JWST lensed quasar dark matter survey IV: Stringent warm dark matter constraints from the joint reconstruction of extended lensed arcs and quasar flux ratios

TL;DR

This work uses JWST lensed quasars to tightly constrain warm dark matter by jointly reconstructing extended lensed arcs and quasar flux ratios across 28 quadruply imaged systems. A forward-modeling Bayesian framework incorporates full populations of subhalos, line-of-sight halos, and globular clusters, with subhalo tidal evolution and free-streaming effects, evaluated via decoupled multi-plane lensing and importance sampling of imaging data. Imposing arcs constraints breaks degeneracies between substructure abundance and the dark-matter free-streaming scale, yielding m_hm < 10^{7.4} M_sun (Galacticus prior) and m_hm < 10^{7.2} M_sun (N-body prior), corresponding to thermal relic masses of 7.4–8.4 keV, with 95% exclusion limits around 11 keV. In CDM, the inferred subhalo surface density is Sigma_sub ≈ 1.7^{+2.6}_{-1.2} × 10^7 M_sun kpc^{-2}, with a projected subhalo fraction f_sub ≈ 3% (95% CL), broadly consistent with semi-analytic predictions but mildly higher than some N-body results. The analysis demonstrates the strongest WDM bounds to date from strong lensing and highlights the power of combining arc and flux-ratio information, paving the way for larger samples from Euclid, Rubin, and Roman.

Abstract

We present a measurement of the free-streaming length of dark matter (DM) and subhalo abundance around 28 quadruple image strong lenses using observations from JWST MIRI presented in Paper III of this series. We improve on previous inferences on DM properties from lensed quasars by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications (flux ratios). Our forward modeling framework generates full populations of subhalos, line-of-sight halos, and globular clusters, uses an accurate model for subhalo tidal evolution, and accounts for free-streaming effects on halo abundance and concentration. Modeling lensed arcs leads to more-precise model-predicted flux ratios, breaking covariance between subhalo abundance and the free-streaming scale parameterized by the half-mode mass $m_{\rm{hm}}$. Assuming subhalo abundance predicted by the semi-analytic model {\tt{galacticus}} ($N$-body simulations), we infer (Bayes factor of 10:1) $m_{\rm{hm}} < 10^{7.4} \mathrm{M}_{\odot}$ ($m_{\rm{hm}} < 10^{7.2} \mathrm{M}_{\odot}$), a 0.4 dex improvement relative to omitting lensed arcs. These bounds correspond to lower limits on thermal relic DM particle masses of $7.4$ and $8.4$ keV, respectively. Conversely, assuming DM is cold, we infer a projected mass in subhalos ($10^6 < m/M_{\odot}<10^{10.7}$) of $1.7_{-1.2}^{+2.6} \times 10^7 \ \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$ at $95 \%$ confidence. This is consistent with {\tt{galacticus}} predictions ($0.9 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$), but in mild tension with recent $N$-body simulations ($0.6 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$). Our results are among the strongest bounds on WDM, and the most precise measurement of subhalo abundance around strong lenses. Further improvements will follow from the large sample of lenses to be discovered by Euclid, Rubin, and Roman.

Figures (26)

