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Draft version July 13, 2021Typeset using LATEX default style in AASTeX631
Long-term spectra of the blazars Mrk 421 and Mrk 501 at TeV energies seen by HAWC
A. Albert ,1 R. Alfaro ,2 C. Alvarez,3 J.R. Angeles Camacho,2 J.C. Arteaga-Velazquez,4 K.P. Arunbabu,5
D. Avila Rojas ,2 H.A. Ayala Solares ,6 V. Baghmanyan ,7 E. Belmont-Moreno ,2
K.S. Caballero-Mora ,3 T. Capistran ,8 A. Carraminana ,9 S. Casanova ,7 U. Cotti ,4 J. Cotzomi ,10
S. Coutino de Leon ,9 E. De la Fuente ,11 R. Diaz Hernandez,9 M.A. DuVernois ,12 M. Durocher ,1
J.C. Dıaz-Velez ,11 K. Engel ,13 C. Espinoza ,2 K.L. Fan,13 M. Fernandez Alonso,6 N. Fraija ,8
D. Garcia,2 J.A. Garcıa-Gonzalez ,14 F. Garfias ,8 M.M. Gonzalez ,8 J.A. Goodman ,13 J.P. Harding ,1
B. Hona ,15 D. Huang ,16 F. Hueyotl-Zahuantitla ,3 P. Huntemeyer,16 A. Iriarte ,8 V. Joshi ,17
A. Lara ,5 W.H. Lee ,8 J. Lee,18 H. Leon Vargas ,2 A.L. Longinotti ,8 G. Luis-Raya ,19 K. Malone ,1
O. Martinez ,10 J. Martınez-Castro ,20 J.A. Matthews ,21 P. Miranda-Romagnoli ,22 E. Moreno ,10
M. Mostafa ,6 A. Nayerhoda ,7 L. Nellen ,23 M. Newbold ,15 R. Noriega-Papaqui ,22 A. Peisker,24
Y. Perez Araujo ,8 E.G. Perez-Perez ,19 C.D. Rho ,18 D. Rosa-Gonzalez ,9 H. Salazar,10
F. Salesa Greus ,7 A. Sandoval ,2 M. Schneider ,13 J. Serna-Franco,2 A.J. Smith ,13 R.W. Springer ,15
K. Tollefson ,24 I. Torres ,9 R. Torres-Escobedo,11 F. Urena-Mena ,9 L. Villasenor ,10 X. Wang,16
T. Weisgarber,12 E. Willox ,13 H. Zhou ,25 C. de Leon ,4
THE HAWC COLLABORATION
1Physics Division, Los Alamos National Laboratory, Los Alamos, NM, USA2Instituto de Fısica, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico, Mexico
3Universidad Autonoma de Chiapas, Tuxtla Gutierrez, Chiapas, Mexico4Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mexico
5Instituto de Geofısica, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico, Mexico6Department of Physics, Pennsylvania State University, University Park, PA, USA
7Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 IFJ-PAN, Krakow, Poland8Instituto de Astronomıa, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico, Mexico
9Instituto Nacional de Astrofısica, Optica y Electronica, Puebla, Mexico10Facultad de Ciencias Fısico Matematicas, Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
11Departamento de Fısica, Centro Universitario de Ciencias Exactase Ingenierias, Universidad de Guadalajara, Guadalajara, Mexico12Department of Physics, University of Wisconsin-Madison, Madison, WI, USA
13Department of Physics, University of Maryland, College Park, MD, USA14Tecnologico de Monterrey, Escuela de Ingenierıa y Ciencias, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., Mexico, 64849
15Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, USA16Department of Physics, Michigan Technological University, Houghton, MI, USA
17Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universitat Erlangen-Nurnberg, Erlangen, Germany18University of Seoul, Seoul, Rep. of Korea
19Universidad Politecnica de Pachuca, Pachuca, Hgo, Mexico20Centro de Investigacion en Computacion, Instituto Politecnico Nacional, Mexico City, Mexico.
21Dept of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA22Universidad Autonoma del Estado de Hidalgo, Pachuca, Mexico
23Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico, Mexico24Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
25Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China
Corresponding author: Sara Coutinno de Leon
Corresponding author: Alberto Carraminana
Corresponding author: Daniel Rosa-Gonzalez
Corresponding author: Anna Lia Longinotti
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2 THE HAWC COLLABORATION
Submitted to ApJ
Abstract
The High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory surveys the very high energy
sky in the 300 GeV to > 100 TeV energy range. HAWC has detected two blazars above 11σ, Markarian
421 (Mrk 421) and Markarian 501 (Mrk 501). The observations are comprised of data taken in the
period between June 2015 and July 2018, resulting in a ∼ 1038 days of exposure. In this work we
report the time-averaged spectral analysis for both sources above 0.5 TeV. Taking into account the
flux attenuation due to the extragalactic background light (EBL), the intrinsic spectrum of Mrk 421 is
described by a power law with an exponential energy cut-off with index α = 2.26± (0.12)stat(+0.17−0.2 )sys
and energy cut-off Ec = 5.1± (1.6)stat(+1.4−2.5)sys TeV, while the intrinsic spectrum of Mrk 501 is better
described by a simple power law with index α = 2.61± (0.11)stat(+0.01−0.07)sys. The maximum energies at
which the Mrk 421 and Mrk 501 signals are detected are 9 and 12 TeV, respectively. This makes these
some of the highest energy detections to date for spectra averaged over years-long timescales. Since the
observation of gamma radiation from blazars provides information about the physical processes that
take place in their relativistic jets, it is important to study the broad-band spectral energy distribution
(SED) of these objects. To this purpose, contemporaneous data from the Large Area Telescope on
board the Fermi satellite and literature data, in the radio to X-ray range, were used to build time-
averaged SEDs that were modeled within a synchrotron self-Compton leptonic scenario to derive the
physical parameters that describe the nature of the respective jets.
