Using the variability of light from pulsating stars to study the internal physics is a field called asteroseismology. γ-Doradus stars were the class of pulsators chosen, because of their unique pulsation mechanism. They are categorised as g-mode pulsators because the restoring force is gravity; this means the pulsations originate from deep inside the stellar interior, which provides us with important information about stellar structure. Using high-resolution spectroscopic data, the frequencies and modes from three γ-Doradus pulsating variable stars, HD 139095 and HD 48501 and HD 197541 have been determined. Long term observations have yielded 257 specrta for HD 139095, 165 spectra for HD48501 and 309 spectra for HD 197541. The data were obtained from the 1.m McLellan telescope at The University of Canterbury Mount John Observatory using the High Efficiency and Resolution Canterbury University Large Echelle Spectograph. The data were processed using a cross correlation technique that maximises the signal-to-noise ratio of the spectral line profiles. The non-radial pulsation modes of these profiles have been determined using a pixel-by-pixel Fourier parameter fit method. HD 139095 had five significant frequencies f1=1.22624 ± 0.00001 d−1, f2=0.59456 ± 0.00002 d−1, f3=1.38710 ± 0.00002 d−1, f4=1.13233 ± 0.00001 d−1 and f5=0.49500 ± 0.00002 d−1. Modes of (1,1), (2,-2), (3,0) and (2,-2) were identified for f1, f2, f3 and f4 respectively. HD 197541 had six frequencies of f1=0.71409±0.00001 d−1, f2=1.01804±0.00002 d−1, f3=0.82275±0.000007 d−1, f4=0.76269±0.00002 d−1, f5=1.11593±0.00002 d−1 and f6=2.52637±0.00003 d−1. Frequencies f1, f2, f3, f4 and f6 had the modes (3,-2), (2,-2), (3,-3), (3,-2) and (3,-1) respectively. HD 48501 had four frequencies f1=1.29042 ± 0.00003 d−1, f2=1.09386 ± 0.00005 d−1, f3=1.35816 ± 0.0002 d−1 and f4=1.23804 ± 0.0002 d−1. All the frequencies had modes of (2,-2), (2,-2), (2,-2) and (3,-3) respectively. It can be confidently stated that the target stars had full frequency and mode identification performed upon them, an important step to understanding these complex pulsation modes of γ-Doradus stars.
