A lepto-hadronic model for high-energy emission from FR I radiogalaxies
Key Words.:Galaxies: radio galaxies: individual: Cen A, M87; heavy jet: lepto-hadronic high energy emission
Context:The well known radiogalaxy Cen A has been recently detected as a source of very high energy (VHE) -rays by the HESS experiment just before Fermi/LAT detected it at high energies (HE). The detection, together with that of M87, established radiogalaxies as VHE -ray emitters.
Aims:The aim of this work is to present a lepto-hadronic model for the VHE emission from the relativistic jets in FR I radiogalaxies.
Methods:We consider that protons and electrons are accelerated in a compact region near the base of the jet, and they cool emitting multi wavelength radiation as propagating along the jet. The proton and electron distributions are obtained through steady-state transport equation taking into account acceleration, radiative and non-radiative cooling processes, as well as particle transport by convection.
Results:Considering the effects of photon absorption at different wavelengths, we calculate the radiation emitted by the primary protons and electrons, as well as the contribution of secondaries particles (, s and s ). The expected high-energy neutrino signal is also obtained and the possibility of detections with KM3NeT and IceCube is discussed.
Conclusions:The spectral energy distribution obtained in our model with an appropriate set of parameters for an extended emission zone can account for much of the observed spectra for both AGNs.
The non-thermal high-energy emission from Active Galactic Nuclei (AGNs) has been widely studied in recent years at different wavelength ranges through both satellite-borne and ground-based detectors (e.g. Urry & Padovani 1995). Several theoretical models have been proposed to explain the electromagnetic emission of these objects. It is commonly accepted that the high-energy radiation is emitted by particles accelerated in the relativistic jets launched from the inner parts of an accretion disk that surrounds the central black hole. In general, the high-energy spectral energy distribution (SED) of AGNs presents two characteristic bumps. The lower energy bump, located at optical to X-ray energies, is usually explained as synchrotron emission of electrons while the origin of the high-energy peak in the SED is still under debate (see e.g. (e.g. Böttcher 2007) for a review). Leptonic models attribute this component to inverse-Compton up-scattering off synchrotron or external photons from the disk and/or radiation reprocessed in nearby clouds (see e.g. Katarzyński et al. 2001; Lenain et al. 2008; Ghisellini et al. 2005). In hadronic models, interactions of highly relativistic protons in the jet with ambient matter and photon fields, proton-induced cascades, or synchrotron radiation of protons, are responsible for the high-energy photons (see e.g. Mücke et al. 2000; Mücke & Protheroe 2001; Reimer et al. 2004; Costamante et al. 2008; Hardcastle et al. 2009; Romero et al. 1996; Orellana & Romero 2009). There also exist models which are not based on the emission of accelerated particles in the relativistic jet and assume the production of TeV -rays in a pulsar-like cascade mechanism in the magnetosphere of the black hole (e.g. Neronov & Aharonian 2007; Rieger & Aharonian 2008b).
The recently reported detection by HESS of the nearby radiogalaxy Cen A (Aharonian et al. 2009) is of great relevance since it establishes radiogalaxies as VHE -ray emitters. Cen A is the second non-blazar AGN discovered at VHE, after the HEGRA detection of -rays from M 87 (Aharonian et al. 2003) and the later confirmation by HESS (Aharonian et al. 2006). A great variety of leptonic and hadronic models has been already applied to this kind of sources and a full review is beyond the scope of this work. During the first year of operation, Fermi/LAT has detected HE emission from Centaurus A (Abdo et al. 2009a) and M 87 (Abdo et al. 2009c), providing new constraints to the models.
In this work we present a lepto-hadronic model for the emission from FR I radiogalaxies. Section 2 contains a brief description of observational facts on this type of sources. In Section 3 we present the outline of our scenario, describing its most relevant characteristics. Section 4 is devoted to the description of the model. In Section 5 we present the application to Centaurus A, whereas in Section 6 the results for M87 are given. Finally, in Section 7 we discuss the model implications and perspectives.
2 FR I radiogalaxies
According to the unification model of AGNs (e.g. Urry & Padovani 1995) FR I radiogalaxies, with their jet axis at a large angle with the line-of-sight, are the parent population of BL Lac objects whose jets are closely aligned to the line of sight. We concentrate here on the only two of them observed until now in the VHE range.
