ABSTRACT

NGC 253 is a nearby starburst galaxy in the Sculptor group located at a distance of ∼3.5 Mpc that has been suggested by some authors as a potential site for cosmic ray acceleration up to ultrahigh energies. Its nuclear region is heavily obscured by gas and dust, which prevents establishing whether or not the galaxy harbours a supermassive black hole coexisting with the starburst. Some sources have been proposed in the literature as candidates for an active nucleus. In this work, we aim at determining the implications that the presence of a supermassive black hole at the nucleus of NGC 253 might have on cosmic ray acceleration. With this aim, we model the accretion flow on to the putative active nucleus, and we evaluate the feasibility of particle acceleration by the black hole dynamo mechanism. As a by-product, we explore the potential contribution from non-thermal particles in the accretion flow to the high-energy emission of the galaxy. We found that in the three most plausible nucleus candidates, the emission of the accretion flow would inhibit the black hole dynamo mechanism. To rule out completely the influence that a putative nucleus in NGC 253 might have in cosmic ray acceleration, a better clarification concerning the true nature of the nucleus is needed.

1 INTRODUCTION

Starburst galaxies are characterized by an ongoing enhanced rate of star formation that results in the existence of a large number of hot, massive stars and stellar remnants concentrated into a small region. The many supernova remnants in this region give rise to a high density of locally accelerated cosmic rays that produce non-thermal electromagnetic radiation from radio up to gamma-rays (e.g. Paglione et al. 1996; Bykov 2001; Romero & Torres 2003; Domingo-Santamaría & Torres 2005; Rephaeli, Arieli & Persic 2010). The two nearest starburst galaxies, NGC 253 and M82, have been both detected in the high-energy and the very high energy gamma-ray bands (Acero et al. 2009; Abdo et al. 2010a; Ackermann et al. 2012) confirming the early theoretical predictions. The gamma-ray emission is usually interpreted as the effect of cosmic ray interactions with the dense gas of the disc, although a large-scale contribution from the galactic superwind might also be present (Romero, Müller & Roth 2018).

The existence of a superwind caused by the collective effects of stars and supernovae in starburst galaxies was suggested long ago by Chevalier & Clegg (1985). Today, the presence of a superwind can be directly established by line and continuum observations in nearby galaxies such as NGC 253 (see e.g. Veilleux, Cecil & Bland-Hawthorn 2005, and references therein). The reverse shock of these superwinds has been proposed as a possible site for the acceleration of cosmic rays up to ultrahigh energies (Anchordoqui, Romero & Combi 1999; Anchordoqui 2018). The idea is attractive because the large size of the acceleration region can easily satisfy the Hillas criterion and radiative losses in the tenuous medium of the galactic halo are not as significant as they are in the disc. Moreover, investigations on the composition of the cosmic rays at the end of the spectrum (e.g. Aab et al. 2017) seem to show a trend towards heavy elements in accordance with the predictions of Anchordoqui et al. (1999). Recent results obtained by the Pierre Auger Observatory also suggest a marginally significant excess of events in the direction of some starburst galaxies (Aab et al. 2018). However, Romero et al. (2018) have investigated the case of NGC 253 using the new available information on the wind and its mass load obtained with the help of ALMA observatory (Bolatto et al. 2013) along with radio and X-ray observations and concluded that even under the most optimistic assumptions the superwind of this starburst cannot accelerate cosmic rays beyond energies of ∼1016 eV for protons and ∼4 × 1017 eV for iron nuclei. These results are in accordance with independent estimates by Bustard, Zweibel & Cotter (2017). Acceleration up to 100 EeV would require completely unrealistic magnetic fields outside this galaxy. In light of such a situation, Romero et al. (2018) suggested that ultrahigh-energy cosmic ray (UHECR) acceleration in NGC 253 would still be possible if it is achieved by compact objects, either in a starved supermassive black hole at the galactic centre or in young pulsars in the disc.

In this paper, we shall explore the first of these possibilities, namely we investigate the feasibility of cosmic ray acceleration up to extreme energies in a putative hidden low-luminosity active galactic nucleus (LLAGN) of NGC 253. With such an aim, we shall model the typical environment of such a nucleus. This involves a hot accretion flow that supplies matter to the vicinity of the central black hole and a magnetosphere where particles can be accelerated under certain conditions. As a by-product, we shall estimate the gamma-ray contribution of the AGN to the overall high-energy radiation emitted by the galaxy.

The structure of the paper is as follows. In Section 2, we summarize the main characteristics of the sources in the central region of NGC 253 that have been proposed to harbour a supermassive black hole. In Section 3, we summarize the main characteristics of the accretion model we assume for these sources. In Section 4, we describe the black hole dynamo mechanism and the conditions under which it is able to accelerate cosmic rays to very high energies. In Section 5, we apply the accretion flow model to the different nucleus candidates and probe the black hole dynamo mechanism. In Section 6, we discuss the implication of these results in the context of cosmic rays and gamma-rays. We end the article presenting a summary in Section 7.

2 THE NEARBY STARBURST NGC 253 AND ITS CENTRAL REGION

NGC 253 is a nearby edge-on starburst galaxy located in the Sculptor group (α ∼ 00h47m, δ ∼ −25°17′) at a distance of 3.5 ± 0.2 Mpc (Rekola et al. 2005). Along with M82, NGC 253 is the best-studied starburst galaxy, and it has been detected at all wavelengths, from radio to high-energy gamma-rays. The starburst of NGC 253 is believed to be fed by a 6 kpc bar that funnels gas into the nucleus (Engelbracht et al. 1998). A high number of neighbouring galaxies contain both starbursts and AGNs, and it is not clear what is the physical connection between them (Levenson, Weaver & Heckman 2001). In the case of NGC 253, it is unknown whether an AGN coexists with the starburst or not. The physical properties and the nature of its nucleus are far from clear and have been discussed in the literature for many years. The central region of the galaxy is heavily obscured by gas and dust, and the effects of strong stellar winds affect kinematic studies. Historically, the most plausible nucleus candidate considered was the strongest compact radio source in the central region (21 mJy at 1.3 cm), named TH2 after Turner & Ho (1985). However, later studies did not find any counterpart in the infrared (IR), optical, or X-rays for this source. This lack of detection at other wavelengths led Fernández-Ontiveros, Prieto & Acosta-Pulido (2009) to state that if TH2 holds a black hole, it has to be in a dormant state; they proposed that it could be a scaled-up version of Sgr A*.

