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We performed a theoretical analysis on the relevance of the small frequencyseparation $\delta \nu$ in determining stellar ages, masses, and radii. Weadopted the SCEPtER pipeline for low-mass stars, [0.7, 1.05] Msun. Syntheticstars were generated and reconstructed assuming different relative precision in$\delta \nu$ (5% and 2%). The quantification of the systematic errors arisingfrom a mismatch between synthetic stars and the recovery grid was alsoperformed. The biases were negligible. The statistical error in age estimateswas strongly dependent on the stellar evolutionary phase. It is at its maximumat ZAMS and decreases to about 11% and 6% ($\delta \nu$ at 5% and 2% level)when stars reach the 30% of their evolutionary MS lifetime, then vanishes inthe last 20% of the MS. For mass and radius estimates we detected nearlyidentical behavior for an observational uncertainty of 5%. No benefit wasdetected for mass and radius determinations from a reduction $\delta \nu$precision to 2%. The impact on the age of the initial helium abundance resultedin negligible results. On the other hand greater bias (2% and 1%) in mass andradius estimates were detected whenever $\delta \nu$ is in the observationalpool. This result, together with the presence of further unexplored uncertaintysources, suggest that precision in the derived stellar quantities below thesethresholds may possibly be overoptimistic. [...] Finally, we compared theestimates by the SCEPtER pipeline for 13 Kepler asteroseismic LEGACY samplestars with those given by six different pipelines. Overall, on the LEGACYsample data, we obtained a multi-pipeline precision of about 4.4%, 1.7%, and11% on the estimated masses, radii, and ages, respectively.

astronomy and astrophysics

Relevance of the small frequency separation for asteroseismic stellar  age, mass, and radius. A statistical investigation for main-sequence low-mass  stars