Dissipative SIDM: Halo Cooling & Collapse

• Dissipative SIDM is a class of dark matter models where self-interactions remove kinetic energy via inelastic transitions, fundamentally altering halo dynamics.
• Analytical studies and simulations show that even modest dissipative effects can accelerate halo core collapse and steepen density profiles on astrophysical timescales.
• Observational and numerical studies indicate that dSIDM yields distinct kinematic signatures and structural changes compared to elastic SIDM, offering new avenues for empirical constraints.

Dissipative self-interacting dark matter (dSIDM) is the class of self-interacting dark matter models in which dark matter collisions do not merely exchange momentum, but also remove kinetic energy from the halo through inelastic transitions or radiative processes. In astrophysical halos this adds an irreversible cooling channel to the conductive heat transport familiar from elastic SIDM, altering density profiles, velocity dispersion profiles, collapse timescales, shapes, and kinematics. Across semianalytical gravothermal models, isolated $N$-body calculations, cosmological baryonic zoom-ins, and recent microscopic treatments in the Born regime, the defining result is that dissipation can convert long-lived SIDM cores into rapidly contracting, cuspy, or collapsed inner halos on astrophysically short timescales (Essig et al., 2018, Huo et al., 2019, Shen et al., 2021, Lankester--Broche et al., 15 Sep 2025, Schmidt et al., 17 Jun 2026).

1. Definition and microscopic realizations

In dSIDM, the self-interaction is intrinsically non-conservative at the halo level: scattering redistributes momentum, but part of the center-of-momentum kinetic energy is lost to invisible dark radiation or to decay products that escape the halo. This distinguishes dSIDM from collisionless cold dark matter, which has neither heat transport nor dissipation, and from non-dissipative elastic SIDM, which thermalizes inner halos without net energy loss (Huo et al., 2019, Shen et al., 2021).

One explicit realization introduces two dark-sector states, $\chi$ and a slightly heavier $\chi'$. Elastic scattering $\chi\chi \to \chi\chi$ competes with inelastic up-scattering $\chi\chi \to \chi'\chi'$, and $\chi'$ is assumed to decay promptly into $\chi$ plus an invisible massless particle that escapes the halo. The inelastic channel is kinematically allowed only when

$$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$

with threshold velocity

$$v_\text{th}\equiv c\sqrt{\frac{2(m_{\chi'}-m_{\chi})}{m_\chi}}, \qquad v_\text{rel}>2v_\text{th},$$

and post-collision speed

$v_f=\sqrt{v_i^2-v_\text{th}^2}.$

In this parameterization, $\chi$0 simultaneously controls which particles can dissipatively scatter and how much energy is extracted when they do (Huo et al., 2019).

A second, deliberately phenomenological parameterization treats each collision as removing a fixed fraction of the center-of-momentum kinetic energy. In the FIRE-2 dSIDM simulations the model is specified by a self-interaction cross-section per unit mass $\chi$1 and a dimensionless dissipation fraction $\chi$2, with fiducial choice $\chi$3. The energy loss per unit mass is written as

$\chi$4

and the framework is studied for both constant and velocity-dependent cross sections (Shen et al., 2021, Shen et al., 2022).

A more microscopic formulation was developed in the Born regime for genuinely radiative $\chi$5 processes of the form

$\chi$6

the dark-sector analogue of Bremsstrahlung. That treatment considers six dissipative scenarios with vector or scalar emission, for distinguishable and identical scatterers, and derives closed-form energy-differential cross sections in the non-relativistic limit. The leading dipole emission amplitude is model-independent up to trivial prefactors for massless emission, while model dependence enters for massive emission and at next-to-leading order through quadrupole terms (Lankester--Broche et al., 15 Sep 2025).

2. Gravothermal evolution and thermodynamic structure

The central dynamical idea is the competition between gravitational contraction and collisional energy loss. As the inner halo loses energy, it becomes more bound and contracts; that contraction converts gravitational potential energy into kinetic energy and tends to heat the center. Dissipative self-interactions act in the opposite direction by removing kinetic energy whenever an inelastic or radiative event occurs. The resulting evolution is qualitatively different from standard elastic SIDM because the halo is not merely transporting heat internally; it is coupled to an energy sink (Huo et al., 2019).

