11institutetext: INAF – Osservatorio Astronomico di Roma, Via Frascati 33,
I-00078 Monte Porzio Catone (RM), Italy 22institutetext: “Sapienza” Università
di Roma – Dip. di Fisica, P.le A. Moro 5, I-00185 Roma, Italy 33institutetext:
Università degli Studi di Roma “Tor Vergata” – Dip. di Fisica, Via della
Ricerca Scientifica 1, I-00133 Roma, Italy 44institutetext: INFN – Roma Tor
Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy 55institutetext:
University of Maryland – Dept. of Astronomy, College Park, MD-20742, USA
66institutetext: NASA – Goddard Space Flight Center, Greenbelt Rd. 8800,
MD-20771 Greenbelt, USA 77institutetext: ASI – Space Science Data Center, Via
del Politecnico snc, I-00133 Roma, Italy 88institutetext: Scuola Normale
Superiore di Pisa, P.zza dei Cavalieri 7, I-56126 Pisa, Italy

# Unveiling the periodic variability patterns of the X-ray emission from the
blazar PG 1553+113

T. Aniello 112233 L. A. Antonelli 11 F. Tombesi 1133445566 A. Lamastra 11 R.
Middei 1177 M. Perri 1177 F. G. Saturni 1177 A. Stamerra 1188 F. Verrecchia
1177

(Received 18 March 2024; accepted 5 April 2024)

The search for periodicity in the multi-wavelength high variable emission of
blazars is a key feature to understand dynamical processes at work in this
class of active galactic nuclei. The blazar PG 1553+113 is an attractive
target due to the evidence of periodic oscillations observed at different
wavelengths, with a solid proof of a 2.2-year modulation detected in the
$\gamma$-ray, UV and optical bands. We aim at investigating the variability
pattern of the PG 1553+113 X-ray emission using a more than 10-years long
light curve, in order to robustly assess the presence or lack of a periodic
behavior whose evidence is only marginal so far. We conducted detailed
statistical analyses, studying in particular the variability properties of the
X-ray emission of PG 1553+113 by computing the Lomb-Scargle periodograms,
which are suited for the analyses of unevenly sampled time series, and
adopting epoch folding techniques. We find out a modulation pattern in the
X-ray light curve of PG 1553+113 with a period of $\sim$1.4 years, about 35%
shorter than the one observed in the $\gamma$-ray domain. Our finding is in
agreement with the recent spectro-polarimetric analyses and supports the
presence of more dynamical phenomena simultaneously at work in the central
engine of this quasar.

###### Key Words.:

black hole physics — galaxies: active — BL Lacertae objects: general — BL
Lacertae objects: individual: PG 1553+113 — X-rays: general — X-rays: galaxies
— X-rays: individual: PG 1553+113

##  1 Introduction

Blazars are a class of active galactic nuclei (AGN) characterized by extreme
luminosity and variability over the entire electromagnetic spectrum. Their
emission is dominated by a single component, i.e. a jet of relativistic
particles directly pointing towards the observer (Urry & Padovani, 1995). From
a spectroscopic point of view, these sources show a peculiar spectral energy
distribution (SED) that is characterized by a double-humped shape. The low-
frequency peak, that can be observed from the radio up to the X-ray domain, is
attributed to synchrotron radiation arising from high-energy electrons that
spiral around magnetic field lines (Padovani & Giommi, 1995); its properties
mainly depend on the strength of the magnetic field and on the energy
distribution of the relativistic electrons in the jet (Maraschi et al., 1992).
The second hump is usually observed in the X-to-$\gamma$-ray range, and its
origin is commonly associated with inverse Compton (IC) emission (Ghisellini
et al., 1992; Abdo et al., 2011a; Zdziarski & Bottcher, 2015), or synchotron
self-Compton where the seed photons emerge from either external radiation
fields (external Compton; EC) or the synchrotron radiation of the jet itself,
respectively. Several evidences, from SED modeling (e.g., Abdo et al., 2011b)
and energetic considerations (Zdziarski & Bottcher, 2015; Liodakis &
Petropoulou, 2020) to observations of correlated flux variations across
different wavebands (e.g., Agudo et al., 2011b, a; Liodakis et al., 2018),
and, recently, polarimetry (Middei et al., 2023a; Peirson et al., 2023),
support the leptonic origin of the second hump of the blazars SED.

