Dancing in the dark: probing Dark Matter through the dynamics of eccentric binary pulsars

Abstract

We investigate the dynamics of eccentric binary pulsars embedded in dark matter environments. While previous studies have primarily focused on circular orbits in collisionless dark matter halos, we extend this framework to eccentric systems and explore their interaction with ultralight scalar fields. Adopting a perturbative approach, we compute the modifications to the orbital period induced by dark matter-driven dynamical friction. Our results show that orbital eccentricity amplifies the imprints of non-vacuum environments on binary dynamics, underscoring the potential of such systems as sensitive probes for dark matter signatures.

Figures (4)

• Figure 1: (Top Row) Absolute value of the secular change in the orbital period as a function of $\alpha$ for binary pulsars with $m_1=1.3M_\odot$ and $m_2=0.3M_\odot$ and different values of eccentricity. For all configurations we assume $\beta=\pi/2$ and $P_b=100$ days. Solid and dashed curves refer to DM wind speed of $v_w=100$ km/s and $v_w=200$ km/s, while left and right panel to velocity dispersion of $\sigma=50$ km/s and $\sigma=150$ km/s, respectively. (Bottom Row) Secular change in the orbital period for the same configurations shown in the top panels. Horizontal dashed black lines identify specific values of $\dot{P}_b$. Gray and white regions correspond to parameter space in which $\dot{P}_b>0$ and $\dot{P}_b<0$, respectively.
• Figure 2: Secular change in the orbital period as given from Eq. \ref{['eq:Pdot-sec']} for binaries on eccentric orbits, normalized to the circular case, as a function of the angle $\alpha$. Each panel corresponds to a different choice of the DM wind velocity $v_w$ and of the velocity dispersion $\sigma$. Values of $\dot{P}_{b}$ are obtained for a binary pulsar with component masses $m_1=1.3M_\odot$ and $m_2=0.3M_\odot$. The lower solid (upper dashed) curve of each colored band identify binaries with orbital period of $P_b=100$ ($P_b=200$) days. For all panels we fix $\beta=\pi/2$.
• Figure 3: Same as Fig. \ref{['Fig2']} but fixing $\alpha=\pi/2$ and varying $\beta$.
• Figure 4: Density plots for the change in the orbital period for binaries on eccentric orbits (left panel: $e=0.3$; right panel: $e=0.9$), normalized to the circular case, as a function of $m_1$ and the mass ratio $m_2/m_1$. In both panels, we fix $\alpha=\beta=\pi/2$, $P_b = 100$ days, $\sigma = 100~\unit{km/s}$, and $v_w = 250~\unit{km/s}$. The yellow star identifies the case discussed in Figs. \ref{['Fig1']}--\ref{['Fig2']}, with $m_1 = 1.3\,M_\odot$ and $m_2 = 0.3\,M_\odot$.