The accurate determination of galaxy relative distances is extremely important for the empirical calibration of the uncertain metallicity dependence of some standard candles like Cepheid stars , or for studying the galaxy space distribution and peculiar velocities .
Here we have investigated the reliability of the widely used I -band Tip of the Red Giant Branch ( TRGB ) relative distances for a sample of Local Group galaxies with complex Star Formation Histories ( SFRs ) and Age Metallicity Relationships ( AMRs ) namely the LMC , SMC and LGS3 .
The use of the K -band is also discussed .
By employing theoretical stellar population synthesis techniques , we find that using actual determinations of SFR and AMR of the LMC and SMC , their RGB is populated by stars much younger ( by \sim 9 Gyr ) than the Galactic globular cluster counterparts , on which the I -band ( and K -band ) TRGB absolute magnitude is calibrated .
This age difference induces a bias in both the photometric metallicity estimates based on the comparison of RGB colours with globular cluster ones , and the TRGB distances .
The extent of the distance bias – which is not influenced by the actual value of the TRGB absolute magnitude zero point – is strongly dependent on the specific TRGB technique applied , and on the assumed I -band bolometric correction ( BC _ { I } ) scale adopted ; the correction to apply to the SMC–LMC distance modulus ranges from 0 mag up to +0.10 mag .
LGS3 is an example of galaxy populated mainly by old stars , so that photometric metallicity and distance estimates using globular cluster calibrations are reliable .
However , the relative distance moduli between Magellanic Clouds and LGS3 are affected by the population effects discussed for the LMC and SMC .
The correction to apply to the LGS3–LMC distance modulus ranges between -0.05 mag and to +0.14 mag , whereas in case of the LGS3–SMC distance modulus it goes from - 0.07 mag to + 0.04 mag .
In case of all three relative distances discussed before , the correction to apply to the K -band TRGB distances are larger than the I -band case .

Our results clearly show that the presence of a well developed RGB in the Colour Magnitude Diagram of a stellar system with a complex SFR does not guarantee that it is populated by globular cluster-like red giants , and therefore the TRGB method for distance determination has to be applied with caution .
A definitive assessment of the appropriate corrections for population effects on TRGB distances has however to wait for a substantial reduction in the uncertainties on the BC _ { I } scale for cold stars .