Hints of Dark Matter Spikes in Low-mass X-ray Binaries: a critical assessment

TL;DR

This paper tests the DM-spike hypothesis as an explanation for anomalously fast orbital decay in three BH-LMXBs by performing $N$-body simulations of binaries embedded in DM spikes with varying density slopes $\gamma$. By explicitly modelling the feedback of the binary on the spike, the authors find rapid depletion of DM near the orbit and show that much steeper spikes than previously claimed are required to reproduce the observed $\dot{P}$, with lower limits $\gamma \gtrsim 2.15$–$2.20$ for Systems A and B and $\gamma \gtrsim 2.3$ for System C. The results imply that simple shallow spikes cannot explain the decays once depletion is accounted for, challenging prior DM-based interpretations, though steeper spikes or different long-term evolutions could still accommodate the observations. The work highlights the importance of spike feedback and motivates longer, higher-resolution simulations to refine the admissible DM-density profiles around stellar-mass black holes and their formation scenarios.

Abstract

Three black-hole low-mass X-ray binaries (LMXBs) in the Milky Way show rates of period decay which cannot be easily explained by standard mechanisms. Recently, it has been claimed that the anomalous period decays in two of these systems may be explained by dynamical friction due to very high dark matter (DM) densities around the black holes. We critically assess these claims by performing $N$-body simulations of binaries embedded in dense DM ``spikes". We simulate the previously-studied systems XTE J1118+480 and A0620--00, as well as studying the third binary Nova Muscae 1991 for the first time in this context. These simulations show that feedback on the DM distribution plays a crucial role and we rule out previously-claimed shallow DM spikes. We set lower limits on the steepness $γ$ of DM density profiles required to explain the period decay in these LMXBs, requiring $γ\gtrsim 2.15-2.20$ in XTE J1118+480 and A0620--00 and $γ\gtrsim 2.3$ in Nova Muscae 1991. Improved modeling of the long-term evolution of binaries embedded in DM spikes may allow us to exclude even larger densities in future.

Figures (6)

• Figure 1: Estimated disruption timescales for DM spikes in the three binary systems. This timescale is obtained by comparing the total gravitational binding energy of a spike with slope $\gamma$ to the rate of energy injection inferred from the observed value of $\dot{P}$. A DM-related explanation of the anomalous inspiral rates is ruled out in the grey shaded region; here, the spike is likely to be completely disrupted on timescales shorter than the duration of observation of these systems, $T_\mathrm{obs} \sim 20 \,\mathrm{yr}$.
• Figure 2: Time evolution of the DM density profile around the BH, for one realisation of system A with initial density profile index $\gamma=9/4$. The red band around the orbital radius indicates the size of the star. Dotted lines indicate the BH softening scale $r_\mathrm{soft}$ and the truncation radius $r_\mathrm{t}$. Thin lines are ten orbits apart, the simulation spans 6000 orbits. Left: DM density as a function of radius. Right: ratio of the final and initial density profiles. Notice that the variation of the orbital radius over 6000 orbits is much too small to be appreciated on this figure.
• Figure 3: Evolution of the orbital period for 16 realisations of System A, assuming a spike index of $\gamma=9/4$ (same as \ref{['fig:depletion']}). Left: fractional change of the orbital period $P$ with respect to the initial value $P_0$, as a function of time. Right: period decay rate $\dot{P}$ as a function of time, averaged over 1000 orbits to reduce noise. The final points of each line (6000 orbits) correspond to our estimates of the period decay rate $\dot{P}_\gamma$.
• Figure 4: Period decay rates extracted from simulations as a function of the spike index $\gamma$. Diamonds mark the decay rates inferred from single realisations, while the vertical error bars span the interval covered by the 11 most central ones, corresponding to $\approx 68\%$ of points. In each panel, the horizontal band shows the observational $1\sigma$ constraint. Values of the spike index that predict a period decay rate lower than the observed one are unable to explain the anomalous decay rates. Arrows indicate the $\gamma$ range that is ruled out by this criterium.
• Figure 5: Limits on dark matter density profiles compatible with the observed decay rates of Systems A, B and C. The DM density predicted by Eq. \ref{['eq:spikes']} is shown as a function of the distance from the BH, for a set of values of the power-law index $\gamma$. The three points indicate, for each system, the value of the density at the orbital radius inferred through \ref{['eq:Pdot']}, neglecting the effects of feedback. The green and blue dots, obtained for Systems A and B respectively, are consistent with the density values inferred by Ref. Chan:2022gqd. The coloured bars indicate the lower limits obtained from simulations, accounting for the depletion of the DM spike by the star. Simulations on longer timescales may lead to further depletion and potentially push these limits to larger DM densities. To avoid overcrowding, in the main panel the density profiles are shown only for System A. The small differences between profiles for the three systems can be appreciated in the inset, where they are shown in different colours.