# Ultraconfined Plasmons in Atomically Thin Crystalline Silver Nanostructures

Vahagn Mkhitaryan  ICFO-Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
Andrew P. Weber  ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute
of Science and Technology, 08860 Castelldefels (Barcelona), Spain  Donostia
International Physics Center, Paseo Manuel Lardizabal 4, 20018 Donostia-San
Sebastián, Spain  Saad Abdullah  ICFO-Institut de Ciencies Fotoniques, The
Barcelona Institute of Science and Technology, 08860 Castelldefels
(Barcelona), Spain  Laura Fernández  Centro de Física de Materiales CSIC-
UPV/EHU and Materials Physics Center, 20018 San Sebastián, Spain  Zakaria M.
Abd El-Fattah  Physics Department, Faculty of Science, Al-Azhar University,
Nasr City, E-11884 Cairo, Egypt  Ignacio Piquero-Zulaica  Centro de Física de
Materiales CSIC-UPV/EHU and Materials Physics Center, 20018 San Sebastián,
Spain  Hitesh Agarwal  ICFO-Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
Kevin García Díez  Centro de Física de Materiales CSIC-UPV/EHU and Materials
Physics Center, 20018 San Sebastián, Spain  Frederik Schiller  Centro de
Física de Materiales CSIC-UPV/EHU and Materials Physics Center, 20018 San
Sebastián, Spain  J. Enrique Ortega<EMAIL_ADDRESS>Donostia
International Physics Center, Paseo Manuel Lardizabal 4, 20018 Donostia-San
Sebastián, Spain  Centro de Física de Materiales CSIC-UPV/EHU and Materials
Physics Center, 20018 San Sebastián, Spain  Departamento de Física Aplicada I,
Universidad del País Vasco, 20018 San Sebastián, Spain  F. Javier García de
Abajo<EMAIL_ADDRESS>ICFO-Institut de Ciencies
Fotoniques, The Barcelona Institute of Science and Technology, 08860
Castelldefels (Barcelona), Spain  ICREA-Institució Catalana de Recerca i
Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain

###### Abstract

The ability to confine light down to atomic scales is critical for the
development of applications in optoelectronics and optical sensing as well as
for the exploration of nanoscale quantum phenomena. Plasmons in metallic
nanostructures can achieve this type of confinement, although fabrication
imperfections down to the subnanometer scale hinder actual developments. Here,
we demonstrate narrow plasmons in atomically thin crystalline silver
nanostructures fabricated by prepatterning silicon substrates and epitaxially
depositing silver films of just a few atomic layers in thickness. Combined
with on-demand lateral shaping, this procedure allows for an unprecedented
control over optical field confinement in the near-infrared spectral region.
Specifically, we observe fundamental and higher-order plasmons featuring
extreme spatial confinement and high-quality factors that reflect the
crystallinity of the metal. Our approach holds potential for the design and
exploitation of atomic-scale nanoplasmonic devices in optoelectronics,
sensing, and quantum-physics applications.

##  I INTRODUCTION

A large deal of work has been devoted to the confinement of light down to
deep-subwavelength spatial regions as a powerful strategy to enhance nonlinear
interactions with matter [1], enable efficient single-molecule sensing [2],
and explore quantum optics phenomena at the nanoscale [3]. Efforts have thus
focused on localized and surface-propagating optical modes that are robust,
long-lived, spatially compressed relative to free-space light, and lying
within a spectral range of technological interest such as the near-infrared
(NIR). Unfortunately, finding a single platform that combines these appealing
properties is a hard task. Partial success has been obtained by engineering
lossless dielectric structures [4], although the mode sizes are yet far from
the few-nanometer realm, particularly in the NIR. For example, polaritons in
two-dimensional (2D) materials [5, 6] (e.g., plasmons in graphene [7, 8] and
phononic modes in hexagonal BN [9] and MoO3 [10]) are long-lived, extremely
confined, and amenable to active tunability [11, 12], but they only exist at
mid-infrared frequencies.

Atomic-scale confinement of NIR light requires hybridization with electronic
excitations, with the ultimate limit of spatial compression being represented
by individual atoms and molecules, although their application is in practice
hindered by weak coupling to light compared with coupling to atomic vibrations
in any host material unless cryogenic temperatures are introduced [13].
Analogously, excitons in transition metal dichalcogenides operate in the
visible domain and are active at room temperature, but only within narrow
spectral bands [14, 15].

Visible and NIR plasmons in noble metals are collective broadband electron
excitations of bosonic nature, capable of strongly localizing optical energy
down to the few-nanometer scale in all three spatial directions [16], and
commonly displaying large transition strengths that are contributed by a large
number of electrons. Through a sustained series of advances in colloid
chemistry [17] and nanolithography [18], the plasmon mode frequency and
spatial distribution can be tuned at will by adjusting the size and morphology
of the supporting structure. Although inelastic losses limit the lifetimes of
noble-metal plasmons down to tens of femtoseconds, their strong spatial
confinement renders them as excellent nonlinear elements for harmonic
generation [1, 19] and wave mixing [20, 21], as well as an optimum choice for
optical sensing based on surface-enhanced Raman spectroscopy [22]. In
addition, the robustness and strong coupling to light displayed by noble-metal
plasmons have been instrumental in the success of plasmonics in areas such as
optical signal communications [23], light modulation [24, 25, 26], biosensing
[27, 28, 29, 30], structural coloring [31, 32], and control of thermal
emission [33, 34], in spite of the fact that most studies have relied on
amorphous or polycrystalline samples. In this respect, it is well-known that
defects and grain boundaries increase inelastic losses, and this effect can be
dramatically reduced in single-crystal structures [35].

Visible and NIR plasmons in 2D metals combine robustness with an intrinsically
high degree of spatial confinement [36, 37, 38, 39] that makes them attractive
as a platform for nonlinear nanophotonics [40] and optoelectronics [41].
Previously, we demonstrated plasmons in silver structures as thin as eight
(111) atomic monolayers (MLs) on Si(111) with a high crystalline quality
revealed by the measurement of sharp electronic quantum-well states and
electron diffraction patterns, as well as a record-high surface conductance
[38]. Plasmons in 2D metals are characterized by short wavelengths compared to
free-space light, and therefore, a source of momentum is required to excite
them, such as that provided by external tips [42, 43] or through the
evanescent field supplied by electron beams [44]. However, we are generally
interested in shaping the metal structure to gain control over the near field
associated with plasmon guiding, localization, coupling to external light, and
interaction with other structures. Electron beam lithography and focused ion
beam are commonly employed to this end, and although these techniques are
perfectly suited for patterning thick metal films, they produce damage and
contamination in 2D materials. For example, the measured quality factor of
ultrathin plasmons has been reported to be $\sim 4$ in $<2$ nm silver [38] and
$\sim 1$ in $\approx 3$ nm gold [39]. Ultimately, the quality factor of deep-
subwavelength plasmons is limited by intrinsic material properties, quantified
in a Drude damping $\hbar\gamma\sim 20$ meV in silver and $\sim 70$ meV in
gold [45], such that, at the telecom wavelength of $\sim 1550~{}$nm
($\hbar\omega=0.8$ eV photon energy), we have an upper bound of the quality
factor $Q=\omega/\gamma\approx$ 40 and 10 in silver and gold, respectively. In
pursuit of these limits, alternative patterning methods that can minimize
metal damage are highly desirable.

Here, we observe plasmons in few-atomic-layer-thick crystalline silver
nanostructures with an unprecedented combination of spatial confinement and
lifetime. Our samples are made possible through the development of a
fabrication method consisting in lithographically prepatterning the desired
morphologies on a silicon wafer and subsequently evaporating silver films of
epitaxial quality. We observe silver plasmons with quality factors approaching
10 in $\sim 3$ nm-thick silver bowties, with the modes being laterally
confined down to a $\sim 10$ nm gap region. The flexibility of our fabrication
method is illustrated by a wide range of NIR spectral features exhibited by
particles of various designated shapes and sizes. In addition, we compare
particle arrays with different periodicities and reveal radiative losses
driven by inter-particle interactions even for well-separated structures.
These results open a practical approach to high-quality NIR plasmonics on the
few-nanometer scale, enabling applications in optical sensing, light
modulation, and nonlinear nanophotonics by bridging the gap between
traditional noble-metal nanostructures and 2D materials.

##  II RESULTS

Figure 1: Prepatterned silicon for high-quality ultrathin crystalline silver
nanoplasmonics. (a) Schematic representation of a ribbon array consisting of
flat-top and rough-bottom Si(111) regions covered with an ultrathin Ag(111)
film. (b) SEM images of representative samples with two different ribbon
widths $W$ (see labels). (c,d) Measured optical extinction spectra for 14 ML
$\approx 3.3$ nm (c) and 18 ML $\approx 4.3$ nm (d) silver films with
different ribbon widths $W$ (see top legend) combined with an array period
$a=3\,W$ (dashed curves with markers) or $a=4\,W$ (solid curves). (e,f)
Simulations corresponding to panels (c,d), respectively. (g,h) Dipolar plasmon
energies extracted from (c-f).

