[Paper Review] Forward modelling of quasar light curves and the cosmological matter power spectrum on milliparsec scales

Mansour Karami, Niayesh Afshordi+1 more|arXiv (Cornell University)|May 17, 2018

Galaxies: Formation, Evolution, Phenomena21 references6 citations

TL;DR

This paper presents a novel Monte Carlo Markov Chain (MCMC) method to jointly model time delays, intrinsic quasar variability, and gravitational lensing fluctuations in strongly lensed quasar light curves. It achieves the strongest constraint to date on the primordial scalar power spectrum at small scales, with $\mathcal{P}_{\mathcal{R}} < 3 \times 10^{-9}$ at $k_{\rm L} \sim 3~\mathrm{pc}^{-1}$, consistent with $\Lambda\mathrm{CDM}$ predictions.

ABSTRACT

We devise an optimal method to measure the temporal power spectrum of the lensing and intrinsic fluctuations of multiply-imaged strongly lensed quasar light curves, along with the associated time delays. The method is based on a Monte-Carlo Markov Chain (MCMC) sampling of a putative gaussian likelihood, and accurately recovers the input properties of simulated light curves, as well as the "Time Delay Challenge". We apply this method to constrain the dimensionless cosmological (non-linear) matter power spectrum on milliparsec scales (comparable to the size of the solar system), to $Δ_{ m NL}^2&lt; 4 imes 10^7$ at $k_{ m NL} \sim 10^3 { m pc}^{-1}$. Using a semi-analytic nonlinear clustering model which is calibrated to simulations, the corresponding constraint on the primordial (linear) scalar power spectrum is ${\cal P}_{\cal R} &lt; 3 imes 10^{-9}$ at $k_{ m L}\sim$ 3 pc$^{-1}$. This is the strongest constraint on primordial power spectrum at these scales, and is within an order of magnitude from the standard $Λ$CDM prediction. We also report measurements of temporal spectra for intrinsic variabilities of quasar light curves, which can be used to constrain the size of the emitting region in accretion disks. Future cadenced optical imaging surveys, such as LSST, should increase the number of observed strongly lensed quasars by 3 orders of magnitude and significantly improve these measurements, even though improvements in modelling quasar accretion and stellar microlensing are necessary.

Motivation & Objective

• To develop a robust, forward modeling framework that simultaneously fits time delays, intrinsic quasar variability, and lensing-induced fluctuations in multiply-imaged quasar light curves.
• To constrain the nonlinear cosmological matter power spectrum on milliparsec scales using observed temporal power spectra from lensed quasars.
• To translate constraints on the nonlinear matter power spectrum into bounds on the primordial linear scalar power spectrum using a calibrated semi-analytic model.
• To measure the temporal power spectrum of intrinsic quasar variability, providing insights into accretion disk size and emission structure.
• To assess the feasibility of detecting transient weak lensing from dark matter nanostructures using current and future optical surveys.

Proposed method

• Employs a Monte Carlo Markov Chain (MCMC) sampling technique to explore a Gaussian likelihood function constructed from observed light curves.
• Models the observed light curves as a sum of three components: intrinsic quasar variability, time delays between lensed images, and lensing fluctuations from stellar microlensing and dark matter substructures.
• Uses a semi-analytic model (P2SAD) calibrated to N-body simulations to relate the nonlinear matter power spectrum to the linear primordial power spectrum.
• Incorporates a finite-size emission region model for quasar accretion disks, with size as a free parameter in the fitting process.
• Validates the method on the Time Delay Challenge (TDC) dataset, demonstrating accurate recovery of time delays and power spectra.
• Applies the method to real COSMOGRAIL light curves from six strongly lensed quasar systems to derive upper limits on the matter power spectrum.

Experimental results

Research questions

• RQ1 Can a unified forward modeling approach accurately recover time delays, intrinsic variability, and lensing fluctuations from quasar light curves?
• RQ2 What are the tightest constraints on the nonlinear matter power spectrum on milliparsec scales from current optical light curves?
• RQ3 How do uncertainties in the quasar emission region size affect constraints on the matter power spectrum and primordial power spectrum?
• RQ4 Can the temporal power spectrum of intrinsic quasar variability be reliably measured and used to infer accretion disk size?
• RQ5 To what extent can future surveys like LSST improve constraints on dark matter substructures and the primordial power spectrum?

Key findings

• The method successfully recovers time delays and power spectra in the Time Delay Challenge dataset with sub-percent accuracy, validating its robustness.
• The strongest constraint on the dimensionless nonlinear matter power spectrum is $\Delta_{\rm NL}^2 < 4 \times 10^7$ at $k_{\rm NL} \sim 10^3~\mathrm{pc}^{-1}$, corresponding to milliparsec scales.
• Using the P2SAD model, this translates to a constraint on the primordial scalar power spectrum of $\mathcal{P}_{\mathcal{R}} < 3 \times 10^{-9}$ at $k_{\rm L} \sim 3~\mathrm{pc}^{-1}$, the tightest such limit to date.
• The constraint on the primordial power spectrum is within an order of magnitude of the $\Lambda\mathrm{CDM}$ prediction, supporting the standard model at small scales.
• The intrinsic variability power spectrum is measured for multiple quasars, with implications for estimating accretion disk sizes, especially in systems like J1206+4332.
• Future surveys such as LSST are expected to increase the number of observed strongly lensed quasars by three orders of magnitude, enabling significant improvements in statistical precision.