# Stellar clustering shapes the architecture of planetary systems

## Abstract

Planet formation is generally described in terms of a system containing the host star and a protoplanetary disk1,2,3, of which the internal properties (for example, mass and metallicity) determine the properties of the resulting planetary system4. However, (proto)planetary systems are predicted5,6 and observed7,8 to be affected by the spatially clustered stellar formation environment, through either dynamical star–star interactions or external photoevaporation by nearby massive stars9. It is challenging to quantify how the architecture of planetary sysems is affected by these environmental processes, because stellar groups spatially disperse within less than a billion years10, well below the ages of most known exoplanets. Here we identify old, co-moving stellar groups around exoplanet host stars in the astrometric data from the Gaia satellite11,12 and demonstrate that the architecture of planetary systems exhibits a strong dependence on local stellar clustering in position-velocity phase space. After controlling for host stellar age, mass, metallicity and distance from the star, we obtain highly significant differences (with p values of 10−5 to 10−2) in planetary system properties between phase space overdensities (composed of a greater number of co-moving stars than unstructured space) and the field. The median semi-major axis and orbital period of planets in phase space overdensities are 0.087 astronomical units and 9.6 days, respectively, compared to 0.81 astronomical units and 154 days, respectively, for planets around field stars. ‘Hot Jupiters’ (massive, short-period exoplanets) predominantly exist in stellar phase space overdensities, strongly suggesting that their extreme orbits originate from environmental perturbations rather than internal migration13,14 or planet–planet scattering15,16. Our findings reveal that stellar clustering is a key factor setting the architectures of planetary systems.

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## Data availability

The Gaia data used in this work are publicly available through the Gaia archive (https://gea.esac.esa.int/archive/). The exoplanetary catalogue used in this work is publicly available through the NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/). Results of the calculations performed as part of this work are either available in the Supplementary Information, or from the authors upon request. A table containing the planet properties, host star properties, and the phase space decomposition is publicly available at https://github.com/ajw278/astrophasesplit with file name planetdata (2).csv.

## Code availability

The code used for the phase space decomposition is publicly available at https://github.com/ajw278/astrophasesplit.

## References

1. 1.

Armitage, P. J. Dynamics of protoplanetary disks. Annu. Rev. Astron. Astrophys. 49, 195–236 (2011).

2. 2.

Williams, J. P. & Cieza, L. A. Protoplanetary disks and their evolution. Annu. Rev. Astron. Astrophys. 49, 67–117 (2011).

3. 3.

Winn, J. N. & Fabrycky, D. C. The occurrence and architecture of exoplanetary systems. Annu. Rev. Astron. Astrophys. 53, 409–447 (2015).

4. 4.

Mordasini, C., Alibert, Y., Benz, W., Klahr, H. & Henning, T. Extrasolar planet population synthesis. IV. Correlations with disk metallicity, mass, and lifetime. Astron. Astrophys. 541, A97 (2012).

5. 5.

Adams, F. C., Hollenbach, D., Laughlin, G. & Gorti, U. Photoevaporation of circumstellar disks due to external far-ultraviolet radiation in stellar aggregates. Astrophys. J. 611, 360–379 (2004).

6. 6.

Cai, M. X., Portegies Zwart, S. & van Elteren, A. The signatures of the parental cluster on field planetary systems. Mon. Not. R. Astron. Soc. 474, 5114–5121 (2018).

7. 7.

de Juan Ovelar, M. et al. Can habitable planets form in clustered environments? Astron. Astrophys. 546, L1 (2012).

8. 8.

Ansdell, M. et al. An ALMA survey of protoplanetary disks in the σ Orionis cluster. Astron. J. 153, 240 (2017).

9. 9.

Winter, A. J., Kruijssen, J. M. D., Chevance, M., Keller, B. W. & Longmore, S. N. Prevalent externally driven protoplanetary disc dispersal as a function of the galactic environment. Mon. Not. R. Astron. Soc. 491, 903–922 (2020).

10. 10.

Krumholz, M. R., McKee, C. F. & Bland-Hawthorn, J. Star clusters across cosmic time. Annu. Rev. Astron. Astrophys. 57, 227–303 (2019).

11. 11.

Gaia Collaboration et al. The Gaia mission. Astron. Astrophys. 595, A1 (2016).

12. 12.

