Fractional error δ = (Q_fit − Q_numKG07)/Q_numKG07 for temperatures concerning low-mass RGB stars, where Q_fit is the neutrino emissivity calculated with the H94 (red lines) or KG07 (blue lines) fitting formulae, and Q_numKG07 is the neutrino emissivity calculated numerically by KG07. Vertical black lines indicate the log (ρ/μ_e) value in the center of three stars (Y = 0.245, and the labeled initial mass and metallicity) along their evolution through the RGB phase, when the center reaches the labeled temperature. In the panel for log T = 8, vertical lines indicate the density for the maximum temperature reached in the center (log T ~ 7.87). The log (ρ/μ_e) ranges are determined by the limits of the KG07 numerical values.