# The Cosmological Constant Potential:
a resolution to the Hubble tension via the cosmological sound horizon

Nima Khosravi<EMAIL_ADDRESS>Department of Physics, Sharif University of
Technology, Tehran 11155-9161, Iran  Department of Physics, Shahid Beheshti
University, 1983969411, Tehran, Iran

###### Abstract

The cosmological constant term can be seen as a constant potential for a
(scalar) field. In this viewpoint, at late times, the field is stopped rolling
and behaves as a cosmological constant ($w=-1$). While at the early universe,
its kinetic term can be dominant and behaves as a stiff fluid ($w=+1$). This
new phase lowers the cosmological sound horizon by increasing the Hubble
parameter for very high redshifts. Consequently, the lower cosmological sound
horizon results in the higher Hubble constant at the present time. This early
phase ends before the photon decoupling, so we do not expect any new physics
after the last scattering surface. We checked this model in the presence of
(reduced) CMB, BAO’s and $H_{0}$ datasets and could show the Hubble tension is
fully relieved.

##  I Introduction:

The tensions and anomalies can lead us to understand better and deeper our
theoretical models as well as observations. In recent years the Hubble
($H_{0}$) tension in cosmology made us to think more about the standard model
of cosmology $\Lambda$CDM which includes the cosmological constant ($\Lambda$)
and the cold dark matter (CDM) as main ingredients. The $H_{0}$ tension shows
a discrepancy between the local direct measurements of $H_{0}$ by distance
ladders Riess et al. (2016, 2019, 2022) and the inferred value by the cosmic
microwave background (CMB) Aghanim et al. (2020). Although, the CMB is an
indirect measurement which means one needs to assume the $\Lambda$CDM to
connect physics of early universe to the present time observations. Though
$H_{0}$ tension seems to be the most severe one but there are many other
reported tensions and anomalies: the $S_{8}$ tension Heymans et al. (2021),
the lensing anomaly Aghanim et al. (2020) and the spatial anomalies Schwarz et
al. (2016); Akrami et al. (2020). However our main focus will be on the
$H_{0}$ tension in this work.

If these tensions are not statistical flukes or systematics then there is a
request to explain them by new theoretical models, the models beyond the
standard $\Lambda$CDM Di Valentino et al. (2021). There are a vast literature
trying to address the $H_{0}$ tension by modifying different parts of the
standard model. The natural scenarios seem those which are related to the late
time dark energy Di Valentino et al. (2021). But there are some
counterarguments against them Efstathiou (2021). A way to see the problem is
to look at BAO’s: BAO’s share the same physics with CMB. This makes solving
the $H_{0}$ tension by the late time modifications hard since it seems the
late time modifications affect CMB and BAO differently. Then (based on this
argument) there are early modification of cosmological constitutes
Kamionkowski and Riess (2023); Knox and Millea (2020); Poulin et al. (2019).
The idea is to modify the sound horizon scale, $r_{s}$, and since the CMB put
constraint on a combination of $H_{0}$ and $r_{s}$ then one can be able to
address the Hubble tension indirectly. Again there is still some arguments
against these models Vagnozzi (2023).

In this work, we study (maybe) the simplest possible model i.e. the standard
$\Lambda$CDM but we change our viewpoint on the cosmological constant term. We
look at this constant as a constant potential where its associated (scalar)
field stoped rolling at the late times. The early dynamics of this field can
affect the cosmological expansion and consequently $r_{s}$ and $H_{0}$ as we
will show.

##  II Model:

The model is (almost) exactly the standard $\Lambda$CDM model with a twist of
interpretation on the cosmological constant, $\Lambda$, which opens a new way
to look at. We assume the $\Lambda$ term is a potential of a (scalar) field
i.e. $V(\phi)=\Lambda$. This means we have a very specific case of
quintessence model

$\displaystyle{\cal{L}}=\sqrt{-g}\,\bigg{[}R-\partial_{\mu}\phi\,\partial^{\mu}\phi\,-\,V(\phi)\bigg{]}$
(1)

where as mentioned above $V(\phi)=\Lambda$ is a constant. Now the equation of
motion for the scalar field will be

$\displaystyle\Box\phi+V_{,\phi}=0$ (2)

which for our scenario reduces to $\Box\phi=0$ with two solutions (in the case
of isotropic and homogeneous cosmological background)

$\displaystyle\phi$ $\displaystyle=$ $\displaystyle\text{constant},$ (3)
$\displaystyle\phi$ $\displaystyle\propto$ $\displaystyle a^{-3}$ (4)

where $a$ is the scale factor for the FRW metric. The first solution gives
exactly the standard $\Lambda$CDM model but the second one has some non-
trivial and interesting properties. However since the equation in linear in
$\phi$ so the superposition of both is a solution. To go further let’s switch
to the perfect fluid prescription for the scalar fields

$\displaystyle\rho_{\phi}$ $\displaystyle=$
$\displaystyle\partial_{\mu}\phi\,\partial^{\mu}\phi\,+\,V(\phi)\doteq\partial_{\mu}\phi\,\partial^{\mu}\phi\,+\Lambda,$
(5) $\displaystyle p_{\phi}$ $\displaystyle=$
$\displaystyle\partial_{\mu}\phi\,\partial^{\mu}\phi\,-\,V(\phi)\doteq\partial_{\mu}\phi\,\partial^{\mu}\phi\,-\Lambda$
(6)

where $\doteq$ means in our scenario. So for the case of background cosmology
we will have

$\displaystyle\rho_{\phi}$ $\displaystyle=$
$\displaystyle\alpha\,a^{-6}+\Lambda,$ (7) $\displaystyle p_{\phi}$
$\displaystyle=$ $\displaystyle\alpha\,a^{-6}-\Lambda$ (8)

where $\alpha$ is an integration constant. The above relation says for very
large $a$’s we have the cosmological constant. The $\alpha$ term is
representing non-vanishing initial velocity of the scalar field
$\dot{\phi}\neq 0$. This non-vanishing initial velocity term is diluted very
rapidly by $a^{-6}$. The corresponding equation of state, $w_{CCPot}$, is
given by

$\displaystyle
w_{CCPot}=\frac{\alpha\,a^{-6}-\Lambda}{\alpha\,a^{-6}+\Lambda}=\frac{e^{-\beta}-a^{6}}{e^{-\beta}+a^{6}},$
(9)

where $e^{-\beta}\equiv\alpha/\Lambda$. This means we are dealing with a fluid
which transits from a stiff matter era ($w=+1$) at the very early times
($a\rightarrow 0$) to the cosmological constant ($w=-1$) for the late times
($a\rightarrow 1$). The equation of state of the stiff matter, $w=+1$, is at
the border of satisfying the causality. For $w>1$ the speed of sound exceeds
the speed of light which is not acceptable though there are some arguments
Ellis et al. (2007). The cosmology of stiff matter is studied in Chavanis
(2015) for a specific scenario and earlier in Zel’dovich (1961). The same
behavior can also happen in the ultra slow roll inflation Dimopoulos (2017)
where we will make a comment on it later.

##  III The Hubble tension and/or the $r_{s}$ tension

The Hubble tension states the local direct measurement of the Hubble constant
is not consistent with the derived one from the CMB measurements. In this
direction, we would like to focus on the derived $H_{0}$ value from the CMB.
The CMB cannot directly constrain “$H_{0}$” but its constraint is on
“$r_{s}\times H_{0}$” Knox and Millea (2020). It is the reason that the
$r_{s}$ tension is also studied directly Aylor et al. (2019).

So this degeneracy in the CMB measurement suggests a solution for the $H_{0}$
tension: instead of increasing $H_{0}$ try to decrease $r_{s}$. This is the
main idea behind the early modifications of $\Lambda$CDM model including. This
effectively means the last scattering surface is closer to the big-bang. This
distance is given by

$\displaystyle
r_{s}^{\star}=\int_{z_{\star}}^{\infty}\,c_{s}(z)\,\frac{1}{H(z)}\,dz,$ (10)

where $c_{s}$ is the speed of sound of the photon-baryon fluid and $z_{\star}$
is the redshift of the CMB last scattering. So what we can do alongside
reducing $r_{s}$ is to play with the Hubble parameter $H(z)$ and the speed of
sound $c_{s}(z)$ at early times (i.e. $z>z_{\star}$). For the case of
modification on $c_{s}(z)$ there are many examples including Jedamzik and
Pogosian (2020); Sekiguchi and Takahashi (2021). The modification of $H(z)$ at
early times is the main idea behind different approaches of early dark energy
Kamionkowski and Riess (2023).

##  IV The $H_{0}$ tension in the CCPot model

In the CCPot model, the stiff matter era makes the early cosmological
evolution modified. Consequently, it shows its effects on the sound horizon,
$r^{\star}_{s}$. The effect is in the reduction of $r^{\star}_{s}$ as it could
be guessed due to larger $H(z)$ for very high redshifts. This may give a
chance to have higher $H_{0}$ values and address the Hubble tension.

###  IV.1 Datasets

In this work, we use the CMB, BAO and local $H_{0}$ datasets to constrain our
model. It is important to mention that for the CMB we have not used the full
dataset but the reduced. It has been shown that the reduced CMB dataset
captures the main information in the CMB and is useful to check the models
beyond the $\Lambda$CDM Mukherjee et al. (2008); Tutusaus et al. (2023). The
reduced CMB dataset includes the angular scale of the sound horizon at the
last scattering surface $\theta_{\star}$, the CMB shift parameter
$R=\sqrt{\Omega_{m}H_{0}^{2}}D_{M}(z^{\star})$ and the baryon density and the
spectral index. Since our model does not affect the spectral index and the
baryonic physics, we do not expect any modification in these two parameters
and we fix them same as their best values from Planck Aghanim et al. (2020).
We also do not use the CMB shift parameter to constrain our model but will
show that our final prediction for it is compatible with its value from Planck
$R=1.7478\pm 0.0046$ Tutusaus et al. (2023). So from the CMB, we use the
acoustic angular angle $\theta_{\star}=1.04090\pm 0.00031$ which is very well
constrained Aghanim et al. (2020). To have more information about the sound
horizon, we also use the late time BAO observations. For our purposes, the
BAO’s are very crucial. Their main physics is exactly the CMB physics but they
are far from the last scattering surface. This property is one of the reasons
that makes late time solution to the Hubble tension very hard. Since any late
time modification in the cosmological distances may affect the CMB distance
(and consequently the $H_{0}$ deduced from CMB) but cannot change the
distances given by the BAO’s. Because of this reason we have used some
independent BAO datasets: $r_{d}/D_{V}=0.336\pm 0.015$ Beutler et al. (2011);
$D_{A}/(1.81r_{d})=10.75\pm 0.43$ Abbott et al. (2019); $D_{V}/r_{d}=4.466\pm
0.168$ Ross et al. (2015); $D_{V}/r_{d}=11.548\pm 0.559$,
$D_{V}/r_{d}=14.946\pm 0.68\pm 0.559$, $D_{V}/r_{d}=16.931\pm 0.579$ Kazin et
al. (2014); $D_{V}/r_{d}=16.085\pm 0.406$ Bautista et al. (2018);
$D_{M}/r_{d}=36.6\pm 1.35$, $D_{H}/r_{d}=8.94\pm 0.225$ du Mas des Bourboux et
al. (2017); $D_{H}/r_{d}=9.07\pm.031$ Bautista et al. (2017);
$D_{V}/r_{d}=9.995\pm 0.108$, $D_{V}/r_{d}=12.701\pm 0.129$,
$D_{V}/r_{d}=14.481\pm 0.149$ Alam et al. (2017); $r_{d}\,H=25500\pm 1800$,
$D_{M}/(2.25r_{d})=12.58\pm 0.70$ Ata et al. (2018). Note that the
measurements are at different redshifts. For the direct local measurement of
the $H_{0}$ we use $H_{0}=73.30\pm 1.04$ Riess et al. (2022). First we check
the CCPot model’s parameters against $\theta+BAO$ (i.e. reduced CMB and all
the BAO’s). Then if the model was compatible with higher values of $H_{0}$, we
are allowed to add the local $H_{0}$ measurement.

