Comparing the Near-infrared Spectral Energy Distributions from Different Stellar Population Synthesis Models with SPHEREx Observations

While stellar population synthesis (SPS) models have been widely used for spectral analysis in optical wavelengths, their characteristics remain uncertain in the near-infrared (NIR) due to a relative lack of observed NIR spectra. The spectrophotometric data from SPHEREx are well-suited for investigating the performance of SPS models in the NIR, thanks to its wide wavelength coverage over $0.7-5.0~{\rm \mu m}$. In this work, we compare the observed SPHEREx data of SDSS compact galaxies, including 2,726 non-emission-line galaxies and 1,163 emission-line galaxies, to the NIR SEDs predicted from the full spectrum fitting of SDSS optical spectra. We use four different SPS models that extend into the NIR: E-MILES, Bruzual \& Charlot (BC03), Charlot \& Bruzual (CB19), and FSPS. We find that all four models tend to overpredict the stellar continuum at $2.4-5~{\rm \mu m}$ by $0.1-0.3~{\rm mag}$. This trend is particularly prominent for intermediate-age stellar populations ($\sim1-5~{\rm Gyr}$), suggesting a systematic bias in the NIR SED predictions of current SPS models. For stellar populations older than $5~{\rm Gyr}$, E-MILES shows relatively smaller offsets at $3.8-5~{\rm \mu m}$ compared to other models. Meanwhile, for emission-line galaxies, the SPS models underestimate the SED by up to $\sim0.5~{\rm mag}$ at longer wavelengths due to the contribution of non-stellar emission. Overall, these results highlight the necessity of refining the NIR stellar spectral features in SPS models, such as emissions from thermally pulsating asymptotic giant branch stars or molecular absorptions from cool stars.