# TeV Analysis of a Source Rich Region with HAWC Observatory: Is HESS
J1809-193 a Potential Hadronic PeVatron?

A. Albert  Physics Division, Los Alamos National Laboratory, Los Alamos, NM,
USA  R. Alfaro  Instituto de F’isica, Universidad Nacional Autónoma de México,
Ciudad de Mexico, Mexico  C. Alvarez  Universidad Autónoma de Chiapas, Tuxtla
Gutiérrez, Chiapas, México  J.C. Arteaga-Velázquez  Universidad Michoacana de
San Nicolás de Hidalgo, Morelia, Mexico  D. Avila Rojas  Instituto de F’isica,
Universidad Nacional Autónoma de México, Ciudad de Mexico, Mexico  R. Babu
Department of Physics, Michigan Technological University, Houghton, MI, USA
Department of Physics and Astronomy, Michigan State University, East Lansing,
MI, USA  E. Belmont-Moreno  Instituto de F’isica, Universidad Nacional
Autónoma de México, Ciudad de Mexico, Mexico  A. Bernal  Instituto de
Astronom’ia, Universidad Nacional Autónoma de México, Ciudad de Mexico, Mexico
M. Breuhaus  Max-Planck Institute for Nuclear Physics, 69117 Heidelberg,
Germany  K.S. Caballero-Mora  Universidad Autónoma de Chiapas, Tuxtla
Gutiérrez, Chiapas, México  T. Capistrán  Instituto de Astronom’ia,
Universidad Nacional Autónoma de México, Ciudad de Mexico, Mexico  A.
Carramiñana  Instituto Nacional de Astrof’isica, Óptica y Electrónica, Puebla,
Mexico  S. Casanova  Instytut Fizyki Jadrowej im Henryka Niewodniczanskiego
Polskiej Akademii Nauk, IFJ-PAN, Krakow, Poland  J. Cotzomi  Facultad de
Ciencias F’isico Matemáticas, Benemérita Universidad Autónoma de Puebla,
Puebla, Mexico  E. De la Fuente  Departamento de F’isica, Centro Universitario
de Ciencias Exactase Ingenierias, Universidad de Guadalajara, Guadalajara,
Mexico  D. Depaoli  Max-Planck Institute for Nuclear Physics, 69117
Heidelberg, Germany  N. Di Lalla  Department of Physics, Stanford University:
Stanford, CA 94305–4060, USA  R. Diaz Hernandez  Instituto Nacional de
Astrof’isica, Óptica y Electrónica, Puebla, Mexico  B.L. Dingus  Physics
Division, Los Alamos National Laboratory, Los Alamos, NM, USA  M.A. DuVernois
Department of Physics, University of Wisconsin-Madison, Madison, WI, USA  C.
Espinoza  Instituto de F’isica, Universidad Nacional Autónoma de México,
Ciudad de Mexico, Mexico  K.L. Fan  Department of Physics, University of
Maryland, College Park, MD, USA  K. Fang  Department of Physics, University of
Wisconsin-Madison, Madison, WI, USA  B. Fick  Department of Physics, Michigan
Technological University, Houghton, MI, USA  N. Fraija  Instituto de
Astronom’ia, Universidad Nacional Autónoma de México, Ciudad de Mexico, Mexico
J.A. García-González  Tecnologico de Monterrey, Escuela de Ingeniería y
Ciencias, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., Mexico, 64849  F.
Garfias  Instituto de Astronom’ia, Universidad Nacional Autónoma de México,
Ciudad de Mexico, Mexico  A. Gonzalez Muñoz  Instituto de F’isica, Universidad
Nacional Autónoma de México, Ciudad de Mexico, Mexico  M.M. González
Instituto de Astronom’ia, Universidad Nacional Autónoma de México, Ciudad de
Mexico, Mexico  J.A. Goodman  Department of Physics, University of Maryland,
College Park, MD, USA  S. Groetsch  Department of Physics, Michigan
Technological University, Houghton, MI, USA  J.P. Harding  Physics Division,
Los Alamos National Laboratory, Los Alamos, NM, USA  S. Hernández-Cadena
Instituto de F’isica, Universidad Nacional Autónoma de México, Ciudad de
Mexico, Mexico  I. Herzog  Department of Physics and Astronomy, Michigan State
University, East Lansing, MI, USA  D. Huang  Department of Physics, University
of Maryland, College Park, MD, USA  F. Hueyotl-Zahuantitla  Universidad
Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas, México  P. Hüntemeyer
Department of Physics, Michigan Technological University, Houghton, MI, USA
A. Iriarte  Instituto de Astronom’ia, Universidad Nacional Autónoma de México,
Ciudad de Mexico, Mexico  V. Joshi  Erlangen Centre for Astroparticle Physics,
Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany  S.
Kaufmann  Universidad Politecnica de Pachuca, Pachuca, Hgo, Mexico  A. Lara
Instituto de Geof’isica, Universidad Nacional Autónoma de México, Ciudad de
Mexico, Mexico  J. Lee  University of Seoul, Seoul, Rep. of Korea  H. León
Vargas  Instituto de F’isica, Universidad Nacional Autónoma de México, Ciudad
de Mexico, Mexico  A.L. Longinotti  Instituto de Astronom’ia, Universidad
Nacional Autónoma de México, Ciudad de Mexico, Mexico  G. Luis-Raya
Universidad Politecnica de Pachuca, Pachuca, Hgo, Mexico  K. Malone  Physics
Division, Los Alamos National Laboratory, Los Alamos, NM, USA  J. Martínez-
Castro  Centro de Investigaci’on en Computaci’on, Instituto Polit’ecnico
Nacional, M’exico City, M’exico.  J.A. Matthews  Dept of Physics and
Astronomy, University of New Mexico, Albuquerque, NM, USA  P. Miranda-
Romagnoli  Universidad Autónoma del Estado de Hidalgo, Pachuca, Mexico  J.A.
Montes  Instituto de Astronom’ia, Universidad Nacional Autónoma de México,
Ciudad de Mexico, Mexico  J.A. Morales-Soto  Universidad Michoacana de San
Nicolás de Hidalgo, Morelia, Mexico  E. Moreno  Facultad de Ciencias F’isico
Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico  M.
Mostafá  Department of Physics, Temple University, Philadelphia, Pennsylvania,
USA  L. Nellen  Instituto de Ciencias Nucleares, Universidad Nacional Autónoma
de Mexico, Ciudad de Mexico, Mexico  M. Newbold  Department of Physics and
Astronomy, University of Utah, Salt Lake City, UT, USA  M.U. Nisa  Department
of Physics and Astronomy, Michigan State University, East Lansing, MI, USA  R.
Noriega-Papaqui  Universidad Autónoma del Estado de Hidalgo, Pachuca, Mexico
M. Osorio  Instituto de Astronom’ia, Universidad Nacional Autónoma de México,
Ciudad de Mexico, Mexico  Y. Pérez Araujo  Instituto de F’isica, Universidad
Nacional Autónoma de México, Ciudad de Mexico, Mexico  E.G. Pérez-Pérez
Universidad Politecnica de Pachuca, Pachuca, Hgo, Mexico  C.D. Rho  Department
of Physics, Sungkyunkwan University, Suwon 16419, South Korea  D. Rosa-
González  Instituto Nacional de Astrof’isica, Óptica y Electrónica, Puebla,
Mexico  E. Ruiz-Velasco  Max-Planck Institute for Nuclear Physics, 69117
Heidelberg, Germany  H. Salazar  Facultad de Ciencias F’isico Matemáticas,
Benemérita Universidad Autónoma de Puebla, Puebla, Mexico  A. Sandoval
Instituto de F’isica, Universidad Nacional Autónoma de México, Ciudad de
Mexico, Mexico  M. Schneider  Department of Physics, University of Maryland,
College Park, MD, USA  J. Serna-Franco  Instituto de F’isica, Universidad
Nacional Autónoma de México, Ciudad de Mexico, Mexico  A.J. Smith  Department
of Physics, University of Maryland, College Park, MD, USA  Y. Son  University
of Seoul, Seoul, Rep. of Korea  R.W. Springer  Department of Physics and
Astronomy, University of Utah, Salt Lake City, UT, USA  O. Tibolla
Universidad Politecnica de Pachuca, Pachuca, Hgo, Mexico  K. Tollefson
Department of Physics and Astronomy, Michigan State University, East Lansing,
MI, USA  I. Torres  Instituto Nacional de Astrof’isica, Óptica y Electrónica,
Puebla, Mexico  R. Torres-Escobedo  Tsung-Dao Lee Institute & School of
Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China  R.
Turner  Department of Physics, Michigan Technological University, Houghton,
MI, USA  F. Ureña-Mena  Instituto Nacional de Astrof’isica, Óptica y
Electrónica, Puebla, Mexico  E. Varela  Facultad de Ciencias F’isico
Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico  X.
Wang  Department of Physics, Michigan Technological University, Houghton, MI,
USA  I.J. Watson  University of Seoul, Seoul, Rep. of Korea  E. Willox
Department of Physics, University of Maryland, College Park, MD, USA  S. Yun-
Cárcamo  Department of Physics, University of Maryland, College Park, MD, USA
H. Zhou  Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai
Jiao Tong University, Shanghai, China R. Babu<EMAIL_ADDRESS>
###### Abstract

