0.02 | 0.12 | 0.2 | 0.84
AR3(1,1) | -0.11 | 0.15 | -0.72 | 0.47
AR3(2,1) | 0.22 | 0.21 | 1.08 | 0.28
AR3(3,1) | -0.15 | 0.11 | -1.32 | 0.19
AR3(4,1) | 0 | 0.01 | 0.45 | 0.65
AR3(1,2) | -0.1 | 0.09 | -1.21 | 0.23
AR3(2,2) | -0.07 | 0.12 | -0.62 | 0.54
AR3(3,2) | 0.01 | 0.06 | 0.15 | 0.88
AR3(4,2) | -0.02*** | 0 | -4.2 | 0
AR3(1,3) | -0.14 | 0.14 | -1 | 0.32
AR3(2,3) | 0.26 | 0.2 | 1.3 | 0.19
AR3(3,3) | 0.26* | 0.11 | 2.46 | 0.01
AR3(4,3) | 0 | 0.01 | -0.39 | 0.7
AR3(1,4) | 3.37 | 2.52 | 1.34 | 0.18
AR3(2,4) | 3.45 | 3.51 | 0.98 | 0.33
AR3(3,4) | 2.77 | 1.86 | 1.49 | 0.14
AR3(4,4) | 0.38** | 0.12 | 3.27 | 0
AR4(1,1) | 0.12 | 0.13 | 0.97 | 0.33
AR4(2,1) | -0.04 | 0.18 | -0.22 | 0.83
AR4(3,1) | 0.09 | 0.1 | 0.94 | 0.35
AR4(4,1) | 0 | 0.01 | 0.43 | 0.67
Table 4: VAR: ARx(y,z) ”x” is the lag, ”y” is affecting variable, and ”z” is
affected variable
| Value | Standard Error | TStatistic | PValue
---|---|---|---|---
AR4(1,2) | 0.15 | 0.09 | 1.79 | 0.07
AR4(2,2) | 0.13 | 0.12 | 1.06 | 0.29
AR4(3,2) | -0.04 | 0.06 | -0.58 | 0.56
AR4(4,2) | 0.02*** | 0 | 4.68 | 0
AR4(1,3) | 0 | 0.14 | -0.03 | 0.98
AR4(2,3) | 0.06 | 0.2 | 0.28 | 0.78
AR4(3,3) | -0.04 | 0.1 | -0.43 | 0.67
AR4(4,3) | -0.01 | 0.01 | -0.87 | 0.39
AR4(1,4) | -1.03 | 2.17 | -0.47 | 0.64
AR4(2,4) | -3.85 | 3.03 | -1.27 | 0.2
AR4(3,4) | 0.19 | 1.6 | 0.12 | 0.91
AR4(4,4) | -0.21* | 0.1 | -2.1 | 0.04

##  5 Conclusion

We have documented the evolution of mentions of climate change in different
environments: policy, sciences, and the general public (proxied by news
media). We have also postulated a model about how those different environments
influence one another and then estimated the model’s parameters. We find large
fluctuations of interest and interesting cross influences. A particularly
salient one is related to how GDP evolution affects the interest in climate
change. These observations could be a useful tool for timing activists and
other groups interested in influencing social debate.

Future research could expand our results by doing a more fine grained analysis
of the connections inside the different groups, potentially using tools from
social complex network analysis.

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## Appendix A. A CCI for each country.

#### United Kingdom

We use the keywords ”Climate Change” for The Guardian, The Times, The Sun, and
The Independent.

Figure 5: Share of Articles in the British Media

#### Spain

We use the keywords ”Cambio Climático (Climate Change)” for El Mundo, El País,
and ABC.

Figure 6: Share of Articles in the Spanish Media

#### Germany

We use the keywords ”Klimawandel (Climate Change)” and how much they have been
used in Bild and DIE ZEIT.

Figure 7: Share of Articles in the German Media

#### France

We use the keywords ”Changement Climatique (Climate Change)” and how much they
have been used in Le Figaro and Les Echos

Figure 8: Share of Articles in the French Media

#### Italy

We use the keywords ”Cambiamento Climatico (Climate Change)” and how much they
have been used in Corriere della Sera, and La Repubblica.

Figure 9: Share of Articles in the Italian Media Figure 10: Climate Change
Index for the European Countries

## Appendix B. Natural Science Journals.

#### Science

We count the number of articles (total) published in Science and Nature that
use ”Climate Change” in their abstract for the period 1995-2021.

Figure 11: Quarterly Share of Articles in Science containing ”Climate Change”.

## Appendix C

Figure 12: Share of Speeches from the ECB containing the words ”Climate
Change”

In the following table we show a comparison of mentions over time in ECB
presidential speeches of climate change with taxex and inequality.

| date | n | climate | global | tax | taxes | inequality
---|---|---|---|---|---|---|---
|  |  | change | warming |  |  |
1 | 1997 Q1 | 2 | 0 | 0 | 2 | 0 | 0
2 | 1997 Q2 | 6 | 0 | 0 | 1 | 1 | 0
3 | 1997 Q3 | 2 | 0 | 0 | 0 | 0 | 0
4 | 1997 Q4 | 9 | 0 | 0 | 4 | 1 | 0
5 | 1998 Q1 | 7 | 0 | 0 | 2 | 1 | 0
6 | 1998 Q2 | 1 | 0 | 0 | 0 | 0 | 0
7 | 1998 Q3 | 8 | 0 | 0 | 1 | 1 | 0
8 | 1998 Q4 | 22 | 0 | 0 | 9 | 6 | 0
9 | 1999 Q1 | 20 | 0 | 0 | 8 | 4 | 0
10 | 1999 Q2 | 27 | 0 | 1 | 14 | 3 | 0
11 | 1999 Q3 | 18 | 0 | 0 | 7 | 3 | 0
12 | 1999 Q4 | 27 | 0 | 0 | 11 | 3 | 0
13 | 2000 Q1 | 14 | 0 | 0 | 7 | 2 | 0
14 | 2000 Q2 | 18 | 0 | 0 | 8 | 3 | 0
15 | 2000 Q3 | 17 | 1 | 0 | 8 | 2 | 0
16 | 2000 Q4 | 21 | 0 | 0 | 8 | 2 | 0
17 | 2001 Q1 | 14 | 0 | 0 | 9 | 2 | 1
18 | 2001 Q2 | 16 | 0 | 0 | 8 | 3 | 0
19 | 2001 Q3 | 13 | 0 | 0 | 3 | 0 | 0
20 | 2001 Q4 | 22 | 0 | 0 | 4 | 1 | 0
21 | 2002 Q1 | 20 | 0 | 1 | 9 | 4 | 0
22 | 2002 Q2 | 18 | 0 | 0 | 6 | 1 | 0
23 | 2002 Q3 | 8 | 0 | 0 | 3 | 2 | 0
24 | 2002 Q4 | 19 | 0 | 0 | 5 | 1 | 0
25 | 2003 Q1 | 12 | 0 | 0 | 5 | 3 | 0
26 | 2003 Q2 | 18 | 0 | 0 | 5 | 3 | 0
27 | 2003 Q3 | 10 | 0 | 0 | 2 | 0 | 0
28 | 2003 Q4 | 24 | 0 | 0 | 7 | 3 | 0
29 | 2004 Q1 | 16 | 0 | 0 | 9 | 6 | 0
30 | 2004 Q2 | 31 | 0 | 0 | 18 | 9 | 0

