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

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× 10¹¹\, M and an inner halo slope γ ᵢₙʰᵃˡᵒ = 1.04+0.10-0.14. The halo mass is M₂₀₀ʰᵃˡᵒ = 1.11+0.37-0.32× 10¹³\, M, implying log 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.