###  IV.2 Results

In the CCPot model, we have an additional $\beta$ parameter as it appeared in
(9). In addition to this parameter, we allow the dark matter density
($\Omega_{c}$) and the Hubble constant ($H_{0}$) to be free parameters. We do
not assume the other parameters as baryon density ($\Omega_{b}$), spectral
index ($n_{s}$) and etc. to be free parameters as we mentioned above. We also
impose spatial flatness which results in

$\displaystyle H^{2}$ $\displaystyle=$ $\displaystyle
H_{0}^{2}\bigg{[}\Omega_{r}\,(1+z)^{4}+\Omega_{m}\,(1+z)^{3}$ $\displaystyle+$
$\displaystyle(1-\Omega_{r}-\Omega_{m})\,\bigg{(}(1+e^{-\beta}(1+z)^{6})/(1+e^{-\beta})\bigg{)}\bigg{]}$

as the Friedmann equation where $\Omega_{r}=\Omega_{\gamma}+\Omega_{\nu}$ and
$\Omega_{m}=\Omega_{b}+\Omega_{c}$.

The figure 1 shows the $1\sigma$ posterior on our free parameters when the
CCPot is constrained by all the datasets $\theta+BAO$ and late $H_{0}$
measurement. The result is very consistent with the higher value of the late
$H_{0}$ measurements which means there is no Hubble tension in our model.
However, it should be emphasized that before allowing to add datasets together
we had to check their consistencies. In figure 2 we have checked the CCPot
against $\theta+BAO$ without $H_{0}$ dataset. The figure shows that the
posterior for the CCPot is big enough to contain higher value of $H_{0}$. Note
that it is not just because of larger variance but also is due to higher value
for the mean value of $H_{0}$. The $\Lambda$CDM as a limit of the CCPot (for
$\beta\rightarrow 0$) is at the border of $1\sigma$ region. Back to figure 1,
we can see that for a fixed value of $\beta$, we can see the expected anti-
correlation of $H_{0}$ and $\Omega_{m}$. The best values and their $1\sigma$
variances are reported in Table 1. As an independent check, we checked the
CCPot results against the CMB shift parameter which is almost model
independent Mukherjee et al. (2008); Tutusaus et al. (2023) as we already
mentioned. The CCPot prediction (when we use the best fit parameters) is
$R=1.7462$ which is in $1\sigma$ prediction by Planck results $R=1.7478\pm
0.0046$.

Figure 1: This plot shows the $1\sigma$ contour in the $H_{0}-\Omega_{m}$ plane while the color dots (bar) is representing the $\beta$ parameter. In this plot all the $\theta+BAO$ and $H_{0}$ datasets are used. The results are totally compatible with higher $H_{0}$ values while has no conflict with the $\theta+BAO$. It is obvious that for a fixed $\beta$ value (a fixed color) the expected anti-correlation between $H_{0}$ and $\Omega_{m}$ is seen. Figure 2: The blue region is $1\sigma$ likelihood for the CCPot model which is constrained by only $\theta+BAO$ dataset. Obviously, it is compatible with the higher local values of $H_{0}$ which allows us to constrain the CCPot model with $\theta+BAO+H_{0}$ dataset. For this case, the green region is the $1\sigma$ likelihood for the CCPot model. The orange region is the standard $\Lambda$CDM model which is constrained by $\theta+BAO$ that shows inconsistency with the local $H_{0}$ value. The $\Lambda$CDM is compatible with the CCPot as we could expect (because it is the $\beta\rightarrow\infty$ limit of the CCPot). But in general the CCPot prefers higher values for the $H_{0}$. This means not also the variance but the mean of the $H_{0}$ increases. The green region, is plotted in figure 1 in more details.  Figure 3: The solid line is the CCPot fluid time dependence in the history of the cosmos. At the late time it is the standard cosmological constant ($w=-1$) and becomes dominant. The same fluid is dominant in the very early universe due to its similarities to the stiff matter ($w=+1$). The figure is plotted for the best values of parameters reported in Table 1. Figure 4: The (effective) equation of state for the CCPot fluid is plotted for the best fit parameters. The transition between the stiff matter ($w=+1$) and the cosmological constant ($w=-1$) is obvious. $H_{0}$ | $\Omega_{m}$ | $\beta$
---|---|---
$73.31^{+1.83}_{-1.88}$ | $0.2578^{+0.111}_{-0.121}$ | $30.80^{+1.13}_{-0.62}$
Table 1: The best fit values of our free parameters as well as their $1\sigma$
variances is reported. The parameters are constrained by using the full
datasets: $\theta+BAO$ and $H_{0}$.

In figure 3, the fraction of each energy content is plotted against redshift.
As we expected the new fluid is dominant before $z\sim 10^{5}$ and after
$z\sim 0.3$. The former phase is the one which makes the $r_{s}$ less than the
standard scenario. This phase predicts higher values for the Hubble parameter
in redshifts above $10^{4}-10^{5}$. On the other hand since the interaction
rates $\Gamma$ are coming from the independent physics of particles so we
expect them to be the same as the standard cosmology. In conclusion, we expect
the particles be out of the equilibrium sooner with respect to the standard
$\Lambda$CDM. This does not true for the photon decoupling since the
cosmological modifications due to the CCPot are very small at the decoupling
redshift and so the last scattering surface distance from us should be the
same as the standard one. However, we have to say that the physics before the
last scattering surface in our model needs more consideration which remains
for the future works. In figure 4, we can see the effective equation of state
$w(z)$. The transition redshift between $w=+1$ and $w=-1$ is around $z\sim
150$ for the best fit parameters’ values. It seems hard to make observational
constraint in these redshifts. To go further in this direction, we need to use
full CMB dataset to look for more details of the CCPot model in
early/intermediate/late times, which remains for the future.

##  V Concluding remarks

The cosmological constant, which is a constant in the Lagrangian, can explain
the late time acceleration perfectly. But by another view, this constant is
the remnant of the field rolling on a constant potential. In this viewpoint at
the early times, the field (which is assumed to be scalar) behaves as a stiff
fluid with $w=+1$ while it stops rolling due to the Hubble friction and
results in a fluid with $w=-1$. We studied this model and could show that it
can resolve the Hubble tension by reducing the sound horizon at the early
times. We checked our model against the (reduced) CMB as well as BAO and they
are consistent with each other and the late time measurements of the Hubble
constant. However for the future works we would like to check the full model
against the full CMB dataset.

In the theoretical side, the cosmological constant potential can be seen as
the leftover of the early inflation. The inflaton field is rolling down the
potential to give the inflationary phase and at the end it reaches a constant
potential. The initial conditions of the CCPot part is the final conditions of
the inflationary phase. This scenario needs more consideration and can be
interesting if it can be related to the PBH production at the end of
inflation. This idea seems natural to come to mind since the PBH production
can be efficient if there is an ultra slow roll regime which has effectively
$w=+1$.

Acknowledgments: I would like to thank Shant Baghram, Abdolali Banihashemi and
Sara Khatibi for useful discussions about this paper. I am also grateful to
Abdolali Banihashemi for allowing me to use his MCMC code.

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# An XMM-Newton study of active-inactive galaxy pairs

Matteo Guainazzi${}^{1},$ Alessandra De Rosa2, Stefano Bianchi3, Bernd
Husemann4, Tamara Bogdanovic5, Stefanie Komossa6, Nora Loiseau7, Zsolt
Paragi8, Miguel Pérez-Torres9, Enrico Piconcelli10, Cristian Vignali11
1ESA European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201
AZ, Noordwijk, The Netherlands
2INAF - Istituto di Astrofisica e Planetologia Spaziali (IAPS), via Fosso del
Cavaliere, I-133 Roma, Italy
3Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, via
della Vasca Navale 84, I-00146 Roma, Italy
4Max Planck Institute for Astronomy, Königstuhl 17, 69117, Heidelberg, Germany
5Center for Relativistic Astrophysics, School of Physics, Georgia Institute of
Technology, 837 State Street, Atlanta, GA 30332-0430, United States
6Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-521 Bonn,
Germany
7ESA - European Space Astronomy Centre (ESAC), E-28692 Villanueva de la
Cañada, Madrid, Spain
8Joint Institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD, Dwingeloo,
The Netherlands
9Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía
s/n, 18008 Granada, Spain
10Osservatorio Astronomico di Roma (INAF), via Frascati 33, 00040, Monte
Porzio Catone, Roma, Italy
11Dipartimento di Fisica e Astronomia, Alma Mater Studiorum, Università degli
Studi di Bologna, Via Gobetti 93/2, 40129, Bologna, Italy E-mail:
<EMAIL_ADDRESS>
(Accepted 2021 March 15. Received 2021 March 1; in original form 2020 December
10)

###### Abstract

While theory and simulations indicate that galaxy mergers play an important
role in the cosmological evolution of accreting black holes and their host
galaxies, samples of Active Galactic Nuclei (AGN) in galaxies at close
separations are still small. In order to increase the sample of AGN pairs, we
undertook an archival project to investigate the X-ray properties of a SDSS-
selected sample of 32 galaxy pairs with separations $\leq$150 kpc containing
one optically-identified AGN, that were serendipitously observed by XMM-
Newton. We discovered only one X-ray counterpart among the optically
classified non-active galaxies, with a weak X-ray luminosity
($\simeq$5$\times$1041 erg s-1). 59% (19 out of 32) of the AGN in our galaxy
pair sample exhibit an X-ray counterpart, covering a wide range in absorption
corrected X-ray luminosity (5$\times$1041–2$\times$1044 erg s-1). More than
79% of these AGN are obscured (column density $N_{H}>$1022 cm-2), with more
than half thereof (i.e., about 47% of the total AGN sample) being Compton-
thick. AGN/no-AGN pairs are therefore more frequently X-ray obscured (by a
factor $\simeq$1.5) than isolated AGN. When compared to a luminosity and
redshift-matched sample of bona fide dual AGN, AGN/no-AGN pairs exhibit one
order-of-magnitude lower X-ray column density in the same separation range
($>$10 kpc). A small sample (4 objects) of AGN/no-AGN pairs with sub-pc
separation are all heavily obscured, driving a formal anti-correlation between
the X-ray column density and the galaxy pair separation in these systems.
These findings suggest that the galactic environment has a key influence on
the triggering of nuclear activity in merging galaxies.

