#  Supramassive dark objects with neutron star origin

M. Vikiaris1 V. Petousis2 M. Veselský2 Ch.C. Moustakidis1 1Department of
Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki,
Greece
2Institute of Experimental and Applied Physics, Czech Technical University

###### Abstract

Till today, the nature of Dark Matter (DM) remains elusive despite all our
efforts. This missing matter of the universe has not been observed by the
already operating DM direct-detection experiments, but we can infer its
gravitational effects. Galaxies and clusters of galaxies are most likely to
contain DM trapped to their gravitational field. This leads us to the natural
assumption that compact objects might contain DM too. Among the compact
objects exist in galaxies, neutron stars considered as natural laboratories,
where theories can be tested, and observational data can be received. Thus,
many models of DM they have proposed it’s presence in those stars. By
employing the two fluid model, we discovered a stable area in the M-R diagram
of a celestial formation consisting of neutron and DM that is substantial in
size and vast in dimensions. This formation spans hundreds of kilometers in
diameter and possesses a mass equivalent to 100 or more times that of our sun.
To elucidate, this entity resembles an enormous celestial body of DM, with a
neutron star at its core. This implies that a supramassive stellar compact
entity can exist without encountering any issues of stability and without
undergoing a collapse into a black hole. In any case, the present theoretical
prediction can, if combined with corresponding observations, shed light on the
existence of DM and even more on its basic properties.

Neutron stars, Dark matter, Two fluid model, Supramassive compact objects

##  I Introduction

The mystery concerning the Dark Matter (DM) nature, is still today one of the
most challenging subjects in astrophysics and cosmology in general. Two
scenarios of DM exist today, either its self annihilating and through this
procedure temperature gradient could be produced, or its not self annihilating
and then the DM could cluster in blobs. But what is the possibility to have
non self annihilating DM captured and existing inside astrophysical compact
objects ?

We know that among the compact objects exist in galaxies, neutron stars
considered as natural laboratories, where theories can be tested, and
observational data can be received [1, 2, 3]. If its possible that DM could
clump in a sufficient with nuclear matter in neutron stars, then this mixing
could influence its neutron stars measurable properties. Thus, many models of
DM they have proposed it’s presence in those stars [4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42]. This suggests the exciting
possibility that neutron stars could act as laboratories for indirectly
measuring DM properties. Another important question is how DM could become
mixed with ordinary matter in a neutron star. One well studied possibility is
through capture as described in the [43, 44, 45, 46, 47, 48, 49].

It is very useful to treat the mixing between nuclear matter and DM as a two-
fluid systems, in which the first fluid describes the nuclear matter through
an Equation of State (EoS) for a neutron star without DM and the second fluid
describes the DM. The properties such as the mass and radius of the neutron
star can be determined by solving the multi-fluid Tolman-Oppenheimer-Volkoff
(TOV) equations [50, 51, 52].

Until today, no results were found from DM direct detection experiments [53,
54, 55] and thus have have placed strict constraints on the DM to the nucleons
coupling strength. From the perspective of the TOV equations, this is
generally taken to mean that the coupling strength its negligibly small [56,
57, 58, 59] and that DM admixed neutron stars are two-fluid systems in which
the only inter-fluid interactions are gravitational. Through this paper, we
mostly focusing on the bulk properties of the neutron star, such as its mass
and its radius and its possibility for mixing nuclear matter with DM in mind.

Applying the two fluid model in our study, we came to an surprising
possibility of a stable area in the M-R diagram of a celestial formation
consisting of neutron and DM that is substantial in size and vast in
dimensions. This formation spans hundreds of kilometers in diameter and
possesses a mass equivalent to 100 or more times that of our sun. To
elucidate, this entity resembles an enormous celestial body of DM, with a
neutron star at its core.

This possibility, implies that a supramassive stellar compact entity can exist
without encountering any issues of stability and without undergoing a collapse
into a black hole. It seems that the existence of such objects may demands
mass of DM particle $m_{\chi}<1~{}$GeV. The lower the $m_{\chi}$ the higher
the $M_{max}$ and $R_{max}$. But before we claim something like this in our
study, several crucial questions which they need convinced answers arise:

a) How stable are these objects ? [60] b) which is their compactness ? c) is
there a consistency with the values of central pressure of the neutron star
that do not exceed the accepted limits of the nuclear EoS ? d) is valid the
crucial assumption for our investigation, that the fermions are stable on the
time scale comparable with the lifetime of the universe, ($\tau\geq
H_{0}^{-1}\approx 14$ Gyr, where $H_{0}$ is the value of the Hubble constant)
? or in other words, holds the assumption that the fermions constituting the
new compact object are conserved ? [61] e) when and how the possible
supramassive compact objects, made of exotic fermions, could be formed ? One
could speculate that this happened after the inflation era. Large objects
could serve as primary seeds clumping nuclear matter after the radiation
decoupling era. Perhaps could be possible the formation of some hybrid objects
where the exotic fermionic stars might be surrounded by the halo of ordinary
matter.

Answering most of the aforementioned questions, forms a large part of our
research on the subject, especially the stability issue. Also in addition, the
motivation behind our present work is to extend the recent study concerning
the trapped DM in the interior of neutron stars and far beyond it. It can be
considered that the present study is an extension and generalization of the
study done in the paper [61]. In the aforementioned paper the study focused on
compact stars consisting of one kind of fermions with arbitrary masses and
interaction strengths. The present study include a similar study by
considering a two fluid model the one consist of neutron star matter and the
other a DM fluid consist by fermions or bosons.

We investigate the possibility to gain useful information and constraints of
some possible DM candidates as well. Using a two-fluid model for neutron stars
admixture with DM particles, we focus both on fermionic and bosonic DM where
their mass and the self-interaction are treated as free parameters. Using this
approach, we predict the properties of this new compact object including mass
and radius. All of our findings are rigorously guided from the stability
conditions of which these new objects must obey.

The paper is organized as follows: in Section 2, we briefly describe the Two-
fluid model used, accompanied with subsections dedicated to self interacting
DM Equations of State (EoS), for fermionic and bosonic DM particles. In
Section 3, we discuss the important topic of stability and in Section 4, we
display and discuss the results of the present study. In Section 5, we
finalize our investigation with the concluding remarks.

##  II Two-fluids model

In the present work we study compacts objects made by a) non-self annihilating
DM particles admixed with b) neutron star matter (including mainly neutrons
and a small fraction of protons and electrons). We consider also that the
total matter, described by these two fluids, interact each other only
gravitationally. In order to predict the bulk properties of the objects
consists of the aforementioned two fluids, one has to solve the coupled
Tolman-Oppenheimer-Volkov (TOV) equations (two for each fluid) simultaneously.
These four equations are defined below [51, 50]:

$\displaystyle\frac{dP_{\rm NS}(r)}{dr}$ $\displaystyle=$
$\displaystyle-\frac{G{\cal E}_{\rm
NS}(r)M(r)}{c^{2}r^{2}}\left(1+\frac{P_{\rm NS}(r)}{{\cal E}_{\rm
NS}(r)}\right)$ (1) $\displaystyle\times$ $\displaystyle\left(1+\frac{4\pi
P(r)r^{3}}{M(r)c^{2}}\right)\left(1-\frac{2GM(r)}{c^{2}r}\right)^{-1}$
$\frac{dM_{\rm NS}(r)}{dr}=\frac{4\pi r^{2}}{c^{2}}{\cal E}_{\rm NS}(r)$ (2)
$\displaystyle\frac{dP_{\rm DM}(r)}{dr}$ $\displaystyle=$
$\displaystyle-\frac{G{\cal E}_{\rm
DM}(r)M(r)}{c^{2}r^{2}}\left(1+\frac{P_{\rm DM}(r)}{{\cal E}_{\rm
DM}(r)}\right)$ (3) $\displaystyle\times$ $\displaystyle\left(1+\frac{4\pi
P(r)r^{3}}{M(r)c^{2}}\right)\left(1-\frac{2GM(r)}{c^{2}r}\right)^{-1}$
$\frac{dM_{\rm DM}(r)}{dr}=\frac{4\pi r^{2}}{c^{2}}{\cal E}_{\rm DM}(r)$ (4)

where also $M(r)=M_{\rm NS}(r)+M_{\rm DM}$ and $P(r)=P_{\rm NS}(r)+P_{\rm
DM}(r)$ (the subscripts $\rm NS$ and $\rm DM$ stand for the neutron star and
dark matter respectively).

##  III Neutron star matter and dark matter equations of state

In the present work, in order to describe the neutron star matter we use the
Equation of State (EoS) derived by Akmal et al. [62](hereafter APR) in
particular the model A18+UIX. This is an EoS with microscopic origin which and
its predictions are in very good agreement with both the measured maximum
masses and radii. It is worth to notice here that the present study mainly
focuses on the EoS of DM and its properties. Nevertheless, the use of a
realistic EoS for neutron stars provides a guarantee for the reliability of
our results.

