Herschel discovery of far-infrared emission from the hotspot D in the radio galaxy Cygnus A

The far-infrared counterpart of hotspot D, the terminal hotspot of the eastern jet hosted by the radio galaxy Cygnus A, is detected with Herschel Aperture photometry of the source performed in 5 photometric bands covering the wavelength range of 70-350 mu m. After removing the contamination from another nearby hotspot, E, the far-infrared intensity of hotspot D is derived as 83 +/- 13 and 269 +/- 66 mJy at 160 and 350 mu m, respectively. Since the far-infrared spectrum of the object smoothly connects to the radio one, the far-infrared emission is attributed to the synchrotron radiation from the radio-emitting electron population. The radio-to-near-infrared spectrum is confirmed to exhibit a far-infrared break feature at the frequency of nu(br) = 2.0(-0.8)(+1.2) x 10(12) Hz. The change in energy index at the break (Delta alpha = 0.5) is interpreted as the impact of radiative cooling on an electron distribution sustained by continuous injection from diffusive shock acceleration. By ascribing the derived break to this cooling break, the magnetic field, B, in the hotspot is determined as a function of its radius, R within a uniform one-zone model combined with the strong relativistic shock condition. An independent B-R constraint is obtained by assuming the X-ray spectrum is wholly due to synchrotron self-Compton emission. By combining these conditions, the two parameters are tightly determined as B = 120-150 mu G and R = 1.3-1.6 kpc. A further investigation into the two conditions indicates the observed X-ray flux is highly dominated by the synchrotron self-Compton emission.