Solution to the Conflict between the Estimations of Resolved and Unresolved Galaxy Stellar Mass from the Perspective of JWST

The CEERS program (S. L. Finkelstein et al. 2023, in preparation.) is one of the early release science surveys of JWST. The mosaicked images and weight maps utilized in this study were processed by Valentino et al. (2023), based on the public grizli software package (Brammer 2022). The HST images in the same field were also processed by Valentino et al. (2023). For this investigation, we employ imaging mosaics obtained from JWST in six broadband filters (F115W, F150W, F200W, F277W, F356W, and F444W). Due to the proximity of the central wavelengths of filters JWST/F115W and HST/F125W, and filters JWST/F150W and HST/F160W, we do not include these two HST filters in this study, that is, only the F435W, F606W, and F814W filters from HST are utilized.

Our galaxy sample is constructed based on the 3D-HST catalog (Brammer et al. 2012; Skelton et al. 2014; Momcheva et al. 2016). This fits galaxy SEDs in the wavelength range 0.3–8.0 μm to estimate photometric redshift and other physical properties of galaxies. For a more detailed description, we refer readers to the papers cited. Our sample comprises galaxies within the CEERS field that are bright and massive enough to facilitate reliable SED fitting. We require the result from the 3D-HST catalog to be reliable by setting use_phot = 1 and flags ≤ 2 and restrict our sample to galaxies with $\mathrm{log}({M}_{* }/{M}_{\odot })\gt 9$ at 0.2 < z < 3.0. Additionally, we only include galaxies that are detected (signal-to-noise ratio S/N > 3) in all six JWST filters and in at least two HST filters. Sources at the boundary of the field are removed. Our final sample contains 1060 galaxies.

In this section, we provide a brief overview of the method employed to construct the stellar mass maps in our study. To begin, we adopt the models of point-spread function (PSF) from the grizli-psf-library provided by G. B. Brammer et al. (2023, in preparation) and create convolution kernels with the photutils package (Bradley et al. 2022) by optimizing the measurements of kernel performance proposed by Aniano et al. (2011). The shorter-wavelength images are then PSF-matched to the F444W band since the PSF FWHM of this band is the largest. Subsequently, the final images used to generate the spatially resolved stellar mass maps are resampled to a common pixel scale of 004. The images used in this work are also corrected for the Milky Way extinction (Schlafly & Finkbeiner 2011) assuming the Fitzpatrick (1999) extinction curve with R_V = 3.1.

For each galaxy in our sample, we generate a cutout that is 1.5 times larger than the segmentation map provided by Valentino et al. (2023). Within this cutout, we perform SED fitting on all pixels to obtain the stellar mass map of the galaxy. We fix the redshift of all pixels to z_best retrieved from the 3D-HST catalog and utilize the CIGALE program (Boquien et al. 2019) to estimate M_* of each pixel. In brief, we adopt the delayed-τ star formation history, Bruzual & Charlot (2003) stellar population models, Inoue (2011) nebular emission-line models, and Charlot & Fall (2000) dust attenuation law in the fitting. In Figure 1, we show the multiband images and the corresponding stellar mass maps of a few example galaxies.

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The SED fitting result can be influenced by many factors, such as the treatment of the thermally pulsating asymptotic giant branch stage, the choice of IMF, and assumptions regarding the star formation history (e.g., Sawicki & Yee 1998; Maraston et al. 2006, 2010; Pforr et al. 2012), leading to large model-dependent systematic uncertainties in estimating M_*. However, the aim of this study is to study the difference between M_*,resolved and M_*,unresolved under the same model assumptions. Therefore, the systematic bias due to the model selection will not be considered in this study. Fortunately, once the redshift is well determined, M_* is one of the most robust parameters estimated from the SED fitting, while other parameters are generally more difficult to estimate because of the degeneracy (e.g., Caputi et al. 2015; Pacifici et al. 2023). Thanks to the richness of multiband observations, the uncertainty of the photometric redshifts in the 3D-HST catalog is σ_Δz/(1+z) ∼ 0.02, which is small enough to ensure reliable M_* estimations. Additionally, within our sample, we have 82 sources with spectroscopic redshifts. In the subsequent analysis, we also independently verify the results using the subset of sources with spectroscopic redshifts and find that they align with the results obtained from the entire sample.

