Velocity Dependence Of Cross Sections Research Articles

Dianoga SIDM: Galaxy cluster self-interacting dark matter simulations

Context. Self-interacting dark matter (SIDM) can tackle or alleviate small-scale issues within the cosmological standard model ΛCDM, and diverse flavours of SIDM can produce unique astrophysical predictions, resulting in different possible signatures which can be used to test these models with dedicated observations of galaxy clusters. Aims. This work aims to assess the impact of dark matter self-interactions on the properties of galaxy clusters. In particular, the goal is to study the angular dependence of the cross section by testing rare (large angle scattering) and frequent (small angle scattering) SIDM models with velocity-dependent cross sections. Methods. We re-simulated six galaxy cluster zoom-in initial conditions with a dark matter-only run and with full-physics set-up simulations that include a self-consistent treatment of baryon physics. We tested the dark matter-only setup and the full physics setup with the collisionless cold dark matter, rare self-interacting dark matter, and frequent self-interacting dark matter models. We then studied their matter density profiles as well as their subhalo population. Results. Our dark matter-only SIDM simulations agree with theoretical models, and when baryons are included in simulations, our SIDM models substantially increase the central density of galaxy cluster cores compared to full-physics simulations using collisionless dark matter. SIDM subhalo suppression in full-physics simulations is milder compared to the one found in the dark matter-only simulations because of the cuspier baryonic potential that prevents subhalo disruption. Moreover, SIDM with small-angle scattering significantly suppresses a larger number of subhaloes compared to large-angle scattering SIDM models. Additionally, SIDM models generate a broader range of subhalo concentration values, including a tail of more diffuse subhaloes in the outskirts of galaxy clusters and a population of more compact subhaloes in the cluster cores.

Simulations of galaxy cluster mergers with velocity-dependent, rare, and frequent self-interactions

ABSTRACT Self-interacting dark matter (SIDM) has been proposed to solve small-scale problems in $\rm {\Lambda CDM}$ cosmology. In previous work, constraints on the self-interaction cross-section of dark matter have been derived assuming that the self-interaction cross-section is independent of velocity. However, a velocity-dependent cross-section is more natural in most theories of SIDM. Using idealized N-body simulations without baryons, we study merging clusters with velocity-dependent SIDM. In addition to the usual rare scattering in the isotropic limit, we also simulate these systems with anisotropic, small-angle (frequent) scatterings. We find that the collisionless brightest cluster galaxy (BCG) has an offset from the DM peak that grows at later stages. Finally, we also extend the existing upper bounds on the velocity-independent, isotropic self-interaction cross-section to the parameter space of rare and frequent velocity-dependent self-interactions by studying the central densities of dark matter-only isolated haloes. For these upper-bound parameters, the DM-BCG offsets just after the first pericentre in the dark matter-only simulations are found to be ≲10 kpc. On the other hand, because of BCG oscillations, we speculate that the distribution of BCG offsets in a relaxed cluster is a statistically viable probe. Therefore, this motivates further studies of BCG off-centring in hydrodynamic cosmological simulations.

Cosmological and idealized simulations of dark matter haloes with velocity-dependent, rare and frequent self-interactions

ABSTRACT Dark matter self-interactions may have the capability to solve or at least mitigate small-scale problems of the cosmological standard model, Lambda cold dark matter. There are a variety of self-interacting dark matter models that lead to distinguishable astrophysical predictions and hence varying success in explaining observations. Studies of dark matter (DM) density cores on various mass scales suggest a velocity-dependent scattering cross-section. In this work, we investigate how a velocity dependence alters the evolution of the DM distribution for frequent DM scatterings and compare to the velocity-independent case. We demonstrate that these cases are qualitatively different using a test problem. Moreover, we study the evolution of the density profile of idealized DM haloes and find that a velocity dependence can lead to larger core sizes and different time-scales of core formation and core collapse. In cosmological simulations, we investigate the effect of velocity-dependent self-interaction on haloes and satellites in the mass range of ≈1011–$10^{14} \, \mathrm{M_\odot }$. We study the abundance of satellites, density, and shape profiles and try to infer qualitative differences between velocity-dependent and velocity-independent scatterings as well as between frequent and rare self-interactions. We find that a strongly velocity-dependent cross-section can significantly amplify the diversity of rotation curves, independent of the angular dependence of the differential cross-section. We further find that the abundance of satellites in general depends on both the velocity dependence and the scattering angle, although the latter is less important for strongly velocity-dependent cross-sections.

