* Eigenthaler et al. (2018) Eigenthaler, P., Puzia, T. H., Taylor, M. A., et al. 2018, ApJ, 855, 142
  * Esquej et al. (2008) Esquej, P., Saxton, R. D., Komossa, S., et al. 2008, A&A, 489, 543
  * Fahrion et al. (2022) Fahrion, K., Bulichi, T.-E., Hilker, M., et al. 2022, A&A, 667, A101
  * Fahrion et al. (2021) Fahrion, K., Lyubenova, M., van de Ven, G., et al. 2021, A&A, 650, A137
  * Frank & Rees (1976) Frank, J. & Rees, M. J. 1976, MNRAS, 176, 633
  * Frederick et al. (2021) Frederick, S., Gezari, S., Graham, M. J., et al. 2021, ApJ, 920, 56
  * French et al. (2016) French, K. D., Arcavi, I., & Zabludoff, A. 2016, ApJ, 818, L21
  * French et al. (2017) French, K. D., Arcavi, I., & Zabludoff, A. 2017, ApJ, 835, 176
  * French et al. (2020a) French, K. D., Arcavi, I., Zabludoff, A. I., et al. 2020a, ApJ, 891, 93
  * French et al. (2020b) French, K. D., Wevers, T., Law-Smith, J., Graur, O., & Zabludoff, A. I. 2020b, Space Sci. Rev., 216, 32
  * Gadotti (2009) Gadotti, D. A. 2009, MNRAS, 393, 1531
  * Gallo & Sesana (2019) Gallo, E. & Sesana, A. 2019, ApJ, 883, L18
  * Gebhardt et al. (2001) Gebhardt, K., Lauer, T. R., Kormendy, J., et al. 2001, AJ, 122, 2469
  * Generozov & Perets (2023) Generozov, A. & Perets, H. B. 2023, MNRAS, 522, 1763
  * Georgiev et al. (2016) Georgiev, I. Y., Böker, T., Leigh, N., Lützgendorf, N., & Neumayer, N. 2016, MNRAS, 457, 2122
  * Gezari et al. (2008) Gezari, S., Basa, S., Martin, D. C., et al. 2008, ApJ, 676, 944
  * Gezari et al. (2006) Gezari, S., Martin, D. C., Milliard, B., et al. 2006, ApJ, 653, L25
  * Goldtooth et al. (2023) Goldtooth, A., Zabludoff, A. I., Wen, S., et al. 2023, PASP, 135, 034101
  * Graham & Spitler (2009) Graham, A. W. & Spitler, L. R. 2009, MNRAS, 397, 2148
  * Graur et al. (2018) Graur, O., French, K. D., Zahid, H. J., et al. 2018, ApJ, 853, 39
  * Greene (2012) Greene, J. E. 2012, Nature Communications, 3, 1304
  * Greene et al. (2020) Greene, J. E., Strader, J., & Ho, L. C. 2020, ARA&A, 58, 257
  * Guillochon & Ramirez-Ruiz (2013) Guillochon, J. & Ramirez-Ruiz, E. 2013, ApJ, 767, 25
  * Guo et al. (2011) Guo, Q., White, S., Boylan-Kolchin, M., et al. 2011, MNRAS, 413, 101
  * Guolo et al. (2023) Guolo, M., Gezari, S., Yao, Y., et al. 2023, arXiv e-prints, arXiv:2308.13019
  * Haiman et al. (1997) Haiman, Z., Rees, M. J., & Loeb, A. 1997, ApJ, 476, 458
  * Hambleton et al. (2023) Hambleton, K. M., Bianco, F. B., Street, R., et al. 2023, PASP, 135, 105002
  * Hammerstein et al. (2021) Hammerstein, E., Gezari, S., van Velzen, S., et al. 2021, ApJ, 908, L20
  * Hammerstein et al. (2023) Hammerstein, E., van Velzen, S., Gezari, S., et al. 2023, ApJ, 942, 9
  * Hartmann et al. (2011) Hartmann, M., Debattista, V. P., Seth, A., Cappellari, M., & Quinn, T. R. 2011, MNRAS, 418, 2697
  * Henriques et al. (2015) Henriques, B. M. B., White, S. D. M., Thomas, P. A., et al. 2015, MNRAS, 451, 2663
  * Henriques et al. (2020) Henriques, B. M. B., Yates, R. M., Fu, J., et al. 2020, MNRAS, 491, 5795
  * Hills (1975) Hills, J. G. 1975, Nature, 254, 295
  * Hinkle et al. (2021) Hinkle, J. T., Holoien, T. W. S., Auchettl, K., et al. 2021, MNRAS, 500, 1673
  * Hinkle et al. (2022) Hinkle, J. T., Holoien, T. W. S., Shappee, B. J., et al. 2022, ApJ, 930, 12
  * Homan et al. (2023) Homan, D., Krumpe, M., Markowitz, A., et al. 2023, A&A, 672, A167
  * Hoyer et al. (2021) Hoyer, N., Neumayer, N., Georgiev, I. Y., Seth, A. C., & Greene, J. E. 2021, MNRAS, 507, 3246
  * Hoyer et al. (2023) Hoyer, N., Neumayer, N., Seth, A. C., Georgiev, I. Y., & Greene, J. E. 2023, MNRAS, 520, 4664
  * Huang & Lu (2024) Huang, H.-T. & Lu, W. 2024, MNRAS, 527, 1865
