On the Encounter Rate of Open Star Clusters

TL;DR

This study models the past and future close encounters of open star clusters in the Milky Way, revealing their frequency and potential influence on stellar populations, using orbit integration with the galpy package.

Contribution

It provides the first detailed estimates of encounter rates of open clusters over 64 million years in the Galaxy using orbit integration.

Findings

Cluster encounters occur at 35-40 events per Myr near the Sun.

Encounters between clusters of different ages happen at 15 events per Myr.

Close approaches of cluster pairs are actively occurring, with 29 pairs currently at their closest approach.

Abstract

Probable past and future close encounters of open clusters with known characteristics over 64 million years have been calculated by integrating the orbits of cluster centers in the Galactic potential using the _galpy_ package. It has been shown that in the Galactic neighborhood of the Sun, pairwise cluster encounters at distances comparable to or smaller than their sizes occur at a characteristic rate of 35 to 40 events per 1 Myr. Close encounters between open clusters with a significant age difference occur at a rate of 15 events per Myr. It can be expected that in the Galaxy as a whole, such events occur an order of magnitude more frequently per unit time. Thus, dynamical interactions between stellar ensembles of different ages may not be too rare and could influence the properties of stellar populations. A pair of clusters with similar ages: HSC 1428 and Gulliver 22 was identified as a likely physically bound binary cluster system. A forecast of expected close encounters over the next 32 Myr has been provided for 490 pairs of clusters. Currently, 29 pairs of clusters are at their closest approach.

Tables

Table 1. Table 1 : Close encounters of open star clusters.

