* [57] E. Del Gado, A Fierro, L. de Arcangelis, and A Coniglio.  A unifying model for chemical and colloidal gels.  Europhys. Lett., 63(1):1–7, July 2003.
  * [58] Ludovic Berthier and Giulio Biroli.  Theoretical perspective on the glass transition and amorphous materials.  Rev. Mod. Phys., 83(2):587–645, June 2011.
  * [59] S. Manley, Benny Davidovitch, Neil R. Davies, L. Cipelletti, A. E. Bailey, R. J. Christianson, U. Gasser, V. Prasad, P. N. Segre, M. P. Doherty, S. Sankaran, A. L. Jankovsky, B. Shiley, J. Bowen, J. Eggers, C. Kurta, T. Lorik, and D. A. Weitz.  Time-Dependent Strength of Colloidal Gels.  Phys. Rev. Lett., 95(4):048302, July 2005.
  * [60] Naveen Krishna Reddy, Zhenkun Zhang, M. Paul Lettinga, Jan K. G. Dhont, and Jan Vermant.  Probing structure in colloidal gels of thermoreversible rodlike virus particles: Rheology and scattering.  Journal of Rheology, 56(5):1153–1174, September 2012.
  * [61] Malcolm A. Faers, Tahsin H. Choudhury, Bobby Lau, Kevin McAllister, and Paul F. Luckham.  Syneresis and rheology of weak colloidal particle gels.  Colloids and Surfaces A: Physicochemical and Engineering Aspects, 288(1-3):170–179, October 2006.
  * [62] L Starrs, W C K Poon, D J Hibberd, and M M Robins.  Collapse of transient gels in colloid-polymer mixtures.  J. Phys.: Condens. Matter, 14(10):2485–2505, March 2002.
  * [63] Paul Bartlett, Lisa J. Teece, and Malcolm A. Faers.  Sudden collapse of a colloidal gel.  Phys. Rev. E, 85(2):021404, February 2012.
  * [64] M. Carpineti and M. Giglio.  Spinodal–Type Dynamics in Fractal Aggregation of Collodal Clusters.  Phys. Rev. Lett., 68:3327–3330, 1992.
  * [65] Luca Cipelletti, S. Manley, R. C. Ball, and D. A. Weitz.  Universal Aging Features in the Restructuring of Fractal Colloidal Gels.  Phys. Rev. Lett., 84(10):2275–2278, March 2000.
  * [66] Nynke A M Verhaegh, Daniela Asnaghi, and Henk N W Lekkerkerker.  Transient gels in colloid–polymer mixtures studied with uorescence confocal scanning laser microscopy.  Phys. A, page 11, 1999.
  * [67] Chaikin, P. M. and Lubeneksy, T. C.  Principles of Consdensed Matter Physics.  Cambridge University Press, 1995.
  * [68] Cahn, J, and Hilliard, J.  Free Energy of a Nonuniform System III. Nucleation in a Two–Component Incompressible Fluid.  J. Chem. Phys., 31:688–699, 1959.
  * [69] Andrea Cavagna.  Supercooled liquids for pedestrians.  Physics Reports, 476(4-6):51–124, June 2009.
  * [70] C. Patrick Royall and Stephen R. Williams.  The role of local structure in dynamical arrest.  Physics Reports, 560:1–75, February 2015.
  * [71] C Patrick Royall, Francesco Turci, Soichi Tatsumi, John Russo, and Joshua Robinson.  The race to the bottom: Approaching the ideal glass?  J. Phys.: Condens. Matter, 30(36):363001, September 2018.
  * [72] Ludovic Berthier and Mark D. Ediger.  Facets of glass physics.  Physics Today, 69(1):40–46, January 2016.
  * [73] Giulio Biroli and Juan P. Garrahan.  Perspective: The glass transition.  The Journal of Chemical Physics, 138(12):12A301, March 2013.
  * [74] Pablo G. Debenedetti and Frank H Stillinger.  Debenedetti, P. & Stillinger, F. Supercooled liquids and the glass transition.  Nature, 410:259–267, 2001.
  * [75] C. Patrick Royall, Francesco Turci, and Thomas Speck.  Dynamical phase transitions and their relation to structural and thermodynamic aspects of glass physics.  J. Chem. Phys., 153(9):090901, September 2020.
  * [76] Patrick Charbonneau, Jorge Kurchan, Giorgio Parisi, Pierfrancesco Urbani, and Francesco Zamponi.  Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions.  Annu. Rev. Condens. Matter Phys., 8(1):265–288, March 2017.
  * [77] S. Manley, H. M. Wyss, K. Miyazaki, J. C. Conrad, V. Trappe, L. J. Kaufman, D. R. Reichman, and D. A. Weitz.  Glasslike Arrest in Spinodal Decomposition as a Route to Colloidal Gelation.  Phys. Rev. Lett., 95(23):238302, December 2005.
  * [78] Peter J. Lu, Emanuela Zaccarelli, Fabio Ciulla, Andrew B. Schofield, Francesco Sciortino, and David A. Weitz.  Gelation of particles with short-range attraction.  Nature, 453(7194):499–503, May 2008.
  * [79] Emanuela Zaccarelli, Peter J Lu, Fabio Ciulla, David A Weitz, and Francesco Sciortino.  Gelation as arrested phase separation in short-ranged attractive colloid–polymer mixtures.  J. Phys.: Condens. Matter, 20(49):494242, December 2008.
  * [80] Samuel Griffiths, Francesco Turci, and C. Patrick Royall.  Local structure of percolating gels at very low volume fractions.  The Journal of Chemical Physics, 146(1):014905, January 2017.
  * [81] E. A. G. Jamie, R. P. A. Dullens, and D. G. A. L. Aarts.  Spinodal decomposition of a confined colloid-polymer system.  The Journal of Chemical Physics, 137(20):204902, November 2012.
  * [82] Christopher J. Fullerton and Ludovic Berthier.  Glassy behaviour of sticky spheres: What lies beyond experimental timescales?  ArXiv200714165 Cond-Mat, July 2020.
