Red-Herschel Sources in FIR Surveys

Updated 3 December 2025

Red-Herschel sources are defined by FIR flux densities that rise from 250 μm to 500 μm, effectively isolating high-redshift dusty star-forming galaxies including lensed ULIRGs and protoclusters.
They are identified using precise flux thresholds, confusion-noise suppression, and deblending techniques, ensuring minimal contamination from AGN and foreground objects.
Their extreme infrared luminosities and high star formation rates provide critical tests for galaxy evolution models and inform the study of cosmic structure formation at early epochs.

Red-Herschel sources are a rare population identified via their distinct far-infrared (FIR) colors in Herschel/SPIRE data: rising flux densities through the 250, 350, and 500 μm bands—typically referred to as "500 μm-risers." These sources efficiently isolate dusty star-forming galaxies (DSFGs) at high redshifts (z ≳ 2–6), including protoclusters, galaxy overdensities, and lensed ultraluminous infrared galaxies (ULIRGs). Red-Herschel selection methods underpin extragalactic surveys tracing the earliest peaks of dust-embedded star formation, and form the observational backbone for galaxy evolution studies at cosmic noon and beyond.

1. Selection Criteria and Definitions

Red-Herschel sources are characterized by monotonically rising SPIRE flux densities, formalized as $S_{500} > S_{350} > S_{250}$ , where $S_{250}$ , $S_{350}$ , $S_{500}$ are the measured flux densities at 250 μm, 350 μm, and 500 μm, respectively (Asboth et al., 2016, Yan et al., 2019, Quirós-Rojas et al., 22 Jun 2024). For practical catalog construction, additional thresholds are imposed:

Minimum $S_{500}$ : typically $> 52$ mJy for robust selection (Asboth et al., 2016), or $> 30$ mJy for efficiency in smaller fields (Dowell et al., 2013).
No radio-loud AGN or blazar counterparts, established via cross-matches with FIRST/NVSS (Duivenvoorden et al., 2018).
Band-merged catalogs and confusion-noise suppression via matched filtering are standard, with selection often performed in a difference map, $D = 0.92M_{500} - 0.392M_{250}$ , which reduces confusion to $\sigma_{\text{conf},D} \sim 3.5$ mJy (Asboth et al., 2016).

Extensions to longer wavelengths (e.g., SCUBA-2 850 μm) identify "SPIRE dropouts," sources undetected in SPIRE but bright at 850 μm, indicative of $z\gtrsim 6$ (Yan et al., 2019).

The table summarizes principal selection criteria:

Criterion	Typical Value/Range	Context
SPIRE color	$S_{500} > S_{350} > S_{250}$	Core definition
Flux cut ( $S_{500}$ )	$> 52$ mJy, $> 30$ mJy, $> 20$ mJy	Varies by survey, field
Confusion noise (D-map)	$\sim 3.5$ mJy	Matched-filter map
Ancillary AGN rejection	NVSS/FIRST non-detection	Purity control

These color criteria select galaxies whose FIR SEDs peak longward of observed wavelengths, a signature of cold, dust-enshrouded starbursts redshifted into the SPIRE regime.

2. Source Multiplicity, Deblending, and Physical Association

Herschel’s SPIRE beam ( $\sim$ 18–36″ FWHM) blends multiple DSFGs, particularly in overdense regions or along lines of sight through massive halos. ALMA interferometric follow-up shows that:

73% of red-Herschel detections are single (point-like) sources at $\sim$ 1″ resolution; 20% are genuine multiples ( $\geq$ 2 sources separated by $>$ 3″), and ~5% are candidate lenses or close mergers (Quirós-Rojas et al., 22 Jun 2024, Quirós-Rojas et al., 30 Nov 2025).
In double/multiple systems, only 13% of doubles and 8% of triples are likely physically associated ( $\Delta z < 0.01$ ), yet 47–67% of triple/quadruple systems contain at least one potentially associated pair (Quirós-Rojas et al., 30 Nov 2025).
The brightest component generally dominates the flux, contributing 64% (doubles), 48% (triples), and 42% (quads).

This multiplicity analysis suggests that the enhanced SFRs typical of red-Herschel sources are primarily internally driven rather than the result of large-scale interactions, though the catalogs serve as potential proto-cluster targets (Quirós-Rojas et al., 30 Nov 2025).

3. Redshift, SED Properties, and Star Formation Activity

Red-Herschel sources have extreme infrared luminosities and high redshifts:

ALMA+SPIRE SED modeling yields median $L_{\text{IR}} \sim 8.9 \times 10^{12}\ L_\odot$ , SFR $\sim 1.3 \times 10^{3}\ M_\odot\,\text{yr}^{-1}$ , and $M_{\text{gas}} \sim 4 \times 10^{11}\ M_\odot$ (Quirós-Rojas et al., 22 Jun 2024).
The redshift distribution for single systems peaks at $z \approx 2.8$ , lensed systems at $z \approx 3.3$ , with detections out to $z \sim 6$ (Quirós-Rojas et al., 22 Jun 2024, Dowell et al., 2013, Yan et al., 2019).
Depletion times are short ( $\sim 0.3$ Gyr), consistent with a starburst population.