###### keywords:

Galaxies:active – galaxies:interactions – galaxies:nuclei – X-ray:galaxies

††pubyear: 2020††pagerange: An XMM-Newton study of active-inactive galaxy
pairs–References

##  1 Introduction

The tight empirical correlations between the mass of super-massive black
holes, and observable quantities related to the host galaxy size (such as the
"M-$\sigma$ relation; Ferrarese & Merritt 2000; McConnell & Ma 2013; Kormendy
& Ho 2013) have been interpreted as signature of the cosmological co-evolution
of accreting black holes and host galaxies. In this context, galaxy merging
could play an important role in triggering the formation of black holes via
direct gas collapse (Begelman et al., 2006; Mayer et al., 2010), generating
gas instabilities that allow the nuclear gas to lose angular momentum and
efficiently feed the black hole (Di Matteo et al., 2005), or even shape the
environment and clustering properties of quasars (Kauffmann & Haehnelt, 2000;
Alexander & Hickox, 2012). However, it remains unclear if there is a relation
between galaxy interaction and nuclear activity. Results from X-ray and IR
surveys indicate an increase of the fraction of Active Galactic Nuclei (AGN)
in the population of merging galaxies for decreasing nuclear separation below
100 kpc (Ellison et al., 2011; Silverman et al., 2011; Satyapal et al., 2014).
Also the fraction of "dual AGN" - close galaxy companions hosting both
actively accreting black holes - increases with decreasing separation, and
their X-ray luminosity increases (Koss et al., 2012). However, these
conclusions are based on relatively small samples. Dual AGN are rare, and many
of the known specimen of this class have been discovered serendipitously. A
robust comparison with models of galaxy mergers evolution is often cumbersome
(De Rosa et al., 2019).

One of the main observational biases is the fact the AGN pairs are often
heavily dust-enshrouded. It has been recently demonstrated that obscured AGN
show a significant excess of late-stage nuclear mergers when compared to a
control sample of inactive galaxies (Koss et al., 2018). Identifying dual AGN
via optical spectroscopy is therefore hard. Together with IR (Imanishi &
Saito, 2014), X-rays are an efficient way to detect accretion-powered
processes in low-to-moderately obscured sources (i.e. Compton-thin; column
density $N_{H}$ $\leq$ 1024 cm-2), and even heavily obscured sources can be
identified in deep exposures (through optically-thick reprocessing spectral
components; see , e.g., Piconcelli et al. (2010)), or through measurements
above 10 keV (Bianchi et al., 2008; Koss et al., 2011; Iwasawa et al., 2018).
Interestingly, X-ray obscuration seems also to increase with decreasing AGN
separation (Ricci et al., 2017; De Rosa et al., 2018; Pfeifle et al., 2019).
This is in agreement with numerical simulations (Capelo et al., 2017), even
though they typically probe spatial scales ($\geq$ 50 pc) much larger than the
scale of the torus where the bulk of X-ray obscuration is assumed to occur.
However, these results are somewhat dependent on the sample selection
criteria. Optically-selected dual AGN samples tend to show a larger fraction
of unobscured or moderately obscured AGN than X-ray selected samples (Green et
al., 2011; Gross et al., 2019). Whether this is the correction of a bias, or a
bias in itself it is still to be ascertained.

In order to increase the size of well-defined AGN pair samples, we undertook
an archival project to investigate the X-ray properties of a SDSS-selected
sample of galaxy pairs with separations $\leq$150 kpc containing one
optically-identified AGN and serendipitously observed by XMM-Newton (Jansen et
al., 2001). The original goal of the study was identifying dual AGN pairs that
may have been missed because the nuclear activity in the optical inactive
galaxy remains undetected due to, for instance, heavy nuclear obscuration. The
results of the study yield new observational constraints on the trigger
mechanism of supermassive black holes in merging galaxies at separations
$\leq$100 kpc.

The paper is structured as follows. In § 2 we present the sample selection
criteria. A re-analysis of the SDSS imaging and spectroscopy data is presented
in § 3; this is required to validate the nature of the galaxy pairs discussed
in this paper. The X-ray data analysis is presented in § 4. Our results are
discussed in § 5 and the main conclusions are summarized in § 6.

##  2 Sample selection

In order to select the AGN/no-AGN pairs discussed in this paper, we took the
SDSS DR7 galaxy sample from the MPA-JHU value added catalogs and classified
all emission line galaxies into star forming galaxies, LINERs and Seyfert 2
galaxies using classical BPT diagnostics (Baldwin et al., 1981). All galaxies
with too weak emission lines for a BPT classification (S/N<3), were assigned
the class "UNCLEAR". Furthermore, we considered 3600 unobscured AGN from the
SDSS DR7 derived catalog of Stern et al. (2012) as Seyfert 1 galaxies. Based
on the combined Seyfert 1 and Seyfert 2 catalog we identified potential
companion galaxies, classified as star forming, LINERs, or UNCLEAR, with a
projected separation, $R$, of 5 kpc$<$R$<$200 kpc and a redshift difference of
$\Delta$z$<0.01$. This leads to 698 Seyfert-SF pairs, 71 Seyfert-LINER pairs
and 780 Seyfert-UNCLEAR pairs. We have then searched in the archive of XMM-
Newton observations all the fields where each pair was observed at least once
with at least one of the EPIC cameras. This search yielded 41 matches. 9 of
these sources were later discarded because a reanalysis of the SDSS imaging
and spectroscopic data did not confirm the original classification (cf. § 3).
The final list includes 32 pairs, whose coordinates and redshifts are shown in
Tab. LABEL:tab_ul. The galaxy pairs with at least one X-ray counterpart (cf. §
4.1) cover a range in black hole separation up to $\simeq$150 kpc, with a
median separation of $\simeq$40 kpc (Fig. 1). All 32 sky positions were
observed by XMM-Newton only once, and only a few of them were at the boresight
of the corresponding observation.

Figure 1: Histogram of the galaxy separations for the galaxies in our sample
with at least one XMM-Newton observations (empty bars) and for those with at
least one X-ray counterpart (filled bars) (cf. Tab. 2)

Our optical selection biases the sample against heavily-obscured (buried) AGN,
whose ionizing photons cannot create a NLR. On the other hand, using X-ray
spectroscopic data taken with the EPIC camera on board XMM-Newton for the
spectral fitting may also prevent us from detecting objects whose X-ray
emission is suppressed by heavy obscuration. Thus, the fraction of obscured
AGN that we derive from our sample is likely to constitute a lower limit to
that of the parent sample of galaxy pairs with at least one AGN. We discuss in
§ 3 a way to at least partly alleviate the latter bias.

##  3 Optical spectroscopy

Aware of possible inaccuracies in the SDSS spectroscopic classification of
close galaxy pairs due to the spillover of the primary flux to the secondary
fibre (Husemann et al., 2020), we retrieved the SDSS DR12 spectra (Alam et
al., 2015) at the location of the galaxies, as reported in Table LABEL:tab_ul,
from the survey webpage111http://skyserver.sdss3.org/dr12.. We analyse the
full-band optical spectra with the software package QSFit 1.3.0 (Calderone et
al., 2017), which automatically takes into account both the AGN and the host
galaxy emission, together with a number of broad and narrow emission lines. In
particular, we extracted the intensities of the the primary diagnostic narrow
emission lines such as H$\beta$, [OIII] $\lambda 5007$, [OI] $\lambda 6300$,
H$\alpha$, [NII] $\lambda 6583$ and [SII] $\lambda\lambda 6717,6730$. Five
sources (namely SSDSSJ002920.35-001028.9, SDSSJ011254.91+00031.0,
SDSSJ011448.67-002946.0, SDSSJ111830.28+402554.0, SDSSJ170601.86+601732.3)
show unambiguously the presence of dominant broad components of the Balmer
lines, and are therefore included in our sample. For all the other sources,
the line flux ratios were then plotted in the BPT diagrams shown in Fig. 2,
where the separations between Seyfert galaxies, starburst galaxies, and low-
ionization nuclear emission-line regions (LINERs) are as in Kewley et al.
(2006). Sources with at least one BPT diagram indicating an AGN are kept in
our sample, while LINERs and all the other cases are excluded.

Figure 2: BPT diagrams for all the sources of our sample. See text for
details.

The ratio between the observed 2–10 keV and [OIII]$\lambda 5007$ luminosity in
AGN is often used as a proxy of X-ray obscuration (Bassani et al., 1999), that
is one of the objectives of our study. The X-ray luminosity of our sample will
be discussed in the sect. 4.2, while to derive the L[OIII] corrected for
extinction, we assumed the Cardelli et al. (1989) extinction law and an
intrinsic Balmer decrement (H$\alpha$/H$\beta$) equal to 3, which represents
the case for the Narrow Line Region (NLR) (Osterbrock & Ferland, 2006). We
then will use the ratio between the X-ray and ${\rm[OIII]}$ $\lambda$5007
luminosity as an indirect measurement of NH, to be compared with the value
obtained through X-ray spectroscopy (see Sect.4.2).

##  4 X-ray data analysis

For each of the XMM-Newton observations we extracted the Observation Data
Files (ODF) from the XMM-Newton Science Archive (XSA). The list of Observation
Identifiers (Obs.#) is shown in Tab. LABEL:tab_ul. The data of the EPIC
cameras (Strüder et al., 2001; Turner et al., 2001) were reduced using SAS
version 16.0 (Gabriel et al., 2004), and the most updated calibration files
available at the time the reduction was performed. Calibrated event lists were
generated with the data reduction meta-tasks epproc and emproc for the EPIC-pn
and the EPIC-MOS cameras, respectively. Intervals of high particle background
were removed by applying a standard threshold on a representative curve of
this background component, extracted using single events with energies larger
than 10 keV (10–12 keV for EPIC-pn). The value of the thresholds were 0.4 and
0.35 counts per second in EPIC-pn and EPIC-MOS, respectively.