  * Huang et al. (2023) Huang, S., Jiang, N., Lin, Z., Zhu, J., & Wang, T. 2023, MNRAS, 525, 4057
  * Ito et al. (2023) Ito, K., Valentino, F., Brammer, G., et al. 2023, arXiv e-prints, arXiv:2307.06994
  * Izquierdo-Villalba et al. (2020) Izquierdo-Villalba, D., Bonoli, S., Dotti, M., et al. 2020, MNRAS, 495, 4681
  * Izquierdo-Villalba et al. (2019) Izquierdo-Villalba, D., Bonoli, S., Spinoso, D., et al. 2019, MNRAS, 488, 609
  * Izquierdo-Villalba et al. (2022) Izquierdo-Villalba, D., Sesana, A., Bonoli, S., & Colpi, M. 2022, MNRAS, 509, 3488
  * Jankovič et al. (2023) Jankovič, T., Bonnerot, C., & Gomboc, A. 2023, arXiv e-prints, arXiv:2303.16230
  * Johnston et al. (2020) Johnston, E. J., Puzia, T. H., D’Ago, G., et al. 2020, MNRAS, 495, 2247
  * Kacharov et al. (2018) Kacharov, N., Neumayer, N., Seth, A. C., et al. 2018, MNRAS, 480, 1973
  * Karas & Šubr (2007) Karas, V. & Šubr, L. 2007, A&A, 470, 11
  * Kaviraj et al. (2007) Kaviraj, S., Kirkby, L. A., Silk, J., & Sarzi, M. 2007, MNRAS, 382, 960
  * Kawamuro et al. (2016) Kawamuro, T., Ueda, Y., Shidatsu, M., et al. 2016, PASJ, 68, 58
  * Kesden (2012) Kesden, M. 2012, Phys. Rev. D, 85, 024037
  * Khan & Holley-Bockelmann (2021) Khan, F. M. & Holley-Bockelmann, K. 2021, MNRAS, 508, 1174
  * Kim et al. (2018) Kim, E., Kim, S. S., Choi, Y.-Y., et al. 2018, MNRAS, 479, 562
  * Kimbrell et al. (2021) Kimbrell, S. J., Reines, A. E., Schutte, Z., Greene, J. E., & Geha, M. 2021, ApJ, 911, 134
  * Kıroğlu et al. (2023) Kıroğlu, F., Lombardi, J. C., Kremer, K., et al. 2023, ApJ, 948, 89
  * Kochanek (2016) Kochanek, C. S. 2016, MNRAS, 461, 371
  * Komossa & Bade (1999) Komossa, S. & Bade, N. 1999, A&A, 343, 775
  * Kool et al. (2020) Kool, E. C., Reynolds, T. M., Mattila, S., et al. 2020, MNRAS, 498, 2167
  * Kormendy & Ho (2013) Kormendy, J. & Ho, L. C. 2013, ARA&A, 51, 511
  * Kritos et al. (2023) Kritos, K., Berti, E., & Silk, J. 2023, Phys. Rev. D, 108, 083012
  * Krolik et al. (2020) Krolik, J., Piran, T., & Ryu, T. 2020, ApJ, 904, 68
  * Krolik et al. (2016) Krolik, J., Piran, T., Svirski, G., & Cheng, R. M. 2016, ApJ, 827, 127
  * Kroupa (2001) Kroupa, P. 2001, MNRAS, 322, 231
  * Law-Smith et al. (2017) Law-Smith, J., Ramirez-Ruiz, E., Ellison, S. L., & Foley, R. J. 2017, ApJ, 850, 22
  * Leaman & van de Ven (2022) Leaman, R. & van de Ven, G. 2022, MNRAS, 516, 4691
  * Lee et al. (2023) Lee, S., Kim, J.-h., & Oh, B. K. 2023, ApJ, 943, 77
  * Li et al. (2023) Li, J., Wang, Z.-X., Zheng, D., et al. 2023, Research in Astronomy and Astrophysics, 23, 025012
  * Li et al. (2017) Li, S., Liu, F. K., Berczik, P., & Spurzem, R. 2017, ApJ, 834, 195
  * Lin et al. (2022) Lin, Z., Jiang, N., Kong, X., et al. 2022, ApJ, 939, L33
  * Liu et al. (2023) Liu, C., Mockler, B., Ramirez-Ruiz, E., et al. 2023, ApJ, 944, 184
  * Liu et al. (2020) Liu, Z., Li, D., Liu, H.-Y., et al. 2020, ApJ, 894, 93
  * Lohmann et al. (2023) Lohmann, F. S., Schnorr-Müller, A., Trevisan, M., Ricci, T. V., & Clerici, K. S. 2023, MNRAS, 524, 5266
  * MacLeod et al. (2012) MacLeod, M., Guillochon, J., & Ramirez-Ruiz, E. 2012, ApJ, 757, 134
  * Madigan et al. (2018) Madigan, A.-M., Halle, A., Moody, M., et al. 2018, ApJ, 853, 141
  * Magorrian & Tremaine (1999) Magorrian, J. & Tremaine, S. 1999, MNRAS, 309, 447
  * Mainetti et al. (2017) Mainetti, D., Lupi, A., Campana, S., et al. 2017, A&A, 600, A124
  * Makrygianni et al. (2023) Makrygianni, L., Trakhtenbrot, B., Arcavi, I., et al. 2023, ApJ, 953, 32
  * Malyali et al. (2023) Malyali, A., Liu, Z., Rau, A., et al. 2023, MNRAS, 520, 3549
