The proton low-mass microquasar: high-energy emission

Microquasars (MQs) are accreting X-ray binaries that produce jets of relativistic particles (e.g., Mirabel & Rodríguez 1999). According to the type of donor star, microquasars can be classified into high-mass and low-mass microquasars (HMMQs and LMMQs, respectively). Soon after their discovery by Mirabel et al. (1992), it was proposed that MQs might be sources of gamma rays, as it is the case for some active galactic nuclei, in particular, flat-spectrum radio quasars and BL Lacertae (BL Lac) objects (Levinson & Blandford 1996). A variety of models were then developed for HMMQs, mostly based on interactions between relativistic particles in the jets (both leptons and hadrons) and matter and photon fields from the hot, massive primary star (see Romero 2005, and references therein; Bosch-Ramon et al. 2006; Bosch-Ramon 2007, and references therein). The primary motivation for these models was to explain the existence of a population of variable and unidentified gamma-ray sources on the galactic plane (Romero 2001; Kaufman Bernadó et al. 2002; Bosch-Ramon et al. 2005). These sources are young and mostly located in the inner spiral arms of the Galaxy. Imaging air Cherenkov telescopes have recently detected HMMQs (e.g., Cygnus X-1 and LS I +61 303 by the Major Atmospheric Gamma-ray Imaging Cherenkov telescope, MAGIC, Albert et al. 2006, 2007; and LS 5039 by the High-Energy Stereoscopic System, HESS, Aharonian et al. 2005). There is some controversy around the nature of some of these objects, especially of LS I +61 303; we refer the reader to Romero et al. (2007) for a discussion.

There is a population of variable unidentified sources forming a halo around the Galactic center (Grenier 2001, Nolan et al. 2003). It is expected that this group of sources is old and presents a distribution similar to that of the globular clusters, but with no direct positional correspondence. Since they are extremely variable, it has been suggested that they might be LMMQs (i.e., compact objects) expelled from globular clusters or the galactic plane (Grenier 2001, 2005).

Different types of models have been proposed to explain gamma-ray emission in LMMQs, where the external fields to the jet itself are exiguous. Aharonian & Atoyan (1998) and Atoyan & Aharonian (1999) developed time-dependent synchrotron self-Compton (SSC) models for bursting sources. Bosch-Ramon et al. (2006) explored SSC models for the case of sources with steady inhomogeneous jets. Markoff et al. (2001) presented a synchrotron model with emission reaching the hard X-rays. Grenier et al. (2005), on the other hand, calculated the interaction of a relativistic leptonic jet with the photon fields from the corona, the accretion disk and the dim star, concluding that external inverse Compton interactions cannot be invoked to explain the high gamma-ray luminosities (in the range $10^{34}-10^{36}$ erg s^-1) inferred from the Energetic Gamma-Ray Experiment Telescope (EGRET) detections.

Hadronic models based on inelastic proton-proton collisions (e.g., Romero et al. 2003) are not expected to work in the bare environment of old and cold stars as those of LMMQs. However, Levinson & Waxman (2001) proposed that photopion production could be important in MQs if strong synchrotron radiation fields are generated at the base of the jets. These authors developed a simple model to predict the neutrino emission of MQs, where the neutrinos are generated through the decay of charged pions created in proton-photon interactions.

Here we explore in more detail a proton model for LMMQs, with emphasis on the electromagnetic output. We consider a system where the jets have a content in relativistic protons, which are accelerated by shocks in a compact region close to the accreting object. Electrons are accelerated as well in this region. We study models with different ratios of primary relativistic protons to electrons. The jet itself is considered as a mildly relativistic macroscopic fluid launched by some type of magneto-centrifugal mechanism, and hence it is initially assumed to be in equipartition with the magnetic field (as considered, e.g., by Bosch-Ramon et al. 2006). The jet power is taken as a fraction of the accretion power. In the case of advective accretion flows, the spectral energy distribution will be dominated by the non-thermal emission. Among the processes that cool the relativistic particles we consider synchrotron radiation for both electrons and protons¹¹1The potential of proton synchrotron radiation in the context of AGNs has been explored by Aharonian (2002)., inverse Compton (IC) interactions with the locally produced fields, photopair and photopion production, and adiabatic losses. The results show that proton microquasars might be detected by forthcoming satellites like the Gamma-Ray Large Area Space Telescope (GLAST) and by ground-based air Cherenkov telescopes with a low-energy threshold.