Before investigating the disparity between M_*,resolved and M_*,unresolved, we conduct an examination of the influence of the rest-frame NIR data on the M_* estimation. The total flux catalog extracted by Valentino et al. (2023) is used to estimate M_* here via the CIGALE program with the configuration described in Section 2.2. For simplicity, M_* derived from the fittings using photometry with and without the long-wavelength (LW) bands (i.e., F200W, F277W, F356W, and F444W) is denoted as M_{*,with LW} and M_{*,without LW}, respectively. The comparison between them is presented in Figure 2.

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In Figure 2(a), we present the distribution of M_{*,without LW} and M_{*,with LW} for our sample color-coded by redshift. It is evident that M_{*,without LW} tends to be larger than M_{*,with LW}. To further investigate this issue, we examine the difference between them (i.e., $\mathrm{log}({M}_{* ,\mathrm{without}\,\mathrm{LW}}/{M}_{* ,\mathrm{with}\,\mathrm{LW}})$) as a function of redshift in Figure 2(b). The solid black line represents the median difference, while the red shaded region represents the 1σ uncertainty estimated by the bootstrapping method. It can be seen that there is no significant difference between the two at z < 0.5. However, at higher redshift, a notable disparity emerges, reaching up to 0.2 dex. We attribute this redshift trend to the fact that the longest bands involved in the fitting without LW bands (i.e., F150W) can no longer trace the rest-frame NIR emission (≳10000 Å) at z ≳ 0.5. Interestingly, a similar trend was reported by Ilbert et al. (2010), in which the authors compared M_* estimated with and without IRAC data, akin to our comparison with and without LW bands. In their work, at z < 1.5, the IRAC data have a negligible impact on the M_* estimation, since the K band (the longest band available except for the IRAC data) can still cover the rest-frame NIR data. However, at z > 1.5, lack of IRAC data could lead to an overestimation of M_* up to 0.1 dex since the K band only covers rest-frame ∼9000 Å in this redshift range.

Moreover, we have further validated this result using simulated data. Using the CIGALE program, we construct a sophisticated Stellar Population Synthesis library and randomly select a sample of 1500 SEDs from it. The model employed in this simulation is the same as the one mentioned in Section 2.2. By fixing the redshift to 2, we are able to scrutinize the ramifications of incorporating rest-frame NIR data, employing the same filters as the observation. Recognizing the inherent variations in median flux errors across different filters in real observations, the standard deviation (σ) of the Gaussian noise has been tailored to match the median flux error of each band. Subsequently, we have proceeded to derive stellar mass from the perturbed fluxes, leveraging the capabilities of the CIGALE software. With these simulated data, the median deviation between the estimated stellar mass and the true one is approximately 0.08 dex in the absence of rest-frame NIR data, while this discrepancy reduces to a mere 0.02 dex when incorporating rest-frame NIR data. Furthermore, the dispersion in mass estimates is diminished when rest-frame NIR data are utilized. Specifically, the standard deviation amounts to 0.04 dex with NIR inclusion, compared to 0.14 dex when NIR is absent from the fitting. This indicates that without the rest-frame NIR data, the measurement of M_* is indeed biased statistically.

There are several potential factors that could contribute to an overestimation of M_* in the absence of the rest-frame NIR data. Since M_* is determined by multiplying the galaxy's luminosity by the M_*/L ratio, the inclusion or exclusion of rest-frame NIR data may impact the derived M_*/L ratio. Numerous studies have demonstrated that factors such as stellar age and dust attenuation can influence the observed M_*/L ratio (e.g., Leja et al. 2019; Miller et al. 2022). Using galaxies at z ∼ 2, we compare the distributions of stellar age and dust attenuation (A_V ) obtained from the fittings with and without LW bands and present them in Figure 3. Evidently, both the stellar age and A_V tend to be overestimated when performing SED fitting without rest-frame NIR data. The median stellar age and A_V are 0.76 (0.88) Gyr and 0.37 (0.50) mag, respectively, for the results with (without) LW bands. To assess the statistical significance of the differences between them, we apply the Kolmogorov–Smirnov test and find that the p-values for stellar age and A_V are both smaller than 10⁻³, suggesting substantial differences between the two distributions. We thus conclude that the stellar age and A_V are indeed overestimated when the rest-frame NIR data are not included in the SED fitting. For a given luminosity, an older stellar population and a large A_V can lead to a larger observed M_*/L and consequently an overestimation of M_*. The physical reason for these differences when lacking rest-frame observations at wavelengths ≳10000 Å deserves further investigation.