  * Masterson et al. (2024) Masterson, M., De, K., Panagiotou, C., et al. 2024, arXiv e-prints, arXiv:2401.01403
  * Mattila et al. (2018) Mattila, S., Pérez-Torres, M., Efstathiou, A., et al. 2018, Science, 361, 482
  * Mayes et al. (2021) Mayes, R. J., Drinkwater, M. J., Pfeffer, J., et al. 2021, MNRAS, 506, 2459
  * McKernan et al. (2022) McKernan, B., Ford, K. E. S., Cantiello, M., et al. 2022, MNRAS, 514, 4102
  * Merloni & Heinz (2008) Merloni, A. & Heinz, S. 2008, MNRAS, 388, 1011
  * Merritt (2009) Merritt, D. 2009, ApJ, 694, 959
  * Merritt (2013) Merritt, D. 2013, Classical and Quantum Gravity, 30, 244005
  * Merritt et al. (2001) Merritt, D., Ferrarese, L., & Joseph, C. L. 2001, Science, 293, 1116
  * Mezcua et al. (2018) Mezcua, M., Civano, F., Marchesi, S., et al. 2018, MNRAS, 478, 2576
  * Mezcua & Domínguez Sánchez (2020) Mezcua, M. & Domínguez Sánchez, H. 2020, ApJ, 898, L30
  * Miller & Davies (2012) Miller, M. C. & Davies, M. B. 2012, ApJ, 755, 81
  * Milosavljević et al. (2006) Milosavljević, M., Merritt, D., & Ho, L. C. 2006, ApJ, 652, 120
  * Mockler et al. (2023) Mockler, B., Melchor, D., Naoz, S., & Ramirez-Ruiz, E. 2023, ApJ, 959, 18
  * Mockler & Ramirez-Ruiz (2021) Mockler, B. & Ramirez-Ruiz, E. 2021, ApJ, 906, 101
  * Mockler et al. (2022) Mockler, B., Twum, A. A., Auchettl, K., et al. 2022, ApJ, 924, 70
  * Moustakas et al. (2013) Moustakas, J., Coil, A. L., Aird, J., et al. 2013, ApJ, 767, 50
  * Muñoz et al. (2015) Muñoz, R. P., Eigenthaler, P., Puzia, T. H., et al. 2015, ApJ, 813, L15
  * Mummery (2024) Mummery, A. 2024, MNRAS, 527, 6233
  * Mummery & Balbus (2020) Mummery, A. & Balbus, S. A. 2020, MNRAS, 497, L13
  * Mummery et al. (2024) Mummery, A., van Velzen, S., Nathan, E., et al. 2024, MNRAS, 527, 2452
  * Mutlu-Pakdil et al. (2016) Mutlu-Pakdil, B., Seigar, M. S., & Davis, B. L. 2016, ApJ, 830, 117
  * Naiman et al. (2015) Naiman, J. P., Ramirez-Ruiz, E., Debuhr, J., & Ma, C. P. 2015, ApJ, 803, 81
  * Nasim et al. (2023) Nasim, S. S., Fabj, G., Caban, F., et al. 2023, MNRAS, 522, 5393
  * Neumayer et al. (2020) Neumayer, N., Seth, A., & Böker, T. 2020, A&A Rev., 28, 4
  * Neumayer & Walcher (2012) Neumayer, N. & Walcher, C. J. 2012, Advances in Astronomy, 2012, 709038
  * Nguyen et al. (2022) Nguyen, D. D., Bureau, M., Thater, S., et al. 2022, MNRAS, 509, 2920
  * Nguyen et al. (2018) Nguyen, D. D., Seth, A. C., Neumayer, N., et al. 2018, ApJ, 858, 118
  * Oates et al. (2023) Oates, S. R., Kuin, N. P. M., Nicholl, M., et al. 2023, arXiv e-prints, arXiv:2307.01044
  * Panagiotou et al. (2023) Panagiotou, C., De, K., Masterson, M., et al. 2023, ApJ, 948, L5
  * Pandya et al. (2023) Pandya, V., Zhang, H., Huertas-Company, M., et al. 2023, arXiv e-prints, arXiv:2310.15232
  * Park & Hayasaki (2020) Park, G. & Hayasaki, K. 2020, ApJ, 900, 3
  * Payne et al. (2021) Payne, A. V., Shappee, B. J., Hinkle, J. T., et al. 2021, ApJ, 910, 125
  * Pechetti et al. (2020) Pechetti, R., Seth, A., Neumayer, N., et al. 2020, ApJ, 900, 32
  * Pérez-González et al. (2008) Pérez-González, P. G., Trujillo, I., Barro, G., et al. 2008, ApJ, 687, 50
  * Pfeffer et al. (2014) Pfeffer, J., Griffen, B. F., Baumgardt, H., & Hilker, M. 2014, MNRAS, 444, 3670
  * Pfister et al. (2021) Pfister, H., Dai, J. L., Volonteri, M., et al. 2021, MNRAS, 500, 3944
  * Pfister et al. (2022) Pfister, H., Toscani, M., Wong, T. H. T., et al. 2022, MNRAS, 510, 2025
  * Pfister et al. (2020) Pfister, H., Volonteri, M., Dai, J. L., & Colpi, M. 2020, MNRAS, 497, 2276
  * Phinney (1989) Phinney, E. S. 1989, in The Center of the Galaxy, ed. M. Morris, Vol. 136, 543
