Superhumps and post-outburst rebrightening episodes in the AM CVn star SDSS J012940.05+384210.4

We report unfiltered photometry of the first confirmed outburst of the AM CVn system SDSS J012940.05+384210.4 during 2009 December. At its brightest the star was magnitude 14.5, 5.4 magnitudes above mean quiescence. Although the first part of the outburst was not observed, six remarkable rebrightening events were observed during the course of the outburst. Forty-one days after the outburst was detected, the star was still 1.7 magnitudes above quiescence. Superhumps were observed during the outburst with a peak-to-peak amplitude of 0.06 mag and Psh = 37.9(2) min. We also used archival data to show that another AM CVn system, SDSS J124058.03-015919.2, has also undergone at least one outburst, with an amplitude of ~4.6 magnitudes.