Another galactic nucleus candidate proposed in the literature is the strong hard X-ray source X-1 (Weaver et al. 2002). Chandra observations show that this source is heavily absorbed (NH = 7.5 × 1023 cm−2) and presents a very low F0.5–2 keV/F2–10 keV ratio (∼10−3). Based on this, Müller-Sánchez et al. (2010) hypothesized that this source might be a hidden LLAGN, similar to, but weaker than, the one found in NGC 4945 (Marconi et al. 2000). They estimated an intrinsic 2–10 keV luminosity of ∼1040 erg s−1.

Recently, based on near-IR observations, Günthardt et al. (2015) proposed a third nucleus candidate: the IR peak known as IRC. This source is coincident with the radio source TH7 (Ulvestad & Antonucci 1997), with the second strongest X-ray source, X-2, and with a massive star cluster of 1.4 × 107 M. They proposed that such a cluster can hide a ∼106 M black hole.

Whichever of these sources is the true galactic nucleus, the corresponding black hole must be in a low-activity state and hence it would be powered by a radiatively inefficient accretion flow (RIAF; see Yuan & Narayan 2014, for a recent review). In what follows, we shall assume this LLAGN scenario and we shall investigate the potential impact of the presence of a starved central black hole on cosmic ray acceleration and gamma-ray production in NGC 253.

3 ACCRETION FLOW MODEL

We assume that the accretion flow around the supermassive black hole is in the form of an RIAF. We follow the standard semi-analytical modelling of these systems in the quiescent state. The standard model considers a steady axisymmetric hot, geometrically thick, optically thin, two-temperature flow with a low radiative efficiency (Narayan, Barret & McClintock 1997; Yuan et al. 2000). It is also well established that RIAFs present strong magnetocentrifugal-driven winds (Narayan & Yi 1995; Stone, Pringle & Begelman 1999; Yuan, Bu & Wu 2012). To take into account the mass-loss of this wind, we follow Blandford & Begelman (1999) and make the accretion rate to depend on the radius via the parameter s as
(1)
where Rout and |$\dot{M}_{\rm out}$| are the outer radius of the flow and the outer accretion rate, respectively. Both numerical simulations (Stone et al. 1999; Yuan et al. 2012) and observational studies (Quataert & Gruzinov 2000; Wang et al. 2013) suggest that 0.1 ≲ s ≲ 1. The original works on radiatively inefficient advection-dominated accretion flows (ADAFs) considered δ, the energy released by turbulence that directly heats electrons, to be small (δ ∼ 10−3; Narayan & Yi 1995), but later works argued that this parameter is much higher, more likely lying in the range 0.1 ≲ δ ≲ 0.5 (e.g. Quataert & Gruzinov 1999; Sharma, Quataert & Stone 2007). The other parameters that determine the hydrodynamic structure of the flow are the viscosity parameter α, the gas pressure to magnetic pressure ratio β, and the black hole mass MBH. Given the poor observational constraints on the sources, we conservatively adopt standard values for most of the parameters, namely α = 0.1, β = 1 (equipartition), δ = 0.1, and s = 0.3. We allow the black hole mass to vary between 106 and 107 solar masses, and we adjust the accretion rate to fit the observational data. Given the parameters above, obtaining the global hydrodynamical solution is a two-point boundary value problem. We solve the equations numerically using the shooting method with appropriate boundary conditions, as outlined in Yuan et al. (2000). The flow extends from the Schwarzschild radius Rschw up to Rout = 104 Rschw, where the temperatures of ions and electrons are Tout,i = 0.2Tvir and Tout,e = 0.19Tvir, respectively, and the Mach number is λ ≡ v/cs = 0.2; the virial temperature is given by Tvir = 3.6 × 1012(Rschw/R) K. Once we obtain the density, pressure, magnetic field, and velocity of the flow, and the temperatures of both electrons and ions at each radius, we calculate the spectrum of the emission solving the radiative transfer equation via the ‘plane-parallel rays’ method with boundary conditions for a non-illuminated atmosphere (Mihalas 1978; see Özel, Psaltis & Narayan 2000; Yuan, Quataert & Narayan 2003, for more details). The emission processes considered for the thermal electrons are synchrotron emission, bremsstrahlung (free–free) radiation, and inverse Compton upscattering of the seed photons produced by those two processes.

3.1 Jet component

We also allow the possibility that a small fraction of the matter that reaches the black hole is launched into a collimated outflow. We consider a simple one-zone leptonic model in which the jet starts magnetically dominated and at some distance from the hole develops internal shocks. A fraction qrel < 1 of the jet power goes to non-thermal electrons, which emit synchrotron radiation (for more details, see e.g. Bosch-Ramon, Romero & Paredes 2006; Vila & Romero 2010). Following the ‘disc–jet symbiosis’ hypothesis of Falcke & Biermann (1995) (see also Körding, Fender & Migliari 2006), the total power of the jet is a fraction of the accretion power,
(2)
where qjet < 1. The other parameters of the model are the jet bulk Lorentz factor Γjet, the viewing angle i, the distance from the black hole to the base of the acceleration region zacc, the opening angle of the jet θjet, the minimum Lorentz factor of the non-thermal leptons γmin, and the particle spectral index α. We choose standard values used for AGNs (see e.g. Spada et al. 2001): Γjet = 2.3, θjet = 0.1 rad, |$i=30\deg$|⁠, and γmin = 2.0, and we adjust the remaining parameters to fit the data when required.

