Revisiting The Cosmological Time Dilation of Distant Quasars: Influence of Source Properties and Evolution

TL;DR

This work tests whether cosmological time dilation is present in quasar variability while accounting for source properties and possible evolution. By modeling a continuous intrinsic timescale surface that depends on rest-frame wavelength and bolometric luminosity, plus an intrinsic scatter and a carefully constructed asymmetric likelihood, the authors infer a cosmological scaling $\Delta t_{ m obs} = \Delta t_{ m int} (1 + z)^n$ with $n = 1.14 \pm 0.34$, consistent with relativistic expansion. The analysis shows timescales increase with wavelength and luminosity, while black-hole mass has no additional explanatory power once $\lambda$ and $L_{\rm bol}$ are included; tests allow for evolution but find it to be small or negligible, and a model with standard cosmology and no evolution is most supported by the data. Overall, the results reaffirm cosmological time dilation in quasar variability and constrain potential evolution, underscoring the importance of robust modelling choices and future large surveys for tighter limits.

Abstract

After decades of searching, cosmological time dilation was recently identified in the timescale of variability seen in distant quasars. Here, we expand on the previous analysis to disentangle this cosmological signal from the influence of the properties of the source population, specifically the quasar bolometric luminosity and the rest-frame emission wavelength at which the variability was observed. Furthermore, we consider the potential influence of the evolution of the quasar population over cosmic time. We find that a significant intrinsic scatter of 0.288 +- 0.021 dex in the variability timescales, which was not considered in the previous analysis, is favoured by the data. This slightly increases the uncertainty in the results. However, the expected cosmological dependence of the variability timescales is confirmed to be robust to changes in the underlying assumptions. We find that the variability timescales increase smoothly with both wavelength and bolometric luminosity, and that black hole mass has no effect on the variability timescale once rest wavelength and bolometric luminosity are accounted for. Moreover, if the standard cosmological model is correct, governed by relativistic expansion, we also find very little cosmological evolution in the intrinsic variability timescales of distant quasars.

Figures (5)

• Figure 1: A corner plot corner of the posterior distribution for the parameters. The most substantial dependence is a negative correlation between $\beta_2$ and $n$.
• Figure 2: The posterior mean regression surface at $z=0$, showing the $\log_{10}$ of the intrinsic variation timescale as a function of wavelength and bolometric luminosity. Each point in the plot represents a measurement, so there are three points per quasar. The typical variation timescale in the rest frame is a little below $10^3$ days and increases smoothly as a function of rest wavelength and bolometric luminosity.
• Figure 3: The joint posterior distribution of $\beta_3$ (the coefficient of an evolution term), and $n$, the cosmological dependence. There is a very strong dependence between these two parameters. Taking a vertical slice at $\beta_3=0$ reproduces the main model's results.
• Figure 4: The posterior distribution of $\beta_3$ (the coefficient of an evolution term), under model $M_6$. The parameter $n$ was fixed to 1, i.e., standard cosmology. The inferred value of $\beta_3$ is small and consistent with zero (vertical dashed line).
• Figure 5: An example of an asymmetric exponential distribution (proportional to our likelihood function) with quantiles set at $x=(2.5, 3.0, 3.4)$.