Probing the Sea of Cosmic Rays by Measuring Gamma-Ray Emission from Passive Giant Molecular Clouds with HAWC
A. Albert, R. Alfaro, C. Alvarez, J.R. Angeles Camacho, J.C. Arteaga-Velázquez, K.P. Arunbabu, D. Avila Rojas, H.A. Ayala Solares, V. Baghmanyan, E. Belmont-Moreno, S.Y. BenZvi, C. Brisbois, K.S. Caballero-Mora, T. Capistrán, A. Carramiñana, S. Casanova, U. Cotti, J. Cotzomi, S. Coutiño de León, E. De la Fuente, R. Diaz Hernandez, B.L. Dingus, M.A. DuVernois, M. Durocher, J.C. Díaz-Vélez, R.W. Ellsworth, K. Engel, C. Espinoza, K.L. Fan, M. Fernández Alonso, N. Fraija, A. Galván-Gámez, D. Garcia, J.A. García-González F. Garfias M.M. González, J.A. Goodman, J.P. Harding, S. Hernandez, B. Hona, D. Huang, F. Hueyotl-Zahuantitla, P. Hüntemeyer, A. Iriarte, V. Joshi, D. Kieda, A. Lara, W.H. Lee, J. Lee, H. León Vargas, J.T. Linnemann, A.L. Longinotti, G. Luis-Raya, J. Lundeen, K. Malone, O. Martinez, J. Martínez-Castro, J.A. Matthews, P. Miranda-Romagnoli, J.A. Morales-Soto, E. Moreno, M. Mostafá, A. Nayerhoda, L. Nellen, M. Newbold, M.U. Nisa, R. Noriega-Papaqui, N. Omodei, A. Peisker, Y. Pérez Araujo, E.G. Pérez-Pérez, C.D. Rho, D. Rosa-González, E. Ruiz-Velasco, F. Salesa Greus, A. Sandoval, M. Schneider, J. Serna-Franco, A.J. Smith, R.W. Springer, P. Surajbali, M. Tanner, K. Tollefson, I. Torres, R. Torres-Escobedo, R. Turner, F. Ureña-Mena, L. Villaseñor, T. Weisgarber, E. Willox, H. Zhou, C. de León
DDraft version January 22, 2021
Typeset using L A TEX preprint2 style in AASTeX61
PROBING THE SEA OF COSMIC RAYS BY MEASURING GAMMA-RAY EMISSION FROMPASSIVE GIANT MOLECULAR CLOUDS
A. Albert, R. Alfaro, C. Alvarez, J.R. Angeles Camacho, J.C. Arteaga-Vel´azquez, K.P. Arunbabu, D. Avila Rojas, H.A. Ayala Solares, V. Baghmanyan, E. Belmont-Moreno, S.Y. BenZvi, C. Brisbois, K.S. Caballero-Mora, T. Capistr´an, A. Carrami˜nana, S. Casanova, U. Cotti, J. Cotzomi, S. Couti˜no de Le´on, E. De la Fuente, R. Diaz Hernandez, B.L. Dingus, M.A. DuVernois, M. Durocher, J.C. D´ıaz-V´elez, R.W. Ellsworth, K. Engel, C. Espinoza, K.L. Fan, M. Fern´andez Alonso, N. Fraija, A. Galv´an-G´amez, D. Garcia, J.A. Garc´ıa-Gonz´alez, F. Garfias, M.M. Gonz´alez, J.A. Goodman, J.P. Harding, S. Hernandez, B. Hona, D. Huang, F. Hueyotl-Zahuantitla, P. H¨untemeyer, A. Iriarte, V. Joshi, D. Kieda, A. Lara, W.H. Lee, J. Lee, H. Le´on Vargas, J.T. Linnemann, A.L. Longinotti, G. Luis-Raya, J. Lundeen, K. Malone, O. Martinez, J. Mart´ınez-Castro, J.A. Matthews, P. Miranda-Romagnoli, J.A. Morales-Soto, E. Moreno, M. Mostaf´a, A. Nayerhoda, L. Nellen, M. Newbold, M.U. Nisa, R. Noriega-Papaqui, N. Omodei, A. Peisker, Y. P´erez Araujo, E.G. P´erez-P´erez, C.D. Rho, D. Rosa-Gonz´alez, E. Ruiz-Velasco, F. Salesa Greus,
12, 30
A. Sandoval, M. Schneider, J. Serna-Franco, A.J. Smith, R.W. Springer, P. Surajbali, M. Tanner, K. Tollefson, I. Torres, R. Torres-Escobedo, R. Turner, F. Ure˜na-Mena, L. Villase˜nor, T. Weisgarber, E. Willox, H. Zhou, and C. de Le´on HAWC Collaboration Physics Division, Los Alamos National Laboratory, Los Alamos, NM, USA Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico, Ciudad de M´exico, M´exico Universidad Aut´onoma de Chiapas, Tuxtla Guti´errez, Chiapas, M´exico Universidad Michoacana de San Nicol´as de Hidalgo, Morelia, M´exico Instituto de Geof´ısica, Universidad Nacional Aut´onoma de M´exico, Ciudad de M´exico, M´exico Department of Physics, Pennsylvania State University, University Park, PA, USA Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 IFJ-PAN, Krakow, Poland Department of Physics & Astronomy, University of Rochester, Rochester, NY , USA Dept. of Physics, University of Maryland, College Park, MD 20742, USA Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, Ciudad de M´exico, M´exico Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica, Puebla, M´exico Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 IFJ-PAN, Krakow, Poland Facultad de Ciencias F´ısico Matem´aticas, Benem´erita Universidad Aut´onoma de Puebla, Puebla, M´exico Departamento de F´ısica, Centro Universitario de Ciencias Exactas e Ingenierias, Universidad de Guadalajara,Guadalajara, M´exico Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
