MBM 12 and MBM 16 distances

Among the multitude of intrinsic SDSS index vs. index diagrams the $(g-r) \ vs. \ (r-i)$ diagram is characterized by showing only minor $(g-r)$ variation for the M dwarfs. The $(g-r) \ vs. \ (r-i)$ reddening vector has a slope almost identical to the slope of the main sequence earlier than $\approx$M2, meaning that dwarfs later than $\sim$M2 are not contaminated by reddened dwarfs of earlier type. Chemical composition, stellar activity and evolution have only minor effects on the location of the M2$-$M7 dwarfs in the $(g-r) \ vs. \ (r-i)$ diagram implying that reddening may be isolated in a rather unique way. From $r$, $M_{r,(r-i)_0}$ and $E_{g-r}$ we may construct distance vs. $A_r$ diagrams. This purely photometric method is applied on SDSS DR8 data in the MBM 12 region. We derive individual stellar distances with a precision $\approx20-26$%. For extinctions in the $r-band$ the estimate is better than 0.2 mag for $\approx 67%$ and between 0.3 and 0.4 for the remaining $\approx 33%$. The extinction discontinuities noticed in the distance vs. $A_r$ diagrams suggest that MBM 12 is at $\approx$160 pc and MBM 16 at a somewhat smaller distance $\approx$100 pc. The distance for which $\Delta (A_r)/\sigma (\Delta(A_r))$ = 3, where $\Delta (A_r)$ refers to $\bar{A_{r, on}}-\bar{A_{r, off}}$, may possibly be used as an indicator for the cloud distance as well: For MBM 12 and 16 these distance estimates equal 160 and 100 pc, respectively