Modeling The Distribution Of Dark Matter And Its Connection To Galaxies
Creators: name: Mao, Yao-Yuan
Publisher: name: Zenodo
Year: 2016
Subjects: astronomy
astrophysics
cosmology
dark matter
galaxies
simulations

description: Despite the mysterious nature of dark matter and dark energy, the Lambda-Cold Dark Matter (LCDM) model provides a reasonably accurate description of the evolution of the cosmos and the distribution of galaxies. Today, we are set to tackle more specific and quantitative questions about the galaxy formation physics, the nature of dark matter, and the connection between the dark and the visible components. The answers to these questions are however elusive, because dark matter is not directly observable, and various unknowns lie between what we can observe and what we can calculate. Hence, mathematical models that bridge the observable and the calculable are essential for the study of modern cosmology. The aim of my thesis work is to improve existing models and also to construct new models for various aspects of the dark matter distribution, as dark matter structures the cosmic web and forms the nests of visible galaxies. Utilizing a series of cosmological dark matter simulations which span a wide dynamical range and a statistical sample of zoom-in simulations which focus on individual dark matter halos, we develop models for the spatial and velocity distribution of dark matter particles, the abundance of dark substructures, and the empirical connection between dark matter and galaxies. As more precise observational results become available, more accurate models are then required to test the consistency between these results and the LCDM predictions. For all the models we investigate, we find that the formation history of dark matter halos always plays a crucial role. Neglecting the halo formation history would result in systematic biases when we interpret various observational results, including dark matter direct detection experiments, the detection of dark substructures with strong-lensed systems, the large-scale spatial clustering of galaxies, and the abundance of dwarf galaxies. Rectifying this, our work will enable us to fully utilize the complementary power of diverse observational datasets to test the LCDM model and to seek new physics.
description: {"references": ["Aalseth, C. E., Barbeau, P. S., Bowden, N. S., et al. 2011, Physical Review Letters, 106, 131301", "Abazajian, K. N., Adelman-McCarthy, J. K., Ag\u00fceros, M. A., et al. 2009, ApJS, 182, 543", "Abel, T., Hahn, O., &amp; Kaehler, R. 2012, MNRAS, 427, 61", "Agnese, R., Ahmed, Z., Anderson, A. J., et al. 2013, Physical Review Letters, 111, 251301", "Akerib, D. S., Ara\u00fajo, H. M., Bai, X., et al. 2014, Physical Review Letters, 112, 091303", "Allgood, B., Flores, R. A., Primack, J. R., et al. 2006, MNRAS, 367, 