New model for the 0957 + 561 gravitational lens system - Bounds on masses of a possible black hole and dark matter and prospects for estimation of H0

We present a simple model that accounts for the known properties of the gravitational lens system 0957 + 561, but assumes little about the galaxies that constitute the lens. The brightest galaxy, G1, is represented as a circularly symmetric, smooth, King-type surface density profile, with core radius θc_, velocity dispersion σᵥ_, accompanied by a compact nucleus with mass Mc_. The compact nucleus is indispensable in our model, because surface density profiles in common use are not sufficiently centrally condensed to account for the image observables, in particular their relative magnification. Other galaxies that contribute to the light deflection are assumed to be embedded in smoothly distributed "dark matter" with surface mass density σₛ_. The light deflection attributable to these galaxies and to dark matter is represented with a series approximation that excludes all terms higher than linear in the distance to the center of G1. This series has two parameters: an astigmatism QA_ and a corresponding position angle γ. Our estimate of θc_ is 2. 8" +/- 0. 1", significantly larger than that found by Stockton for the light emitted by G1, and perhaps indicating the presence of "dark matter" in Gl. Based on our model and on the work of Malumuth and Kirshner, we infer relatively weak limits for σᵥ_: 200 km s^-1^ <~ σᵥ_ <= 390 km s^-1^. For H₀_ = 100h km s^-1^ Mpc^-1^, these limits imply corresponding ones on Mc_, QA_, and σₛ_: 3 <~ Mc_/ (10¹0ʰ^-1^ Mₛun_) <=11 0. 4 <~QA_/ (10¹0ʰ^-1^ Mₛunₐrcsec^-2^) <=1. 2 and 0 <= σₛ_/ (10¹0ʰ^-1^ Mₛun_ arcsec^-2^) <~ 3. Our estimate for the position angle that corresponds to QA_ is γ = 63ᵈeg^ +/- 1ᵈeg^. From our results for G1 and the other galaxies, we infer H₀_ = (90 +/- 10) (σᵥ_/390 km s^-1^) ²^ (DELTAτBA_/1 yr) ^-1^ km s^-1^ Mpc^-1^, where DELTAτBA_ is the difference in light propagation times from the source to the observer, via the images A and B. The main contribution to the uncertainty in the coefficient of this expression for H₀_ is due to the weakness of the constraint the image observables place on the mass distributions of G1 and of the other galaxies and dark matter. A measurement of σᵥ_ would yield "point" estimates for Mc_, QA_ and σₛ_, and would, for example, determine the amount of "dark matter" in the deflector, all within the context of our simple model. If standard errors in future measurements of σᵥ_ and DELTAτBA_ were each 10% or less, H₀_ could be determined from our expression with a standard error of under 25%.