Numerical estimation of the capture ability of Neptunian mean motion resonances

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Table 1

Estimated numbers of objects in various MMRs provided by previous observational works.

MMR	Nominal location (au)	Population (D ≳ 100 km)
4:5	34.8	$160_{- 140}^{+ 700}$ $Mathematical equation: $160^{+700}_{-140}$$
3:4	36.3	$800_{- 600}^{+ 1100}$ $Mathematical equation: $800^{+1100}_{-600}$$
2:3	39.3	$10 000_{- 3000}^{+ 3600}$ $Mathematical equation: $10~000^{+3600}_{-3000}$$
3:5	42.2	$5000_{- 3000}^{+ 5200}$ $Mathematical equation: $5000^{+5200}_{-3000}$$
4:7	43.6	$3000_{- 2000}^{+ 4000}$ $Mathematical equation: $3000^{+4000}_{-2000}$$
1:2	47.6	$4400_{- 1100}^{+ 1500}$ $Mathematical equation: $4400^{+1500}_{-1100}$$
8:17	49.6	$700_{- 700}^{+ 3100}$ $Mathematical equation: $700^{+3100}_{-700}$$
6:13	50.2	$1700_{- 1400}^{+ 4300}$ $Mathematical equation: $1700^{+4300}_{-1400}$$
5:11	50.7	$2100_{- 1800}^{+ 4900}$ $Mathematical equation: $2100^{+4900}_{-1800}$$
3:7	52.8	$3000_{- 2300}^{+ 5000}$ $Mathematical equation: $3000^{+5000}_{-2300}$$
5:12	53.8	$2400_{- 2000}^{+ 5600}$ $Mathematical equation: $2400^{+5600}_{-2000}$$
2:5	55.3	$6600_{- 3000}^{+ 4100}$ $Mathematical equation: $6600^{+4100}_{-3000}$$
5:13	56.7	$1200_{- 1200}^{+ 4800}$ $Mathematical equation: $1200^{+4800}_{-1200}$$
3:8	57.7	$2300_{- 2000}^{+ 5000}$ $Mathematical equation: $2300^{+5000}_{-2000}$$
4:11	58.9	$3900_{- 3400}^{+ 9000}$ $Mathematical equation: $3900^{+9000}_{-3400}$$
1:3	62.4	$17 000_{- 8000}^{+ 11 000}$ $Mathematical equation: $17~000^{+11~000}_{-8000}$$
3:10	66.9	$1400_{- 1400}^{+ 6000}$ $Mathematical equation: $1400^{+6000}_{-1400}$$
2:7	69.2	$2300_{- 1900}^{+ 5400}$ $Mathematical equation: $2300^{+5400}_{-1900}$$
4:15	72.4	$2600_{- 2500}^{+ 12 000}$ $Mathematical equation: $2600^{+12~000}_{-2500}$$
6:23	73.5	$1800_{- 1800}^{+ 7400}$ $Mathematical equation: $1800^{+7400}_{-1800}$$
1:4	75.6	$13 000_{- 8000}^{+ 15 000}$ $Mathematical equation: $13~000^{+15~000}_{-8000}$$
4:17	78.7	$3100_{- 3000}^{+ 12 000}$ $Mathematical equation: $3100^{+12~000}_{-3000}$$
8:35	80.2	$2600_{- 2500}^{+ 11 000}$ $Mathematical equation: $2600^{+11~000}_{-2500}$$
2:9	81.8	$1100_{- 1100}^{+ 6000}$ $Mathematical equation: $1100^{+6000}_{-1100}$$
5:24	85.4	$2500_{- 2400}^{+ 11 000}$ $Mathematical equation: $2500^{+11~000}_{-2400}$$
1:5	87.7	$11 000_{- 8000}^{+ 19 000}$ $Mathematical equation: $11~000^{+19~000}_{-8000}$$
4:27	107.1	$5000_{- 4800}^{+ 23 000}$ $Mathematical equation: $5000^{+23~000}_{-4800}$$
1:9	129.8	$18 000_{- 15 000}^{+ 39 000}$ $Mathematical equation: $18~000^{+39~000}_{-15~000}$$
2:23	152.8	$4000_{- 4000}^{+ 15 000}$ $Mathematical equation: $4000^{+15~000}_{-4000}$$

Notes. The results for the 4:5, 3:4, 3:5, and 4:7 MMRs come from Gladman et al. (2012); the result for the 2:3 MMR comes from Volk et al. (2016); the result for the 1:2 MMR comes from Chen et al. (2019); and the others are from Crompvoets et al. (2022). The magnitude range estimated by Gladman et al. (2012) is H_g < 9.16, while the other studies use H_r < 8.66. These two thresholds are roughly consistent, both corresponding to small bodies with diameters D ≳ 100 km.

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