Now, concerning the DM particles we consider that they are relativistic
fermions, which interact each other through a repulsive force. In particular,
we consider Yukawa type interaction on the form [59]:

$V(r)=\frac{{\rm g}_{\chi}^{2}}{4\pi r}\exp\left[-\frac{m_{\phi}c^{2}}{\hbar
c}r\right]$ (5)

where ${\rm g}_{\chi}$ is the coupling constant and $m_{\phi}$ is the mediator
mass. It is worth to mention that in the majority of the similar studies, the
DM considered as a non-interacting gas of fermions. However, as we will see in
the present study, the role of interaction is decisive for the creation and
stability of supramassive objects. The contribution on the energy density of
the self-interaction is given by:

${\cal E}_{SI}(n_{\chi})=\frac{y^{2}}{2}(\hbar c)^{3}n_{\chi}^{2}$ (6)

where $y={\rm g}_{\chi}/m_{\phi}c^{2}$. In this case the total energy density
of the DM particles is given by [61]:

$\displaystyle{\cal E}_{\rm DM}(n_{\chi})$ $\displaystyle=$
$\displaystyle\frac{(m_{\chi}c^{2})^{4}}{(\hbar
c)^{3}8\pi^{2}}\left[x\sqrt{1+x^{2}}(1+2x^{2})\right.$ (7) $\displaystyle-$
$\displaystyle\left.\ln(x+\sqrt{1+x^{2}})\right]+\frac{y^{2}}{2}(\hbar
c)^{3}n_{\chi}^{2}$

The corresponding pressure is calculate straightforward using the definition:

$P_{\rm DM}(n_{\chi})=n_{\chi}\frac{d{\cal E}_{\rm
DM}(n_{\chi})}{dn_{\chi}}-{\cal E}_{\rm DM}(n_{\chi})$ (8)

and is given by:

$\displaystyle P_{\rm DM}(n_{\chi})$ $\displaystyle=$
$\displaystyle\frac{(m_{\chi}c^{2})^{4}}{(\hbar
c)^{3}8\pi^{2}}\left[x\sqrt{1+x^{2}}(2x^{2}/3-1)\right.$ (9) $\displaystyle+$
$\displaystyle\left.\ln(x+\sqrt{1+x^{2}})\right]+\frac{y^{2}}{2}(\hbar
c)^{3}n_{\chi}^{2}$

where $m_{\chi}$ is the particle mass and

$x=\frac{(\hbar c)(3\pi^{2}n_{\chi})^{1/3}}{m_{\chi}c^{2}}.$

The total energy density and pressure of the two fluid mixing, considering
that the contribution of neutron star matter are defined as ${\cal E}_{\rm
NS}(n_{b})$ and $P_{\rm NS}(n_{b})$ where both are functions of the baryon
density $n_{b}$ (for more details see Ref. [62]), are given simple by the
following sums:

${\cal E}(n_{b},n_{\chi})={\cal E}_{\rm NS}(n_{b})+{\cal E}_{\rm
DM}(n_{\chi})$ (10) $P(n_{b},n_{\chi})=P_{\rm NS}(n_{b})+P_{\rm DM}(n_{\chi})$
(11)

With the aim of enriching the possible DM candidates, we will also consider
the case where it consists of bosonic particles. We use in this case, the EoS
provided recently in Ref. [33]) where energy density and pressure are given
respectively by:

$\displaystyle{\cal E}_{\rm DM}(n_{\chi})$ $\displaystyle=$ $\displaystyle
m_{\chi}c^{2}n_{\chi}+\frac{u^{2}}{2}(\hbar c)^{3}n_{\chi}^{2},$
$\displaystyle P_{\rm DM}(n_{\chi})$ $\displaystyle=$
$\displaystyle\frac{u^{2}}{2}(\hbar c)^{3}n_{\chi}^{2}$ (12)

where the quantity $u=g_{\chi}/m_{\phi}c^{2}$ defines the strength of the
interaction.

##  IV Stability

The most usual method to study the stability is to perturb the static
solution. In particular, in order to check the stability of a given
configuration, one has to consider small radial perturbations of the
equilibrium configuration by solving the Sturm-Liouville eigenvalue equation,
which yields eigenfrequencies $\omega_{n}$ [1]. The eigenfrequencies of the
different modes form a discrete hierarchy $\omega_{n}^{2}<\omega_{n+1}^{2}$
$n=0,1,2\cdots$ …being real numbers [63]. A negative value of $\omega_{n}^{2}$
leads to an exponential growth of the radial perturbation and collapse of the
star. Only when all eigenfrequencies are positive the star will be stable [64]
(see also the relevant discussion in Ref [63].)

In the present work we employ the method developed by Henriques, Liddle and
Moothouse which used for the study of boson-fermion star [65, 66, 67]. This
method has been elaborated and extended through the years for similar studies
[60, 69, 70, 68]. According to this method, the stability analysis is carried
out by examining the behaviour of baryons and DM particles, yet fixing the
total mass $M$ values. In particular, the stability curve is formed with the
pair of central values of pressures $\\{P_{c}^{\rm NS},P_{c}^{\rm DM}$}
exactly in the point where the number of particles reached the minimum and
maximum values. This critical curves identify the transition from linear,
stable and unstable with respect to perturbations that conserve the mass and
the particle number. Hence fulfill the following conditions [68]:

$\displaystyle\left(\frac{\partial N_{b}}{\partial P_{c}^{\rm NS}}\right)_{\rm
M=const}=\left(\frac{\partial N_{\chi}}{\partial P_{c}^{\rm NS}}\right)_{\rm
M=const}=0$ $\displaystyle\left(\frac{\partial N_{b}}{\partial P_{c}^{\rm
DM}}\right)_{\rm M=const}=\left(\frac{\partial N_{\chi}}{\partial P_{c}^{\rm
NS}}\right)_{\rm M=const}=0$ (13)

where $N_{b}$ and $N_{\chi}$ are the numbers of baryons and DM particles
respectively. Now, the stability analysis can be summarized as follows [70]:
The configurations whose particle is located to the left of that point, where
the maximum and minimum of $N_{b}$ and $N_{\chi}$ coalesce, considered as
stable, where the corresponding located on the right point are unstable. In
fact it is sufficient (and this is what we do in this paper), to simply study
the dependence of $n_{\chi}$ on the central pressure $P_{c}^{\rm DM}$ to
identify the stability-instability critical points.

##  V Results and Discussion

Actually, there is an infinite number of possible configuration of the DMNS
object. This is due to the use of three independent parameters, that is the DM
mass $m_{\chi}$, the strength of the self-interaction and the fraction
$f=P_{DM}^{c}/P_{NS}^{c}$ of the central densities. Basically, all of them are
unconstrained. In the present study we focus on a few stable configurations
which prove and confirm our hypothesis for the existence of supramassive dark
objects, with neutron star origin, in the universe.

It is proper to clarify here that, by supramassive compact objects, we mean
those whose compactness $C=GM/Rc^{2}$ is in the neutron star region, i.e.
[0.15-0.25] or at least greater than the value 0.1 but less than the maximum
upper limit $C_{\rm max}=4/9$ where the objects collapse to a black hole. In
any case, the effects of the general relativity are important and moreover the
curvature of spacetime in the neighborhood of these objects is noticeable.
This has the consequence that they can be perceived in this way.

It is worth to notice that the majority of the relevant studies dedicated to
the specific cases, where the hybrid object consist mainly by hadronic matter
and a small fraction of DM, leading to configurations with mass similar to
neutron stars but with DM halo extended even to a few tens of kilometers.

To be more specific, in the present study we investigated the possibility of
very massive hybrid objects with masses ranging from ten to even hundred solar
masses and radii also for tens to even thousand of kilometers. In principle
there is no ad-hoc limitation to these configurations except for the stability
condition. Some additional constraints can be introduced by the absorption
rate of DM (in particular of the DM particle-neutron scattering cross
section), in a neutron star and the associated time scales, or by the density
distribution of DM in the universe. Besides, compact DM objects with large
masses and corresponding radii have already been studied (for a systematic
review see reference [61]. The motivation of the present work is to study the
corresponding supramassive compact objects, where a neutron star sits at their
center triggering the accretion of DM in and around it.

In general, as already pointed out, calculating the stability of these objects
is computationally a difficult and time-consuming problem. Since we are
initially interested in proving the stability of these objects we will choose
some special cases whose stability we will confirm. A more systematic and
extensive study may determine the stable range (concerning the mass and
radius), of such objects as a function of the mass, the interaction and the
fraction.

Now, since the DM contributes the a larger fraction on the total mass, some
useful approximation, concerning the total number of the fermions, can be
inferred by applying the analytical solution of the TOV equations, that is the
Tolman VII solution [71]. According to this solution, the energy density
varies in the interior of the star according the rule ${\cal
E}(r)\sim(1-(r/R)^{2})$. In this case the binding energy,
$BE/c^{2}=N_{\chi}m_{x}-M$, is given by [72]

$\frac{BE}{Mc^{2}}=1+f(C),\quad
f(C)=\frac{11C}{21}+\frac{7187C^{2}}{18018}+\cdots$ (14)

where $f(C)$ is a function of the compactness of the star $C=GM/Rc^{2}$. After
some algebra, we get the following approximation, for the critical number of
fermions which corresponds to the stability limit:

$N_{\chi}^{\rm cr}=1.144\times
10^{51}\left(0.627+0.27\tilde{y}\right)\left(1+f(C_{\rm
cr})\right)\left(\frac{100\ {\rm GeV}}{m_{\chi}}\right)^{3}$ (15)

where $C_{\rm cr}=GM_{\rm max}/R_{\rm min}c^{2}$ The values $M_{\rm max}$ and
$R_{\rm min}$ are taken from Ref. [61] where:

$M_{\rm max}=\left(0.384+0.165\times\tilde{y}\right)\times\left(\frac{\rm
GeV}{m_{\chi}}\right)^{2}\times 1.632M_{\odot}$ (16) $R_{\rm
min}=\left(3.367+0.979\times\tilde{y}\right)\times\left(\frac{\rm
GeV}{m_{\chi}}\right)^{2}\times 2.410\ ({\rm km})$ (17)

The expression (15) is similar to that found in Ref. [24] (using a Newtonian
apprach) where:

$N_{\chi}^{\rm cr}\simeq 1.8\times 10^{51}\left(\frac{100\ {\rm
GeV}}{m_{\chi}}\right)^{3}$ (18)

When the number of DM particle, concentrated in a neutron stars exceed the
Chandrasekhar limit the compact object collapse into a black hole [24]. It is
concluded then that the observations of old neutron stars can be used as a
laboratory to constrain the DM - neutron scattering cross section [24].