Figure 1: MWL LCs of PG1153+113 in B (yellow dots), M2 (blue dots), X-ray (red
dots) bands and spectral index (dark blue dots) from 2012 to 2023 of Swift
satellite. The X-ray fluxes are in 0.2-10 keV band. B, M2 and X-rays LCs are
showed along with the corresponding 1$\sigma$ uncertainties.

A hallmark of the blazar phenomenon is the prominent flux and spectral
variability, which is thought to arise from changes in the jet properties such
its particle density, magnetic field strength and orientation (Padovani &
Giommi, 1995). Variability can be observed over different timescales from
hours up to decades (Kellermann, 1992). In this context, the search of
periodic signals is object of growing attention, and the high synchrotron
peaked source PG 1553+113 represents one of the most interesting cases. PG
1553+113, a blazar with optical magnitude $V\,\sim\,14.5$ at redshift
$z\,\sim\,0.4\div 0.5$ (Danforth et al., 2010), shows evidence of a
periodicity ($T\sim 2.2$ yr) in the $\gamma$-ray band ($E\geq\,100\,\rm MeV$)
sampled by the Fermi-LAT satellite and at lower frequencies ($R$-band;
Ackermann et al., 2015; Sobacchi et al., 2017; Peñil et al., 2024). A possible
explanation for the periodic signal was proposed by Sobacchi et al. (2017),
who discussed a scenario where a couple of asymmetric super massive black
holes (SMBHs), of which the smallest carries a jet, interacts producing a
precession of the jet itself.

The temporal properties of the PG 1553+113 X-ray emission are instead more
debated: Huang et al. (2021) claimed the finding of the same periodicity with
respect to the $\gamma$-ray emission within a scenario in which both SMBHs
possess a jet. Conversely, Peñil et al. (2024), working on a blazar sample,
identified a periodicity of $\sim$1.5 years with a significance of
$\sim$2$\sigma$. In this paper, we report on the temporal properties of PG
1553+113 by investigating the data collected in the rich Swift archive, which
provides 617 X-ray and $>$400 optical/UV observations. By constructing the
source multi-wavelength (MWL) light curves (LCs), we correlate the various
emission bands and search for an unambiguous periodic signal at each
wavelength with robust methods of time series analysis, such as the
construction of the Lomb-Scargle periodograms (Lomb, 1976; Scargle, 1982) and
the application of epoch folding techniques (e.g., Larsson, 1996), with a
particular attention to the X-ray signal in order to identify with enough
significance an associated periodicity.

The paper is organised as follows: in Sect. 2 we illustrate the data selection
and reduction; in Sect. 3 we compute correlations between different bands; in
Sect. 4 we present the X-ray variability analysis; in Sect. 6 we discuss our
findings; finally, in Sect. 7 we summarize the obtained results. Throughout
the text, we adopt a concordance cosmology with $H_{0}=70$ km s-1 Mpc-1,
$\Omega_{M}=0.3$ and $\Omega_{\Lambda}=0.7$.

##  2 Observations and data reduction

Launched in 2004, the Swift satellite carries the X-ray Telescope (XRT), which
is sensitive in the $0.2\div 10$ keV energy band, and the UV/Optical Telescope
(UVOT), capable of observations in the $170\div 600$ nm band. XRT has high
spatial resolution of 18′′, allowing for precise localization of celestial
objects. XRT and UVOT operate simultaneously, to enable concurrent
observations in different electromagnetic bands (Roming et al., 2005; Burrows
et al., 2005). Since our e retrieved the X-ray, UV and optical reduced data
from 2005 to 2023 from the Swift public mirror archive 111Available at
https://swift.ssdc.asi.it/. of the Space Science Data Center (SSDC) at the
Italian Space Agency (ASI). In this analysis, we excluded the data taken
before 2012, characterized by a sparse temporal sampling, to avoid the
introduction of biases that could be ascribed to time intervals containing no
data points.