The sketch in Fig. 1a shows an example of our fabricated structures,
consisting of silver ribbons deposited on a prepatterned silicon wafer and
covered with a $\sim 1$ nm passivating silica layer (not shown; see Methods).
The lower regions in the structures are rough because we use a combination of
chemical and physical dry etching, and accordingly, silver is also rough in
those areas. In contrast, the upper silicon surfaces remain smooth because
they are protected by a resist mask during etching (see also Supplementary
Figs. S5-S8 for an extended surface-science analysis of our films). Examples
of two fabricated ribbon arrays with widths $W=150$ and $250$ nm are shown in
the scanning electron microscope (SEM) images of Fig. 1b. For ultrathin
Ag(111) films consisting of 14 and 18 MLs ($\approx 3.3$ and 4.3 nm,
respectively), we collect extinction spectra that reveal well-defined plasmons
over a wide range of ribbon widths $W=40-100$ nm (Fig. 1c,d). An expected
redshift is observed as the ribbon aspect ratio is increased by either
reducing the film thickness or making the width larger. In addition, the
inter-ribbon separation plays an important role that we analyze by comparing
structures with different periods: $a=3\,W$ (Fig. 1c,d dashed curves) and
$a=4\,W$ (solid curves). In brief, shorter periods produce an attractive
interaction between the modes of neighboring ribbons that translates into an
observable redshift that becomes clearer when comparing the plasmon energies
for the two period-to-width ratios under consideration (Fig. 1g,h). In
addition, for a given plasmon energy, modes sustained by structures with a
larger $a/W$ ratio are narrower, in agreement with the fact that the plasmon
width receives a radiative contribution proportional to $\sim 1/a$ [38].

We also show electromagnetic simulations of these structures based on a
finite-difference method in the frequency domain (COMSOL), which are in
excellent agreement with our measurements, as shown in Fig. 1e,f, particularly
for the dipolar plasmon energies of the thicker sample (see Fig. 1h), although
the experimental peaks are blue-shifted with respect to theory for the 14 ML
films (Fig. 1g), presumably because of the effect of de-wetting in the rough
metal deposited in the grooves at such small thicknesses, which changes its
behavior from a continuous metallic layer to an effective dielectric composed
of nonpercolated metal particles [46]. The redshift produced by the attractive
interaction of ribbon plasmons with the extended metal regions in the grooves
is corroborated in our simulations (see Supplementary Fig. S9). We also
observe an extra broadening in the experiment with respect to theory, which we
attribute mainly to a finite distribution in the size of the fabricated
ribbons.

Inelastic losses in the metal can also contribute to broadening, although the
overall effect when contrasting experiments (Fig. 1c,d) and theory (Fig. 1e,f)
is smaller for samples fabricated through the present prepatterning approach
than what one finds when following a fabrication procedure based on
lithography of previously deposited flat silver films [38]. We thus understand
that the high crystalline quality of the metal is better preserved by using
the methods here reported. Supporting this conclusion, a decent preservation
of silver quality is revealed by the observation of electronic quantum wells
in angle-resolved photoemission spectroscopy (ARPES) measurements of patterned
structures, comparable to those of extended unpatterned films (see
Supplementary Figs. S5 and S8).

Figure 2: Plasmon diversity in ultrathin crystalline silver nanostructures. We
study doubly periodic arrays of disks (a-c), triangles (d-f), bars (g-i), and
bowtie antennas (j-l). The structures and geometrical parameters are
illustrated in the top panels (a,d,g,j), accompanied by SEM images of
representative fabricated samples (b,e,h,k). The measured extinction of these
structures is shown in the bottom panels (c,f,i,l) for different lattice
periods and structure sizes (see labels), combined with a silver film
thickness of 14 ML (dashed curves) or 18 ML (solid curves). Disks and
triangles are arranged in square lattices. Spacings for disks are indicated in
the legend of (c). We set $a=2\,W$ for triangles (f), $a_{x}=2\,W_{x}$ and
$a_{y}=3\,W_{y}$ for rods (i), and $a_{x}=3\,W$ and $a_{y}=2\,W$ for bowties
(l). The gap in the latter is $\sim 10$ nm.

The flexibility of the prepatterning approach allows us to fabricate a wide
variety of ultrathin crystalline silver morphologies, whose plasmonic
properties are analyzed in Fig. 2. We consider doubly periodic arrays of disks
(Fig. 2a-c), triangles (d-f), bars (g-i), and bowtie antennas (j-l), whose
geometrical parameters are defined in the upper sketches (Fig. 2a,d,g,j,
respectively), along with SEM images of representative structures (Fig.
2b,e,h,k) that corroborate an excellent degree of quality. The corresponding
extinction spectra (Fig. 2c,f,i,l) for silver thicknesses of 14 ML (dashed
curves) and 18 ML (solid curves) display pronounced features associated with
plasmon modes in the structures, revealing again a redshift in thinner
structures relative to thicker ones. A change in morphology produces a radical
redistribution in the position and arrangement of the observed spectral
features. Interestingly, besides the main dipolar resonance peaks, additional
modes are emerging in the upper energy range of the spectra under
investigation, corresponding to higher-order plasmons that are more localized
and, consequently, less radiative than dipolar plasmons. Such higher-order
plasmons are thus spectrally narrower and exhibit larger quality factors,
although, due to their weaker radiative coupling, their extinction cross
sections are comparatively reduced. In addition, higher-order modes are
associated with shorter plasmon wavelengths, which render them more sensitive
to structural defects. The observation of high-quality, higher-order modes is
thus clear evidence of the excellent quality of our fabricated silver
structures.

Figure 3: Large quality factors in high-order plasmons. (a) Selection of
measured extinction spectra featuring high-order modes for different structure
morphologies. (b,c) Quality factors (b) and plasmon widths (c) extracted from
measured samples with different shapes (see legend) over the range of
geometrical parameters considered in Fig. 2 for a silver film thickness of 14
ML (open symbols) and 18 ML (solid symbols). Measuremed values for ribbon
arrays are included for completeness. In (c), we show the intrinsic silver
width of 21 meV (blue line).

Figure 3a shows a selection of spectra in different structures that sustain
high-energy modes, from which we obtain the corresponding quality factor
$Q_{j}=\omega_{j}/\gamma_{j}$ for each mode $j$ by fitting to a series of
pseudo-Voigt line shapes and extracting the peak positions $\omega_{j}$ and
resonance widths $\gamma_{j}$. Applying this procedure to a varied set of
particle shapes and sizes, we obtain the quality factors and plasmon widths
presented in Figs. 3b and 3c, respectively. We find quality factors $Q>9$ in
rods and bowties at relatively large energy ($\gtrsim 0.7$ eV) in the NIR
spectral range. A part of the observed plasmon broadening is directly
inherited from the intrinsic optical Drude damping of the material, which is
21 meV [45] for bulk silver (blue line in Fig.s 3c). Additional damping is
introduced by material defects, which act as an extra source of inelastic
coupling from plasmons to electron-hole pairs. This effect is important when
the structures are fabricated by patterning previously deposited metal films
[38], but its magnitude is reduced for prepatterned structures in the present
study, allowing us to reach substantially higher plasmon quality factors.
Again, radiative damping contributes to the plasmon width when the structures
are placed in close proximity, so that they are allowed to interact: for an
individual structure (e.g., one of our ribbons or other shapes), coupling to
radiation plays a negligible role because the lateral size is much smaller
than the light wavelength; in contrast, when the distance between neighboring
structures is reduced, the overall extinction takes substantial values (Fig.s
3a), and by reciprocity, coupling from plasmons to radiation is also becoming
significant. For ribbon arrays, the contribution of radiative damping scales
as the width-to-period ratio $\propto W/a$ [38], while for 2D arrays it goes
as $\propto(W/a)^{2}$. The different scaling of ribbon and 2D particle arrays
explains why, for the same metal thickness, the plasmon widths of ribbon
arrays are generally larger than those of 2D arrays within the larger range of
plasmon energies under consideration (Fig. 3c).

Figure 4: Near-field distribution and Purcell factor simulated for bowtie
structures. (a,b) Electric near-field amplitude distribution for a silver
bowtie of 18 ML thickness illuminated under normal incidence with light of
2.72 $\mu$m wavelength polarized along the gap direction. (c) Purcell factor
for a dipolar emitter placed at the gap center of bowties with 10, 15, and 20
ML silver thickness. (d) Near-field distribution associated with features A-D
in the 10 ML bowtie of (c). Triangles are equilateral with 200 nm side length
and 10 nm gap separation in all cases.

Prepatterning of atomically thin films allows us to control not only the
plasmon spectral properties but also the near-field distributions and the
degree of localization of optical hotspots, such as in the bowtie structures
presented in Fig. 2j-l. As an example, we theoretically explore in Fig. 4
bowties made of equilateral triangles with $W=200$ nm side length. The near
field associated with the lowest-order gap plasmon is illustrated in Fig. 4a,b
for a 18 ML structure with a $\sim 10$ nm gap at 2.72 $\mu$m light wavelength,
showing that the field is primarily confined to the gap, with some intense
features also emerging at distant corners of the structure, which can be
attributed to the effect of charge redistribution guaranteeing neutrality in
each of the two triangles. The gap-plasmon energy is very sensitive to
geometrical details, such as the film thickness, with the associated Purcell
factor (i.e., the decay rate of an emitter at the gap center relative to the
rate in free space) taking high values of $\sim 10^{5}$ within the fabricated
range of thicknesses (Fig. 4c). Such high Purcell factors are the result of
both the relatively narrow plasmon lines and the small volume contained in the
gap regions. The calculated plasmon width is smaller than what we measure in
the experiment (Fig. 2l), an observation that we attribute to the effect of
averaging over a large number of structures in the spectrometer, which present
unintended variations in geometrical parameters within the precision of the
fabrication method. Incidentally, the bowtie structures also sustain higher-
order modes with a small degree of field concentration in the gap compared to
the fundamental gap mode (Fig. 4d).