Name 1	Name 2	t	Min_dist, пк	$R_1$, пк	$R_2$, пк	$V_{rel}$, км/c	dlogAge
UBC_1558	UBC_550	0	19.9	12.0	10.6	34.8	0.84
NGC_2311	HSC_1723	0	16.2	8.5	5.9	30.5	1.01
Melotte_22	HSC_1318	0	19.8	35.6	7.2	24.3	1.34
IC_2395	HSC_2147	0	12.6	26.2	15.3	16.3	1.04
UPK_535	CWNU_1134	0	18.6	16.1	25.3	20.5	0.94
HSC_883	Aveni-Hunter_1	0	19.7	23.2	37.9	23.7	0.89
UPK_194	HSC_853	0	18.3	13.7	14.5	6.7	0.76
HSC_2976	HSC_103	0	19.5	10.7	12.5	23.1	0.78
HSC_1991	HSC_1977	0	19.0	15.7	7.5	23.4	0.75
HSC_2468	HSC_2394	0	12.4	24.3	17.4	14.8	1.04
HSC_2085	HSC_2082	0	11.9	15.3	14.3	25.2	1.7
Theia_67	OCSN_99	0	17.5	11.1	82.8	15.9	0.9
NGC_2354	CWNU_1064	0	6.9	35.5	17.9	16.8	1.8
OCSN_100	HSC_2919	0	14.3	5.1	4.8	9.3	0.88
HSC_2976	HSC_2971	0	9.7	10.7	41.0	18.3	0.98
UBC_17a	OC_0339	0	14.3	11.2	4.9	17.5	1.23
NGC_6193	CWNU_1842	0	19.2	12.3	8.8	37.5	1.36
HSC_674	CWNU_1216	0	11.9	30.3	29.5	12.6	0.74
Teutsch_182	NGC_7429	0	18.1	17.3	11.0	20.8	1.06
Theia_7	HSC_1318	0	11.6	8.0	7.2	10.6	1.53
HSC_1636	CWNU_158	0	16.4	8.5	28.2	17.7	0.74
HSC_1262	HSC_1257	0	18.9	13.6	17.2	32.9	1.35
HSC_570	HSC_558	0	18.9	22.5	19.8	12.3	0.93
HSC_1644	CWNU_1015	0	13.7	10.9	38.6	22.6	1.56
Theia_70	HSC_95	0	19.4	15.7	85.4	19.4	1.29
HSC_1667	HSC_1644	0	16.8	13.8	10.9	20.1	2.04
OC_0339	ASCC_19	0	13.0	4.9	5.5	17.5	1.03
HSC_1709	ASCC_24	0	16.7	20.5	13.6	35.4	0.93
OC_0128	Bica_2	0	19.9	14.2	6.3	12.9	1.14
Theia_1147	Haffner_13	2	14.3	27.1	58.6	34.3	1.66
HSC_480	CWNU_1813	2	12.4	46.9	11.7	38.6	1.63
Theia_1891	HSC_2824	2	15.1	17.7	45.0	34.6	0.77
UBC_338	HSC_76	2	9.5	7.3	13.0	41.8	1.24
Theia_3099	Majaess_90	2	13.2	12.0	11.8	16.1	1.57
Theia_65	HSC_1347	2	17.6	18.8	42.7	9.2	1.42
HSC_157	HSC_103	2	10.7	34.8	12.5	25.3	1.69
Theia_710	NGC_7429	2	19.6	37.3	11.0	8.0	1.12
Theia_3582	HSC_1385	2	17.2	40.8	22.0	37.7	0.9
UPK_567	HSC_2449	2	11.2	46.5	47.5	28.7	0.85
FSR_1421	CWNU_182	2	6.2	20.5	30.1	17.9	1.19
UBC_168	OC_0181	2	17.4	37.4	4.4	30.6	1.6
UBC_96	ASCC_94	2	13.7	8.4	16.4	18.0	0.9
Theia_710	HSC_803	2	16.8	37.3	26.7	25.8	0.88
UPK_198	CWNU_1228	2	12.0	36.2	7.6	34.4	1.4
OCSN_99	HSC_2900	2	18.8	82.8	7.7	12.4	1.1
UBC_541	HSC_2754	2	15.0	10.1	7.6	42.6	0.93
IC_348	HSC_1257	2	10.9	21.5	17.2	24.3	1.28
COIN-Gaia_18	ASCC_14	2	17.4	8.3	16.2	18.6	0.74
HSC_1134	HSC_1127	2	15.7	8.9	14.3	16.6	1.03
Theia_67	HSC_157	2	18.8	11.1	34.8	15.2	1.24
Platais_10	HSC_2529	2	14.2	116.1	20.4	29.2	1.24
Theia_65	Melotte_25	2	6.7	18.8	55.1	32.8	1.79
Collinder_106	Basel_8	2	17.0	9.6	15.2	26.2	0.87
OC_0339	NGC_2068	2	19.3	4.9	12.4	23.4	1.13
Theia_4	HSC_892	2	11.2	10.3	8.3	17.8	1.72
OCSN_91	HSC_2816	2	17.7	4.9	12.1	1.5	2.39
HSC_1630	CWNU_1057	2	14.1	90.0	33.1	9.3	1.02
OCSN_91	HSC_2733	2	16.1	4.9	31.1	5.3	2.34
OCSN_61	OC_0339	2	19.1	10.0	4.9	4.9	0.83
NGC_6883	ASCC_110	2	19.3	15.0	25.5	47.8	1.66
NGC_1333	HSC_1257	2	19.7	4.5	17.2	32.8	1.33
HSC_1495	HSC_1437	2	14.8	19.2	15.8	9.3	1.11
FSR_0551	COIN-Gaia_34	4	8.0	14.4	15.3	16.4	1.21
XDOCC_9	Theia_38	4	11.0	18.3	49.0	15.4	1.4
NGC_2451A	HSC_1746	4	13.7	17.6	79.2	23.8	0.84
OCSN_92	HSC_2784	4	14.0	18.9	28.0	27.0	1.35
Theia_667	CWNU_58	4	8.7	36.7	12.3	29.1	1.18
Theia_230	NGC_1662	4	13.7	39.3	93.1	25.3	1.32
HSC_815	FSR_0416	4	13.4	12.2	4.4	46.3	1.32
HSC_892	CWNU_1228	4	15.2	8.3	7.6	24.4	1.84
Theia_72	HSC_1849	4	14.7	31.2	43.9	15.4	1.2
HSC_1989	Alessi_3	4	6.6	38.6	20.5	28.3	1.53
Theia_1797	HSC_1590	4	10.8	33.9	23.5	11.2	1.08
HSC_1977	CWNU_1013	4	12.4	7.5	13.4	16.7	1.23
Teutsch_145	HSC_262	4	14.0	6.5	31.0	10.8	1.42
NGC_743	HSC_1049	4	18.3	21.7	24.5	14.6	1.02
HSC_1714	HSC_1640	4	14.7	26.6	38.9	12.5	0.99
HSC_1644	HSC_1640	4	19.9	10.9	38.9	16.9	1.88
UBC_168	Theia_4	4	19.1	37.4	10.3	29.0	1.42
UBC_168	HSC_862	4	16.0	37.4	8.2	33.9	1.32
UBC_415	CWNU_77	4	16.1	7.5	52.1	12.0	0.85
HSC_2986	HSC_2705	4	16.2	19.7	50.0	20.8	1.46
UBC_168	HSC_835	4	18.5	37.4	13.3	22.7	1.39
UFMG_24	HSC_2910	4	19.4	4.2	20.5	16.5	1.26
UPK_198	OC_0185	4	17.9	36.2	41.9	18.2	1.15
UPK_198	CWNU_1126	4	16.3	36.2	11.5	21.6	0.76
UBC_1184	Gulliver_19	4	10.4	17.3	32.0	57.4	0.95
HSC_1733	CWNU_1013	6	19.3	52.2	13.4	22.6	0.8
UBC_97	NGC_6561	6	15.7	7.9	6.1	18.8	0.85
HSC_1470	HSC_1460	6	5.9	17.2	6.1	7.6	1.27
HSC_1463	HSC_1361	6	18.3	33.3	18.6	20.3	2.05
Theia_29	HSC_2615	6	18.3	8.2	17.5	13.6	0.73
Theia_2897	FSR_0398	6	18.2	14.8	20.0	30.0	0.73
OC_0227	HSC_1037	6	19.7	12.9	9.7	33.7	1.4
HSC_2244	Gulliver_9	6	15.7	26.7	28.4	24.2	0.93
Theia_19	HSC_1067	6	9.8	5.5	44.0	25.9	1.77
HSC_613	Aveni-Hunter_1	6	8.0	19.3	37.9	40.9	1.32
HSC_1390	HSC_1318	6	18.0	13.4	7.2	13.5	2.6
OC_0018	HSC_87	6	12.6	5.8	9.3	112.7	1.26
Theia_65	HSC_1254	6	18.1	18.8	14.5	7.3	1.09
Theia_558	Collinder_95	6	16.5	60.5	11.9	13.2	1.67
UPK_617	HSC_2675	6	13.0	10.8	25.2	43.6	0.96
HSC_2907	HSC_157	6	17.6	23.7	34.8	13.0	1.32
HSC_2931	HSC_157	6	17.3	4.3	34.8	13.8	1.51
FSR_0817	CWNU_255	6	11.8	14.7	16.9	17.5	1.64
HSC_1977	HSC_1840	6	7.0	7.5	22.0	19.0	0.84
HSC_1105	CWNU_1029	6	11.4	44.3	9.3	19.1	1.52
FSR_1744	ESO_332-13	6	8.6	10.9	10.9	11.6	1.6
HSC_1119	HSC_704	6	7.6	8.5	21.7	62.3	1.7
OCSN_98	HSC_157	6	17.3	5.6	34.8	15.3	1.66
HSC_2327	HSC_2263	6	19.8	31.5	26.3	12.0	0.98
HSC_157	CWNU_1143	8	9.9	34.8	17.3	11.1	1.04
HSC_447	HSC_437	8	18.8	14.7	6.6	18.8	0.88
HSC_1715	HSC_1566	8	18.0	15.7	26.9	5.3	0.85
HSC_450	ASCC_107	8	16.7	18.4	14.1	6.6	0.96
HSC_1874	FSR_1129	8	18.6	28.0	17.5	59.9	1.21
HSC_1961	HSC_1920	8	15.2	47.4	40.1	5.8	0.77
HSC_2106	HSC_2071	8	12.5	23.0	10.3	8.6	0.94
HSC_406	CWNU_2024	8	17.9	18.3	7.5	24.4	1.36
HSC_873	HSC_725	8	19.8	8.7	13.9	19.5	1.54
CWNU_2825	CWNU_1841	8	18.8	8.0	10.6	33.5	1.13
HSC_782	HSC_594	8	19.8	20.8	31.0	11.6	0.83
Theia_72	HSC_2026	8	17.9	31.2	19.3	18.1	1.02
Theia_4069	FSR_0238	8	19.0	40.3	27.5	38.4	1.01
