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Bulge Growth Through Disc Instabilities in High-Redshift Galaxies

  • Frédéric BournaudEmail author
Part of the Astrophysics and Space Science Library book series (ASSL, volume 418)

Abstract

The role of disc instabilities, such as bars and spiral arms, and the associated resonances, in growing bulges in the inner regions of disc galaxies have long been studied in the low-redshift nearby Universe. There it has long been probed observationally, in particular through peanut-shaped bulges (Chap.  14). This secular growth of bulges in modern disc galaxies is driven by weak, non-axisymmetric instabilities: it mostly produces pseudobulges at slow rates and with long star-formation timescales. Disc instabilities at high redshift (z > 1) in moderate-mass to massive galaxies (1010 to a few 1011 M of stars) are very different from those found in modern spiral galaxies. High-redshift discs are globally unstable and fragment into giant clumps containing 108−9 M of gas and stars each, which results in highly irregular galaxy morphologies. The clumps and other features associated to the violent instability drive disc evolution and bulge growth through various mechanisms on short timescales. The giant clumps can migrate inward and coalesce into the bulge in a few 108 years. The instability in the very turbulent media drives intense gas inflows toward the bulge and nuclear region. Thick discs and supermassive black holes can grow concurrently as a result of the violent instability. This chapter reviews the properties of high-redshift disc instabilities, the evolution of giant clumps and other features associated to the instability, and the resulting growth of bulges and associated sub-galactic components.

Keywords

Star Formation Stellar Mass Star Formation Rate Thick Disc Host Galaxy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I am grateful to Anna Cibinel, Jared Gabor, Marie Martig, Valentin Perret and Florent Renaud for providing some of the figures and material used in this review, and to Avishai Dekel and Bruce Elmegreen for triggering many new studies on the instability of high-redshift galaxies and the associated growth of bulges. The simulations shown in Fig. 13.7 were carried out on the GENCI computing resources and TGCC/Curie, under allocation GENCI-2015-04-2192.

References

  1. Abraham, R. G., van den Bergh, S., Glazebrook, K., et al. 1996, ApJS, 107, 1ADSCrossRefGoogle Scholar
  2. Abraham, R. G., Merrifield, M. R., Ellis, R. S., Tanvir, N. R., & Brinchmann, J. 1999, MNRAS, 308, 569ADSCrossRefGoogle Scholar
  3. Agertz, O., Teyssier, R., & Moore, B. 2009, MNRAS, 397, L64ADSCrossRefGoogle Scholar
  4. Agertz, O., Teyssier, R., & Moore, B. 2011, MNRAS, 410, 1391ADSCrossRefGoogle Scholar
  5. Barro, G., Faber, S. M., Pérez-González, P. G., et al. 2014, ApJ, 791, 52ADSCrossRefGoogle Scholar
  6. Behrendt, M., Burkert, A., & Schartmann, M. 2014, arXiv:1408.5902Google Scholar
