colour transformations. The XMM-OM $u$ band is characterized by:

-   a strong sensitivity in the 3100-3300 Å region, where the ground-based Johnson’s $U$ is essentially blind;

-   a reduced sensitivity in the critical Balmer decrement region (3850-4100 Å), leading to untransformability between both bands for stars showing Balmer jump (see Sects. 3.1.1, 3.1.6, 3.1.7). As we show later, $(U-u)$ can be evaluated thanks to $uvw1$.

Fig. 1b allows comparison between XMM-OM and standard $U$, $B$ and $V$ filters.

The UV XMM-OM filters do not correspond to any pre-existing standard system. No transmission measurements below 1800 Å  are given in the XMM flight simulator software files, so we added a point with $\sim0\%$ transmission at 1700 Å in the UV filters.

The stellar spectra
-------------------

The spectra we used for the synthetic photometry are those of the Kurucz’ ATLAS 9 atmosphere models (Kurucz 1992), reddened by the Cardelli interstellar extinction model (Cardelli et al. 1989) with an average reddening law ($R_{\rm V}~=~A_{\rm   V}/E(B-V)~=~3.1$) when necessary. Except when otherwise stated, the set of spectra we chose mimics an unreddened solar composition main sequence (MS) since these 55 spectra possess the following characteristics: $A_{\rm V}~=~0.$; $[\rm Fe/H]~=~0.$; $\log~g~=~4.$; $3500\,$K$~\leq~T_{\rm eff}~\leq~35000\,$K. Stars we refer 