docs: correct sigma_LT/sigma_0 attribution in dPIE docstrings

The sqrt(3/2) relation between Lenstool's fiducial dispersion (sigma_LT) and
the central dispersion (sigma_0) was attributed to Elíasdóttir et al. (2007)
as if it were that paper's physical definition. Per the contributed
derivation note (H. Ding 2026, "On the definitions of b0 and velocity
dispersion in Lenstool / dPIE"), it is Lenstool's parameter convention:
Lenstool computes b0 = 6*pia_c2*sigma^2 (an E07-style coefficient) but
evaluates deflections with the Kassiola & Kovner (1993) / Limousin et al.
(2005) amplitude, so the input sigma must be read through the L05
parameterization. Docstrings now state this, and give the equivalent
central-dispersion form b0 = 4*648000*(sigma_0/c)^2*(D_LS/D_S).

No numerical behaviour changes — documentation only; the sigma_LT
parameterization is retained deliberately for Lenstool results-table parity.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_012Eacj9naBWSKrevsqnVJWR

Author: claude

autogalaxy/profiles/mass/total/dual_pseudo_isothermal_mass.py

@@ -571,9 +571,10 @@ def from_lenstool(
 
         - ``sigma`` is Lenstool's **fiducial** velocity dispersion ``v_disp`` (sigma_LT),
           *not* the central velocity dispersion sigma_0 of the dPIE profile. They differ
-          by sigma_0 = sqrt(3/2) * sigma_LT (Eliasdottir et al. 2007, App. A; Bergamini
-          et al. 2019, Eq. 5) — quoting a measured central/aperture dispersion here
-          overestimates the mass by 50%. The lens strength is
+          by sigma_0 = sqrt(3/2) * sigma_LT — a Lenstool parameter convention (E07-style
+          b0 coefficient paired with the K93/L05 deflection amplitude; see the dPIEMass
+          class docstring), quoted by Bergamini et al. 2019, Eq. 5 — so a measured
+          central/aperture dispersion entered here overestimates the mass by 50%. The lens strength is
           b0 = 6 * 648000 * (sigma_LT / c)^2 * (D_LS / D_S) arcsec, where Lenstool's
           stored ``b0 = 6 * pia_c2 * sigma^2`` (``set_potfile.c``) carries no distance
           ratio — Lenstool applies D_LS / D_S separately at deflection time
@@ -1095,18 +1096,27 @@ class dPIEMass(dPIEMassB0):
       must be handled when ingesting real-data catalogues).
     - ``sigma`` — Lenstool's **fiducial** velocity dispersion ``v_disp``
       (sigma_LT, km/s), *not* the central dispersion:
-      sigma_0 = sqrt(3/2) * sigma_LT (Elíasdóttir et al. 2007, App. A;
-      Bergamini et al. 2019, Eq. 5). Quoting a measured stellar dispersion here
-      overestimates the mass by 50%.
+      sigma_0 = sqrt(3/2) * sigma_LT (the relation quoted by Bergamini et al.
+      2019, Eq. 5). The sqrt(3/2) is Lenstool's parameter convention, not a
+      physical definition from Elíasdóttir et al. (2007): it arises because
+      Lenstool computes ``b0 = 6 * pia_c2 * sigma^2`` (an E07-style
+      coefficient, ``set_potfile.c``) but evaluates deflections with the
+      Kassiola & Kovner (1993) / Limousin et al. (2005) amplitude, so the
+      input sigma must be read through the L05 parameterization (see the
+      contributed derivation note "On the definitions of b0 and velocity
+      dispersion in Lenstool / dPIE", H. Ding 2026). Quoting a measured
+      stellar dispersion here overestimates the mass by 50%.
     - ``r_core`` / ``r_cut`` — Lenstool ``core_radius`` / ``cut_radius`` in
       arcseconds (the internal ``ra`` / ``rs``). For ``.par`` files using the kpc
       variants, pre-convert with
       ``r_core = r_core_kpc / cosmology.kpc_per_arcsec_from(redshift=redshift_object)``.
 
     The lens strength is fully normalized internally:
     b0 = 6 * 648000 * (sigma_LT / c)^2 * (D_LS / D_S) arcsec — equivalently
-    E_0 = 6 pi (D_LS / D_S) (sigma_LT / c)^2 in radians (Elíasdóttir et al. 2007,
-    Eq. A24) with the E_0-to-b0 prefactor folded in. Lenstool stores its ``b0``
+    E_0 = 6 pi (D_LS / D_S) (sigma_LT / c)^2 in radians (the coefficient of
+    Elíasdóttir et al. 2007, Eq. A24) with the E_0-to-b0 prefactor folded in;
+    written in the central dispersion this is
+    b0 = 4 * 648000 * (sigma_0 / c)^2 * (D_LS / D_S). Lenstool stores its ``b0``
     without the distance ratio and applies D_LS / D_S at deflection time
     (``e_grad.c``); the two conventions are verified equivalent against the
     Lenstool C source and reference deflections