GravSphere2: A higher order Jeans method for mass modeling spherical stellar systems

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Table 1

Priors implemented in DYNESTY for our analysis.

Parameter	Units	Prior	Range
${\tilde{β}}_{0}, {\tilde{β}}_{0}^{'}$ $\widetilde{\beta}_{0}, \widetilde{\beta}_{0}^{\prime}$	None	Flat	[−0.01, 0.01] (G) [−1, 1] (F)
${\tilde{β}}_{\infty}, {\tilde{β}}_{\infty}^{'}$ $\widetilde{\beta}_{\infty}, \widetilde{\beta}_{\infty}^{\prime}$	None	Flat	[−0.1, 1](G)
			[−1, 1] (F)
$r_{β}, r_{β}^{'}$ $r_{\beta}, r_{\beta}^{\prime}$	log₁₀ kpc	Flat	[−2, 1]
η, η^′	None	Flat	[1, 3]
M₂₀₀	log₁₀ M_⊙	Flat	[7.5, 11.5]
c₂₀₀	None	Flat	[1, 100] (G) [1, 50] (F)
r_c	log₁₀ kpc	Flat	[−2, 1]
n	None	Flat	[0, 1]
r_t	log₁₀ kpc	Flat	[0, log₁₀(20)]
δ	None	Flat	[3.01, 5]
M_*	10⁷ M_⊙	Flat	4.3 ± 25%(F)
ρ_p	kpc⁻³	Flat	Truth ± 50%(G)
	kpc (G)		Truth ± 50%(G)
r_p	log₁₀ kpc (F)	Flat	R_1/2 ± 1 dex (F)
α	None	Flat	Truth ± 50%(G) [0.1, 4] (F)
β	None	Flat	Truth ± 50%(G) [3.1, 7] (F)
γ	None	Flat	Truth ± 50%(G) [0, 2.9] (F)

Notes. The parenthesized “G” denotes priors specific to the Gaia Challenge mocks, while “F” corresponds to the simulated Fornax dwarf analog. For both cases, there are 19 fitting parameters in total (for Fornax, we marginalize over the additional stellar mass M_*, but do not use a density scale for the photometry, since we fit stars individually, rather than from a profile). Primed quantities (rows 1−4) denote the parameters of the fourth-order counterpart of the anisotropy. For the Gaia Challenge mocks, the exponents α, β, γ are also ensured not to exceed the broad convergence limits used for the Fornax case. The full implementation of these priors, with initialization files and data, are included in the GRAVSPHERE2 public release repository on GitHub.

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