Infalling ultra-faint dwarfs as emissaries of the Axiverse

TL;DR

The paper addresses the puzzling bimodality between ultra-faint dwarfs (UFDs) and classical dwarf spheroidals (dSphs) by embedding them in a two-field wave dark matter (2ψDM) Axiverse framework, where a discrete spectrum of axion masses yields two dominant DM components. It analyzes Leo K and M as UFD representatives, fits their stellar profiles with a soliton core plus halo, and uses two-field simulations to show how a heavy boson ($m_\psi \sim 3\times 10^{-21}$ eV) drives UFD cores while a lighter boson ($m_\psi \sim 10^{-22}$ eV) dominates larger galaxies, predicting distinct velocity dispersions and core radii. The results reproduce the observed bimodality in core density–core radius space and offer concrete, testable pulsar-timing signals with the Square Kilometer Array, arising from the two Compton frequencies $2 m_\psi c^2/h$ for the heavy and light bosons. While promising, the work also highlights current simulation limitations (mass ratios, resolution, lack of baryons) and calls for higher-resolution, baryon-inclusive models to robustly extend the predictions to $z\approx 0$ and to sharpen the observational tests.

Abstract

Recent discoveries of ultra-faint dwarf galaxies (UFDs) infalling onto the Milky Way, namely Leo K \& M at $r \simeq 450$kpc, considerably strengthens the case that UFDs constitute a distinct galaxy class that is inherently smaller and fainter, and metal-poorer than the classical dwarf spheroidals (dSph). This distinction is at odds with the inherent continuity of galaxy halo masses formed under scale-free gravity for any standard dark-matter (DM) model. Here, we show that distinct galaxy classes do evolve in cosmological simulations of multiple light bosons representing the ``Axiverse'' proposal of string theory, where a discrete mass spectrum of axions is generically predicted to span many decades in mass. In this context, the observed UFD class we show corresponds to a relatively heavy boson of $3\times 10^{-21}$ eV, including Leo K \& M, whereas a lighter axion of $10^{-22}$ eV comprises the bulk of DM in all larger galaxies including the dSphs. Although Leo M is larger in size than Leo K, we predict its velocity dispersion to be smaller $(\simeq 1.7$km/s) than that of Leo K $(\simeq 4.5$km/s) because of the inverse de Broglie scale dependence on momentum. This scenario can be definitively tested using millisecond pulsars close to the Galactic center, where the Compton frequencies of the heavy and light bosons imprint monotone timing residuals that may be detected by the Square Kilometre Array (SKA) on timescales of approximately one week and four months, respectively.

Figures (7)

