A possible YORP effect on C and S Main Belt Asteroids

A rotating frequency analysis in a previous paper, showed that two samples of C and S-type asteroids belonging to the Main Belt, but not to any families, present two different values for the transition diameter to a Maxwellian distribution of the rotation frequency, respectively 48 and 33 km. In this paper, after a more detailed statistical analysis, aiming to verify that the result is physically relevant, we found a better estimate for the transition diameter, respectively $D_C = 44 \pm 2$ km and $D_S = 30 \pm 1$ km. The ratio between these estimated transition diameters, $D_C/D_S = 1.5 \pm 0.1$, can be supported with the help of the YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect, although other physical causes can not be completely ruled out. In this paper we have derived a simple scaling law for YORP which, taking into account the different average heliocentric distance, the bulk density, the albedo and the asteroid <<asymmetry surface factor>>, has enabled us to reasonably justify the ratio between the diameters transition of C-type and S-type asteroids. The same scaling law can be used to estimate a new ratio between the bulk densities of S and C asteroids samples (giving $\rho_S/\rho_C \approx 2.9 \pm 0.3$), and can explain why the asteroids near the transition diameter have about the same absolute magnitude. For C-type asteroids, using the found density ratio and other estimates of S-type density, it is also possible to estimate an average bulk density equal to $0.9 \pm 0.1$ g cm-3, a value compatible with icy composition. The suggested explanation for the difference of the transition diameters is a plausible hypothesis, consistent with the data, but it needs to be studied more in depth with further observations.