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

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 $20–100M_{\odot }$ window. We show that strong gravitational lensing of extragalactic fast radio bursts (FRBs) by MACHOs of masses larger than $\sim 20M_{\odot }$ would result in repeated FRBs with an observable time delay. Strong lensing of a FRB by a lens of mass $M_L$ induces two images, separated by a typical time delay $\sim \text{few}\times (M_L/30M_{\odot })\mathrm{msec}$. Considering the expected FRB detection rate by upcoming experiments, such as canadian hydrogen intensity mapping experiment (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 $f_{\mathrm{DM}}$ of dark matter in MACHOs to $f_{\mathrm{DM}}\lesssim 0.08$ for $M_L\gtrsim 20M_{\odot }$.

Figure 1

A histogram of the 17 FRBs observed to date, with inferred redshifts [23]. FRB redshift distributions are plotted assuming a constant comoving density (solid red curve) and following the star-formation history (dashed blue curve), both with a cutoff at $z_{\text{cut}}=0.5$, 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 $z_{\text{cut}}=0.5$. In dashed, solid, and dotted lines, we require a time delay $\mathrm{\Delta }t>0.3$, 1, and 3 ms, respectively. In all cases, $f_{\mathrm{DM}}=1$.

Figure 3

Joint probability distribution for the flux ratio $R_f$ and time delay $\mathrm{\Delta }t$ between the two peaks of a FRB lensed by a $30M_{\odot }$ MACHO. On the right, we marginalize over $R_f$ and show the probability to find a time delay $\mathrm{\Delta }t$. The shaded region corresponds to time delays smaller than 1 ms, too short to be detectable.

Figure 4

Fraction $f_{\mathrm{DM}}$ of dark matter allowed in the form of point lenses of mass $M_L$, if no events out of $N_{\mathrm{FRB}}=10^4$ are lensed, where the FRBs have a constant comoving density with a cutoff at $z_{\text{cut}}=0.5$. In dashed, solid, and dotted black lines, we show our constraints when we require a time delay $\mathrm{\Delta }t>0.3$, 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.