Eleven nearby (<300 pc), short-period (50-130 days) asymptotic giant branch (AGB) stars were observed in the CO J = (2-1) line. Detections were made towards objects that have evidence for dust production (Ks-[22] >~ 0.55 mag; AK Hya, V744 Cen, RU Crt, alpha Her). Stars below this limit were not detected (BQ Gem, eps Oct, NU Pav, II Hya, CL Hyi, ET Vir, SX Pav). Ks-[22] colour is found to trace mass-loss rate to well within an order of magnitude. This confirms existing results, indicating a factor of 100 increase in AGB-star mass-loss rates at a pulsation period of ~60 days, similar to the known superwind trigger at ~300 days. Between ~60 and ~300 days, an approximately constant mass-loss rate and wind velocity of ~3.7 x 10^-7 solar masses per year and ~8 km/s is found. While this has not been corrected for observational biases, this rapid increase in mass-loss rate suggests a need to recalibrate the treatment of AGB mass loss in stellar evolution models. The comparative lack of correlation between mass-loss rate and luminosity (for L <~ 6300 solar luminosities) suggests that the mass-loss rates of low-luminosity AGB-star winds are set predominantly by pulsations, not radiation pressure on dust, which sets only the outflow velocity. We predict that mass-loss rates from low-luminosity AGB stars, which exhibit optically thin winds, should be largely independent of metallicity, but may be strongly dependent on stellar mass.
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