Magnetic Cycles and Rotation Periods of Late Type Stars from photometric time series

We investigate the photometric modulation induced by magnetic activity cycles and study the relationship between rotation period and activity cycle(s) in late-type (FGKM) stars. We analyse light-curves spanning up to 9 years of 125 nearby stars provided by the ASAS survey. The sample is mainly conformed by low-activity main sequence late A to mid M-type stars. A search is performed for short (days) and long-term (years) periodic variations in the photometry. We modelled with combinations of sinusoids the light-curves to measure the properties of these periodic signals. To provide a better statistical interpretation of our results we complement them with the results from previous similar works. We have been able to measure long-term photometric cycles of 47 stars. Rotational modulation was also detected and rotational periods measured in 36 stars. For 28 stars we have simultaneous measurements of both, activity cycles and rotational periods, being 17 of them M-type stars. From sinusoidal fits we measured both photometric amplitudes and periods. The measured cycle periods range from 2 up to 14 yr with photometric amplitudes in the range of 5-20 mmag. We have found that the distribution of cycle lengths for the different spectral types is similar. On the other hand the distribution of rotation periods is completely different, trending to longer periods for later type stars. The amplitudes induced by magnetic cycles and rotation show a clear correlation. A trend of photometric amplitudes with rotation period is also outlined in the data. For a given activity index the amplitudes of the photometric variability induced by activity cycles of main sequence GK stars are lower than those of early and mid-M dwarfs. Using spectroscopic data we also provide an update in the empirical relationship between the level of chromospheric activity as given by log(Rhk) and the rotation periods.