<figure><img src="image_10.png" /><figcaption>**Figure 8.** SFR-$\sigma_{\delta}$ (overdensity) relation for all spectroscopically confirmed galaxies that fall in the redshift range of interest $4.2 < z < 4.93$. The SFR for these galaxies are estimated with CIGALE, an SED fitting code (see 5.1). The orange squares are the median SFR plotted at the median overdensity for each bin such that each bin contains approximately equal number of galaxies. The spread on the median is calculated using $\sigma_{\text{NMAD}}$. The Spearman correlation coefficient is positive indicating a weak correlation between local galaxy density and the SFR.</figcaption></figure>

images for 179 candidate protoclusters at $z \sim 4$, selected from the HSC Subaru Strategic Program, with the combined IR emission in the observed 12–850 µm wavelength range. The SFR of LBG-selected protocluster candidates from this study was converted into SFRD by using a spherical volume with a radius of 10.2 cMpc. Albeit at different redshifts, we find a good agreement between our results and the results of these studies (see Section 7 for more discussion).

It is tempting to attribute the elevated SFRD of the Taralay protocluster compared to the field solely to the fact that the protocluster hosts a great number of star-forming galaxies in a relatively small volume. Here we focus on the SFR-$\sigma_{\delta}$ relation in order to investigate whether the high SFRD<sub>pc</sub> comes simply from having a large number of galaxies in the protocluster or if it is also a product of the protocluster galaxy members genuinely having an elevated SFR relative to their counterparts in the field. The SFR-$\sigma_{\delta}$ relation shown in Fig. 8 for galaxies in this sample reveals a positive correlation between the SFR and overdensity. A Spearman test results in a correlation coefficient of 0.286 and a p-value of 0.002. An identical exercise is performed with respect to SM later in this section. Lemaux et al. (2022) found a weak but significant trend for SFR-overdensity for the full VUDS+ sample of 6730 star-forming galaxies over the redshift range $2 \le z \le 5$. The strength of the correlation seen in our sample is >2 times higher than that measured in Lemaux et al. (2022; $\rho = 0.29$ versus $\rho = 0.13$) indicating that members of the Taralay protocluster are even more likely to have an increase in the SFR as in denser environments than the overall star-forming galaxy population at $2 \le z \le 5$.

To disentangle the fraction of SFRD that results from the protocluster having a higher number of galaxies versus the fraction that results from the protocluster galaxies having higher SFR on average, we investigated a scenario where we assumed that the average SFR of the protocluster galaxies is the same as the average SFR of the coeval field galaxies. In Fig. 8, the average $\log(SFR/M_{\odot} \text{yr}^{-1})$ increases 0.22 for galaxies in the protocluster relative to those in the field—$\log(SFRD/M_{\odot} \text{yr}^{-1} \text{Mpc}^{-3}) = 1.25$ versus 1.47. We then reduce the SFRD<sub>pc</sub> by the ratio between the average SFR of protocluster members and that of field galaxies, which results in a $\log(SFRD_{pc}/M_{\odot} \text{yr}^{-1} \text{Mpc}^{-3}) = 0.04$ as compared to the derived value of 0.26. This

means that even if protocluster members had the same average SFR as field galaxies, the SFRD<sub>pc</sub> would still be higher than the SFRD<sub>field</sub> by 7.3 times instead of 12. In other words, 43 per cent of the difference in the SFRD<sub>pc</sub> and the SFRD<sub>field</sub> is as a result of the elevated SFR of the protocluster members relative to that of field galaxies, with the remaining 57 per cent resulting from the higher galaxy number density.

In principle, it is possible that this increase in the SFR is due to an increase in the SM (e.g. Davé 2008; Sobral et al. 2014; Salmon et al. 2015; Tomczak et al. 2016) as the environment gets denser. However, performing a comparable calculation with respect to SM results in no significant evidence of correlation between the SM and overdensity. The Spearman correlation coefficient is weaker (0.155) with a p value of 0.09. We recast these results in the next section.

## 6.3 SFRD of the $\sigma_{\delta} \ge 5$ peaks of Taralay

We calculate the SFRD of the peaks of Taralay to be $\log(SFRD_{\text{peak}}/M_{\odot} \text{yr}^{-1} \text{Mpc}^{-3}) = 0.87_{-0.32}^{+0.18}$. Similar to the full Taralay protocluster, the $\sigma_{\delta} \ge 5$ peaks of this protocluster also show SFRD well in excess of the coeval field value.

Fig. 9 shows the cumulative distribution function (CDF) of the SFR, SM and the number of galaxies as a function of $\sigma_{\delta}$. It is obvious on inspection that the CDF of SFR in the protocluster is skewed toward higher values in the central regions than that of the average number of galaxies, while the CDF of SM tracks the average number of galaxies throughout the entire protocluster. For example, about 68 per cent of the total SFR in the protocluster (SFR<sub>pc</sub>) takes place in the $\sigma_{\delta} \ge 5$ peaks while the inner most regions of the peak ($\sigma_{\delta} \ge 10$) contains 50 per cent of the SFR<sub>pc</sub>. This points to the galaxies in the peaks having accelerated evolution and is highly suggestive of inside-out growth. These galaxies might become the more quiescent galaxies that are seen ~850 Myr later at $z \sim 3$ (e.g. Franco et al. 2020; Forrest et al. 2020a,b; Shen et al. 2021; McConachie et al. 2022; Ito et al. 2023)

The high SFR in the peaks cannot be attributed only to the large number of galaxies in these regions as less than 30 per cent protocluster member galaxies are in the inner most regions of the peaks with the entire $\sigma_{\delta} \ge 5$ peaks hosting less than 50 per cent of the total protocluster member galaxies. The SM in the peaks is < 50 per cent of the total SM encased in the protocluster, which largely rules out higher SFR of the galaxies in the peak being a result of those galaxies having higher SMs than counterparts in more rarefied regions. The segregation observed in SFR between the densest regions of the protocluster, the protocluster outskirts, and the field, and the lack of SM segregation strongly indicate that the protocluster members, especially those in densest regions, are just beginning to ramp up their star formation activity. If such activity was sustained for even a relatively short time early in the formation history of the protocluster, SM segregation would almost certainly also be observed.

## 6.4 Fractional contribution of the protoclusters at $z \sim 4.57$ to the cosmic SFRD

We also estimate the fractional contribution from protoclusters to the cosmic SFRD at $z \sim 4.57$ using Taralay as a representative of a sample of protoclusters at these redshifts (although see Appendix A6 for discussion about using such a massive protocluster as a proxy). We estimate this fraction using the following formula:

$$ \text{SFRD}_{\text{pc}} \text{ fraction} = \frac{\text{SFRD}_{\text{pc}} \times \text{vol}_{\text{pc}}}{\text{SFRD}_{\text{pc}} \times \text{vol}_{\text{pc}} + \text{SFRD}_{\text{field}} \times (1 - \text{vol}_{\text{pc}})} \quad (6) $$
<figure><img src="image_9.png" /><figcaption>**Figure 9.** The cumulative distribution function (CDF) of the average total SFR, the average total SM and the average number of galaxies as a function of $\sigma_8$. The average for all quantities is taken from 100 iterations of Monte Carlo. The distribution of the average number of galaxies shown on the right hand y-axis for both panels is slightly imprecise due to the statistical nature of the Monte Carlo process. The shaded blue region indicates the peak region of the Taralay protocluster and the $2 \le \sigma_8 \le 5$ area shows the outskirts of the protocluster for both panels.</figcaption></figure>

where vol<sub>pc</sub> refers to the volume occupied by protoclusters. At $z \sim 4.57$, the volume filling factor for protoclusters calculated by Chiang et al. (2017) is 0.04.<fnref n="6" /> This makes the fractional contribution to SFRD from protoclusters at $z \sim 4.57$ to be 33.5 per cent<sup>+8.0</sup><sub>-4.3</sub> per cent.<fnref n="7" /> The uncertainty on the SFRD<sub>pc</sub> fraction comes from the uncertainty on the SFR from performing Monte Carlo on redshifts (Section 3.2), and change in the SFR and volume of the protocluster due to varying the boundary of the protocluster (Section 3.3).

We compare this result with the predictions from Chiang et al. (2017). The estimated SFRD<sub>pc</sub> fraction in this study is 2.6σ and 1.7σ in excess of the predicted ~22 per cent and ~26 per cent from (Guo et al. 2013) and (Henriques et al. 2015) simulations, respectively. Though our SFRD<sub>pc</sub> fraction shows moderate tension with the predictions from simulations, we would like to note that there are several caveats when comparing observational data and simulations. We discuss how the definition for a protocluster that we adopt in this study varies from the definition adopted in Chiang et al. (2017) in Appendix A5. We also remind the reader that semi-analytic models (SAMs) assign the SFR to galaxies using a prescription that differs from SED fitting results. However, regardless of these considerations, the simulations, other observational studies, and our measurements of Taralay all indicate that protoclusters at $z \ge 2$ contribute significantly to the SM growth of the universe.

