6. BEYOND THERMAL EQUILIBRIUM

The intra-cluster medium is usually assumed to be in collisional ionization equilibrium (CIE). Plasma in CIE is optically thin for its own radiation and external radiation fields do not affect the ionization balance which is entirely determined by the temperature of the plasma. The ionization and recombination rates in CIE plasma have come to a balance and the electron and ion temperatures are in equilibrium. The energy distribution of the electrons in the ICM is usually described by a Maxwellian.

These assumptions are mostly justified but there are certain situations when the plasma deviates from the thermal equilibrium. The shock heated plasma in the cluster outskirts with densities n_e 10^-4 cm^-3 is likely to be out of ionization balance. The equilibration time scale at those low densities is longer than the age of the cluster and therefore the gas may still ionize. At the lowest density parts of warm-hot intergalactic medium filaments photoionization by the diffuse radiation field of galaxies and the cosmic background becomes important. Deviations from a Maxwellian electron distribution could occur in the cooling cores of clusters where multiple gas phases are present. If electrons diffuse from a hotter into a cooler phase they over-ionize the gas. Plasma could also be out of equilibrium in the vicinity of shocks, which may alter the electron/ion equilibrium. Shocks could also accelerate electrons and produce non-Maxwellian tails in the ICM electron distribution. Future observatories with large photon collecting area and high spectral resolution will be able to study the spectral signature of these non-equilibrium effects in detail. Moreover, radio observations of clusters reveal the presence of relativistic electrons emitting synchrotron radio emission. This relativistic plasma in clusters may also emit Inverse-Compton radiation in the form of a power law shaped X-ray continuum.

Below we briefly describe what are the spectral signatures of non-equilibrium effects in the multiphase plasma and around shocks, and we summarize the state of observations of X-ray emission from relativistic plasma.

6.1. Multiphase plasma

High signal-to-noise X-ray spectra reveal that multiple spatially unresolved gas phases are present in the cooling cores of clusters (Kaastra et al. 2004, Sanders & Fabian 2007, Simionescu et al. 2008b). In M87 and Perseus, the most nearby and the brightest cooling cores, images obtained by Chandra reveal filaments and blobs in soft X-rays (Forman et al. 2007, Fabian et al. 2006). But the multi-phase extends to much lower temperatures. Narrow band optical observations of cooling cores reveal H emitting warm (10⁴ K) gas which both in M87 and in Perseus is often associated with soft X-ray filaments (Sparks et al. 2004, Fabian et al. 2006). The H filaments in Perseus are composed of gas with temperatures of 10⁴ K down to 50 K (Hatch et al. 2005). Sanders & Fabian (2007) showed that they are surrounded and possibly mixed with soft X-ray emitting plasma with temperatures of 0.5-1 keV.

If electrons penetrate from the hotter to the cooler phase they over-ionize the "cool" plasma which may result in observable low energy X-ray line emission. In Fig. 38 we show a simulated EPIC/pn spectrum (100 ks) of the Eastern X-ray arm of M87. Within this extraction region, we assume the presence of a filament with a diameter of 60 pc and length of 3.5 kpc filled with 10⁴ K gas with an average density of n_e = 10 cm^-3. We assume that 0.05% of all the electrons within the filament have penetrated there from the ambient ICM and have a Maxwellian energy distribution with a temperature of 2 keV. As the spectrum in Fig. 38 shows, a deep observation with a well calibrated instrument would even at medium spectral resolution reveal the line emission from Ne III-VI at 0.85-0.9 keV, O IV-VII at ~ 0.55 keV, N III-VI between 0.40-0.42 keV, C IV-V at 0.35, 0.37 keV, and at 0.30-0.31 keV. This exercise demonstrates the potential of X-ray spectroscopy in constraining the diffusion of electrons from the hot ICM phase into the warm filaments. In reality such attempts are hampered by the complicated multi-temperature structure of the ICM around the filaments. Detailed studies of the electron diffusion will be possible with future micro-calorimeters or transition-edge sensors sensitive at low energies.

Figure 38. Simulated EPIC/pn spectrum of the Eastern X-ray arm of M87 assuming a presence of a filament with a diameter of 60 pc and length of 3.5 kpc filled with 104 K gas with an average density of ne = 10 cm-3. We assumed that 0.05% of all the electrons within the filament penetrated there from the ambient ICM and have a Maxwellian distribution with a temperature of 2 keV. The model plotted with the red line shows the emission from the ambient hot ICM. Assuming a well calibrated instrument the excess line emission at ~ 0.85 keV would be clearly revealed.

6.2. Shocks and non-equilibrium

In the downstream regions of shock fronts the electron and ion temperatures of the plasma might be different and the ICM is out of ionization equilibrium.

