Secondary Radio and X-Ray Emissions from Galaxy Mergers

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SECONDARY RADIO AND X-RAY EMISSIONS FROM GALAXY MERGERS

Chengchao Yuan1, Kohta Murase1,2, and Peter Mesz´ aros´ 1

1Department of Physics; Department of Astronomy and Astrophysics; Center for Particle and Gravitational Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA 2Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

ABSTRACT Shocks arising in galaxy mergers could accelerate cosmic-ray (CR) ions to TeV-PeV energies. While propagating in the intergalactic medium, these CRs can produce high-energy neutrinos, electron- positron pairs and gamma-rays. In the presence of intergalactic magnetic fields, the secondary pairs will radiate observable emissions through synchrotron radiation and inverse Compton scattering. In this paper, we demonstrate that these emissions can explain the radio and X-ray fluxes of merging galaxies such as NGC 660 and NGC 3256. Using our model in combination with the observations, we can constrain the gas mass, shock velocity, magnetic field and the CR spectral index s of these systems. For NGC 660 a single-zone model with a spectral index 2.1 ∼< s ∼< 2.2 is able to reproduce simultaneously the radio and X-ray observations, while a simple one-zone scenario with s ∼ 2 can describe the radio and a large fraction of X-ray observations of NGC 3256. Our work provides a useful approach for studying the dynamics and physical parameters of galaxy mergers, which can play an important part in future multi-messenger studies of similar and related extragalactic sources. Keywords: cosmic rays — galaxies: interactions — galaxies: individual (NGC 660, NGC 3256) — radio continuum: galaxies — X-rays: galaxies

1. INTRODUCTION electron-positron pairs produced by the CR interactions Star-forming galaxies including starbursts have been in such systems. Here the EIC is caused by scatter- considered as possible reservoirs of cosmic rays (CRs) ings with the cosmic microwave background (CMB), and sources of associated neutrinos and gamma rays infrared/optical starlight (SL) and extragalactic back- (e.g., Loeb & Waxman 2006; Thompson et al. 2007; ground light (EBL). In addition, since the radiation Murase et al. 2013), in which the CRs can be supplied spectrum of the merging galaxies is determined by the by not only supernovae but also hypernovae, superbub- dynamics of the galaxy interactions and the resulting bles and active galactic nuclei (Senno et al. 2015; Xiao physical conditions, this enables us to provide con- et al. 2016; Tamborra et al. 2014; Wang & Loeb 2016; straints on the magnetic field B, shock velocity vs, gas Lamastra et al. 2017; Liu et al. 2018). Interacting galax- mass Mg, etc. Different from Lisenfeld & Voelk(2010) ies, which may be accompanied by starburst activities, where shock-accelerated electrons are employed to de- have also been considered as additional accelerators of scribe the radio emissions of two colliding galaxies, UGC CRs (Kashiyama & Mészáros 2014; Yuan et al. 2018). 12914/5 and UGC 813/6, we present an alternative Under the conditions typical of galaxy merger systems model based on the secondary emission from inelastic pp collisions to reproduce simultaneously the radio and arXiv:1810.04155v4 [astro-ph.HE] 24 Jun 2019 synchrotron emission can extend from the radio band to the X-ray regime, while the inverse Compton scatter- X-ray observations of NGC 660 and NGC 3256. In gen- ing may be important in the ultraviolet (UV) and up to eral, secondary electrons are more natural to explain the beyond the X-ray band. electromagnetic emissions in merging galaxies. For the In this work we formulate a model which is ca- observed CRs, the electron acceleration efficiency, the pable of reproducing the radio and X-ray obser- fraction of plasma energy deposited to electrons, is at vations of specific systems using synchrotron and least two orders lower than the proton acceleration ef- −4 −2 synchrotron self-Compton (SSC) or external inverse ficiency, e.g. Ke/p = e/p ∼ 10 − 10 (Jones 2011; Compton (EIC) emissions from high-energy secondary Morlino & Caprioli 2012). This value is also consistent with the observations of Galactic supernova remnants. Furthermore, the recent particle-in-cell simulation shows −3 [email protected] a similar value, Ke/p ' 10 (Katz & Waxman 2008; 2 Yuan, Murase and Mesz´ aros´

Caprioli & Spitkovsky 2014; Park et al. 2015a). The ra- tio of the primary electrons (from shock accelerations) and the secondary electrons and positrons is approximately γ, ν Ee,primary 6e −1 ' ∼< 10 . e± Ee,sec min[1, fpp,g]p Radio/X − ray R p, π0, π± 2 g where fpp,g is the effective pp optical depth in the emitting region. Therefore in our model with the typical electron/proton acceleration efficiencies, emission from primary electrons directly accelerated in shocks is sub- Diffusive Shock dominant compared to that from secondary electrons and positrons from pp collisions and pion decays. This is consistent with Murase et al.(2018) where they sug- gest that the secondary emissions overwhelm the primary component in nearly proton calorimetric sources. Figure 1. Schematic figure showing the merger of two galax- It is possible that primary electrons can provide a non- ies. The shock was simplified as a straight line across the negligible contribution if K > 0.1, considering that dense core region. It is also in the core region where inter- e/p ∼ actions occur and neutrinos as well as electromagnetic radi- Ke/p is poorly constrained theoretically and observa- ation are produced. tionally for this system. In the following text, we focus on the primary electron/positron scenario and omit the The pions produced in the pp collisions between shock- primary electron contribution. accelerated CR ions and the galaxy gas generate, besides As a well-studied interacting system, NGC 660 is a high-energy neutrinos and γ-rays, also copious quanti- galaxy formed by the collision of two galaxies (van Driel ties of high-energy electron-positron pairs. These high- et al. 1995), which has been observed in both radio (e.g., energy leptons may produce observable synchrotron Douglas et al. 1996; Large et al. 1981; Condon et al. emissions while propagating inside the galactic mag- 2002, 1998; Dressel & Condon 1978; Bennett et al. 1986; netic fields. Here, considering the conservation of lep- Becker et al. 1991; Gregory & Condon 1991; Sramek ton numbers and muon decays, we approximate the to- 1975), microwave, infrared, UV and X-ray (e.g., Frater- tal electron-positron injection spectrum to be the same nali et al. 2004; Liu 2010; Brightman & Nandra 2011; with the neutrino production spectrum. Following the White et al. 2000) bands. Also, the magnetic field in the procedure in Yuan et al.(2018), the electron injection core region of NGC 660 is constrained in the range of spectrum can be written as 16 ± 5 µG through polarization studies (Drzazga et al. 2011). In this paper, we take NGC 660 as an example 2 1 2 dNν 1 −1 2 ε Ne(ε) = ε = pC Mgv and use our model to reproduce the radio, UV and X-ray 3 dε 12 s (1) fluxes. We also apply our model to constrain the shock × min [1, f ] , pp,g εp'20ε velocity and gas mass of the core region of NGC 660 by using the magnetic field 16 ± 5 µG as a precondition. where p is the CR ion acceleration efficiency (nor- To show that our model’s applicability can be extended mally fixed as 0.1), C = ln(εp,max/εp,min) is the normal- −2 to other similar systems, we also consider another well- ization coefficient for a ε spectrum, Mg is the gas mass studied galaxy formed through a merger, NGC 3256, as of the merging region, vs is the shock/collision veloc- a supplementary template. ity and fpp,g = κppcngσ(εp) min[tesc, tdyn] is pp optical This paper is organized as follows. In §2, we formu- depth inside the galaxy. In this expression, κpp = 0.5 is late the secondary electron-positron spectrum and calcu- the proton inelasticity, c is the speed of light, ng is the late resulting electromagnetic emissions, including syn- gas density, tesc is the escape time of CRs, tdyn ' Rg/vs chrotron radiation and SSC/EIC components. In §3 , we is the dynamic time of the merger and σ(εp) is the pp apply the formalism in §2 to the core regions of NGC cross section given by Kafexhiu et al.(2014). As galaxies 660 and NGC 3256. A summary and discussion, in- merge, strong shocks occur with a complicated morphol- cluding comparison with previous work in the context ogy over a galaxy scale, while merging cores of the two of starburst galaxies, is given in §4. galaxies lead to a dense core region. Particles are accelerated by the shocks, and then will be distributed in a galaxy scale. The CRs diffusing in the core region will 2. SECONDARY ELECTRON SPECTRUM AND make neutrinos and gamma rays efficiently. In this work, ELECTROMAGNETIC EMISSIONS as a simplified approximation without covering the de- Secondary Radio and X-ray Emissions from Galaxy Mergers 3