Keywords: Active galactic nuclei (16), Gamma-ray sources (633), BL Lacertae objects (158)
1. INTRODUCTION
Blazars are a particular class of radio-loud Active Galactic Nuclei (AGN), characterized by ultra relativistic jets
escaping from a super massive black hole (SMBH) that are oriented very close to the observer’s line of sight (Urry &
Padovani 1995). The spectral energy distribution (SED) of blazars is characterized by two peaks: the first at low to
medium energies (radio to X-ray), and the second at high energies (gamma-ray) (Fossati et al. 1998a). The first peak is
produced by synchrotron emission from ultra-relativistic electrons embedded in a magnetic field within the plasma jet.
The high-energy peak is thought to be produced by inverse Compton (IC) scattering of low-energy photons by the same
electron population that generates the synchrotron emission. This mechanism is known as synchrotron-self-Compton
(SSC) (Jones et al. 1974) and it is the simplest and most commonly used model in a leptonic scenario. The relativistic
jets are a key piece to understanding the nature of black holes and their environment; however, little is known about
their composition, production and how gravitational energy is transported to the dissipation zone, where radiation
is generated. Therefore to constrain the physical parameters of the jet, such as the size of the emission region and
magnetic field, emission models have to be applied to gamma-ray observations. However, the observation of blazars
have been often motivated by flaring activities, and so the very high-energy (VHE; & 0.1 TeV) data tend to be biased
to high-activity periods. Modeling the sources during these states can help to understand the physical processes that
trigger this activity.
On the other hand, the average activity level of blazars has been poorly characterized, and therefore satellites and
extensive air shower (EAS) arrays are the best instrumentation to get averaged spectra in long periods of time, due
to their large duty cycle and wide field of view.
The blazars Mrk 421 (z = 0.031) and Mrk 501 (z = 0.034) were first detected in the VHE range by the Whipple
Observatory, Mrk 421 in 1992 above 0.5 TeV (Punch et al. 1992) and the Mrk 501 in 1996 above 300 GeV (Quinn
et al. 1996). Their gamma-ray flux has been measured extensively with imaging atmospheric Cherenkov telescopes
(IACTs) during different activity periods in the 0.1-10 TeV energy range. Also both sources are continuously detected
by the Large Area Telescope on board NASA’s Fermi Gamma-ray Space Telescope (Fermi -LAT) in the 50 MeV to 1
TeV energy range (Abdollahi et al. 2020). In the literature, the quasi-contemporaneous multi-wavelength spectra have
been measured mainly through observation campaigns.
Mrk 421 has been extensively studied in the VHE range. Between 2004 and 2005 MAGIC performed a total of 25.6
hours of observations during a period where Mrk 421 had low energy flux, identifying an energy cut-off and setting
Mrk 421 & Mrk 501 TeV spectra with HAWC 3
upper limits for energies at and above 4 TeV (Albert et al. 2007a). With the same telescope, in 2006 the average
spectra of Mrk 421 was observed during a high energy flux state for 8 nights (12.7 h in total) where the highest energy
detection was reported at 3.3 TeV (Aleksic et al. 2010). Between 2006 and 2008 observations of the source were
carried out with the VERITAS telescope where different periods of activity were identified, having a total of 35.19
hours of observations, of which 9% correspond to observations made when the source had a high activity state (Acciari
et al. 2011a). The ARGO-YBJ experiment used 676 days of observation to report four different averaged spectra of
Mrk 421 between 2007 and 2010, where simultaneous X-ray data were used to find correlations between the different
states of activity of the source; the highest energy signal was reported at 10 TeV (Bartoli et al. 2011). In 2009, the
MAGIC telescope observed Mrk 421 for 27.7 hours as part of the multi-wavelength campaign organized by the Fermi
collaboration, detecting the source at 4 TeV; emission models were fit to the SED and the results differed from those
obtained in previous works since they were based on observations when the source was in a state of high activity (Abdo
et al. 2011a). Recently, using 4.5 years of data, the ARGO-YBJ experiment reported the averaged spectrum of Mrk
421 for observations performed between 2008 and 2013; the highest energy signal detected was reported at 4.5 TeV
(Bartoli et al. 2016).