Theia_5292	Teutsch_175	8	12.6	24.6	7.1	24.4	0.89
IC_4651	HSC_2769	8	9.7	13.8	12.7	28.9	1.94
UBC_415	HSC_1052	8	17.7	7.5	7.9	4.7	0.83
UBC_415	CWNU_466	8	12.7	7.5	13.9	18.2	0.95
Theia_117	Teutsch_182	8	18.0	12.6	17.3	24.6	1.11
Theia_178	Teutsch_181	8	12.2	34.3	29.5	7.9	0.77
Theia_11	OCSN_24	8	16.3	10.4	18.0	27.1	1.01
OCSN_88	HSC_2068	8	16.3	224.5	15.8	11.5	0.91
HSC_2653	HSC_2641	8	16.4	34.8	23.4	14.2	0.88
HSC_2622	HSC_2612	8	12.2	8.4	26.0	18.1	0.74
UPK_438	OC_0343	8	17.1	15.9	20.0	29.6	1.02
Theia_933	HSC_1224	8	15.0	17.7	75.5	23.9	0.73
HSC_180	HSC_67	10	19.9	27.0	7.0	12.6	1.31
Harvard_13	CWNU_1538	10	18.8	27.6	6.8	48.3	1.03
Pozzo_1	HSC_2452	10	19.2	12.1	51.8	21.6	1.22
Stock_1	OCSN_32	10	14.7	36.5	14.3	28.9	1.48
UPK_189	HSC_881	10	15.3	27.1	13.1	30.0	0.86
Pismis_5	HSC_2179	10	11.9	8.0	8.6	18.8	1.79
HSC_2585	Chamaleon_I	10	12.0	63.2	11.6	14.0	1.06
OC_0673	NGC_6204	10	14.2	4.1	8.0	42.4	1.05
UPK_116	Stock_1	10	17.4	20.1	36.5	13.8	0.77
HSC_1666	HSC_1344	10	13.8	91.9	25.1	41.8	1.03
Mamajek_1	HSC_719	10	14.9	4.8	20.0	19.3	1.82
BDSB_93	ASCC_28	10	11.1	17.2	17.5	33.2	1.11
Theia_26	HSC_889	10	19.8	24.7	21.6	28.3	1.29
HSC_2237	HSC_1989	10	11.2	9.5	38.6	12.9	1.62
HSC_1369	HSC_1257	10	14.8	17.9	17.2	18.0	0.74
Theia_69	Platais_10	10	12.3	11.0	116.1	25.8	0.9
HSC_823	CWNU_1107	10	16.4	8.4	11.1	4.6	1.77
Theia_622	CWNU_236	10	16.3	22.5	12.9	8.9	0.95
HSC_2662	HSC_2630	10	13.9	25.1	25.0	9.1	1.11
HSC_427	HSC_252	10	17.9	17.0	38.3	45.7	1.13
Teutsch_182	CWNU_1216	10	14.3	17.3	29.5	19.0	1.42
NGC_6167	UBC_311	10	19.9	20.4	18.3	15.6	0.98
Theia_1038	HSC_255	10	19.0	28.3	25.4	23.5	0.86
Theia_110	HSC_2136	10	13.1	38.7	6.6	15.3	2.0
HSC_1460	HSC_865	10	4.2	6.1	29.1	20.0	0.96
Stock_2	HSC_1262	10	17.4	90.2	13.6	20.4	1.76
IC_2602	HSC_2464	10	15.9	35.6	11.7	10.6	0.96
HSC_2871	HSC_2816	12	10.8	18.7	12.1	13.7	1.62
HSC_2712	HSC_2690	12	18.4	25.9	3.8	13.3	1.19
UPK_535	Melotte_22	12	15.6	16.1	35.6	29.6	0.74
HSC_2260	HSC_2028	12	13.8	38.1	15.0	18.0	1.98
HSC_725	CWNU_1144	12	12.6	13.9	47.5	34.6	1.51
Theia_436	BH_164	12	19.8	19.2	131.2	16.8	0.77
Theia_1858	CWNU_128	12	19.0	18.4	21.9	38.3	1.01
HSC_2597	Alessi_9	12	17.5	63.0	31.4	9.1	1.06
HSC_2712	HSC_171	12	13.2	25.9	12.5	23.9	1.04
HSC_2971	CWNU_1205	12	14.8	41.0	24.7	22.2	1.07
HSC_2662	HSC_2529	12	14.8	25.1	20.4	8.6	1.13
HSC_94	ESO_522-05	12	11.7	7.1	4.7	6.2	1.49
UPK_38	Theia_622	12	14.6	12.9	22.5	8.3	1.48
HXHWL_5	HSC_1791	12	5.4	11.6	23.9	17.0	0.75
NGC_6633	Gaia_8	12	15.0	22.5	24.8	14.6	1.35
UPK_629	Theia_1643	12	16.5	18.1	23.6	23.6	1.7
HSC_1481	HSC_1447	12	15.4	57.5	95.1	13.3	0.73
OCSN_49	Delta_Cephei_Cluster	12.0	9.1	86.1	35.8	20.3	0.84
NGC_6334	HSC_11	12	4.3	12.5	3.5	30.0	1.01
Pozzo_1	HSC_1746	12	15.6	12.1	79.2	21.7	1.28
LISC-III_3668	HSC_2174	12	9.3	54.2	11.5	19.6	0.86
OCSN_70	HSC_1707	12	17.8	3.4	20.1	18.1	1.28
OCSN_70	ASCC_24	12	13.1	3.4	13.6	20.1	0.72
Theia_222	Theia_70	12	15.4	21.2	15.7	10.9	0.95
HSC_1942	CWNU_1134	12	5.5	13.2	25.3	12.0	0.74
OCSN_91	HSC_2871	12	8.1	4.9	18.7	15.4	0.77
Pismis_5	NGC_2546	12	16.6	8.0	27.3	6.6	1.58
OC_0497	CWNU_1163	12	17.0	5.6	9.8	23.1	1.33
HSC_1470	CWNU_1178	12	19.3	17.2	27.6	9.8	1.08
HSC_1871	CWNU_1057	12	18.1	14.1	33.1	16.8	0.8
Platais_12	HSC_2529	12	16.9	46.2	20.4	20.3	1.31
Platais_12	HSC_2630	12	9.9	46.2	25.0	22.4	1.29
OC_0017	HSC_79	12	11.8	11.3	6.7	72.4	1.34
HSC_1840	FSR_1017	12	15.0	22.0	17.7	19.8	1.02
NGC_6281	HSC_2915	12	19.3	39.4	6.7	71.4	1.2
Pismis_5	HSC_2234	12	13.6	8.0	10.1	23.5	1.14
Theia_169	CWNU_1088	14	15.6	123.5	17.9	11.7	0.74
IC_4665	HSC_2705	14	8.4	23.7	50.0	25.6	0.8
CWNU_58	Alessi_37	14	16.2	12.3	63.6	18.7	1.18
HSC_2687	HSC_2120	14	12.8	16.3	53.1	28.1	0.73
HSC_1986	CWNU_1066	14	14.2	66.4	29.2	11.0	0.82
Theia_1528	ADS_16795	14	14.0	11.6	30.8	7.7	1.11
Theia_5	HSC_986	14	16.8	54.5	17.9	17.8	1.26
Theia_29	HSC_2609	14	16.0	8.2	23.3	12.1	0.77
NGC_2215	Collinder_132	14	16.5	13.3	31.4	33.0	1.51
HSC_1523	HSC_1314	14	16.4	10.3	73.6	10.5	0.95
UPK_144	Theia_713	14	16.7	7.0	94.3	20.5	1.1
HSC_1119	HSC_295	14	18.5	8.5	39.2	49.2	0.95
Collinder_471	ASCC_99	14	18.2	17.2	40.4	32.9	1.27
HSC_2907	HSC_188	14	15.5	23.7	12.7	7.1	1.65
HSC_2239	Gulliver_9	14	16.8	14.7	28.4	14.1	1.04
HSC_1465	HSC_782	14	15.5	22.9	20.8	27.2	2.29
Theia_247	HSC_238	14	12.2	70.2	16.4	17.5	0.99
HSC_2983	Collinder_394	14	14.9	6.7	22.3	24.4	0.78
OCSN_98	HSC_376	14	19.4	5.6	17.1	19.6	1.14
OCSN_100	HSC_376	14	15.6	5.1	17.1	19.9	1.23
Ruprecht_53	HSC_2092	14	17.1	14.6	10.9	20.5	1.15
HSC_2610	HSC_2068	14	17.0	43.3	15.8	10.6	1.48
HSC_2645	BH_164	14	15.2	38.5	131.2	20.0	1.52
HSC_2641	HSC_171	14	14.0	23.4	12.5	24.5	1.0
Gulliver_9	DBSB_64	14	19.5	28.4	10.9	36.4	1.01
OC_0124	Berkeley_90	14	16.6	10.3	27.7	64.3	0.93
OCSN_92	HSC_2871	14	17.5	18.9	18.7	12.2	1.59
Roslund_6	Aveni-Hunter_1	14	15.5	25.2	37.9	16.4	1.17
HSC_2452	CWNU_1224	14	16.8	51.8	21.3	19.4	1.06
HSC_94	CWNU_448	14	11.5	7.1	16.1	26.5	1.07
HSC_1894	HSC_1843	16	16.9	15.6	27.8	15.1	0.92
Theia_54	HSC_1710	16	19.3	13.6	29.5	8.2	1.48
OCSN_32	ASCC_100	16	17.7	14.3	21.2	20.8	0.88
HSC_2763	HSC_2618	16	13.5	8.8	20.7	6.8	1.39
HSC_2335	HSC_1347	16	18.8	19.0	42.7	14.3	0.74
HSC_2103	HSC_2020	16	18.6	17.9	22.8	25.9	1.86
Theia_366	HSC_1894	16	16.7	19.6	15.6	12.9	0.91
HSC_2314	ASCC_85	16	19.6	34.3	41.4	59.6	1.68
NGC_6800	HSC_618	16	12.4	20.4	10.1	21.7	1.69
HSC_2298	Gulliver_9	16	15.2	24.1	28.4	12.0	1.0
LK_10	Bica_2	16	15.8	9.9	6.3	7.0	1.78
IC_1396	CWNU_460	16	15.1	14.7	16.7	24.1	1.43
HSC_2303	HSC_1648	16	16.5	70.9	24.9	20.8	0.87
UPK_156	BDSB_30	16	9.6	11.1	8.8	10.6	1.37
OCSN_59	CWNU_1054	16	8.7	15.0	18.9	6.8	1.31
Theia_472	HSC_2469	16	17.0	21.2	37.1	53.7	1.15
Theia_181	ASCC_79	16	16.5	41.0	15.8	16.3	1.31
