The Opposition Effect of the Asteroid 4 Vesta
  We present the results of photometric observations carried out with four small telescopes of the asteroid 4 Vesta in the $B$, $R_{\rm C}$, and $z'$ bands at a minimum phase angle of 0.1 $\timeform{D}$. The magnitudes, reduced to unit distance and zero phase angle, were $M_{B}(1, 1, 0) = 3.83 \pm 0.01, M_{R_{\rm C}}(1, 1, 0) = 2.67 \pm 0.01$, and $M_{z'}(1, 1, 0) = 3.03 \pm 0.01$ mag. The absolute magnitude obtained from the IAU $H$--$G$ function is $\sim$0.1 mag darker than the magnitude at a phase angle of 0$\timeform{D}$ determined from the Shevchenko function and Hapke models with the coherent backscattering effect term. Our photometric measurements allowed us to derive geometric albedos of 0.35 in the $B$ band, 0.41 in the $R_{\rm C}$ band, and 0.31 in the $z'$ bands by using the Hapke model with the coherent backscattering effect term. Using the Hapke model, the porosity of the optically active regolith on Vesta was estimated to be $\rho$ = 0.4--0.7, yielding the bluk density of 0.9--2.0 $\times$ $10^3$ kg $\mathrm{m^{-3}}$. It is evident that the opposition effect for Vesta makes a contribution to not only the shadow-hiding effect, but also the coherent backscattering effect that appears from ca. $1\timeform{D}$. The amplitude of the coherent backscatter opposition effect for Vesta increases with a brightening of reflectance. By comparison with other solar system bodies, we suggest that multiple-scattering on an optically active scale may contribute to the amplitude of the coherent backscatter opposition effect ($B_{C0}$). 
Sunao Hasegawa, Seidai Miyasaka, Noritaka Tokimasa, Akito Sogame,   Mansur A. Ibrahimov, Fumi Yoshida, Shinobu Ozaki, Masana...
astro-ph.EP