Corresponding author: H.A. Ayala [email protected] a r X i v : . [ a s t r o - ph . H E ] J a n HAWC Collaboration Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, Ciudad de M´exico, M´exico Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, USA Department of Physics, Michigan Technological University, Houghton, MI, USA Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg, D-91058 Erlangen,Germany Natural Science Research Institute, University of Seoul, Seoul, Republic of Korea Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Universidad Politecnica de Pachuca, Pachuca, Hgo, M´exico Facultad de Ciencias F´ısico Matem´aticas, Benem´erita Universidad Aut´onoma de Puebla, Puebla, M´exico Centro de Investigaci´on en Computaci´on, Instituto Polit´ecnico Nacional, Mexico City, Mexico. Dept of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA Universidad Aut´onoma del Estado de Hidalgo, Pachuca, M´exico Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, Ciudad de M´exico, M´exico Department of Physics, Stanford University: Stanford, CA 94305–4060, USA Max-Planck Institute for Nuclear Physics, 69117 Heidelberg, Germany Instituto de F´ısica Corpuscular, CSIC, Universitat de Val`encia, E-46980, Paterna, Valencia, Spain Facultad de Ciencias F´ısico Matem´aticas, Benem´erita Universidad Aut´onoma de Puebla, Puebla, M´exico Department of Chemistry and Physics, California University of Pennsylvania, California, Pennsylvania, USA Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
ABSTRACTThe study of high-energy gamma rays from passive Giant Molecular Clouds (GMCs) in our Galaxyis an indirect way to characterize and probe the paradigm of the “sea” of cosmic rays in distant partsof the Galaxy. By using data from the High Altitude Water Cherenkov (HAWC) observatory, wemeasure the gamma-ray flux above 1 TeV of a set of these clouds to test the paradigm.We selected high-galactic latitude clouds that are in HAWC’s field-of-view and which are within1 kpc distance from the Sun. We find no significant excess emission in the cloud regions, nor when weperform a stacked log-likelihood analysis of GMCs that are considered part of the Gould Belt. Usinga Bayesian approach, we calculate 95% credible intervals upper limits together with the sensitivity ofHAWC. These are the first limits to constrain gamma-ray emission in the multi-TeV energy range ( > Keywords:
Astroparticle physics — gamma rays: diffuse background — cosmic rays —Gamma-Ray Astronomy eV gamma rays from passive Giant Molecular Clouds INTRODUCTIONDirect observations of cosmic rays measurethe spectrum surrounding the vicinity of thesolar system (Aguilar et al. 2015). It is gen-erally assumed that this spectrum is represen-tative of the cosmic-ray flux across the Galaxyand it is usually referred as the “sea” of cosmicrays. This assumption comes from the fact thatcosmic rays diffuse through the Galaxy due tothe deflecting effect of the interstellar magneticfield to alter the path of charged particles. Ifthis process occurs on a timescale of millions ofyears, their distribution becomes homogeneousand isotropic (Strong et al. 2007).A way to probe the paradigm of the “sea”of cosmic rays is by using gamma-ray data.Since the beginning of high-energy gamma-rayastrophysics, it was recognized that the ob-servation of gamma rays gives us the oppor-tunity to measure the propagation and distri-bution of cosmic rays in distant parts of theGalaxy, since these can interact with the in-terstellar matter and radiation fields generatinggamma-ray emission (Issa & Wolfendale 1981;Aharonian 2001; Casanova et al. 2010). A sim-ple idea, suggested by Casanova et al. (2010),is to look for regions that act as targets forcosmic rays: clouds that are part of the in-terstellar medium. We focus on passive giantmolecular clouds (GMCs), i.e. clouds with nocosmic-ray accelerators inside of them (Issa &Wolfendale 1981). These clouds are large reser-voirs of gas (mainly molecular hydrogen) anddust. Masses of these complexes are of the or-der of ∼ M (cid:12) . Their average density is ahundred to a thousand times greater than theaverage density in the solar vicinity which isof the order of one to ten particles per cubiccentimetre (Ferri`ere 2001). It is assumed that,due to the lack of cosmic-ray sources inside theGMCs, the main gamma-ray production mech-anism in these sources is the decay of neutralpions, which are produced by the collision of high-energy cosmic rays with interstellar mat-ter in the clouds.The flux of gamma rays is proportional to theflux of cosmic rays Φ CR , as well as the totalmass M of the GMC, and inversely proportionalto the distance square d of the GMC (see forexample Casanova et al. 2010): F γ ∝ Md Φ CR . (1)It is then important to know the masses anddistances of the GMCs. Equation 1 has beenused in other analyses using data from the Fermi -LAT telescope. For example, in Yanget al. (2014), gamma-ray spectra above 300MeV were used to extract the cosmic-ray spec-tra from eight massive clouds. They showedthat the derived spectral indices and absolutefluxes of cosmic-ray protons in the energy in-terval 10 - 100 GeV agree with the direct mea-surements of local cosmic rays by the PAMELAexperiment(Adriani et al. 2011).A similar study was published by Aharonianet al. (2020). With their observations, theyfound that the flux of cosmic rays at distancesfrom 0.6 kpc to 12.5 kpc also agrees with the lo-cally measured cosmic-ray flux measured by theAlpha Magnetic Spectrometer (AMS) (Aguilaret al. 2015).The