Correlation | Pearson coeff. | Degrees of freedom
---|---|---
U/X | 0.54 | 265
B/X | 0.50 | 264
V/X | 0.48 | 254
W1/X | 0.57 | 279
M2/X | 0.58 | 269
W2/X | 0.60 | 278
X PhIdx/flux | 0.55 | 303

Table 1: Results of the correlation analysis (Pearson correlation coefficients
and number of degrees of freedom) between pairs of wavebands, and between the
X-ray photon index and flux.

The Swift-XRT observations were carried out in the Windowed Timing (WT) and
Photon Counting (PC) readout modes. The data were first reprocessed locally
with the XRTDAS software package (version v3.7.0), developed by the ASI-SSDC
and included in the NASA-HEASARC HEASoft package222Available at
https://heasarc.gsfc.nasa.gov/docs/software/heasoft/. (version v6.31.1).
Standard calibration and filtering processing steps were applied to the data
using the xrtpipeline task. The calibration files available from the Swift-XRT
CALDB (version 20220803) were used. Events for the temporal and spectral
analysis were selected within a circle of 20-pixel ($\sim$47′′) radius, while
the background was estimated from nearby circular regions with a radius of 40
pixels. For each observation, the X-ray energy spectrum was first binned with
the grppha tool of the FTOOLS package333Available at
https://heasarc.gsfc.nasa.gov/ftools/. to ensure a minimum of 20 counts per
bin, and then modeled using the XSPEC software package444Available at
https://heasarc.gsfc.nasa.gov/xanadu/xspec/. adopting a single power-law
model.

We obtained dereddened UV and optical fluxes with a dedicated ASI-SSDC
pipeline for the analysis of UVOT sky images (Giommi et al., 2012). We first
executed the aperture photometry task included in the UVOT official software
from the HEASoft package (version v6.26), extracting source counts within a
standard 5$\arcsec$ circular aperture and the background counts from three
circular 18$\arcsec$ apertures that were selected to exclude nearby stars. We
then derived the source dereddened fluxes by applying the official UVOT
calibrations from the CALDB (Breeveld et al., 2011), and adopting a standard
UV/optical mean interstellar extinction law (Fitzpatrick, 1999) with a mean
$E(B-V)$ value of 0.0447 mag (Schlafly & Finkbeiner, 2011). We show the X-ray,
UV (M2 filter) and optical ($B$-band) LCs obtained in this way in Fig. 1,
along with the X-ray photon index: a visual inspection already reveals
considerable flux variability. Furthermore, while the UV and optical trends
can be overlapped, the X-ray band exhibits some peaks that do not appear in
the other bands, hinting to a possible X-ray periodicity that is different
with respect to the optical/UV one.

##  3 Correlations between different bands, and between photon index and X-ray
flux

Figure 2: PG 1553+113 X-ray photon index–to-flux correlation. The two linear
fits of photon index versus flux and vice-versa (red dotted lines) are shown
along with the corresponding bisector fit (red dashed line). The data points
are color-coded on the basis of their MJD.

We first proceeded studying the correlations among the various bands, and
between X-ray photon index and flux. The photon index and the X-ray flux of PG
1553+113 in the 0.3-10 keV band are moderately anti-correlated (see Fig. 2) as
we computed a Pearson coefficient (Bevington & Robinson, 2003) of $r=-0.55$
and an associated null-hypothesis probability $p($¿$r)=3.6\times 10^{-24}$
(see Tab. 1). The X-ray photon index is flatter as the source flux increases.
This is commonly observed in blazars (the so-called “harder when brighter”
behavior; e.g., Giommi et al., 2021), and is expected when particles are
injected and accelerated in the jet (Abdo et al., 2010).

