Concerto Suite: SIDM & CDM Simulations

• Concerto Suite is a robust compilation of 14 high-resolution, DM-only zoom-in simulations that contrast CDM and SIDM models across a broad range of host masses.
• It employs state-of-the-art numerical methods with MUSIC, modified Gadget-2, and Rockstar to ensure consistent halo identification and controlled comparisons across environments.
• The suite benchmarks SIDM predictions against observations by revealing key trends like ~50% subhalo mass function suppression and diverse inner density structures impacting strong lensing and stellar stream studies.

Concerto Suite, in the form released as SIDM Concerto, is a compilation and public data release of 14 high-resolution, cosmological DM-only zoom-in simulations run in cold dark matter (CDM) and self-interacting dark matter (SIDM) models. It pairs CDM with strong, velocity-dependent SIDM models across LMC-mass, Milky Way-mass, Group-mass, and low-mass cluster hosts at matched resolution, with each host resolved by approximately $2\times 10^7$ particles in the high-resolution region. The suite builds on the Symphony and Milky Way-est suites, unifies prior SIDM zoom-ins, and provides a benchmark for testing SIDM predictions with observations of field and satellite galaxies, strong lensing systems, and stellar streams (Nadler et al., 13 Mar 2025).

1. Composition and provenance

The suite consists of side-by-side CDM and SIDM realizations of six host systems, for a total of 14 zoom-ins. Each host is simulated in CDM and one or more SIDM variants, enabling controlled comparisons across host mass and cross-section model. The host sample covers roughly four decades in host mass, from an LMC-mass halo to a low-mass cluster (Nadler et al., 13 Mar 2025).

Host scale	Halo IDs and virial masses	Runs
LMC-mass	Halo104, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$	CDM; GroupSIDM
Milky Way analogs	Halo004, $M_{\rm vir}\approx 10^{12.0}\,M_\odot$; Halo416, $M_{\rm vir}\approx 10^{12.2}\,M_\odot$	Halo004: CDM; GroupSIDM; MilkyWaySIDM. Halo416: CDM; MilkyWaySIDM
Group-mass hosts	Halo352, $M_{\rm vir}\approx 10^{13.1}\,M_\odot$; Halo962, $M_{\rm vir}\approx 10^{13.5}\,M_\odot$	Halo352: CDM; GroupSIDM; GroupSIDM-70. Halo962: CDM; GroupSIDM-70
Low-mass cluster	Halo000, $M_{\rm vir}\approx 10^{14.2}\,M_\odot$	CDM; GroupSIDM

The compilation incorporates previously published SIDM zoom-ins and adds new hosts. The provenance identified for the suite includes MW Halo416 in MilkyWaySIDM (Yang et al. 2022), Group Halo352 in GroupSIDM (Nadler et al. 2023), and MW Halo004 in MilkyWaySIDM/CDM (COZMIC III; Nadler et al. 2024). Newly added systems are LMC Halo104 SIDM/CDM, Group Halo962 SIDM/CDM, and L-Cluster Halo000 SIDM/CDM (Nadler et al., 13 Mar 2025).

This organization makes the suite a unified comparative framework rather than a collection of isolated simulations. A plausible implication is that the design is intended to separate environmental effects from SIDM-model dependence by matching resolution and analysis methodology across host categories.

2. Numerical realization and SIDM parameterization

All runs are DM-only, with initial conditions generated with MUSIC and with gravity and SIDM scattering implemented in modified Gadget-2. The high-resolution region extends to a zoom size of approximately $10\,R_{\rm vir}$. For the LMC, MW, and Group suites, the adopted cosmology is $h=0.7$, $\Omega_m=0.286$, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$0, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$1, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$2; for the L-Cluster, it is $M_{\rm vir}\approx 10^{10.9}\,M_\odot$3, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$4, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$5, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$6, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$7. Virial quantities adopt the Bryan & Norman overdensity (Nadler et al., 13 Mar 2025).