In a collisional plasma, protons are heated dissipatively at the shock layer which has approximately the width of the collisional mean free path, but the faster moving electrons do not feel the shock (for Mach numbers smaller than ~ 40), they get adiabatically compressed and equilibrate with the ions via Coulomb collisions reaching the post-shock temperature predicted by the Rankine-Hugoniot jump condition. Astrophysical shocks in a magnetized plasma, like the ICM, are expected to be "collisionless". Which means that the electron and ion temperature jump occurs on a spatial scale much smaller than the collisional mean free path, but ions and electrons are heated by the shock to different temperatures. In heliospheric shocks with moderate Mach numbers electrons are heated much less than protons, barely above the adiabatic compression temperature (Schwartz et al. 1988). The plasma behind the shocks is thus expected to be in electron/ion temperature non-equilibrium. Assuming that no kinetic energy goes into acceleration of cosmic rays, the post-shock temperature after the Coulomb equilibration time scale reaches the same temperature as the one predicted by the Rankine-Hugoniot jump condition.

Markevitch (2006) used the bow shock in the "Bullet cluster" (1E 0657-56) to determine whether the electrons in the intra-cluster plasma are heated directly at the shock to the equilibrium temperature (instant-equilibration), or whether they equilibrate via Coulomb collisions with protons. They measure the temperature in front of the shock front seen as a gas density jump, from which, using the adiabatic and Rankine-Hugoniot jump conditions, they determine the expected post shock adiabatic and instant-equilibration electron temperatures which they directly compare with observed data. The shock in the "Bullet cluster" is happening approximately in the plane of the sky, which means that the downstream velocity of the shocked gas spreads out the time dependence of the electron temperature in the plane of the sky. The measured temperatures behind the shock in the bullet cluster are consistent with instant heating of electrons. Adiabatic compression followed by equilibration on the collisional time scale is excluded at the 95% confidence level (see Fig. 39).

Figure 39. Left panel: Electron-ion equilibration in 1E 0657-56 (the "Bullet cluster"). The two data points show the deprojected electron temperature for two narrow post shock regions. The data points are overlaid on the model predictions for instant equilibration (light gray) and for adiabatic compression followed by collisional equilibration (dark gray). The velocity of the post-shock gas relative to the shock front is ~ 1600 km s -1. (From Markevitch 2006). Right panel: The 6.9-7.0 keV part (rest frame energies) of a simulated Astro-H micro-calorimeter spectrum of the downstream region of a M = 2.2 shock propagating through a 108 K plasma. The Fe XXVJ satellite line is clearly stronger (with a significance of 3 for these simulations) than that predicted by the thermal model with a Maxwellian electron distribution indicated by the full line. (From Kaastra et al. 2009).

Shocks and turbulence in the magnetized ICM are believed to be sides of non-thermal particle acceleration in clusters (for reviews on particle acceleration see e.g. Petrosian & Bykov 2008, Bykov et al. 2008). Stochastic turbulence in the ICM can create a non-thermal tail to the Maxwellian electron distribution (Bykov & Uvarov 1999. The low energy end of the power-law electron distribution enhances the ionization rates and modifies the degree of the ionization of the plasma. Porquet et al. (2001) showed that the plasma is always more ionized for hybrid (Maxwellian plus power-law) electron distribution than for a Maxwellian distribution and the mean charge of a given element at a given temperature is increased. The effect is more pronounced at lower temperatures. In groups of galaxies, low mass clusters or in cooling cores a peculiar ionization state of Fe which is inconsistent with the temperature determined from continuum emission can potentially be a good tool to reveal such non-thermal tails in the electron distribution. Kaastra et al. (2009) show that a non-Maxwellian tail in the electron distribution behind a shock front propagating through 10⁸ K plasma cannot be revealed by current detectors. They simulate the electron distribution and the resulting X-ray spectra of the downstream region of a M = 2.2 shock in a X-ray bright hot cluster and show that a good indicator of hard non-thermal electrons is the enhancement of the equivalent widths of satellite lines which may be possible to detect with the X-ray micro-calorimeters on the future Astro-H satellite or on the proposed International X-ray Observatory (IXO). In the right panel of Fig. 39, we show the 6.9-7.0 keV part (rest frame energies) of a simulated 100 ks Astro-H spectrum of the downstream region of a M = 2.2 shock propagating through the ICM in a cluster similar to Abell 2029. The Fe XXVI Ly lines and the Fe XXVJ satellite line are visible in the spectrum and the satellite line is clearly stronger than that predicted by the thermal model with a Maxwellian electron distribution indicated by the full line.