We also compare our results with the SFRD<sub>pc</sub> fractions based on the SFRD values of Popescu et al. (2023) in Fig. 10. To obtain the

<figure><img src="image_10.png" /><figcaption>**Figure 10.** Comparison of the fraction of SFRD from protoclusters at $z \sim 4.57$ estimated using Taralay protocluster as a proxy of all protoclusters at this redshift with the fraction of protocluster SFRD predicted through Chiang et al. (2017) simulation. The olive stars show the fraction of SFRD from protoclusters at $z = 2$ and $z = 3$ obtained from Popescu et al. (2023). The solid lines is the fraction predicted for all protoclusters in the simulations with two different SAMs from Henriques et al. (2015) and Guo et al. (2013). The dotted lines show the fraction predicted for only the protocluster cores with SAMs mentioned above.</figcaption></figure>

SFRD<sub>pc</sub> fractions corresponding to the SFRD values listed in this study at $z = 2$ and $z = 3$, we first measure SFRD<sub>field</sub> at $z = 2$ and $z = 3$ based on the SFRD values in the $1.8 < z < 2.2$ redshift range from Dahlen et al. (2007), Gruppioni et al. (2013, 2020), Magnelli et al. (2013), Koprowski et al. (2017), and Wang et al. (2019b) and SFRD values in the $2.8 < z < 3.2$ redshift range from Gruppioni et al. (2013, 2020) and Koprowski et al. (2017), respectively. The median, 16th and 84th percentile of these samples give us the SFRD<sub>field</sub> and errors at $z = 2$ and $z = 3$ respectively. We find a good agreement between the SFRD<sub>pc</sub> fraction of this study and the SFRD<sub>pc</sub> fractions we calculate based on the SFRD values of Popescu et al. (2023).

<footnote n="6">⁶The volume filling factor in our data is 0.018 when only Taralay is considered and increases to 0.022 if S1 and S2 are included. The volume filling factor is obtained by dividing the volume of the overdense structure(s) by the volume of the coeval field reported in Section 4.</footnote>

<footnote n="7">⁷Adopting the volume filling factor of our data, 0.022, rather than that of simulations, 0.04, recovered a fractional contribution to SFRD from protoclusters at $z \sim 4.57$ of ~21 per cent. This value is also consistent with the equivalent value from simulations. However, the filling factor estimated from our data is subject to cosmic variance to a much higher level than that of the simulation.</footnote>
<figure><img src="image_11.png" /><figcaption>**Figure 9.** The cumulative distribution function (CDF) of the average total SFR, the average total SM and the average number of galaxies as a function of $\sigma_8$. The average for all quantities is taken from 100 iterations of Monte Carlo. The distribution of the average number of galaxies shown on the right hand y-axis for both panels is slightly imprecise due to the statistical nature of the Monte Carlo process. The shaded blue region indicates the peak region of the Taralay protocluster and the $2 \le \sigma_8 \le 5$ area shows the outskirts of the protocluster for both panels.</figcaption></figure>

where vol<sub>pc</sub> refers to the volume occupied by protoclusters. At $z \sim 4.57$, the volume filling factor for protoclusters calculated by Chiang et al. (2017) is 0.04.<sup>6</sup> This makes the fractional contribution to SFRD from protoclusters at $z \sim 4.57$ to be 33.5 per cent<sup>+8.0</sup><sub>-4.3</sub> per cent.<sup>7</sup> The uncertainty on the SFRD<sub>pc</sub> fraction comes from the uncertainty on the SFR from performing Monte Carlo on redshifts (Section 3.2), and change in the SFR and volume of the protocluster due to varying the boundary of the protocluster (Section 3.3).

We compare this result with the predictions from Chiang et al. (2017). The estimated SFRD<sub>pc</sub> fraction in this study is $2.6\sigma$ and $1.7\sigma$ in excess of the predicted $\sim 22$ per cent and $\sim 26$ per cent from (Guo et al. 2013) and (Henriques et al. 2015) simulations, respectively. Though our SFRD<sub>pc</sub> fraction shows moderate tension with the predictions from simulations, we would like to note that there are several caveats when comparing observational data and simulations. We discuss how the definition for a protocluster that we adopt in this study varies from the definition adopted in Chiang et al. (2017) in Appendix A5. We also remind the reader that semi-analytic models (SAMs) assign the SFR to galaxies using a prescription that differs from SED fitting results. However, regardless of these considerations, the simulations, other observational studies, and our measurements of Taralay all indicate that protoclusters at $z \ge 2$ contribute significantly to the SM growth of the universe.

We also compare our results with the SFRD<sub>pc</sub> fractions based on the SFRD values of Popescu et al. (2023) in Fig. 10. To obtain the

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Comparison of the fraction of SFRD from protoclusters at $z \sim 4.57$ estimated using Taralay protocluster as a proxy of all protoclusters at this redshift with the fraction of protocluster SFRD predicted through Chiang et al. (2017) simulation. The olive stars show the fraction of SFRD from protoclusters at $z = 2$ and $z = 3$ obtained from Popescu et al. (2023). The solid lines is the fraction predicted for all protoclusters in the simulations with two different SAMs from Henriques et al. (2015) and Guo et al. (2013). The dotted lines show the fraction predicted for only the protocluster cores with SAMs mentioned above.</figcaption></figure>

SFRD<sub>pc</sub> fractions corresponding to the SFRD values listed in this study at $z = 2$ and $z = 3$, we first measure SFRD<sub>field</sub> at $z = 2$ and $z = 3$ based on the SFRD values in the $1.8 < z < 2.2$ redshift range from Dahlen et al. (2007), Gruppioni et al. (2013, 2020), Magnelli et al. (2013), Koprowski et al. (2017), and Wang et al. (2019b) and SFRD values in the $2.8 < z < 3.2$ redshift range from Gruppioni et al. (2013, 2020) and Koprowski et al. (2017), respectively. The median, 16th and 84th percentile of these samples give us the SFRD<sub>field</sub> and errors at $z = 2$ and $z = 3$ respectively. We find a good agreement between the SFRD<sub>pc</sub> fraction of this study and the SFRD<sub>pc</sub> fractions we calculate based on the SFRD values of Popescu et al. (2023).

<footnote n="6"><sup>6</sup>The volume filling factor in our data is 0.018 when only Taralay is considered and increases to 0.022 if S1 and S2 are included. The volume filling factor is obtained by dividing the volume of the overdense structure(s) by the volume of the coeval field reported in Section 4.</footnote>

<footnote n="7"><sup>7</sup>Adopting the volume filling factor of our data, 0.022, rather than that of simulations, 0.04, recovered a fractional contribution to SFRD from protoclusters at $z \sim 4.57$ of $\sim 21$ per cent. This value is also consistent with the equivalent value from simulations. However, the filling factor estimated from our data is subject to cosmic variance to a much higher level than that of the simulation.</footnote>
We further discuss these results with respect to additional literature in Section 7.

We also calculate the fractional contribution from the $\sigma_s \ge 5$ peaks of protoclusters to the cosmic SFRD using equation

$$ SFRD_{\text{peak}} \text{ fraction} = \frac{SFRD_{\text{peak}} \times \text{vol}_{\text{peak}}}{SFRD_{\text{pc}} \times \text{vol}_{\text{pc}} + SFRD_{\text{field}} \times (1 - \text{vol}_{\text{pc}})} \quad (7) $$

where vol$_{peak}$ is calculated by as the ratio of volume of peaks estimated with density mapping (~2060 cMpc$^3$) divided by the volume of the entire protocluster (~12 620 cMpc$^3$) and then multiplying this ratio by the volume filling factor for protoclusters, 0.04. The estimated SFRD$_{peak}$ fraction is 22.2 per cent$^{+5.4}_{-7.3}$ per cent, a significant portion of the SFRD$_{pc}$ fraction, which is indicative of the inside-out growth of protoclusters as discussed in Chiang et al. (2017). Note that we do not use the volume filling factor for the protocluster cores as outlined in Chiang et al. (2017) as their definition of core differs from our definition of peaks, discussed in Section A5.

## 7 DISCUSSION

The SFRD$_{pc}$ we report in this study is based on optical/Near-IR data. To obtain the total SFR for each galaxy, we perform SED fitting that includes a dust correction. We find that our value is in agreement with the value reported in Popescu et al. (2023), a study that focuses on the stacked Far-IR data for 211 protoclusters at $2 < z < 3$ to estimate the SFR of galaxies using SED fitting (see Section 6.2 for a brief description of analysis employed by Popescu et al. (2023) to obtain the SFRD values). Because this study concentrates on the Far-IR emission of protocluster galaxies, they are only sensitive to obscured star formation activity. At such redshifts the emission in the FIR is, perhaps, a good proxy of the total SFR at $2 < z < 3$, as obscured star formation activity is predicted and measured to be an order of magnitude higher than the unobscured SFRD at these redshifts on average (see, e.g. Algera et al. 2023 and references therein). By contrast, at $z \sim 4.5$, the unobscured SFRD is thought to be in excess or comparable to the obscured SFRD (e.g. Khusanova et al. 2021; Algera et al. 2023), which makes it a reasonable approximation of the total SFRD when corrections for extinction are applied. Note, however, that there are some clear exceptions in protocluster environments, which we discuss in the next paragraph. Although the relative contribution of the unobscured and obscured SFRD in the field and in protoclusters has yet to be studied in great detail, a comparison of our results with those of Popescu et al. (2023) shows a good agreement between the obscured SFRD of protocluster galaxies at redshifts $z \sim 2.5$ with the extinction-corrected unobscured SFRD derived for Taralay at $z \sim 4.5$.

