The proton microquasar
We present a model for high-energy emission in microquasars where the energy content of the jets is dominated by relativistic protons. We also include a primary leptonic component. Particles are accelerated up to relativistic energies in a compact region located near the base of the jet, where most of the emission is produced.
We calculate the production spectrum due to proton and electron synchrotron radiation and photohadronic interactions. The target field for proton-photon collisions is provided by the synchrotron radiation in the acceleration region. In models with a significant leptonic component, strong internal photon-photon absorption can attenuate the emission spectrum at high energies.
Depending on the values of the parameters, our model predicts luminosities in the range erg s up to GeV energies, with a high-energy tail that can extend up to eV. In some cases, however, absorption effects can completely suppress the emission above 10 GeV, giving rise to different spectral shapes. These results can be tested in the near future by observations with instruments like GLAST-Fermi, HESS II and MAGIC II.
Keywords:X-ray binaries – -ray sources – -ray
:97.80.Jp, 98.70.Rz, 95.85.Pw
Microquasars are binary systems formed by a donor star that feeds a compact object (black hole or neutron star), where part of the accreted matter is ejected from the system as two collimated non-thermal jets. Depending on the mass of the donor star, microquasars are classified into high-mass or low-mass systems. The emission spectrum of microquasars covers almost the entire electromagnetic spectrum, from radio wavelengths to hard X-rays. Three high-mass X-ray binaries have also been detected at Tev gamma rays gamma-rays. The gamma rays can be produced by interaction of relativistic particles in the jet with the radiation field and the matter in the winds of the companion star. Several models to explain the gamma-ray emission in high-mass microquasars can be found in the literature, see for example Romero2005 , BR2006 and BR2007 . However, in the case of low-mass microquasars, the density of the radiation and matter fields supplied by the donor star is much lower, and the same type of mechanisms proposed for high-mass systems turns out to be inefficient Grenier2005 . Here we present a model for the high-energy emission of low-mass microquasars, based on the interaction of relativistic particles in the jets with the internal radiation, matter and magnetic field of the jet itself. The model can be also applied to high-mass microquasars, taking into account the effect of the external fields. In our model the high-energy emission is mostly due to hadronic interactions, though we also take into account the contribution of primary and secondary electrons. The results show that, under certain physical conditions, low-mass microquasars can be sources of gamma rays detectable by the satellite GLAST-Fermi, or Cherenkov telescope arrays like HESS II and MAGIC II.
2 Model description
We consider a conical jet, perpendicular to the orbital plane of the binary. A scheme of the jet launching region is shown in Figure 1. The jet is launched at a distance from the compact object and has an initial radius . The outflow is assumed to be only mildly relativistic, with a bulk Lorentz factor . It carries a fraction of the accretion power, erg s. We further assume that a fraction of the jet kinetic power is in the form of relativistic protons and leptons, . We relate the injected power in protons and electrons through the parameter , .
Particles are accelerated by diffusive shock acceleration leading to a power-law injection,
The acceleration region is compact, extending from the base of the jet up to . The efficiency of the acceleration mechanism is characterized by the parameter , so that the rate of energy gain for a particle of energy is
Here we assume an efficient accelerator with .
The magnetic field in the jet decreases as
We determine by requiring equipartition between magnetic and kinetic energy densities,
where is the jet bulk velocity. Equation (4) yields G .
Figure 2 shows the acceleration rate and the cooling rates for the different processes of energy loss. The only relevant cooling channel for leptons is synchrotron radiation. This is also true for high-energy protons, whereas at low energies proton cooling is dominated by inelastic proton-proton () collisions and adiabatic losses. The maximum energy of the particles is fixed equating acceleration rate and the sum of the cooling rates. This condition yields eV and eV.