The structure of the paper is as follows. In Sect. 2 we outline the basics of the model and we introduce all the relevant radiative processes. In Section 3 we present the results of our calculations for a number of specific models. Section 4 presents the effects of internal photon-photon absorption on the production spectra. Section 5 contains a discussion of the results. We close in Sect. 6 with a brief summary and the prospects of our model for future applications.

Figures 4 and 5 show the spectral energy distributions (SEDs) calculated for different values of the model parameters. In Fig. 4 the spectral index of the injection function has the canonical value $\alpha=2.2$, whereas in Fig. 5 we considered a harder injection with $\alpha=1.5$. For each case, we show four representative spectra obtained by varying the value of the remaining parameters within a physically reasonable range. The main contributions to the SEDs are always due to synchrotron radiation of leptons and protons. The relative importance of each contribution depends on the value of the ratio $a=L_{p}/L_{e}$. The proton synchrotron spectra are hardly affected by changes in $a$, peaking at $\sim 10^{35-36}$ erg s^-1 for $E_{\gamma}\sim 10^{8-9}$ eV; lepton synchrotron luminosities range from $\sim 10^{34}$ erg s^-1 for a completely proton-dominated jet ($a=10^{3}$) to $\sim 10^{37}$ erg s^-1 in the case of equipartition ($a=1$). In fact, lepton energy losses are so strong that they radiate almost all their available energy budget in each case.

The efficiency of the acceleration $\eta$ fixes the maximum particle energy and therefore has a direct effect on the high-energy cutoff of the SEDs. Synchrotron spectra extend up to $E_{\gamma}\sim 10^{12}$ eV in the case of protons and up to $E_{\gamma}\sim 10^{9}$ eV in the case of leptons for $\eta=0.1$; when a poor acceleration efficiency $\eta=10^{-4}$ is considered, only energies of about three orders of magnitude smaller are reached. In the same way, modifying the minimum particle energy accordingly changes the low-energy cutoff of the spectra.

The IC contribution is always negligible and, for $a>1$, IC luminosities are below $\sim 10^{30}$ erg s^-1 as the leptonic content of the jet is reduced. Photopion production ($p\gamma_{\pi^{0}}$) yields a very hard energy tail to the SEDs, peaking at energies $E_{\gamma}\sim 10^{14-15}$ eV. The highest value of the $p\gamma_{\pi^{0}}$ luminosity is sensible to $a$, since the target photons for $p\gamma$ collisions are provided mostly by the lepton synchrotron radiation field. Luminosities as large as $10^{35-36}$ erg s^-1 can be reached at very high energies. Synchrotron radiation from $e^{\pm}$ produced in $p\gamma_{e^{\pm},\pi^{\pm}}$ can be important in those models with relatively low barion content, as it can be seen from the different SEDs in Figs. 4 and 5. In general, these contributions have luminosities not too different from those obtained from $p\gamma_{\pi^{0}}$ but they cover a lower energy range.

Internal photon-photon absorption might be important in some of the models we have calculated. In particular, TeV gamma-rays can be efficiently absorbed by IR synchrotron photons. This might initiate an electromagnetic cascade in the emission region of those cases where there are significant photon fields at low energies as could happen in blazars (e.g., Blandford & Levinson 1995). In the context of microquasars, however, a strong magnetic field can quench a pure IC cascade. This is the result of synchrotron losses for the first few generations of pairs, which then cannot produce photons energetic enough to sustain the electromagnetic avalanche (Khangulyan et al. 2008). The photon absorption, nonetheless, might change the gamma-ray spectrum depending on the specific model. This, in turn, can yield a variety of slopes in the spectra to be observed by GLAST or other instruments sensitive in the MeV-up-to-TeV energy range (see, e.g., Aharonian et al. 2008 for a recent discussion in the context of extragalactic jets).

The opacity of a photon field of density $n(\epsilon,z)$ given by Eq. (24) to the propagation of a gamma-ray photon of energy $E_{\gamma}$ is (Gould & Schréder 1966):

The threshold energy $\epsilon_{\rm th}$ is defined by the condition $\beta=1$ with $\vartheta=0$.

We have calculated the attenuation factor $\exp(-\tau)$ for the different models presented in the previous section. Some results are shown in Fig. 6.

We notice that in all cases with significant leptonic synchrotron emission, the radiation is completely suppressed above 10 GeV. For proton-dominated models, which are characterized by a prominent proton synchrotron peak, the attenuation is quite moderate.

