Read and colleagues in their paper showed that gravitational potential fluctuations driven by bursty star formation can kinematically ‘heat up’ dark matter at the centres of dwarf galaxies. They estimated pre-infall halo masses for their sample of dwarfs, using HI rotation curve measurements for the gas rich dwarf irregular galaxies (dIrrs) sample and abundance matching for the gas-poor dwarf spheroidal galaxies (dSphs) sample. With this, they showed that their ρDM(150 pc) as a function of M200 is in good agreement with models in which DM is kinematically ‘heated up’ by bursty star formation.
The standard Λ Cold Dark Matter (ΛCDM) cosmological model gives a remarkable description of the growth of structure in the Universe on large scales. Yet, on smaller scales inside the dark matter halos of galaxies, there have been long-standing tensions. The oldest of these is the ‘cusp-core’ problem. Pure dark matter (DM) structure formation simulations in ΛCDM predict a universal DM halo profile that has a dense ‘cusp’ at the centre, with inner density ρDM ∝ r-¹. By contrast, observations of gas rich dwarf galaxy rotation curves have long favoured DM ‘cores’, with ρDM ∼ constant.
The cusp-core problem has generated substantial interest over the past two decades because it may point to physics beyond the collisionless ‘Cold Dark Matter’ (CDM) typically assumed to date. Spergel & Steinhardt, were the first to suggest that ‘Self Interacting Dark Matter’ (SIDM) – that invokes a new force acting purely in the dark sector – could transform a dense cusp to a core through energy transfer between the DM particles. Warm Dark Matter (WDM) has also been proposed as a solution to the cusp-core problem. Other solutions include ‘fuzzy DM’, ‘fluid’ DM and ‘wave-like’ DM.
However, there is a more prosaic explanation for the cusp-core problem. If gas is slowly accreted onto a dwarf galaxy and then suddenly removed (for example by stellar winds or supernovae feedback) this causes the DM halo to expand, irreversibly lowering its central density. In 2002, Gnedin & Zhao showed that, for reasonable gas fractions and collapse factors, the overall effect of this ‘DM heating’ is small. However, if the effect repeats over several cycles of star formation, it accumulates, leading eventually to complete DM core formation. Indeed, recent numerical simulations of dwarf galaxies that resolve the impact of individual supernovae on the interstellar medium find that the gas mass within the projected half light radius of the stars, R1/2, naturally rises and falls on a timescale comparable to the local dynamical time, transforming an initial DM cusp to a core. Such simulations have already made several testable predictions. In 2013, Teyssier et al. showed that the gas flows that transform DM cusps to cores lead to a bursty star formation history, with a peak-to-trough ratio of 5-10 and a duty cycle comparable to the local dynamical time. Furthermore, the stars are dynamically ‘heated’ similarly to the DM, leading to a stellar velocity dispersion that approaches the local rotational velocity of the stars (v/σ ∼ 1) inside R1/2. Both of these predictions are supported by observations of dwarf galaxies. Further evidences for ‘DM heating’ come from the observed age gradients in dwarfs.
While there is strong evidence that dwarf galaxies have bursty star formation histories, this is only circumstantial evidence for DM heating. The real ‘smoking gun’ for DM cusp-core transformations lies in another key prediction from recent numerical models: DM core formation requires several cycles of gas inflow and outflow. Thus, at fixed halo mass, galaxies that have formed more stars (i.e. that have undergone more gas inflow-outflow cycles) will have a lower central DM density. By contrast, solutions to the cusp-core problem that invoke exotic DM predict no relationship between the central DM densities of dwarfs and their star formation histories (SFHs).
Whether or not a dwarf will form a DM core depends primarily on the number and amplitude of gas inflow-outflow cycles, & on the amount of DM that needs to be evacuated from the centre of the dwarf to form the core. This can be posed in the form of an energy argument, whereby the total energy available to move gas around depends on the total stellar mass formed, M∗, while the energy required to unbind the DM cusp depends on the DM halo mass, M200. Thus, whether or not a DM core will form in a given dwarf galaxy depends primarily on its stellar mass to halo mass ratio, M∗/M200. However, since M200 is challenging to extrapolate from the data, in this paper, read and colleagues consider also a proxy for the ratio M∗/M200: the star formation ‘truncation time’, ttrunc. They define this to be the time when the dwarf’s star formation rate (SFR) fell by a factor of two from its peak value. This can be used as a proxy for M∗/M200 so long as the SFR is approximately constant (as is the case for the sample of dwarfs that they consider in this paper). In this case, dwarfs with ttrunc → 0 Gyrs have M∗/M200 → 0, while those with ttrunc →13.8 Gyrs (i.e. the age of the Universe) have formed stars for as long as possible and have, therefore, maximised both M∗/M200 and their ability to produce a DM core. Unlike M200, however, ttrunc has the advantage that it is readily estimated from the dwarf’s star formation history.