1781", "An, J., Evans, N. W., &amp; Deason, A. J. 2012, MNRAS, 420, 2562", "An, J., &amp; Zhao, H. 2013, MNRAS, 428, 2805", "Angloher, G., Bauer, M., Bavykina, I., et al. 2012, European Physical Journal C, 72, 1971", "Angulo, R. E., Lacey, C. G., Baugh, C. M., &amp; Frenk, C. S. 2009, MNRAS, 399, 983", "Aprile, E., Arisaka, K., Arneodo, F., et al. 2011, Physical Review Letters, 107, 131302", "Aprile, E., Alfonsi, M., Arisaka, K., et al. 2012, Physical Review Letters, 109, 181301", "Avila, S., Knebe, A., Pearce, F. R., et al. 2014, MNRAS, 441, 3488", "Bechtol, K., Drlica-Wagner, A., Balbinot, E., et al. 2015, ApJ, 807, 50", "Behroozi, P. S., Conroy, C., &amp; Wechsler, R. H. 2010, ApJ, 717, 379", "Behroozi, P. S., Wechsler, R. H., Lu, Y., et al. 2014, ApJ, 787, 156", "Behroozi, P. S., Wechsler, R. H., &amp; Wu, H.-Y. 2013a, ApJ, 762, 109", "Behroozi, P. S., Wechsler, R. H., Wu, H.-Y., et al. 2013b, ApJ, 763, 18", "Berlind, A. A., &amp; Weinberg, D. H. 2002, ApJ, 575, 587", "Bernabei, R., Belli, P., Cappella, F., et al. 2008, European Physical Journal C, 56, 333", "Bernabei, R., Belli, P., Cappella, F., et al. 2010, European Physical Journal C, 67, 39", "Bertone, G. 2010, Particle Dark Matter : Observations, Models and Searches (Cambridge University Press)", "Bertone, G., Hooper, D., &amp; Silk, J. 2005, Phys. Rep., 405, 279", "Bhattacharjee, P., Chaudhury, S., Kundu, S., &amp; Majumdar, S. 2013, Phys. Rev. D, 87, 083525", "Binney, J., &amp; Tremaine, S. 2008, Galactic Dynamics: Second Edition (Princeton University Press)", "Bjornson, E., Hammarwall, D., &amp; Ottersten, B. 2009, IEEE Transactions on Signal Processing, 57, 4027", "Blanton, M. R., Lupton, R. H., Schlegel, D. J., et al. 2005a, ApJ, 631, 208", "Blanton, M. R., Hogg, D. W., Bahcall, N. A., et al. 2003, ApJ, 592, 819", "Blanton, M. R., Schlegel, D. J., Strauss, M. A., et al. 2005b, AJ, 129, 2562", "Bovy, J., &amp; Tremaine, S. 2012, ApJ, 756, 89", "Bower, R. G., Benson, A. J., Malbon, R., et al. 2006, MNRAS, 370, 645", "Boylan-Kolchin, M., Bullock, J. S., &amp; Kaplinghat, M. 2011, MNRAS, 415, L40", "Boylan-Kolchin, M., Springel, V., White, S. D. M., &amp; Jenkins, A. 2010, MNRAS, 406, 896", "Bozorgnia, N., Calore, F., Schaller, M., et al. 2016, J. Cosmology Astropart. Phys., 5, 024", "Brown, W. R., Geller, M. J., Kenyon, S. J., &amp; Diaferio, A. 2010, AJ, 139, 59", "Bruch, T., Read, J., Baudis, L., &amp; Lake, G. 2009, ApJ, 696, 920", "Bryan, G. L., &amp; Norman, M. L. 1998, ApJ, 495, 80", "Bullock, J. S. 2010, ArXiv e-prints, arXiv:1009.4505 [astro-ph.CO]", "Bullock, J. S., Kolatt, T. S., Sigad, Y., et al. 2001, MNRAS, 321, 559", "Bullock, J. S., Wechsler, R. H., &amp; Somerville, R. S. 2002, MNRAS, 329, 246", "Busha, M. T., Marshall, P. J., Wechsler, R. H., Klypin, A., &amp; Primack, J. 2011a, ApJ, 743, 40", "Busha, M. T., Wechsler, R. H., Behroozi, P. S., et al. 2011b, ApJ, 743, 