Early Results from GLASS-JWST. XI. Stellar Masses and Mass-to-light Ratio of z > 7 Galaxies

Stellar masses and the other physical parameters, including the observed absolute UV magnitudes at 1500 Å (M₁₅₀₀), were measured by fitting synthetic stellar templates to the seven-band NIRCam photometry with zphot (Fontana et al. 2000). When the nominal flux errors are smaller than 0.05 mag, we set a minimum photometric uncertainty in all bands corresponding to this threshold to account for uncertainties in the NIRCam calibration. We adopt in the following the photometric redshifts computed by Leethochawalit et al. (2022) and Castellano et al. (2022). We fixed the redshift to the EAzY z_peak value, with the exception of two of the z > 9 color-selected galaxies (GHZ3 and GHZ5 in Castellano et al. 2022), for which EAzY prefers a lower-redshift solution while zphot fits them at z > 9. We use the zphot redshifts for these sources. We built the stellar library following the assumptions of Merlin et al. (2021). We adopt Bruzual & Charlot (2003) models, including nebular emission lines according to Castellano et al. (2014) and Schaerer & de Barros (2009). We do not include Lyα emission because it is most likely absorbed by the intergalactic medium at these redshifts, although for clarity it is drawn in the spectral energy distributions (SEDs) shown in Figure 1. We assume delayed exponentially declining star formation histories (SFH(t) $\propto \,({t}^{2}/\tau )\cdot \exp (-t/\tau )$) with τ ranging from 0.1 to 7 Gyr (the adoption of more complicated SFHs, e.g., including recent bursts, will be addressed in a future analysis). We let the age range from 10 Myr to the age of the universe at each galaxy redshift. Metallicity is allowed to be 0.02, 0.2, and 1 times solar, and dust extinction is assumed to follow a Calzetti et al. (2000) law with E(B − V) varying from 0 to 1.1. We compute 1σ uncertainties on the physical parameters by retaining for each object the minimum and maximum fitted masses among all the solutions with a probability P(χ²) > 32% of being correct, both fixing the redshift to the best-fit value and allowing it to vary within its 1σ and 2σ ranges. For this analysis, for simplicity, we consider uncertainties at fixed redshifts. We will explore any residual degeneracy with redshift in future work.

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We have compared the stellar masses computed with zphot with those computed at the very same redshift with Bagpipes (Carnall et al. 2018) assuming a log-normal SFH, used by Leethochawalit et al. (2022). We find good agreement between the two, with some discrepancy only for a few low-mass galaxies. These discrepancies arise in objects with very small 4000 Å break (D4000). For these objects, the photometry at long wavelengths depends critically on the assumptions about emission lines, which are different for the two codes. This is clearly a topic that will deserve further attention as larger samples of spectra at z > 7 become available to calibrate the models.

We show in Figure 1 a few examples of the SED and best-fit templates of our candidates: two z ∼ 7.5–8 candidates, one with high M/L and a pronounced D4000 (ID1470), and another one with a low M/L and a D4000 smaller than 1 (ID5001), and the two most robust candidates at z > 10, namely GHZ1 and GHZ2 presented by Castellano et al. (2022). We note that two out of these four galaxies exhibit D4000 < 1, which is indicative of extremely young stellar populations and a spectrum dominated by nebular continuum. While the optical rest frame is nicely sampled at z < 10—and also marginally at z ∼ 10—at higher redshift we are limited to the spectral region blueward of the break. For these galaxies, longer-wavelength observations with MIRI will be a valuable addition.

Remarkably, GHZ2 shows a characteristic U-shape pattern (Carnall et al. 2022) (i.e., an extremely blue UV slope with the Balmer break seen in emission) that allows us to nicely constrain its SED. Despite its extremely high redshift, its intrinsic luminosity allows for accurate physical characterization.

Modest lensing magnification is expected to be present in the parallel fields (Medezinski et al. 2016; Bergamini et al. 2022) so that the stellar masses and UV luminosities should be taken as lower limits. In this initial set of papers, we ignore this effect. The issue will be revisited after the completion of the campaign.

In any case, the main results of the present Letter are independent of the lensing magnification. In particular, lensing affects masses and luminosities in the same way, so the M/L is free from magnification uncertainties. Furthermore, relative uncertainties on the stellar mass are also independent of magnification.