##  III CONCLUSIONS

The possibility of having damage-free, ultrathin, crystalline metal films
marks a new upper bound in our ability to manipulate light at unprecedentedly
small length scales. In this context, silver still holds a paramount position
as a relatively low-loss plasmonic material, but its optical performance is
limited by defects in noncrystalline samples, which introduce undesired
inelastic losses. We demonstrate a low-damage fabrication method of ultrathin
crystalline silver nanostructures with great flexibility to produce any
desired lateral morphologies by epitaxially growing films with a controlled
number of atomic layers on prepatterned silicon wafers. Using far-field near-
infrared spectroscopy, we experimentally identify narrow plasmon modes
supported in these structures with a quality factor approaching $Q\sim 10$. We
remark that high-order modes beyond dipolar features are also observed, thus
increasing the level of spatial confinement down to a small fraction of the
fabricated nanostructures. This is the case of bowties, which host gap modes
with extreme spatial localization, while still retaining relatively high
quality factors. Our results represent a substantial step towards the ultimate
achievable level of quality factor for ultraconfined optical modes in the
near-infrared spectral region, which is only limited by intrinsic metal losses
in such deep-subwavelength plasmons (i.e., a Drude damping $\hbar\gamma=21$
meV in silver [45], for which $Q=\omega/\gamma\sim 40$ and 80 at 1550 and 800
nm light wavelength, respectively). At small particle sizes, plasmon
confinement is further limited by nonlocal effects, which introduce additional
damping mechanisms for sizes approaching $W\sim 1$ nm [47], and thus, we
envision the ultimate degree of combined confinement and lifetime in silver
structures of $\sim 10$ nm lateral size resonating at a light wavelength
$\lambda_{0}\sim 1$ $\mu$m with an in-plane plasmon wavelength $\lambda_{\rm
p}\sim 2W$ and an out-of-plane extension $\sim\lambda_{\rm p}/2\pi$ [38],
resulting in a mode volume $\sim 10^{-7}\,\lambda_{0}^{3}$. The present work
represents a solid step in that direction, holding potential for the
realization of sought-after nanoplasmonic applications in optoelectronics,
optical sensing, and the exploration of quantum-optics phenomena at the few-
nanometer length scale.

## METHODS

Sample Preparation. Silicon chips were prepatterned through a combination of
electron-beam lithography (EBL) and dry reactive ion etching (RIE). Samples
were first cleaned by ultrasound sonication in acetone and isopropanol for
5-10 min in each solvent, followed by blow-drying using nitrogen gas, and
subsequent baking for 5 min at 150°C on a hot plate to remove any remaining
water before a negative-tone AR-N-7520 EBL resist was spin-coated at 4000 rpm.
The desired patterns were transferred to the resist using a Crestec
lithography setup, followed by development in AR-300 for 1 min and rinsing in
de-ionized water for 30 s. The patterned resist then served as a mask for
etching the silicon in a RIE Oxford Plasmalab 80 Plus system employing a
mixture of C4F8 and SF6. With gas flows of 90 sccm for C4F8 and 30 sccm for
SF6, combined with a fixed radiofrequency power of 10 W and a coil power of
600 W, we obtained an etching rate of 80 nm/min as well as rather straight
side wall profiles in the etched silicon structures. Etched samples were then
washed in reagent-grade acetone and isopropanol for $>15$ min each. The native
silica surface layer was removed in a commercial (iDonus) vapor-based etching
system, using a solution of 40% HF (by mass) in de-ionized water as the
etchant, or by direct immersion in 2% aqueous HF solution. Samples were etched
for either 1 hr or $\approx 90$ s when following vapor- or solution-based
approaches, respectively, and then rinsed twice by immersion in de-ionized
water for 5 min, dried under a stream of nitrogen, loaded into the ultrahigh
vacuum (UHV) chamber within 12 min, degassed at a temperature in the
$150-250$°C range for several hours, and heated to $>680$°C for over 2 min
until a well-ordered Si(111)$-(7\times 7)$ surface was identified by low-
energy electron diffraction (LEED, see Supplementary Fig. S6). Silver was then
sublimated from an electron-bombardment evaporator onto the Si(111)$-(7\times
7)$ surface. The deposition, which we monitored with monolayer accuracy using
a quartz microbalance whose response to a given silver flux was calibrated by
probing the quantum-well state binding energies of silver films grown on
Au(111) [48], was carried out at a rate of $\approx 0.4$ ML/min with the
sample kept at a temperature of 110 K. Samples were then annealed to room
temperature and the film thickness and quality were verified by photoemission
measurements, followed by deposition of 1 nm of Si before removal from the UHV
chamber, when oxidation transformed it into a passivating silica layer [38].

Sample Characterization. ARPES was performed using a SPECS Phoibos 150
electron analyzer equipped with a monochromatized He gas discharge lamp
operating at the He I$\alpha$ excitation energy (21.22 eV), with an electron
energy and angular resolution better than 40 meV and 0.4°, respectively. ARPES
measurements (see Supplementary Fig. S5) were made with the sample at 110 K.
X-ray photoelectron spectroscopy was also collected using a monochromatized Al
K$\alpha$ source (1486.71 eV) to corroborate a low degree of carbon and oxygen
surface contamination (see Supplementary Fig. S7).

Optical Measurements and Analysis. Plasmon spectra were acquired in the far
field using a Bruker Hyperion Fourier-transform infrared (FTIR) spectrometer
operating over a spectral range of $0.074-0.99$ eV. A multi-peak procedure was
followed to assimilate the measured FTIR spectra to a combination of
asymmetric pseudo-Voigt peak profiles. Plasmon resonance positions $\omega$
and FWHM $\Delta\omega$ were then extracted, from which the quality factors
were calculated as $Q=\omega/\Delta\omega$.

Figure S5: Characterization of the silver film quality on H-passivated
prepatterned Si(111). (a-c) Low-energy electron diffraction (LEED) images
providing a surface structural characterization of the procedure for preparing
silver films on H-passivated prepatterned Si(111) in ultrahigh vacuum. The
H/Si(111) surface presents $1\times 1$ order until hydrogen desorption is
induced by heating to a temperature above 550 ∘C, leaving a bare
Si(111)$-(7\times 7)$ surface [49]. Although our H/Si(111) surface shows sharp
LEED spots in (a), there is a moderate background due to diffuse (and possibly
inelastic) scattering by surface contaminants. To produce a clean
Si(111)$-(7\times 7)$ surface for high-quality silver epitaxy, the samples
were gradually heated and kept at the maximum temperature of $650$ ∘C for
$12-15$ min. Following the procedure in Ref. [38], the samples were then
cooled below 120 K for silver deposition. (d-e) Angle-resolved photoelectron
spectroscopy (ARPES) measurements showing the photoemission intensity as a
function of binding energy relative to the Fermi level ${E_{\rm F}}$ and in-
plane wave vector for forms consisting of 14 ML (d) and 18 ML (e) of Ag(111)
deposited on prepatterned silicon. The incident electron beam energy is 32 eV
in (a,b) and 51 eV in (c). The ARPES photon energy is 21.22 eV. Figure S6:
LEED characterization of Si(111)$-(7\times 7)$ surfaces. (a) Diffraction from
a fully $7\times 7$ ordered surface obtained by successive heating cycles with
a high maximum temperature of $>1000$ ∘C, as used previously on unpatterned Si
substrates [38]. (b) Incomplete $7\times 7$ ordering (exhibiting only faint
reconstruction spots) obtained by annealing a patterned H/Si(111) substrate at
650 ∘C. Degreasing and HF etching are performed in a standard chemistry lab
fume hood for this sample. The $7\times 7$ pattern does not form as readily as
in the previous samples. (c) Improved $7\times 7$ order obtained after
successive heating cycles limited to a maximum temperature of $850$ ∘C. The
electron beam energy is 51 eV in all cases. Figure S7: X-ray photoemission
spectroscopy (XPS) of (a) a clean Si(111)$-(7\times 7)$ surface prepared on an
unpatterned substrate following the method in Ref. [38] and (b) a patterned
H/Si(111) substrate prepared as the described in Fig. S6. In (b), the spectra
collected immediately after loading into an ultrahigh vacuum (UHV) chamber and
after heating are plotted in red and blue, respectively. In all cases, the Si
2p and 2s core levels appear near 100 and 150 eV binding energy, respectively,
each of them accompanied by a set of bulk-plasmon loss peaks, as well as a
shoulder produced by the $\approx 4$ eV chemical shift produced by a small
remaining part of the native surface oxide [50]. The as-loaded H/Si(111)
sample exhibits lower core-level peak intensities, a higher background, and
some intensity appearing around 285 eV binding energy arising from C 1s, which
is not detectable in (a). Labeled insets in (b) show the XPS signal in narrow
ranges around the C 1s and O 1s core levels, which are clearly resolved. This
is in contrast to Ref. [49], where an extensively degreased, thick thermal
oxide surface was used as a starting point for obtaining H/Si(111). Heating
the sample in (b) nearly eliminates the oxygen contribution, although some
carbon contamination remains with a chemical shift to $\approx 283$ eV binding
energy, consistent with SiC [50]. These remaining carbide impurities are
likely the primary hindrance to $7\times 7$ ordering, which limits the quality
of the fabrication process compared with higher-temperature methods in which
carbon is diffused into the bulk. Figure S8: Comparison of ARPES spectra
collected from unpatterned (a-d) and patterned (e-h) substrates either before
(a-b,e-f) or after (c-d,g-h) growth of 18 ML of Ag(111). We plot results for a
narrow energy range within 3 eV of ${E_{\rm F}}$ in panels (a,c,e,g) and over
a wide energy sweep of the valence bands in panels (b,d,f,h). In general, we
observe broader features increasing toward higher binding energies and a
larger inelastic background in the patterned sample. The surface states of the
$7\times 7$ silicon surface around 0.25 and 0.8 eV below the Fermi level also
show weaker intensity for the patterned sample. Both of these observations are
consistent with the roughness imposed by etching most of the surface area of
the substrate (away from the patterns), as well as a degradation off perfect
long-range atomic ordering introduced by the presence of carbide, as discussed
in Fig. S7. Figure S9: Effect produced by silver deposition in the groove
region on the ribbon plasmon energies. We show the plasmon energies calculated
under the same conditions as in Fig. 1 in the main text for 14 ML (a) and 18
ML (b) silver films with a period-to-width ratio $a/W=3$ and 4 (see labels)
and assuming the presence or absence of silver on the lower groove regions
(with and without gap Ag, respectively). A substantial redshift is produced in
the ribbon plasmon energies by interaction with the metal in the groove
regions.

