Satellites around Milky Way Analogs: Tension in the Number and Fraction of Quiescent Satellites Seen in Observations versus Simulations

Characterizing the satellite populations around Milky Way (MW)–like hosts is a key component of understanding galaxy formation and evolution. Owing to the unrivaled depth and completeness of observations of its satellite population, the MW has been the default test bed for simulations aiming to probe the underlying physics of dwarf galaxy evolution. The environmental dependence of the satellite star-forming fraction therein is well established: with few massive (M_* ≳ 10⁸ M_⊙) exceptions, satellites are quiescent within the virial radius and star-forming farther out (Grcevich & Putman 2009; Spekkens et al. 2014; Putman et al. 2021), implying that satellites are quenched by their hosts. Indeed, it has been demonstrated that the observed Local Group (LG) satellite quenched fraction transitions from ∼100% to 0% between 10^6.5 ≲ M_*/M_⊙ ≲ 10⁹, suggesting a mass dependence to the underlying mechanisms (Fillingham et al. 2015; Wetzel et al. 2015, see also Slater & Bell 2014; Wheeler et al. 2014). Whether or not the star-forming properties of satellites around MW-mass hosts beyond the LG are consistent with those within the LG can provide important constraints on cosmological galaxy formation simulations.

Observationally, searches for the satellite populations around nearby MW analogs were pioneered by Zaritsky et al. (1993, 1997) and are now being pursued by various groups (e.g., Crnojević et al. 2016; Javanmardi et al. 2016; Bennet et al. 2019; Carlsten et al. 2020). One of the most extensive of these campaigns is the ongoing Satellites Around Galactic Analogs (SAGA; Geha et al. 2017) survey, which aims to detect and characterize all satellites brighter than the Leo i dwarf (M_* ∼ 10^6.6 M_⊙) around 100 MW-like hosts. The SAGA Stage ii (SAGA-ii) release presented in Mao et al. (2021, hereafter M21) shows that the vast majority of confirmed satellites within the virial radii of the 36 hosts surveyed so far are star-forming rather than quenched. While this result is commensurate with some earlier surveys of brighter satellites across a broader host mass range (e.g., Guo et al. 2013; Phillips et al. 2015; Davies et al. 2019), it is in strong contrast to the fainter satellites in the LG. This discrepancy between the LG and other observed systems may have important implications for models that aim to replicate the trends seen in the LG.

Theoretically, a variety of cosmological zoom-in simulation suites can now probe star formation and quenching physics in satellites around MW analog hosts down to Leo i masses (Wetzel & Hopkins 2016; Garrison-Kimmel et al. 2019; Akins et al. 2021). In particular, galaxy properties in APOSTLE (Fattahi et al. 2016; Sawala et al. 2016) and Auriga (Grand et al. 2017) are interesting to contrast given their similar resolutions and suite sizes but different host selection, hydrodynamical schemes (SPH versus moving-mesh), and evolutionary models. One focus has been the comparison of the simulated satellite quenched fraction to that in the LG. The agreement between simulations is generally good, with most studies suggesting a characteristic mass (M_* ∼ 10⁸−10⁹ M_⊙) below which satellites are more readily quenched by their hosts (e.g., Fillingham et al. 2016; Simpson et al. 2018; Akins et al. 2021; Joshi et al. 2021).

The consistency of simulated satellite populations with those in the LG combined with the stark contrast between the quenched fractions in the MW and SAGA-ii strongly motivates direct comparisons between theory and other MW analogs in order to build robust models of galaxy formation. This requires selecting star-forming objects consistently across observed and simulated samples.

In this letter, we compare star-forming satellites and quenched fractions in the SAGA-ii observations to those in the APOSTLE and Auriga simulations. The observations and simulations have similar host numbers, host masses, and satellite selection functions (Section 2). We use archival UV imaging and simulated star formation rates (SFRs) to select star-forming satellites in SAGA-ii and APOSTLE/Auriga, respectively, comparing SFRs to gauge consistency across samples (Section 3). We then compare quenched fractions in the observed and simulated samples (Section 4) and discuss possible explanations for the significant discrepancies we find (Section 5).