There exist some rare systems that contain overdensities of sub-mm galaxies that exhibit extreme star formation activity, such as the SPT2349-56 protocluster, which was discovered in the South Pole Telescope (SPT)'s extragalactic mm-wave point-source catalogue (Vieira et al. 2010, Mocanu et al. 2013, Everett et al. 2020) and followed up with the ALMA telescope (Miller et al. 2018). This protocluster has over 30 submillimetre-bright galaxies along with LAEs and LBGs and SFRD of over $10^5 M_{\odot}yr^{-1}Mpc^{-3}$ at $z \sim 4$ (Hill et al. 2022). Such rare systems with high star formation activities also exist at lower redshifts, e.g., a system from Wang et al. (2016) at $z \sim 2.5$ that has nine starburst galaxies in the center whose SFR amounts to 3400 $M_{\odot}yr^{-1}$ within an 80 kpc region, and four enormous Ly$\alpha$ nebulae from Nowotka et al. (2022) at $2 < z < 3$ with an SFRD of $1200 \pm 300 M_{\odot}yr^{-1}Mpc^{-3}$; however, the SPT2349-56 protocluster is one of the only few systems yet discovered at a comparable redshift to Taralay (see Alberts & Noble 2022 and references therein) that shows an extremely high star formation activity. The SFRD of such systems, while high in the region of the universe that they exist, averaged over the entire sky is probably much less than typical optical/Near-IR selected systems as such types of systems are extremely rare (e.g. Negrello et al. 2017, Lammers et al. 2022). In this way, Taralay might be a better representative of the underlying population of massive protoclusters at this epoch. More work is needed in the future to compare SFRD of Taralay with an ensemble of protoclusters at these redshifts.

Although the optical/Near-IR selection may lead to a sample of protoclusters that are more representative of an underlying galaxy populations, one of the disadvantages of this approach is that the optical/Near-IR diminished/dark galaxies get left out of the sample. If such galaxies, sometimes called HST-dark galaxies, i.e. the galaxies that are undetected in the current HST surveys due to being effectively invisible in the rest-frame ultrablue to the typical depths of HST survey observations (e.g. Franco et al. 2018, Wang et al. 2019a), exist in the region that is targeted in this study, Barrufet et al. (2023) shows that their presence will contribute approximately an order of magnitude less than the rest-frame UV/optically selected galaxies to the total SFRD at these redshifts. Due to the volume of the protocluster being a lot smaller than the field, the contribution of the HST-dark galaxies may affect the SFRD of the protocluster more than the field widening the gap between SFRD$_{pc}$ and SFRD$_{field}$. The effect of these galaxies on the gap between SFRD$_{pc}$ and SFRD$_{field}$ will depend on the location preferred by the galaxies.

Studies such as Blain et al. (2004), Almeida, Baugh & Lacey (2011), Smolčić et al. (2017), Zhou et al. (2020) claim association of sub-millimeter galaxies with overdensities, though it is not clear if these sources are fractionally over represented in protoclusters relative to the field. There is some indication from the ALPINE-ALMA survey that there might be a higher number of extremely dusty star-forming galaxies at elevated redshifts in denser environments compared to the field, including around $z \sim 4.57$ (e.g. Romano et al. 2020, Loiacono et al. 2021, Fujimoto et al. 2023). If such galaxies are more prevalent in rich environments relative to the field, the SFRD$_{pc}$ we calculate here will be a lower limit as will its fractional contribution to the overall SFRD at this redshift.

The observational SFRD$_{pc}$ fraction we found in this study is none the less quite large, even in excess of the predictions from simulations and indicates that the protoclusters are a significant contributors to the cosmic SFRD at high redshifts. Ito et al. (2020) also found protoclusters as a driver of SM growth in the early universe. They calculated rest-frame ultra-blue luminosity function of g-dropout galaxies in 177 protocluster candidates at $z \sim 4$ selected in the HSC Subaru Strategic Program (Aihara et al. 2018); though their SFRD fraction, 6 per cent–20 per cent, is not as high as the finding of this study.

At $z \sim 4.57$, the number density of quiescent galaxies is small (e.g. Steinhardt et al. 2014, Tasca et al. 2015, Davidzon et al. 2017, Gould et al. 2023). All such galaxies may not be detected in our combined spectroscopic and photometric sample. However, their impact on our results are minimal, as their contribution to the SFR is expected to be very low. For example, a massive quiescent galaxy in an overdense environment at $z = 4.53$ in the COSMOS field that was observed with MOSFIRE on Keck has SFR an order of magnitude less than the SFR of main-sequence galaxies at $z = 4.5$ (Kakimoto et al. 2023). This galaxy is ~6 proper Mpc away from the center of the PC1 of Taralay and may or may not be associated with Taralay.
We further discuss these results with respect to additional literature in Section 7.

We also calculate the fractional contribution from the $\sigma_s \ge 5$ peaks of protoclusters to the cosmic SFRD using equation

$$SFRD_{\text{peak}} \text{ fraction} = \frac{SFRD_{\text{peak}} \times \text{vol}_{\text{peak}}}{SFRD_{\text{pc}} \times \text{vol}_{\text{pc}} + SFRD_{\text{field}} \times (1 - \text{vol}_{\text{pc}})} \quad (7)$$

where vol$_{peak}$ is calculated by as the ratio of volume of peaks estimated with density mapping (~2060 cMpc$^3$) divided by the volume of the entire protocluster (~12 620 cMpc$^3$) and then multiplying this ratio by the volume filling factor for protoclusters, 0.04. The estimated SFRD$_{peak}$ fraction is 22.2 per cent$^{+5.4}_{-7.3}$ per cent, a significant portion of the SFRD$_{pc}$ fraction, which is indicative of the inside-out growth of protoclusters as discussed in Chiang et al. (2017). Note that we do not use the volume filling factor for the protocluster cores as outlined in Chiang et al. (2017) as their definition of core differs from our definition of peaks, discussed in Section A5.

## 7 DISCUSSION

The SFRD$_{pc}$ we report in this study is based on optical/Near-IR data. To obtain the total SFR for each galaxy, we perform SED fitting that includes a dust correction. We find that our value is in agreement with the value reported in Popescu et al. (2023), a study that focuses on the stacked Far-IR data for 211 protoclusters at $2 < z < 3$ to estimate the SFR of galaxies using SED fitting (see Section 6.2 for a brief description of analysis employed by Popescu et al. (2023) to obtain the SFRD values). Because this study concentrates on the Far-IR emission of protocluster galaxies, they are only sensitive to obscured star formation activity. At such redshifts the emission in the FIR is, perhaps, a good proxy of the total SFR at $2 < z < 3$, as obscured star formation activity is predicted and measured to be an order of magnitude higher than the unobscured SFRD at these redshifts on average (see, e.g. Algera et al. 2023 and references therein). By contrast, at $z \sim 4.5$, the unobscured SFRD is thought to be in excess or comparable to the obscured SFRD (e.g. Khusanova et al. 2021; Algera et al. 2023), which makes it a reasonable approximation of the total SFRD when corrections for extinction are applied. Note, however, that there are some clear exceptions in protocluster environments, which we discuss in the next paragraph. Although the relative contribution of the unobscured and obscured SFRD in the field and in protoclusters has yet to be studied in great detail, a comparison of our results with those of Popescu et al. (2023) shows a good agreement between the obscured SFRD of protocluster galaxies at redshifts $z \sim 2.5$ with the extinction-corrected unobscured SFRD derived for Taralay at $z \sim 4.5$.

There exist some rare systems that contain overdensities of sub-mm galaxies that exhibit extreme star formation activity, such as the SPT2349-56 protocluster, which was discovered in the South Pole Telescope (SPT)'s extragalactic mm-wave point-source catalogue (Vieira et al. 2010, Mocanu et al. 2013, Everett et al. 2020) and followed up with the ALMA telescope (Miller et al. 2018). This protocluster has over 30 submillimetre-bright galaxies along with LAEs and LBGs and SFRD of over $10^5 M_{\odot}yr^{-1}Mpc^{-3}$ at $z \sim 4$ (Hill et al. 2022). Such rare systems with high star formation activities also exist at lower redshifts, e.g., a system from Wang et al. (2016) at $z \sim 2.5$ that has nine starburst galaxies in the center whose SFR amounts to 3400 $M_{\odot}yr^{-1}$ within an 80 kpc region, and four enormous Ly$\alpha$ nebulae from Nowotka et al. (2022) at $2 < z < 3$ with an SFRD of $1200 \pm 300 M_{\odot}yr^{-1}Mpc^{-3}$; however, the SPT2349-

56 protocluster is one of the only few systems yet discovered at a comparable redshift to Taralay (see Alberts & Noble 2022 and references therein) that shows an extremely high star formation activity. The SFRD of such systems, while high in the region of the universe that they exist, averaged over the entire sky is probably much less than typical optical/Near-IR selected systems as such types of systems are extremely rare (e.g. Negrello et al. 2017, Lammers et al. 2022). In this way, Taralay might be a better representative of the underlying population of massive protoclusters at this epoch. More work is needed in the future to compare SFRD of Taralay with an ensemble of protoclusters at these redshifts.

Although the optical/Near-IR selection may lead to a sample of protoclusters that are more representative of an underlying galaxy populations, one of the disadvantages of this approach is that the optical/Near-IR diminished/dark galaxies get left out of the sample. If such galaxies, sometimes called HST-dark galaxies, i.e. the galaxies that are undetected in the current HST surveys due to being effectively invisible in the rest-frame ultrablue to the typical depths of HST survey observations (e.g. Franco et al. 2018, Wang et al. 2019a), exist in the region that is targeted in this study, Barrufet et al. (2023) shows that their presence will contribute approximately an order of magnitude less than the rest-frame UV/optically selected galaxies to the total SFRD at these redshifts. Due to the volume of the protocluster being a lot smaller than the field, the contribution of the HST-dark galaxies may affect the SFRD of the protocluster more than the field widening the gap between SFRD$_{pc}$ and SFRD$_{field}$. The effect of these galaxies on the gap between SFRD$_{pc}$ and SFRD$_{field}$ will depend on the location preferred by the galaxies.

