GPU-Accelerated Gravitational Lensing and Dynamical (GLaD) modeling for cosmology and galaxies

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Volume 701 (September 2025)

A&A, 701 (2025) A280

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Table 4.

Inferred H₀ and key parameters for the models.

Model	D_d [Mpc]	D_Δt, int [Mpc]	λ_int	β_ani	P(H₀ \| D_d)	P(H₀ \| D_Δt, int)	P(H₀ \| D_d, D_Δt, int)	χ_dyn²
Full FoV (52 bins)
Ideal Kinematics with M_BH in [10⁹, 10¹⁰] M_⊙	$781_{- 29}^{+ 30}$ $781_{-29}^{+30}$	$1857_{- 78}^{+ 137}$ $1857_{-78}^{+137}$	$0 . 98_{- 0.07}^{+ 0.04}$ $0.98_{-0.07}^{+0.04}$	$0 . 21_{- 0.14}^{+ 0.07}$ $0.21_{-0.14}^{+0.07}$	$83 . 1_{- 2.9}^{+ 3.7}$ $83.1_{-2.9}^{+3.7}$	$81 . 0_{- 6.4}^{+ 4.4}$ $81.0_{-6.4}^{+4.4}$	$82 . 5_{- 3.1}^{+ 3.2}$ $82.5_{-3.1}^{+3.2}$	50

Ideal Kinematics with M_BH = 5 × 10⁹ M_⊙*	$769_{- 18}^{+ 18}$ $769_{-18}^{+18}$	$1868_{- 80}^{+ 140}$ $1868_{-80}^{+140}$	$0 . 98_{- 0.07}^{+ 0.04}$ $0.98_{-0.07}^{+0.04}$	$0 . 13_{- 0.04}^{+ 0.04}$ $0.13_{-0.04}^{+0.04}$	$83 . 5_{- 2.9}^{+ 3.1}$ $83.5_{-2.9}^{+3.1}$	$80 . 9_{- 6.3}^{+ 4.6}$ $80.9_{-6.3}^{+4.6}$	$83 . 3_{- 3.0}^{+ 3.0}$ $83.3_{-3.0}^{+3.0}$	51

Ideal Kinematics with no BH	$785_{- 11}^{+ 12}$ $785_{-11}^{+12}$	$1770_{- 39}^{+ 54}$ $1770_{-39}^{+54}$	$1 . 00_{- 0.03}^{+ 0.02}$ $1.00_{-0.03}^{+0.02}$	$0 . 29_{- 0.006}^{+ 0.003}$ $0.29_{-0.006}^{+0.003}$	$81 . 3_{- 3.1}^{+ 3.1}$ $81.3_{-3.1}^{+3.1}$	$85 . 3_{- 3.6}^{+ 3.0}$ $85.3_{-3.6}^{+3.0}$	$83 . 2_{- 3.0}^{+ 2.3}$ $83.2_{-3.0}^{+2.3}$	64

Ideal Kinematics with M_BH = 7 × 10⁹ M_⊙	$742_{- 17}^{+ 20}$ $742_{-17}^{+20}$	$1876_{- 78}^{+ 144}$ $1876_{-78}^{+144}$	$0 . 98_{- 0.07}^{+ 0.04}$ $0.98_{-0.07}^{+0.04}$	$- 0 . 028_{- 0.05}^{+ 0.06}$ $-0.028_{-0.05}^{+0.06}$	$86 . 9_{- 1.8}^{+ 2.0}$ $86.9_{-1.8}^{+2.0}$	$80 . 4_{- 6.6}^{+ 4.6}$ $80.4_{-6.6}^{+4.6}$	$85 . 0_{- 2.4}^{+ 2.5}$ $85.0_{-2.4}^{+2.5}$	53

Kinematics with a 5% bias with M_BH in [10⁹, 10¹⁰] M_⊙	$706_{- 27}^{+ 20}$ $706_{-27}^{+20}$	$1863_{- 82}^{+ 149}$ $1863_{-82}^{+149}$	$0 . 97_{- 0.07}^{+ 0.04}$ $0.97_{-0.07}^{+0.04}$	$0 . 19_{- 0.15}^{+ 0.08}$ $0.19_{-0.15}^{+0.08}$	$93 . 7_{- 2.0}^{+ 3.0}$ $93.7_{-2.0}^{+3.0}$	$80 . 5_{- 6.6}^{+ 4.4}$ $80.5_{-6.6}^{+4.4}$	$87 . 4_{- 2.0}^{+ 2.2}$ $87.4_{-2.0}^{+2.2}$	50

Full FoV without the inner region (43 bins)
Ideal Kinematics with no BH	$777_{- 19}^{+ 18}$ $777_{-19}^{+18}$	$1804_{- 54}^{+ 96}$ $1804_{-54}^{+96}$	$0 . 99_{- 0.06}^{+ 0.03}$ $0.99_{-0.06}^{+0.03}$	$0 . 23_{- 0.06}^{+ 0.05}$ $0.23_{-0.06}^{+0.05}$	$82 . 9_{- 2.7}^{+ 3.0}$ $82.9_{-2.7}^{+3.0}$	$83 . 4_{- 5.3}^{+ 3.8}$ $83.4_{-5.3}^{+3.8}$	$83 . 3_{- 3.2}^{+ 2.9}$ $83.3_{-3.2}^{+2.9}$	34

Ideal kinematics with M_BH = 7 × 10⁹ M_⊙	$752_{- 30}^{+ 34}$ $752_{-30}^{+34}$	$1903_{- 97}^{+ 176}$ $1903_{-97}^{+176}$	$0 . 97_{- 0.08}^{+ 0.05}$ $0.97_{-0.08}^{+0.05}$	$0 . 019_{- 0.15}^{+ 0.13}$ $0.019_{-0.15}^{+0.13}$	$85 . 5_{- 2.7}^{+ 2.7}$ $85.5_{-2.7}^{+2.7}$	$79 . 6_{- 7.0}^{+ 5.1}$ $79.6_{-7.0}^{+5.1}$	$84 . 1_{- 3.3}^{+ 3.1}$ $84.1_{-3.3}^{+3.1}$	42

Notes. Important parameters and the inferred H₀ [ ${kms}^{- 1} {Mpc}^{- 1}$ $\rm kms^{-1}~Mpc^{-1}$ ] from the different joint models. In the individual models, we present the marginalized values of H₀ constrained by P(D_d), P(D_Δt, int), and P(D_d, D_Δt, int), respectively. We also provide the marginalized distance values for D_d and D_Δt, int. The 1σ uncertainties are calculated from the 16th, 50th, and 84th percentiles of the distribution. The input mock values are $H_{0} = 82.5 km s^{- 1} {Mpc}^{- 1}$ $H_0 = 82.5~\rm km~s^{-1}~Mpc^{-1}$ , D_d = 775 Mpc and D_Δt, int = 1823 Mpc. The star symbol denotes joint modeling that includes the BH mass, which is the mock input.

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