117", "Cautun, M., Frenk, C. S., van de Weygaert, R., Hellwing, W. A., &amp; Jones, B. J. T. 2014a, MNRAS, 445, 2049", "Cautun, M., Hellwing, W. A., van de Weygaert, R., et al. 2014b, MNRAS, 445, 1820", "CDMS II Collaboration, Ahmed, Z., Akerib, D. S., et al. 2010, Science, 327, 1619", "Chaves-Montero, J., Angulo, R. E., Schaye, J., et al. 2015, ArXiv e-prints, arXiv:1507.01948", "Collar, J. I., &amp; Fields, N. E. 2012, ArXiv e-prints, arXiv:1204.3559 [astro-ph.CO]", "Conroy, C., Wechsler, R. H., &amp; Kravtsov, A. V. 2006, ApJ, 647, 201", "Cooray, A., &amp; Sheth, R. 2002, Phys. Rep., 372, 1", "Crocce, M., Pueblas, S., &amp; Scoccimarro, R. 2006, MNRAS, 373, 369", "Croton, D. J., Gao, L., &amp; White, S. D. M. 2007, MNRAS, 374, 1303", "Croton, D. J., Springel, V., White, S. D. M., et al. 2006, MNRAS, 365, 11", "Cui, W., Borgani, S., Dolag, K., Murante, G., &amp; Tornatore, L. 2012, MNRAS, 423, 2279", "Dariush, A. A., Raychaudhury, S., Ponman, T. J., et al. 2010, MNRAS, 405, 1873", "Deason, A. J., Belokurov, V., Evans, N. W., &amp; An, J. 2012, MNRAS, 424, L44", "Deason, A. J., Conroy, C., Wetzel, A. R., &amp; Tinker, J. L. 2013, ApJ, 777, 154", "Desmond, H., &amp; Wechsler, R. H. 2015, MNRAS, 454, 322", "Diemer, B., &amp; Kravtsov, A. V. 2015, ApJ, 799, 108", "D\u2019Onghia, E., Sommer-Larsen, J., Romeo, A. D., et al. 2005, ApJ, 630, L109", "Driver, S. P., Hill, D. T., Kelvin, L. S., et al. 2011, MNRAS, 413, 971", "Drlica-Wagner, A., Bechtol, K., Rykoff, E. S., et al. 2015, ApJ, 813, 109", "Dutton, A. A., &amp; Macci\u00f2, A. V. 2014, MNRAS, 441, 3359", "Eddington, A. S. 1916, MNRAS, 76, 572", "Essig, R., Mardon, J., &amp; Volansky, T. 2012, Phys. Rev. D, 85, 076007", "Evans, N. W., &amp; An, J. H. 2006, Phys. Rev. D, 73, 023524", "Feng, J. L. 2010, ARA&amp;A, 48, 495", "Feng, J. L., Kumar, J., Marfatia, D., &amp; Sanford, D. 2011, Physics Letters B, 703, 124", "Feng, J. L., Kumar, J., &amp; Strigari, L. E. 2008, Physics Letters B, 670, 37", "Fox, P. J., Liu, J., &amp; Weiner, N. 2011, Phys. Rev. D, 83, 103514", "Frandsen, M. T., Kahlhoefer, F., McCabe, C., Sarkar, S., &amp; Schmidt-Hoberg, K. 2012, J. Cosmology Astropart. Phys., 1, 024", "Frandsen, M. T., Kahlhoefer, F., McCabe, C., Sarkar, S., &amp; Schmidt-Hoberg, K. 2013, J. Cosmology Astropart. Phys., 7, 023", "Friedland, A., &amp; Shoemaker, I. M. 2013, Physics Letters B, 724, 183", "Gao, L., Navarro, J. F., Frenk, C. S., et al. 2012, MNRAS, 425, 2169", "Gao, L., Springel, V., &amp; White, S. D. M. 2005a, MNRAS, 363, L66", "Gao, L., &amp; White, S. D. M. 2007, MNRAS, 377, L5", "Gao, L., White, S. D. M., Jenkins, A., Frenk, C. S., &amp; Springel, V. 2005b, MNRAS, 363, 379", "Gao, L., White, S. D. M., Jenkins, A., Stoehr, F., &amp; Springel, V. 2004, MNRAS, 355, 819", "Garbari, S., Liu, C., Read, J. I., &amp; Lake, G. 2012, MNRAS, 425, 