High Energy Astronomy: Particle Acceleration and Nonthermal Emission.

For many centuries astronomers could only study objects visible by the naked eye. The invention of a telescope in the seventeen century was really a great achievement for the astronomy, as it has led to many wonderful discoveries and to substantial changes in the conventional picture of the world. The science and technology breakthrough achieved in the 20th century made a new revolution in the astronomy. Now astronomy deals not only with optical observations but with observations in very broad photon energy ranges that lie far beyond the optical range as well. The best example here is radio astronomy that is no older than eighty years but now is as well developed as optical astronomy. The possibility to bring telescopes into space out of the Earth atmosphere made it possible to observe Universe in photon energy ranges previously unavailable or hardly available from Earth, such as infrared, ultraviolet, x-rays and gamma-rays. This expansion of the observable energy range dramatically increased the quality and quantity of the obtained data. In the last decades x-ray and gamma-ray astronomy draws the closest attention of of the scientific society. The reason is that space-based telescopes together with the great progress in high energy detectors technology made a breakthrough in observable energy range as well as in angular and energy spectral resolution.

All recent multiwavelength observations show that many astrophysical objects have nonthermal components in their spectra or even have totally nonthermal spectra. The full list of the objects is very long and includes supernova remnants (SNR), high velocity clouds (HVC), gamma-ray bursts, barsters, masers and so on. The processes responsible for the nonthermal emission in all those objects could be absolutely different. But the characteristics of their nonthermal radiation give us very valuable information about the objects where it originates from. So studying of nonthermal radiation is a very useful method in researching many different astrophysical objects.

As it was mentioned above, there are different mechanisms to generate nonthermal emission. The following will be devoted to the nonthermal emission produced by nonthermal particles, mostly by nonthermal electrons. This generation mechanism has close links to the question about the origin of Cosmic Rays (CRs) - a nonthermal particle flux (protons, electrons, nuclei) observed in the neighborhood of the Earth. The reason is that the sources of the Cosmic Rays must be the sources of nonthermal emission and likewise, some sources of nonthermal emission are plausible candidates to be Cosmic Ray sources as well.

Nonthermal particles can generate nonthermal radiation by different radiation processes: synchrotron radiation in a magnetic field, inverse Compton scattering, bremsstrahlung radiation, secondary p₀ decay. The secondary p₀ decay occurs during high energy nuclei interaction with the interstellar medium and this is an emission process that is possible only for nuclei (mostly for protons because of their higher concentration). All other processes are more effective for electrons because their mass is much lower then the proton mass. Positrons can also add to this emission but usually positron concentration and fluxes are much smaller then the electron ones, so the addition can be neglected.

If we want to calculate emission by any of the described processes we need to know the nonthermal particle spectrum in the radiation source. And here we see a big difference between a nonthermal distribution function and the equilibrium Maxwell particle distribution function which is described only by temperature and concentration. A nonthermal spectrum characterizes a nonequilibrium state and depends not only on the parameters of the initial equilibrium state but also on the way of its evolution. The evolution depends on the mechanism of particle acceleration and energy losses. Thus, in order to calculate a particle distribution function it is necessary to know the acceleration mechanisms. That is why investigations of the mechanisms of particle acceleration in astrophysical conditions have a lot of practical implications in astrophysics.

There are different ways to accelerate particles. We will shortly describe the only one of them - particle acceleration on shock fronts also named "first order Fermi acceleration". Let us consider an extended object with a high energy release. In this case usually at least few shock waves are formed. We will focus on the SNRs, HVCs, and shocks in the interplanetary medium. In the case of SNRs the initial energy release is produced by a supernova explosion, in the case of HVCs an energy emission is produced by the interaction of the clouds with gas in the Galaxy halo and in the Solar wind shocks energy is supplied by the energetic processes on the Sun.