2.1 Cen A
Cen A is the closest FR I radiogalaxy ( Mpc, Harris et al. 1984; Hui et al. 1993) and its proximity makes it uniquely observable among such objects, eventhough its bolometric luminosity is not high as compared to other AGNs. It is very active at radio wavelengths presenting a rich jet structure. We can distinguish in its structure two components: inner jets at a kpc scale and giants lobes covering 10 in the sky. A detailed description of the radio morphology can be found in Meier et al. (1989). The inner kpc jet has also been detected in X-rays (Kraft et al. 2002) with an structure of knots and diffuse emission. Recently Croston et al. (2009) reported the detection of non-thermal X-ray emission from the shock of the southwest inner radio lobe from deep Chandra observations.
The supermassive black hole at the center of the active galaxy has an estimated mass of about (Neumayer et al. 2007; Cappellari et al. 2009; Israel 1998) to (Silge et al. 2005; Marconi et al. 2001). The black hole host galaxy is an elliptical one (NGC 5128) with a twisted disk which obscures the central engine at optical wavelengths.
Cen A was observed by the Compton Gamma Ray Observatory (CGRO) with all its instruments from MeV to GeV energies (Gehrels & Cheung 1992; Kinzer et al. 1995; Paciesas et al. 1993; Steinle et al. 1998; Thompson et al. 1995). In this period, this source exhibited X-ray variability (Bond et al. 1996) and also some soft -ray variability (Bond et al. 1996; Kinzer et al. 1995; Steinle et al. 1998). However, Sreekumar et al. (1999) found that the EGRET flux was stable during the whole period of CGRO observations.
In 1999 the new Chandra X-ray Observatory took images of Cen A with an unprecedented resolution. More than 200 X-ray point sources were identified in those images (Kraft et al. 2001).
Cen A as a possible source of UHE cosmic rays was early proposed by (Romero et al. 1996). Recently, the Pierre Auger Collaboration reported the existence of anisotropy on the arrival directions of UHE cosmic rays (Abraham et al. 2007), remarking that at least 2 of this events can be correlated with the Cen A position ( circle). Further works have claimed that there are several events that can be associated with Cen A and its big radio lobes (Gorbunov et al. 2008; Fargion 2008; Wibig & Wolfendale 2007) but this correlation is still statistically weak.
Finally, Fermi/LAT has detected Cen A in the first three months of survey with a significance above 10 (Abdo et al. 2009b).
The giant radiogalaxy M87 is located at 16.7 Mpc within the Virgo cluster (Macri et al. 1999). It presents a one-sided jet which is inclined with respect to the line of sight an angle between 20 - 40 (Biretta et al. 1995, 1999). In addition to its bright and well resolved jet, M87 harbors a very massive black hole (6.0 0.5) 10 M (Gebhardt & Thomas 2009) which is thought to power the relativistic outflow. Given its proximity, the substructures inside the jet could be resolved in the X-ray, optical, and radio wavebands (Wilson & Yang 2002). High frequency VLBI observations have resolved the inner jet up to about 70 Schwarzschild radii (Junor et al. 1999). Along the jet, nearly stationary components (Marscher et al. 2008) and features moving at superluminal speeds (Ly et al. 2007; Kovalev et al. 2007) were observed (100 pc-scale).
M87 is also a well-known VHE -rays emitter (Aharonian et al. 2003, 2006; Acciari et al. 2008; Albert et al. 2008) showing a -ray flux variability on short time scales with flaring phenomena in VHE, radio, and X-ray wavebands simultaneously (Acciari et al. 2009). Recently, it was detected by Fermi/LAT with a significance greater than 10 in 10 months of observations (Abdo et al. 2009c).
Rapid variability constrains the emission region extent to less than , where is the relativistic Doppler factor. Some suggested explanations for the VHE -ray emission were ruled out (e.g. dark matter annihilation (Baltz et al. 2000)) At the same time, various VHE -ray jet emission models were proposed: leptonic (Georganopoulos et al. 2005; Lenain et al. 2008) and hadronic (Reimer et al. 2004) ones. However, the location of the emission region is still unknown. The nucleus (Neronov & Aharonian 2007; Rieger & Aharonian 2008a) , the inner jet (Tavecchio & Ghisellini 2008), or larger structures in the jet such as the knot HST-1, have been discussed as possible sites of particle acceleration (Cheung et al. 2007).
3 Basic Scenario
We assume that a population of relativistic particles can be accelerated to very high energies close to the base of the AGN jet. These primary electrons and protons carry a fraction of the total kinetic power of the jet , and as they are dragged along with the jet, they cool giving rise to electromagnetic emission and neutrinos.
