Don't cross the streams: caustics from Fuzzy Dark Matter

Abstract

We study how tidal streams from globular clusters may be used to constrain the mass of ultra-light dark matter particles, called 'fuzzy' dark matter (FDM). A general feature of FDM models is the presence of ubiquitous density fluctuations in bound, virialized dark matter structures, on the scale of the de Broglie wavelength, arising from wave interference in the evolving dark matter distribution. These time-varying fluctuations can disturb the motions of stars, leading to potentially observable signatures in cold thin tidal streams in our own Galaxy. The study of this effect has been hindered by the difficulty in simulating the FDM wavefunction in Milky Way-sized systems. We present a simple method to evolve realistic wavefunctions in nearly static potentials, that should provide an accurate estimate of this granulation effect. We quantify the impact of FDM perturbations on tidal streams, and show that initially, while stream perturbations are small in amplitude, their power spectra exhibit a sharp cutoff corresponding to the de Broglie wavelength of the FDM potential fluctuations. Eventually, when stream perturbations become nonlinear, fold caustics generically arise that lead to density fluctuations with universal behavior. This erases the signature of the de Broglie wavelength in the stream density power spectrum, but we show that it will still be possible to determine the FDM mass in this regime, by considering the fluctuations in quantities like angular momenta or actions.

Wave Dark Matter

“…It would be useful to quantify it with wave simulations (see discussion at the end of Section 4.2). Moreover, wave interference granules-not virialized subhalos-could by themselves give rise to these signals, such as the scattering of stellar streams (Dalal et al 2020). Their effects should be taken into account.…”

“…49 Are the same measurements consistent with fuzzy dark mater? To answer this question, one must account for scattering by both the subhalo contents (Schutz 2020) and the interference substructures (Dalal et al 2020). In addition, it is important to clarify to what extent the tidal stream density fluctuations can be attributed to the tidal disruption process itself (Kuepper et al 2010, Ibata et al 2020.…”

“…In addition, it is important to clarify to what extent the tidal stream density fluctuations can be attributed to the tidal disruption process itself (Kuepper et al 2010, Ibata et al 2020. More measurements spanning different orbital radii would be helpful in differentiating between models: scattering by interference substructures is expected to be more important at small radii relative to scattering by subhalos (Dalal et al 2020). It is also worth noting there are other statistics that might have different sensitivity to the mass and compactness of subhalos (e.g.…”

On $N$-body simulations of globular cluster stream

“…While we have used 𝑁-body simulations to determine the expected power spectrum of stream density variations in the presence of a population of massive 𝑁-body particles, when the entire halo is made up off 𝑁 = 𝑀 halo /𝑀 res particles with mass 𝑀 res , the number of impacts on a stream is high enough that we can estimate the induced power using simple statistical calculations. Following Appendix B of Dalal et al (2020), who work out the expected stream density power spectrum for a population of CDM subhalos, we can determine the approximate scaling of the power spectrum with mass. As shown by Dalal et al (2020), for perturbers of a single mass 𝑀 res with a spatial density n, the expected power spectrum is 𝑃 𝛿 𝛿 ∝ 𝑀 2 res n. When the entire halo consists of substructure of mass 𝑚, then n = 𝜌/𝑀 res , where 𝜌 is the dark matter density and 𝑃 𝛿 𝛿 ∝ 𝑀 res (where we drop the 𝜌 dependence because it does not change with resolution).…”

“…Following Appendix B of Dalal et al (2020), who work out the expected stream density power spectrum for a population of CDM subhalos, we can determine the approximate scaling of the power spectrum with mass. As shown by Dalal et al (2020), for perturbers of a single mass 𝑀 res with a spatial density n, the expected power spectrum is 𝑃 𝛿 𝛿 ∝ 𝑀 2 res n. When the entire halo consists of substructure of mass 𝑚, then n = 𝜌/𝑀 res , where 𝜌 is the dark matter density and 𝑃 𝛿 𝛿 ∝ 𝑀 res (where we drop the 𝜌 dependence because it does not change with resolution). This scaling holds down to angular scales 𝜃 ≈ 𝑅/𝑟, where 𝑅 is the size of the perturber and 𝑟 is the Galactocentric radius (that is, 𝜃 is the angular size of perturbers as seen from the Galactic center); below this scale the power spectrum drops to zero quickly.…”