As was shown in [1,2] shock waves are an effective particle accelerator due to the first order Fermi [3] mechanism. Particles that are crossing the shock front from upstream to downstream and reverse in average are gaining energy in these cycles. It should be mentioned here that in the astrophysical conditions a medium density is very low so the mean free path due to Coulomb interactions is much shorter than a mean free path due to diffusion on electro-magnetic field fluctuations. The structure of these collisionless shock waves is different from the structure of the usual hydrodynamic shocks and it was studied by several authors [4,5] that used the so called "hybrid code" numerical simulation method. In this method electrons are treated as a fluid while proton trajectories are calculated numerically by solving their dynamical equations. It was shown that the structure of a quasi-parallel (magnetic field vector is almost parallel to the shock front normal) and quasi-perpendicular (magnetic field vector is almost parallel to the shock front plain) shock waves is different. Below we will consider only the case of the quasi-parallel shocks. These shock waves have an extended shock front with a characteristic width of a few hundred ion plasma lengths. In this region ("transition region") strong magnetic field fluctuations are formed. The magnitude of the magnetic field in these fluctuations could be much higher than the mean magnetic field values in upstream and downstream plasma flows. A particle with a mean free path that is greater than the width of the transition region is effectively injected in the Fermi mechanism. For typical astrophysical conditions it is true for protons with an energy only slightly higher than the thermal energy. It could be thought that protons acceleration by Fermi mechanism may be considered in this test particle approximation, but this is not right. There is a strong nonlinear interaction between protons and electro-magnetic fluctuations in the transition region. These fluctuations are formed by Alfven waves that are generated by plasma instabilities induced by proton flows. Protons themselves scatter very effectively on these fluctuations. This nonlinear problem has not been solved analytically and only numerical modeling by hybrid codes is now feasible [4,5]. And there is even more complication here. Accelerated high energy particles in the upstream zone produce an additional pressure to the thermal plasma pressure. This pressure makes an additional deceleration of the incoming plasma in the upstream region. All this leads to creation of the shock precursor - a smooth decrease of plasma velocity (and increase of density) in the upstream flow with the characteristic length a few orders higher than the width of the transition region. This length depends on the upstream diffusion coefficient and flow velocity. The formation of the shock precursor was studied in [6,7]. The usual way to study it is to solve a system of hydrodynamic equations taking into account the additional pressure from high energy accelerated particles. It looks like that a precursor is formed only in strong shocks (shocks with high Mach number).

If a shock is strong enough then its structure is defined by proton kinetic instabilities. Such shocks are called supercritical. In this case we can consider electrons as test particles because of their much lower mass. But again, because of their lower mass, the mean free path of the thermal electrons is much shorter than either thermal proton mean free path and the width of the transition region. So electrons are not directly involved in the Fermi acceleration mechanism, and here appears a question about a mechanism of electrons preacceleration up to the energies from which they are effectively involved into the Fermi acceleration mechanism, or by other words, a question of an injection mechanism.

Different injection mechanisms are possible. Levinson [8] suggested a mechanism of injection by whistlers for the case of very strong shocks with Mach number M>M_*=sqrt(4pP/B²Mp/Me) and anisotropic electron distribution function. We [9] suggested and considered the injection mechanism due to electron scattering on the magnetic field fluctuations in the transition region. This is an appropriate injection for shocks with Mach numbers 1<M<M_*. The electron distribution function in this case could be considered isotropic with a good accuracy, and diffusion approximation is appropriate. Below there is a short description of our model that is presented in detail in [9].

In our model we use a shock wave structure obtained in [5]. We find electron distribution function as a numerical solution of a kinetic equation describing convection, diffusion in coordinate and momentum spaces and energy losses. We solve this equation in the upstream and downstream plasma flows and in the transition region with conditions of continuous distribution function and flux together with appropriate boundary conditions on the system borders. We as well obtain the electron distribution function taking into account injection process, Fermi mechanism and energy looses. In our model injection occurs due to second order Fermi acceleration in the transition region where electrons scatter on magnetic field fluctuations co-moving with the plasma flow and it is described as diffusion in the momentum space.

