We present magnetic flux measurements in seven rapidly rotating M dwarfs. Our sample stars have X-ray and H-alpha emission indicative of saturated emission, i.e., emission at a high level independent of rotation rate. Our measurements are made using near-infrared FeH molecular spectra observed with HIRES at Keck. Because of their large convective overturn times, the rotation velocity of M stars with small Rossby numbers is relatively slow and does not hamper the measurement of Zeeman splitting. The Rossby numbers of our sample stars are as small as 0.01. All our sample stars exhibit magnetic flux of kilo-Gauss strength. We find that the magnetic flux saturates in the same regime as saturation of coronal and chromospheric emission, at a critical Rossby number of around 0.1. The filling factors of both field and emission are near unity by then. We conclude that the strength of surface magnetic fields remains independent of rotation rate below that; making the Rossby number yet smaller by a factor of ten has little effect. These saturated M-star dynamos generate an integrated magnetic flux of roughly 3 kG, with a scatter of about 1 kG. The relation between emission and flux also has substantial scatter.
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