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Many previous studies showed that M_*,unresolved is underestimated compared to M_*,resolved, particularly at high redshift (e.g., Zibetti et al. 2009; Martínez-García 2017; Sorba & Sawicki 2018; Mosleh et al. 2020). However, as mentioned above, obtaining measurements of M_*,resolved relies on high-spatial-resolution images, primarily obtained from HST. It is important to note that the reddest filter of HST is F160W, which can only trace the rest-frame optical (≲8000 Å) emission at z > 1. Consequently, relying solely on these observations may lead to an overestimation of M_* for each pixel (see Section 3.1).

To address this issue and mitigate the potential bias in M_* estimation, it is crucial to include rest-frame NIR observations, such as those provided by JWST. Here, we use PSF-matched HST and JWST images (from F435W to F444W) to further investigate the difference between M_*,resolved and M_*,unresolved. Before deriving M_*,resolved, we need to account for the potential bias introduced by the poor S/N of individual pixels during the SED fitting, as discussed in Gallazzi & Bell (2009). To this end, we only consider pixels with S/N larger than 3 in all six JWST bands. Regarding the HST data in the CEERS field, we find that the S/N, particularly in the F435W band, is generally much lower than for the JWST images. Applying a similar S/N threshold to the HST images leads to a significant reduction of the sample size. To obtain a galaxy sample with a reasonable size, we determined not to impose the S/N restrictions on the HST images. However, even if such restrictions are applied, we still obtain almost unchanged conclusions. Nonetheless, as in Sorba & Sawicki (2018), the pixel number included in the analysis for each galaxy is required to be ≥64 since the uncertainty in mass estimation becomes inordinately large below this threshold. Finally, 535 galaxies in total are included in the following analysis. To estimate M_*,resolved, we sum the stellar masses of all pixels within the segmentation map that satisfy the aforementioned criteria. Then we estimate M_*,unresolved by summing the fluxes from all the corresponding pixels and performing SED fitting with the same parameter configuration.

The comparison between the resolved and unresolved stellar mass is depicted in Figure 4. Notably, after incorporating JWST data, there is no significant difference observed between the resolved and unresolved stellar masses. This result is further emphasized in the lower panel of Figure 4, in which we plot the difference between M_*,resolved and M_*,unresolved (i.e., $\mathrm{log}({M}_{* ,\mathrm{resolved}}/{M}_{* ,\mathrm{unresolved}})$) as a function of redshift. It is evident that, when accounting for the associated errors, M_*,resolved and M_*,unresolved agree well, while the median bias and its 1σ uncertainty are all about 0.02 dex. We calculate the mass-weighted age by weighting the stellar ages of all selected pixels by their stellar masses within one galaxy and find that the median mass-weighted age of the sample from the resolved fitting (0.83 Gyr) is slightly smaller than the one obtained from the unresolved photometry (0.97 Gyr), which is consistent with the tiny difference that M_*,resolved is slightly smaller than M_*,unresolved. Note that outshining would expect a larger resolved mass-weighted age than the unresolved one. Although outshining might have an effect on the M_* estimation when the rest-frame NIR data are not included, our result suggests that incorporating the rest-frame NIR data in the fitting could correct for the potential impact of outshining (if any) and return a reliable measurement of M_*, regardless of whether spatially resolved or unresolved photometry is used.

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Different SED fitting codes may employ different data handling methods. To validate our findings, we conduct similar analyses using the FAST (Kriek et al. 2009) and BAGPIPES (Carnall et al. 2018) programs. Remarkably, the results obtained from these alternative programs still align with those obtained from the CIGALE fitting. By incorporating the JWST data, we consistently find no significant difference between the resolved and unresolved stellar masses. Moreover, different stellar populations may also produce notable differences in stellar mass estimates. We have also estimated both resolved and unresolved stellar masses for our sample, employing the CIGALE program, with the stellar population shifting from Bruzual & Charlot (2003) to Maraston (2005). With this new model, there is also no significant difference between M_*,resolved and M_*,unresolved. Further efforts are still needed to examine the consistency between estimations of M_*,resolved and M_*,unresolved with other stellar population models.