2 dNγ 2 2 dNν tails of the shock structure, we assume that shocks are spectrum are correlated by ε = ε |ε =2ε . γ dεγ 3 ν dεν γ ν CR accelerators, which inject high energy CRs to the From energy conservation, we may approximately relate core region of the merging systems and initiate subse- the electron-positron injection rate to the gamma-ray quent interactions. Figure1 shows the schematic. After production rate, and the former spectrum can be writ- leaving the accelerator, the particles can propagate dif- ten as fusively or get advected away through galactic winds, 2 γγ 2 dNγ 1 2 dNν cut therefore the net escape rate is the sum of diffusion ε Ne (εe) = 2ε |εγ =2εe = ε |εν =εe , εe > εγγ /2. dεγ 3 dεν −1 −1 −1 rate and advection rate, e.g. tesc ≈ tdiff + tad . Al- (3) though the maximum CR energy εp,max and effective The total electron-positron injection spectrum is pp optical depth fpp,g depend on the geometry of the therefore the summation of Equations1 and3, or equiv- colliding galaxies, for simplicity and consistency, we as- alently we can introduce a modification factor χ(ε) = sume that the neutrinos are produced inside the core re- cut 1 + exp(−εγγ /2ε) to Equation1. gion of the interacting system and calculate the electro- With these preparatory work, we can now derive the magnetic radiation therein. This hypothesis is in good secondary electron-positron distributions and calculate agreement with the radio maps of NGC 660 and NGC the synchrotron and inverse Compton emissions. Con- 3256. Hence, to fully depict the physical condition of the sidering the dynamic time tdyn = Rg/vs, we have the core region, we introduce several quantities, the radius rate of lepton production Rg, the average magnetic field B as well as the previ- t−t Ne(ε)χ(ε) − dyn ously defined gas mass Mg and shock velocity vs. Us- Q(ε, t) = × min{1, e tesc }, (4) ing these parameters, we can write down the maximum tdyn CR energy, gas density and diffusion time explicitly as where the exponential factor describes the escape of CRs 3 vs 4 3 εp,max = 20 eBsRg c (Drury 1983), ng = Mg/( 3 πmpRg) after the dynamical time scale and is obtained through 2 and tdiff = Rg/(6Dg), respectively. Here, mp is the pro- the equation ∂N/∂t = −N/tesc. To get the electron ton mass, Dg is the diffusion coefficient and Bs is the distribution inside the galaxy, we solve the transport post-shock magnetic field which can be parameterized equation of a simplified leaky-box model 2 1 2 as a fraction of the ram pressure Bs /8π = 2 Bngmpvs ∂Ne Ne ∂ (Kashiyama & Mészáros 2014). As for the diffusion co- = Q(ε, t) − + [b(ε)Ne(ε, t)] (5) ∂t tesc ∂ε efficient Dg, we use a combined large and small angle diffusion equation as in Senno et al.(2015); Casse et al. where b(ε) is the electron energy loss rate due to (2001) and Yuan et al.(2018) and then it can be written synchrotron radiation, SSC/EIC and advection (bad ' explicitly as ε/tad). In our calculations, we assume Q and the diffusion coefficient Dg do not depend on the positions in R 2 D −1 the merging system. t '4.28 Myr g 0 diff 29 2 −1 In the synchrotron limit γ 1, the synchrotron ra- 3 kpc 10 cm s (2) e −1 diation power in the frequency range ω to ω + dω by h 1/2 2i × (ε/εc,g) + (ε/εc,g) one electron with Lorentz factor γe can be written in the well-known formula where D is defined by D ' cl /20, l ' 0.1R is √ 0 0 c c g 3e3B sin θ the coherence length of the magnetic field fluctuations p Psyn(ω, γe)dω = 2 F (X)dω (6) 2πmec and εc,g ≈ eBlc is the characteristic energy. As for the advection, the typical values of wind velocity in where θp is the angle between the electron velocity star-forming galaxies and star burst galaxies range from and the magnetic field, which is assumed to be π/2 in 500 km s−1 (Crocker 2012; Keeney et al. 2006) to 1500 our case, −1 ω 3 eB km s (Strickland & Heckman 2009). Here, we use a X = , ω = γ2 . −1 c e moderate value vw ≈ 1000 km s for interacting galax- ωc 2 mec ies since these galaxies may enter star-forming/starburst The function F (X) is given by phase. In this case we have the advection time t ' ad ∞ −1 Z 6 vw Rg Rg/vw ≈ 2.94 × 10 yr 1000 km s−1 3 kpc . F (X) = X K5/3(ξ)dξ. Inside the galaxy, the electron-positron injection spec- X trum can be modified due to additional injections via Then, it is straightforward to write down the inte- two-photon annihilation, γγ → e−e+, since the core re- grated radiation power gion can be opaque to high-energy gamma-ray photons Z 2 cut bsyn(ε) = Psyn(ω, ε/mec )dω. above a certain threshold energy εγγ . In the pion de- cay scenario, the gamma-ray spectrum and the neutrino 4 Yuan, Murase and Mesz´ aros´

ing. Now with the preparations on synchrotron radiation, we are able to solve the kinetic equation. One μ 1 1μ special solution to the diﬀerential equation is the steady 1 μ state solution (∂Ne/∂t = 0), 1 1 1 1 −1

1 1 steady 1 1 Ne = Q(ε, t) + (8) tesc tsyn 1 1 1 To verify this expression, it is worthwhile to solve the