  * Pinna et al. (2021) Pinna, F., Neumayer, N., Seth, A., et al. 2021, ApJ, 921, 8
  * Planck Collaboration et al. (2020) Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6
  * Prasad et al. (2023) Prasad, C., Wang, Y., Perna, R., Ford, K. E. S., & McKernan, B. 2023, arXiv e-prints, arXiv:2310.00020
  * Rantala & Naab (2023) Rantala, A. & Naab, T. 2023, arXiv e-prints, arXiv:2308.12344
  * Rauch & Tremaine (1996) Rauch, K. P. & Tremaine, S. 1996, New A, 1, 149
  * Rees (1988) Rees, M. J. 1988, Nature, 333, 523
  * Reines & Volonteri (2015) Reines, A. E. & Volonteri, M. 2015, ApJ, 813, 82
  * Reynolds (2021) Reynolds, C. S. 2021, ARA&A, 59, 117
  * Reynolds et al. (2022) Reynolds, T. M., Mattila, S., Efstathiou, A., et al. 2022, A&A, 664, A158
  * Ricci & Trakhtenbrot (2023) Ricci, C. & Trakhtenbrot, B. 2023, Nature Astronomy, 7, 1282
  * Rizzuto et al. (2023) Rizzuto, F. P., Naab, T., Rantala, A., et al. 2023, MNRAS, 521, 2930
  * Roediger & Courteau (2015) Roediger, J. C. & Courteau, S. 2015, MNRAS, 452, 3209
  * Ryu et al. (2023a) Ryu, T., Krolik, J., & Piran, T. 2023a, ApJ, 946, L33
  * Ryu et al. (2020a) Ryu, T., Krolik, J., Piran, T., & Noble, S. C. 2020a, ApJ, 904, 98
  * Ryu et al. (2020b) Ryu, T., Krolik, J., Piran, T., & Noble, S. C. 2020b, ApJ, 904, 100
  * Ryu et al. (2023b) Ryu, T., McKernan, B., Ford, K. E. S., et al. 2023b, MNRAS[arXiv:2310.00610]
  * Ryu et al. (2022) Ryu, T., Trani, A. A., & Leigh, N. W. C. 2022, MNRAS, 515, 2430
  * Saha (1992) Saha, P. 1992, MNRAS, 254, 132
  * Sánchez-Janssen et al. (2019) Sánchez-Janssen, R., Côté, P., Ferrarese, L., et al. 2019, ApJ, 878, 18
  * Saracco et al. (2010) Saracco, P., Longhetti, M., & Gargiulo, A. 2010, MNRAS, 408, L21
  * Sazonov et al. (2021) Sazonov, S., Gilfanov, M., Medvedev, P., et al. 2021, MNRAS, 508, 3820
  * Seth et al. (2008) Seth, A., Agüeros, M., Lee, D., & Basu-Zych, A. 2008, ApJ, 678, 116
  * Setton et al. (2022) Setton, D. J., Verrico, M., Bezanson, R., et al. 2022, ApJ, 931, 51
  * Shankar et al. (2019) Shankar, F., Bernardi, M., Richardson, K., et al. 2019, MNRAS, 485, 1278
  * Shankar et al. (2016) Shankar, F., Bernardi, M., Sheth, R. K., et al. 2016, MNRAS, 460, 3119
  * Shankar et al. (2009) Shankar, F., Weinberg, D. H., & Miralda-Escudé, J. 2009, ApJ, 690, 20
  * Shankar et al. (2013) Shankar, F., Weinberg, D. H., & Miralda-Escudé, J. 2013, MNRAS, 428, 421
  * Shen et al. (2003) Shen, S., Mo, H. J., White, S. D. M., et al. 2003, MNRAS, 343, 978
  * Singh & Kesden (2023) Singh, T. & Kesden, M. 2023, arXiv e-prints, arXiv:2306.08054
  * Siudek et al. (2023) Siudek, M., Mezcua, M., & Krywult, J. 2023, MNRAS, 518, 724
  * Somalwar et al. (2023a) Somalwar, J. J., Ravi, V., & Lu, W. 2023a, arXiv e-prints, arXiv:2310.03795
  * Somalwar et al. (2023b) Somalwar, J. J., Ravi, V., Yao, Y., et al. 2023b, arXiv e-prints, arXiv:2310.03782
  * Spergel et al. (2003) Spergel, D. N., Verde, L., Peiris, H. V., et al. 2003, ApJS, 148, 175
  * Spinoso et al. (2023) Spinoso, D., Bonoli, S., Valiante, R., Schneider, R., & Izquierdo-Villalba, D. 2023, MNRAS, 518, 4672
  * Springel et al. (2005) Springel, V., White, S. D. M., Jenkins, A., et al. 2005, Nature, 435, 629
  * Steinberg & Stone (2022) Steinberg, E. & Stone, N. C. 2022, arXiv e-prints, arXiv:2206.10641
  * Stone et al. (2013) Stone, N., Sari, R., & Loeb, A. 2013, MNRAS, 435, 1809
  * Stone et al. (2018) Stone, N. C., Generozov, A., Vasiliev, E., & Metzger, B. D. 2018, MNRAS, 480, 5060
  * Stone et al. (2019) Stone, N. C., Kesden, M., Cheng, R. M., & van Velzen, S. 2019, General Relativity and Gravitation, 51, 30
