J-PLUS: Reconstructing the Milky Way disc's star formation history with 12-filter photometry

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Volume 706 (February 2026)

A&A, 706 (2026) A74

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Table 2

Variables entering our hierarchical model.

Pop. parameter	a		Stellar fraction vector
parameters (β)	ρ_n	pc	Theoretical heliocentric distance
	$J_{n}^{k}$ $J_{n}^{k}$	mag	Theoretical absolute magnitude
	${\hat{ϖ}}_{n} = 1 / ρ_{n}$ $\hat{\varpi}_{n}=1/\rho_{n}$	mas	Predicted parallax
	${\hat{m}}_{J, n}^{k} = J_{n}^{k} + f (ρ_{n})$ $\hat{m}_{J,n}^{k}=J_{n}^{k}+f(\rho_n)$	mag	Predicted apparent magnitude

Data (d)	$ϖ_{n}$ $\varpi_{n}$	mas	Observed parallax
	$e_{ϖ, n}$ $e_{\varpi,n}$	mas	Parallax error
	$m_{J, n}^{k}$ $m_{J,n}^{k}$	mag	Observed apparent magnitude
	$e_{J, n}^{k}$ $e_{J,n}^{k}$	mag	Apparent magnitude error

Fixed quantities	p(ρ)	mas	Distance prior
	$J_{i}^{k}$ $\mathcal{J}_{i}^{k}$	mag	Isochrone absolute magnitude
	$σ_{i}^{k}$ $\sigma_{i}^{k}$	mag	Isochrone tolerance
	φ(M)		Initial mass function

Notes. Subscripts i = 1,..., I and n = 1,..., N indicate the i^th isochrone and the n^th star, respectively, where I is the number of selected isochrones and N the number of observed stars. Superscript k = 1,2,..., K refers to the J-PLUS photometric filters as indicated in Table A.1.

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