Alessi_37	ASCC_125	16	17.3	63.6	4.2	16.9	1.53
UBC_1105	HSC_643	16	19.7	19.4	10.8	94.9	1.18
Platais_12	HSC_2636	16	14.2	46.2	19.0	19.6	1.18
UPK_25	HSC_911	16	16.8	17.7	20.1	39.4	0.97
RSG_8	HSC_956	16	17.4	21.7	23.0	16.9	0.87
UFMG_66	BH_211	16	19.9	11.8	9.2	19.2	1.1
Teutsch_39	NGC_7438	16	4.7	11.2	32.0	22.5	1.21
HSC_415	HSC_106	16	19.9	20.2	5.9	62.5	0.75
UBC_534	Harvard_13	16	17.2	19.7	27.6	41.3	0.91
UBC_162	HSC_779	16	16.8	15.6	13.7	12.5	0.99
HSC_1146	FSR_0686	16	15.9	6.4	10.0	15.5	1.09
Theia_925	ASCC_127	16	18.1	37.9	27.8	26.1	1.12
RSG_8	HSC_1125	16	15.4	21.7	17.4	24.9	1.03
OCSN_92	Mamajek_2	18	19.3	18.9	45.4	7.0	1.03
HSC_1732	HSC_1719	18	17.2	23.8	21.8	20.4	0.97
Theia_171	Teutsch_181	18	13.7	90.9	29.5	17.9	0.94
UPK_82	Teutsch_39	18	12.3	20.7	11.2	19.1	0.73
UPK_172	HSC_533	18	14.5	21.9	24.8	29.3	0.76
HSC_1224	ASCC_20	18	11.7	75.5	10.3	21.4	0.97
UPK_169	Theia_269	18	12.1	20.0	14.9	38.1	1.34
HSC_1481	HSC_1047	18	13.4	57.5	15.4	12.8	1.21
HSC_2442	CWNU_1265	18	11.9	32.3	10.6	7.8	1.65
HSC_2630	CWNU_513	18	16.3	25.0	13.8	10.2	1.41
HSC_764	CWNU_174	18	5.87	72.6	60.2	27.5	0.97
UPK_640	HSC_844	18	10.0	43.3	16.9	68.3	1.01
Theia_118	ASCC_24	18	17.5	19.1	13.6	5.0	1.77
Theia_7	HSC_2229	18	10.7	8.0	49.0	16.7	1.41
Theia_101	HSC_1465	18	18.0	31.5	22.9	34.0	1.49
Theia_1232	HSC_1469	18	16.2	14.5	31.1	21.4	1.13
HSC_1765	HSC_926	18	7.9	18.4	35.1	22.3	0.74
HSC_1390	HSC_926	18	19.3	13.4	35.1	15.7	1.01
Theia_4310	Theia_850	18	11.3	15.4	26.1	29.6	1.07
UBC_159	HSC_658	18	19.6	12.4	7.4	38.3	1.72
NGC_7031	CWNU_1276	18	9.2	14.6	15.7	54.9	1.03
CWNU_1107	CWNU_460	18	10.1	11.1	16.7	26.4	1.15
HSC_440	HSC_238	18	13.4	18.1	16.4	13.1	1.03
HSC_2028	ASCC_58	18	14.0	15.0	30.4	15.9	2.08
Theia_227	OCSN_12	18	18.8	39.5	29.8	17.4	0.77
Teutsch_28	Dolidze_1	20	14.6	15.3	12.7	45.7	0.84
Teutsch_182	HSC_2846	20	13.4	17.3	47.4	23.2	0.89
NGC_5822	CWNU_1173	20	19.9	25.6	45.3	22.0	1.02
HSC_534	Gaia_8	20	19.1	10.4	24.8	4.2	1.02
UBC_1618	HSC_2080	20	17.5	14.6	9.1	5.5	1.21
HSC_2237	HSC_2056	20	17.4	9.5	24.0	10.7	1.45
HSC_1667	ASCC_73	20	11.8	13.8	38.9	31.9	1.14
HSC_2784	HSC_1648	20	9.1	28.0	24.9	24.4	1.28
Theia_4	HSC_736	20	13.6	10.3	5.6	18.1	1.48
UPK_113	LDN_988e	20	17.8	31.3	16.7	12.0	0.9
NGC_2215	HSC_2046	20	7.9	13.3	20.7	30.8	1.27
HSC_2028	CWNU_287	20	19.8	15.0	12.6	12.7	1.83
HSC_884	HSC_842	20	10.7	10.3	12.5	10.1	0.95
UPK_438	Mon_OB1-D	20	12.1	15.9	3.8	16.1	1.75
UPK_191	Roslund_5	20	17.6	11.7	27.7	25.4	1.49
Theia_1232	Theia_229	20	10.3	14.5	62.2	30.3	0.95
Theia_1256	HSC_1958	20	11.9	11.7	13.6	21.8	1.65
HSC_188	CWNU_1004	20	6.4	12.7	4.2	8.6	1.88
Theia_71	Alessi_3	20	11.9	8.1	20.5	14.3	1.6
Theia_1224	OCSN_82	20	19.4	31.7	35.5	26.5	1.18
Theia_759	HSC_1920	20	19.9	26.9	40.1	14.5	1.15
HSC_696	FSR_0369	20	13.6	15.7	3.9	16.2	1.46
HSC_1058	Alessi_20	22	11.6	75.7	13.6	10.5	1.24
Theia_865	HSC_2587	22	16.2	62.7	10.6	8.8	0.8
UBC_179	HSC_576	22	18.9	35.7	15.6	34.4	1.21
HSC_2983	Alessi_80B	22	16.5	6.7	14.1	28.3	1.24
Teutsch_182	HSC_629	22	17.7	17.3	18.7	13.0	1.38
HSC_1213	ASCC_21	22	19.9	31.8	10.6	20.1	1.5
HSC_1370	HSC_1239	22	19.9	10.3	27.1	33.8	1.13
NGC_2423	HSC_2412	22	17.5	26.7	10.5	41.0	0.79
OC_0018	HSC_305	22	18.4	5.8	18.7	62.6	1.36
NGC_6530	CWNU_101	22	8.3	11.4	9.2	17.2	1.1
NGC_7789	HSC_877	22	19.1	28.4	19.2	46.6	0.87
HSC_2648	Alessi_20	22	20.0	9.3	13.6	32.3	1.63
NGC_6735	FSR_0165	22	19.5	27.9	11.1	53.9	0.8
Majaess_90	HSC_1974	22	18.7	11.8	26.8	6.8	1.06
OC_0652	HSC_381	22	12.6	9.7	37.9	37.2	0.83
HSC_1648	HSC_878	22	16.7	24.9	35.5	22.1	0.91
HSC_1542	ASCC_19	22	17.1	52.9	5.5	11.8	1.38
HSC_1469	HSC_1460	22	14.4	31.1	6.1	7.8	0.91
UPK_118	Czernik_2	22	16.1	15.9	21.8	60.2	0.93
UPK_594	Majaess_160	22	7.0	24.6	11.3	9.8	0.86
Theia_227	NGC_6568	22	18.3	39.5	7.9	26.6	1.24
Theia_648	ASCC_21	22	16.9	19.6	10.6	13.4	1.28
UPK_540	HSC_1724	22	13.6	26.4	21.7	15.3	1.87
Theia_862	HSC_1253	22	14.3	62.4	25.3	13.9	0.88
Theia_345	HSC_1112	22	15.8	24.6	17.9	18.7	1.35
UBC_294	CWNU_1362	22	17.5	12.7	8.7	70.6	1.0
Theia_229	HSC_782	22	11.8	62.2	20.8	25.4	0.79
Haffner_13	CWNU_2407	22	7.0	58.6	14.2	51.2	0.92
Theia_863	Theia_5	22	11.8	37.9	54.5	22.0	1.28
HSC_2247	HSC_453	22	15.3	32.2	69.7	24.7	1.25
Theia_874	OCSN_70	22	15.7	45.5	3.4	24.1	1.72
Theia_1188	ASCC_111	22	4.8	26.4	26.8	29.9	0.86
UPK_492	CWNU_331	22	15.7	21.4	7.8	23.9	1.5
HSC_2315	FSR_1452	22	11.9	24.0	23.3	28.3	0.81
Theia_1232	HSC_2718	22	8.8	14.5	81.2	24.6	0.88
Theia_1528	HSC_1640	22	18.5	11.6	38.9	22.4	1.64
Theia_8014	HSC_899	22	11.6	24.1	9.1	18.3	1.7
HSC_691	BDSB_30	22	12.7	17.5	8.8	17.8	1.23
HSC_2881	Bochum_13	22	4.6	5.6	15.4	22.5	1.23
Theia_874	OCSN_82	24	16.7	45.5	35.5	28.6	1.13
NGC_6882	HSC_544	24	16.3	40.2	16.2	6.4	1.07
HSC_381	FSR_0416	24	13.1	37.9	4.4	30.3	0.81
UPK_317	UBC_51	24	10.7	17.4	11.6	15.6	1.15
HSC_1941	CWNU_1032	24	12.6	12.9	37.9	28.9	0.81
Theia_401	HSC_835	24	5.1	72.2	13.3	17.0	1.47
Theia_93	HSC_1840	24	15.9	22.9	22.0	9.6	1.16
HSC_1640	HSC_725	24	19.3	38.9	13.9	17.6	1.66
OCSN_28	HSC_396	24	17.1	27.1	67.1	16.1	0.87
Trumpler_3	ASCC_125	24	5.9	64.4	4.2	17.5	1.02
UPK_45	HSC_419	24	17.6	24.6	18.8	32.5	0.95
HSC_1692	CWNU_1096	24	11.8	16.4	9.2	12.4	1.1
Theia_1890	HSC_1867	24	16.1	17.3	9.8	22.2	0.88
Theia_1528	HSC_106	24	2.9	11.6	5.9	50.8	2.1
Theia_1408	CWNU_172	24	13.3	18.5	14.0	23.4	0.78
Mon_OB1-D	CWNU_410	24	14.8	3.8	22.1	15.7	1.12
OCSN_70	HSC_1169	24	15.3	3.4	22.2	24.1	1.03
HSC_1973	Alessi_170	24	16.6	13.5	39.6	34.1	1.23
UBC_169	Theia_420	24	12.4	10.8	26.2	26.6	1.07
HSC_2796	ASCC_87	26	16.2	16.0	16.8	39.2	1.6
HSC_2144	Gulliver_40	26	18.9	13.2	10.6	32.0	0.96
Majaess_90	CWNU_212	26	18.1	11.8	15.1	14.2	1.2
OC_0395	HSC_1693	26	9.4	21.2	13.7	14.1	0.86