Mrk 501 is also a very well studied VHE source. Shortly after its detection at VHE, during a period of intense
high activity in 1997, the HEGRA collaboration reported the averaged spectra from this source for 140- and 85-hour
observations performed with the Cherenkov telescopes CT1 and CT2, respectively; with the highest energy detection
above 10 TeV (Aharonian et al. 1999). In 2005 the MAGIC telescope made observations of Mrk 501 where it reported
variability in its energy flux, identifying three states of activity; the average spectrum during the period of low activity
was obtained with 17.2 hours of observations, the intermediate with 11 hours and the high with 1.52 hours, with
the highest energy detection at approximately 4.5 TeV (Albert et al. 2007b). Between 2005 and 2006, the TACTIC
telescope observed Mrk 501 for a total of 112.5 hours, reporting an average spectrum in the energy range of 400 GeV
to 6 TeV (Godambe et al. 2008). A multi-wavelength campaign to study the low activity state of Mrk 501 was carried
out in 2005 where the MAGIC telescope observed the source for 9.1 hours detecting it at up to 2 TeV; the obtained
SED, using Fermi and Suzaku data in X-rays, was fitted with an SSC model and suggested that the high activity
states could be due to variations in the electron population (Anderhub et al. 2009). A few years later, the Fermi
collaboration organized in 2009 a multi-wavelength campaign to study the Mrk 501 SED, which was built with data
from radio to gamma rays; the MAGIC telescope participated with 16.2 hours of observation and the VERITAS array
telescopes with 9.7 hours, of which 2.4 hours were during a high activity state of the source; a SSC model was fit to the
data showing that relativistic proton shock waves are related to the bulk of the energy dissipation within the source
emission zone (Abdo et al. 2011b).
The average spectrum of Mrk 501 was also reported by the ARGO-YBJ experiment using 1179.6 days of data taken
between 2008 and 2012. This was done for different periods of activity; it was deduced that there was a correlation
between the X-ray and gamma-ray fluxes, as well as a hardening of the spectra when the flux increased, thus favoring
the SSC model to explain the physical processes of this source (Bartoli et al. 2012).
From the works cited above we can summarize a range of physical parameters that describe the jet of each source
such as the emission zone which is assumed to be spherical with a radius R that moves at a relativistic speed v = βc
throughout the jet with a bulk Lorentz factor Γ, so the observed radiation is amplified by a Doppler factor δ =
(Γ(1− β cos θ))−1, where θ is the jet inclination angle. For Mrk 421 the Doppler factor value, which accounts for the
relativistic effects and depends on the speed of the emission zone and pitch angle of the jet, ranges from δ = 15−50, the
magnetic field varies between B = 39− 200 mG, and the size of the emission zone ranges from R = (0.25− 5.2)× 1016
cm. For Mrk 501 the value for the Doppler factor varies between δ = 12−25, the range of the magnetic field goes from
B = 15 − 310 mG, and the size of the emission zone varies from R = (0.1 − 13) × 1016 cm. It should be mentioned
that the values for the highest δ and B and the lowest R values, for both sources, correspond to models fitted to
observations carried out in short periods of time, mainly by IACTs.
Both Mrk 421 and Mrk 501 have been by the High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory
above 300 GeV. Each source is observed in average during 6.2 hours per day within the field of view of the observatory.
HAWC first published the detection of these sources in Abeysekara et al. (2017a) which reported on the monitoring
carried out over a period of 513 days of observation. The spectral analysis did not consider the EBL attenuation and
was performed taking into account only the size of the air shower, which is weakly related to the energy of the primary
gamma rays. In the second HAWC catalog of VHE sources (Abeysekara et al. 2017b), which comprised 507 days of
observations, the detection of both sources was also reported. The energy spectrum of Mrk 421 and Mrk 501 was
4 THE HAWC COLLABORATION
recently reported using a preliminary implementation of the energy estimators developed by the HAWC collaboration,
according to which the spectrum of each source was divided into energy bins for the first time (Coutino de Leon et al.
2019). That analysis comprised a period of 837 days and was carried out by using a different framework than the one
used in this work (see Section 2.1).
In this work we report the observations of Mrk 421 and Mrk 501 during ∼ 1038 days of exposure and the spectral
analysis above 0.5 TeV with HAWC and we include the systematic uncertainties calculation. We built a contempora-
neous SED with Fermi -LAT data with the aim of modelling it with a SSC model in order to improve the constraints
on the physical parameters of the blazars jet.
The paper is organized as follows, in Section 2 the HAWC observatory is described along with the method to measure
the energy flux, in Section 3 the energy spectra of each source is presented, in Section 4 a comparison with previous
results is made, in Section 5 the results are used to build a multi-wavelength SED to test a one-zone leptonic blazar
emission model, and finally a summary and future work are presented in Section 6.
2. THE HAWC GAMMA-RAY OBSERVATORY
HAWC is located at latitude +19N and at an altitude of 4100 meters in Puebla, Mexico. It consists of 300 water
Cherenkov detectors (WCD), of 7.3 m diameter and 4.5 m height covering an area larger than 22,000 m2. Each WCD is
filled with 180,000 liters of water and instrumented with four photo-multiplier tubes (PMTs) that measure the arrival
time and direction of cosmic and gamma-ray primaries mostly above 300 GeV, within its ∼ 2 sr field of view.