In their paper, Read and colleagues set out to test the above key prediction of DM heating models, that dwarfs with ‘extended star formation’ (i.e. ttrunc → 13.8 Gyrs and maximal M∗/M200) have DM cores, while those with ‘truncated star formation’ (i.e. ttrunc → 0 Gyrs and minimal M∗/M200) have DM cusps. To achieve this, they estimated the central DM density, M∗, ttrunc and M200 for a sample of nearby dwarf galaxies with a wide range of star formation histories (SFHs). Their sample includes gas-poor dwarf spheroidal galaxies (dSphs) whose star formation ceased shortly after the beginning of the Universe, dSphs with extended star formation that shut down only very recently, and gas rich dwarf irregular galaxies (dIrrs) that are still forming stars today. This requires them to accurately infer the DM distribution in both gas rich and gas poor galaxies. For the former, they used HI rotation curves as in their previous paper; for the latter, they used line of sight stellar kinematics. However, with only line of sight velocities, there is a well-known degeneracy between the radial density profile (that they would like to measure) and the velocity anisotropy of the dwarf.
In 2017 and 2018 paper i.e. Read & Steger (2017) and Read et al. (2018), Read introduced a new mass modelling tool – GravSphere – that breaks this degeneracy by using ‘Virial Shape Parameters’ (VSPs). They used a large suite of mock data to demonstrate that with ∼ 500 radial velocities, GravSphere is able to correctly infer the dark matter density profile over the radial range 0.5 < r/R1/2 < 2, within its 95% confidence intervals. Here, in this paper, they used GravSphere to infer the inner DM density of eight Milky Way dSphs and eight dwarf irregular (dIrr) galaxies with a wide range of star formation histories. Their key findings are as follows:
• For all galaxies, they estimated the dark matter density at a common radius of 150 pc, ρDM(150pc) and found that their sample of dwarfs falls into two distinct classes. Galaxies with only old stars (> 6 Gyrs old) had central DM densities, ρDM(150 pc) > 10^8 M kpc-³, consistent with DM cusps; those with star formation until at least 3 Gyrs ago had ρDM(150 pc) < 10^8 Mkpc-³, consistent with DM cores (Figure 1).
• They estimated pre-infall halo masses for their sample of dwarfs, using HI rotation curve measurements for the dIrr sample and abundance matching for the dSph sample. With this, they showed that their ρDM(150 pc) as a function of M200 is in good agreement with models in which DM is kinematically ‘heated up’ by bursty star formation. The dwarfs with only old-age stars lay along the track predicted by the NFW profile in ΛCDM, consistent with having undergone no measurable DM heating. By contrast, those with extended star formation lay along the track predicted by the coreNFW profile from Read et al. (2016a), consistent with maximal DM heating (Figure 2, left panel).
• They found that ρDM(150 pc) for their sample of dwarfs is anti-correlated with their stellar mass to pre-infall halo mass ratio, M∗/M200 (Figure 2, right panel) i.e. using abundance matching to infer pre-infall halo masses, M200, they showed that this dichotomy is in excellent agreement with models in which dark matter is heated up by bursty star formation. In particular, they found that ρDM(150 pc) steadily decreases with increasing stellar mass-to-halo mass ratio, M∗/M200.
Their results suggested that, to leading order, dark matter is a cold, collisionless, fluid that can be kinematically ‘heated up’ and moved around.
Reference: J. I. Read, M. G. Walker, P. Steger, “Dark matter heats up in dwarf galaxies”, Monthly Notices of the Royal Astronomical Society, Volume 484, Issue 1, March 2019, Pages 1401–1420, https://doi.org/10.1093/mnras/sty3404 https://academic.oup.com/mnras/article/484/1/1401/5265085
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