Table 1: Galaxy pair sample. The "Minimum separation" indicates the separation (in arcminutes and kpc) between the AGN and the closest galaxy in the pair. The "…" sign indicates that the values of the corresponding AGN in the system shall be applied. Obs.# | SDSS name | RA | Dec. | z | Minimum separation
---|---|---|---|---|---
|  |  |  |  | (") | (kpc)
04060101 | SDSSJ002920.36-00102 | 7.33482 | -0.17469 | 0.061 | 43.6 | 59.7
… | N/D | 7.34739 | -0.16365 | 0.060 | … | …
… | N/D | 7.32722 | -0.18411 | 0.060 | … | …
… | N/D | 7.34890 | -0.17187 | 0.060 | … | …
0747390139 | SDSSJ010951.34+00024 | 17.46393 | 0.04618 | 0.086 | 54.6 | 107.2
… | N/D | 17.45529 | 0.03373 | 0.090 | … | …
0747400142 | SDSSJ011254.92+000 | 18.22883 | 0.05361 | 0.239 | 23.7 | 142.1
… | N/D | 18.22787 | 0.04709 | 0.240 | … | …
0404410201 | SDSSJ011429.87+00125 | 18.62445 | 0.21521 | 0.046 | 38.6 | 39.4
… | N/D | 18.62415 | 0.20448 | 0.050 | … | …
0747400132 | SDSSJ011448.68-00294 | 18.70279 | -0.49611 | 0.034 | 8.4 | 6.3
… | N/D | 18.70754 | -0.49558 | 0.030 | … | …
0747400150 | SDSSJ011659.07+00193 | 19.24612 | 0.32593 | 0.078 | 10.1 | 17.9
… | N/D | 19.24880 | 0.32673 | 0.080 | … | …
0747430138 | SDSSJ014402.61-00070 | 26.01089 | -0.11915 | 0.079 | 55.0 | 98.7
… | N/D | 26.02399 | -0.12703 | 0.080 | … | …
0142610101 | SDSSJ030639.57+00034 | 46.66483 | 0.06197 | 0.107 | 56.5 | 139.9
… | N/D | 46.68293 | 0.06610 | 0.110 | … | …
… | N/D | 46.67869 | 0.06935 | 0.110 | … | …
0201120101 | SDSSJ030655.63-00014 | 46.781 | -0.02805 | 0.112 | 50.4 | 1.1
… | N/D | 46.730 | -0.01412 | 0.110 | … | …
… | N/D | 46.72687 | -0.04465 | 0.110 | … | …
0206340101 | SDSSJ0852.70+16261 | 133.30290 | 16.43763 | 0.065 | 6.4 | 9.4
… | N/D | 133.30148 | 16.43875 | 0.060 | … | …
0725300159 | SDSSJ090255.53+01464 | 135.735 | 1.77980 | 0.118 | 22.4 | 61.6
… | N/D | 135.73344 | 1.77393 | 0.120 | … | …
06750401 | SDSSJ091507.48+29562 | 138.78117 | 29.94010 | 0.1 | 23.0 | 70.8
… | N/D | 138.75716 | 29.93708 | 0.130 | … | …
… | N/D | 138.77386 | 29.939 | 0.130 | … | …
0306050201 | SDSSJ094046.29+03393 | 145.19287 | 3.65839 | 0.087 | 40.4 | 80.3
… | N/D | 145.18353 | 3.66466 | 0.090 | … | …
0504101701 | SDSSJ101858.47+37180 | 154.74361 | 37.30021 | 0.048 | .0 | 33.1
… | N/D | 154.73328 | 37.28583 | 0.050 | … | …
… | N/D | 154.74774 | 37.30816 | 0.050 | … | …
0556211401 | SDSSJ104856.96+59282 | 162.23734 | 59.47383 | 0.093 | 34.9 | 74.4
… | N/D | 162.25620 | 59.47245 | 0.090 | … | …
0111290301 | SDSSJ111830.29+40255 | 169.62616 | 40.467 | 0.155 | 5.5 | 20.4
… | N/D | 169.62616 | 40.467 | 0.160 | … | …
0047540601 | SDSSJ114713.50+47325 | 176.80624 | 47.54950 | 0.074 | 52.5 | 87.9
… | N/D | 176.79112 | 47.55992 | 0.070 | … | …
0744040301 | SDSSJ115852.20+42432 | 179.71750 | 42.72242 | 0.002 | 16.4 | 0.7
… | N/D | 179.64188 | 42.73404 | 0.000 | … | …
0601780601 | SDSSJ120443.32+103 | 181.18051 | .17729 | 0.025 | 59.7 | 32.6
… | N/D | 181.18834 | .19248 | 0.030 | … | …
… | N/D | 181.18861 | .15791 | 0.030 | … | …
… | N/D | 181.18861 | .15772 | 0.030 | … | …
… | N/D | 181.18834 | .19248 | 0.030 | … | …
0601780901 | SDSSJ121044.28+38201 | 182.68446 | 38.33617 | 0.023 | 50.9 | 25.5
… | N/D | 182.69930 | 38.34421 | 0.020 | … | …
0722670201 | SDSSJ122846.68+07275 | 187.19452 | 7.46599 | 0.085 | 8.0 | 15.5
… | N/D | 187.19670 | 7.46651 | 0.080 | … | …
0202180301 | SDSSJ124210.61+370 | 190.54420 | 33.28405 | 0.044 | 55.1 | 53.7
… | N/D | 190.52699 | 33.27884 | 0.040 | … | …
0691610301 | SDSSJ125729.99+28111 | 194.42943 | 27.60787 | 0.068 | 48.7 | 74.6
… | N/D | 194.41422 | 27.60609 | 0.070 | … | …
… | N/D | 194.42854 | 27.62137 | 0.070 | … | …
0055990501 | SDSSJ133817.28+48163 | 204.57198 | 48.27563 | 0.028 | 10.1 | 6.2
… | N/D | 204.57404 | 48.27807 | 0.030 | … | …
0671150501 | SDSSJ134736.41+17340 | 206.90169 | 17.56796 | 0.045 | 10.0 | 10.0
… | N/D | 206.90462 | 17.56780 | 0.050 | … | …
0164560701 | None | 211.496 | 54.41608 | 0.083 | 54.6 | 103.2
… | N/D | 211.30116 | 54.42896 | 0.080 | … | …
0091140201 | SDSSJ1451.76+16552 | 223.29903 | 16.92345 | 0.045 | 49.5 | 49.4
… | N/D | 223.30621 | 16.93537 | 0.050 | … | …
0721820201 | SDSSJ145840.74+38273 | 224.66077 | 38.45776 | 0.136 | 25.7 | 82.4
… | N/D | 224.66972 | 38.45910 | 0.140 | … | …
0150680101 | SDSSJ151811.57+172 | 229.54819 | .28951 | 0.108 | 30.4 | 76.0
… | N/D | 229.53943 | .29341 | 0.110 | … | …
0147210301 | SDSSJ160515.86+17422 | 241.604 | 17.70761 | 0.0 | 59.7 | 40.6
… | N/D | 241.442 | 17.72411 | 0.030 | … | …
0305750301 | SDSSJ170601.87+60173 | 256.50778 | 60.29233 | 0.130 | 13.5 | 41.2
… | N/D | 256.50061 | 60.29357 | 0.130 | … | …
0744410801 | SDSSJ171715.74+64154 | 259.558 | 64.26115 | 0.035 | 33.5 | 25.8
… | N/D | 259.32224 | 64.27000 | 0.030 | … | …
0673000147 | SDSSJ221839.93-00240 | 334.66635 | -0.40052 | 0.095 | 30.8 | 67.2
… | N/D | 334.67072 | -0.398 | 0.090 | … | …

###  4.1 XMM-Newton source detection and photometry

The first step of our analysis aimed at identifying the X-ray counterparts of
the sample sources. For each optically identified pair member we run the
standard source detection algorithm in the SAS, through the meta-task
edetect_chain. In a nutshell, this task employs the detection algorithm in
Cruddace et al. (1988) on an image whose background is determined through a
2-D spline of field-of-view map from which sources had been removed on the
basis of a prior detection run. We run the detection algorithm simultaneously
on EPIC-pn and EPIC-MOS images in the 0.3–10 keV energy band extracted on a
square box of 2’ size around the nominal coordinates of the optically-
identified AGN. We used a edetect_chain option allowing to simultaneously
fitting the telescope Point Spread Function (PSF) in the so-called "multi-
source mode" (with input parameters nmulsou = 2 and scut = 200), where
neighbouring sources with overlapping PSFs are fitted simultaneously. Our
choice is driven by the fact that the distance between the components of some
of the pairs in our sample is comparable with the telescope angular
resolution. Following Rosen et al. (2016), we assume that an X-ray source is a
bona fide counterpart of an optical galaxy if the centroid distance is
$\leq$3.5".

We show the results of our X-ray photometric analysis in Tab. 2. For each
optically-identified AGN we list one row for each of the potentially
associated AGN/non-AGN pair members. We significantly detect 19 X-ray sources
among the optically identified AGN. For completeness, in the other cases we
show the distance of the closest X-ray source in the 2’ side detection box, if
any.

Table 2: Total 0.3–10 keV count rate of the X-ray counterparts of the bona fide optically identified AGN in our sample, as estimated from the combined EPIC images of the corresponding XMM-Newton observation. Rows in bold indicate AGN with an identified bona fide X-ray counterpart. An upper limit at the optical position (1$\sigma$-level) is shown if the closest X-ray source is located at a distance larger than the astrometric error of the XMM-Newton EPIC serendipitous source catalogue (3.5" at the 90% confidence level). The "Distance" is between the AGN optical position and the closest X-ray source in the 2$\times$2 acrminutes2 detection box. The dots indicates AGN optical positions for which no meaningful X-ray count rate upper limit could be estimated and/or no X-ray source was detected in the detection box. Source ID | Rate | Net counts | Distance
---|---|---|---
| (s-1) |  | (")
SDSSJ002920.36-00102 | 0.688$\pm$0.040 | 2533$\pm$125 | 0.1$\pm$ 2.9
SDSSJ010951.34+00024 | 0.115$\pm$0.017 | 222$\pm$ | 5.8$\pm$ 4.3
SDSSJ011254.92+000 | 0.630$\pm$0.017 | 1477$\pm$40 | 0.7$\pm$ 0.2
SDSSJ011429.87+00125 |  $\leq$0.023 | 6632$\pm$ 199 | 12.8$\pm$ 1.2
SDSSJ011448.68-00294 | … | … | …
SDSSJ011659.07+00193 | 0.152$\pm$0.014 | 326$\pm$28 | 6.1$\pm$ 3.4
SDSSJ014402.61-00070 | 0.042$\pm$0.005 | 110$\pm$12 | 1.1$\pm$ 1.0
SDSSJ030639.57+00034 | 0.948$\pm$0.005 | 33992$\pm$189 | 0.9$\pm$ 0.0
SDSSJ030655.63-00014 | 0.729$\pm$0.046 | 4564$\pm$286 | 2.9$\pm$ 2.8
SDSSJ0852.70+16261 | 0.223$\pm$0.008 | 2332$\pm$73 | 1.3$\pm$ 0.8
SDSSJ090255.53+01464 |  $\leq$0.039 | 13$\pm$ 5 | 77.4$\pm$ 7.2
SDSSJ091507.48+29562 |  $\leq$0.022 | 1604$\pm$ 100 | 19.6$\pm$ 2.7
SDSSJ094046.29+03393 |  $\leq$0.019 | 2097$\pm$ 93 | 56.5$\pm$ 0.8
SDSSJ101858.47+37180 | 0.522$\pm$0.023 | 2379$\pm$103 | 0.6$\pm$ 0.9
SDSSJ104856.96+59282 | 0.289$\pm$0.009 | 1129$\pm$36 | 1.4$\pm$ 0.3
SDSSJ111830.29+40255 |  $\leq$2.553 | 6046$\pm$ 343 | 56.3$\pm$ 0.0
SDSSJ114713.50+47325 |  $\leq$0.014 | 762$\pm$ 259 | 69.0$\pm$ 1.4
SDSSJ115852.20+42432 | 0.1$\pm$0.005 | 1249$\pm$43 | 2.1$\pm$ 0.7
SDSSJ120443.32+103 | 0.648$\pm$0.006 | 15460$\pm$129 | 0.5$\pm$ 0.1
SDSSJ121044.28+38201 | 0.601$\pm$0.040 | 1858$\pm$47 | 1.3$\pm$ 0.2
SDSSJ122846.68+07275 | … | … | …
SDSSJ124210.61+370 | 7.121$\pm$0.028 | 66480$\pm$258 | 0.6$\pm$ 0.0
SDSSJ125729.99+28111 | 0.433$\pm$0.011 | 5324$\pm$126 | 3.6$\pm$ 1.1
SDSSJ133817.28+48163 |  $\leq$0.266 | 3911$\pm$ 270 | 19.6$\pm$ 0.2
SDSSJ134736.41+17340 | 0.145$\pm$0.005 | 887$\pm$33 | 1.6$\pm$ 0.3
SDSSJ1451.76+16552 |  $\leq$0.022 | 3237$\pm$ 262 | 9.0$\pm$ 1.3
SDSSJ145840.74+38273 | 0.356$\pm$0.015 | 3681$\pm$155 | 3.5$\pm$ 2.6
SDSSJ151811.57+172 |  $\leq$0.021 | 3652$\pm$ 170 | 71.6$\pm$ 1.7
SDSSJ160515.86+17422 | 0.711$\pm$0.026 | 4360$\pm$ 146 | 5.2$\pm$ 0.7
SDSSJ170601.87+60173 | 0.241$\pm$0.056 | 48$\pm$7 | 1.4$\pm$ 1.2
SDSSJ171715.74+64154 | 0.004$\pm$0.002 | 52$\pm$13 | 4.0$\pm$ 0.7
SDSSJ221839.93-00240 |  $\leq$0.025 |  $\leq$ 41 | 8.5$\pm$ 1.4

