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The major sources of the Soft X-ray Background (SXRB), besides distinctstructures as supernovae and superbubbles (e.g. Loop I), are: (i) an absorbedextragalactic emission following a power law, (ii) an absorbed thermalcomponent ~2x10^6 K) from the galactic disk and halo, (iii) an unabsorbedthermal component, supposedly at 10^6 K, attributed to the Local Bubble and(iv) the very recently identified unabsorbed Solar Wind Charge-eXchange (SWCX)emission from the heliosphere and the geocorona. We study the SWCX heliosphericcomponent and its contribution to observed data. In a first part, we apply aSWCX heliospheric simulation to model the oxygen lines (3/4 keV) localintensities during shadowing observations of the MBM12 molecular cloud and adense filament in the south galactic hemisphere with Chandra, XMM-Newton, andSuzaku telescopes. In a second part, we present a preliminary comparison ofSWCX model results with ROSAT and Wisconsin surveys data in the 1/4 keV band.We conclude that, in the 3/4 keV band, the total local intensity is entirelyheliospheric, while in the 1/4 keV band, the heliospheric component seems tocontribute significantly to the local SXRB intensity and has potentially astrong influence on the interpretation of the ROSAT and Wisconsin surveys datain terms of Local Bubble hot gas temperature.

The Solar Wind Charge-eXchange contribution to the Local Soft X-ray Background. Model to data comparison in the 0.1-1.0 keV band