Explanation of the exceptionally strong timing noise of PSR J0337+1715 by a circum-ternary planet and consequences for gravity tests

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Volume 693 (January 2025)

A&A, 693 (2025) A143

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Table 1.

Mean values of model-specific parameters of the MCMC runs assuming the PL3 (left) and Planet (right) models with their 68% confidence intervals.

Parameter	Symbol	PL3GR	PlanetGR	Symbol	Parameter
Fitted values

Fundamental frequency (day⁻¹)	ν	$3.44 {(28)}_{- 54}^{+ 61} \times 10^{- 4}$ $3.44(28)_{-54}^{+61} \times 10^{-4}$	$3310_{- 260}^{+ 280}$ $3310_{-260}^{+280}$	P_Π	Orbital period (d)
Amplitude at ν (μs)	A_ν	$4.4 {(82)}_{- 19}^{+ 22}$ $4.4(82)_{-19}^{+22}$	${(6.5)}_{- 1.4}^{+ 1.6} \times 10^{- 6}$ $(6.5)_{-1.4}^{+1.6} \times 10^{-6}$	a_tsini_Π	Projected semi-major axis (lt-s)
Power-law index	γ	$2.73 {(26)}_{- 61}^{+ 68}$ $2.73(26)_{-61}^{+68}$	$- {(1.5)}_{- 1.6}^{+ 1.4} \times 10^{- 5}$ $-(1.5)_{-1.6}^{+1.4} \times 10^{-5}$	a_tcosi_Π	Co-projected semi-major axis (lt-s)
Phase 1 (rad)	ϕ₁	$- 0.21 {(54)}_{- 17}^{+ 19}$ $-0.21(54)_{-17}^{+19}$	$0.2 {(51)}_{- 37}^{+ 32}$ $0.2(51)_{-37}^{+32}$	e_Πsinω_t	Laplace-Lagrange
Phase 2 (rad)	ϕ₂	$- 0.77 {(74)}_{- 61}^{+ 68}$ $-0.77(74)_{-61}^{+68}$	${(5.7)}_{- 2.4}^{+ 2.4} \times 10^{- 2}$ $(5.7)_{-2.4}^{+2.4} \times 10^{-2}$	e_Πcosω_t	Laplace-Lagrange
Phase 3 (rad)	ϕ₃	$- 1.42 {(21)}_{- 61}^{+ 68}$ $-1.42(21)_{-61}^{+68}$	$56549_{- 20}^{+ 3333}$ $56549_{-20}^{+3333}$	t_asc_t	Time of ascending node (MJD)
			$1 . {(25)}_{- 53}^{+ 62} \times 10^{2}$ $1.(25)_{-53}^{+62} \times 10^{2}$	Ω_t	Longitude of planet ascending node (°)

Derived values

Fundamental period (days)	1/ν	$2904 . 6_{- 5.1}^{+ 4.6}$ $2904.6_{-5.1}^{+4.6}$	${(1.65)}_{- 0.89}^{+ 1.6} \times 10^{- 5}$ $(1.65)_{-0.89}^{+1.6} \times 10^{-5}$	a_π	Semi-major axis (lt-s)
Amplitude at 1 yr⁻¹ (μs)	$A_{1 yr}^{- 1}$ $A_{1\,\mathrm{yr}^{-1}}$	$1.55 {(16)}_{- 68}^{+ 61} \times 10^{- 2}$ $1.55(16)_{-68}^{+61} \times 10^{-2}$	$157_{- 54}^{+ 11}$ $157_{-54}^{+11}$	i_Π	Orbital inclination w.r.t. plane of sky (°)
			$119_{- 42}^{+ 16} \times 10^{2}$ $119_{-42}^{+16} \times 10^{2}$	δi_Π	Orbital inclination w.r.t. triple system (°)
			$0.2 {(57)}_{- 31}^{+ 29}$ $0.2(57)_{-31}^{+29}$	e_Π	Orbital eccentricity
			$77 . 2_{- 7.2}^{+ 6.0}$ $77.2_{-7.2}^{+6.0}$	ω_t	Longitude of periastron (°)
			$57258_{- 77}^{+ 3270} \times 10^{4}$ $57258_{-77}^{+3270} \times 10^{4}$	t_p_Π	Time of periastron passage (MJD)
			${(1.23)}_{- 0.66}^{+ 1.1} \times 10^{- 8}$ $(1.23)_{-0.66}^{+1.1} \times 10^{-8}$	m_π	Planet-companion mass (M_⊙)

Notes. Uncertainties apply to the digits between parenthesis and delimit the 68% median confidence region, namely the interval excluding 16% of the distribution above and below it. The central value quoted is the best-fit value. The upper-case index Π refers to the planet binary. The lower-case index π refers to the planet, and t refers to the triple-system centre of mass. Data spans MJD 56492 − 59480. Solar System ephemeris is DE430. Parameters common to both models are reported in Table E.1.

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