Euclid Quick Data Release (Q1). The average far-infrared properties of Euclid-selected star-forming galaxies

Technical Summary: The Average Far-Infrared Properties of Euclid-Selected Star-Forming Galaxies

Problem and Motivation
The Euclid mission's first Quick Data Release (Q1) provides an unprecedented optical and near-infrared (NIR) dataset, containing millions of galaxies with robust photometric redshifts, stellar masses, and star-formation rates (SFRs) derived from spectral energy distribution (SED) fitting. However, these optical/NIR-derived SFRs rely on assumptions about dust attenuation and the underlying stellar population. To independently constrain the average far-infrared (far-IR) properties of these galaxies and verify the consistency of SFR estimates, this study investigates the thermal emission from dust grains. While previous stacking analyses of far-IR data (e.g., in UDS, COSMOS, or GAMA fields) have been limited by small sky areas or redshift ranges, the Euclid Q1 catalogue allows for the stacking of millions of galaxies across tens of square degrees, enabling a statistically robust characterization of the main sequence (MS) of star-forming galaxies out to $z \approx 3$.

Methodology
The authors utilized the Euclid Q1 merging catalogue (specifically the sample described by Euclid Collaboration: Enia et al. 2025), selecting star-forming galaxies within the redshift range $0.2 < z < 3.0$ and stellar mass range $8.3 < \log_{10}(M_*/M_\odot) < 11.5$. The sample was cross-matched with existing far-IR imaging from the Herschel Space Observatory (PACS at 100/160 $\mu$m; SPIRE at 250/350/500 $\mu$m) and the SCUBA-2 instrument (450/850 $\mu$m). The analysis covered a total overlapping area of 17.6 deg$^2$ for SPIRE and 2.4 deg$^2$ for SCUBA-2.

To address the coarse angular resolution of far-IR instruments (10–30 arcseconds) compared to Euclid's resolution (~0.2 arcseconds), the authors employed a stacking analysis using the SimStack algorithm. This method simultaneously solves for the average flux densities of multiple bins defined by stellar mass and redshift. Key methodological features included:

• SimStack Implementation: Solving a linear system $y = S_1 X_1 + \dots + S_N X_N$ to determine stacking amplitudes ($S_b$) for $N$ bins, accounting for galaxy clustering and bin-to-bin correlations without assuming a Poisson distribution.
• Masking: Rigorous masking of regions contaminated by bright stars, edge effects, and Galactic sources (e.g., NGC 6543) to prevent bias in the stacked flux.
• SED Fitting: The stacked flux densities were fitted with a modified blackbody model transitioning to a power law at high frequencies. The dust emissivity index ($\beta$) and power-law slope ($\alpha$) were fixed to values derived from local far-IR-selected galaxies ($\beta=1.96, \alpha=2.3$) due to limited photometric constraints.
• Parameter Derivation: From the best-fit SEDs, the authors derived mean dust temperatures ($T_d$), dust masses ($M_d$), and far-IR-derived SFRs.

Key Results

1. SFR Consistency: The far-IR-derived SFRs show good agreement with the SFRs predicted by the star-forming main sequence (MS) derived from optical/NIR photometry, with a weighted mean ratio of 1.0.
2. Dust Temperature Evolution: The average dust temperature ($T_d$) decreases with cosmic time (increasing redshift). The evolution is well-described by the function $T_d(t) = T_2 + (T_1 - T_2)e^{-t/\tau}$, where $T_1 = 79.7 \pm 7.4$ K (extrapolated to $t=0$), $T_2 = 23.2 \pm 0.1$ K (asymptotic value), and $\tau = 1.6 \pm 0.1$ Gyr.
   • Crucially, $T_d$ is found to be independent of stellar mass across the bins studied.
   • The convergence to a non-zero value ($T_2 \approx 23$ K) below $z=1$ suggests that dust in MS galaxies is increasingly heated by the existing cooler, older stellar population rather than solely by hot young stars in star-forming regions.
3. Dust Mass and Ratios: Dust masses ($M_d$) and dust-to-stellar mass ratios ($M_d/M_*$) increase from $z=0.2$ to $z \approx 1$, after which they plateau or decline. The dust-to-stellar mass ratio decreases with increasing stellar mass at all redshifts, attributed to lower specific SFRs (sSFRs) in more massive galaxies.
4. Cosmic Infrared Background (CIB): The Euclid Q1 catalogue resolves more than 60% of the CIB at 250, 350, and 500 $\mu$m. At 100 $\mu$m, the resolved fraction is estimated at 30–80%, while at 850 $\mu$m it is 30–40%.
5. Comparison with Simulations: When compared to the MAMBO mock catalogue (based on the Millennium Simulation and Empirical Galaxy Generator), the simulated dust masses and SFRs agree reasonably well. However, the simulation predicts a monotonic decrease in dust temperature with time, failing to reproduce the observed plateau at low redshifts ($z < 1$).

Significance and Claims
The paper claims that this study represents the largest stacking analysis of its kind to date, leveraging the unique depth and area of the Euclid Q1 release. The primary significance lies in the discovery that the average dust temperature of star-forming galaxies converges to a constant value at low redshifts, independent of stellar mass. This finding challenges models where dust temperature is strictly proportional to SFR or sSFR, suggesting a transition in the heating mechanism of dust from young, massive stars to the general interstellar radiation field of older stellar populations as the universe ages.

Furthermore, the authors demonstrate that the correlation between dust temperature and SFR is mediated by stellar mass, as $T_d$ itself is mass-independent. The results also provide a benchmark for future Euclid data releases, indicating that deeper imaging will be required to fully resolve the CIB and probe the far-IR properties of galaxies at higher redshifts ($z > 1.5$) and lower stellar masses. The study concludes that while the current Q1 data does not resolve the entire CIB, it accounts for the majority of the background at SPIRE wavelengths, validating the potential of Euclid to map the thermal history of the universe's star-forming population.