Universal gravothermal evolution of isolated self-interacting dark matter halos for velocity-dependent cross-sections

ABSTRACT We study the evolution of isolated self-interacting dark matter halos using spherically symmetric gravothermal equations allowing for the scattering cross-section to be velocity dependent. We focus our attention on the large class of models where the core is in the long mean free path regime for a substantial time. We find that the temporal evolution exhibits an approximate universality that allows velocity-dependent models to be mapped onto velocity-independent models in a well-defined way using the scattering time-scale computed when the halo achieves its minimum central density. We show how this time-scale depends on the halo parameters and an average cross-section computed at the central velocity dispersion when the central density is minimum. The predicted collapse time is fully defined by the scattering time-scale, with negligible variation due to the velocity dependence of the cross-section. We derive new self-similar solutions that provide an analytic understanding of the numerical results.

XQC and CSR constraints on strongly interacting dark matter with spin and velocity dependent cross sections

Dark matter that interacts strongly with baryons can avoid the stringent dark matter direct detection constraints, because, like baryons, they are likely to be absorbed when traversing the rocks, leading to a suppressed flux in deep underground labs. Such strongly interacting dark matter, however, can be probed by dark matter experiments or other experiments operated on the ground level or in the atmosphere. In this paper we carry out systematic analysis of two of these experiments, XQC and CSR, to compute the experimental constraints on the strongly interacting dark matter in the following three scenarios: (1) spin-independent and spin-dependent interactions; (2) different velocity dependent cross sections; (3) different dark matter mass fractions. Some of the scenarios are first analyzed in the literature. We find that the XQC exclusion region has some non-trivial dependencies on the various parameters and the limits in the spin-dependent case is quite different from the spin-independent case. A peculiar region in the parameter space, where the XQC constraint disappears, is also found in our Monte Carlo simulations. This occurs in the case where the interaction cross section is proportional to the square of the velocity. We further compare our XQC and CSR limits to other experimental constraints, and find that a large parameter space is allowed by various experiments if the dark matter mass fraction is sufficiently small, fχ ≲ 10-4.

Gravothermal Solutions of SIDM Halos: Mapping from Constant to Velocity-dependent Cross Section

The scale-free gravothermal fluid formalism has long proved effective in describing the evolution of self-interacting dark matter halos with a constant dark matter particle cross section. However, whether the gravothermal fluid solutions match numerical simulations for velocity-dependent cross-section scenarios remains untested. In this work, we provide a fast mapping method that relates the constant-cross-section gravothermal solution to models with arbitrary velocity dependence in the cross section. We show that the gravothermal solutions after mapping are in good agreement with Arepo N-body simulation results. We illustrate the power of this approach by applying this fast mapping method to a halo hosting a low-surface-brightness galaxy, UGC 128. We show that this fast mapping method can be used to constrain free parameters in a physically motivated cross-section model and illustrate the parameter space favored by the rotation curve measurement.

Orbital evolution of satellite galaxies in self-interacting dark matter models

Dark matter self-interactions can leave distinctive signatures on the properties of satellite galaxies around Milky Way--like hosts through their impact on tidal stripping, ram pressure, and gravothermal collapse. We delineate the regions of self-interacting dark matter parameter space---specified by interaction cross section and a velocity scale---where each of these effects dominates and show how the relative mass loss depends on the satellite's initial mass, density profile, and orbit. We obtain novel, conservative constraints in this parameter space using Milky Way satellite galaxies with notably high central densities and small pericenter distances. Our results for self-interacting dark matter models, in combination with constraints from clusters of galaxies, favor either velocity-dependent cross sections that lead to gravothermal core collapse in the densest satellites or small cross sections which more closely resemble cold and collisionless dark matter.

