2.3 Formation models for cluster diffuse emission
2.3.1 Reacceleration models
Also called primary electron models, reacceleration models are based on the notion that pre- existing populations of relativistic electrons exist in the cluster environment from previous or existing AGN activity from quasars and radio galaxies (Miley and Perola, 1975; Brunetti et al., 2001), or supernovae events and galactic winds during star formation in normal galaxies (V¨olk et al., 1996; Jones, 2011; Morlino and Caprioli, 2012), and that the seed CRe population under- goes second order Fermi acceleration processes (Fermi, 1949; Clarke et al., 2001) to reaccelerate the particles to the required energies. In the case of cool-core clusters, most of them contain a radio-loud central, dominant galaxy which can provide the necessary CRe (Burns, 1990; Best et al., 2007; Mittal et al., 2009). Certain models have also considered the possibility that the seed population is non-relativistic (e.g. Dogiel et al., 2007, and references therein).
There are two primary mechanisms to transfer energy from the ICM to the reaccelerated cosmic rays: cluster turbulence and cluster shocks, both of which occur during mergers.
2.3.1.1 Turbulence
During a cluster merger, ICM electrons can be reaccelerated to relativistic speeds via interactions with large scale (∼ Mpc) MHD turbulence (e.g. Schlickeiser et al., 1987; Ensslin et al., 1998;
Petrosian, 2001; Fujita et al., 2003; Brunetti et al., 2004; Xu et al., 2010; Brunetti and Lazarian, 2011). This turbulent energy is provided by gas sloshing in cluster cores, shearing instabilities, and from intricate interplay among structure formation and merger shocks which develop in the ICM (Vazza et al., 2010a, 2009b; Dolag et al., 2005b; Iapichino and Niemeyer, 2008; Keshet et al., 2010; Iapichino et al., 2011; Paul et al., 2011; ZuHone et al., 2011b; Hallman and Jeltema, 2011; Vazza et al., 2011a, 2012b; Nagai et al., 2013; Miniati, 2014). Numerical simulations show that a combination of these mechanisms can indeed drive MHD turbulence throughout the cluster region (Miniati, 2014; Beresnyak et al., 2013). These processes are the foundation for the turbulent reacceleration model for radio halos and radio mini-halos.
As a second-order Fermi process, turbulent acceleration is not very efficient and is only pro- ductive in re-energising CRe for a few hundred Myr. Any resulting observable radio emission is therefore expected to coincide with ongoing or very recent merger events (Brown et al., 2011a;
Feretti et al., 2004a; Enßlin et al., 2011), which should leave observable traces in the thermal ICM. The turbulent reacceleration model thus successfully predicts the observed correlation be- tween radio halos and cluster mergers as discussed in§2.2.1.3, as well as the existence of USS- RHs as discussed in §2.2.1.1. Once the turbulent energy loses efficiency, i.e. after a certain point in the merger, the spectrum of the reaccelerated particles will become dominated by syn- chrotron and IC energy losses and steepen accordingly. The observations that radio halos are not very common structures (e.g. Kuo et al., 2004), and the observed bimodality in the radio halo P1.4GHz−LXplane are also in line with MHD turbulence being the driving factor in radio halo formation (Brunetti et al., 2009).
Models of turbulence-driven particle acceleration predict that the resulting population of rel- ativistic electrons will have an energy distribution with a maximum Lorentz factor ofγ ∼ 105 (Brunetti, 2004). This will cause a high-frequency cut-off in the population synchrotron spectrum and these models therefore anticipate a steepening of the radio halo spectrum at high frequencies.
Furthermore, since MHD turbulence is not uniform throughout the cluster region, with different turbulent processes being stronger or weaker in different parts of the cluster, the spectral index distribution of the radio emission will likely be of a complex and irregular nature. Observations of radio halo spectra agree with these predictions and thus support the turbulent reacceleration model for radio halos.
These models can also explain radio mini-halos. In this case MHD turbulence in the cool cores of clusters can drive the reacceleration of particles from a variety of potential seed pop- ulations in the central cluster region, as discussed in§2.2.3.2, which is consistent with the few observations of mini-halo spectra and the apparent correlation between their radio power and the cooling rate power of the host cluster (Gitti et al., 2004). Turbulent energy to form radio mini- halos may also be generated by gas sloshing (Mazzotta and Giacintucci, 2008; ZuHone et al., 2011a), a theory that is supported by spiral-shaped cold fronts in high resolution X-ray imaging of cluster cool-cores (Giacintucci et al., 2011).