2.1. Observed Sample: SAGA-ii

2.2. Simulated Samples: APOSTLE and Auriga

With the satellite samples established in Section 2, we now outline our method to select observed (Section 3.1) and simulated (Section 3.2) star-forming satellites within them. We check for consistency of our star-forming satellite definitions across the observations and the simulations in Section 3.3.

3.1. Observed Star-forming Satellites

We use UV emission as the primary indicator of star formation in the observed satellites from SAGA-ii with archival GALEX imaging (see Table 1). We take a curve-of-growth approach using the Astropy Photutils package (Bradley et al. 2020) to detect statistically significant UV emission. Our method is illustrated in Figure 1, and the corresponding measurements are in Table 1.

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We start by masking bright sources near the satellite targets in each 12 wide GALEX tile and measuring the mean and standard deviation of the flux within 1000 randomly placed circular regions across them. The region radius is the satellite effective radius r_eff from the SAGA-ii photometry. Working from the (generally deeper) NUV tile, we measure background-subtracted fluxes within circular apertures about the optical position of each satellite starting from r = 0.5 r_eff. We increase the aperture size in steps of 075 (3'') for less (more) extended sources until the background-subtracted fluxes in adjacent apertures change by less than the noise difference between them. We compute the signal-to-noise ratio S/N_NUV in the smaller of these regions (with a radius r_COG reported in Table 1) and place an identical region on the FUV tile to measure S/N_FUV.

We consider measured fluxes with S/N > 2 as detections in a given band. By this definition, 115/119 satellites with GALEX coverage have associated NUV emission, and 104/113 have associated FUV emission. We use standard equations (Morrissey et al. 2007) to convert to apparent AB magnitudes m_NUV and m_FUV (see Table 1), correcting for foreground extinction using E(B − V) from Schlafly & Finkbeiner (2011) with R_NUV = 8.2, R_FUV = 8.24 (Wyder et al. 2007).

Not only do the vast majority of the SAGA-ii satellites with UV coverage show emission in one or both bands, but the correspondence between satellites with Hα equivalent widths EW ≥ 2 Å (M21) is also very high: 98/113 satellites with observations in NUV, FUV, and Hα are detected in all three tracers. We posit that the majority of nondetections stem from observational limitations (such as image depth/sensitivity combined with satellite distances or Hα fiber position) rather than physical differences. The strong correlation between UV and Hα star formation tracers, despite the difference in the timescales they probe, is common in dwarf galaxies (e.g., Lee et al. 2011), and suggests that quenching is rapid at these masses (e.g., Wetzel et al. 2015).

We define an observed satellite to be star-forming either if it is detected in the UV or if it has EW ≥ 2Å as reported by M21. Because we find 12 (6) satellites with NUV (FUV) emission that do not satisfy the Hα criterion but only 2 satellites (1 NUV, 1 FUV) for which the inverse is true, the fraction of star-forming satellites in Table 1, 120/127, is marginally higher than that reported by M21. We discuss the implications of these numbers for the quenched fraction in Section 4.

3.2. Simulated Star-forming Satellites

We consider two SFR measures to identify star-forming satellites in the simulations. Our fiducial metric, the "instantaneous" rate, , is estimated using the gas particles associated with the satellite subhalo determined by SUBFIND at z = 0 and corresponding SFR relations for APOSTLE (Schaye et al. 2015) and Auriga (Springel & Hernquist 2003; Grand et al. 2017), with the former using a gas pressure threshold and the latter using a gas density threshold. These SFRs have previously been shown to reproduce observed trends (Vogelsberger et al. 2013; Furlong et al. 2015; Schaye et al. 2015). We also consider the average mass of star particles formed over the last gigayear as a measure of SFR. Like this metric is less susceptible to shot noise than estimates over shorter time intervals, but, unlike the observational tracers, it averages over a significant fraction of a satellite orbit. We demonstrate in the Appendix that both metrics produce similar results and adopt to select simulated star-forming satellites throughout.