Data are divided in 9 analysis bins (fhit) according to the fraction of PMTs that are triggered in each shower event
(Abeysekara et al. 2017c). Recently developed energy estimators are used to divide the these fhit bins into 12 quarter-
decade energy bins covering the 0.316-316 TeV range. In this paper we use the ground parameter method presented
in Abeysekara et al. (2019), which uses the measured charge 40 meters from the air shower axis, along with the zenith
angle of the air shower, to estimate the primary gamma-ray energy. The binning scheme is identical to Abeysekara
et al. (2019). The data used for this analysis go from June 2015 to July 2018.
2.1. Fitting technique
A forward-folding method is performed to fit the spectral shape of the sources using a maximum-likelihood technique,
maximizing the test statistics (TS) so the input parameters have the highest likelihood of providing a good description
of the observed data. Assuming a point source model, the TS is defined as follows:
TS ≡ 2 lnL(H1)
L(H0), (1)
where L is the likelihood function, H0 is the background hypothesis, H1 is the signal plus background hypothesis,
which depends on the spectral parameters assumed to describe the sources. The significance maps (Figure 1) are
obtained as explained in Abeysekara et al. (2017b) at the sources position, maximizing the TS value in each pixel
of a Nsize = 1024 HEALPix grid (Gorski et al. 2005). The likelihood calculation is performed as in Younk et al.
(2016) using the multi-mission maximum likelihood (3ML) framework (Vianello et al. 2015) along with the HAWC
accelerated likelihood (HAL)1 plugin.
Since the sources are of extragalactic origin, the attenuation due to the extragalactic background light (EBL) is
taken into account. The input spectral model is assumed to be the intrinsic one and it is then attenuated using an
EBL model. The resulting spectrum is then convolved with the detector response to be compared with the observed
counts. This way, the output parameters correspond to the intrinsic ones. The EBL model used to perform the fits in
this work is from Gilmore et al. (2012) .
The spectral shapes tested were a simple power law (PL, equation 2) and a power law with an exponential energy
cut-off (PL+CO, equation 3).
dN
dE= N0
(E
E0
)−α
× exp(−τ), (2)
dN
dE= N0
(E
E0
)−α
× exp
(−EEc
)× exp(−τ), (3)
1 https://github.com/threeML/hawc hal
Mrk 421 & Mrk 501 TeV spectra with HAWC 5
Mrk 421 Mrk 501
Figure 1. Significance maps of Mrk 421 (left panel) and Mrk 501 (right panel) for 1038 day of effective exposure correspondingto energies above 0.5 TeV, obtained with HAWC data. The cross indicates the coordinates of the source, for Mrk 421 atRA= 166.11 and DEC= 38.2 (Fey et al. 2004); and for Mrk 501 at RA= 253.47 and DEC= 39.7 (Johnston et al. 1995)equatorial J2000.0.
where N0 is the normalization flux [TeV−1cm−2s−1], E0 is the pivot energy fixed at 1 TeV, α is the spectral index, Ecis the energy cut-off [TeV], and τ is the opacity value given by EBL model, and which is an increasing function of E
and the source redshift, z.
Depending on the TS values in the global fit using all the available energy bins, a preferred spectral shape is chosen.
The flux points are estimated as in Abeysekara et al. (2019), by fitting N0 in each energy bin with α and Ec fixed
using the resulting values from the global fit. If a fit from an individual energy bin has a TS < 4, an upper limit at a
95% confidence interval is set.
2.2. Energy range
To determine the maximum energy at which a source is detected, the spectral model that best describes the source is
multiplied by a step function to simulate an abrupt energy cut-off. This upper energy cut-off is set as an additional free
parameter in the fit so as to provide a lower limit on the maximum detected energy when the log likelihood decreases
by 2σ from the nominal case (without the step function). This method has been previously used in Abeysekara et al.
(2017d).
2.3. Systematic uncertainties
The systematic uncertainties taken into account for this analysis are carried out the same way as in Abeysekara et al.
(2019). The size of the uncertainties depends on the detection significance of each source and spectral models chosen
to describe the sources, since weaker sources naturally will show larger uncertainties and because spectral models
also assign different weights in each energy bin. It is important to mention that even for sources detected at high
significance, the number of free parameters affects the size of systematic uncertainties.
3. HAWC RESULTS
6 THE HAWC COLLABORATION
3.1. Mrk 421
All best fit parameters are quoted with their respective statistical and systematic errors. Above 0.5 TeV, the
intrinsic spectra of Mrk 421 is better described by a PL+CO with N0 = [4.0±(0.3)stat(+0.9−0.2)sys]×10−11 TeV−1cm−2s−1,
α = 2.26±(0.12)stat(+0.17−0.39)sys and Ec = 5.10±(1.60)stat(
+1.4−2.5)sys TeV (Table 1). The intrinsic and observed differential
energy spectra are shown in Figure 2. After integrating equation 3 above 0.5 TeV, the observed integrated photon
flux is Nobs(> 0.5 TeV) = (44.1 ± 5.8) × 10−12 cm−2s−1. The intrinsic energy flux is fE(> 0.5 TeV) = (105 ± 20) ×10−12 erg−1cm−2s−1; and the luminosity per solid angle L(> 0.5 TeV)/∆Ω = fEdL
2 = (1.70±0.30)×1043 ergs−1sr−1,
where dL is the luminosity distance. The maximum energy at which the source is detected is 9 TeV at a 2σ level.
