Long-term monitoring of WASP-19 b: Signs of apsidal precession and molecular signatures

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Volume 708 (April 2026)

A&A, 708 (2026) A313

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Table 3

Comparison of linear, quadratic, and cubic ephemeris model for WASP-19b.

Quantity	Linear ephemeris	Quadratic ephemeris	Cubic ephemeris
Reference time (T₀; BJD(TDB)-2 400 000)	55183.167643±0.000061	55183.167527±0.000074	55183.167368±0.000080
Period (P_b; days)	${0.788839059}_{- 0.000000024}^{+ 0.000000023}$ $Mathematical equation: $0.788839059^{+0.000000023}_{-0.000000024}$$	${0.788839224}_{- 0.000000069}^{+ 0.000000068}$ $Mathematical equation: $0.788839224^{+0.000000068}_{-0.000000069}$$	${0.788839703}_{- 0.000000135}^{+ 0.000000136}$ $Mathematical equation: $0.788839703^{+0.000000136}_{- 0.000000135}$$
Quadratic term (p 1)		${- 3.1536 \times 10^{- 11}}_{- 1.2321 \times 10^{- 11}}^{+ 1.2297 \times 10^{- 11}}$ $Mathematical equation: $-3.1536 $\times$ 10$^{-11}$ $^{+1.2297 \times 10^{-11}} _{-1.2321 \times 10^{-11}}$$	${- 2.5574 \times 10^{- 10}}_{- 5.6958 \times 10^{- 11}}^{+ 5.7502 \times 10^{- 11}}$ $Mathematical equation: -2.5574 $\times$ 10$^{-10}$ $^{+5.7502 \times 10^{-11}} _{-5.6958 \times 10^{-11}}$$
Cubic term (p2)			${2.946 \times 10^{- 14}}_{- 6.364 \times 10^{- 15}}^{+ 6.419 \times 10^{- 15}}$ $Mathematical equation: 2.946 $\times$ 10$^{-14}$ $^{+6.419 \times 10^{-15}} _{-6.364 \times 10^{-15}}$$
χ²	547.02	516.29	468.47
$χ_{ν}^{2}$ $Mathematical equation: $\chi^{2}_{\nu}$$	4.84	4.61	4.22
AIC	551.02	522.29	476.47
BIC	556.51	530.53	487.45
r.m.s. of residuals (s)	48.54	47.51	46.31

Notes. The models are fitted to the full set of mid-transit times spanning 2008-2025 (Table A.2). The table lists the raw χ², reduced $χ_{ν}^{2}$ $Mathematical equation: $\chi^{2}_{\nu}$$ , Akaike information criterion (AIC), and Bayesian information criterion (BIC) values computed directly from the measured timing uncertainties. While none of the models fully reproduces the observed scatter in the timing residuals, the cubic ephemeris yields the lowest information-criterion values among the tested models.

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