Lensing of Fast Radio Bursts as a Probe of Compact Dark Matter

Abstract: The possibility that part of the dark matter is made of massive compact halo objects (MACHOs) remains poorly constrained over a wide range of masses, and especially in the $20-100\, M_\odot$ window. We show that strong gravitational lensing of extragalactic fast radio bursts (FRBs) by MACHOs of masses larger than $\sim20\,M_\odot$ would result in repeated FRBs with an observable time delay. Strong lensing of an FRB by a lens of mass $M_L$ induces two images, separated by a typical time delay $\sim$ few $\times(M_L/30\, M_\odot)$ milliseconds. Considering the expected FRB detection rate by upcoming experiments, such as CHIME, of $10^4$ FRBs per year, we should observe from tens to hundreds of repeated bursts yearly, if MACHOs in this window make up all the dark matter. A null search for echoes with just $10^4$ FRBs, would constrain the fraction $f_{\rm DM}$ of dark matter in MACHOs to $f_{\rm DM}\lesssim 0.08$ for $M_L\gtrsim 20\,M_\odot$.

Lensing of Fast Radio Bursts as a Probe of Compact Dark Matter

The exploration of dark matter composition continues to be a pivotal topic in astrophysics, with Massive Compact Halo Objects (MACHOs) remaining a viable candidate to form part of the elusive dark matter. Despite significant advancements in constraining MACHO presence within certain mass ranges, particularly within the low and high ends of the spectrum, there exists a mass window from approximately 20 to 100 ( M_\odot ) that remains relatively unbounded. The paper discussed proposes leveraging the gravitational lensing of extragalactic Fast Radio Bursts (FRBs) as a novel method for probing MACHOs within this enigmatic mass range.

Key Insights

1. Gravitational Lensing Basics:

   • Strong lensing by MACHOs would result in repeated FRBs, exhibiting observable time delays due to their compact and massive nature.
   • For lenses with mass ( M_L ), the time delay between images scales as several milliseconds multiplied by ( M_L/30\,M_\odot ), offering a detectable difference if the time delay surpasses the typically narrow pulse width of FRBs.

2. Potential Observations:

   • The upcoming CHIME experiment anticipates a detection rate of around ( 10^4 ) FRBs per year. If MACHOs constitute all dark matter, tens to hundreds of repeated FRB events should be observable annually.
   • A null result from these observations could constrain the MACHO fraction of dark matter, ( f_{\rm DM} ), to a value below 0.08 for masses above 20 ( M_\odot ).

3. Implications for Dark Matter:

   • Current constraints allow MACHOs to form a significant fraction of cosmic dark matter only within the specified mass window.
   • Using FRB lensing as a probe provides a unique method to either confirm significant MACHO presence within dark matter composition or further restrict their contribution.

Practical and Theoretical Implications

The successful application of FRB lensing to identify MACHOs would offer a profound insight into dark matter's nature, corroborating the hypothesis of these compact objects as primary constituents. Such data could provide substantial support for theories suggesting primordial black holes (PBHs) in these mass ranges, ultimately aligning with gravitational wave observations postulated to arise from PBH binaries coalescing.

On a practical level, integrating FRB lens observations with data from projects like CHIME could refine the understanding of cosmic structures and inform future telescopic surveys aimed at incremental mass precision and distribution.

Future Directions

Looking ahead, refining detection methods and improving time resolution on FRB observations will be crucial. Given the constraints observed from current MACHO surveys via Galactic microlensing, FRB lensing might offer a complementary pathway to confine MACHO contributions across broader mass ranges.

Moreover, the burgeoning interdisciplinary field of astrophysics and cosmology stands to benefit from advancements in computational techniques that simulate lensing effects more precisely, aiding in methodological accuracy when assessing lensing-induced periods or magnitudes.

Ultimately, the study of FRB lensing presents an exciting frontier that may substantially advance the understanding of MACHOs and their role within dark matter frameworks. Continued research and observational diligence will be instrumental in exploring the boundaries of current theories and enriching the scientific narrative of our universe's composition.