Matching the mass function of Milky Way satellites in competing dark matter models

ABSTRACT Any successful model of dark matter must explain the diversity of observed Milky Way (MW) satellite density profiles, from very dense ultrafaints to low-density satellites so large that they could be larger than their inferred dark matter haloes. Predictions for these density profiles are complicated by the limitations of simulation resolution in the stripping of subhaloes by the MW system. We consider cold dark matter (CDM), warm dark matter (WDM, 3.3 keV thermal relic power spectrum), and a self-interacting dark matter model (SIDM) that induces gravothermal collapse in low-mass subhaloes. Using N-body simulations combined with a halo stripping algorithm, we find that most CDM and WDM subhaloes of mass >108 ${\, \rm M_\odot }$ are large enough after stripping to fit most satellites; however, the required amount of stripping often requires a stronger tidal field than is available on the subhalo’s orbit. The lower concentrations of WDM subhaloes enable more stripping to take place, even on orbits with large pericentres. SIDM cores offer the best fits to massive, low-density satellites at the expense of predicting >109 ${\, \rm M_\odot }$ subhaloes to host low-density satellites with no observed analogue. The agreement of the total number of satellites with observations in CDM and WDM depends strongly on the assumptions made to draw the observational estimates. We conclude that an SIDM model must have a very high velocity-dependent cross-section in order to match all satellites, and that WDM offers a marginally better fit than CDM to the MW satellite mass function.

Ion-molecule charge exchange in Io's extended atmosphere: Velocity dependence

The Io plasma torus is mostly composed of electrons and ions of O and S, singly and multiply-charged. These ions interact with the neutral species of Io's atmosphere (S, O, SO2 and SO) through symmetrical (e.g., O+ + O ⇒ O + O+) and asymmetrical (e.g., S+ + O ⇒ S + O+) charge exchange reactions. Moreover, molecular ions (SO2+, SO+) produced in Io's atmosphere by ionization or charge exchange are accelerated as they are picked up by the local plasma flow and eventually also charge exchange with the atmospheric neutrals (e.g., SO2+ + SO2 ⇒ SO2 + SO2+).Cross sections for many charge exchange reactions were estimated in Johnson and Strobel (1982) and McGrath and Johnson (1989) for ion speeds of 60 km/s appropriate for torus/neutral cloud interactions where the plasma is approximately at corotation in Io's reference frame. But close to Io, the flow velocity and ion temperature are drastically reduced (Vflow < 10 km/s and Tion < 50 eV) and greatly increased on its flanks (∼80 km/s and 400 eV). Thus, velocity-dependent charge exchange cross sections are critical for numerical simulations of the Io plasma/atmosphere interaction.We provide estimates of charge exchange cross sections of ions on molecular neutrals and of molecular ions on neutrals for the range of velocity [5–120] km/s representative of ion velocities at Io. We combine several methods valid at the low and higher velocities in this range: Two-state impact parameter approximation, quasi-thermal rate constant extrapolation, Langevin orbiting cross sections and scaling from experimental data. We describe these methods in details.Our estimates at 60 km/s are 2–3 times smaller or larger than previously published values, depending on the reaction. Most are generally large (∼60–90 Å2) at small velocities. We discuss the most important reactions relevant to Io's interaction and where improvements and experimental values are needed. We anticipate the effect of these velocity-dependent cross sections in numerical simulations of Io's interaction and show that some of these reactions are of critical importance regarding the plasma composition close to Io, the plasma supply to the torus and the neutral supply to Io's corona and to the giant neutral clouds that extend along Io's orbit.

Motivations for a large self-interacting dark matter cross-section from Milky Way satellites

ABSTRACT We explore the properties of Milky Way (MW) subhaloes in self-interacting dark matter models for moderate cross-sections of 1–5 cm2 g−1 using high-resolution zoom-in N-body simulations. We include the gravitational potential of a baryonic disc and bulge matched to the MW, which is critical for getting accurate predictions. The predicted number and distribution of subhaloes within the host halo are similar for 1 and 5 cm2 g−1 models, and they agree with observations of MW satellite galaxies only if subhaloes with peak circular velocity over all time &amp;gt;7 km s−1 are able to form galaxies. We do not find distinctive signatures in the pericentre distribution of the subhaloes that could help distinguish the models. Using an analytical model to extend the simulation results, we are able to show that subhaloes in models with cross-sections between 1 and 5 cm2 g−1 are not dense enough to match the densest ultrafaint and classical dwarf spheroidal galaxies in the MW. This motivates exploring velocity-dependent cross-sections with values larger than 5 cm2 g−1 at the velocities relevant for the satellites such that core collapse would occur in some of the ultrafaint and classical dwarf spheroidals.