  * [83] Y. Gao and M. L. Kilfoil.  Direct Imaging of Dynamical Heterogeneities near the Colloid-Gel Transition.  Phys. Rev. Lett., 99(7):078301, August 2007.
  * [84] Clare J Dibble, Michael Kogan, and Michael J Solomon.  Structural origins of dynamical heterogeneity in colloidal gels.  Phys. Rev. E, 77:050401R, 2008.
  * [85] C. Patrick Royall, Stephen R. Williams, Takehiro Ohtsuka, and Hajime Tanaka.  Direct observation of a local structural mechanism for dynamic arrest.  Nature Mater, 7(7):556–561, July 2008.
  * [86] Isla Zhang, C. Patrick Royall, Malcolm A. Faers, and Paul Bartlett.  Phase separation dynamics in colloid–polymer mixtures: The effect of interaction range.  Soft Matter, 9(6):2076, 2013.
  * [87] A. van Blaaderen and P. Wiltzius.  Real-Space Structure of Colloidal Hard-Sphere Glasses.  Science, 270(5239):1177–1179, November 1995.
  * [88] Eric R Weeks, J C Crocker, Andrew C Levitt, Andrew Schofield, and D A Weitz.  Three-Dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition.  Science, 287:627, 2000.
  * [89] James E Hallett, Francesco Turci, and C Patrick Royall.  The devil is in the details: Pentagonal bipyramids and dynamic arrest.  J. Stat. Mech., 2020(1):014001, January 2020.
  * [90] T. S. Kuhn.  The Structure of Scientific Revolutions.  1962\.
  * [91] W. Goetze.  Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory.  Oxford Univ. Press, 2009.
  * [92] David R Reichman and Patrick Charbonneau.  Mode-coupling theory.  J. Stat. Mech., 2005(05):P05013, May 2005.
  * [93] G. Brambilla, D. El Masri, M. Pierno, L. Berthier, L. Cipelletti, G. Petekidis, and A. B. Schofield.  Probing the Equilibrium Dynamics of Colloidal Hard Spheres above the Mode-Coupling Glass Transition.  Phys. Rev. Lett., 102(8):085703, February 2009.
  * [94] James E. Hallett, Francesco Turci, and C. Patrick Royall.  Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations.  Nat Commun, 9(1):3272, December 2018.
  * [95] Liesbeth M. C. Janssen and David R. Reichman.  Microscopic Dynamics of Supercooled Liquids from First Principles.  Phys. Rev. Lett., 115(20):205701, November 2015.
  * [96] Adam, G. and Gibbs, J.  On the temperature dependence of relaxation phenomena in glass-forming liquids.  J. Chem. Phys., 43:139–146, 1965.
  * [97] Vassiliy Lubchenko and Peter G. Wolynes.  Theory of Structural Glasses and Supercooled Liquids.  Annu. Rev. Phys. Chem., 58(1):235–266, May 2007.
  * [98] Giorgio Parisi and Francesco Zamponi.  Mean-field theory of hard sphere glasses and jamming.  Rev Mod Phys, 82(1):57, 2010.
  * [99] G Tarjus, S A Kivelson, Z Nussinov, and P Viot.  The frustration-based approach of supercooled liquids and the glass transition: A review and critical assessment.  J. Phys.: Condens. Matter, 17(50):R1143–R1182, December 2005.
  * [100] David Chandler and Juan P. Garrahan.  Dynamics on the Way to Forming Glass: Bubbles in Space-Time.  Annu. Rev. Phys. Chem., 61(1):191–217, March 2010.
  * [101] Francesco Turci, C. Patrick Royall, and Thomas Speck.  Nonequilibrium Phase Transition in an Atomistic Glassformer: The Connection to Thermodynamics.  Phys. Rev. X, 7(3):031028, August 2017.
  * [102] Tina Hecksher, Albena I. Nielsen, Niels Boye Olsen, and Jeppe C. Dyre.  Little evidence for dynamic divergences in ultraviscous molecular liquids.  Nature Phys, 4(9):737–741, September 2008.
  * [103] Misaki Ozawa, Camille Scalliet, Andrea Ninarello, and Ludovic Berthier.  Does the Adam-Gibbs relation hold in simulated supercooled liquids?  J. Chem. Phys., 151(8):084504, August 2019.
  * [104] M E Cates, M Fuchs, K Kroy, W C K Poon, and A M Puertas.  Theory and simulation of gelation, arrest and yielding in attracting colloids.  J. Phys.: Condens. Matter, 16(42):S4861–S4875, October 2004.
  * [105] R. C. Ball, D. A. Weitz, T. A. Witten, and F. Leyvraz.  Universal kinetics in reaction-limited aggregation.  Phys. Rev. Lett., 58:274–277, 1987.
  * [106] K. Kroy, M. E. Cates, and W. C. K. Poon.  Cluster Mode-Coupling Approach to Weak Gelation in Attractive Colloids.  Phys. Rev. Lett., 92(14):148302, April 2004.
  * [107] A. P. R. Eberle, N. J. Wagner, and R. Castaneda-Priego.  Dynamical arrest transition in nanoparticle dispersions with short-range interactions.  Phys. Rev. Lett., 106:105704, 2011.
  * [108] M. Laurati, G. Petekidis, N. Koumakis, F. Cardinaux, A. B. Schofield, J. M. Brader, M. Fuchs, and S. U. Egelhaaf.  Structure, dynamics, and rheology of colloid-polymer mixtures: From liquids to gels.  J. Chem. Phys., 130(13):134907, April 2009.
  * [109] V Gopalakrishnan, K S Schweizer, and C F Zukoski.  Linking single particle rearrangements to delayed collapse times in transient depletion gels.  J. Phys.: Condens. Matter, 18(50):11531–11550, December 2006.
  * [110] N. J. Mewis, J. & Wagner.  Thixotropy.  Adv. Coll. Interf. Sci.,, 147–148:214–227, 2009.
  * [111] S M Fielding.  Shear banding in soft glassy materials.  Rep. Prog. Phys., 77(10):102601, October 2014.
  * [112] Daniel Bonn, Morton M. Denn, Ludovic Berthier, Thibaut Divoux, and Sébastien Manneville.  Yield stress materials in soft condensed matter.  Rev. Mod. Phys., 89(3):035005, August 2017.
