Constraints on the collimated X-ray emission of SS 433 from the reflection on molecular clouds

We calculate X-ray signal that should arise due to reflection of the putative collimated X-ray emission of the Galactic supercritical accretor SS 433 on molecular clouds in its vicinity. The molecular gas distribution in the region of interest has been constructed based on the data of the BU-FCRAO GRS in $^{13}$CO $J=1\rightarrow0$ emission line, while the collimated emission was assumed to be aligned with the direction of the relativistic jets, which are continuously launched by the system. We consider all the available $Chandra$ observations covering the regions possibly containing the reflection signal and put constraints on the apparent face-on luminosity of SS 433 above 4 keV. No signatures of the predicted signal have been found in the analysed regions down to a 4-8 keV surface brightness level of $\sim 10^{-11}$ erg/s/cm$^2$/deg$^2$. This translates into the limit on the apparent face-on 2-10 keV luminosity of SS 433 $L_{X,2-10}\lesssim 8\times10^{38}$ erg/s, provided that the considered clouds do fall inside the illumination cone of the collimated emission. This, however, might not be the case due to persisting uncertainty in the line-of-sight distances to SS 433 $d_{SS433}$ (4.5-5.5 kpc) and to the considered molecular clouds. For half-opening angle of the collimation cone larger than or comparable to the amplitude of the jets' precession ($\approx21\deg$), the stringent upper limit quoted above is most relevant if $d_{SS433}<5$ kpc, provided that the kinematic distances to the considered molecular clouds are sufficiently accurate. Dropping the last assumption, a more conservative constraint is $L_{X,2-10}\lesssim10^{40}$ erg/s for $d_{SS433}=4.65-4.85$ kpc (and yet worse outside this range). We conclude that SS 433 is not likely to belong to the brightest ultraluminous X-ray sources if it could be observed face-on, unless its X-ray emission is highly collimated. (Abridged)