Impact of kinetic and potential self-interactions on scalar dark matter

We consider models of scalar dark matter with a generic interaction potential and noncanonical kinetic terms of the K-essence type that are subleading with respect to the canonical term. We analyze the low-energy regime and derive, in the nonrelativistic limit, the effective equations of motions. In the fluid approximation they reduce to the conservation of matter and to the Euler equation for the velocity field. We focus on the case where the scalar field mass ${10}^{-21}\ll m\lesssim {10}^{-4}\mathrm{eV}$ is much larger than for fuzzy dark matter, so that the quantum pressure is negligible on cosmological and galactic scales, while the self-interaction potential and noncanonical kinetic terms generate a significant repulsive pressure. At the level of cosmological perturbations, this provides a dark-matter density-dependent speed of sound. At the nonlinear level, the hydrostatic equilibrium obtained by balancing the gravitational and scalar interactions imply that virialized structures have a solitonic core of finite size depending on the speed of sound of the dark matter fluid. For the most relevant potential in ${\lambda }_4{\varphi }^4/4$ or K-essence with a $(\partial \varphi {)}^4$ interaction, the size of such stable cores cannot exceed 60 kpc. Structures with a density contrast larger than $10^6$ can be accommodated with a speed of sound $c_s\lesssim {10}^{-6}$. We also consider the case of a cosine self-interaction, as an example of bounded nonpolynomial self-interaction. This gives similar results in low-mass and low-density halos whereas solitonic cores are shown to be absent in massive halos.

Figure 1

Range of interest in the plane $(m,{\lambda }_4)$. The left and upper exclusion regions correspond to Eqs. (24), (26) and (27). The diagonal lines labeled “20 kpc” and “1 kpc” correspond to Eq. (29), with $r_a=20\mathrm{kpc}$ and $r_a=1\mathrm{kpc}$.

Figure 2

Profiles of the nonrelativistic self-interaction potential ${\mathrm{\Phi }}_{\mathrm{I}}$ (upper panel) and of the density $\rho$ (lower panel) for the power-law cases $n=2$, 3, and 4.

Figure 3

Nonrelativistic self-interaction potential ${\mathrm{\Phi }}_{\mathrm{I}}(\rho )$ for a cosine scalar field potential $V_{\mathrm{I}}(\varphi )$.

Figure 4

Dark matter halo profiles at redshift $z=0$ for halos of mass $M={10}^{14}$, $10^{12}$, and $10^{10}{h}^{-1}{M}_{\odot }$. Upper panel: Dark matter density $\rho$ in units of the critical density ${\rho }_c$. Middle panel: circular velocity $v$. Lower panel: Newtonian force $-F_{\mathrm{N}}$ and dark-matter force $F_{\mathrm{I}}$ (lines with squares), in units of $(\mathrm{km}/\mathrm{s}{)}^2/\mathrm{kpc}$.

Figure 5

Dark matter halo density profiles at redshifts $z=3$ (upper panel) and $z=6$ (lower panel).

Figure 6

Mass ratio $M_{\star }/M$ of the solitonic core to the total halo mass $M$ at redshifts $z=0$, $z=3$ and $z=6$.

Figure 7

Dark matter halo profiles at redshift $z=0$ for halos of mass $M={10}^{14}$, $10^{12}$, and $10^{10}{h}^{-1}{M}_{\odot }$. Upper panel left: Dark matter density $\rho$ in units of the critical density ${\rho }_c$. Upper right panel: Circular velocity $v$. Lower left panel: Newtonian force $-F_{\mathrm{N}}$ and dark-matter force $F_{\mathrm{I}}$ (lines with squares), in units of $(\mathrm{km}/\mathrm{s}{)}^2/\mathrm{kpc}$. Lower right panel: Newtonian potential $\mathrm{\Phi }$ and dark-matter potential ${\mathrm{\Phi }}_{\mathrm{I}}$ (lines with squares).

Figure 8

Dark matter halo density profiles at redshifts $z=3$ (upper panel) and $z=6$ (lower panel).

Figure 9

Mass ratio $M_{\star }/M$ of the solitonic core to the total halo mass $M$ at redshifts $z=0$, $z=3$ and $z=6$.