  * [113] Alexandre Nicolas, Ezequiel E. Ferrero, Kirsten Martens, and Jean-Louis Barrat.  Deformation and flow of amorphous solids: Insights from elastoplastic models.  Rev. Mod. Phys., 90(4):045006, December 2018.
  * [114] Marjolein Dijkstra, Joseph M Brader, and Robert Evans.  Phase behaviour and structure of model colloid-polymer mixtures.  J. Phys.: Condens. Matter, 11(50):10079–10106, December 1999.
  * [115] Marjolein Dijkstra, Rene van Roij, and Robert Evans.  Effective interactions, structure, and isothermal compressibility of colloidal suspensions.  J Chem Phys, 113(11):9, 2000.
  * [116] Jade Taffs, Alex Malins, Stephen R Williams, and C Patrick Royall.  A structural comparison of models of colloid–polymer mixtures.  J. Phys.: Condens. Matter, 22(10):104119, March 2010.
  * [117] A D Dinsmore and D A Weitz.  Direct imaging of three-dimensional structure and topology of colloidal gels.  J. Phys.: Condens. Matter, 14(33):7581–7597, August 2002.
  * [118] G L Hunter and E R Weeks.  The physics of the colloidal glass transition.  Rep Prog Phys, page 31, 2012.
  * [119] Peter J Lu and David A. Weitz.  Colloidal Particles: Crystals, Glasses, and Gels.  Annu. Rev. Condens. Matter Phys., 4(1):217–233, April 2013.
  * [120] Peter J Yunker, Ke Chen, Matthew D Gratale, Matthew A Lohr, Tim Still, and A G Yodh.  Physics in ordered and disordered colloidal matter composed of poly( _N_ -isopropylacrylamide) microgel particles.  Rep. Prog. Phys., 77(5):056601, May 2014.
  * [121] Alfons van Blaaderen, Arnout Imhof, W. Hage, and A. Vrij.  Van Blaaderen, A.; Imhof, A.; Hage, W. & Vrij, A. Three-Dimensional Imaging of Submicrometer Colloidal Particles in Concentrated Suspensions Using Confocal Scanning Laser Microscopy.  Langmuir, 8:1514–1517, 1992.
  * [122] U. Gasser.  Real-Space Imaging of Nucleation and Growth in Colloidal Crystallization.  Science, 292(5515):258–262, April 2001.
  * [123] Jade Taffs, Stephen R. Williams, Hajime Tanaka, and C. Patrick Royall.  Structure and kinetics in the freezing of nearly hard spheres.  Soft Matter, 9:297–305, 2013.
  * [124] John C. Crocker and David G. Grier.  Methods of Digital Video Microscopy for Colloidal Studies.  Journal of Colloid and Interface Science, 179(1):298–310, April 1996.
  * [125] Mathieu Leocmach and Hajime Tanaka.  A novel particle tracking method with individual particle size measurement and its application to ordering in glassy hard sphere colloids.  Soft Matter, 9(5):1447–1457, 2013.
  * [126] Yongxiang Gao and Maria L. Kilfoil.  Accurate detection and complete tracking of large populations of features in three dimensions.  Opt. Express, 17(6):4685, March 2009.
  * [127] Matthew Bierbaum, Brian D. Leahy, Alexander A. Alemi, Itai Cohen, and James P. Sethna.  Light Microscopy at Maximal Precision.  Phys. Rev. X, 7(4):041007, October 2017.
  * [128] Rei Kurita and Eric R. Weeks.  Measuring every particle’s size from three-dimensional imaging experiments.  Nat Commun, 3(1):1127, January 2012.
  * [129] G. H. Koenderink, G. A. Vliegenthart, S. G. J. M. Kluijtmans, A. van Blaaderen, A. P. Philipse, and H. N. W. Lekkerkerker.  Depletion-Induced Crystallization in Colloidal Rod-Sphere Mixtures.  Langmuir, 15(14):4693–4696, July 1999.
  * [130] V. A. Tolpekin, M. H. G. Duits, D. van den Ende, and J. Mellema.  Aggregation and Breakup of Colloidal Particle Aggregates in Shear Flow, Studied with Video Microscopy.  Langmuir, 20(7):2614–2627, March 2004.
  * [131] E. H. A. de Hoog, W. K. Kegel, A. van Blaaderen, and H. N. W. Lekkerkerker.  Direct observation of crystallization and aggregation in a phase-separating colloid-polymer suspension.  Phys. Rev. E, 64(2):021407, July 2001.
  * [132] P. N. Pusey and van Megen, W.  Phase behaviour of concentrated suspensions of nearly hard colloidal spheres.  Nature, 320:340–342, 1986.
  * [133] Wilson C K Poon, Eric R Weeks, and C Patrick Royall.  On measuring colloidal volume fractions.  Soft Matter, 8:21–30, 2012.
  * [134] C. Patrick Royall, Wilson C. K. Poon, and Eric R. Weeks.  In search of colloidal hard spheres.  Soft Matter, 9(1):17–27, 2013.
  * [135] C P Royall, R van Roij, and A van Blaaderen.  Extended sedimentation profiles in charged colloids: The gravitational length, entropy, and electrostatics.  J. Phys.: Condens. Matter, 17(15):2315–2326, April 2005.
  * [136] C P Royall, M E Leunissen, and A van Blaaderen.  A new colloidal model system to study long-range interactions quantitatively in real space.  J. Phys.: Condens. Matter, 15(48):S3581–S3596, December 2003.
  * [137] Christian L. Klix, C. Patrick Royall, and Hajime Tanaka.  Structural and Dynamical Features of Multiple Metastable Glassy States in a Colloidal System with Competing Interactions.  Phys. Rev. Lett., 104(16):165702, April 2010.
  * [138] C. Patrick Royall.  Hunting mermaids in real space: Known knowns, known unknowns and unknown unknowns.  Soft Matter, 14(20):4020–4028, 2018.
