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The TESS space telescope is collecting continuous, high-precision opticalphotometry of stars throughout the sky, including thousands of RR Lyrae stars.In this paper, we present results for an initial sample of 118 nearby RR Lyraestars observed in TESS Sectors 1 and 2. We use differential-image photometry togenerate light curves and analyse their mode content and modulation properties.We combine accurate light curve parameters from TESS with parallax and colorinformation from the Gaia mission to create a comprehensive classificationscheme. We build a clean sample, preserving RR Lyrae stars with unusual lightcurve shapes, while separating other types of pulsating stars. We find that alarge fraction of RR Lyrae stars exhibit various low-amplitude modes, but thedistribution of those modes is markedly different from those of the bulgestars. This suggests that differences in physical parameters have an observableeffect on the excitation of extra modes, potentially offering a way to uncoverthe origins of these signals. However, mode identification is hindered byuncertainties when identifying the true pulsation frequencies of the extramodes. We compare mode amplitude ratios in classical double-mode stars to starswith extra modes at low amplitudes and find that they separate into twodistinct groups. Finally, we find a high percentage of modulated stars amongthe fundamental-mode pulsators, but also find that at least 28% of them do notexhibit modulation, confirming that a significant fraction of stars lack theBlazhko effect.

First results on RR Lyrae stars with the TESS space telescope: untangling the connections between mode content, colors and distances