OCSN_54	HSC_1112	26	14.2	18.9	17.9	14.6	1.82
HSC_2468	HSC_1991	26	18.7	24.3	15.7	6.4	1.2
Theia_704	HSC_2437	26	19.4	30.5	30.6	11.5	1.07
HSC_460	CWNU_446	26	11.9	15.4	8.2	36.4	2.07
UPK_120	ASCC_125	26	19.7	24.0	4.2	14.7	1.24
HSC_2202	HSC_1958	26	19.6	10.2	13.6	21.0	1.72
Theia_280	HSC_789	26	16.5	52.3	11.3	13.6	1.54
HSC_1894	CWNU_1087	26	18.6	15.6	9.4	16.9	0.9
HSC_1067	HSC_824	26	16.8	44.0	4.8	17.3	1.76
Theia_648	NGC_2068	26	19.9	19.6	12.4	11.0	1.35
UPK_126	CWNU_209	26	16.1	5.6	11.3	24.1	1.6
Theia_1890	NGC_2539	26	16.4	17.3	16.4	28.2	1.62
OC_0018	HSC_2231	26	9.8	5.8	11.6	67.9	2.26
Teutsch_182	HSC_883	26	18.3	17.3	23.2	9.0	1.11
HSC_957	ASCC_125	26	12.2	18.0	4.2	16.9	1.62
OCSN_91	HSC_2850	26	14.0	4.9	36.5	8.7	1.36
HSC_507	HSC_207	26	14.2	28.9	15.1	13.6	0.96
HSC_2785	HSC_283	26	16.5	11.2	24.0	40.0	1.08
Theia_345	Teutsch_5	26	11.3	24.6	10.3	62.3	0.98
UBC_1592	HSC_2638	26	19.8	9.6	13.6	24.5	0.75
HSC_703	CWNU_1240	26	17.5	37.3	11.0	32.3	1.06
HSC_272	CWNU_1292	26	19.9	18.7	14.1	30.7	1.09
UPK_540	HSC_229	26	10.8	26.4	18.3	24.2	1.95
HSC_1908	CWNU_232	26	8.2	15.4	31.2	19.6	1.33
HSC_2693	HSC_2139	26	13.3	17.4	24.1	50.2	1.73
UBC_302	Collinder_272	26	19.6	8.6	19.0	40.5	0.91
Theia_403	HSC_2283	26	19.7	18.0	67.4	20.4	0.77
Theia_366	Ruprecht_26	26	10.2	19.6	15.6	10.4	0.75
HSC_2636	HSC_883	26	19.8	19.0	23.2	22.6	0.95
Theia_3796	OC_0497	28	18.3	5.5	5.6	51.4	1.45
Theia_3715	CWNU_164	28	5.1	13.6	13.5	38.5	1.31
HSC_725	CWNU_168	28	17.6	13.9	13.9	30.7	1.53
CWNU_2419	CWNU_207	28	19.5	40.0	9.7	61.7	1.09
HSC_926	Collinder_135	28	19.8	35.1	14.1	21.1	0.85
Theia_6	OC_0257	28	15.9	18.8	11.9	11.5	1.25
Theia_6599	CWNU_1111	28	14.6	34.3	14.3	41.0	0.75
OCSN_28	HSC_598	28	19.2	27.1	33.1	13.9	0.96
HSC_926	Alessi_36	28	19.6	35.1	9.8	19.8	0.87
HSC_1234	HSC_1040	28	18.3	17.3	12.2	9.6	1.9
UPK_614	UFMG_66	28	16.5	13.7	11.8	37.6	0.95
UPK_606	Mamajek_2	28	11.6	14.6	45.4	6.9	1.01
HSC_894	HSC_627	28	19.3	17.0	4.9	30.6	1.88
HSC_2022	HSC_1913	28	19.0	7.2	8.2	18.1	1.91
Theia_3980	CWNU_406	28	14.5	20.5	15.7	15.1	1.21
HSC_1122	HSC_926	28	18.7	45.7	35.1	71.3	1.09
UBC_182	NGC_7082	28	19.3	15.2	14.2	28.3	0.8
OCSN_28	ASCC_101	28	4.0	27.1	47.9	9.8	1.02
UPK_72	HSC_1385	28	10.4	31.5	22.0	37.2	1.11
OCSN_41	CWNU_1216	28	18.3	7.0	29.5	7.7	1.42
OC_0339	COIN-Gaia_12	28	10.3	4.9	27.9	25.9	0.83
UPK_470	OC_0289	28	18.6	41.1	22.8	43.5	1.14
FSR_1527	CWNU_246	28	13.2	22.2	36.3	56.0	1.71
Theia_246	Alessi_36	28	16.0	31.5	9.8	10.0	0.82
UBC_1622	UBC_482	28	19.1	14.3	27.8	27.5	1.15
Teutsch_5	HSC_1523	28	8.5	10.3	10.3	64.0	1.89
Theia_85	ASCC_125	28	18.8	24.5	4.2	18.0	1.2
HSC_1667	HSC_1347	28	14.9	13.8	42.7	6.3	1.33
HSC_2068	HSC_453	28	12.0	15.8	69.7	8.8	0.97
OC_0158	HSC_620	28	16.8	6.7	10.7	21.9	1.14
UBC_1295	BDSB_93	28	17.6	20.6	17.2	39.1	1.22
HSC_1052	HSC_465	28	18.6	7.9	13.1	36.2	1.35
HSC_204	CWNU_236	28	19.6	22.1	12.9	6.4	0.94
UBC_374	UBC_373	28	17.2	15.5	12.8	12.6	1.24
HSC_2587	HSC_2461	28	8.4	10.6	11.1	20.3	0.96
Theia_665	HSC_1958	30	17.5	22.1	13.6	19.5	1.49
Theia_6680	HSC_190	30	5.6	23.1	15.3	24.8	0.97
Stock_8	Ruprecht_145	30	19.6	21.7	65.7	81.3	1.77
UPK_562	BH_56	30	10.0	13.8	12.4	11.9	1.82
OCSN_70	HSC_977	30	19.8	3.4	23.4	29.8	1.13
NGC_1960	HSC_142	30	13.2	23.2	6.6	89.1	0.75
UBC_669	ESO_226-06	30	14.4	7.7	11.6	13.9	0.76
UBC_1004	CWNU_1920	30	19.8	16.8	29.5	32.4	0.8
UPK_639	CWNU_2145	30	15.6	70.9	20.3	70.8	1.08
Theia_4877	Gulliver_24	30	9.7	22.1	11.3	35.1	0.76
Theia_6	HSC_1194	30	17.4	18.8	11.0	14.2	1.28
Theia_361	HSC_1314	30	12.6	6.9	73.6	21.6	1.55
Theia_3397	Theia_1424	30	19.9	68.6	29.5	47.0	0.82
Theia_72	CWNU_1134	30	8.8	31.2	25.3	7.1	0.84
IC_2391	HSC_1378	30	18.6	31.5	16.5	32.4	0.87
HSC_2603	HSC_1724	30	18.3	22.5	21.7	9.7	1.37
Theia_361	CWNU_1129	30	13.6	6.9	21.7	23.1	2.44
UBC_255	OC_0322	30	14.6	21.0	13.9	31.5	2.26
HSC_1314	CWNU_1129	30	18.7	73.6	21.7	5.7	0.89
HXHWL_7	ASCC_90	30	13.3	7.5	60.2	26.0	0.78
UPK_127	UBC_10b	30	14.2	8.1	13.5	12.1	1.14
UPK_535	HSC_1774	30	15.7	16.1	27.5	22.8	0.8
HSC_2784	HSC_2458	30	19.1	28.0	8.9	12.0	0.76
PHOC_24	Majaess_88	30	18.6	15.3	12.9	31.8	0.78
Theia_1038	OCSN_3	30	20.0	28.3	12.6	11.7	0.96
UPK_172	Theia_1140	30	17.6	21.9	17.8	26.7	0.93
UPK_185	HSC_747	30	9.8	23.4	10.0	11.1	1.47
CWNU_1801	CWNU_1227	30	13.9	19.4	29.0	32.4	1.8
OC_0470	HSC_1426	30	18.8	18.4	28.3	13.4	1.06
HSC_1900	HSC_453	30	19.6	15.7	69.7	7.5	0.96
OCSN_27	Melotte_111	30	15.2	38.6	61.4	18.1	1.64
Theia_246	Collinder_135	30	11.8	31.5	14.1	9.5	0.81
UPK_422	Teutsch_5	30	19.1	46.7	10.3	59.7	1.83
HSC_2503	Gulliver_9	30	18.6	18.0	28.4	25.4	1.47
HSC_606	CWNU_58	30	15.8	25.2	12.3	21.0	1.09
HSC_894	ASCC_114	30	16.5	17.0	11.8	25.3	1.26
HSC_974	HSC_932	32	12.3	26.4	15.0	9.8	0.73
Theia_387	NGC_752	32	13.2	72.9	82.9	14.5	1.11
IC_1396	HXHWL_8	32	17.0	14.7	30.8	16.8	1.55
HSC_2662	HSC_558	32	11.2	25.1	19.8	16.8	1.31
UPK_169	UPK_53	32	19.4	20.0	17.1	18.8	1.43
HSC_1827	HSC_1658	32	19.5	10.6	25.3	3.7	0.89
UBC_1456	Loden_46	32	17.5	14.8	18.2	33.4	0.99
HSC_618	HSC_343	32	12.4	10.1	19.7	20.8	1.36
Theia_713	Riddle_6	32	11.9	94.3	6.2	17.5	1.54
Harvard_13	HSC_2719	32	13.5	27.6	22.1	32.6	0.98
UPK_369	HSC_2453	32	15.5	14.8	85.9	24.4	0.77
Theia_6599	NGC_2232	32	12.0	34.3	17.6	40.0	0.96
Theia_4877	HSC_862	32	16.7	22.1	8.2	29.5	2.07
HSC_2022	CWNU_384	32	10.9	7.2	15.5	7.8	0.97
Theia_66	Kronberger_92	32	17.0	11.7	13.2	33.0	1.42
HSC_2971	HSC_2836	32	19.8	41.0	18.8	30.9	1.05
Theia_66	OC_0370	32	18.6	11.7	10.4	26.5	1.41
HSC_1516	CWNU_1129	32	17.2	13.8	21.7	24.2	0.89
Theia_71	ASCC_99	32	11.9	8.1	40.4	14.1	0.76
OCSN_89	HSC_453	32	13.6	34.9	69.7	15.2	0.82
CWNU_338	Alessi_170	32	11.6	36.1	39.6	31.7	1.72
NGC_6793	FSR_0551	32	18.3	47.4	14.4	25.7	1.32