The mass resolution and softening vary by host scale. The quoted values are $M_{\rm vir}\approx 10^{10.9}\,M_\odot$8, $M_{\rm vir}\approx 10^{10.9}\,M_\odot$9 for the LMC halo; $M_{\rm vir}\approx 10^{12.0}\,M_\odot$0, $M_{\rm vir}\approx 10^{12.0}\,M_\odot$1 for the MW halos; $M_{\rm vir}\approx 10^{12.0}\,M_\odot$2, $M_{\rm vir}\approx 10^{12.0}\,M_\odot$3 for the Group halos; and $M_{\rm vir}\approx 10^{12.0}\,M_\odot$4, $M_{\rm vir}\approx 10^{12.0}\,M_\odot$5 for the L-Cluster (Nadler et al., 13 Mar 2025).

The SIDM model is defined through an angular-dependent differential elastic scattering cross section,

$M_{\rm vir}\approx 10^{12.0}\,M_\odot$6

where $M_{\rm vir}\approx 10^{12.0}\,M_\odot$7 is the relative velocity, $M_{\rm vir}\approx 10^{12.0}\,M_\odot$8 is the scattering angle, $M_{\rm vir}\approx 10^{12.0}\,M_\odot$9 sets the amplitude, and $M_{\rm vir}\approx 10^{12.2}\,M_\odot$0 sets the transition velocity scale between the $M_{\rm vir}\approx 10^{12.2}\,M_\odot$1 and $M_{\rm vir}\approx 10^{12.2}\,M_\odot$2 regimes (Nadler et al., 13 Mar 2025).

The parameter choices in the suite are:

• GroupSIDM: $M_{\rm vir}\approx 10^{12.2}\,M_\odot$3, $M_{\rm vir}\approx 10^{12.2}\,M_\odot$4
• GroupSIDM-70: $M_{\rm vir}\approx 10^{12.2}\,M_\odot$5, $M_{\rm vir}\approx 10^{12.2}\,M_\odot$6
• MilkyWaySIDM: $M_{\rm vir}\approx 10^{12.2}\,M_\odot$7, $M_{\rm vir}\approx 10^{12.2}\,M_\odot$8

The effective cross section is described by the approximation

$M_{\rm vir}\approx 10^{12.2}\,M_\odot$9

The models were chosen so that subhalos and hosts at different mass scales probe different parts of $M_{\rm vir}\approx 10^{13.1}\,M_\odot$0, enabling both core formation in high-velocity environments and gravothermal core collapse in lower-velocity halos (Nadler et al., 13 Mar 2025).

3. Analysis pipeline, observables, and gravothermal classification

Halo identification and merger trees are produced uniformly with Rockstar + Consistent Trees. Subhalos are analyzed within $M_{\rm vir}\approx 10^{13.1}\,M_\odot$1 of the $M_{\rm vir}\approx 10^{13.1}\,M_\odot$2 host, while isolated halos are analyzed within $M_{\rm vir}\approx 10^{13.1}\,M_\odot$3 of each host, corresponding to high-resolution regions with negligible low-resolution contamination (Nadler et al., 13 Mar 2025).

The suite uses standard structural diagnostics. Circular velocity is defined by

$M_{\rm vir}\approx 10^{13.1}\,M_\odot$4

and

$M_{\rm vir}\approx 10^{13.1}\,M_\odot$5

The evolutionary diagnostic $M_{\rm vir}\approx 10^{13.1}\,M_\odot$6 is the maximum of $M_{\rm vir}\approx 10^{13.1}\,M_\odot$7 over a halo’s history. The inner density slope is

$M_{\rm vir}\approx 10^{13.1}\,M_\odot$8

measured via spline fits at $M_{\rm vir}\approx 10^{13.1}\,M_\odot$9, subject to the spatial resolution criterion $M_{\rm vir}\approx 10^{13.5}\,M_\odot$0 (Nadler et al., 13 Mar 2025).