  7. Bekki, K., & Cioni, M.-R. L. 2007, MNRAS, 377, L20ADSCrossRefGoogle Scholar
  8. Block, D. L., Bournaud, F., Combes, F., Puerari, I., & Buta, R. 2002, A&A, 394, L35ADSCrossRefGoogle Scholar
  9. Bois, M., Bournaud, F., Emsellem, E., et al. 2010, MNRAS, 406, 2405ADSCrossRefGoogle Scholar
  10. Bouché, N., Dekel, A., Genzel, R., et al. 2010, ApJ, 718, 1001ADSCrossRefGoogle Scholar
  11. Bournaud, F., Combes, F., & Semelin, B. 2005, MNRAS, 364, L18ADSCrossRefGoogle Scholar
  12. Bournaud, F., Elmegreen, B. G., & Elmegreen, D. M. 2007, ApJ, 670, 237ADSCrossRefGoogle Scholar
  13. Bournaud, F., Daddi, E., Elmegreen, B. G., et al. 2008, A&A, 486, 741ADSCrossRefGoogle Scholar
  14. Bournaud, F., & Elmegreen, B. G. 2009, ApJ, 694, L158ADSCrossRefGoogle Scholar
  15. Bournaud, F., Elmegreen, B. G., & Martig, M. 2009, ApJ, 707, L1ADSCrossRefGoogle Scholar
  16. Bournaud, F. 2010, Galaxy Wars: Stellar Populations and Star Formation in Interacting Galaxies, 423, 177ADSGoogle Scholar
  17. Bournaud, F., Chapon, D., Teyssier, R., et al. 2011, ApJ, 730, 4ADSCrossRefGoogle Scholar
  18. Bournaud, F., Dekel, A., Teyssier, R., et al. 2011, ApJ, 741, L33ADSCrossRefGoogle Scholar
  19. Bournaud, F., Juneau, S., Le Floc’h, E., et al. 2012, ApJ, 757, 81ADSCrossRefGoogle Scholar
  20. Bournaud, F., Perret, V., Renaud, F., et al. 2014, ApJ, 780, 57ADSCrossRefGoogle Scholar
  21. Bournaud, F., Daddi, E., Weiß, A., et al. 2015, A&A, 575, AA56ADSCrossRefGoogle Scholar
  22. Brooks, A. M., Governato, F., Quinn, T., Brook, C. B., & Wadsley, J. 2009, ApJ, 694, 396ADSCrossRefGoogle Scholar
  23. Cameron, E., Carollo, C. M., Oesch, P., et al. 2010, MNRAS, 409, 346ADSCrossRefGoogle Scholar
  24. Comerón, S., Elmegreen, B. G., Salo, H., et al. 2014, A&A, 571, AA58ADSCrossRefGoogle Scholar
  25. Ceverino, D., Dekel, A., & Bournaud, F. 2010, MNRAS, 404, 2151ADSGoogle Scholar
  26. Ceverino, D., Dekel, A., Mandelker, N., et al. 2012, MNRAS, 420, 3490ADSCrossRefGoogle Scholar
  27. Ceverino, D., Klypin, A., Klimek, E. S., et al. 2014, MNRAS, 442, 1545ADSCrossRefGoogle Scholar
  28. Ceverino, D., Dekel, A., Tweed, D., & Primack, J. 2014, arXiv:1409.2622Google Scholar
  29. Chiappini, C., Górny, S. K., Stasińska, G., & Barbuy, B. 2009, A&A, 494, 591ADSCrossRefGoogle Scholar
  30. Chiappini, C. 2009, IAU Symposium, 254, 191ADSGoogle Scholar
  31. Cibinel, A., Le Floc’h, E., Perret, V., et al. 2015Google Scholar
  32. Coelho, P., & Gadotti, D. A. 2011, ApJ, 743, L13ADSCrossRefGoogle Scholar
  33. Combes, F., & Gerin, M. 1985, A&A, 150, 327ADSGoogle Scholar
  34. Combes, F. 2001, Advanced Lectures on the Starburst-AGN, 223 (arXiv:0010570)Google Scholar
  35. Combes, F., García-Burillo, S., Braine, J., et al. 2013, A&A, 550, AA41ADSCrossRefGoogle Scholar
  36. Combes, F. 2014, A&A, 571, AA82ADSCrossRefGoogle Scholar
  37. Conselice, C. J., Bershady, M. A., Dickinson, M., & Papovich, C. 2003, AJ, 126, 1183ADSCrossRefGoogle Scholar
