Systematics in metallicity gradient measurements. I. Angular resolution, signal to noise, and annular binning

With the rapid progress in metallicity gradient studies at high redshift, it is imperative that we thoroughly understand the systematics in these measurements. This work investigates how the [N II]/Hα-ratio-based metallicity gradients change with angular resolution, signal to noise (S/N), and annular binning parameters. Two approaches are used: (1) we downgrade the high angular resolution integral-field data of a gravitationally lensed galaxy and re-derive the metallicity gradients at different angular resolution; (2) we simulate high-redshift integral field spectroscopy observations under different angular resolution and S/N conditions using a local galaxy with a known gradient. We find that the measured metallicity gradient changes systematically with angular resolution and annular binning. Seeing-limited observations produce significantly flatter gradients than higher angular resolution observations. There is a critical angular resolution limit beyond which the measured metallicity gradient is substantially different to the intrinsic gradient. This critical angular resolution depends on the intrinsic gradient of the galaxy and is ≤0.″02 for our simulated galaxy. We show that seeing-limited high-redshift metallicity gradients are likely to be strongly affected by resolution-driven gradient flattening. Annular binning with a small number of annuli produces a more flattened gradient than the intrinsic gradient due to weak line smearing. For three-annulus bins, a minimum S/N of 5 on the [N II] line is required for the faintest annulus to constrain the gradients with meaningful errors.