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# Study of Blazar activity in 10 year Fermi-LAT data and implications for TeV
neutrino expectations

J. R. Sacahui  11affiliation: Instituto de Investigación en Ciencias Físicas y
Matemáticas, USAC, Guatemala. A. V. Penacchioni  22affiliation: Instituto de
Física de La Plata (IFLP)- CONICET, La Plata, Argentina. 88affiliation: Dept.
of Physics, University of La Plata, Argentina. A. Marinelli  33affiliation:
Instituto Nazionale di Fisica Nucleare, Sezione di Napoli, Italy. A. Sharma
44affiliation: Dept. of Physics and Astronomy, Uppsala University, Sweden. M.
Castro  55affiliation: Instituto Nacional de Pesquisas Espaciais (INPE)-
Divisão de Astrofísica, Brazil. 99affiliation: Universidade Estadual de
Campinas (UNICAMP)-Instituto de Computação, Campinas, Brazil. J. M. Osorio
66affiliation: Instituto de Astronomía, UNAM, México. and M. A.
Morales77affiliation: Instituto Balseiro, Universidad Nacional de Cuyo,
Argentina. M. A. Morales: Instituto Balseiro, Universidad Nacional de Cuyo -
CNEA, 8400 S. C. Bariloche, Río Negro, Argentina. (marco.morales@ib.edu.ar).
J. M. Osorio: Instituto de Astronomía, Universidad National Autónoma de
México, Mexico 04510, Mexico. (jmosorio@astro.unam.mx). M. Castro: Instituto
Nacional de Pesquisas Espaciais (INPE)- Divisão de Astrofísica, 12227-010, São
José dos Campos, São Paulo, Brazil. Universidade Estadual de Campinas
(UNICAMP)-Instituto de Computação, 13083-852, Campinas, São Paulo, Brazil.
(manuel.castro@inpe.br). A. Sharma: Dept. of Physics and Astronomy, Uppsala
University, Box 516, S-75120 Uppsala, Sweden. (ankur.sharma@physics.uu.se). A.
Marinelli: Instituto Nazionale di Fisica Nucleare, Sezione di Napoli,
Complesso Universitario di Monte S. Angelo, Via Cintia ed.G, Napoli, 80126
Italy. (antonio.marinelli@na.infn.it). A. V. Penacchioni: Instituto de Física
de La Plata (IFLP)- CONICET, La Plata, Argentina. Dept. of Physics, University
of La Plata, c.c. 67, (1900) La Plata, Argentina. (la,
ana.penacchioni@fisica.unlp.edu.ar). J. R. Sacahui: Instituto de Investigación
en Ciencias Físicas y Matemáticas, ed. T-1, Ciudad Universtiaria, zona 12,
Guatemala. (jrsacahui@profesor.usac.edu.gt).

###### Abstract

Blazars are the most active extragalactic gamma-ray sources. They show
sporadic bursts of activity, lasting from hours to months. In this work we
present a 10-year analysis of a sample of bright sources detected by Fermi-LAT
(100 MeV - 300 GeV). Using 2-week binned lightcurves (LC) we estimated the
Duty Cycle (DC): fraction of time that the source spends in an active state.
The objects present different DC values, with an average of $22.74\%$ and
$23.08\%$ when considering (and not) the Extragalactic Background Light (
EBL). Additionally we study the so called “blazar sequence” trend for the
sample of selected blazars in the ten years of data. This analysis constrains
a possible counterpart of sub-PeV neutrino emission during the quiescent
states, leaving the possibility to explain the observed IceCube signal during
the flaring states.

Los blazares son las fuentes de rayos gamma más activas. Presentan períodos
esporádicos de actividad, con duraciones de horas a meses. En este trabajo
presentamos un análisis de una muestra de fuentes brillantes detectadas por
Fermi-LAT (100 MeV- 300 GeV) durante una década. Usando curvas de luz con
episodios de 2 semanas estimamos el ciclo de actividad (DC): la fracción de
tiempo que la fuente pasa en el estado activo. Los objetos presentan
diferentes valores del DC, con promedio de $22.74\%$ y $23.08\%$ cuando se
considera y no se considera el fondo de luz difusa. Adicionalmente estudiamos
la tendencia conocida como ”secuencia de blazares”. Este análisis restringe
una posible contraparte de neutrinos con energías de sub-PeV durante los
estados estacionarios, dejando la posibilidad de explicar las observaciones de
IceCube durante períodos de fase activa.

Astrophysical Neutrinos Blazars Duty Cycle Extragalactic gamma-rays Fermi-LAT

##  0.1 Introduction

Blazars are the most variable and luminous type of Active Galactic Nuclei
(AGN). They are among the most powerful emitters in the Universe, and they are
thought to be powered by material falling onto a supermassive ($10^{6}$ \-
$10^{10}$ $M_{\odot}$) black hole (BH) at the center of the host galaxy
through an accretion disc. The strong, non-thermal electromagnetic emission is
generally detected in all observable bands, from radio to gamma-rays, and is
dominated by a relativistic jet pointing in the direction of the observer
(when the jet is not pointing in this direction, they are catalogued as radio
galaxies). Blazars thus reveal the energetic processes occurring in the center
of active galaxies. The most compelling mechanism for the emission in the
range from radio to optical is synchrotron emission, while gamma-rays are
produced via Inverse Compton (IC) by the same relativistic electrons producing
the synchrotron emission (Sikora et al., 1994; Sikora, M. et al, 2009).

Many blazars were first identified as irregular variable stars in our own
galaxy. Their luminosity changes in periods that go from days to years, but
without a pattern. With the development of radio astronomy many bright radio
sources were discovered, most of them with optical counterparts. This led to
the discovery of quasars and blazars in the late 50’s. The first redshift
measurement was done for blazar 3C 273 (Schmidt, 1963). The Fermi satellite,
launched in 2008, paved the way for the beginning of a new blazar era thanks
to its Large Area Telescope (LAT), which detects sources in the $0.1$ \- $300$
GeV energy range (Atwood, W. B. et al, 2009) with much higher sensitivity than
its predecessors. Blazars present high variability in this energy range, with
periods in which the flux increases considerably (Abdo, A. A. et al, 2009).
Detailed studies of blazar spectra, and in particular their spectral
variability (Urry, 1996a, b), are fundamental tools to determine the physical
processes responsible for particle acceleration and emission in the jet.

Blazars are often divided into two subclasses: BL Lacs (Stickel, M. et al,
1991) and flat spectrum radio quasars (FSRQs) (Angel & Stockman, 1980),
although up to date there is no complete agreement in the selection criteria.
BL Lacs are named after their prototype, BL Lacertae. They are characterized
by rapid, large-amplitude flux variability and significant optical
polarization. One of their defining features is the weakness or absence of
emission lines; therefore their redshifts can only be determined from features
in their host galaxies’ spectra. Besides, their spectra are dominated by a
relatively featureless non-thermal emission continuum over the entire
electromagnetic range. The nearby BL Lacs, which are associated to elliptical
galaxies with typical absorption spectra, sometimes have narrow emission
lines, while the more distant BL Lacs, whose host galaxies have never been
detected, present broad emission lines. All known BL Lacs are associated with
core-dominated radio sources.

Another type of source are Flat Spectrum Radio Quasars (FSRQ). They are
usually more distant, more luminous, and have stronger emission lines than BL
Lacs but, due to their similar continuum properties, they are collectivelly
called blazars, together with BL Lacs. There are three suggestions regarding
their classification: i) FSRQ evolve into BL Lacs, ii) they are different
manifestations of the same physical object, and iii) BL Lacs are
gravitationally micro-lensed FSRQ (Urry & Padovani, 1995). An example of FSRQ
is the source 3C 279 (also known as PKS 1253-05). It presents very high
variability in the visible, radio and X-ray bands. It is also one of the
brightest sources in the gamma-ray sky monitored by the Fermi Space Telescope.

Blazars have been strong candidate sources of astrophysical neutrinos since
2017, when IceCube reported the first neutrino EHE event (IC-170922A) (Kopper
& Blaufuss, 2017) with energy $\sim$ 290 TeV associated with a flare from
blazar TXS 0506+056 (Aartsen, 2018). This opened the possibility to establish
a link between the neutrino signal and the electromagnetic emission at
different energy ranges, which is of key importance in the search for the
privileged target of hadronic interaction processes as well as for a pion
decay component at VHE.

However, the blazar contribution to the diffuse astrophysical flux measured by
IceCube is still a matter of debate (Aartsen, M.G. et al., 2017). The diffuse
Galactic contribution (Gaggero et al., 2015) is constrained by recent analyses
from IceCube and ANTARES (Aartsen, 2017; Albert et al., 2017) to just $8.5\%$
of the full sky measured neutrino flux, and large room remains for other AGNs
(Atoyan & Dermer, 2001; Padovani et al., 2016; Murase & Waxman, 2016) and
Starbursts galaxies (Tamborra et al., 2014; Peretti et al., 2020). In this
work we investigate whether the long term observation, which is mainly
characterized by the quiescent states, is well described by a leptonic
scenario. On the other hand, by concentrating on a possible hadronic component
during the flaring states, we remark the importance of the estimation of a DC
factor to obtain long term neutrino expectations.