4 ACCELERATION BY THE BLACK HOLE DYNAMO MECHANISM

General relativity magnetohydrodynamic simulations of accretion flows around rotating black holes show that a magnetically dominated funnel forms above the polar region of the black hole. Provided the force-free condition is fulfilled in this region, the rotational energy of the black hole can be extracted as an outwards Poynting flux via the Blandford–Znajek (BZ) mechanism (Blandford & Znajek 1977). The initial poloidal field lines are twisted in the ergosphere of the black hole and develop a toroidal component. Plasma with negative energy falls into the hole decreasing its energy and a magnetically dominated flux is evacuated along the rotation axis. The total power of this flux is |$L_{\rm BZ}\sim c (B^2/8\pi) \pi r_{\rm g}^2 \propto B^2 r_{\rm g}^2$|⁠, where rg = GM/c2 is the gravitational radius of the black hole. In convenient units and introducing the black hole spin parameter a*, this can be written as
(3)

Since the plasma of the accretion flows cannot enter into the funnel because of the magnetocentrifugal barrier, another mechanism must be responsible for providing the charge density required for a force-free plasma, namely the Goldreich––Julian charge density ρGJ (Goldreich & Julian 1969). One possibility to fill the magnetosphere is that MeV photons produced in the accretion flow collide between themselves and decay into electron–positron pairs in the funnel. However, if the luminosity of the disc is too low, as is the case in RIAFs, the number of MeV photons could not be high enough to provide the magnetosphere with the Goldreich–Julian charge density. This lack of charges in some regions of the magnetosphere allows the formation of an unscreened electrostatic potential gap. The formation of this gap is located more likely near the region where ρGJ ∼ 0 (see Fig. 1).

Goldreich–Julian charge density colour map for a black hole magnetosphere under the split-monopole magnetic field configuration. The green line shows the black hole event horizon and the cyan line shows the surface where ρGJ = 0 (see, e.g., Ptitsyna & Neronov (2016)). The plot is only schematic and the colour map scale is arbitrary.
Figure 1.

Goldreich–Julian charge density colour map for a black hole magnetosphere under the split-monopole magnetic field configuration. The green line shows the black hole event horizon and the cyan line shows the surface where ρGJ = 0 (see, e.g., Ptitsyna & Neronov (2016)). The plot is only schematic and the colour map scale is arbitrary.

For a nearly maximally rotating black hole, the potential drop in the gap can be estimated as
(4)
where M6 = M/106 M, B4 = B/104 G, h is the gap height, and rg is the gravitational radius as before (Znajek 1978; Levinson 2000). The magnetic field is expected to be in equipartition with the accreting matter (Boldt & Ghosh 1999). This assumption leads to
(5)
where |$\dot{m}$| is the accretion rate at the horizon in Eddington units.
Thus, in principle, a charged nucleus of atomic number Z entering into the gap can be accelerated up to very high energies,
(6)
A strong limiting condition for this acceleration mechanism is that the gap height must be of the order of rg for the process to be efficient. If electrons or positrons are also accelerated in the gap, they may close the gap or limit its extension via the emission of gamma-rays through inverse Compton with a background photon field. These gamma-rays would collide with the same soft photon field giving rise to electron–positron pairs, which in turn emit more gamma-rays. If this process is efficient enough, an electromagnetic cascade develops and the pairs created screen the electrostatic potential drop, thus inhibiting the acceleration. To account for the possibility of gap closure, we impose the condition that the multiplicity of pairs |$\mathcal {M}$| (number of pairs created per lepton) should not be larger than 1 (Hirotani & Pu 2016).
The equation that governs the energy evolution of a lepton in the gap is
(7)
where the first term on the right-hand side accounts for the acceleration, and the second and third terms are the energy losses by inverse Compton and curvature radiation, respectively. The curvature losses depend on the curvature radius, which we choose as Rcrg (Ford, Keenan & Medvedev 2018). For an electron of energy E, the number of pairs created via the inverse Compton process is
(8)
where
(9)
and
(10)
In equations (9) and (10), dNIC/dt dεγ is the inverse Compton emissivity (e.g. Blumenthal & Gould 1970), σγγγ, εph) is the photo-pair creation cross-section (Aharonian, Atoyan & Nagapetyan 1983), and nphph) is the spectral density of external soft photons in the gap. In our scenarios, this photon field is provided by the emission of the RIAF1 (see Section 3). We locate the inner gap boundary at zgap = 2rg (Ford et al. 2018) and assume homogeneity along its extension. Then, we obtain iteratively h in each scenario by solving equations (7) and (8) imposing the gap closure condition |$\mathcal {M}_{\rm IC}=1$|⁠.2

5 APPLICATION TO NGC 253

5.1 Accretion flow

We shall model now the physical scenario around the different black hole candidates in order to investigate the particle acceleration by the black hole dynamo mechanism. The uncertainties about the nature of the emission in these objects are important. We apply the hot accretion flow model assuming that the emission observed is powered by the black hole. This could not be the case, of course, and this does not rule out the possibility that one of these sources harbours a dormant black hole not responsible for the emission. The values adopted for the different parameters are shown in Table 1.

Table 1.

Parameters of the hot accretion flow and the jet (when necessary) for the galactic nucleus candidates.

Accretion flowJet
 SourceMBH (106 M)|$\dot{M}_{\rm acc}$||$(\dot{M}_{\rm Edd})$|qjetαzacc (RS)
TH2101.1 × 10−4|$10 \%$|2.8100
X-111.5 × 10−2
IRC/TH7/X-212.5 × 10−3|$8 \%$|2.3104
Accretion flowJet
 SourceMBH (106 M)|$\dot{M}_{\rm acc}$||$(\dot{M}_{\rm Edd})$|qjetαzacc (RS)
TH2101.1 × 10−4|$10 \%$|2.8100
X-111.5 × 10−2
IRC/TH7/X-212.5 × 10−3|$8 \%$|2.3104
Table 1.