Studies such as Blain et al. (2004), Almeida, Baugh & Lacey (2011), Smolčić et al. (2017), Zhou et al. (2020) claim association of sub-millimeter galaxies with overdensities, though it is not clear if these sources are fractionally over represented in protoclusters relative to the field. There is some indication from the ALPINE-ALMA survey that there might be a higher number of extremely dusty star-forming galaxies at elevated redshifts in denser environments compared to the field, including around $z \sim 4.57$ (e.g. Romano et al. 2020, Loiacono et al. 2021, Fujimoto et al. 2023). If such galaxies are more prevalent in rich environments relative to the field, the SFRD$_{pc}$ we calculate here will be a lower limit as will its fractional contribution to the overall SFRD at this redshift.

The observational SFRD$_{pc}$ fraction we found in this study is none the less quite large, even in excess of the predictions from simulations and indicates that the protoclusters are a significant contributors to the cosmic SFRD at high redshifts. Ito et al. (2020) also found protoclusters as a driver of SM growth in the early universe. They calculated rest-frame ultra-blue luminosity function of g-dropout galaxies in 177 protocluster candidates at $z \sim 4$ selected in the HSC Subaru Strategic Program (Aihara et al. 2018); though their SFRD fraction, 6 per cent–20 per cent, is not as high as the finding of this study.

At $z \sim 4.57$, the number density of quiescent galaxies is small (e.g. Steinhardt et al. 2014, Tasca et al. 2015, Davidzon et al. 2017, Gould et al. 2023). All such galaxies may not be detected in our combined spectroscopic and photometric sample. However, their impact on our results are minimal, as their contribution to the SFR is expected to be very low. For example, a massive quiescent galaxy in an overdense environment at $z = 4.53$ in the COSMOS field that was observed with MOSFIRE on Keck has SFR an order of magnitude less than the SFR of main-sequence galaxies at $z = 4.5$ (Kakimoto et al. 2023). This galaxy is ~6 proper Mpc away from the center of the PC1 of Taralay and may or may not be associated with Taralay.
# 8 SUMMARY AND CONCLUSION

This study was performed in order to conduct one of the first observational tests of whether the protocluster regions in the high redshift universe contribute significantly to the overall mass assembly of the universe as predicted by simulations. We chose the Taralay protocluster at $z \sim 4.57$ in the COSMOS field as the target of a large Keck/DEIMOS campaign as part of the C3VO (Lemaux et al. 2022) survey. With the total integration time of $\sim$28 h, we obtained 44 new secure spectral redshifts in the redshift range of the protocluster as compared to the nine secure spectral redshifts from VUDS at the time of the discovery. We also reported on 46 new secure spectral redshifts obtained in the redshift range of the coeval field. We combined this spectroscopic data with spectral redshifts from other spectral surveys and a variety of photometric catalogs in the COSMOS field. Using this wealth of data, we measured the SFRD of the Taralay protocluster and the surrounding field. Following are the main conclusions of this paper:

(i) Using the density mapping technique, we mapped out the Taralay protocluster at $z \sim 4.57$, established its internal structure and characterized its properties. Taralay protocluster displays two sub structures PC1 and PC2 for a density isopleth of $\sigma_\delta \ge 2$ that we use as a boundary to define the outline of this protocluster. While PC1 hosts two $\sigma_\delta \ge 5$ overdense peaks, PC2, the smaller substructure only hosts one $\sigma_\delta \ge 5$ overdense peak.

(ii) The mass of Taralay protocluster is estimated to be $1.74_{-0.77}^{+1.36} \times 10^{15} M_\odot$, which makes it exceptionally massive at these redshifts. This protocluster occupies a comoving volume $12620_{-956}^{+1042} \text{ cMpc}^3$.

(iii) We measured the SFRD of the field surrounding the Taralay protocluster to be $\log(\text{SFRD}/M_\odot \text{ yr}^{-1} \text{ Mpc}^{-3}) = -0.82_{-0.29}^{+0.19}$ and found it to be consistent with the most comparable study at these redshifts (Khusanova et al. 2021) but in moderate tension with that of Madau & Dickinson (2014).

(iv) We compare the masses estimated from overdensities calculated with the density mapping technique to the dynamical masses estimated from the LoS velocity dispersion for the protocluster, two $\sigma_\delta \ge 4.5$ regions and one $\sigma_\delta \ge 2.8$ region. We find that the masses estimated from the LoS velocity dispersion show a deficit in the range of $1.5-4\sigma$ with an average deficit of $2.5\sigma$.

(v) The SFRD of the $z \sim 4.57$ Taralay galaxy members is $\sim 12$ times higher or $\log(\text{SFRD}/M_\odot \text{ yr}^{-1} \text{ Mpc}^{-3}) = 1.08 \pm 0.32$ in excess of the SFRD of the coeval field galaxies signifying that the environment does play a crucial role in driving the SFRD. Protoclusters like Taralay are clearly drivers of SM growth in the early universe.

(vi) We provide one of the first observational tests of simulation predictions that protoclusters contribute significantly to the fraction of cosmic SFR density in the early universe. Our findings indicate that protoclusters drive the SM growth in the early universe contributing $33.5 \text{ per cent}^{+8.0}_{-4.3} \text{ per cent}$ to the cosmic SFRD at $z \sim 4.57$, in $2.67\sigma$ excess over the $\sim 22 \text{ per cent}$ value predicted from simulations.

(vii) We find that the contribution to the cosmic SFRD from the $\sigma_\delta \ge 5$ peaks of the Taralay protocluster is $22.2 \text{ per cent}^{+5.4}_{-7.3} \text{ per cent}$, a significant portion of the total SFRD of the protocluster and indicative of the inside-out growth pattern as predicted by simulations.

(viii) We find that the $\sigma_\delta \ge 5$ peaks of the Taralay protocluster encase 68 per cent of the SFR while hosting less than 50 per cent of the galaxies. The SFRD of $\sigma_\delta \ge 5$ peaks is $\log(\text{SFRD}/M_\odot \text{ yr}^{-1} \text{ Mpc}^{-3}) = 0.87_{-0.32}^{+0.18}$.

(ix) We find a moderately strong, significant positive correlation between SFR and overdensity for galaxies in and around the Taralay protocluster.

In the future, we will be expanding this work to ensembles of protoclusters. With an ensemble of protoclusters, it is possible to divide the protoclusters by mass, dynamical state, redshift, etc. in order to better understand the underlying mechanisms which drive and quench the rapid SM growth. We also plan on including sub-millimetre observations to attempt to characterize the role of highly dusty star-forming galaxies in protocluster environments. It appears that such sources may prefer overdense environments (e.g. Romano et al. 2020, Loiacono et al. 2021, Fujimoto et al. 2023). The inclusion of these highly dusty star-forming galaxies has the potential to significantly increase the estimated SFRD of this protocluster, and thus its contribution to the overall SFRD of the universe at these redshifts. The results we have presented in Taralay are tantalizing and, if Taralay is indeed an exemplar of massive protoclusters at these redshifts, our results indicate that protoclusters play a key role in driving SM growth in the early universe.

# ACKNOWLEDGEMENTS

We thank the anonymous referee for their valuable feedback. This work was supported by the National Science Foundation under grant no. 1908422. YF acknowledges support from JSPS KAKENHI Grant Number JP23K13149. We thank the late Olivier Le Févre for his pioneering work with galaxy redshift surveys, including the VIMOS Ultra-Deep Survey, without which this work would have likely not been possible. PS thanks Matthew Staab for providing crucial programming support that made the analysis of this paper possible. We thank the teams that did the hard work of compiling the various photometric catalogs in the COSMOS field for making these catalogs and their associated quantities public. A part of this work is based on the Galaxy Evolution Explorer (GALEX) satellite, Canada-France-Hawaii Telescope (CFHT), Hubble Space Telescope (HST), Subaru telescope, Visible and Infrared Survey Telescope for Astronomy (VISTA), and Spitzer Space Telescope. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

# 9. DATA AVAILABILITY

The data used for this study will be shared upon a reasonable request.

# REFERENCES

* Adams S. M., Martini P., Croxall K. V., Overzier R. A., Silverman J. D., 2015, MNRAS, 448, 1335

* Aihara H. et al., 2018, PASJ, 70, S4

* Alberts S., Noble A., 2022, Universe, 8, 554

* Algera H. S. B. et al., 2023, MNRAS, 518, 6142

* Almeida C., Baugh C. M., Lacey C. G., 2011, MNRAS, 417, 2057

* Arnouts S. et al., 2002, MNRAS, 329, 355

* Ata M., Kitaura F.-S., Lee K.-G., Lemaux B. C., Kashino D., Cucciati O., Hernández-Sánchez M., Le Fèvre O., 2021, MNRAS, 500, 3194

* Bañados E., Venemans B., Walter F., Kurk J., Overzier R., Ouchi M., 2013, ApJ, 773, 178
# 8 SUMMARY AND CONCLUSION

This study was performed in order to conduct one of the first observational tests of whether the protocluster regions in the high redshift universe contribute significantly to the overall mass assembly of the universe as predicted by simulations. We chose the Taralay protocluster at $z \sim 4.57$ in the COSMOS field as the target of a large Keck/DEIMOS campaign as part of the C3VO (Lemaux et al. 2022) survey. With the total integration time of $\sim$28 h, we obtained 44 new secure spectral redshifts in the redshift range of the protocluster as compared to the nine secure spectral redshifts from VUDS at the time of the discovery. We also reported on 46 new secure spectral redshifts obtained in the redshift range of the coeval field. We combined this spectroscopic data with spectral redshifts from other spectral surveys and a variety of photometric catalogs in the COSMOS field. Using this wealth of data, we measured the SFRD of the Taralay protocluster and the surrounding field. Following are the main conclusions of this paper:

(i) Using the density mapping technique, we mapped out the Taralay protocluster at $z \sim 4.57$, established its internal structure and characterized its properties. Taralay protocluster displays two sub structures PC1 and PC2 for a density isopleth of $\sigma_\delta \ge 2$ that we use as a boundary to define the outline of this protocluster. While PC1 hosts two $\sigma_\delta \ge 5$ overdense peaks, PC2, the smaller substructure only hosts one $\sigma_\delta \ge 5$ overdense peak.