In this paper we analyze a sample of 38 bright blazars: 19 FSRQ and 19 BL Lacs
from the Fermi 3FGL catalog (Acero, F. et al., 2015), through 10 years of data
(from 2008 to 2018). We made a first selection of the blazars with the highest
flux values and, from them, we selected the ones with ’good’ LC (not dominated
by upper limits). The paper is organized as follows: in Section 0.2 we analyse
the LC for each source and identify the active states. Following two different
procedures, we distinguish the steady-state phase from the active phase for
each of the sources of the sample. In Section 0.3 we calculate the duty cycle
(DC) according to the baseline flux obtained with each procedure. In Section
0.4 we discuss about a possible negative correlation between the blazar’s
synchrotron peak frequency and the gamma-ray luminosity. In Section 0.5 we
consider the DC value and the blazar sequence trend from Section 0.4 as useful
tools to better understand the physical processes at play in the potential
neutrino sources. In Section 0.6 we show our results. Finally, in Section 0.7
we present our discussion and conclusions.

##  0.2 Data analysis

We selected 38 of the blazars with highest flux values from the Fermi 3FGL
catalog (Acero, F. et al., 2015) as listed in Table 1. Among these, there are
2 with no reported redshift. Figure 1 shows the redshift distribution of the
sample. The redshift and spectral type of each source were taken from
(Ackermann et al., 2015). In order to perform the data analysis we made use of
the tool Enrico (Sanchez & Deil, 2013) from the Fermi Science Tools (FSSC)
software, version
v11r5p3111http://fermi.gsfc.nasa.gov/ssc/data/analysis/software (Asercion,
2018). The analysis was performed in the energy range of 0.1 - 300 GeV, in a
RoI (region of interest) with radius of 20∘, considering the isotropic and
Galactic diffuse emission components (iso_P8R2_SOURCE_v6_v06.txt and
gll_iem_v06.fits222http://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html)
falling within the RoI. For the cases in which we considered the Extragalactic
Background Light (EBL) absorption, we used the model by Franceschini et al.
(2008) as reference.

Figure 1: Redshift distribution of the sample of blazars considered in this
work.

We generated the LC for the 10-year period with two-month, one-month, two-week
and one-week time bins. From these, we selected the two-week binning, since it
allowed us to see periods of activity with good resolution while minimizing
the number of upper limits (UL). Figure 2 shows the LC for the sources 3C 66A,
a BL Lac in the Andromeda constellation, and Mkn 421, a BL Lac located in the
constellation Ursa Major. We consider them as benchmark sources since they
have been intensively studied in the last decade, they are relatively nearby
sources ($z=0.444$ (Miller et al., 1978) and $z=0.03$ (de Vaucouleurs, G. et
al., 1991), respectively) and both flux and spectral information are available
over the entire electromagnetic spectrum.

3FGL name | Other name | Classification | Redshift | Spectral Type
---|---|---|---|---
J1015.0+4925 | 1H 1013+498 | BL Lac | 0.212 | PowerLaw
J1229.1+0202 | 3C 273 | FSRQ | 0.16 | LogParabola
J1256.1-0547 | 3C 279 | FSRQ | 0.5362 | LogParabola
J2254.0+1608 | 3C 454.3 | FSRQ | 0.859 | PLExpCutoff
J0222.6+4301 | 3C 66A | BL Lac | 0.444 | LogParabola
J1058.5+0133 | 4C +01.28 | BL Lac | 0.89 | LogParabola
J1224.9+2122 | 4C +21.35 | FSRQ | 0.435 | LogParabola
J0237.9+2848 | 4C +28.07 | FSRQ | 1.206 | LogParabola
J1635.2+3809 | 4C +38.41 | FSRQ | 1.8139 | LogParabola
J0238.6+1636 | AO 0235+164 | BL Lac | 0.94 | LogParabola
J1522.1+3144 | B2 1520+31 | FSRQ | 1.4886 | LogParabola
J2202.7+4217 | BL Lacertae | BL Lac | 0.686 | LogParabola
J2001.1+4352 | MG4 J2001.1+4352 | BL Lac | - | PowerLaw
J1104.4+3812 | Mkn421 | BL Lac | 0.031 | PowerLaw
J1653.9+3945 | Mkn 501 | BL Lac | 0.0337 | PowerLaw
J1555.7+1111 | PG 1553+113 | BL Lac | 0.5 | LogParabola
J0428.6-3756 | PKS 0426-380 | BL Lac | 1.111 | LogParabola
J0449.4-4350 | PKS 0447-439 | BL Lac | 0.205 | PowerLaw
J0457.0-2324 | PKS 0454-234 | FSRQ | 1.003 | LogParabola
J0538.8-4405 | PKS 0537-441 | BL Lac | 0.892 | LogParabola
J0730.2-1141 | PKS 0727-11 | FSRQ | 1.591 | LogParabola
J0808.2-0751 | PKS 0805-07 | FSRQ | 1.8369 | LogParabola
J1246.7-2547 | PKS 1244-255 | FSRQ | 0.638 | LogParabola
J1427.0+2347 | PKS 1424+240 | BL Lac | - | LogParabola
J1504.4+1029 | PKS 1502+106 | FSRQ | 1.8379 | LogParabola
J1512.8-0906 | PKS 1510-08 | FSRQ | 0.3599 | LogParabola
J1625.7-2527 | PKS 1622-253 | FSRQ | 0.7860 | LogParabola
J1833.6-2103 | PKS 1830-211 | FSRQ | 2.507 | LogParabola
J2158.8-3013 | PKS 2155-304 | BL Lac | 0.116 | LogParabola
J2236.5-1432 | PKS 2233-148 | BL Lac | 0.3250 | LogParabola
J2329.3-4955 | PKS 2326-502 | FSRQ | 0.518 | LogParabola
J1427.9-4206 | PKS B1424-418 | FSRQ | 1.5220 | LogParabola
J1802.6-3940 | PMN J1802-3940 | FSRQ | 1.319 | LogParabola
J2345.2-1554 | PMN J2345-1555 | FRSQ | 0.621 | LogParabola
J0112.1+2245 | S2 0109+22 | BL Lac | 0.265 | LogParabola
J0721.9+7120 | S5 0716+71 | BL Lac | 0.300 | LogParabola
J0509.4+0541 | TXS 0506+056 | BL Lac | 0.3365 | PowerLaw
J0521.7+2113 | TXS 0518+211 | BL Lac | 0.108 | PowerLaw
Table 1: List of our sample of blazars. The redshift value ($z$) is indicated
when available, and marked with ’-’ when unknown.

Figure 2: Flux light curves (considering EBL absorption) for the sources 3C
66A and Mkn 421 using a two-week binning. The red dashed-dotted line and the
black solid line the threshold flux $F_{thr}$ calculated according to
Vercellone’s criterion and the $\mu_{G}+3\sigma$ criterion (Tluczykont).

##  0.3 Duty Cycle

The duty cycle is the level of activity of a source. It is obtained by
calculating the fraction of time that the source is in the active phase (or
flaring state, with the flux above a given threshold) with respect to the
total observation period $T_{obs}$ as a function of the flux:

$\rm{Duty\,cycle}=DC=\frac{\sum_{i}t_{i}}{T_{obs}}.$ (1)

Here, $t_{i}$ is each of the time intervals the source spends in the flaring
state (Vercellone et al., 2004). The baseline phase (or steady state) is
defined as the fraction of time the flux remains below a given threshold.

In order to separate the active phase from the steady-state phase, we need to
define a threshold value for the flux. There are different criteria to do
this.

###  0.3.1 Vercellone’s criterion

Following the work of Vercellone et al. (2004), we define the threshold flux
$F_{\rm{thr}}$ as $1.5$ times the average flux of the source:

$F_{\rm{thr}}=1.5\,\,\overline{F}$ (2)

(see red-dotted lines in Figure 2). A source is in the active state when the
flux of the ith time bin is $>F_{\rm{thr}}$ and the $1\sigma$ uncertainty of
the ith time bin is smaller than the difference between the datapoint and
$F_{\rm{thr}}$ (Jorstad et al., 2001).

The average flux $\overline{F}$ is defined as the weighted mean of all the
detections and UL, with weight $w(\sigma)=1/\sigma$, where $\sigma$ is the
uncertainty of the measurement. In the case of UL, $\sigma$ is equal to the UL
value. $\overline{F}$ can be decomposed into the fluence from the baseline
states (flux below $F_{\rm{thr}}$) and the fluence from the flaring states
(flux above $F_{\rm{thr}}$) , respectively:

$\overline{F}\times T_{\rm{obs}}=F_{\rm{baseline}}\times
T_{\rm{baseline}}+\sum_{i}F_{\rm{flare},i}\,t_{i}.$ (3)

Here, $T_{{\rm{baseline}}}$ is the total time the source spends in the
baseline state, $F_{\rm{baseline}}$ is the flux of the baseline state, i.e.,
the weighted average flux of the non-flaring state (below the threshold
$F_{\rm{thr}}$), $F_{\rm{flare},i}$ is the average flux of the ith flare and
$t_{i}$ is the duration of each flare. Note that, for Vercelone’s criterion,
the value of $F_{\rm{baseline}}$ is fixed once we fix the value of
$F_{\rm{thr}}$.

