Euclid preparation: TBD. Cosmic Dawn Survey: evolution of the galaxy stellar mass function across 0.2<z<6.5 measured over 10 square degrees

1. Problem Statement

The evolution of the galaxy stellar mass function (SMF) is a fundamental framework for understanding galaxy growth, star formation efficiency, and feedback mechanisms. However, previous studies of the high-redshift universe ($z > 3$) have been limited by:

• Small Survey Areas: Space-based surveys (e.g., HST, JWST) are deep but cover tiny fields of view, leading to large cosmic variance (statistical uncertainty due to sampling a small volume of the universe).
• Inability to Constrain Massive Galaxies: The number density of massive galaxies ($M > M_*$) drops exponentially. Small surveys often lack the statistical power to constrain the abundance of these rare objects, resulting in only upper limits rather than firm measurements.
• Selection Biases: Many high-redshift surveys rely on near-infrared (NIR) selection, which can miss intrinsically red or dusty galaxies if not paired with sufficient mid-infrared (MIR) data to constrain stellar masses.

There is a critical need for a survey that combines large volume (to reduce cosmic variance) with deep MIR imaging (to accurately measure stellar masses) to characterize the growth of massive galaxies across cosmic time.

2. Methodology

Data Source: The Cosmic Dawn Survey (Pre-Launch)

The study utilizes the DAWN PL (Pre-Launch) catalogues, covering the Euclid Deep Field North (EDF-N) and Euclid Deep Field Fornax (EDF-F).

• Area: Effective area of 10.13 deg² (after masking).
• Depth: Uniform deep Spitzer/IRAC data at $m \sim 25$ mag (5$\sigma$) in [3.6$\mu$m] and [4.5$\mu$m]. This is the largest area covered to these depths in the MIR.
• Optical/UV: Depth-matched UV/optical imaging from CFHT (u-band) and Subaru HSC (griz bands), reaching $\sim 27$ mag.
• Volume: The sampled comoving volume is 0.62 Gpc³, an order of magnitude larger than previous comparable works (e.g., Weaver et al. 2023a).

Sample Selection & Photometry

• Detection: Sources detected on a composite stack of HSC $r+i+z$ images.
• Photometry: Measured using The Farmer (a model-based photometry code built on The Tractor), which handles crowded fields and varying PSFs self-consistently.
• Redshifts & Masses: Derived using LePHARE (SED fitting). LePHARE was chosen over EAZY to avoid unphysical rest-frame colors caused by the wavelength gap between HSC $z$ and Spitzer/IRAC.
• Selection Criteria:
  • Sources must have $S/N \ge 3$ in HSC $r, i, z$ and Spitzer/IRAC bands (relaxed for $r$ at $z > 3.5$).
  • Redshift probability distribution must contain 68% of the probability within $z_{phot} \pm 0.5$.
  • $\chi^2$ cuts applied to remove poor SED fits.
  • Star-Forming vs. Quiescent: Classified using the $NUV-r, r-J$ diagram (Ilbert et al. 2013) for $z \le 3$.

Stellar Mass Limits & Completeness

• Mass limits were determined empirically using the Pozzetti et al. (2010) method, rescaling masses based on the limiting magnitude of the HSC $z$-band.
• Limits: $M_{lim} \approx 4.3 \times 10^8 (1+z)^{1.74} M_\odot$ for the total sample.
• Caveat: The sample is optically selected; intrinsically red/dusty galaxies at $z > 1.5$ may be incomplete, though massive galaxies ($M > 10^{10} M_\odot$) are well-constrained.

Uncertainty Analysis

The total uncertainty ($\sigma_\Phi$) combines three components:

1. Poisson Uncertainty: Reduced by the large survey area (factor of $\sim 3$ improvement over COSMOS).
2. Cosmic Variance ($\sigma_{CV}$): Estimated using the UniverseMachine simulations (Jespersen et al. 2024), providing robust estimates for massive galaxies at high $z$.
3. SED Fitting Uncertainty ($\sigma_{SED}$): Estimated via Monte Carlo simulations (1000 realizations) varying redshifts and masses to account for covariance.

Modeling the SMF

• Formalism: The intrinsic SMF is inferred by deconvolving the observed SMF with an Eddington bias kernel (Gaussian + Lorentzian) to correct for scatter in stellar mass estimates.
• Fitting: A Schechter function (or double-Schechter for $z \le 2$) is fitted using Markov Chain Monte Carlo (MCMC) methods.
• Priors: Low-mass slopes ($\alpha$) are constrained by priors from literature to handle the incompleteness at the low-mass end.