| date | n | climate | global | tax | taxes | inequality
---|---|---|---|---|---|---|---
|  |  | change | warming |  |  |
31 | 2004 Q3 | 14 | 0 | 0 | 6 | 6 | 0
32 | 2004 Q4 | 30 | 0 | 0 | 12 | 7 | 0
33 | 2005 Q1 | 13 | 0 | 0 | 7 | 2 | 0
34 | 2005 Q2 | 29 | 0 | 0 | 13 | 9 | 1
35 | 2005 Q3 | 13 | 0 | 0 | 5 | 4 | 0
36 | 2005 Q4 | 26 | 0 | 0 | 8 | 5 | 0
37 | 2006 Q1 | 20 | 0 | 0 | 12 | 5 | 0
38 | 2006 Q2 | 31 | 0 | 0 | 16 | 7 | 0
39 | 2006 Q3 | 16 | 0 | 0 | 9 | 5 | 0
40 | 2006 Q4 | 29 | 0 | 0 | 14 | 7 | 0
41 | 2007 Q1 | 22 | 1 | 0 | 7 | 3 | 1
42 | 2007 Q2 | 33 | 0 | 0 | 8 | 4 | 2
43 | 2007 Q3 | 26 | 1 | 0 | 6 | 3 | 0
44 | 2007 Q4 | 37 | 1 | 0 | 14 | 4 | 1
45 | 2008 Q1 | 29 | 1 | 0 | 7 | 6 | 0
46 | 2008 Q2 | 40 | 3 | 0 | 10 | 6 | 0
47 | 2008 Q3 | 29 | 0 | 0 | 11 | 4 | 1
48 | 2008 Q4 | 34 | 0 | 0 | 13 | 3 | 2
49 | 2009 Q1 | 26 | 0 | 0 | 7 | 1 | 0
50 | 2009 Q2 | 34 | 0 | 0 | 5 | 2 | 0
51 | 2009 Q3 | 20 | 0 | 0 | 6 | 1 | 0
52 | 2009 Q4 | 32 | 1 | 1 | 7 | 0 | 0
53 | 2010 Q1 | 22 | 0 | 0 | 7 | 2 | 0
54 | 2010 Q2 | 42 | 1 | 0 | 14 | 2 | 0
55 | 2010 Q3 | 24 | 0 | 0 | 10 | 4 | 1
56 | 2010 Q4 | 30 | 1 | 0 | 6 | 1 | 4
57 | 2011 Q1 | 28 | 0 | 0 | 11 | 3 | 1
58 | 2011 Q2 | 45 | 0 | 0 | 11 | 2 | 1
59 | 2011 Q3 | 13 | 0 | 0 | 5 | 0 | 1
60 | 2011 Q4 | 33 | 1 | 0 | 13 | 3 | 0

| date | n | climate | global | tax | taxes | inequality
---|---|---|---|---|---|---|---
|  |  | change | warming |  |  |
61 | 2012 Q1 | 11 | 0 | 0 | 5 | 0 | 0
62 | 2012 Q2 | 33 | 0 | 0 | 13 | 5 | 0
63 | 2012 Q3 | 17 | 0 | 0 | 6 | 1 | 0
64 | 2012 Q4 | 30 | 0 | 0 | 17 | 4 | 1
65 | 2013 Q1 | 29 | 1 | 0 | 12 | 5 | 0
66 | 2013 Q2 | 42 | 0 | 0 | 22 | 3 | 3
67 | 2013 Q3 | 25 | 0 | 0 | 10 | 1 | 1
68 | 2013 Q4 | 37 | 0 | 0 | 20 | 4 | 3
69 | 2014 Q1 | 20 | 0 | 0 | 6 | 3 | 1
70 | 2014 Q2 | 31 | 0 | 0 | 14 | 3 | 1
71 | 2014 Q3 | 23 | 0 | 0 | 10 | 3 | 0
72 | 2014 Q4 | 30 | 0 | 0 | 9 | 4 | 1
73 | 2015 Q1 | 20 | 0 | 0 | 6 | 1 | 1
74 | 2015 Q2 | 25 | 0 | 0 | 12 | 3 | 3
75 | 2015 Q3 | 17 | 0 | 0 | 5 | 0 | 1
76 | 2015 Q4 | 42 | 1 | 0 | 12 | 3 | 1
77 | 2016 Q1 | 23 | 1 | 0 | 9 | 5 | 0
78 | 2016 Q2 | 32 | 1 | 0 | 12 | 1 | 3
79 | 2016 Q3 | 21 | 1 | 0 | 10 | 1 | 1
80 | 2016 Q4 | 34 | 0 | 0 | 19 | 2 | 4
81 | 2017 Q1 | 34 | 1 | 0 | 9 | 1 | 2
82 | 2017 Q2 | 45 | 2 | 0 | 10 | 3 | 1
83 | 2017 Q3 | 30 | 0 | 0 | 6 | 1 | 4
84 | 2017 Q4 | 39 | 0 | 0 | 10 | 2 | 4
85 | 2018 Q1 | 29 | 0 | 0 | 8 | 1 | 2
86 | 2018 Q2 | 28 | 1 | 0 | 13 | 8 | 4
87 | 2018 Q3 | 20 | 0 | 0 | 5 | 0 | 1
88 | 2018 Q4 | 36 | 5 | 1 | 11 | 1 | 2
89 | 2019 Q1 | 30 | 1 | 0 | 9 | 1 | 3
90 | 2019 Q2 | 26 | 4 | 0 | 8 | 1 | 2

