What is the closest black hole to the Sun?

International audienceWe examine the distance of the two galactic microquasars GRO J1655-40 and A 0620-00 which are potentially the two closest black holes to the Sun. We aim to provide a picture as wide and complete as possible of the problem of measuring the distance of microquasars in our Galaxy. The purpose of this work is to fairly and critically review in great detail every distance method used for these two microquasars in order to show that the distances of probably all microquasars in our Galaxy are much more uncertain than currently admitted. Moreover, we show that many confirmations of quantitative results are often entangled and rely on very uncertain measurements. We also present a new determination of the maximum distance of GRO J1655-40 using red clump giant stars, and show that it confirms our earlier result of a distance less than 2 kpc instead of 3.2 kpc. Because, it then becomes more likely that GRO J1655-40 could originate from the stellar cluster NGC 6242, located at 1.0 kpc, we review the distance estimations of A 0620-00, which is so far the closest black hole with an average distance of about 1.0 kpc. We show that the distance methods used for A 0620-00 are also problematic. Finally, we present a new analysis of spectroscopic and astrometric archival data on this microquasar, and apply the maximum distance method of Foellmi et al. [Foellmi, C., Depagne, E., Dall, T.H., Mirabel, I.F., 2006b. A&A 457, 249]. It appears that A 0620-00 could indeed be even closer to the Sun than currently estimated, and consequently would be the closest known black hole to the Sun