[Paper Review] Coexistence Test of Primordial Black Holes and Particle Dark Matter from Diffractive Lensing

Han Gil Choi, Sunghoon Jung+2 more|arXiv (Cornell University)|Nov 29, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes using diffractive lensing of gravitational waves from binary black hole mergers to detect and distinguish 'dressed primordial black holes' (dPBHs)—PBHs embedded in particle dark matter halos—thereby testing the coexistence of primordial black holes and particle dark matter. The method enables event-by-event discrimination between dPBHs and bare PBHs via frequency-dependent wavefront distortions, uniquely identifying subdominant PBHs in a particle DM background.

ABSTRACT

If dark matter (DM) consists of primordial black holes (PBHs) and particles simultaneously, PBHs are generically embedded within particle DM halos. Such ``dressed PBHs'' (dPBHs) are subject to modified constraints compared to PBHs and can contribute to significant DM abundance in the mass range $10^{-1} - 10^2 M_\odot$. We show that diffractive lensing of chirping gravitational waves (GWs) from binary mergers can not only discover, but can also identify dPBH lenses and discriminate them from bare PBHs on the event-by-event basis, with potential to definitively establish the coexistence of subdominant PBHs and particle DM.

Motivation & Objective

• To test the coexistence of primordial black holes (PBHs) and particle dark matter (DM) by identifying dPBHs—PBHs embedded in particle DM halos.
• To overcome the degeneracy in distinguishing dPBHs from bare PBHs using conventional lensing methods.
• To develop a model-independent method to probe the mass profile of PBH lenses via gravitational wave diffractive lensing.
• To establish a unique observational signature for primordial origin of PBHs through halo-induced lensing effects.

Proposed method

• Utilizes diffractive lensing of chirping gravitational wave (GW) signals from binary mergers, which distorts the wavefront over a broad frequency band.
• Applies high-precision GW waveform modeling to extract frequency-dependent amplification effects caused by extended mass profiles of dPBHs.
• Employs Bayesian inference with a Poisson likelihood model to compute upper limits on PBH abundance $f_{\text{PBH}}$ under null detection.
• Uses the optimal signal-to-noise ratio (SNR) $\rho_0(M,\eta,z_s)$ to compute lensing optical depth $\langle\tau(z_s)\rangle$ for binary black hole populations.
• Assumes a flat $\Lambda$CDM cosmology with $H_0=67.74~\mathrm{km~s^{-1}~Mpc^{-1}}$, $\Omega_m=0.3075$, and $\Omega_{\mathrm{CDM}}=0.2575$ to compute comoving volume and merger rates.
• Applies a uniform prior on $f_{\text{PBH}}$ and computes the 90% upper limit via posterior distribution under null detection ($k=0$).

Experimental results

Research questions

• RQ1 Can diffractive lensing of gravitational waves distinguish 'dressed' primordial black holes (dPBHs) from bare PBHs on an event-by-event basis?
• RQ2 Does the presence of a particle dark matter halo around PBHs produce a unique, detectable frequency-dependent distortion in GW waveforms?
• RQ3 Can this method uniquely establish the coexistence of subdominant PBHs and particle dark matter without relying on specific particle DM interactions?
• RQ4 What is the projected sensitivity of future GW detectors (e.g., Cosmic Explorer, Einstein Telescope) to dPBHs via this lensing signature?
• RQ5 How does the halo mass profile of dPBHs, derived from spherical collapse theory, affect the lensing observables?

Key findings

• Diffractive lensing enables event-by-event discrimination between dPBHs and bare PBHs through frequency-dependent wavefront distortions, uniquely identifying dPBHs.
• The halo mass of dPBHs is estimated as $M_h \simeq 97 \left(\frac{31}{1+z_c}\right) M_{\text{PBH}}$, with a density profile $\rho_h(r) \propto (R_h/r)^{9/4}$, consistent with N-body simulations.
• The method is sensitive to PBH masses in the $10^{-1} \sim 10^2 M_\odot$ range, optimal for LIGO-band frequencies.
• Under null detection ($k=0$) over 5 years, the 90% upper limit on $f_{\text{PBH}}$ is computed via the posterior distribution $p(f_{\text{PBH}}|0) = \nu_L \frac{e^{-f_{\text{PBH}} \nu_L}}{1 - e^{-\nu_L}}$, with $\nu_L$ derived from merger rates and lensing optical depth.
• The approach provides a model-independent probe of the coexistence scenario, avoiding reliance on specific particle DM interaction models.
• The method uniquely establishes the primordial origin of PBHs by detecting the extended mass profile of dPBHs, which astrophysical black holes do not form.