Gaia Collaboration et al. Gaia Data Release 2. Summary of the contents and survey properties. Astron. Astrophys. 616, A1 (2018).

13. 13.

Batygin, K. A primordial origin for misalignments between stellar spin axes and planetary orbits. Nature 491, 418–420 (2012).

14. 14.

Baruteau, C. et al. Planet-disk interactions and early evolution of planetary systems. In Protostars and Planets VI (eds Beuther, H., Klessen, R. S., Dullemond, C. P. & Henning, T.) 667 (2014).

15. 15.

Triaud, A. H. M. J. et al. Spin-orbit angle measurements for six southern transiting planets. New insights into the dynamical origins of hot Jupiters. Astron. Astrophys. 524, A25 (2010).

16. 16.

Albrecht, S. et al. Obliquities of hot Jupiter host stars: evidence for tidal interactions and primordial misalignments. Astrophys. J. 757, 18 (2012).

17. 17.

Kruijssen, J. M. D. On the fraction of star formation occurring in bound stellar clusters. Mon. Not. R. Astron. Soc. 426, 3008–3040 (2012).

18. 18.

Hopkins, P. F. Why do stars form in clusters? An analytic model for stellar correlation functions. Mon. Not. R. Astron. Soc. 428, 1950–1957 (2013).

19. 19.

Quillen, A. C. et al. Spiral arm crossings inferred from ridges in Gaia stellar velocity distributions. Mon. Not. R. Astron. Soc. 480, 3132–3139 (2018).

20. 20.

Fragkoudi, F. et al. On the ridges, undulations, and streams in Gaia DR2: linking the topography of phase space to the orbital structure of an N-body bar. Mon. Not. R. Astron. Soc. 488, 3324–3339 (2019).

21. 21.

Composite Planet Data Table https://catcopy.ipac.caltech.edu/dois/doi.php?id=10.26133/NEA2 (NASA Exoplanet Archive, 2019).

22. 22.

Johnson, J. A. et al. Retired A stars and their companions: exoplanets orbiting three intermediate-mass subgiants. Astrophys. J. 665, 785–793 (2007).

23. 23.

Hebb, L. et al. WASP-12b: the hottest transiting extrasolar planet yet discovered. Astrophys. J. 693, 1920–1928 (2009).

24. 24.

Johnson, J. A., Aller, K. M., Howard, A. W. & Crepp, J. R. Giant planet occurrence in the stellar mass-metallicity plane. Publ. Astron. Soc. Pacif. 122, 905 (2010).

25. 25.

Wyatt, M. C. & Jackson, A. P. Insights into planet formation from debris disks. II. Giant impacts in extrasolar planetary systems. Space Sci. Rev. 205, 231–265 (2016).

26. 26.

Madhusudhan, N., Amin, M. A. & Kennedy, G. M. Toward chemical constraints on hot Jupiter migration. Astrophys. J. Lett. 794, L12 (2014).

27. 27.

Dawson, R. I. & Johnson, J. A. Origins of Hot Jupiters. Annu. Rev. Astron. Astrophys. 56, 175–221 (2018).

28. 28.

Jackson, B., Greenberg, R. & Barnes, R. Tidal evolution of close-in extrasolar planets. Astrophys. J. 678, 1396–1406 (2008).

29. 29.

Rasio, F. A. & Ford, E. B. Dynamical instabilities and the formation of extrasolar planetary systems. Science 274, 954–956 (1996).

30. 30.

Morbidelli, A., Lunine, J. I., O’Brien, D. P., Raymond, S. N. & Walsh, K. J. Building terrestrial planets. Annu. Rev. Earth Planet. Sci. 40, 251–275 (2012).

31. 31.

Minchev, I., Boily, C., Siebert, A. & Bienayme, O. Low-velocity streams in the solar neighbourhood caused by the Galactic bar. Mon. Not. R. Astron. Soc. 407, 2122–2130 (2010).

32. 32.

Kruijssen, J. M. D. et al. Fast and inefficient star formation due to short-lived molecular clouds and rapid feedback. Nature 569, 519–522 (2019).

33. 33.

Chevance, M. et al. The lifecycle of molecular clouds in nearby star-forming disc galaxies. Mon. Not. R. Astron. Soc. 493, 2872–2909 (2020).

34. 34.

