One-dimensional fluid model simulations are performed to investigate how the secondary electron emission arising from ions (γ i ), metastable atoms (γ m ), and photons (γ p ) affect Townsend's second ionization coefficient (γ ) in argon dielectric barrier discharges. Since Townsend's breakdown criterion determines the value of γ , it is naturally affected by the discharge condition such as the reduced electric field (E /p) as well as the combination of γ i , γ m , and γ p . It also depends on the other contributions from the indirect ionization processes such as cumulative ionizations or metastable-metastable collision ionizations. When the nonionic electron-yielding processes such as the effects of γ m , γ p , and the indirect ionizations are considered, the calculated γ increases largely under the higher pd (pressure times distance) branch of the Paschen curve. Since the experimental characteristics of γ , which decreases with E /p, can hardly be explained without such nonionic processes, the contributions of those processes can be quite important in Townsend discharges especially under high pd conditions. These processes tend not to appear and γ tends to converge to γ i under the lower pd branch of the Paschen curve. The value of γ i can possibly be estimated by using γ under the lower pd condition.