# Probing motion of fast radio burst sources by timing strongly lensed repeaters

## TL;DR

This paper proposes a method using high-precision timing of strongly lensed repeating FRBs to detect tiny motions of the emission source, providing insights into their physical environment and nature.

## Contribution

It introduces a lens-independent timing technique to probe non-uniform source motions of FRBs through measurable time-delay variations.

## Key findings

- Timing precision of ~1 ms allows detection of small source displacements.
- Earth's orbital motion effects can be accurately subtracted from delay measurements.
- Non-uniform source motion of 0.1-1 AU is detectable over hundreds of days.

## Abstract

Given the possible repetitive nature of fast radio bursts (FRBs), their cosmological origin, and their high occurrence, detection of strongly lensed sources due to intervening galaxy lenses is possible with forthcoming radio surveys. We show that if multiple images of a repeating source are resolved with VLBI, using a method independent of lens modeling, accurate timing could reveal non-uniform motion, either physical or apparent, of the emission spot. This can probe the physical nature of FRBs and their surrounding environments, constraining scenarios including orbital motion around a stellar companion if FRBs require a compact star in a special system, and jet-medium interactions for which the location of the emission spot may randomly vary. The high timing precision possible for FRBs ($\sim {\rm ms}$) compared to the typical time delays between images in galaxy lensing ($\gtrsim 10\, {\rm days}$) enables the measurement of tiny fractional changes in the delays ($\sim 10^{-9}$), and hence the detection of time-delay variations induced by relative motions between the source, the lens, and the Earth. We show that uniform cosmic peculiar velocities only cause the delay time to drift linearly, and that the effect from the Earth's orbital motion can be accurately subtracted, thus enabling a search for non-trivial source motion. For a timing accuracy of $\sim 1\,$ms and a repetition rate (of detected bursts) $\sim 0.05$ per day of a single FRB source, non-uniform displacement $\gtrsim 0.1 - 1\,$AU of the emission spot perpendicular to the line of sight is detectable if repetitions are seen over a period of hundreds of days.