We present an in-depth analysis of stellar activity and its effects on radial velocity (RV) for the M2 dwarf GJ 176 based on spectra taken over 10 years from the High Resolution Spectrograph on the Hobby-Eberly Telescope. These data are supplemented with spectra from previous observations with the HIRES and HARPS spectrographs, and V- and R-band photometry taken over 6 years at the Dyer and Fairborn observatories. Previous studies of GJ 176 revealed a super-Earth exoplanet in an 8.8-day orbit. However, the velocities of this star are also known to be contaminated by activity, particularly at the 39-day stellar rotation period. We have examined the magnetic activity of GJ 176 using the sodium I D lines, which have been shown to be a sensitive activity tracer in cool stars. In addition to rotational modulation, we see evidence of a long-term trend in our Na I D index, which may be part of a long-period activity cycle. The sodium index is well correlated with our RVs, and we show that this activity trend drives a corresponding slope in RV. Interestingly, the rotation signal remains in phase in photometry, but not in the spectral activity indicators. We interpret this phenomenon as the result of one or more large spot complexes or active regions which dominate the photometric variability, while the spectral indices are driven by the overall magnetic activity across the stellar surface. In light of these results, we discuss the potential for correcting activity signals in the RVs of M dwarfs.
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