1 time evolution of electron-positron spectra numerically. 9 11 For illustration purposes, we assume Mg = 10 M , v = 100 km s−1, R = 5 kpc and εcut = 1 TeV. Figure 11 s g γγ 1 −1 2 shows the synchrotron cooling rate (tsyn; solid lines) as 11 1 1 1 11 111 11 11 11 functions of lepton energy for different galactic magnetic ε −1 fields as well as the escape rate (tesc) and the reciprocal of dynamic time (t−1 ; dashed lines). As the magnetic Figure 2. Electron loss rates versus electron energy εe. Solid dyn lines correspond to cooling rates due to synchrotron radiation field becomes stronger, the synchrotron cooling tends to in different magnetic fields, e.g. 5µG (green), 15µG (red) be faster since P (ω, γe) increases. Using the finite differ- and 30µG (black). The cyan dash-dotted line is the cooling ence method, the time evolution of pair spectra for the rate of inverse Compton scattering (SSC+EIC). Blue and magenta dotted lines illustrate the contributions of CMB and magnetic field B = 5 µG is shown in the Figure3, where EBL to the EIC cooling rate, while the black, red and green we use the parameter η = t/tdyn to label the stages of dotted lines are SSC cooling rates at the magnetic fields 5µG pair injection. The thick red solid line corresponds to (green), 15µG (red) and 30µG (cyan), respectively. Magenta and blue dashed lines are the escape rate and the reciprocal the steady electron distribution given by the Equation8. of dynamic time, respectively. The theoretical steady distribution almost coincide with the numerical steady solutions. To show this, we mul- steady tiply the theoretical solution Ne by a factor of ten to separate these curves. Figure3 also illustrates the

1 evolution of the cumulative number of electron inside the core region. From this ﬁgure, we conclude that the 1 electron injection enters the steady phase when η ∼> 0.2.

1 Inverse Compton scattering between high-energy

1 electron-positron pairs and external CMB/SL/EBL 1 1 photons (denoted by EIC) as well as SSC may become

ε 1 1 1 more pronouncing in lepton cooling process when the

electron-positron spectrum becomes harder. Here we 1 1 formulate the SSC/EIC power per unit comoving vol- 11 1 1 ume as (e.g., Murase et al. 2011), 1 1 1 1 11 111 11 11 Z Z dNx dNe dnγ 0 dσIC ε E = dγe dεγ E c (9) dEdt dγe dεγ x dE Figure 3. Secondary electron-positron spectra at different times assuming the magnetic field B = 5 µG. The parame- where x = SSC or EIC, and the differential cross sec- ter η = t/tdyn represents the time of electron-positron injection is (Blumenthal & Gould 1970): tion. Thin lines are numerical solutions to the CR transport equation while the thick red line is the analytical steady- steady steady dσIC 0 3 1 state solution Ne . To separate Ne from numerical c = σT c × steady 2 solutions, we multiply Ne by a factor of 10. dE 4 γe εγ v2w2(1 − v) 1 + v − 2v2 + + 2v ln v . 2(1 + vw) It is useful to define the synchrotron cooling time (10) ε tsyn(ε) = . (7) bsyn(ε) In the expression of the cross section, σT is the Thom- E 2 son cross section, v = 2 , ξ = E/(γemec ) and While SSC and EIC also play a role in electron- 4εγe (1−ξ) 4εγ γe positron cooling, we will show later that these pro- w = 2 . For SSC, dnγ /dεγ corresponds to the photon mec cesses are subdominant comparing to synchrotron cool- spectrum of synchrotron emission and it can be written Secondary Radio and X-ray Emissions from Galaxy Mergers 5 as where the coefficient 2π and Planck constant h come from |dω/dν| and |dE/dν|, respectively. In general, we dn 1 Z ε ε γ = P ε / , e N (ε )dε need to keep in mind that inverse Compton (or more γ dε 2R2ch syn γ ~ m c2 e e e γ SSC g e especially SSC) emission can be significant at some fre- (11) quency even when the magnetic field is strong and the The intergalactic starlight photon density can be es- core region is more compact such that the synchrotron timated by using the IR/optical spectral energy density photon field is more intense. We will show later that (SED; see the inset of the left panel of Figure5), e.g. 2 2 SSC and EIC can also be important for NGC 3256. εγ (dn/dεγ )SL ∼ 2dLFν,SL/(Rgch), where dL is the luminosity distance of the galaxy. In this paper, we use 3. RADIO AND X-RAY CONSTRAINTS ON MG two modified Planck functions to approximate the left AND VS and right bulks of the IR/optical data, With the above, we are able to calculate the syn- ζ chrotron and SSC/EIC fluxes. The spectrum of syn- X hν i 1 Fν,SL(ν) = Ai . (12) chrotron radiation extends broadly from radio band to 1eV exp( hν ) − 1 i=L,R εi X-ray regime while SSC/EIC may become important from optical band to X-ray band. In this section we As for EIC, (dnγ /dεγ )EIC is given by the summation investigate the possibility of explaining the radio and of CMB black body spectrum, (dn/dεγ )SL and the EBL X-ray observations simultaneously using the formalism photon density spectrum provided by ”model C” from presented in §2. Since in our model the physical state of Finke et al.(2010). the core region of merging galaxies is determined by five Like the synchrotron radiation, we can define the cool- parameters: the radius Rg, the magnetic field B, the gas ing time for SSC and EIC, mass Mg, the shock velocity vs and the time parameter Z Z −1 η = t/tdyn, our model provides one useful method to dnγ 0 dσIC tx(εe) = εe dE dεγ E c , study the dynamics of galaxy mergers. In this section, dεγ dE εe x γe= mec2 we present an application to the interacting system NGC (13) 660 and show that our model can be used to reproduce The cyan dash-dotted line in Figure2 shows the com- the radio and X-ray observation. In addition, we find −1 −1 −1 bined cooling rate tIC = tSSC +tEIC as a function of elec- that Mg and vs in the core region of NGC 660 can be tron energy. Figure2 illustrates also the components of constrained under appropriate assumptions. To show the total IC cooling rate, e.g. CMB (blue dotted line), that our model can be used widely to general galaxy EBL (magenta dotted line) and SSC at the magnetic merging systems, we consider also the galaxy NGC 3256. fields 30 µG (black dotted line), 15 µG (red dotted line) From Figure3, we find that the interacting system can and 5 µG (green dotted line). The flattening of the EIC be approximately treated as a steady state. Hence, to loss rate is due to the Klein-Nishina regimes as the elec- simplify the constraint, we employ a steady state so- tron Lorentz factor increases. From this figure, we find lution to approximate the secondary electron-positron that the cooling process is dominated by synchrotron ra- distribution throughout the paper. diation and the cooling due to EIC is predominant comparing to SSC. Hence, in the following section where the 3.1. NGC 660 application to NGC 660 is discussed, we only consider NGC 660 is usually believed as a galaxy formed by the tsyn in the CR transport equation (Equation5). In gen- collision and merger of two galaxies. The distance to us eral, for a power-law electron distribution, the SSC cool- is dL ∼ 12.3Mpc and the HI extent is 47 kpc. Radio ing rate should have the same slope. However, in Figure maps by VLA reveal a smooth core region (Condon et al. 2, the physical cause of the slight slowing down of the 1982). Filho et al.(2004) showed that the de-convoluted growth of the SSC cooling rate is that the steady-state angular size of the radio and X-ray emitting region is electron spectrum becomes steeper due to synchrotron less than 10 arcsec or equivalently the radius Rg ∼< 0.5 cooling (see the red line in Figure3) and this can influ- kpc. Hence, in our calculations, we use Rg ' 0.5 kpc ence the synchrotron photon density spectrum through as the fiducial radius of the core region. In addition, Equation 11. With the equations above, we can write Drzazga et al.(2011) studied the magnetic fields using down the equations for synchrotron and SSC/EIC fluxes VLA data in 16 interacting galaxies and they find that the average magnetic field of NGC 660 is 16 ± 5 µG. Z In the X-ray regime, the data from Chandra telescope syn 1 εe +0.37 −13 −3 −1 Fν = 2 2π · Psyn 2πν, 2 N(εe)dεe gives the X-ray flux 1.24−0.54 × 10 erg cm s 4πdL mec (14) (Argo et al. 2015) in the range 0.5 − 10 keV. In mid- x h dNx 2013, a radio outburst was observed using e-MERLIN Fν = 2 E , x = SSC or EIC, 4πdL dEdt E=hν 6 Yuan, Murase and Mesz´ aros´

