Period variation and spot model for the W UMa type binary TY UMa

We present the full VRI light curves and the times of minima of TY UMa to provide a complete photometric solution and a long-term trend of period variation. The light curves show a high degree of asymmetry (the O'Connell effect). The maxima at 0.25 phase (Max I) are 0.021, 0.015, and 0.020 mag fainter than those at 0.75 phase (Max II) in V, R, and I, respectively. The period of TY UMa has varied in a sinusoidal way, superimposed on the long-term upward parabolic variation. The secularly increasing rate of the period is deduced as 1.83 s per century (P˙/P=5.788×10^-10 d d^-1). The period of sinusoidal variation is about 57.4 yr. The spot model has been applied to fit the asymmetric light curves of TY UMa, to explain light variations. By changing only the spot parameters, the model light curves can fit the observed light curves for three epochs. This indicates that the variation of the spot location and size is the main reason for changing the shape of light curves, including two different maxima and the interchanging depths of occultation and transit minima.