Euclid preparation. Far-infrared predictions for Euclid galaxy catalogues: cluster, protocluster, and field

Abstract: The MAMBO mock galaxy catalogue, based on the Millennium Simulation with empirically assigned galaxy properties, provides predictions of FIR fluxes and physical parameters of Euclid-detectable galaxies. Predicted FIR flux distributions confirm that only the brightest Euclid sources will be detectable in existing FIR surveys. We employ stacking to measure the mean dust properties as a function of stellar mass and redshift. We find dust temperatures and infrared luminosities increase with redshift across all mass bins, while dust masses remain roughly constant. FIR number counts from MAMBO show overall good agreement with observations, and the total infrared luminosity function reproduces published estimates across most redshift ranges, extending to z~10. Comparing the Euclid Wide and Deep Surveys, we find that the EDS recovers the total IRLF to fainter luminosities and higher redshifts (up to z~6 in $I_E$), although its detectability falls below 80% at z>4, whereas the EWS becomes strongly incomplete beyond z~2. We also examine the dependence of the IRLF on environment. Schechter fits indicate that the faint-end slope $α$ flattens with redshift for cluster and protocluster galaxies, while remaining approximately constant for field populations. Imposing additional detection limits from Herschel-PACS and SPIRE shows that only the most luminous ($L_{IR}$ > $10<sup>{12.5}$ $L_{\odot}$) galaxies remain detectable at z~4, but the limited MAMBO area (3.14$deg<sup>2$) is inadequate for statistically robust (>3$σ$) constraints. Survey areas at least 30 times larger are required. Overall, the MAMBO FIR extension reproduces key number count and IRLF trends, provides realistic predictions for FIR-detected Euclid galaxies, and highlights the importance of synergies with current and future FIR/sub-mm facilities to probe environmental dependence with sufficient depth and area.

• The paper extends the MAMBO mock catalogue with far-infrared predictions for 7.9 million galaxies across 3.14 deg² and validates its number counts and infrared luminosity functions against observations from z≈0 to beyond 6.
• Euclid Wide Survey completeness exceeds 80% for IR galaxies above 10¹⁰ L☉ only at low redshift, while the deeper survey reaches 100% above 10⁹·⁵ L☉ to z≈2 and remains useful to z≈6, making stacking essential for most FIR studies.
• The paper finds that IR luminosity-function slopes evolve differently in clusters, protoclusters, and the field, but robust environmental FIR constraints require sources brighter than 10¹²·⁵ L☉ at z≈3.5–4 and survey areas roughly 30 times larger than the mock.

The Euclid mission's optical and near-infrared surveys will deliver unprecedented samples of galaxies, but the dust-obscured component of star formation that these galaxies host is only directly observable in the far-infrared (FIR) and sub-millimetre. This paper by Parmar et al. (2603.13195) presents FIR predictions for the MAMBO mock galaxy catalogue — a lightcone built on the Millennium Simulation with empirically assigned galaxy properties via the Empirical Galaxy Generator — covering 3.14 deg$^2$ and roughly 7.9 million galaxies from $z = 0.02$ to 10. The work validates the mock against observed FIR number counts and infrared luminosity functions (IRLFs), quantifies the completeness of the Euclid Wide Survey (EWS) and Deep Survey (EDS) for IR-luminous galaxies, and provides the first FIR predictions for environment-dependent (cluster, protocluster, field) Euclid IRLFs.

The MAMBO lightcone and its FIR extension

MAMBO assigns stellar masses to dark matter sub-haloes through a stellar-to-halo mass relation calibrated on SDSS, COSMOS, and CANDELS stellar mass functions, then classifies galaxies as quiescent or star-forming and derives SFRs, metallicities, and photometry through observed scaling relations implemented in a modified EGG pipeline. Dust emission SEDs are parameterised by $L_{\rm IR}$, dust temperature, and the IR8 ratio, with both quantities tied to redshift and stellar mass. The lightcone preserves halo clustering and merger trees, which is what enables the protocluster analysis: protocluster members are galaxies that share a $z=0$ descendant halo with $M \geq 10^{14}\,M_\odot$, while cluster members reside at observation in haloes of $M \geq 10^{13.25}\,M_\odot$. Two structural limitations should be noted up front: the catalogue contains no AGN contribution, and the cluster sample is restricted to $1.5 \leq z \leq 4$ by the underlying GAEA lightcone constraints.

