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PIEMass.potential_2d_from: implement the missing lensing potential

Type: feature Target: PyAutoGalaxy Difficulty: too-large Autonomy: supervised Priority: normal Status: formalised Filed: 2026-06-05 (backfilled from git)

Follow-up from the dark-matter potential work (PyAutoGalaxy feature/dark-matter-potentials). That branch implemented potential_2d_from for every elliptical/spherical NFW/gNFW variant and fixed NFWSph. PIEMass was deliberately scoped out because, unlike the NFW family, it has no decomposition hook to reuse.

Symptom

PIEMass (the Lenstool-ported Pseudo-Isothermal Elliptical Mass Distribution, Kassiola & Kovner 1993) has deflections_yx_2d_from and convergence_2d_from but no potential_2d_from. It therefore inherits the abstract base MassProfile.potential_2d_from, which now raises a clean NotImplementedError (post feature/dark-matter-potentials; it previously raised a confusing TypeError: ... unexpected keyword argument 'xp'). Any tracer/galaxy containing a PIEMass crashes when the visualizer writes the potential extension to tracer.fits.

This is the same class of bug as the original NFW report (visualization calls tracer.potential_2d_from; the likelihood path never does), just for a different profile.

Where the code lives

autogalaxy/profiles/mass/total/dual_pseudo_isothermal_mass.py, class PIEMass (~line 218). The sibling dPIEMass (~line 359) in the same file does implement an analytic potential_2d_from (~line 586) — PIEMass is the single-core limit of dPIEMass.

Why MGE doesn't drop in

The NFW family reuses MGEDecomposer(mass_profile=self).potential_2d_via_mge_from(...), but PIEMass has neither decompose_convergence_via_mge nor decompose_convergence_via_cse (verified: both hasattr return False), so the MGE route raises NotImplementedError.

Plan (two options)

  1. Analytic (preferred). Port the PIE lensing potential from Kassiola & Kovner (1993) / Lenstool, or specialise dPIEMass.potential_2d_from to the r_s -> infinity (no-truncation) limit — note the convergence normalisations differ (dPIE carries an r_s/(r_s-r_a) factor), so it is not a verbatim copy.
  2. MGE convergence hook. Add a decompose_convergence_via_mge (2D, three_D=False) hook to PIEMass so the existing potential_2d_via_mge_from can integrate it.

Validation

Self-consistency via finite differencing (the dark.py pattern in autolens_workspace_test/scripts/mass/, or a new total.py case): grad(psi)=alpha and lap(psi)=2 kappa must agree to ~1e-3 (med). Add a test__potential_2d_from to test_autogalaxy/profiles/mass/total/. If the analytic route is taken, also cross-check it against an MGE potential of the same profile at zero/low ellipticity.