3. Key Contributions

1. Unprecedented Volume: This is the first study to measure the SMF over $\sim 10$ deg² with deep MIR data, reducing cosmic variance by an order of magnitude compared to previous high-$z$ studies.
2. Firm Constraints on Massive Galaxies: Replaces upper limits with firm number density estimates for galaxies with $M > 10^{11} M_\odot$ up to $z \sim 6.5$.
3. Environmental Dependence: Provides the first evidence of environmental dependence (overdensity vs. underdensity) in the SMF out to $z \sim 3.5$.
4. Benchmark for Euclid: Serves as a "pre-launch" benchmark, demonstrating the power of combining deep optical (HSC) and deep MIR (Spitzer) data before Euclid's NIR data becomes available.

4. Key Results

Evolution of the Stellar Mass Function

• Rapid Early Growth: The abundance of massive galaxies ($M \sim 10^{10.5} M_\odot$) increased by a factor of $\ge 100$ between $z \sim 6$ and $z \sim 3.25$ (a 1 Gyr span), followed by slower growth ($\times 10$) over the next 7.7 Gyr. This confirms the "downsizing" effect.
• Consistency: The total SMF agrees well with literature (D17, W23, G15, W24) up to $z \sim 3.5$.
• High-$z$ Excess: At $z > 3.5$, DAWN PL detects a significant population of massive galaxies ($M > 10^{11} M_\odot$) that were previously only upper limits in smaller surveys.

Star-Forming vs. Quiescent

• Quiescent Galaxies: A significant fraction of the most massive quiescent galaxies ($M > 10^{11.7} M_\odot$) are already in place by $z \sim 2.5$.
• Stagnation: The number density of these massive quiescent systems shows little change from $z \sim 2.5$ to $z \sim 0.2$, suggesting their growth is halted by feedback mechanisms and they grow primarily through minor mergers rather than major ones.
• Selection Bias: The optical selection function limits the detection of quiescent galaxies at $z > 3$ (where the Balmer break moves out of the observed bands), but the massive ones detected are robust.

Star-Formation Efficiency (SFE) & Dark Matter Connection

• High Efficiency at High $z$: Comparing the SMF to the Dark Matter Halo Mass Function (HMF) reveals that massive galaxies at $z > 3.5$ require integrated star-formation efficiencies ($\epsilon = M_*/M_h f_b$) of $\epsilon \gtrsim 0.25 - 0.5$.
• Implication: This exceeds the "universal peak efficiency" ($\sim 0.2$) seen at low redshift. It implies that feedback mechanisms (AGN and stellar) were ineffective at regulating star formation in massive halos during the early universe ($z > 3.5$).
• Ultra-Massive Candidates: The study identifies candidates with $\epsilon > 1$ (requiring more baryons than available in the halo), though these are rare and may be subject to systematic uncertainties or represent extreme evolutionary paths.

Environmental Dependence

• Density-Dependent SMF: Evidence is found that massive galaxies are preferentially located in high-density environments (clusters/protoclusters) out to $z \sim 3.5$.
• Low-Mass Bias: Low-mass galaxies are more abundant in low-density environments.
• Quenching: At $z \sim 1$, low-mass quiescent galaxies are found in high-density regions, supporting "environmental quenching" mechanisms.

5. Significance

• Cosmological Constraints: The results challenge standard models of galaxy formation that assume feedback is effective early on. The high SFE suggests a "feedback-free" or "feedback-delayed" era for massive galaxies in the early universe.
• Validation of Future Surveys: The DAWN PL results validate the strategy of using deep optical + deep MIR data to study high-$z$ galaxies. It sets the stage for the Euclid mission, which will provide NIR data to complete the picture (detecting red/dusty galaxies and improving photo-zs).
• Statistical Power: By reducing cosmic variance, this work provides the first statistically robust census of the most massive galaxies in the first 2-3 billion years of the universe, moving beyond anecdotal "rare object" discoveries to population-level statistics.

Conclusion: The paper demonstrates that massive galaxies formed with extreme efficiency in the early universe, likely due to ineffective feedback, and that their abundance is tightly linked to their environment. The unique volume of the DAWN survey allows for these conclusions with a level of statistical confidence previously unattainable.