We define a simulated satellite as star-forming if . A total of 54/229 APOSTLE and 152/411 Auriga satellites meet this criterion, and their properties are illustrated in Figure 2. The left-hand panel of Figure 2 shows the relation of star-forming satellites and the stellar mass distribution of the quenched ones. The right-hand panel of Figure 2 shows the cumulative number of star-forming and quenched satellites per simulated host. Considering the differences between the simulations (see Section 2.2), there is good agreement between them despite the different host environments: star-forming satellites in both APOSTLE and Auriga follow similar relations, and both populations become increasingly dominated by quenched systems at low M_*. These trends are qualitatively similar if a specific SFR threshold is adopted instead of a nonzero (i.e. Akins et al. 2021).

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The mild difference between the APOSTLE and Auriga satellite samples in the right panel of Figure 2 likely stems from the different galaxy formation prescriptions adopted by the simulations. For example, APOSTLE halos may more readily remove gas from lower-mass subhalos leaving them permanently quenched, while Auriga subhalos may reaccrete expelled gas, allowing them to be more long lived. Additionally, the earlier onset of the UV background in the APOSTLE simulations may further contribute to fewer star-forming satellites per host at lower M_*.

3.3. Comparing Star-forming Satellites

With star-forming satellites identified and their consistency checked, we proceed to compare observed and simulated quenched fractions.

Because most SAGA-ii candidates are confirmed in the Hα emission line (see Section 2.1), Table 1 is likely missing quenched satellites even in regions where the spectroscopic coverage is high. Interloping field galaxies are also more likely to be star-forming than quenched given their relative ubiquity (Geha et al. 2012). Correcting for both effects would systematically raise the observed quenched fraction relative to that calculated directly from Table 1. M21 model them in detail, deriving a (dominant) incompleteness correction by assuming that all spectroscopically targeted but undetected candidates are quenched satellites, and a (subdominant) interloper correction by drawing mock samples from gravity-only simulations. We use the M21 corrections directly from their Figure 11 (in the same M_* bins), retaining the interloper correction despite comparing to simulations (for which it should not be required). The incompleteness/interloper-corrected quenched fractions we adopt are therefore conservative upper limits on the observed values implied by SAGA-ii.

Figures 3 and 4 plot the observed and simulated quenched fractions in two different ways. In Figure 3, the SAGA-ii quenched fractions (purple stars with dark bars showing random counting uncertainties ¹⁸ and light bars showing systematic incompleteness/interloper corrections) are compared to those in APOSTLE (cyan band and squares) and Auriga (pink band and triangles). Figure 4 plots M_* as a function of projected host distance D_proj for star-forming (stars) and quenched (circles) satellites in the APOSTLE (cyan) and Auriga (pink) samples. The M_* bin definitions in M21 and Figure 3 are shown as a gradient of purple horizontal bands in Figure 4. The average simulated quenched fraction in those bins is directly to their right, and the range of observed quenched fractions bracketed by the ratios from Table 1 (smaller value) and the incompleteness/interloper-corrected ratios (larger value) are in parentheses. In both plots, the dotted (dashed–dotted) lines show the SAGA-ii 100% (80%) spectroscopic coverage.

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Figures 3 and 4 illustrate that, despite their differences (i.e., hydrodynamic schemes, galaxy formation and evolution models, and host environments), there is a striking correspondence between the quenched fractions from the APOSTLE and Auriga simulations as a function of M_* and D_proj for 10⁶ ≲ M_*/M_⊙ ≲ 10¹⁰. It is also clear that, even when conservatively accounting for both incompleteness and interlopers as in M21, the observed satellite quenched fraction is lower than in the simulations across the M_* range considered. The difference is largest for 10⁷ ≲ M_*/M_⊙ ≲ 10⁸, where the SAGA-ii spectroscopic coverage is essentially complete and the incompleteness/interloper-corrected observed quenched fraction is 2–3 times lower than in the simulations. We discuss the implications of this result in the following section.

Finally, the median projected separation for the SAGA-ii quenched and star-forming objects is shown at the bottom of Figure 4 by short, white lines. These separations are relatively consistent with the simulations where star-forming satellites have larger projected separations than quenched satellites; however, the scarcity and incompleteness of the observed quenched satellites limits this comparison. This perspective illustrates a distance dependence in both simulated samples beginning at intermediate masses (10⁸ ≲ M_*/M_⊙ ≲ 10⁹) where quenched satellites are located at lower projected distances and become more ubiquitous at lower stellar masses, similar to previous trends reported around more massive hosts and in the LG (Guo et al. 2013; Wang et al. 2014; Fillingham et al. 2018).

