We present the correlations between the spectroscopic metallicities and ninety-three different intrinsic colors of M31 globular clusters , including seventy-eight BATC colors and fifteen SDSS and near infrared ugriz K colors .
The BATC colors were derived from the archival images of thirteen filters ( from c to p ) , which were taken by Beijing-Arizona-Taiwan-Connecticut ( BATC ) Multicolor Sky Survey with a 60/90 cm f/3 Schmidt telescope .
The spectroscopic metallicities adopted in our work were from literature .
We fitted the correlations of seventy-eight different BATC colors and the metallicities for 123 old confirmed globular clusters , and the result implies that correlation coefficients of twenty-three colors r > 0.7 .
Especially , for the colors ( f - k ) _ { 0 } , ( f - o ) _ { 0 } , and ( h - k ) _ { 0 } , the correlation coefficients are r > 0.8 .
Meanwhile , we also note that the correlation coefficients ( r ) approach zero for ( g - h ) _ { 0 } , ( k - m ) _ { 0 } , ( k - n ) _ { 0 } , and ( m - n ) _ { 0 } , which are likely to be independent of metallicity .
Similarity , we fitted the correlations of metallicity and ugriz K colors for 127 old confirmed GCs .
The result indicates that all these colors are metal-sensitive ( r > 0.7 ) , of which ( u - K ) _ { 0 } is the most metal-sensitive color .
Our work provides an easy way to simply estimate the metallicity from colors .