SinFoniA: Empirical Galaxy Cluster Calibration

• SinFoniA is a data-driven selection function extractor that applies Monte Carlo methods and AMICO probabilistic memberships to calibrate galaxy and cluster catalogs.
• It generates mock catalogs by resampling observed survey data—preserving masks, galaxy density, photometry, and photo-z behavior—to maintain survey realism.
• The framework enables precise estimation of purity, completeness, and observable scatter, underpinning accurate cosmological inference from cluster counts.

Searching arXiv for SinFoniA and closely related AMICO papers to ground the article in current literature. SinFoniA is the Selection Function extrActor, a Monte Carlo, data-driven machinery used within the AMICO ecosystem to derive sample purity, completeness, observable scatter, and the selection function of optically selected galaxy-group and galaxy-cluster catalogs from the data themselves rather than from fully synthetic numerical simulations. In the recent KiDS-DR4 cosmological cluster sample, SinFoniA is explicitly described as the mechanism that turns the observed galaxy catalog and AMICO probabilistic memberships into a survey-realistic calibration of the detected sample, preserving the actual masks, galaxy density, photometry, photo-$z$ behavior, and depth variations of the survey (Maturi et al., 18 Jul 2025). In the COSMOS-Web deep group catalog, SinFoniA is similarly used to generate data-driven mock catalogs directly from the observed data and the AMICO output, providing the truth-table framework needed to quantify reliability and selection effects up to $z=3.7$ (Toni et al., 15 Jan 2025).

1. Definition and conceptual role

SinFoniA is introduced in the KiDS-DR4 AMICO cluster analysis through the statement that “The sample purity and selection function are derived from the analysis of mock data using the data-driven approach implemented in the Selection Function extrActor (SinFoniA) code” (Maturi et al., 18 Jul 2025). The same paper gives its methodological core more explicitly: SinFoniA “relies on a Monte Carlo approach, using the probabilistic galaxy memberships provided by AMICO to generate a mock galaxy catalog that distinguishes between field galaxies and cluster members,” while reproducing “the actual masks, galaxy density, photometry and photo-$z$s” (Maturi et al., 18 Jul 2025).

In the COSMOS-Web group catalog, SinFoniA is described as a method that “exploits a Monte Carlo approach to create realizations of the universe and generate realistic mocks directly from the data,” with the stated purpose of deriving purity and completeness of the AMICO sample (Toni et al., 15 Jan 2025). Across both applications, SinFoniA is not presented as a generic structure-formation simulator, nor as a cluster finder. AMICO performs the detection; SinFoniA is the downstream calibration layer that characterizes the detected catalog.

This usage defines SinFoniA operationally as an empirical selection-function extractor. Its central function is to answer, as a function of redshift and observable, which fraction of real systems is recovered and which fraction of detections corresponds to real systems. A plausible implication is that SinFoniA occupies the interface between catalog construction and inference, especially where cluster counts or group statistics require explicit selection modeling.

2. Placement within the AMICO workflow

The KiDS-DR4 paper states the pipeline in practical terms: a homogeneous KiDS-DR4 galaxy sample is constructed; AMICO is run on the real survey to detect clusters and assign probabilistic memberships; those memberships and the observed survey properties are then passed to SinFoniA; SinFoniA generates mock realizations of the galaxy catalog; AMICO is rerun on those mocks exactly as on the data; the resulting mock detections are matched to the injected mock clusters; purity, completeness, and scatter in observables are then derived from the matching (Maturi et al., 18 Jul 2025).

The same logical chain appears in the COSMOS-Web work. There, the authors state that the mocks are generated “based on the input dataset used for the creation of our candidate catalog, which is already divided into field and group galaxies via the association probability returned by AMICO,” and that “the AMICO algorithm is applied to the mock galaxy catalog in the same way as was done for the real data,” after which the mock groups are used as a “truth table” to study the detected catalog (Toni et al., 15 Jan 2025).

