Period-luminosity relations of pulsating M giants in the solar neighbourhood and the Magellanic Clouds

We analyse the results of a 5.5-yr photometric campaign that monitored 247 southern, semi-regular variables with relatively precise Hipparcos parallaxes to demonstrate an unambiguous detection of Red Giant Branch (RGB) pulsations in the solar neighbourhood. We show that Sequence A' contains a mixture of AGB and RGB stars, as indicated by a temperature related shift at the TRGB. Large Magellanic Cloud (LMC) and Galactic sequences are compared in several ways to show that the P-L sequence zero-points have a negligible metallicity dependence. We describe a new method to determine absolute magnitudes from pulsation periods and calibrate the LMC distance modulus using Hipparcos parallaxes to find \mu (LMC) = 18.54 +- 0.03 mag. Several sources of systematic error are discussed to explain discrepancies between the MACHO and OGLE sequences in the LMC. We derive a relative distance modulus of the Small Magellanic Cloud (SMC) relative to the LMC of \Delta \mu = 0.41 +- 0.02 mag. A comparison of other pulsation properties, including period-amplitude and luminosity-amplitude relations, confirms that RGB pulsation properties are consistent and universal, indicating that the RGB sequences are suitable as high-precision distance indicators. The M giants with the shortest periods bridge the gap between G and K giant solar-like oscillations and M-giant pulsation, revealing a smooth continuity as we ascend the giant branch.