(ii) The mass of Taralay protocluster is estimated to be $1.74_{-0.77}^{+1.36} \times 10^{15} M_\odot$, which makes it exceptionally massive at these redshifts. This protocluster occupies a comoving volume $12620_{-956}^{+1042} \text{ cMpc}^3$.

(iii) We measured the SFRD of the field surrounding the Taralay protocluster to be $\log(\text{SFRD}/M_\odot \text{ yr}^{-1} \text{ Mpc}^{-3}) = -0.82_{-0.29}^{+0.19}$ and found it to be consistent with the most comparable study at these redshifts (Khusanova et al. 2021) but in moderate tension with that of Madau & Dickinson (2014).

(iv) We compare the masses estimated from overdensities calculated with the density mapping technique to the dynamical masses estimated from the LoS velocity dispersion for the protocluster, two $\sigma_\delta \ge 4.5$ regions and one $\sigma_\delta \ge 2.8$ region. We find that the masses estimated from the LoS velocity dispersion show a deficit in the range of $1.5-4\sigma$ with an average deficit of $2.5\sigma$.

(v) The SFRD of the $z \sim 4.57$ Taralay galaxy members is $\sim 12$ times higher or $\log(\text{SFRD}/M_\odot \text{ yr}^{-1} \text{ Mpc}^{-3}) = 1.08 \pm 0.32$ in excess of the SFRD of the coeval field galaxies signifying that the environment does play a crucial role in driving the SFRD. Protoclusters like Taralay are clearly drivers of SM growth in the early universe.

(vi) We provide one of the first observational tests of simulation predictions that protoclusters contribute significantly to the fraction of cosmic SFR density in the early universe. Our findings indicate that protoclusters drive the SM growth in the early universe contributing $33.5 \text{ per cent}^{+8.0}_{-4.3} \text{ per cent}$ to the cosmic SFRD at $z \sim 4.57$, in $2.67\sigma$ excess over the $\sim 22 \text{ per cent}$ value predicted from simulations.

(vii) We find that the contribution to the cosmic SFRD from the $\sigma_\delta \ge 5$ peaks of the Taralay protocluster is $22.2 \text{ per cent}^{+5.4}_{-7.3} \text{ per cent}$, a significant portion of the total SFRD of the protocluster and indicative of the inside-out growth pattern as predicted by simulations.

(viii) We find that the $\sigma_\delta \ge 5$ peaks of the Taralay protocluster encase 68 per cent of the SFR while hosting less than 50 per cent of the galaxies. The SFRD of $\sigma_\delta \ge 5$ peaks is $\log(\text{SFRD}/M_\odot \text{ yr}^{-1} \text{ Mpc}^{-3}) = 0.87_{-0.32}^{+0.18}$.

(ix) We find a moderately strong, significant positive correlation between SFR and overdensity for galaxies in and around the Taralay protocluster.

In the future, we will be expanding this work to ensembles of protoclusters. With an ensemble of protoclusters, it is possible to divide the protoclusters by mass, dynamical state, redshift, etc. in order to better understand the underlying mechanisms which drive and quench the rapid SM growth. We also plan on including sub-millimetre observations to attempt to characterize the role of highly dusty star-forming galaxies in protocluster environments. It appears that such sources may prefer overdense environments (e.g. Romano et al. 2020, Loiacono et al. 2021, Fujimoto et al. 2023). The inclusion of these highly dusty star-forming galaxies has the potential to significantly increase the estimated SFRD of this protocluster, and thus its contribution to the overall SFRD of the universe at these redshifts. The results we have presented in Taralay are tantalizing and, if Taralay is indeed an exemplar of massive protoclusters at these redshifts, our results indicate that protoclusters play a key role in driving SM growth in the early universe.

# ACKNOWLEDGEMENTS

We thank the anonymous referee for their valuable feedback. This work was supported by the National Science Foundation under grant no. 1908422. YF acknowledges support from JSPS KAKENHI Grant Number JP23K13149. We thank the late Olivier Le Févre for his pioneering work with galaxy redshift surveys, including the VIMOS Ultra-Deep Survey, without which this work would have likely not been possible. PS thanks Matthew Staab for providing crucial programming support that made the analysis of this paper possible. We thank the teams that did the hard work of compiling the various photometric catalogs in the COSMOS field for making these catalogs and their associated quantities public. A part of this work is based on the Galaxy Evolution Explorer (GALEX) satellite, Canada-France-Hawaii Telescope (CFHT), Hubble Space Telescope (HST), Subaru telescope, Visible and Infrared Survey Telescope for Astronomy (VISTA), and Spitzer Space Telescope. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

# 9. DATA AVAILABILITY

The data used for this study will be shared upon a reasonable request.

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## APPENDIX A: CAVEATS

Here we discuss some of the key caveats that should be considered when interpreting the results of our study.

### A1 Estimating the overdensity

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Mei S. et al., 2023, A&A, 670, A58

Miley G., De Breuck C., 2008, A&AR, 15, 67

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Sanders D. B. et al., 2007, ApJS, 172, 86

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Schechter P., 1976, ApJ, 203, 297

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Scoville N. et al., 2007, ApJS, 172, 38

Shah E. A. et al., 2023, Identification and Characterization of Six Spectroscopically Confirmed Massive Protostructures at $2.5 < z < 4.5$, preprint (arXiv:2312.04634)

Shapley A. E., Steidel C. C., Pettini M., Adelberger K. L., 2003, ApJ, 588, 65

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Shi K., Toshikawa J., Cai Z., Lee K.-S., Fang T., 2020, ApJ, 899, 79

Shi K., Toshikawa J., Lee K.-S., Wang T., Cai Z., Fang T., 2021, ApJ, 911, 46

Smolčić V. et al., 2017, A&A, 597, A4

Sobral D., Best P. N., Smail I., Mobasher B., Stott J., Nisbet D., 2014, MNRAS, 437, 3516

Steidel C. C., Adelberger K. L., Shapley A. E., Erb D. K., Reddy N. A., Pettini M., 2005, ApJ, 626, 44

Steinhardt C. L. et al., 2014, ApJ, 791, L25

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Tasca L. A. M. et al., 2015, A&A, 581, A54

Thomas R. et al., 2017, A&A, 602, A35

Tomczak A. R. et al., 2016, ApJ, 817, 118

Tomczak A. R. et al., 2017, MNRAS, 472, 3512

Tomczak A. R. et al., 2019, MNRAS, 484, 4695

Toshikawa J. et al., 2012, ApJ, 750, 137

Toshikawa J. et al., 2016, ApJ, 826, 114

Toshikawa J., Malkan M. A., Kashikawa N., Overzier R., Uchiyama H., Ota K., Ishikawa S., Ito K., 2020, ApJ, 888, 89

Uchiyama H. et al., 2022, PASJ, 74, L27

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Vieira J. D. et al., 2010, ApJ, 719, 763

Vizgan D. et al., 2022, ApJ, 929, 92

Wagner C. R., Courteau S., Brodwin M., Stanford S. A., Snyder G. F., Stern D., 2017, ApJ, 834, 53

Wang T. et al., 2016, ApJ, 828, 56

Wang T. et al., 2019a, Nature, 572, 211

Wang L., Pearson W. J., Cowley W., Trayford J. W., Béthermin M., Gruppioni C., Hurley P., Michałowski M. J., 2019b, A&A, 624, A98

Weaver J. R. et al., 2022, ApJS, 258, 11

Werner M. W. et al., 2004, ApJS, 154, 1

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Zhou L. et al., 2020, A&A, 642, A155

de La Vieuille G. et al., 2019, A&A, 628, A3

van Dokkum P. G., 2008, ApJ, 674, 29

von der Linden A., Wild V., Kauffmann G., White S. D. M., Weinmann S., 2010, MNRAS, 404, 1231

## APPENDIX A: CAVEATS

Here we discuss some of the key caveats that should be considered when interpreting the results of our study.

### A1 Estimating the overdensity

In this study, we assume that galaxies can serve as tracers of the underlying matter density field and measure the overdensity in terms of galaxies (e.g. Cucciati et al. 2014). Different types of galaxies, such as quiescent or star forming, trace the matter density field differently. Sometimes matter density is not traced very well by UV-selected galaxies, as in the case of Newman et al. (2022), which finds unexpectedly low galaxy overdensity where large-scale Lyα absorption is strongest indicating high matter density. Moreover, observations might not trace the true underlying galaxy population as low-luminosity galaxies are harder to detect, especially at high redshifts. By considering the mass of galaxies and their SFRs, we determine an appropriate bias factor from simulations that scales the
galaxy overdensity to the matter overdensity. For this study, we use
a bias factor of $b = 3.6$, which is based on previous research (e.g.
Chiang et al. 2013, Durkalec et al. 2018) and the upper and lower
limit for the bias factor are 4.5 and 3.12, respectively, obtained from
Einasto et al. (2023) and Ata et al. (2021).