The AMICO–SinFoniA division of labor is therefore stable across wide-field cluster and deep-field group applications. AMICO returns detections, amplitudes, richness estimators, redshifts, and probabilistic memberships. SinFoniA consumes those outputs together with the observed survey properties and produces calibrated mocks that enable post-detection performance estimation. This suggests that SinFoniA is best understood as a catalog-characterization framework attached to a matched-filter detector rather than as an independent mock-generation code in the abstract.

3. Inputs, probabilistic ingredients, and mock construction

The inputs emphasized in the KiDS-DR4 analysis are the galaxy catalog, AMICO detections, AMICO probabilistic memberships $P_i(j)$, survey masks and tile properties, galaxy photometry, photo-$z$ information, and depth variations (Maturi et al., 18 Jul 2025). A key probabilistic ingredient is the field probability, written in the paper in garbled form but intended as the probability that galaxy $i$ belongs to the field being one minus the sum of its membership probabilities over detections (Maturi et al., 18 Jul 2025). For mock-cluster member extraction, galaxies are drawn according to the AMICO membership probabilities $P_i(j)$, so galaxies with larger membership probability are more likely to be selected into mock systems (Maturi et al., 18 Jul 2025).

In the COSMOS-Web paper, the membership formalism is written explicitly as

$$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$

where $F_i$ is the probability of belonging to the field, $A$ is the signal amplitude, $z=3.7$0 is the cluster model, $z=3.7$1 is the redshift probability at the detection redshift, and $z=3.7$2 is the noise (Toni et al., 15 Jan 2025). In that application, $z=3.7$3 is used to sample field galaxies, while $z=3.7$4 is used to sample mock members.

Both studies emphasize that mock groups or clusters are not produced by imposing a hard reality criterion on detections. Instead, detections are probabilistically selected into the mock truth population through cumulative-distribution-function weighting based on a signal-to-noise variable. In KiDS-DR4 the relevant quantity is SN_NO_CLUSTER, and the extraction probability is

$z=3.7$5

in redshift bins (Maturi et al., 18 Jul 2025). The COSMOS-Web implementation follows the same principle with the CDF of $z=3.7$6, again in redshift bins, explicitly to avoid a sharp cut when deciding which detections to treat as real in the mock universe (Toni et al., 15 Jan 2025).

Once a detection is selected to seed a mock system, its key properties are inherited from the real detection. In KiDS-DR4, the number, position, redshift, and richness are based on the real detection, with apparent richness $z=3.7$7 held fixed (Maturi et al., 18 Jul 2025). Position and redshift are then perturbed within $z=3.7$8 kpc/h and $z=3.7$9, chosen so nearby clusters can nearly overlap without erasing spatial correlations (Maturi et al., 18 Jul 2025). In COSMOS-Web, mock group positions and redshifts are shuffled by at most 0.25 $z$0 and 0.01 in redshift, again to preserve large-scale structure while avoiding exact duplication (Toni et al., 15 Jan 2025).

A common structural feature is empirical binning of member pools. In KiDS-DR4, mock-member stacks are binned by parent detection redshift $z$1, apparent richness $z$2, and an additional dimension related to tile depth, with fine-grained bins $z$3 and $z$4, plus grouping into sets of 50 tiles with similar survey depth (Maturi et al., 18 Jul 2025). In COSMOS-Web, galaxies are collected into bins of apparent richness and redshift with

$z$5

before drawing members for mock groups (Toni et al., 15 Jan 2025).

Both studies also preserve field-galaxy structure directly from the observed catalog. KiDS-DR4 explicitly states that field-galaxy angular positions are not perturbed, preserving intrinsic clustering properties and hence “the three-dimensional correlation of the noise” (Maturi et al., 18 Jul 2025). COSMOS-Web likewise keeps original positions and redshifts of field galaxies “to maintain the noise spatial correlation and so the main features of the large-scale structure” (Toni et al., 15 Jan 2025).