Equations

$$E=\frac{{\left|v_1-v_2\right|}^2}{2}-\frac{GM}{S},$$

$$M=M_1+M_2$$

Full text

On the Encounter Rate of Open Star Clusters

A. D. Grinenko

Moscow State University, Moscow, 119991 Russia

Institute of Astronomy, Russian Academy of Sciences, Moscow, 119017 Russia

  

D. A. Kovaleva

Institute of Astronomy, Russian Academy of Sciences, Moscow, 119017 Russia

open star clusters, dynamical evolution of the Galaxy, Gaia

Probable past and future close encounters of open clusters with known characteristics over 64 million years have been calculated by integrating the orbits of cluster centers in the Galactic potential using the galpy package. It has been shown that in the Galactic neighborhood of the Sun, pairwise cluster encounters at distances comparable to or smaller than their sizes occur at a characteristic rate of 35–40 events per 1 Myr. Close encounters between open clusters with a significant age difference occur at a rate of 15 events per Myr. It can be expected that in the Galaxy as a whole, such events occur an order of magnitude more frequently per unit time. Thus, dynamical interactions between stellar ensembles of different ages may not be too rare and could influence the properties of stellar populations. A pair of clusters with similar ages: HSC 1428 and Gulliver 22 was identified as a likely physically bound binary cluster system. A forecast of expected close encounters over the next 32 Myr has been provided for 490 pairs of clusters. Currently, 29 pairs of clusters are at their closest approach.

