A Salpeter IMF and an NFW halo: Disentangling the dark and stellar mass of an elliptical galaxy through precise lens modelling of a double-source-plane system

Abstract

We present a strong lensing analysis of the double source plane lens J0946+1006 (colloquially "Jackpot" lens) to measure the inner dark matter density profile, the stellar-to-halo mass ratio, and the stellar initial mass function normalisation using a two component stellar plus dark matter mass model. The stellar mass follows a multi-Gaussian expansion light model with a free global mass-to-light ratio and an allowed radial $M/L$ gradient, while the dark matter is described by an elliptical generalised NFW halo. The double-source-plane geometry provides additional leverage against the mass-sheet transformation and helps constrain the radial mass profile. Despite allowing both a radial stellar $M/L$ gradient and a generalised NFW halo, the data prefer the canonical picture: an approximately constant stellar mass-to-light ratio with a Salpeter-like IMF normalisation, and a dark matter halo consistent with NFW. We infer $M_{\star }=4.4_{-0.39}^{+0.25}\times 10^{11}{M}_{\odot }$ and an inner halo slope ${\gamma }_{\mathrm{in}}^{\mathrm{halo}}=1.04_{-0.14}^{+0.10}$. The halo mass is $M_{200}^{\mathrm{halo}}=1.11_{-0.32}^{+0.37}\times 10^{13}{M}_{\odot }$, implying ${\log }_{10}(M_{200}/M_{\star })=1.41_{-0.14}^{+0.13}$. At fixed halo mass, the inferred stellar mass lies $\sim 0.1$ dex above typical literature stellar halo mass relations at similar redshift, which is comparable to the intrinsic scatter of these relations. We expect this approach to provide a practical template for future dark matter studies with the large double-source-plane lens samples from Euclid.

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