| date | n | climate | global | tax | taxes | inequality
---|---|---|---|---|---|---|---
|  |  | change | warming |  |  |
91 | 2019 Q3 | 17 | 0 | 0 | 4 | 0 | 1
92 | 2019 Q4 | 34 | 10 | 1 | 13 | 6 | 6
93 | 2020 Q1 | 20 | 9 | 1 | 8 | 2 | 3
94 | 2020 Q2 | 15 | 2 | 0 | 1 | 0 | 0
95 | 2020 Q3 | 20 | 7 | 2 | 6 | 0 | 3
96 | 2020 Q4 | 27 | 3 | 0 | 6 | 0 | 3
97 | 2021 Q1 | 19 | 7 | 0 | 4 | 2 | 1
98 | 2021 Q2 | 19 | 11 | 4 | 5 | 0 | 2
99 | 2021 Q3 | 12 | 4 | 1 | 4 | 1 | 3
100 | 2021 Q4 | 11 | 8 | 2 | 3 | 0 | 1
date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
1997-02-01 | 1 | 0 | 0 | 1 | 0 | 0
1997-03-01 | 1 | 0 | 0 | 1 | 0 | 0
1997-04-01 | 2 | 0 | 0 | 2 | 0 | 0
1997-05-01 | 1 | 0 | 0 | 1 | 0 | 0
1997-06-01 | 3 | 0 | 0 | 2 | 1 | 0
1997-09-01 | 2 | 0 | 0 | 2 | 0 | 0
1997-10-01 | 4 | 0 | 0 | 4 | 1 | 0
1997-11-01 | 5 | 0 | 0 | 5 | 0 | 0
1998-01-01 | 4 | 0 | 0 | 4 | 1 | 0
1998-02-01 | 2 | 0 | 0 | 2 | 0 | 0
1998-03-01 | 1 | 0 | 0 | 1 | 0 | 0
1998-06-01 | 1 | 0 | 0 | 1 | 0 | 0
1998-07-01 | 3 | 0 | 0 | 3 | 0 | 0
1998-09-01 | 5 | 0 | 0 | 4 | 1 | 0
1998-10-01 | 4 | 0 | 0 | 4 | 1 | 0
1998-11-01 | 9 | 0 | 0 | 9 | 2 | 0
1998-12-01 | 9 | 0 | 0 | 8 | 3 | 0
1999-01-01 | 6 | 0 | 0 | 6 | 0 | 0
1999-02-01 | 7 | 0 | 0 | 7 | 2 | 0
1999-03-01 | 7 | 0 | 0 | 7 | 2 | 0
1999-04-01 | 7 | 0 | 0 | 6 | 0 | 0
1999-05-01 | 10 | 0 | 0 | 10 | 2 | 0
1999-06-01 | 10 | 0 | 0 | 9 | 1 | 0
1999-07-01 | 5 | 0 | 0 | 5 | 1 | 0
1999-08-01 | 2 | 0 | 0 | 2 | 1 | 0
1999-09-01 | 11 | 0 | 0 | 11 | 1 | 0
1999-10-01 | 7 | 0 | 0 | 7 | 0 | 0
1999-11-01 | 16 | 0 | 0 | 14 | 3 | 0
1999-12-01 | 4 | 0 | 0 | 4 | 0 | 0
Table 5:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2000-01-01 | 5 | 0 | 0 | 5 | 1 | 0
2000-02-01 | 4 | 0 | 0 | 3 | 0 | 0
2000-03-01 | 5 | 0 | 0 | 5 | 1 | 0
2000-04-01 | 4 | 0 | 0 | 3 | 0 | 0
2000-05-01 | 7 | 0 | 0 | 6 | 2 | 0
2000-06-01 | 7 | 0 | 0 | 6 | 1 | 0
2000-07-01 | 1 | 0 | 0 | 1 | 0 | 0
2000-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2000-09-01 | 15 | 1 | 0 | 15 | 2 | 0
2000-10-01 | 6 | 0 | 0 | 6 | 0 | 0
2000-11-01 | 10 | 0 | 0 | 10 | 1 | 0
2000-12-01 | 5 | 0 | 0 | 4 | 1 | 0
2001-01-01 | 5 | 0 | 0 | 5 | 0 | 0
2001-02-01 | 6 | 0 | 0 | 6 | 1 | 0
2001-03-01 | 3 | 0 | 0 | 2 | 1 | 1
2001-04-01 | 2 | 0 | 0 | 1 | 0 | 0
2001-05-01 | 8 | 0 | 0 | 7 | 3 | 0
2001-06-01 | 6 | 0 | 0 | 6 | 0 | 0
2001-07-01 | 1 | 0 | 0 | 1 | 0 | 0
2001-08-01 | 4 | 0 | 0 | 2 | 0 | 0
2001-09-01 | 8 | 0 | 0 | 8 | 0 | 0
2001-10-01 | 8 | 0 | 0 | 8 | 0 | 0
2001-11-01 | 9 | 0 | 0 | 8 | 0 | 0
2001-12-01 | 5 | 0 | 0 | 5 | 1 | 0
2002-01-01 | 4 | 0 | 0 | 4 | 1 | 0
2002-02-01 | 7 | 0 | 0 | 7 | 2 | 0
2002-03-01 | 9 | 0 | 0 | 8 | 1 | 0
2002-04-01 | 7 | 0 | 0 | 6 | 0 | 0
2002-05-01 | 7 | 0 | 0 | 6 | 1 | 0
2002-06-01 | 4 | 0 | 0 | 2 | 0 | 0
Table 6:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2002-07-01 | 5 | 0 | 0 | 4 | 1 | 0
2002-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2002-09-01 | 2 | 0 | 0 | 1 | 1 | 0
2002-10-01 | 5 | 0 | 0 | 5 | 0 | 0
2002-11-01 | 8 | 0 | 0 | 7 | 0 | 0
2002-12-01 | 6 | 0 | 0 | 5 | 1 | 0
2003-01-01 | 1 | 0 | 0 | 1 | 0 | 0
2003-02-01 | 5 | 0 | 0 | 5 | 3 | 0
2003-03-01 | 6 | 0 | 0 | 5 | 0 | 0
2003-04-01 | 5 | 0 | 0 | 4 | 1 | 0
2003-05-01 | 4 | 0 | 0 | 4 | 0 | 0
2003-06-01 | 9 | 0 | 0 | 8 | 2 | 0
2003-07-01 | 5 | 0 | 0 | 5 | 0 | 0
2003-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2003-09-01 | 4 | 0 | 0 | 4 | 0 | 0
2003-10-01 | 9 | 0 | 0 | 6 | 0 | 0
2003-11-01 | 12 | 0 | 0 | 10 | 2 | 0
2003-12-01 | 3 | 0 | 0 | 2 | 1 | 0
2004-01-01 | 6 | 0 | 0 | 4 | 3 | 0
2004-02-01 | 6 | 0 | 0 | 5 | 2 | 0
2004-03-01 | 4 | 0 | 0 | 4 | 1 | 0
2004-04-01 | 10 | 0 | 0 | 9 | 5 | 0
2004-05-01 | 13 | 0 | 0 | 12 | 3 | 0
2004-06-01 | 8 | 0 | 0 | 5 | 1 | 0
2004-07-01 | 3 | 0 | 0 | 3 | 3 | 0
2004-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2004-09-01 | 10 | 0 | 0 | 8 | 3 | 0
2004-10-01 | 11 | 0 | 0 | 9 | 2 | 0
2004-11-01 | 10 | 0 | 0 | 8 | 3 | 0
2004-12-01 | 9 | 0 | 0 | 8 | 2 | 0
Table 7:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2005-01-01 | 5 | 0 | 0 | 3 | 1 | 0
2005-02-01 | 2 | 0 | 0 | 1 | 0 | 0
2005-03-01 | 6 | 0 | 0 | 6 | 1 | 0
2005-04-01 | 7 | 0 | 0 | 6 | 2 | 0
2005-05-01 | 10 | 0 | 0 | 9 | 5 | 0
2005-06-01 | 12 | 0 | 0 | 12 | 2 | 1
2005-07-01 | 5 | 0 | 0 | 4 | 1 | 0
2005-08-01 | 2 | 0 | 0 | 1 | 0 | 0
2005-09-01 | 6 | 0 | 0 | 5 | 3 | 0
2005-10-01 | 12 | 0 | 0 | 9 | 2 | 0
2005-11-01 | 11 | 0 | 0 | 9 | 3 | 0
2005-12-01 | 3 | 0 | 0 | 3 | 0 | 0
2006-01-01 | 3 | 0 | 0 | 2 | 0 | 0
2006-02-01 | 8 | 0 | 0 | 6 | 4 | 0
2006-03-01 | 9 | 0 | 0 | 7 | 1 | 0
2006-04-01 | 6 | 0 | 0 | 6 | 1 | 0
2006-05-01 | 13 | 0 | 0 | 12 | 4 | 0
2006-06-01 | 12 | 0 | 0 | 11 | 2 | 0
2006-07-01 | 6 | 0 | 0 | 4 | 1 | 0
2006-09-01 | 10 | 0 | 0 | 8 | 4 | 0
2006-10-01 | 11 | 0 | 0 | 10 | 4 | 0
2006-11-01 | 12 | 0 | 0 | 11 | 1 | 0
2006-12-01 | 6 | 0 | 0 | 6 | 2 | 0
2007-01-01 | 8 | 0 | 0 | 7 | 1 | 1
2007-02-01 | 6 | 0 | 0 | 4 | 0 | 0
2007-03-01 | 8 | 1 | 0 | 6 | 2 | 0
2007-04-01 | 6 | 0 | 0 | 6 | 1 | 0
2007-05-01 | 12 | 0 | 0 | 9 | 0 | 2
2007-06-01 | 15 | 0 | 0 | 14 | 3 | 0
Table 8:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2007-07-01 | 8 | 0 | 0 | 8 | 1 | 0
2007-08-01 | 1 | 0 | 0 | 1 | 1 | 0
2007-09-01 | 17 | 1 | 0 | 15 | 1 | 0
2007-10-01 | 14 | 0 | 0 | 14 | 2 | 0
2007-11-01 | 14 | 1 | 0 | 13 | 1 | 0
2007-12-01 | 9 | 0 | 0 | 8 | 1 | 1
2008-01-01 | 13 | 0 | 0 | 10 | 3 | 0
2008-02-01 | 9 | 1 | 0 | 7 | 1 | 0
2008-03-01 | 7 | 0 | 0 | 6 | 2 | 0
2008-04-01 | 18 | 0 | 0 | 17 | 3 | 0
2008-05-01 | 8 | 1 | 0 | 6 | 2 | 0
2008-06-01 | 14 | 2 | 0 | 14 | 1 | 0
2008-07-01 | 5 | 0 | 0 | 4 | 2 | 0
2008-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2008-09-01 | 23 | 0 | 0 | 18 | 2 | 1
2008-10-01 | 9 | 0 | 0 | 8 | 1 | 1
2008-11-01 | 16 | 0 | 0 | 14 | 2 | 1
2008-12-01 | 9 | 0 | 0 | 9 | 0 | 0
2009-01-01 | 7 | 0 | 0 | 6 | 0 | 0
2009-02-01 | 10 | 0 | 0 | 7 | 1 | 0
2009-03-01 | 9 | 0 | 0 | 9 | 0 | 0
2009-04-01 | 7 | 0 | 0 | 6 | 0 | 0
2009-05-01 | 8 | 0 | 0 | 6 | 1 | 0
2009-06-01 | 19 | 0 | 0 | 17 | 1 | 0
2009-07-01 | 4 | 0 | 0 | 1 | 0 | 0