  * [139] Djamel El Masri, Teun Vissers, Stephane Badaire, Johan C. P. Stiefelhagen, Hanumantha Rao Vutukuri, Peter Helfferich, Tian Hui Zhang, Willem K. Kegel, Arnout Imhof, and Alfons van Blaaderen.  A qualitative confocal microscopy study on a range of colloidal processes by simulating microgravity conditions through slow rotations.  Soft Matter, 8(26):6979, 2012.
  * [140] H Sedgwick, S U Egelhaaf, and W C K Poon.  Clusters and gels in systems of sticky particles.  J. Phys.: Condens. Matter, 16(42):S4913–S4922, October 2004.
  * [141] Andrew I. Campbell, Valerie J. Anderson, Jeroen S. van Duijneveldt, and Paul Bartlett.  Dynamical Arrest in Attractive Colloids: The Effect of Long-Range Repulsion.  Phys. Rev. Lett., 94(20):208301, May 2005.
  * [142] Anand Yethiraj and Alfons van Blaaderen.  A colloidal model system with an interaction tunable from hard sphere to soft and dipolar.  Nature, 421(6922):513–517, January 2003.
  * [143] I. Rios de Anda, A. Statt, F. Turci, and C.P. Royall.  Low-Density Crystals in Charged Colloids: Comparison with Yukawa Theory: Low-Density Crystals in Charged Colloids: Comparison with Yukawa Theory.  Contrib. Plasma Phys., 55(2-3):172–179, February 2015.
  * [144] M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, and P. M. Chaikin.  Electrostatics at the oil-water interface, stability, and order in emulsions and colloids.  Proceedings of the National Academy of Sciences, 104(8):2585–2590, February 2007.
  * [145] A. D. Dinsmore, V. Prasad, I. Y. Wong, and D. A. Weitz.  Microscopic Structure and Elasticity of Weakly Aggregated Colloidal Gels.  Phys. Rev. Lett., 96(18):185502, May 2006.
  * [146] Kun Zhao and Thomas G. Mason.  Directing Colloidal Self-Assembly through Roughness-Controlled Depletion Attractions.  Phys. Rev. Lett., 99(26):268301, December 2007.
  * [147] Peter J. Lu, Jacinta C. Conrad, Hans M. Wyss, Andrew B. Schofield, and David A. Weitz.  Fluids of Clusters in Attractive Colloids.  Phys. Rev. Lett., 96(2):028306, January 2006.
  * [148] Mirjam E. Leunissen.  Manipulating Colloids with Charge and Electric Fields.  PhD thesis, Utrecht, 2006.
  * [149] C Patrick Royall, Dirk G A L Aarts, and Hajime Tanaka.  Fluid structure in colloid–polymer mixtures: The competition between electrostatics and depletion.  J. Phys.: Condens. Matter, 17(45):S3401–S3408, November 2005.
  * [150] Jan Groenewold and Willem K. Kegel.  Anomalously Large Equilibrium Clusters of Colloids †.  J. Phys. Chem. B, 105(47):11702–11709, November 2001.
  * [151] Anna Stradner, Helen Sedgwick, Frédéric Cardinaux, Wilson C. K. Poon, Stefan U. Egelhaaf, and Peter Schurtenberger.  Equilibrium cluster formation in concentrated protein solutions and colloids.  Nature, 432(7016):492–495, November 2004.
  * [152] Anna Stradner.  Potential and limits of a colloid approach to protein solutions.  Soft Matter, page 17, 2020.
  * [153] Saskia Bucciarelli, Lucía Casal-Dujat, Cristiano De Michele, Francesco Sciortino, Jan Dhont, Johan Bergenholtz, Bela Farago, Peter Schurtenberger, and Anna Stradner.  Unusual Dynamics of Concentration Fluctuations in Solutions of Weakly Attractive Globular Proteins.  J. Phys. Chem. Lett., 6(22):4470–4474, November 2015.
  * [154] Saskia Bucciarelli, Jin Suk Myung, Bela Farago, Shibananda Das, Gerard A. Vliegenthart, Olaf Holderer, Roland G. Winkler, Peter Schurtenberger, Gerhard Gompper, and Anna Stradner.  Dramatic influence of patchy attractions on short-time protein diffusion under crowded conditions.  Sci. Adv., 2(12):e1601432, December 2016.
  * [155] Jin Suk Myung, Felix Roosen-Runge, Roland G. Winkler, Gerhard Gompper, Peter Schurtenberger, and Anna Stradner.  Weak Shape Anisotropy Leads to a Nonmonotonic Contribution to Crowding, Impacting Protein Dynamics under Physiologically Relevant Conditions.  J. Phys. Chem. B, 122(51):12396–12402, December 2018.
  * [156] Anuj Shukla, Efstratios Mylonas, Emanuela Di Cola, Stephanie Finet, Peter Timmins, Theyencheri Narayanan, and Dmitri I. Svergun.  Absence of equilibrium cluster phase in concentrated lysozyme solutions.  PNAS, 105(13):5075–5080, April 2008.
  * [157] F. Zhang, M. W. A. Skoda, R. M. J. Jacobs, S. Zorn, R. A. Martin, C. M. Martin, G. F. Clark, S. Weggler, A. Hildebrandt, O. Kohlbacher, and F. Schreiber.  Reentrant Condensation of Proteins in Solution Induced by Multivalent Counterions.  Phys. Rev. Lett., 101(14):148101, September 2008.
  * [158] Matti M. van Schooneveld, Volkert W. A. de Villeneuve, Roel P. A Dullens, Dirk G. A. L. Aarts, Mirjam E. Leunissen, and Willem K. Kegel.  Structure, Stability, and Formation Pathways of Colloidal Gels in Systems with Short-Range Attraction and Long-Range Repulsion.  J. Phys. Chem. B, 113(14):4560–4564, April 2009.
  * [159] Christian L. Klix, Ken-ichiro Murata, Hajime Tanaka, Stephen R. Williams, Alex Malins, and C. Patrick Royall.  Novel kinetic trapping in charged colloidal clusters due to self-induced surface charge organization.  Sci Rep, 3(1):2072, December 2013.
