Modeling the non-thermal component

We have found with good confidence that the hard X-ray flux detected withINTEGRALis non-thermal. Moreover, comparison with theChandra image (see Fig. 5.7) indicates that significant contamination of the observed spectrum by point sources is unlikely. Therefore, we conclude that there exists diffuse non-thermal emission from relativistic electrons in the cluster (see Chapt. 2). The natural explanation for the excess is inverse-Compton (IC) scattering with the Cosmic Microwave Background (CMB) of the same electrons which produce the radio emission through synchrotron radiation. In this framework, we used the compilation of existing radio data presented by Johnston et al. (1981) to constrain the shape of the Spectral Energy Distribution (SED) of the non-thermal emission from the cluster, and tried to model the resulting SED. To construct our models, we assumed a relativistic electron population with a power-law distribution with spectral index of 2.0, as is typical for shock-accelerated electrons, and a high-energy cut-offE_cut. Unfortunately, the existing radio data are old, and were measured by several instruments with very different beam size, so the exact shape of the radio spectrum could not be constrained.

Nevertheless, by comparing the strength of the radio and hard X-ray emissions, and using the formula

where P_sync,P_IC is the power emitted through synchrotron, respectively IC emission, B is the mean magnetic field strength and u_{CM B} is the well-known energy density of the Cosmic Microwave Background, we can constrain the mean magnetic field value in the cluster. The bottom panel of Fig. 5.9 shows the SED models computed for different values of magnetic field B and electron cut-off energy E_cut. Based on these models, we estimate the magnetic field strength to be

B ∼0.1−0.2µG. (5.5)

This value is consistent with the value obtained with the same method by Fusco-Femiano et al. (1999) in the Coma cluster (see Sect. 2.7.3). However, it is one order of magnitude lower than the typical magnetic field strengths deduced from Faraday rotation measures (see Sect. 2.7.1). Unfortunately, no polarization measurement and high-resolution maps are yet available on the Ophiuchus cluster. With the help of the new generation of low-frequency radio arrays (GMRT, LOFAR), we will be able to probe the population of high-energy electrons and the magnetic field structure in the Ophiuchus cluster. In order to achieve this goal, we proposed a 30 hours Giant Metrewave Radio Telescope (GMRT) observation of the Ophiuchus cluster, which was accepted by the GMRT time allocation comitee, and will be performed in August 26-30, 2008. The GMRT array consists of 30 antennae with a diameter of 45 m, with an excellent sensitivity (0.02 mJy at 610 MHz) and angular resolution (5 arcsec at 610 MHz). Thanks to the good sensitivity and angular res-olution, we will be able to study the morphology of the radio source. We will also perform the observation at several different frequencies, which will enable us to better constrain the radio spectrum. Finally, we will also measure the polarization of a background source at different frequencies, which will enable us to measure the magnetic field of the cluster through Farady rotation measure, and compare the result with the value inferred from synchrotron/IC flux ratio. This is extremely important to determine if the origin of the emission detected byINTEGRALindeed comes from the same electron population as the radio emission.

On the other hand, if the mean magnetic field in the cluster is of the order of 1 µG as it is usually found from Faraday rotation measure, the inverse-Compton model for the HXR emission falls short of the observed value by about 1 order of magnitude. In this case, we have to consider other models for the origin of the HXR emission. In particular, the emission could be due to synchrotron emission from another population of electrons with very high energies (E ∼ 100 TeV, see Sect. 2.5). The top panel of Fig. 5.9 shows several models for the SED of the non-thermal emission for different values of magnetic field B and cut-off energy E_cut. For magnetic field strengths B = 1−10µG and cut-off energies E_cut ∼ 0.1 PeV, this model can explain the observed level of hard X-ray emission. Unfortunately, the lack of multi-wavelength information does not allow us to constrain this model any further. In the TeV γ-ray range, the figure also shows the 10 mCrab flux level, which corresponds more or less to the sensitivity level of the HESS Cherenkov telescope array. We can see that the relatively high level of TeVγ-ray emission predicted by this model could be detectable by HESS if the mean magnetic field value is not too high. Therefore, observations of the Ophiuchus cluster with HESS would bring an important input to the understanding of the INTEGRAL observations, even in the case of a non-detection. The main problem resides in the fact that the HESS instrument is

5.4. Broad-band spectrum of the cluster 89

Figure 5.9: Models for the Spectral Energy Distribution (SED) of the non-thermal emis-sion from the Ophiuchus cluster. The radio data are from Johnston et al. (1981). The black triangle represents the INTEGRAL measurement of non-thermal emission (this work). In the top panel, we considered a high-energy electron population of E ∼ PeV electrons ra-diating in the HXR range through synchrotron emission and in the TeV range through IC scattering, while in the bottom panel, a more conventional modeling withE ∼ GeV elec-trons was performed. The dashed lines above∼10 TeV shows attenuation of the spectrum by interaction of the γ-ray photons with the extragalactic infra-red and CMB radiation fields.

operated by a consortium of institutes, and does not work as an observatory. Hence, the observation possibilities for scientists which are not members of the HESS consortium are very small. Nevertheless, we also submitted an observation proposal to the HESS guest observer program, which was unfortunately rejected. We hope that a similar proposal will be accepted in the future for observation in the TeV γ-ray domain by a Cherenkov telescope.

5.5 Discussion