Uncertainties in asteroseismic grid-based estimates of the ages of halo stars

Context. Stellar age determinations for field stars are crucial for studying the evolutionary history of the Galaxy. The vast majority of the research in this area has so far been focused on stars with typical disk characteristics.Aims. Nowadays, the availability of high-quality asteroseismic data for stars with typical halo characteristics makes it possible to extend such investigations. The aim of this paper is to study the precision and theoretical biases in the age determinations of halo stars adopting both asteroseismic and classic observational constraints.Methods. We adopt the well-tested SCEPtER pipeline, covering evolutionary phases up to the red giant branch (RGB). The fitting grids contain stars with mass in the range of [0.7; 1.0] M-circle dot and metallicity [Fe/H] from -2.5 to -0.5, which are typical ranges seen in the halo population. We investigate several scenarios characterised by different adopted observational uncertainties. We also assess the impact of systematic discrepancies between the recovery grid models and target stars by computing several synthetic grids of stellar models with perturbed input physics.Results. We achieve more precise asteroseismic age estimates for old metal-poor stars than for more metallic stars. In our reference scenario (errors in Delta nu and nu(max) of 2.5% and 5% respectively), we recover ages for stars in the main sequence (MS) or subgiant branch (SGB) with a typical 10%-20% precision, while we recover those of RGB stars with a precision of about 60%. However, recent observations allow tighter constraints on asteroseismic parameters by about a factor of 3. With this assumption, the age precision in RGB improved to 20%, while few modifications occur in the other analysed evolutionary phases. Our investigation of the relevance of systematic discrepancies between grid models and target stars shows that a mismatch in the mixing-length parameter value between grids and targets (from 1.9 to 1.74) leads to significant bias in the age estimations for MS stars (about 10%), but this bias is smaller for SGB and RGB stars. Neglecting the microscopic diffusion effect in the recovery grid leads to a typical 40% bias in age estimates for stars on the MS. Finally, we applied the age estimation technique to stars in globular clusters, adopting typical observational uncertainties from the literature. We find a precision in age estimates of around 20% for MS stars and up to 40% for RGB stars. These uncertainties are greater than those obtained with classical methods, which are therefore still to be preferred. We also applied the SCEPtER pipeline to the age determination of the stars of the cluster M4, relying on asteroseismic data for seven RGB stars from the literature. We obtain a cluster age of 11.9 +/- 1.5 Gyr and a mass at the turn-of off 0.86 +/- 0.04 M-circle dot, which are in good agreement with literature results.