Figure 2. Energy spectrum of Mrk 421. The intrinsic spectrum is represented with the blue dashed line and band (statisticaluncertainty), the observed spectrum is represented with a black line and grey band (statistical uncertainty) along with theobserved flux points. For both spectra the pink band correspond to the systematic uncertainties that are calculated as inAbeysekara et al. (2019).
3.2. Mrk 501
For Mrk 501, the PL and PL+CO spectral models result in a very similar TS value; however the fitted energy cut-off
is larger than 700 TeV, so within the HAWC energy range the intrinsic spectrum can be modeled with a single PL
with N0 = [6.6 ± (0.9)stat(+0.9−0.6)sys] × 10−12 TeV−1cm−2s−1 and α = 2.61 ± (0.11)stat(
+0.01−0.07)sys. Mrk 501 is detected
up to 12 TeV at a 2σ level (Table 1). Integrating equation 2 above 0.5 TeV, the observed integrated photon flux
is Nobs(> 0.5 TeV) = (9.14 ± 1.25) × 10−12 cm−2s−1. The intrinsic energy flux is fE(> 0.5 TeV) = (25.4 ± 4.2) ×10−12 erg−1cm−2s−1; and the luminosity per solid angle L(> 0.5 TeV)/∆Ω = (4.96 ± 0.80) × 1043 ergs−1sr−1. The
intrinsic and observed spectrum is shown in Figure 3.
4. COMPARISON WITH PREVIOUS RESULTS
Mrk 421 & Mrk 501 TeV spectra with HAWC 7
Figure 3. Energy spectrum of Mrk 501. The intrinsic spectrum is represented with the blue dashed line and band (statisticaluncertainty), the observed spectrum is represented with a black line and grey band (statistical uncertainty) along with theobserved flux points, and the pink bands correspond to the systematic uncertainties that are calculated as in Abeysekara et al.(2019).
Table 1. Best fit spectral parameters for Mrk 421 and Mrk 501 following the method described in section 2.1. The photonEmax value corresponds to the maximum energy at which the signal is detected at a 2σ level.
Mrk 421 Mrk 501√TS 48 12
N0 [TeV−1cm−2s−1] [4.0± (0.3)stat(+0.9−0.2)sys]× 10−11 [6.6± (0.9)stat(
+0.9−0.6)sys]× 10−12
α 2.26± (0.12)stat(+0.17−0.39)sys 2.61± (0.11)stat(
+0.01−0.07)sys
Ec [TeV] 5.1± (1.6)stat(+1.4−2.5)sys ∞
Emax [TeV] 9 12
4.1. Mrk 421
The intrinsic spectrum of Mrk 421 is in good agreement within the statistical and systematic errors with the spectra
previously reported by HAWC (Coutino de Leon et al. 2019), and with the averaged spectra reported in Albert et al.
(2007a) and Bartoli et al. (2011). As mentioned before, most of the IACT observations are biased to high-state
activity of the source, showing not only a higher flux but a harder spectrum, following a “brighter-harder” relation.
This can be seen in Figure 4 (left panel) where the spectral index is plotted against the normalization flux for different
observations. The fitted values in this work for Mrk 421 lie between the values from time-averaged observations or low
activity states. The observed spectra of Mrk 421 reported in the literature that best coincide with our flux points are
those reported by VERITAS for a very low activity state (Acciari et al. 2011a), the spectrum measured by MAGIC
8 THE HAWC COLLABORATION
Index vs. Normalization flux Energy cut-off vs. Normalization flux
Figure 4. Mrk 421. Spectral index vs. normalization flux (left panel) and energy cut-off vs normalization flux (right panel)for reported values in the literature. The black circle correspond to the results in this work, the blue downward triangles areresults reported for low activity states or time-averaged spectra from IACTs and EAS, and the grey squares are the reportedvalues from observations when the source presented a high activity state.
during the Fermi multi-wavelength campaign which was fitted to a single log-parabola (Abdo et al. 2011a), and the
average spectrum reported by the ARGO-YBJ experiment (Bartoli et al. 2016) fitted with a single PL.
The energy of the last flux point in the HAWC spectrum for Mrk 421 is at 8.8 TeV. This value is one of the
highest energy detections for a long-term time-averaged spectrum reported to date. The high-energy (HE) part of the
spectrum, in the MeV-GeV regime, can be obtained with the Fermi -LAT data. Using Fermipy (Wood et al. 2017) we
obtained the contemporary Fermi spectrum of Mrk 421 to complete the IC peak of the SED. The highest energy bin
from Fermi -LAT is at 430 GeV, while the median energy of the lowest-energy bin from HAWC spectrum is at 830 GeV
leaving an energy gap of 400 GeV between both data sets. The Figure 5 shows the flux points for Mrk 421 reported
in this work with the contemporaneous data from Fermi -LAT data (black circles and squares). This plot also shows
the reported observed spectra from different IACTs and EAS.
4.2. Mrk 501
For Mrk 501 the intrinsic spectrum is in agreement with previous results obtained by HAWC (Coutino de Leon et al.
