Constraining Dissipative Dark Matter Self-Interactions

We study the gravothermal evolution of dark matter halos in the presence of dissipative dark matter self-interactions. Dissipative interactions are present in many particle-physics realizations of the dark-sector paradigm and can significantly accelerate the gravothermal collapse of halos compared to purely elastic dark matter self-interactions. This is the case even when the dissipative interaction timescale is longer than the free-fall time of the halo. Using a semianalytical fluid model calibrated with isolated and cosmological $N$-body simulations, we calculate the evolution of the halo properties—including its density profile and velocity dispersion profile—as well as the core-collapse time as a function of the particle model parameters that describe the interactions. A key property is that the inner density profile at late times becomes cuspy again. Using 18 dwarf galaxies that exhibit a corelike dark matter density profile, we derive constraints on the strength of the dissipative interactions and the energy loss per collision.

Figure 1

The evolution of the density profiles for an SIDM halo, LSB F583-1, assuming purely elastic DM self-interactions (“no cooling,” blue) and self-interactions with an additional dissipative interaction (“with cooling,” red). Numbers show the Knudsen number for the innermost shell at a given time. We project the evolution of the density of the innermost shell on to the $\rho -t$ plane and mark the separation of stages $1\to 2$ and $2\to 3$ with diamond and star, respectively. We take $\beta =0.60$.

Figure 2

Left: Dimensionless collapse time ${\widehat{t}}_c$ multiplied by $\beta$ as a function of $\widehat{\sigma }$ when cooling is absent with $\beta =0.75$ (black), 0.60 (blue), and 0.45 (gray). We also show the results recasted from $N$-body simulations [49] and fluid-model predictions [50], where $\beta =0.75$ were used. In this work, we focus on $\widehat{\sigma }\le {10}^{-1}$ (solid). Right: Ratio of the collapse time, $\xi \equiv t_c^{\prime }/t_c$, as a function of ${\widehat{\nu }}_{\mathrm{loss}}$ for different values of ${\sigma }^{\prime }/(\beta \sigma )$, where we take $\widehat{\sigma }={10}^{-2}$ with $\beta =0.60$. For the range of $\widehat{\sigma }={10}^{-4}–{10}^{-1}$ we have checked, ${\sigma }^{\prime }/(\beta \sigma )$ well characterizes the $\xi -{\widehat{\nu }}_{\mathrm{loss}}$ relation.

Figure 3

Constraints on the dissipative parameters from the absence of core collapse in individual dwarf galaxies (yellow) within 10 Gyr and its overall boundary for the sample (purple). We take the fitted halo parameters of the galaxies from Ref. [33], also listed in the Supplemental Material [42] and labeled for the outer ones, and $\beta =0.60$ in our fluid simulations. See text for detailed discussion on LSB F583-1 (gray) and the four benchmark cases (marked with numbers). We focus on the ${\sigma }^{\prime }/\sigma \le 1$ region, where the fluid model is applicable.