Assuming that a fraction of the Eddington luminosity is carried by the jet and a counter jet, the jet kinetic power is
This power can be very high if the jet is launched by a dissipationless accretion disk (Bogovalov & Kelner 2010).
Most of the jet content is in the form of a thermal plasma with a constant bulk Lorentz factor . This plasma is initially in equipartition with a tangled magnetic field at the Alfvn surface ( from the central black hole) (e.g. McKinney 2006). The highly disorganized magnetic field has a root mean square value at a distance from the black hole in the observer frame, such that . The magnetic energy density for is then with . Equating the magnetic to the kinetic energy density, yields:
where is the distance to the black hole, is the jet velocity, and is the radius of the jet assuming that it has a conical shape with half-opening angle . A widely accepted view is that jets are accelerated through the conversion of magnetic energy into kinetic energy (e.g. Komissarov et al. 2007). We adopt a phenomenological dependence on the distance to the black hole for the magnetic field (e.g. Krolik 1999),
Since the density of cold material within the jet decays as , using an exponent in the above expression implies that, as increases, the magnetic energy decreases more rapidly than the kinetic one. The corresponding increase in the bulk Lorentz factor is taken into account as described in Appendix A. In the following, we will write simply , but it actually depends on .
The particle acceleration takes place in a compact but inhomogeneous region of size near the base of the jet, at a distance away from the black hole. The value of is fixed by requiring the magnetic energy density to be in sub-partition with the jet kinetic energy density. This condition enables strong shocks to develop (Gaisser 1990). Assuming that at the magnetic energy is a fraction of its value at , it follows that
For example, if , , and , using yields a distance .
The power injected in the form of relativistic particles () is considered to be a small fraction of the total jet kinetic power and the relation between proton and electron powers is given by the parameter such that (see e. g. Romero & Vila 2008; Vila & Romero 2010).
These parameters are constrained by the available observational data on each source and reasonable theoretical considerations. In the following section, we describe the procedure used to obtain the particle distributions along the jet and the radiative output that then arises.
The existence of heavy jets magnetically driven in AGN and microquasars has been supported by several scientific works in the last few years. For example, Sa̧dowski & Sikora (2010) conclude that mildly relativistic proton-electron jets might be formed by magnetocentrifugal launching by inner portion of magnetized disks around rotating black holes. This leads to a triple-component jet structure: proton-electron component sourrounded by the relativistic pair-dominated sheat. The final speed of this centrifugal outflow depends strongly on the disk vertical structure (see e.g. Wardle & Koenigl 1993) which is certainly unknown. However, for barionic outflows to reach mildly relativistic speeds, some inital boost would be neccesary, which would be produced by heating or mechanically, by flaring activity and/or by radiation pressure. Previous work by Heinz (2008) has proved the existence of a relativistic and baryon-loaded jet in Cygnus X-1 and that the bulk of the kinetic energy is carried by cold protons, as in the case of SS 433. For further information about magnetically launched jets see (Spruit 2010), where the production, acceleration, collimation, and composition of jets are well explained.
4 Description of the model
The model developed for this work is based on the energy distribution of the different particle populations along the jet. These are obtained as solutions of a 1-dimensional steady-state transport equation that includes the relevant cooling terms and a convective one. The radiative output is obtained in the jet reference frame, where the particle distributions are isotropic, and the result is transformed back to the observer frame.
The procedure begins with the calculation of the distribution of primary electrons along the jet taking into account synchrotron and adiabatic cooling. After that, the synchrotron radiation emitted by the primary electrons can be calculated. To check that the electron distribution is consistent with the energy loss mechanisms operating, the synchrotron cooling rate must be much greater than the inverse Compton (IC) one due to electrons interacting with the synchrotron photons (SSC). If this is the case, it means that the main cooling is due to synchrotron radiation, and neglecting the IC energy loss is a valid approximation to obtain the electron distribution. If the SSC cooling can not be neglected, then the transport equation becomes more complicated and a different approach is needed (e.g. Schlickeiser 2009).
