That the RR Lyrae star period – K-band luminosity relation is a promising tool as a distance indicator in the Milky Way and Local Group of Galaxies is apparent on observational and theoretical grounds in the literature .
Less clear is the sensitivity of the relation , and consequently the physics of horizontal branch stars , to differences in stellar environment .
In this paper , the first measurement of the ( fundamental ) period – K-band luminosity relation for the central region of a globular cluster is presented .
It is based on a sample of seven RR Lyrae stars imaged with adaptive optics .
In addition , the relation for the outer region has been reanalyzed , and is found to be in good agreement with both the previous estimate by Longmore et al .
( 1990 ) , and with the inner region relation , especially when irregular and double-mode RR Lyrae stars are excluded .
Importantly , there is no difference between the slope of the inner and outer region relation within measurement uncertainties , suggesting no difference in evolutionary state ( luminosity ) .
Taking the M3 distance modulus as 15.0 \pm 0.07 mag , the period–absolute K-band magnitude relation derived by linear least squares fitting is : { M _ { K } = -0.96 \hskip { 2.845276 pt } ( \pm 0.10 ) -2.42 \hskip { 2.845276 pt } ( \pm 0.16 ) % \hskip { 2.845276 pt } Log P _ { o } } for the inner region .
Excluding irregular variable stars , the outer region relation is : { M _ { K } = -1.07 ( \pm 0.10 ) -2.38 \hskip { 2.845276 pt } ( \pm 0.15 ) \hskip { 2.845276 pt% } Log P _ { o } } .
This good agreement provides further strong support for the near-IR period-luminosity relation as a distance indicator .