Parameters of the hot accretion flow and the jet (when necessary) for the galactic nucleus candidates.

Accretion flowJet
 SourceMBH (106 M)|$\dot{M}_{\rm acc}$||$(\dot{M}_{\rm Edd})$|qjetαzacc (RS)
TH2101.1 × 10−4|$10 \%$|2.8100
X-111.5 × 10−2
IRC/TH7/X-212.5 × 10−3|$8 \%$|2.3104
Accretion flowJet
 SourceMBH (106 M)|$\dot{M}_{\rm acc}$||$(\dot{M}_{\rm Edd})$|qjetαzacc (RS)
TH2101.1 × 10−4|$10 \%$|2.8100
X-111.5 × 10−2
IRC/TH7/X-212.5 × 10−3|$8 \%$|2.3104

5.1.1 TH2

Despite TH2 being the strongest compact radio source in the nuclear region of NGC 253, it has no counterpart at other wavelengths. Hence, if this source corresponds to a supermassive black hole, this has to be accreting at very low rates. Given this starvation, we propose that the accretion flow on to the black hole is an RIAF similar to the one in Sgr A* (Narayan et al. 1998; Yuan et al. 2003) but with a higher mass. Fernández-Ontiveros et al. (2009) estimated a mass of ≈7 × 106 M; given the uncertainties, we adopt MBH = 107 M. The thermal synchrotron emission of an RIAF around a supermassive black hole of this mass has its peak at submillimetre wavelengths and cannot be responsible for the detected centimetre flux. This emission, however, can be reproduced with the additional assumption that a weak jet is also present (see Section 3.1). We take |$q_{\rm jet}=10{{\ \rm per\ cent}}$|⁠, a spectral index for the non-thermal distribution in the jet of α = 2.8, and an outer accretion rate for the accretion flow of |$\dot{M}_{\rm out}=1.1\times 10^{-4} \dot{M}_{\rm Edd}$|⁠. We assume that the acceleration of particles takes place at a distance of zacc ≈ 100rg from the black hole horizon. Fig. 2 shows the spectral energy distribution (SED) of the RIAF + jet model that yields the best fit of the data. Though the RIAF emission is not seen, the jet power is linked to that of the accretion flow.

SED of the hot accretion flow for the source TH2. The radio data are from Ulvestad & Antonucci (1997), and the IR background limits are from Fernández-Ontiveros et al. (2009).
Figure 2.

SED of the hot accretion flow for the source TH2. The radio data are from Ulvestad & Antonucci (1997), and the IR background limits are from Fernández-Ontiveros et al. (2009).

5.1.2 X-1

X-1 is a strong hard X-ray source in the nucleus of NGC 253. Early studies considered it to be the X-ray counterpart of TH2, thus reinforcing the AGN nature of the latter (Weaver et al. 2002), but further reprocessing of the Chandra data by Müller-Sánchez et al. (2010) demonstrated that both sources are not associated with each other, being separated by ∼1 arcsec. Moreover, X-1 has no counterpart at other wavelengths, and it is only detected at energies >2 keV. Müller-Sánchez et al. (2010) stated that if X-1 is the true galactic nucleus, the simplest explanation is that it is a hidden LLAGN. Hidden AGNs are characterized by extremely high obscuration up to mid-IR wavelengths, and they do not fit in the standard unified AGN model (Antonucci 1993). The prototype of this class of AGN is the Seyfert 2 galaxy NGC 4945 (Marconi et al. 2000). Müller-Sánchez et al. (2010) estimated the intrinsic luminosity of X-1 in the 2–10 keV band to be ∼1040 erg s−1. In 2013, simultaneous Chandra and NuSTAR observations of the central region of NGC 253 did not detect emission at the X-1 position (Lehmer et al. 2013). This fact plus the upper limit imposed by NuSTAR (L10–40 keV ≲ 0.3 × 1039 erg s−1) seem to disfavour the AGN hypothesis. Lehmer et al. (2013) suggested that if this source is a hidden AGN, it was in a low-activity state during the 2013 observing campaign. Adopting this assumption, we model the emission of X-1 as an RIAF with a mass of M ≈ 106 M and an outer accretion rate of |$\approx \! 1.5\times 10^{-2} \dot{M}_{\rm Edd}$|⁠. Fig. 3 shows the SED of the RIAF.

SED of the hot accretion flow for the source X-1. The X-ray data point is from Müller-Sánchez et al. (2010).
Figure 3.

SED of the hot accretion flow for the source X-1. The X-ray data point is from Müller-Sánchez et al. (2010).

5.1.3 IRC/TH7/X-2

IRC is the brightest near-IR and mid-IR source, as well as the most powerful soft X-ray source in the central region of NGC 253 (the source is dubbed X-2 in Müller-Sánchez et al. 2010). It has a radio counterpart (TH7 in Ulvestad & Antonucci 1997), and it is coincident with a superstellar cluster (SSC) of ∼107 M. Günthardt et al. (2015) presented evidence suggesting that this source could be the true galactic nucleus and that in this case the SSC might harbour a ≈106 M low-luminosity accreting black hole. The luminosity in the Chandra band is ∼1038 erg s−1 (Müller-Sánchez et al. 2010) and can be reproduced by an RIAF with a black hole mass of 106 M and an outer accretion rate of |$\dot{M}_{\rm out}\approx 2.5 \times 10^{-3}~ \dot{M}_{\rm Edd}$|⁠. Given the flatness of the radio emission, Sν ∼ ν−0.8, the region in the jet that produces it should be located far from the black hole. We fit these data with a phenomenological jet model with zacc ≈ 2 × 104rg, α = 2.3, and |$q_{\rm jet}=8{{\ \rm per\ cent}}$|⁠. Fig. 4 shows the SED for the RIAF + jet model. The IR luminosity of the source is very high (≳1042 erg s−1 at the Ks band) and it is very likely produced by the heated dust in the SSC and not related to the AGN; hence, it is not shown in Fig. 4.