The selection thresholds are explicit. Halo and subhalo abundances are analyzed for $M_{\rm vir}\approx 10^{13.5}\,M_\odot$1, with thresholds of $M_{\rm vir}\approx 10^{13.5}\,M_\odot$2, $M_{\rm vir}\approx 10^{13.5}\,M_\odot$3, $M_{\rm vir}\approx 10^{13.5}\,M_\odot$4, and $M_{\rm vir}\approx 10^{13.5}\,M_\odot$5 for the LMC, MW, Group, and L-Cluster hosts, respectively. Internal properties and profiles use $M_{\rm vir}\approx 10^{13.5}\,M_\odot$6, corresponding to $M_{\rm vir}\approx 10^{13.5}\,M_\odot$7, $M_{\rm vir}\approx 10^{13.5}\,M_\odot$8, $M_{\rm vir}\approx 10^{13.5}\,M_\odot$9, and $M_{\rm vir}\approx 10^{14.2}\,M_\odot$0 (Nadler et al., 13 Mar 2025).

The suite also uses a parametric SIDM gravothermal model. The dimensionless gravothermal time is

$M_{\rm vir}\approx 10^{14.2}\,M_\odot$1

where $M_{\rm vir}\approx 10^{14.2}\,M_\odot$2 is the formation time and $M_{\rm vir}\approx 10^{14.2}\,M_\odot$3 is the model-dependent core-collapse timescale. Objects are classified as core-forming for $M_{\rm vir}\approx 10^{14.2}\,M_\odot$4 and core-collapsed for $M_{\rm vir}\approx 10^{14.2}\,M_\odot$5; the model is calibrated up to $M_{\rm vir}\approx 10^{14.2}\,M_\odot$6 (Nadler et al., 13 Mar 2025).

The local SIDM kinetics used in the interpretation are

$M_{\rm vir}\approx 10^{14.2}\,M_\odot$7

and

$M_{\rm vir}\approx 10^{14.2}\,M_\odot$8

The collapse-timescale scaling is written as

$M_{\rm vir}\approx 10^{14.2}\,M_\odot$9

with $10\,R_{\rm vir}$0 (Nadler et al., 13 Mar 2025). In the $10\,R_{\rm vir}$1 regime, $10\,R_{\rm vir}$2 grows with mass; in the $10\,R_{\rm vir}$3 regime, it increases as mass decreases once the weak mass–concentration dependence is included.

4. Principal results across environments

A central result of the suite is a turnover in the core-collapsed fraction as a function of halo velocity scale, tied to the transition in $10\,R_{\rm vir}$4 from $10\,R_{\rm vir}$5 to $10\,R_{\rm vir}$6. In the GroupSIDM model, the core-collapsed fraction peaks around $10\,R_{\rm vir}$7 for isolated halos and around $10\,R_{\rm vir}$8 for subhalos. At lower velocities, where the effective cross section is in the constant regime, the fraction declines; bootstrap confidence bands indicate that this low-$10\,R_{\rm vir}$9 decline is statistically significant (Nadler et al., 13 Mar 2025).

The suite also quantifies suppression of the subhalo mass function (SHMF). In GroupSIDM, cumulative SHMFs evaluated with both present-day and peak mass show that subhalo abundances are suppressed by approximately 50% relative to CDM in LMC, MW, and Group hosts across the resolved mass range $h=0.7$0. The suppression is milder in MilkyWaySIDM and GroupSIDM-70, reflecting dependence on both the amplitude and transition velocity of $h=0.7$1. In the L-Cluster host, SIDM SHMFs are statistically consistent with CDM given Poisson uncertainties, with a hint of a slight overabundance in SIDM at the highest subhalo masses (Nadler et al., 13 Mar 2025).