• Figure 1: Illustrations of the various steps in the calculation of the likelihood function, as detailed in Section \ref{['ssec:likelihood']}. This example shows one lens model constructed for GRAL1131+4419. The calculations depicted here are performed millions of times per lens to compute the likelihood function (Equation \ref{['eqn:likelihood']}). Top row: Observed (left) and reconstructed (center) image of GRAL1131+4419. The imaging data importance weight (Equation \ref{['eqn:imageweights']}) is given in the center panel. On the right we show effective convergence (Equation \ref{['eqn:effectivekappa']}) for this lens model. The dark matter hyper-parameters $\qsub$ (see Section \ref{['sec:dmmodel']} for details on the dark matter model) and the strength of the multipole perturbations to the macromodel (see Section \ref{['ssec:macromodel']} for discussion on the macromodel) are quoted in the upper left and right corners, respectively. The black line is the critical curve. Center row: Zoomed in regions around each lensed image showing the effective convergence near the image. Subhalos and field halos at $z \leq z_{\rm{d}}$ appear round in the convergence maps, while halos behind the main deflector, whose lensing effects are amplified by the macromodel, appear elongated along the tangential direction of the critical curve. Bottom row: Model-predicted quasar images obtained by ray tracing through the lens system to a background source with a size 1.3 pc, characteristic of the compact warm dust region from which we measure flux ratios. We compute image magnifications (quoted in the top left) by computing the total integrated flux on a high resolution grid (416 by 416 pixels, resolution 0.00011 arcsec/pixel). The panels show how a lensed image would appear, as seen through a telescope with exquisite angular resolution and deconvolution with a perfectly-known PSF.
• Figure 2: Distributions of macromodel parameters that illustrate the role of the importance sampling weights (Equation \ref{['eqn:imageweights']}) used to incorporate constraints from lensed arcs. Solid (dashed) contours are $68 \%$ ($95 \%$) confidence intervals. Left: Parameters inferred for GRAL1131 (see Figure \ref{['fig:1131zooms']}) include the main deflector axis ratio $q$, external shear strength $\gamma_{\rm{ext}}$, the logarithmic profile slope of the main deflector mass profile $\gamma$, the strength of $m=3$ and $m=4$ multipole perturbations, and the mass of satellite galaxy near J0607, $\theta_{\rm{E},G2}$. The gray distribution shows the prior $p\left(\xlens\right)$ updated with constraints from the astrometric likelihood. The blue distributions shows the inference from image positions and lensed arcs. The green distribution represents the importance weights $w_{\rm{img}}$ defined in Equation \ref{['eqn:imageweights']}, marginalized over $\xlight$, that encode new information from the imaging data (gray $\times$ green = blue). Right: The same as the left panel, but showing parameters for J0607 (see second row of Figure \ref{['fig:mosaic']}), including the mass of its satellite galaxy $\theta_{\rm{E},G2}$.
• Figure 3: The model-predicted flux ratios for GRAL1131 (left) and J0607 (right) obtained by propagating the image data importance weights $w_{\rm{img}}$ through the inference pipeline. The gray distribution corresponds to the gray distribution in Figure \ref{['fig:wimgpdfs']}, and shows model-predicted flux ratios given the prior $p\left(\xlens\right)$ and the astrometric likelihood. The blue distributions, which correspond to the blue distributions in Figure \ref{['fig:wimgpdfs']}, show the flux ratios after weighting by $w_{\rm{img}}$. The improved precision in the model predicted flux ratios enables stronger constraints on dark matter properties. Red crosshairs are measured values.
• Figure 4: Left: The infall (solid lines) and bound (dashed and dotted lines) subhalo mass functions predicted by our tidal evolution model for $m_{\rm{hm}}=10^8 \mathrm{M}_{\odot}$. To suppress sample variance we show the median across 100 realizations with $\Sigma_{\rm{sub}} = 0.1 \ \rm{kpc^{-2}}$ in a circular aperture with an area $1086 \ \rm{kpc^2}$. The cyan (black) curves correspond to WDM (CDM). Linestyles correspond to bound mass functions with different assumed concentration--mass relations: The dashed black curve uses a CDM-like concentration--mass relation, the dashed cyan curve uses a WDM-like concentration--mass relation (Equation \ref{['eqn:wdmmc']}), and the dotted cyan curve assumes a CDM-like concentration--mass relation. Right: Suppression of the subhalo bound mass function as a function of infall mass assuming $m_{\rm{hm}}=10^8 \mathrm{M}_{\odot}$. Solid curves show the amplitude of the infall mass functions relative to the CDM infall mass function. The dashed black (cyan) curve shows the bound mass function in CDM (WDM), relative to the infall mass function in CDM (WDM). Shaded regions encompass $1 \sigma$ scatter. The extra suppression on small scales in WDM occurs due to the dependence of tidal stripping on infall concentration: because WDM halos have lower concentrations, they lose more mass.
• Figure 5: Top: The density profiles of halos and subhalos in CDM (black), and in a WDM (cyan) model with $m_{\rm{hm}} = 10^{8.5} \mathrm{M}_{\odot}$. The field halos, with density profiles constructed at $z=2$ (solid lines), have a total mass $10^9 \mathrm{M}_{\odot}$. The scale radius of the CDM field halo is $r_\mathrm{s} = 1.6 \ \rm{kpc}$, and the CDM subhalo has this same scale radius at infall. Due to free-streaming effects, the WDM halo and subhalo have a lower concentration, with $r_\mathrm{s} = 2.7 \ \rm{kpc}$. The dashed curves show density profiles of subhalos with $m_{\rm{infall}}=10^9 \mathrm{M}_{\odot}$ obtained with our tidal stripping model Du++25, which predicts that this WDM subhalo loses twice as much mass by $z=0.5$. The panel under the x-axis shows the density profile of the tidally-evolved subhalos, relative to the density profiles in the field or at infall, and clearly shows the effects of additional mass loss due to more efficient tidal stripping. Bottom: The logarithmic profile slope of the field halos and subhalos shown in the top panel. Our tidal stripping model predicts most subhalos have logarithmic profile slopes $|d \log \rho / d \log r| \sim 2-4$ at $r_\mathrm{s}$.