Effects of New Forces on Scalar Dark Matter Solitons

TL;DR

The paper investigates whether a light scalar mediator can induce a new long-range force between scalar dark matter particles and how this affects galactic-core solitons (boson stars). It develops a nonrelativistic, mean-field framework with a DM field $\phi$ of mass $m_\phi$ coupled to a mediator $\chi$ of mass $m_\chi$, solving the coupled Schrödinger–Poisson system and its Yukawa-like extension for static, spherically symmetric solitons. The key result is that the additional force modifies the core-density–core-radius relation, yielding a crossover between regimes where the effective gravitational coupling is $G_{\rm eff}=(1+g_\chi)G$ for $R_c\ll m_\chi^{-1}$ and $G_{\rm eff}=G$ for $R_c\gg m_\chi^{-1}$, with a characteristic prefactor $\zeta \approx 0.226$ in the asymptotic scaling $\rho_c\propto 1/R_c^4$. Extending the analysis to two mediators shows a stepped enhancement of the effective gravity as mediator thresholds are crossed, offering modest improvements in fits to galactic core data for couplings of order $G$, and outlining directions for exploring larger couplings and additional mediators in future work.

Abstract

New long range forces acting on ordinary matter are highly constrained. However it is possible such forces act on dark matter, as it is less constrained observationally. In this work, we consider dark matter to be made of light bosons, such as axions. We introduce a mediator that communicates a new force between dark matter particles, in addition to gravity. The mediator is taken to be light, but not massless, so that it can affect small scale galactic behavior, but not current cosmological behavior. As a concrete application of this idea, we analyze the effects on scalar dark matter solitons bound by gravitation, i.e., boson stars, which have been claimed to potentially provide cores of galaxies. We numerically determine the soliton's profiles in the presence of this new force. We also extend the analysis to multiple mediators. We show that this new force alters the relation between core density and core radius in a way that can provide improvement in fitting data to observed galactic cores, but for couplings of order the gravitational strength, the improvement is only modest.

Figures (4)

• Figure 1: Representative plots of fields $\tilde{f}, \tilde{\phi}_N , \tilde{\chi}$ versus dimensionless radius $\tilde{r}$ evaluated at $\beta' = 0.287 \sim 0.3$, $\beta' = 1.278 \sim 1.3$ and $\beta' = 5.683 \sim 5.7$. In the left (right) column, we have set the coupling of the new force to be $g_\chi=1$ ($g_\chi=2)$.
• Figure 2: Top: Core density $\rho_c$ (in units of $m_\chi^4/(G \,m_\phi^2)$) of the soliton versus core radius $R_c$ (in units of $m_\chi^{-1}$). Bottom: Rescaled core density $\rho_c\, R_c^4$ (in units of $(G\, m_\phi^2)^{-1}$) of the soliton versus core radius $R_c$ (in units of $m_\chi^{-1}$). Small $R_c\ll m_\chi^{-1}$ and large $R_c\gg m_\chi^{-1}$ asymptotes are given in orange and red lines, respectively. Also a fit function of the form in Eq. (\ref{['fit']}) is given in the bottom plot. In the left (right) column, we have set the coupling of the new force to be $g_\chi=1$ ($g_\chi=2)$ .
• Figure 3: First two rows: Representative plots of fields $\tilde{f}$, $\tilde{\phi}_N$, $\tilde{\chi}_1$ and $\tilde{\chi}_2$ evaluated at $\beta'=0.287\sim0.3$. In one curve, we have the case of only a single mediator $\chi_1$. In the other two curves, we have the case of two mediators $\chi_1$ and $\chi_2$, with $m_{\chi_2}=3\,m_{\chi_1}$ and $m_{\chi_2}=30\, m_{\chi_1}$. Final row: Representative plot of $\tilde{\chi}_2$ for different $\beta'$ with $m_{\chi_2}=30\,m_{\chi_1}$. We have set the couplings to be $g_{\chi_1}=g_{\chi_2}=2$.
• Figure 4: Top: Core density $\rho_c$ (in units of $m_{\chi_1}^4/(G \,m_\phi^2)$) of the soliton versus core radius $R_c$ (in units of $m_{\chi_1}^{-1}$) in the presence of two mediators $\chi_1$ and $\chi_2$. Bottom: Rescaled core density $\rho_c\, R_c^4$ (in units of $(G\, m_\phi^2)^{-1}$) of the soliton versus core radius $R_c$ (in units of $m_\chi^{-1}$). Small $R_c\ll m_{\chi_2}^{-1}$, intermediate $m_{\chi_2}^{-1}\ll R_c\ll m_{\chi_1}^{-1}$ and large $R_c\gg m_{\chi_1}^{-1}$ asymptotes are given in green, orange and red lines, respectively. We have set the couplings to be $g_{\chi_1}=g_{\chi_2}=2$ and the ratio of the masses to be $m_{\chi_2}=30\, m_{\chi_1}$.