Among the galaxies optically classified as "non-AGN", only one X-ray source is
detected within the aforementioned astrometric error: a galaxy with
coordinates (RA,Dec.) = (133.30148,16.43875), companion to the AGN SDSS
J0852.70+16261 in Obs.#0206340101. Its total 0.3–10 keV count rate is
(9$\pm$3)$\times$10-3 s-1. It belongs to the galaxy pair in our sample
corresponding to the smallest separation (6.4"), comparable to the angular
resolution of the X-ray telescope. This casts doubts on the robustness of the
detection that could be affected by uncertainties in the Point Spread Function
modelling (Fig. 3). For all the other non-AGN galaxies, upper limits on an
X-ray counterpart vary in the range between 0.011 and 5 s-1 depending on the
source position in the EPIC field-of-view and the observation exposure time.

Figure 3: SDSS i-filter image superposed to the count contours of the EPIC
image (green dashed lines; 6 levels in logarithmic scale in the 10–42 net EPIC
counts per pixel range) for the only galaxy pair where an X-ray counterpart
spatially coincident with each member of the pair is detected: SDSS
J0852.70+16261.

###  4.2 XMM-Newton spectroscopy

For each of the X-ray counterparts, we performed a formal forward-folding
spectral analysis. Our main goal is to estimate the X-ray luminosity and the
column density obscuring the primary emission of the AGN. EPIC source spectra
were extracted from a circular region of 20" radius around the SDSS optical
position. Background spectra were extracted from boxes in detector coordinates
of of 50"$\times$75" and 50"$\times$150" once a circle around the AGN had been
removed with a radius comprised between 30" and 40" depending on the source
count rate to avoid that the background region is contaminated by the source
PSF wings. From the background regions circles were also excised around any
serendipitous source (including the position of the non-active SDSS AGN).
Instrument responses were generated for each individual source using the
standard SAS tasks rmfgen and arfgen taking into account the corresponding
time- and spatial-dependent calibration.

Table 3: List of models used in the spectroscopic analysis of the AGN counterpart. $A$ is the power-law normalization. $G(E)$ is a Gaussian profile in emission. $C(E)$ describes the emission of an optically-thin, collisionally ionized plasma in thermal equilibrium (Smith et al., 2001). $R(E)$ is a Compton-reflection model after Magdziarz & Zdziarski (1995).  ID | Model
---|---
1 | $e^{-\sigma N_{H}}A_{1}E^{-\Gamma}$
2 | $A_{1}E^{-\Gamma}+e^{-\sigma N_{H}}A_{2}E^{-\Gamma}$
3 | $A_{1}E^{-\Gamma}+e^{-\sigma N_{H}}A_{2}E^{-\Gamma}+G(E)$
4 | $C(E)+e^{-\sigma N_{H}}AE^{-\Gamma}$
5 | $C(E)+R(E)+G(E)$

Spectra were rebinned according to the instrumental resolution following the
prescription in Kaastra & Bleeker (2016). Spectra were analyzed in the 0.3–10
keV energy range using the Cash statistics (Cash, 1976; Kaastra, 2017). We
have employed a set of phenomenological models as described in Tab. 3222In the
analysis we used a wider set of trial models than shown in Tab. 3, which
include only those yielding the best-fit on at least one of the sources in
Tab. 4.. They are sufficient to describe the spectral shapes observed in the
X-ray spectra of the AGN on our sample. While a detailed physical description
of the astrophysical nature of each object is beyond the scope of this paper,
the proposed parameterization is sufficient to allow us to estimate the
quantities we are interested in (X-ray luminosity and obscuring column
density), keeping the systematic uncertainties due to the models lower than
the statistical errors. As far as the Compton-reflection model is concerned
($R(E)$ in Tab. 3), we used pexrav (Magdziarz & Zdziarski, 1995) for
consistency with the results published in the literature on sources of similar
statistical quality and for simplicity, even if we are well aware of the
existence of more recent and sophisticated models to describe the emission
from the AGN torus (see, e.g., the discussion in Murphy & Yaqoob 2009). As we
are not interested in this paper in understanding the detailed properties of
the reprocessing material (that would be anyway very hard to determine given
the quality of the spectroscopic data) we consider this approximation
acceptable. In using pexrav we have assumed that the spectral index of the
primary illuminating continuum is the same as that of the primary continuum,
and that the cut-off energy is 100 keV. This value is consistent with the
measurement in several nearby AGN observed with NuSTAR (Tortosa et al., 2018;
Middei et al., 2019). the exact value of this parameter does not have an
impact on the results discussed in this paper. Likewise, we employed models of
optically-thin, collisionally ionized plasma (apec; Smith et al. 2001) to
model any "soft excess" component above the extrapolation of the hard X-ray
power-law (assumed of nuclear origin) not to unduly over-fit the spectroscopic
data, even if there is now overwhelming evidence that any "soft excess" in
obscured AGN is due to the emission of photoionized gas in the X-ray Extended
NLR (Kinkhabwala et al., 2002; Guainazzi & Bianchi, 2007; Bianchi et al.,
2019), while the origin of the soft excess in unobscured AGN is still debated
(Crummy et al., 2006; Fabian et al., 2009; Done et al., 2012). None of these
assumptions affects substantially the main conclusions of this paper.

As the Cash goodness-of-fit test does not allow us to estimate the absolute
quality of the fit, the best-fit model was chosen by applying an empirical
criterion to models differing by one component corresponding to the the 99%
confidence level of the F-test calculated on the basis of the $\chi^{2}$
difference between the two models, taking the caveats after Protassov et al.
(2002) into account. We applied the $\chi^{2}$ on spectra rebinned to a
minimum number of 10 counts per background-subtracted spectral channel to
minimize biases due to the non-Gaussian nature of the count distribution.

The quality of the X-ray spectroscopic data is insufficient to constrain the
primary photon index when: a) the hard X-ray spectrum is dominated by a
Compton-reflection component (Model #5 in Tab. 3); b) in a few sources where
the primary continuum is heavily obscured and therefore the number of counts
above the photoelectric cut-off energy is too low. In these cases we have
assumed a photon index fixed to the value $\Gamma$ = 1.7, the median value
observed in a sample of nearby AGN with good quality X-ray spectroscopy data
with XMM-Newton (Bianchi et al., 2008). In two objects (SDSS J002920.36-00102
and SDSS J011254.92+00) the AGN photon index can be measured, but is
marginally inconsistent with this value because it is too hard. We attribute
this discrepancy to poor signal-to-noise (in the latter case in presence of a
steeper soft X-ray component). We estimate that the corresponding systematic
error on the AGN X-ray luminosity is $\leq$20% if $\Gamma$ = 1.7 is the true
value. In SDSS J120443.32+103 a flat spectral index $\Gamma\simeq 1.2$ is
measured in a good signal-to-noise spectrum. In this case, we interpret this
results as due to a too simple parameterization of the X-ray absorber as a
single layer. While more complex X-ray absorption structures are not required
by the fit, it is possible that deep X-ray observations at higher energies may
unveil an additional, higher column density component. If this is the case,
our measurement of the column density in this object, $\simeq$6$\times$1022
cm-2, is likely to represent a lower limit to the true column density covering
the AGN.

The best-fit values on 2-10 keV observed luminosity, photon index, and column
density absorbing the primary continuum are shown in Tab. 4.

Table 4: Best-fit parameters for the X-ray counterparts of the optically classified AGN. $N_{H}$ is the column density covering the primary continuum; $L_{X}$ is the 2–10 keV luminosity of the primary continuum corrected for absorption; $\Gamma$ is the photon index of the primary power-law continuum; $\log([OIII])$ is the [OIII]$\lambda 5007$ luminosity; $BD$ is the Balmer Decrement; $\log(R)$ is the logarithm of the ratio between the observed 2–10 keV and BD-corrected [OIII] luminosity (cf. Sect. 3). N/A indicates that the [OIII] measurement is not available. The Model IDs follow Tab. 3. Source | $\log(L_{X})$ | $\log(N_{H})$ | $\Gamma$ | $\log(L_{[OIII]})$ | $\log(BD)$ | $\log(R)$ | Model | C/$\nu$
---|---|---|---|---|---|---|---|---
SDSSJ002920.36-00102 | $42.29\pm^{0.38}_{0.17}$ | $22.91\pm^{0.88}_{1.16}$ | $0.57\pm^{1.07}_{1.34}$ | 39.67 | -0.7 | 2.6 | 3 | 103.9/87
SDSSJ010951.34+00024 | $43.55\pm^{0.33}_{0.50}$ | $\geq 24.20$ | 1.7† | 41.77 | 0.7 | -0.1 | 5 | 11.5/15
SDSSJ011254.92+000 | $43.49\pm^{0.13}_{0.28}$ | $\leq 24.25$ | $0.28\pm^{1.37}_{0.87}$ | 39.45 | -2.2 | 4.0 | 2 | 190.2/217
SDSSJ011659.07+00193 | $43.23\pm^{0.53}_{0.67}$ | $\geq 24.20$ | 1.7† | 41.65 | 1.6 | -0.3 | 1 | 38.8/25
SDSSJ014402.61-00070 | $\leq 43.35$ | $\geq 24.20$ | 1.7† | 41.56 | 1.4 |  $\leq$-0.2 | 5 | 56.1/44
SDSSJ030639.57+00034 | $42.77\pm^{0.92}_{0.18}$ | $21.55\pm^{0.25}_{0.74}$ | $1.84\pm^{0.05}_{0.04}$ | 41.34 | -0.2 | 1.4 | 2 | 543.8/494
SDSSJ030655.63-00014 | $44.\pm^{0.25}_{0.24}$ | $\geq 24.20$ | 1.7† | 42.24 | 1.4 | 0.2 | 5 | 96.7/97
SDSSJ0852.70+16261 | $42.58\pm^{0.10}_{0.08}$ | $23.00\pm^{0.18}_{0.20}$ | $1.48\pm^{0.64}_{0.55}$ | 41.05 | 0.4 | 1.5 | 2 | 284.0/277
SDSSJ101858.47+37180 | $43.09\pm^{0.23}_{0.24}$ | $\geq 24.20$ | 1.7† | 41.43 | 0.6 | -0.2 | 1 | 95.6/90
SDSSJ104856.96+59282 | $42.85\pm^{0.07}_{0.07}$ | $21.11\pm^{0.19}_{0.}$ | $1.61\pm^{0.18}_{0.17}$ | 40.91 | 0.1 | 1.9 | 1 | 263.5/247
SDSSJ115852.20+42432 | $40.66\pm^{0.14}_{0.14}$ | $\geq 24.20$ | 1.7† | 39.24 | 1.2 | -0.4 | 4 | 439.4/149
SDSSJ120443.32+103 | $42.61\pm^{0.01}_{0.02}$ | $22.76\pm^{0.04}_{0.05}$ | $1.23\pm^{0.09}_{0.11}$ | 41.57 | 0.4 | 1.0 | 3 | 653.4/523
SDSSJ121044.28+38201 | $42.55\pm^{0.45}_{0.37}$ | $23.17\pm^{0.13}_{0.13}$ | $1.48\pm^{0.67}_{0.72}$ | 39.80 | -1.0 | 2.7 | 2 | 277.5/304
SDSSJ124210.61+370 | $43.20\pm^{0.02}_{0.02}$ | $22.06\pm^{0.08}_{0.06}$ | $1.79\pm^{0.08}_{0.06}$ | 41.45 | 0.0 | 1.8 | 3 | 802.6/498
SDSSJ125729.99+28111 | $42.18\pm^{0.10}_{0.}$ | $22.48\pm^{0.14}_{0.13}$ | $1.48\pm^{1.26}_{0.84}$ | N/A | N/A | N/A | 2 | 197.6/185
SDSSJ134736.41+17340 | $41.73\pm^{0.24}_{0.34}$ | $\geq 24.20$ | 1.7† | 41.44 | 0.5 | -1.6 | 1 | 195.6/167
SDSSJ145840.74+38273 | $42.21\pm^{0.36}_{0.52}$ | $\geq 24.20$ | 1.7† | N/A | N/A | N/A | 5 | 214.6/199
SDSSJ170601.87+60173 | $42.27\pm^{0.69}_{0.71}$ | $\leq 21.82$ | $3.53\pm^{1.99}_{1.09}$ | 41.08 | 0.2 | 1.2 | 1 | 16.9/22
SDSSJ171715.74+64154 | $41.97\pm^{0.65}_{1.40}$ | $\geq 24.20$ | 1.7† | 41.90 | 1.8 | -1.8 | 1 | 93.0/64

