Prospects for detecting asteroid-mass primordial black holes in extreme mass-ratio inspirals with continuous gravitational waves

TL;DR

The paper targets the largely unconstrained asteroid-mass PBH dark matter window by proposing continuous gravitational-wave searches for very slowly evolving EMRIs, where a PBH companion orbits a stellar-mass object. It develops a semi-analytic sensitivity framework based on the frequency-Hough method to translate non-detections into constraints on the PBH DM fraction, expressed through the parameter $\tilde{f}=f_{\rm PBH}[f_{\rm sup}f(m_1)f(m_2)]^{37/53}$, and evaluates projected limits for ET and NEMO across mass, frequency, and eccentricity. The analysis shows that higher GW frequencies contribute most to constraints for small PBH masses, while lower frequencies matter for larger masses, and that relaxing linearity or improving time-frequency tracking could dramatically improve current capabilities. The findings indicate that next-generation detectors like ET and NEMO could set stringent limits on asteroid-mass PBHs that are complementary to microlensing probes, especially when analysis methods are adapted to non-linear and transient CW signals.

Abstract

Despite decades of research, the existence of asteroid-mass primordial black holes (PBHs) remains almost completely unconstrained and thus could still comprise the totality of dark matter (DM). In this paper, we show that standard searches for continuous gravitational waves -- long-lived, quasi-monochromatic signals -- could detect extreme mass-ratio inspirals of asteroid-mass PBHs in orbit around a stellar-mass companion using future gravitational-wave (GW) data from Einstein Telescope (ET) and the Neutron Star Extreme Matter Observatory (NEMO). We evaluate the robustness of our projected constraints against the eccentricity of the binary, the choice of the mass of the primary object, and the GW frequency range that we analyze. Furthermore, to determine whether there could be ways to detect asteroid-mass PBHs using current GW data, we quantify the impact of changes in current techniques on the sensitivity towards asteroid-mass PBHs. We show that methods that allow for signals with increased and more complicated frequency drifts over time could obtain much more stringent constraints now than those derived from standard techniques, though at slightly larger computational cost, potentially constraining the fraction of DM that certain asteroid-mass PBHs could compose to be less than one with current detectors.

Figures (9)

• Figure 1: Synthetic upper limits obtained using \ref{['eqn:h0min']} in each 1 Hz band using an ET sensitivity curve and the following analysis parameters: $T_\text{FFT}=1.5$ days; $T_\text{obs}=1$ year; $\Gamma=0.95$, $CR_\text{thr}=5$, and $\theta_\text{thr}=2.5$ .
• Figure 2: Using \ref{['eqn:dmax95']} and the ET power spectral density curve, we have computed the expected luminosity distance reach (left) and $\tilde{f}$ (right) as a function of $m_1$ and $m_2$, enforcing the criteria that $\dot{f}\leq\dot{f}_{\rm max}=10^{-9}$ Hz/s and that the linear approximation in \ref{['eqn:ftay']} holds. We have only plotted points in which $\tilde{f}<1$, and have assumed that the eccentricity is negligible, an assumption that will be relaxed later in \ref{['sec:anacons']}.
• Figure 3: Left: Varying the maximum spin-up to which CW searches are sensitive results in different constraints on $\tilde{f}$. Current searches consider $\dot{f}_{\rm max}=10^{-9}$ Hz/s. We can see that smaller $\dot{f}$ indicates not only a poorer sensitivity at small $m_2$, but also an inability to reach higher values of $m_2$, since the signal spin up will increase to be higher than $\dot{f}_{\rm max}$ during $T_\text{obs}$. The degradation in sensitivity of smaller $\dot{f}_{\rm max}$ occurs because signals at higher frequencies cannot contribute to the sum in \ref{['eqn:ratedenssolved']}, since the signal would either take on $\dot{f}\geq\dot{f}_{\rm max}$, and/or the GW frequency evolution cannot be described by \ref{['eqn:ftay']} anymore. Right: A comparison showing how much the constraints would improve if no $\dot{f}_{\rm max}$ existed, that is, if the signal could be searched for at arbitrarily high $\dot{f}$ with a frequency evolution following \ref{['eqn:powlaws']}. In both plots, we have set $\delta f =1$ Hz, which represents the approximate spacing in upper limits that is obtained through injections in CW searches KAGRA:2022dwb.
• Figure 4: We vary the eccentricity and compute the expected constraint on $\tilde{f}$ for a fixed $m_1=2.5M_\odot\xspace$ for a search that assumes $\dot{f}_{\rm max}=10^{-9}$ Hz/s and using the ET power spectral density. Highly eccentric systems are much harder to constrain with standard CW searches than lower ones, $\dot{f}_{\rm ecc}$ exceeds $\dot{f}_{\rm max}$ much more easily than for low-eccentricity systems.
• Figure 5: Accumulated rate density constraint as a function of which frequency we begin to sum the distance reaches in \ref{['eqn:ratedenssolved']} up to a maximum given by the right-most frequency on each curve. This has been computed using the ET power spectral density and assuming $m_1=2.5M_\odot\xspace$. The frequency on the x-axis represents the minimum frequency considered in the range $[f_\text{min},f_\text{max}]$. For all values of $m_2$ plotted here, it is clear that the rate density saturates at a particular minimum frequency, which means that it is no longer beneficial to consider frequencies below $f_\text{min}$ in the sum to compute constraints on the rate density.