2009-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2009-09-01 | 15 | 0 | 0 | 12 | 1 | 0
2009-10-01 | 9 | 0 | 0 | 8 | 0 | 0
2009-11-01 | 14 | 0 | 0 | 11 | 0 | 0
2009-12-01 | 9 | 1 | 0 | 6 | 0 | 0
Table 9:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2010-01-01 | 5 | 0 | 0 | 4 | 0 | 0
2010-02-01 | 7 | 0 | 0 | 6 | 1 | 0
2010-03-01 | 10 | 0 | 0 | 7 | 1 | 0
2010-04-01 | 16 | 1 | 0 | 13 | 1 | 0
2010-05-01 | 12 | 0 | 0 | 9 | 0 | 0
2010-06-01 | 14 | 0 | 0 | 12 | 1 | 0
2010-07-01 | 6 | 0 | 0 | 5 | 2 | 0
2010-08-01 | 1 | 0 | 0 | 1 | 1 | 1
2010-09-01 | 17 | 0 | 0 | 10 | 1 | 0
2010-10-01 | 12 | 0 | 0 | 10 | 0 | 2
2010-11-01 | 14 | 0 | 0 | 12 | 1 | 1
2010-12-01 | 4 | 1 | 0 | 4 | 0 | 1
2011-01-01 | 6 | 0 | 0 | 6 | 0 | 0
2011-02-01 | 10 | 0 | 0 | 8 | 0 | 0
2011-03-01 | 12 | 0 | 0 | 7 | 3 | 1
2011-04-01 | 5 | 0 | 0 | 4 | 0 | 0
2011-05-01 | 20 | 0 | 0 | 17 | 1 | 1
2011-06-01 | 20 | 0 | 0 | 17 | 1 | 0
2011-07-01 | 3 | 0 | 0 | 0 | 0 | 0
2011-08-01 | 3 | 0 | 0 | 2 | 0 | 1
2011-09-01 | 7 | 0 | 0 | 5 | 0 | 0
2011-10-01 | 14 | 1 | 0 | 13 | 1 | 0
2011-11-01 | 12 | 0 | 0 | 10 | 0 | 0
2011-12-01 | 7 | 0 | 0 | 7 | 2 | 0
2012-02-01 | 4 | 0 | 0 | 4 | 0 | 0
2012-03-01 | 7 | 0 | 0 | 5 | 0 | 0
2012-04-01 | 12 | 0 | 0 | 11 | 4 | 0
2012-05-01 | 11 | 0 | 0 | 9 | 1 | 0
2012-06-01 | 10 | 0 | 0 | 8 | 0 | 0
Table 10:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2012-07-01 | 7 | 0 | 0 | 2 | 1 | 0
2012-08-01 | 2 | 0 | 0 | 2 | 0 | 0
2012-09-01 | 8 | 0 | 0 | 7 | 0 | 0
2012-10-01 | 12 | 0 | 0 | 10 | 3 | 1
2012-11-01 | 11 | 0 | 0 | 9 | 1 | 0
2012-12-01 | 7 | 0 | 0 | 5 | 0 | 0
2013-01-01 | 9 | 0 | 0 | 7 | 1 | 0
2013-02-01 | 11 | 1 | 0 | 10 | 3 | 0
2013-03-01 | 9 | 0 | 0 | 4 | 1 | 0
2013-04-01 | 14 | 0 | 0 | 10 | 2 | 1
2013-05-01 | 13 | 0 | 0 | 9 | 1 | 0
2013-06-01 | 15 | 0 | 0 | 13 | 0 | 2
2013-07-01 | 9 | 0 | 0 | 5 | 1 | 0
2013-08-01 | 2 | 0 | 0 | 2 | 0 | 0
2013-09-01 | 14 | 0 | 0 | 12 | 0 | 1
2013-10-01 | 12 | 0 | 0 | 10 | 3 | 3
2013-11-01 | 17 | 0 | 0 | 11 | 0 | 0
2013-12-01 | 8 | 0 | 0 | 7 | 1 | 0
2014-01-01 | 7 | 0 | 0 | 4 | 1 | 0
2014-02-01 | 7 | 0 | 0 | 6 | 1 | 1
2014-03-01 | 6 | 0 | 0 | 5 | 1 | 0
2014-04-01 | 11 | 0 | 0 | 11 | 0 | 1
2014-05-01 | 14 | 0 | 0 | 12 | 1 | 0
2014-06-01 | 6 | 0 | 0 | 6 | 2 | 0
2014-07-01 | 9 | 0 | 0 | 8 | 1 | 0
2014-08-01 | 1 | 0 | 0 | 1 | 1 | 0
2014-09-01 | 13 | 0 | 0 | 9 | 1 | 0
2014-10-01 | 12 | 0 | 0 | 9 | 1 | 1
2014-11-01 | 15 | 0 | 0 | 11 | 2 | 0
2014-12-01 | 3 | 0 | 0 | 3 | 1 | 0
Table 11:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2015-01-01 | 2 | 0 | 0 | 1 | 0 | 0
2015-02-01 | 6 | 0 | 0 | 4 | 0 | 0
2015-03-01 | 12 | 0 | 0 | 10 | 1 | 1
2015-04-01 | 9 | 0 | 0 | 8 | 1 | 0
2015-05-01 | 8 | 0 | 0 | 8 | 1 | 1
2015-06-01 | 8 | 0 | 0 | 5 | 1 | 2
2015-07-01 | 4 | 0 | 0 | 2 | 0 | 0
2015-08-01 | 3 | 0 | 0 | 3 | 0 | 1
2015-09-01 | 10 | 0 | 0 | 4 | 0 | 0
2015-10-01 | 16 | 1 | 0 | 10 | 0 | 0
2015-11-01 | 22 | 0 | 0 | 11 | 3 | 1
2015-12-01 | 4 | 0 | 0 | 3 | 0 | 0
2016-01-01 | 9 | 0 | 0 | 5 | 3 | 0
2016-02-01 | 8 | 1 | 0 | 8 | 0 | 0
2016-03-01 | 6 | 0 | 0 | 5 | 2 | 0
2016-04-01 | 11 | 0 | 0 | 9 | 1 | 1
2016-05-01 | 5 | 0 | 0 | 3 | 0 | 1
2016-06-01 | 16 | 1 | 0 | 10 | 0 | 1
2016-07-01 | 6 | 0 | 0 | 5 | 0 | 0
2016-08-01 | 2 | 0 | 0 | 2 | 0 | 0
2016-09-01 | 13 | 1 | 0 | 9 | 1 | 1
2016-10-01 | 14 | 0 | 0 | 13 | 0 | 2
2016-11-01 | 18 | 0 | 0 | 15 | 2 | 2
2016-12-01 | 2 | 0 | 0 | 1 | 0 | 0
2017-01-01 | 10 | 0 | 0 | 5 | 0 | 1
2017-02-01 | 9 | 1 | 0 | 9 | 1 | 1
2017-03-01 | 15 | 0 | 0 | 9 | 0 | 0
2017-04-01 | 15 | 0 | 0 | 9 | 1 | 1
2017-05-01 | 20 | 1 | 0 | 15 | 2 | 0
2017-06-01 | 10 | 1 | 0 | 6 | 0 | 0
Table 12:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2017-07-01 | 8 | 0 | 0 | 7 | 0 | 0
2017-08-01 | 3 | 0 | 0 | 2 | 1 | 2
2017-09-01 | 19 | 0 | 0 | 12 | 0 | 2
2017-10-01 | 15 | 0 | 0 | 10 | 0 | 2
2017-11-01 | 22 | 0 | 0 | 15 | 1 | 2
2017-12-01 | 2 | 0 | 0 | 2 | 1 | 0
2018-01-01 | 4 | 0 | 0 | 3 | 1 | 0
2018-02-01 | 15 | 0 | 0 | 10 | 0 | 2
2018-03-01 | 10 | 0 | 0 | 6 | 0 | 0
2018-04-01 | 9 | 0 | 0 | 8 | 2 | 1
2018-05-01 | 14 | 1 | 0 | 13 | 6 | 3
2018-06-01 | 5 | 0 | 0 | 5 | 0 | 0
2018-07-01 | 7 | 0 | 0 | 4 | 0 | 1
2018-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2018-09-01 | 12 | 0 | 0 | 10 | 0 | 0
2018-10-01 | 11 | 2 | 0 | 11 | 0 | 1
2018-11-01 | 20 | 3 | 0 | 13 | 1 | 1
2018-12-01 | 5 | 0 | 0 | 2 | 0 | 0
2019-01-01 | 8 | 1 | 0 | 4 | 0 | 0
2019-02-01 | 11 | 0 | 0 | 8 | 0 | 1
2019-03-01 | 11 | 0 | 0 | 9 | 1 | 2
2019-04-01 | 4 | 1 | 0 | 2 | 0 | 0
2019-05-01 | 13 | 2 | 0 | 7 | 1 | 2
2019-06-01 | 9 | 1 | 0 | 5 | 0 | 0
2019-07-01 | 5 | 0 | 0 | 5 | 0 | 0
2019-08-01 | 1 | 0 | 0 | 1 | 0 | 0
2019-09-01 | 11 | 0 | 0 | 6 | 0 | 1
2019-10-01 | 10 | 3 | 0 | 9 | 3 | 3
2019-11-01 | 18 | 4 | 0 | 12 | 2 | 2
2019-12-01 | 6 | 3 | 0 | 5 | 1 | 1
Table 13:  ECB Speeches. 1997-2022 date | n | climate change | covid | price | taxes | inequality
---|---|---|---|---|---|---
2020-01-01 | 4 | 2 | 0 | 1 | 0 | 1
2020-02-01 | 15 | 7 | 0 | 14 | 2 | 2
2020-03-01 | 1 | 0 | 0 | 1 | 0 | 0
2020-04-01 | 2 | 0 | 2 | 2 | 0 | 0
2020-05-01 | 5 | 1 | 3 | 4 | 0 | 0
2020-06-01 | 8 | 1 | 7 | 8 | 0 | 0
2020-07-01 | 6 | 1 | 5 | 3 | 0 | 0
2020-08-01 | 2 | 1 | 2 | 2 | 0 | 0
2020-09-01 | 12 | 5 | 10 | 8 | 0 | 3
2020-10-01 | 9 | 1 | 5 | 4 | 0 | 1
2020-11-01 | 14 | 2 | 11 | 13 | 0 | 1
2020-12-01 | 4 | 0 | 4 | 1 | 0 | 1
2021-01-01 | 5 | 3 | 3 | 3 | 1 | 1
2021-02-01 | 5 | 2 | 4 | 4 | 1 | 0
2021-03-01 | 9 | 2 | 8 | 5 | 0 | 0
2021-04-01 | 6 | 3 | 5 | 5 | 0 | 1
2021-05-01 | 4 | 3 | 1 | 3 | 0 | 1
2021-06-01 | 9 | 5 | 6 | 5 | 0 | 0
2021-07-01 | 3 | 2 | 2 | 3 | 0 | 2
2021-08-01 | 1 | 0 | 1 | 1 | 0 | 0
2021-09-01 | 8 | 2 | 4 | 7 | 1 | 1
2021-10-01 | 11 | 8 | 6 | 8 | 0 | 1
2021-11-01 | 18 | 8 | 9 | 13 | 2 | 3
2021-12-01 | 4 | 2 | 4 | 4 | 0 | 1
2022-01-01 | 3 | 2 | 2 | 3 | 1 | 0
2022-02-01 | 11 | 3 | 3 | 8 | 0 | 1
2022-03-01 | 10 | 4 | 4 | 9 | 2 | 1
2022-04-01 | 10 | 6 | 4 | 10 | 2 | 1
2022-05-01 | 6 | 0 | 2 | 6 | 0 | 1
2022-06-01 | 9 | 2 | 2 | 6 | 0 | 0
Table 14:  ECB Speeches. 1997-2022


