Gravitational-Wave Fringes at LIGO: Detecting Compact Dark Matter by Gravitational Lensing

Abstract

Utilizing gravitational-wave (GW) lensing opens a new way to understand the small-scale structure of the universe. We show that, in spite of its coarse angular resolution and short duration of observation, LIGO can detect the GW lensing induced by compact structures, in particular by compact dark matter (DM) or primordial black holes of 10 − 10 5 M , which remain interesting DM candidates. The lensing is detected through GW frequency chirping, creating the natural and rapid change of lensing patterns: frequency-dependent amplification and modulation of GW waveforms. As a highest-frequency GW detector, LIGO is a unique GW lab to probe such light compact DM. With the design sensitivity of Advanced LIGO, one-year observation by three detectors can optimistically constrain the compact DM density fraction fDM to the level of a few percent.Introduction. The GW from far-away binary mergers [1, 2] is a new way to see the universe with gravitational interaction. Not only is it revealing astrophysics of solar-mass black holes and neutron stars, but the GW can also carry information of intervening masses and the evolution of the universe through gravitational lensing. Having the long wavelength λ, the GW is usually expected to be lensed by heaviest structures (such as galaxies and their clusters) with large enough Schwarzschild radii, 2GM/c 2 = 2M λ 2 × 10 3 (100 Hz/f ) M . Their prototypical lensing signal is strongly time-delayed GW images [3,4] or statistical correlations [5].

Constraining the gravitational coupling of axion dark matter at LIGO

“…The width m a γ is very narrow [see Eq. (10)] so that k ≈ m a =2. This relation is consistent with the particle interpretation of the phenomenon as a stimulated axion decay into two gravitons.…”

“…Since it has a well predicted waveform chirping in time and frequency domains in a particular way, even small perturbations to the chirping can be confidently detected. Example studies with dark matter perturbations are [9][10][11][12][13][14], one of which is probing coherently oscillating light dark matter around binary mergers [15].…”

Gamma-ray burst lensing parallax: Closing the primordial black hole dark matter mass window

“…1. Supernova lensing magnification can be detected as a deviation in the brightness-redshift relation (result with current data is shown [9]); FRB and GRB pulses can be strongly time-delayed or angular separated (10 4 FRBs up to z ≤ 0.5 [10]); and GW lensing fringes in chirping waveforms can be detected at aLIGO (∼ 10 3 mergers for 1 yr [11]) probing the mass range corresponding to the LIGO frequency band.…”

“…Among several proposals, basically only microlensing of nearby stars have been thoroughly measured, constraining 10 −11 M ∼ 10 M [3][4][5][6][7]; see also [8]. Heavier PBHs are expected to be probed by strong lensing of supernova [9]/FRB [10]/GRB and lensing fringes of GW at aLIGO [11]. On the other hand, lensing cannot efficiently probe lighter PBHs in the range 10 −16 M -10 −11 M , as lensing is typically too weak and fragile to be resolved; in particular, source size and wave-optics effects are limitations [12,13].…”

“…Thus, different brightness with the same energy spectra between simultaneous measurements is a basic signal of lensing. However, the interference fringe (in the energy spectrum) [11,15,16] becomes relevant when the wavelength λ is about to be too long to probe small PBHs with mass M , i.e. λ ∼ O(GM/c 2 ) (equivalently, c∆t d /λ ∼ O(1)).…”