We used our model for calculation of the electron energy spectrum in the vicinity of shocks in the interplanetary medium, supernova remnants (SNR), regions of interaction of high velocity clouds (HVC) with the Galactic halo. The results of modeling of the electron spectrum in the interplanetary medium are discussed in [9]. This is a very interesting application itself because spacecraft measurements could directly test our model predictions as well as the theory describing the structure of collisionless shock waves. Below we will concentrate on applications to SNRs and HVCs. In these cases we not only obtain the electron spectrum but also use it for calculation of the emission from these objects due to synchrotron, bremsstrahlung and inverse Compton radiation processes.

The question about the origin of the high energy radiation from SNRs is broadly discussed in the literature. High energy radiation is often interpreted as synchrotron emission. This interpretation was suggested in [11] for SN1006. Another possible interpretation was suggested by Asvarov et. al. in [12] who interpreted the high energy emission as nonthermal bremsstrahlung radiation. We applied our model to the modeling of the SNR IC443 [10]. This is a shell structure SNR that was repeatedly observed in different spectral ranges including optical, radio, x-ray and gamma-ray bands. This remnant is a very interesting object. The molecular lines emission registered from the shell of this SNR shows that it is interacting with high density molecular clouds. We calculated the total emission from the IC443 due to synchrotron, bremsstrahlung and inverse Compton radiation using our model of the electron injection and acceleration to obtain the electron energy spectrum [10].

In figure 1 one can see the calculated fluxes measured on Earth for the case of injection from the thermal initial upstream spectrum in comparison with the experimental data. The experimental points were taken from papers [15] (radio), [16] (OSSE, EGRET), [17] (WHIPPLE). For synchrotron radiation free-free absorption was taken into account.

Figure 2 is similar but shows fluxes calculated in assumption that the initial upstream spectrum was a spectrum of the CR electrons. The CR spectrum becomes flatter on low energies. To take this into account we suggested a plateau in the initial CR electron distribution function normalized by p²dp on low energies up to an energy Ec. The curves 1, 2, 3 were calculated for Ec equal to 3 MeV, 8 MeV, 50 MeV. It is necessary to mention that the whole spectrum of the IC443 could be thus explained by leptonic emission only. And it is impossible to conclude if an addition from secondary pion decay is present in the observable spectrum. Thus, a direct confirmation of an effective proton acceleration in the SNR IC443 cannot be done yet. This confirmation could be very important for the theory that considers SNR remnants as the sources of cosmic rays.

One more very interesting application for our model is prediction and explanation of the nonthermal radiation from high velocity clouds. These clouds were first observed by the emission of neutral hydrogen as gas clouds falling on the Galaxy plain with the velocities of about 100-150 km/s. This velocity differs from the velocity of the Galaxy gas flow. The distance to these objects is not yet well defined, but there are some estimations [13] giving the distance of a few kpc. So it looks like these clouds are the clouds of hydrogen with masses near 10⁵ Solar masses that are really falling onto the Galaxy plain. If we use Galactic halo temperature and density values we find that these clouds should produce shock waves with Mach numbers M around 3 while interacting with Galactic halo. These shocks are relatively weak but, nevertheless, they could be particle accelerators. In [14] we calculated the flux of the high energy radiation from an ensemble of these clouds. The excess of the nonthermal flux in a few MeV energy range was observed by COMPTEL [14].

In figure 3 the radiation flux from the HVC ensemble calculated according to our model is shown together with COMPTEL data points for different assumptions about total angular size of the ensemble. There is a good consistency of our predictions with COMPTEL observations.

The presented results show that our model based on very simple physical principles is able to describe the process of electron acceleration in various extended astrophysical objects. The new generation of high energy telescopes with better spatial and energy resolution in the nearest future will supply much more observational data which will help us to make an advance in our understanding of physics of the extended nonthermal radiation sources and will provide more opportunities for testing of our model.

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