Semianalytical gravothermal treatments organize the halo evolution into three stages: core expansion, self-similar collapse, and post-self-similar collapse. In the elastic case, core collapse often occurs only for very large cross sections or on timescales much longer than a Hubble time. With dissipation, however, even modest cooling can dramatically shorten collapse. A useful parameterization introduces a dissipative cross section $\chi$7 and an energy loss per collision $\chi$8, with associated “velocity loss”

$\chi$9

The collapse-time ratio

$\chi'$0

depends on $\chi'$1 and on the dimensionless $\chi'$2, and the strongest reduction occurs near $\chi'$3. In that regime the paper reports that dissipative scattering can shorten collapse by as much as a factor of $\chi'$4 (Essig et al., 2018).

Controlled isolated-halo simulations reach a closely related conclusion. For reasonable dissipative parameters, collapse times are shortened by a factor of $\chi'$5 relative to purely elastic SIDM, and the effect is maximized when the energy loss per collision is comparable to the characteristic kinetic energy of dark matter particles in the halo. In the Milky Way benchmark explored there, $\chi'$6 can produce collapse in much less than $\chi'$7, whereas the corresponding elastic collapse time is of order $\chi'$8 (Huo et al., 2019).

Recent dissipative frequent-small-angle SIDM calculations sharpen the thermodynamic picture further. They find that dissipation does not merely accelerate the elastic pathway; sufficiently strong central cooling can suppress isothermal-core formation altogether. The velocity-dispersion profile can retain a positive central gradient, so heat conduction remains directed inward throughout the evolution. Outer halo regions beyond the scale radius can cool efficiently rather than being heated by conduction, which enlarges the infall region and weakens the usual indentation between the core and the outer halo in the final density profile. These effects depend strongly on the cooling rate and are comparatively insensitive to the angular dependence of the self-interaction cross section (Schmidt et al., 17 Jun 2026).

This body of work rules out a common simplification: dSIDM collapse is not simply elastic gravothermal catastrophe with a larger effective cross section. In low-mass cosmological dwarfs, the inner cusp can instead be interpreted as a dissipation-driven inflow cusp. In the FIRE-2 study, once $\chi'$9, the slope asymptotes to $\chi\chi \to \chi\chi$0, explained as a dark matter “cooling flow” with $\chi\chi \to \chi\chi$1, rather than as the standard elastic gravothermal-collapse cusp (Shen et al., 2021).

3. Modeling frameworks and numerical methods

dSIDM has been studied with several complementary methodologies that encode dissipation differently but converge on the same qualitative phenomenon: irreversible energy loss steepens and contracts halo centers.

Framework	Dissipation variable	Representative application
Thresholded inelastic scattering	$\chi\chi \to \chi\chi$2, $\chi\chi \to \chi\chi$3	Isolated NFW halos in Gadget2 (Huo et al., 2019)
Fixed-fraction dissipation	$\chi\chi \to \chi\chi$4, $\chi\chi \to \chi\chi$5	Cosmological FIRE-2 dwarf zoom-ins (Shen et al., 2021)
Radiative Born-limit dSIDM	$\chi\chi \to \chi\chi$6 scalar/vector emission	Analytic energy-differential cross sections (Lankester--Broche et al., 15 Sep 2025)
Dissipative fSIDM	$\chi\chi \to \chi\chi$7-enhanced drag	Isolated halos and compact perturbers (Schmidt et al., 17 Jun 2026)

The semianalytical gravothermal fluid approach describes the halo in spherical symmetry through enclosed mass, hydrostatic equilibrium, and energy transport, with elastic interactions entering through conductivity and inelastic processes through a volumetric cooling term. It is solved numerically in dimensionless variables built from the NFW scale parameters $\chi\chi \to \chi\chi$8, using a Lagrangian shell method with $\chi\chi \to \chi\chi$9 log-spaced shells and iterative re-thermalization after each timestep (Essig et al., 2018).

The isolated $\chi\chi \to \chi'\chi'$0-body study of halo structure implemented a deterministic algorithm in Gadget2. It examined three benchmark halos initialized with NFW profiles: a dwarf halo with $\chi\chi \to \chi'\chi'$1, a Milky Way halo with $\chi\chi \to \chi'\chi'$2, and a cluster halo with $\chi\chi \to \chi'\chi'$3, each realized with $\chi\chi \to \chi'\chi'$4 particles; a Milky Way convergence test used $\chi\chi \to \chi'\chi'$5 particles. The principal diagnostics were density profiles $\chi\chi \to \chi'\chi'$6, velocity-dispersion profiles, and the time evolution of the average density within the inner $\chi\chi \to \chi'\chi'$7 (Huo et al., 2019).

