Velocity dispersion profiles of dwarf spheroidal galaxies with self-interacting ultralight dark matter

TL;DR

This study tests self-interacting ultralight dark matter (ULDM) by fitting velocity-dispersion profiles of seven Milky Way dwarf spheroidal galaxies. ULDM halos are modeled as Bose-Einstein condensate solitons described by the Gross-Pitaevskii-Poisson system, with a Gaussian density profile and a mass-radius relation that is modified by baryonic gravity. The analysis finds two viable ULDM regimes: (i) nearly non-interacting ULDM with boson mass $m\sim1.6\times10^{-22}$ eV when self-interactions are repulsive and (ii) attractively interacting ULDM with $m\sim1.3\times10^{-22}$ eV and negative scattering length $a_{\rm s}\sim-10^{-78}$ m, where self-interactions significantly shape the halo. Accounting for baryons alters the mass-radius relation and the inferred parameters, highlighting the importance of baryonic potential in halo hydrostatics. Overall, ULDM remains compatible with the velocity-dispersion data, though it faces external constraints (e.g., de Broglie wavelength considerations and Lyman-$\alpha$ limits) that motivate more detailed, realistic modeling of baryons and coherence effects in dwarf galaxies.

Abstract

Dark-matter-dominated dwarf galaxies provide an excellent laboratory for testing dark matter models at small scale and, in particular, the ultralight dark matter (ULDM) class of models. Within the framework of self-interacting bosonic dark matter, we use the observed velocity-dispersion pro- files of seven dwarf spheroidal galaxies to constrain the parameters of ULDM. In our modeling, we account for the impact of the baryonic component on the velocity dispersion and ULDM halo structure. We find that in the regime of repulsively interacting ULDM, the self-interaction, which fits the observations, is almost negligible, consistent with non-interacting ULDM with a boson mass of approximately 1.6*10^(-22) eV. In contrast, for attractively interacting ULDM, the best fit corre- sponds to a smaller boson mass of about 1.3*10^(-22) eV, with self-interaction playing a significant role in shaping the dark-matter halo and thereby influencing the interpretation of observations.

Figures (7)

• Figure 1: The function of $b/R_\textrm{DM}$ which defines the relative contribution of baryonic matter in Eq. (\ref{['eq: R(M) perturbed by bulge']}).
• Figure 2: The mass-radius relation for repulsively interacting ULDM. Black solid line shows the best fit, corresponding to the minimum of $\chi^2$-error, while the gray shaded region depicts to $M_\textrm{DM}-R$ relations within confidence intervals for $m$ and $a_\textrm{s}$. Colorful points depict dSphs with the errorbars corresponding to the confidence intervals for halo masses $M_\textrm{DM}$.
• Figure 3: The mass-radius relation for attractively interacting ULDM. The black solid line shows the best fit, corresponding to the minimum of $\chi^2$-error, while the gray shaded region depicts $M_\textrm{DM}-R$ relations within confidence intervals for $m$ and $a_\textrm{s}$. Colorful points depict dSphs with the errorbars corresponding to the confidence intervals for halo masses $M_\textrm{DM}$.
• Figure 4: The mass-radius relation for repulsively interacting ULDM. The solid lines show the best fits for different baryonic matter parameters $M_\textrm{b}$ and $b$, while the gray shaded regions correspond to $M_\textrm{DM}-R$ relations within confidence intervals for $m$ and $a_\textrm{s}$. Colorful points depict dSphs with the errorbars corresponding to the confidence intervals for halo masses $M_\textrm{DM}$.
• Figure 5: The mass-radius relation for attractively interacting ULDM. The solid lines show the best fits for different baryonic matter parameters $M_\textrm{b}$ and $b$, while the gray shaded regions correspond to $M-R$ relations within confidence intervals for $m$ and $a_\textrm{s}$. Colorful points depict dSphs with the errorbars corresponding to the confidence intervals for halo masses $M$.