We have identified star-forming satellites around MW analogs in observed and simulated samples, which have similar sizes and similar host masses, and which are selected in a similar manner (Section 2). We used UV emission in confirmed SAGA-ii satellites (Figure 1) and an instantaneous SFR in APOSTLE and Auriga satellites to define observed and simulated star-forming objects, respectively, which were checked for consistency (Section 3 and Figure 2). We compared quenched fractions in the resulting samples and find that the incompleteness/interloper-corrected observed values are ∼2–3 times lower than the simulated ones for 10⁷ ≲ M_*/M_⊙ ≲ 10⁸ (Section 4 and Figures 3 and 4). The observed and simulated quenched fractions are therefore strongly discrepant in a mass range that is well probed in both samples.

The comparisons presented here are broadly consistent with previous investigations of satellite quenched fractions. Observationally, our quenched fractions differ only slightly from those found by M21, which Akins et al. (2021) report to be lower than those of satellites around four MW-like hosts in the Justice League simulations. Furthermore, we note that this discrepancy extends to other nearby systems that are similar to the MW/M31 with respect to quenched satellites (Chiboucas et al. 2013; Carlsten et al. 2021), and it can also be inferred from the star formation histories of satellites from the FIRE-2 simulations (Garrison-Kimmel et al. 2019). More broadly, as the quenched fractions in the LG have been shown to agree with simulations (e.g., Fillingham et al. 2016; Simpson et al. 2018; Akins et al. 2021; Joshi et al. 2021) and the LG and SAGA-ii have been shown to disagree (Geha et al. 2017; M21), the discrepancy in quenched fractions between SAGA-ii and the APOSTLE and Auriga simulations is unsurprising. Here, we have demonstrated the degree to which the observations and simulations are inconsistent with large, comparably sized samples, and that the discrepancy is robust against different choices of observed or simulated star formation tracers as well as a variety of simulation parameters (Section 3.2 and the Appendix).

The agreement between the SFR–M_* relations and cumulative M_* distributions in Figure 2 combined with the discrepant quenched fractions in Figures 3 and 4 suggests that the difference between the observed and simulated samples stems from the number of quenched satellites in each. For 10^6.6 ≲ M_*/M_⊙ ≲ 10^7.8, the APOSTLE and Auriga samples, respectively, have an average of 3.5 and 4.9 satellites per host, comparable to the LG (McConnachie 2012) but greater than the incompleteness/interloper-corrected SAGA-ii value ¹⁹ of ∼2 (M21). The star-forming satellite counts, quenched fractions, and total satellite counts presented here are therefore all broadly consistent at 10^6.6 ≲ M_*/M_⊙ ≲ 10^7.8 if there are 50–100 additional quenched satellites in the simulated samples compared to that estimated for the incompleteness/interloper-corrected observed sample.

One possibility is that the quenched satellite number difference is observationally driven: in this scenario, the SAGA-ii incompleteness correction underestimates the number of quenched satellites with 10^6.6 ≲ M_*/M_⊙ ≲ 10^7.8, with the deficit increasing toward the low-mass end (c.f. Figure 2, right). The nearly complete SAGA-ii spectroscopic coverage and the conservative M21 incompleteness correction suggest that the quenched satellites would most likely be missing from the imaging catalogs from which spectroscopic targets are drawn.

It is plausible that low surface brightness (LSB) satellites are missing from the SAGA-ii imaging catalogs from which follow-up targets are drawn because they are not developed for LSB detection. M21's comparisons to deeper overlapping catalogs argue against this scenario, although quantitative photometric completeness simulations (e.g., Bennet et al. 2017) have not been carried out. It is also plausible that a larger fraction of the 70 detected diffuse LSB galaxies (dLSBGs) without redshifts are actually satellites than the 25%–30% assumed in the M21 incompleteness correction. If all of these dLSBGs were satellites, it may remedy the discrepancy at the lowest masses; however, the total number of quenched satellites per host would still be low compared to that in the simulations. Extending these investigations of surface brightness effects to simulations may provide some additional insight (e.g., Font et al. 2021). We conclude that observational effects are unlikely to fully explain the quenched fraction discrepancy reported here.

