We quantitatively examine the significance of star formation triggered in the swept-up shell around an expanding H II region .
If the swept-up molecular gas is sufficiently massive , new OB stars massive enough to repeat the triggering process will form in the shell .
We determine the lower limit ( M _ { thr } ) for the mass of the star that sweeps up the molecular gas , where at least one new star with mass M _ { * } > M _ { thr } forms after the shell fragmentation .
To calculate the threshold stellar mass , M _ { thr } , we examine how massive molecular shells can form around various central stars , by performing detailed numerical radiation hydrodynamics calculations .
The mass of the photodissociated gas is generally larger than the mass of the photoionized gas .
However , the swept-up molecular mass exceeds the photodissociated mass with a higher-mass star of M _ { * } \gtrsim 20 ~ { } M _ { \odot } .
The accumulated molecular mass generally increases with the stellar mass , and amounts to 10 ^ { 4 - 5 } ~ { } M _ { \odot } for M _ { * } \gtrsim 20 ~ { } M _ { \odot } with an ambient density of n \sim 10 ^ { 2 } ~ { } { cm } ^ { -3 } .
The threshold stellar mass is M _ { thr } \sim 18 ~ { } M _ { \odot } with the star-formation efficiency of \epsilon \sim 0.1 and n \sim 10 ^ { 2 } ~ { } { cm } ^ { -3 } .
We examine the generality of this mode of run-away triggering for different sets of parameters , and found that M _ { thr } \sim 15 - 20 ~ { } M _ { \odot } in various situations .
If the ambient density is too high or the star-formation efficiency is too low , the triggering is not run-away , but a single event .