On the origin of Fanaroff-Riley classification of radio galaxies: Deceleration of supersonic radio lobes

We argue that the origin of "FRI/FRI{-.1em}I dichotomy" -- the division between Fanaroff-Riley class I (FRI) with subsonic lobes and class I{-.1em}I (FRI{-.1em}I) radio sources with supersonic lobes is sharp in the radio-optical luminosity plane (Owen-White diagram) -- can be explained by the deceleration of advancing radio lobes. The deceleration is caused by the growth of the effective cross-sectional area of radio lobes. We derive the condition in which an initially supersonic lobe turns into a subsonic lobe, combining the ram-pressure equilibrium between the hot spots and the ambient medium with the relation between "the hot spot radius" and "the linear size of radio sources" obtained from the radio observations. We find that the dividing line between the supersonic lobes and subsonic ones is determined by the ratio of the jet power $L_{\rm j}$ to the number density of the ambient matter at the core radius of the host galaxy $\bar{n}_{\rm a}$. It is also found that there exists the maximal ratio of $(L_{\rm j}/\bar{n}_{\rm a})$ and its value resides in $(L_{\rm j}/\bar{n}_{\rm a})_{\rm max}\approx 10^{44-47} {\rm erg} {\rm s}^{-1} {\rm cm}^{3}$, taking account of considerable uncertainties. This suggests that the maximal value $(L_{\rm j}/\bar{n}_{\rm a})_{\rm max}$ separates between FRIs and FRI{-.1em}Is.