B = 11 G B = 16 G B = 21 G 103 103 103 UV UV UV 2 2 2 . 6 . 6 . 6 0 . 0 0 . 0 0 . 0 0 . 0 . 0 . = 1 Radio = 1 Radio = 1 Radio g = g = g = , = , = , = g g g p p p , g , g , g f p p , f p p , f p p , f p p 3 X-ray f p p 3 X-ray f p p 3 X-ray f p f p f p m m m c c c 0 0 0 0 0 0 1 1 1 ] ] ] 1 1 1 g g g n n n s s s m m m k k k [ 2 T = 104 K, 10 [ 2 T = 104 K, 10 [ 2 T = 104 K, 10 SSC+BIC s 10 s 10 s 10 v v v

T = 103 K, 10 T = 103 K, 10 T = 103 K, 10

107 108 109 1010 1011 107 108 109 1010 1011 107 108 109 1010 1011

Mg [M ] Mg [M ] Mg [M ]

Figure 4. Constraints on Mg −vs plane from radio, UV and X-ray tolerance areas. From left to right, magnetic fields are assumed to be B = 11 µG, 16 µG and 21 µG. In each figure, blue and red areas correspond to the radio and X-ray constraints and the black line shows the upper boundary under the UV constraint. The vertical dashed line and gray area show the constraints from −3 the core region gas density ng ∼< 100 cm , whereas the horizontal dashed lines and gray area correspond to the strong shock requirements (M' 10) for the temperature 104 K and 103 K. The magenta dash-dotted contours correspond to different pp −1 8 optical depth fpp,g. The orange star in the overlapping region labels the test case: B = 21 µG, vs = 240 km s ,Mg = 10 M .

Energy [eV] 1 10 100 1000 10000 8 1 Mg = 10 M , vs = 240 km s 30 B = 16 G, s = 2.3 B = 16 G, s = 2.1 B = 21 G, s = 2.0 X-ray 10 13 ] 2

m 20 c ] 1 G s [ g

14 B r 10 9 16

e 10 [ F 10 11

10 13 10 Radio IR/optical 15 10 10 15 1010 1012 1014 1016 5 108 1010 1012 1014 1016 1018 1.9 2.0 2.1 2.2 2.3 2.4 Frequency [Hz] Spectral index s

Figure 5. Left panel shows the spectral energy distribution for NGC 660, extending from the radio band to the X-ray regime. Blue points are radio ﬂuxes at various frequencies and the red points are X-ray data in the energy range 0.2−10 keV. Observations from microwave to UV are illustrated as magenta points in the inset. The gray line is the Planck-function approximation to the IR/optical data. The bulk of the microwave, IR and optical spectrum is due to starlight and dust re-radiation. The ﬁtting areas of radio, UV and X-ray data are shown as the blue, magenta and red areas, respectively. The black, cyan and orange lines are spectra that correspond to the black wedge, cyan circle and orange star in the right panel. In the right panel, the gray and green areas are X-ray and radio constraints on s − B plane. The red area shows the constraints on the magnetic from previous polarization studies, 16 ± 5 µG.

and after the outburst the X-ray flux also increased to don 1978), 4.78 GHz (Bennett et al. 1986), 4.85 GHz +0.19 −13 −3 −1 1.85−0.16 × 10 erg cm s . The origin of the out- (Becker et al. 1991; Gregory & Condon 1991) and 5 burst was investigated in mid-2013 and it might be pro- GHz (Sramek 1975). The red points are X-ray data duced by AGN activities in the galaxy center. In our before the radio burst in the energy range 0.2 − 10 keV, work, we focus on the emissions from the smooth core which are provided by Chandra (Fraternali et al. 2004; region, therefore we use the data recorded before the Liu 2010), XMM-Newton (Brightman & Nandra 2011) outburst. Above all, with the magnetic field estimated and ROSAT (White et al. 2000). Since this source was by Drzazga et al.(2011), the parameters left to be de- observed with short exposure times, the photon count termined are Mg and vs. rates were converted to the X-ray fluxes by assuming a The left panel of Figure5 shows the spectral energy spectral index in the energy range for each red bar in distribution for NGC 660 from radio band to X-ray this figure. More details on the data reductions can be band. Blue points are radio fluxes at 365 MHz (Dou- found in the corresponding references. In our model, the glas et al. 1996), 408 MHz (Large et al. 1981), 1.4 GHz synchrotron spectrum can reproduce the slope of radio (Condon et al. 2002, 1998) 2.38 GHz (Dressel & Con- spectra, which is the primary motivation of our work. Secondary Radio and X-ray Emissions from Galaxy Mergers 7