Fermi -LAT collaboration presented theirown studies to understand the cosmic-ray prop-agation through gamma-ray data of the Orionmolecular cloud (Ackermann et al. 2012a), andof the molecular clouds Chamaleon, R Coro-nae Australis, Cepheus and Polaris (Ackermannet al. 2012b). In both publications the authorscalculated gamma-ray emissivities and molecu-lar mass conversion factors for X CO .Other studies using Fermi -LAT data includethe work by Neronov et al. (2012) and Neronovet al. (2017), where they look at high-galacticlatitude clouds that are part of the Gould Belt.They calculate the average cosmic-ray spectrumin the Galaxy. A recent publication by Bagh-
HAWC Collaboration manyan et al. (2020), also used
Fermi -LATdata to find discrepancies between the measuredcosmic-ray flux at Earth and the cosmic-ray fluxin distant regions of the Galaxy. They reportthat in three GMCs (Aquila Rift, Ophiuchi andCepheus) they observe higher gamma-ray emis-sion with respect to the expected emission fromthe “sea of cosmic rays”. Most of this publica-tions have presented results of gamma rays upto 300 GeV.The present work is the first attempt to mea-sure the “sea of cosmic rays” using high-energygamma rays above 1 TeV. In this paper wepresent measurements of gamma rays that havemedian energies of the order of ∼ THE GIANT MOLECULAR CLOUDSFollowing a similar procedure as the one pre-sented in Yang et al. (2014), we selected sevenmassive clouds identified by the CO Galacticsurvey of Dame et al. (1987) with the CfA 1.2 mmillimetre-wave Telescope. The selected cloudsare Taurus, Orion, Perseus, Ophiuchi, Mono-ceros, Aquila Rift, and Hercules. Their proper-ties are listed in Table 1. All of them are locatedless than 1 kpc away from the solar system. Onepart of the analysis focuses on each cloud indi-vidually.The first four clouds that appear in Table 1(Taurus, Orion, Perseus and Ophiuchi) are con-sidered as part of the Gould Belt according toDzib et al. (2018). The Gould Belt is a region inthe Galaxy composed of gas and young stars. Inthe sky it appears as a ring with an inclinationangle of ∼ o with respect to the galactic plane, although according to Guillout et al. (1998), itcan be considered a disk-like structure. Theclouds Aquila and Hercules do not line up withthis structure and the Monoceros cloud is toofar to be considered part of the belt. However,a recent study by Alves et al. (2020), has putinto question the Gould Belt structure and sub-stitutes it by the so called Radcliff Wave. In thiscase, the first three clouds in Table 1 are part ofthe Radcliff Wave, while the fourth cloud is partof the Local Arm. Assuming that these cloudshave similar properties we combine the gamma-ray emission of the clouds that belong to theGould Belt and the Radcliff Wave in a stackedanalysis to increase the sensitivity of the probe . OBSERVATIONS AND DATA ANALYSIS3.1.
The HAWC Data
The HAWC Observatory is a gamma-ray de-tector built in Sierra Negra in the mexican stateof Puebla at an altitude of 4100 m above sealevel. It is a wide field-of-view array of 300 waterCherenkov detectors (WCDs), with four photo-multiplier tubes (PMTs) facing upwards in eachWCD. The WCDs are cylindrical water tanks4.5 m high and 7.3 m wide. The PMTs detectthe Cherenkov light in the water from the pas-sage of secondary particles, which are producedby gamma rays and cosmic rays interacting withthe atmosphere. HAWC triggers with a rate of25 kHz and has a duty cycle of > A study of a Gould-belt-like structure in M83 makescomparisons including Monoceros as part of the MilkyWay’s Gould Belt (Comer´on 2001). For the present pa-per, we will still consider Monoceros separately from theGould Belt for the present paper. As it will be seen in §
4, the results of the stackedclouds are similar due to the fact that Ophiuchi is athigh zenith values for HAWC and hence HAWC has lesssensitivity in this region. eV gamma rays from passive Giant Molecular Clouds Table 1.