1 Introduction

The abundance of double and multiple stars in the field of the Galaxy is usually considered as a consequence of the process of formation of stars in groups (Duchêne and Kraus, 2013).Thus, the components of binary star systems have a common origin, the same or very similar age, and initial abundance of chemical elements. The most common processes of binary star formation are considered to be the formation of bound systems during the fragmentation of a molecular cloud or during the fragmentation of a protostellar disk surrounding a formed star (see detailed discussion in Bate (2015), Tutukov and Cherepashchuk (2020)). It is also possible for binaries to form during inelastic collisions in the parent cluster, provided that excess kinetic energy can be released through interaction with a third body Cournoyer-Cloutier et al. (2021), tidal interactions (for very close pairs), or, most often, through a protostellar disk. Some wide pairs have been shown to form during the disintegration of open star clusters due to the low relative velocity of stars leaving the cluster relative to each other (Kouwenhoven et al., 2011, Tokovinin, 2020, Rozner and Perets, 2023). The components of pairs formed in such events may have an age difference determined by the duration of the star formation process in the cluster (up to several million years; see, for example, Smilgys and Bonnell (2017), Jerabkova et al. (2019)). However, there are known cases where the observational characteristics of the components of a binary system lead to significantly different estimates of the ages of the components (see discussion in Valle et al. (2016), Malkov and Kniazev (2022)). Such events are usually explained by inaccuracies in the definition of observational characteristics or evolutionary models. However, the interaction of a binary system with a single star, a binary star, or a high-multiplicity stellar system is theoretically possible during encounters outside the parent star cluster, including encounters between star clusters. Open star clusters are an important component of the Galaxy, and their evolution largely determines the characteristics of the stellar population (Lindegren and Dravins, 2003, Krumholz et al., 2019). In particular, in clusters, a significant fraction of binary and multiple stars is formed (Bate, 2015, Kouwenhoven et al., 2011, Rozner and Perets, 2023). The publication of data from the Gaia space mission (Gaia Collaboration et al., 2016) has led to an abundance of new information on the number of open star clusters and moving groups of stars in the solar neighborhood, as well as to a significant increase in the accuracy of determining their characteristics. High-precision astrometric and photometric data from Gaia for more than 1.5 billion stars in our Galaxy have served as the basis for many projects using methods for automatically searching for regions of increased density in the 5D parameter space, including celestial coordinates, proper motions, and parallaxes, to search for clusters (see, e.g., Cantat-Gaudin et al. (2018), Cantat-Gaudin and Anders (2020), Cantat-Gaudin et al. (2020), Castro-Ginard et al. (2020), Liu and Pang (2019), Sim et al. (2019), He et al. (2021), Castro-Ginard et al. (2021) and others; a review of the used methods and the obtained results is given in Cantat-Gaudin and Casamiquela (2024)). The most complete homogeneous catalogue of star clusters discovered using automated search algorithms and machine learning methods applied to Gaia DR3 data (Gaia Collaboration et al., 2021, 2022), is the one authored by Hunt & Reffert (Hunt and Reffert, 2024), and hereafter referred to as HR24.

New studies of the open star cluster population have revealed that, although some previously thought to exist clusters have turned out to be mirages (Cantat-Gaudin, 2022), their number even at hundreds of parsecs from the Sun is significantly greater than previously thought, especially if we take into account stellar groups with common motion, which can be difficult to distinguish from clusters. Besides, the sizes of open clusters turned out to be significantly larger than previously thought. In this regard, in the Galaxy, unlike earlier ideas (de La Fuente Marcos and de La Fuente Marcos, 2009, see, e.g., discussion in), a noticeable number of pairs of clusters that are located at a small physical distance from each other and interact gravitationally (e.g., Kovaleva et al. (2020), Camargo (2021), Ye et al. (2022), Casado (2022), Qin et al. (2023); see also reviews by Vereshchagin et al. (2022), Angelo et al. (2022)) were discovered. Typically, the clusters in these pairs are very similar in age and formed in the same giant molecular cloud. However, there are also other reliable examples of clusters and stellar groups of very different ages that are close to each other or approaching each other and have significant velocities relative to each other. Several examples of such encounters of different ages known to date can be listed: the approaching cluster Coma Ber and a moving stellar group (Fürnkranz et al., 2019, Tang et al., 2019, Sapozhnikov and Kovaleva, 2021); the cluster NGC 1605 AB, which, as was stated by Camargo (2021), is the result of mixing of the populations of two clusters of different ages (this opinion has been opposed, though, by Anders et al. (2022)); the ongoing collision of the clusters IC 4665 and Collinder 350 (Piatti and Malhan, 2022); etc.

If the populations of such clusters mix, it may be possible to form linked stellar systems whose components will have different ages. In this paper, we aim to answer the question of how frequent are the encounters of open star clusters, and what is the fraction of encounters between clusters of different ages. To do this, we construct a simplified model in which known clusters are considered as material points moving in the gravitational potential of the Galaxy, integrate their galactic orbits, and record the moments of approach. In Section 2, the data, approximations, and used methods are described; In Section 3, we present the obtained results, Section 4 is devoted to their discussion, and in Section 5, conclusions are provided.

2 Data and methods

We used data on clusters and their characteristics from the most complete modern homogeneous catalog of open star clusters (Hunt and Reffert, 2024), HR24, which is the result of a systematic search for star clusters among the sources of the Gaia DR3 catalog and their comprehensive homogeneous study. The HR24 catalogue contains data for 7167 star clusters (including 134 globular clusters) at distances of up to 10 kpc from the Sun. In this case, radial velocities were determined for 5749 open star clusters, and we limit further consideration to them.

The following cluster parameters from HR24 were used to integrate the galactic orbits:

• •

coordinates RA_ICRS, DE_ICRS;

• •

parallaxes Plx;

• •

proper motions pmRA, pmDE;

• •

radial velocities RV.

For subsequent analysis of the encounters, other characteristics of clusters from the HR24 catalogue were also used:

• •

cluster radii in parsecs: total $rtotpc$, Jacobi radius $rJtotpc$, core radius $rcpc$;

• •

logarithms of ages (median, first and third quartile): logAge16, logAge50, logAge84;

• •

total masses of clusters: MassTot.

galpy programming package (Bovy, 2015) allows to integrate the orbits of objects in the gravitational potential of the Galaxy, provided that their three-dimensional coordinates and velocities at the present time are known. In the calculations, the three-component model of the galactic potential MWPotential2014 for our Galaxy was used. MWPotential2014 represents some simplification of the model Bovy and Rix (2013) and includes

• •

a bulge with a power density profile with an exponential cutoff, with the power degree is equal to –1.8, and the cutoff radius is 1.9 kpc;

• •

disk in the form of the Miyamoto–Nagai potential (Miyamoto and Nagai, 1975);

• •

a dark matter halo described by the Navarro–Frank–White potential (Navarro et al., 1996).

The numerical parameters of these three components, the disk and halo size scales are selected to best match important observable characteristics of the Galactic population (Bovy, 2015).

Orbits were integrated for each center of open clusters with determination of spatial-kinematic characteristics at the nodes of time scale with a step of 2 million years from the present moment to 32 million years into the past and into the future. In this way, positions were calculated for all 5749 open star clusters with known radial velocities. At each step, mutual distances were calculated for all pairs of clusters.

3 Results

For the purposes of this study, a convergence of a pair of clusters was considered to be a position, in which the centers of the pair of clusters were located at a distance of no more than 20 pc from each other. The catalogue contains 146 pairs of clusters, the distance between the centers of which is currently ( ) is 20 pc or less. At distance from the present moment both into the past and into the future, the calculated number of approaches tends to decrease 1), which is associated with the blurring in space of the ensemble of open star clusters observed in the vicinity of the Sun today, and the replacement of some of them by other clusters not yet included in the catalogs of known ones.

We considered the values of significant age differences to be 0.72. The selection of this criterion was determined by the following considerations. In the HR24 catalogue, the distribution of age estimates for the same cluster is characterized by a median interquartile distance of 0.24 dex. Taking this value as an analogue of the standard deviation (SD) for a symmetric distribution, we select a deviation greater than three SDs as significant. To date ( ), 38 pairs of approaching clusters out of 146 have a significant age difference. The distribution of approaches by the difference in ages of clusters in the approaching pair is shown in Fig. 2.

The detected approaches are shown in Fig. 3 in coordinates: the distance between the centers of the clusters at the moment of approach–the sum of the total radii of the approaching clusters. All calculated encounters are shown in grey, with encounters currently observed highlighted in yellow ( ). To distinguish pairs located close to each other at formation from true encounters, in Fig. 4 the same events in the same coordinates are marked with a color that is darker the greater the difference in age for the two clusters participating in the encounter. The same pair may correspond to several points if the convergence is observed in more than one time node.

