Into the lair: gravitational-wave signatures of dark matter

Abstract

The nature and properties of dark matter (DM) are both outstanding issues in physics. Besides clustering in halos, the universal character of gravity implies that self-gravitating compact DM configurations might be spread throughout the universe. The astrophysical signature of these objects may be used to probe fundamental particle physics, or even to provide an alternative description of compact objects in active galactic nuclei. Here we discuss the most promising dissection tool of these configurations: the inspiral of a compact stellar-size object and consequent gravitational-wave emission. The inward motion of this "test probe" encodes unique information about the nature of the central, supermassive DM configuration. When the probe travels through some compact DM profile we show that, within a Newtonian approximation, the quasi-adiabatic evolution of the inspiral is mainly driven by DM accretion into the small compact object and by dynamical friction, rather than by gravitational-wave radiation-reaction. These effects circularize the orbits and leave a peculiar imprint on the gravitational waves emitted at late time. When accretion dominates, the frequency and the amplitude of the gravitational-wave signal produced during the latest stages of the inspiral are nearly constant. In the exterior region we study a relativistic model in which the inspiral is driven by the emission of gravitational and scalar waves. Resonances in the energy flux appear whenever the orbital frequency matches the mass of the DM particle and they correspond to the excitation of the central object's quasinormal frequencies. Unexpectedly, these resonances can lead to large dephasing with respect to standard inspiral templates, to such an extent as to prevent detection with matched filtering techniques. We discuss some observational consequences of these effects for gravitational-wave detection.

Figures (6)

• Figure 1: Level plots corresponding to the ratio $R_p/\ell=1,10^{-4},10^{-8}$ in the $(\sigma_{\rm DM},m_{\rm DM})$ plane, where $\sigma_{\rm DM}$ is the total self-interaction cross section for DM and $m_{\rm DM}$ is the mass of the DM particle. In the left-uppermost part of the parameter space the radius of the small compact object $R_p$ is much larger than the mean free path $\ell$ and accretion occurs at the Bondi-Hoyle rate \ref{['Bondi']}. In the lower-rightmost part of the diagram $R_p\ll\ell$ and accretion is governed by Eq. \ref{['eqmu']}. Straight lines refer to $\mu_p/M=10^{-6}$ and $R=2M$, but they have a simple scaling with the inverse of the mass ratio and with the compactness of the central object.
• Figure 2: Secular evolution of the orbital parameters of a point particle orbiting a constant density, Newtonian star with radius $R=6M$. The particle starts at $r(0)=8M$ with initial eccentricity $e_i\equiv e(t=0)=0.1$. When $r>R$ (blue curves), the evolution is radiation-driven through the quadrupole formula (cf. Appendix \ref{['app:Newtonian_ext']}). When $r<R$ (red curves) the evolution is driven by dynamical friction and by (i) collisionless accretion (left panels, cf. Eq. \ref{['eqmu']}) or ii) Bondi-Hoyle accretion (right panels, cf. Eq. \ref{['Bondi']}). Upper panels: $c_s=0.6$ and the motion is always subsonic. In the interior the orbits circularize quickly. Lower panels: $c_s=0.2$; the inspiral in the interior starts supersonic and the evolution is dominated by dynamical friction. When $v<c_s$, the evolution proceeds qualitatively as in the upper panel. In the small left panels we show (from top to bottom): the radial position in polar coordinates, the module of the particle's velocity and the time evolution of the mass-ratio. The evolution does not qualitatively depend on the accretion rate formula used.
• Figure 3: Gravitational-wave amplitude $h_+ \tilde{r}$ along $(\iota,0)=(\pi/2,0)$ as a function of time when collisionless accretion (left panels) and Bondi accretion (right panels) are considered, respectively. Small panels refer to: a) usual radiation-driven inspiral (neglecting accretion and dynamical friction); b) accretion-driven inspiral (neglecting radiation and dynamical friction); c) inspiral driven by accretion and dynamical friction (neglecting radiation) with $c_s=0.6$, which corresponds to the orbits shown in the top panels of Fig. \ref{['fig:orbits_accretion']}; d) same as panel c) but with $c_s=0.5$; e) supersonic regime with $c_s=0.2$, which corresponds to the orbits shown in the bottom panels of Fig. \ref{['fig:orbits_accretion']}. Remaining parameters as in Fig. \ref{['fig:orbits_accretion']}.
• Figure 4: Circular geodesic motion for different BS models and configurations (cf. Table \ref{['tableconf']}). In the top, middle and lower row we show the orbital frequency $\Omega$, the energy $E_c$ and the specific angular momentum $L_c$, respectively. Each column refers to a different BS model. From left to right: mini-BS, massive-BS and solitonic BS. For each model, we compare the geodesic quantities to those of a Schwarzschild BH and for the solitonic BS model we also compare to the metric elements of a uniform density star with $R=3M$. In the last column, the markers indicate the outer last stable orbit for solitonic BS configurations, which is approximately given by $r\approx 6M$ and $M\Omega_{isco}\approx 0.06804$. The light-rings are given by $r_{l-}\approx2.72093M$ and $r_{m}\approx2.9812M$, with $M\Omega_{l-} \approx 0.188818$ and $M\Omega_{l+}\approx 0.192453$, for the first configuration and $r_{l-}\approx 1.91163M$ and $r_{m}\approx2.99883M$, with $M\Omega_{l-} \approx 0.184590$ and $M\Omega_{l+}\approx 0.192452$, for the second one.
• Figure 5: Dominant $l=2$, $m=1$ contribution to the axial gravitational flux emitted by a point-particle orbiting a BS for the stable BS configurations used in this work, compared to that of a Schwarzschild BH. The most compact configurations are closer to the BH case, and both solitonic configurations for $r>3M$ have basically the same values of the BH case.