Inner density structure is substantially more diverse in SIDM than in CDM. In LMC, MW, and Group hosts, many surviving SIDM subhalos are in or near collapse, showing $h=0.7$2 cores interior to $h=0.7$3, while others remain cored with $h=0.7$4 out to $h=0.7$5. The distribution of inner slopes $h=0.7$6 is significantly shifted relative to CDM. GroupSIDM yields more negative slopes in LMC, MW, and Group hosts and shallower slopes in the L-Cluster, in agreement with the $h=0.7$7–$h=0.7$8 shifts. Two-sample KS tests confirm significant differences between SIDM and CDM slope distributions, with p-values ranging from $h=0.7$9 down to $\Omega_m=0.286$0 depending on host (Nadler et al., 13 Mar 2025).

Additional structural diagnostics are consistent with mixed populations of cored and collapsed objects. The $\Omega_m=0.286$1–$\Omega_m=0.286$2 relations show larger scatter in SIDM than in CDM at all host masses. In lower-mass hosts, many subhalos shift toward higher $\Omega_m=0.286$3 and smaller $\Omega_m=0.286$4, consistent with collapse; in the L-Cluster, they shift toward lower $\Omega_m=0.286$5 and larger $\Omega_m=0.286$6, consistent with core formation. The suite further attributes enhanced differences in subhalo–host interactions at MW and Group scales to host–subhalo encounter velocities probing $\Omega_m=0.286$7 regimes for $\Omega_m=0.286$8 (Nadler et al., 13 Mar 2025).

5. Observational interfaces and strong-lensing applications

The suite was constructed as a bridge between SIDM microphysics and astrophysical observables. The released analysis identifies implications for field and satellite galaxy kinematics, strong lensing substructure, and stellar stream perturbations. Diverse central densities, including both cores and collapsed cusps, are mapped onto the observed diversity of dwarf rotation curves and MW satellite dispersions. The approximately 50% SHMF suppression at MW and Group scales, together with the emergence of extremely dense collapsed subhalos, is linked to lensing flux-ratio statistics, gravitational imaging, and dense substructures such as the SDSSJ0946+1006 perturber. The presence of highly compact collapsed SIDM subhalos is also identified as a natural explanation for dense stream perturbers such as GD-1, with the LMC–MW environment specifically supporting predictions for stream–subhalo interactions enhanced near the Clouds (Nadler et al., 13 Mar 2025).

A dedicated follow-up study, "Strong Lensing Perturbers from the SIDM Concerto Suite", uses Concerto to examine the projected properties most relevant for gravitational imaging, especially the projected enclosed mass

$\Omega_m=0.286$9

and the projected inner slope

$M_{\rm vir}\approx 10^{10.9}\,M_\odot$00

evaluated by averaging between $M_{\rm vir}\approx 10^{10.9}\,M_\odot$01. That study analyzes Group, MW, and LMC hosts, generates 1000 random orientations per subhalo, and emphasizes that SIDM halos evolve continuously through core-expansion and core-collapse phases, whereas CDM inner profiles remain nearly static after formation (Kong et al., 1 Oct 2025).

The lensing analysis identifies several concrete correspondences between simulated SIDM subhalos and observed low-mass perturbers. For SDSS J0946+1006, CDM subhalos rarely reach the inferred steep projected slope, while SIDM produces broad $M_{\rm vir}\approx 10^{10.9}\,M_\odot$02 distributions that encompass $M_{\rm vir}\approx 10^{10.9}\,M_\odot$03, and several core-collapsed SIDM subhalos have both high $M_{\rm vir}\approx 10^{10.9}\,M_\odot$04 at 1 kpc and $M_{\rm vir}\approx 10^{10.9}\,M_\odot$05 near $M_{\rm vir}\approx 10^{10.9}\,M_\odot$06. For JVAS B1938+666, the higher-resolution LMC zoom-in shows that deeply collapsed SIDM field halos can reach central densities consistent with the inferred perturber, although the analysis explicitly notes that CDM cannot be ruled out because of resolution and extrapolation systematics. For SDP.81, many core-collapsed SIDM subhalos reach inner densities and slopes comparable to the originally inferred pseudo-Jaffe-like perturber, but the comparison is treated as conditional because a recent re-analysis did not confirm a subhalo detection. For SPT2147−50, CDM subhalos with $M_{\rm vir}\approx 10^{10.9}\,M_\odot$07 often match the NFW perturber with median concentration, while in SIDM most subhalos in this mass range are still core-forming at $M_{\rm vir}\approx 10^{10.9}\,M_\odot$08, although some lower-mass $M_{\rm vir}\approx 10^{10.9}\,M_\odot$09 SIDM subhalos are already deeply collapsed (Kong et al., 1 Oct 2025).

