---
title: 'Concerto Suite: SIDM & CDM Simulations'
url: https://www.emergentmind.com/topics/concerto-suite
type: topic
---

# Concerto Suite: SIDM & CDM Simulations

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 [2503.10748].

## 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** [2503.10748].

| 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** [2503.10748].

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 **$h=0.7$, $\Omega_m=0.286$, $\Omega_\Lambda=0.714$, $\sigma_8=0.82$, $n_s=0.96$**; for the L-Cluster, it is **$h=0.7$, $\Omega_m=0.3$, $\Omega_\Lambda=0.7$, $\sigma_8=0.85$, $n_s=0.96$**. Virial quantities adopt the **Bryan & Norman overdensity** [2503.10748].

The mass resolution and softening vary by host scale. The quoted values are **$m_{\rm part}=6.3\times 10^3\,M_\odot$, $\epsilon=40\,{\rm pc}\ h^{-1}$** for the LMC halo; **$m_{\rm part}=5.0\times 10^4\,M_\odot$, $\epsilon=80\,{\rm pc}\ h^{-1}$** for the MW halos; **$m_{\rm part}=4.0\times 10^5\,M_\odot$, $\epsilon=170\,{\rm pc}\ h^{-1}$** for the Group halos; and **$m_{\rm part}=2.7\times 10^7\,M_\odot$, $\epsilon=600\,{\rm pc}\ h^{-1}$** for the L-Cluster [2503.10748].

The SIDM model is defined through an angular-dependent differential elastic scattering cross section,
$$
\frac{{\rm d}\sigma}{{\rm d}\cos\theta}
=
\frac{\sigma_0\,w^4}{2\left[w^2+v^2\sin^2(\theta/2)\right]^2},
$$
where $v$ is the relative velocity, $\theta$ is the scattering angle, $\sigma_0$ sets the amplitude, and $w$ sets the transition velocity scale between the **$v^{-4}$** and **$v^0$** regimes [2503.10748].

The parameter choices in the suite are:

- **GroupSIDM**: $\sigma_0/m = 147.1~{\rm cm}^2\,{\rm g}^{-1}$, $w=120~{\rm km\,s}^{-1}$  
- **GroupSIDM-70**: $\sigma_0/m = 70~{\rm cm}^2\,{\rm g}^{-1}$, $w=120~{\rm km\,s}^{-1}$  
- **MilkyWaySIDM**: $\sigma_0/m = 147.1~{\rm cm}^2\,{\rm g}^{-1}$, $w=24.3~{\rm km\,s}^{-1}$

The effective cross section is described by the approximation
$$
\left(\frac{\sigma_{\rm eff}}{m}\right)(v)\simeq
\begin{cases}
\sigma_0/m, & v\lesssim v_{\rm trans}\simeq w,\\[4pt]
(\sigma_0/m)\,(w/v)^4, & v\gtrsim v_{\rm trans}\simeq w.
\end{cases}
$$
The models were chosen so that subhalos and hosts at different mass scales probe different parts of $\sigma_{\rm eff}(v)$, enabling both **core formation in high-velocity environments** and **gravothermal core collapse in lower-velocity halos** [2503.10748].

## 3. Analysis pipeline, observables, and gravothermal classification

Halo identification and merger trees are produced uniformly with **Rockstar + Consistent Trees**. Subhalos are analyzed within **$R_{\rm vir}$ of the $z=0$ host**, while isolated halos are analyzed within **$10\,R_{\rm vir}$** of each host, corresponding to high-resolution regions with negligible low-resolution contamination [2503.10748].

The suite uses standard structural diagnostics. Circular velocity is defined by
$$
V_{\rm circ}(r)=\sqrt{\frac{G\,M(<r)}{r}},
$$
and
$$
V_{\max}=\max_r\,V_{\rm circ}(r).
$$
The evolutionary diagnostic **$V_{\rm peak}$** is the maximum of $V_{\max}(t)$ over a halo’s history. The inner density slope is
$$
\alpha(r)\equiv \frac{{\rm d}\ln\rho}{{\rm d}\ln r},
$$
measured via spline fits at **$r=0.02\,R_{\rm vir}$**, subject to the spatial resolution criterion **$r\geq 2.8\epsilon$** [2503.10748].

The selection thresholds are explicit. Halo and subhalo abundances are analyzed for **$M_{\rm vir}(z=0)>300\,m_{\rm part}$**, with thresholds of **$1.9\times 10^6\,M_\odot$**, **$1.5\times 10^7\,M_\odot$**, **$1.2\times 10^8\,M_\odot$**, and **$8.1\times 10^9\,M_\odot$** for the LMC, MW, Group, and L-Cluster hosts, respectively. Internal properties and profiles use **$M_{\rm vir}(z=0)>2000\,m_{\rm part}$**, corresponding to **$1.3\times 10^7\,M_\odot$**, **$1\times 10^8\,M_\odot$**, **$8\times 10^8\,M_\odot$**, and **$5.4\times 10^{10}\,M_\odot$** [2503.10748].