In Fig. 1(a), we display the M-R dependence for the case of pure fermionic DM
and DMNM object for $m_{\chi}=100$ MeV, $y=0.5$ and fraction $f=5\cdot
10^{-5}$. Obviously there is an infinite number of possible configurations but
we focus on the indicated case $M=925.05M_{\odot}$ and $R=7540.42$ Km with a
neutron star $M=1.73M_{\odot}$ and $R=12.26$ Km in the center. This is an
objects with compactness $C=0.18$. In Fig. 1(b), we confirm the stability of
this object, with the help of $N_{\chi}-P_{\chi}^{c}$ diagram, since
corresponds to stability region.

In Fig. 2(a), we investigate the case of a heavier DM particle with mass
$m_{\chi}=1500$ MeV and also with $y=0.5$ and fraction $f=0.01$. We select the
indicated case $M=56.28M_{\odot}$ and $R=504.04$ Km with a neutron star
$M=1.4M_{\odot}$ and $R=12.31$ Km in the center. Again, in Fig. 2(b), we
confirm the stability of this object. Moreover, in Fig. 3 we display the
dependence of the pressure (which corresponds to neutron star matter and DM)
on the radius $r$ for the specific configuration denoted in Fig. 2(a).

In Fig. 4(a), we consider the case of a bosonic DM with mass $m_{\chi}=100$
MeV, interaction $u=0.5$ and fraction $f=4.1\cdot 10^{-5}$. We select the
specific configuration which corresponds to total mass $M=864.27M_{\odot}$,
$R=7813.37$ Km and compactness $C=0.164$ (with a neutron star with mass
$M=1.64M_{\odot}$ and radius $R=12.33$ Km in the center). This object is
stable as one can see in Fig.4(b).

Finally, in Fig. 5(a) we select the case of a particle with mass
$m_{\chi}=1500$ MeV, interaction $u=0.5$ and fraction $f=0.01$. We select the
configuration where $M=56.24M_{\odot}$, $R=502.97$ Km and $C=0.165$ (with a
neutron star with mass $M=1.42M_{\odot}$ and radius $R=12.31$ Km in the
center). This object is stable as confirmed in Fig. 5(b).

##  VI Concluding Remarks

We investigated possible supramassive dark objects stable configurations, with
neutron star origin. We used EoS of self-interactive fermions and bosons and
one of the most reliable EoS for the neutron star matter. Unlike other similar
studies, we did not focus on the cases of neutron stars surrounded by a DM
halo of a few kilometers and of low relative mass contribution of the DM. We
found that there are an infinite numbers of these configurations (just we
select few of them to present), which are also stable against perturbations.
This means that may exist in the universe. An extension of this study is to
include interactions between DM particles and baryons. This is an interesting
perspective to be studied in future work.

In the present work we do not indent to answer on the question ”how these
objects are created?”. There are few speculations related with this question.
A relevant discussion is provided in Ref.[63]. For example the accretion
mechanism of DM into neutron stars as by the primordial formation of DM clumps
surrounded by ordinary matter. Another possibility is of having dark compact
object originated from DM perturbations growing from primordial over-
densities. Finally, another possibility is copious production and capture of
DM in the core-collapse supernova of neutron stars progenitor [56]. In any
case, there is no any strong theoretical prediction which argues strongly
against the creation of these supramassive DM objects.

The most critical question, as far as the objects are concerned, is how we can
locate them. The most powerful tool in this case is the gravitational lensing
which is based on space-time distortion which is caused by these objects.
Another possibility is to detect a possible merger event, by the well known
detectors (LIGO-VIRGO-KARGA collaboration) which include two cases: a) merger
between two dark compact objects or b) merger between one of them and another
compact object including pure neutron star or black hole. The signal of the
corresponding gravitational waves will transfer useful information for the
structure of these objects [73].

## Acknowledgments

This work is supported by the Czech Science Foundation (GACR Contract No.
21-24281S).

Figure 1: (a) The M-R dependence for the case of pure fermionic DM (dashed
line) DMNS object (solid line) of a lighter particle with mass $m_{\chi}=100$
MeV, interaction $y=0.5$ and fraction $f=5\cdot 10^{-5}$. The arrow indicate
the specific case where $M=925.05M_{\odot}$ and $R=7540.42$ Km (correspond to
a neutron star with mass $M=1.73M_{\odot}$ and radius $R=12.26$ Km in the
center). (b) The dependence of the ratio $N_{\chi}/N_{\chi}^{\rm max}$ for the
fixed mass $M=925.05M_{\odot}$ as a function of the central value of the DM
pressure $P_{\rm DM}^{c}$. Since the configuration belong to the stability
curve we conclude stability of this specific compact star case.

Figure 2: (a) The M-R dependence for the case of pure fermionic DM (dashed
line) and DMNS object (solid line) for DM mass $m_{\chi}=1500$ MeV,
interaction parameter $y=0.5$ and fraction of central pressure $f=0.01$. We
indicate the specific case $M=56.27M_{\odot}$ and $R=504$ Km, which include a
neutron star in the center with mass $M=1.4M_{\odot}$ and $R=12.32$ Km. (b)
The same as in Fig. 1(b).
Figure 3: The pressure of DM and neutron star matter as a function of the
distance $r$ for the specific configuration denoted in Fig. 2(a)

Figure 4:  (a) The M-R dependence for the case of pure bosonic DM (dashed
line) DMNS object (solid line) of a particle with mass $m_{\chi}=100$ MeV,
interaction $y=0.5$ and fraction $f=4.1\cdot 10^{-5}$. The arrow indicate the
specific case where $M=864.27M_{\odot}$ and $R=7813.37$ Km (correspond to a
neutron star with mass $M=1.64M_{\odot}$ and radius $R=12.3$ Km in the
center). (b) The same as in Fig. 1(b).

Figure 5: (a) The M-R dependence for the case of pure bosonic DM (dashed line)
DMNS object (solid line) of a particle with mass $m_{\chi}=1500$ MeV,
interaction $y=0.5$ and fraction $f=0.01$. The arrow indicate the specific
case where $M=56.24M_{\odot}$ and $R=503.41$ Km (correspond to a neutron star
with mass $M=1.42M_{\odot}$ and radius $R=12.31$ Km in the center). (b) The
same as in Fig. 1(b).

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# Same Words, Different Meanings: Semantic Polarization in Broadcast Media
Language Forecasts Polarization on Social Media Discourse

Xiaohan Ding,1 Mike Horning, 2 Eugenia H. Rho 1

###### Abstract

With the growth of online news over the past decade, empirical studies on
political discourse and news consumption have focused on the phenomenon of
filter bubbles and echo chambers. Yet recently, scholars have revealed limited
evidence around the impact of such phenomenon, leading some to argue that
partisan segregation across news audiences cannot be fully explained by online
news consumption alone and that the role of traditional legacy media may be as
salient in polarizing public discourse around current events. In this work, we
expand the scope of analysis to include both online and more traditional media
by investigating the relationship between broadcast news media language and
social media discourse. By analyzing a decade’s worth of closed captions (2.1
million speaker turns) from CNN and Fox News along with topically
corresponding discourse from Twitter, we provide a novel framework for
measuring semantic polarization between America’s two major broadcast networks
to demonstrate how semantic polarization between these outlets has evolved
(Study 1), peaked (Study 2) and influenced partisan discussions on Twitter
(Study 3) across the last decade. Our results demonstrate a sharp increase in
polarization in how topically important keywords are discussed between the two
channels, especially after 2016, with overall highest peaks occurring in 2020.
The two stations discuss identical topics in drastically distinct contexts in
2020, to the extent that there is barely any linguistic overlap in how
identical keywords are contextually discussed. Further, we demonstrate at-
scale, how such partisan division in broadcast media language significantly
shapes semantic polarity trends on Twitter (and vice-versa), empirically
linking for the first time, how online discussions are influenced by televised
media. We show how the language characterizing opposing media narratives about
similar news events on TV can increase levels of partisan discourse online. To
this end, our work has implications for how media polarization on TV plays a
significant role in impeding rather than supporting online democratic
discourse.

