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Infrared excess around nearby RGB stars and Reimers law

(Abridged) The spectral energy distributions of a well-defined sample of 54 RGB stars are constructed, and fitted with the dust radiative transfer model DUSTY. The central stars are modeled by MARCS model atmospheres. In a first step, the best-fit MARCS model is derived, determining the effective temperature. In a second step, models with a finite dust optical depth are fitted and it is determined whether the reduction in chi2 in such models with one additional free parameter is statistically significant. 23 stars are found to have a significant infrared excess, which is interpreted as mass loss. The dust optical depths are translated into mass-loss rates assuming a typical expansion velocity of 10 km/s and a dust-to-gas ratio of 0.005. The mass-loss rates are compared to those derived for luminous stars in globular clusters, by fitting both the infrared excess, as in the present paper, and the chromospheric lines. There is excellent agreement between these values and the mass-loss rates derived from the chromospheric activity. There is a systematic difference with the literature mass-loss rates derived from modeling the infrared excess, and this has been traced to technical details on how the DUSTY radiative transfer model is run. If the present results are combined with those from modeling the chromospheric emission lines, we obtain the fits Log Mdot = (1.0 +- 0.3) Log L + (-12.0 +- 0.9) and Log Mdot = (0.6 +- 0.2) Log (LR/M) + (-11.9 +- 0.9). The predictions of these mass-loss rate formula are tested against the RGB mass loss determination in NGC 6791. Using a scaling factor of (8 +- 5), both relations can fit this value. That the scaling factor is larger than unity suggests that the expansion velocity and/or dust-to-gas ratio, or even the dust opacities, are different from the values adopted.