Properties of the GMCs. Masses obtained from Dame et al. (1987) ∗ , Yang et al.(2014) ∗∗ and calculated using the Planck survey † (See appendix A for mass calculations).Distances obtained from Dame et al. (1987) and Schlafly (2014) . The sky positions cor-respond to the center of the regions of interest that are analyzed. The first four molecularclouds are part of the Gould Belt.GMC Mass/Planck [10 M (cid:12) ] Distance [pc] l[ ◦ ] b[ ◦ ] Dec. [ ◦ ] RA [ ◦ ]Taurus 0.3 ∗ /0.23 † ±
30 171.6 -15.8 26.2 66.5Orion 3.3 ∗ /3.0 † ±
50 -151.0 -15.5 -3.6 87.3Perseus 0.41 ∗∗ /0.38 † ±
32 159.0 -20.5 30.9 52.9Ophiuchi 0.12 ∗∗ /0.12 † ±
18 -5.7 16.8 -23.5 247.5Monoceros 1.2 ∗ /1.4 † ±
83 -145.8 -12.4 -6.8 92.3Aquila Rift 1.5 ∗ /1.50 † ±
55 22.5 11.8 -3.72 267.6Hercules 0.08 † ±
30 46.0 9.0 15.7 280.6
For the analysis presented here, we use adataset that started on 11/2014 and ended on06/2019. The total integration time of the datais 1523 days. As it was done in previous analy-ses, we apply gamma-hadron cuts to our datasetand divide the data in 9 bins. These bins are de-fined by the ratio of the number of PMTs thatwere triggered by the air-shower event to thetotal number of active PMTs in the array. Wewill refer to them as fractional bins f hit . Thisis a proxy to an energy variable, where a lower f hit bin corresponds to a lower energy gamma-ray. The definition of the gamma-hadron cutsand the bins can be found in Abeysekara et al.(2017b). 3.2. Analysis Method
The analysis is performed using the Multi-Mission Maximum Likelihood (3ML) Vianelloet al. (2015) framework together with theHAWC Accelerated Likelihood (HAL) frame-work . We perform both individual cloud and astacked analyses, and assume the same spectral https://github.com/threeML/hawc_hal model for each cloud as a function of energywith the form F γ ( E ) = A C (cid:18) EE (cid:19) − α , (2)where α is the spectral index, E is the pivotenergy, and C is the normalization factor. Thefactor A , defined as M /d ( M = M/ M (cid:12) ; d kpc = d/ M , and distance in kpc, d kpc . This factor quantifies the weighted con-tribution of each cloud when we perform thestacking log-likelihood analysis.We fixed the spectral index to 2.7 assumingthat gamma rays at these energies still followthe spectral shape of the “sea” of cosmic rays(Aguilar et al. 2015). We also include morphol-ogy information from each cloud based on tem-plates generated using the Planck survey (SeeAppendix B on how we built the templates).This information is combined, together withHAWC’s detector response, to obtain an ex-pected number of events in each f hit bin usedin the likelihood calculation. HAWC Collaboration
For each cloud we create a log-likelihood pro-file as a function of C . For individual clouds,we use this profile to find the value ˆ C that opti-mizes the log-likelihood. For the stacking anal-ysis, we add the log-likelihood profiles and thenwe find the value ˆ C that optimizes this profile.A test statistic value T S is calculated to checkfor a significant excess.
T S = 2 L ( S ( ˆ C ) + B ) L ( B ) , (3)where S is the signal from the source model,while B is the background model, which corre-sponds to the background estimated from thedata using direct integration (See Abeysekaraet al. 2017a).The best value ˆ C is then used as an input toa Markov-Chain Monte Carlo (MCMC) to es-timate a probability distribution. Since we ob-serve a non-significant detection (i.e. TS < C .We compute a limit for the E − . spectrummodel (refer afterwards as 2.7-model) andquasi-differential limits on the normalizationin a similar way as previous HAWC analysesAbeysekara et al. (2017c, 2018). The main dif-ference between these two limits is that thequasi-differential limits are independent of anymodel assumption, while the limit for a broadenergy range is model dependent. However, thequasi-differential limits are more conservativedue to the lowering of the statistical power bydividing the data. For the 2.7-model limit, weuse the energy band going above 1 TeV. For thequasi-differential limits, we define three energyhalf decade bands, between 1 TeV and 31.6 TeVand an overflow bin above 31.6 TeV. The range The f hit bins used in the analysis overlap when trans-lated into energy space. Although this is taken into ac-count in the analysis, the limits are therefore not strictlydifferential. of the bands and the pivot energy, E , used ineach range are shown in Table 2. The pivotenergy is set at 10 TeV for the 2.7-model limit. RESULTS AND DISCUSSIONWe did not find significant emission from thestudied regions (See Appendix C). Therefore,we proceed to calculate the 95% credible inter-vals (C.I.) as explained in § σ confidence bands, aswell as the median of the upper limits expectedfrom a background-only scenario.Figure 1 shows the quasi-differential upperlimits. Figure 2 shows the 2.7-model upperlimits at 10 TeV. These measurements can becompared with the gamma-ray flux expectedfrom hadronic interactions producing gammarays from neutral pion decay. The models wereproduced by using the parametrization of the pp cross section ( dσdE γ ) process from Kafexhiuet al. (2014). We use the cosmic-ray measure-ments from the AMS experiment (Aguilar et al.2015) and extrapolate the AMS fit to highercosmic-ray energies, with the assumption thatit will maintain its spectral shape. We calculatethe expected gamma-ray flux by convolving thecosmic-ray flux with the pp cross section (Aha-ronian et al. 2020) : F γ ( E γ ) = ξ N m p A (cid:90) dE p dσdE γ F p ( E p ) , (4)where A is the same factor as equation 2, ξ N isthe nuclear enhancement factor and assumed tobe equal to 1.8 as in Aharonian et al. (2020),and m p is the proton mass. As can be seen inthe Figures 1 and 2, the overlap between the The software used to calculate the gamma-ray fluxwas Naima (Zabalza 2015) and libppgam (Kafexhiuet al. 2014). We show the results of both software pack-ages as the blue band in Figures 1 eV gamma rays from passive Giant Molecular Clouds
Systematic uncertainties
We quantify systematic uncertainties by re-running the analysis with a range of differentdetector response files corresponding to our bestunderstanding of PMT performance, detectorcalibration, and uncertainties in the point-spread function (Abeysekara et al. 2017b),resulting in a systematic relative uncertaintyranging from 15% to 35%. This effects are dueto systematics from mis-modeling the detector.4.2.