However as for the X-ray data, the slope is quite uncer- fpp,g in the vs − M plane (magenta dash-dotted lines tain and depends on different observations and models. in Figure4). As we can see, pp interactions are more Therefore in the X-ray band we attempt to explain in- efficient in a region with large gas mass and low shock tegrated fluxes from different observations in the energy velocity vs due to the higher gas density ng and longer range 0.2 − 10 keV. The broadband observations from collision time. When vs decreases to one critical value, microwaves to UV are shows as magenta points in the which is determined by tdyn = tesc, the particle escape inset.1. The gray line shows the approximation to the dominates the interaction time. Therefore, the oblique IR/optical data using Equation 12, with the parameters lines become vertical. 10 AL = 5.15 × 10 Jy, ζL = 3.9, εL = 0.004 eV; AR = Considering the uncertainty of magnetic field, we se- 3.44 Jy, ζR = 1.8, εL = 0.3 eV. To measure the con- lect B = 11 µG, 16 µG and 21 µG as three fiducial sistency between synchrotron spectrum and the obser- values. Figure4 shows the constraints on Mg − vs vations, we set three fitting areas, as shown in the left plane from the radio, UV and the X-ray error toler- panel of Figure5. The blue and red areas correspond to ances (see the blue, magenta and red areas in Figure5). the error tolerances of radio and X-ray data respectively. From these figures, we find that the permissible areas As for the microwave, infrared and UV data points, we in the Mg − vs plane overlap only at higher magnetic need to keep in mind that the dust in the galaxy and star fields, which means that to fit the radio, UV and X-ray forming activities may dominate the emissions in these data simultaneously, a stronger magnetic field is favored. bands. Hence we assume the secondary radiation in the This conclusion is also consistent with the orange line shock region merely contributes to the background and in the left panel of Figure5, which shows the flux pre- use the UV data as the upper limit in our model (see dicted by our model for the test point, the orange star 8 −1 the magenta area). One vexing problem of the UV limit (B = 21 µG,Mg = 10 M , vs = 240 km s ), in is that the dust absorption in the host galaxy cannot be the overlapping region of Figure4. Meanwhile, we find neglected and the photometry correction is model de- that the contributions from SSC and EIC are subdomi- pendent. Hence, in our calculation, we use the UV limit nant comparing with synchrotron emissions in the case just as a reference. of NGC 660. For a lower magnetic field, the tension be- NGC 660 has been identified as a star- tween radio data and X-ray data is inevitable. To fit the forming/starburst galaxy (van Driel et al. 1995), radio data, the synchrotron spectrum will overshoot X- which provides one complementary constraint on the ray flux and UV upper limit. On the other hand, to alle- gas mass once the radius Rg is specified. The gas den- viate the tension, we need to make the synchrotron spec- −2 sity in starburst galaxies can be up to ng ' 100 cm trum higher in the radio regime while keeping the X-ray and thus we conclude that the gas mass in the core flux unchanged. This can be achieved by increasing the 4π 3 region satisfies Mg ∼< 3 µmpngRg, where µ ' 1.24 magnetic field, since the synchrotron spectra converge is the mean molecular weight. The vertical dashed at high energy band (e.g. X-ray) even if we increase the lines and the gray areas in Figure4 illustrate the gas magnetic field. We provide one brief proof here. From density constraint. Another caveat is that a strong Figure2, we see that synchrotron cooling dominate the −1 −1 shock with the Mach number M ∼> 10 is required to electron spectrum (tsyn tesc) when the electron energy produce a power-law electron spectrum with index steady εeQ(εe,t) is high, which means Ne ' Q(εe, t)tsyn = . 2 2 bsyn(εe) s ' 2(M + 1)/(M − 1) ' 2. Observations reveal Combining N steady with Equations6 and 14, we obtain that NGC 660 has the dust temperature and kinetic e temperature around 40 K and 200 K (van Driel et al. Z 1995; Mangum et al. 2013), respectively. Here, we syn P (ω, εe) 4 Fν ∝ εeQ(εe, t)R 0 0 dεe use T ' 10 K as an optimized value since the core P (ω , εe)dω (15) region may contain warm gas and evaluate the lower Z F (X) q γkB T ∝ εeQ(εe, t)R dεe. limit of the shock velocity vs > M which is F (X0)dω0 ∼ µmp shown as the upper horizontal dashed lines and gray areas in Figure4. For illustration purpose, we show At high energy limit,√ the function F (X) has the asymp- −X also the constraint obtained by assuming a relatively totic form F (X) ' 2πXe and the flux no longer lower temperature T = 103 K (the lower dashed lines). depends on the magnetic field. A more physical in- Meanwhile, we include the contours of pp optical depth terpretation is that once B is high enough, the energy of electrons is radiated away through synchrotron fast cooling. In this case, the flux only depends on the elec- 1 A full list of references can be found in the page NED:INDEX tron injection rate. Meanwhile, it’s easy to see that the NGC 660 flux will increase as B increases in a lower energy band (e.g. radio regime) since electrons lose more energy in a 8 Yuan, Murase and Mesz´ aros´ stronger magnetic field. Above all, for a flat CR spec- 0.009364 (Meyer et al. 2004). In a ΛCDM universe −1 −1 trum with the spectral index s ∼ 2, a higher magnetic with Ωm = 0.286 and H0 = 69.6 km s Mpc , the field will keep the X-ray flux unchanged with increasing luminosity distance to us is dL = 40.6 Mpc. It pro- the radio flux and therefore can be used to fit the radio vides a nearby template for studying the properties of and X-ray data simultaneously. merging galaxies. Nearly infrared observations (Skrut- This simple single-zone model meets difficulty explain- skie et al. 2006) reveal that the major axis and minor ing the radio and X-ray observations at the same time axis sizes are a =1.277 arcmin and b =1.251 arcmin with a relatively lower B. This motivates us to exploit respectively. In our calculation,√ we assume an equiv- the chance of improving the fitting by varying the CR alent angular size θg = ab = 1.264 arcmin and the spectral index s in the range 1.8-2.4. As s deviates from corresponding radius R = 14.92 kpc. However, instead 2.0, the normalization coefficient in Equation1 changes of using the galaxy radius, we focus on the core/nucleus 2−s 2−s 2−s to (εmax − εmin )/(2 − s) and a correction factor ε region where collisions occur. Laine et al.(2003) investi- should be applied to the electron spectrum. To demon- gated the morphology of many merging galaxies includ- strate the impact of s and B on the fitting, we select ing NGC 3256 using Hubble Space Telescope WFPC2 8 and fix the gas mass and shock velocity to be 10 M camera and the radius of the core region of NGC 3256 is and 240 km s−1, the orange star in the overlapping re- approximately 3 kpc. In the following calculations, we gion in Figure4. The right panel of Figure5 shows the adopt Rg = 3 kpc. Like NGC 660, Drzazga et al.(2011) constraints in the s − B plane from polarization studies also provided the average magnetic field for NGC 3256, (red area), radio (green area) and X-ray (gray area) ob- which is 25 ± 8 µG. Therefore, in this section we us servations. Firstly, we find that magnetic field almost 17 µG, 25 µG and 33 µG as three fiducial values of the does not influence the X-ray results, which is consistent magnetic field. In the 0.3 − 10 keV band, NGC 3256 with the previous analysis. There exist a cut off around has been observed by ASCA Medium Sensitivity Sur- s = 2.35, beyond which the X-ray flux could be too vey (Ueda et al. 2001), XMM-Newton (Pereira-Santaella low to explain the observations. Secondly, as the index et al. 2011; Jenkins et al. 2004) and ROSAT (Brinkmann s increases, the electron spectrum becomes steeper, or et al. 1994). As for the radio band, we use the data on other words, more low-energy electrons are injected. from broad-band observations in the frequency range 80 Consequently, radio flux got flattened while X-ray flux MHz to 5.0 GHz (Slee 1995; Large et al. 1981; Con- steepened. Therefore, a low magnetic field is required to don et al. 1996; Wright et al. 1994; Whiteoak 1970). counteract radio flux increase and as a result we expect Blue and red points in left panel of Figure6 show the the green area for radio constraint. One straightforward radio and X-ray fluxes respectively. In this figure, we conclusion we can make from this figure is that, a rela- also plot the fluxes from infrared to UV bands as ma- tive larger spectral index can be used to reproduce the genta points 2. The gray line in this figure is our ap- radio and X-ray data simultaneously, e.g. the parallelo- proximation to the IR/optical data with the parameters 10 gram region formed by the green and red areas. To show AL = 6.87 × 10 Jy, ζL = 3.9, εL = 0.004 eV; AR = that explicitly, we select three representative points in 2.06 Jy, ζR = 1.0, εL = 0.7 eV. the s − B plane, e.g. orange star (s = 2.0,B = 21 µG), Using the same procedure for NGC 660, we attempt cyan circle (s = 2.1,B = 16 µG) and black wedge to reproduce the observations of NGC 3256. We find (s = 2.3,B = 16 µG). The corresponding X-ray and that we can fit the radio and X-ray data simultaneously radio fluxes are shown in the left panel of Figure5. Obvi- in the whole magnetic field range 17 µG − 33 µG by ously, from this figure, a moderately larger s in the range using a simple CR spectral index s = 2. The right ∼ 2.1−2.2 with the optimized magnetic field B = 16 µG panel illustrates the constraints from X-ray and radio can provide a good fitting. These indices are also con- observations. The X-ray constraint (yellow area) re- sistent with the observations of starburst galaxies such mains unchanged as consequence that the flux in X- as M82 and NGC 253. ray band is not sensitive to the magnetic field. Radio From the discussions above, we showed that our one- constraints at 17 µG, 25 µG and 33 µG are shown as zone model can be used to explain the radio, UV and blue, green and red areas. Like Figure4, the gray ar- X-ray observations of the NGC 660 core region. Given eas and black dashed lines correspond to the gas den- our model is correct, one can constrain the gas mass sity and strong shock constraints. Using the magnetic Mg, magnetic field B, CR spectral index s and collision field given by polarization studies, our model can ex- velocity vs in that region. plain a significant fraction of X-ray flux. Left panel