Classification of gamma-ray targets for velocity-dependent and subhalo-boosted dark-matter annihilation

Gamma-ray observations have long been used to constrain the properties of dark matter (DM), with a strong focus on weakly interacting massive particles annihilating through velocity-independent processes. However, in the absence of clear-cut observational evidence for the simplest candidates, the interest of the community in more complex DM scenarios involving a velocity-dependent cross-section has been growing steadily over the past few years. We present the first systematic study of velocity-dependent DM annihilation (in particular p-wave annihilation and Sommerfeld enhancement) in a variety of astrophysical objects, not only including the well-studied Milky Way dwarf satellite galaxies, but nearby dwarf irregular galaxies and local galaxy clusters as well. Particular attention is given to the interplay between velocity dependence and DM halo substructure. Uncertainties related to halo mass, phase-space and substructure modelling are also discussed in this velocity-dependent context. We show that, for s-wave annihilation, extremely large subhalo boost factors are to be expected, up to 1011 in clusters and up to 106–107 in dwarf galaxies where subhalos are usually assumed not to play an important role. Boost factors for p-wave annihilation are smaller but can still reach 103 in clusters. The angular extension of the DM signal is also significantly impacted, with e.g. the cluster typical emission radius increasing by a factor of order 10 in the s-wave case. We also compute the signal contrast of the objects in our sample with respect to annihilation happening in the Milky Way halo. Overall, we find that the hierarchy between the brightest considered targets depends on the specific details of the assumed particle-physics model.

J -factors for velocity-dependent dark matter annihilation

If dark matter annihilates with a velocity-dependent cross section within a subhalo, then the magnitude and angular distribution of the resulting photon signal will change. These effects are encoded in the $J$-factor. In this work we compute the $J$-factor for a variety of choices for the cross section velocity-dependence, and for a variety of choices for the dark matter profile, including generalized Navarro-Frenk-White (NFW), Einasto, Burkert and Moore. We include the results of these computations as data products alongside the article. We find that the angular distribution of a future signal would depend on the velocity-dependence of the annihilation cross section more strongly for cuspy profiles than for cored profiles. Interestingly, we find that for a density profile with an inner slope power law steeper than 4/3, Sommerfeld-enhanced annihilation in the Coulomb limit leads to a divergence at the center, requiring a more detailed treatment of departure from the Coulomb limit.

The Signatures of Self-interacting Dark Matter and Subhalo Disruption on Cluster Substructure

The abundance, distribution, and inner structure of satellites of galaxy clusters can be sensitive probes of the properties of dark matter. We run 30 cosmological zoom-in simulations with self-interacting dark matter (SIDM), with a velocity-dependent cross section, to study the properties of subhalos within cluster-mass hosts. We find that the abundance of subhalos that survive in the SIDM simulations are suppressed relative to their cold dark matter (CDM) counterparts. Once the population of disrupted subhalos—which may host orphan galaxies—is taken into account, satellite galaxy populations in CDM and SIDM models can be reconciled. However, even in this case, the inner structures of subhalos are significantly different in the two dark matter models. We study the feasibility of using the weak-lensing signal from the subhalo density profiles to distinguish between the cold and self-interacting dark matter while accounting for the potential contribution of orphan galaxies. We find that the effects of self-interactions on the density profile of subhalos can appear degenerate with subhalo disruption in CDM, when orphans are accounted for. With current error bars from the Subaru Hyper Suprime-Cam Strategic Program, we find that subhalos in the outskirts of clusters (where disruption is less prevalent) can be used to constrain dark matter physics. In the future, the Vera C. Rubin Observatory Legacy Survey of Space and Time will give precise measurements of the weak-lensing profile and can be used to constrain σ T /m at the ∼1 cm2 g−1 level at v ∼ 2000 km s−1.