We have complemented the results of the X-ray spectral analysis through a
study of the ratio between the observed 2–10 keV and [OIII]$\lambda 5007$
luminosities. This is known to be a sensitive diagnostic of X-ray obscuration
(Bassani et al. 1999; cf. Sect. 3 for the derivation of the [OIII]
luminosity). The selection criteria of our sample, extracted from optically-
classified AGN/no-AGN pairs (cf. § 2), ensure that we can use it as a proxy
for X-ray obscuration. The Lx/L[OIII] ratio has been investigated using
different samples of type 1 and type 2 AGN (Heckman et al., 2005; Mulchaey et
al., 1994; Bassani et al., 1999; Lamastra et al., 2009; Vignali et al., 2010).
In particular, in a sample of Compton-thick AGN Marinucci et al. (2012)
measured log (Lx/L[OIII])=-0.76 (0.1 dex dispersion), while for Compton-thin
AGN Lamastra et al. (2009) found log (Lx/L[OIII])=1.09 (0.63 dex dispersion).
We will use these thresholds to shed further light on the source
classification based on the X-ray spectral analysis. We assumed a threshold of
log (Lx/L[OIII])$\leq$0.43 to classify a source as Compton-thick. Out of the
bona fide AGN of our sample, eight sources have a ratio value indicative of
Compton-thick obscuration. For these sources we estimate a 2–10 intrinsic
luminosity larger than the observed one by a factor of 70, following Lamastra
et al. (2009); Marinucci et al. (2012). We have also verified a posteriori
that all sources with a log (Lx/L[OIII]) between 0.43 and 1.72 are consistent
with being Compton-thin according to the X-ray spectral analysis, except one
for which only a $\log(N_{H})\leq 21.82$ upper limit on the X-ray column
density (for a rather steep photon index: $\Gamma$$\geq$2.4) could be
determined.

We did not perform any spectral analysis on the only X-ray counterpart of the
SDSS non-active member of the pairs due to the low statistical quality of the
detection (cf. Sect. 4.1). Its count rate corresponds to an observed flux of
(6$\pm$2)$\times$10-14 erg s-1 cm-2, or an observed rest-frame luminosity of
(5.3$\pm$1.8)$\times$1041 erg s-1, for a typical unobscured ($N_{H}$ =
5$\times$1020 cm-2) AGN power-law spectrum with a $\Gamma$=2 photon index.

###  4.3 Radio emission

We correlated the position of the AGN in the parent sample of 32 galaxy pairs
with the Faint Images of the Radio Sky at Twenty-Centimers (FIRST; Helfand et
al. 2015) and the NRAO VLA Sky Survey (NVSS; Condon et al. 1998) 1.4 GHz radio
surveys, using a matching radius of $\leq$3.5" driven by the X-ray astrometric
accuracy. 12 of the X-ray sources exhibit a radio counterpart. A radio source
is present at the position of 5 additional AGN with no detected X-ray
counterpart. About half of the AGN are X-ray over-luminous with respect to the
radio luminosity when compared to the relation derived from a sample of local
Seyfert 1 galaxies [$L_{X}$=(11.60$\pm$0.72)+(0.81$\pm$0.02)$\times$$L_{R}$]
(Fig. 4; Panessa et al. 2007).

Figure 4: X-ray ($L_{x}$) versus 1.4 GHz luminosity ($L_{R}$) for the AGN in
the galaxy pair sample discussed in the paper. Downwards triangles indicate
upper limits on the X-ray luminosity. The red lines represent the best-fit
linear relation (dashed) and the envelope corresponding to the 1$\sigma$
uncertainty on the best-fit parameters (dot-dashed) of the relation between
the 2-10 keV luminosity and the 20 cm radio luminosity on the sample of local
Seyfert galaxies after Panessa et al. (2007).

##  5 Discussion

###  5.1 The X-ray counterparts of inactive galaxies

Only 1 out of 32 galaxies optically classified as non-AGN is our sample has a
bona fide X-ray counterpart. It is the companion galaxy of the AGN SDSS
J0852.70+16261. The detection is at the 3$\sigma$ level only (110$\pm$40 total
net counts) preventing a detailed spectral analysis. Moreover, it corresponds
to the galaxy pair with the smallest separation in our sample (6.4"),
comparable to the angular resolution of the X-ray telescope. Assuming it is a
bona fide detection, and a standard unobscured AGN spectrum, its observed
rest-frame luminosity ($\simeq$5$\times$1041 erg s-1) is consistent with a
weak AGN, a heavily obscured Seyfert galaxy, emission from starbursts
(although in this case it would correspond to a rather extreme Far Infrared
Luminosity of $\sim$1045 erg s-1 for the local Universe; Ranalli et al. 2003),
or even an extreme Ultra-Luminous X-ray (ULX) source. Its WISE colours (Tab.
5) correspond to an intermediate region where obscured AGN may be located
(Weston et al., 2017; Ricci et al., 2017). They are close to the WISE colours
of the pair of X-ray obscured AGN ESO509-IG066 (Guainazzi et al., 2005).

Table 5: WISE colors for SDSS J0852.70+16261 and its companion galaxy.  WISE name | W1-W2 | W2-W3
---|---|---
J0852.38+162619.7 | 0.355 | 4.064
J0852.87+162615.7 | 0.845 | 3.145

The nature of the X-ray emission in galaxies without detected X-ray
counterparts remains elusive. In Fig. 5

Figure 5: 90% confidence level upper limits on the 0.3–10 keV observed rest
frame luminosity at the position of the galaxies optically classified as "non-
AGN" is our sample.

we show the upper limits on the 0.3–10 keV observed rest frame luminosity at
the position of the galaxy optical centroid. In all cases, the upper limits
exceed 1041 erg s-1, and 1042 erg s-1 for $>$90% of the sample. Deeper
observations would be needed to either detect AGN still confused in the
observation noise, or to rule out with certainty the presence of weak of
heavily obscured AGN in these optically inactive galaxies. Further
observations with Chandra would also surely help in ensuring that weak sources
are not confused by the comparatively large and complex PSF of the XMM-Newton
telescope.

###  5.2 AGN triggering in AGN/no-AGN galaxy pairs

In order to make a statistical analysis of the obscuration in merging
galaxies, we collected from literature the systems hosting AGN/no-AGN pairs
and for which a measure of the absorption column density can be derived from
X-ray observations. We selected from literature additional 14 pairs AGN-galaxy
in different wavebands, (Satyapal et al., 2017; Ricci et al., 2017; Pfeifle et
al., 2019; Hou et al., 2019). Together with our systems with measured value of
NH, we collected a total sample of 33 systems (see Tab. 4, and Tab. 6). We
compared this enlarged sample with both a sample of dual AGN (the $\simeq$60
objects extracted from an heterogeneous literature sample by De Rosa et al.
(2018); see also Ricci et al. (2017)) and with a sample of isolated AGN (728
non blazar AGN extracted from the 70-month catalogue of the Swift/BAT; Ricci
et al. (2015)) in the same range of X-ray luminosities
(5$\times$1040–2$\times$1044 erg s-1).

In Fig. 6 we show the evolution of the X-ray column density as a function of
galaxy separation. The data points represent the AGN/no-AGN sample. Given the
large number of censored data, we fit the data with a Monte-Carlo method,
whereby 10,000 sets of simulated data sets were drawn from the observed data
set by: a) replacing each column density constrained measurement with the sum
of the best-fit value and the statistical error multiplied by a random number
extracted from a Gaussian distribution of mean zero and unitary standard
deviation; b) replacing each column density censored measurement with a value
randomly extracted from a uniform distribution in the [LL,1019 cm-2] and [UL,
1026 cm-2] for Lower Limits (LL) and Upper Limits (UL), respectively. The
curves in Fig. 6 represent the average of the fit on the 10,000 simulated data
sets (dotted) and the 1$\sigma$ envelope (dashed-dotted) of the best-fit
curves distribution. Formally, a strong anti-correlation between X-ray
obscuration and galaxy separation is found, with average $N_{H}$ decreasing
from a few 1023 cm-2 to $\sim$1022 cm-2 from the sub-kpc to the $\sim$100 kpc
scale. However, a few caveats shall be borne in mind. The correlation is
driven by a few heavily obscured sources at sub-kpc scale. If they are removed
from the fit, the anti-correlation between X-ray obscuration and galaxy
separation in the AGN/no-AGN systems becomes statistically not significant.
Furthermore, at separations larger than 10 kpc a sizeable number of Compton-
thick objects are found. However, the formal anti-correlation is only
marginally affected by the inclusion/removal of the Compton-thick sources (due
to their homogeneous distribution along the separation axis).

Figure 6: X-ray nuclear column density versus galaxy separation for the
AGN/no-AGN sample. The light silver data points represent the measurements
presented in this paper augmented of the literature systems listed in Tab. 6.
Upwards (downwards) triangles represent lower (upper) limits. The black lines
represent the best-fit (dotted and the envelope corresponding to the 1$\sigma$
statistical uncertainties (details of the fit procedure in text). The red
lines represent the same fit for a sample of bona fide dual AGN (data not
shown).

