When Tiny Halos Stir Spacetime: Gravitational Waves from Fifth-Force Mergers

Abstract

Dark matter fermions interacting via attractive fifth forces mediated by a light mediator can form dark matter halos in the very early universe. We show that bound systems composed of these halos are capable of generating gravitational wave (GW) signals detectable today, even when the individual halos are very light. The Yukawa force dominates the dynamics of these halo binaries, rather than gravity. As a result, large GW signals can be produced at initially extremely high frequencies, which are then redshifted to frequency bands accessible to current or future GW observatories. In addition, the resulting GW signals carry distinctive features that enable future observations to distinguish them from conventional ones. Notably, even if only a tiny fraction of dark matter experiences strong fifth-force interactions, such effects provide a new avenue to discover self-interacting dark matter through GW observations.

Figures (6)

• Figure 1: The characteristic strain of the SGWB from halo mergers is plotted, alongside sensitivity curves of both current and planned GW surveys and constraints. Parameters are fixed at $y=0.1$ and $m_{\mathrm{h}}=10^{-10}M_{\mathrm{y}}$ (as in Fig. \ref{['parameterspace1']}), with $(m_\psi, m_\phi)$ corresponding to the colored dots in Fig. \ref{['parameterspace1']}. In the plot, we consider a total comoving merger density $R(z)\delta z=3\times 10^{-6}(M_{\odot}/m_{\mathrm{h}})/\mathrm{Gpc}^3$. Sensitivity curves are taken from PTAs Kuroda:2015owv, LISA Robson:2018ifk, and aLIGO LIGO_T1800044_v5_2018. The light-red region shows the signal and constraints from the NANOGrav best-fit SIGW from BSMBH inspirals NANOGrav:2023gor. The light-blue region is the constraint on the SGWB coming from Big Bang Nucleosynthesis (BBN).
• Figure 2: Contour of the time ratio $t_{\mathrm{cool}}/t_\mathrm{c}$ for a Yukawa-bound binary halo. We fix $y=0.1$ and $m_1=m_2=m_h=10^{-10}M_{\mathrm{y}}$, where $M_{\mathrm{y}}$ is the total mass of $\psi$ fermions enclosed within the Yukawa range $l_{\mathrm{y}}$ at the end of halo formation, defined in Eq. (\ref{['my']}). The initial orbit is circular with separation $d=l_{\mathrm{y}}$ and halo radius $R=l_{\mathrm{y}}(m_{\mathrm{h}}/M_{\mathrm{y}})^{1/3}$. The red solid line denotes $t_{\mathrm{cool}}=t_{\mathrm{c}}$, with $t_{\mathrm{cool}}>t_\mathrm{c}$ ($<t_\mathrm{c}$) on the left (right). Stable inspirals satisfying $\min(t_{\mathrm{cool}},t_\mathrm{c})>T_0$ occupy the region above the black curve; category A systems ($t_{\mathrm{cool}}>t_\mathrm{c}>T_0$) are enclosed by red dashed lines. White areas are excluded where assumptions break down, and the blue-shaded region is ruled out by observational constraints from Bullet Cluster (left), and $\gamma$-ray and BBN on evaporating PBHs (right). The black dashed contours indicate where halos cannot collapse into black holes without additional mass growth, since the Schwarzschild radius would be smaller than the Compton wavelength of $\psi$. The square marker denotes a case with uncertain post-cooling effective charge retention: the final state could either retain most of its effective charge or lose it significantly, depending on the underlying theory. In Fig. \ref{['hcz']}, we treat this case as in Category B. A more detailed analysis will be presented in future work.
• Figure 3: Total gravitational--wave energy $\Delta E$ from the prompt merger calculated using Eq. (\ref{['deltaEresult']}). The plot is obtained for halo masses $m_1=m_2=2\times10^{17}\,\mathrm{g}$, mediator mass $m_\psi=m_1/q_1=10^{10}\,\mathrm{GeV}$, halo radius $R=3\times10^{-3}\,\mathrm{m}=2\times10^{-10}Gm_1$, initial separation $d_0=\infty$, and coupling constant $y=0.1$. The black solid curve shows the result if full numerical integral, the blue dashed curve the ultrarelativistic approximation, and the red dotted curve the non-relativistic approximation.
• Figure 4: Relativistic beaming effect in gravitational--wave burst scenarios. The contours show the angular distribution of the emitted power, $\mathrm{d}P/\mathrm{d}\Omega\propto A^2$, for different Lorentz factors $\gamma$.
• Figure 5: The trajectory of the black hole in a bound system for different types of initial conditions. The blue-shaded area shows the effective range of the Yukawa force. The black dots show the initial position of the two halos, with one halo fixed at the origin. The red lines show the trajectory of another halo on the plane.