A comparison of pendulum models for large-amplitude longitudinal prominence oscillations

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Table 1.

Inference results.

	Observations	Uniform priors			Gaussian prior on n
	P ± ΔP [min]	B_M₁ [G]	B_M₂ [G]	B_avg [G]	B_M₁ [G]	B_M₂ [G]	B_avg [G]

Synthetic	30 ± 10	9 $_{- 4}^{+ 4}$ $Mathematical equation: $ ^{+4}_{-4} $$	9 $_{- 4}^{+ 4}$ $Mathematical equation: $ ^{+4}_{-4} $$	9 $_{- 4}^{+ 4}$ $Mathematical equation: $ ^{+4}_{-4} $$	3 $_{- 1}^{+ 1}$ $Mathematical equation: $ ^{+1}_{-1} $$	4 $_{- 1}^{+ 1}$ $Mathematical equation: $ ^{+1}_{-1} $$	4 $_{- 1}^{+ 1}$ $Mathematical equation: $ ^{+1}_{-1} $$
Synthetic	60 ± 10	19 $_{- 6}^{+ 5}$ $Mathematical equation: $ ^{+5}_{-6} $$	21 $_{- 7}^{+ 6}$ $Mathematical equation: $ ^{+6}_{-7} $$	20 $_{- 6}^{+ 6}$ $Mathematical equation: $ ^{+6}_{-6} $$	8 $_{- 1}^{+ 1}$ $Mathematical equation: $ ^{+1}_{-1} $$	8 $_{- 1}^{+ 2}$ $Mathematical equation: $ ^{+2}_{-1} $$	8 $_{- 1}^{+ 1}$ $Mathematical equation: $ ^{+1}_{-1} $$
Synthetic	90 ± 10	30 $_{- 9}^{+ 7}$ $Mathematical equation: $ ^{+7}_{-9} $$	36 $_{- 11}^{+ 10}$ $Mathematical equation: $ ^{+10}_{-11} $$	33 $_{- 10}^{+ 10}$ $Mathematical equation: $ ^{+10}_{-10} $$	12 $_{- 1}^{+ 1}$ $Mathematical equation: $ ^{+1}_{-1} $$	14 $_{- 2}^{+ 3}$ $Mathematical equation: $ ^{+3}_{-2} $$	13 $_{- 2}^{+ 3}$ $Mathematical equation: $ ^{+3}_{-2} $$
Synthetic	120 ± 10	40 $_{- 12}^{+ 8}$ $Mathematical equation: $ ^{+8}_{-12} $$	60 $_{- 19}^{+ 19}$ $Mathematical equation: $ ^{+19}_{-19} $$	53 $_{- 17}^{+ 20}$ $Mathematical equation: $ ^{+20}_{-17} $$	16 $_{- 2}^{+ 2}$ $Mathematical equation: $ ^{+2}_{-2} $$	24 $_{- 4}^{+ 6}$ $Mathematical equation: $ ^{+6}_{-4} $$	23 $_{- 6}^{+ 6}$ $Mathematical equation: $ ^{+6}_{-6} $$
Zhang et al. (2017)	99 ± 10	33 $_{- 10}^{+ 7}$ $Mathematical equation: $ ^{+7}_{-10} $$	42 $_{- 13}^{+ 11}$ $Mathematical equation: $ ^{+11}_{-13} $$	38 $_{- 12}^{+ 12}$ $Mathematical equation: $ ^{+12}_{-12} $$	27 $_{- 3}^{+ 4}$ $Mathematical equation: $ ^{+4}_{-3} $$	35 $_{- 6}^{+ 7}$ $Mathematical equation: $ ^{+7}_{-6} $$	32 $_{- 6}^{+ 8}$ $Mathematical equation: $ ^{+8}_{-6} $$

Notes. Posterior summaries for different synthetic periods and one observed event under the two considered models and the two adopted sets of priors. The corresponding marginal posteriors are displayed in Figure 3 for the synthetic observations and in Figure 5 for the event observed by Zhang et al. (2017). Posterior summaries are given as the median and upper and lower bounds at the 68% credible interval. We note that the Gaussian prior in density for the synthetic cases is 𝒢(n [cm⁻³]; μ_n, σ_n), with μ_n = 10¹⁰ cm⁻³ and σ_n = 0.2μ_n, while for the observed event, it is 𝒢(n [cm⁻³]; μ_n, σ_n), with μ_n = 4.25 × 10¹⁰ cm⁻³ and σ_n = 0.2μ_n.

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