## Introduction

Mass media plays a vital role in democratic processes by influencing how
institutions operate, political leaders communicate, and most importantly, how
citizens engage in politics (McLeod, Scheufele, and Moy 1999). Although it is
no surprise that America’s two political divides speak different languages
(Westfall et al. 2015), research has also shown that partisan language in news
media has sharply increased in recent years, particularly in broadcast news
(Horning 2018). This is concerning given that news consumption is critical for
helping the public understand the events around them. According to Agenda
Setting Theory, the language used by the media to frame and present current
events impacts how the public perceives what issues are important (McCombs
1997; Russell Neuman et al. 2014).
While some may have the impression that mainstream legacy media is decreasing
in relevancy amid the explosive growth of online news via websites and social
media, American news consumption is still overwhelmingly from television,
accounting for nearly five times as much as online news consumption across the
public (Allen et al. 2020). Despite the notion that TV news consumption is
more “passive” than reading the news, research shows that people tend to
recall televised news better than online news (Eveland, Seo, and Marton 2002).
Further, a recent study comparing TV vs. internet news consumption found that
there are four times as many Americans who are partisan-segregated via TV than
via online news. In fact, TV news audiences are several times more likely to
maintain their partisan news diets overtime, and are much narrower in their
sources while even partisan online news readers tend to consume from a variety
of sources (Muise et al. 2022).
Yet studies on media polarization and ensuing public discourse are
overwhelmingly based on online content (Garimella et al. 2021). For example,
even research that analyzes data from traditional news outlets, solely relies
on tweets from the official Twitter accounts of newspapers, TV shows, and
radio programs rather than the direct transcription of content from these
legacy media sources (Recuero, Soares, and Gruzd 2020). This is due to the
fact that unlike online information, legacy media data (e.g., closed captions)
are harder to collect, exist in formats incompatible for quick pre-processing
(e.g., srt files), and scattered across institutions that lack incentives to
share data with academics. Hence, much of how mainstream legacy media affects
online discourse is unknown.
In that sense, our analysis of a decade’s worth of closed captions from 24hr-
broadcast TV news programs from America’s two largest news stations presents a
unique opportunity to empirically demonstrate how linguistic polarization in
broadcast media has evolved over time, and how it has impacted social media
discourse. In this work, we examine how semantic differences in broadcast
media language have evolved over the last $11$ years between CNN and Fox News
(Study 1), what words are characteristic of the semantic polarity peaks in
broadcast media language (Study 2), whether semantic polarity in TV news
language forecasts polarization trends in social media discourse, and how
language plays a role in driving relational patterns from one to the other
(Study 3).
In Study 1, we leverage techniques in natural language processing (NLP) to
develop a method that quantitatively captures how semantic polarization
between CNN and Fox News has evolved from 2010 to 2020 by calculating the
semantic polarity of how socially important, yet politically divided topics
(racism, Black Lives Matter, police, immigration, climate change, and health
care) are discussed by the two news channels. We then use a model
interpretation technique in deep learning to linguistically unpack what may be
driving these spikes by extracting contextual tokens that are most predictive
of how each station discusses topical keywords in 2020 (Study 2). To
investigate whether partisan trends in broadcast media language influence
polarity patterns in social media discourse, we use Granger causality to test
whether and how semantic polarization between the two TV news stations
forecasts polarization across Twitter audiences replying to @CNN and @FoxNews
(Study 3). Finally to understand the language that drives the Granger-causal
relations in how semantic polarity trends in televised news affect that across
Twitter users (and vice-versa), we identify tokens that are most predictive of
how topical keywords are discussed on TV vs. Twitter, separated by lag lengths
that correspond to Granger-causality significance. Our contributions are as
follows:

  * •

We provide a novel framework for quantifying semantic polarization between two
entities by considering the temporality associated with how semantic
polarization evolves over time. Prior research that quantifies polarization as
an aggregate measure from a single longitudinal data dump often leaves out key
temporal dynamics and contexts around how polarity unfolds across time. Our
framework incorporates temporal fluctuations by computing diachronic shifts
using contextual word embeddings with temporal features.

  * •

In showing how semantic polarization in broadcast media has evolved over the
last 11 years, we go beyond providing a mere quantification of polarization as
a metric by using Integrated Gradients to identify attributive tokens as a
proxy to understand the contextual language that drives the 2020 ascent in
semantic polarity between the two news stations.

  * •

We address the question of whether and how polarization in televised news
language forecasts semantic polarity trends across Twitter, providing new
evidence around how online audiences are shaped in their discourse by TV news
language — an important link that has not been empirically established at-
scale in prior research.

  * •

Finally, we use model interpretation to extract lexical features from
different entities, to show which words drive significant Granger-causal
patterns in how broadcast media language shapes Twitter discourse and vice-
versa, thereby highlighting the manner in which language plays a key role in
driving semantic polarity relations between online discussions and broadcast
media language.

Our findings are one of the first to quantify how language characterizing
opposing media narratives about similar news events on TV can increase levels
of partisan discourse online. Results from this work lend support to recent
scholarship in communications research, which theorizes that both media and
public agendas can influence each other, and that such dynamics can polarize
the manner in which the public engages in discourse, thereby influencing
democratic decision-making at-large.

## Related Work

### Temporal Dynamics in Linguistic Polarization

Scholars have measured linguistic polarization through stance (Dash et al.
2022), toxicity (Sap et al. 2019), sentiment detection (Yang et al. 2017),
topic modeling (Ebeling et al. 2022), and lexicon-dictionaries (Polignano et
al. 2022). Such methods typically capture an aggregated snapshot of
polarization across large textual corpora, providing a static quantification
of media bias based on preset criteria. As a result, such approaches seldom
capture temporal fluctuations in semantic polarity. Only a few research to
date quantify linguistic polarization over time. For example, researchers have
measured partisan trends in congressional speech by defining polarization as
the expected posterior probability that a neutral observer would infer a
speaker’s political party from a randomly selected utterance (Gentzkow,
Shapiro, and Taddy 2019) across various issues. Demszky et al. use this
Bayesian approach to capture how social media discussions on mass shootings
become increasingly divisive (2020).

Such methods, however, capture linguistic polarization as a general metric
across nearly all aggregated words within a textual corpus. Given the powerful
salience of certain topical keywords that are inseparable from American
politics, unlike prior work, we focus on how specific keywords polarize over
time. We depart from previous approaches by devising a framework that captures
semantic polarity as a function of how two different entities semantically
diverge across time in their contextual use of identical words that are
central to the American public discourse. Specifically, we measure linguistic
polarization by capturing the diachronic shifts in how two news stations use
the same topical words on their news programs over an 11-year period.

Further, in effort to understand the linguistic drivers behind how and why
semantic polarization evolves, we aim to identify the source of diachronic
shifts based on how two different entities use identical, politically
contentious keywords. Few research has endeavored to detect causal factors
underlying how the meaning of words changes over time, which remains an open
challenge in NLP scholarship (Kutuzov et al. 2018). Hamilton et al. show how
word meanings change between consecutive decades due to cultural shifts (e.g.,
change in the meaning of “cell” driven by technological advancement: prison
cell vs. cell phone) (2016). Yet such research typically makes a priori
assumptions that the language between two textual corpora of comparison are
significantly related without statistically demonstrating how so. On the other
hand, research that do provide evidence of statistical relations between two
separate textual data (Dutta, Ma, and Choudhury 2018), generally do not
explain what words drive the direction of semantic influence from one corpus
to another. We overcome these limitations: first, we statistically validate
the existence of a significant semantic relationship between two textual
corpora, TV news language and social media discourse, through Granger-
causality (Study 3). Then, we strategically separate our data by lag-times
associated with significant Granger-causal relations and apply a deep learning
interpretation technique to demonstrate which contextual words from TV news
language influences Twitter discussions around specific topical keywords (and
vice-versa) over time.

### Who Influences Who? Setting a Media Agenda

On any given day, newsrooms select news on a wide range of topics that cover a
variety of issues. According to Agenda Setting Theory, this selection process
leads audiences to see certain issues as more significant than others (McCombs
1997). Agenda Setting was particularly useful in decades past when media was
much more consolidated. In the U.S. for example, three major networks (NBC,
ABC, and CBS) provided the bulk of broadcast news content, and so their news
agendas had broad influence on what audiences saw as important. However,
today’s media landscape is much more fragmented. People receive their news
from any number of sources including television, newspapers, radio, online
websites, and social media. In such an environment, Agenda Setting has certain
limitations as the theory assumes that audiences are relatively passive and
simply receive information from the media. This was true when news flowed one-
way from the media to the mass public.

Topic | Topical Keywords
---|---
1 | Racism | racism, racist
2 | Black Lives Matter | blacklivesmatter
3 | Police | police
4 | Immigration | immigration, immigrants
5 | Climate Change | climate change, global warming
6 | Health Care | health care

Table 1: Our data consists of speaker turns that contain 9 target keywords
pertaining to six core topics.

By contrast nowadays, the two-way form of communication afforded by the
internet and social media makes it possible for the public to both influence
media agendas and be influenced by them (Papacharissi 2009; Barnard 2018). As
a result, new scholarship has argued through Intermedia Agenda Setting Theory
that media agendas do not come entirely from within their own organizations,
but from two other sources: other media and the mass audience. In the latter
case, for example, audiences themselves can influence media agendas through
online affordances (e.g., retweeting, commenting, sharing), to raise certain
issues to prominence online (Rogstad 2016). In this work, we explore these new
emerging dynamics with an interest in not only understanding how news agendas
are constructed, but how the possible adoption of different agendas might
influence agenda dynamics as media interact with the public online.

## Study 1: Evolution of Semantic Polarity in Broadcast Media Language
(2010-2020)

NLP researchers studying diachronic shifts have been leveraging word
embeddings from language models to understand how the meaning of a given word
changes over time (Kutuzov et al. 2018). In Study 1, we adapt methodological
intuitions from such prior work to calculate how semantic polarization — the
semantic distance between how two entities contextually use an identical word
— evolves over time. While scholars have examined online polarization in the
context of understanding partisan framing and public discourse around current
events, our work is the first to quantify and capture the evolution of
semantic polarization in broadcast media language.

### Dataset

Our data consists of transcribed closed captions from news shows that were
broadcast 24-7 by CNN and Fox News from January 1, 2010 to December 31, 2020,
which was provided by the Internet Archive and the Stanford Cable TV News
Analyzer. We computationally extracted closed captions pertaining to each
televised segment from a total of $181K$ SRT (SubRip Subtitle) files —
consisting of $23.8$ million speaker turns or $297$ billion words spoken
across the decade (Figure 1). To focus our analysis on how socially important
yet politically controversial topics were discussed between the two major news
networks, we narrowed down our sample of speaker turns to those that contained
keywords associated with six politically contentious topics: racism, Black
Lives Matter, police, immigration, climate change, and health care (Table 1).
We extracted all sentences containing one of the nine topical keywords, giving
us a final corpus of $2.1$ million speaker turns or $19.4$ billion words. All
closed captions pertaining to commercials were removed using a matching search
algorithm. (Tuba, Akashe, and Joshi 2020).