• Figure 1: Star-count profiles. The binned star counts for Leo K and M McQuinn:2024 are compared with the standard Plummer profile shown as the red dashed curve that can be seen to be increasingly in tension at a large radius. The $\psi$DM profile is shown by the green band for our Markov Chain Monte Carlo (MCMC)-based range of acceptable fits, with its soliton core component and an outer Navarro-Frank-White (NFW) profile. The radius of the soliton component is set by the de Broglie scale, and there is a characteristic sharp density drop between the core and the halo predicted in the simulations to be typically a factor of $\simeq 30$, which we mark as the transition radius by the vertical orange band. Note that the right panel has a linear-log scale that helps us appreciate the extent of the outer halo present in the data. In the bottom row, we plot the sum of all star count profiles of recognized UFDs in the Local Group, showing the clear core-halo form and best fitting $\psi$DM profile derived by Pozo:2024 to illustrate the similarity with Leo K and M.
• Figure 2: Density versus core radius. The central density is plotted within the fit core radius for each dwarf, estimated as $(\sigma_c / r_c)^2$. Since the values of $\sigma_c$ are not available for the galaxy dataset, we used $\sigma_{los}$ instead. A clear separation between UFD´s and classical dSph´s is apparent with both populations following parallel trends. The slope $d\log \rho_c / d\log r_c = -4$ corresponds to the time-independent soliton solution of the Schrödinger–Poisson equation, where more massive solitons produce narrower cores. The blue lines represent the predicted relation for the UFD´s and dSph´s, whereas the green lines correspond to the input boson masses of the simulation and can be compared with the star symbols (simulated halos) and halo ID number. In the case of halos, $12_2$ and $13_2$ represent halos 12 and 13 in a scenario where they do not experience tidal forces. Note how the dSph galaxies and the non-tidally affected extrapolated UFDs follow their theoretical trend lines. We also mark Leo K ($r_c=0.034^{+0.002}_{-0.019}$Kpc) and Leo M ($r_c=0.081^{+0.01}_{-0.01}$Kpc) galaxies and color-code them by luminosity; this plot provides a prediction of their predicted velocity dispersions, which are as yet unmeasured. Crater II is marked with a white point.
• Figure 3: Velocity dispersion versus core radius. The observed velocity dispersion is plotted against the core radius for all dSph and UFD dwarfs, comparing them with the inverse relation, $d\log \sigma_c/d\log r_c=-1$, required by the uncertainty principle; this is shown via diagonal lines. Since the values of $\sigma_c$ are not available for the galaxy dataset, we used $\sigma_{los}$ instead. The best fits to the UFD and dSPh dwarfs are indicated in blue, with the corresponding boson masses of $\psi$DM derived from the normalization listed in the legend. The parallel green lines correspond to the boson masses adopted in our simulation, which do not coincide precisely with the best-fit values found in the data (as indicated by the blue lines). Also overlaid is an approximate CDM-related prediction Walker:2009 as a dotted gray curve, where galaxies with NFW profiles are naturally predicted to be larger with increasing galaxy mass, i.e., with the opposite sign to the negative-slope $\psi$DM relation. Crater II is marked with a white point.
• Figure 4: Evolution of virial mass (left), radius (center), and virial mass versus radius (right). Solid lines trace the evolution of these quantities across all simulation snapshots (as projected in Fig. \ref{['Fig:Box']}), with extrapolation to $z = 0$ shown as dashed lines, as described in the appendix. Right panel shows virial mass versus radius (left), with the last snapshot marked with red squares (z=3.4), to illustrate that the predicted bimodality is inherent rather than a product of our extrapolations to z = 0. Arrows in the right panel indicate the evolutionary trend for the two galaxy classes (orange for dSphs and purple for UFDs), with the green area encompassing formation values. The low-mass galaxies all suffer some level of tidal stripping of one or both boson components, and we highlight the sensitivity to tidal effects for the heavy boson-dominated halos 12 and 13 by extrapolating two possible scenarios: one in which they experience tidal stripping similarly to the other UFDs (purple arrow) and another in which they remain unaffected (orange arrow). The latter case is represented by the markers $12_2$ and $13_2$, with the corresponding dotted lines in the figure. All quantities are shown in physical units.
• Figure 5: Top left panel: Histogram of luminosities of both galaxy classes. Each galaxy population has been colored differently—yellow for dSphs and purple for UFDs, respectively. We observe that, overall, both classes show a clear distinction in terms of luminosities, forming two separate groups. However, there is no sharp discrete transition between the classes, as some galaxies lie in an overlapping region. Top right panel: Histogram of metallicities of both galaxy classes. We observe the same trend as with the luminosities. Bottom panel: Luminosity versus 2D-projected half-light radius for simulated and observed galaxies. We compare our results (extrapolated to $z=0$ from our latest simulation outputs at $z=3.4$, marked with star-shaped points) with updated catalogs of observed UFD and dwarf galaxies from several works McConnachie:2012Simon:2019Richstein:2022Richstein:2024, as well as with simulated galaxies from various studies Jeon:2017Jeon:2021Wheeler:2019Applebaum:2021Prgomet:2022Sanati:2023Ko:2024. Additionally, we included the galaxies analyzed in our previous work Pozo:2024. For our simulations, we derived the half-light-radius values based on typical proportions corresponding to each dwarf population Pozo:2024. We mark Leo K and Leo M with red squares and the locations of halos $12_2$ and $13_2$ with light-green star-shaped points. Note how these two halos still fall within the UFD range, with halo $12_2$ showing similar properties to the recently discovered isolated Leo M UFD (halos $12_2$ and $13_2$ represent halos 12 and 13 in a scenario where they do not experience tidal forces; see Fig. \ref{['Fig:evolution']}).