3.2. NGC 3256 NGC 3256 is also a galaxy formed by the collision 2 A full list of references can be found in the page NED:INDEX for NGC 3256 of two galaxies and the redshift of NGC 3256 is z ≈ Secondary Radio and X-ray Emissions from Galaxy Mergers 9

Energy [eV] 1 10 100 1000 10000 10 8 103 B = 17 G 2 . 6 B = 25 G 0 . 0 0 . 9 = 1 10 g = , = B = 33 G p g , g f p p , f p p f p 3

10 m

10 c 0 0 1 ]

11 1

10 g n s m

12 k

10 [ Flux [Jy] 2 T = 104 K, 10 s 10 v

10 13

X-ray 10 14 Radio, B = 17 G Radio, B = 25 G T = 103 K, 10 Radio, B = 33 G 10 15 107 109 1011 1013 1015 1017 1019 109 1010 1011 1012 Frequency [Hz] Mg [M ]

Figure 6. Left panel: The spectral energy distribution for NGC 3256. Blue and red points are radio and X-ray fluxes, respectively. The observations from the infrared band to the UV band, which are mainly attributed to dust and starlight, are shown as magenta points. The blue, green and red lines are best-fitting spectra obtained from three selected points in the right panel for different magnetic fields. The dashed and dash-dotted lines correspond to the synchrotron and IC components. The right panel shows the X-ray (yellow area) and radio constraints for the magnetic fields 17 µG (blue area), 25 µG (green area) and 33 µG (red area). The gray areas, black dashed lines and magenta dash-dotted lines have the same meaning with Figure4. shows the spectra of three test points in the right panel, magnetic field 16 µG ∼< B ∼< 21 µG is required, which 10 −1 e.g. blue wedge (17 µG, 10 M , 250 km s ), green is consistent with the uncertainty of the magnetic field 10 −1 circle (25 µG, 10 M , 210 km s ) and red star given by Drzazga et al.(2011). Utilizing 16 µG ∼< B ∼< 10 −1 (33 µG, 10 M , 180 km s ). As anticipated, to fit 21 µG as the fiducial range of magnetic field, we have the radio data, a stronger magnetic field implies a lower found that the permissible ranges for the gas mass and X-ray flux (see the red line). As for NGC 3256, since the shock velocity are constrained to the reasonable ranges 8 11 −1 −1 radius of the nucleus is smaller and the starlight photon 10 M ∼ 10 M and 500 km s ∼ 40 km s , re- 2 density is proportional to (dL/Rg) , the starlight contri- spectively. Moreover, a steeper CR distribution with the bution to EIC is more significant than NGC 660. Mean- spectral index 2.1 ∼< s ∼< 2.2 could be helpful to resolve while, considering that strong magnetic field can also the tensions between radio and X-ray observations. On boost SSC, in this case inverse Compton scattering is the other hand, for NGC 3256, contributions from in- no longer negligible. The dashed lines and dash-dotted verse Compton scattering could be significant since the lines in the left panel of Figure6 show the synchrotron the core region is compact in the sense of photons. With and IC contributions for various magnetic fields. the constraint 17 µG ∼< B ∼< 33 µG, our model with a Above all, our simple one-zone model with s ∼ 2 can hard spectral index s ∼ 2 can explain the radio and X- be used to explain the radio and a large fraction of X- ray data simultaneously. From these two examples, we ray observation and the constraint is in good agreement show that our simple one-zone model can reproduce the with previous magnetic studies. radio and X-ray observations of galaxy merger systems. Considering the complexity and the diversity observed 4. SUMMARY AND DISCUSSION from system to system, each merging galaxy should be In this paper, we have investigated the synchrotron diagnosed independently. We note that since the factor and SSC/EIC emissions from secondary electron- 1 2 2 Mgvs dominates the electron injections, as can be seen positron pairs in merging galaxies and found that these in Equation1, Mg and vs are degenerate in our model. emissions can be used to reproduce the radio and X-ray Despite this, our model provides one useful approach to observations of such systems, as calculated in detail for reproduce the radio and X-ray observations and to study two of the best-studied galaxies formed by galaxy merg- the dynamics of galaxy mergers as well as the physical ers, NGC 660 and NGC 3256. Combining the magnetic parameters of the shock regions. field in the core regions measured through polarization Unavoidably, pp collisions in our model can produce analyses, we showed that our model can be used to con- gamma rays through π0 decays. In the framework of strain the gas mass Mg and shock velocity vs under hadronic process, we estimate the gamma-ray flux from a steady-state approximation for the electron-positron distribution. For NGC 660, in order to alleviate the tensions between the radio and X-ray constraints, a higher 10 Yuan, Murase and Mesz´ aros´