Figure 1: Volume of televised closed captions (word count) from CNN and Fox
News stations from 2010 to 2020.

### Method and Analysis

Figure 2: Methodological framework of deriving semantic polarization (how CNN
& Fox News use the keyword racist in 2010). Figure 3: Evolution of semantic
polarization in how CNN and Fox News use topically contentious keywords from
2010 to 2020.

With more recent advances in deep learning, researchers have leveraged the
ability of transformer-based language models to generate contextualized
embeddings to detect the semantic change of words across time (Kutuzov et al.
2018). Similarly, we leverage contextual word representations from BERT
(Bidirectional Encoder Representations from Transformers) (Devlin et al. 2019)
to calculate the semantic polarity in how CNN and Fox News use topical
keywords over time.

First, we use BERT to learn a set of embeddings for each keyword from the
hidden layers of the model for every year from 2010 to 2020, to quantify how
much the embeddings for a given topical keyword from CNN semantically differ
from those of Fox across an 11-year period. We extracted all contextual word
representations from our corpus of $2.1$ million speaker turns. Then, for
every occurrence of the $9$ topical keywords in the data, we calculated the
semantic distance between each contextual word representation from CNN and Fox
using cosine values. The use of cosine values of BERT word embeddings is
standard in machine translation and other NLP domains for computing contextual
similarities in how tokens are used in sentences (Zhang et al. 2020). Our
calculation of semantic polarization between how CNN vs. Fox News uses a
topical keyword for a given year is as follows.

Given the set of word embeddings for a keyword in a given year $t$ from CNN:

$C_{t}=\left\\{w^{c}_{1},w^{c}_{2},w^{c}_{3},\ldots\right\\}$ (1)

and the set of word embeddings for a keyword in a given year $t$ from Fox
News:

$F_{t}=\left\\{w^{f}_{1},w^{f}_{2},w^{f}_{3},\ldots\right\\}$ (2)

we define the semantic polarity (SP) between CNN and Fox News as:

$\operatorname{SP}\left(C_{t},F_{t}\right)=\frac{\sum_{w^{c}_{i}\in
C_{t},w^{f}_{j}\in F_{t}}1-\cos\left(w^{c}_{i},w^{f}_{j}\right)}{n_{1}n_{2}}$
(3)

where:

$C_{t}$ | ${}:{}$ |  set of word embeddings from CNN
---|---|---
$F_{t}$ | ${}:{}$ |  set of word embeddings from Fox News
$w^{c}_{i}$ | ${}:{}$ |  word embedding of a keyword from CNN
$w^{f}_{j}$ | ${}:{}$ |  word embedding of a keyword from Fox News
$n_{1}$ | ${}:{}$ |  number of word embeddings from CNN
$n_{2}$ | ${}:{}$ |  number of word embeddings from Fox News

In Figure 2, we visualize our methodological framework to illustrate how we
derive the semantic polarization (SP) score in how CNN vs. Fox News uses the
keyword, “racist” in 2010. First, we extract all contextual word embeddings
(each of which is a $768\times 1$ tensor) associated with every occurrence of
the word “racist” in our corpus of speaker turns from Fox and CNN in 2010.
Next, we calculate the cosine distance between the tensors associated with the
word representation “racist” in the CNN corpus and those from the Fox News
corpus. Finally, we use Equation 3 to calculate the average of all cosine
distance values to obtain the semantic polarization score or the semantic
distance between how Fox News and CNN uses the word “racist” in 2010.

### Results

Between 2010 and 2020, semantic polarity between America’s two largest TV news
stations increased with a significant upward trend starting in 2015 and 2016
(Figure 3). Over the past decade, CNN and Fox News became increasingly
semantically divergent in how they used the topical keywords “racist”,
“racism”, “police”, “blackbivesmatter”, “immigrant”, “immigration”, “climate
change”,“global warming”, and “health care” in their broadcasting language.
Though there is a general dip in semantic polarity around 2013-14 across all
keywords with the exception of “health care”, semantic polarity between the
two stations starts to sharply increase every year on average by $112\%$
across all keywords starting in 2016. These results corroborate findings from
a recent study analyzing the airtime of partisan actors on CNN and Fox, which
shows that the two stations became more polarized in terms of visibility bias
particularly following the 2016 election (Kim, Lelkes, and McCrain 2022).
Further, the highest peaks generally occur in 2020 for the terms “racism”,
“racist”, “blacklivesmatter”, “police”, along with “immigrant”, and “global
warming” (Table 2). Specifically, semantic polarity is highest for the keyword
“police” in 2020, denoting that across the nine keywords, CNN and Fox were
most polarized in how they semantically used the word “police” in their news
programs in 2020.

Keywords | Min SP | Max SP
---|---|---
racism | 0.095(2014) | 0.289(2020)
racist | 0.100 (2014) | 0.341(2020)
blacklivesmatter | 0.148(2015) | 0.320(2020)
police | 0.119(2014) | 0.574(2020)
immigration | 0.103(2013) | 0.362(2016)
immigrant | 0.157(2013) | 0.383(2020)
climate change | 0.144(2013) | 0.334(2018)
global warming | 0.175(2014) | 0.401(2020)
health care | 0.076(2010) | 0.496(2018)

Table 2: Range of 2020 semantic polarity scores.

## Study 2: Words that Characterize Semantic Polarity between Fox News & CNN
in 2020

### Method and Analysis

Semantic polarity between Fox and CNN is predominantly high in 2020, echoing
the series of highly publicized events in the media (e.g., COVID-19, George
Floyd, and BLM demonstrations) that reified a widening ideological gap among
the American public on a number of issues. Hence, in Study 2, we aim to go
beyond providing a mere quantification of polarization by examining how the
language surrounding the use of contentious keywords by CNN and Fox
contributes to the 2020 peak in semantic polarity. In other words, how does
CNN and Fox News contextually differ in their use of topical keywords on their
news programs in 2020? To answer this question, we identified attributive
words or contextual tokens that are most predictive of whether a speaker turn
containing a topical keyword was from CNN or Fox in 2020. This task entailed a
two-step process. First, we trained a BERT-based classifier using the 2020
corpus of closed captions from both stations to predict whether a speaker turn
was from CNN or Fox. Then, we used a model interpretation technique called
Integrated Gradients (Sundararajan, Taly, and Yan 2017) to identify which
words (except for the topical keyword) in each speaker turn contributed most
to the classification decision.

#### Classifying 2020 Speaker Turns.

To identify whether a speaker turn was broadcast from Fox or CNN in 2020, we
built six BERT-based classifiers pertaining to each topic. First, we merged
the 2020 corpus of speaker turns, each containing one of the nine topical
keywords by topic (e.g., speaker turns containing “racism” or “racist” were
merged into one topical corpus).
For each of the six topical corpora, we trained BERT (BERT-Base-Uncased) by
masking $15\%$ of the words in each speaker turn and trained the model to fill
in the masked words using a standard cross-entropy loss function. We then
fine-tuned the adapted model to predict whether a speaker turn was from CNN or
Fox News. For this step, we split the data into $80\%$ training, $10\%$
validation, and $10\%$ test sets. We set batch sizes to $16$, training epochs
to 6 with $3$-fold cross-validation, and used AdamW for optimization with a
learning rate of $2\mathrm{e}{-05}$. We used PyTorch for all model
implementations.

#### Model Interpretation.

To identify the contextual language or the attributive words that contributed
most to the 2020 semantic polarity between CNN and Fox News, we used
Integrated Gradients (IG) to interpret the classification results from our
BERT-classifier in the previous step. IG is an attribution method that allows
us to understand how much an input feature contributes to the output result of
a deep neural network (Sundararajan, Taly, and Yan 2017). This post-hoc
interpretability technique combines the input’s gradients by interpolating in
short increments along a straight line between a baseline $x$ (usually a
vector with all zeros) and the input $x^{\prime}$. Formally, if
$F:R_{n}\rightarrow[0,1]$ represents BERT, then the integrated gradient (IG)
of the $i^{th}$ dimension of $x$ is:

$IG_{i}(x)=\left(x_{i}-x_{i}^{\prime}\right)\times\int_{\alpha=0}^{1}\frac{\partial
F\left(x^{\prime}+\alpha\left(x-x^{\prime}\right)\right)}{\partial
x_{i}}d\alpha$ (4)

Large pre-trained transformer-based language models, such as BERT may have
strong predictive powers, but their multiple nonlinearities prevent users from
directly attributing model outputs to various input features. To overcome this
lack of interpretive insight, we leverage IG to identify words that are most
attributable to each predicted class. Thus, we identify which contextual words
within a speaker turn (input features of a classifier) contribute most to, or
are most predictive of the output decision, namely, whether the speaker turn
is from CNN or Fox News in 2020.

### Results

Our BERT-classifier distinguishes 2020 speaker turns from CNN and Fox News
with a mean accuracy of $75.3\%$ across all six topics (Table 3). Model
performance is highest for speaker turns topically focused on the police,
corresponding to Study 1 findings demonstrating highest SP scores for “police”
across all keywords in 2020.

Topic | Acc. | F1 | Prec. | Recall
---|---|---|---|---
Racism | 0.710 | 0.709 | 0.707 | 0.712
BLM | 0.724 | 0.726 | 0.710 | 0.743
Police | 0.826 | 0.829 | 0.815 | 0.845
Immigration | 0.773 | 0.780 | 0.762 | 0.800
Climate change | 0.737 | 0.710 | 0.750 | 0.675
Health care | 0.750 | 0.752 | 0.748 | 0.757

Table 3: Model performance for station classification.