Consistent explanation for the cosmic-ray positron excess in p-wave Breit\u2013Wigner enhanced dark matter annihilation

Dark matter (DM) annihilation in the galactic halo can be enhanced relative to that in the early Universe due to the Breit–Wigner enhancement, if the DM particles annihilate through a narrow resonance. Although the s-wave Breit–Wigner enhancement can provide a consistent explanation for both the observed cosmic-ray (CR) positron excess and the DM thermal relic density, it is severely constrained by the observations of gamma rays from dwarf spheroidal satellite galaxies (dSphs) and the cosmic microwave background (CMB), which have relatively lower allowed DM annihilation cross section and typical DM velocities than that in the galactic halo. Furthermore, in the s-wave Breit–Wigner enhancement, the case where the resonance mass is below a threshold (twice the DM mass) is ruled out due to the monotonically increasing annihilation cross section with decreasing DM velocity. In this work, we consider Breit–Wigner enhanced p-wave DM annihilation. We explore the parameter regions which can simultaneously account for the CR positron excess and DM thermal relic density without violating the constraints from dSphs gamma rays and CMB. We show that the velocity-dependent cross section in this scenario can peak around the typical DM velocity in the galactic halo for the resonance mass both above and below the threshold. Moreover, the highly suppressed annihilation cross section at extremely low DM velocity can evade the constraints from dSphs gamma rays and CMB easily, which results in larger allowed parameter regions than that in the s-wave case.

Dissipative dark matter on FIRE – I. Structural and kinematic properties of dwarf galaxies

ABSTRACT We present the first set of cosmological baryonic zoom-in simulations of galaxies including dissipative self-interacting dark matter (dSIDM). These simulations utilize the Feedback In Realistic Environments galaxy formation physics, but allow the dark matter to have dissipative self-interactions analogous to standard model forces, parametrized by the self-interaction cross-section per unit mass, (σ/m), and the dimensionless degree of dissipation, 0 &amp;lt; fdiss &amp;lt; 1. We survey this parameter space, including constant and velocity-dependent cross-sections, and focus on structural and kinematic properties of dwarf galaxies with $M_{\rm halo} \sim 10^{10-11}{\, \rm M_\odot }$ and $M_{\ast } \sim 10^{5-8}{\, \rm M_\odot }$. Central density profiles (parametrized as ρ ∝ rα) of simulated dwarfs become cuspy when $(\sigma /m)_{\rm eff} \gtrsim 0.1\, {\rm cm^{2}\, g^{-1}}$ (and fdiss = 0.5 as fiducial). The power-law slopes asymptote to α ≈ −1.5 in low-mass dwarfs independent of cross-section, which arises from a dark matter ‘cooling flow’. Through comparisons with dark matter only simulations, we find the profile in this regime is insensitive to the inclusion of baryons. However, when $(\sigma /m)_{\rm eff} \ll 0.1\, {\rm cm^{2}\, g^{-1}}$, baryonic effects can produce cored density profiles comparable to non-dissipative cold dark matter (CDM) runs but at smaller radii. Simulated galaxies with $(\sigma /m) \gtrsim 10\, {\rm cm^{2}\, g^{-1}}$ and the fiducial fdiss develop significant coherent rotation of dark matter, accompanied by halo deformation, but this is unlike the well-defined thin ‘dark discs’ often attributed to baryon-like dSIDM. The density profiles in this high cross-section model exhibit lower normalizations given the onset of halo deformation. For our surveyed dSIDM parameters, halo masses and galaxy stellar masses do not show appreciable difference from CDM, but dark matter kinematics and halo concentrations/shapes can differ.

On the Capture of Interstellar Objects by Our Solar System

Abstract Motivated by recent visits from interstellar comets, along with continuing discoveries of minor bodies in orbit of the Sun, this paper studies the capture of objects on initially hyperbolic orbits by our solar system. Using an ensemble of ∼500 million numerical experiments, this work generalizes previous treatments by calculating the capture cross section as a function of asymptotic speed. The resulting velocity-dependent cross section can then be convolved with any distribution of relative speeds to determine the capture rate for incoming bodies. This convolution is carried out for the usual Maxwellian distribution, as well as the velocity distribution expected for rocky debris ejected from planetary systems. We also construct an analytic description of the capture process that provides an explanation for the functional form of the capture cross section in both the high- and low-velocity limits.