HESS J1809-193 is an unidentified TeV source, first detected by the High
Energy Stereoscopic System (H.E.S.S.) Collaboration. The emission originates
in a source-rich region that includes several Supernova Remnants (SNR) and
Pulsars (PSR) including SNR G11.1+0.1, SNR G11.0-0.0, and the young radio
pulsar J1809-1917. Originally classified as a pulsar wind nebula (PWN)
candidate, recent studies show the peak of the TeV region overlapping with a
system of molecular clouds. This resulted in the revision of the original
leptonic scenario to look for alternate hadronic scenarios. Marked as a
potential PeVatron candidate, this region has been studied extensively by
H.E.S.S. due to its emission extending up-to several tens of TeV. In this
work, we use 2398 days of data from the High Altitude Water Cherenkov (HAWC)
observatory to carry out a systematic source search for the HESS J1809-193
region. We were able to resolve emission detected as an extended component
(modelled as a Symmetric Gaussian with a 1$\sigma$ radius of 0.21∘) with no
clear cutoff at high energies and emitting photons up-to 210 TeV. We model the
multi-wavelength observations for the region HESS J1809-193 using a time-
dependent leptonic model and a lepto-hadronic model. Our model indicates that
both scenarios could explain the observed data within the region of HESS
J1809-193.

##  1 Introduction

###  1.1 Previous TeV measurements

HESS J1809-193 was originally discovered by the High Energy Stereoscopic
System (H.E.S.S.) detector in 2007(Aharonian et al., 2007) as a part of a
systematic search for very-high-energy emission from energetic pulsars in the
Galactic plane in the very-high-energy range (up to 30TeV). H.E.S.S.
originally reported that it is an extended source with a fairly hard spectral
index ($\sim$2.2) that could be possibly associated with a Pulsar Wind Nebula
(PWN) powered by the pulsar PSR J1809-1917.

HESS J1809-193 was detected by the High Altitude Water Cherenkov Detector
(HAWC) Observatory in the HAWC second source catalog on TeV sources
(Abeysekara et al., 2017) as 2HWC J1809-190 and also in the third catalog of
TeV sources (Albert et al., 2020) with the source name as 3HWC J1809-190. The
emission of 3HWC J1809-190 is centered at (R.A, Decl.) of (272.46∘, -19.04∘)
with a 16$\sigma$ significance(pre-trials) using 1523 days of HAWC data.

The H.E.S.S. Collaboration, in 2023, updated their observations with a total
of 93.2 hours of observation time above 0.27 TeV (H.E.S.S. Collaboration et
al., 2023). They were able to resolve the emission into two components: an
extended Component A, and a compact Component B. The extended Component A was
modelled as an elongated Gaussian with a 1$\sigma$ semi-major/semi-minor axis
of $\sim$ 0.62∘ / $\sim$ 0.35∘, that shows a spectral cutoff at $\sim$ 12 TeV.
Component B is modelled as a symmetric Gaussian with a 1$\sigma$ radius of
$\sim$ 0.1∘ modelled with a hard spectrum and shows no spectral cutoff. The
location of Component B is closer to PSR J1809-1917. H.E.S.S. Collaboration et
al. (2023) modelled the region using a time-dependent leptonic scenario based
on three generations of electrons: a halo of ‘relic’ electrons associated with
the extended Component A, ‘medium-age’ electrons associated with the compact
Component B and the ‘young’ electrons associated with an X-ray nebula(Anada et
al., 2010).

Fermi-LAT observations of the region, performed by Araya (2018) and H.E.S.S.
Collaboration et al. (2023) using 3FGL and 4FGL data releases respectively,
list two sources in the region. As noted in H.E.S.S. Collaboration et al.
(2023), the two sources in the region are:(i) 4FGL J1810.3-1925e, which is
modelled as an extended source(Gaussian morphology) with a LogParabola
spectral curvature model, (ii) 4FGL J1811.5-1925 is modelled as a point source
and a power-law spectral model. 4FGL J1810.3-1925e’s best-fit position is
closer to PSR J1809-1917 and the two H.E.S.S. components, indicating an
association with the emission observed by H.E.S.S. The extension of the Fermi
source ($\sigma\sim 0.3^{\circ}$) is also comparable to the extension of the
extended H.E.S.S. Component A ($\sigma\sim 0.6^{\circ}$). 4FGL J1811.5-1925 is
positionally coincident with PSR J1811-1925, which indicates the association
of the source with the pulsar. Therefore the emission from this region is not
considered to contribute towards the bulk emission from HESS J1809-193.

HESS J1809-193 is also reported by the Large High Altitude Air Shower
Observatory (LHAASO) Collaboration in 2023 as an ultra high-energy source
1LHAASO J1809-1918u (Cao et al., 2023). LHAASO WCDA array detected the region
as an extended gaussian with a 1$\sigma$ radius of $\sim$ 0.35∘, with a
spectral index of 2.24 between 1-25 TeV. The KM2A array detects the region as
a point source with a 1$\sigma$ radius of $\sim$ 0.22∘ as an upper limit, with
a soft spectral index of 3.51, at energies above 25 TeV. The source was
detected by KM2A with a significance of 9.4 $\sigma$ at energies greater than
100 TeV, it is marked as an ultra-high-energy source.

Recently HAWC also reported that the HESS J1809-193 region is one of the few
sources emitting above 56 TeV in its high-energy source catalog (Abeysekara et
al., 2020). Figure 2 shows the HAWC significance map of the region using 2398
days of data, with possible counterparts within the region. It is also noted
from the catalog that there is a clear indication of emission from this region
above 100 TeV with significance slightly below the threshold of confirmation
($5\sigma)$. At energies above 56 TeV, the source emission remains extended
with a gaussian width of 0.34∘.

The high energy emission from similar objects is particularly intriguing to
study the cosmic rays near the ”knee” of the cosmic ray spectrum around 1 PeV
energy. The true origin of such cosmic rays is a mystery. The acceleration
process of these particles continues to be a question, given that cosmic-ray
accelerators produce gamma rays near their source of origin. A fraction of the
energy of these cosmic rays is transferred to the gamma rays and are detected
on Earth. In this work, we will explore particle acceleration in the region
using a lepto-hadronic scenario and a time-dependent leptonic scenario.