  38. Cowie, L. L., Songaila, A., Hu, E. M., & Cohen, J. G. 1996, AJ, 112, 839ADSCrossRefGoogle Scholar
  39. Daddi, E., Cimatti, A., Renzini, A., et al. 2004, ApJ, 617, 746ADSCrossRefGoogle Scholar
  40. Daddi, E., Dickinson, M., Morrison, G., et al. 2007, ApJ, 670, 156ADSCrossRefGoogle Scholar
  41. Daddi, E., Dannerbauer, H., Elbaz, D., et al. 2008, ApJ, 673, L21ADSCrossRefGoogle Scholar
  42. Daddi, E., Bournaud, F., Walter, F., et al. 2010, ApJ, 713, 686ADSCrossRefGoogle Scholar
  43. Daddi, E., Dannerbauer, H., Liu, D., et al. 2014, ApJ in press (arXiv:1409.8158)Google Scholar
  44. Dalcanton, J. J., & Bernstein, R. A. 2002, AJ, 124, 1328ADSCrossRefGoogle Scholar
  45. Danovich, M., Dekel, A., Hahn, O., Ceverino, D., & Primack, J. 2014, arXiv:1407.7129Google Scholar
  46. DeGraf, C., Dekel, A., Gabor, J., & Bournaud, F. 2014, arXiv:1412.3819Google Scholar
  47. Dekel, A., Birnboim, Y., Engel, G., et al. 2009a, Nature, 457, 451ADSCrossRefGoogle Scholar
  48. Dekel, A., Sari, R., & Ceverino, D. 2009b, ApJ, 703, 785ADSCrossRefGoogle Scholar
  49. Dekel, A., & Krumholz, M. R. 2013, MNRAS, 432, 455ADSCrossRefGoogle Scholar
  50. Dekel, A., & Burkert, A. 2014, MNRAS, 438, 1870ADSCrossRefGoogle Scholar
  51. Dekel, A., & Mandelker, N. 2014, MNRAS, 444, 2071ADSCrossRefGoogle Scholar
  52. Di Matteo, P., Lehnert, M. D., Qu, Y., & van Driel, W. 2011, A&A, 525, LL3CrossRefGoogle Scholar
  53. Di Matteo, T., Khandai, N., DeGraf, C., et al. 2012, ApJ, 745, LL29CrossRefGoogle Scholar
  54. Dubois, Y., Pichon, C., Haehnelt, M., et al. 2012, MNRAS, 423, 3616ADSCrossRefGoogle Scholar
  55. Dubois, Y., Volonteri, M., & Silk, J. 2013, arXiv:1304.4583Google Scholar
  56. Elbaz, D., Dickinson, M., Hwang, H. S., et al. 2011, A&A, 533, A119ADSCrossRefGoogle Scholar
  57. Elmegreen, D. M., Elmegreen, B. G., & Hirst, A. C. 2004, ApJ, 604, L21ADSCrossRefGoogle Scholar
  58. Elmegreen, B. G., & Elmegreen, D. M. 2005, ApJ, 627, 632ADSCrossRefGoogle Scholar
  59. Elmegreen, B. G., Elmegreen, D. M., Vollbach, D. R., Foster, E. R., & Ferguson, T. E. 2005, ApJ, 634, 101ADSCrossRefGoogle Scholar
  60. Elmegreen, D. M., Elmegreen, B. G., & Ferguson, T. E. 2005, ApJ, 623, L71ADSCrossRefGoogle Scholar
  61. Elmegreen, B. G., & Elmegreen, D. M. 2006, ApJ, 650, 644ADSCrossRefGoogle Scholar
  62. Elmegreen, D. M., Elmegreen, B. G., Ravindranath, S., & Coe, D. A. 2007, ApJ, 658, 763ADSCrossRefGoogle Scholar
  63. Elmegreen, D. M., Elmegreen, B. G., Ravindranath, S., & Coe, D. A. 2007, ApJ, 658, 763ADSCrossRefGoogle Scholar
  64. Elmegreen, B. G., Bournaud, F., & Elmegreen, D. M. 2008, ApJ, 684, 829ADSCrossRefGoogle Scholar
  65. Elmegreen, B. G., Bournaud, F., & Elmegreen, D. M. 2008, ApJ, 688, 67ADSCrossRefGoogle Scholar
  66. Elmegreen, B. G., Elmegreen, D. M., Fernandez, M. X., & Lemonias, J. J. 2009, ApJ, 692, 12ADSCrossRefGoogle Scholar
  67. Elmegreen, B. G., & Burkert, A. 2010, ApJ, 712, 294ADSCrossRefGoogle Scholar