In Table 4, we show the top 10 words most predictive of how CNN and Fox News
discuss the six topics on their news programs in 2020. To avoid noise caused
by low-frequency words, we limited our token selection to words with a
frequency above the $95$th percentile. We categorized the tokens with the
highest and lowest attribution scores ranging from positive (attributed to
CNN) to negative (attributed to Fox News) values for each topic. As shown,
across all topics, none of the top tokens overlap between the two stations,
indicating the drastically distinct contexts in which the two channels discuss
key topics in 2020. For example, words like “illegal”, “enforcement”, and
“order” contextualize immigration discussions in a rather legalistic manner on
Fox News whereas, “parents”, “family”, “children”, “daughter”, and
“communities” - humanizing words connotative of family relations best predict
how CNN discusses the same topic. Both stations may be discussing the same
topic with identical keywords, but the contextual language surrounding their
discussion is strikingly different. Such divergence sheds light on the
underlying differences in the linguistic signature of televised media language
that help explain the 2020 peak in semantic polarity between the two stations.

## Study 3: How Semantic Polarization in Broadcast Media Language Forecasts
Semantic Polarity in Social Media Discourse

Study 1 shows that semantic polarization in broadcast media language has been
increasing in recent years and overall peaking closer to 2020 during which the
two major stations use starkly contrasting language in their discussion of
identical words (Study 2). Such partisan divide in televised news language is
similarly observed online where public discourse is becoming increasingly
fraught with political polarization (Chinn, Hart, and Soroka 2020). To what
degree is broadcast media one of the causes of online polarization in today’s
agora of public discourse on social media? Do the temporal changes in semantic
polarity in broadcast media significantly predict ensuing temporal changes in
the semantic polarization across social media discourse?

To answer this, we used Granger causality to test whether semantic polarity
between CNN and Fox News broadcast media language over the last decade
Granger-causes the semantic polarity between Twitter users who follow and
mention @CNN or @FoxNews in their tweets that contain one of the nine keywords
(“racist”, “racism”, “police”, “blackbivesmatter”, “immigrant”, “immigration”,
“climate change”,“global warming”, and “health care”) over the same time
period.

### Twitter Dataset

For our social media corpus, we collected all tweets between 2010 and 2020
based on the following criteria: (1) written by users who follow both @CNN and
@FoxNews; (2) mention or are replying to either @CNN or @FoxNews; (3) contain
one of the nine keywords. Our final corpus amounted to $131,627$ tweets
spanning over a decade. The volume of tweets and mean word count per tweet are
shown in Table 5.

Racism | Black Lives Matter | Climate Change
---|---|---
CNN | Fox News | CNN | Fox News | CNN | Fox News
Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr.
president | 0.457 | called | -0.482 | confederate | 0.717 | party | -0.505 | human | 0.483 | gun | -0.440
whitehouse | 0.348 | anti | -0.442 | people | 0.350 | video | -0.475 | science | 0.435 | left | -0.419
senator | 0.224 | crime | -0.413 | we | 0.285 | shooting | -0.454 | scientists | 0.289 | democrats | -0.385
there | 0.155 | left | -0.398 | symbol | 0.281 | mayor | -0.440 | states | 0.259 | democratic | -0.369
protests | 0.153 | accused | -0.380 | saw | 0.261 | anti | -0.400 | today | 0.244 | agenda | -0.352
comments | 0.146 | school | -0.376 | thousands | 0.255 | weekend | -0.394 | climate | 0.236 | party | -0.349
he | 0.141 | criminal | -0.330 | came | 0.249 | night | -0.351 | california | 0.207 | progressive | -0.324
conversation | 0.128 | democratic | -0.325 | players | 0.247 | democratic | -0.349 | believe | 0.207 | right | -0.276
brutality | 0.111 | government | -0.319 | know | 0.240 | police | -0.340 | issues | 0.203 | voters | -0.264
ago | 0.102 | bad | -0.302 | they | 0.240 | democrats | -0.335 | important | 0.199 | Obama | -0.264
Police | Immigration | Health Care
CNN | Fox News | CNN | Fox News | CNN | Fox News
Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr.
different | 0.414 | seattle | -0.641 | racist | 0.370 | illegal | -0.787 | vaccines | 0.735 | illegal | -0.647
they | 0.351 | city | -0.537 | Trump | 0.298 | laws | -0.422 | vaccine | 0.525 | businesses | -0.568
certainly | 0.346 | portland | -0.512 | parents | 0.254 | enforcement | -0.367 | va | 0.453 | free | -0.477
racial | 0.295 | minnesota | -0.489 | obama | 0.252 | police | -0.308 | masks | 0.386 | business | -0.459
actually | 0.285 | chicago | -0.446 | pan | 0.212 | legal | -0.303 | deaths | 0.336 | open | -0.361
understand | 0.285 | left | -0.414 | family | 0.210 | order | -0.288 | virus | 0.323 | pay | -0.352
know | 0.285 | street | -0.406 | vice | 0.208 | million | -0.278 | faucci | 0.295 | economy | -0.338
shows | 0.278 | riots | -0.401 | daughter | 0.186 | protect | -0.261 | climate | 0.283 | jobs | -0.328
hands | 0.269 | democratic | -0.397 | children | 0.167 | wants | -0.222 | weeks | 0.273 | safe | -0.318
we | 0.267 | crime | -0.395 | communities | 0.167 | law | -0.213 | Trump | 0.259 | city | -0.311

Table 4: Top 10 tokens with the highest (attributed to CNN) and lowest
(attributed to Fox News) attribution scores as a proxy for understanding words
that linguistically characterize the 2020 semantic polarity between Fox News
and CNN across six topics.

### Hypothesis Testing with Granger Causality

To test whether temporal patterns in semantic polarity in TV news language
significantly predict semantic polarity trends across Twitter users, we
conducted a Granger causality analysis. Granger causality is a statistical
test to determine whether a time series $X$ is meaningful in forecasting
another time series $Y$ (Granger 1980). Simply, for two aligned time series
$X$ and $Y$, it can be said that $X$ Granger-causes $Y$ if past values
$X_{t-l}\in X$ lead to better predictions of the current $Y_{t}\in Y$ than do
the past values $Y_{t-l}\in Y$ alone, where $t$ is the time point and $l$ is
the lag time or the time interval unit in which changes in $X$ are observed in
$Y$. Using this logic, we tested the following hypotheses:

  * H1. Semantic polarization on TV news significantly Granger-causes semantic polarization on Twitter.

  * H2. Semantic polarization on Twitter significantly Granger-causes semantic polarization on TV.

| Tweet Volume |  Avg. Word Count (per Tweet)
---|---|---
Keyword | FoxNews | CNN | FoxNews | CNN
racism | 8,787 | 8,944 | 24 | 22
racist | 7,887 | 8,795 | 27 | 22
blacklivesmatter | 4,863 | 4,528 | 21 | 23
police | 8,731 | 8,670 | 24 | 22
immigration | 8,163 | 7,883 | 19 | 21
immigrant | 8,239 | 7,721 | 20 | 28
climate change | 7,536 | 7,140 | 21 | 22
global warming | 5,042 | 5,140 | 18 | 17
health care | 7,612 | 6,943 | 20 | 19

Table 5: Volume of tweets and mean word account.

### Method and Analysis

First, we computed the monthly semantic polarity (SP) scores spanning from
2010 to 2020 for a total of $132$ time points (12 months $\times$ 11 years)
for each topical keyword for both the televised closed caption and Twitter
data. We then built $18$ time series using the monthly SP values for each of
the $9$ keywords across $11$ years derived from the closed captions and the
tweets. We then paired each of the TV news language time series with the
Twitter time series by keyword, giving us a total of 9 causality tests per
hypothesis. As a prerequisite for Granger causality testing, we conducted the
Augmented Dickey-Fuller (ADF) test (Cheung and Lai 1995) to ensure that the
value of the time series was not merely a function of time (see Appendix). We
used the serial difference method (Cheung and Lai 1995) to obtain stationarity
for $\Delta TwS_{racism}$ and $\Delta TvS_{BLM}$, which were the only two time
series with an ADF test value greater than the 5% threshold. In total, we
conducted 18 time series analyses to test whether there was a Granger-causal
relationship between the monthly SP values of broadcast media language
($SP_{tv}$) and that of Twitter ($SP_{tw}$) by each of the 9 keywords to
determine the extent to which semantic polarization on TV drives semantic
polarization on Twitter (H1) and vice versa (H2). For both hypotheses, we used
a time-lag ranging from 1-12 months.

Keyword |  Hypos |  Lag |  $F$-value |  $p$-value
---|---|---|---|---
racism | H1 | 2 | 1.70 | 0.0386
H2 | 2 | 0.19 | 0.4526
racist | H1 | 2 | 3.17 | 0.0101
H2 | 5 | 0.36 | 0.8730
blacklivesmatter | H1 | 3 | 2.90 | 0.0376
H2 | 3 | 3.25 | 0.0241
police | H1 | 3 | 0.75 | 0.5189
H2 | 5 | 0.50 | 0.7747
immigration | H1 | 3 | 2.13 | 0.0333
H2 | 1 | 1.11 | 0.2929
immigrant | H1 | 3 | 2.19 | 0.0325
H2 | 1 | 1.11 | 0.2929
climate change | H1 | 7 | 2.00 | 0.0502
H2 | 3 | 3.18 | 0.0262
global warming | H1 | 8 | 0.96 | 0.4691
H2 | 4 | 2.15 | 0.0213
heath care | H1 | 4 | 0.58 | 0.6738
H2 | 3 | 0.72 | 0.5377

Table 6: H1 and H2 results using Granger causality tests. H1: $SP_{tv}$
$\not\to\mathcal{}$ $SP_{tw}$; H2: $SP_{tw}$ $\not\to\mathcal{}$ $SP_{tv}$.