1445", "Garrison-Kimmel, S., Boylan-Kolchin, M., Bullock, J. S., &amp; Lee, K. 2014, MNRAS, 438, 2578", "Ghez, A. M., Salim, S., Weinberg, N. N., et al. 2008, ApJ, 689, 1044", "Gillessen, S., Eisenhauer, F., Trippe, S., et al. 2009, ApJ, 692, 1075", "Giocoli, C., Pieri, L., &amp; Tormen, G. 2008, MNRAS, 387, 689", "Gnedin, O. Y., Brown, W. R., Geller, M. J., &amp; Kenyon, S. J. 2010, ApJ, 720, L108", "Gondolo, P., &amp; Gelmini, G. B. 2012, J. Cosmology Astropart. Phys., 12, 015", "Green, A. M. 2012, Modern Physics Letters A, 27, 1230004", "Guo, H., Zheng, Z., Behroozi, P. S., et al. 2016, MNRAS, 459, 3040", "Hahn, O., &amp; Abel, T. 2011, MNRAS, 415, 2101", "Hansen, S. H., Moore, B., Zemp, M., &amp; Stadel, J. 2006, J. Cosmology Astropart. Phys., 1, 014", "Hearin, A. P., Watson, D. F., Becker, M. R., et al. 2014, MNRAS, 444, 729", "Hearin, A. P., Zentner, A. R., Berlind, A. A., &amp; Newman, J. A. 2013a, MNRAS, 433, 659", "Hearin, A. P., Zentner, A. R., Newman, J. A., &amp; Berlind, A. A. 2013b, MNRAS, 430, 1238", "Hearin, A. P., Zentner, A. R., van den Bosch, F. C., Campbell, D., &amp; Tollerud, E. 2016, MNRAS, arXiv:1512.03050", "Helmi, A., White, S. D. M., &amp; Springel, V. 2003, MNRAS, 339, 834", "Henriques, B. M. B., White, S. D. M., Thomas, P. A., et al. 2015, MNRAS, 451, 2663", "Hezaveh, Y. D., Dalal, N., Marrone, D. P., et al. 2016, ArXiv e-prints, arXiv:1601.01388", "Ishiyama, T., Fukushige, T., &amp; Makino, J. 2009, ApJ, 696, 2115", "Ishiyama, T., Rieder, S., Makino, J., et al. 2013, ApJ, 767, 146", "Jiang, F., &amp; van den Bosch, F. C. 2014, ArXiv e-prints, arXiv:1403.6827", "Jungman, G., Kamionkowski, M., &amp; Griest, K. 1996, Phys. Rep., 267, 195", "Kaehler, R., Hahn, O., &amp; Abel, T. 2012, ArXiv e-prints, arXiv:1208.3206 [astro-ph.IM]", "Kafle, P. R., Sharma, S., Lewis, G. F., &amp; Bland-Hawthorn, J. 2012, ApJ, 761, 98", "Kaplan, D. E., Luty, M. A., &amp; Zurek, K. M. 2009, Phys. Rev. D, 79, 115016", "Kauffmann, G., White, S. D. M., &amp; Guiderdoni, B. 1993, MNRAS, 264, 201", "Kavanagh, B. J., &amp; Green, A. M. 2013, Physical Review Letters, 111, 031302", "Kelso, C., Hooper, D., &amp; Buckley, M. R. 2012, Phys. Rev. D, 85, 043515", "Kim, D., &amp; Jerjen, H. 2015, ApJ, 808, L39", "Klypin, A., Gottl\u00f6ber, S., Kravtsov, A. V., &amp; Khokhlov, A. M. 1999a, ApJ, 516, 530", "Klypin, A., Kravtsov, A. V., Valenzuela, O., &amp; Prada, F. 1999b, ApJ, 522, 82", "Klypin, A., Yepes, G., Gottlober, S., Prada, F., &amp; Hess, S. 2014, ArXiv e-prints, arXiv:1411.4001", "Klypin, A., Zhao, H., &amp; Somerville, R. S. 2002, ApJ, 573, 597", "Klypin, A. A., Trujillo-Gomez, S., &amp; Primack, J. 2011, ApJ, 740, 102", "Koposov, S. E., Belokurov, V., Torrealba, G., &amp; Evans, N. W. 2015, ApJ, 805, 130", "Kravtsov, A. V., Berlind, A. A., Wechsler, R. H., et al. 2004, ApJ, 609, 35", "Kuhlen, M., Lisanti, M., &amp; Spergel, D. N. 2012, Phys. Rev. D, 86, 063505", "Kuhlen, M., Weiner, N., Diemand, J., et al. 2010, J. Cosmology Astropart. Phys., 2, 030", "Kulier, A., &amp; Ostriker, J. P. 2015, MNRAS, 452, 4013", "Lehmann, B. V., Mao, Y.