SED for the accretion flow in IRC. The radio data are from Ulvestad & Antonucci (1997), the 2–10 keV data are from Müller-Sánchez et al. (2010), and the NuSTAR upper limits are from Lehmer et al. (2013).
Figure 4.

SED for the accretion flow in IRC. The radio data are from Ulvestad & Antonucci (1997), the 2–10 keV data are from Müller-Sánchez et al. (2010), and the NuSTAR upper limits are from Lehmer et al. (2013).

5.2 Electrostatic gaps

To probe the potential of the black hole dynamo mechanism to accelerate cosmic rays in this scenario, we must take into account the influence of the RIAF photon field on the gap extension. We impose the condition that an electron injected in the gap does not trigger an exponential growth of pairs via the emission of gamma-rays (see Section 4). We take into account inverse Compton and curvature losses that limit the maximum energy of the leptons. From the sources considered, we find that even for the low-luminosity RIAF considered for TH2 the gap height is heavily reduced: h ≈ 0.01rg. For a magnetic field B ≈ 600 G as there is in its innermost region, the maximum energy that a charged nucleus can achieve is
(11)

For cosmic rays to be accelerated to higher energies in the electrostatic gap, a lower RIAF luminosity is required. Despite the shape of the spectrum changes as the luminosity of the RIAF increases or decreases, at low accretion rates the most relevant seed photons are those of the submillimetre peak. Hence, to study how the gap height is affected by the background radiation it is a good approximation to take the photon spectrum from the RIAF in TH2 and scale it to different situations. In Fig. 5, we show the dependence of the gap height with the intensity of the background photon field parametrized by f such that the photon density is |$n_{\rm ph} = f n_{\rm ph}^{\rm (TH2)}$|⁠. The little bump in the plot is related to the change from the Thomson regime to the Klein–Nishina regime in the inverse Compton emission of the electron. We see that for the gap height to be ∼1 a photon density approximately two orders of magnitude lower would be required. In the case of TH2, it could be in principle that such a fainter accretion flow is present but, since the emission of the jet is linked to that of the RIAF by the jet–disc symbiosis, the jet power should be much higher than |$10{{\ \rm per\,cent}}$| of the accretion power or its emission should be strongly beamed, which is not expected in this scenario. We conclude that if TH2 harbours a starved black hole that is powering the radio emission, the potential of the black hole dynamo mechanism to accelerate cosmic rays in this source is heavily limited because of the emission of the accretion flow. The RIAFs we considered for X-1 and IRC are both quite brighter than the one in TH2. So, if any of these sources is related to the true active nucleus, the gap would be even shorter and the acceleration less efficient. This rules out the putative LLAGN as a viable alternative for UHECR acceleration in NGC 253.

Gap height as a function of the parameter f that parametrizes the photon density, $n_{\rm ph} = f n_{\rm ph}^{\rm (TH2)}$, for different values of the magnetic field intensity. The dotted red line shows the location in the plot of the parameters for the source TH2 (see Table 1).
Figure 5.

Gap height as a function of the parameter f that parametrizes the photon density, |$n_{\rm ph} = f n_{\rm ph}^{\rm (TH2)}$|⁠, for different values of the magnetic field intensity. The dotted red line shows the location in the plot of the parameters for the source TH2 (see Table 1).

There is still an open window for an extremely dormant black hole, either coincident with these sources or not, which cannot be completely ruled out until the true nature of the galactic nucleus in NGC 253 is clarified.

6 DISCUSSION

6.1 Cosmic rays

The presence of a hidden AGN in NGC 253 cannot explain the origin of UHECRs in this source. According to equation (11), the maximum energy attainable by iron nuclei entering into the electrostatic gap of the black hole magnetosphere would be ∼2 × 1015 eV. This is even less than what Romero et al. (2018) estimated for particle acceleration in the superwind. If NGC 253 and other starbursts are confirmed as sources of UHECRs of high metallicity, then the cosmic rays should probably be originated in compact objects located in the star-forming region. Among the candidates we can mention engine-driven supernovae (Zhang & Murase 2019), a recent tidal disruption event (Guépin et al. 2018), magnetars (Singh, Ma & Arons 2004), and gamma-ray bursts (Waxman 2006).

6.2 Different contributions to gamma-rays

NGC 253 has been detected at high-energy gamma-rays by the LAT instrument onboard of the Fermi satellite (Abdo et al. 2010b) and at very high energies by HESS (Acero et al. 2009). The overall gamma-ray emission is analysed by Abramowski et al. (2012). At a distance of 3.5 Mpc, the integrated flux above 200 MeV yields a luminosity of L(E > 200 MeV) ∼ 7.8 × 1039 erg s−1. The high-energy spectrum is well fitted as a power law of index Γ = 2.24 ± 0.14stat ± 0.03sys. The very high energy spectrum observed by HESS is also a power law with a similar index of Γ = 2.14 ± 0.18stat ± 0.30sys. Both spectra are compatible with an overall spectrum fitted by a power law of index Γ = 2.34 ± 0.03. However, a slight break cannot be ruled out with a lightly harder spectrum at higher energies.

The observations with the best resolution in gamma-rays are those of HESS. The detection is consistent with the galactic centre and with a source whose extension is of less than 2.4 arcmin at 3σ confidence level (Abramowski et al. 2012). Since the extension of the starburst region is ∼0.4 arcmin × 1.0 arcmin, there is some room for contributions from the base of the superwind as suggested by Romero et al. (2018). GeV gamma-rays might also be produced in the superwind, but Fermi resolution does not allow to disentangle this radiation if present. On the other hand, the observed IR–radio correlation of star-forming galaxies has led to the idea that cosmic ray electrons accelerated by supernovae are responsible for the radio emission of these sources. In addition, cosmic ray protons produced also by supernovae might be responsible for the gamma-ray emission through inelastic collisions with ambient gas (Anchordoqui et al. 1999; Domingo-Santamaría & Torres 2005; Rephaeli et al. 2010; Paglione & Abrahams 2012; Yoast-Hull et al. 2013). Other sources of locally accelerated protons, such as the stellar winds of massive stars, might also contribute to the overall gamma-ray luminosity (e.g. Romero & Torres 2003; Yoast-Hull, Gallagher & Zweibel 2014b).

