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Soft excess emission, defined here as excess emission over the usual thermal emission from hot intracluster gas at energies below 1 keV, has been detected significantly in ~30% of clusters of galaxies. This value is based on the two largest cluster soft excess samples (Bonamente et al. 2003, Kaastra et al. 2003). However, as described above, such detections are difficult because of instrumental issues and for many objects a controversy remains.

Thermal and non-thermal models have been proposed to account for this soft excess emission. We will briefly summarise them below using Coma and Sérsic 159-03 as examples.

7.1. Thermal models

7.1.1 WHIM in Coma

The massive soft excess halo around Coma (Bonamente et al. 2003) is not well accounted for by a non-thermal model. Furthermore, Finoguenov et al. (2003) detected O VII and O VIII line emission in the outskirts of Coma. Thus Coma is a good case for a cluster where the soft excess is dominantly of thermal nature. Bonamente et al. (2003) proposed that the soft component may reside in external filamentary structures of warm-hot intergalactic medium (WHIM). These filaments are predicted by hydrodynamic simulations of formation and evolution of large-scale structures, extending for several megaparsecs, containing a large fraction of the current epoch's baryons (e.g. Cen & Ostriker 1999, Davé et al. 2001, Yoshikawa & Sasaki 2006). In WHIM simulations, the temperatures are in the range 105 - 107 K, consistent with the soft excess properties found in Coma. Assuming a filamentary geometry, Bonamente et al. (2003) derived densities of n ~ 10-5 - 10-4 cm-3 for the warm gas in Coma. These values are consistent with those in the WHIM simulations (10-7 - 10-4 cm-3). Assuming n = 10-4 cm-3, the implied mass of the filament exceeds that of the hot gas by a factor of 3.

7.1.2 Soft emission from merging sub-halos

In Sérsic 159-03, detailed WHIM filament calculations showed that unrealistically long structures (~ 100 - 1000 Mpc), projected on the line of sight of the cluster, are required to explain the soft excess detected in XMM-Newton data (Bonamente et al. 2005a). The assumption that the warm gas occupies the same volume as the hot gas has the problem that there is a pressure difference between the two components, and that the cooling time is short. As proposed by these authors, this problem can be avoided if one assumes that the warm gas is not distributed evenly but rather in high density 10-2 - 10-3 cm-3 clumps with a volume filling factor f << 1. Such a distribution is predicted by the simulations of Cheng et al. (2005), in which the soft excess emission comes from high-density and low entropy gas associated with merging sub-groups, which preserve their identity before being destroyed and thermalised in the hot ICM. The simulated 0.2-1.0 keV band soft excess in the radial range of 0-0.5 rvir is consistent with that published in Bonamente et al. (2005a) for Sérsic 159-03. This scenario yields a warm gas mass of 25% of the hot gas mass for Sérsic 159-03.

However, Werner et al. (2007) show that the soft excess emission peaks at the position of the central cD galaxy and does not show any significant azimuthal variations. Moreover the soft excess in Sérsic 159-03 is observed out to radii of at least 1 Mpc. If this soft excess is associated with the gas of an infalling group, then this group is moving exactly along the line of sight. However, such an infalling group cannot explain the presence of the soft excess emission at large radii. Therefore the soft excess observed in Sérsic 159-03 is most probably not of thermal origin.

7.2. Non-thermal models

Inverse Compton models of energetic electrons on CMB photons and/or on galaxy starlight have been developed by various authors to account for the soft excess observed in several of the objects presented here.

Non-thermal inverse Compton emission has a power-law spectrum with a relative flux which in the 0.3-10.0 keV band may account for more than 30% of the cluster emission. The best-fit power-law photon indices of soft excess clusters are typically between alphaph ~ 2.0-2.5. In the IC model, this corresponds to a differential relativistic electron number distribution dN / dE = N0 E(-µ) with µ = 3-4. These are steeper than the distribution of the Galactic cosmic-ray electrons (µ ~ 2.7). The steeper power-law distribution might indicate that the relativistic electrons suffered radiative losses (Sarazin 1999). Relativistic electrons in this energy range have relatively long lifetimes of tIC = 2.3 × 109 (gamma / 103)-1(1 + z)-4 yr and tsyn = 2.4 × 1010(gamma / 103)-1(B / (1 µG))-2 yr for inverse-Compton and synchrotron processes respectively.