Particle distributions in steady state (in units of erg cm) are calculated solving the transport equation in the one-zone approximation Khang2007 ,
We consider several photon production mechanisms: proton and electron synchrotron radiation, electron relativistic Bremsstrahlung, proton-proton inelastic collisions, inverse Compton scattering (IC) and proton-photon collisions on the synchrotron radiation fields of both protons and electrons. Both and interactions create neutral -mesons that then decay to give gamma-rays,
To estimate the spectrum from the decay we followed Refs. Kelner2006 and AD2003 for the cases of and collisions, respectively (for more accurate expressions in the latter case see KA2008 ). Proton-photon and proton-proton collisions also inject high-energy secondary electron-positron pairs, product of the decay of charged pions. Pairs are also injected directly through photopair production,
These secondary leptons also contribute to the gamma-ray emission through synchrotron radiation. To calculate the spectrum of pairs, we used the formulae given by Refs. Ch1992 and Mast2005 . The IC spectra were calculated in the local approximation of Ref. Ghis1985 , whereas for synchrotron and Bremsstrahlung radiation we used classical expressions, see for example Ref. BG1970 .
All calculations, except those of interactions with matter (for these see Reynoso2008 ), were performed in the jet co-moving reference frame and the results were transformed to the observer frame using the appropriate Doppler factor . We fixed for the viewing angle. See Table 1 for detailed values of the model parameters.
|Jet injection point||cm111|
|Jet initial radius||cm|
|Size of acceleration region|
|Jet bulk Lorentz factor|
|Jet kinetic power||erg s|
|Proton-to-lepton energy ratio|
|Magnetic field at||G|
|Minimum proton/electron energy|
|Maximum proton/electron energy||eV222|
Finally, we studied possible modifications of the production spectrum due to internal absorption effects: high-energy radiation in the jet can be self-absorbed by photon-photon annihilation,
We calculated the opacity for a gamma ray to escape from the emission region, and then corrected the production spectra through the attenuation factor . The cross section for photon-photon annihilation and expression for the opacity can be found in Levinson2006 and GS1966 . Cascades are expected to be suppressed by the strong magnetic fields, see Khang2008 .
Figure 3 shows some of the spectral energy distributions (SEDs) obtained for different values of the model parameters. At energies below 1 GeV, the emission is dominated by the synchrotron radiation of protons and primary leptons. The relative importance of the leptonic contribution depends sensibly on the parameter , that fixes the proton-to-lepton total energy ratio. The electron synchrotron luminosity ranges from erg s in a proton-dominated jet (cases (a) and (b)), to erg s in the case of equipartition ( , case (c)). Case (c) is the only case where IC and Bremsstrahlung are significant, since the electron population is larger and there is an intense synchrotron photon field that serves as target for IC scattering. At energies above 1 GeV, in cases (a) and (b) the main contribution to the spectrum is due to the decay of -mesons created in collisions, reaching unabsorbed luminosities of up to erg s. For , the synchrotron emission of secondary pairs created in interactions is relevant as well. The target field for collisions is also the synchrotron field of primary leptons, and therefore these contributions are not relevant for . For additional details the reader is referred to RV2008 .
Absorption effects modify strongly the emission spectrum in the case with a strong synchrotron radiation field. In fact, as it can be seen in Figure 3 (d), high-energy emission above GeV is completely suppressed for . In the rest of the cases, the absorption is moderate and does not result in significant changes of the emission spectrum.
According to the results presented in this work, low-mass microquasars could be sources of high-energy radiation. Currrent atmospheric Cherenkov telescopes are not likely to detect them, since they are sensible to photons of energy above several hundreds of GeV, and in our models emission in this energy range is completely absorbed, or the peak in the luminosity is well below the detection threshold of the detectors. However, proton microquasars could be observed by AGILE and GLAST at MeV-GeV energies, and in the future by enhanced Cherenkov arrays like MAGIC II and HESS II. Systems like those with high-levels of photomeson production should also be strong high-energy (¿1 TeV) neutrino sources, since neutrinos are not affected by gamma-gamma absorption.
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