Quenched fractions in the IllustrisTNG simulations: comparison with observations and other theoretical models

We make an in-depth comparison of the IllustrisTNG simulations with observational data on the quenched fractions of central and satellite galaxies, for $M_*=10^{9-12}M_{\odot}$ at $0\leq z\leq3$. We study how analysis methodologies and observational effects impact this comparison. This includes measurement choices -- aperture, quenched definition, star formation rate (SFR) indicator timescale -- as well as observational uncertainties and sample selection issues: projection effects, satellite/central misclassification, and host mass distribution sampling. The definition used to separate quenched and star-forming galaxies produces differences of up to 70 (30)$\%$ for centrals (satellites) $>\sim 10^{10.5} M_{\odot}$. Increasing the aperture within which SFR is measured can suppress the quenched fractions by up to $\sim50\%$, particularly at $z\gtrsim2$. Proper consideration of the stellar and host mass distributions is crucial: naive comparisons to volume-limited samples from simulations lead to misinterpretation of the quenched fractions as a function of $z$ by up to 20$\%$. Including observational uncertainties to theoretical values of $M_*$ and SFR changes the quenched fraction values and their trend and/or slope with mass. Taking projected rather than 3D distances for satellites decreases the quenched fractions by up to 10$\%$ due to field contamination. Comparing with data, TNG produces quenched fractions broadly consistent with observations. TNG predicts quenched fractions up to $\sim80-90\%$ for centrals at $z\leq2-3$, in line with recent observations, and notably higher than other theoretical models. The quantitative agreement of TNG and SDSS for satellite quenched fractions in groups and clusters depends strongly on the galaxy and host mass range. Our mock comparison between TNG and SDSS highlights the importance of properly accounting for observational effects and biases.