A second possibility is that the observed and simulated quenched fraction difference is simulation driven: in this scenario, the simulations overpredict the number of quenched satellites around MW analogs. The correspondence between APOSTLE and Auriga in Figures 3 and 4 as well as similar results from other simulations (Akins et al. 2021; Joshi et al. 2021) imply that the effect is somewhat model agnostic. This consistency is not necessarily predictable: while tides are relatively similar across simulation suites, the interstellar medium (ISM), star formation feedback-dependent physics, and hydrodynamical schemes producing the ram pressure that begins to dominate the quenching of 10⁷ ≲ M_*/M_⊙ ≲ 10⁸ satellites (Wetzel et al. 2015; Fillingham et al. 2016) are not (e.g., Agertz et al. 2007; Sijacki et al. 2012). Furthermore, Digby et al. (2019) find all intermediate-mass (10⁷ ≲ M_*/M_⊙ ≲ 10⁹) dwarfs in APOSTLE and Auriga have young (τ_form ≲ 6 Gyr ago) stellar populations. This suggests that any form of quenching in these satellites, as implied in this work, must have occurred recently and rapidly, consistent with previous similar investigations (e.g., Wetzel et al. 2015; Fillingham et al. 2016).

Whether or not the agreement between simulated quenched fractions presented here has a common physical origin or stems from a confluence of disparate effects with a similar net outcome is unclear. Nonetheless, it is plausible that the ISM gas densities simulated here with state-of-the-art resolution and star formation feedback physics in the simulations generically produce satellites that are less resilient to ram pressure stripping than in nature. A separate detailed study is required to determine if this mechanism quantitatively explains the discrepancy reported here (e.g., Bose et al. 2019; Digby et al. 2019).

We conclude that the dearth of observed quenched satellites relative to simulated ones in Figures 3 and 4 is not readily explained by vagaries in the samples considered here. There is apparently a genuine discrepancy between the satellite populations of the MW, M31, and their simulated analogs on the one hand and of the SAGA-ii host galaxies on the other. This highlights the fact that while the ability to reproduce the properties of the LG is a necessary feature of any complete model of galaxy formation and evolution, exclusive reliance on the LG as the benchmark for faint satellites risks introducing severe biases in the models. More detailed comparisons between observed and simulated satellites will further elucidate the origin of this discrepancy. This requires larger, more observationally complete samples that probe even further down the luminosity function (e.g Bennet et al. 2019; Carlsten et al. 2020), and large samples of simulated satellites (e.g., this work; Font et al. 2021; Joshi et al. 2021) at higher resolutions (e.g., Wetzel & Hopkins 2016; Wheeler et al. 2019) and self-consistent star-forming ISMs. Both will be available soon.

We thank the anonymous referee for their thoughtful and useful comments that helped improve this manuscript. K.S. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC). K.A.O. acknowledges support by the European Research Council (ERC) through Advanced Investigator grant to C.S. Frenk, DMIDAS (GA 786910). A.F. is supported by a UKRI Future Leaders Fellowship (grant no MR/T042362/1). The simulation used in this work used the DiRAC@Durham facility managed by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The equipment was funded by BEIS capital funding via STFC capital grants ST/K00042X/1, ST/P002293/1, ST/R002371/1, and ST/S002502/1; Durham University; and STFC operations grant ST/R000832/1. DiRAC is part of the National e-Infrastructure. D.J.S. acknowledges support from NSF grants AST-1821967 and 1813708. F.A.G. acknowledges financial support from CONICYT through the project FONDECYT Regular Nr. 1211370. F.A.G. acknowledges funding from the Max Planck Society through a Partner Group grant. F.M. acknowledges support through the Program "Rita Levi Montalcini" of the Italian MUR. B.M.P. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2001663.

