Macroscopic states in Bose-Einstein condensate dark matter model with axionlike interaction

TL;DR

This work addresses DM halos formed from ultralight bosons with an axionlike self-interaction by developing a statistical, thermodynamic treatment of stationary BEC configurations under gravity. The authors derive and analyze a dimensionless Gross–Pitaevskii–Poisson model with an axionlike potential, constructing a $p-\\mu$ phase diagram that reveals stable, metastable and unstable bands separated by critical amplitudes $a_n$, and they predict a first-order transition between dense and rarefied DM phases driven by quantum-fluctuation pressure. They apply the framework to the dwarf galaxy NGC 2366, fitting its rotation curve to extract a DM particle mass $m \simeq 0.1171\\times10^{-22}$ eV/$c^2$, a decay constant $f_a \simeq 3.50\\times10^{19}$ eV, and a central density $\\rho_c$, and they find a dense solitonic core containing about 19% of the DM mass in about 4.7% of the halo volume, with the core stabilizing the halo against fluctuations. The work provides a thermodynamic diagnostic for discerning DM configurations, linking core-to-halo structure to phase behavior and offering a complementary perspective to time-dependent simulations in axisymmetric BEC DM models.

Abstract

The phase diagrams of ultralight dark matter (DM), modeled as a self-gravitating Bose-Einstein condensate with axionlike interaction, are studied. We classify stable, metastable, and unstable DM states over a wide range of condensate wave function amplitudes. It is shown that the axionlike interaction causes instability and an imaginary speed of sound at low amplitudes, whereas, in a specific high-amplitude band, DM attains a stable state capable of forming a dense solitonic core and suppressing quantum fluctuations in the surrounding galactic DM halo. These findings are corroborated by evaluating thermodynamic functions for DM in the dwarf galaxy NGC 2366 and its hypothetical analogs with different core-to-halo mass ratios. Distinct DM phase compositions respond differently to fluctuation-induced partial pressure, resulting in a first-order phase transition in a certain range of an interaction parameter. While the DM properties in NGC 2366 lie within the supercritical regime, the phase transition nonetheless provides a thermodynamic marker separating stable from unstable DM configurations. Once a dense core forms - reaching a threshold of about 12% of the total mass - the enhanced gravitation stabilizes the DM halo against fluctuations, while the internal pressure ensures core stability. In particular, we find that NGC 2366's dense DM comprises roughly 19% of the DM mass while occupying only 4.7% of its total volume.

Figures (13)

• Figure 1: Grand canonical potential density $\omega$ as a function of order parameter $\chi$ for various $\nu$. The curve numbers $i=\overline{1,5}$ correspond to $\nu_i=b_i$, see (\ref{['nums']}), and curve 6 is for $\nu=0$. The two dotted curves passing through the minima of $\omega$ define the ranges of existence of phase-1 and phase-2.
• Figure 2: Solution to the equation $j_0(\pi x)=j_0(\pi y)$ in the domain $x,y\in[0;5]$. Red sections correspond to positive values, $j_0(\pi x)\geq0$, while the blue ones are for $j_0(\pi x)<0$.
• Figure 3: Chemical potential $\mu$ versus internal pressure $p$, which are parametrized by $\chi$ in the range of $\chi\in[0; 4.5\pi]$. Segments $AB$ and $CD$ are unstable states; $BO$ and $OE$ represent stable states of phase-1 and phase-2; $OC$ and $DO$ correspond to metastable states of phase-1 and -2. The first-order phase transition between phase-1 and -2 occurs at point $O$.
• Figure 4: Wave functions at $A=4.5\times10^{-3}$ and $\chi(0)=6.551147852$. Red line is the solution of Eqs. (\ref{['TF1']})-(\ref{['TF2']}) at $\nu=0.04041539748$, and it terminates at $\xi_B=3.0747465$, indicated by the vertical dashed line. Blue curve represents the solution of Eqs. (\ref{['feq1']})-(\ref{['feq2']}) at $\nu=0.36$.
• Figure 5: Black curves represent the solutions of Eq. (\ref{['icon']}) for $A=4.5\times10^{-3}$. The red cross marks the initial condition for the blue curve in Fig. \ref{['sols']}.