  * [160] Ronja F. Capellmann, Néstor E. Valadez-Pérez, Benedikt Simon, Stefan U. Egelhaaf, Marco Laurati, and Ramón Castañeda-Priego.  Structure of colloidal gels at intermediate concentrations: The role of competing interactions.  Soft Matter, 12(46):9303–9313, 2016.
  * [161] Takehiro Ohtsuka, C. Patrick Royall, and Hajime Tanaka.  Local structure and dynamics in colloidal fluids and gels.  Europhys. Lett., 84(4):46002, November 2008.
  * [162] F. Sciortino, P. Tartaglia, and E. Zaccarelli.  One-Dimensional Cluster Growth and Branching Gels in Colloidal Systems with Short-Range Depletion Attraction and Screened Electrostatic Repulsion.  J. Phys. Chem. B, 109(46):21942–21953, November 2005.
  * [163] M. Kohl, R. F. Capellmann, M. Laurati, S. U. Egelhaaf, and M. Schmiedeberg.  Directed percolation identified as equilibrium pre-transition towards non-equilibrium arrested gel states.  Nat Commun, 7(1):11817, September 2016.
  * [164] Jung Min Kim, Jun Fang, Aaron P. R. Eberle, Ramón Castañeda-Priego, and Norman J. Wagner.  Gel Transition in Adhesive Hard-Sphere Colloidal Dispersions: The Role of Gravitational Effects.  Phys. Rev. Lett., 110(20):208302, May 2013.
  * [165] David Richard, C. Patrick Royall, and Thomas Speck.  Communication: Is directed percolation in colloid-polymer mixtures linked to dynamic arrest?  The Journal of Chemical Physics, 148(24):241101, June 2018.
  * [166] Massimo G. Noro and Daan Frenkel.  Extended corresponding-states behavior for particles with variable range attractions.  The Journal of Chemical Physics, 113(8):2941–2944, August 2000\.
  * [167] W. van Megen, T. C. Mortensen, S. R. Williams, and J. Müller.  Measurement of the self-intermediate scattering function of suspensions of hard spherical particles near the glass transition.  Phys. Rev. E, 58(5):6073–6085, November 1998.
  * [168] F. Charles Frank.  Supercooling of Liquids.  Proc. R. Soc. A., 215:43–46, 1952.
  * [169] P. J. Steinhardt, David R. Nelson, and M. Ronchetti.  Bond-Orientational Order In Liquids And Glasses.  Phys. Rev. B, 28:784–805, 1983.
  * [170] Joshua F. Robinson, Francesco Turci, Roland Roth, and C. Patrick Royall.  Morphometric Approach to Many-Body Correlations in Hard Spheres.  Phys. Rev. Lett., 122(6):068004, February 2019.
  * [171] G. Meng, N. Arkus, M. P. Brenner, and V. N. Manoharan.  The Free-Energy Landscape of Clusters of Attractive Hard Spheres.  Science, 327(5965):560–563, January 2010.
  * [172] Alex Malins, Stephen R Williams, Jens Eggers, Hajime Tanaka, and C Patrick Royall.  Geometric frustration in small colloidal clusters.  J. Phys.: Condens. Matter, 21(42):425103, October 2009.
  * [173] Mark A. Miller, Jonathan P. K. Doye, and David J. Wales.  Structural relaxation in Morse clusters: Energy landscapes.  The Journal of Chemical Physics, 110(1):328–334, January 1999.
  * [174] Jonathan P. K. Doye, David J. Wales, and R. Stephen Berry.  The effect of the range of the potential on the structures of clusters.  The Journal of Chemical Physics, 103(10):4234–4249, September 1995\.
  * [175] S. Mossa and G. Tarjus.  Locally preferred structure in simple atomic liquids.  The Journal of Chemical Physics, 119(15):8069–8074, October 2003\.
  * [176] Jade Taffs, Alex Malins, Stephen R. Williams, and C. Patrick Royall.  The effect of attractions on the local structure of liquids and colloidal fluids.  The Journal of Chemical Physics, 133(24):244901, December 2010.
  * [177] C. Patrick Royall, Alex Malins, Andrew J. Dunleavy, and Rhiannon Pinney.  Strong geometric frustration in model glassformers.  Journal of Non-Crystalline Solids, 407:34–43, January 2015.
  * [178] Alex Malins, Jens Eggers, C. Patrick Royall, Stephen R. Williams, and Hajime Tanaka.  Identification of long-lived clusters and their link to slow dynamics in a model glass former.  The Journal of Chemical Physics, 138(12):12A535, March 2013.
  * [179] Alex Malins, Jens Eggers, Hajime Tanaka, and C. Patrick Royall.  Lifetimes and lengthscales of structural motifs in a model glassformer.  Faraday Discuss., 167:405, 2013.
  * [180] Alex Malins, Stephen R Williams, Jens Eggers, and C Patrick Royall.  Identification of structure in condensed matter with the topological cluster classification.  J Chem Phys, page 21, 2013.
  * [181] C. Patrick Royall, Stephen R. Williams, Takehiro Ohtsuka, Hajime Tanaka, Michio Tokuyama, Irwin Oppenheim, and Hideya Nishiyama.  Direct Observation of Low-Energy Clusters in a Colloidal Gel.  In AIP Conference Proceedings, volume 982, pages 97–101. AIP, 2008.
  * [182] L. C. Hsiao, R. S. Newman, S. C. Glotzer, and M. J. Solomon.  Role of isostaticity and load-bearing microstructure in the elasticity of yielded colloidal gels.  Proceedings of the National Academy of Sciences, 109(40):16029–16034, October 2012.
  * [183] Hideyo Tsurusawa, Mathieu Leocmach, John Russo, and Hajime Tanaka.  Gelation as condensation frustrated by hydrodynamics and mechanical isostaticity.  ArXiv180404370 Cond-Mat, April 2018.
  * [184] Kathryn A. Whitaker, Zsigmond Varga, Lilian C. Hsiao, Michael J. Solomon, James W. Swan, and Eric M. Furst.  Colloidal gel elasticity arises from the packing of locally glassy clusters.  Nat Commun, 10(1):2237, December 2019.