4. Geometric modeling, survey realism, and the meaning of “data driven”

A notable issue in membership-stacking approaches is that combining members from many observed systems tends to suppress intrinsic projected asymmetries. Both papers address this by introducing ellipsoidal projected shapes. In KiDS-DR4 the coordinate transformation is

$z$6

with $z$7 random and ellipticity

$z$8

drawn from a distribution motivated by dark-matter halos in N-body simulations (Maturi et al., 18 Jul 2025). The paper explicitly notes that this ellipticity distribution is not based on direct measurements from the observational data. COSMOS-Web describes the same corrective idea more generically as a coordinate transformation that preserves density while introducing ellipsoidal shapes resembling halo shapes in simulations (Toni et al., 15 Jan 2025).

This aspect is important because the papers repeatedly describe SinFoniA as “data-driven,” yet they also make clear that the method is not literally assumption-free. The KiDS-DR4 study argues that SinFoniA avoids “strong assumptions embedded in numerical simulations” and reduces dependence on cosmological and astrophysical assumptions by constructing mock catalogs from the observed dataset itself (Maturi et al., 18 Jul 2025). The COSMOS-Web paper goes further rhetorically, stating that the generated mocks “are not based on any model or assumption” (Toni et al., 15 Jan 2025). However, within the same paper, the actual implementation includes CDF-based truth selection, richness–redshift binning, ellipsoidal shape restoration, and small redshift/position shuffles (Toni et al., 15 Jan 2025).

A careful synthesis therefore supports a narrower interpretation: SinFoniA is data-driven in the sense that it preserves empirical survey complexity—masks, galaxy density, depth, field clustering, photometry, and photo-$z$9 behavior—while importing substantially fewer theoretical assumptions than end-to-end numerical simulations. This suggests a contrast not between “model” and “no model,” but between survey-anchored weak modeling and fully synthetic cosmology-dependent simulation.

5. Matching strategy and definitions of purity, completeness, and scatter

After generating the mock galaxy catalogs, both studies rerun AMICO on the mocks with exactly the same setup used on the real data. The subsequent comparison between recovered detections and injected mock truth objects defines the calibration outputs.

In KiDS-DR4, 3D matching is performed with angular distance smaller than $P_i(j)$0 Mpc/h and redshift difference $P_i(j)$1, after sorting detections and mock clusters by descending apparent richness (Maturi et al., 18 Jul 2025). In COSMOS-Web, the authors first use loose tolerances,

$P_i(j)$2

then inspect the empirical separation distribution and identify the region

$P_i(j)$3

as the effective concentration of genuine matches (Toni et al., 15 Jan 2025). They model the 2D scatter distribution with signal plus constant background and find the random-match background negligible within the adopted rectangle (Toni et al., 15 Jan 2025).

The definitions of the key performance metrics are aligned across the two papers. KiDS-DR4 defines sample purity as “the ratio between the detections with a matched counterpart in the mocks and the total number of detections,” and completeness as “the ratio between the detections with a matched counterpart in the mocks and the total number of clusters in the mocks” (Maturi et al., 18 Jul 2025). COSMOS-Web gives the same definitions in equivalent language: purity is matched detections over all detections, and completeness is matched detections over all true objects (Toni et al., 15 Jan 2025).

Observable scatter is also measured from the mock-truth comparison. In COSMOS-Web the difference is explicitly written as

$P_i(j)$4

for observables such as $P_i(j)$5, $P_i(j)$6, and $P_i(j)$7 (Toni et al., 15 Jan 2025). KiDS-DR4 extends the same logic to amplitude $P_i(j)$8, apparent richness $P_i(j)$9, intrinsic richness $z$0, redshift, and positional offset or miscentering (Maturi et al., 18 Jul 2025).

A plausible implication is that SinFoniA produces not only a selection function in the narrow sense but an empirical transfer function from true to measured cluster or group properties under the exact survey and detection conditions.

6. Empirical outputs in recent applications

The two recent applications illustrate SinFoniA’s quantitative role in different observational regimes.

KiDS-DR4 AMICO cosmological cluster sample

Using AMICO on KiDS-DR4, the authors identify 23965 clusters over an effective area of about 839 deg$z$1 in the redshift range $z$2, with $z$3, and then use SinFoniA to estimate sample purity, completeness, observable scatter, and the selection function (Maturi et al., 18 Jul 2025). Purity is evaluated in bins of true redshift and observed $z$4, $z$5, $z$6, $z$7, and SN_NO_CLUSTER (Maturi et al., 18 Jul 2025). A key result is that, for a fixed purity, all observables exhibit redshift dependence except SN_NO_CLUSTER (Maturi et al., 18 Jul 2025). This gives SN_NO_CLUSTER a special status as a redshift-stable purity selector.

