Pushing the limits of detectability: mixed dark matter from strong gravitational lenses

Abstract

One of the frontiers for advancing what is known about dark matter lies in using strong gravitational lenses to characterize the population of the smallest dark matter haloes. There is a large volume of information in strong gravitational lens images - the question we seek to answer is to what extent we can refine this information. To this end, we forecast the detectability of a mixed warm and cold dark matter scenario using the anomalous flux ratio method from strong gravitational lensed images. The halo mass function of the mixed dark matter scenario is suppressed relative to cold dark matter but still predicts numerous low-mass dark matter haloes relative to warm dark matter. Since the strong lensing signal receives a contribution from a range of dark matter halo masses and since the signal is sensitive to the specific configuration of dark matter haloes, not just the halo mass function, degeneracies between different forms of suppression in the halo mass function, relative to cold dark matter, can arise. We find that, with a set of lenses with different configurations of the main deflector and hence different sensitivities to different mass ranges of the halo mass function, the different forms of suppression of the halo mass function between the warm dark matter model and the mixed dark matter model can be distinguished with 40 lenses with Bayesian odds of 30:1.

Keywords: dark matter; galaxies: structure; gravitational lensing: strong; methods: statistical.

Figure 1.

Example halo mass functions for CDM (blue), WDM (green), and MixDM (red) cases, where the warm component of the MixDM case has the same mass as the WDM case, specifically, that the M_hm = 10^8.5 M_⊙ for both models.

Figure 2.

Example 2D histograms of flux ratios (f_i are the flux ratios of individual images) for CDM, WDM, and MixDM cases. The width of the distributions corresponds to the statistical signal that we seek to use to differentiate these models.

Figure 3.

On the left, we show likelihoods of the Z-statistic for various half-mode masses for the WDM and MixDM cases for our first mock lens. Some of these distributions are identical, which would mean, no matter how many observations drawn from the distribution, they should be indistinguishable. On the right, we show likelihoods for M_hm = 10¹⁰ M_⊙ for the MixDM model and M_hm = 10^9.5M_⊙ for the WDM model, which overlap for the first lens, and likelihoods for the same parameters and models for the second lens, which do not overlap. Thus, if we combine information from different lenses with different lens configurations, we will be able to break these degeneracies.

Figure 4.

Configurations of the two lenses (lens 1 left, lens 2 right) in question and labelled by the flux ratios for each image. The critical curves are also displayed.

Figure 5.

Posteriors for the half-mode mass and normalization of the subhalo mass function for 40 mock lenses for the WDM case (left) and for the MixDM case (right). The green line denotes the true parameters of the MixDM model that was used to generate the data.

Figure 6.

Cumulative Bayes factor between the MixDM and WDM models as a function of number of lenses. This surpasses the Jeffreys scale threshold for a ‘strong’ preference at 25 lenses, and at 40 lenses, prefers the MixDM model by a factor of 30:1. The red line corresponds to the forecasted statistical preference for the 31 lenses we will observe with upcoming JWST observations.

Figure 7.

Posterior for the case where the CDM fraction f is varied alongside the half-mode mass M_hm and the normalization of the subhalo mass function Σ_sub.