Blazhko effect in the Galactic bulge fundamental mode RR Lyrae stars - I. Incidence rate and differences between modulated and non-modulated stars

We present the first paper of a series focused on the Blazhko effect in RR Lyrae type stars pulsating in the fundamental mode that are located in the Galactic bulge. A comprehensive overview of the incidence rate and light-curve characteristics of the Blazhko stars is given. We analysed 8282 stars having the best quality data in the OGLE-IV survey, and found that at least 40.3 per cent of the stars show modulation of their light curves. The number of Blazhko stars we identified is 3341, which is the largest sample ever studied, implying that these are the most relevant statistical results currently available. Using combined data sets with OGLE-III observations, we found that 50 per cent of the stars that show unresolved peaks close to the main component in OGLE-IV are actually Blazhko stars with extremely long periods. Blazhko stars with modulation occur preferentially among RR Lyrae stars with shorter pulsation periods in the Galactic bulge. Fourier amplitude and phase coefficients based on the mean light curves appear to be substantially lower for Blazhko stars than for stars with an unmodulated light curve on average. We derived new relations for the compatibility parameter Dm in the I passband and relations that allow for differentiating modulated and non-modulated stars easily based on R31, ϕ21 and ϕ31. Photometric metallicities, intrinsic colours and absolute magnitudes computed using empirical relations are the same for Blazhko and non-modulated stars in the Galactic bulge, suggesting there is no correlation between the occurrence of the Blazhko effect and these parameters