We present a new set of horizontal-branch ( HB ) models computed with the MESA stellar evolution code .
The models adopt \alpha -enhanced ( ) metals mixtures and include the gravitational settling of He .
They are used in our HB population synthesis tool to generate theoretical distributions of HB stars in order to describe the multiple stellar populations in the globular clusters 47 Tuc , M 3 , and M 13 .
The observed HB in 47 Tuc is reproduced very well by our simulations for [ Fe/H ] = -0.70 and [ \alpha /Fe ] = +0.4 if the initial helium mass fraction varies by \Delta Y _ { 0 } \sim 0.03 and approximately 21 % , 37 % , and 42 % of the stars have Y _ { 0 } = 0.257 , 0.270 , and 0.287 , respectively .
These simulations yield ( m - M ) _ { V } = 13.27 , implying an age near 13.0 Gyr .
In the case of M 3 and M 13 , our synthetic HBs for [ Fe/H ] = -1.55 and [ \alpha /Fe ] = 0.4 match the observed ones quite well if M 3 has \Delta Y _ { 0 } \sim 0.01 and ( m - M ) _ { V } = 15.02 , resulting in an age of 12.6 Gyr , whereas M 13 has \Delta Y _ { 0 } \sim 0.08 and ( m - M ) _ { V } = 14.42 , implying an age of 12.9 Gyr .
Mass loss during giant-branch evolution and \Delta Y _ { 0 } appear to be the primary second parameters for M 3 and M 13 .
New observations for 7 of the 9 known RR Lyrae in M 13 are also reported .
Surprisingly , periods predicted for the c -type variables tend to be too high ( by up to \sim 0.1 d ) .