For the brightest confirmed sources, SED fits return $T_d \sim 50$ –65 K, $L_{\text{IR}} \sim 1$ – $6 \times 10^{13} L_\odot$ , and SFRs up to $10^4\ M_\odot\,\text{yr}^{-1}$ (Dowell et al., 2013). For protostellar sources (PACS Bright Red sources or PBRs), modified black-body fits to $\lambda \geq 70\,\mu$ m yield dust temperatures $T_{MBB} = 16$ –27 K, envelope masses $0.2$– $2\,M_\odot$ , and luminosities $0.7$– $10\,L_\odot$ (Stutz et al., 2013).

4. Spatial Density, Clustering, and Protoclusters

Extensive surveys quantify the sky density and clustering of red-Herschel sources:

In HerMES/HeLMS, surface densities range from $1.7$–$8.2$ deg $^{-2}$ at $S_{500} \geq 52$ –$20$ mJy (Asboth et al., 2016, Yan et al., 2019). At $S_{500} \geq 30$ mJy, densities are $3.3 \pm 0.8$ deg $^{-2}$ (Dowell et al., 2013).
Lensed ULIRGs are rare, comprising $<1$ –$5$\% of surveyed fields, while $20$–$21$\% of fields host significant protocluster candidates, characterized by $>3\sigma$ galaxy or red-galaxy overdensities (Lammers et al., 2022, Collaboration et al., 2015).
Planck–Herschel studies find median overdensity contrasts of $\delta_{500} \sim 5$ , often with $10$ SPIRE sources per structure, yielding aggregate SFRs up to $7 \times 10^{3}\ M_\odot\,\text{yr}^{-1}$ (Collaboration et al., 2015).

Stacked profiles indicate widely distributed star formation over projected Mpc scales at $z\sim2$ ; the highest-z protocluster peaks are both more intense and more extended than those found in lower-z cluster surveys (Lammers et al., 2022).

5. Comparison to Galaxy Evolution Models and Implications

Observed red-Herschel number counts and source properties systematically exceed predictions from established backward-evolution models (Béthermin+, Franceschini+, Valiante+):

Measured $dN/dS$ for red sources at $S_{500} \sim 60$ mJy exceed model predictions by factors of $10$–$20$ (Asboth et al., 2016, Dowell et al., 2013).
Even invoking extreme lensing boosts, models do not reproduce the observed bright, high-z population (Dowell et al., 2013).
Simulations show that noise boosting (Eddington bias) and blending have significant effects, but corrections via Monte Carlo injection-recovery analyses can self-consistently match observed counts with phenomenological models (e.g., Gruppioni+13 luminosity function, SIDES) once confusion and selection biases are incorporated (Duivenvoorden et al., 2018, Yan et al., 2019).

The abundance and properties of red-Herschel sources necessitate revisions to evolutionary scenarios, including the population of highly dust-obscured starbursts at $z \gtrsim 4$ and the role of gravitational lensing at high flux densities.

6. Lensing, Contamination, and AGN Fraction

Gravitational lensing is pervasive among the brightest red-Herschel sources:

All galaxies with $S_{500} > 100$ mJy or $S_{1.3\,\text{mm}} \geq 13$ mJy are found to be gravitationally amplified (Quirós-Rojas et al., 22 Jun 2024).
Statistical analyses reveal a $\sim3\times$ excess of foreground WISE/SDSS sources within $7''$ of red-Herschel fields, indicating weak or strong lensing in up to $\sim50$ \% of bright DSFGs (Duivenvoorden et al., 2018).
Machine-learning classifiers trained on SPIRE fluxes (input: $S_{250}$ , $S_{350}$ , $S_{500}$ ) efficiently separate high-SFR lenses ( $>100$ mJy) from protoclusters and normal star-formers (Lammers et al., 2022).

Radio-loud AGN contamination is low ( $\lesssim1.2\%$ ), and visual inspection of maps removes 10–15\% of severe blends (Yan et al., 2019).

7. Variants: PACS Red Sources and Low-Redshift Analogs

“Red” source selection is applied in other Herschel bands and contexts:

PACS Bright Red Sources (PBRs) are defined by $\log_{10}[\lambda F_{\lambda,70}/\lambda F_{\lambda,24}]>1.65$ , mapping to extreme Class 0 protostars in the Orion complex (Stutz et al., 2013). These sources exhibit SEDs peaking beyond 70 μm, cold dust envelopes, and high mass-infall rates.
At low redshift ( $z \leq 0.2$ ), optically “red” galaxies detected in SPIRE include both dust-reddened inclined spirals and passive ellipticals with external cold dust reservoirs; these form $\sim$ 4.2\% of massive submm detections (Dariush et al., 2015).

Additionally, PACS 160 μm ("Red band") surveys reach deep flux thresholds and resolve up to 60% of the cosmic infrared background, with LIRGs dominating the counts in the $5$–$100$ mJy regime (Pearson et al., 2018).

Red-Herschel sources form a unique window into the dusty, star-forming universe at early epochs, constraining the evolutionary trajectory of massive galaxies, the relative contribution of obscured starbursts to cosmic star formation rates, and a critical testbed for cosmological structure formation models. Their selection, physical properties, and multiplicity are intimately tied to survey methodologies and instrumental capabilities, with ongoing ALMA/JWST follow-up promising refined measurements of clustering, lensing, and SFR activity across cosmic time.