6.3. Non-thermal x-ray emission from relativistic plasma

Direct evidence for the presence of electrons accelerated up to relativistic energies comes from observations of radio emission in clusters. Large-scale diffuse extended radio emission in the form of halos or relics has been observed in about 50 known clusters of galaxies (Feretti & Giovannini 2007). This radiation is associated with the ICM and has no connection to the cluster galaxies. It is clearly produced by synchrotron emission by a population of relativistic electrons in the ICM. Since the energy density of the cosmic microwave background (CMB) radiation (~ 4 × 10^-13 erg cm^-3) is higher than the energy density in the intra-cluster magnetic field (3 × 10^-14(B / µG)² erg cm^-3), these relativistic electrons will radiate away most of their energy via inverse-Compton scattering of the CMB photons, producing a power-law shaped X-ray continuum emission (Rephaeli 1977). The detection of both the non-thermal X-ray emission and the radio emission would be a powerful tool, which would allow us to determine both the volume averaged magnetic field in clusters and the energy in the population of relativistic electrons. But for the observed radio fluxes, detectable hard X-ray emission can only be produced if the magnetic fields are of the order of 0.1 µG. Faraday rotation measurements indicate that the intra-cluster magnetic fields are much stronger - of the order of 1-10 µG. The volume averaged magnetic field might, however, be weaker than the strong magnetic field measured by Faraday rotation along our line of sight.

Non-thermal X-ray emission could in principle also originate in non-thermal bremsstrahlung of shock accelerated supra-thermal electrons in the ICM. However, such non-thermal bremsstrahlung phase must be very short lived. Petrosian (2001) points out that in order to explain the reported hard X-ray luminosity in the Coma cluster (see later) by bremsstrahlung emission, the continuous input of energy into the ICM would increase the ICM temperature to 10¹⁰ K in Hubble time. Also the high-energy electrons > 50 keV can not be confined by the gravitational potential of the cluster and will escape in a crossing time of < 1.5 × 10⁷ years, unless they are confined by the intra-cluster magnetic field. Alternatively, hard X-ray emission with power-law spectra of ~ 1.5 could be produced by synchrotron emission from ultra-relativistic electrons and positrons produced by the interaction of relativistic protons with the CMB (Inoue et al. 2005).

The nearest hot massive cluster of galaxies with a big radio halo is the Coma cluster (Feretti & Giovannini 1998). Therefore, Coma has been the primary target to identify non-thermal X-rays. Their detection has been reported with both BeppoSAX (Fusco-Femiano et al. 1999) and RXTE (Rephaeli & Gruber 2002). More recently, Coma has also been observed with the INTEGRAL satellite (Eckert et al. 2007). A combined analysis of XMM-Newton and INTEGRAL data revealed the presence of hotter (~ 12 keV) gas in the south-west region overlapping with a radio halo. This hot gas was probably heated in a merger (Eckert et al. 2007). Analysing INTEGRAL, ROSAT, and RXTE data, Lutovinov et al. (2008) found that the global Coma spectrum is well fitted with a thermal model and the evidence for a hard excess is very marginal (1.6). Ajello et al. (2009) analysed combined XMM-Newton and hard X-ray Swift-BAT spectra and even though they could not rule out the presence of non-thermal hard X-ray emission outside of their 10' region, within their field of view they found a good fit with two thermal models, with no need for a non-thermal component. Wik et al. (2009) analyzed combined Suzaku Hard X-ray Detector (HXD-PIN) and XMM-Newton mosaic spectra of a larger 34' × 34' region centered on the Coma cluster. They found no statistically significant evidence for non-thermal emission implying a lower limit of 0.15 µG on the cluster averaged magnetic field.

Suzaku observations of the bright radio relic in the merging cluster Abell 3667 show that, at least in some cases, magnetic fields can be high even at distances of ~ 1 Mpc from the cluster core. The upper limits on the non-thermal emission from Suzaku put a lower limit of 2.3 µG on the magnetic field in the radio relic. The non-thermal energy density in the relics is > 7% of the thermal energy density and likely near 20% (Nakazawa et al. 2009).

Ajello et al. (2009) analysed the spectra of 10 clusters of galaxies detected above 15 keV with the Swift-BAT. Except of the Perseus cluster the spectrum of which is probably contaminated by hard X-ray emission from the central AGN, the spectra of all clusters are well fitted by a simple thermal model. Their stacked spectrum of 8 clusters (except Perseus and Coma) also confirms the absence of any non-thermal high energy component down to a flux of 1.9 × 10^-12 erg cm^-2s^-1 in the 50-100 keV band.

Although there have been several other reports claiming the detection of both hard and soft X-ray emission in excess to the ICM emission, interpreted as being possibly of non-thermal origin (for reviews see Rephaeli et al. 2008, Durret et al. 2008), a solid identification of non-thermal X-rays from clusters is still lacking. In the relatively near future, X-ray satellites with imaging hard X-ray optics sensitive up to 40 keV will be launched: Astro-H, NuSTAR, Simbol-X. They will shed more light on the presence of very hot thermal gas, non-thermal and supra-thermal electron populations, and on intra-cluster magnetic fields. The Fermi Gamma- ray Large Array Space Telescope (GLAST) might detect gamma ray emission associated with relativistic intra-cluster ions. These missions promise a big progress in our understanding of the non-thermal particle population in clusters of galaxies.