Core-envelope haloes in scalar field dark matter with repulsive self-interaction: fluid dynamics beyond the de Broglie wavelength

Abstract

Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger-Poisson equations. In the free-field (“fuzzy”) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have “solitonic” cores of radius ∼λdeB, surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length scale, λSI, with λSI > λdeB called the Thomas-Fermi (TF) regime. FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-λdeB limit, however, we can model all three by fluid conservation equations for a compressible, γ = 5/3 ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, PSI∝ρ2. We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of RTF, the radius of an SI-pressure-supported (n = 1)-polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the [“too-big-to-fail” + “core-cusp”]-test if RTF ≳ 1 kpc.

Orbits and adiabatic contraction in scalar field dark matter halos: revisiting the cusp-core problem in dwarf galaxies

“…While already anticipated earlier, e.g. in the papers by Rindler-Daller & Shapiro (2014), Chavanis (2019), Padilla et al (2021), the actual confirmation of a core-envelope halo structure in the opposite regime of strongly-interacting, repulsive SFDM-TF has only been established very recently in Dawoodbhoy, Shapiro & Rindler-Daller (2021). There, the outcome of halo formation simulations from 1D spherical collapse starting with Jeans-unstable initial conditions in a static background has been calculated, where the combination of a 1D Lagrangian code along with a smart modelling scheme allows 1 However, as the 1D simulations of Zimmermann et al (2021) show, the nature of the central object and its properties depend on how the dimensional reduction from 3D to 1D is carried out, so caution is advised.…”

“…For these reasons, we will employ a "semi-analytic" modelling approach, where we include the SI-pressure in (11) in an exact manner, but approximate the physics of the 𝑄-pressure term in (10) in a coarse-grained way. The fundamental formalism of this approach has been derived and laid out in detail in Dawoodbhoy et al (2021), whose main results we discussed already in the Introduction. Importantly, this approach works for SFDM models with strong, repulsive SI, thus "SFDM-TF", i.e.…”

“…For the purpose of the work in this paper, we will only use here one of the "semi-analytic" type of models of Dawoodbhoy et al (2021) that was mostly applied for the sake of comparison to the simulated halos. However, it has been shown there that this model is a good approximation for the accurate SFDM-TF halo profiles, and we will summarize it below.…”

“…(We note that the 1D results actually allow a cleaner analysis of the various sections of the calculated halo profiles, which is complicated to work out for the 3D simulations mentioned earlier and, in fact this has not nearly been worked out yet at the same degree of detail than it was for 1D). Furthermore, the work of Dawoodbhoy et al (2021) explains why the halo envelopes in SFDM-TF, as well as in FDM, are close to those of CDM: essentially, the novel dynamics caused by "quantum pressure" which acts on scales of 𝜆 dB can be coarse-grained such that it gives rise to an effective "velocity dispersion pressure" which stabilizes the halo envelope at large against gravity. The applied smoothing scale is much larger than the de Broglie scale, which is a justified procedure for the halo envelopes at large, as long as the latter are much larger than the de Broglie scale.…”

“…However, when doing the same comparison with typical "cusp-core halos" which are more massive, 𝑀 200 = 10 10 −10 11.15 𝑀 , and using the same FDM parameters than before, then FDM clearly fails in explaining the data. Subsequently, Dawoodbhoy et al (2021) also performed such a comparison, but including SFDM-TF as a further model. Indeed, while they confirm that CDM fails, and FDM fails with respect to the cusp-core halos, SFDM-TF halos can explain the data of both halo mass ranges, if the TF radius of the central core of those halos is large enough; e.g.…”