We then tested the correlation properties between the UV, optical and X-ray
bands, respectively. Moderate correlations were found as shown in Fig. 3 and
Tab. 1. Such a study highlights the typical behavior of the radiation emitted
from blazars in adjacent wavebands such as the X-rays and the optical/UV,
since the respective emitting regions are partially overlapping in the jet and
produce photons through the same underlying physical process (i.e. the
synchrotron or IC radiation) – or by processes that make it varying in a
quasi-simultaneous way (Dhiman et al., 2021).

Figure 3: Correlations of the UV-to-X-ray and optical-to-X-ray bands of PG
1553+113. As in Fig. 2, the two linear correlation fits (red dotted lines) are
shown along with the corresponding bisector fit (red dashed line).

##  4 Multi-wavelength variability analysis

To investigate the periodic behavior of the X-ray emission in PG 1553+113, we
performed an analysis of the LC through the employment of numerical methods
that are commonly used in studies of time series. In particular, we mainly
relied on the construction of the Lomb-Scargle (LS) periodogram (Lomb, 1976;
Scargle, 1982), a technique that is widely adopted to search for periodic
signals in astronomical data sets (e.g., VanderPlas, 2018; Vio et al., 2013)
and especially suited for analysing unevenly sampled time series (Baluev,
2008). This method consists in the calculation of the power spectral density
(PSD) of a time series, estimating the signal likelihood at each frequency on
the basis of a least-squares fit of a sinusoidal model to the data. For our
analysis, we adopted the LS routines contained inside the AstroPy (v5.0)
Python package (Astropy Collaboration et al., 2022).

In carrying on our analysis, we already knew that the optical (and the
associated UV) LCs exhibit a $\sim$2.2-yr period (Sobacchi et al., 2017);
therefore, we expected that the calculation of the LS periodogram for such LCs
should yield a comparable result as a confirmation of the goodness of the
method. We thus computed the LS periodograms associated with the PG 1553+113
X-ray, UV and optical LCs, and identified prominent peaks in the PSD. We show
the results in the left panels of Fig. 4: a visual inspection reveals that,
while the main peak associated with the optical and UV variability patterns is
located at the same frequency, a clearly prominent peak also appears for the
X-ray signal, but – at variance with the optical/UV case – is shifted at a
larger frequency (corresponding to a shorter period).

We found that such a peak was located at a frequency of $\sim$2.3 $\times
10^{-8}$ Hz, corresponding to $T_{\rm X}\sim 1.4$ years. This value is
significantly lower of $\sim$35% than the $\gamma$-ray period $T_{\gamma}\sim
2.2$ years identified in the Fermi-LAT data by Ackermann et al. (2015) and in
the optical LC by Sobacchi et al. (2017), thus hinting at the presence of a
different periodic process. To quantify the significance of this peak, we then
estimated its false alarm probability (FAP) level, i.e. the probability of
accidentally obtaining a given peak power due to noise fluctuations. We
considered statistically significant only those peaks whose FAP level was
falling below $\sim$10% (Sturrock & Scargle, 2010), setting the corresponding
LS power of $\sim$0.04 to be our 1$\sigma$ significance; in doing so, we
obtained a significance of 9.2$\sigma$ for the 1.4-yr X-ray peak. We also
repeated the procedure on the entire PG 1553+113 X-ray LC from 2005 to 2023,
i.e. including those data that were discarded in the selection described in
Sect. 2, to check the persistence of the peak in the LS periodogram: the test
yielded the same $T_{\rm X}$ with a significance of 7.5$\sigma$. We argue that
this lower significance is due to the presence of large time gaps in the
complete X-ray LC (see Fig. 1).

Figure 4: Left panels: PG 1553+113 LS periodograms of the X-ray, UV (W2) and
optical bands ($V$; blue solid lines). In each panel, the frequency of the
main peak (black dashed line) is highlighted, and its value is reported (see
legend). Right panels: X-ray, UV and optical LCs (blue points), along with the
relative sinusoids of periods corresponding to the LS most significant
frequencies (red dashed lines). In such panels, the sinusoid maxima
approximately coinciding with flux peaks in the LCs (grey dot-dashed lines)
are marked, and the corresponding period is reported (see legend).