Predicted FIR fluxes and stacked dust properties

The predicted flux distributions of EWS-detectable galaxies span sub-$\mu$Jy to hundreds of mJy and generally decline in mean flux with redshift. Comparisons with instrument limits are sobering: the PACS $3\sigma$ confusion limits (5–12.7 mJy) sit above the mean predicted fluxes at $z \sim 1$–5, and by $z = 0.02$0 the entire predicted flux range falls below the PACS thresholds; SPIRE confusion limits similarly exclude all but the brightest sources. Only through stacking can the bulk of the Euclid population be characterised in the FIR.

The stacking analysis, binned to match the Q1 analysis of Euclid-selected star-forming galaxies, yields three robust trends: mean dust temperature rises from roughly 20 K at $z = 0.02$1 to 40 K at $z = 0.02$2; $z = 0.02$3 increases by more than three orders of magnitude over the same interval; and $z = 0.02$4 remains approximately constant with redshift while scaling with stellar mass. The authors verify internal consistency by showing that SED fits to the stacked fluxes recover the input parameterisations of Schreiber et al. — the recovered dust temperatures follow the prescribed $z = 0.02$5 relation and the inferred SFRs match the star-forming main sequence used to generate the mock. This circularity is a strength for internal consistency but means the exercise cannot independently test the underlying dust prescriptions against observation.

FIR number counts

The Euclideanised differential counts agree broadly with published measurements across MIPS, PACS, SPIRE, SCUBA-2, LABOCA, AzTEC, and ALMA bands, and in places extend to fainter fluxes than existing data. Notable discrepancies are quantified and partly diagnosed:

Band	Discrepancy	Maximum deviation	Plausible cause
MIPS/PACS 70 $z = 0.02$6m	MAMBO overpredicts bright end	5–6$z = 0.02$7	Excess hot dust on the Wien tail
PACS 100 $z = 0.02$8m	Overpredicts above 40 mJy	2–3$z = 0.02$9	Same hot-dust effect
SPIRE 350/500 $L_{\rm IR}$0m	Underpredicts at 10–50 mJy	—	Source blending in SPIRE beam (cf. Béthermin et al.)
SCUBA-2 450 $L_{\rm IR}$1m	Overpredicts near 7 mJy	4$L_{\rm IR}$2	Model transmission curve lacking atmospheric absorption
ALMA Band 9	Overpredicts bright end	7$L_{\rm IR}$3	Idealised source extraction, no confusion

The 450 $L_{\rm IR}$4m discrepancy is a concrete, correctable artefact: the mock used the model (not as-measured) SCUBA-2 transmission curve, overestimating throughput. The SPIRE shortfall mirrors a known issue in other simulations and could be addressed by generating simulated maps with beam and clustering effects, which the authors identify as unexplored follow-up work.

The total and survey-limited IRLF

Using the $L_{\rm IR}$5 method with a cut at $L_{\rm IR}$6, the total IRLF shows excellent agreement with the literature from $L_{\rm IR}$7 to beyond 6, extending in some bins below the luminosities probed observationally. Two tensions stand out. At $L_{\rm IR}$8–7.5, MAMBO lies up to 4$L_{\rm IR}$9 above the Barrufet et al. UV-selected IRLF — an expected consequence of UV selection missing heavily dust-obscured sources, but also a genuine model uncertainty. Conversely, Fujimoto et al.'s ALMA-based results consistently show a steeper faint-end slope than MAMBO at 2$z=0$0 level; the authors candidly note they cannot rule out that MAMBO underestimates the density of faint sources.

