We numerically investigate abundance properties of the Galactic globular clusters ( GCs ) by adopting a new “ external pollution ” scenario .
In this framework , GCs are assumed to originate in forming low-mass dwarfs embedded in dark matter subhalos at very high redshifts ( z ) and thus be chemically influenced by field AGB stars of the dwarfs during early GC formation processes .
GCs within a dwarf galaxy therefore can be formed from the mixture of ( i ) gas ejected from the field AGB stars formed earlier in the dwarf and ( ii ) the interstellar gas infalling to the central region of the dwarf .
In this external pollution scenario , the ratio of the total mass of infalling gas to that of AGB ejecta during GC formation in a dwarf ( s ) and the time scale of gas infall ( { \sigma } _ { I } ) are the most important key parameters that can determine abundance properties of GCs .
We mainly investigate the abundance inhomogeneity among light elements ( e.g. , C , N , O , Na , and Al ) of stars in GCs by using the latest stellar yield models of metal-poor AGB stars with and without third dredge-up . Our principal results for the models with no third dredge-up , which are more consistent with observations , are as follows .

( 1 ) Both [ N/Fe ] and [ C/Fe ] can be diverse among stars within a GC owing to chemical pollution from field AGB stars .
[ N/Fe ] distributions in some GCs can clearly show bimodality whereas [ C/Fe ] is monomodal in most models .
[ N/Fe ] distributions depend on s such that models with smaller s ( i.e. , larger mass fraction of AGB ejecta used for GC formation ) show the [ N/Fe ] bimodality more clearly .

( 2 ) N-rich , C-poor stars in GCs also have higher He abundances owing to pollution from massive AGB stars with He-rich ejecta .
The number fraction of He-rich stars ( Y > 0.30 ) is higher for the models with smaller s and shorter { \sigma } _ { I } for 3 \leq s \leq 24 and 10 ^ { 5 } \leq { \sigma } _ { I } \leq 10 ^ { 7 } yr .
He abundances of stars correlate with [ N/Fe ] and [ Al/Fe ] and anticorrelate with [ C/Fe ] , [ O/Fe ] , and [ Na/Fe ] within GCs in our models .

( 3 ) Although our model can much better explain the observed C-N and Mg-Al anticorrelations than previous theoretical models , it is in strong disagreement with the observed O-Na anticorrelation .

( 4 ) This model naturally provides an explanation for the large fraction of CN-strong stars without recourse to an implausible IMF .

Based on these results for the above external pollution scenario , we discuss the long-standing problem of the CN-bimodality prevalent in the Galactic GCs , the possible helium abundance inhomogeneity in these systems , and their horizontal branch morphologies .