# The Extragalactic Gamma-Ray Background from Core Dominated Radio Galaxies

Floyd W. Stecker11affiliation: Astrophysics Science Division, NASA/Goddard
Space Flight Center, Greenbelt, MD 20771 22affiliation: Department of Physics
and Astronomy, University of California, Los Angeles, Los Angeles, CA
90095-1547 , Chris R. Shrader11affiliation: Astrophysics Science Division,
NASA/Goddard Space Flight Center, Greenbelt, MD 20771 33affiliation: Physics
Department, Catholic University of America, Washington, DC 20064 , Matthew. A.
Malkan22affiliation: Department of Physics and Astronomy, University of
California, Los Angeles, Los Angeles, CA 90095-1547

###### Abstract

Recent radio surveys have discovered a large number of low luminosity core
dominated radio galaxies that are much more abundant than those at higher
luminosities. These objects will be too faint in $\gamma$-rays to be detected
individually by Fermi. Nevertheless, they may contribute significantly to the
unresolved extragalactic $\gamma$-ray background. We consider here the
possible contribution of these core dominated radio galaxies to the diffuse
extragalactic $\gamma$-ray background. Using published data available for all
45 of the radiogalaxies listed as detected counterparts in the Fermi FL8Y
source list update to the 3FGL catalog, we have searched for radio maps which
can resolve the core flux from the total source flux. Using high resolution
radio maps we were able to obtain core fluxes for virtually every source. We
then derived a relation between core radio flux and $\gamma$-ray flux that we
extrapolated to sources with low radio luminosities that are known to be
highly core dominated. We then employed a very recent determination of the
luminosity function for core dominated radio galaxies in order to obtain the
contribution of all possible $\gamma$-ray emitting radio galaxies to the
unresolved extragalactic $\gamma$-ray background. We find this contribution to
be a possibly non-negligible, $4\%-18\%$ of the unresolved $\gamma$-ray
background observed using the Fermi-LAT telescope.

###### Subject headings:

Gamma rays: diffuse background – Gamma rays: radio galaxies: active galaxies

##  1\. Introduction

The Large Area Telescope on the Fermi Gamma-ray Space Telescope (hereafter
called Fermi) has measured the diffuse unresolved extragalactic $\gamma$-ray
background (hereafter, EGB) at energies between 0.1 GeV and 820 GeV (Ackermann
et al 2015). The photon spectrum of the EGB is found to follow an approximate
power-law of spectral index $\sim$ 2.3 below $\sim$ 200 GeV, with a total flux
above 0.1 GeV of $\sim 7\times 10^{-6}$ cm-2 s-1 sr-1. It appears that $\sim$
85% of the EGB at energies above 50 GeV is from unresolved blazars (Ackermann
et al. 2016). Below 50 GeV, the EGB may be made up of various unresolved
extragalactic $\gamma$-ray sources such as blazars (e.g., Stecker 1993;
Padovanni et al. 1993; Stecker & Salamon 1996; Stecker & Venters 2011) and
star forming galaxies (Pavlidou & Fields 2001,2002; Stecker 2007; Fields 2010;
Makiya et al. 2011; Stecker & Venters 2011; Tamborra et al. 2014; Linden
2017). Star forming galaxies emit $\gamma$-rays at energies above 0.1 GeV,
such $\gamma$-rays being produced by interactions of cosmic rays accelerated
in supernova explosions of young massive stars with interstellar gas (Stecker
1971, 1976). If one lists the number of $\gamma$-ray point sources by AGN type
one finds that the gamma-ray sky is dominated by radio-loud blazars that have
their jets aligned within $\sim 20^{\circ}$ of the direction of the Earth. No
radio quiet AGN, other than nearby ones with active star formation, have been
detected by Fermi.

In addition to blazars and star forming galaxies, a number of $\gamma$-ray
emitting radio galaxies have been detected by Fermi, indicating that radio
galaxies can also contribute to the EGB (e.g., Inoue 2012; di Mauro et al.
2014; Hooper et al. 2016). These galaxies are believed to be AGN whose jets
are ”mis-aligned” with the direction of the Earth (Inoue 2011).111There is no
standard definition of ”mis-alligned”. As opposed to blazars (see above), we
can take this criterion to be $\sim>20^{\circ}$ of the direction of the Earth.
In this study, we specifically consider the more recently discovered
relatively abundant classes of low luminosity core dominated radio galaxies.
We thus make here the hypothesis that low luminosity core dominated radio
galaxies may contribute significantly to the unresolved extragalactic
$\gamma$-ray background. In order to examine this hypothesis we derive a new
relation between core radio and $\gamma$-ray luminosity based on an updated
list of Fermi-detected radio galaxies. This relation implies that lower
luminosity $\gamma$-ray emitting radio galaxies are expected to have
proportionally lower $\gamma$-ray luminosities so that they cannot be detected
individually by Fermi. However, their high relative abundance implies that
they can contribute to the unresolved (diffuse) $\gamma$-ray background. In
order to examine this hypothesis we need to derive a new relation between core
radio and $\gamma$-ray luminosity.

In Section 2 we discuss how we determined estimated core radio fluxes from
radio maps for the $\gamma$-ray emitting radio sources given in the Fermi FL8Y
source list. The FL8Y source list, which is based on the first eight years of
Fermi data in the 100 MeV - 1 TeV energy range, includes 5523 sources observed
by Fermi as having a significance $>4\sigma$.

In section 3 we use the expanded Fermi FL8Y source list, together with the
results from Section 2, to derive a new log-linear relation between
$\gamma$-ray luminosity and core radio luminosity for Fermi-detected radio
galaxies.

In Section 4 we make the case for the importance of the potential contribution
of classes of low luminosity radio sources to the diffuse EGB; such sources
being too weak to be individually detected by Fermi.

Section 5 gives our choice for luminosity functions for core dominated radio
galaxies at different redshifts. This includes the classes of low luminosity
radio sources considered in Section 4.

Section 6 outlines our calculation of the EGB from $\gamma$-ray emitting radio
galaxies. Section 7 concludes with a discussion of our results.

##  2\. Core Luminosities for our Data Set of Gamma-ray Emitting Radio
Galaxies

As a first step in our program to determine the EGB from core dominated radio
galaxies, we examined the published radio and $\gamma$-ray data available for
all 45 of the radio galaxies listed as detected counterparts in the Fermi FL8Y
source list update to the Fermi 3FGL source catalog 222The FL8Y list is based
on 8 years of sky survey data. It is a precursor to the forthcoming 4FGL
catalog. 333https://fermi.gsfc.nasa.gov/ssc/data/access/lat/fl8y/. We employed
this updated list of 45 sources, in conjunction with their corresponding radio
data discussed in Section 2, to derive a new radio (core) to gamma-ray
luminosity relation.