6.3 Contribution from a hidden LLAGN to the gamma-ray emission

NGC 4945, the prototype of hidden AGN, is one of the few radio-quiet AGNs detected by the Fermi-LAT telescope (Abdo et al. 2010a). Interestingly, despite this galaxy having also a starburst in its central region, recent evidence suggests that the high-energy emission could be powered by the accretion flow around the central supermassive black hole (Wojaczyński & Niedźwiecki 2017). Motivated by this, we explore here what would be the maximum contribution to the gamma-ray emission expectable from a similar but weaker hidden AGN in NGC 253, as the one that might be responsible for the emission in X-1.

Since RIAFs are plasmas in the collisionless regime, it is not clear whether particles in them are thermal or not (Mahadevan & Quataert 1997). Moreover, at least in some LLAGNs, there is evidence that points to the presence of a non-thermal component (Yuan et al. 2003; Inoue & Doi 2018). We explore the most favourable scenario for gamma-ray production in a hot accretion flow around a ∼106 M black hole with a luminosity ∼1040 erg s−1 in the Chandra band (see Section 5.1.2). We assume that a fraction of the energy density of both electrons and ions follows a non-thermal distribution of spectral index p. Some plausible acceleration mechanisms in these plasmas are turbulent magnetic reconnection (see Hoshino & Lyubarsky 2012, for a review), stochastic acceleration (Dermer, Miller & Li 1996), or diffusive shock acceleration (e.g. Drury 1983; Blandford & Eichler 1987). Electrons cool locally by synchrotron radiation, so their cooled spectrum is steeper with an increased index of p + 1 (N(E) ∝ E−(p+1)). On the other hand, ions do not cool efficiently and are advected towards the hole; as a consequence, they preserve the original spectral index. We explore a leptonic scenario where |$10{{\ \rm per\ cent}}$| of the electrons (this fraction cannot be much higher or the low-energy emission would be overestimated) follow a non-thermal distribution with p = 2, and a hadronic scenario where all ions are non-thermal, following a harder power-law distribution of index p = 1.5, and we estimate the associated gamma-ray emission in both cases. Electrons emit by synchrotron radiation and inverse Compton radiation, while ions emit synchrotron and also produce pion-decay gamma-rays via pp interactions; however, the latter process produces photons at energies where they are completely self-absorbed. The detailed description of the model is not the aim of this work and it will be presented in a forthcoming paper (Gutiérrez et al., in preparation). Fig. 6 shows the high-energy SED for the parameters above in the leptonic scenario. The electrons are able to produce |$\approx \! 10 {{\ \rm per\ cent}}$| of the GeV emission detected from NGC 253. Photons with higher energies will be internally absorbed. Fig. 7 shows the hadronic case; given the high magnetic fields, if an efficient acceleration mechanism occurs, protons are able to emit GeV synchrotron photons with a luminosity comparable to the total emission detected from NGC 253 at this band.

Leptonic scenario for the gamma-ray emission associated with a hidden LLAGN in X-1 during a high-activity state (see Table 1). The dotted line is synchrotron emission, the dashed line is inverse Compton emission, and the dot–dashed line is the thermal RIAF emission. The solid line is the total non-thermal emission including photo-pair absorption. The data points are from the Fermi-LAT (Abdo et al. 2010b) and HESS (Acero et al. 2009).
Figure 6.

Leptonic scenario for the gamma-ray emission associated with a hidden LLAGN in X-1 during a high-activity state (see Table 1). The dotted line is synchrotron emission, the dashed line is inverse Compton emission, and the dot–dashed line is the thermal RIAF emission. The solid line is the total non-thermal emission including photo-pair absorption. The data points are from the Fermi-LAT (Abdo et al. 2010b) and HESS (Acero et al. 2009).

Hadronic scenario for the gamma-ray emission associated with a hidden LLAGN in X-1 during a high-activity state (see Table 1). The dotted line is synchrotron emission internally produced and the solid line is the final outgoing non-thermal emission including photo-pair absorption. The data points are from the Fermi-LAT (Abdo et al. 2010b) and HESS (Acero et al. 2009).
Figure 7.

Hadronic scenario for the gamma-ray emission associated with a hidden LLAGN in X-1 during a high-activity state (see Table 1). The dotted line is synchrotron emission internally produced and the solid line is the final outgoing non-thermal emission including photo-pair absorption. The data points are from the Fermi-LAT (Abdo et al. 2010b) and HESS (Acero et al. 2009).

The above predictions should be taken as upper limits for the contribution of a central AGN to the high-energy emission of NGC 253, since we are adopting the most favourable sets of values for the parameters. Nevertheless, given the low contribution of the RIAF in the GeV band and the lack of emission in the HESS energy range, the non-thermal processes in the RIAF are unlikely to ease the difficulties found in the joint fit of radio and gamma-rays in the context of the calorimeter model for NGC 253 (Yoast-Hull et al. 2014a).

To constrain the content of high-energy hadrons, a self-consistent study of the neutrino production should be performed. We will calculate the neutrino emission self-consistently with the gamma radiation in a subsequent work. Neutrinos might provide also a powerful test to investigate the relative contribution of starburst and AGNs to the high-energy regime in galaxies where the two phenomena coexist; both starburst galaxies and LLAGNs have been considered as possible sources of very high energy neutrinos. Moreover, recently some authors have proposed that RIAFs might play a role in the neutrino emission of LLAGNs (e.g. Kimura, Murase & Toma 2015; Kimura, Murase & Mészáros 2019).