In Fig. 7, we present two spectral energy distributions modified by the effects of the photon-photon absorption. In the left panel, we show a case with $a=1$ (strong attenuation). The internal opacity to gamma-ray propagation results in a significant softening of the spectrum between $\sim 10$ MeV and $\sim 10$ GeV, with a cutoff beyond the latter energy. This is consistent with the type of very soft spectra observed by EGRET in some variable halo sources (e.g., Thompson et al. 2000, Grenier 2001). In the right panel of the same figure, we show the SED for a proton-dominated microquasar, which is basically not modified by absorption effects.

In all cases the emission at TeV energies is either suppressed or too weak, and hence no detection with current Cherenkov telescope arrays should be expected for these objects unless very high acceleration efficiencies could be achieved in proton-dominated cases³³3A high acceleration efficiency would move the high-energy cutoff of the synchrotron peak into the TeV regime.. Neutrino propagation is not affected by the effects discussed in this section.

From the results presented in the previous sections is clear that proton low-mass microquasars can be significant gamma-ray sources in the MeV-GeV range, and perhaps in some cases even at TeV energies. According to the ratio $a$ of primary protons to leptons, we can obtain different types of low-energy counterparts. Such counterparts range from sources with radio luminosities of $10^{29}-10^{30}$ erg s^-1 and strong X-ray emission (e.g., the model shown in the left upper panel of Fig. 5), up to sources with weak luminosities dominated by proton synchrotron emission between 100 MeV and 100 GeV (e.g., the model shown in the right upper panel of Fig. 5). Since the cutoff of the synchrotron peak always occurs at energies below 1 TeV, and the high-energy emission due to photopion production is beyond 10 TeV in all models, detection with ground-based Cherenkov telescopes with a threshold of around 1 TeV would be difficult. In cases with strong leptonic synchrotron emission, the TeV radiation is directly suppressed by internal absorption. The telescope GLAST, on the contrary, with its energy window of 100 MeV $-$ 300 GeV is especially suitable for the detection of these objects. Actually, we suggest that many of the unidentified EGRET sources detected off the galactic plane around the Galactic center, might be proton microquasars. Variability, one of the outstanding properties of these sources (Nolan et al. 2003), can be easily introduced in our model through a variable accretion rate, precessing jets, or internal shocks (in this latter case, there would be very rapid variability, superposed to longer variations with timescales from hours to days). The Astro-rivelatore Gamma a Immagini LEggero (AGILE) satellite might provide a more accurate location for some of these sources in the immediate future. Low-threshold, ground-based gamma-ray Cherenkov telescope arrays like HESS II and MAGIC II could also detect hadronic LMMQs at $E\geq 100$ GeV. In particular, the tail of the proton synchrotron peak from models with large values of $a$ might be detectable, displaying a soft spectra. So, observations of LMMQs with Cherenkov telescopes can be useful to constrain the parameter $a$.

An additional prediction of our model is the production of high-energy ($E>1$ TeV) neutrinos, with luminosities in the range $10^{33}-10^{35}$ erg s^-1. In the cases of the highest luminosities, if the MQ is located not too far away (say, around 2 kpc as it is the case of XTE J1118+480) the expected flux could be similar to those estimated for HMMQs (e.g., Levinson & Waxman 2001; Romero et al. 2003; Christiansen et al. 2006; Aharonian et al. 2006). We notice that heavily absorbed sources are precisely those with the highest neutrino luminosities, so a correlation between gamma-ray and neutrino fluxes should not necessarily be expected. Finally, we mention that some features related to electron/positron annihilation could be observable in cases with strong absorption (e.g., Romero 1996; Punsly et al. 2000; Levinson 2006).

We have developed a simple model for proton low-mass microquasars that predicts significant gamma-ray emission in the MeV and GeV domain for these objects. Observations with GLAST will help to establish some fundamental parameters such as the ratio of relativistic protons to electrons in the sources and the effects of internal absorption. Proton low-mass microquasars also produce very high-energy gamma-rays (well within the TeV range) and neutrinos, that in some cases might be detectable by km³-detectors like IceCube or Nemo. Proton microquasars might also present very weak low energy counterparts, and hence they are suitable candidates to explain the unidentified gamma-ray sources detected by EGRET in the galactic halo.

Future developments of the model should include a more sophisticated treatment of the acceleration region and time-dependent calculations. These topics will be included in a forthcoming communication.