We combine variability information from the MAssive Compact Halo Objects ( MACHO ) survey of the Large Magellanic Cloud ( LMC ) with infrared photometry from the Spitzer Space Telescope Surveying the Agents of a Galaxy ’ s Evolution ( SAGE ) survey to create a dataset of \sim 30 000 variable red sources .
We photometrically classify these sources as being on the first ascent of the Red Giant Branch ( RGB ) , or as being in one of three stages along the Asymptotic Giant Branch ( AGB ) : oxygen-rich , carbon-rich , or highly reddened with indeterminate chemistry ( “ extreme ” AGB candidates ) .
We present linear period-luminosity relationships for these sources using 8 separate infrared bands ( J , H , K _ { s } , 3.6 , 4.5 , 5.8 , 8.0 , and 24 \mu m ) as proxies for the luminosity .
We find that the wavelength dependence of the slope of the period-luminosity relationship is different for different photometrically determined classes of AGB stars .
Stars photometrically classified as O-rich show the least variation of slope with wavelength , while dust enshrouded extreme AGB stars show a pronounced trend toward steeper slopes with increasing wavelength .
We find that O-rich AGB stars pulsating in the fundamental mode obey a period-magnitude relation with a slope of -3.41 \pm 0.04 when magnitude is measured in the 3.6 \mu m band , in contrast to C-rich AGB stars , which obey a relation of slope -3.77 \pm 0.05 .