Figure 1:  Figure 2: HAWC sky significance map (assuming an index of 2.7 with
a point source morphology) of the region shows the emission from HAWC
J1809-1919. The distance between PSR J1809-1917 and HAWC fit is
0.05${}^{\circ}\pm$0.28. The red dashed circle shows the 1-$\sigma$ gaussian
width of the HAWC source. The maximum significance is 27$\sigma$. The upper
labels show the sources in the region. The lower labels indicate the location
of TeV sources observed by H.E.S.S., LHAASO, and HAWC (this work).

###  1.2 Multi-wavelength observations

The region in the sky in the direction of HESS J1809-193 is a source-rich
region, consisting of several supernova remnants (SNR) and pulsars. The radio
SNR G11.0-0.05, which is a partial shell type SNR is suggested to be located
at a distance of 2.4 $\pm$ 0.7 kpc(Shan et al., 2018). The radio SNR
G11.1+0.08 is also located within the TeV emission region. Both of these radio
SNR were discovered using the Very Large Array (VLA) observations at 1465 MHz
along with the Giant Metrewave Radio Telescope (GMRT) at 235 MHz (Brogan et
al., 2004). The region also consists of a powerful high spin-down energy
pulsar with a period of 82.7 ms. PSR J1809-1917 discovered by the Parkes
Multibeam Pulsar Survey (Morris et al., 2002)111See
https://www.atnf.csiro.au/research/pulsar/psrcat/ is coincident with the
H.E.S.S. and HAWC peak emission location. The X-ray diffuse emission
discovered around SNR G11.0-0.08 (Bamba et al., 2003) was thought to be
associated with the pulsar wind nebula(PWN) and consequently, the TeV emission
was assumed to be of a PWN origin. X-ray observations from Suzaku in the 2-10
KeV band, confirmed the detection of an elongated hard, non-thermal extended
emission (Anada et al., 2010). The characteristic age of PSR J1809-1917 is
51kyr (Morris et al., 2002)while the age of the SNR G11.0-0.08 is unknown
which makes the association of the pulsar to SNR G11.0-0.08 difficult. Another
energetic pulsar, PSR J1811-1925 is located at the eastern edge of the TeV
emission, at the center of SNR G11.2-0.3 (Manchester et al., 2005). Rangelov
et al. (2014) mentioned that this pulsar and SNR along with X-ray binary XTE
J1810-189 and the binary candidate Suzaku J1811-1900 are not responsible for
the bulk of the observed TeV emission. This arises from the large location
offset for PSR J1811-1925 location from the center of the emission region and
XTE J1810-189 is an ordinary type I X-ray burster, and such objects have not
been found to produce TeV $\gamma$-rays.

In 2016, using the Expanded Karl G. Jansky Very Large Array (JVLA),
Castelletti, G. et al. (2016) produced deep full-synthesis imaging at 1.4 GHz
images near the vicinity of PSR J1809-1917. Along with 12CO observations from
the James Clerk Maxwell telescope in the transition line J(3$\rightarrow$2)
and atomic hydrogen data from the Southern Galactic Plane Survey (SGPS), a
system of molecular clouds on the edge of the shock front of SNR G11.0-0.0 was
discovered. This is spatially coincident with the peak emission of the source
HESS J1809-193 although there are no radio counterparts detected for the PWN
associated with PSR J1809-1917. They proposed that the most probable origin of
the TeV emission comes from the protons of the SNR interacting with the
molecular clouds in its vicinity. The density of the molecular clouds ($\sim
2-3\times 10^{3}\mathrm{cm}^{-3}$) interacting with the SNR G11.0-0.0 is found
to be sufficient to produce the observed TeV gamma-ray emission in the region.
As stated earlier, two unidentified LAT sources, 4FGL J1810.3-1925e and 4FGL
J1811.5-1925 (Ballet et al., 2020) could have possible associations with the
TeV source.

##  2 HAWC Observatory and Description of HAWC data

In this analysis, we use data from the HAWC Observatory to study HESS
J1809-193. The HAWC detector located in the state of Puebla, Mexico at an
altitude of 4100 m, consists of 300 water Cherenkov detector tanks and covers
a total area of 22000 m2. Each tank contains four photo-multiplier tubes
designed to detect Cherenkov light emitted when particles travel through water
at a speed greater than the speed of light in the medium. HAWC is sensitive to
sources within declinations of -26∘ and +64∘and capable of continuously
monitoring the sky with a total duty cycle of 95%.

This analysis uses 2398 days of data above 1 TeV energy, collected between
June 2015 and June 2022 (Abeysekara et al. (2023)). The data is binned using a
2D binning scheme of the estimated energy and the fraction of HAWC array
triggered during an event as described in Abeysekara et al. (2019). The data
is reconstructed using the neural network energy estimator(Abeysekara et al.,
2019). This energy estimator algorithm uses artificial neural networks to
estimate the energies of photons during an event based on the input parameters
which rely on air shower characteristics such as the energy deposited by the
air shower in the array, the extent of the shower footprint within the
detector, and degree of attenuation of the shower by the atmosphere. The
energy resolution and the angular resolution, at 10 TeV, for the neural
network energy estimator at the declination of HESS J1809-193 is $\sim$15% in
logE scale and 0.4∘ (68% containment radius) respectively.

##  3 Modeling and Results

###  3.1 Methodology

The $\gamma$-ray source morphology and spectrum are fit simultaneously with a
multi-source fitting procedure using the Multi-Mission Maximum Likelihood
(3ML)222https://github.com/threeML/threeML framework and HAWC Accelerated
Plugin (HAL)333https://github.com/threeML/hawc$\\_$hal (Vianello et al.
(2015), Abeysekara et al. (2022)). The analysis is performed using a
rectangular region of interest (ROI) normal to the galactic plane and defined
as 9∘ $<$ l $<$ 13∘ and -4∘ $<$ b $<$ 4∘ where l, b are galactic latitude and
longitude respectively. The data within the ROI, shown in Figure 4, is used
for this analysis.

Figure 3:  Figure 4: HAWC sky significance map(assuming an index of 2.7 with a
point source morphology) of the region showing the ROI in the green rectangle.

In this analysis, we used a test statistic (TS) to calculate the pre-trial
statistical significance of a model using the free model parameters. TS
provides a statistical measure of how well an alternate hypothesis performs
over a null hypothesis. TS is defined as:

$\mathrm{TS}=2\ln\biggl{(}\frac{\mathrm{L}_{\mathrm{alt}}}{\mathrm{L}_{\mathrm{null}}}\biggl{)},$
(1)

where Lalt and Lnull are likelihood values for the alternate hypothesis and
null hypothesis respectively. Using Wilks’ theorem (Wilks, 1938), a pre-trial
significance $\sigma$, which is computed as $\sigma\simeq\sqrt{\mathrm{TS}}$,
which is used to denote the significance of a source (alternate hypothesis)
over background (null hypothesis).

Inspired by the Fermi-LAT Extended Source Search Catalog (Ackermann et al.,
2017), a source search method is carried out using a systematic multi-source
search analysis pipeline. The pipeline to search for point sources and
extended sources within the ROI is described as follows:

  1. 1.

The initial phase of the pipeline analysis involves creating a TS map for the
ROI assuming point-source morphology and a spectral index of 2.7.
Contributions from unresolved sources and diffuse galactic background
emissions, Unresolved Radiation Model (URM), are modelled using a 2D Gaussian
spatial template model centered 0∘ along the galactic longitude. The URM model
is fit to the data using 3ML and following the fitting process, the model is
subtracted from the data. The resulting TS maps are checked for any remaining
positive excess.

