We have applied the image subtraction method to the M3 dataset previously analyzed by Corwin & Carney (2001; CC01). The new analysis produced light curves and periods for 15 variables, bringing to 222 the total number of RR Lyrae stars in CC01 M3 dataset. We have identified three new candidate double-mode (RRd) variables (V13, V200, and V251) in M3. Of the newly discovered RRds V13 is unusual in that it has the fundamental as the dominant pulsation mode. Two of the new candidate RRds (V13 and V200) have period ratios as low as 0.738-0.739. They lie separated from all previously known RRds in the Petersen diagram, in positions implying a large spread in mass and/or, less likely, in heavy element mass fraction, among the M3 horizontal branch (HB) stars. We explore mass transfer and helium enhancement as possible explanations for the apparent spread in HB masses. We also note that the masses derived from the RRd analyses now favor little mass loss on the red giant branch. V200 has changed its dominant pulsation mode from fundamental to first overtone, while V251 has changed its dominant mode from first overtone to fundamental in the interval 1992 to 1993. Together with M3-V166 this is the first time that RRd variables are observed to switch their dominant pulsation modes while remaining RRds. The phenomenon is found to occur in a one year time-span thus suggesting that these stars are undergoing a rapid evolutionary phase, and that both redward and blueward evolution may take place among the HB stars in M3. The unusual behavior of the M3 RRds is discussed and compared to that of the RRds identified so far in globular clusters and in the field of our and other Local Group galaxies. We find lack of correlation between the presence of RRd variables and any of the cluster structural parameters.
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