MOCK KSZ OBSERVATIONS: SUPPLEMENTAL MATERIALS
A.1 Mock Observation Pipeline Validation .1 Constraint Validation.1Constraint Validation
A.1.3 Validation of Cluster Member Galaxy Model
Here, we describe our model of the dust emission from cluster member galaxies, as introduced in Section 2.3.1. Cai et al. (2013) use a collection of infrared and submillimeter observations to provide IR luminosity functions and SEDs for four different types of sources: warm dusty galaxies, cool dusty galaxies, and active galactic nuclei (AGN) of types 1 and 2. The “cool” dusty galaxies are the most common type of galaxy, sometimes called late-type galaxies, which follow the galactic main sequence in the relation between star formation rate and total stellar mass (see, e.g., Rodighiero et al., 2011). The “warm” variety, which are known as starburst galaxies, are outliers from the main sequence, having significantly higher star formation rates per stellar mass. The two AGN types are distinguished by their level of dust obscuration; according to the standard unified AGN model (e.g., Antonucci, 1993), these types are in fact the same class of object as viewed from different angles relative to the dusty torus, with type 1 AGN being viewed through torus’s axis (and thus having low dust obscuration) and type 2 AGN being viewed through the lobes (high dust obscuration).
To implement the cluster member dust model, we must scale the Cai et al. (2013) luminosity functions by the local matter overdensity within the cluster. To do this, we infer a mass profile for the cluster’s total matter distribution based on the known mass (𝑀500) and redshift of the cluster. We assume that the mass density profile is described by an NFW model (Navarro et al., 1996; Navarro et al., 1997), and we calculate the model’s scale radius from the concentration-mass scaling relation of Child et al. (2018). However, it is not sufficient to simply scale the field luminosity function by the overdensity: we must also adjust for the abundance of different types of galaxies relative to the field. Alberts et al. (2016) measured this “field- relative fraction” of galaxies within clusters usingHerschel/PACS and Spitzer data, reporting abundance of each galaxy type as a function of radius and redshift. Thus, we scale the Cai et al. (2013) luminosity functions by the Alberts et al. (2016) field- relative fraction for each type. Finally, Alberts et al. (2014) found that the infrared
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(a) Cold sources
Figure A.2: Fitted SEDs for a selection of 60 sources detected by the removal pipeline in a mock observation with the 30m telescope. A.2a and A.2b are the 30 sources with the lowest fitted values of 𝑇/(1+ 𝑧), while A.2c and A.2d were randomly chosen among the remaining sources. The orange dashed curves represent the SED fits, while the blue points represent photometry values for each bandpass with estimated uncertainties.
(b) Cold sources
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(c) Warm Sources
(d) Warm Sources
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Figure A.3: Comparison of the normalized projected NFW profile with the mean normalized simulated cluster profiles with (right) and without the (left) Alberts et al.
(2016) correction applied.
luminosity of cluster members differs from the field in a redshift-dependent way.
We follow the Melin et al. (2018) interpretation of the Alberts et al. (2014) findings and rescale each galaxy’s luminosity by the function
𝑓(𝑧) =5.77e−0.34𝑡Gyr(𝑧), (A.1) where𝑡Gyris the cosmic time at redshift z.
Below, we include a few validation checks of our cluster member galaxy model.
As one caveat, these checks all depend on the assumption of azimuthal symmetry, which may not be fully valid (Deshev et al., 2020).
Check 1 (Figure A.3): Comparison of the expected normalized projected NFW profile to the mean normalized profile from the simulated cluster samples generated with and without Alberts et al. (2016) correction applied.
Figure A.4: Alberts et al. (2016) radial distribution corrections for each redshift range and galaxy type. The values at𝑟 =0 are extrapolated from Figure 5 in Alberts et al. (2016). Right: Empirical values of the same radial distribution correction for our simulated clusters, calculated as the ratio (with Alberts et al. (2016) correction / without Alberts et al. (2016) correction) and sorted by galaxy type. Redshifts used in simulating clusters with and without the Alberts et al. (2016) correction applied are given in Figure A.5.
Figure A.5: Redshifts used for simulated cluster samples with (right) and without (left) Alberts et al. (2016) correction applied. In both cases, redshifts used in the simulated clusters are consistently at𝑧 < 1.
Check 2 (Figure A.4): Comparison of the ratio of normalized profiles for sim- ulated clusters generated with and without Alberts et al. (2016) correction applied with the expected Alberts et al. (2016) radial distribution correction.
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Figure A.6: 857 GHz surface brightness profile for the simulated cluster sample.
Right: 857 GHz stacked PSZ2 profiles (Melin et al., 2018).
Check 3 (Figure A.6): 857 GHz simulated surface brightness profile comparison with Melin et al. (2018) stacked PSZ2 profiles in the 857 GHzPlanck band. The simulated surface brightness profile is calculated using the SEDs from Cai et al.
(2013) and evaluated in 10radial bins. While the overall normalization is consistent between our profile and that of Melin et al. (2018), their shapes are somewhat discrepant. There are are some differences between the algorithm of our work and the one used by Melin et al. (2018)—e.g., Melin et al. (2018) apply the Alberts et al.
(2016) correction at the cluster level while we apply it as a function of radius—
though we have not conclusively determined that the discrepancy is fully explained by algorithmic differences.