Although MHD turbulence is a good fit to the radio halo and mini-halo data, the intricacies of the physical mechanisms involved are still not perfectly understood. Our knowledge will be improved once X-ray observations are deep enough to place tight constraints on the physics of turbulence in dynamically disturbed clusters (Schuecker et al., 2004; Sanders et al., 2013). The ASTRO-H satellite is expected to achieve this by observing, among other things, the Doppler broadening and shifting of metal lines in the ICM created by turbulent motions (Dolag et al., 2005b; Nagai et al., 2013; Sunyaev et al., 2003; Vazza et al., 2010b; Takahashi et al., 2010;
Zhuravleva et al., 2012, 2013).
2.3.1.2 Shocks
Current observations of radio relics imply they are strongly connected with cluster shocks (Sarazin, 1999; Keshet et al., 2004). Shock acceleration, a first order Fermi process, has been identified as the process responsible for supernovae synchrotron emission (Jones, 2011; Morlino and Caprioli, 2012). In the cluster context, cosmological simulations have shown that out-going shock waves with moderate Mach numbers, M ∼ 2 - 3, occur on the peripheral regions of clusters due to
merger activity (Miniati et al., 2000; Ryu et al., 2003; Pfrommer et al., 2006; Skillman et al., 2008; Ryu et al., 2008; Vazza et al., 2009a, 2010a; Kang et al., 2007; Vazza et al., 2011b). The Mach number is the primary determinant of the shock acceleration efficiency. Strong shocks, M>3, are efficient particle accelerators, but only occur at very large distances (several Mpcs) from the cluster centre where the density is low and there is minimal energy available to interact with the shocks. Although weaker shocks are less efficient in accelerating particles, they are found closer to cluster cores where the density is higher and thus there is more accessible energy.
In fact, a high percentage of the gravitational energy is dissipated at the relatively weak merger- driven shocks. If even a small amount of this energy is converted into non-thermal particles, then the ICM could host populations of non-thermal cosmic ray particles that have sufficient energy to create diffuse radio emission (Miniati et al., 2001b; Ryu et al., 2003; Blasi et al., 2007; Pfrommer et al., 2007; Vazza et al., 2012a). This is the basis of the shock-driven reacceleration model for radio relics, where the pre-existing relativistic electrons are thought to be from the thermal ICM itself (Ensslin et al., 1998), or remnants of previous AGN activity (Enßlin and Gopal-Krishna, 2001; Enßlin and Br¨uggen, 2002; Hoeft et al., 2004).
Diffuse shock acceleration (DSA) theory is commonly used to describe the energisation of cosmic rays at shock locations (Bell, 1978; Drury, 1983; Blandford and Eichler, 1987; Jones and Ellison, 1991). In this framework, if the seed particles have finite scattering lengths much larger than the width of the shock, they are trapped at the shock front until convection downstream of the shock allows them to escape. While the particles are held in this shock flow, they gain energy each time they are reflected back across the shock with a rate proportional to the energy itself.
Since electrons suffer from strong synchrotron and IC losses, their short radiative lifetimes limit visible radio emission to the region in the immediate vicinity of the shock fronts, causing fairly narrow widths. The downstream diffusion of particles once they are released from the shock-flow causes the oldest and least energetic population of cosmic rays to be the furthest away from the shock front, leading to a flatter radio spectrum at the shock edge. Moreover, DSA models predict that the magnetic field lines involved in the synchrotron emission are aligned with the shock front. These model predictions are consistent with the observed structures, relative locations, and polarization of elongated radio relics (§2.2.2.1).
DSA theories cannot exclude the possibility that shock acceleration could be effective at certain locations of radio halo emission (Markevitch, 2010). However, since radio halos cover large volumes of the ICM, it is unlikely that this emission is purely driven by localised shocks.
Another possible link between shocks and radio halos is indicated by the spatial correlation between radio halo emission and the hot gas of the ICM (§2.2.1.2) that has been found for some clusters (e.g. Govoni et al., 2004). However this is not a strong link as the spatial correlation does not appear to be a generic feature of observed radio halos.