This research made use of data from the SAGA Survey (sagasurvey.org). The SAGA Survey was supported by NSF collaborative grants AST-1517148 and AST-1517422 and by Heising-Simons Foundation grant 2019–1402.

The Legacy Surveys consist of three individual and complementary projects: the Dark Energy Camera Legacy Survey (DECaLS; NOAO Proposal ID # 2014B-0404; PIs: David Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Proposal ID # 2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy Survey (MzLS; NOAO Proposal ID # 2016A-0453; PI: Arjun Dey). DECaLS, BASS, and MzLS together include data obtained, respectively, at the Blanco telescope, Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory (NOAO); the Bok telescope, Steward Observatory, University of Arizona; and the Mayall telescope, Kitt Peak National Observatory, NOAO. The Legacy Surveys project is honored to be permitted to conduct astronomical research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation.

NOAO is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.

This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, and the Ministério da Ciência, Tecnologia e Inovações, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l'Espai (IEEC/CSIC), the Institut de Fisica d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universitat Munchen and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A&M University.

BASS is a key project of the Telescope Access Program (TAP), which has been funded by the National Astronomical Observatories of China, the Chinese Academy of Sciences (the Strategic Priority Research Program "The Emergence of Cosmological Structures" grant # XDB09000000), and the Special Fund for Astronomy from the Ministry of Finance. The BASS is also supported by the External Cooperation Program of the Chinese Academy of Sciences (grant # 114A11KYSB20160057), and the Chinese National Natural Science Foundation (grant # 11433005).

The Legacy Survey team makes use of data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by the National Aeronautics and Space Administration.

The Legacy Surveys imaging of the DESI footprint is supported by the Director, Office of Science, Office of High Energy Physics of the US Department of Energy under contract No. DE-AC02-05CH1123, by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract; and by the US National Science Foundation, Division of Astronomical Sciences under contract No. AST-0950945 to NOAO.

Software: astropy (Astropy Collaboration et al. 2013; Price-Whelan et al. 2018); Photutils (Bradley et al. 2020).

Facilities: GALEX - Galaxy Evolution Explorer satellite, DiRAC. -

To test our results for convergence with resolution, we consider five high-resolution (L1) volumes (10 hosts) from the APOSTLE simulations with m_DM ∼ 5 × 10⁴ M_⊙ and m_star ∼ 1 × 10⁴ M_⊙ and six high-resolution (Level 3) hosts from Auriga with m_DM ∼ 4 × 10⁴ M_⊙ and m_star ∼ 6 × 10³ M_⊙. The satellites in these sets of simulations are treated as in Section 2.2: subhalos are selected with SUBFIND, the SAGA-ii spatial selection criteria are applied, and all physical properties are defined identically.

We also test for any dependence on our star formation metric, i.e., SFR estimated from the gas particles/cells. We repeat our quenched fraction estimates using the SFR calculated based on the average number of star particles created over the last gigayear (SFR-1Gyr). This measure provides a more accurate estimate of a satellite's SFR compared to SFR derived from star particles on shorter timescales that are susceptible to shot noise given the time and particle resolutions in the simulations. However, this measure will lead to a marginally higher number of star-forming satellites relative to our fiducial as it will include satellites that may have ceased forming stars within the last gigayear.

The results of these tests are shown in Figure 5. The left column shows the quenched fractions as a function of stellar mass for the APOSTLE (top) and Auriga (bottom) samples using our fiducial SFR definition, i.e., . The shaded regions show the 68% confidence intervals and correspond to the total sample at the standard (filled; 229 APOSTLE satellites and 411 Auriga satellites), the subset simulated at higher resolution (diagonal hatched pattern; 123 APOSTLE satellites and 92 Auriga satellites), and the matching subset of volumes at the standard resolution (grid-hatched pattern; 98 APOSTLE satellites and 79 Auriga satellites). The right column of Figure 5 plots the same samples except using the alternative SFR based on the star particles, i.e. SFR_1Gyr > 0 M_⊙ yr⁻¹. In all four panels, we can see that the discrepancy in quenched fractions as a function of stellar mass, our primary result, remains between the observed and simulated samples at higher resolution and with an alternative star formation definition.

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