  * [185] David Richard, James Hallett, Thomas Speck, and C. Patrick Royall.  Coupling between criticality and gelation in “sticky” spheres: A structural analysis.  Soft Matter, 14(27):5554–5564, 2018.
  * [186] C. Patrick Royall, Dirk G. A. L. Aarts, and Hajime Tanaka.  Bridging length scales in colloidal liquids and interfaces from near-critical divergence to single particles.  Nature Phys, 3(9):636–640, September 2007.
  * [187] C. Patrick Royall, Ard A. Louis, and Hajime Tanaka.  Measuring colloidal interactions with confocal microscopy.  The Journal of Chemical Physics, 127(4):044507, July 2007.
  * [188] Hurley, M. M. and Harrowell, P.  Kinetic structure of a two-dimensional liquid.  Phys. Rev. E., 52:1694–1698, 1995.
  * [189] C. Patrick Royall, Jens Eggers, Akira Furukawa, and Hajime Tanaka.  Probing Colloidal Gels at Multiple Length Scales: The Role of Hydrodynamics.  Phys. Rev. Lett., 114(25):258302, June 2015.
  * [190] V Prasad, V Trappe, A D Dinsmore, P N Segre, L Cipelletti, and D A Weitz.  Universal features of the fluid to solid transition for attractive colloidal particles.  Faraday Discuss, page 12, 2003.
  * [191] Jan Maarten van Doorn, Joanne E. Verweij, Joris Sprakel, and Jasper van der Gucht.  Strand Plasticity Governs Fatigue in Colloidal Gels.  Phys. Rev. Lett., 120(20):208005, May 2018.
  * [192] Joanne E. Verweij, Frans A. M. Leermakers, Joris Sprakel, and Jasper van der Gucht.  Plasticity in colloidal gel strands.  Soft Matter, 15(32):6447–6454, 2019.
  * [193] Akira Furukawa and Hajime Tanaka.  Key Role of Hydrodynamic Interactions in Colloidal Gelation.  Phys. Rev. Lett., page 4, 2010.
  * [194] Hideyo Tsurusawa, Mathieu Leocmach, John Russo, and Hajime Tanaka.  Direct link between mechanical stability in gels and percolation of isostatic particles.  Sci. Adv., 5(5):eaav6090, May 2019.
  * [195] S. Manley, L. Cipelletti, V. Trappe, A. E. Bailey, R. J. Christianson, U. Gasser, V. Prasad, P. N. Segre, M. P. Doherty, S. Sankaran, A. L. Jankovsky, B. Shiley, J. Bowen, J. Eggers, C. Kurta, T. Lorik, and D. A. Weitz.  Limits to Gelation in Colloidal Aggregation.  Phys. Rev. Lett., 93(10):108302, September 2004.
  * [196] Hajime Tanaka, Yuya Nishikawa, and Takehito Koyama.  Network-forming phase separation of colloidal suspensions.  J. Phys.: Condens. Matter, 17(15):L143–L153, April 2005.
  * [197] Tian Hui Zhang, Jan Klok, R. Hans Tromp, Jan Groenewold, and Willem K. Kegel.  Non-equilibrium cluster states in colloids with competing interactions.  Soft Matter, 8(3):667–672, 2012.
  * [198] C. Patrick Royall.  Kinetic crystallisation instability in liquids with short-ranged attractions.  Molecular Physics, 116(21-22):3076–3084, November 2018.
  * [199] C. P. Royall and A. Malins.  The role of quench rate in colloidal gels.  Faraday Discuss., 158:301–311, 2012.
  * [200] Peter Sollich and Nigel B. Wilding.  Crystalline Phases of Polydisperse Spheres.  Phys. Rev. Lett., 104(11):118302, March 2010.
  * [201] Pieter Rein ten Wolde and Daan Frenkel.  Enhancement of Protein Crystal Nucleation by Critical Density Fluctuations.  Science, 277(5334):1975–1978, September 1997.
  * [202] J. R. Savage and A. D. Dinsmore.  Experimental Evidence for Two-Step Nucleation in Colloidal Crystallization.  Phys. Rev. Lett., 102(19):198302, May 2009.
  * [203] Shelley L Taylor, Robert Evans, and C Patrick Royall.  Temperature as an external field for colloid–polymer mixtures: ‘quenching’ by heating and ‘melting’ by cooling.  J. Phys.: Condens. Matter, 24(46):464128, November 2012.
  * [204] Hideyo Tsurusawa, John Russo, Mathieu Leocmach, and Hajime Tanaka.  Formation of porous crystals via viscoelastic phase separation.  Nat. Mater., 16(10):1022–1028, October 2017.
  * [205] W C K Poon and M M Robins.  Delayed sedimentation of transient gels in colloid–polymer mixtures : Dark-üeld observation, rheology and dynamic light scattering studies.  Faraday Discuss, page 12, 1999.
  * [206] Richard Buscall, Tahsin H. Choudhury, Malcolm A. Faers, James W. Goodwin, Paul A. Luckham, and Susan J. Partridge.  Towards rationalising collapse times for the delayed sedimentation of weakly-aggregated colloidal gels.  Soft Matter, 5(7):1345, 2009.
  * [207] Lisa J. Teece, James M. Hart, Kerry Yen Ni Hsu, Stephen Gilligan, Malcolm A. Faers, and Paul Bartlett.  Gels under stress: The origins of delayed collapse.  Colloids and Surfaces A: Physicochemical and Engineering Aspects, 458:126–133, September 2014.
  * [208] Roberto Piazza, Stefano Buzzaccaro, and Eleonora Secchi.  The unbearable heaviness of colloids: Facts, surprises, and puzzles in sedimentation.  J. Phys.: Condens. Matter, 24(28):284109, July 2012.
  * [209] Roberto Piazza.  Settled and unsettled issues in particle settling.  Rep. Prog. Phys., 77(5):056602, May 2014.
  * [210] Azaima Razali, Christopher J. Fullerton, Francesco Turci, James E. Hallett, Robert L. Jack, and C. Patrick Royall.  Effects of vertical confinement on gelation and sedimentation of colloids.  Soft Matter, 13(17):3230–3239, 2017.