Completeness is treated as the selection function and evaluated in bins of true redshift and expected input cluster properties (Maturi et al., 18 Jul 2025). The public paper withholds the unblinded $z$8-based selection function but reports approximate amplitude-based completeness values at $z$9: $i$0, $i$1, and $i$2 completeness are achieved for amplitudes larger than $i$3, $i$4, and $i$5, respectively (Maturi et al., 18 Jul 2025).

SinFoniA is also used to characterize observable biases. Incomplete low-observable regions show selection bias, described as Malmquist bias, where “preferentially noise-scattered high estimates are selected” (Maturi et al., 18 Jul 2025). Within the completeness regime, $i$6 is reported as unbiased across the full sample; $i$7 shows a slight negative bias at $i$8; and $i$9 shows a small trend from positive to negative bias with negligible bias in $P_i(j)$0 (Maturi et al., 18 Jul 2025). For redshift scatter, the paper finds

$P_i(j)$1

while explicitly cautioning that this is likely slightly underestimated relative to spectroscopic calibration because the mock redshifts are inherently defined in the photo-$P_i(j)$2 space (Maturi et al., 18 Jul 2025). For centering, the algorithmic positional scatter is quoted as $P_i(j)$3, $P_i(j)$4, and $P_i(j)$5 arcmin in the redshift bins $P_i(j)$6, $P_i(j)$7, and $P_i(j)$8, corresponding to $P_i(j)$9, $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$0, and $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$1 Mpc/h (Maturi et al., 18 Jul 2025).

The KiDS-DR4 study also reports internal validation of the mock realism. Mock tiles reproduce the total number of galaxies with maximum deviation well below $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$2, with only three tiles exceeding $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$3 (Maturi et al., 18 Jul 2025). However, the number of detections per tile shows residual discrepancies: roughly a $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$4 excess of high-$$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$5 detections in mocks and deficits up to $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$6 at lower $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$7 in $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$8 (Maturi et al., 18 Jul 2025). The authors attribute this pattern to the injected mock clusters, suggesting that larger mock clusters are somewhat easier to detect, while smaller ones are more difficult than in the real data (Maturi et al., 18 Jul 2025).

COSMOS-Web deep group catalog

In COSMOS-Web, SinFoniA is used to characterize AMICO detections up to $$P_{i,j}= F_{i}\frac{A M_c(\boldsymbol{x}_i)p(z_j)}{A M_c(\boldsymbol{x}_i)p(z_j)+N} \, ,$$9 over an effective area of 0.45 deg$F_i$0 (Toni et al., 15 Jan 2025). The catalog contains 1678 detected groups, and the mock-based analysis yields an overall purity of $F_i$1 for the full sample (Toni et al., 15 Jan 2025). The study emphasizes that $F_i$2 is the detection quantity with the best redshift stability for purity calibration (Toni et al., 15 Jan 2025).

The most practical outputs are the purity-calibrated thresholds. The paper reports that a cut at

$F_i$3

selects 200 detections with $F_i$4 purity, while a cut at

$F_i$5

selects 756 detections with $F_i$6 purity (Toni et al., 15 Jan 2025). The operational catalog threshold itself is

$F_i$7

(Toni et al., 15 Jan 2025).

For observable performance, the mock-truth comparison shows no significant bias in $F_i$8, $F_i$9, or $A$0 across the sample, but the paper identifies Malmquist bias at the low-observable end, approximately for

$A$1

with slight redshift dependence for the amplitude threshold (Toni et al., 15 Jan 2025). The authors also note that the scatter in redshift inferred from the mocks is underestimated relative to spectroscopic redshift scatter (Toni et al., 15 Jan 2025).