  2. 2.

A point source model is added to the URM model at the pixel’s location
corresponding to the highest TS peak on the residual map. The data is then
refitted using both the point source model and the diffuse template model. If
the TS between this model and the previous model (URM only) is greater than
16, then this model is chosen as the new seed model, and the residual is
examined for any positive excess. An additional point source model is added to
the new seed model at the location of the highest TS peak in the residual, and
the fitting process is repeated. This sequence is repeated until the TS of the
additional point sources is less than 16 or residual TS maps no longer show
significant excess (TS$<$16).

  3. 3.

All sources, regardless of their extension, must be initially detected as a
point source. Here we start checking the extension of point sources
iteratively starting from the source with the maximum test statistic using the
final point source model as the seed model. If the difference in the TS
between the extended model and the seed model is greater than 25, then the
extended model becomes the seed model for the next source extension test.
Throughout the extension testing phase, if the TS of any sources becomes
smaller than 16, they are removed from the model. The localization, extension
and spectrum of the remaining sources are refit. This process continues until
the extension tests cover all the sources inside the ROI.

  4. 4.

A similar approach, based on the source extension test, is adopted to test the
spectrum of all sources. We test the spectrum of the model using a powerlaw
(Eqn 2), powerlaw with exponential cutoff (Eqn 3) and a log-parabola spectrum
(Eqn 4)

$\phi(E)=\phi_{0}\left(\frac{E}{E_{0}}\right)^{-\Gamma}$ (2)
$\phi(E)=\phi_{0}\left(\frac{E}{E_{0}}\right)^{-\Gamma}\exp{\left(\frac{-E}{E_{c}}\right)}$
(3)
$\phi(E)=\phi_{0}\left(\frac{E}{E_{0}}\right)^{-\alpha-\beta\log{\left(\frac{E}{E_{0}}\right)}}$
(4)

where $\phi_{0}$ is the differential flux at a pivot energy of $E_{0}$,
$\Gamma$ is the spectral index, $E_{c}$ is the cutoff energy. $\alpha$ is the
spectral index and $\beta$ is the curvature parameter for the log-parabola
spectrum respectively. The pivot energy $E_{0}$ used in this study is chosen
as 10 TeV, to minimize correlation between the spectral parameters.

Figure 5: (a): A significance map of the best-fit model described in Table 1.
(b): A residual map produced by subtracting the best-fit model.

###  3.2 Results and Comparison to H.E.S.S.

The best-fit results of the source search pipeline analysis for HESS J1809-193
above 1 TeV, reveal an extended source ($\sigma$=0.21$\pm
0.016_{\text{stat}}\pm 0.67_{\text{sys}}$) in the region with a symmetric
Gaussian morphology located at (RA, Dec) = (272.38∘$\pm 0.021_{\text{stat}}\pm
0.086_{\text{sys}}$, -19.33∘$\pm 0.019_{\text{stat}}\pm 0.051_{\text{sys}}$)
and a power-law spectrum with an index of $\Gamma=2.42\pm
0.05_{\text{stat}}\pm 0.21_{\text{sys}}$. The spectral energy distribution
(SED) of the source is shown in Figure 7) with the corresponding data points
from H.E.S.S.(H.E.S.S. Collaboration et al., 2023) and LHAASO(Cao et al.,
2023). The flux points obtained from this work, show signs of a potential
steepening of spectrum above 100 TeV, consistent with the spectrum observed by
LHAASO above 25 TeV. Therefore we also tested the source with an ECPL model
and a LGP model. We found that both complex models have a similar statistical
significance, $\sim 1\sigma$ and $\sim 1.2\sigma$ respectively compared to the
power-law, and are not preferred over the power-law model by $3\sigma$
significance. Therefore we adopted the simpler power-law model to best
describe the region. More data at higher energies is needed to make conclusive
evidence for the curvature of the spectrum.

Figure 5(a) shows the model map for the region and Figure 5(b) shows the
residual map after the subtraction of model from the data map. Table 1 shows
the best-fit parameters from modeling the source at a pivot energy of 10TeV,
along with their statistical and systematic uncertainties (Abeysekara et al.,
2019). Systematic uncertainties related to the modeling of the HAWC detector
are investigated as described in Abeysekara et al. (2019). The effects of the
detector systematic uncertainties are shown as the yellow band in Figure 7.
The energy range for this source is determined by adding a step function
cutoff to the best-fit model, and calculating the maximum and minimum energies
with a 1$\sigma$ confidence level.

The analysis was repeated using data above 56 TeV. We find that the source
becomes softer above 56 TeV, with a best-fit index of $\Gamma$ = 2.94 $\pm$
0.29stat, and remains extended with a symmetric Gaussian morphology with a
1-$\sigma$ extension of 0.186${}^{\circ}\pm$ 0.023stat. An energy dependent
morphology study for HESS J1809-193 based on the methodology explained in
Section 4. of Albert et al. (2021) was done. The results of the energy-
dependent morphology lacks conclusive evidence for change in morphology with
increasing energy, primarily due to the large uncertainties in the
measurements attributing from poor angular resolution of HAWC at the
declination of the source. This may be improved through additional data in the
future, along with HAWCs outrigger array(Marandon et al., 2019).

Figure 6:  Figure 7: HAWC SED for HESS J1809-193. We compare the HAWC spectrum
and flux points in gray triangles to spectra observed by H.E.S.S. (H.E.S.S.
Collaboration et al., 2023) for the extended H.E.S.S. component A and the
compact H.E.S.S. component B, in green and purple respectively. The LHAASO:
WCDA and KM2A spectra taken from Cao et al. (2023) are shown in red and blue
respectively. HAWC spectrum (gray) shows the best-fit PL model with the
statistical uncertainties. HAWC spectrum (yellow) shows the best-fit PL model
with systematical uncertainties.

In contrast to the detection of a two-source model from H.E.S.S. (H.E.S.S.
Collaboration et al., 2023) (with an angular resolution of <0.1∘ above 1 TeV),
HAWC (with an angular resolution of 0.55∘ (68% containment radius) above 1 TeV
at the declination of HESS J1809-193), detects a single extended source which
is likely due to the different energy ranges and angular resolution of the two
instruments. The comparison of spectral results suggests that the spectrum of
the observed HAWC source is similar to that of the more brighter component,
Component A, as detected by H.E.S.S.

Fit parameters | Best fit values
---|---
TS | 392
RA(∘) | 272.38$\pm 0.021_{\text{stat}}\pm 0.086_{\text{sys}}$
Dec(∘) | -19.33$\pm 0.019_{\text{stat}}\pm 0.051_{\text{sys}}$
$\phi_{0}$(TeV-1 cm-2 s-1) | 3.53$\pm 0.31_{\text{stat}}\pm 1.19_{\text{sys}}\times 10^{-14}$
Index | 2.42$\pm 0.05_{\text{stat}}\pm 0.21_{\text{sys}}$
$\sigma$(∘) | 0.21$\pm 0.016_{\text{stat}}\pm 0.67_{\text{sys}}$
Table 1: Best-fit parameters and their statistical and systematic
uncertainties for HAWC J1809-1919. $\phi_{0}$ is the flux normalization at a
pivot energy of 10 TeV. Also given is the 1$\sigma$ radius of the Gaussian
morphological model.

