The multimessenger observations of NGC 1068 dictate the need for multiple emission zones. In this work, we will capture its inner microparsecs referring to a spherically symmetric structure for the corona of the AGN as well as an outer starburst ring with a radius of ∼1 kpc (see Figure 1). Note, that in between these two emission sites NGC 1068 shows strong indications of a jet structure on scales of up to about 1 kpc (e.g., Wilson & Ulvestad 1982; Gallimore et al. 2004, 2006), which however is not included in this work. Due to mathematical convenience we treat both spatial regions as homogeneous. For particle acceleration processes that take place on considerably shorter timescales than the energy loss in these zones, we can disentangle these processes and only describe the steady-state transport of nonthermal, accelerated electrons and protons. Hereby, we suppose that in both zones some acceleration mechanism yields a differential source rate q(T) of relativistic protons and primary electrons that can be described by a power-law distribution in momentum space up to a certain maximal kinetic energy 



Tˆ

, which depends on the competing energy-loss timescales in these zones. In the case of the starburst zone, we suppose that a certain fraction 



fSN

 of the total energy of the SN that releases about 1051 erg and occurs with an approximate rate
5


5
Supposing a SN rate 



νSN≃0.02[SFR/(1M⊙/yr)]yr−1

 (note that Condon1992 suggested a value of 0.04 instead of 0.02 for normal galaxies) where the star formation rate SFR ≃ 17[L
IR/(1011
L
⊙)] M
⊙yr−1. (Veilleux et al. 2005) 



νSN≃0.34[LIR/(1011L⊙)]yr−1

 dependent on the IR luminosity L
IR gets accelerated into CRs according to diffusive shock acceleration (DSA; e.g., Drury 1983; Protheroe 1999) by individual supernova remnants (SNR; e.g., Bell 2014, and references therein). In general, many starburst galaxies—NGC 253 is a prominent example—show a galactic superwind (e.g., Veilleux et al. 2005, and references therein) as a result of a large number of core-collapse SNe. These winds introduce another source of acceleration
6


6
Note that in these phenomena also stochastic diffuse acceleration may become relevant due to the presence of a turbulent plasma within the wind bubbles. (e.g., Anchordoqui et al. 1999; Romero et al. 2018), however, we are not aware of any observational indications of such a superwind in the starburst ring of NGC 1068. For the AGN corona, we suppose that a fraction f
inj ≪ 1 of the mass accretion rate 



Ṁ=Lbol/(ηradc2)

, with a radiation efficiency of η
rad = 0.1 (Kato et al. 2008), goes into relativistic protons via stochastic diffuse acceleration (SDA; e.g., Lemoine & Malkov 2020, and references therein). For both zones, the nonthermal primary electrons are normalized by the nonthermal proton rates due to the requested quasi-neutral total charge number of the injection spectra of primary CRs above a characteristic kinetic energy of 



Tˇ≃10keV

 (Schlickeiser 2002; Eichmann & Becker Tjus2016; Merten et al. 2017). Note that this corresponds to a quasi-neutral acceleration site; however, CR transport can subsequently remove CR electrons and protons in different amounts from the nonthermal energy regime. Nevertheless their charge stays conserved. Transforming the source rates from momentum space into kinetic energy T, we obtain
1



qp(T)≡dNdVdTdt=qp,0Tˇ2+2TˇEp,0×T+Ep,0T2+2TEp,0T2+2TEp,0Tˇ2+2TˇEp,0−s/2exp[−T/Tˆ],

for the injected nonthermal protons, and
2



qe±(T)=qe−,0Tˇ2+2TˇEe,0T+Ee,0T2+2TEe,0×T2+2TEe,0Tˇ2+2TˇEe,0−s/2exp[−T/Tˆ]+qe±2nd(T),

for the nonthermal electrons (e
−) and positrons (e
+). Here, the latter term 



qe±2nd(T)

 introduces the source rate of secondary electrons and positrons that are generated by hadronic interaction processes, as discussed in the following. Thus, the steady-state behavior of the differential nonthermal electron and proton density n(T) in the AGN corona and the starburst zone, respectively, can be approximated by
3



−∂∂TTn(T)τcool(T)=q(T)−n(T)τesc(T).

Here, τ

cool
 refers to the total continuous energy-loss timescale, which in the case of the relativistic electrons is given by the inverse of the sum of the synchrotron (syn), inverse Compton (IC), nonthermal Bremsstrahlung (brems), and Coulomb (C) loss rates, according to
4



τcool(e)=[τsyn(e)−1+τic−1+τbrems−1+τC(e)−1]−1,

and in the case of the relativistic protons we use
5



τcool(p)=[τsyn(p)−1+τC(p)−1+τpγπ−1+τBH−1+τpp−1]−1,

including the photopion (π), Bethe–Heitler pairs (BH), and hadronic pion (pp) production loss rates. Proton synchrotron losses—as well as the associated radiation—are negligible for the considered environments. Note that these processes require additional information on the associated interaction medium, which is one of the following targets:(i)A magnetic field, which is assumed to be uniform on small scales (with respect to the particles’ gyro radius) and randomly oriented on significantly larger scales (due to isotropic Alfvénic turbulence).(ii)A photon target, which is in the case of the starburst zone dominated by the thermal IR emission due to the rescattered starlight by dust grains with a temperature θ
dust and can be described by an isotropic, diluted modified blackbody radiation field
6



nIR(E)=Cdilπ2ℏc3E2exp(E/(kBθdust))−1EE0,

where the dust clouds become optically thick above a critical energy E
0 = 8.2 meV (Yun & Carilli 2002). The constant dilution factor C

dil
 is determined from the observed IR luminosity L
IR according to the relation 



LIR/(πRstr2c)=∫dEEnIR(E)

.
7


7
A more accurate approach to the IR photon spectrum has been proposed by Casey (2012), where a coupled modified greybody plus a mid-infrared power law has been used, but these modifications have no impact on our results. In case of the coronal region we used a parametrized model (Ho 2008) above 1 eV that accounts for the optical and UV emission by the disk as well as the Comptonized X-ray emission by hot thermal electrons in the corona. Hereby, the parameterization depends on the Eddington ratio (L
bol/L
Edd), i.e., the ratio of the bolometric over the Eddington luminosity, and we adopt the relation of Hopkins et al. (2007) to determine L
bol based on the intrinsic X-ray luminosity L
X between (2 and 10)keV.(iii)A thermal gas target with a given temperature θ, which is due to mathematical convenience assumed to be homogeneously distributed in both regions. For the starburst ring, Spinoglio et al. (2012) determine θ = 127 K, a gas density of n(H2) = 102.9 cm−3, and a molecular hydrogen mass of M(H2) ∼ 3.5 × 108
M
⊙.More details on the individual energy-loss timescales can be found in Appendix A.
Citation: Protheroe 1999
Citation function: Uses