0 π decays ity 0.21 ∼< Lcr,merger/Lcr,SN ∼< 4.15, which indicates that our model can explain a significant part of the gamma- 2 ray observation. εγ Fεγ (εγ ) = εν Fεν (εν )|εγ =2εν 3 Various authors, e.g., Thompson et al.(2007) and (16) 1 −1 2 Lacki et al.(2014), have investigated the contribu- ∼< 2 pC Mgvs . 24πdLtdyn tions from secondary particles (e.g., pions and electrons/positrons) in star-forming/starburst galaxies to As for NGC 660, we have ε F < 1.7 × γ εγ ∼ the MeV-GeV gamma-ray background and found that −13 −1 −2 10 erg s cm while the gamma-ray flux of NGC these sources can describe a significant portion of the 3256 satisfies ε F < 2.9 × 10−13 erg s−1 cm−2. Both γ εγ ∼ extragalactic gamma-ray background. In this paper, our of these fluxes are lower than the flux sensitivities of work has expanded the scope of the applicability of the 3 current gamma-ray detectors, such as F ermi LAT , secondary particle interaction model to galaxy merging H.E.S.S (Holler et al. 2015), MAGIC (Aleksić et al. systems by introducing a phenomenological approach 2016), HAWC (Abeysekara et al. 2017) and VERITAS where CR productions, electron-positron distributions (Park et al. 2015b). In the future, the 50-hour sensitiv- and electromagnetic emissions can be predicted from the ity of the proposed Cherenkov Telescope Array (CTA) basic parameters of the merging regions. This enables −13 −1 −2 in the TeV range can reach ∼ 10 erg s cm us, furthermore, to constrain the gas mass, shock veloc- 4 (Bernlöhret al. 2013) and our model for the merg- ity and magnetic field given that supernova CR lumi- ing galaxies can be further constrained by gamma-ray nosities and star-formation rates are revealed. observations. Since galaxy mergers are also promising sources of Secondary particle interactions can produce observ- high-energy neutrinos, these systems may be detected able emissions not only in interacting galaxy systems by astrophysical neutrino detectors, such as the Ice- but also in star-forming and/or starburst galaxies, where Cube Neutrino Observatory (e.g., Gaisser & Halzen supernovae can accelerate high-energy CRs and trigger 2014; Halzen 2017, for reviews). So far, IceCube has subsequent particle interactions. Previous studies incor- detected the diffuse astrophysical high-energy neutrino 0 porating π decays, bremsstrahlung, inverse Compton background (Aartsen et al. 2013a,b, 2014, 2015), as well and synchrotron emissions have shown that CR inter- as one possible source, blazar TXS 0506+056 (Aart- actions can be used to explain the gamma-ray obser- sen et al. 2018). The physical origin of the bulk of vations of the starburst galaxy M82 (Yoast-Hull et al. these neutrinos is still under debate, but the success 2013), the Cygnus X region (Yoast-Hull et al. 2017b) and of multi-messenger obswervations following IceCube- the ultra-luminous infrared galaxy Arp 220 (Yoast-Hull 170922A show that neutrino astronomy has become an et al. 2017a). Interestingly, for Arp 220 we can esti- important and indispensable part of multi-messenger as- mate the CR luminosity density from a galaxy merger trophysics (Keivani et al. 2018). Our model for high- scenario in the central molecular zone as Lcr,merger ' energy emissions from galaxy mergers connects the elec- −1 3 1 2 R 43 vs −1 pMgv ≈ 9.87 × 10 −1 erg s , tromagnetic emissions from merging regions to the neu- 2 s vs 500km s 8 trino emission and CR acceleration. With the prospects using the gas mass Mg = 6 × 10 M (Sakamoto et al. 2008) and R = 70 pc (Downes & Eckart 2007), for detecting or setting the limits on their high-energy which is roughly twice as much as the best-fitting super- neutrino emission by current and/or next-generation neutrino detectors (Murase & Waxman 2016; Yuan et al. nova CR luminosity Yoast-Hull et al.(2015), Lcr,SNe ' 43 −1 2018), our work will be able to provide a new perspec- Ecr,SNRSN ≈ 4.76 × 10 erg s , for a typical CR en- 50 tive on future multi-messenger studies of the evolution ergy injected by supernovae of Ecr,SN ≈ 10 erg and −1 of galaxies. a supernova rate RSN ≈ 15 yr . This demonstrates that our galaxy merger scenario can fill the gap between the observed gamma-ray flux of Arp 220 and the 2015 We are grateful to Shigeo Kimura and Zhao-Wei gamma-ray prediction from the supernova model (see Zhang for useful discussions. The authors would like to Yoast-Hull et al. 2015, 2017a). Even more conserva- thank the referee for constructive comments and sugges- tively, taking the uncertainty in the supernova CR in- tions. This research was partially supported by NASA 49 51 jection energy 5 × 10 erg ∼

3 The Pass 8 sensitivity: https://www.slac.stanford.edu/ cta-observatory.org/science/cta-performance/ exp/glast/groups/canda/lat_Performance.htm 4 The sensitivity can be also found in http://www. Secondary Radio and X-ray Emissions from Galaxy Mergers 11