##  4 Spectral Modeling

Due to the number of SNRs along with potential PWNs in the region, it is
unclear whether the observed $\gamma$-rays have a hadronic or leptonic origin.
Studies performed by Castelletti, G. et al. (2016) using 12CO data in the
region of HESS J1809-193 revealed a system of molecular clouds positionally
coincident with the peak of the observed $\gamma$-ray emission from the
H.E.S.S. observations. X-ray observations by Suzaku (Anada et al., 2010)
reveal a hard non-thermal spectrum(photon index $\Gamma\approx 1.7$).
Therefore in section 4.1 we investigate the lepto-hadronic scenario for the
multi-wavelength observations from the contribution of SNR-molecular gas cloud
interaction and the pulsar PSR J1809-1917 injecting particles into the system
using NAIMA (Zabalza, 2015)framework. In section 4.2, we investigate a time-
dependent leptonic scenario for the PWN associated with PSR J1809-1917 using
GAMERA (Hahn et al., 2022) framework. We also note that the associations made
to the multiwavelength data are used to explain the SED alone and not the
spatial features.

###  4.1 Lepto-hadronic scenario

Observations of molecular clouds by Castelletti, G. et al. (2016) and Voisin
et al. (2019) along with the presence of SNRs, increase the probability of
cosmic rays accelerating in the SNR shocks and interacting with the molecular
clouds in the region. Figure 9 shows the 12CO (J=1-0) FUGIN line emission
contours overlaid with the HAWC and H.E.S.S. extensions that show the
morphology of the molecular clouds detected within the region. The distance
estimates for SNR G011.0-0.0, as reported in the studies, include
approximately 3.7 kpc according to Voisin et al. (2019), around 3.0 kpc based
on Castelletti, G. et al. (2016), 2.4$\pm$0.7 according to Shan et al. (2018),
and 2.6 kpc according to Bamba et al. (2003). These estimates are closer to
the distance estimations for PSR J1809-1917, which is approximately 3.7 kpc.
The distance estimate for SNR G011.1+00.1 is 17 kpc, with a 40% fractional
error (Brogan et al., 2004). This would, unrealistically, place SNR
G011.1+00.1 outside the boundaries of the galaxy. Hence for this study, we do
not consider the emissions from SNR G011.1+00.1. Since SNR G011.0-0.0 is
believed to be the progenitor of PSR J1809-1917, we show the integrated radio
flux points from SNR G011.0-0.0 calculated by Brogan et al. (2006), for
comparison in the multiwavelength analysis.

Figure 8:  Figure 9: 12CO (J=1-0) FUGIN line emission map (Umemoto et al.,
2017) for the HESS J1809-193 region. The blue triangle represents the location
of PSR J1809-1917, the green dot and circle represent the HAWC source position
and the 1-$\sigma$ extension, and the yellow square and ellipse represent the
H.E.S.S. extended source respectively.

H.E.S.S. detection of two components along with the break in the spectra in
the GeV energy range motivates using a complex model, involving contributions
from both leptonic and hadronic models(lepto-hadronic model), over a simple
hadronic model. This model assumes the SNR/molecular cloud interaction for the
hadronic mechanism motivated by the overlap of the HAWC and the molecular
cloud morphologies from Figure 9 (no spatial information is used in the
study). For the leptonic scenario, we assume the electrons injected into the
PWN by the pulsar, PSR J1809-1917. For this physical scenario, we use NAIMA to
model the multi-wavelength observations.

The very high-energy $\gamma$-rays observations from HAWC and the H.E.S.S.
extended source component(Component A) are modelled with a hadronic
population. Even though the molecular cloud density in the region shows a
gradient (Castelletti, G. et al., 2016), seen in Figure 9, the TeV morphology
does not show any similar characteristics across the region of HAWC
J1809-1919. Therefore we calculate an average ambient density that can produce
the detected TeV photons from the region. To quantify the ambient density
within the region, we first calculate the $\gamma$-ray flux for HAWC
J1809-1919 above 1 TeV by taking into account the power-law spectrum of this
source (d$\phi_{\gamma}$(E)/dE=$\phi_{0}$(E/10 TeV)-Γ) with $\phi_{0}$ and
$\Gamma$ values from Table(1), which implies a
F${}_{\gamma}(>1\text{TeV})=6.4\times 10^{-12}\text{ph cm}^{-2}\text{s}^{-1}$.
Assuming the fraction of the total supernova explosion energy converted to
cosmic-ray energies, $\theta$=10% (Dermer & Powale, 2013), the distance to the
SNR, d$\sim$3.5 kpc and the supernova energy output of $10^{51}$ erg, we
calculate the required ambient density in the region to produce the observed
$\gamma$-ray emission, using Eq.(16) of Torres et al. (2003). We find that a
minimum ambient density of $n\sim 40\text{cm}^{-3}$ at a distance of 3.5 kpc,
is required to produce the $\gamma$-ray emission detected above 1 TeV. This
calculated value is below the density of cloud in the range of 2-3$\times
10^{3}\mathrm{cm}^{-3}$estimated by Castelletti, G. et al. (2016), using 12CO
observations.

The Suzaku X-ray observations are modelled using a leptonic population and the
radio observations are used only for comparison. The X-ray flux is measured in
the vicinity of the nebula(regions 2, 3, 6 and 7 in Table 4 of Anada et al.
(2010)). The same leptonic population can produce TeV emissions through the
Inverse Compton (IC) mechanism(assuming cosmic microwave background (CMB),
Far-infrared radiation (FIR), and Near-infrared radiation (NIR) photon fields
as seed photons with their values set to (2.72 K, 0.261 eV/cm3), (30 K, 0.5
eV/cm3) and (3000 K, 1 eV/cm3) respectively, obtained from GALPROP). We also
consider the same leptonic population interacting with the molecular cloud
(with a ambient ion density n${}_{\text{ion}}\sim 40$ cm-3) undergoing a non-
thermal Bremmstrahlung process to reproduce the observed Fermi data points
obtained by H.E.S.S. Collaboration et al. (2023). The parent particle spectrum
is assumed to follow an exponential cut-off power-law, motivated by the
spectrum break between LHASSO KM2A and WCDA (used only for comparison), and
with an assumed distance of 3.5 kpc distance to the source.

The model parameters are fitted to the multiwavelength data using the Markov
Chain Monte-Carlo (MCMC) procedure to obtain probability distributions for the
parameters of the parent particle populations. The fit parameters for the
model are summarised in Table 2 and the resulting spectra are shown in Figure
10. Figure 10(a) shows the total SED for the resultant model, while Figure
10(b) shows the SED in the GeV-TeV. LHAASO WCDA and KM2A spectra from LHAASO’s
catalog (Cao et al., 2023) are also plotted for comparison. We observe the
total spectrum can reproduce all the observed emissions including the highest
energy HAWC and LHAASO data.

We tested the hadronic component in Naima with two different maximum proton
energies, Ep, at 800 TeV and 1 PeV, and found that a proton energy of at least
1 PeV is required to explain the TeV $\gamma$-rays. The hadronic component
prefers a relatively hard index of $\Gamma_{p}=2.00\pm 0.03$ with a cutoff of
350 TeV. Integrating the spectrum above 1 GeV gives a total proton energy of
$W_{p}\sim 1.23\times 10^{49}\text{erg}$, which is a very small fraction of
the calculated energy released in a supernova explosion of $\sim 10^{51}$ erg
(Ginzburg & Ptuskin, 1976). Considering the gas density gradient across the
HAWC 1$\sigma$ width of 0.21∘ observed by FUGIN(Figure 9), cosmic rays
accelerated by SNR G011.0-0.0 can potentially reach the dense molecular clouds
in the region ($n_{h}\sim 40\ \mathrm{cm}^{-3}$) and produce the observed
$\gamma$-rays. In the case of the proton-proton interaction scenario, the
presence of secondary synchrotron component from the secondary electrons
produced in the process is expected. Observations of the region with larger
field-of-view with X-ray telescopes would provide evidence of such an
emission.

The secondary electrons in the pp scenario is not adding complexity to the
model, they are just expected to be present. They need to be mentioned even
their synchrotron emission is not computed.