  68. Elmegreen, B. G. 2011, ApJ, 737, 10ADSCrossRefGoogle Scholar
  69. Elmegreen, B. G., Elmegreen, D. M., Sánchez Almeida, J., et al. 2013, ApJ, 774, 86ADSCrossRefGoogle Scholar
  70. Emsellem, E., Cappellari, M., Krajnović, D., et al. 2007, MNRAS, 379, 401ADSCrossRefGoogle Scholar
  71. Emsellem, E., Renaud, F., Bournaud, F., et al. 2015, MNRAS, 446, 2468ADSCrossRefGoogle Scholar
  72. Epinat, B., Tasca, L., Amram, P., et al. 2012, A&A, 539, A92ADSCrossRefGoogle Scholar
  73. Eskridge, P. B., Frogel, J. A., Pogge, R. W., et al. 2000, AJ, 119, 536ADSCrossRefGoogle Scholar
  74. Förster Schreiber, N. M., Genzel, R., Lehnert, M. D., et al. 2006, ApJ, 645, 1062ADSCrossRefGoogle Scholar
  75. Förster Schreiber, N. M., Genzel, R., Bouché, N., et al. 2009, ApJ, 706, 1364ADSCrossRefGoogle Scholar
  76. Förster Schreiber, N. M., Shapley, A. E., Genzel, R., et al. 2011, ApJ, 739, 45ADSCrossRefGoogle Scholar
  77. Förster Schreiber, N. M., Genzel, R., Newman, S. F., et al. 2014, ApJ, 787, 38ADSCrossRefGoogle Scholar
  78. Gabor, J. M., & Bournaud, F. 2013, MNRAS, 434, 606ADSCrossRefGoogle Scholar
  79. Gabor, J. M., & Bournaud, F. 2014, MNRAS, 437, L56ADSCrossRefGoogle Scholar
  80. Gabor, J. M., & Bournaud, F. 2014, MNRAS, 441, 1615ADSCrossRefGoogle Scholar
  81. Gao, Y., & Solomon, P. M. 2004, ApJ, 606, 271ADSCrossRefGoogle Scholar
  82. García-Burillo, S., Usero, A., Alonso-Herrero, A., et al. 2012, A&A, 539, A8ADSCrossRefGoogle Scholar
  83. Genel, S., Naab, T., Genzel, R., et al. 2012, ApJ, 745, 11ADSCrossRefGoogle Scholar
  84. Genel, S., Dekel, A., & Cacciato, M. 2012, MNRAS, 425, 788ADSCrossRefGoogle Scholar
  85. Genzel, R., Tacconi, L. J., Eisenhauer, F., et al. 2006, Nature, 442, 786ADSCrossRefGoogle Scholar
  86. Genzel, R., Burkert, A., Bouché, N., et al. 2008, ApJ, 687, 59ADSCrossRefGoogle Scholar
  87. Genzel, R., Newman, S., Jones, T., et al. 2011, ApJ, 733, 101ADSCrossRefGoogle Scholar
  88. Genzel, R., Tacconi, L. J., Lutz, D., et al. 2015, ApJ, 800, 20ADSCrossRefGoogle Scholar
  89. Guedes, J., Callegari, S., Madau, P., & Mayer, L. 2011, ApJ, 742, 76ADSCrossRefGoogle Scholar
  90. Guo, Q., White, S., Boylan-Kolchin, M., et al. 2011, MNRAS, 413, 101ADSCrossRefGoogle Scholar
  91. Guo, Y., Giavalisco, M., Ferguson, H. C., Cassata, P., & Koekemoer, A. M. 2012, ApJ, 757, 120ADSCrossRefGoogle Scholar
  92. Guo, Y., Ferguson, H. C., Bell, E. F., et al. 2014, arXiv:1410.7398Google Scholar
  93. Hennebelle, P., & Falgarone, E. 2012, Ann. Rev. of Astron. and Astrophys., 20, 55CrossRefGoogle Scholar
  94. Hopkins, P. F., Kereš, D., Murray, N., Quataert, E., & Hernquist, L. 2012, MNRAS, 427, 968ADSCrossRefGoogle Scholar
  95. Hopkins, P. F., Kereš, D., & Murray, N. 2013, MNRAS, 432, 2639ADSCrossRefGoogle Scholar
  96. Immeli, A., Samland, M., Westera, P., & Gerhard, O. 2004a, ApJ, 611, 20ADSCrossRefGoogle Scholar