JWST observations allow for a significant reduction of the uncertainties on the stellar-mass measurement. Figure 2 shows the relative uncertainty ΔM/M at a 1σ level as a function of stellar mass and redshift. The error ${\rm{\Delta }}M=({M}_{\max }-{M}_{\min })/2$ is computed by scanning all models with acceptable χ² as described above.

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The ΔM/M inferred from GLASS observations is compared with the uncertainty affecting the stellar masses in three of the highest-quality and most exploited data sets that were available before the advent of JWST. All of them are obtained with a combination of HST, Spitzer, and ground-based data covering approximately the same spectral range as this work, but with much lower depth and S/N longward 1.6 μm. These are (i) the 43 band catalog of the CANDELS GOODS-S field by Merlin et al. (2021), (ii) the 43 band CANDELS COSMOS catalog of Nayyeri et al. (2017), and (iii) the 10 band catalog of Hubble Frontier Field (HFF) A2744 parallel by Merlin et al. (2016) and Castellano et al. (2016). The 5σ limiting magnitudes in the CH1 and CH2 IRAC bands are 25.5–25.6 ((i), total magnitudes), 24.4 ((ii), aperture photometry within a 1 FWHM radius), and ∼24.85 ((iii), calculated as described in Merlin et al. 2016), to be compared with the 29.3–29.7 depth (5σ limiting point-source magnitudes in 01 radius) of the F356W and F444W GLASS observations (Merlin et al. 2021). In all cases, we restricted to the galaxies of similar redshift (z > 6.9) and mass (7.2 < $\mathrm{log}M/{M}_{\odot }$ < 9.3) to the GLASS sample. In addition, we cleaned the catalogs by removing all sources flagged in the original catalogs due to photometric issues as well as spectroscopic and photometric stars. The latter were identified by requiring S/N(H160) > 10 and either (a) SExtractor (Bertin & Arnouts 1996) class_star > 0.95 or (b) class_star > 0.8 and populating the stellar locus of the BzK diagram (Daddi et al. 2004). For the GOODS-S and COSMOS catalogs, we also removed X-ray-selected AGNs according to the official CANDELS selection.

We remark that the computation of the error on mass depends on the code and on the library adopted. For this reason, we have used exactly the same code and template library, but for safety, the comparison should be considered as an estimate of the relative improvement that can be obtained via JWST optical rest-frame photometry.

Figure 2 shows that, in the redshift and mass range considered here, JWST observations improve the accuracy of the stellar-mass measurements by factors ranging from ≃2 to ≃30 on average compared to measurements based on Spitzer, HST, and ground-based observations only, at a given stellar mass or redshift. The improvement is more significant with respect to the HFF data set. The HFF catalog lacks IRAC CH3 and CH4 bands, which are instead included in the CANDELS catalogs, and suffers from shorter exposure times with Spitzer. Therefore, the deeper HST photometry of HFF compared to CANDELS is not complemented by similarly deeper IRAC CH1 and CH2 observations. In any case, we need to emphasize that the exposure times of the Spitzer data are significantly larger than those of JWST here, up to more than 100 hr in the case of GOODS-S.

Unsurprisingly, the accuracy improves for more massive objects, which are on average brighter and proportionally less affected by the (uncertain) contribution of nebular emission lines. The relative improvement compared to HFF is even more significant if analyzed as a function of redshift, increasing up to a factor of ≃30–50. Most importantly, as shown in the previous section, JWST data enable not only the detection of z > 10 galaxies, but also an accurate estimate of their stellar mass.

We revisit here the so-called mass–luminosity correlation for LBGs and characterize for the first time whether it is valid, and what is the scatter around the relation, by means of JWST data.

Prior to JWST, numerous studies have relied on the UV stellar luminosities to estimate the stellar mass of high-redshift galaxies, lacking rest-frame optical and near-infrared data, by adopting an average (stellar) mass–(UV) luminosity correlation. This correlation has been used to estimate the stellar-mass function by converting the UV luminosity function (e.g., González et al. 2011; Song et al. 2016; Kikuchihara et al.2020).

Figure 3 shows the mass–luminosity relation compared with previous estimates from the literature. At variance with previous works, our data do not show a correlation between mass and UV absolute magnitude, with a Pearson coefficient equal to −0.37 (a similar value is obtained by limiting the fit to z < 9 sources for a cleaner comparison with previous studies). We note that the luminosity range probed by our data is limited due to the small volume of our observations, insufficient to include the brighter and rarer sources. Nevertheless, the scatter at M₁₅₀₀ > −20 is very large (a factor of 50 in mass). This happens despite the fact that our sample is biased in favor of LBGs and against galaxies with older/dustier stellar populations (none of our candidates has a best-fit E(B − V) larger than 0.2), whose search requires a different strategy. Should these galaxies be detected in future JWST analysis, we expect the measured scatter in M/L to further increase.