Eisenstein, D. J. & Hut, P. HOP: a new group-finding algorithm for N-body simulations. Astrophys. J. 498, 137–142 (1998).

35. 35.

Maciejewski, M., Colombi, S., Springel, V., Alard, C. & Bouchet, F. R. Phase-space structures. II. Hierarchical structure finder. Mon. Not. R. Astron. Soc. 396, 1329–1348 (2009).

36. 36.

Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).

37. 37.

Seabroke, G. M. & Gilmore, G. Revisiting the relations: Galactic thin disc age-velocity dispersion relation. Mon. Not. R. Astron. Soc. 380, 1348–1368 (2007).

38. 38.

Kamdar, H. et al. Stars that move together were born together. Astrophys. J. Lett. 884, L42 (2019).

39. 39.

Pfeffer, J. et al. Young star cluster populations in the E-MOSAICS simulations. Mon. Not. R. Astron. Soc. 490, 1714–1733 (2019).

40. 40.

Adamo, A. et al. Star clusters near and far; tracing star formation across cosmic time. Space Sci. Rev. 216, 69 (2020).

41. 41.

Antoja, T., Figueras, F., Fernández, D. & Torra, J. Origin and evolution of moving groups. I. Characterization in the observational kinematic-age-metallicity space. Astron. Astrophys. 490, 135–150 (2008).

42. 42.

Fürnkranz, V., Meingast, S. & Alves, J. Extended stellar systems in the solar neighborhood. III. Like ships in the night: the Coma Berenices neighbor moving group. Astron. Astrophys. 624, L11 (2019).

43. 43.

Meingast, S., Alves, J. & Fürnkranz, V. Extended stellar systems in the solar neighborhood. II. Discovery of a nearby 120° stellar stream in Gaia DR2. Astron. Astrophys. 622, L13 (2019).

44. 44.

Price-Jones, N. et al. Strong chemical tagging with APOGEE: 21 candidate star clusters that have dissolved across the Milky Way disc. Mon. Not. R. Astron. Soc. 496, 5101–5115 (2020).

45. 45.

Famaey, B., Siebert, A. & Jorissen, A. On the age heterogeneity of the Pleiades, Hyades, and Sirius moving groups. Astron. Astrophys. 483, 453–459 (2008).

46. 46.

Lépine, J. R. D., Michtchenko, T. A., Barros, D. A. & Vieira, R. S. S. The dynamical origin of the local arm and the Sun’s trapped orbit. Astrophys. J. 843, 48 (2017).

47. 47.

Kamdar, H. et al. A dynamical model for clustered star formation in the Galactic disk. Astrophys. J. 884, 173 (2019).

48. 48.

Oh, S., Price-Whelan, A. M., Hogg, D. W., Morton, T. D. & Spergel, D. N. Comoving stars in Gaia DR1: an abundance of very wide separation comoving pairs. Astron. J. 153, 257 (2017).

49. 49.

Haisch, J., Karl, E., Lada, E. A. & Lada, C. J. Disk frequencies and lifetimes in young clusters. Astrophys. J. Lett. 553, L153–L156 (2001).

50. 50.

Holland, W. S. et al. Submillimetre images of dusty debris around nearby stars. Nature 392, 788–791 (1998).

51. 51.

Halliday, A. N. A young Moon-forming giant impact at 70-110 million years accompanied by late-stage mixing, core formation and degassing of the Earth. Phil. Trans. R. Soc. Lond. A 366, 4163–4181 (2008).

52. 52.

Kennedy, G. M. & Wyatt, M. C. The bright end of the exo-Zodi luminosity function: disc evolution and implications for exo-Earth detectability. Mon. Not. R. Astron. Soc. 433, 2334–2356 (2013).

53. 53.

Snaith, O. et al. Reconstructing the star formation history of the Milky Way disc(s) from chemical abundances. Astron. Astrophys. 578, A87 (2015).

54. 54.

Portegies Zwart, S. F., McMillan, S. L. W. & Gieles, M. Young massive star clusters. Annu. Rev. Astron. Astrophys. 48, 431–493 (2010).

55. 55.

Fischer, D. A. & Valenti, J. The planet-metallicity correlation. Astrophys. J. 622, 1102–1117 (2005).

56. 56.