In order to obtain the core fluxes for these 45 sources, we searched for radio
maps of these sources which can resolve the core flux from the total source
flux. For virtually every source we were able to find these measurements. We
sought radio observations the highest angular resolution available. In the
majority of cases this was provided by interferometry at the Very Large Array
(VLA).444For those sources which are too far south for the VLA to observe, we
found maps from the Australia Telescope Compact Array (ATCA). We were also
able to obtain results from Multi-Element Radio Linked Interferometer Network
(MERLIN). Nearly all of the sources have a detectable compact core with a
measured flux. The core observed fluxes range from making up $>$ 90% of the
total source flux, down to 10 % or less.

In a few cases, no distinct ’core’ component is visible. For such radio
galaxies we used radio maps to set strict upper limits to the possible core
flux, which is typically 5% or less of the total flux.555Only 3 of the Fermi-
detected radiogalaxies show no detectable cores, only diffuse extended
(usually double) radio emission: and MRC0522-239, MRC1303-215, and MRC
2327-215. For these we adopted conservative upper limits to the possible flux
of a faint core. Most of the maps were made at an observing frequency of 5
GHz. Where these were not available, we used 1.4 GHz maps. References to each
of the publications used to determine the core fluxes are given in Table 1 and
more fully in the reference list.

##  3\. Radio Luminosity - Gamma Ray Luminosity Correlation

We now derive a relationship between the expected $\gamma$-ray luminosity of a
radio galaxy and its radio luminosity. Fortunately, such a relationship has
been found to exist that spans the entire radio luminosity range, regardless
of type (such as FRI and FRII), provided one considers only the core
luminosity of the radio sources (here designated by $L_{R}$) rather than their
total luminosity (Inoue 2011; di Mauro et al. 2014; Hooper et al. 2016). This
relation can be understood conceptually. The radio core emission is directly
associated with the power produced by non-thermal processes in the central
engine of the AGN in the vicinity of the black hole and the base of the jet.
The physics of such jets is analogous to that of the more familiar
$\gamma$-ray emitting blazars such as BL Lac objects. In fact, it appears that
Fermi-detected $\gamma$-ray emitting blazars are more core dominated than
those not detected by Fermi (Pei et al. 2018).

We have updated the relation between $\gamma$-ray luminosity and core radio
luminosity using our expanded data set as discussed in the previous section.
We therefore will adopt the reasonable assumption of extrapolating our new
relation between radio core and $\gamma$-ray luminosities to lower core radio
luminosities.

For $\gamma$-ray emitting radio galaxies, di Mauro et al. (2014) and Hooper et
al. (2016) found a relation between the radio (core) and $\gamma$-ray
luminosities. Those authors found an approximate log-linear relation to hold,
i.e.

$\log(L_{\gamma})=A\log(L_{R})+B.$ (1)

Subsequent to those previous determinations, the total Fermi sky exposure has
doubled. In addition to this increase in exposure, the entire dataset recently
underwent a full reprocessing, applying refined instrumental calibrations and
event selections. This recalibration, which followed procedures as described
in (Atwood et al. 2013), lead to significant improvement in sensitivity and
source localization and resulted in the FL8Y source list used here.

We have updated the relation between $\gamma$-ray luminosity and core radio
luminosity using our expanded data set as discussed in Section 2 in order to
derive an new core radio to $\gamma$-ray luminosity relation. Using our new
data set we find a best fit to the relation shown in Fig. 1 to be of the form
of equation (1) with derived values of $A=0.89$ and $B=7.15$. Figure 1 shows
the luminosity data overlaid with our derived correlation. The previous
results of di Mauro et al.(2014) and Hooper et al. (2016), are also shown for
comparison in Figure 1.666Previous results were based on the smaller (3FGL)
sample with about half the number of detections, and both incorporated upper
limits in to their analysis. In calculating the parameters of the luminosity
correlation, we have not included sources with only $\gamma$-ray flux upper
limits. However, our result agrees well with that of di Mauro (2014).

##  4\. Low Luminosity Core Dominated Radio Galaxies

In roughly the past decade populations of low luminosity compact core
dominated radio sources have been revealed through a combination of wide
field-of-view $\sim$ GHz surveys and follow up interferometric mapping. These
abundant sources have been designated ”miniature RGs” or ”Core Galaxies”
(CoreG) with typical luminosities in the range $10^{20}-10^{22}$ W/Hz at 1.4
GHz and ”FR0 galaxies” with luminosities in the range $10^{22}-10^{24}$ W/Hz
at 1.4 GHz (Balmaverde & Capetti 2006). These highly core-dominated radio
sources are found mostly in luminous, red, early type galaxies (Herrera Ruiz
et al. 2017; Baldi, Capetti, & Massaro, 2018). They are classified
predominantly as LERGs (low-excitation radio galaxies) (see, e.g. Best &
Heckman (2012a). FR0 galaxies, although of lower radio luminosity than FRI
galaxies, have been found to be five times more numerous than FRI galaxies in
the local universe (Baldi et al. 2018).

Core G and FR0 galaxies are faint radio sources, having luminosities below
$10^{25}$ W/Hz. Because of their relatively low luminosity, they are expected
to be extremely difficult to detect as individual $\gamma$-ray sources, as
follows from relation (1)777There has been one claimed detection of an FR0
designated as Toll 326-379 as a $\gamma$-ray source (Grandi, Capetti & Baldi
2016). However, with the refined positional determination of this gamma-ray
source in the FL8Y source list the association with Toll 1326-379 is now very
questionable.. In fact, even at radio frequencies these galaxies have not been
observed at redshifts above $\sim$ 0.5. However, owing to their abundance, we
consider core-dominant Core G and FR0 galaxies to be candidates to contribute
significantly to the unresolved extragalactic $\gamma$-ray background.

We have searched the literature as well as the Sloan Digital Sky Survey (SDSS)
database for optical spectroscopy of the Fermi-detected radiogalaxies. The
majority of them have an available optical spectrum which allows us to
classify $\sim$93% of these radiogalaxies as either ”HERGs” (high excitation
radio galaxies) or ”LERGs”. Whereas HERGs typically have accretion rates of
$\sim$ 1-10 % Eddington, LERGs have typical accretion rates below $\sim$ 1 %
Eddington (Heckman & Best 2012). Using their optical spectra to classify the
radio galaxies detected by Fermi, we classify $\sim$70% of them as LERGs and
$\sim$30% as HERGs. The later are usually indicated by their broad permitted
lines, which make them either quasars or Seyfert 1 AGN.

Baldi et al. (2018) chose their sample of 108 FR0 galaxies to be limited to
redshifts $z\leq 0.05$ to optimize spatial resolution, and to fluxes
$F_{r}\geq$ 5 mJy. The Baldi et al. FR0 sample peaks in the range 20 mJy $\geq
F_{r}$ 30 mJy. Given their resolution, they find their observed FR0s to be
very strongly core dominated.

We have examined optical spectra of the FR0 sources which have available
observations from SDSS. Of those, somewhat more than 80% are likely LERGs.
Their population is therefore likely to show the relatively weak redshift
dependence typical of LERGs (Best, et al. 2014; Pracy et al. 2016; Yuan et al.
2017), in contrast with the strong redshift-evolution seen for HERGs. 888Given
the LERG predominance among the FR0 sample, we note that the converse is not
necessarily true, i.e., one cannot conclude LERGs as a population are not
predominantly FR0s.

Since FR0s are low redshift sources, with an expected weak redshift
dependence, we make the reasonable conservative assumption of a Euclidean
source count for these sources. This assumption is supported by the fact that
FR0s are predominantly LERGs. It is known that LERGs have little redshift
dependence (e.g., Pracy et al. 2016).

Figure 2 shows the integral source count distribution obtained by Baldi et al.
(2018) for the 108 FR0 galaxies in their sample. A Euclidean distribution
extrapolation is also shown in the figure. Thus, it would be difficult to
obtain the contribution of FR0s alone to the EGB from this sample.

We wish to estimate the possible contribution of all core dominated radio
sources to the EGB based on a more complete picture. This would include low
luminosity sources such as FR0s, but also higher luminosity core dominated
sources. Our method for doing this will be discussed in the next section.

##  5\. Luminosity Function (LF) of Radio Core Emission

Traditionally galaxy radio luminosity functions are derived based on the
total; i.e. spatially integrated or, more commonly unresolved radio emission.
In recent years combined radio and spectroscopic surveys have led to
statistically complete samples comprising $\sim 10^{4}$ objects (e.g., Best &
Heckman (2012); Pracy et al. 2016) from which rigorously determined radio
luminosity functions have been derived, but most of these sample objects are
unresolved.