Constraints on the cosmic-ray energydensity
With the assumption that the gamma-rayemission is produced by pion decay, we esti-mate constraints in the cosmic-ray energy den-sity from these distant regions and compare itto that measured in the local neighborhood. Us-ing the same expression as in Abramowski et al.(2016), and using the same energy bins as in Ta-ble 2, we can modify our spectral model, Equa-tion 2, so that our free parameter is the cosmic-ray energy density (in eV / cm ) ρ CR = 1 . × − (cid:0) ξ N . (cid:1) − (cid:16) L γ erg / s (cid:17) (cid:16) M M (cid:12) (cid:17) − , (5) where ξ N accounts for nuclei heavier than hy-drogen in both cosmic rays and interstellar mat-ter, L γ is the luminosity of gamma rays, and M is the mass of the region. The luminosity is ob-tained as L γ ( E < E γ < E f ) = 4 πd (cid:90) E f E E γ F ( E γ ) dE γ , (6)where d is the distance to the region. We theninsert Equation 6 into Equation 5. After doingthe algebra and taking care of units, we obtain ρ CR = 4 . C E α ( E − α +2 i − E − α +2 f ) , (7)where α is the index, E is the mid-point ofthe energy bin and E i , E f are the edges of theenergy bins. Equation 2 now can be rewrittenso that the free parameter is ρ CR . We applythe procedure in § ± σ uncertainty region of the extrapolation.Table 3 contains the observed and expected up-per limits for each of the clouds and stackedanalyses.From these limits we do not have evidencethat there is any deviation from the paradigm ofthe sea of cosmic rays permeating our Galaxy.It is also important to remark again that thegamma-ray expectation is based on an extrap-olation of cosmic-ray data, so these estimatedlimits give a constraint on the cosmic ray en-ergy density at energies of E CR ∼ E γ (see forexample Kelner et al. 2006), assuming purelypion decay photons. CONCLUSIONS
HAWC Collaboration
Table 2.
Observed 95% credible upper limits on the gamma-ray emission from the GMCs, together with the expectedmedian upper limits, as well as the 68% and 95% containment bands for the expected limits. > > × − ] 5.62 TeV [ × − ] 17.8 TeV [ × − ] 56.2 TeV [ × − ] 10 TeV [ × − ]U.L. Expected Limit U.L. Expected Limit U.L. Expected Limit U.L. Expected Limit U.L. Expected Limit StackedI +1 . − . , +3 . − . ) 2.3 1.8( +0 . − . , +1 . − . ) 13.5 8.7( +3 . − . , +7 . − . ) 9.4 6.1( +2 . − . , +5 . − . ) 18.0 13.5( +4 . − . , +11 . − . ) StackedII +1 . − . , +2 . − . ) 1.8 1.4( +0 . − . , +1 . − . ) 10.3 7.0( +2 . − . , +5 . − . ) 7.4 4.9( +1 . − . , +4 . − . ) 13.8 11.0( +4 . − . , +7 . − . ) Taurus +0 . − . , +1 . − . ) 1.0 0.8( +0 . − . , +0 . − . ) 6.4 4.1( +1 . − . , +3 . − . ) 5.0 3.1( +1 . − . , +2 . − . ) 7.8 5.6( +2 . − . , +5 . − . ) Orion +0 . − . , +2 . − . ) 1.0 1.0( +0 . − . , +1 . − . ) 4.8 5.2( +2 . − . , +4 . − . ) 3.0 3.3( +1 . − . , +3 . − . ) 7.1 8.2( +3 . − . , +7 . − . ) Perseus +0 . − . , +0 . − . ) 0.74 0.5( +0 . − . , +0 . − . ) 4.0 2.4( +1 . − . , +2 . − . ) 2.9 1.7( +0 . − . , +1 . − . ) 5.8 3.4( +1 . − . , +2 . − . ) Ophiuchi [x100] +2 . − . , +6 . − . ) 1.4 1.9( +0 . − . , +1 . − . ) 5.2 7.8( +2 . − . , +5 . − . ) 2.5 3.0( +1 . − . , +2 . − . +5 . − . , +9 . − . ) Monoceros +0 . − . , +1 . − . ) 0.52 0.6( +0 . − . , +0 . − . ) 1.7 3.1( +1 . − . , +2 . − . ) 1.2 1.9( +0 . − . , +1 . − . ) 3.4 4.6( +1 . − . , +3 . − . ) Aquila +1 . − . , +3 . − . ) 1.3 2.0( +0 . − . , +1 . − . ) 6.9 10.1( +3 . − . , +8 . − . ) 4.2 6.5( +2 . − . , +6 . − . ) 9.8 14.7( +5 . − . , +13 . − . ) Hercules +0 . − . , +0 . − . ) 0.5 0.5( +0 . − . , +0 . − . ) 3.2 3.0( +1 . − . , +2 . − . ) 2.9 2.3( +0 . − . , +1 . − . ) 4.2 4.1( +1 . − . , +3 . − . ) Note.
