Preprint typeset using LATEX style AASTeX6 v. 1.0 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 & M´esz´aros 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 approxi- mately 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 emit- ting 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 pri- mary 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 " Ne(") = " = pC Mgv and use our model to reproduce the radio, UV and X-ray 3 d" 12 s (1) fluxes. We also apply our model to constrain the shock × min [1; f ] ; pp;g "p'20" 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("p;max="p;min) is the normal- −2 to other similar systems, we also consider another well- ization coefficient for a " 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("p) min[tesc; tdyn] is pp optical This paper is organized as follows. In x2, 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 x3 , we is the dynamic time of the merger and σ("p) is the pp apply the formalism in x2 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 x4. galaxies lead to a dense core region. Particles are accel- erated 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 " = " j" =2" : γ d"γ 3 ν d"ν 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 " Ne ("e) = 2" j"γ =2"e = " j"ν ="e ;"e > "γγ =2: d"γ 3 d"ν −1 −1 −1 rate and advection rate, e.g.