For the leptonic model, we get an index of $\Gamma_{e}=2.49\pm 0.06$ and a
relatively low magnetic field of B=2.8 $\pm 0.11\mathrm{\mu}$G. The
synchrotron emission from the leptonic model shows good agreement with the
Suzaku X-ray data. We also observe that this same population of electrons at
higher energies can reproduce the spectrum of the compact component detected
by H.E.S.S. (H.E.S.S. Component B) through the IC mechanism. This could
explain the X-ray component along with H.E.S.S. component B, and is compatible
with the emission surrounding the PWN associated with PSR J1809-1917. The same
leptonic population could interact with the molecular cloud in the vicinity
undergoing a Bremmstrahlung mechanism to reproduce the $\leq$100 GeV
$\gamma$-ray emission observed by Fermi.

###  4.2 Time-dependent leptonic model

In this section, we explain the spectra assuming a leptonic scenario, where
the emission originates from a PWN powered by the pulsar PSR J1809-1917. The
observed period ($P$) and the period time derivative ($\dot{P}$) are 82.7 ms
and $2.553\times 10^{-14}$(Manchester et al., 2005). The characteristic age,
$\tau_{c}$, of the pulsar is 51.3 kyr which is an estimated measure for the
pulsar age, provided the assumption of pulsar braking index n=3 and the birth
period ($P_{0}$) is less than the observed period $P$ holds true (Gaensler &
Slane, 2006). The distance used to calculate the flux in this model is assumed
to be 3.5 kpc. We found that a model with a minimum of three particle
populations is required describe the observed TeV and X-ray data. The radio
flux data is shown only for comparison and is not included in the fit. In this
model, the fraction of the pulsar spin-down luminosity converted to electrons
($\theta$-fraction), particle cut-off energy ($E_{c}$), and the birth period
($P_{0}$) are treated as unknown parameters used to describe the injected
electron spectrum. The true age of the system,$\tau$, is calculated as a
function of $P_{0}$ using equation(5).

$\tau=\frac{P}{(n-1)\dot{P}}\left[1-\left(\frac{P_{0}}{P}\right)^{n-1}\right]$
(5)

We use the GAMERA package(Hahn et al., 2022) to model the spectrum of the
radiation produced by the particles. GAMERA can produce a time-dependent model
of relativistic electrons, including its injection and cooling, producing
photon emission in different wavelengths. In this model we consider a power-
law with an exponential cutoff for the injected electrons. The seed radiation
fields used to calculate the IC spectrum are calculated from Popescu et al.
(2017) for the location of PSR J1809-1917. (Gaensler & Slane, 2006) specifies
the conditions for the time evolution for $B$, $\dot{E}$ and $P$. The time-
dependent modelling approach is similar to the approach outlined in Albert et
al. (2021) and H.E.S.S. Collaboration et al. (2023). The parameters of the
model are described in Table(3).

We fit the model to three generations of electrons: relic, middle-age and
recently injected ‘young electrons’. Relic electrons are electrons injected
into the ISM by the PWN over the lifetime of the system, in this case the
result of the fit gives the age of the system as $\tau\sim$26.5 kyr, and is
associated with the HAWC, H.E.S.S. Component A and LHAASO WCDA components.
Medium-age electrons are electrons injected into the system in the last 10.2
kyr and associated with the compact H.E.S.S. Component B. Young electrons are
electrons injected into the system in the last $\sim$3.1 kyr and is associated
with the X-ray nebula. We also see that the evolved spectra has an index of
$\Gamma$=2.1 and an evolved present day magnetic field, B$\sim$3.2 $\mu$G and
about 67% of the pulsars spin-down luminosity is converted to electrons. This
signifies that the spin-down energy of the pulsar is sufficient to maintain
the energy of electrons and positrons in the wind of the pulsar powering the
entire multiwavelength observations.

Figure 10: Multi-wavelength SEDs for the lepto-hadronic scenario of HESS J1809-193 region obtained with NAIMA. The data shown includes the 90 cm radio observations of the SNR G11.0-0.0 with the Very Large Array survey points in teal (Brogan et al., 2004), the Suzaku butterfly spectra in purple (Anada et al., 2010), the Fermi-LAT, H.E.S.S. Component A and H.E.S.S. Component B flux points, in brown, orange and green respectively (H.E.S.S. Collaboration et al., 2023), and the HAWC flux points from this work in blue. Figure(a) shows the full SED for the region. The primary synchrotron is shown in dashed pink line. Total inverse compton SED is show in dashed red line while the individual seed photon components for IC: CMB and interstellar radiation fields (IRF) are shown in dashed brown and orange tomato colors respectively. p-p emission is shown in green and the non-thermal Bremsstrahlung emission is shown in blue dashed lines.The total SED is represented in gray. Figure(b): Zoomed in version of the SED for $\gamma$-ray observations. Shown for comparison, but not used in the fit, is the spectrum for the ultra high-energy source 1LHAASO J1809-1918u from the (Cao et al., 2023) and the radio flux points from SNR G11.0+0.0 Figure 11: Multiwavelength SED for the time dependent leptonic model of HESS J1809-193 obtained with GAMERA. The presented data is identical to the one shown in Fig(10). Fig(a) shows the full SED for the region for the three generations of electrons. The solid line indicates the old ’relic’ electrons. The dashed lines and curved lines correspond to the medium-age and young electrons injected into the system respectively. Fig(b) shows the zoomed-in $\gamma$-ray observations and their MCMC results. Shown for comparison(but not used in the fit is the spectrum for the ultra high-energy source 1LHAASO J1809-1918u from Cao et al. (2023). Parameters | Fit values
---|---
Leptonic fit
log($A$[1/TeV]) | 43.81 $\pm$ 1.14
$E_{0}$[TeV] | 10
$\Gamma_{e}$ | 2.49 $\pm$ 0.06
$E_{\text{cutoff}}$[TeV] | 630.54 $\pm$ 185
B-field[$\mu$G] | 2.80 $\pm$ 0.11
W $>$ 1 GeV[erg] | $2.35^{+1.19}_{-0.95}{}\times 10^{48}$
Hadronic
log($A$[1/TeV]) | 45.91 $\pm$ 1.17
$E_{0}$[TeV] | 10
$\Gamma_{p}$ | 2.00 $\pm$ 0.03
$E_{\text{cutoff}}$[TeV] | 349.05 $\pm$ 65.33
W $>$ 1 GeV[erg] | $1.23^{+0.09}_{-0.1}{}\times 10^{49}$
Table 2: Naima best-fit parameters for the spectral models shown in Figure 10. Note that $E_{0}$ is fixed here. Parameter | Parameter description | Fit values
---|---|---
| Pulsar Parameters |
$\dot{\text{E}}$ | Spin down power | $1.8\times 10^{36}\ \text{erg s}^{-1}$
$\tau_{c}$ | Characteristic age | 51 kyr
P | Pulsar period | 82.76 ms
$\dot{\text{P}}$ | Pulsar period derivative | $2.55\times 10^{-14}\text{s s}^{-1}$
d | Distance to pulsar | 3.3 kpc
n | Braking index | 3
| Fitting parameters |
$\theta$ | Power fraction | 0.67
$\text{E}_{c}$ | Particle Cut-off energy | 794 TeV
$\alpha$ | Particle injection index | 2.1
B | Magnetic field | $3.2\ \mu\text{G}$
$\text{P}_{0}$ | Pulsar birth period | $47\ \text{ms}$
$\tau_{\text{young}}$ | Age of young electrons | 3.1 kyr
$\tau_{\text{med}}$ | Age of middle-age electrons | 10.2 kyr
$\tau_{\text{relic}}$ | Age of relic electrons | 26.5 kyr
Table 3: Pulsar parameters and fit parameters for the time-dependent PWN
model. The listed values are the Pulsar parameters taken from ATNF catalog
(Manchester et al., 2005) and the fit parameters obtained from an MCMC fit to
the spectral data using GAMERA.