-Y., Becker, M. R., Skillman, S. W., &amp; Wechsler, R. H. 2015, ArXiv e-prints, arXiv:1510.05651", "Levi, M., Bebek, C., Beers, T., et al. 2013, ArXiv e-prints, arXiv:1308.0847 [astro-ph.CO]", "Lewin, J. D., &amp; Smith, P. F. 1996, Astroparticle Physics, 6, 87", "Lin, Y.-T., Mandelbaum, R., Huang, Y.-H., et al. 2016, ApJ, 819, 119", "Ling, F.-S., Nezri, E., Athanassoula, E., &amp; Teyssier, R. 2010, J. Cosmology Astropart. Phys., 2, 012", "Lisanti, M., Strigari, L. E., Wacker, J. G., &amp; Wechsler, R. H. 2011, Phys. Rev. D, 83, 023519", "\u0141okas, E. L., &amp; Mamon, G. A. 2001, MNRAS, 321, 155", "Lu, Y., Mo, H. J., Katz, N., &amp; Weinberg, M. D. 2006, MNRAS, 368, 1931", "Lu, Y., Yang, X., &amp; Shen, S. 2015, ApJ, 804, 55", "Lu, Y., Wechsler, R. H., Somerville, R. S., et al. 2014, ApJ, 795, 123", "Ludlow, A. D., Navarro, J. F., Angulo, R. E., et al. 2014, MNRAS, 441, 378", "Ludlow, A. D., Navarro, J. F., Li, M., et al. 2012, MNRAS, 427, 1322", "Lynden-Bell, D. 1967, MNRAS, 136, 101", "Macci\u00f2, A. V., Dutton, A. A., &amp; van den Bosch, F. C. 2008, MNRAS, 391, 1940", "Macci\u00f2, A. V., Dutton, A. A., van den Bosch, F. C., et al. 2007, MNRAS, 378, 55", "Maciejewski, M., Vogelsberger, M., White, S. D. M., &amp; Springel, V. 2011, MNRAS, 415, 2475", "Mandelbaum, R., Seljak, U., Kauffmann, G., Hirata, C. M., &amp; Brinkmann, J. 2006, MNRAS, 368, 715", "Mao, Y.-Y., Strigari, L. E., &amp; Wechsler, R. H. 2014, Phys. Rev. D, 89, 063513", "Mao, Y.-Y., Strigari, L. E., Wechsler, R. H., Wu, H.-Y., &amp; Hahn, O. 2013, ApJ, 764, 35", "Mao, Y.-Y., Williamson, M., &amp; Wechsler, R. H. 2015, ApJ, 810, 21", "Mar\u00edn, F. A., Wechsler, R. H., Frieman, J. A., &amp; Nichol, R. C. 2008, ApJ, 672, 849", "McCabe, C. 2010, Phys. Rev. D, 82, 023530", "Merritt, D. 1985, AJ, 90, 1027", "Miyatake, H., More, S., Mandelbaum, R., et al. 2015, ApJ, 806, 1", "Moore, B., Ghigna, S., Governato, F., et al. 1999, ApJ, 524, L19", "More, S. 2012, ApJ, 761, 127", "More, S., van den Bosch, F. C., Cacciato, M., et al. 2009, MNRAS, 392, 801", "More, S., Miyatake, H., Takada, M., et al. 2016, ArXiv e-prints, arXiv:1601.06063", "Navarro, J. F., Frenk, C. S., &amp; White, S. D. M. 1996, ApJ, 462, 563", "Navarro, J. F., Frenk, C. S., &amp; White, S. D. M. 1997, ApJ, 490, 493", "Navarro, J. F., Ludlow, A., Springel, V., et al. 2010, MNRAS, 402, 21", "Neistein, E., &amp; Khochfar, S. 2012, ArXiv e-prints, arXiv:1209.0463 [astro-ph.CO]", "Neistein, E., Li, C., Khochfar, S., et al. 2011, MNRAS, 416, 1486", "Norberg, P., Baugh, C. M., Gazta\u00f1aga, E., &amp; Croton, D. J. 2009, MNRAS, 396, 19", "Oguri, M., &amp; Lin, Y.