The cosmological FIRE-2 program embedded dSIDM into baryonic zoom-ins with GIZMO, mesh-free Lagrangian hydrodynamics, metal-line and primordial cooling, UV background heating, star formation in dense self-gravitating molecular gas, and stellar feedback including supernovae, winds, radiation, and photoheating. That suite contains $\chi\chi \to \chi'\chi'$8 zoom-ins spanning ultra-faint dwarfs through Milky Way-mass halos, with the primary focus on dwarf galaxies of $\chi\chi \to \chi'\chi'$9 (Shen et al., 2021).

The latest algorithmic advance is the first extension of the frequent small-angle SIDM $\chi'$0-body formalism to include effective dissipation. In that framework dissipation enhances the effective drag by a factor $\chi'$1, reduces the timestep relative to the elastic case, and explicitly breaks energy conservation in a way consistent with radiative cooling. Comparison to a dissipative gravothermal fluid model shows good agreement on qualitative trends, while also identifying regimes where the fluid model underpredicts central densities or mischaracterizes the core-formation phase (Schmidt et al., 17 Jun 2026).

4. Halo structure, kinematics, and the role of baryons

In purely elastic SIDM, a benchmark cross section such as $\chi'$2 produces the familiar large constant-density core and nearly isothermal central velocity dispersion. Once dissipative scattering is turned on, the inner halo loses energy, the central velocity dispersion drops, and the density profile becomes much steeper than either the initial NFW cusp or the elastic SIDM core. For $\chi'$3, the fastest collapse occurs when $\chi'$4 is comparable to the characteristic halo velocity; in purely dissipative Milky Way runs with $\chi'$5, $\chi'$6 causes collapse to begin essentially immediately and the central density to rise monotonically (Huo et al., 2019).

The cosmological dwarf simulations generalize this result to live baryonic environments. A major threshold appears near

$\chi'$7

above which central density profiles become cuspy rather than cored. At higher effective interaction strengths the steepening saturates, and in low-mass dwarfs the inner slope approaches $\chi'$8. Below this threshold, baryonic feedback can still create core-like profiles, but the cores are smaller and the central density remains higher than in CDM. The same simulations show that once dissipation is strong enough, dark-matter self-interactions dominate over baryonic feedback: the full-physics and dark-matter-only dSIDM runs become very similar (Shen et al., 2021).

The baryonic response is not monotonic with interaction strength. In isolated dwarfs, moderate dissipation with $\chi'$9 makes galaxies more compact than in CDM and promotes stellar and neutral-gas disk formation, while remaining broadly consistent with observed dwarf size–mass relations. In the strongest dissipative case $\chi$0, halos develop coherent rotation and oblate shapes, the spherically measured central density normalization can drop, and the stellar component becomes fluffier or more extended (Shen et al., 2022).

High-cross-section dSIDM also has distinct kinematic signatures. For $\chi$1, the inner halo can develop coherent rotation with $\chi$2 in some galaxies, the velocity anisotropy parameter $\chi$3 drops below zero, and the halo becomes more oblate. The FIRE analysis emphasizes that these systems are not thin, baryon-like “dark disks”: in the explored parameter space the dissipation time remains much longer than the dynamical time, the system does not undergo rapid fragmentation, and the outcome is an oblate, rotating spheroid rather than a razor-thin rotationally supported disk (Shen et al., 2021).

5. Observational signatures and empirical constraints

The most direct empirical lever on dSIDM is the existence of galaxies whose inner dark-matter profiles remain cored. A semianalytical study calibrated to isolated and cosmological $\chi$4-body simulations used 18 dwarf and low-surface-brightness galaxies with core-like profiles and required the dissipative collapse time to satisfy

$\chi$5

For the benchmark elastic cross section $\chi$6, it found that roughly

$\chi$7

is disfavored, because such halos would have developed cusps too early (Essig et al., 2018).