  * [211] Stephen W. Kamp and Maria L. Kilfoil.  Universal behaviour in the mechanical properties of weakly aggregated colloidal particles.  Soft Matter, 5(12):2438, 2009.
  * [212] Malcolm A. Faers.  The importance of the interfacial stabilising layer on the macroscopic flow properties of suspensions dispersed in non-adsorbing polymer solution.  Advances in Colloid and Interface Science, 106(1-3):23–54, December 2003.
  * [213] M. Laurati, S. U. Egelhaaf, and G. Petekidis.  Nonlinear rheology of colloidal gels with intermediate volume fraction.  Journal of Rheology, 55(3):673–706, April 2011.
  * [214] Nick Koumakis, Esmaeel Moghimi, Rut Besseling, Wilson C. K. Poon, John F. Brady, and George Petekidis.  Tuning colloidal gels by shear.  Soft Matter, 11(23):4640–4648, 2015.
  * [215] P. A. Smith, G. Petekidis, S. U. Egelhaaf, and W. C. K. Poon.  Yielding and crystallization of colloidal gels under oscillatory shear.  Phys. Rev. E, 76(4):041402, October 2007.
  * [216] Neil Y. C. Lin, Jonathan H. McCoy, Xiang Cheng, Brian Leahy, Jacob N. Israelachvili, and Itai Cohen.  A multi-axis confocal rheoscope for studying shear flow of structured fluids.  Review of Scientific Instruments, 85(3):033905, March 2014.
  * [217] Lucio Isa, Rut Besseling, and Wilson C K Poon.  Shear Zones and Wall Slip in the Capillary Flow of Concentrated Colloidal Suspensions.  Phys. Rev. Lett., 98(19):198305, May 2007.
  * [218] Rahul Pandey, Melissa Spannuth, and Jacinta C. Conrad.  Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures.  JoVE J. Vis. Exp., (87):e51461, May 2014.
  * [219] Matthias Kohl and Michael Schmiedeberg.  Shear-induced slab-like domains in a directed percolated colloidal gel.  Eur. Phys. J. E, 40(8):71, August 2017.
  * [220] Eric M. Schwen, Meera Ramaswamy, Chieh-Min Cheng, Linda Jan, and Itai Cohen.  Embedding orthogonal memories in a colloidal gel through oscillatory shear.  Soft Matter, 16(15):3746–3752, April 2020.
  * [221] P. C. F. Møller, S. Rodts, M. A. J. Michels, and Daniel Bonn.  Shear banding and yield stress in soft glassy materials.  Phys. Rev. E, 77(4):041507, April 2008.
  * [222] Abdoulaye Fall, Jose Paredes, and Daniel Bonn.  Yielding and Shear Banding in Soft Glassy Materials.  Phys. Rev. Lett., 105(22):225502, November 2010.
  * [223] Joris Sprakel, Stefan B. Lindström, Thomas E. Kodger, and David A. Weitz.  Stress Enhancement in the Delayed Yielding of Colloidal Gels.  Phys. Rev. Lett., 106(24):248303, June 2011.
  * [224] Ming Han, Jonathan K. Whitmer, and Erik Luijten.  Dynamics and structure of colloidal aggregates under microchannel flow.  Soft Matter, 15(4):744–751, January 2019.
  * [225] Jacinta C. Conrad and Jennifer A. Lewis.  Structure of Colloidal Gels during Microchannel Flow.  Langmuir, 24(15):7628–7634, August 2008.
  * [226] Jacinta C. Conrad and Jennifer A. Lewis.  Structural Evolution of Colloidal Gels During Constricted Microchannel Flow.  Langmuir, 26(9):6102–6107, May 2010.
  * [227] Michael J. Solomon and Patrick T. Spicer.  Microstructural regimes of colloidal rod suspensions, gels, and glasses.  Soft Matter, 6(7):1391, 2010.
  * [228] T. Schilling, S. Jungblut, and Mark A. Miller.  Depletion-Induced Percolation in Networks of Nanorods.  Phys. Rev. Lett., 98(10):108303, March 2007.
  * [229] Andriy V. Kyrylyuk, Marie Claire Hermant, Tanja Schilling, Bert Klumperman, Cor E. Koning, and Paul van der Schoot.  Controlling electrical percolation in multicomponent carbon nanotube dispersions.  Nature Nanotech, 6(6):364–369, June 2011.
  * [230] H N W Lekkerkerker and Remco Tuinier.  Colloids and the Depletion Interaction, volume 833 of Lecture Notes in Physics.  2011\.
  * [231] Lilian C. Hsiao, Benjamin A. Schultz, Jens Glaser, Michael Engel, Megan E. Szakasits, Sharon C. Glotzer, and Michael J. Solomon.  Metastable orientational order of colloidal discoids.  Nat Commun, 6(1):8507, December 2015.
  * [232] Georgina M. H. Wilkins, Patrick T. Spicer, and Michael J. Solomon.  Colloidal System To Explore Structural and Dynamical Transitions in Rod Networks, Gels, and Glasses.  Langmuir, 25(16):8951–8959, August 2009.
  * [233] Rebecca Rice, Roland Roth, and C. Patrick Royall.  Polyhedral colloidal ‘rocks’: Low-dimensional networks.  Soft Matter, 8(4):1163–1167, 2012.
  * [234] Isla Zhang, Rattachai Pinchaipat, Nigel B Wilding, Malcolm A Faers, Paul Bartlett, Robert Evans, and C Patrick Royall.  Composition inversion in mixtures of binary colloids and polymer.  J Chem Phys, page 11, 2018.
  * [235] Michael E. Cates and Paul S. Clegg.  Bijels: A new class of soft materials.  Soft Matter, 4(11):2132, 2008.
  * [236] F. Varrato, L. Di Michele, M. Belushkin, N. Dorsaz, S. H. Nathan, E. Eiser, and G. Foffi.  Arrested demixing opens route to bigels.  Proceedings of the National Academy of Sciences, 109(47):19155–19160, November 2012.