The suite also uses a parametric SIDM gravothermal model. The dimensionless gravothermal time is
$$
\tau_0=\int_{t_f}^{t_0}\frac{{\rm d}t}{t_c(t)},
\qquad t_0=13.6~{\rm Gyr},
$$
where $t_f$ is the formation time and $t_c(t)$ is the model-dependent core-collapse timescale. Objects are classified as **core-forming** for **$\tau_0<0.15$** and **core-collapsed** for **$\tau_0>0.75$**; the model is calibrated up to **$\tau_0\lesssim 1.1$** [2503.10748].

The local SIDM kinetics used in the interpretation are
$$
\Gamma(r)=\rho(r)\left(\frac{\sigma_{\rm eff}}{m}\right)v(r),
\qquad
\lambda(r)=\left[\rho(r)\left(\frac{\sigma_{\rm eff}}{m}\right)\right]^{-1},
$$
and
$$
t_{\rm relax}(r)\sim \frac{1}{\rho(r)(\sigma_{\rm eff}/m)\,v(r)}.
$$
The collapse-timescale scaling is written as
$$
t_c \propto
\left(\frac{\sigma_0}{m}\right)^{-1}
M^{(n-1)/3}c^{(n-7)/2},
$$
with $\sigma_{\rm eff}/m\propto v^{-n}$ [2503.10748]. In the **$n=4$** regime, $t_c$ grows with mass; in the **$n=0$** 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 $\sigma_{\rm eff}/m(v)$ from **$v^{-4}$** to **$v^0$**. In the **GroupSIDM** model, the core-collapsed fraction peaks around **$V_{\rm peak}\approx 30~{\rm km\,s}^{-1}$** for isolated halos and around **$V_{\rm peak}\approx 60~{\rm km\,s}^{-1}$** 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-$V_{\rm peak}$ decline is statistically significant [2503.10748].

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 **$M_{\rm vir}\gtrsim 300\,m_{\rm part}$**. The suppression is milder in **MilkyWaySIDM** and **GroupSIDM-70**, reflecting dependence on both the amplitude and transition velocity of $\sigma_{\rm eff}/m(v)$. 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 [2503.10748].

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 **$\rho\propto r^{-2}$** cores interior to **$\sim 0.02\,R_{\rm vir}$**, while others remain cored with **$\rho\sim r^0$** out to **$\sim 0.1\,R_{\rm vir}$**. The distribution of inner slopes **$\alpha(0.02\,R_{\rm vir})$** 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 **$R_{\max}$–$V_{\max}$** shifts. Two-sample KS tests confirm significant differences between SIDM and CDM slope distributions, with p-values ranging from **$\lesssim 0.07$ down to $<10^{-5}$** depending on host [2503.10748].

Additional structural diagnostics are consistent with mixed populations of cored and collapsed objects. The **$R_{\max}$–$V_{\max}$** relations show larger scatter in SIDM than in CDM at all host masses. In lower-mass hosts, many subhalos shift toward **higher $V_{\max}$ and smaller $R_{\max}$**, consistent with collapse; in the L-Cluster, they shift toward **lower $V_{\max}$ and larger $R_{\max}$**, 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 **$\mathcal{O}(1{-}10)\,{\rm cm}^2\,{\rm g}^{-1}$** regimes for $\sigma_{\rm eff}/m$ [2503.10748].

## 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 [2503.10748].

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**
$$
M_{2D}(<R)=\int_0^R 2\pi R'\Sigma(R')\,{\rm d}R'
$$
and the projected inner slope
$$
\gamma_{2D}(R)=\frac{{\rm d}\ln \Sigma(R)}{{\rm d}\ln R},
$$
evaluated by averaging between **$R=1\pm 0.25~{\rm kpc}$**. 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 [2510.01491].

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 $\gamma_{2D}$ distributions that encompass **$\gamma_{2D}\approx -2$**, and several core-collapsed SIDM subhalos have both high **$M_{2D}$ at 1 kpc** and **$\gamma_{2D}$ near $-2$**. 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 **$M_{\rm vir}>5\times 10^9\,M_\odot$** often match the NFW perturber with median concentration, while in SIDM most subhalos in this mass range are still core-forming at **$z\approx 0.85$**, although some lower-mass **$\sim 10^9\,M_\odot$** SIDM subhalos are already deeply collapsed [2510.01491].

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 **$\gamma_{2D}$** and **$M_{2D}$**, together with the presence or absence of early collapsed cores, constrains the turnover velocity **$w$** and the amplitude **$\sigma_0/m$**.

## 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 **$\tau_0$** and core-forming/core-collapsed flags; and metadata describing cosmology, initial conditions, resolution, and run configuration [2503.10748].

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 **$r\geq 2.8\epsilon$**, evaluating inner slopes at **$r=0.02\,R_{\rm vir}$**, deriving **$V_{\rm peak}$** from **$V_{\max}(t)$** histories in the merger trees, and using the released **$\tau_0$** thresholds for gravothermal classification [2503.10748].

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 **$R_{\max}$** near **$r\sim 2.8\epsilon$**. 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 [2503.10748].

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 [2503.10748].

Source: https://www.emergentmind.com/topics/concerto-suite