Flux units are in TeV − cm − s − . Note.
StackedI includes Taurus, Orion, Perseus, and Ophiuchi; StackedII includes Taurus, Orion, and Perseus. Notice that the flux values ofOphiuchi are a hundred times higher.
Table 3.
Observed 95% credible upper limits on the gamma-ray emission from the GMCs, together withthe expected median upper limits, as well as the 68% and 95% containment bands for the expected limits. > StackedI +3 . − . , +11 . − . ) 7.7 6.0( +2 . − . , +5 . − . ) 4.6 2.9( +1 . − . , +2 . − . ) 3.1 1.9( +0 . − . , +1 . − . ) StackedII +5 . − . , +13 . − . ) 7.6 6.2( +2 . − . , +5 . − . ) 4.6 2.9( +1 . − . , +2 . − . ) 3.1 1.8( +0 . − . , +1 . − . ) Taurus +6 . − . , +14 . − . ) 9.8 7.9( +2 . − . , . − . ) 6.5 4.1( +1 . − . , +3 . − . ) 4.9 2.8( +1 . − . , +2 . − . ) Orion +9 . − . , +20 . − . ) 8.6 9.9( +3 . − . , +8 . − . ) 4.0 4.6( +1 . − . , +3 . − . ) 2.3 2.8( +0 . − . , +2 . − . ) Perseus +17 . − . , +38 . − . ) 34.7 20.0( +7 . − . , +16 . − . ) 19.8 10.1( +3 . − . , +8 . − . ) 14.0 6.7( +2 . − . , +5 . − . ) Ophiuchi [x100] +36 . − . , +98 . − . ) 20.0 33.1( +12 . − . , +37 . − . ) 7.2 10.8( +4 . − . , +9 . − . ) 3.2 4.3( +1 . − . , +3 . − . ) Monoceros +46 . − . , +156 . − . ) 38.1 43.3( +14 . − . , +34 . − . ) 16.5 20.1( +6 . − . , +16 . − . ) 5.9 11.5( +4 . − . , +9 . − . ) Aquila +7 . − . , +16 . − . ) 5.0 8.0( +3 . − . , +6 . − . ) 2.2 3.9( +1 . − . , +3 . − . ) 1.2 2.4( +1 . − . , +1 . − . ) Hercules +23 . − . , +46 . − . ) 26.0 27.8( +10 . − . , +23 . − . ) 15 14.5( +5 . − . , +12 . − . ) 12.0 9.9( +3 . − . , +8 . − . ) Note.
Units are in[ × − eV cm − ]. Note.
StackedI includes Taurus, Orion, Perseus, and Ophiuchi; StackedII includes Taurus, Orion, and Perseus. Notice that theenergy density values of Ophiuchi are a hundred times higher. eV gamma rays from passive Giant Molecular Clouds (a) StackedI (b) StackedII(c) Taurus (d) Orion Figure 1.
95% C.I. upper limits on the gamma-ray flux of the giant molecular clouds studied. Stackedclouds include Taurus, Orion, Perseus and Ophiuchi. The gray band represents the statistical uncertainty inthe U.L.(68% and 90% containment). The blue band is the expectation for the gamma-ray spectrum of theclouds based on local cosmic-ray meeasuerments (Equation 4). The width of the band corresponds to theuse of two different software implementations to calculate the gamma flux (Zabalza 2015; Kafexhiu et al.2014). HAWC Collaboration (e) Perseus (f) Ophiuchi(g) Monoceros (h) Aquila(i) Hercules
Figure 1.
