Radial velocity signatures of Zeeman broadening

Stellar activity signatures such as spots and plages can significantly limit the search for extrasolar planets. Current models of activity-induced radial velocity (RV) signals focus on the impact of temperature contrast in spots according to which they predict the signal to diminish toward longer wavelengths. The Zeeman effect on RV measurements counteracts this: the relative importance of the Zeeman effect on RV measurements should grow with wavelength because the Zeeman displacement itself grows with lambda, and because a magnetic and cool spot contributes more to the total flux at longer wavelengths. In this paper, we model the impact of active regions on stellar RV measurements including both temperature contrast in spots and line broadening by the Zeeman effect. We calculate stellar line profiles using polarized radiative transfer models including atomic and molecular Zeeman splitting over large wavelength regions from 0.5 to 2.3 mu m. Our results show that the amplitude of the RV signal caused by the Zeeman effect alone can be comparable to that caused by temperature contrast; a spot magnetic field of similar to 1000 G can produce a similar RV amplitude as a spot temperature contrast of similar to 1000 K. Furthermore, the RV signal caused by cool and magnetic spots increases with wavelength, in contrast to the expectation from temperature contrast alone. We also calculate the RV signal caused by variations in average magnetic field strength from one observation to the next, for example due to a magnetic cycle, but find it unlikely that this can significantly influence the search for extrasolar planets. As an example, we derive the RV amplitude of the active M dwarf AD Leo as a function of wavelength using data from the HARPS spectrograph. Across this limited wavelength range, the RV signal does not diminish at longer wavelengths but shows evidence for the opposite behavior, consistent with a strong influence of the Zeeman effect. We conclude that the RV signal of active stars does not vanish at longer wavelength but sensitively depends on the combination of spot temperature and magnetic field; in active low-mass stars, it is even likely to grow with wavelength.