2019); it is also in agreement with the intrinsic spectrum of the ARGO-YBJ experiment for a 1179.6-day observation
period where α = 2.59 ± 0.27 (Bartoli et al. 2012). The trend of having a harder spectrum when the source is in a
high activity state is not as noticeable as with Mrk 421, as shown in Figure 6 where the spectral index is plotted vs.
the normalization flux from reported spectra in the literature for different activity states.
The energy of the last flux point bin is at 10.90 TeV, which is also one of the highest energy detections for time-
averaged spectra to date. As with Mrk 421, the contemporaneous spectrum of Mrk 501 was obtained with Fermi -LAT.
The highest energy flux point from Fermi data is at 430 GeV and the median energy from the lowest energy bin from
HAWC is 750 GeV, having an energy gap between the two data sets of 320 GeV. The obtained flux points with HAWC
data compared to previous observations made with IACTs and ARGO-YBJ, along with the HE part, is shown in
Figure 7, where the HAWC flux points at higher energies are below previous observations by a factor of ∼ 6− 7. This
difference can be explained in terms of the Mrk 501 activity state during those observations, such as those reported in
Abdo et al. (2011b) where a high energy state was detected.
5. SPECTRAL ENERGY DISTRIBUTION MODELING
Mrk 421 and Mrk 501 are blazars classified as high-synchrotron–peaked (HBL) BL Lacs (Padovani & Giommi 1995;
Fossati et al. 1998b). These types of objects are characterized by emitting most of their power in the UV and X-ray
range. HBL blazars are also characterized by having a low luminosity, so it is thought that the only seed photons that
Mrk 421 & Mrk 501 TeV spectra with HAWC 9
Figure 5. HE and VHE spectrum of Mrk 421. The HE part is constituted of data from Fermi-LAT, and the VHE part ismade up of data from IACTs (Albert et al. 2007a; Acciari et al. 2011a), ARGO-YBJ (Bartoli et al. 2011) and HAWC. Blacksquares and circles correspond to the contemporary data from Fermi and HAWC, the green right triangle and crosses are thesemi-simultaneous data from Fermi and MAGIC for the 2009 observation campaign (Abdo et al. 2011a), and the yellow lefttriangles and x symbols are the contemporaneous data from Fermi-LAT and ARGO-YBJ for a 4.5 year period between 2008and 2012 (Bartoli et al. 2016).
are scattered at very high energies are synchrotron photons, that is, there is no contribution from external photons
from the torus or the accretion disk (Madejski & Sikora 2016). For this reason the SSC is the chosen scenario for this
work.
Assuming that the same physical process occurs in both sources, the simplest model is a SSC mechanism. The
electron population within the emission zone has a total energy given by
We =
∫ Emax
Emin
EedNedEe
dEe, (4)
where Emin and Emax are the minimum and maximum electron energies respectively, and dNe/dEe is the particle
distribution embedded in a magnetic field B. The electron population is accelerated to relativistic velocities by the
magnetic field producing synchrotron radiation, which is then used as a seed photon field for the inverse Compton
(IC) scattering.
The total radiative energy output of the jet Ljet = Le + Lp + LB is the sum of the radiative output carried by
electrons, protons (under the assumption of one cold proton per emitting relativistic electron) and the magnetic field
which are defined as
Li ' πR2c Γ2Ui, i = e, p,B (5)
with Ue = 3We/4πR3, Up = mpNp, and UB = B2/8π are the energy densities; being mp the proton mass (Celotti &
Ghisellini 2008).
10 THE HAWC COLLABORATION
Figure 6. Mrk 501. Spectral index vs. normalization flux for reported values in the literature. The black circle correspondto the results in this work, the blue downward triangles are results reported for low activity states or time-averaged spectrafrom IACTs and EAS, and the grey squares are the reported values from observations when the source presented a high activitystate.
To build the synchrotron SED peak in the radio to X-ray range of Mrk 421 and Mrk 501, we use the data collected
in Abdo et al. (2011a) and Abdo et al. (2011b), respectively, as these are one of the most complete average SED data
sets to date. For both sources the IC peak is built with the contemporaneous data from Fermi -LAT and HAWC. We
use Naima, a python package developed by Zabalza (2015) that calculates the non-thermal radiation from a population
of charged particles. It performs a fit to the data using the Markov Chain Monte Carlo (MCMC) technique to sample
the likelihood distribution of each parameter. Naima also provides the Bayesian information criterion (BIC) in each
fit, so the smallest BIC value among different fits is chosen in order to define the model that best describes the data.
Since Naima performs the fits in the rest frame of the sources, the data have to be corrected by relativistic effects.
Therefore, to find the Doppler factor that best represents the observed SED, we defined a set of δ values in the range
of 10 to 40 and performed the fits assuming different electron energy distributions; then the Doppler factor that results
in a better fit is chosen. The tested electron energy distributions were a broken power law (BKPL) and a power law
with an exponential energy cut-off (PL+CO), where the spectral parameters, Emin and Emax were left free to vary.
For the synchrotron and IC flux calculation we also left the magnetic field B and the radius of the emission zone R
as free parameters. The IC flux is attenuated using the EBL model from Gilmore et al. (2012) to properly reproduce
the obtained flux points with HAWC.