###  0.3.2 $3\sigma$ or Tluczykont criterion

According to Tluczykont, M. et al (2010), we organized the data into a flux
histogram, as shown in Figure 3. A flux state is defined as the integrated
flux value in each time bin, obtained from the source LC. We then organized
the data into a flux histogram (flux vs. number of events with that value of
the flux) and fit them with the sum of a Gaussian and Log-Normal
distributions333Here, $\rm{x}$ represents the values of the flux for a given
blazar, while $f_{G}(\rm{x})$ and $f_{LN}(\rm{x})$ represent the number of
occurrences (number of time intervals that have a flux $\rm{x}$).,
$f_{G}+f_{LN}$. The Gaussian

$f_{G}(\rm{x})=\frac{A_{G}}{\sigma_{G}\sqrt{2\pi}}\rm{exp}\left(\frac{-(x-\mu_{G})^{2}}{2\,\sigma_{G}^{2}}\right)$
(4)

represents the baseline state and the Log-Normal

$f_{LN}(\rm{x})=\frac{A_{LN}}{x\sigma_{LN}\sqrt{2\pi}}\rm{exp}\left(\frac{-(log(x)-\mu_{LN})^{2}}{2\,\sigma_{LN}^{2}}\right)$
(5)

describes the active-state phases. The parameters $\mu_{G}$, $\sigma_{G}$ and
$A_{G}$ are the mean, standard deviation and normalization for the Gaussian
distribution, while $\mu_{LN}$, $\sigma_{LN}$ and $A_{LN}$ are the mean,
standard deviation and normalization for the Log-Normal distribution. The
parameters of the fits of the entire sample can be found in Appendix 0.8.

According to Tluczykont’s criterion, the source threshold flux $F_{thr}$ is a
variable in the range from $3\,\sigma_{G}$ to $\mu_{G}+3\,\sigma_{G}$. We
define the flux $F_{baseline}$ as the mean value of all the non-flaring
states:

$F_{baseline}=\frac{\int_{0}^{F_{thr}}x\,f_{G}(x)\,dx}{\int_{0}^{F_{thr}}f_{G}(x)\,dx}.$
(6)

If the flux is $>F_{\rm{thr}}$ the source is considered to be in the active
phase. We recall that

$T_{\rm{baseline}}=T_{\rm{obs}}-T_{\rm{flare}},$ (7)

with $T_{\rm{flare}}=\sum_{i}t_{i}$.

Following the work of Abdo, A. A. et al (2014), we calculated the average
flare flux

$\langle
F_{flare}\rangle=\frac{\int_{F_{\rm{thr}}}^{F_{\rm{max}}}x\,f_{LN}(x)\,dx}{\int_{F_{\rm{thr}}}^{F_{\rm{max}}}f_{LN}(x)\,dx}$
(8)

as a function of $F_{\rm{thr}}$ and $F_{\rm{max}}$, the maximum flux detected.

In order to obtain the average flux of the flaring states we need to replace
$F_{flare}$ by $\langle F_{flare}\rangle$. Substituting these quantities in
Eq. (3) we obtain

$DC=\frac{T_{\rm{flare}}}{T_{\rm[obs]}}=\frac{\overline{F}-F_{\rm{baseline}}}{\langle
F_{\rm{flare}}\rangle-F_{\rm{baseline}}}.$ (9)

Figure 3: Flux distribution for the source 3C 66A and Mkn 421 considering EBL
absorption. The black dotted line is the fit with the Log-Normal distribution,
the black solid line is the fit with the Gaussian distribution, the red solid
line is the fit with the sum of both distributions and the blue dotted line
represents the threshold value.

Figure 4 shows the plots of the DC obtained for 3C 66A and Mkn 421. In
particular, the value of the DC obtained for Mrk 421 (av DC= 24.7%) is
consistent with the results reported by (Patricelli, B. et al., 2014; Abdo, A.
A. et al, 2014) using 3 year Milagro data in the TeV energy range. The DC
plots for the whole sample are shown in Appendix 0.9.

The threshold flux calculated for 3C 66A is $F_{\rm{thr}}=1.4\times 10^{-7}$
ph cm-2 s-1 (Tluczykont criterion, black solid line in Figure 2) and
$F_{\rm{thr}}=1.06\times 10^{-7}$ ph cm-2 s-1 (Vercellone’s criterion, red
dashed-dotted line in Figure 2). In the case of Mkn 421,
$F_{\rm{thr}}=3.87\times 10^{-7}$ ph cm-2 s-1 (Tluczykont criterion) and
$F_{\rm{thr}}=3.52\times 10^{-7}$ ph cm-2 s-1 (Vercellone’s criterion). We
recall that these values of $F_{\rm{thr}}$ have been calculated considering
EBL absorption.

Figure 4: DC vs. flux with (left panels) and without (right panels) EBL
absorption, for 3C 66A (upper panels) and Mkn 421 (lower panels). The blue
(black) lines represent the DC range inferred from Tluczykont (Vercellone’s)
criterion.

##  0.4 Blazar sequence

Fossati et al. (1998), Kubo et al. (1998) and Donato et al. (2001) observed a
negative correlation between the peak frequency of the synchrotron emission
from blazars and their bolometric luminosities (traced through their radio
luminosities in their observations). It was named the observational blazar
sequence, and was thought to be an evidence in favor of leptonic emission from
the source. This was later revealed to be a result of selection bias, although
the existence of a physical blazar sequence (Ghisellini et al., 1998) was
explained due to the different cooling experienced by the electrons under
different environments in BL Lacs and FSRQs.

Figure 5: Correlation between the synchrotron peak frequency and gamma-ray
luminosity (0.1 - 300 GeV) for our sample. BL Lacs are shown in blue and FSRQs
in red. The red line represents the best fit for the combined sub-sets.

In the case of blazars, the gamma-ray luminosity can be a better indicator of
the integrated bolometric luminosity than the radio luminosity (Fossati et
al., 1998; Wang, Z. et al., 2017). It is thus possible to explore this
relationship between the two variables for our sample, using Fermi-LAT data
accumulated over 10 years. Figure 5 shows the integrated gamma-ray luminosity
($L_{\gamma}$) in the 0.1 - 300 GeV range, averaged over 10 years of
observation, vs. the synchrotron peak frequency (${\nu^{s}}_{\rm{peak}}$) for
each source. The value of ${\nu^{s}}_{\rm{peak}}$ has been obtained from the
3FHL catalog (Ajello, M; Atwood, W. B.; Baldini, L. et al., 2017) when
available. Luminosities have been calculated assuming a $\Lambda$CDM Universe
with standard cosmological parameters ($H_{0}$ = $67.8$, $\Omega_{m}$ =
$0.308$, $\Omega_{\lambda}$ = $0.692$).

The two sub-samples of BL Lacs and FSRQs show a negative correlation trend,
the FSRQs having higher luminosity and lower peak frequency on average as
compared to the set of BL Lacs. The combined sample of BL Lacs and FSRQs has a
Pearson coefficient of -0.3, with a best-fit slope of $-1.0025\pm 0.0003$.
This moderate correlation trend can be interpreted in the context of leptonic
emission favored in the inner part of the jet, providing information on the
sub-PeV neutrino emission from this region (Murase et al., 2014). Other
authors (Finke, 2013) argue that there is a correlation between Compton
dominance and the peak frequency of the synchrotron component, which is also
consistent with the blazar sequence.

##  0.5 The Multimessenger case and very high energy neutrino emission

In this work, two important multimessenger aspects of gamma-ray emission from
blazars were analyzed: the DC value and the blazar sequence trend. In
particular, they can be used to better understand the physical processes
responsible for the gamma-ray emission and to constrain a possible VHE
neutrino counterpart. The first parameter represents a duty factor of the
blazar activity, and it is considered a crucial factor whenever a long term
unblinded analysis is done with a neutrino telescope, taking into account one
or more VHE emitting blazars. In particular, under the assumption that the
hadronic emission can be amplified during the VHE flaring states, it is worth
using this value to set the expected neutrino observations. Figure 6 shows the
value of average DCs of the samples obtained with 10 years of Fermi-LAT data.
Taking them into account, the known ULs of full-sky neutrino emission expected
from blazars can change by a factor $>2$. In fact, the full sky upper limit
reported by IceCube collaboration for blazars considering the unblinded point-
like searches (Aartsen, M.G. et al., 2017) does not consider the DC for the
weighting factor $(w_{\gamma/\nu})$ when deducing possible neutrino flux from
the gamma-ray emission.

Figure 6: DC distribution of our samples according to Tluczykont’s (left
panels) and Vercellone’s (right panels) criteria, considering EBL absortion
(upper panels) and not considering it (lower panels).

More in detail, the contribution to the diffuse astrophysical neutrino flux
observed by IceCube (Aartsen, M. G., IceCube Collaboration et al., 2017;
Aartsen, M.G. et al, 2016; Aartsen, M. G., Ackermann, M., Ice Cube
Collaboration et al., 2020) attributed to blazars will decrease from 27% to 7%
in Aartsen, M.G. et al. (2017), for energies $>10$ TeV, and from 40-80% to
10-20% in Aartsen et al. (2018) for energies $>200$ TeV, when an average DC of
26% is considered. This decreasing factor on the expected neutrino flux will
be quite independent of the blazar gamma-ray luminosity reached during the
flaring periods even though the possibility to observe it during such activity
period is strictly dependent of that, under the assumption of an amplified
hadronic emission on active states.
While the DC can represent a temporal constraint on the hadronic activity from
BL-lacs and FSRQs, the blazar sequence trend can constrain the emitting
process as well as the energy range of VHE neutrinos produced, limiting the
production of sub-PeV neutrinos (Murase et al., 2014) by the interaction of
jet accelerated protons with the ambient photon fields. The trend shown in
Figure 5 can be explained assuming that a self-synchrotron Compton (SSC)
emission scenario takes place in the inner part of the jet. Assuming the
results of (Murase et al., 2014), Figure 5 favors FSRQs with respect to BL
Lacs as the main candidates for neutrino production in the range 1-100 PeV.
Moreover, it is worth highlighting the fact that the blazar sequence reported
here takes into account the full Fermi-LAT dataset, which is dominated by the
quiescent periods and does not exclude a different emission scenario during
the flaring periods. If that were the case, Figure 7 shows that we cannot
discriminate which class of blazars, BL Lacs or FSRQs, can produce a higher
neutrino fluence over a longer observational period.

