A&A 426, 777 (2004)
DOI: 10.1051/0004-6361:20041826

Erratum

Constraining the population of cosmic ray protons in cooling flow clusters with $\gamma$-ray and radio observations: Are radio mini-halos of hadronic origin?

C. Pfrommer - T. A. Enßlin

Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str.1, Postfach 1317, 85741 Garching, Germany

A&A 413, 17-36 (2004), DOI: 10.1051/0004-6361:20031464

Key words: errata, addenda - galaxies: cooling flows - galaxies: clusters: general - galaxies: clusters: individual: Perseus (A426) - radiation mechanisms: non-thermal

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The normalization of the inverse Compton (IC) flux induced by secondary cosmic ray electrons (CRe) in Fig. 3 has been incorrectly computed. The correct ratio of $\gamma$-ray flux resulting from decaying pions relative to IC flux from secondary CRe is 1.5 $\times$ 10^-1 ( $\alpha_{\rm p}= 2.1$) and 1.7 $\times$ 10^-3 ( $\alpha_{\rm p}= 2.7$) at $E_\gamma = 1~\mbox{GeV}$. This is illustrated in Fig. 1, which replaces Fig. 3 of our paper.

This induces a minor change in the expected IC emission (cf. Sect. 4.1.) of hadronically originating CRe in the Perseus cluster. Assuming a cosmic ray proton (CRp) spectral index of $\alpha_{\rm p}= 2.3$ and taking the CRp normalization obtained by comparing the hadronically induced synchrotron emission to the observed radio mini-halo of Perseus, the secondary IC emission ought to have read as

$$% \frac{{\rm d}\mathcal{F}}{{\rm d}E} (20 \mbox{ keV})= \math... ...-7} ~\gamma \mbox{ cm}^{-2} \mbox{ s}^{-1} \mbox{ keV}^{-1},$$ (1)

with $\mathcal{F}_{{\rm IC}} = 8.4,$ 4.2, and 2.3 for $B_0 = 5~\mu \mbox{G}, 10~\mu \mbox{G},$ and $20~\mu \mbox{G}$. Comparing these results to the post-launch spectral sensitivity of $4\times 10^{-6} ~\gamma \mbox{ s}^{-1} \mbox{ cm}^{-2} \mbox{ keV}^{-1}$ to the continuum at 20 keV for an observation time of 10⁶ s ($3\sigma$ detection), there is only a minor chance to detect IC emission of CRe as previously concluded. All other figures, formulae, and conclusions remain unchanged.

Figure 1: The simulated differential flux of $\gamma$-rays from Perseus reaching the Earth. Shown are upper limits of the IC emission of secondary CRe (power-laws, assuming zero magnetic field) as well as pion decay induced $\gamma$-ray emission (represented by broad distribution centered on $E_{{\rm peak}}\simeq 67.5 \mbox{ MeV}$). The normalization of the spectra differing in their values of the CRp spectral index $\alpha _\gamma =\alpha _{\rm p}$ (Dermer's model) depends on the assumed scaling between CRp and thermal energy density. We fix this scaling parameter  $X_{\rm CRp}$ assuming the isobaric model by comparing the integrated flux above 100 MeV to EGRET upper limits (see Reimer et al. 2003).

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References

• Reimer, O., Pohl, M., Sreekumar, P., & Mattox, J. R. 2003, ApJ, 588, 155 [NASA ADS] [CrossRef]