In this work, considering the impact of a supernova remnant (SNR) with a neutral magnetized cloud we derived a set of conditions that are favorable for driving gravitational instability in the cloud and thus star formation.
Using these conditions, we have built diagrams of the SNR radius versus the initial cloud density that constrain a domain in the parameter space where star formation is allowed. The diagrams are also tested with fully 3-D MHD radiative cooling simulations involving a SNR and a self-gravitating cloud and we find that the numerical analysis is consistent with the results predicted by the diagrams. While the inclusion of a homogeneous magnetic field approximately perpendicular to the impact velocity of the SNR with an intensity of 1 micro-G within the cloud results only a small shrinking of the star formation zone in the diagram relative to that without magnetic field, a
larger magnetic field (10 micro-G) causes a significant shrinking, as expected. These diagrams provide a useful tool for identifying sites where
star formation could be triggered by the impact of a SN blast wave. Applications of them to few regions of our own galaxy (e.g., the large CO
shell in the direction of Cassiopeia, and the Edge Cloud 2 in the direction of the Scorpious constellation) have revealed that star formation in those sites could have been triggered by shock waves from SNRs. Finally, we have evaluated
the effective star formation efficiency for this sort of interactions and found that it is generally smaller than the observed values in our own Galaxy (sfe $= 0.01-0.3$). This result (which is consistent with previous work in the literature) suggests that the mechanism presently investigated, though very powerful to drive structure formation, supersonic turbulence and
eventually, local star formation, does not seem to be sufficient to drive GLOBAL star formation in normal star forming galaxies, nor even when the
magnetic field in the neutral clouds is neglected.