##  0.6 Results

Tables 2 and 3 show the DC values for all the sources with and without EBL
absortion, according to Tluczykont and Vercellone’s criteria. We calculated
the DC in the 0.1-300 GeV energy range for $\sim$ 10 years of Fermi-LAT data
(2008 - 2018). The table includes: for Tluczykont criterion, the DC obtained
considering the maximum baseline flux (DCbl%), the DC obtained assuming 0 as
the baseline flux (DC0%), and the average DC for each source (DCav%). For
Vercellone’s criterion the DC value and its error. The distribution of the
values presented in the tables is shown in Figure 6.

Table 2: DC values calculated for each source considering EBL absorption. For objects without a known redshift, DC has not been calculated Source Name | Tluczykont | Vercellone
---|---|---
|  DCbl% |  DC0% |  DCav% | DC % | error DC %
1H 1013+498 | 8.59 | 18.18 | 13.39 | 5.81 | 0.01
3C 273 | 15.73 | 19.47 | 17.6 | 17.05 | 0.03
3C 279 | 14.32 | 15.94 | 15.13 | 22.69 | 0.04
3C 454.3 | 16.20 | 16.82 | 16.51 | 11.63 | 0.02
3C 66A | 5.29 | 40.53 | 22.91 | 19.77 | 0.04
4C +01.28 | 37.12 | 38.73 | 37.93 | 32.56 | 0.06
4C +21.35 | 12.06 | 12.66 | 12.36 | 27.31 | 0.06
4C +28.07 | 14.47 | 15.96 | 15.21 | 23.05 | 0.05
4C +38.41 | 20.47 | 22.49 | 21.48 | 28.96 | 0.06
AO 0235+164 | 18.66 | 20.68 | 19.67 | 22.48 | 0.04
B2 1520+31 | 29.00 | 35.86 | 32.43 | 21.58 | 0.05
BL Lacertae | 38.86 | 46.33 | 42.60 | 26.36 | 0.5
MG4 J2001.1+4352 | - | - | - | - | -
Mkn 421 | 9.21 | 30.01 | 19.61 | 8.49 | 0.02
Mkn 501 | 15.03 | 37.15 | 26.09 | 7.39 | 0.01
PG 1553+113 | 4.11 | 27.40 | 15.76 | 3.46 | 0.01
PKS 0426-380 | 40.62 | 43.57 | 42.10 | 25.1 | 0.05
PKS 0447-439 | 16.7 | 29.31 | 23.01 | 12.69 | 0.03
PKS 0454-234 | 35.2 | 37.03 | 36.12 | 25.49 | 0.05
PKS 0537-441 | 29.43 | 34.52 | 31.97 | 26.54 | 0.05
PKS 0727-11 | 16.95 | 23.43 | 20.19 | 19.52 | 0.04
PKS 0805-07 | 12.75 | 13.44 | 13.09 | 20.08 | 0.04
PKS 1244-255 | 20.64 | 27.46 | 24.05 | 18.99 | 0.04
PKS 1424+240 | - | - | - | - | -
PKS 1502+106 | 35.32 | 40.84 | 38.08 | 23.17 | 0.05
PKS 1510+089 | 16.64 | 20.14 | 18.39 | 19.62 | 0.04
PKS 1622-253 | 31.86 | 33.38 | 32.62 | 28.4 | 0.06
PKS 1830-211 | 16.11 | 23.56 | 19.83 | 12.79 | 0.03
PKS 2155-304 | 11.53 | 20.31 | 15.92 | 14.62 | 0.03
PKS 2233-148 | 12.25 | 13.13 | 12.69 | 22.83 | 0.05
PKS 2326-502 | 14.87 | 23.12 | 18.99 | 41.09 | 0.08
PKS B1424-418 | 14.57 | 21.51 | 18.04 | 19.18 | 0.04
PMN J1802-3940 | 21.75 | 22.22 | 21.98 | 30.24 | 0.06
PMN J2345-1555 | 19.39 | 28.6 | 24.00 | 16.33 | 0.04
S2 0109+22 | 2.75 | 58.24 | 30.49 | 25 | 0.05
S5 0716+71 | 0.7 | 15.89 | 8.3 | 16.02 | 0.03
TXS 0506+056 | 14.16 | 26.3 | 20.23 | 13.51 | 0.03
TXS 0518+211 | 13.54 | 26.41 | 19.98 | 13.33 | 0.03
Mean values | 18.24 | 27.24 | 22.74 | 20.09 |
Table 3: DC values calculated for each source without EBL absorption. Source Name | Tluczykont | Vercellone
---|---|---
|  DCbl% |  DC0% |  DCav% | DC % | error DC %
1H 1013+498 | 11.46 | 40.14 | 25.80 | 3.49 | 0.01
3C 273 | 16.63 | 21.03 | 18.83 | 16.99 | 0.03
3C 279 | 14.04 | 14.99 | 14.52 | 7.72 | 0.02
3C 454.3 | 16.2 | 16.82 | 16.51 | 11.63 | 0.02
3C 66A | 8.12 | 41.42 | 24.77 | 20.16 | 0.04
4C +01.28 | 31.52 | 32.12 | 31.82 | 32.56 | 0.07
4C +21.35 | 15.54 | 16.70 | 16.12 | 4.64 | 0.01
4C +28.07 | 19.39 | 23.24 | 21.32 | 23.83 | 0.05
4C +38.41 | 12.86 | 14.93 | 13.89 | 4.26 | 0.01
AO 0235+164 | 18.37 | 20.87 | 19.62 | 26.25 | 0.05
B2 1520+31 | 35.27 | 43.21 | 39.24 | 22.78 | 0.04
BL Lacertae | 41.20 | 49.60 | 45.4 | 26.36 | 0.05
MG4 J2001.1+4352 | 7.40 | 13.24 | 10.32 | 13.18 | 0.03
Mkn 421 | 8.67 | 35.93 | 22.3 | 8.49 | 0.02
Mkn 501 | 12.97 | 33.92 | 23.45 | 6.98 | 0.01
PG 1553+113 | 13.52 | 22.35 | 17.93 | 11.58 | 0.02
PKS 0426-380 | 37.2 | 41.14 | 39.17 | 53.46 | 0.1
PKS 0447-439 | 13.59 | 27.59 | 20.59 | 12.69 | 0.03
PKS 0454-234 | 33.71 | 40.53 | 37.12 | 21.24 | 0.05
PKS 0537-441 | 28.36 | 31.41 | 29.88 | 55.21 | 0.1
PKS 0727-11 | 27.75 | 37.59 | 32.67 | 18.38 | 0.04
PKS 0805-07 | 2.32 | 3.49 | 2.9 | 39.15 | 0.08
PKS 1244-255 | 11.33 | 16.95 | 14.14 | 62.16 | 0.1
PKS 1424+240 | 16.24 | 25.36 | 20.80 | 40.15 | 0.08
PKS 1502+106 | 16.34 | 17.68 | 17.53 | 18.08 | 0.04
PKS 1510+089 | 13.80 | 16.10 | 14.95 | 15.77 | 0.03
PKS 1622-253 | 32.17 | 33.78 | 32.98 | 28 | 0.06
PKS 1830-211 | 19.38 | 25.96 | 22.67 | 14.01 | 0.03
PKS 2155-304 | 13.44 | 23.43 | 18.44 | 13.46 | 0.03
PKS 2233-148 | 17.81 | 20.03 | 18.92 | 21.2 | 0.04
PKS 2326-502 | 22.75 | 24.98 | 23.87 | 41.08 | 0.08
PKS B1424-418 | 14.31 | 19.41 | 16.86 | 17.83 | 0.04
PMN J1802-3940 | 23.82 | 24.32 | 24.07 | 32.13 | 0.07
PMN J2345-1555 | 26.37 | 33.71 | 29.67 | 36.54 | 0.07
S2 0109+22 | 0.84 | 53.99 | 27.41 | 25 | 0.05
S5 0716+71 | 0.70 | 15.89 | 8.30 | 16.02 | 0.03
TXS 0506+056 | 19.96 | 35.59 | 27.78 | 10.81 | 0.02
TXS 0518+211 | 26.78 | 42.29 | 34.54 | 12.74 | 0.03
Mean values | 18.47 | 27.67 | 23.08 | 22.27 |

Figure 7: Relation between flare duration ($T_{flare}$), Duty Cycle (DC) and
flare luminosity ($L_{ff}$) for BL Lac type (left panel) and FSRQ type blazars
(right panel).

Following Tluczykont criterion, the average DC for the sample when considering
EBL absorption (and not) is 22.74% (23.08%). According to Vercellone’s
criterion we obtained values of 20.09% (22.27%). The blazars PKS 0426-380 and
BL Lacertae have the highest DC values (considering EBL absorption), with an
average DC of $\sim$ $42\%$ and $43\%$, respectively (Tluczykont’s criterion).
On the ther hand, the lowest value of DC obtained corresponds to blazar S5
0716+71 with a DCav value of $\sim 8\%$ considering EBL absorption
(Tluczykont’s criterion).

At this point, we must consider the following: choosing a flare flux threshold
in terms of the time average flux (Vercellone’s criterion) does not allow a
direct comparison of DC between sources to be made, because the time average
flux is influenced by the level of activity. In the case of a highly active
source, the time average flux, and consequently its flare flux threshold,
would be much higher than the baseline flux, so the DC only refers to the
highest flux states. On the contrary, for a less active source the time
average flux is close to the baseline flux, so the DC refers to almost all the
flaring states. Since the DC of an active source includes only the highest
flux-flaring states, it is possible to obtain a DC value smaller than the one
for a less active source and erroneously conclude that the latter is more
active than the former. In general, Tluczykont criterion leads to a higher DC
average value than Vercellone’s criterion.