  * Stone et al. (2017) Stone, N. C., Küpper, A. H. W., & Ostriker, J. P. 2017, MNRAS, 467, 4180
  * Stone & Metzger (2016) Stone, N. C. & Metzger, B. D. 2016, MNRAS, 455, 859
  * Stone et al. (2020) Stone, N. C., Vasiliev, E., Kesden, M., et al. 2020, Space Sci. Rev., 216, 35
  * Sutherland & Dopita (1993) Sutherland, R. S. & Dopita, M. A. 1993, ApJS, 88, 253
  * Syer & Ulmer (1999) Syer, D. & Ulmer, A. 1999, MNRAS, 306, 35
  * Tadhunter et al. (2017) Tadhunter, C., Spence, R., Rose, M., Mullaney, J., & Crowther, P. 2017, Nature Astronomy, 1, 0061
  * Teboul et al. (2024) Teboul, O., Stone, N. C., & Ostriker, J. P. 2024, MNRAS, 527, 3094
  * Thater et al. (2023) Thater, S., Lyubenova, M., Fahrion, K., et al. 2023, A&A, 675, A18
  * Trani et al. (2018) Trani, A. A., Mapelli, M., & Ballone, A. 2018, ApJ, 864, 17
  * Tremmel et al. (2023) Tremmel, M., Ricarte, A., Natarajan, P., et al. 2023, arXiv e-prints, arXiv:2306.12813
  * Trump et al. (2015) Trump, J. R., Sun, M., Zeimann, G. R., et al. 2015, ApJ, 811, 26
  * Urquhart et al. (2022) Urquhart, R., McDermott, L. I., Strader, J., et al. 2022, ApJ, 940, 111
  * Valiante et al. (2016) Valiante, R., Schneider, R., Volonteri, M., & Omukai, K. 2016, MNRAS, 457, 3356
  * Valluri et al. (2005) Valluri, M., Ferrarese, L., Merritt, D., & Joseph, C. L. 2005, ApJ, 628, 137
  * van Donkelaar et al. (2023) van Donkelaar, F., Mayer, L., Capelo, P. R., et al. 2023, arXiv e-prints, arXiv:2303.12828
  * van Velzen (2018) van Velzen, S. 2018, ApJ, 852, 72
  * van Velzen & Farrar (2014) van Velzen, S. & Farrar, G. R. 2014, ApJ, 792, 53
  * van Velzen et al. (2011) van Velzen, S., Farrar, G. R., Gezari, S., et al. 2011, ApJ, 741, 73
  * Vasiliev (2017) Vasiliev, E. 2017, ApJ, 848, 10
  * Vasiliev (2019) Vasiliev, E. 2019, MNRAS, 482, 1525
  * Vasiliev & Merritt (2013) Vasiliev, E. & Merritt, D. 2013, ApJ, 774, 87
  * Vika et al. (2009) Vika, M., Driver, S. P., Graham, A. W., & Liske, J. 2009, MNRAS, 400, 1451
  * Wang & Merritt (2004) Wang, J. & Merritt, D. 2004, ApJ, 600, 149
  * Wang et al. (2024) Wang, M., Ma, Y., Wu, Q., & Jiang, N. 2024, ApJ, 960, 69
  * Wang et al. (2022) Wang, Y., Jiang, N., Wang, T., et al. 2022, ApJ, 930, L4
  * Weissbein & Sari (2017) Weissbein, A. & Sari, R. 2017, MNRAS, 468, 1760
  * Wevers et al. (2022) Wevers, T., Nicholl, M., Guolo, M., et al. 2022, A&A, 666, A6
  * Wevers et al. (2019) Wevers, T., Stone, N. C., van Velzen, S., et al. 2019, MNRAS, 487, 4136
  * White & Frenk (1991) White, S. D. M. & Frenk, C. S. 1991, ApJ, 379, 52
  * White & Rees (1978) White, S. D. M. & Rees, M. J. 1978, MNRAS, 183, 341
  * Wild et al. (2016) Wild, V., Almaini, O., Dunlop, J., et al. 2016, MNRAS, 463, 832
  * Wild et al. (2020) Wild, V., Taj Aldeen, L., Carnall, A., et al. 2020, MNRAS, 494, 529
  * Wong et al. (2022) Wong, T. H. T., Pfister, H., & Dai, L. 2022, ApJ, 927, L19
  * Wu & Yuan (2018) Wu, X.-J. & Yuan, Y.-F. 2018, MNRAS, 479, 1569
  * XueGuang (2022) XueGuang, Z. 2022, arXiv e-prints, arXiv:2209.09037
  * Yao et al. (2023) Yao, Y., Ravi, V., Gezari, S., et al. 2023, ApJ, 955, L6
  * Zajaček et al. (2023) Zajaček, M., Czerny, B., Jaiswal, V. K., et al. 2023, arXiv e-prints, arXiv:2306.15082
  * Zanatta et al. (2021) Zanatta, E., Sánchez-Janssen, R., Chies-Santos, A. L., de Souza, R. S., & Blakeslee, J. P. 2021, MNRAS, 508, 986
  * Zanazzi & Ogilvie (2020) Zanazzi, J. J. & Ogilvie, G. I. 2020, MNRAS, 499, 5562
  * Zhao (1996) Zhao, H. 1996, MNRAS, 278, 488
  * Zhong et al. (2022) Zhong, S., Li, S., Berczik, P., & Spurzem, R. 2022, ApJ, 933, 96
  * Zou et al. (2023) Zou, F., Brandt, W. N., Ni, Q., et al. 2023, ApJ, 950, 136