Winn, J. N., Fabrycky, D., Albrecht, S. & Johnson, J. A. Hot stars with hot Jupiters have high obliquities. Astrophys. J. Lett. 718, L145–L149 (2010).

57. 57.

Reffert, S., Bergmann, C., Quirrenbach, A., Trifonov, T. & Künstler, A. Precise radial velocities of giant stars. VII. Occurrence rate of giant extrasolar planets as a function of mass and metallicity. Astron. Astrophys. 574, A116 (2015).

58. 58.

Kaib, N. A., Raymond, S. N. & Duncan, M. Planetary system disruption by Galactic perturbations to wide binary stars. Nature 493, 381–384 (2013).

59. 59.

Veras, D., Georgakarakos, N., Dobbs-Dixon, I. & Gänsicke, B. T. Binary star influence on post-main-sequence multi-planet stability. Mon. Not. R. Astron. Soc. 465, 2053–2059 (2017).

60. 60.

Kervella, P., Arenou, F., Mignard, F. & Thévenin, F. Stellar and substellar companions of nearby stars from Gaia DR2. Binarity from proper motion anomaly. Astron. Astrophys. 623, A72 (2019).

61. 61.

Fontanive, C. et al. A high binary fraction for the most massive close-in giant planets and brown dwarf desert members. Mon. Not. R. Astron. Soc. 485, 4967–4996 (2019).

62. 62.

Evans, D. F. Evidence for unresolved exoplanet-hosting binaries in Gaia DR2. Res. Not. Am. Astron. Soc. 2, 20 (2018).

63. 63.

Belokurov, V. et al. Unresolved stellar companions with Gaia DR2 astrometry. Mon. Not. R. Astron. Soc. 496, 1922–1940 (2020).

64. 64.

Johnstone, D., Hollenbach, D. & Bally, J. Photoevaporation of disks and clumps by nearby massive stars: application to disk destruction in the Orion nebula. Astrophys. J. 499, 758–776 (1998).

65. 65.

Knutson, H. A. et al. Friends of hot Jupiters. I. A radial velocity search for massive, long-period companions to close-in gas giant planets. Astrophys. J. 785, 126 (2014).

66. 66.

Davies, M. B. et al. The long-term dynamical evolution of planetary systems. In Protostars and Planets VI (University of Arizona Press, 2014).

67. 67.

Pál, A. et al. HAT-P-7b: an extremely hot massive planet transiting a bright star in the Kepler field. Astrophys. J. 680, 1450–1456 (2008).

68. 68.

Hartman, J. D. et al. HAT-P-12b: a low-density sub-Saturn mass planet transiting a metal-poor K dwarf. Astrophys. J. 706, 785–796 (2009).

69. 69.

Vogt, S. S. et al. Ten low-mass companions from the Keck Precision Velocity Survey. Astrophys. J. 568, 352–362 (2002).

70. 70.

Da Silva, R. et al. Elodie metallicity-biased search for transiting Hot Jupiters. I. Two hot Jupiters orbiting the slightly evolved stars HD 118203 and HD 149143. Astron. Astrophys. 446, 717–722 (2006).

71. 71.

Moutou, C. et al. The SOPHIE search for northern extrasolar planets. VI. Three new hot Jupiters in multi-planet extrasolar systems. Astron. Astrophys. 563, A22 (2014).

72. 72.

O’Donovan, F. T. et al. TrES-3: a nearby, massive, transiting hot Jupiter in a 31 hour orbit. Astrophys. J. Lett. 663, L37–L40 (2007).

73. 73.

Hellier, C. et al. Three WASP-South transiting exoplanets: WASP-74b, WASP-83b, and WASP-89b. Astron. J. 150, 18 (2015).

74. 74.

Hellier, C. et al. Transiting hot Jupiters from WASP-South, Euler and TRAPPIST: WASP-95b to WASP-101b. Mon. Not. R. Astron. Soc. 440, 1982–1992 (2014).

75. 75.

Winn, J. N. et al. HAT-P-7: a retrograde or polar orbit, and a third body. Astrophys. J. Lett. 703, L99–L103 (2009).

76. 76.

Mugrauer, M. Search for stellar companions of exoplanet host stars by exploring the second ESA-Gaia data release. Mon. Not. R. Astron. Soc. 490, 5088–5102 (2019).

77. 77.