As discussed earlier, the core radio emission in radio galaxies is what is
physically most directly associated with the central AGN activity. As such a
luminosity function based on a large, flux limited statistically complete
sample of resolved radio galaxy core luminosities would be greater value for
many applications involving AGN and related high-energy properties such as
their $\gamma$-ray emission and contribution to the EGB. In practical terms
however, the task of obtaining VLBI maps for a large sample of say $10^{3}$ to
$10^{4}$ galaxies is a daunting one, and thus progress has remained limited.
The previous efforts to estimate the radio-galaxy contribution to the EGB have
invoked scaling relations to estimate the radio core luminosity function from
the total one (e.g., Fig 4 of di Mauro et al. 2014), however relations have
necessarily been based on limited statistics. Thus, uncertainties are inherent
in estimates of the EGB.

Recently, Yuan et al (2018) have made progress in towards improving estimates
of the core radio luminosity function by employing a large sample of radio
galaxies in conjunction with statistical methods. They find a relatively weak
luminosity dependent evolution in comparison to other derivations of the total
luminosity functions. We note that their derivation incorporates both FRI and
II subclasses which are delineated in terms of luminosity, but the total-to-
core correction for the combined luminosity distribution is smoothly
interpolated. The sample also extends to the low-luminosity extreme core
dominant FR0 population, which may in fact be the predominant population
locally (Baldi, Capetti, A. & Massaro, 2018). The resulting radio galaxy core
luminosity function has thus been obtained by Yuan et al. (2018). Yuan et al.
also show that relatively low luminosity, low redshift radio sources below
$10^{25}$ W/Hz are core dominated. This luminosity function at low
luminosities is consistent with the Euclidean number flux distribution shown
in Figure 2.

We thus chose to compute our estimate of the radio galaxy contribution to the
EGB based on the Yuan et al (2018) luminosity function. We use the LFs for
sources at higher redshifts as also derived by Yuan et al (2018) in Figure 5
of their Section 5. The higher redshift LFs derived by Yuan et al. show a very
weak redshift evolution as typical of LERGS, with the number density peaking
at $z\sim 0.8$. This resonates with our results in Section 4 where we found
that both FR0s and $\gamma$-ray -loud radio galaxies are primarily LERGs.

##  6\. Gamma-ray Background from Core Dominated CoreG, FR0 and FRI Galaxies

We proceeded by deriving a $\gamma$-ray luminosity function based on our
$L_{\gamma}$ to $L_{R}$ correlation presented in section 3 and the radio
galaxy core luminosity function of Yuan (2018) as discussed in Section 5.
Specifically, we have used the parametric form of that LF and their fitted
parameters for the radio galaxy population. From that we compute the
$\gamma$-ray LF as

$\Phi_{\gamma}(L_{\gamma},z)=\Phi_{R}(L_{R}(L_{\gamma}),z)d\log L_{R}d\log
L_{\gamma},$ (2)

with equation (2) being evaluated using the relation (1), extrapolated to
lower luminosities than were detected by Fermi. Here and elsewhere $L_{R}$
refers to the core luminosity at a frequency of 5 GHz. We then compute the EGB
contribution at a given energy according equation (3), except that we have not
included the photon-photon opacity term. Also, we have included a point source
detection efficiency term which effectively removes the contribution from the
brightest sources. Such sources would presumably be above the point-source
threshold such as the 45 detections used in our gamma-to-radio luminosity
relation and would be masked in the empirical EGB measurement process. For
this procedure we follow the methodology of Abdo et al.(2010).

We now calculate the $\gamma$-ray background from core dominated radio
galaxies. We assume that these sources have $\gamma$-ray spectra of
approximate power-law form $KE^{-\Gamma}$ in the energy range $0.1<100$ GeV.
We assume a distribution of $\gamma$-ray spectral indexes, $\Gamma$, for the
45 non-blazar radio loud AGN taken from the Fermi FL8Y compilation, fit to a
Gaussian distribution with $\sigma$ = 0.35 around a mean value of 2.3. This is
shown in Figure 3. Our Gaussian assumption produce a slightly concave
$\gamma$-ray spectrum (e.g., Stecker & Salamon 1996). We note that, despite
the limited statistics, this our mean value matches precisely the measured EGB
slope over the nominal 1-100 GeV range (Ackermann et al. 2015).

We use the luminosity function $\Phi_{R}(L,z)$ taken from Yuan et al. (2018)
together with equation (2) to obtain the $\gamma$-ray luminosity function for
core dominated radio galaxies. The $\gamma$-ray background is then given by

$\begin{array}[]{c}I(E_{\gamma})=\int_{\Gamma_{min}}^{\Gamma_{max}}\frac{dn(\Gamma)}{d\Gamma}d\Gamma\int_{0}^{z_{\mathrm{max}}}dz\int_{L_{\gamma,\mathrm{min}}}^{L_{\gamma,\mathrm{max}}}\frac{dL_{\gamma}}{\ln(10)L_{\gamma}}\times\\\
\\\ \frac{d^{2}V}{d\Omega
dz}\Phi_{\gamma,Core}(L_{\gamma},z)\frac{dF_{\gamma}(L_{\gamma},(1+z)E_{\gamma},z)}{dE_{\gamma}}\
e^{-\tau(E_{\gamma},z)}\end{array}$ (3)

In order to calculate the EGB from core dominated radio galaxies, we carried
out the integration of equation (3) over the range of observed spectral
indices and with limits of integration in redshift and luminosity that covered
the pertinent ranges. The $\gamma$-ray luminosity range used, viz. 0.1 - 300
GeV, corresponds to the range of radio galaxy core luminosities (in erg/s)
$36.0<\log L_{\gamma}<45.0$ (see Figure 1). We evaluated the comoving volume
integration from redshift $z=0$ to $z=3.0$.

Aside from our basic assumption regarding the low-luminosity core-dominant
radio galaxy population as $\gamma$-ray emitters, the largest source of
uncertainty in our calculation is the inherent scatter in the $\gamma$-ray-to-
radio luminosity correlation as given by equation (1). This scatter is shown
in Figure 1. To quantify this scatter, we considered a parallel band of
uncertainty about the red curve of Fig. 1 spanning a factor of 2 (or 0.3 dex).
We then computed the EGB, separately varying the parameters A and B in
equation (1), with the curves constrained to lie within this certainty band.
By comparison, the uncertainty bands of the Yuan et al (2018) luminosity
functions employed in our calculation have uncertainty bands less than 0.1 dex
in vertical extent at most and less than 0.05 dex near the knee where most of
the contribution to the total luminosity occurs. Thus, the uncertainty in the
luminosity function comprises a much smaller contribution to our uncertainty
than the scatter in the gamma-ray to radio correlation.

Taking these uncertainties into account, we find that our evaluation using
equations (1) - (3) gives a range of flux values from $\sim$ $11\%\pm 7\%$ of
the observed EGB between 100 MeV and 100 GeV. This is shown by the pink
uncertainty band depicted in Figure 5. Our results thus indicate that the
total $\gamma$-ray flux from core dominated radio galaxies can account for a
minor, but non-negligible, $11\pm 7\%$ of the unresolved $\gamma$-ray
background observed using the Fermi-LAT telescope.

##  7\. Conclusions

Using radio maps we determined estimated core radio fluxes for the
$\gamma$-ray emitting radio sources given in the expanded Fermi FL8Y source
list. We used those results, to derive a new log-linear relation between
$\gamma$-ray luminosity and core radio luminosity for Fermi-detected radio
galaxies. We then considered the importance of the potential contribution of
the recently studied classes of low luminosity radio sources to the diffuse
GRB; such sources being too weak to be individually detected by Fermi. Using
luminosity functions for core dominated radio galaxies at different redshifts,
including the classes of low luminosity sources discussed in Section 4, we
determined the contribution to the EGB from unresolved radio galaxies.

In comparing our results with the unresolved EGB derived by the Fermi
collaboration (referred to by Ackermann et al. 2015 as the IGRB), we note that
the spectral index of the observed background is consistent with $E^{-2.3}$ so
that the fraction of the background that we may attribute to core dominated
radio galaxies is roughly independent of energy. However, the unresolved
background derived by Ackermann et al. (2015) has a steep drop off above
$\sim$ 350 GeV. This drop off is probably due to a combination of (a)
decreased sensitivity at the highest energies, (b) uncertainty in the analysis
of the galactic foreground, and (c) some possible absorption from interactions
with EBL photons (e.g., Stecker, Scully and Malkan 2016). For this reason, we
do not calculate our results for energies above $\sim$ 100 GeV. In this
regard, we note that the Fermi group has determined that $\sim$ 85% of the
unresolved $\gamma$-ray background above 50 GeV is from blazars (Ackermann, M.
et al. 2016).