-T. 2015, ApJ, 801, 94", "Old, L., Skibba, R. A., Pearce, F. R., et al. 2014, MNRAS, 441, 1513", "Old, L., Wojtak, R., Mamon, G. A., et al. 2015, MNRAS, 449, 1897", "Onions, J., Knebe, A., Pearce, F. R., et al. 2012, MNRAS, 423, 1200", "Osipkov, L. P. 1979, Pisma v Astronomicheskii Zhurnal, 5, 77", "Padmanabhan, N., Schlegel, D. J., Finkbeiner, D. P., et al. 2008, ApJ, 674, 1217", "Paranjape, A., Kova\u010d, K., Hartley, W. G., &amp; Pahwa, I. 2015, MNRAS, 454, 3030", "Pato, M., Baudis, L., Bertone, G., et al. 2011, Phys. Rev. D, 83, 083505", "Pato, M., Strigari, L. E., Trotta, R., &amp; Bertone, G. 2013, J. Cosmology Astropart. Phys., 2, 041", "Peacock, J. A., &amp; Smith, R. E. 2000, MNRAS, 318, 1144", "Peter, A. H. G. 2010, Phys. Rev. D, 81, 087301", "Pillepich, A., Kuhlen, M., Guedes, J., &amp; Madau, P. 2014, ApJ, 784, 161", "Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2015, ArXiv e-prints, arXiv:1502.01589", "Prada, F., Klypin, A. A., Cuesta, A. J., Betancort-Rijo, J. E., &amp; Primack, J. 2012, MNRAS, 423, 3018", "Press, W. H., &amp; Schechter, P. 1974, ApJ, 187, 425", "Purcell, C. W., &amp; Zentner, A. R. 2012, J. Cosmology Astropart. Phys., 12, 007", "Purcell, C. W., Zentner, A. R., &amp; Wang, M.-Y. 2012, J. Cosmology Astropart. Phys., 8, 027", "Read, J. I., Lake, G., Agertz, O., &amp; Debattista, V. P. 2008, MNRAS, 389, 1041", "Reddick, R. M., Wechsler, R. H., Tinker, J. L., &amp; Behroozi, P. S. 2013, ApJ, 771, 30", "Reed, D. S., Koushiappas, S. M., &amp; Gao, L. 2011, MNRAS, 415, 3177", "Reid, B. A., Seo, H.-J., Leauthaud, A., Tinker, J. L., &amp; White, M. 2014, MNRAS, 444, 476", "Reyes, R., Mandelbaum, R., Hirata, C., Bahcall, N., &amp; Seljak, U. 2008, MNRAS, 390, 1157", "Rodr\u00edguez-Puebla, A., Avila-Reese, V., &amp; Drory, N. 2013a, ApJ, 767, 92", "Rodr\u00edguez-Puebla, A., Avila-Reese, V., &amp; Drory, N. 2013b, ApJ, 773, 172", "Rodr\u00edguez-Puebla, A., Drory, N., &amp; Avila-Reese, V. 2012, ApJ, 756, 2", "Rozo, E., Rykoff, E. S., Bartlett, J. G., &amp; Melin, J.-B. 2015, MNRAS, 450, 592", "Rozo, E., Rykoff, E. S., Koester, B. P., et al. 2009, ApJ, 703, 601", "Rozo, E., Wechsler, R. H., Rykoff, E. S., et al. 2010, ApJ, 708, 645", "Rykoff, E. S., Rozo, E., Busha, M. T., et al. 2014, ApJ, 785, 104", "Saito, S., Leauthaud, A., Hearin, A. P., et al. 2016, MNRAS, arXiv:1509.00482", "Scoccimarro, R., Sheth, R. K., Hui, L., &amp; Jain, B. 2001, ApJ, 546, 20", "Seljak, U. 2000, MNRAS, 318, 203", "Sheth, R. K., Mo, H. J., &amp; Tormen, G. 2001, MNRAS, 323, 1", "Sheth, R. K., &amp; Tormen, G. 1999, MNRAS, 308, 119", "Skillman, S. W., Warren, M. S., Turk, M. J., et al. 2014, ArXiv e-prints, arXiv:1407.2600", "Smith, M. C., Ruchti, G. R., Helmi, A., et al. 2007, MNRAS, 379, 755", "Somerville, R. S., Hopkins, P. F., Cox, T. J., Robertson, B. E., &amp; Hernquist, L. 2008, MNRAS, 391, 481", "Sorensen, P. 2012, Phys. Rev. D, 86, 