Having obtained the electron distribution, the next step is to calculate the distribution of primary protons taking into account the cooling due to synchrotron emission, adiabatic expansion, and interactions. The latter two types of interactions yield the production of secondary pions, muons, and electron-positron pairs. These three populations of particles are also described with the transport equation, and the radiative output that they produce is also considered. According to, e.g. Khangulyan et al. (2008) and Pellizza et al. (2010), it can be seen that in the present scenario, IC cascades are suppressed by the synchrotron cooling of secondary , since the magnetic field is greater than G in the regions of the jet where emission takes place. Therefore, we neglect the effect of IC cascading and calculate the synchrotron emission of the secondary electrons and positrons.
In this section we present all the relevant expressions used in this model. We discuss on the injection of primary particles, the relevant cooling rates, the transport equation used, the injection of secondary particles, and the emission of photons and neutrinos.
4.1 Injection of primary particles
At a distance to the black hole taken in the reference frame of the observer, we adopt an injection function in terms of the particle energy in the co-moving reference frame of the jet:
Here, represents the total number of relativistic electrons () or protons (), and the cut-off energy is obtained from the balance of particle gains and losses. These processes are described below.
The injection function can be transformed to the observer frame by taking into account that
where the energy in the jet frame is given in terms of the energy in the observer frame , and the angle between the particle momentum and the bulk velocity of the jet :
The normalization constant is found in each case using the power in relativistic species , integrating in the energy, solid angle, and volume of the acceleration zone ():
4.2 Accelerating and cooling processes
To determine the maximum energies, it is necessary to account for the particles acceleration and cooling rates .
We assume that in the acceleration zone, particles are accelerated by a diffusive shock-modulated mechanism with a rate (e.g. Begelman et al. 1990):
where is the efficiency of the mechanism. The magnetic field in the jet frame is assumed to be random and with no preferred direction. represents the root mean square field in the jet frame: . As considered also in Heinz & Begelman (2000), the average of each component of the magnetic field is supposed to vanish in the jet frame: . Assuming that there is no electric field in the jet frame, the components of the magnetic field in the observer frame are related to the ones in the jet frame as , , and , which yields111Note that Eq.(12) is consistent with Eq. (3) of Heinz & Begelman (2000) if the radial component of their flow velocity can be neglected.
where is given by Eq.(3).
As for the energy loss processes, particles emit synchrotron radiation at a rate
The lateral expansion of the jet implies an adiabatic cooling rate (Bosch-Ramon et al. 2006) in the observer frame given by
The density of cold matter at a distance from the black hole is, in observer frame,
where the mass loss rate in the jet is
In the jet frame, the cold matter density is
Relativistic protons in the jet undergo collisions with these cold protons at a rate
where and .
4.2.1 Synchrotron radiation and Inverse Compton interactions
To consider IC interactions of primary electrons with synchrotron photons in the jet (SSC), it is necessary to know the particle distribution of the synchrotron emitting particles, , which is obtained by solving the transport equation described below. Actually, the synchrotron emission of electrons dominates the low energy photon background which is a good target for IC and interactions. Since in the cases considered here, IC cooling is much less efficient than synchrotron cooling, the electron distribution can be obtained to a good approximation without considering IC cooling. In the jet frame, the background radiation density, in units , has been approximated locally as
where is the power per unit energy per unit volume of the synchrotron photons,
Here, the synchrotron power per unit energy emitted by the electrons is given by (Blumenthal & Gould 1970):
where is the modified Bessel function of order and
The factor in parenthesis in Eq. (19) accounts for the effect of synchrotron self-absorption (SSA) within the jet, with an optical depth
where is such that , and the SSA coefficient is given by (Rybicki & Lightman 1979):
After all these considerations, the cooling rate due to IC scattering for electrons of energy in the jet frame can be obtained by integrating in the target photon energy and in energy of the scattered photon (Blumenthal & Gould 1970):
where is the lowest energy of the available background of synchrotron photons, and
4.2.2 Proton-photon interactions
Proton interactions with the photon background can be an important cooling process, with a rate appoximated as
Here, MeV and we use the expressions for the cross section and the inelasticity given in Begelman et al. (1990).
4.3 Particle distributions in the jet
This equation includes the effects of convection with a speed , and particle cooling with an energy loss . Particle decay with a timescale is also considered in the cases of secondary pions and muons. We note that the energy in the above equation corresponds to the co-moving frame, where the particle distributions are isotropic, while the spatial coordinate corresponds to the observer frame (e.g. Jokipii & Parker 1970; Kirk et al. 1988). The source term is given by a function , which in the case of primary particles is given by Eq. (6), while for secondaries it is obtained using the parent particle distribution () along with the secondary particle production rates (see Section 4.3.1).