Casertano, S. & Hut, P. Core radius and density measurements in N-body experiments. Connections with theoretical and observational definitions. Astrophys. J. 298, 80–94 (1985).

78. 78.

Ester, M., Kriegel, H.-P., Sander, J. & Xu, X. A density-based algorithm for discovering clusters in large spatial databases with noise. In Proc. 2nd Int. Conf. on Knowledge Discovery and Data Mining (KDD’96) 226–231 (AAAI Press, 1996).

79. 79.

Sharma, S. & Johnston, K. V. A group finding algorithm for multidimensional data sets. Astrophys. J. 703, 1061–1077 (2009).

80. 80.

Myeong, G. C., Evans, N. W., Belokurov, V., Amorisco, N. C. & Koposov, S. E. Halo substructure in the SDSS-Gaia catalogue: streams and clumps. Mon. Not. R. Astron. Soc. 475, 1537–1548 (2018).

81. 81.

Spergel, D. et al. Wide-field infrarred survey telescope-astrophysics focused telescope assets WFIRST-AFTA 2015 report. Preprint at https://arxiv.org/abs/1503.03757 (2015).

82. 82.

Fang, M. et al. Star formation and disk properties in Pismis 24. Astron. Astrophys. 539, A119 (2012).

83. 83.

Guarcello, M. G. et al. Photoevaporation and close encounters: how the environment around Cygnus OB2 affects the evolution of protoplanetary disks. Preprint at https://arxiv.org/abs/1605.01773 (2016).

84. 84.

Winter, A. J., Ansdell, M., Haworth, T. J. & Kruijssen, J. M. D. Testing viscous disc theory using the balance between stellar accretion and external photoevaporation of protoplanetary discs. Mon. Not. R. Astron. Soc. 497, L40–L45 (2020).

85. 85.

van Terwisga, S. E., Hacar, A. & van Dishoeck, E. F. Disk masses in the Orion Molecular Cloud-2: distinguishing time and environment. Astron. Astrophys. 628, A85 (2019).

86. 86.

Clarke, C. J. & Pringle, J. E. Accretion disc response to a stellar fly-by. Mon. Not. R. Astron. Soc. 261, 190–202 (1993).

87. 87.

Ostriker, E. C. Capture and induced disk accretion in young star encounters. Astrophys. J. 424, 292 (1994).

88. 88.

Bate, M. R. On the diversity and statistical properties of protostellar discs. Mon. Not. R. Astron. Soc. 475, 5618–5658 (2018).

89. 89.

Anderson, K. R., Adams, F. C. & Calvet, N. Viscous evolution and photoevaporation of circumstellar disks due to external far ultraviolet radiation fields. Astrophys. J. 774, 9 (2013).

90. 90.

Facchini, S., Clarke, C. J. & Bisbas, T. G. External photoevaporation of protoplanetary discs in sparse stellar groups: the impact of dust growth. Mon. Not. R. Astron. Soc. 457, 3593–3610 (2016).

91. 91.

Winter, A. J. et al. Protoplanetary disc truncation mechanisms in stellar clusters: comparing external photoevaporation and tidal encounters. Mon. Not. R. Astron. Soc. 478, 2700–2722 (2018).

92. 92.

Haworth, T. J., Clarke, C. J., Rahman, W., Winter, A. J. & Facchini, S. The FRIED grid of mass-loss rates for externally irradiated protoplanetary discs. Mon. Not. R. Astron. Soc. 481, 452–466 (2018).

93. 93.

Concha-Ramírez, F., Wilhelm, M. J. C., Portegies Zwart, S. & Haworth, T. J. External photoevaporation of circumstellar discs constrains the time-scale for planet formation. Mon. Not. R. Astron. Soc. 490, 5678–5690 (2019).

94. 94.

Fatuzzo, M. & Adams, F. C. UV radiation fields produced by young embedded star clusters. Astrophys. J. 675, 1361–1374 (2008).

95. 95.

O’dell, C. R. & Wen, Z. Postrefurbishment mission Hubble Space Telescope images of the core of the Orion Nebula: Proplyds, Herbig-Haro Objects, and measurements of a circumstellar disk. Astrophys. J. 436, 194 (1994).

96. 96.

Winter, A. J., Clarke, C. J. & Rosotti, G. P. External photoevaporation of protoplanetary discs in Cygnus OB2: linking discs to star formation dynamical history. Mon. Not. R. Astron. Soc. 485, 1489–1507 (2019).

