Luminosity-duration relation of fast radio bursts

Abstract

Nature of dark energy remains unknown. Especially, to constrain the time variability of the dark-energy, a new, standardisable candle that can reach more distant Universe has been awaited. Here we propose a new distance measure using fast radio bursts (FRBs), which are a new emerging population of $\sim$ ms time scale radio bursts that can reach high-$z$ in quantity. We show an empirical positive correlation between the time-integrated luminosity (L${}_{\nu }$) and rest-frame intrinsic duration ($w_{\mathrm{int},\mathrm{rest}}$) of FRBs. The L${}_{\nu }-w_{\mathrm{int},\mathrm{rest}}$ correlation is with a weak strength but statistically very significant, i.e., Pearson coefficient is $\sim$ 0.5 with p-value of $\sim$0.038, despite the smallness of the current sample. This correlation can be used to measure intrinsic luminosity of FRBs from the observed $w_{\mathrm{int},\mathrm{rest}}$. By comparing the luminosity with observed flux, we measure luminosity distances to FRBs, and thereby construct the Hubble diagram. This FRB cosmology with the L${}_{\nu }-w_{\mathrm{int},\mathrm{rest}}$ relation has several advantages over SNe Ia, Gamma-Ray Burst (GRB), and well-known FRB dispersion measure (DM)-$z$ cosmology; (i) access to higher redshift Universe beyond the SNe Ia, (ii) high event rate that is $\sim$ 3 order of magnitude more frequent than GRBs, and (iii) it is free from the uncertainty from intergalactic electron density models, i.e., we can remove the largest uncertainty in the well-debated DM-$z$ cosmology of FRB. Our simulation suggests that the L${}_{\nu }-w_{\mathrm{int},\mathrm{rest}}$ relation provides us with useful constraints on the time variability of the dark energy when the next generation radio telescopes start to find FRBs in quantity.

arXiv commentAccepted in MNRAS. Summary of the paper can be found at https://youtu.be/1gBBujgiNuQ

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