95% C.I. upper limits on the gamma-ray flux of the giant molecular clouds studied. Stackedclouds include Taurus, Orion, Perseus and Ophiuchi. The gray band represents the statistical uncertainty inthe U.L.(68% and 90% containment). The blue band is the expectation for the gamma-ray spectrum of theclouds based on local cosmic-ray meeasuerments (Equation 4). The width of the band corresponds to theuse of two different software implementations to calculate the gamma flux (Zabalza 2015; Kafexhiu et al.2014). (Continued)
With the purpose to test the cosmic-ray seaparadigm and probe if its density is indepen-dent of the location, we performed measure-ments of giant molecular clouds using data fromthe HAWC observatory. Since no significant ex-cess was observed, we calculated upper limits at the 95% credible interval, for individual andstacked gamma-ray emission of clouds that arepart of the Gould Belt as described in §
2. Thegamma-ray flux expected from pure hadronicinteractions of the cosmic-ray flux with passivemolecular clouds is below 10 − TeV − cm − s − eV gamma rays from passive Giant Molecular Clouds E F (10TeV) [TeV cm s ]StackedStackedIITaurusOrionPerseusOphiuchiMonocerosAquilaHercules 95% CIHAWC expected limit68% containment95% containmentExpectation Figure 2.
95% C.I. upper limit on the gamma-ray flux between 1 and 100 TeV, assuming a pivot energy of10 TeV and an E − . spectrum. The gray and blue bands are calculated the same way as for Figure 1. (a) StackedI (b) StackedII Figure 3.
95% C.I. upper limits on the cosmic-ray energy density from the stacked analyses (Gould Beltand Radcliff Wave structures) as a function of gamma-ray energy. The corresponding cosmic-energy densitycan be estimated based on the assumption that E CR ∼ E γ (see for example Kelner et al. 2006). Grayband represents the statistical uncertainty in the U.L. (68% and 90% containment). Blue band correspondsto the the ± σ uncertainty region of the cosmic ray energy density using data (and extrapolating) fromAMS. above 10 TeV. The upper limit value for the fluxnormalization, in the case of the stacked analy- sis, is overlapping with the values predicted fora cosmic-ray flux energy density similar to the2 HAWC Collaboration one measured at Earth. The differential limitsare less than a factor of 10 higher than the pre-diction. The same is observed for the individualclouds Taurus, Orion and Aquila.Using the same analysis method for the differ-ential gamma-ray limits, we also estimated thecosmic-ray energy density of the clouds. Usingthe data from AMS and extrapolating the re-sults to HAWC energies, we see that the HAWClimits are higher by a factor of less than 10 forthe case of the stacked clouds as wells as Taurus,Orion and Aquila.With current detector settings, as describedin § Abeysekara, A. U., Albert, A., Alfaro, R., et al.2017a, ApJ, 843, 21—. 2017b, ApJ, 843, 39—. 2017c, ApJ, 842, 9—. 2018, ApJ, 853, 154Abramowski, A., Aharonian, F., Benkhali, F. A.,et al. 2016, Nature, 531, 476Ackermann, M., Ajello, M., Allafort, M., et al.2012a, ApJ, 756, 4—. 2012b, ApJ, 755, 22Adriani, O., Barbarino, G. C., Bazilevskaya,G. A., et al. 2011, Science, 332, 69Aguilar, M., Aisa, D., Alpat, B., et al. 2015, Phys.Rev. Lett., 114, 171103Aharonian, F. 2001, Space Science Reviews, 99,187 Aharonian, F., Peron, G., Yang, R., Casanova, S.,& Zanin, R. 2020, Phys. Rev. D, 101, 083018Alves, J., et al. 2020, Nature, 578, 237Baghmanyan, V., Peron, G., Casanova, S.,Aharonian, F., & Zanin, R. 2020, TheAstrophysical Journal, 901, L4Casanova, S., Aharonian, F. A., Fukui, Y., et al.2010, Publications of the Astronomical Societyof Japan, 62, 769Comer´on, F. 2001, A&A, 365, 417Dame, T. M., Ungerechts, H., Cohen, R. S., et al.1987, ApJ, 322, 706Dzib, S. A., Loinard, L., Ortiz-Le´on, G. N.,Rodr´ıguez, L. F., & Galli, P. A. B. 2018, ApJ,867, 151Ferri`ere, K. M. 2001, Rev. Mod. Phys., 73, 1031 eV gamma rays from passive Giant Molecular Clouds Guillout, P., Sterzik, M. F., Schmitt, J. H. M. M.,Motch, C., & Neuhaeuser, R. 1998, AAP, 337,113Issa, M., & Wolfendale, A. W. 1981, Nature, 292,430Kafexhiu, E., Aharonian, F., Taylor, A. M., &Vila, G. S. 2014, PRD, 90, 123014Kelner, S. R., Aharonian, F. A., & Bugayov, V. V.2006, PhRvD, 74, 034018Neronov, A., Malyshev, D., & Semikoz, D. V.2017, A&A, 606, A22 Neronov, A., Semikoz, D. V., & Taylor, A. M.2012, PRL, 108, 051105Planck Collaboration, et al. 2011, A&A, 536, 16Schlafly. 2014, ApJStrong, A., Moskalenko, I. V., & Ptuskin, V. S.2007, Ann. Rev. Sci., 57, 285Vianello, G., Lauer, R. J., Younk, P. W., et al.2015, arXiv e-prints, arXiv:1508.07479Yang, R., de Ona Wilhelmi, E., & Aharonian, F.2014, A&A, 566Zabalza, V. 2015, Proc. of International CosmicRay Conference 2015, 922 HAWC Collaboration
