Scaling relations for gamma-ray burst afterglow light curves and centroid motion independent of jet structure and dynamics

Hendrik Van Eerten, Geoffrey Ryan

Research output: Contribution to journalArticlepeer-review


Models for gamma-ray burst afterglow dynamics and synchrotron spectra are known to exhibit various scale invariances, owing to the scale-free nature of fluid dynamics and the power-law shape of synchrotron spectra. Since GRB 170817A, off-axis jet models including a lateral energy structure in the initial outflow geometry have gained in prominence. Here, we demonstrate how the scale invariance for arbitrary jet structure and dynamical stage can be expressed locally as a function of jet temporal light-curve slope. We provide afterglow flux expressions and demonstrate their use to quickly assess the physical implications of observations. We apply the scaling expressions to the Swift X-ray Telescope sample, which shows a spread in observed fluxes, binned by light-curve slope at time of observation, that increases with increasing light-curve slope. According to the scaling relations, this pattern is inconsistent with a large spread in environment densities if these were the dominant factor determining the variability of light curves. We further show how the late deep Newtonian afterglow stage remains scale-invariant but adds distinct spectral scaling regimes. Finally, we show that for given jet structure a universal curve can be constructed of the centroid offset, image size, and ellipticity (that can be measured using very large baseline interferometry) versus observer angle, in a manner independent of explosion energy and circumburst density. Our results apply to any synchrotron transient characterized by a release of energy in an external medium, including supernova remnants, kilonova afterglows, and soft gamma-repeater flares.

Original languageEnglish
Pages (from-to)4094-4106
Number of pages13
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
Early online date27 Apr 2024
Publication statusE-pub ahead of print - 27 Apr 2024

Data Availability Statement

No new data were generated or analysed in support of this research.


  • gamma-ray burst: general
  • gamma-ray bursts: individual: 170817A
  • radiation mechanisms: non-thermal

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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