### Results

We observe that changes in semantic polarity patterns on Twitter can be
significantly predicted by semantic polarity trends in broadcast media
language and vice-versa. Table 6, shows Granger causality results for
hypotheses 1 and 2 with corresponding significant lag lengths ($p<0.05$).

#### Hypothesis 1.

As shown in Table 6, semantic polarity trends in broadcast media’s discussion
on racism (keywords: “racism”, “racist”) and immigration (keywords:
“immigration” and “immigrant”) significantly forecasts semantic polarity
shifts in how people discuss these topics on Twitter with a time lag of 2 and
3 months, respectively. In other words, it takes about 2 months for the
influence of semantic polarization in broadcast media language to manifest
across how Twitter users semantically diverge in their discussion on racism,
and about 3 months in how they talk about keywords linked to immigration.

#### Hypothesis 2.

To test whether the directionality of influence is not only such that semantic
polarization in televised news shapes polarity across Twitter conversations,
but also vice-versa, we tested H2. Our results show that for “climate change”
and “global warming”, semantic polarization across how people discuss these
keywords on Twitter Granger-causes how CNN and Fox News semantically diverge
in their use of these words on their shows with a lag of 3 months. This may be
due to the fact that discussions on climate change and global warming have
become increasingly political and less scientific on Twitter (Jang and Hart
2015; Chinn, Hart, and Soroka 2020), therefore raising online prominence of
the topic through controversial political sound bites that may in return, draw
attention from mainstream media outlets as a source for news reporting.

#### Bidirectional Causality.

For Black Lives Matter, there is bidirectional causality, meaning semantic
polarity in how the keyword “blacklivesmatter” is discussed on televised news
programs shapes semantic polarity trends in how users talk about the topic and
vice-versa. This may be due to the fact that BLM is an online social movement,
largely powered by discursive networks on social media. Hence, while users may
draw upon the narratives generated by traditional media outlets in their
Twitter discussions, journalists and broadcast media companies too, may be
attuned to how online users discuss BLM issues on social media.

### Words That Characterize the Relational Trends in Semantic Polarization
Between Broadcast Media and Twitter Discourse

To understand the manner in which language plays a role in how semantic
polarity trends in broadcast media forecasts polarization patterns on Twitter,
for topical keywords with significant Granger-causality results, we identified
contextual tokens that are most characteristic of how each topical keyword is
discussed on TV vs. Twitter separated by the corresponding lag lengths based
on results shown in Table 6.

Hence, given the 132 time points (12 months $\times$ 11 years) represented by
$t_{ij}$, where $i$ represents the month $(i\in[1,12])$, $j$ is the year
$(j\in[1,11])$, and $l$ is the value of the lag length in months corresponding
to significant Granger coefficients $(l\in[1,8])$, we first re-organized our
TV news data with $t_{i^{\prime}j}$ time points, where ${i^{\prime}}$
represents the value of the maximum month minus $l$ with the range:
$\left(i^{\prime}\in[1,12-l]\right)$ and our Twitter data with
$t_{i^{\prime\prime}j}$ time points, where ${i^{\prime\prime}}$ represents the
value of the minimum month plus $l$ with the range:
$\left(i^{\prime\prime}\in[1+l,12]\right)$. For topical keywords where
semantic polarity in Twitter Granger-causes semantic polarity trends in
broadcast media language, we interchange the values of $i^{\prime}$ and
$i^{\prime\prime}$. Next, following a similar approach to Study 2, we
separately fed the TV news and Twitter corpora into a BERT-classifier and used
Integrated Gradients to identify the top 10 most predictive tokens for each
topical keyword.

Results are shown in Tables 8 \- 11 (Appendix) where we demonstrate the top 10
contextual tokens that are most attributive of how each topical keyword is
used either by a speaker from CNN or Fox News stations or by a user responding
to @CNN or @FoxNews in their tweet during time periods separated by monthly
lag lengths corresponding to significant Granger-causal relationships.

As shown by the bolded tokens, a fair proportion of the top 10 words most
characteristic of how televised news programs (CNN vs. Fox News) and Twitter
users (replying to @CNN vs. @FoxNews) discuss topical keywords overlap quite a
bit, suggesting that these tokens are semantically indicative of how
linguistic polarity in one media manifests in another over time. For example,
six of the top 10 tokens predictive of how CNN broadcast news contextually
uses the keyword “racism” are identical to that of how users on Twitter,
replying to @CNN, use “racism” in their tweets: “believe”, “today”,
“president”, “Trump”, “campaign”, “history”, “issue”.

For “blacklivesmatter” where the Granger-causality relationship is
bidirectional, words most predictive of semantic polarity in broadcast news
that drive polarized discourse on Twitter are different from the tokens on
Twitter that drive polarity in televised news language. For example, the set
of tokens (“violence”, “matter”, “white”, “support”, “blacks”) most predictive
of how TV news programs on Fox News talk about BLM that appear three months
later in tweets replying to @FoxNews, are strikingly different from the set of
words (“blacks”, “cities”, “democrats”, “lives”, “moral”, “organization”, and
“shoot”) that best characterize the tweets replying to @FoxNews, which appear
three months later on the Fox News channel.

## Discussion

The rising levels of semantic polarity between the two major broadcast news
organizations, as demonstrated in our work may render people’s ability to
reach across partisan divides and to perceive and solve issues democratically
more difficult. The way CNN and Fox News discuss identical keywords on their
programs is remarkably distinct in 2020 where semantic polarity between the
two stations reaches its peak over an 11-year period, corroborating the
widening partisan media gap highlighted by recent scholarship. Framing Theory
argues that even subtle changes in the wording around how an issue is
described by the media can significantly influence how audiences interpret the
issue (Scheufele 2000; Entman 2003). Yet, our findings show that the
contextual language driving semantic polarization in broadcast media is not
nuanced at all. The surrounding words that characterize how each station
discusses topically important keywords are drastically different, to the
extent that identical words seem to reflect different meanings altogether.
This is a crucial point of consideration, as linguistic cues in the media can
play a powerful role in selectively reifying certain aspects of the perceived
reality of an issue while downplaying others. Our findings suggest that TV
news language does not only shape how online audiences perceive issues, but
also how they talk about them.

In linguistics, collocation is the property of language where two or more
words appear in each other’s company with greater than random chance (Hoey
2005), such as “illegal” and “immigrants” in Fox News and “climate change” and
“science” from CNN, as shown in our findings. Repeated encounters with
collocated words drive what linguists call lexical priming (Hoey 2005), in
which a priming word (e.g., ”blacklivesmatter”) provokes a particular target
word (“protests” for CNN and “violence” for Fox) more strongly and quickly
than disparate words encountered more rarely. In this vein, online audiences
who consume very different perceived realities from the media may be lexically
primed through repeated exposure to collocated words that frame identical
issues in acutely contrasting contexts. This may help theorize why TV news
language can shape how online audiences engage in public discourse as
demonstrated in this work. Semantic polarization in televised media not only
forecasts semantic polarity trends on Twitter, but the words that characterize
broadcast media polarization re-appear across Twitter discussions, separated
by significant lag months. Our results demonstrate that the language
characterizing opposing media narratives around topically similar news events
on TV can be linguistically mimicked in how social media users are polarized
in their discourse around important social issues.

Limitations. Differences in cosine values between contextual word
representations stem not only from semantic, but also from positional
differences of words in sentences. Although word embeddings generally embody
contextual nuances, we acknowledge that our work predominantly considers
semantic rather than syntactic aspects, and that to some extent our
calculation of semantic polarity could embody syntactic differences in how
keywords are discussed. Furthermore, our findings pertain to American
political contexts, which might not be generalizable to foreign public
discourse and media language. For future work, we aim to apply our model to
relevant textual corpora in other languages by incorporating cross-lingual
transfer learning methods to better understand the generalizability of our
model by comparing distributional differences with cross-lingual data.

## Ethics Statement

We aim to strictly adhere to the AAAI Code of Ethics and Conduct by ensuring
that no personal information of Twitter users was collected nor compromised
throughout our project. All data in this work are securely stored on servers
only accessible by the authors. Our semantic polarization framework is made
publicly available on the authors’ GitHub page and can be applied on a variety
of textual corpora with diachronic and contrastive properties.

##  Appendix A Appendix

Time Series | ADF |  Threshold (1%) |  Threshold (5%) | Conclusion
---|---|---|---|---
$TwS_{1}$ | -8.52 | -3.48 | -2.88 | stat
$TwS_{2}$ | -1.86 | -3.45 | -2.88 | non-stat
$\Delta TwS_{2}$ | -5.28 | -2.69 | -1.85 | stat
$TwS_{3}$ | -4.12 | -3.43 | -2.82 | stat
$TwS_{4}$ | -7.43 | -3.48 | -2.87 | stat
$TwS_{5}$ | -8.01 | -3.48 | -2.85 | stat
$TwS_{6}$ | -6.80 | -3.47 | -2.88 | stat
$TwS_{7}$ | -4.12 | -3.48 | -2.82 | stat
$TwS_{8}$ | -7.78 | -3.46 | -2.84 | stat
$TwS_{9}$ | -5.78 | -3.48 | -2.82 | stat
$TvS_{1}$ | -4.48 | -3.48 | -2.88 | stat
$TvS_{2}$ | -7.87 | -3.48 | -2.87 |  stat
$TvS_{3}$ | -2.30 | -3.21 | -2.88 | non-stat
$\Delta TvS_{3}$ | -8.53 | -2.35 | -1.74 | stat
$TvS_{4}$ | -3.59 | -3.43 | -2.83 | stat
$TvS_{5}$ | -8.85 | -3.48 | -2.83 | stat
$TvS_{6}$ | -3.79 | -3.41 | -2.86 | stat
$TwS_{7}$ | -5.22 | -3.42 | -2.81 | stat
$TwS_{8}$ | -7.17 | -3.42 | -2.89 | stat
$TwS_{9}$ | -4.45 | -3.49 | -2.88 | stat

Table 7: ADF test results showing whether the Twitter and TV news time series
data are stationary (stat) or non-stationary (non-stat).