7 SUMMARY AND CONCLUSIONS

We have investigated the feasibility of cosmic ray acceleration via the black hole dynamo mechanism in a putative active nucleus of NGC 253. We have considered the three most plausible candidates in the galactic centre region for a 106–107 M black hole. Whichever the black hole is, it should be accreting at low rates and hence it would be powered by an RIAF. We modelled the electromagnetic emission of these flows to reproduce the observational data; for two sources, TH2 and IRC, we also assumed the presence of a small jet component to account for the radio emission. We have studied the viability of cosmic ray acceleration to very high energies by an electrostatic potential gap in the polar region of the black hole magnetosphere. Charges accelerated in the gap emit gamma-rays that collide with the soft photons from the RIAF and pair-create, thus closing the gap. Taking into account this effect, we have found that even in the least luminous of the three flows studied, that of TH2, the RIAF luminosity is high enough to limit heavily the extension of the gap, avoiding cosmic rays to be accelerated to energies higher than 1015 eV. This effect rules out the AGN scenario as a candidate for UHECR acceleration in the case that the nucleus is powering the emission of one of the source candidates considered in the literature. There is still the possibility of an extremely weakly accreting nucleus, which is not seen in any way, to play some role in cosmic ray acceleration. To rule out this latter possibility, it would be necessary to provide either a clarification concerning the true nature of the NGC 253 nucleus or a robust alternative explanation for the UHECR origin.

Finally, as a by-product of the modelling of the source X-1, we have estimated the contribution from non-thermal particles in the accretion flow to the overall gamma-ray emission of NGC 253. In the most favourable scenario, protons might produce a luminosity comparable to the one detected by the Fermi-LAT telescope at ≈1 GeV.

ACKNOWLEDGEMENTS

This work was supported by the Argentine agency CONICET (PIP 2014-00338), the National Agency for Scientific and Technological Promotion (PICT 2017-0898), and the Spanish Ministerio de Economía y Competitividad (MINECO/FEDER, UE) under grant AYA2016-76012-C3-1-P.

Footnotes

1

The IR emission of the starburst also provides seed photons to the inverse Compton process but in regions close to the black hole the energy density of these photon fields is approximately 10 orders of magnitude lower than those produced by the RIAF.

2

Curvature radiation could also produce gamma-rays and subsequent pair creation, but this process is subdominant (Hirotani & Pu 2016).

REFERENCES

Aab
A.
et al. .,
2017
,
J. Cosmol. Astropart. Phys.
,
4
,
038

Aab
A.
et al. .,
2018
,
ApJ
,
853
,
L29

Abdo
A. A.
et al. .,
2010a
,
ApJS
,
188
,
405

Abdo
A. A.
et al. .,
2010b
,
ApJ
,
709
,
L152

Abramowski
A.
et al. .,
2012
,
ApJ
,
757
,
158

Acero
F.
et al. .,
2009
,
Science
,
326
,
1080

Ackermann
M.
et al. .,
2012
,
ApJ
,
755
,
164

Aharonian
F. A.
,
Atoyan
A. M.
,
Nagapetyan
A. M.
,
1983
,
Astrophysics
,
19
,
187

Anchordoqui
L. A.
,
2018
,
Phys. Rev. D
,
97
,
063010

Anchordoqui
L. A.
,
Romero
G. E.
,
Combi
J. A.
,
1999
,
Phys. Rev. D
,
60
,
103001

Antonucci
R.
,
1993
,
ARA&A
,
31
,
473

Blandford
R. D.
,
Begelman
M. C.
,
1999
,
MNRAS
,
303
,
L1

Blandford
R. D.
,
Eichler
D.
,
1987
,
Phys. Rep.
,
154
,
1

Blandford
R. D.
,
Znajek
R. L.
,
1977
,
MNRAS
,
179
,
433

Blumenthal
G. R.
,
Gould
R. J.
,
1970
,
Rev. Mod. Phys.
,
42
,
237

Bolatto
A. D.
et al. .,
2013
,
Nature
,
499
,
450

Boldt
E.
,
Ghosh
P.
,
1999
,
MNRAS
,
307
,
491

Bosch-Ramon
V.
,
Romero
G. E.
,
Paredes
J. M.
,
2006
,
A&A
,
447
,
263

Bustard
C.
,
Zweibel
E. G.
,
Cotter
C.
,
2017
,
ApJ
,
835
,
72

Bykov
A. M.
,
2001
,
Space Sci. Rev.
,
99
,
317

Chevalier
R. A.
,
Clegg
A. W.
,
1985
,
Nature
,
317
,
44

Dermer
C. D.
,
Miller
J. A.
,
Li
H.
,
1996
,
ApJ
,
456
,
106

Domingo-Santamaría
E.
,
Torres
D. F.
,
2005
,
A&A
,
444
,
403

Drury
L. O.
,
1983
,
Rep. Prog. Phys.
,
46
,
973

Engelbracht
C. W.
,
Rieke
M. J.
,
Rieke
G. H.
,
Kelly
D. M.
,
Achtermann
J. M.
,
1998
,
ApJ
,
505
,
639

Falcke
H.
,
Biermann
P. L.
,
1995
,
A&A
,
293
,
665

Fernández-Ontiveros
J. A.
,
Prieto
M. A.
,
Acosta-Pulido
J. A.
,
2009
,
MNRAS
,
392
,
L16

Ford
A. L.
,
Keenan
B. D.
,
Medvedev
M. V.
,
2018
,
Phys. Rev. D
,
98
,
063016

Goldreich
P.
,
Julian
W. H.
,
1969
,
ApJ
,
157
,
869

Guépin
C.
,
Kotera
K.
,
Barausse
E.
,
Fang
K.
,
Murase
K.
,
2018
,
A&A
,
616
,
A179

Günthardt
G. I.
,
Agüero
M. P.
,
Camperi
J. A.
,
Díaz
R. J.
,
Gomez
P. L.
,
Bosch
G.
,
Schirmer
M.
,
2015
,
AJ
,
150
,
139