In the UV and optical LS periodograms, we found a frequency of the most
significant peak of $\sim$1.5 $\times 10^{-8}$ Hz that corresponds to $T_{\rm
opt}\sim 2.1$ years with a significance of 5.8$\sigma$ (see Fig. 4). For
completeness, we also tested the LS analysis on the publicly available Fermi-
LAT $\gamma$-ray data555Available at
https://fermi.gsfc.nasa.gov/ssc/data/access/. from 2008 to 2023: in doing so,
we again obtained the peak at a frequency of $\sim$1.5 $\times 10^{-8}$ Hz
with a significance of 7.3$\sigma$, corresponding to the well-known
$T_{\gamma}\sim 2.2$ years found by Ackermann et al. (2015). In light of
having retrieved a comparable result with that reported in the literature for
the PG 1553+113 joint optical/$\gamma$-ray signal (Sobacchi et al., 2017),
this analysis strengthens our finding of a discrepant $T_{\rm X}$ with respect
to the variability period of the LCs at other wavebands.

To further confirm the temporal properties of the PG 1553+113 X-ray emission,
we applied two different methods. First, we used the timing tasks provided by
the Xronos software package666Available at
https://heasarc.gsfc.nasa.gov/xanadu/xronos/xronos.html., designed for the
analysis of high-energy astrophysical data (Stella & Angelini, 1992). We
started from the power spectrum (powerspec) method to calculate the PSD of the
LCs in each energy band; in this way, we identified the significant peaks
corresponding to potential periods in the X-ray LC that match the results
obtained with the LS analysis. Then, we applied the epoch-folding search
(efsearch) method to perform the calculation of the posterior distribution of
the LC periodicities: the distribution peak yielded a best-fit period of
$\sim$1.4 years, further confirming the LS findings. Finally, we employed the
epoch folding (efold) method to generate folded LCs at the specific periods of
interest. We show the outcome of this cross-check in Fig. 5.

Then, we also used the “significance spectrum” (SigSpec) algorithm developed
for asteroseismology (Reegen, 2007; Chang et al., 2011; Maceroni et al.,
2014), which is based on the analysis of frequency- and phase-dependent
spectral significance levels $S$ of peaks in a discrete Fourier transform of
the signal, through the computation of the probability density function and
its associated FAP due to white noise. Like the LS analysis, this method is
particularly suited for periodicity studies on sparse data. We thus executed
the SigSpec algorithm on the UVOT W2 and $V$ time series and finally on the
X-ray time series, obtaining the highest significance periods $T_{\rm W2}\sim
2.08$ years ($S_{\rm W2}\sim 28.0$), $T_{V}\sim 2.11$ years ($S_{V}\sim 29.6$)
and $P_{\rm X}\sim 1.39$ years ($S_{\rm X}\sim 27.5$), respectively. Also such
values are in agreement with those obtained with the LS, thus confirming the
goodness of our result.

Figure 5: Left panel: PG 1553+113 PSD of the X-ray LC obtained with the
powerspec package of Xronos. Middle panel: best-fit period (solid line) of the
PG 1553+113 X-ray LC obtained with the efsearch task, along with its numerical
value in seconds corresponding to $\sim$1.4 years (see text). Right panel:
epoch folding of the PG 1553+113 X-ray LC obtained with the efold method on
the basis of the best-fit period determined by efsearch.

