Dynamical friction on binary stars in dark matter dominated environments

Abstract

We study binary stars moving through a uniform dark matter background and experiencing dynamical friction. The centre-of-mass motion of the pairs is taken into account. We derive formulas and timescales for the secular evolution of the orbital parameters for both wide and close binaries. We apply these results to environments typical of dark matter dominated ultra-faint dwarf galaxies and show that some binaries undergo significant eccentricity oscillations, while their semi-major axes decrease more gradually. We consider a simple binary star population and find that dynamical friction, notably, can enhance the bias from unresolved binaries in velocity dispersion measurements. With future, more detailed theoretical studies and improving observational capabilities, binary stars may serve as a tool to probe the dark matter content of some of the faintest galaxies.

Figures (4)

• Figure 1: Evolution of the semi-major axis (red) and eccentricity (blue) of a wide binary with $m_1 = 1.5 M_\odot$ and $m_2 = 0.5 M_\odot$, initial values $a_0 = 10^4$ AU and $e_0 = 0.25$, and CoM velocity $v_\text{cm} = 3$ km/s, in an environment with $\rho_\text{dm} = 100$ GeV/cm$^3$ and $\sigma = 3$ km/s. Solid curves show the full evolution obtained by integrating Eqs. \ref{['eq:E_evo_wide']} and \ref{['eq:params_evo_wide']}, while the dotted line shows the idealised analytical solution from Eq. \ref{['eq:analytical_evo_wide']}. The orbital parameters $i$, $\Omega$, and $\omega$ also evolve but are not shown; changing their initial values leads to different evolutionary tracks.
• Figure 2: Evolution of the semi-major axis (red) and eccentricity (blue) of a close binary of solar-mass stars with initial values $a_0=1$ AU and $e_0=0.25$, in a environment with $\rho_\text{dm}=10^4$ GeV$/$cm$^3$ and $\sigma=5$ km$/$s. Solid curves show the result of numerically integrating Eq. \ref{['eq:a_tight']}, dashed curves correspond to the solution of Eq. \ref{['eq:E_and_L_evo_tight']}, and the dotted curve shows the solution of Eq. \ref{['eq:analytical_evo_tight']}.
• Figure 3: Distribution of the initial (blue) and final (red) semi-major axes (left panel) and eccentricities (right panel) for a population of 1000 low-mass binaries evolved for 13 Gyr under dark matter dynamical friction, assuming $\rho_\text{dm}=133\text{ GeV}$ and $\sigma=2.1\text{ km/s}$. The inset histograms highlight the 178 binaries with total mass $M > 0.8\,M_\odot$.
• Figure 4: Comparison of various dynamical timescales for wide binaries in an UFD galaxy. The upper grey region corresponds to times longer than the age of the Universe. The left green region indicates where DM dynamical friction dominates the long-term evolution of wide binaries. The right red region marks where at least one of the two wide-binary timescales exceeds the tidal timescale.