Cosmology with supernova Encore in the strong lensing cluster MACS J0138–2155 - Lens model comparison and H0 measurement

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Table B.1.

Overview of the lens mass models from the seven independent modeling approaches using the gold image positions as constraints.

Description	GLAFIC	GLEE	GLEE `-baseline`	`Lenstool` I	`Lenstool` II	ZITRIN-ANALYTIC	`MrMARTIAN`	WSLAP+
BCG profile	Hernquist	dPIE	dPIE	dPIE	dPIE	dPIE	— (hybrid)	— (free-form)
Number of DM halos	1	2	2	1	1	2	1 + grid	— (free-form)
DM halo profile	NFW	various^a	isothermal	dPIE	dPIE	isothermal	NFW + grid	— (free-form)
External shear	Yes	No	No	Yes	Yes	No	—	—
Galaxy scaling relation
α	0.25	0.25^b	0.25^b	0.25	0.21^b	0.25	—	—
β	0.5	0.7	0.7	0.5	0.71	0.5	—	—
Galaxies not in scaling relation	fg, JF-1	multiple^c	multiple^c	multiple^d	multiple^e	multiple^f	—	—
positional error boost factor	1	1	1	2.2	1.5	3	1	1

Notes.

Various halo profiles were explored, including isothermal, power-law and NFW; one model also included a mass sheet.

The parameter α of the scaling relation (Eq. 1) was optimized using cluster member galaxies with velocity dispersion measurements in the GLEE (Granata et al. 2025; Ertl et al. 2025) and LENSTOOL II (Acebron et al. 2025) models, whereas α was fixed to the tabulated values in the other models.

The multiple objects excluded from the galaxy scaling relation of the GLEE model are: BCG, object ID = 116, JF-1, JF-2, JF-3, fg, and bg (see Ertl et al. 2025).

The multiple objects excluded from the galaxy scaling relation of the LENSTOOL I model are: object at (RA, Dec) = $(24 \overset{°}{.} 51662331, - 21 \overset{°}{.} 92448273)$ $Mathematical equation: $ (24{{\overset{\circ}{.}}}51662331, -21{{\overset{\circ}{.}}}92448273) $$ , JF-1, JF-2, JF-3, and fg.

The multiple objects excluded from the galaxy scaling relation of the LENSTOOL II model are: JF-1, JF-2, JF-3, fg, and bg.

Four objects excluded from the galaxy scaling relation of the ZITRIN-ANALYTIC model are located at (RA, Dec) = $(24 \overset{°}{.} 5114258, - 21 \overset{°}{.} 9213075)$ $Mathematical equation: $ (24{{\overset{\circ}{.}}}5114258, -21{{\overset{\circ}{.}}}9213075) $$ , $(24 \overset{°}{.} 5129665, - 21 \overset{°}{.} 9203688)$ $Mathematical equation: $ (24{{\overset{\circ}{.}}}5129665, -21{{\overset{\circ}{.}}}9203688) $$ , $(24 \overset{°}{.} 5156305, - 21 \overset{°}{.} 9227688)$ $Mathematical equation: $ (24{{\overset{\circ}{.}}}5156305, -21{{\overset{\circ}{.}}}9227688) $$ , and $(24 \overset{°}{.} 5076146, - 21 \overset{°}{.} 9271504)$ $Mathematical equation: $ (24{{\overset{\circ}{.}}}5076146, -21{{\overset{\circ}{.}}}9271504) $$ .

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