##  5 X-ray period uncertainty estimate and red-noise bias analysis

The calculation of the LS periodogram does not provide any estimate of the
uncertainty on the position of the significant peaks. To estimate this
quantity, we performed an extensive LS analysis over many altered versions of
the PG 1553+113 X-ray LC, in which we replaced each point with a new observing
epoch and flux level that differ from the original ones by random amounts
extracted from appropriate distributions centered on the actual data. For
altering the observing epochs, we adopted uniform distributions, with widths
equal to the full width at half maximum (FWHM) of $\sim$1 year derived from
the Gaussian fit to the distribution of best-fit periods computed by the
efsearch task (see Fig. 5); for the flux values, we instead adopted Gaussian
distributions with standard deviations equal to the associated 1$\sigma$
errors. In this way, we produced $10^{3}$ realizations of the PG 1553+113
X-ray LC; for each realization, we then computed the LS periodogram, and
derived the posterior distribution of frequencies of the most significant
peak. The statistical analysis of this distribution yielded a best estimate of
the PG 1553+113 X-ray period of $T_{\rm X}=1.41\pm 0.68$ years.

Despite the high significance level of our results, we are unable to
automatically exclude that the LS analysis is biased by sources of uncertainty
that could produce fake signals in the periodogram. This could be due e.g. to
non-periodic processes that can mimic a periodic temporal behavior on the time
scales of our interest, such as random variability in the AGN flux that is
usually distributed according to a red noise spectrum (Bhatta, 2017; Vaughan
et al., 2016). Since the PSD of blazar LCs is of the red-noise type (Vaughan,
2005), the power level – and thus the FAP – is expected to increase at low
frequencies. To assess that our results are not biased by red-noise processes,
we simulated the response of the LS analysis to a sample of mock LCs generated
according to a pure red noise PSD.

To this aim, we generated such LCs by extracting, from a red-noise spectral
distribution (e.g., Gardiner, 1994), a number of fake flux points
corresponding to the amount of X-ray data at our disposal, and associating
each of them to an MJD time of our observations. We iterated this process
$10^{5}$ times to reach statistical significance of the results; for each mock
LC produced in this way, we computed the associated LS periodogram using the
same methodology described in Sect. 4. Requesting a minimum LS power of
$\sim$0.04 as our 1$\sigma$ level – i.e. the same amount associated with the
threshold FAP of our real data (see Sect. 4) – we found that at most
$\sim$16$\%$ of our mock LCs rise above 5$\sigma$ in the frequency range of
interest $(2\div 3)\times 10^{-8}$ Hz (see Fig. 6). Such a fraction is non-
negligible, and thus suggests some caution to be adopted in claiming a firm
discovery of the $\sim$1.4-year periodicity; nevertheless, these findings
point toward the plausible detection of a true periodic signal in the X-ray LC
of PG 1553+113 at an $\sim$84% confidence level.

##  6 Discussion

The presence of multiple periodic patterns in the MWL LCs of PG 1553+113 has
been object of various studies (Ackermann et al., 2015; Sobacchi et al., 2017;
Huang et al., 2021; Peñil et al., 2022; Adhikari et al., 2023); recently,
there has also been the indication of a potential long-term variability trend
in the $\gamma$-ray emission ($\sim$22 years; Adhikari et al., 2023; Peñil et
al., 2024). Different scenarios have been proposed to explain this behaviour:
the most widely accepted one relies upon the presence, inside the PG 1553+113
central engine, of a binary system of SMBHs in which one of the two carries a
jet that is gravitationally affected by the SMBH motions (Ackermann et al.,
2015). This may happen in several ways, such as (i) a jet precession (Sobacchi
et al., 2017), (ii) a helical shaping of the jet (Abdo et al., 2010), or (iii)
instabilities in the jet structure (Huang et al., 2021). Alternatively, (iv)
accretion modulations (Tavani et al., 2018) and (v) evaporation processes
possibly coexisting with disk overdensities (Adhikari et al., 2023) may also
lead to similar results.

The $\gamma$-ray and optical period was already modeled by Sobacchi et al.
(2017), considering a jet precession with a period $T_{\gamma}\sim 2.2$ years.
To account for an overall different X-ray period, Huang et al. (2021) fit the
Swift-XRT LC with a two-jet model, each carried by one of the PG 1553+113
SMBHs, assuming a precession with $T_{X}\sim 2.2$ years acting on both jets;
however, their result is based on the analysis of a less extended X-ray LC
with respect to ours. Also Peñil et al. (2024), by analyzing the Swift-XRT
data of a sample of $\gamma$-ray detected blazars, found for PG 1553+113 an
X-ray period of $\sim$1.5 years with a significance of $\sim$2$\sigma$ after
averaging on the temporal properties of the entire sample.

