Why color choice decides cluster-member identification
Galaxy clusters are the largest gravitationally bound structures in the Universe, and their baryonic component can be traced through observables such as galaxy richness, X-ray emission, and the Sunyaev-Zeldovich effect. To use galaxy richness as a tracer of stellar mass, a pipeline has to decide which detected galaxies are actually bound to the cluster rather than sitting in front of or behind it.
Cluster members share photometric properties that make this possible. They tend to have predominantly older stellar populations and relatively low star-formation rates, and successive generations of star formation build up heavier elements that produce a prominent 4000 Angstrom break in their spectra. In a color-magnitude diagram this break appears as the red sequence line, so a color that measures the break cleanly lets a pipeline select likely members with less contamination.
SuperBIT flew in April 2023 and imaged thirty merging galaxy clusters in three blue-end optical bands: F400W (u), F480W (b), and F600W (g). Those three bands yield three possible colors, (u-b), (b-g), and (u-g), and any of them could in principle be used to locate the red sequence for a sample spanning redshifts of roughly 0.1 to 0.5. The paper's question is which one does the job most accurately.
Spectroscopic members anchor the red-sequence fit
The identification procedure starts from SuperBIT detections that already have external spectroscopic redshifts consistent with the target cluster. Those redshifts come from the Dark Energy Spectroscopic Instrument (DESI DR1) and the NASA/IPAC Extragalactic Database (NED). An object counts as a spectroscopically identified cluster member when its external redshift satisfies |z_spec - z_cluster| < 0.02.
Those known members are then placed on each cluster's color-magnitude diagram, and the red sequence line is characterized by fitting a linear relation to their colors. Candidate photometric members are selected within a color window of width 0.1 on either side of the best-fit line, with an additional upper magnitude limit that depends on cluster redshift to reduce contamination from faint background objects.
Because the red-sequence fit is anchored on the spectroscopically identified members, the precision of their colors sets how tightly the selection window can be drawn. The paper therefore measures the 1-sigma color scatter of those members separately for (u-b), (b-g), and (u-g), and treats that scatter as the first performance metric.
Scatter and purity measure different failure modes
The two metrics in this paper answer different questions and should not be substituted for one another. The 1-sigma color scatter describes how tightly the spectroscopically identified members cluster around the red sequence in a given color; it is a property of the member population's colors, expressed in magnitudes.
Purity describes what happens when the selection is actually applied. It is defined as P = N_member / (N_member + N_non-member), where N_member is the number of spectroscopically identified cluster members falling inside the red-sequence selection region and N_non-member is the number of spectroscopically identified non-members falling inside that same region. In the color-magnitude diagram these correspond to the known members and known non-members inside the selection box.
A color can therefore be precise in the sense of a narrow member distribution and still admit interlopers, and the paper reports both quantities rather than collapsing them into a single score. The scatter is measured on members only; purity is measured on the mix of members and non-members that the selection captures.
(b-g) wins on both scatter and purity
For Abell 1689, used as the worked example, the color distributions of the spectroscopically identified members are compared across (u-b), (b-g), and (u-g). The (b-g) distribution is the narrowest of the three, indicating the smallest color scatter for the identified members of that cluster.
The full-sample comparison is summarized as the 1-sigma color scatter of the spectroscopically identified members against cluster redshift, with each vertical grouping of three points corresponding to one cluster and the three points representing (b-g), (u-b), and (u-g). The number of spectroscopically identified members available for each cluster is annotated next to its grouping, so the reader can see how much spectroscopic support each cluster contributes. The same figure set reports red-sequence purity for the three colors as a function of redshift.
Across the full sample and over the redshift range probed by SuperBIT, (b-g) consistently exhibits the smallest scatter of the three color combinations and correspondingly tends to yield the highest purity. The paper's own reading of this pattern is that (b-g) provides the most precise color measurement of the red-sequence population in the SuperBIT data, which is why it becomes the preferred choice for the cluster-member identification algorithm.
Filter throughput explains why (b-g) wins
The paper attributes the ranking not only to the spectral information each filter pair captures but also to the quality of the photometry in each band. Filter transmission efficiency and sky background both feed into the photometric uncertainties, and the two do not favor the same bands equally.
Among the SuperBIT bands, F480W (b) provides the best combination of transmission efficiency and sky-background performance, followed by F600W (g). Because (b-g) pairs the two best-performing bands, it ends up with the smallest photometric scatter among the three color combinations considered. This is the mechanism the paper offers for the empirical ranking, and it is a statement about SuperBIT's specific band set rather than about color selection in general.
Where the (b-g) preference does and does not transfer
The result is bounded by the data it was measured on. The benchmark uses spectroscopically identified members across the SuperBIT cluster sample, which consists of thirty merging galaxy clusters plus five calibration fields with photometry in all three bands, and it covers the redshift range probed by SuperBIT, roughly 0.1 to 0.5. The spectroscopic redshifts that define members and non-members come from DESI DR1 and NED, so the purity measurement inherits whatever those catalogs supply for these fields.
The scatter and purity comparisons are also made at the level of the red-sequence selection used here: a linear fit to the known members, a color window of width 0.1 on either side of that fit, and a redshift-dependent upper magnitude limit. A different selection width or magnitude cut would change the member and non-member counts that enter the purity fraction, even though the underlying color scatter of the members would not change.
Within those bounds, the paper adopts (b-g) as the primary color for photometric cluster-member identification in the follow-up weak-lensing analysis, using it in the color-magnitude selection to construct cluster-member number-density maps. Those maps let the team compare the spatial distribution of the stellar population traced by red-sequence galaxies against the weak-lensing signal from the same SuperBIT observations, and they are also intended as input for future coherence analyses with SuperBIT data.
What to carry forward from this comparison
The practical takeaway is a ranking with a stated basis, not a universal rule. For SuperBIT's three blue-end bands, (b-g) is the color to use when building red-sequence cluster-member selections, because it combines the narrowest member color distribution with the highest purity across the sample and over the redshifts SuperBIT observed.
The reason to prefer it over (u-g) is not that (u-g) lacks spectral leverage but that it pairs a well-performing band with a weaker one, while (b-g) pairs the two bands with the best transmission efficiency and sky-background performance. That distinction matters for anyone deciding how to weight photometric quality against wavelength coverage when choosing a color for red-sequence selection.
The paper's own next step is to use (b-g) in the color-magnitude selection that produces cluster-member number-density maps for the weak-lensing analysis, so the value of this comparison will show up as the fidelity of those maps rather than as a standalone color ranking.
Sources used in this answer
Optimizing Color Selection for Cluster-Member Identification with SuperBIT
Across the SuperBIT cluster sample and over the redshift range probed by SuperBIT, the (b-g) color consistently shows the smallest 1-sigma color scatter among spectroscopically identified cluster members and tends to yield the highest red-sequence purity, making it the preferred color for red-sequence-based cluster-member identification.