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State of the art radial-velocity (RV) exoplanet searches are currentlylimited by RV signals arising from stellar magnetic activity. We analyze solarobservations acquired over a 3-year period during the decline of CarringtonCycle 24 to test models of RV variation of Sun-like stars. A purpose-builtsolar telescope at the High Accuracy Radial velocity Planet Searcher for theNorthern hemisphere (HARPS-N) provides disk-integrated solar spectra, fromwhich we extract RVs and $\log{R'_{\rm HK}}$. The Solar Dynamics Observatory(SDO) provides disk-resolved images of magnetic activity. The Solar Radiationand Climate Experiment (SORCE) provides near-continuous solar photometry,analogous to a Kepler light curve. We verify that the SORCE photometry andHARPS-N $\log{R'_{\rm HK}}$ correlate strongly with the SDO-derived magneticfilling factor, while the HARPS-N RV variations do not. To explain thisdiscrepancy, we test existing models of RV variations. We estimate thecontributions of the suppression of convective blueshift and the rotationalimbalance due to brightness inhomogeneities to the observed HARPS-N RVs. Weinvestigate the time variation of these contributions over several rotationperiods, and how these contributions depend on the area of active regions. Wefind that magnetic active regions smaller than $60 \ \rm Mm^2$ do notsignificantly suppress convective blueshift. Our area-dependent model reducesthe amplitude of activity-induced RV variations by a factor of two. The presentstudy highlights the need to identify a proxy that correlates specifically withlarge, bright magnetic regions on the surfaces of exoplanet-hosting stars.

HARPS-N Solar Radial-Velocity Variations Are Dominated By Large, Bright Magnetic Regions