  97. Immeli, A., Samland, M., Gerhard, O., & Westera, P. 2004b, A&A, 413, 547ADSCrossRefGoogle Scholar
  98. Inoue, S., & Saitoh, T. R. 2011, MNRAS, 418, 2527ADSCrossRefGoogle Scholar
  99. Inoue, S., & Saitoh, T. R. 2011, MNRAS, 418, 2527ADSCrossRefGoogle Scholar
  100. Inoue, S., & Saitoh, T. R. 2012, MNRAS, 422, 1902ADSCrossRefGoogle Scholar
  101. Inoue, S., & Saitoh, T. R. 2014, MNRAS, 441, 243ADSCrossRefGoogle Scholar
  102. Jog, C. J. 1996, MNRAS, 278, 209ADSCrossRefGoogle Scholar
  103. Kereš, D., Vogelsberger, M., Sijacki, D., Springel, V., & Hernquist, L. 2012, MNRAS, 425, 2027ADSCrossRefGoogle Scholar
  104. Kocevski, D. D., Faber, S. M., Mozena, M., et al. 2012, ApJ, 744, 148ADSCrossRefGoogle Scholar
  105. Kraljic, K., Bournaud, F., & Martig, M. 2012, ApJ, 757, 60ADSCrossRefGoogle Scholar
  106. Krumholz, M. R., & McKee, C. F. 2005, ApJ, 630, 250ADSCrossRefGoogle Scholar
  107. Krumholz, M., & Burkert, A. 2010, ApJ, 724, 895ADSCrossRefGoogle Scholar
  108. Lotz, J. M., Primack, J., & Madau, P. 2004, AJ, 128, 163ADSCrossRefGoogle Scholar
  109. Mac Low, M.-M. 1999, ApJ, 524, 169ADSCrossRefGoogle Scholar
  110. Magnelli, B., Lutz, D., Saintonge, A., et al. 2014, A&A, 561, A86ADSCrossRefGoogle Scholar
  111. Mandelker, N., Dekel, A., Ceverino, D., et al. 2014, MNRAS, 443, 3675ADSCrossRefGoogle Scholar
  112. Maraston, C., Pforr, J., Renzini, A., et al. 2010, MNRAS, 407, 830ADSCrossRefGoogle Scholar
  113. Martig, M., Bournaud, F., Teyssier, R., & Dekel, A. 2009, ApJ, 707, 250ADSCrossRefGoogle Scholar
  114. Martig, M., Bournaud, F., Croton, D. J., Dekel, A., & Teyssier, R. 2012, ApJ, 756, 26ADSCrossRefGoogle Scholar
  115. Melvin, T., Masters, K., Lintott, C., et al. 2014, MNRAS, 438, 2882ADSCrossRefGoogle Scholar
  116. Mullaney, J. R., Daddi, E., Béthermin, M., et al. 2012, ApJ, 753, L30ADSCrossRefGoogle Scholar
  117. Murray, N., Ménard, B., & Thompson, T. A. 2011, ApJ, 735, 66ADSCrossRefGoogle Scholar
  118. Murray, N. 2011, ApJ, 729, 133ADSCrossRefGoogle Scholar
  119. Naab, T., Oser, L., Emsellem, E., et al. 2014, MNRAS, 444, 3357ADSCrossRefGoogle Scholar
  120. Nelson, D., Vogelsberger, M., Genel, S., et al. 2013, MNRAS, 429, 3353ADSCrossRefGoogle Scholar
  121. Newman, S. F., Genzel, R., Förster-Schreiber, N. M., et al. 2012, ApJ, 761, 43ADSCrossRefGoogle Scholar
  122. Noguchi, M. 1999, ApJ, 514, 77ADSCrossRefGoogle Scholar
  123. Oppenheimer, B. D., & Davé, R. 2006, MNRAS, 373, 1265ADSCrossRefGoogle Scholar
  124. Padoan, P., Bally, J., Billawala, Y., Juvela, M., & Nordlund, Å. 1999, ApJ, 525, 318ADSCrossRefGoogle Scholar
  125. Perez, J., Valenzuela, O., Tissera, P. B., & Michel-Dansac, L. 2013, MNRAS, 436, 259ADSCrossRefGoogle Scholar
  126. Perret, V., Renaud, F., Epinat, B., et al. 2014, A&A, 562, A1ADSCrossRefGoogle Scholar
  127. Puech, M. 2010, MNRAS, 406, 535ADSCrossRefGoogle Scholar
  128. Renaud, F., Bournaud, F., Emsellem, E., et al. 2013, MNRAS, 436, 1836ADSCrossRefGoogle Scholar