These results give strong lensing a specific role in the Concerto framework: it directly probes projected mass on kiloparsec and sub-kiloparsec scales, where SIDM gravothermal evolution produces either shallow cores at early times or compact collapsed centers at later times. A plausible implication is that the redshift evolution of $M_{\rm vir}\approx 10^{10.9}\,M_\odot$10 and $M_{\rm vir}\approx 10^{10.9}\,M_\odot$11, together with the presence or absence of early collapsed cores, constrains the turnover velocity $M_{\rm vir}\approx 10^{10.9}\,M_\odot$12 and the amplitude $M_{\rm vir}\approx 10^{10.9}\,M_\odot$13.

6. Data products, usage, limitations, and position within SIDM simulation programs

The public data release is archived at https://doi.org/10.5281/zenodo.14933624. Included products are particle snapshots in Gadget-2 format for CDM and SIDM runs; halo catalogs and merger trees produced with Rockstar and Consistent Trees; derived structure measurements such as density profiles and spline-fit inner slopes; parametric gravothermal model outputs including $M_{\rm vir}\approx 10^{10.9}\,M_\odot$14 and core-forming/core-collapsed flags; and metadata describing cosmology, initial conditions, resolution, and run configuration (Nadler et al., 13 Mar 2025).

The recommended workflow is explicit. Snapshots are to be read with pynbody; halo catalogs and trees are to be parsed with standard Rockstar/CT readers; and numerical analysis can be performed with NumPy/SciPy. A modified Symfind subhalo tracker is provided at https://github.com/DemaoK/Concerto. Best practices include respecting the convergence criterion $M_{\rm vir}\approx 10^{10.9}\,M_\odot$15, evaluating inner slopes at $M_{\rm vir}\approx 10^{10.9}\,M_\odot$16, deriving $M_{\rm vir}\approx 10^{10.9}\,M_\odot$17 from $M_{\rm vir}\approx 10^{10.9}\,M_\odot$18 histories in the merger trees, and using the released $M_{\rm vir}\approx 10^{10.9}\,M_\odot$19 thresholds for gravothermal classification (Nadler et al., 13 Mar 2025).

The suite’s limitations are also explicit. It is DM-only, so baryonic processes are not included; central potentials and feedback can alter SIDM-only predictions. Finite spatial resolution limits the interpretation of sub-kiloparsec cores and of $M_{\rm vir}\approx 10^{10.9}\,M_\odot$20 near $M_{\rm vir}\approx 10^{10.9}\,M_\odot$21. Deep collapse can be sensitive to energy-conservation systematics in N-body SIDM scattering, and the predictions likely under-estimate the abundance of the deepest collapsed objects. In strongly stripped or collapsed regimes, Consistent Trees and particle-tracking Symfind may differ, so cross-checks are recommended (Nadler et al., 13 Mar 2025).

Within the broader simulation landscape, Concerto complements Symphony and Milky Way-est by spanning four decades in host mass with a unified pipeline and consistent resolution strategy, and by operating at one resolution level higher than the fiducial suites to robustly capture core collapse in low-mass subhalos. It adds a controlled demonstration of the turnover in the core-collapsed fraction versus halo velocity scale, quantifies the approximately 50% SHMF suppression in LMC, MW, and Group hosts for strong SIDM, and makes those results available as a public, analysis-ready resource. Natural extensions identified for the program are hydrodynamic resimulations, expanded host samples, and combined studies of controlled high-resolution subhalo evolution with Concerto merger trees (Nadler et al., 13 Mar 2025).