97. 97.

Tanaka, H., Takeuchi, T. & Ward, W. R. Three-dimensional interaction between a planet and an isothermal gaseous disk. I. Corotation and Lindblad torques and planet migration. Astrophys. J. 565, 1257–1274 (2002).

98. 98.

Kennedy, G. M. & Kenyon, S. J. Planet formation around stars of various masses: hot super-Earths. Astrophys. J. 682, 1264–1276 (2008).

99. 99.

Ida, S. & Lin, D. N. C. Toward a deterministic model of planetary formation. VI. Dynamical interaction and coagulation of multiple rocky embryos and super-Earth systems around solar-type stars. Astrophys. J. 719, 810–830 (2010).

100. 100.

Johansen, A. & Lambrechts, M. Forming planets via pebble accretion. Annu. Rev. Earth Planet. Sci. 45, 359–387 (2017).

101. 101.

Lambrechts, M. et al. Formation of planetary systems by pebble accretion and migration. How the radial pebble flux determines a terrestrial-planet or super-Earth growth mode. Astron. Astrophys. 627, A83 (2019).

102. 102.

Ward, W. R. Protoplanet migration by nebula tides. Icarus 126, 261–281 (1997).

103. 103.

Ragusa, E. et al. Eccentricity evolution during planet-disc interaction. Mon. Not. R. Astron. Soc. 474, 4460–4476 (2018).

104. 104.

Pu, B. & Lai, D. Eccentricities and inclinations of multiplanet systems with external perturbers. Mon. Not. R. Astron. Soc. 478, 197–217 (2018).

105. 105.

Dwarkadas, V. V., Dauphas, N., Meyer, B., Boyajian, P. & Bojazi, M. Triggered star formation inside the shell of a Wolf-Rayet bubble as the origin of the Solar System. Astrophys. J. 851, 147 (2017).

106. 106.

Lichtenberg, T. et al. A water budget dichotomy of rocky protoplanets from 26Al-heating. Nat. Astron. 3, 307–313 (2019).

107. 107.

Malmberg, D., Davies, M. B. & Heggie, D. C. The effects of fly-bys on planetary systems. Mon. Not. R. Astron. Soc. 411, 859–877 (2011).

108. 108.

van Elteren, A., Portegies Zwart, S., Pelupessy, I., Cai, M. X. & McMillan, S. L. W. Survivability of planetary systems in young and dense star clusters. Astron. Astrophys. 624, A120 (2019).

109. 109.

Chatterjee, S., Ford, E. B., Matsumura, S. & Rasio, F. A. Dynamical outcomes of planet-planet scattering. Astrophys. J. 686, 580–602 (2008).

110. 110.

Owen, J. E. & Lai, D. Photoevaporation and high-eccentricity migration created the sub-Jovian desert. Mon. Not. R. Astron. Soc. 479, 5012–5021 (2018).

111. 111.

Malavolta, L. et al. The GAPS programme with HARPS-N at TNG. XI. Pr 0211 in M 44: the first multi-planet system in an open cluster. Astron. Astrophys. 588, A118 (2016).

112. 112.

Pfalzner, S., Bhandare, A. & Vincke, K. Did a stellar fly-by shape the planetary system around Pr 0211 in the cluster M44? Astron. Astrophys. 610, A33 (2018).

113. 113.

Pfalzner, S., Bhandare, A., Vincke, K. & Lacerda, P. Outer Solar System possibly shaped by a stellar fly-by. Astrophys. J. 863, 45 (2018).

114. 114.

Hamers, A. S. & Tremaine, S. Hot Jupiters driven by high-eccentricity migration in globular clusters. Astron. J. 154, 272 (2017).

115. 115.

Li, D., Mustill, A. J. & Davies, M. B. Fly-by encounters between two planetary systems I: Solar System analogues. Mon. Not. R. Astron. Soc. 488, 1366–1376 (2019).

116. 116.

Fujii, M. S. & Hori, Y. Survival rates of planets in open clusters: the Pleiades, Hyades, and Praesepe clusters. Astron. Astrophys. 624, A110 (2019).

117. 117.

Adams, F. C. The birth environment of the Solar System. Annu. Rev. Astron. Astrophys. 48, 47–85 (2010).