A possible explanation that does not take into account a binary SMBH system
could be the cyclic injection of large quantities of matter from the innermost
regions of the central engine into the jet base (Lewis et al., 2019). If this
input of matter occurs regularly, this could produce the emission of a
modulated X-ray signal with a different period with respect to that of the
$\gamma$-ray, UV and optical emission (due to the jet precession). It is
interesting to note that recent observations from the IXPE satellite (Middei
et al., 2023b) indicate the presence of different emitting regions in the jet
structure, hinting at either a stratified jet or different levels of
turbulence inside the jet structure.

The plausible detection of a different time modulation of the PG 1553+113
X-ray emission with respect to the $\gamma$-ray, UV and optical ones has
further complicated the road to understand the physical mechanisms acting in
the central engine of this blazar. Future MWL observations and studies
involving a more detailed modeling of the PG 1553+113 innermost structure
(SMBH system, accretion disk, jet, and the respective interplay), will be
crucial to eventually explain the origin of its temporal properties.

Figure 6: LS periodograms calculated on randomly generated LCs of pure red
noise. For plotting purposes, we show $10^{2}$ (grey solid lines) out of the
total $10^{5}$ realizations, superimposed to the LS periodogram of the real PG
1553+113 X-ray data (blue dot-dashed line) and the corresponding 5$\sigma$
significance level (black dashed line) (see Sect. 4). The relevant frequency
interval for our analysis of $(2\div 3)\times 10^{-8}$ Hz (black dotted lines)
is also highlighted.

##  7 Summary and future work

In this study, we have conducted a comprehensive analysis of the X-ray, UV and
optical data of the blazar PG 1553+113, aimed at investigating the possible
presence of a characteristic X-ray periodicity that differs from the already
ascertained $\gamma$-ray and optical variability period. We summarize our main
findings below:

  1. 1.

the PG 1553+113 X-ray, UV and optical LCs are all moderately correlated to
each other according to the Pearson analysis ($r\sim 0.5$); the X-ray photon
index is correlated with the X-ray flux in a similar way. This behavior is
typical of blazars, where the light is emitted almost entirely from the jet
due to the synchrotron and IC processes (Padovani & Giommi, 1995; Maraschi et
al., 1992).

  2. 2.

The X-ray LC constructed over $\gtrsim$10 observer-frame years of Swift-XRT
data likely ($>$80% confidence level) exhibits a periodic emission, but with a
shorter characteristic period $T_{\rm X}\sim 1.4$ years with respect to that
found in the optical and $\gamma$-ray bands ($T_{\rm opt}=T_{\rm
UV}=T_{\rm\gamma}\sim 2.2$ years; Ackermann et al., 2015; Sobacchi et al.,
2017; Peñil et al., 2024).

Current scenarios are not able to properly explain such a difference in the
widely accepted framework of a binary system of SMBHs carrying a preceding jet
in the PG 1553+113 central engine (Huang et al., 2021; Tavani et al., 2018;
Sobacchi et al., 2017; Adhikari et al., 2023); therefore, further theoretical
investigations and observational data are needed to better disentangle the
physical mechanisms that lie at the base of the different variability periods
of the PG 1553+113 MWL emission.

###### Acknowledgements.

We thank the anonymous referee for their helpful comments. We acknowledge M.
Imbrogno (INAF-OAR) for useful discussion about the use of the Xronos
software. This article is part of TA’s work for the Ph.D. in Astronomy,
Astrophysics and Space Science, jointly organized by the “Sapienza” University
of Rome, University of Rome “Tor Vergata” and INAF. Reproduced with permission
from Astronomy & Astrophysics, © ESO.

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