Cosmological dwarf simulations convert the same logic into a direct structural bound. For $\chi$8, dSIDM models with constant cross-section $\chi$9 are effectively ruled out in bright dwarfs with $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$0 by circular-velocity constraints. In the same runs, isolated dwarfs with $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$1 show sub-kpc circular velocities enhanced by about a factor of two, still consistent with many Local Group stellar velocity dispersions but in tension with the H I rotation curves of more massive field dwarfs. The authors summarize the bright-dwarf constraint as

$$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$2

which for the fiducial $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$3 corresponds to roughly $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$4 at the relevant velocity scale (Shen et al., 2022).

The strongest signatures advocated for constraining dSIDM are therefore internal rather than global: inner density slopes, central density normalization, halo concentration, coherent rotation, tangential anisotropy, and halo flattening. In the FIRE-2 suite, halo masses and stellar masses do not show appreciable differences from CDM across much of the surveyed parameter space, whereas the internal structure and kinematics can differ sharply (Shen et al., 2021).

dSIDM has also been connected to compact strong-lensing perturbers. The recent dissipative fSIDM study compared evolved halos to the lensing-inferred masses of the perturber in JVAS B1938+666,

$$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$5

and found that both elastic and weakly dissipative SIDM halos can match the observed ratio over a broad range of scales. Dissipation changes the interpretation by allowing the halo to reach the compact, steep-profile state in roughly half the evolution time, or equivalently with a smaller self-interaction cross section than in the elastic case (Schmidt et al., 17 Jun 2026).

6. Relation to elastic SIDM and current scope of the literature

The dSIDM literature is best understood relative to the elastic SIDM baseline. Elastic SIDM in low-mass FIRE dwarfs with $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$6 produces robust central cores and density slopes $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$7, with much weaker sensitivity to baryonic feedback than in CDM (Robles et al., 2017). Elastic SIDM can also generate both cored and core-collapsed halos through gravothermal evolution, depending on concentration, tidal stripping, and halo history; this mechanism has been invoked to explain low-mass halo diversity and compact lens perturbers (Nadler et al., 2023, Ando et al., 17 Mar 2025). Those results are highly relevant analogues, but they do not introduce genuine dark-sector cooling.

This distinction matters because not every hidden-sector SIDM model with a light mediator is a dSIDM model. The PTA-motivated $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$8 construction that ties a MeV-scale mediator mass to a first-order phase transition is an elastic SIDM model with a dark Higgs and broken gauge symmetry rather than a model of explicit halo cooling (Han et al., 2023). Likewise, non-standard cosmology studies with light scalar or vector mediators address relic abundance and direct-detection viability for SIDM, but do not model dark-sector cooling, bound-state formation, or radiative halo dissipation (Dutta, 2023).

The current dSIDM program therefore spans three logically distinct layers. At the microscopic level, Born-regime calculations now provide energy-differential cross sections and energy-loss rates for radiative $$\frac{1}{4} m_\chi v_\text{rel}^2 > 2 (m_{\chi'}-m_\chi)c^2,$$9 processes, including the distinction between dipole- and quadrupole-dominated emission and between short-range and long-range mediation (Lankester--Broche et al., 15 Sep 2025). At the mesoscopic level, dissipative gravothermal fluid models and dissipative frequent-small-angle $$v_\text{th}\equiv c\sqrt{\frac{2(m_{\chi'}-m_{\chi})}{m_\chi}}, \qquad v_\text{rel}>2v_\text{th},$$0-body schemes connect cooling and conduction to evolving halo profiles (Essig et al., 2018, Schmidt et al., 17 Jun 2026). At the galaxy-formation level, FIRE-2 zoom-ins show how those processes appear once baryons, star formation, and feedback are present (Shen et al., 2021, Shen et al., 2022).

A consistent picture emerges across these approaches. dSIDM is not simply “SIDM with faster collapse,” nor is it generically a dark-disk scenario. Rather, it is the regime in which self-interactions endow dark matter halos with both heat transport and an explicit energy sink. That combination can preserve core-like structure when dissipation is weak, generate $$v_\text{th}\equiv c\sqrt{\frac{2(m_{\chi'}-m_{\chi})}{m_\chi}}, \qquad v_\text{rel}>2v_\text{th},$$1 cooling-flow cusps in low-mass dwarfs when dissipation is moderate, and produce accelerated collapse or compact perturbers when dissipation is strong enough but still slower than the free-fall time (Huo et al., 2019, Shen et al., 2021, Schmidt et al., 17 Jun 2026).