7. Cosmological relevance, blinding, and methodological limitations

In the KiDS-DR4 cluster analysis, SinFoniA is directly tied to downstream cosmological inference. The paper states that one of the main scientific drivers is to use the cluster sample to constrain cosmological parameters, and therefore the selection function derived from SinFoniA is itself subjected to blinding (Maturi et al., 18 Jul 2025). The blinding procedure is based on controlled perturbations of the selection function derived from the SinFoniA matching of true and detected clusters (Maturi et al., 18 Jul 2025). The steps reported are: compute a halo-ratio perturbation using the Jenkins mass function between a reference cosmology and a randomly perturbed one; map the perturbation from halo mass onto the AMICO amplitude proxy $A$2; perturb the matching catalog for detections with $A$3; recompute the selection functions for original and perturbed matchings; and smooth them with first-order Chebyshev polynomials of order one and window size three (Maturi et al., 18 Jul 2025).

This makes the role of SinFoniA foundational rather than auxiliary. The unblinded selection function originates from SinFoniA, and the blinded versions are perturbations of that same matched mock catalog. Since cluster-count cosmology depends critically on the relation between true halo population and detected sample, SinFoniA provides the empirical bridge between catalog space and likelihood space (Maturi et al., 18 Jul 2025).

The limitations acknowledged in the papers are equally important. KiDS-DR4 explicitly states that no intrinsic redshift bias can be measured within the SinFoniA approach because mock cluster redshifts are directly based on the original photo-$A$4s (Maturi et al., 18 Jul 2025). The same paper also notes that positional uncertainties inferred from the mocks are purely algorithmic because the mock clusters are smooth ellipsoids without the morphological complexity of real clusters (Maturi et al., 18 Jul 2025). COSMOS-Web likewise reports underestimated redshift scatter relative to spectroscopy and notes, by reference to forthcoming work, the possible under-representation of small and blended objects in the mocks (Toni et al., 15 Jan 2025).

These caveats delimit the scope of the method. SinFoniA preserves survey realism and avoids dependence on fully synthetic numerical simulations, but it inherits the strengths and weaknesses of the observed catalog and of the AMICO probabilistic decomposition from which it is built. This suggests that SinFoniA is most powerful when the dominant challenge is survey realism rather than first-principles forward modeling of halo and galaxy formation.

8. Relation to simulation-based calibration and broader significance

Both papers frame SinFoniA against conventional simulation-based calibration. The KiDS-DR4 work states that the data-driven approach avoids numerical simulations, which “often fail to capture the full complexity of the data and can introduce biases due to the cosmological and astrophysical assumptions they rely on” (Maturi et al., 18 Jul 2025). The COSMOS-Web paper similarly argues that the method reduces biases associated with cosmological assumptions in numerical simulations (Toni et al., 15 Jan 2025). In both cases, the central claim is not that simulations are unnecessary in general, but that empirical resampling of the observed catalog can better preserve masks, depth fluctuations, galaxy density, and photo-$A$5 behavior.

This methodological stance is consequential for large observational programs. In KiDS-DR4, the cluster sample, probabilistic memberships, sample purity, and selection function are intended for public release, indicating that SinFoniA products are part of the scientific data product itself (Maturi et al., 18 Jul 2025). In COSMOS-Web, the method underpins the practical interpretation of a deep group catalog extending into the protocluster regime at high redshift (Toni et al., 15 Jan 2025). The latter paper also notes that SinFoniA “has already been applied to wide-field surveys such as KiDS” and “is currently part of the implementation of the Euclid pipeline” (Toni et al., 15 Jan 2025).

Taken together, the recent literature portrays SinFoniA as a survey-realistic, Monte Carlo, membership-based calibration framework layered on top of AMICO. Its essential products are purity, completeness, observable scatter, and the selection function. Its characteristic feature is the construction of mock galaxy catalogs from the observed data and AMICO’s own probabilistic field/member decomposition, with explicit preservation of real survey complexity. Its scientific role is to convert a detection catalog into a quantitatively characterized sample suitable for astrophysical interpretation and, in cosmological applications, for blinded inference on cluster counts and related observables (Maturi et al., 18 Jul 2025, Toni et al., 15 Jan 2025).