Figure 7 shows the average DC and flare luminosity (Tluczykont criterion) as a
function of the major flare duration, together with flare luminosity vs DC. As
seen from the figure, there is no significant difference between the values of
DC for BL Lacs and FSRQ. We selected the major flares as the ones presenting
the greatest number of consecutive temporal bins with the highest fluence in
the 10-year dataset. We searched for possible correlations between these
variables. However, no correlation was found. Furthermore, we found no
correlation between DC and the source redshift, independently of the criterion
used.

##  0.7 Discussion and conclusion

We have presented the results of 10 years of Fermi-LAT data in the energy
range of 0.1-300 GeV for a sample of 38 bright blazars following the two
criteria presented in Section 0.3. In particular, we have estimated the gamma-
ray variability of the BL Lacs and FSRQs present in the sample as well as the
gamma-ray fluence during the activity periods. We have searched for the
possible origin of this emission when looking at the entire observation time,
dominated by quiescent periods, advocating a more enhanced hadronic component
during the flaring periods. The average DC for the whole sample following
Tluczykont’s criterion varies in the range [$\sim$8-43]% considering EBL
absorption. This implies that blazars present a wide range of activity levels.
Ongoing work aims to make a complete spectral analysis of these sources.

When correlating the gamma-ray activity to the hadronic emission from the
sources, the obtained DC becomes relevant also for the calculation of the
expected neutrino signal over a long observational period, as discussed in
(Marinelli et al., 2019). In particular, the average DC values reported in
Figure 7 can be used as a scaling factor for the expected neutrino fluence. It
is noteworthy however that the variance of the DC inferred considering EBL and
not considering it is negligible, which would imply that the DC is not
affected by the EBL absorption at these energies and distances. Even though
the sample is small, a quick analysis shows that there is no correlation
between DC and redshift (nor between DC and luminosity) for this sample of
blazars. However, further analysis is required in order to make a stronger
statement. Finally, we find that, for this sample, there is no notorious
difference between the DC values inferred for FSRQ and BL Lacs (see Figure 7).

Acknowledgments

JRS acknowledges DIGI-USAC for financial support by grant 4.8.63.4.44 and
DGAPA-UNAM IG101320. AVP acknowledges the National Research Council of
Argentina (CONICET) by the grant PIP 616, and by the Agencia Nacional de
Promoción Científica y Tecnológica (ANPCYT) PICT 140492. AM acknowledges
Istituto Nazionale di Fisica Nucleare (INFN), Ministero dell’ Universitá e
della Ricerca (MIUR), PRIN 2017 program (Grant NAT-NET 2017W4HA7S) Italy. MC
acknowledges Fundação de Ampara à Pesquisa do Estado de São Paulo (FAPESP) for
financial support under grants
#2015/25972-0 and #2017/00968-6.

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##  0.8 Fit parameters

Table 4: LN+G distribution fit parameters. Flux is in units $\times 10^{-8}$.  Source name | EBL Correction | No EBL Correction
---|---|---
| $\mu_{LN}$ | $\sigma_{LN}$ | $\mu_{G}$ | $\sigma_{G}$ | $\mu_{LN}$ | $\sigma_{LN}$ | $\mu_{G}$ | $\sigma_{G}$
1H 1013+498 | 3.43 | 0.93 | 4.87 | 1.83 | 2.97 | 1.02 | 6.31 | 1.54
3C 273 | 4.55 | 1.23 | 12.99 | 5.07 | 4.47 | 1.18 | 13.05 | 4.53
3C 279 | 6.22 | 1.49 | 21.91 | 11.58 | 6.33 | 1.55 | 15.14 | 9.96
3C 66A | 2.12 | 1.01 | 8.70 | 1.83 | 2.35 | 1.1 | 8.11 | 1.42
4C +01.28 | 3.27 | 1.65 | 0.96 | 2.36 | 3.65 | 1.12 | 0.69 | 3.00
4C +21.35 | 17.48 | 4.42 | 8.25 | 10.91 | 10.56 | 3.77 | 4.78 | 1.83
4C +28.07 | 5.09 | 1.66 | 8.83 | 13.90 | 5.18 | 1.81 | 11.59 | 7.69
4C +38.41 | 5.21 | 1.01 | 13.70 | 13.74 | 4.94 | 1.72 | 6.66 | 2.34
AO 0235+164 | 5.72 | 1.93 | 4.67 | 2.33 | 5.91 | 2.13 | 5.08 | 2.36
B2 1520+31 | 3.58 | 0.75 | 9.26 | 8.03 | 4.18 | 0.65 | 15.03 | 8.17
BL Lacertae | 3.95 | 1.04 | 8.58 | 5.19 | 3.89 | 1.05 | 8.47 | 4.52
MG4 J2001.1+4352 | - | - | - | - | 4.52 | 2.31 | 4.35 | 1.92
Mkn421 | 3.95 | 0.60 | 21.34 | 5.77 | 4.34 | 1.13 | 21.48 | 4.32
Mkn 501 1 | 2.58 | 0.51 | 6.06 | 2.16 | 2.74 | 0.42 | 8.13 | 3.37
PG 1553+113 | 3.17 | 0.11 | 12.53 | 4.13 | 2.87 | 0.73 | 4.99 | 2.65
PKS 0426-380 | 3.88 | 0.78 | 4.69 | 7.74 | 3.84 | 0.72 | 6.39 | 8.16
PKS 0447-439 | 3.70 | 0.96 | 8.60 | 3.78 | 3.35 | 0.91 | 9.15 | 4.00
PKS 0454-234 | 3.81 | 1.05 | 2.91 | 8.15 | 3.63 | 0.62 | 8.65 | 5.28
PKS 0537-441 | 4.67 | 1.45 | 6.41 | 2.88 | 4.60 | 1.29 | 5.07 | 3.14
PKS 0727-11 | 4.38 | 1.09 | 12.44 | 7.73 | 4.51 | 0.69 | 23.08 | 12.21
PKS 0805-07 | 4.46 | 1.83 | 1.87 | 3.78 | 0.75 | 1.45 | 5.01 | 4.23
PKS 1244-255 | 4.22 | 1.12 | 7.80 | 3.12 | 0.60 | 1.05 | 7.05 | 3.26
PKS 1424+240 | - | - | - | - | 2.69 | 0.76 | 5.43 | 3.53
PKS 1502+106 | 5.17 | 1.67 | 8.73 | 3.82 | 5.53 | 1.83 | 4.93 | 1.72
PKS 1510-089 | 7.14 | 1.69 | 37.06 | 21.16 | 6.29 | 1.48 | 25.86 | 11.14
PKS 1622-253 | 0.89 | 0.22 | 2.20 | 1.06 | 8.59 | 2.18 | 23.6 | 11.85
PKS 1830-211 | 5.17 | 0.89 | 31.88 | 11.93 | 4.04 | 1.26 | 12.52 | 3.56
PKS 2155-304 | 3.37 | 0.55 | 8.10 | 3.70 | 3.22 | 0.60 | 7.82 | 3.56
PKS 2233-148 | 4.81 | 1.98 | 2.15 | 1.61 | 2.74 | 1.56 | 2.07 | 1.73
PKS 2326-502 | 5.77 | 1.70 | 13.35 | 2.17 | 19.19 | 4.81 | 4.52 | 1.24
PKS B1424-418 | 4.32 | 0.69 | 31.46 | 22.91 | 5.34 | 0.77 | 35.14 | 21.78
PMN J1802-3940 | 12.08 | 2.68 | 13.64 | 7.35 | 22.19 | 4.28 | 12.65 | 6.66
PMN J2345-1555 | 3.32 | 1.17 | 5.9 | 1.8 | 3.32 | 1.08 | 5.32 | 1.90
S2 0109+22 | 2.21 | 1.23 | 9.38 | 1.46 | 2.38 | 1.25 | 9.56 | 1.50
S5 0716+71 | 3.30 | 1.56 | 13.60 | 6.16 | 3.3 | 1.56 | 13.60 | 6.17
TXS 0506+056 | 2.29 | 0.91 | 6.60 | 3.13 | 2.59 | 0.78 | 5.13 | 1.63
TXS 0518+211 | 2.63 | 0.83 | 11.70 | 5.97 | 3.42 | 0.97 | 7.71 | 1.78

##  0.9 Duty Cycle Plots

(a)  (b)  (c)  (d)

(e)  (f)  (g)  (h)

(i)  (j)  (k)  (l)

(m)  (n)  (o)  (p)

(q)  (r)

Figure 8: DC vs. flux conidering EBL absorption. The blue (black) lines
represent the DC range inferred from Tluczykont (Vercellone’s) criterion.

(s)  (t)  (u)  (v)

(w)  (x)  (y)  (z)

(aa)  (ab)  (ac)  (ad)

(ae)  (af)  (ag)  (ah)

(ai)  (aj)

Figure 8: (continued)

(a)  (b)  (c)  (d)

(e)  (f)  (g)  (h)

(i)  (j)  (k)  (l)

(m)  (n)  (o)  (p)

(q)  (r)  (s)

Figure 9: DC vs. flux for each source of the sample, with no EBL absorption.
The blue (black) lines represent the DC range inferred from Tluczykont
(Vercellone’s) criterion.

(t)  (u)  (v)  (w)

(x)  (y)  (z)  (aa)

(ab)  (ac)  (ad)  (ae)

(af)  (ag)  (ah)  (ai)

(aj)  (ak)  (al)

Figure 9: (continued)