APPENDIX A. MASS CALCULATIONAlthough some of the mass values of the clouds can be found in the literature, we calculate themourselves due to the fact that we are building the regions of interest for the analysis, focusing on thehigh-density areas of the clouds where we assume most of the gamma rays originate. As mentionedin the main text, we use data from the Planck survey. We start by calculating the column density: N H = τ D / (cid:18) τ D N H (cid:19) ref (A1)where the reference value used is ( τ D /N H ) ref = 1 . × − cm for 353GHz Planck Collaborationet al. (2011). τ D is the measured dust opacity. The mass of the cloud is then calculated as M dust = N H A cloud m H (A2)The area of the cloud can be expressed as A angular d , where d is the distance to the cloud.We apply a cut on the dust opacity value to select the high-density regions of 5 × − as done inYang et al. (2014). B. TEMPLATESWe generated our molecular cloud templates using the Planck survey. We apply the same method-olgy as in Yang et al. (2014). First we calculate the column density from the dust optical depth mapat 353 GHz from Equation A1. We apply the corresponding cut on the opacity value as mentionedin Appendix A, then we normalize the map to the integral of the column density divided by the sizeof the spatial bin. This procedure ensures that the correct units are derived when the 3ML spatialmodel is used. Figure 4 shows the results after applying this procedure. C. RESULTS OF THE ANALYSISTable 4 shows the TS results, together with the corresponding flux measurements of Table 2. Ascan be seen, none of the results are significant (i.e. TS > eV gamma rays from passive Giant Molecular Clouds
176 174 172 170 168 166-12-14-16-18 166168170172174176 -18-16-14-12Galactic Longitude [ o ] G a l a c t i c L a t i t u d e [ o ] [ s r ] (a) Taurus
215 210 205-12-14-16-18-20 205210215 -20-18-16-14-12Galactic Longitude [ o ] G a l a c t i c L a t i t u d e [ o ] [ s r ] (b) Orion
161 160 159 158 157-18-20-22-24 157158159160161 -24-22-20-18Galactic Longitude [ o ] G a l a c t i c L a t i t u d e [ o ] [ s r ] (c) Perseus
216 215 214 213-11-12-13-14 213214215216 -14-13-12-11Galactic Longitude [ o ] G a l a c t i c L a t i t u d e [ o ] [ s r ] (d) Monoceros
30 25 20 15 101614121086 1015202530 6810121416Galactic Longitude [ o ] G a l a c t i c L a t i t u d e [ o ] [ s r ] (e) Aquila
50 48 46 44 4210987 4244464850 78910Galactic Longitude [ o ] G a l a c t i c L a t i t u d e [ o ] [ s r ] (f) Hercules o ] G a l a c t i c L a t i t u d e [ o ] [ s r ] (g) Ophiuchi Figure 4.
Templates created using the information from the Planck Survey. Colorbar is the normalizedcolumn density divided by the size of the spatial bin. HAWC Collaboration (a) Taurus (b) Orion(c) Perseus (d) Ophiuchi(e) Monocerros (f) Aquila(g) Hercules
Figure 5.
Cosmic-ray density upper limits of the GMCs. eV gamma rays from passive Giant Molecular Clouds T a b l e . G a mm a - r a y flu x m e a s u r e m e n t s a nd % C . I . upp e r li m i t s ( i np a r e n t h e s i s ) . - . T e V . - . T e V . - . T e V > . T e V > T e V . T e V . T e V . T e V . T e V T e V T S F l u x [ × − ] T S F l u x [ × − ] T S F l u x [ × − ] T S F l u x [ × − ] T S F l u x [ × − ] S t a c k e d I - . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) S t a c k e d II - . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) T a u r u s . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) O r i o n - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) P e r s e u s . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) O ph i u c h i[ x ] - . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) M o n o c e r o s . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) A q u il a - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) - . . + . − . ( . ) H e r c u l e s - . . + . − . ( . ) - . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) N o t e . F l u x un i t s a r e i n T e V − c m − s − . N o t e . S t a c k e d I i n c l ud e s T a u r u s , O r i o n , P e r s e u s , a nd O ph i u c h i; S t a c k e d II i n c l ud e s T a u r u s , O r i o n , a nd P e r s e u s HAWC Collaboration T a b l e . C o s m i c - r a y e n e r g y d e n s i t yq u a s i - d i ff e r e n t i a l % C . I . upp e r li m i t s [ × − e V c m − ]i n e a c h e n e r g y b i n . - . T e V . - . T e V . - . T e V > . T e V . T e V . T e V . T e V . T e V T S T S T S T S S t a c k e d I - . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) S t a c k e d II . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) T a u r u s . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . ± . ( . ) O r i o n . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) P e r s e u s . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) O ph i u c h i[ x ] . . + . − . ( . ) . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) M o n o c e r o s . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . . ( . ) A q u il a . . + . − . ( . ) . . + . . ( . ) . . . − . ( . ) . . + . − . ( . ) H e r c u l e s . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( . ) . . + . − . ( .0