## A2 SED fitting

The SFR derived from SED fitting method correlates well with the SFR derived from independent measures such as [CII] lines at intermediate and high redshift (e.g. Schaerer et al. 2020). We checked if this correlation holds for galaxies that we obtained from Y. Fudamoto in private communication based on serendipitously detected [CII] lines with ALMA. These three galaxies have $log(L_{CII}/L_{\odot})$ of 8.99, 9.01, and 9.10, respectively. When we compared the [CII] derived SFR with the SFR values obtained for these three galaxies through SED fitting using the parameter set given in Section 5.1, we found that the SED-fit SFR values are consistently lower than the [CII] derived SFR. If we force the fits such that the best model chooses the high end of the E(B-V) value range, the difference between the [CII]-derived SFR and the SED-fit value decreases. However, such fits are clearly disfavored by comparing their reduced $\chi^2$. Note that recent theoretical and observational studies suggest that [CII] is more tightly connected to the molecular gas mass in a complicated way through Kennicut-Schmidt relation (e.g. Zanella et al. 2018; Madden et al. 2020; Vizgan et al. 2022) than to SFR.

## A3 Absence of FIR data

We tested the reliability of SFR derived from SED fitting with optical/NIR data (used in this study). We selected 12 galaxies from ALPINE survey that fall in the redshift range of $4.2 < z < 4.93$ with significant detection in the continuum around restframe 155 $\mu$m. We performed the SED fitting on these galaxies with the same parameters as listed in Table 10 along with (Casey et al. 2012) dust template. We found that, relative to the fits that include the FIR data, the optical/NIR-only fits show higher SFRs by $\sim$0.2 dex. For these galaxies, the extinction correction is generally overestimated by the optical/NIR-only fits. Because these 12 galaxies may or may not be representative of the true galaxy population, as these galaxies are likely the more massive/more dusty extreme of the ALPINE population, we decided to not make any changes to our analysis. Programs probing sub-mm galaxies in protoclusters are needed in order to get a fuller perspective on the star formation in protoclusters. To check how much the result of our study would change if, indeed, what we find were a generally applicable result, we reduced the SFR of each galaxy in our analysis, SFRs that are derived by optical/NIR-only fitting, by 0.2 dex and performed the analysis again. The result was that the SFRD of Taralay and the field were reduced, but well within the uncertainties. The fractional contribution of Taralay-like systems to overall SFRD at these redshifts remained the same.

## A4 Dust properties of bright and faint galaxies

Here we test our assumption that the bright and faint galaxies experience the same level of dust extinction which let us extrapolate the SFRD results to include the lower luminosity galaxies in Section 5.3. If this assumption is wrong, we are either underestimating or overestimating the SFR of the fainter galaxies. This is because the different dust extinction, through the process of SED fitting, will cause the SFR to be different for the fainter galaxies compared to the SFR of the brighter galaxies. To test this assumption, we analyse

the SED models for nearly 3000 galaxies at $2.5 < z < 3.5$ in the COSMOS field. These galaxies make up our sample because at this redshift range we can probe deeper than $M_{FUV} = -19.3$, the depth of our data, at $4.2 < z < 4.93$. For this exercise, a galaxy is considered bright if its FUV absolute magnitude is less than -19, the delineation point between bright and faint.

We perform a KS test on the $E(B-V)$ distribution of both bright and faint galaxies at $2.5 < z < 3.5$, and find that they prefer the same range of values for the colouër excess of the nebular line light, for both young and old populations. The range for E_BV_lines is presented in Table 10. This finding shows that at $2.5 < z < 3.5$, the SFR traced by FUV photons is similarly affected by the dust properties of both faint and bright galaxies. We assume that this behaviour is consistent for galaxies at $4.2 < z < 4.93$ and make no further changes to our FUV magnitude correction factor.

## A5 Comparison to simulations

Our study diverges from the definition and characterization of protoclusters as outlined in Chiang et al. (2017) in several key aspects. In their work, a protocluster encompasses all the dark matter and baryonic matter that will eventually merge into a cluster by $z=0$, with a mass exceeding $10^{14} M_{\odot}$ within $R_{200}$. The protocluster’s volume encompasses all the matter that will contribute to the formation of the cluster by $z=0$. In contrast, our study defines a protocluster as a structure contained within the $2\sigma$ density isopleth.

Furthermore, while Chiang et al. (2017) designates the most massive halo within the protocluster as its core at any given epoch, having a size of $\sim$0.4 cMpc at $z \sim 4.57$, our study identifies the protocluster core as the region bounded inside a $5\sigma$ density isopleth with a size $\sim$2 cMpc. To put our peaks on the same footing as the core defined in Chiang et al. (2017), our peak size will have to reduce beyond $\sigma_{\delta} > 10$ where we have spectroscopic data only for $\sim$3 galaxies. Hence, we adopt our definition for peaks. It is crucial to acknowledge that these differing definitions of protoclusters may contribute to the measured difference between the observed and simulated data.

## A6 Using a massive protocluster as a proxy

Using the density maps, the estimated mass of Taralay protocluster at $z \sim 4.57$ is $1.74 \times 10^{15} M_{\odot}$ making this structure exceptionally massive at these redshifts.

Using such a massive protocluster, which has highly star-forming galaxies, as a representative sample of all the protoclusters at $z \sim 4.57$ to calculate the fraction of SFRD from protoclusters (see Fig. 10) may lead to an overestimated value for the derived contribution of protoclusters to the SFRD. Nevertheless, there is a possibility that environmental quenching is affecting the galaxies within this protocluster (Lemaux et al. 2018) which could result in a decrease in the SFRD. To draw a definitive conclusion, a large collection of protoclusters is required for comprehensively testing their contribution to the SFRD at high redshift.

# APPENDIX B: EFFECT OF PARAMETER CHOICES ON THE MODEL SPECTRUM

The SFR values that our results are based on come from the SED fitting process. It is important therefore to discuss how the different parameters that are used in the SED fitting process impact the spectrum of a galaxy, affecting the estimated SFR. We discuss this impact here using two different approaches. First, we look at the
galaxy overdensity to the matter overdensity. For this study, we use
a bias factor of $b = 3.6$, which is based on previous research (e.g.
Chiang et al. 2013, Durkalec et al. 2018) and the upper and lower
limit for the bias factor are 4.5 and 3.12, respectively, obtained from
Einasto et al. (2023) and Ata et al. (2021).

## A2 SED fitting

The SFR derived from SED fitting method correlates well with the SFR derived from independent measures such as [CII] lines at intermediate and high redshift (e.g. Schaerer et al. 2020). We checked if this correlation holds for galaxies that we obtained from Y. Fudamoto in private communication based on serendipitously detected [CII] lines with ALMA. These three galaxies have $log(L_{CII}/L_{\odot})$ of 8.99, 9.01, and 9.10, respectively. When we compared the [CII] derived SFR with the SFR values obtained for these three galaxies through SED fitting using the parameter set given in Section 5.1, we found that the SED-fit SFR values are consistently lower than the [CII] derived SFR. If we force the fits such that the best model chooses the high end of the E(B-V) value range, the difference between the [CII]-derived SFR and the SED-fit value decreases. However, such fits are clearly disfavored by comparing their reduced $\chi^2$. Note that recent theoretical and observational studies suggest that [CII] is more tightly connected to the molecular gas mass in a complicated way through Kennicut-Schmidt relation (e.g. Zanella et al. 2018; Madden et al. 2020; Vizgan et al. 2022) than to SFR.

## A3 Absence of FIR data

We tested the reliability of SFR derived from SED fitting with optical/NIR data (used in this study). We selected 12 galaxies from ALPINE survey that fall in the redshift range of $4.2 < z < 4.93$ with significant detection in the continuum around restframe 155 $\mu$m. We performed the SED fitting on these galaxies with the same parameters as listed in Table 10 along with (Casey et al. 2012) dust template. We found that, relative to the fits that include the FIR data, the optical/NIR-only fits show higher SFRs by ~0.2 dex. For these galaxies, the extinction correction is generally overestimated by the optical/NIR-only fits. Because these 12 galaxies may or may not be representative of the true galaxy population, as these galaxies are likely the more massive/more dusty extreme of the ALPINE population, we decided to not make any changes to our analysis. Programs probing sub-mm galaxies in protoclusters are needed in order to get a fuller perspective on the star formation in protoclusters. To check how much the result of our study would change if, indeed, what we find were a generally applicable result, we reduced the SFR of each galaxy in our analysis, SFRs that are derived by optical/NIR-only fitting, by 0.2 dex and performed the analysis again. The result was that the SFRD of Taralay and the field were reduced, but well within the uncertainties. The fractional contribution of Taralay-like systems to overall SFRD at these redshifts remained the same.

## A4 Dust properties of bright and faint galaxies

Here we test our assumption that the bright and faint galaxies experience the same level of dust extinction which let us extrapolate the SFRD results to include the lower luminosity galaxies in Section 5.3. If this assumption is wrong, we are either underestimating or overestimating the SFR of the fainter galaxies. This is because the different dust extinction, through the process of SED fitting, will cause the SFR to be different for the fainter galaxies compared to the SFR of the brighter galaxies. To test this assumption, we analyse

the SED models for nearly 3000 galaxies at $2.5 < z < 3.5$ in the COSMOS field. These galaxies make up our sample because at this redshift range we can probe deeper than $M_{FUV} = -19.3$, the depth of our data, at $4.2 < z < 4.93$. For this exercise, a galaxy is considered bright if its FUV absolute magnitude is less than -19, the delineation point between bright and faint.

