2mass/Hipparcos Extinctions and Distances in the Serpens - Aquila Region.IV. Error Propagation. Individual stars and mean values

We estimate errors from the application of the main sequence $(H-K)_0 \ vs. \ (J-H)_0$ and $(J-K)_0 \ vs. \ M_J$ relations on 2mass photometry to provide stellar extinctions and distances. The error propagation on individual stars in the Serpens -- Aquila star forming region is investigated. Results: errors on the $J-band$ extinction $σ_{A_J}$ are found in the range from 0.05 to 0.20 mag and peak at $\approx$0.1. For the absolute $J-band$ magnitudes the $σ_{M_J}$ range is found from 0.1 to 0.5 mag and the distribution has a pronounced maximum at $\approx$0.3 mag. Individual relative distance errors, $σ_{distance}/distance$, are found in the interval from 8$$ to 25$$ and peak at 15$$. If cloud distances are identified with the location of a local maximum of the $A_J(median)/distance(median)$ variation the Serpens -- Aquila cloud may be at 203$\pm$7 pc. We propose that the median absolute deviation from the median of $A_J$ could be used as a cloud distance indicator

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