##  5 Discussion

The outcome from the SED modelling and analysis suggest two potential models
to describe the observed multiwavelength spectra: (i)a lepto-hadronic
scenario, describing the potential involvement of CRs produced by the SNR and
PWN, (ii) a time-dependent model, with 3 population of electrons injected into
the ISM by the PWN system, each associated with their respective emission
wavelengths (TeV $\gamma$-ray and X-ray).

In the lepto-hadronic scenario for the observed multiwavelength SED, the
protons accelerated at the shocks from SNR G11.0-0.0, SNR G11.1+0.1 or both,
could be responsible for the observed GeV-TeV $\gamma$-ray emission. While the
age of these SNRs remains unclear, measurements done based on the association
of 12CO and HI-self absorption features done by Castelletti, G. et al. (2016)
places the SNR G11.0-0.0 at approximately 3 kpc, within the uncertainties of
the derived kinematic distance. This could indicate the association of SNR
G11.0-0.0 as the progenitor of PSR J1809-1917. Protons accelerated by SNR
G11.0-0.0 could interact with the molecular gas clouds in their immediate
vicinity to produce the observed TeV emission. The total mass and total proton
density , as measured by Castelletti, G. et al. (2016)(taking into account
contributions from both HI and 12CO emissions), from the molecular clouds
estimated to be $\text{M}\approx 3\times 10^{3}M_{\odot}$ and $\eta\approx
7.4\times 10^{3}\ \mathrm{cm}^{-3}$, is found to fulfill the required amount
of target material for hadronic interactions. We conclude that a proton energy
of at least 1 PeV is required for a distance of 3.5 kpc to the source and an
average molecular cloud density for proton interactions of $\sim$40 cm-3 is
required within the region of high-energy $\gamma$-ray emissions for a SNR
shock scenario. This could indicate that the source is a hadronic PeVatron.
The estimated value of the present-day B-field is $\sim 2.8\ \mu$G, which is
low relative to the ISM and it depends on the normalization of the peak of
X-ray synchrotron emission. While the magnetic field is comparatively low, the
synchrotron emission can explain the X-ray data. Considering the X-ray
emission is produced near the PWN, the same population of electrons is also
able to reproduce the TeV emission observed from the compact H.E.S.S.
Component B, which spatially coincident with the pulsar and the PWN.

For the time dependent PWN scenario, we show SEDs obtained for three
generations of electrons. The model describes well the spectra of HAWC and
H.E.S.S. Component A and the X-ray flux from Suzaku. The fit yields an average
present day magnetic field of $\sim 3.2\mu$G and a reasonable index for the
injection spectrum of $\sim 2.1$. A maximum electron energy of several hundred
TeV is also observed from the spectrum fit, which is similar to the maximum
electron energy observed in the lepto-hadronic fit. The model predicts that
the ’relic’ old electrons injected into the system would cool down over time,
which could explain the slight cutoff observed at the highest energies. In the
case of the relic electrons, we find that the observed total synchrotron
emission overshoots the observed SED by a factor of 2-3 at energies between
2-10 keV. This is potentially due to the smaller region of interest ($\sim
0.3^{\circ}\times 0.3^{\circ}$) for the Suzaku observations. Anada et al.
(2010) found diffuse X-ray emission extending beyond south of the PWN.
Therefore if the origin of the TeV $\gamma$-rays is of leptonic origin, then a
diffuse X-ray emission from synchrotron radiation could surround the X-ray PWN
with a morphology similar to the observed TeV one. Therefore to quantify the
flux from this diffuse X-ray region, H.E.S.S. Collaboration et al. (2023)
calculated an upper limit (95% CL) for the X-ray flux shown in Figure(11).
H.E.S.S. Collaboration et al. (2023) observed in their modeling that the
synchrotron emission from relic electrons match the upper limit. Our modeling
results show that the synchrotron flux produced by both relic and middle-age
electrons are well below the X-ray upper-limits at keV energies.

This model scenario however cannot explain the Fermi-LAT observations below
$\sim$10 GeV. This could be attributed to a secondary population of particles,
undergoing a non-thermal Bremsstrahlung process near the pulsar with the gas
density in the region as mentioned previously.

##  6 Conclusions and Outlook

In this work, we perform a detailed spectral and morphological study of HESS
J1809-193 using 2398 days of HAWC data. Unlike the H.E.S.S. observations for
this region, HAWC observations indicate a single extended source in the region
and no conclusive evidence for energy dependent morphology due to the low
angular resolution of the detector at higher zenith angles. The morphology of
the region reveals an extended symmetric gaussian source with a 1-$\sigma$
extension of 0.21$\pm 0.016_{\text{stat}}$ (above 1 TeV) and
0.186${}^{\circ}\pm$ 0.023stat (above 56 TeV). Spectral studies indicate a
power-law spectrum with an index of $\sim$2.44. There could be a potential
steepening of the spectrum at the highest energies indicated by the last flux
point above 200 TeV, which requires more data/statistics. The HAWC spectrum
extends the emission observed by H.E.S.S. well past 56 TeV.

Studies done by H.E.S.S. Collaboration et al. (2023), have considered a time-
dependent leptonic scenario to explain the multiwavelength spectrum of HESS
J1809-193 by invoking the electrons injected into the system by PSR
J1809-1917. A lepto-hadronic model proposed by Boxi & Gupta (2024), was also
used to explain the emission of HESS J1809-193, where the explosion of SNR
G11.0-0.0 injected CR protons and electrons into the region producing the
high-energy gamma-rays. In our studies, we have expanded on the
multiwavelength model proposed by HESS using newer HAWC data and place better
constraints on the model. We also suggested that a lepton-hadronic scenario
involving the SNR injecting CR protons and the PWN produced by PSR J1809-1917
injecting CR electrons into the system, can better explain the observed high-
energy gamma-rays and X-rays simultaneously, except for the Fermi-LAT data
below $\sim$ 10 GeV.

As mentioned earlier, this work is based on spectral association alone and the
detailed study of spatial associations is left for future studies. Hence we
cannot provide conclusive evidence for the origin of the $\gamma$-rays from
the region of HESS J1809-193. Conclusive evidence of $\gamma$-ray production
from the region requires deep morphological and spectral studies of the SNRs
present. Future observations from LHAASO, the upcoming Cherenkov Telescope
Array (CTA), and the Southern Wide-Field Gamma-Ray Observatory (SWGO) could
provide unprecedented observations to enhance our understanding of the region.

##  7 Acknowledgements

We acknowledge the support from: the US National Science Foundation (NSF); the
US Department of Energy Office of High-Energy Physics; the Laboratory Directed
Research and Development (LDRD) program of Los Alamos National Laboratory;
Consejo Nacional de Ciencia y Tecnología (CONACyT), México, grants 271051,
232656, 260378, 179588, 254964, 258865, 243290, 132197, A1-S-46288,
A1-S-22784, CF-2023-I-645, cátedras 873, 1563, 341, 323, Red HAWC, México;
DGAPA-UNAM grants IG101323, IN111716-3, IN111419, IA102019, IN106521,
IN110621, IN110521 , IN102223; VIEP-BUAP; PIFI 2012, 2013, PROFOCIE 2014,
2015; the University of Wisconsin Alumni Research Foundation; the Institute of
Geophysics, Planetary Physics, and Signatures at Los Alamos National
Laboratory; Polish Science Centre grant, DEC-2017/27/B/ST9/02272; Coordinación
de la Investigación Científica de la Universidad Michoacana; Royal Society -
Newton Advanced Fellowship 180385; Generalitat Valenciana, grant
CIDEGENT/2018/034; The Program Management Unit for Human Resources &
Institutional Development, Research and Innovation, NXPO (grant number
B16F630069); Coordinación General Académica e Innovación (CGAI-UdeG), PRODEP-
SEP UDG-CA-499; Institute of Cosmic Ray Research (ICRR), University of Tokyo.
H.F. acknowledges support by NASA under award number 80GSFC21M0002. We also
acknowledge the significant contributions over many years of Stefan
Westerhoff, Gaurang Yodh and Arnulfo Zepeda Dominguez, all deceased members of
the HAWC collaboration. Thanks to Scott Delay, Luciano Díaz and Eduardo
Murrieta for technical support.

