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

TL;DR

It is shown that strong gravitational lensing of extragalactic fast radio bursts (FRBs) by MACHOs of masses larger than ∼20  M_{⊙} would result in repeated FRBs with an observable time delay, which should observe from tens to hundreds of repeated bursts yearly.

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 $M_L\gtrsim 20\,M_\odot$.

Figures (4)

• Figure 1: A histogram of the 17 FRBs observed to date, with inferred redshifts 1601.03547. FRB redshift distributions are plotted assuming a constant comoving density (solid-red), and following the star-formation history (dashed-blue), both with a cutoff at $z_{\rm cut}=0.5$, and normalized to match the total number of detected events.
• Figure 2: Integrated optical depth, with weightings corresponding to a population of FRBs with constant comoving density (red curves) and following the SFH (blue curves), both with a cutoff at $z_{\rm cut}=0.5$. In dashed, solid, and dotted lines we require a time delay $\Delta t>$ 0.3, 1, and 3 ms, respectively. In all cases, $f_{\rm DM}=1$.
• Figure 3: Joint probability distribution for the flux ratio $R_f$ and time delay $\Delta t$ between the two peaks of a FRB lensed by a 30 $M_\odot$ MACHO. On the right, we marginalize over $R_f$, and show the probability to find a time delay $\Delta t$. The shaded region corresponds to time delays smaller than 1 ms, too short to be detectable.
• Figure 4: Fraction $f_{\rm DM}$ of dark matter allowed in the form of point lenses of mass $M_L$, if no events out of $N_{\rm FRB}=10^4$ are lensed, where the FRBs have a constant comoving density with a cutoff at $z_{\rm cut}=0.5$. In dashed, solid, and dotted black we show our constraints when we require a time delay $\Delta t>$ 0.3, 1, and 3 ms, respectively. In red we show the current constraints from the MACHO Collaboration, in green the ones from the EROS Collaboration, and in blue the constraints from galactic wide binaries.