Correcting the fiber-aperture bias affecting galaxy stellar populations in the Legacy Sloan Digital Sky Survey. Aperture corrections to absorption indices based on CALIFA integral field observations

A detailed characterization of stellar population properties is crucial for understanding galaxy evolution. Their inference for statistically representative samples requires deep multi-object spectroscopy, typically obtained with fiber-fed spectrographs integrating only a fraction of galaxy light. The Legacy Sloan Digital Sky Survey (SDSS I-II) represents the most studied local Universe dataset in this context. Its fibers typically collected ∼ 30% of total flux. Ubiquitous stellar population gradients systematically bias SDSS measurements toward central properties by an as-yet-unquantified amount. Our aim is to quantify spectroscopic fiber aperture effects for a representative sample of local Universe galaxies over the SDSS redshift range, and to devise empirical recipes to correct stellar absorption indices from SDSS fiber spectra to aperture-free total values. We leveraged CALIFA integral-field spectroscopy to simulate fiber-fed observations at redshifts z = 0.005--0.4, accounting for seeing effects. We analyzed systematic aperture correction trends across galaxy morphologies and derived correction recipes based on fiber-measured indices, the global g!-!r color, the absolute r-band magnitude M_r, and the physical half-light radius R_ Corrections for absorption indices typically reach ≳ 15% of their dynamical range at z ∼ 0.02, decreasing to ∼ 7% at z ∼ 0.1 (median SDSS redshift) and becoming negligible above z ∼ 0.2. Spiral galaxies exhibit the largest aperture effects due to their strong internal gradients. Our correction recipes, split into first-order terms (from fiber-indices and g!-!r color) and second-order terms (from M_r and R_ and applied to the SDSS-DR7 dataset, significantly reduce the scatter in stellar population diagnostic planes and enhance the bimodality in age-sensitive diagrams. The corrections reveal systematic overestimates of old galaxy fractions by up to 10% and an underestimate by ≳ 0.2,mag of the transition luminosity at which old galaxies become dominant. Aperture corrections significantly impact the observational tracers of stellar populations from fiber spectroscopy and tighten correlations between stellar population properties. Absorption index corrections applied to the SDSS-DR7 dataset will provide a robust local benchmark for galaxy evolution studies.