We note that the Fermi upper limits on non-detected radio galaxies (Di Mauro
et al. 2014) are consistent with relation (1) within our error band. Thus,
while it is possible that not all core-dominated radio sources are
$\gamma$-ray sources, our hypothesis and conclusions are reasonable.

On the other hand, we also note that the LF that we have used, taken from Yuan
et al. (2018), may underestimate the number of lower luminosity radio sources,
e.g., FR0s, owing to incompleteness. The LF below the knee of the LF may
actually be steeper than assumed (see e.g. Falcke, Körding & Nagar 2004).

Our results, shown in Figure 5, show that the total $\gamma$-ray flux from
core dominated radio galaxies can account for a minor, but non-negligible,
$4\%-18\%$ of the $\gamma$-ray background over the main energy range observed
by Fermi. Together with the contributions from blazars and star forming
galaxies (e.g., Stecker & Venters 2011), the entire observed diffuse
$\gamma$-ray background can reasonably be accounted for.

## References

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Table 1Radiogalaxies Detected in 4FGL

|  | $\rm S_{core}$ |  |  |
---|---|---|---|---|---
Fermi ID | Source ID | (Jy) | Ref.**footnotemark:  | Tel/Array | (HERG/LERG)
FL8Y J0030.6-0212 | SDSS J002900.98-01134 | 0.23 | Lee17 | ATCA 20 GHz | LERG
FL8Y J0057.7+3022 | NGC 315 | 1.4 | Mack97 | Effelsberg | LERG
FL8Y J0308.4+0407 | MRC 0305+039 = NGC 1218 | 0.7 | Unger84 | Merlin | HERG
FL8Y J0316.9+4120 | IC 310 | 0.17 | Ahnen17 | VLA | LERG
FL8Y J0319.8+4130 | NGC 1275 | 3–28 | Condon86 | VLA | HERG
FL8Y J0322.6-3712e | MRC 0320-373 = NGC 1316 = Fornax A | 0.12 | Fomalont89 | VLA | LERG
FL8Y J0334.3+3920 | 4C 39.12 | 0.43 | Liuzzo13 | VLA-8GHz | LERG
FL8Y J0418.5+3810 | 3CR 111 | 1.2 | Hardcastle88 | VLA | HERG
FL8Y J0433.0+0522 | MRC 0430+052 = 3C 120 | 1 | Fey96 | VLBA | HERG
FL8Y J0519.7-4546 | Pks 0518-45 = Pictor A | 15.4 | Tingay03 | ATCA 5 GHz | HERG
FL8Y J0521.2+1637 | 3C 138 | 0.88 | Akujor91 | MERLIN | HERG
FL8Y J0522.9-3628 | MRC 0521-365 | 1 | Lee16 | VLA | HERG
FL8Y J0524.7-2405 | MRC 0522-239 |  $<$0.5 | Kapahi98 | VLA | ?
FL8Y J0623.9-5300 | MRC 0620-526 | 1.2 | Chherti13 | ATCA 20 GHz | LERG
FL8Y J0627.1-3529 | MRC 0625-354 | 0.5 | Morganti97 | VLA | LERG
FL8Y J0708.9-3616 | MRC 0707-35 | 0.045 | Saikia99;Yuan+Wang’12 | ATCA 5 GHz | ?
FL8Y J0758.7+3746 | 3C 189 = NGC 2484 | 0 | Condon91 | 5 GHz | LERG
FL8Y J0840.8+1315 | 3C 207 | 0.35 | Kharb10 | VLA | HERG
FL8Y J0858.3+1409 | 3C 208 | 0.51 | Bridle94 | VLA | HERG
FL8Y J0934.3+3926 | 3C 221 |  $<$0.4 | Vigotti99 | 5 GHz | ?
FL8Y J1040.5+0617 | SDSS J103928.21+05361 | 0.2 | Kozeił11 | 1.4 GHz | LERG
FL8Y J1053.6+4930 | SDSS J105344.12+49295 | 0.3 | vanVelzen15 | VLA | LERG
FL8Y J1144.9+1937 | 3C 264 = NGC 3862 | 0.4 | Bridle81 | VLA | LERG
FL8Y J1219.5+0548 | 3C 270 = NGC 4261 | 0.3 | Jones97 | VLA | LERG
FL8Y J1230.8+1223 | 3C 274 = M 87 | 3.9 | Kharb10 | VLA | LERG
FL8Y J1244.5+1616 | 3C 275.1 | 0.2 | Fernini14 | VLA | HERG
FL8Y J1312.6+4828 | SDSS J130248.70+4755105 | 0.033 | Best12b | VLA | LERG
FL8Y J1306.4+1112 | SDSS J130619.24+11133 | 0.2 | Lin10 | VLA | LERG
FL8Y J1306.7-2149 | MRC 1303-215 | 0.1 | Kapahi98 | VLA | LERG
FL8Y J1325.5-4301 | MRC 1322-427 | 7 | Yuan12 | VLA | HERG
FL8Y J1331.0+3031 | 3C 286 | 5.5 | An04 | VLA | HERG
FL8Y J1346.3-6027 | Cen B | 2–6 | Chherti13 | ATCA | LERG
FL8Y J1350.8+3033 | 3C 293 = UGC 8782 | 1.55 | Joshi11 | VLA | LERG
FL8Y J1428.5+4240 | SDSS J142832.60+42402 | 0.2 | Liuzzo13 | VLA | LERG
FL8Y J1443.0+5201 | 3C 303 | 0.13 | Hardcastle88 | VLA | HERG
FL8Y J1454.2+1622 | 3C 306 = IC 4516 | 0.002 | Condon91 | VLA | LERG
FL8Y J1459.0+7139 | 3C 309.1 | 2.4 | Yuan18 | VLA | HERG
FL8Y J1518.7+0202 | SDSS J151640.21+00150 | 0.128 | Lister16 | VLBA | HERG
FL8Y J1518.6+0613 | SDSS J151845.72+06135 | 0.1 | Owen92 | VLA | LERG
FL8Y J1521.2+0421 | Parkes 1518+045 = CGCG 049-138 |  | Duncan93 | VLA | LERG
FL8Y J1631.0+8233 | NGC 6251 | 0.24 | Pushkarev12 | VLA | LERG
FL8Y J1829.5+4846 | 3C 380 | 4.5 | Yuan12 | VLA | HERG
FL8Y J1843.5-4835 | MRC 1839-487 | 0.16 | Yuan12 | VLA | LERG
FL8Y J2004.1-3603 | MRC 1955-357 |  $<$ 0.21 | Chherti13 | ATCA 20 GHz | HERG
FL8Y J2329.7-2117 | MRC 2327-215 |  $<$ 0.1 | Kapahi98 | VLA | LERG

**footnotemark:  See reference list for full references.

Figure 1.— Gamma-ray luminosities of radio galaxies from the Fermi FL8Y source
list vs. estimated core radio luminosities at 5 GHz. All luminosities are
given in $erg/s$. Blue circles denote LERGs and unclassified sources; green
triangles denote HERGs. The red line is our fit (see eq. (1). Previous results
derived using the earlier 3FGL Fermi catalog are also shown by dashed lines
for comparison (Purple:Di Mauro et al. 2014, Yellow:Hooper et al. 2016).
Figure 2.— Flux limited FR0 number-flux distribution from Baldi et al.(2018).
The plot is for the 108 Baldi et al. FR0 galaxies covering one quarter of the
sky. The sample appears to become incomplete below $\sim$ 30 mJy (see text).
We also show our assumed Euclidean distribution extrapolated to 1 mJy. Figure
3.— Distribution of $\gamma$-ray spectral indexes for the 45 non-blazar radio
loud AGN taken from the Fermi FL8Y compilation. The red dotted curve is the
best fit Gaussian distribution with a mean value of 2.3 and a width of 0.35.
Figure 4.— Radio galaxy core luminosity functions at 5 GHz derived from Yuan
et. al. (2018) and used in our calculations as described in the text. The
horizontal axis units are in $ergs/s$. Figure 5.— Fermi measurements of the
unresolved extragalactic $\gamma$-ray background (Ackermann et al. 2015) are
shown in blue. Results of our calculation are shown by the red line and pink
uncertainty band (see text). We find that $11\pm 7$% of the unresolved EGB at
$\sim 1$ GeV can be due to unresolved, core dominant radio galaxies.