##  Appendix A TDE hosts mass functions

Figure 11: Stellar Mass Functions of all galaxies (solid black) and TDE-host
galaxies with the highest TDE rates ($\Gamma_{\rm tot}{>}\,10^{-5}$, grey
dashed) for the fiducial model at $z\,{=}\,0$ and $z\,{=}\,1$. The first is
compared with compiled mass constraints from Henriques et al. (2015) and
Henriques et al. (2020), Baldry et al. (2008), Pérez-González et al. (2008),
and Moustakas et al. (2013) (inset legend). With a thin colored line at lower
masses, the NSC Mass Function of the fiducial model is plotted at the same
redshifts. For comparison, we display the model NSC mass function from
Antonini et al. (2015) at $z\,{=}\,0$ (Ant15 z=0).

Our model can explain the constraints of Yao et al. (2023) on the galaxy
stellar mass distribution of the volumetric rates. We discuss briefly the
reasons for the relatively good agreement and the issues to be addressed
regarding the TDE host mass range in future works.

As observed in Fig. 11 (grey dashed), we reproduce the flat galaxy stellar
mass function expected for TDE host galaxies as inferred from observations
(Law-Smith et al. 2017). Galaxy stellar mass functions are all in good
agreement with one another and with observations at $z\,{=}\,0$, $1$, as
expected by the success of the _L-Galaxies_ models.

In the same plot, we present the NSC mass function at $z\,{=}\,0$ (dotted-
dashed) which is lower compared to the theoretical predictions of Antonini et
al. (2015) by an order of magnitude at lower masses, obviously having a
different slope. The number density provided by this function should be a
theoretical lower limit to reproduce the TDE rates, yet NSCs without MBHs
should also be considered. The model predicts that NSCs do not evolve
significantly with redshift from $z\,{=}\,1$, as they are tightly related to
the nuclear MBHs (that also do not evolve).