118. 118.

Gounelle, M. & Meynet, G. Solar system genealogy revealed by extinct short-lived radionuclides in meteorites. Astron. Astrophys. 545, A4 (2012).

119. 119.

Batygin, K., Adams, F. C., Batygin, Y. K. & Petigura, E. A. Dynamics of planetary systems within star clusters: aspects of the Solar System’s early evolution. Astron. J. 159, 101 (2020).

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## Acknowledgements

A.J.W. thanks R. Alexander for discussions. A.J.W. acknowledges funding from the Alexander von Humboldt Stiftung in the form of a Postdoctoral Research Fellowship and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 681601). J.M.D.K. and M.C. acknowledge funding from the German Research Foundation (DFG) in the form of an Emmy Noether Research Group (grant no. KR4801/1-1) and the DFG Sachbeihilfe (grant no. KR4801/2-1). J.M.D.K. acknowledges funding from the ERC under the European Union’s Horizon 2020 research and innovation programme via the ERC Starting Grant MUSTANG (grant agreement no. 714907). This research made use of data from the European Space Agency mission Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, http://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

## Author information

Authors

### Contributions

A.J.W. led the study, developed the analysis method, and performed the analysis, with contributions from J.M.D.K. and S.N.L. A.J.W. and J.M.D.K. wrote the text, with contributions from S.N.L. and M.C. J.M.D.K. and M.C. developed the initial idea for the project. All authors contributed to aspects of the analysis and the interpretation of the results.

### Corresponding author

Correspondence to Andrew J. Winter.

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### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Probability density functions of the relative phase space density for synthetic stellar populations.

Blue histograms represent the distribution of $${\tilde{\rho }}_{{\rm{M}},20}$$ for a background (‘field’) population, while red histograms represent a population of stars with a spatial density perturbed by a multiplicative factor δρ* (increasing from left to right, a, d, gc, f, i) and with a velocity dispersion perturbed by a multiplicative factor δσv (increasing from top to bottom; a, b, cg, h, i). Outlined purple histograms show the sum of the perturbed and background populations. The solid black line represents a double-lognormal fit to this combined phase space density distribution, with both lognormal components marked by dotted lines. The multiplicative factors by which the density and velocity dispersion are perturbed (numbers in brackets are the values of δρ* and δσv inferred from the phase space density decomposition), as well as the probability that the distribution can be described by a single lognormal (Pnull) are shown.

### Extended Data Fig. 2 Effect of the choice of threshold probability on the median exoplanet properties in environments with low and high phase space density.

The panels show the median orbital period (a), orbital eccentricity (b), and planet mass (c), for the same exoplanet host star sample as in Fig. 3. Exoplanets orbiting field stars (Plow > Pth) are shown in blue, and exoplanets orbiting stars within overdensities (Phigh > Pth) are shown in red. The median of the full sample is shown as a dashed black line, and the chosen Pth = 0.84 (adopted for our main results) is shown as a vertical black line.

### Extended Data Fig. 3 Normalized cumulative distribution functions of planet and host star properties.

The samples are divided into low (blue) and high (red) host star phase space densities, without applying any cuts in host star age or mass (unlike in Fig. 3). The panels are the same as in Fig. 3 (af for exoplanet properties, gj for stellar host properties). The faint lines represent 100 Monte Carlo control experiments, constructed by drawing a star at random from within 40 pc of each exoplanet host and using the phase space density of that star instead. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test for the exoplanet hosts (black) and for the median of all control experiments (grey; including 16th–84th percentile uncertainties) are shown.

### Extended Data Fig. 4 Normalized cumulative distribution functions of exoplanet properties that exhibit bimodal distributions.

The samples are divided into low (blue) and high (red) host star phase space densities. The sample is split across the top and bottom rows by semi-major axes (a, <0.3 au; d, >0.3 au), planet masses (b, <50M; e, >50M), and radii (c, <5R; f, >5R). The distributions are shown for the same exoplanet host sample as in Fig. 3. The faint lines represent 100 Monte Carlo control experiments, constructed by drawing a star at random from within 40 pc of each exoplanet host and using the phase space density of that star instead. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test for the exoplanet hosts (black) and for the median of all control experiments (grey; including 16th–84th percentile uncertainties) are shown.