## References

  * Abeysekara et al. (2017) Abeysekara, A. U., Albert, A., Alfaro, R., et al. 2017, ApJ, 843, 40, doi: 10.3847/1538-4357/aa7556
  * Abeysekara et al. (2019) Abeysekara, A. U., et al. 2019, Astrophys. J., 881, 134, doi: 10.3847/1538-4357/ab2f7d
  * Abeysekara et al. (2020) Abeysekara, A. U., Albert, A., Alfaro, R., et al. 2020, Phys. Rev. Lett., 124, 021102, doi: 10.1103/PhysRevLett.124.021102
  * Abeysekara et al. (2022) Abeysekara, A. U., Albert, A., Alfaro, R., et al. 2022, in 37th International Cosmic Ray Conference, 828, doi: 10.22323/1.395.0828
  * Abeysekara et al. (2023) —. 2023, Nuclear Instruments and Methods in Physics Research A, 1052, 168253, doi: 10.1016/j.nima.2023.168253
  * Ackermann et al. (2017) Ackermann, M., Ajello, M., Baldini, L., et al. 2017, ApJ, 843, 139, doi: 10.3847/1538-4357/aa775a
  * Aharonian et al. (2007) Aharonian, F., Akhperjanian, A. G., Bazer-Bachi, A. R., et al. 2007, A&A, 472, 489, doi: 10.1051/0004-6361:20077280
  * Albert et al. (2020) Albert, A., et al. 2020, Astrophys. J., 905, 76, doi: 10.3847/1538-4357/abc2d8
  * Albert et al. (2021) Albert, A., Alfaro, R., Alvarez, C., et al. 2021, arXiv e-prints, arXiv:2101.01649, doi: 10.48550/arXiv.2101.01649
  * Anada et al. (2010) Anada, T., Bamba, A., Ebisawa, K., & Dotani, T. 2010, PASJ, 62, 179, doi: 10.1093/pasj/62.1.179
  * Araya (2018) Araya, M. 2018, ApJ, 859, 69, doi: 10.3847/1538-4357/aabd7e
  * Ballet et al. (2020) Ballet, J., Burnett, T. H., Digel, S. W., & Lott, B. 2020, Fermi Large Area Telescope Fourth Source Catalog Data Release 2, arXiv, doi: 10.48550/ARXIV.2005.11208
  * Bamba et al. (2003) Bamba, A., Ueno, M., Koyama, K., & Yamauchi, S. 2003, ApJ, 589, 253, doi: 10.1086/374354
  * Boxi & Gupta (2024) Boxi, S., & Gupta, N. 2024, ApJ, 961, 61, doi: 10.3847/1538-4357/ad0da9
  * Brogan et al. (2004) Brogan, C. L., Devine, K. E., Lazio, T. J., et al. 2004, Astron. J., 127, 355, doi: 10.1086/379856
  * Brogan et al. (2004) Brogan, C. L., Devine, K. E., Lazio, T. J., et al. 2004, AJ, 127, 355, doi: 10.1086/379856
  * Brogan et al. (2006) Brogan, C. L., Gelfand, J. D., Gaensler, B. M., Kassim, N. E., & Lazio, T. J. W. 2006, ApJ, 639, L25, doi: 10.1086/501500
  * Cao et al. (2023) Cao, Z., Aharonian, F., An, Q., et al. 2023, arXiv e-prints, arXiv:2305.17030, doi: 10.48550/arXiv.2305.17030
  * Castelletti, G. et al. (2016) Castelletti, G., Giacani, E., & Petriella, A. 2016, A&A, 587, A71, doi: 10.1051/0004-6361/201527578
  * Dermer & Powale (2013) Dermer, C. D., & Powale, G. 2013, A&A, 553, A34, doi: 10.1051/0004-6361/201220394
  * Gaensler & Slane (2006) Gaensler, B. M., & Slane, P. O. 2006, ARA&A, 44, 17, doi: 10.1146/annurev.astro.44.051905.092528
  * Ginzburg & Ptuskin (1976) Ginzburg, V. L., & Ptuskin, V. S. 1976, Rev. Mod. Phys., 48, 161, doi: 10.1103/RevModPhys.48.161
  * Hahn et al. (2022) Hahn, J., Romoli, C., & Breuhaus, M. 2022, GAMERA: Source modeling in gamma astronomy, Astrophysics Source Code Library, record ascl:2203.007.  http://ascl.net/2203.007
  * H.E.S.S. Collaboration et al. (2023) H.E.S.S. Collaboration, Aharonian, F., Ait Benkhali, F., et al. 2023, A&A, 672, A103, doi: 10.1051/0004-6361/202245459
  * Manchester et al. (2005) Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005, AJ, 129, 1993, doi: 10.1086/428488
  * Marandon et al. (2019) Marandon, V., Jardin-Blicq, A., & Schoorlemmer, H. 2019, in International Cosmic Ray Conference, Vol. 36, 36th International Cosmic Ray Conference (ICRC2019), 736, doi: 10.22323/1.358.0736
  * Morris et al. (2002) Morris, D. J., Hobbs, G., Lyne, A. G., et al. 2002, MNRAS, 335, 275, doi: 10.1046/j.1365-8711.2002.05551.x
  * Popescu et al. (2017) Popescu, C. C., Yang, R., Tuffs, R. J., et al. 2017, MNRAS, 470, 2539, doi: 10.1093/mnras/stx1282
  * Rangelov et al. (2014) Rangelov, B., Posselt, B., Kargaltsev, O., et al. 2014, ApJ, 796, 34, doi: 10.1088/0004-637X/796/1/34
  * Shan et al. (2018) Shan, S. S., Zhu, H., Tian, W. W., et al. 2018, ApJS, 238, 35, doi: 10.3847/1538-4365/aae07a
  * Torres et al. (2003) Torres, D. F., Romero, G. E., Dame, T. M., Combi, J. A., & Butt, Y. M. 2003, Phys. Rep., 382, 303, doi: 10.1016/S0370-1573(03)00201-1
  * Umemoto et al. (2017) Umemoto, T., Minamidani, T., Kuno, N., et al. 2017, PASJ, 69, 78, doi: 10.1093/pasj/psx061
  * Vianello et al. (2015) Vianello, G., Lauer, R. J., Younk, P., et al. 2015, arXiv e-prints, arXiv:1507.08343, doi: 10.48550/arXiv.1507.08343
  * Voisin et al. (2019) Voisin, F. J., Rowell, G. P., Burton, M. G., et al. 2019, PASA, 36, e014, doi: 10.1017/pasa.2019.7
  * Wilks (1938) Wilks, S. S. 1938, The Annals of Mathematical Statistics, 9, 60 , doi: 10.1214/aoms/1177732360
  * Zabalza (2015) Zabalza, V. 2015, in International Cosmic Ray Conference, Vol. 34, 34th International Cosmic Ray Conference (ICRC2015), 922, doi: 10.22323/1.236.0922