We perform a KS test on the $E(B-V)$ distribution of both bright and faint galaxies at $2.5 < z < 3.5$, and find that they prefer the same range of values for the colouër excess of the nebular line light, for both young and old populations. The range for E_BV_lines is presented in Table 10. This finding shows that at $2.5 < z < 3.5$, the SFR traced by FUV photons is similarly affected by the dust properties of both faint and bright galaxies. We assume that this behaviour is consistent for galaxies at $4.2 < z < 4.93$ and make no further changes to our FUV magnitude correction factor.

## A5 Comparison to simulations

Our study diverges from the definition and characterization of protoclusters as outlined in Chiang et al. (2017) in several key aspects. In their work, a protocluster encompasses all the dark matter and baryonic matter that will eventually merge into a cluster by $z=0$, with a mass exceeding $10^{14} M_{\odot}$ within $R_{200}$. The protocluster’s volume encompasses all the matter that will contribute to the formation of the cluster by $z=0$. In contrast, our study defines a protocluster as a structure contained within the $2\sigma$ density isopleth.

Furthermore, while Chiang et al. (2017) designates the most massive halo within the protocluster as its core at any given epoch, having a size of ~0.4 cMpc at $z \sim 4.57$, our study identifies the protocluster core as the region bounded inside a $5\sigma$ density isopleth with a size ~2 cMpc. To put our peaks on the same footing as the core defined in Chiang et al. (2017), our peak size will have to reduce beyond $\sigma_{\delta} > 10$ where we have spectroscopic data only for ~3 galaxies. Hence, we adopt our definition for peaks. It is crucial to acknowledge that these differing definitions of protoclusters may contribute to the measured difference between the observed and simulated data.

## A6 Using a massive protocluster as a proxy

Using the density maps, the estimated mass of Taralay protocluster at $z \sim 4.57$ is $1.74 \times 10^{15} M_{\odot}$ making this structure exceptionally massive at these redshifts.

Using such a massive protocluster, which has highly star-forming galaxies, as a representative sample of all the protoclusters at $z \sim 4.57$ to calculate the fraction of SFRD from protoclusters (see Fig. 10) may lead to an overestimated value for the derived contribution of protoclusters to the SFRD. Nevertheless, there is a possibility that environmental quenching is affecting the galaxies within this protocluster (Lemaux et al. 2018) which could result in a decrease in the SFRD. To draw a definitive conclusion, a large collection of protoclusters is required for comprehensively testing their contribution to the SFRD at high redshift.

# APPENDIX B: EFFECT OF PARAMETER CHOICES ON THE MODEL SPECTRUM

The SFR values that our results are based on come from the SED fitting process. It is important therefore to discuss how the different parameters that are used in the SED fitting process impact the spectrum of a galaxy, affecting the estimated SFR. We discuss this impact here using two different approaches. First, we look at the
<figure><img src="image_11.png" /></figure>

**Figure B1.** Comparing SFR values estimated using the ranges of parameters given in Table 10 with the SFR values estimated by forcing metallicity to take on a fix value in the top left-hand panel, changing the range of E(B-V) lines in the top right panel and forcing the powerlaw slope to a fix value in the bottom panel. For each plot, the x-axis represents SFR obtained from SED fitting the galaxies using a range of a particular parameter. These ranges for metallicity, E.BV_lines and powerlaw.slope are shown on the x-axis of each plot. The y-axis represents SFR obtained from SED fitting galaxies using a fixed parameter. For both axes for each plot, the SFR values are in log (SFR/M$_{⊙}$yr$^{-1}$). The $\sigma_{MAD}$ for a distribution in the each figure shows the scatter on the SFR value. The $\sigma_{MAD} = 0$ comes from having a very few outliers with the majority of the galaxies having one to one correlation.

<figure><img src="image_12.png" /></figure>

**Figure B2.** Comparing SFR value obtained from SED fitting using different modules of SFH and SSP. The x-axis of the first plot represents SFR obtained from doing SED fitting with sfhdelayed module while the y-axis represents SFR obtained from doing SED fitting with sfh2exp and sfhperiodic modules. For the second plot, x-axis represents SFR obtained from doing SED fitting with bc03 module with Salpeter IMF while the y-axis represents SFR obtained from doing SED fitting with m2005 module with Salpeter IMF. For both axes for each plot, the SFR values are in log (SFR/M$_{⊙}$yr$^{-1}$). The $\sigma_{MAD}$ for a distribution in the each figure shows the scatter on the SFR value.

scatter on the SFR of a large sample of galaxies which sheds light on how the SFR itself varies with different parameters used for SED fitting. Then we look at a model SED of a single galaxy to understand how the SED is impacted with the changes in one parameter while keeping the rest of the parameter inputs constant.

In Fig. B1, we investigate the change in SFR values by fixing metallicity and powerlaw.slope values and by varying E_BV lines range. The sample chosen to perform this exercise is one hundred galaxies and the same modules are chosen to estimate their SFR with SED fitting as used in the analysis of this study, i.e. sfhdelayed, bc03,
<figure><img src="image_13.png" /><figcaption>**Figure B1.** Comparing SFR values estimated using the ranges of parameters given in Table 10 with the SFR values estimated by forcing metallicity to take on a fix value in the top left-hand panel, changing the range of E(B-V) lines in the top right panel and forcing the powerlaw slope to a fix value in the bottom panel. For each plot, the x-axis represents SFR obtained from SED fitting the galaxies using a range of a particular parameter. These ranges for metallicity, E.BV_lines and powerlaw.slope are shown on the x-axis of each plot. The y-axis represents SFR obtained from SED fitting galaxies using a fixed parameter. For both axes for each plot, the SFR values are in log (SFR/M$_{⊙}$yr$^{-1}$). The $\sigma_{MAD}$ for a distribution in the each figure shows the scatter on the SFR value. The $\sigma_{MAD} = 0$ comes from having a very few outliers with the majority of the galaxies having one to one correlation.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure B2.** Comparing SFR value obtained from SED fitting using different modules of SFH and SSP. The x-axis of the first plot represents SFR obtained from doing SED fitting with sfhdelayed module while the y-axis represents SFR obtained from doing SED fitting with sfh2exp and sfhperiodic modules. For the second plot, x-axis represents SFR obtained from doing SED fitting with bc03 module with Salpeter IMF while the y-axis represents SFR obtained from doing SED fitting with m2005 module with Salpeter IMF. For both axes for each plot, the SFR values are in log (SFR/M$_{⊙}$yr$^{-1}$). The $\sigma_{MAD}$ for a distribution in the each figure shows the scatter on the SFR value.</figcaption></figure>

scatter on the SFR of a large sample of galaxies which sheds light on how the SFR itself varies with different parameters used for SED fitting. Then we look at a model SED of a single galaxy to understand how the SED is impacted with the changes in one parameter while keeping the rest of the parameter inputs constant.

In Fig. B1, we investigate the change in SFR values by fixing metallicity and powerlaw.slope values and by varying E_BV lines range. The sample chosen to perform this exercise is one hundred galaxies and the same modules are chosen to estimate their SFR with SED fitting as used in the analysis of this study, i.e. sfhdelayed, bc03,
<figure><img src="image_13.png" /><figcaption>**Figure B3.** Rest-frame SED for a single galaxy with different parameters (see legends of each panels). The SEDs from each panel are such that they have nearly the same SFRs while changing the parameters indicated in the legends in the panels. Data points at $\lambda_{\text{rest}} = 2000$ Å in each panels indicate typical errors of the observations. The differences in the SED of the galaxy are within the uncertainty except for the SED obtained with age\_main of 1000 Myr and E\_BV\_lines of 0.5.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure B3.** Rest-frame SED for a single galaxy with different parameters (see legends of each panels). The SEDs from each panel are such that they have nearly the same SFRs while changing the parameters indicated in the legends in the panels. Data points at $\lambda_{\text{rest}} = 2000$ Å in each panels indicate typical errors of the observations. The differences in the SED of the galaxy are within the uncertainty except for the SED obtained with age\_main of 1000 Myr and E\_BV\_lines of 0.5.</figcaption></figure>
nebular, dustatt\_modified\_starburst, redshifting (See Section 5.1 for the ranges of these parameters). We find that the scatter on the SFR resulting from changing metallicity is fairly small indicating that a specific value of metallicity is not a strong driver of change in SFR. The scatter on SFR from varying the powerlaw\_slope and E.BV lines is larger indicating these parameters may have an impact on the accuracy of the estimated SFR. The largest systematic uncertainty of ~0.2 dex coming from the powerlaw\_slope value of -0.5 affecting the SFR of both the protocluster and the coeval field galaxies equally. Assuming that factors like IMF, E(B-V), powerlaw\_slope do not dramatically change for the two populations, this uncertainty does not change our results since we compare the SFR of the two populations.

In the left-hand panel of Fig. B2 we compare the SFR estimated with sfhdelayed, the SFH module chosen for perform this study, with two of the other SFH modules available from CIGALE to see how the change in our choice of module can impact our results. We find that the scatter on the SFR is small and a particular choice of SFH is not likely to impact the estimated SFR significantly. In the right-hand panel of this figure, we change the library of SSP to investigate the impact of using bc03 module instead of m2005 module. Because m2005 module is not compatible with the Chabrier IMF originally used in the SED fitting of this study, for this exercise, we use the Salpeter IMF with both bc03 and m2005 module. We do not see a significant difference in the estimated SFR by choosing different SSP modules.