### Extended Data Fig. 5 Normalized cumulative distribution functions of planet and host star properties in our fiducial sample, limiting the sample to systems within 300 pc of the Sun (unlike in Fig. 3).

The samples are divided into low (blue) and high (red) host star phase space densities. The panels are the same as in Fig. 3 (af for exoplanet properties, gj for stellar host properties). The faint lines represent 100 Monte Carlo control experiments, constructed by drawing a star at random from within 40 pc of each exoplanet host and using the phase space density of that star instead. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test for the exoplanet hosts (black) and for the median of all control experiments (grey; including 16th–84th percentile uncertainties) are shown.

### Extended Data Fig. 6 Normalized cumulative distribution functions of the kinematic properties of the host stars.

Panel a shows the distribution of absolute proper motions, whereas panel b shows the same for radial velocities. The distributions are shown for all exoplanet host stars that have age and mass estimates. The sample is split by exoplanet discovery method (radial velocity in green, transit in orange) and both subsamples have the same distance distribution by construction (see Methods). The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test between the two survey types are shown.

### Extended Data Fig. 7 Normalized cumulative distribution functions of host star properties in the complete sample of Extended Data Fig. 3.

The sample is divided into exoplanets discovered by radial velocity (ac) and transit (df) surveys. Red lines indicate exoplanet host stars that occupy a phase space overdensity, whereas blue lines represent host stars in the field. For reference, the distributions of the entire host star sample (including all detection methods) from Extended Data Fig. 3 are shown as dashed lines. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test are shown.

### Extended Data Fig. 8 Distributions of exoplanet semi-major axes and masses split by ambient stellar phase space density for different planet discovery methods.

Columns indicate low (a, c; Plow > 0.84) and high (b, d; Phigh > 0.84) phase space densities (as in Fig. 2), split into rows of exoplanets discovered by transit (a, b) and radial velocity (c, d) surveys. Data points with grey error bars (indicating 1σ uncertainties) show individual planets and contours show a two-dimensional Gaussian kernel density estimate. The dashed black lines in a and c follow $${M}_{{\rm{p}}}\propto {a}_{{\rm{p}}}^{1.5}$$ and illustrate the 1σ scatter around an orthogonal distance regression to all planets orbiting field stars that are not hot Jupiters (see Fig. 2a). For reference, b and d includes the Solar System (Phigh = 0.89) planets within ap < 10 au.

### Extended Data Fig. 9 Phase space distributions of stars near the three exoplanet host stars HD 104067, HAT-P-3 and HD 285968.

Panels ac show the phase space density distributions (purple histograms), together with the best-fitting double-lognormal function (black solid line) and the individual lognormal components (black dashed lines) obtained by Gaussian mixture modelling. Keys list the probability that the density distribution is described by a single lognormal (red line) as Pnull, and the probability that each exoplanet host is associated with a phase space overdensity as Phigh. Panels df show the azimuthal (vϕ) and radial (vr) components of the stellar velocities in galactocentric coordinates. Stars in overdensities are shown in red, whereas field stars are shown in blue. To divide the stars into a low- and high-density population, we apply a Monte Carlo procedure that randomly assigns stars based on their individual probabilities of belonging to either of the two components (equation (5)). The host star velocity is shown as a star symbol. These three host stars illustrate cases of a highly significant (Phigh = 0.05) low phase space density (HD 104067), a highly significant (Phigh = 0.94) phase space overdensity (HAT-P-3) and an ambiguous (Phigh = 0.45) phase space density (HD 285968).

### Extended Data Fig. 10 Age distributions of exoplanet host stars with masses 0.7M☉−2M☉.

The red histogram shows stars in overdensities (Phigh > 0.84) and the blue histogram shows field stars (Plow > 0.84). The faint lines represent the results of performing 200 Monte Carlo realizations of the ages, drawn from normal distributions defined by the measured ages and their uncertainties. The error bars show the 16th–84th percentile range of the resulting age distributions.

## Supplementary information

### Supplementary Table 1

The results of all the calculations we performed for each exoplanet host star in the NASA Exoplanet Archive with available six-dimensional astrometry in Gaia DR2.

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Winter, A.J., Kruijssen, J.M.D., Longmore, S.N. et al. Stellar clustering shapes the architecture of planetary systems. Nature 586, 528–532 (2020). https://doi.org/10.1038/s41586-020-2800-0

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