Out of the 19 sources in our sample for which measurements of the Balmer
Decrement (BD) and of the X-ray obscuration are available, 7 out of 9 objects
with $BD\geq$ 2, and all the 7 objects with $BD\geq$ 3 are X-ray Compton-
thick. For lower values of the Balmer Decrement no correlation with the X-ray
column density is found. This may indicate that the highest obscuration in the
NLR of these systems is associated with the most compact structures
surrounding the active nuclei, possibly the torus. No constraints on the
location of the Compton-thin obscurer can be derived from the data our our
sample. It is well possible that Compton-thick and -thin absorbers in the AGN
our our sample probe entirely different systems, thus complicating the
interpretation of the correlation shown in Fig. 6.

With this caveat in mind, the red curve in Fig. 6 represents the results of
the same fit procedure applied to the dual AGN sample. In the common
separation range ($\geq$10 kpc), dual AGN exhibit an X-ray obscuration higher
by above one order of magnitude than the AGN/no-AGN pairs. The lack of dual
AGN corresponding to sub-kpc galaxy separation prevents us from extending this
comparison to the most compact systems. The total fraction of "obscured" AGN
($N_{H}\geq$1022 cm-2) in the AGN/no-AGN sample is comprised between 79% and
84% (cf. Tab. 4). This is significantly larger than observed in isolated AGN
of comparable nuclear luminosity ($\simeq$45%; Ricci et al. 2015). It is,
however, comparable to the fraction of obscured AGN in a dual AGN sample that
raises slowly from $\simeq$70% at galaxy pair separations larger than 60 kpc
to almost 90% for separations lower than 20 kpc.

In Fig. 7 we show the nuclear X-ray luminosity as a function of galaxy
separation for the bona fine AGN presented in this paper. A linear fit with a
function: $\log(L_{X})=A+B\times s$ (where $s$ is the galaxy pair separation
in kpc) yields a moderate trend for more compact systems to be less luminous:
$A=42.05\pm 0.03$, and $B=0.0178\pm 0.0008$ kpc-1, corresponding to a decrease
of 1 dex in luminosity per $\sim$60 kpc. However, it should be borne in mind
that our sample is neither complete nor unbiased in any sense. It is therefore
hard to assess the significance of such a weak trend on the unknown parent
population.

Figure 7: X-ray nuclear luminosity (in logarithm of cgs units) as a function
of galaxy pair separation in the AGN/no-AGN sample presented in this paper.

Both cosmological (Steinborn et al., 2016; Volonteri et al., 2016) and
idealised hydrodynamic simulations (Blecha et al., 2016; Capelo et al., 2017)
of merging galaxies hosting BH have been extensively investigated in order to
evaluate the main parameters triggering the AGN activity in interacting
galaxies. In particular, numerical simulations show an increase of $N_{\rm H}$
as the distance decreases, due to merger dynamics. The simulation predict a
median value of $N_{\rm H}$ of $\sim$ 3$\times$1023cm-2, that is in good
agreement with the value measured in sample of dual AGN (De Rosa et al.,
2018). It worth noticing that the spatial resolution of the simulation only
allow to probe absorption on relatively large scales (above $\sim$ 50 pc),
this means that absorption from the AGN torus, on typical pc-scale, is not
considered and then the NH value from simulations represents a lower limit.

Simulations of the dynamical evolution of isolated mergers indicate that the
evolution depends in principle on several parameters of these complex systems:
galaxy morphology, bulge-to-disk stellar mass ratio, orbital configuration,
galaxy mass ratio, bulge-to-disk mass ratio, galaxy mass ratio, black hole
mass ratio, and the black hole feedback efficiency (Van Wassenhove et al.,
2012; Blecha et al., 2016; Blecha et al., 2018; Capelo et al., 2017). All
simulations in general agree on the dual AGN phase to be short, primarily
concentrated when the two black holes are separated by less then $\sim$10 kpc.
For typical AGN luminosities $\geq$1042 erg s-1, pairs of merging galaxies are
supposed to spend just a few Myr in a "dual AGN" phase (Capelo et al., 2015).
At black hole separations $\geq$10 kpc, the fraction of the dual active phase
versus the total active phase (i.e., the phase when at least one of the AGN is
actively accreting) goes from a few percent to about 20 percent. As our sample
was pre-selected as galaxy pairs constituted by an active and an inactive
galaxy (according to an optical spectroscopic classification), it does not
allow a direct comparison with the predictions of merging simulations.
However, when this comparison is possible (e.g, against the all-sky Swift-BAT
survey; Koss et al. 2012) consistency between the fraction of dual AGN in a
galaxy sample and the simulation predictions within a factor of two was found.

Table 6: Separations, $s$, and column densities, $N_{H}$ for the additional AGN/no-AGN systems extracted from the literature. Source | $s$ | $\log(N_{H})$
---|---|---
| (kpc) |
IRAS05189-2524 | 0.1 | $23.10\pm^{0.03}_{0.04}$
Mrk2 | 0.1 | $23.16\pm^{0.08}_{0.10}$
NGC34 | 0.1 | $23.72\pm^{0.08}_{0.10}$
UGC05101 | 0.1 | $24.12\pm^{0.09}_{0.12}$
NGC7130 | 0.1 | $24.30\pm^{0.18}_{0.30}$
IRAS120-5453 | 0.1 | $24.50\pm^{0.24}_{0.23}$
J1036+0221 | 2.8 | $21.85\pm^{0.06}_{0.07}$
J2356-1016 | 5.0 | $22.93\pm^{0.08}_{0.10}$
J1147+0945 | 6.8 | $22.41\pm^{0.05}_{0.05}$
J0859+10 | 9.9 | $23.24\pm^{0.11}_{0.12}$
NGC4922N | 10.8 | $\geq 24.20$
CG468-002W | 11.3 | $22.18\pm^{0.03}_{0.03}$
NGC7674 | 20.7 | $\geq 24.20$
NGC7469 | 26.0 | $19.78\pm^{0.12}_{0.18}$

##  6 Conclusions

In this paper, we present an XMM-Newton study of a sample of galaxy pairs,
identified through SDSS spectroscopy as being constituted by an AGN-hosting
and an inactive galaxy. The original main goal of the project was to identify
via X-rays active nuclei in the "inactive" member of the pair that could have
been missed due to heavy obscuration along the line of sight to the nucleus.
For the galaxies hosting an AGN, we discuss in this paper the X-ray
photometric and spectroscopic properties, and put them in context of the
prediction of state-of-the-art hydrodynamical simulations of isolated mergers
on the condition for the triggering of "dual" AGN.

Out of the the parent sample of over 1500 galaxy pairs with an SDSS "AGN–no-
AGN" classification, 32 bona fide pairs are in the field-of-view of the EPIC
cameras (as of March 2018). The main results of our study can be summarized as
follows:

  * •

for only one of the "non-AGN" galaxy in the pair an X-ray counterpart is found
(at the 3$\sigma$ level). Assuming a standard AGN-like X-ray spectrum, its
rest-frame luminosity ($\simeq$5$\times$1041 erg s-1) is consistent with a
weak AGN, a heavily-obscured Seyfert galaxy (consistently with its WISE
colors), emission from starbursts, or even an extreme ULX source

  * •

for 90% of the "non-AGN galaxies" in the pair for which no X-ray counterpart
is found, the derived upper limits on the 2-10 keV luminosities are $\geq$1042
erg s-1, i.e. still consistent with an active nucleus "hidden" in the data
(cf. Fig. 5)

  * •

for 19 "AGN" galaxies in the pair, a bona fide X-ray counterpart is found,
covering a wide range in absorption corrected X-ray luminosity
(5$\times$1040–2$\times$1044 erg s-1; cf. Tab. 4)

  * •

our AGN/no-AGN sample shows only a weak dependence of the AGN X-ray luminosity
on the separation between the members of the galaxy pair, with more compact
systems being marginally less luminous (cf. Fig. 7)

  * •

the bona fide AGN are unevenly split between "unobscured" ($N_{H}$$<$1022
cm-2; 16–26%), "Compton-thin ($10^{22}$$\leq$$N_{H}$ $<$1.6$\times 10^{24}$
cm-2; 32-37%), and "Compton-thick" ($N_{H}\geq 1.6\times 10^{24}$ cm-2; 47%)
obscured (cf. Tab. 4)

  * •

we considered 14 additional systems AGN–non-AGN from literature and compare
the total of 33 (14+19) systems with a sample of bona fide dual AGN (De Rosa
et al., 2018). Dual AGN at separations larger than 10 kpc exhibit on the
average a larger nuclear obscuration by about one order of magnitude with
respect to the AGN/no-AGN systems (cf. Fig. 6)

  * •

galaxy pairs including at least an AGN exhibit a fraction of obscured nuclear
activity larger than 70%. This exceeds by a factor 1.5 the fraction of
obscured objects in a sample of isolated AGN of matching luminosities and
redshifts (Ricci et al., 2015)

While this is suggestive that the galactic environment has a key influence on
the AGN triggering in merging galaxies, deeper studies with a larger number of
objects would be needed in order to perform a more quantitative comparison
with the X-ray predictions of hydrodynamic simulations (Capelo et al., 2015,
2017). We aim at continuing these studies in the future (De Rosa et al.,
2019).

## Acknowledgements

The authors thanks an anonimous referee, whose careful revision of the
manuscript significantly improved the paper. We thank G. Calderone for help
with QSFit. SB, ADR and EP acknowledge financial support from the Italian
Space Agency under grant ASI-INAF 2017-14-H.O. MPT acknowledges support by the
Spanish MCIU through grant PGC2018-098915-B-C21 cofunded with FEDER funds and
from the State Agency for Research of the Spanish MCIU through the “Center of
Excellence Severo Ochoa” award for the Instituto de Astrofísica de Andalucía
(SEV-2017-0709) and through grant PGC2018-098915-B-C21 (MCI/AEI/FEDER, UE).
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS-III Collaboration
including the University of Arizona, the Brazilian Participation Group,
Brookhaven National Laboratory, Carnegie Mellon University, University of
Florida, the French Participation Group, the German Participation Group,
Harvard University, the Instituto de Astrofisica de Canarias, the Michigan
State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence
Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max
Planck Institute for Extraterrestrial Physics, New Mexico State University,
New York University, Ohio State University, Pennsylvania State University,
University of Portsmouth, Princeton University, the Spanish Participation
Group, University of Tokyo, University of Utah, Vanderbilt University,
University of Virginia, University of Washington, and Yale University.

## Appendix A: XMM-Newton/EPIC spectra of bona fide AGN

In Fig. 8 and 9 we show the EPIC spectra, best-fit model (upper panels) and
residuals against the best-fit model in units of data/model ratio for the 19
bona fide AGN in our sample. each data point correspond to a signal-to-noise
ratio larger than three.

Figure 8: Upper panels: EPIC spectra crosses and best-fit models solid lines
for the 19 bona fide AGN spectra in our sample. Lower panels: residuals
against the best-fit model in units of data/model ratio. Black: EPIC-pn; red:
EPIC-MOS1; green: EPIC-MOS2. Each data point corresponds to a minimum signal-
to-noise ratio $\geq$3\.