Keyword: “racism” (lag: 2 months) | Keyword: “racist” (lag: 2 months)
---|---
CNN | FoxNews | CNN | FoxNews
TV | Twitter (+2 months) | TV | Twitter (+2 months) | TV | Twitter (+2 months) | TV | Twitter (+2 months)
Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr.
believe | 0.25 | believe | 0.18 | right | -0.30 | system | -0.17 | systemic | 0.27 | Trump | 0.20 | crime | -0.37 | Africa | -0.22
men | 0.25 | issues | 0.18 | party | -0.29 | basis | -0.13 | president | 0.25 | terrorism | 0.19 | states | -0.36 | politics | -0.20
Americans | 0.24 | history | 0.18 | police | -0.29 | party | -0.12 | hate | 0.22 | children | 0.19 | politics | -0.31 | crime | -0.20
today | 0.24 | he | 0.17 | marginalized | -0.29 | media | -0.12 | country | 0.20 | president | 0.17 | Africa | -0.30 | standard | -0.15
president | 0.22 | presidents | 0.16 | black | -0.29 | Africa | -0.12 | think | 0.18 | hate | 0.14 | black | -0.29 | Africans | -0.14
Trump | 0.22 | we | 0.16 | media | -0.28 | diversity | -0.12 | trying | 0.17 | party | 0.13 | Americans | -0.22 | parents | -0.13
understand | 0.21 | hate | 0.15 | Obama | -0.26 | guilty | -0.11 | Trump | 0.17 | white | 0.12 | right | -0.21 | share | -0.12
campaign | 0.17 | today | 0.14 | anti | -0.21 | right | -0.10 | years | 0.16 | bias | 0.12 | white | -0.20 | please | -0.11
history | 0.17 | campaign | 0.13 | law | -0.21 | suicide | -0.11 | history | 0.16 | years | 0.11 | police | -0.16 | surveillance | -0.08
issue | 0.13 | Trump | 0.11 | problem | -0.20 | black | -0.09 | party | 0.15 | presents | 0.10 | surveillance | -0.15 | reforms | -0.08

Table 8: Top 10 tokens most predictive of how CNN and Fox News TV stations and
Twitter users replying to @CNN and @FoxNews use keywords topically related to
racism.

Keyword: “immigrant” (lag: 3 months) | Keyword: “immigration” (lag: 3 months)
---|---
CNN | FoxNews | CNN | FoxNews
TV | Twitter (+3 months) | TV | Twitter (+3 months) | TV | Twitter (+3 months) | TV | Twitter (+3 months)
Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr.
tax | 0.26 | charged | 0.20 | bid | -0.26 | killer | -0.22 | come | 0.25 | white | 0.22 | law | -0.26 | legally | -0.24
united | 0.26 | make | 0.20 | health | -0.25 | right | -0.21 | family | 0.24 | law | 0.21 | people | -0.24 | scouts | -0.20
Trump | 0.26 | united | 0.19 | immigration | -0.25 | immigration | -0.21 | united | 0.23 | united | 0.19 | policies | -0.22 | policies | -0.17
country | 0.25 | parents | 0.17 | right | -0.24 | healthcare | -0.18 | rights | 0.22 | Russia | 0.18 | public | -0.20 | international | -0.17
care | 0.24 | family | 0.16 | state | -0.20 | American | -0.16 | country | 0.22 | country | 0.17 | president | -0.18 | safety | -0.16
know | 0.24 | temporarily | 0.15 | people | -0.19 | peaceful | -0.14 | security | 0.21 | visa | 0.16 | legally | -0.17 | public | -0.15
think | 0.21 | country | 0.14 | president | -0.15 | health | -0.13 | Trump | 0.21 | security | 0.15 | federal | -0.16 | illegal | -0.14
white | 0.20 | immigrants | 0.14 | American | -0.15 | president | -0.12 | white | 0.20 | court | 0.12 | system | -0.15 | election | -0.14
immigrants | 0.19 | prison | 0.13 | law | -0.11 | liberal | -0.12 | Russia | 0.19 | police | 0.12 | order | -0.15 | praises | -0.11
lawyer | 0.18 | obviously | 0.11 | new | -0.10 | Trump | -0.12 | way | 0.19 | rights | 0.10 | illegal | -0.15 | Trump | -0.10

Table 9: Top 10 tokens most predictive of how CNN and Fox News TV stations and
Twitter users replying to @CNN and @FoxNews use keywords topically related to
immigration.

Keyword: “climate change” (lag: 3 months) | Keyword: “global warming” (lag: 4 months)
---|---
CNN | FoxNews | CNN | FoxNews
TV (+3 months) | Twitter | TV (+3 months) | Twitter | TV (+4 months) | Twitter | TV (+4 months) | Twitter
Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr.
science | 0.28 | years | 0.24 | president | -0.26 | policy | -0.23 | important | 0.24 | human | 0.23 | Obama | -0.23 | Obama | -0.24
years | 0.24 | threatened | 0.23 | right | -0.25 | job | -0.22 | water | 0.23 | drugs | 0.23 | future | -0.23 | hurricanes | -0.24
primarily | 0.24 | science | 0.21 | democrats | -0.22 | struggle | -0.22 | science | 0.23 | government | 0.22 | national | -0.22 | protect | -0.23
time | 0.24 | national | 0.21 | economy | -0.22 | presidential | -0.21 | lives | 0.22 | water | 0.20 | rights | -0.22 | communities | -0.22
people | 0.23 | geography | 0.21 | jobs | -0.22 | right | -0.20 | health | 0.22 | condition | 0.19 | Trump | -0.21 | Trump | -0.22
health | 0.23 | diseases | 0.19 | policy | -0.22 | violence | -0.20 | condition | 0.20 | teenager | 0.18 | gas | -0.20 | forest | -0.21
world | 0.23 | ocean | 0.18 | care | -0.21 | diet | -0.19 | world | 0.19 | health | 0.17 | economy | -0.20 | economy | -0.17
think | 0.22 | issues | 0.13 | energy | -0.20 | economy | -0.19 | fossil | 0.19 | marketing | 0.16 | energy | -0.20 | they | -0.17
ocean | 0.22 | world | 0.11 | Trump | -0.18 | democrats | -0.19 | issue | 0.19 | science | 0.16 | immigration | -0.19 | USA | -0.17
issues | 0.21 | predator | 0.10 | global | -0.16 | Trump | -0.17 | environment | 0.17 | important | 0.14 | green | -0.17 | gas | -0.15

Table 10: Top 10 tokens most predictive of how CNN and Fox News TV stations
and Twitter users replying to @CNN and @FoxNews use keywords topically related
to climate change.

Keyword: “BlackLivesMatter” (lag: 3 months) | Keyword: “BlackLivesMatter” (lag: 3 months)
---|---
CNN | FoxNews | CNN | FoxNews
TV | Twitter (+3 months) | TV | Twitter (+3 months) | TV (+3 months) | Twitter | TV (+3 months) | Twitter
Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr. | Token | Attr.
know | 0.33 | protests | 0.24 | right | -0.24 | Baptist | -0.24 | Americans | 0.25 | Americans | 0.21 | cities | -0.22 | blacks | -0.18
going | 0.32 | people | 0.24 | country | -0.24 | moral | -0.22 | movement | 0.20 | church | 0.21 | democrats | -0.20 | cities | -0.18
people | 0.31 | technology | 0.23 | lot | -0.21 | right | -0.21 | plaza | 0.21 | citizens | 0.18 | lives | -0.20 | democrats | -0.20
plaza | 0.28 | county | 0.21 | violence | -0.20 | toxic | -0.18 | president | 0.23 | movement | 0.23 | mayor | -0.20 | federal | -0.21
lives | 0.27 | movement | 0.21 | way | -0.20 | praising | -0.17 | states | 0.21 | powerful | 0.17 | moral | -0.23 | Jackson | -0.24
that | 0.27 | lives | 0.20 | white | -0.19 | blacks | -0.17 | that | 0.21 | president | 0.14 | officers | -0.21 | liberals | -0.19
movement | 0.24 | family | 0.20 | support | -0.18 | violence | -0.16 | they | 0.21 | protests | 0.20 | organization | -0.19 | lives | -0.24
president | 0.22 | protesters | 0.20 | blacks | -0.18 | support | -0.15 | today | 0.20 | states | 0.24 | party | -0.24 | moral | -0.20
protesters | 0.18 | virus | 0.20 | want | -0.18 | white | -0.15 | world | 0.21 | world | 0.13 | shoot | -0.18 | organization | -0.18
protests | 0.18 | president | 0.19 | homicides | -0.17 | matters | -0.13 | year | 0.24 | year | 0.17 | cities | -0.22 | shoot | -0.21

Table 11: Top 10 tokens most predictive of how CNN and Fox News TV stations
and Twitter users replying to @CNN and @FoxNews use keywords topically related
to Black Lives Matter.

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