Period-luminosity relation for M-type semiregular variables from Hipparcos parallaxes

We have studied the period-luminosity (P-L) relationships of oxygen-rich semiregular (SR) variables in several wavelength bands using Hipparcos parallaxes with an accuracy of better than 10 per cent. We have shown that there is a clear dependence on period of absolute magnitude in the U,B,V,R,I_C,J,H,K,L,M,N, [12], [25], [60] and [100] bands, and that the slope of the linear M_λ- logP relation is a smooth function of wavelength. We point out that this relation can in principle be used to derive absolute bolometric magnitude as a function of period.

The behaviour of the second periods of SR variables in the P-L relation in the V and K bands is also discussed.