We can solve the transport equation using the method of characteristics, i.e., writing
where the first two terms allow us to find a characteristic curve for each pair of interest. Equating the second and third members it follows that
4.3.1 Pion and muon production
As high energy protons interact with background matter and radiation, they produce pions.
The pion injection due to interactions in the jet frame is calculated as
In the same way, the source function for charged pions produced by interactions is
Here is the collision frequency defined as (Atoyan & Dermer 2003):
and the mean number of positive or negative pions is
This number depends on the probabilities of single pion and multi-pion production and . Using the mean inelasticity function , the probability is
where and .
For muon injection, we proceed as (Lipari et al. 2007) and we consider the production of left handed and right handed muons separately, which have different decay spectra:
with and .
The injection function of negative left handed and positive right handed muons is
Given that CP invariance implies that , and since the total distribution obtained for all charged pions is , it follows that the injection for left handed muons is
And in a similar way, the right handed muons injection is
4.4 Electromagnetic radiation
The main radiative processes considered in this work are: synchrotron radiation, IC emission, and interactions. For each emission process we can calculate the injection of photons or radiation emissivity, which is given by the general expression of Eq. (5) and represents the number of photons produced per time unit, per volume unit, per photon energy, and per solid angle. In the observer frame, the corresponding emissivity is given by
where the Doppler factor is and .
In the case of synchrotron radiation, the emissivity in the jet frame is
and the IC emissivity is
where is the classical electron radius, and we integrate in the target photon energy and in the electron energies between
With respect to the hadronic contribution to the total emission, the photon emissivity due to interactions is obtained as
where the function is the same as defined by Kelner et al. (2006), for a proton energy .
For the -ray emissivity due to interactions we use the expression
where , ,
and with the function as tabulated in Kelner & Aharonian (2008).
4.5 Internal and external photon absorption
We consider the absorption of the radiation due to photoionization processes at eV energies, and also due to creation by and interactions at high energies in the source.
For interactions, we take as target the material along the line of sight corresponding to each particular object, which is measured through the column density of neutral hydrogen . The absorption cross section in this case is taken as in Ryter (1996) for keV, assuming that the medium is composed by atomic hydrogen and dust within galactic abundances (see Fig. 1). This cross section includes the effects of photoionizaton for eV and scattering with dust below this energy. In the present work we do not consider recombination, the inverse process of photoionization (see Appendix B ). The resulting optical depth for interactions is approximated as
It can be seen from Fig. 1 that besides the large absorption edge corresponding to the ionization energy of hydrogen, three aditional absorption edges are included in the cross section. They correspond to different ionization energies of helium, K-shell electrons of oxygen, and iron. In the present context, as can be seen below, we find no significant features associated with these aditional absorption edges (e.g. Cruddace et al. 1974; Ghisellini et al. 1999). The possible re-emission of lines is beyond the scope of this work, and could be studied, e.g., as in Ghisellini et al. (1999). For energies above keV we take the cross section from Amsler et al. (2008), to account for Compton scattering and production. In Fig. 1 we show the cross section used for interactions
In the case of interactions, the main radiation target is considered to be the synchrotron photons inside the jet, which are characterized by a radiation density . If a dissipationless accretion disk is present, no other significant photon field is relevant for gamma-ray absorption. The cross section is given by
where is the angle of interaction between the incident photons. For -rays produced at a position in the jet, we assume that they undergo collisions over a length inside the jet with a target radiation field that is isotropic in the jet frame. The corresponding optical depth is calculated using the general expression of Gould & Schréder (1967) to obtain
In Fig. 2 we show the optical depths obtained for the case of Cen A and M87, and , the latter evaluated within the injection zone and also outside it. The absorbing photons outside the injection zone are those of synchrotron emission of protons and secondary , which in that case are also included in . It can be seen from this plot that very important absorption occurs at low energies by photoionization, and also at VHE through internal interactions. The latter effect takes place mainly at the injection zone, since for , the optical depth is much lower.
Taking into account the total optical depth , the differential photon flux at Earth, i.e., the number of photons with energy , per unit energy, per unit area, per unit time, can be calculated as
where is the distance from the source to Earth.
4.6 Neutrino emission
Neutrinos arise from direct pion decays plus muon decays with a total emissivity
which correspond to the observer frame and transforms according to Eq. (39). The contribution from pion decays (, ) is represented in the co-moving frame by
with and .
The neutrino emissivity for muon decays (