5.1. SED modeling results.
The SED of Mrk 421 and the best SSC model (black line) are shown in Figure 8. The best fit Doppler factor value is
δ = 20 for an electron energy distribution that follows a PL+CO with spectral index of α = 2.24± 0.01 and an energy
cut-off of Ec = 167 ± 4 GeV. The minimum and maximum electron energies are fitted to Emin = 529 ± 15 MeV and
Emax = 11.1+0.7−1.0 TeV. According to the IC scattering process, the energy of the VHE photons must not exceed that
Mrk 421 & Mrk 501 TeV spectra with HAWC 11
Figure 7. HE and VHE spectrum of Mrk 501. The HE part is obtained using data from Fermi-LAT , and the VHE partfrom IACTs data (Godambe et al. 2008; Acciari et al. 2011b), ARGO-YBJ (Bartoli et al. 2012) and HAWC. Black squares andcircles are the contemporary data from Fermi-LAT and HAWC, and the green right triangles and crosses are the HE and VHEspectrum reported in Abdo et al. (2011b) for the 2009 multi-wavelength campaign.
of the electrons, so accounting for the Doppler boosting, the Emax value agrees with our observations. The magnetic
field results in a value of B = 35± 5 mG and the best fit of the size of the emission region is R = (4.37± 0.09)× 1016
cm.
Table 2. Fitted parameters in the SSC leptonic model for Mrk 421.
Parameter Symbol Mrk 421
Doppler factor δ 20
Magnetic field B [mG] 35± 5
Radius R × 1016 [cm] 4.37± 0.09
Total electron energy We × 1048 [erg] 3.0± 0.2
Spectral index α 2.24± 0.01
Energy cut-off Ec [GeV] 167± 4
Minimum electron energy Emin [MeV] 529± 15
Maximum electron energy Emax [TeV] 11.1+0.7−1.0
Jet power in electrons Le × 1044 [erg s−1] 4.5
Jet power in protons Lp × 1044 [erg s−1] 6.07
Jet power in magnetic field LB × 1042 [erg s−1] 3.5
12 THE HAWC COLLABORATION
Figure 8. SED of Mrk 421. The yellow triangles correspond to observations performed by the ARGO-YBJ experiment (Bartoliet al. 2016), the green squares are from the multi-wavelength observation campaign in 2009 (Abdo et al. 2011a), and the redpoints are the HAWC data and contemporaneous Fermi-LAT data. The green squares (from the first peak) and red points wereused to perform the fit using a SSC model, being the black line the model that better describes the data. The fitted modelparameters are shown in Table 2.
Table 3. Comparison between previous SSC parameters, δ, B and R, and results in this work for Mrk 421.
δ B R Flux state Reference
[mG] ×1016 [cm]
15 200 1.1 Low Albert et al. (2007a)
15 150 5 High Bartoli et al. (2011)
16 80 5 Low
40 200 0.25 Low-Mid-High Acciari et al. (2011a)
21 38 5.2 Long-term averaged Abdo et al. (2011a)
38+6−4 48± 0.012 1 Long-term averaged Bartoli et al. (2016)
20 35± 5 4.37± 0.09 Long-term averaged This work
For Mrk 501 the SED is better described with Doppler factor value of δ = 10. The electron energy distribution
that results in a better fit is a PL+CO, described with an electron spectral index α = 2.39 ± 0.03 and an energy
cut-off of Ec = 500 ± 40 GeV. The minimum and maximum electron energy are fitted to Emin = 103 ± 13 MeV and
Emax = 60+50−30 TeV. The magnetic field is fitted to a value of B = 25± 3 mG, and the radius of the emission zone is
fitted to R = (1.02± 0.14)× 1017 cm. This model is shown in Figure 9 (black line).
Mrk 421 & Mrk 501 TeV spectra with HAWC 13
In Tables 3 and 5 we provide a comparison between our results and previous analysis using a SSC model for Mrk 421
and Mrk 501, respectively. As can be seen, the most notable difference lies in the value of the magnetic field, which is
up to an order of magnitude larger than our results for analyses that were carried out using VHE data averaged over
short state changes. The difference between our results and those obtained by these analyzes, that include VHE data
averaged over long periods of time, is minimal and in good agreement.
Figure 9. SED of Mrk 501. The yellow triangles correspond to observations performed by the ARGO-YBJ experiment (Bartoliet al. 2012), the green squares are from the multi-wavelength observation campaign in 2009 (Abdo et al. 2011b), and the redpoints are the HAWC data and contemporaneous Fermi-LAT data. The green squares (from the first peak) and red points wereused to perform the fit using a SSC model, being the black line the model that better describes the data. The fitted modelparameters are shown in Table 4.
5.2. Derived jet physical quantities
To constrain the location where most of the energy dissipation takes place in the jet, via electron acceleration,
physical quantities can be derived from the fitted parameters (Tables 2 and 4). Assuming the black hole mass of Mrk
421 and Mrk 501 as M421 = 1.9 × 108 M and M501 = 1.6 × 109 M (Barth et al. 2003), the gravitational radius
Rg, defined as Rg = GM/c2, is 2.8× 1013 cm and 2.4× 1014 cm for Mrk 421 and Mrk 501, respectively, therefore the
emission zone of Mrk 421 is ∼ 1.5× 103Rg and the one of Mrk 501 is ∼ 4× 102Rg. The energy dissipation of the jet
that is converted into radiation occurs at a significant large distance from the black hole, Mrk 421 at d ∼ 3 × 104Rgand Mrk 501 at d ∼ 103Rg, assuming a canonical jet and that the emission is originated from a large fraction of the
cross-section of the jet, so d ∼ R/θ and θ ∼ 1/δ (Abdo et al. 2011a).