The total radii of the clusters $rtotpc$ (Fig. 3, 4 demonstrate the sum of total radii for the pair of clusters $rtotpc_{1}+rtotpc_{2}$) are the estimates of the sizes of clusters from above with allowance for their possible coronas and tidal tails. On the other hand, for the same clusters, the median value of the ratio of the Jacobi radius rJtotpc to total radius of the cluster rtotpc is $rJtotpc/rtotpc=0.58$, while the median value of this ratio for the radius of the core is $rcpc/rtotpc=0.36$. A comparison of the radii of clusters given in the HR24 catalogue with their approach distances shows that in most cases, the sum of the total radii of clusters significantly (two or more times) exceeds the minimal distance between their centers during approach (Figs. 3, 4). Thus, most encounters to a distance of less than 20 pc between cluster centers result in mutual penetration of clusters and mixing of the cluster populations in space.

In the Appendix (Table  LABEL:tab1), a forecast and characteristics of the closest approaches of clusters for the next 32 million years and a list of pairs of clusters that are currently in closest approach are given. The table contains identifiers of approaching clusters (Name 1, Name 2), the epoch of closest approach from 0 to 32 million years, minimal distance between cluster centers $Min\_dist$ in parsecs, full cluster radii $R_{1}$, $R_{2}$ in parsecs, the relative velocity of the clusters at the moment of closest approach $V_{rel}$ in km/s, and the difference in the logarithms of ages (in years) $dlogAge$. Each pair of clusters appears in the list at most once with closest approach characteristics.

4 Discussion

The relative velocity of clusters as they approach each other affects the outcome of their dynamic interaction and the probability of population mixing. The distribution of approach events by the relative velocity of clusters in a pair at a minimal distance between their centers is shown in Fig. 5. Most encounters, both in general and at present, occur with a relative velocity of clusters not exceeding 10–20 km/s (the median approach velocity is 12.9 km/s). Moreover, clusters with a significant difference in age and clusters of similar ages, as is expected, show different distributions. Clusters of similar ages have predominantly low velocities at the moment of approach (a narrow maximum is expressed at 1–3 km/s; for high relative velocities, the frequency of events decreases). Pairs of clusters with a significant age difference show a distribution of relative approach velocities that is close to uniform in the region from two to approximately 25 km/s, with a slight broad maximum in the region of relative velocities of 10–12 km/s.

The approaches of pairs of clusters on a diagram distance between centers–relative velocity of movement, with color marking the difference in the ages of the clusters are shown in Fig. 6. It is clearly seen that the smallest differences in velocities are predominantly, but not exclusively, observed among pairs of similar ages. However, among pairs of clusters with a significant age difference, there are those that are closely approaching each other and those that are approaching each other at a low relative velocity. The distributions of approaches by specific orbital energy of a pair of clusters without and with the distribution of differences in the logarithms of the ages of the components in the pair are shown in Figs. 7, 8. The specific orbital energy (related to the reduced mass) is calculated with no allowance for the size of the clusters and the external galactic field using the formula from [45]: (Vallado, 2007):

[TABLE]

where

[TABLE]

– sum of masses of the clusters in the pair, S – distance between centers of the clusters.

No pairs with negative orbital energy were detected (except for one, which will be mentioned below), so in the used approximation, it is impossible to consider the formation of a gravitationally bound system when the clusters approach each other. However, if we consider a model of approach that takes into account the dynamic interactions of stars in clusters, the pattern may turn out to be significantly more complex. Excess kinetic energy can be spent either on increasing the velocities of cluster members (which can lead to the destruction of clusters or the ejection of individual stars) or on the destruction of binary and multiple systems in clusters. Among the pairs of clusters, there were found two that had an age difference of with $dlogAge>1$ and relatively low specific orbital energy $E$. These are pairs: HSC 92 and HSC 63; SAI 122 and HSC 2695.

Among the approaches, only one pair of clusters was discovered, which in some epochs had a negative specific orbital energy of the system $E$, and is presently in its closest approach (the distance between the centers of the clusters is 5.6 pc): the clusters HSC 1428 and Gulliver 22. However, the difference in the logarithms of ages for this pair of clusters is only 0.107, and cannot be considered significant. Most likely, these are clusters that formed simultaneously close to each other in a single giant molecular cloud, which probably represent a gravitationally bound system.

We present (in the Appendix) a forecast of expected close encounters for 32 million years ahead, involving 490 pairs of clusters. For each pair, the characteristics are indicated only at the moment of closest approach. At the same time, 29 pairs of clusters are in closest proximity at present. Only for the components of 224 pairs, the approach is the only one during the considered period; in the remaining 266 pairs of clusters, one or both components participate in 1–4 more approaches during the considered period. The obtained estimate of the probable encounter frequency of open star clusters is 15 events per 1 million years, if for each pair each encounter is recorded only once, i.e., over 1 million years, 30 clusters participate in an encounter. This means, given the number of clusters in our sample, that on average for one cluster, a close approach can be expected once every 200 million years. This estimate is very close to the estimate made earlier in Fürnkranz et al. (2019) using a model with an isotropic distribution of 50000 clusters in the disk of the Galaxy with a radius of 30 kpc and a velocity dispersion corresponding to the velocity dispersion of the disk stars (one approach per cluster per 250 million years).

In reality, the distribution of open star clusters in the Galaxy apparently obeys a more complex law than the isotropic distribution (Just et al., 2023, Scheepmaker et al., 2009), but the estimate of the total number of open star clusters may be close to that used Fürnkranz et al. (2019). Thus, based on the number of

young massive clusters, based on the number of young massive clusters, 20,000 as the lower limit of the total number of clusters in the Galaxy are cited in Just et al. (2023); based on the estimate of the region of completeness of the sample of clusters [46], under the assumption of exponentially decreasing density, an estimate of 60,000–75,000 for the total number of clusters within a radius of 30 kpc from the center of the Galaxy can be obtained. Thus, the overall frequency of cluster encounters in the Galaxy must be at least an order of magnitude higher (150 new encounters per 1 million years).

5 Conclusions

The integration of the orbits of open star clusters from the HR24 catalogue that are located in the Galaxy mainly in the local neighborhood of the Sun has shown that paired approaches of clusters at distances comparable to their sizes and less occur in the galactic neighborhood of the Sun with a frequency of  35–40 events in 1 million years. At the same time, approaches of unrelated open clusters at distances comparable to their sizes and smaller occur in the galactic neighborhood of the Sun with a frequency of  15 events in 1 million years. The estimate of the total number of open star clusters in the Galaxy and their spatial distribution remains sufficiently uncertain, but it can be expected that the true frequency of cluster encounters in the Galaxy is at least an order of magnitude higher than the estimate for observed clusters.

A pair of clusters of similar age: clusters HSC 1428 and Gulliver 22, which represent a probable physical binary system of clusters, have been discovered. With the exception of this pair, in the used approximation (clusters as material points), no pairs with negative specific orbital energy at the moment of approach have been found. However, it can be assumed that when taking into account the dynamic interaction of cluster stars in a realistic model, hybrid clusters can form.

There are approaching pairs of clusters with large differences in the ages of their components. The formation of binary stars with components of different ages through the interaction of their populations is, therefore, not excluded. A detailed study of this issue requires dynamic modeling of the population of clusters during approach.

We provide in the Appendix a forecast of expected close encounters for 32 million years ahead, involving 490 pairs of clusters. At the same time, 29 pairs of clusters are in closest proximity at present.

The authors would like to thank the anonymous reviewer for insightful comments that helped improve the paper. The work uses data from the European Space Agency’s (ESA) $Gaia$ space mission (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). The interactive graphical visualizer and analyzer for tabular data TOPCAT (Taylor, 2005) was used.

Appendix

A list of pairs of open star clusters in the Galaxy that are currently in closest approach, as well as a forecast and characteristics of closest approaches of clusters for the next 32 million years with a step of two million years, is shown in the table below. The table contains identifiers of approaching clusters (Name 1, Name 2), the epoch of closest approach from 0 to 32 [million years] from the present time, minimum distance between cluster centers $Min\_dist$ in parsecs, total cluster radii $R_{1}$, $R_{2}$ and in parsecs, the relative velocity of the clusters at the moment of closest approach $V_{rel}$ in km/s, and the difference in the logarithms of ages (in years) $dlogAge$. Each pair of clusters is present in the list only once, at maximal proximity.