Velocity-dependent self-interacting dark matter from groups and clusters of galaxies

We probe the self-interactions of dark matter with relaxed galaxy groups and clusters using observational data from strong and weak lensing and stellar kinematics. Our analysis uses the Jeans formalism and considers a wider range of systematic effects than in previous work, including adiabatic contraction and stellar anisotropy, to robustly constrain the self-interaction cross section. For both groups and clusters, our results show a mild preference for a nonzero cross section compared with cold collisionless dark matter. Our groups result, σ/m=0.5±0.2 cm2/g, places the first constraint on self-interacting dark matter (SIDM) at an intermediate scale M200∼ 1014 M⊙ between galaxies and massive clusters. For massive clusters with M200∼ 1015 M⊙, our result is σ/m=0.19±0.09 cm2/g, with an upper limit of σ / m < 0.35 cm2/g (95% CL) . Thus, our results disfavor a velocity-independent cross section of order 1 cm2/g or larger needed to impact small scale structure problems in galaxies, but are consistent with a velocity-dependent cross section that decreases with increasing scattering velocity. Comparing the cross sections with and without the effect of adiabatic contraction, we find that adiabatic contraction produces slightly larger values for our data sample, but they are consistent at the 1σ level. Finally, to validate our approach, we apply our Jeans analysis to a sample of mock data generated from SIDM-plus-baryons simulations with σ/m = 1 cm2/g. This is the first test of the Jeans model at the level of stellar and lensing observables directly measured from simulations. We find our analysis gives a robust determination of the cross section, as well as consistently inferring the true baryon and dark matter density profiles.

Diverse dark matter density at sub-kiloparsec scales in Milky Way satellites: Implications for the nature of dark matter

Milky Way (MW) satellites reside within dark matter (DM) subhalos with a broad distribution of circular velocity profiles. This diversity is enhanced with the inclusion of ultra-faint satellites, which seemingly have very high DM densities, albeit with large systematic uncertainties. We argue that if confirmed, this large diversity in the MW satellite population poses a serious test for the structure formation theory with possible implications for the DM nature. For the Cold Dark Matter model, the diversity might be a signature of the combined effects of subhalo tidal disruption by the MW disk and strong supernova feedback. For models with a dwarf-scale cutoff in the power spectrum, the diversity is a consequence of the lower abundance of dwarf-scale halos. This diversity is most challenging for Self-Interacting Dark Matter (SIDM) models with cross sections $\sigma/m_\chi\gtrsim1~$cm$^2$g$^{-1}$ where subhalos have too low densities to explain the ultra-faint galaxies. We propose a novel solution to explain the diversity of MW satellites based on the gravothermal collapse of SIDM haloes. This solution requires a velocity-dependent cross section that predicts a bimodal distribution of cuspy dense (collapsed) subhaloes consistent with the ultra-faint satellites, and cored lower density subhaloes consistent with the brighter satellites.

Dark matter haloes in the multicomponent model – II. Density profiles of galactic haloes

The multicomponent dark matter model with self-scattering and inter-conversions of species into one another is an alternative dark matter paradigm that is capable of resolving the long-standing problems of $\Lambda$CDM cosmology at small scales. In this paper, we have studied in detail the properties of dark matter halos with $M \sim 4-5 \times10^{11} M_{\odot}$ obtained in $N$-body cosmological simulations with the simplest two-component (2cDM) model. A large set of velocity-dependent cross-section prescriptions for elastic scattering and mass conversions, $\sigma_s(v)\propto v^{a_s}$ and $\sigma_c(v)\propto v^{a_c}$, has been explored and the results were compared with observational data. The results demonstrate that self-interactions with the cross-section per particle mass evaluated at $v=100$ km s$^{-1}$ being in the range of $0.01\lesssim \sigma_0/m\lesssim 1$ cm$^2$g$^{-1}$ robustly suppress central cusps, thus resolving the core-cusp problem. The core radii are controlled by the values of $\sigma_0/m$ and the DM cross-section's velocity-dependent power-law indices $(a_s,a_c)$, but are largely insensitive to the species' mass degeneracy. These values are in full agreement with those resolving the substructure and too-big-to-fail problems. We have also studied the evolution of halos in the 2cDM model with cosmic time.

Structure of dark matter haloes of Milky Way satellite galaxies in SIDM universes

AbstractSelf-interacting dark matter (SIDM) can create sufficiently large cores in dark matter haloes of dwarf galaxies if the self-interaction cross-section is sufficiently large on scales of dwarf galaxies. Such a large cross-section can be realized without changing the densities and shapes of cluster-size haloes by introducing a velocity dependent cross-section. Lowering the central densities of dwarf-size haloes, however, may change the strength of stellar feedback required to reproduce observed properties of dwarf galaxies such as the luminosity function of the Milky Way’s satellite galaxies. We perform simulations of galaxy formation by employing such a velocity dependent self-interaction cross-section to investigate the coupled effect of SIDM and feedback.