The jet power in electrons for both sources is comparable to that of protons, Le ∼ Lp, and both are larger than the
jet power carried by the magnetic field, Le > LB , thus the Poynting flux does not contribute significantly to the total
radiation of the jet. The total radiative energy output of Mrk 421 jet is then Ljet−421 = 6.2 × 1044 erg s−1 which
14 THE HAWC COLLABORATION
Table 4. Fitted parameters in the SSC leptonic model for Mrk 501.
Parameter Symbol Mrk 501
Doppler factor δ 10
Magnetic field B [mG] 25± 3
Radius R × 1016 [cm] 10.2± 1.4
Total electron energy We × 1048 [erg] 12± 3
Spectral index α 2.39± 0.03
Energy cut-off Ec [GeV] 500± 40
Minimum electron energy Emin [MeV] 103± 13
Maximum electron energy Emax [TeV] 60+50−30
Jet power in electrons Le × 1044 [erg s−1] 27
Jet power in protons Lp × 1044 [erg s−1] 28.9
Jet power in magnetic field LB × 1042 [erg s−1] 2.43
Table 5. Comparison between previous SSC parameters, δ, B and R, and results in this work for Mrk 501.
δ B R Flux state Reference
[mG] ×1016 [cm]
25 310 0.1 Low Albert et al. (2007b)
20 313 0.103 Low Anderhub et al. (2009)
12 15 13 Long-term averaged Abdo et al. (2011b)
12 70 3 Long-term averaged Bartoli et al. (2012)
10 100 3 High
10 25± 3 10.2± 1.4 Long-term averaged This work
corresponds to ∼ 4% of the Eddington luminosity and for Mrk 501, Ljet = 5.6 × 1045 erg s−1, which represents the
∼ 3% of its Eddington luminosity.
6. SUMMARY AND OUTLOOK
We report the detection of Mrk 421 and Mrk 501, above 0.5 TeV with the High Altitude Water Cherenkov (HAWC)
Gamma-Ray Observatory using 1038 days of exposure comprising the period between June 2015 and July 2018.
1. For Mrk 421, the VHE intrinsic spectrum is well described by a power law with an exponential energy cut-off.
For Mrk 501 the intrinsic VHE spectrum is described by a single power law.
2. These results are in good agreement with those previously obtained with HAWC on both sources once the EBL
attenuation is taken into account. Additionally, the reported values for the intrinsic spectra in this work are
compatible with those in previous averaged spectra reported by IACTs and EAS experiments, setting this way
a baseline energy spectrum of each source. It is also important to mention that the obtained flux points in this
work are in good agreement with the observed spectra reported in the literature for Mrk 421; however, for Mrk
501 the HAWC flux points lay below the observed spectra reported in the literature, this could be related to the
activity state of the source when it was observed in the past.
3. Compared to previously published results using HAWC data, this is the first time that we estimate the highest
energy of the detected signal, with 9 TeV for Mrk 421 and 12 TeV for Mrk 501 at a 2σ confidence level, which
for both sources, is one of the highest energy detections reported to date, for spectra averaged over long periods
of time. This contributes to the restriction of the energy detection limits of both sources.
4. Using contemporaneous data from Fermi -LAT and previous published data in the radio to X-ray energy range,
a SED was built to model it with a one-zone SSC scenario.
Mrk 421 & Mrk 501 TeV spectra with HAWC 15
5. The estimated physical parameters from the jet are in general agreement with values found in the literature for
long-term observations, confirming that both sources are intrinsically different assuming that the same physical
processes take place.
To characterize the spectrum at VHE of Mrk 421 and Mrk 501 in greater detail, it is important to identify the
periods of variability of both sources and thus carry out the spectral analysis in each of them, this way the physical
processes that give rise to these energy flux variations can be constrained. To achieve this, a time resolved analysis of
the data set used in this work is necessary and will be addressed in future publications.
ACKNOWLEDGMENT
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 Tecnologıa (CONACyT), Mexico, grants 271051, 232656, 260378, 179588,
254964, 258865, 243290, 132197, A1-S-46288, A1-S-22784, catedras 873, 1563, 341, 323, Red HAWC, Mexico; DGAPA-
UNAM grants IG101320, IN111315, IN111716-3, IN111419, IA102019, IN112218; VIEP-BUAP; PIFI 2012, 2013, PRO-
FOCIE 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;
Coordinacion de la Investigacion Cientıfica de la Universidad Michoacana; Royal Society - Newton Advanced Fellow-
ship 180385; Generalitat Valenciana, grant CIDEGENT/2018/034; Chulalongkorn University’s CUniverse (CUAASC)
grant. Thanks to Scott Delay, Luciano Dıaz and Eduardo Murrieta for technical support.
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