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We show in Figure 4 the mass-to-light ratio as a function of redshift. The mass-to-light ratio is plotted in units of a reference M/L (M/L_ref) calculated for a 100 Myr old galaxy, with solar metallicity, no dust, and constant SFH (such a galaxy, according to Bruzual & Charlot 2003 models, has a stellar mass of 7.9 × 10⁷ M_⊙ and a 1500 Å luminosity of 1.3 × 10²⁸ erg s⁻¹ Hz⁻¹ if normalized to a star formation rate (SFR) of 1 M_⊙ yr⁻¹).

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The mass-to-light ratio significantly changes from galaxy to galaxy, spanning two orders of magnitude within our sample, consistent with what is seen in Figure 3. This result implies that the high-z galaxy population is largely heterogeneous, with galaxies observed in different evolutionary stages, as well as experiencing a broad variety of SFHs. In particular, the observed high M/L suggest the presence of evolved stellar populations already existing at these high redshifts, with tantalizing evidence that the aggregation of baryons may proceed at a faster rate than predicted by galaxy formation models.

The wide range of observed M/L implies that previous results based on an average value for large galaxy samples should be revisited and revised and might change significantly once JWST information is included.

As expected, the mass-to-light ratio correlates with the amplitude of the D4000 break, encoded in the color map, with more evolved systems showing higher M/L. Similar behavior is observed also with other galaxy properties that are indicative of the galaxy evolutionary stage, such as the specific SFR or age/2τ. ²⁶

Due to the large error bars, the limited size of the sample, and incompleteness effects, it is difficult to assess or exclude an evolutionary trend.

To gain some insight into this issue, we plot in Figure 4 the predictions from the Santa Cruz semianalytic model (Somerville et al. 2021), showing a decreasing trend all the way to z = 10. Our data encompass and exceed the predicted scatter in M/L. The range of predicted M/L in the model, spanning a factor of ∼10, correlates with the specific SFR, likely due to the combination of bursty and smooth SFHs. While observational uncertainties prevent us from drawing firm conclusions, the significantly larger scatter that we observe suggests that the simulations may underestimate the burstiness of mass growth.

We discuss here the accuracy of cosmic stellar-mass density (SMD) estimates obtained by converting luminosities through an average M/L ratio.

We show in the upper panel of Figure 5 a first attempt to infer the SMD. We calculate the observed SMD (ρ_*) by adding up the stellar masses of all galaxies in two redshift bins (6.9 < z < 8.5 and 8.5 < z < 12.1) and dividing by the cosmological volume of the bins. The associated error bars are obtained by propagating the mass uncertainties.

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Following a common approach at these redshifts, we also compute the SMD (${\rho }_{* }^{M/L}$) by converting UV luminosities through different mass–luminosity relations taken from the literature (Bhatawdekar et al. 2019; Kikuchihara et al. 2020; Stefanon et al. 2021), as well as by means of the mean M/L measured in this study in each redshift bin. The salmon-shaded regions in Figure 5 show the range of SMDs spanned by these indirect measurements.

The ratio between these measurements and ρ_* is shown in the lower panel of Figure 5. This ratio can be as high as a factor of ∼6, in both directions. The actual discrepancy depends on the mass and luminosity distributions of the specific data set, which may be different from the one on which the mass–luminosity relations have been estimated. However, we note that not even the average M/L inferred on the same sample of galaxies is always able to reproduce the measured SMD, depending on the distribution of sources within the redshift bin.

Figure 5 also reports a collection of SMD measurements from the literature. These data show that, while a consensus has been reached at z ≲ 3 (e.g., McLeod et al. 2021), the global picture is much more uncertain at redshifts above z ∼ 7, where more than a factor of 10 variance exists among different studies. In this first paper, we do not attempt to compare our findings with the literature. We defer this comparison to future work once incompleteness and lensing magnification have been properly characterized (these two effects move the points in opposite directions). Nevertheless, we want to draw attention to the level of uncertainty that can be introduced in the SMD when direct stellar-mass measurements are not available. We have demonstrated that the scatter among the results obtained with various estimates of the M/L is a dominant source of uncertainty, which will require the full power of JWST to be contained.