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 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 = 4. 4^+0. 25-₀. ₃₉ 10^11\, M and an inner halo slope ₈₍^ halo = 1. 04^+0. 10-₀. ₁₄. The halo mass is M₂₀₀^ halo = 1. 11^+0. 37-₀. ₃₂ 10^13\, M, implying ₁₀ (M₂₀₀/M) =1. 41^+0. 13-₀. ₁₄. At fixed halo mass, the inferred stellar mass lies ∼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.