The EWS versus EDS comparison quantifies survey completeness. In the first two redshift bins, the EWS recovers more than 80% of IR galaxies at $z=0$1, but completeness falls below 80% thereafter, and the EWS becomes strongly incomplete beyond $z=0$2. The EDS recovers 100% of IR galaxies at $z=0$3 out to $z=0$4 and remains useful to $z=0$5 in $z=0$6, though its detectability drops below 80% at $z=0$7. At $z=0$8 the $z=0$9 band is rendered useless by the redshifted Lyman limit, and only the NIR bands retain sensitivity, with the EWS recovering under 30% of the IR sample there versus roughly 80% for the EDS at $M \geq 10^{14}\,M_\odot$0. An interesting inversion appears at high $M \geq 10^{14}\,M_\odot$1 in the EWS at $M \geq 10^{14}\,M_\odot$2: completeness decreases with luminosity, which the authors attribute to heavily dust-obscured, optically faint systems falling below the $M \geq 10^{14}\,M_\odot$3 threshold — an effect largely absent in the deeper EDS. These detectability ratios constitute a practical correction tool for observed Euclid IRLFs.

Environmental dependence of the IRLF

Restricting to $M \geq 10^{14}\,M_\odot$4 and EWS extended-source limits ($M \geq 10^{14}\,M_\odot$5 or $M \geq 10^{14}\,M_\odot$6), the completeness-corrected, volume-renormalised IRLFs show that the effective faint-end slope $M \geq 10^{14}\,M_\odot$7 (fit over $M \geq 10^{14}\,M_\odot$8) flattens with redshift for cluster and protocluster galaxies while remaining approximately constant for field galaxies. The authors are explicit that these $M \geq 10^{14}\,M_\odot$9 values are effective slopes over a bright luminosity range rather than true faint-end slopes, and that the absolute values are less reliable than the relative trends. Direct comparison with low-redshift cluster studies (Bai et al.; Biviano et al.) is limited by the $M \geq 10^{13.25}\,M_\odot$0 floor of the mock sample.

Applying additional Herschel-PACS and SPIRE detection limits produces the paper's most restrictive forecast: cluster and protocluster galaxies are jointly detectable by EWS and SPIRE (or PACS) only in the $M \geq 10^{13.25}\,M_\odot$1–4 bin and only at $M \geq 10^{13.25}\,M_\odot$2. The EWS+SPIRE field sample is so small — a consequence of the 3.14 deg$M \geq 10^{13.25}\,M_\odot$3 lightcone — that its IRLF carries little statistical weight, and the authors estimate that an area at least 30 times larger (about 90 deg$M \geq 10^{13.25}\,M_\odot$4) is required for $M \geq 10^{13.25}\,M_\odot$5 constraints. The EWS+PACS field sample is more robust but corresponds to observing conditions (GOODS-S depth over MAMBO-like areas) that no existing survey provides. The paper therefore argues that environmental IRLF studies require either wide Herschel archives (HerMES, H-ATLAS) combined with Euclid, millimetre facilities such as ALMA and NOEMA, or future concepts (CCAT, PRIMA).

Limitations and open questions

The paper's limitations are acknowledged with reasonable candour. The absence of AGN in the lightcone is argued to be immaterial at 70 $M \geq 10^{13.25}\,M_\odot$6m, where star formation dominates dust heating, but the claim is not tested. The hot-dust explanation for the 70 $M \geq 10^{13.25}\,M_\odot$7m excess is plausible but unconfirmed. The field-galaxy definition — the residue after removing cluster and protocluster members — can contaminate the field sample with genuinely high-density galaxies and is not a volume-complete selection. The Schechter fits are confined to a bright luminosity window, so the faint-end behaviour that distinguishes environments observationally remains unconstrained. The key open questions are whether MAMBO's faint-end IRLF slope is genuinely too shallow at high redshift, as the Fujimoto et al. comparison suggests, and whether simulated maps with realistic beam and blending effects would resolve the SPIRE 350/500 $M \geq 10^{13.25}\,M_\odot$8m deficit.

Conclusion

This work establishes the FIR-extended MAMBO lightcone as a validated predictive tool for Euclid's dust-obscured galaxy population: number counts and total IRLFs agree with observations across most bands and redshifts, stacked dust properties follow physically expected trends, and the EWS/EDS completeness ratios provide directly usable corrections for future observed IRLFs. The environmental analysis demonstrates that the IRLF slope evolution with redshift differs between dense environments and the field, but also shows that the current mock area is inadequate — by a factor of at least 30 — for statistically robust FIR-detected environmental studies. The results collectively frame the observational requirements, in area and depth, that any FIR facility must meet to exploit Euclid's environmental galaxy samples fully.