  129. Roos, O., Juneau, S., Bournaud, F., & Gabor, J. M. 2014, arXiv:1405.7971Google Scholar
  130. Sargent, M. T., Daddi, E., Béthermin, M., et al. 2014, ApJ, 793, 19ADSCrossRefGoogle Scholar
  131. Scannapieco, C., White, S. D. M., Springel, V., & Tissera, P. B. 2011, MNRAS, 417, 154ADSCrossRefGoogle Scholar
  132. Schreiber, C., Pannella, M., Elbaz, D., et al. 2015, A&A, 575, AA74ADSCrossRefGoogle Scholar
  133. Shapiro, K. L., Genzel, R., Förster Schreiber, N. M., et al. 2008, ApJ, 682, 231ADSCrossRefGoogle Scholar
  134. Shapiro, K. L., Genzel, R., Quataert, E., et al. 2009, ApJ, 701, 955ADSCrossRefGoogle Scholar
  135. Sheth, K., Regan, M. W., Scoville, N. Z., & Strubbe, L. E. 2003, ApJ, 592, L13ADSCrossRefGoogle Scholar
  136. Sheth, K., Elmegreen, D. M., Elmegreen, B. G., et al. 2008, ApJ, 675, 1141ADSCrossRefGoogle Scholar
  137. Shlosman, I., & Noguchi, M. 1993, ApJ, 414, 474ADSCrossRefGoogle Scholar
  138. Simmons, B. D., Melvin, T., Lintott, C., et al. 2014, MNRAS, 445, 3466ADSCrossRefGoogle Scholar
  139. Somerville, R. S., Hopkins, P. F., Cox, T. J., Robertson, B. E., & Hernquist, L. 2008, MNRAS, 391, 481ADSCrossRefGoogle Scholar
  140. Somerville, R. S., & Davé, R. 2014, arXiv:1412.2712Google Scholar
  141. Tacconi, L. J., Genzel, R., Smail, I., et al. 2008, ApJ, 680, 246ADSCrossRefGoogle Scholar
  142. Tacconi, L. J., Genzel, R., Neri, R., et al. 2010, Nature, 463, 781ADSCrossRefGoogle Scholar
  143. Tacconi, L. J., Neri, R., Genzel, R., et al. 2013, ApJ, 768, 74ADSCrossRefGoogle Scholar
  144. Tamburello, V., Mayer, L., Shen, S., & Wadsley, J. 2014, arXiv:1412.3319Google Scholar
  145. Taniguchi, Y., & Shioya, Y. 2001, ApJ, 547, 146ADSCrossRefGoogle Scholar
  146. Teyssier, R. 2002, A&A, 385, 337ADSCrossRefGoogle Scholar
  147. Teyssier, R., Pontzen, A., Dubois, Y., & Read, J. I. 2013, MNRAS, 429, 3068ADSCrossRefGoogle Scholar
  148. Thooris, B., & Pomarède, D. 2011, IAU Symposium, 277, 263ADSGoogle Scholar
  149. Toomre, A. 1964, ApJ, 139, 1217ADSCrossRefGoogle Scholar
  150. Trump, J. R., Barro, G., Juneau, S., et al. 2014, ApJ, 793, 101ADSCrossRefGoogle Scholar
  151. van den Bergh, S., Abraham, R. G., Ellis, R. S., et al. 1996, AJ, 112, 359ADSCrossRefGoogle Scholar
  152. Villalobos, Á., & Helmi, A. 2008, MNRAS, 391, 1806ADSCrossRefGoogle Scholar
  153. Villalobos, Á., Kazantzidis, S., & Helmi, A. 2010, ApJ, 718, 314ADSCrossRefGoogle Scholar
  154. Wuyts, S., Förster Schreiber, N. M., Genzel, R., et al. 2012, ApJ, 753, 114ADSCrossRefGoogle Scholar
  155. Yoachim, P., & Dalcanton, J. J. 2006, AJ, 131, 226ADSCrossRefGoogle Scholar
  156. Zanella, A., Daddi, E., Le Floc’h, E., et al. 2015, Nature in press.Google Scholar
  157. Zolotov, A., Dekel, A., Mandelker, N., et al. 2014, arXiv:1412.4783Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Laboratoire AIM Paris-Saclay, CEA/IRFU/SAp, CNRS/INSUUniversité Paris DiderotGif-sur-Yvette CedexFrance

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