New mid-infrared period-luminosity ( PL ) relations are presented for RR Lyræ variables in the globular cluster M4 ( NGC 6121 ) .
Accurate photometry was obtained for 37 RR Lyræ variables using observations from the Infrared Array Camera onboard the Spitzer Space Telescope .
The dispersion of M4 ’ s PL relations is 0.056 , and the uncertainty in the slope is 0.11 mag .
Additionally , we established calibrated PL relations at 3.6 and 4.5 µm using published Hubble Space Telescope geometric parallaxes of five Galactic RR Lyræ stars .
The resulting band-averaged distance modulus for M4 is \mu = 11.399 \pm 0.007 \textrm { ( stat ) } \pm 0.080 \textrm { ( syst ) } \pm 0.015 \textrm { ( % cal ) } \pm 0.020 \textrm { ( ext ) } .
The systematic uncertainty will be greatly reduced when parallaxes of more stars become available from the GAIA mission .
Optical and infrared period-color ( PC ) relations are also presented , and the lack of a MIR PC relation suggests that RR Lyræ stars are not affected by CO absorption in the 4.5 µm band .