REFERENCES

Aartsen, M., Abbasi, R., Abdou, Y., et al. 2013a, Physical Jones, T. W. 2011, Journal of Astrophysics and Astronomy, 32, review letters, 111, 021103 427 —. 2013b, Science, 342, 1242856 Kafexhiu, E., Aharonian, F., Taylor, A. M., & Vila, G. S. 2014, Aartsen, M., Ackermann, M., Adams, J., et al. 2014, Physical Physical Review D, 90, 123014 review letters, 113, 101101 Kashiyama, K., & Mészáros,P. 2014, The Astrophysical Journal Aartsen, M., Abraham, K., Ackermann, M., et al. 2015, The Letters, 790, L14 Astrophysical Journal, 809, 98 Katz, B., & Waxman, E. 2008, Journal of Cosmology and —. 2018, Science, 361, 147 Astroparticle Physics, 2008, 018 Abeysekara, A., Albert, A., Alfaro, R., et al. 2017, The Keeney, B. A., Danforth, C. W., Stocke, J. T., et al. 2006, The Astrophysical Journal, 843, 39 Astrophysical Journal, 646, 951 Aleksić,J., Ansoldi, S., Antonelli, L., et al. 2016, Astroparticle Keivani, A., et al. 2018, Astrophys. J., 864, 84 Physics, 72, 76 Lacki, B. C., Horiuchi, S., & Beacom, J. F. 2014, The Argo, M. K., van Bemmel, I. M., Connolly, S. D., & Beswick, Astrophysical Journal, 786, 40 R. J. 2015, Monthly Notices of the Royal Astronomical Laine, S., Van Der Marel, R. P., Rossa, J., et al. 2003, The Society, 452, 1081 Astronomical Journal, 126, 2717 Becker, R. H., White, R. L., & Edwards, A. L. 1991, The Lamastra, A., Menci, N., Fiore, F., et al. 2017, A&A, 607, A18 Astrophysical Journal Supplement Series, 75, 1 Large, M., Mills, B., Little, A., Crawford, D., & Sutton, J. 1981, Bennett, C., Lawrence, C., Burke, B., Hewitt, J., & Mahoney, J. Monthly Notices of the Royal Astronomical Society, 194, 693 1986, The Astrophysical Journal Supplement Series, 61, 1 Lisenfeld, U., & Voelk, H. J. 2010, Astronomy & Astrophysics, Bernlöhr,K., Barnacka, A., Becherini, Y., et al. 2013, 524, A27 Astroparticle Physics, 43, 171 Liu, J. 2010, The Astrophysical Journal Supplement Series, 192, Blumenthal, G. R., & Gould, R. J. 1970, Reviews of Modern 10 Physics, 42, 237 Liu, R.-Y., Murase, K., Inoue, S., Ge, C., & Wang, X.-Y. 2018, Brightman, M., & Nandra, K. 2011, Monthly Notices of the Astrophys. J., 858, 9 Royal Astronomical Society, 413, 1206 Loeb, A., & Waxman, E. 2006, JCAP, 0605, 003 Brinkmann, W., Siebert, J., & Boller, T. 1994, Astronomy and Mangum, J. G., Darling, J., Henkel, C., et al. 2013, The Astrophysics, 281, 355 Astrophysical Journal, 779, 33 Caprioli, D., & Spitkovsky, A. 2014, The Astrophysical Journal, Meyer, M. J., Zwaan, M. A., Webster, R. L., et al. 2004, 783, 91 Monthly Notices of the Royal Astronomical Society, 350, 1195 Casse, F., Lemoine, M., & Pelletier, G. 2001, Physical Review D, Morlino, G., & Caprioli, D. 2012, Astronomy & Astrophysics, 65, 023002 538, A81 Condon, J., Condon, M. A., Gisler, G., & Puschell, J. 1982, The Murase, K., Ahlers, M., & Lacki, B. C. 2013, Phys. Rev., D88, Astrophysical Journal, 252, 102 121301 Condon, J., Cotton, W., & Broderick, J. 2002, The Astronomical Murase, K., Franckowiak, A., Maeda, K., Margutti, R., & Journal, 124, 675 Beacom, J. F. 2018, arXiv preprint arXiv:1807.01460 Condon, J., Helou, G., Sanders, D., & Soifer, B. 1996, The Murase, K., Toma, K., Yamazaki, R., & Mészáros,P. 2011, The Astrophysical Journal Supplement Series, 103, 81 Astrophysical Journal, 732, 77 Condon, J. J., Cotton, W., Greisen, E., et al. 1998, The Murase, K., & Waxman, E. 2016, Phys. Rev., D94, 103006 Astronomical Journal, 115, 1693 Park, J., Caprioli, D., & Spitkovsky, A. 2015a, Physical review Crocker, R. M. 2012, Monthly Notices of the Royal Astronomical letters, 114, 085003 Society, 423, 3512 Park, N., et al. 2015b, arXiv preprint arXiv:1508.07070 Douglas, J. N., Bash, F. N., Bozyan, F. A., Torrence, G. W., & Pereira-Santaella, M., Alonso-Herrero, A., Santos-Lleo, M., et al. Wolfe, C. 1996, The Astronomical Journal, 111, 1945 2011, Astronomy & Astrophysics, 535, A93 Downes, D., & Eckart, A. 2007, Astronomy & Astrophysics, 468, Sakamoto, K., Wang, J., Wiedner, M. C., et al. 2008, The L57 Astrophysical Journal, 684, 957 Dressel, L., & Condon, J. 1978, The Astrophysical Journal Senno, N., Mészáros,P., Murase, K., Baerwald, P., & Rees, M. J. Supplement Series, 36, 53 2015, The Astrophysical Journal, 806, 24 Drury, L. O. 1983, Reports on Progress in Physics, 46, 973 Skrutskie, M., Cutri, R., Stiening, R., et al. 2006, The Drzazga, R. T., Chy˙zy, K., Jurusik, W., & Wiorkiewicz, K. 2011, Astronomical Journal, 131, 1163 Astronomy & Astrophysics, 533, A22 Slee, O. 1995, Australian Journal of Physics, 48, 143 Filho, M. E., Fraternali, F., Markoff, S., et al. 2004, Astronomy Sramek, R. 1975, The Astronomical Journal, 80, 771 & Astrophysics, 418, 429 Strickland, D. K., & Heckman, T. M. 2009, The Astrophysical Finke, J. D., Razzaque, S., & Dermer, C. D. 2010, The Journal, 697, 2030 Astrophysical Journal, 712, 238 Tamborra, I., Ando, S., & Murase, K. 2014, JCAP, 1409, 043 Fraternali, F., Markoff, S., Nagar, N. M., et al. 2004, Astronomy Thompson, T. A., Quataert, E., & Waxman, E. 2007, The & Astrophysics, 418, 429 Astrophysical Journal, 654, 219 Gaisser, T., & Halzen, F. 2014, Annual Review of Nuclear and Ueda, Y., Ishisaki, Y., Takahashi, T., Makishima, K., & Ohashi, Particle Science, 64, 101 T. 2001, The Astrophysical Journal Supplement Series, 133, 1 Gregory, P., & Condon, J. 1991, The Astrophysical Journal van Driel, W., Combes, F., Casoli, F., et al. 1995, The Supplement Series, 75, 1011 Astronomical Journal, 109, 942 Halzen, F. 2017, Nature Physics, 13, 232 Wang, X., & Loeb, A. 2016, Nature Physics, 12, 1116 Holler, M., Berge, D., van Eldik, C., et al. 2015, arXiv preprint White, N., Giommi, P., & Angelini, L. 2000, VizieR On-line arXiv:1509.02902 Data Catalog: IX/31. Originally published in: Laboratory for Jenkins, L., Roberts, T., Ward, M., & Zezas, A. 2004, Monthly High Energy Astrophysics (LHEA/NASA), Greenbelt Notices of the Royal Astronomical Society, 352, 1335 Whiteoak, J. 1970, Astrophysical Letters, 5, 29 12 Yuan, Murase and Mesz´ aros´

Wright, A. E., Griffith, M. R., Burke, B., & Ekers, R. 1994, The Yoast-Hull, T. M., Gallagher III, J. S., Halzen, F., Kheirandish, Astrophysical Journal Supplement Series, 91, 111 A., & Zweibel, E. G. 2017b, Physical Review D, 96, 043011 Xiao, D., Mszros, P., Murase, K., & Dai, Z.-g. 2016, Astrophys. Yoast-Hull, T. M., Gallagher III, J. S., & Zweibel, E. G. 2015, J., 826, 133 Monthly Notices of the Royal Astronomical Society, 453, 222 Yoast-Hull, T. M., Everett, J. E., Gallagher III, J., & Zweibel, Yuan, C., Mészáros,P., Murase, K., & Jeong, D. 2018, The E. G. 2013, The Astrophysical Journal, 768, 53 Astrophysical Journal, 857, 50 Yoast-Hull, T. M., Gallagher, J. S., Aalto, S., & Varenius, E. 2017a, Monthly Notices of the Royal Astronomical Society: Letters, 469, L89