101301", "Sparre, M., &amp; Hansen, S. H. 2012, J. Cosmology Astropart. Phys., 10, 049", "Springel, V. 2005, MNRAS, 364, 1105", "Springel, V., Yoshida, N., &amp; White, S. D. M. 2001, New A, 6, 79", "Springel, V., Wang, J., Vogelsberger, M., et al. 2008, MNRAS, 391, 1685", "Srisawat, C., Knebe, A., Pearce, F. R., et al. 2013, MNRAS, 436, 150", "Stiff, D., &amp; Widrow, L. M. 2003, Physical Review Letters, 90, 211301", "Strigari, L. E. 2013, Phys. Rep., 531, 1", "Strigari, L. E., &amp; Trotta, R. 2009, J. Cosmology Astropart. Phys., 11, 019", "Sunayama, T., Hearin, A. P., Padmanabhan, N., &amp; Leauthaud, A. 2016, MNRAS, 458, 1510", "Tasitsiomi, A., Kravtsov, A. V., Wechsler, R. H., &amp; Primack, J. R. 2004, ApJ, 614, 533", "Tinker, J., Wetzel, A., &amp; Conroy, C. 2011, ArXiv e-prints, arXiv:1107.5046 [astro-ph.CO]", "Tinker, J. L., &amp; Conroy, C. 2009, ApJ, 691, 633", "Tinker, J. L., Conroy, C., Norberg, P., et al. 2008, ApJ, 686, 53", "Tinker, J. L., George, M. R., Leauthaud, A., et al. 2012, ApJ, 755, L5", "Trujillo-Gomez, S., Klypin, A., Primack, J., &amp; Romanowsky, A. J. 2011, ApJ, 742, 16", "Vale, A., &amp; Ostriker, J. P. 2004, MNRAS, 353, 189", "Vale, A., &amp; Ostriker, J. P. 2006, MNRAS, 371, 1173", "van den Bosch, F. C., &amp; Jiang, F. 2014, ArXiv e-prints, arXiv:1403.6835", "Vergados, J. D., Hansen, S. H., &amp; Host, O. 2008, Phys. Rev. D, 77, 023509", "Vogelsberger, M., &amp; White, S. D. M. 2011, MNRAS, 413, 1419", "Vogelsberger, M., Helmi, A., Springel, V., et al. 2009, MNRAS, 395, 797", "Vogelsberger, M., Genel, S., Springel, V., et al. 2014, MNRAS, 444, 1518", "Wang, W., Han, J., Cooper, A. P., et al. 2015, MNRAS, 453, 377", "Warren, M. S. 2013, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, SC \u201913 (New York, NY, USA: ACM), 72:1", "Watson, D. F., Berlind, A. A., &amp; Zentner, A. R. 2011, ApJ, 738, 22", "Wechsler, R. H., Bullock, J. S., Primack, J. R., Kravtsov, A. V., &amp; Dekel, A. 2002, ApJ, 568, 52", "Wechsler, R. H., Somerville, R. S., Bullock, J. S., et al. 2001, ApJ, 554, 85", "Wechsler, R. H., Zentner, A. R., Bullock, J. S., Kravtsov, A. V., &amp; Allgood, B. 2006, ApJ, 652, 71", "Wu, H.-Y., Hahn, O., Wechsler, R. H., Behroozi, P. S., &amp; Mao, Y.-Y. 2013a, ApJ, 767, 23", "Wu, H.-Y., Hahn, O., Wechsler, R. H., Mao, Y.-Y., &amp; Behroozi, P. S. 2013b, ApJ, 763, 70", "Xue, X. X., Rix, H. W., Zhao, G., et al. 2008, ApJ, 684, 1143", "Yang, X., Mo, H. J., &amp; van den Bosch, F. C. 2006, ApJ, 638, L55", "Yang, X., Mo, H. J., Zhang, Y., &amp; van den Bosch, F. C. 2011, ApJ, 741, 13", "Zentner, A. R., Berlind, A. A., Bullock, J. S., Kravtsov, A. V., &amp; Wechsler, R. H. 2005, ApJ, 624, 505", "Zentner, A. R., Hearin, A. P., &amp; van den Bosch, F. C. 2014, MNRAS, 443, 3044", "Zhu, G., Zheng, Z., Lin, W. P., et al. 2006, ApJ, 639, L5", "Zehavi, I., Zheng, Z., Weinberg, D. H., et al. 2011, ApJ, 736, 59"]}