At $z\,{=}\,0$ the peak at hosts with high rates within
$M_{\ast}\,=\,10^{9.5}$ \- $10^{10.5}\,\,\mathrm{M_{\odot}}$ is directly
related to hosting massive NSC $M_{\rm
NSC}\,=\,10^{7}$-$10^{8}\,\,\mathrm{M_{\odot}}$ and recently seeded (high per-
galaxy rates, left panel in Fig. 11 for NSC distribution) while the evolving
tail ($M_{\ast}\,{<}\,10^{9}\,\,\mathrm{M_{\odot}}$ from $z\,{=}\,1$ to
$z\,{=}\,0$ is from the contribution of intermediate-mass MBHs and smaller NSC
(right NSC distribution in Fig. 11), and systems with TDE rates decaying with
time. The model predicts mild redshift evolution, a falsifiable argument with
the observations of TDEs up to $z\,{=}\,1$ from the forthcoming LSST samples.

##  Appendix B Useful definitions for Tidal Disruption Event rate
interpretation

An interaction between a massive black hole and a star reaches its proximity
zone of less than one tidal radius $r_{t}$ (Eq. 3 in the main text), at fixed
masses $M_{\bullet}$ and $m_{\ast}$ respectively, will result in a variety of
outcomes, with different energetics and observable signatures depending on
many parameters. How close to the horizon the star is destined to make a
passage is of particular importance (Carter & Luminet 1982; Stone et al. 2013;
Dai et al. 2015). It is useful to quantify this with the penetration parameter
that is defined as

$\beta=r_{t}/r_{p},$

where $r_{p}$ the pericenter of the orbit and

$r_{t}=6.9\times 10^{12}{\rm cm}\;\eta_{\rm
TD}^{2/3}(M_{\bullet}/10^{6}M_{\odot})^{1/3}m_{\ast}^{-1/3}r_{\ast}$

the tidal radius depends on the mass/radius of the star disrupted $m_{\ast}$
and $r_{\ast}$ (units of $1\,\mathrm{M_{\odot}}$ and $1$R⊙). The coefficient
$\eta_{\rm TD}$ depends on the polytropic index of the star and is of the
order unity (Merritt 2013). Penetration factor values range from $\beta_{\rm
min}\,=\,0.5$-$0.6$ as derived from hydrodynamical simulations (Guillochon &
Ramirez-Ruiz 2013) and at which point stars are merely disrupted, to
$\beta_{\rm max}$ at which point stars enter whole into the MBH’s horizon.
Analytical calculation on horizon suppression for a Schwarzchild MBH yields
(Kesden 2012; Mummery 2024)

$\beta_{\rm max}=11.8M_{\bullet,6}^{-2/3}m_{\ast}^{-1/3}r_{\ast}.$ (13)

Also, below a value $\beta_{c}$ the star is not fully disrupted. Therefore,
full TDEs at the interval $\beta_{\rm c}\,{<}\,\beta\,{<}\,\beta_{\rm max}$
while direct captures occur for $\beta\,{>}\,\beta_{\max}(M_{\bullet})$. The
rest of the events are found in the interval $\beta_{\min}\,{<}\,\beta_{c}$
and are considered partial TDEs. The latter are identified by the re-flaring
of their source and less frequently from their differentiation in the fading
power law ($-9/4$ instead of $-5/3$). Ryu et al. (2020a) has shown that the
physical tidal radius at which the star is fully disrupted has both stellar
and MBH mass dependence. For disrupted stars of mass 0.3 and 1 M⊙, we adopt

$\beta_{\rm c}=\beta_{\rm
c,0}\frac{1}{1+C_{0}(M_{\bullet}/10^{6}M_{\odot})^{2/3}}.$ (14)

where $\beta_{\rm c,0}=2.0$,$C_{0}=0.166$ & $\beta_{\rm c,0}=2.65$,
$C_{0}=0.204$ respectively. We set the simple form $\beta_{\rm
c,0}(m_{\ast})=1.6(m_{\ast}+0.45)$ and fix $C_{0}=0.2$ for our simple
calculations here (although there is not a linear transition between stars
with different polytropic indices). For reference, Guillochon & Ramirez-Ruiz
(2013) and Mainetti et al. (2017) values from simulations for convective &
radiation-dominated stars around a $M_{\bullet}=10^{6}\,\mathrm{M_{\odot}}$
MBH translate into $\beta_{\rm c,0}=1.08$ & $2.2$ when fixing $C_{0}=0.2$
respectively. Note that there is a continuous transition from TDEs to direct
captures as $\beta_{\rm
c}(m_{\ast})\rightarrow\beta_{\max}(M_{\bullet},m_{\ast},\chi_{\bullet},t),$
with the Hills mass being rather a range of values for the distribution of
star masses. _This transition is computed solely in the analysis here_ ; in
the main text TDEs are considered as $\beta\,{>}\,\beta_{\rm c}=1$ (all stars
within the tidal radius are disrupted) with $\beta_{\rm max}\rightarrow\infty$
for $M_{\bullet}\,{<}\,10^{8}\,\mathrm{M_{\odot}}$ (direct captures are not
considered separately) and $\beta_{\max}\,{<}\,\beta_{\rm c}$ for higher MBH
masses (all events are considered direct captures).