Figure 9: Continuation of Fig. 8.

## Data availability statement

The high-level data underlying this article are extracted through standard
processing from raw data stored in public archives (SDSS and XMM-Newton), and
will be shared on reasonable request to the corresponding author.

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# Newtonian pulsations of relativistic ONe-core ultra-massive DA white dwarfs

A. H. Córsico,1 L. G. Althaus,1 and M.Camisassa,2

1Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La
Plata, Paseo del Bosque s/n, (1900) La Plata, Argentina;
<EMAIL_ADDRESS>
2Departament de Física, Universitat Politécnica de Catalunya, c/Esteve
Terrades 5, E-08860 Castelldefels, Spain

## Abstract

Ultra-massive H-rich (DA spectral type) white dwarf stars
($M_{\star}>1.05M_{\odot}$) are expected to be substantially crystallized by
the time they reach the ZZ Ceti instability strip ($T_{\rm eff}\sim 12\,000$
K). Crystallization leads to a separation of 16O and 20Ne (or 12C and 16O) in
the core of ultra-massive WDs, which strongly impacts their pulsational
properties. An additional factor to take into account when modeling the
evolution and pulsations of WDs in this range of masses are the relativistic
effects, which induce changes in the cooling times and the stellar masses
derived from the effective temperature and surface gravity. Given the arrival
of large amounts of photometric data from space missions such as Kepler/K2 and
TESS, it is important to assess the impact of General Relativity in the
context of pulsations of ultra-massive ZZ Ceti stars. In this work, we present
results of Newtonian gravity($g$)-mode pulsation calculations in evolutionary
ultra-massive WD models computed in the frame of the General Relativity
theory.

##  1 Introduction

ZZ Ceti stars are pulsating DA (H-rich atmospheres) white dwarfs (WDs) with
effective temperatures in the range $10\,500<T_{\rm eff}<12\,600$ K. These
variable stars exhibit pulsation periods from $\sim 100$ s to $\sim 1400$ s
due to nonradial gravity($g$) modes with harmonic degree $\ell=1$ and $\ell=2$
(Winget & Kepler, 2008; Fontaine & Brassard, 2008; Althaus et al., 2010;
Córsico et al., 2019). Although the vast majority of ZZ Ceti stars are DA WDs
with masses between $\sim 0.5$ and $\sim 0.8M_{\odot}$, $g$-mode pulsations
have also been detected at least in four ultra-massive
($M_{\star}>1.05M_{\odot}$) ZZ Ceti stars so far; they are BPM 37093
($M_{\star}=1.1M_{\odot}$ Kanaan et al., 1992), GD 518
($M_{\star}=1.24M_{\odot}$ Hermes et al., 2013), SDSS J084021
($M_{\star}=1.16M_{\odot}$ Curd et al., 2017), and WD J212402
($M_{\star}=1.16M_{\odot}$ Rowan et al., 2019). It is likely that pulsating
WDs even more massive ($M_{\star}>1.30M_{\odot}$) will be identified in the
coming years with the advent of huge volumes of high-quality photometric data
collected by space missions such as the ongoing TESS mission (Ricker et al.,
2014) and the future PLATO space telescope (Rauer et al., 2014). This big
amount of data is expected to make asteroseismology a promising tool to study
the structure and chemical composition of ultra-massive WDs (Córsico et al.,
2019). The increasing number of ultra-massive WDs with masses beyond
$1.30M_{\odot}$, as well as the immediate prospect of detecting pulsating WDs
with such masses, demand new appropriate theoretical evolutionary models to
analyze them. In particular, it is necessary to calculate models that take
into account relativistic effects and to evaluate the impact of General
Relativity on the pulsational properties of ultra-massive WDs. In this
exploratory investigation, we take the first step in this direction,
calculating Newtonian pulsations on fully relativistic equilibrium models.

Figure 1: The stellar radius (upper panels) and gravity (bottom panels) in
terms of the outer mass fraction coordinate corresponding to ultra-massive DA
WD models with $M_{\star}=1.29M_{\odot}$ (left) and $M_{\star}=1.369M_{\odot}$
(right), for the Newtonian case (black curves) and the fully relativistic case
(red curves), for $T_{\rm eff}\sim 12\,000$ K.

##  2 Relativistic WD models

We have generated ultra-massive WD model sequences with ONe cores taking into
account the full effects General Relativity employing the LPCODE stellar
evolution code (Althaus et al., 2022). We considered realistic initial
chemical profiles as predicted by the progenitor evolutionary history (Siess,
2007, 2010; Camisassa et al., 2019), and computed model sequences of
$1.29,1.31,1.33,1.35$, and $1.369M_{\odot}$ WDs. The standard equations of
stellar structure and evolution have been generalized to include the effects
of General Relativity, following Thorne (1977). For comparison purposes, the
same sequences have been computed but for the Newtonian gravity case. We have
included the energy released during the crystallization process, both due to
latent heat and due to the induced chemical redistribution as in Camisassa et
al. (2019).

We show in Fig. 1 the stellar radius and gravity of ultra-massive DA WD models
with $1.29M_{\odot}$ (left panels) and $1.369M_{\odot}$ (right panels), for
the Newtonian case (black curves) and the fully relativistic case (red
curves). Clearly, general relativity induces smaller radii and larger
gravities, and this effect is more pronounced for larger stellar masses.

##  3 Chemical profiles and the Brunt-Väisälä and Lamb frequencies

Figure 2: Abundances by mass of the different chemical species as a function
of the fractional mass (upper panels), and the logarithm of the squared Brunt-
Väisälä and Lamb ($\ell=1$) frequencies, corresponding to ONe-core DA WD
models with $M_{\star}=1.29M_{\odot}$ (left) and $M_{\star}=1.369M_{\odot}$
(right), for $T_{\rm eff}\sim 12\,000$ K. The gray areas correspond to the
crystallized regions.

The cores of our models are composed mostly of 16O and 20Ne and smaller
amounts of 12C, 23Na, and 24Mg. Since element diffusion and gravitational
settling operate throughout the WD evolution, our models develop pure 1H
envelopes. The 4He content of our WD sequences is given by the evolutionary
history of progenitor star, but instead, the 1H content of our canonical
envelopes [$\log(M_{\rm H}/M_{\star})=-6$] has been set by imposing that the
further evolution does not lead to 1H thermonuclear flashes on the WD cooling
track. The temporal changes of the chemical abundances due to element
diffusion are assessed by using a new full-implicit treatment for time-
dependent element diffusion (Althaus et al., 2020).

The chemical profiles in terms of the fractional mass for $1.29M_{\odot}$ and
$1.369M_{\odot}$ ONe-core WD models at $T_{\rm eff}\sim 12\,000$ K and H
envelope thickness $\log(M_{\rm H}/M_{\star})=-6$ are shown in the upper
panels of Fig. 2. At this effective temperature, typical of the ZZ Ceti
instability strip, the chemical rehomogeneization due to crystallization has
already finished, giving rise to a core where the abundance of 16O increases
and 20Ne decreases outward.

In the lower panels of Fig. 2 we show the squared Brunt-Väisälä and Lamb
($\ell=1$) frequencies corresponding to the same models shown in the upper
panels for the Newtonian case (black curves) and the relativistic case (red
red curves). The triple chemical transition between 12C, 16O, and 20Ne located
at $-\log(1-M_{r}/M_{\star})\sim 1.5$ is within the solid part of the core, so
it has no relevance for the mode-trapping properties of the models. This is
because, according to the “hard-sphere” boundary conditions adopted for the
pulsations (Montgomery & Winget, 1999), the $g$-mode eigenfunctions do not
penetrate the crystallized region (gray areas). In this way, the mode trapping
properties are entirely determined by the presence of the 4He/1H transition,
which is located in more external regions. Note that the Brunt-Väisälä and
Lamb frequencies for the Newtonian and relativistic models are
indistinguishable for the case of $1.29M_{\odot}$, but they notoriously differ
when $M_{\star}=1.369M_{\odot}$.

##  4 Pulsation spectrum of $g$ modes for Newtonian and relativistic ultra-
massive WD models

Figure 3: The $\ell=1$ asymptotic period spacing for WD sequences with
different stellar masses for the Newtonian and relativistic cases in terms of
$T_{\rm eff}$ through the whole ZZ Ceti instability strip.

Figure 4: The $\ell=1$ forward period spacing ($\Delta\Pi=\Pi_{k+1}-\Pi_{k}$,
upper panels), the kinetic energy of oscillation (middle panels), and the rate
of period change (lower panels) for models with $1.29M_{\odot}$ (left) and
$1.369M_{\odot}$ (right) in the relativistic (red) and Newtonian (black) cases
($T_{\rm eff}\sim 12000$ K).

Adiabatic nonradial $g$-mode Newtonian pulsations have been computed with the
LP-PUL pulsation code (Córsico & Althaus, 2006). This code neglects the
oscillations of $g$ modes in the crystallized region of the WD core (hard-
sphere boundary condition; see Montgomery & Winget, 1999; Córsico et al.,
2004). Fig. 3 shows the asymptotic period spacing (computed as in Tassoul et
al., 1990) for the sequences of $1.29,1.31,1.33,1.35$ and $1.369M_{\odot}$ WD
models in terms of the effective temperature all along the ZZ Ceti instability
strip. We note that the asymptotic period spacing is smaller for the case of
the relativistic WD sequences as compared with the Newtonian sequences. This
is what we expect since the asymptotic period spacing is inversely
proportional to the integral of the Brunt-Väisälä frequency divided by the
radius. Since the Brunt-Väisälä frequency is larger for the relativistic case
(see Fig. 2), then the integral is larger and its inverse smaller than in the
Newtonian case. The difference is larger for larger stellar masses.

In Fig. 4 we depict the dipole $\ell=1$ forward period spacing, the kinetic
oscillation energy, and the rate of period change for the models with
$1.29M_{\odot}$ and $1.369M_{\odot}$, at $T_{\rm eff}=12\,000$ K. We can see
that, in general, the period spacing is larger in the Newtonian case, as
expected (see Fig. 3). On the other hand, the oscillation kinetic energy of
the modes is higher in the relativistic case, since the WDs are more compact
and dense than in the Newtonian case. Finally, the rate of change of periods
is larger for the relativistic case, since the cooling timescale is shorter
due to relativistic effects, in comparison with the Newtonian case (Althaus et
al., 2022).

##  5 Summary and conclusions

In order to start the study of the impact of General Relativity on the
pulsations of ultra-massive WDs representative of ZZ Ceti stars, we have
calculated as an initial step the Newtonian $g$-mode pulsations on
relativistic equilibrium WD structures. We have found that the Brunt-Väisälä
frequency, the period spacing, the oscillation kinetic energy, and the rates
of period change are remarkably modified in relation to Newtonian models for
the case of very high masses, close to the Chandrasekhar mass, although the
effects are much less noticeable for lower masses. The next step in this
project is to compute the additional effects of General Relativity on the
stellar pulsations by solving the nonradial stellar pulsation equations in the
relativistic Cowling approximation. This will allow us to assess the combined
effect of General Relativity on the equilibrium structures and on the
pulsation modes.

## Acknowledgments

A.H.C. warmly thanks Klaus Werner and the Local Organizing Committee of the
22th European White Dwarf Workshop for support that allowed him to attend this
conference.

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