To model or not to model: nebular continuum in galaxy spectra

The neglect of modelling both stellar and nebular emission significantly affects the derived physical properties of galaxies, particularly those with high star formation rates. While this issue has been studied, it has not been established a clear threshold for a significant impact on the estimated physical properties of galaxies due to accounting for both stellar and nebular emission. We analyse galaxies from SDSS-DR7 across a wide range of star-forming activity levels, comparing the results obtained from two spectral fitting tools: FADO (which considers both stellar and nebular continuum) and STARLIGHT (only considers the stellar continuum). A strong linear correlation is found between the rest-frame H$\alpha$ and H$\beta$ equivalent widths (EWs) and the optical nebular contribution, identifying these as reliable tracers. The results show that when the nebular contribution exceeds 8% (corresponding to EW(H$\alpha$)$\simeq$500 \r{A} and EW(H$\beta$)$\simeq$110 \r{A}), there is a significant impact on the estimation of galaxy properties, namely stellar mass, age and metallicity. Our results highlight the importance of taking into account both the stellar and nebular continuum when analysing the optical spectra of star-forming galaxies. In particular, this is a fundamental aspect for galaxies with a rest-frame EW(H$\alpha$)$\gtrsim$500 \r{A} (or the scaled value of 375 \r{A} for pseudo-continuum measures). At low redshifts, this mostly impacts extreme emission line galaxies, while at higher redshifts it becomes a dominant aspect given the higher star-forming activity in the younger Universe. In light of current JWST observations and future instruments designed for high-redshift observations, such as MOONS, this reveals as a critical issue to take into consideration.