Hirotani
K.
,
Pu
H.-Y.
,
2016
,
ApJ
,
818
,
50

Hoshino
M.
,
Lyubarsky
Y.
,
2012
,
Space Sci. Rev.
,
173
,
521

Inoue
Y.
,
Doi
A.
,
2018
,
ApJ
,
869
,
114

Kimura
S. S.
,
Murase
K.
,
Toma
K.
,
2015
,
ApJ
,
806
,
159

Kimura
S. S.
,
Murase
K.
,
Mészáros
P.
,
2019
,
Phys. Rev. D
,
100
,
083014

Körding
E. G.
,
Fender
R. P.
,
Migliari
S.
,
2006
,
MNRAS
,
369
,
1451

Lehmer
B. D.
et al. .,
2013
,
ApJ
,
771
,
134

Levenson
N. A.
,
Weaver
K. A.
,
Heckman
T. M.
,
2001
,
ApJ
,
550
,
230

Levinson
A.
,
2000
,
Phys. Rev. Lett.
,
85
,
912

Mahadevan
R.
,
Quataert
E.
,
1997
,
ApJ
,
490
,
605

Marconi
A.
,
Oliva
E.
,
van der Werf
P. P.
,
Maiolino
R.
,
Schreier
E. J.
,
Macchetto
F.
,
Moorwood
A. F. M.
,
2000
,
A&A
,
357
,
24

Mihalas
D.
,
1978
,
Stellar Atmospheres
.
Freeman & Co
,
San Francisco

Müller-Sánchez
F.
,
González-Martín
O.
,
Fernández-Ontiveros
J. A.
,
Acosta-Pulido
J. A.
,
Prieto
M. A.
,
2010
,
ApJ
,
716
,
1166

Narayan
R.
,
Yi
I.
,
1995
,
ApJ
,
444
,
231

Narayan
R.
,
Barret
D.
,
McClintock
J. E.
,
1997
,
ApJ
,
482
,
448

Narayan
R.
,
Mahadevan
R.
,
Grindlay
J. E.
,
Popham
R. G.
,
Gammie
C.
,
1998
,
ApJ
,
492
,
554

Özel
F.
,
Psaltis
D.
,
Narayan
R.
,
2000
,
ApJ
,
541
,
234

Paglione
T. A. D.
,
Abrahams
R. D.
,
2012
,
ApJ
,
755
,
106

Paglione
T. A. D.
,
Marscher
A. P.
,
Jackson
J. M.
,
Bertsch
D. L.
,
1996
,
ApJ
,
460
,
295

Ptitsyna
K.
,
Neronov
A.
,
2016
,
A&A
,
593
,
A8

Quataert
E.
,
Gruzinov
A.
,
1999
,
ApJ
,
520
,
248

Quataert
E.
,
Gruzinov
A.
,
2000
,
ApJ
,
545
,
842

Rekola
R.
,
Richer
M. G.
,
McCall
M. L.
,
Valtonen
M. J.
,
Kotilainen
J. K.
,
Flynn
C.
,
2005
,
MNRAS
,
361
,
330

Rephaeli
Y.
,
Arieli
Y.
,
Persic
M.
,
2010
,
MNRAS
,
401
,
473

Romero
G. E.
,
Torres
D. F.
,
2003
,
ApJ
,
586
,
L33

Romero
G. E.
,
Müller
A. L.
,
Roth
M.
,
2018
,
A&A
,
616
,
A57

Sharma
P.
,
Quataert
E.
,
Stone
J. M.
,
2007
,
ApJ
,
671
,
1696

Singh
S.
,
Ma
C.-P.
,
Arons
J.
,
2004
,
Phys. Rev. D
,
69
,
063003

Spada
M.
,
Ghisellini
G.
,
Lazzati
D.
,
Celotti
A.
,
2001
,
MNRAS
,
325
,
1559

Stone
J. M.
,
Pringle
J. E.
,
Begelman
M. C.
,
1999
,
MNRAS
,
310
,
1002

Turner
J. L.
,
Ho
P. T. P.
,
1985
,
ApJ
,
299
,
L77

Ulvestad
J. S.
,
Antonucci
R. R. J.
,
1997
,
ApJ
,
488
,
621

Veilleux
S.
,
Cecil
G.
,
Bland-Hawthorn
J.
,
2005
,
ARA&A
,
43
,
769

Vila
G. S.
,
Romero
G. E.
,
2010
,
MNRAS
,
403
,
1457

Wang
Q. D.
et al. .,
2013
,
Science
,
341
,
981

Waxman
E.
,
2006
,
Nucl. Phys. B
,
151
,
46

Weaver
K. A.
,
Heckman
T. M.
,
Strickland
D. K.
,
Dahlem
M.
,
2002
,
ApJ
,
576
,
L19

Wojaczyński
R.
,
Niedźwiecki
A.
,
2017
,
ApJ
,
849
,
97

Yoast-Hull
T. M.
,
Everett
J. E.
,
Gallagher
J. S. I.
,
Zweibel
E. G.
,
2013
,
ApJ
,
768
,
53

Yoast-Hull
T. M.
,
Gallagher
J. S. I.
,
Zweibel
E. G.
,
Everett
J. E.
,
2014a
,
ApJ
,
780
,
137

Yoast-Hull
T. M.
,
Gallagher
J. S. I.
,
Zweibel
E. G.
,
2014b
,
ApJ
,
790
,
86

Yuan
F.
,
Narayan
R.
,
2014
,
ARA&A
,
52
,
529

Yuan
F.
,
Peng
Q.
,
Lu
J.-F.
,
Wang
J.
,
2000
,
ApJ
,
537
,
236

Yuan
F.
,
Quataert
E.
,
Narayan
R.
,
2003
,
ApJ
,
598
,
301

Yuan
F.
,
Bu
D.
,
Wu
M.
,
2012
,
ApJ
,
761
,
130

Zhang
B. T.
,
Murase
K.
,
2019
,
Phys. Rev. D
,
100
,
103004

Znajek
R. L.
,
1978
,
MNRAS
,
185
,
833

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