Next, we investigate the impact of using different parameter ranges on the spectrum of a single galaxy. The SED of the example galaxy in Fig. B3 changes drastically in the rest-frame UV (shaded region) covered by our data for age\_main of 1000 Myr and E.BV\_lines of 0.5 showing that it is mainly these two factors that can affect the spectrum of a galaxy. However, our data cannot differentiate between the models with age\_main differences of ~100 Myr and E.BV\_lines differences of ~0.05 as the variations in the models are within the uncertainty of our data (typically of order ~$1e^{-5}$ mJy for this example).

## APPENDIX C: SED FITTING WITH CIGALE VERSUS LEPHARE

We compare various physical parameters obtained from SED fitting with CIGALE using the parameter set given in Section 5.1 to the

best-fitting parameters given in the COSMOS2020 catalog (Weaver et al. 2022) and find no significant difference that can be attributed to the choice of using a particular SED fitting software. Here we show this comparison for SM and SFR. The sample used for comparison consists of 106 galaxies in the redshift range of $4.2 < z < 4.93$ that have secure spectroscopic redshifts. This sample has also undergone an IRAC channel 1 and/or IRAC channel 2 cut such that the 106 galaxies have magnitudes brighter than the IRAC channel 1 and/or IRAC channel 2 completeness limit listed in (Weaver et al. 2022).

<figure><img src="image_14.png" /><figcaption>**Figure C1.** Difference between SM and SFR estimated with CIGALE and LePhare, two SED fitting software. The $\sigma_{NMAD}$, catastrophic outlier rate ($\eta = |\log(X_{LePhare}) - \log(X_{CIGALE})|/(1 + \log(X_{LePhare}) > 3\sigma_{NMAD})$, and bias which is defined as the median of the difference between $\log(X_{LePhare})$ and $\log(X_{CIGALE})$ are shown for both panels where X represents SM/M$_{\odot}$ for the left-hand panel and SFR/M$_{\odot}$ yr$^{-1}$ for the right-hand panel.</figcaption></figure>

<footnote n="1">¹Department of Physics and Astronomy, University of California, Davis, One Shields Ave., Davis, CA 95616, USA</footnote>

<footnote n="2">²Gemini Observatory, NSF's NOIRLab, 670 N. A'ohoku Place, Hilo, HI 96720, USA</footnote>

<footnote n="3">³INAF Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy</footnote>

<footnote n="4">⁴University of Hawai'i, Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822, USA</footnote>

<footnote n="5">⁵Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242 USA</footnote>

<footnote n="6">⁶George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242 USA</footnote>

<footnote n="7">⁷Aix Marseille Université, CNRS, LAM (Laboratoire d'Astrophysique de Marseille) UMR 7326, F-13388 Marseille, France</footnote>

<footnote n="8">⁸Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany</footnote>

<footnote n="9">⁹INAF-IASF Milano, Via Alfonso Corti 12, I-20159 Milano, Italy</footnote>

<footnote n="10">¹⁰Dipartimento di Fisica e Astronomia Galileo Galilei, Università degli Studi di Padova, Vicolo dell'Osservatorio 3, I-35122 Padova Italy</footnote>

<footnote n="11">¹¹Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan</footnote>

<footnote n="12">¹²Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan</footnote>

<footnote n="13">¹³Department of Pure and Applied Physics, Graduate School of Advanced Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan</footnote>

<footnote n="14">¹⁴INAF-IASF, via Bassini 15, I-20133, Milano, Italy</footnote>

<footnote n="15">¹⁵Astronomy Department, University of Massachusetts, Amherst, MA, 01003 USA</footnote>

<footnote n="16">¹⁶Instituto de Astrofisica, Departamento de Ciencias Fisicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Fernandez Concha 700, Las Condes, Santiago RM, Chile</footnote>

<footnote n="17">¹⁷University of Bologna – Department of Physics and Astronomy ‘Augusto Righi’ (DIFA, Via Gobetti 93/2, I-40129 Bologna, Italy)</footnote>
nebular, dustatt\_modified\_starburst, redshifting (See Section 5.1 for the ranges of these parameters). We find that the scatter on the SFR resulting from changing metallicity is fairly small indicating that a specific value of metallicity is not a strong driver of change in SFR. The scatter on SFR from varying the powerlaw\_slope and E.BV lines is larger indicating these parameters may have an impact on the accuracy of the estimated SFR. The largest systematic uncertainty of ~0.2 dex coming from the powerlaw\_slope value of -0.5 affecting the SFR of both the protocluster and the coeval field galaxies equally. Assuming that factors like IMF, E(B-V), powerlaw\_slope do not dramatically change for the two populations, this uncertainty does not change our results since we compare the SFR of the two populations.

In the left-hand panel of Fig. B2 we compare the SFR estimated with sfhdelayed, the SFH module chosen for perform this study, with two of the other SFH modules available from CIGALE to see how the change in our choice of module can impact our results. We find that the scatter on the SFR is small and a particular choice of SFH is not likely to impact the estimated SFR significantly. In the right-hand panel of this figure, we change the library of SSP to investigate the impact of using bc03 module instead of m2005 module. Because m2005 module is not compatible with the Chabrier IMF originally used in the SED fitting of this study, for this exercise, we use the Salpeter IMF with both bc03 and m2005 module. We do not see a significant difference in the estimated SFR by choosing different SSP modules.

Next, we investigate the impact of using different parameter ranges on the spectrum of a single galaxy. The SED of the example galaxy in Fig. B3 changes drastically in the rest-frame UV (shaded region) covered by our data for age\_main of 1000 Myr and E.BV\_lines of 0.5 showing that it is mainly these two factors that can affect the spectrum of a galaxy. However, our data cannot differentiate between the models with age\_main differences of ~100 Myr and E.BV\_lines differences of ~0.05 as the variations in the models are within the uncertainty of our data (typically of order ~$1e^{-5}$ mJy for this example).

## APPENDIX C: SED FITTING WITH CIGALE VERSUS LEPHARE

We compare various physical parameters obtained from SED fitting with CIGALE using the parameter set given in Section 5.1 to the

best-fitting parameters given in the COSMOS2020 catalog (Weaver et al. 2022) and find no significant difference that can be attributed to the choice of using a particular SED fitting software. Here we show this comparison for SM and SFR. The sample used for comparison consists of 106 galaxies in the redshift range of $4.2 < z < 4.93$ that have secure spectroscopic redshifts. This sample has also undergone an IRAC channel 1 and/or IRAC channel 2 cut such that the 106 galaxies have magnitudes brighter than the IRAC channel 1 and/or IRAC channel 2 completeness limit listed in (Weaver et al. 2022).

<figure><img src="image_16.png" /><figcaption>**Figure C1.** Difference between SM and SFR estimated with CIGALE and LePhare, two SED fitting software. The $\sigma_{NMAD}$, catastrophic outlier rate ($\eta = |\log(X_{LePhare}) - \log(X_{CIGALE})|/(1 + \log(X_{LePhare}) > 3\sigma_{NMAD})$, and bias which is defined as the median of the difference between $\log(X_{LePhare})$ and $\log(X_{CIGALE})$ are shown for both panels where X represents SM/M$_{\odot}$ for the left-hand panel and SFR/M$_{\odot}$ yr$^{-1}$ for the right-hand panel.</figcaption></figure>

<footnote n="1">¹Department of Physics and Astronomy, University of California, Davis, One Shields Ave., Davis, CA 95616, USA</footnote>

<footnote n="2">²Gemini Observatory, NSF's NOIRLab, 670 N. A'ohoku Place, Hilo, HI 96720, USA</footnote>

<footnote n="3">³INAF Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy</footnote>

<footnote n="4">⁴University of Hawai'i, Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822, USA</footnote>

<footnote n="5">⁵Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242 USA</footnote>

<footnote n="6">⁶George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242 USA</footnote>

<footnote n="7">⁷Aix Marseille Université, CNRS, LAM (Laboratoire d'Astrophysique de Marseille) UMR 7326, F-13388 Marseille, France</footnote>

<footnote n="8">⁸Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany</footnote>

<footnote n="9">⁹INAF-IASF Milano, Via Alfonso Corti 12, I-20159 Milano, Italy</footnote>

<footnote n="10">¹⁰Dipartimento di Fisica e Astronomia Galileo Galilei, Università degli Studi di Padova, Vicolo dell'Osservatorio 3, I-35122 Padova Italy</footnote>

<footnote n="11">¹¹Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan</footnote>

<footnote n="12">¹²Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan</footnote>

<footnote n="13">¹³Department of Pure and Applied Physics, Graduate School of Advanced Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan</footnote>

<footnote n="14">¹⁴INAF-IASF, via Bassini 15, I-20133, Milano, Italy</footnote>

<footnote n="15">¹⁵Astronomy Department, University of Massachusetts, Amherst, MA, 01003 USA</footnote>

<footnote n="16">¹⁶Instituto de Astrofisica, Departamento de Ciencias Fisicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Fernandez Concha 700, Las Condes, Santiago RM, Chile</footnote>

<footnote n="17">¹⁷University of Bologna – Department of Physics and Astronomy ‘Augusto Righi’ (DIFA, Via Gobetti 93/2, I-40129 Bologna, Italy)</footnote>
¹⁸Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

¹⁹Institute for Advanced Research, Nagoya University, Nagoya 464-8601, Japan

²⁰Department of Physics, Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan

²¹California Institute of Technology, MC 249-17, 1200 East California Blvd., Pasadena, CA 91125, USA

This paper has been typeset from a TEX/LATEX file prepared by the author.
¹⁸Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

¹⁹Institute for Advanced Research, Nagoya University, Nagoya 464-8601, Japan

²⁰Department of Physics, Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan

²¹California Institute of Technology, MC 249-17, 1200 East California Blvd., Pasadena, CA 91125, USA

This paper has been typeset from a TEX/LATEX file prepared by the author.