As mentioned earlier, Werner et al. (2007) conclude that a non-thermal model best explains the observed properties of the soft excess in Sérsic 159-03. The total energy in relativistic electrons needed to explain the excess emission within the radius of 600 kpc does not exceed 1 × 1061 erg, while the total thermal energy within the same radius is 3 × 1063 erg. This means that even if the energy in relativistic ions is as much as ~ 30 times larger than that in relativistic electrons, the total energy in cosmic ray particles will only account for 10% of the thermal energy of the ICM.

Models that may account for the observed soft excess can also be found in the following list: Enßlin et al. (1999), Atoyan & Völk (2000), Sarazin & Kempner (2000), Takizawa & Naito (2000), Fujita & Sarazin (2001), Petrosian (2001), De Paolis et al. (2003), Bowyer et al. (2004a), Petrosian et al. (2008) - Chapter 10, this volume.

7.3. Some problems and open questions

In the Virgo cluster a strong soft excess was detected in the extreme ultraviolet with EUVE (Lieu et al. 1996a, Berghöfer & Bowyer 2000a, Bonamente et al. 2001b, Durret et al. 2002) and in the 0.2-0.4 keV band with ROSAT (Bonamente et al. 2002). However, the observations with XMM-Newton did not confirm the existence of this soft excess: a thermal model for the hot cluster emission with Galactic absorption describes the soft band X-ray spectra (above 0.3 keV) of Virgo obtained with XMM-Newton sufficiently well (Kaastra et al. 2003, Matshushita et al. 2002).

Arabadjis & Bregman (1999) claimed that some of the X-ray absorption cross sections were wrong, and that soft excesses would disappear when using the proper values. However, it is surprising that this claim has neither been confirmed nor refuted ever since. During some time, there have been wrong He cross sections by Balucinska-Church & McCammon (1992) in the XSPEC software (see Arabadjis & Bregman refer to those wrong cross sections. They have been improved by Yan et al. (1998) nd are now included properly for example in Wilms' cross sections that are in XSPEC. They are also properly included in the SPEX software. Note that Wilms' more recent cross sections agree quite well with the older Morrison & McCammon (1983) work (see the discussion in Wilms et al. 2000). Lesson to be learned: it is important to check for each paper which cross sections / absorption model have been used!

Several searches for far-ultraviolet emission lines expected from a 106 K gas were performed with the FUSE satellite on the cores of several clusters. Oegerle et al. (2001) have reported the detection of O VI lambda1032 Å in Abell 2597 (z = 0.0824), implying a mass inflow rate of about 40 Modot / yr. However, FUSE has not detected warm gas in five other clusters: Abell 1795 (Oegerle et al. 2001), Coma and Virgo (Dixon et al. 2001), and Abell 2029 (z = 0.0775) and Abell 3112 (Lecavelier des Etangs 2004); the upper limits on the inflow rates for these five clusters were of the order 25 Modot / yr.

A recent review by Bregman (2007) summarises current knowledge on the search for missing baryons at low redshift. Note however that in his Fig. 9 (already in Bregman & Lloyd-Davies 2006) he claims that the soft excess found in some clusters by Kaastra et al. (2003) is an artefact due to wrong background subtraction. The argument is that there is a correlation between the Rosat R12 (low energy) count rate and the presence or absence of a soft excess. However, a closer inspection shows that this correlation is driven by a few clusters with strong Galactic absorption. As Kaastra et al. (2003) pointed out, in addition to the atomic gas visible at 21 cm these clusters also have significant X-ray opacity contributions due to dust or molecules, which naturally explains the observed flux deficit. When these clusters are excluded, the correlation fades away.

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