The number of orbits per penetration factor bin $dN(\beta)/d\beta$ takes the
analytical form of a power-law for the full loss-cone regime (the system just
started to relax). By assuming uniformity of the orbits over $r_{p}$ gives a
power-law dependence of $\,{\propto}\,\beta^{-2}$ (Stone et al. 2020). When
the relativistic gravity is taken into account, this power law drops to
$\beta^{-10/3}$ (Coughlin & Nixon 2022) for maximally-spinning MBHs (Kerr
metric). Also, we consider the scenario where orbits are distributed uniformly
over surface $2\pi r_{p}dr_{p}$ and the probability function scales as
$\,{\propto}\,\beta^{-3}$ (Bricman & Gomboc 2020). At the empty loss-cone
regime (the system has relaxed) there is a weak (logarithmic) dependence of
rates on $\beta$, so essentially we can assume $\,{\propto}\,\beta^{0}$ for
this case. For simplicity, we assume that the distribution of orbits destined
to do partial TDEs follows from one of the full TDEs as inferred for the
disruption of normal stars from Zhong et al. (2022).

We can now write the fraction of full TDEs as the integral of a power-law
probability $\beta^{-S_{\beta}-1}$ in the value intervals mentioned above:

$f_{\rm FTDE}(m_{\ast},M_{\bullet})=\frac{\beta_{\rm
c}(m_{\ast},M_{\bullet})^{-S_{\beta}}-\beta_{\max}(m_{\ast},M_{\bullet})^{-S_{\beta}}}{\beta_{\min}^{-S_{\beta}}-\beta_{\max}(m_{\ast},M_{\bullet})^{-S_{\beta}}}$
(15)

where the generic power-law $S_{\beta}$ is in the range $S_{\beta}\in[1,2]$
for our calculations, for a non-empty loss cone (for all types of events). For
the empty loss-cone regime, $S_{\beta}=-1$ and events at all $\beta$ should be
equally rare.

Now, we can estimate a general correction for our calculated rates of full
disruption stars to the rate of all disruptions by using Eq.15, for the regime
where $\beta_{\rm min}\,{\gg}\,\beta_{c}\,{\gg}\,\beta_{\max}$ get that
full/total TDE rate converges as $f_{\rm FTDE}\rightarrow(\beta_{\rm
min}\,{/}\,\beta_{\rm c})^{S_{\beta}}$. For $\beta_{\rm min}=0.6$ and
$M_{\bullet}\,{\lesssim}\,10^{6}\,\mathrm{M_{\odot}}$ yields almost
invariably232323This refers to both convection-dominated and radiation-
dominated stars since the fraction of full TDE rates is already is over-
estimated by a factor of $(\beta_{c})^{S_{\beta}}$ when assuming the TDE rates
of 0.38 M⊙ stars hold for more massive stars PhaseFlow. Also, the weak
dependence of $\beta_{c}$ on MBH mass in the regime is neglected. a correction
factor of

$1/f_{\rm FTDE}\in[2,4]$

for $S_{\beta}\in[1,2]$. This correction could be applied only to “young”
systems relaxing only for the last $<100\,\mathrm{Myr}$ that have not emptied
their loss-cone. However, the physics of circularization could be different
for TDEs varying in $\beta$, especially for the unknown regime of lower MBH
masses (Kıroğlu et al. 2023,
$M_{\bullet}=10^{2}\,{-}\,10^{4}\,\mathrm{M_{\odot}}$) and the rates may be
modified accordingly (Wong et al. 2022). These simulations242424Both studies
use general relativistic hydrodynamics and initial conditions from the stellar
code MESA. show a critical value greater than the one adopted from studies at
$M_{\bullet}\,=\,10^{6}\,\mathrm{M_{\odot}}$, namely
$\beta_{c}\,{\sim}\,10\,{/}\,3\,{>}47\,{/}\,19.1$, making the fraction of full
disruptions even smaller and this correction greater. Furthermore, this
correction factor can be a few tens ($>1$ dex), as demonstrated by the self-
consistent work on partial disruption events by Bortolas et al. (2023). By
visual inspection, in the optical sample of Yao et al. (2023) there are more
than a few light curves that show a re-flaring activity, instead of a
monotonic drop of luminosity. Caution should be drawn when comparing model
event rates with samples of TDEs.