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Register a new userGalactic Rotation Curves vs. Ultra-Light Dark Matter: Implications of the Soliton -- Host Halo Relation
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Bosonic ultra-light dark matter (ULDM) would form cored density distributions at the center of galaxies. These cores, seen in numerical simulations, admit analytic description as the lowest energy bound state solution (soliton) of the Schroedinger-Poisson equations. Numerical simulations of ULDM galactic halos found empirical scaling relations between the mass of the large-scale host halo and the mass of the central soliton. We discuss how the simulation results of different groups can be understood in terms of the basic properties of the soliton. Importantly, simulations imply that the energy per unit mass in the soliton and in the virialised host halo should be approximately equal. This relation lends itself to observational tests, because it predicts that the peak circular velocity, measured for the host halo in the outskirts of the galaxy, should approximately repeat itself in the central region. Contrasting this prediction to the measured rotation curves of well-resolved near-by galaxies, we show that ULDM in the mass range $msim (10^{-22}div 10^{-21})$ eV, which has been invoked as a possible solution to the small-scale puzzles of $Lambda$CDM, is in tension with the data. We suggest that a dedicated analysis of the Milky Way inner gravitational potential could probe ULDM up to $mlesssim 10^{-19}$ eV.
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Analytic arguments and numerical simulations show that bosonic ultra-light dark matter (ULDM) would form cored density distributions (`solitons) at the center of galaxies. ULDM solitons offer a promising way to exclude or detect ULDM by looking for a distinctive feature in the central region of galactic rotation curves. Baryonic contributions to the gravitational potential pose an obstacle to such analyses, being (i) dynamically important in the inner galaxy and (ii) highly non-spherical in rotation-supported galaxies, resulting in non-spherical solitons. We present an algorithm for finding the ground state soliton solution in the presence of stationary non-spherical background baryonic mass distribution. We quantify the impact of baryons on the predicted ULDM soliton in the Milky Way and in low surface-brightness galaxies from the SPARC database.
A Fuzzy Dark Matter (FDM) halo consists of a soliton core close to the center and an NFW-like density profile in the outer region. Previous investigations found that the soliton core exhibits temporal oscillations and random walk excursions around the halo center. Analyzing a set of numerical simulations, we show that both phenomena can be understood as the results of wave interference -- a suitable superposition of the ground (solitonic) state and excited states in a fixed potential suffices to account for the main features of these phenomena. Such an eigenmode analysis can shed light on the evolution of a satellite halo undergoing tidal disruption. As the outer halo is stripped away, reducing the amplitudes of the excited states, the ground state evolves adiabatically. This suggests diminished soliton oscillations and random walk excursions, an effect to consider in deducing constraints from stellar heating.
Low-acceleration space-time scale invariant dynamics (SID, Milgrom 2009a) predicts two fundamental correlations known from observational galactic dynamics: the baryonic Tully-Fisher relation (BTFR) and a correlation between the observed mass discrepancy and acceleration (MDA) in the low acceleration regime for disc galaxies. SID corresponds to the deep MOdified Newtonian Dynamics (MOND) limit. The MDA data emerging in cold/warm dark matter (C/WDM) cosmological simulations disagree significantly with the tight MDA correlation of the observed galaxies. Therefore, the most modern simulated disc galaxies, which are delicately selected to have a quiet merging history in a standard dark-matter-cosmological model, still do not represent the correct rotation curves. Also, the observed tight correlation contradicts the postulated stochastic formation of galaxies in low-mass DM halos. Moreover, we find that SID predicts a baryonic to apparent virial halo (dark matter) mass relation which agrees well with the correlation deduced observationally assuming Newtonian dynamics to be valid, while the baryonic to halo mass relation predicted from CDM models does not. The distribution of the observed ratios of dark-matter halo masses to baryonic masses may be empirical evidence for the external field effect, which is predicted in SID as a consequence of the forces acting between two galaxies depending on the position and mass of a third galaxy. Applying the external field effect, we predict the masses of galaxies in the proximity of the dwarf galaxies in the Miller et al. sample. Classical non-relativistic gravitational dynamics is thus best described as being Milgromian, rather than Newtonian.
Fuzzy dark matter (FDM) has been a promising alternative to standard cold dark matter. The model consists of ultralight bosons with mass $m_b sim 10^{-22}$ eV and features a quantum-pressure-supported solitonic core that oscillates. In this work, we show that the soliton density oscillations persist even after significant tidal stripping of the outer halo. We report two intrinsic yet distinct timescales associated, respectively, with the ground-state soliton wavefunction $tau_{00}$ and the soliton density oscillations $tau_text{soliton}$, obeying $tau_text{soliton} /tau_{00} simeq 2.3$. The central star cluster (SC) in Eridanus II has a characteristic timescale $tau_text{soliton} / tau_text{SC} sim 2$ to $3$ that deviates substantially from unity. As a result, we demonstrate, both analytically and numerically with three-dimensional self-consistent FDM simulations, that the gravitational heating of the SC owing to soliton density oscillations is negligible irrespective of $m_b$. We also show that the subhalo mass function to form Eridanus II does not place a strong constraint on $m_b$. These results are contrary to the previous findings by Marsh & Niemeyer (2019).
Studies of flux anomalies statistics and perturbations in stellar streams have the potential to constrain models of warm dark matter (WDM), including sterile neutrinos. Producing these constraints requires a parametrization of the WDM mass function relative to that of the cold dark matter (CDM) equivalent. We use five WDM models with half-mode masses, $M_mathrm{hm}=[1.3,35]times10^{8}$~$M_{odot}$, spread across simulations of the Local Group, lensing ellipticals and the $z=2$ universe, to generate such a parametrization: we fit parameters to a functional form for the WDM-to-CDM halo mass function ratio, $n_mathrm{WDM}(M_{X})/n_mathrm{CDM}(M_{X})$, of ($1+(alpha M_mathrm{hm}/M_{X})^{beta})^{gamma}$. For $M_{X}equiv$ virial mass of central halos we obtain $alpha=2.3$, $beta=0.8$, and $gamma=-1.0$, and this fit is steeper than the extended Press-Schechter formalism predicts. For $M_{X}equiv$ mass of subhalos we instead obtain $alpha=4.2$, $beta=2.5$ and $gamma=-0.2$; in both mass definitions the scatter is $sim20$~per~cent. The second fit typically underestimates the relative abundance of $z=2$ WDM subhaloes at the tens of per cent level. We caution that robust constraints will require bespoke simulations and a careful definition of halo mass, particularly for subhalos of mass $<10^{8}M_{odot}$.
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