  * [237] E. M. Herzig, K. A. White, A. B. Schofield, W. C. K. Poon, and P. S. Clegg.  Bicontinuous emulsions stabilized solely by colloidal particles.  Nature Mater, 6(12):966–971, December 2007.
  * [238] Mohammed Filali, Mohamed Jamil Ouazzani, Eric Michel, Raymond Aznar, Grégoire Porte, and Jacqueline Appell.  Robust Phase Behavior of Model Transient Networks.  J. Phys. Chem. B, 105(43):10528–10535, November 2001.
  * [239] S L Fussell, C P Royall, and J S van Duijneveldt.  Controlling phase separation in microgel-polymeric micelle mixtures using variable quench rates.  Soft Matter, page 12, 2021.
  * [240] Alice Blumlein and Jennifer J. McManus.  Bigels formed via spinodal decomposition of unfolded protein.  J. Mater. Chem. B, 3(17):3429–3435, 2015.
  * [241] R. Cheng, I. Rios de Anda, T. W. C. Taylor, M. A. Faers, J. L. R. Anderson, A. M. Seddon, and C. P. Royall.  Protein–polymer mixtures in the colloid limit: Aggregation, sedimentation.  submitted to J. Chem. Phys., 2021.
  * [242] Clemens Bechinger, Roberto Di Leonardo, Hartmut Löwen, Charles Reichhardt, Giorgio Volpe, and Giovanni Volpe.  Active Particles in Complex and Crowded Environments.  Rev. Mod. Phys., 88(4):045006, November 2016.
  * [243] M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, Madan Rao, and R. Aditi Simha.  Hydrodynamics of soft active matter.  Rev. Mod. Phys., 85(3):1143–1189, July 2013.
  * [244] U Dassanayake, S Fraden, and A van Blaaderen.  Structure of electrorheological fluids.  J. Chem. Phys., 112:3851–3858, 2000.
  * [245] Stefano Aime, Laurence Ramos, and Luca Cipelletti.  Microscopic dynamics and failure precursors of a gel under mechanical load.  PNAS, 115(14):3587–3592, April 2018.
  * [246] R. Harich, T. W. Blythe, M. Hermes, E. Zaccarelli, A. J. Sederman, L. F. Gladden, and W. C. K. Poon.  Gravitational collapse of depletion-induced colloidal gels.  Soft Matter, 12(19):4300–4308, 2016.
  * [247] Zsigmond Varga and James Swan.  Hydrodynamic interactions enhance gelation in dispersions of colloids with short-ranged attraction and long-ranged repulsion.  Soft Matter, 12(36):7670–7681, 2016.
  * [248] R. J. Allen, C. Valeriani, and P. Rein ten Wolde.  Forward flux sampling for rare event simulations.  J. Phys. Cond. Matt., 21:463102, 2009.
  * [249] Patrick Charbonneau, Jorge Kurchan, Giorgio Parisi, Pierfrancesco Urbani, and Francesco Zamponi.  Fractal free energy landscapes in structural glasses.  Nat Commun, 5(1):3725, September 2014.
  * [250] Natsuda Klongvessa, Félix Ginot, Christophe Ybert, Cécile Cottin-Bizonne, and Mathieu Leocmach.  Active Glass: Ergodicity Breaking Dramatically Affects Response to Self-Propulsion.  Phys. Rev. Lett., 123(24):248004, December 2019.


# Evidence for Episodic Black Hole Growth of Reionization-Era Quasars observed
with Magellan/FIRE

Leah Bigwood,1,2 Anna-Christina Eilers,3 Robert A. Simcoe,3
1 Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
2 Institute of Astronomy, Madingley Road, Cambridge, CB3 OHA
3 MIT Kavli Institute for Astrophysics and Space Research, 77 Massachusetts
Ave., Cambridge, MA 02139, USA
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Observations of high-redshift quasars hosting billion solar mass black holes
at $z\gtrsim 6$ challenge our understanding of early supermassive black hole
(SMBH) growth. In this work, we conduct a near-infrared spectroscopic study of
$19$ quasars at $6.2\lesssim z\lesssim 7.5$, using the Folded-port InfraRed
Echellette (FIRE) instrument on the $6.5$-meter Magellan/Baade Telescope. We
estimate the single-epoch masses of the quasars’ SMBHs by means of the Mg ii
emission line and find black hole masses of
$M_{\text{BH}}\approx(0.2-4.8)\,\times\,10^{9}\,M_{\odot}$. Furthermore, we
measure the sizes of the quasars’ proximity zones, which are regions of
enhanced transmitted flux bluewards of the Ly$\alpha\,$emission line, ionized
by the quasars’ radiation itself. While it has been shown that the proximity
zone sizes correlate with the quasars’ lifetimes due to the finite response
time of the intergalactic medium to the quasars’ radiation, we do not find any
correlation between the proximity zone sizes and the black hole mass, which
suggests that quasar activity and the concomitant black hole growth are
intermittent and episodic.

###### keywords:

quasars: supermassive black holes – quasars: emission lines – methods: data
analysis

††pubyear: 2024††pagerange: Evidence for Episodic Black Hole Growth of
Reionization-Era Quasars observed with Magellan/FIRE–A

##  1 Introduction

Quasars are the most luminous, non-transient sources in the observable
Universe, and thus they have been observed well into the epoch of
reionization. To date more than $200$ quasars above a redshift of $z\gtrsim 6$
have been discovered (Fan et al., 2022), with the current redshift-record
holder at $z=7.64$ (Wang et al., 2021), which is at a time when the universe
is only $\approx 700$ Myr old. It is well established that their emission is
powered by the accretion of material onto a central super-massive black hole
(SMBH) from the surrounding accretion disk (e.g. Salpeter, 1964; Lynden-Bell,
1969; Kormendy & Richstone, 1995; Richstone et al., 1998). Analyses of the
quasars’ rest-frame UV and optical spectra, including those discovered in the
reionization era, have demonstrated that the quasars host SMBHs with masses
exceeding $M_{\text{BH}}\sim 10^{9}M_{\odot}$ (e.g. Mortlock et al., 2011;
Mazzucchelli et al., 2017; Eilers et al., 2020).

The existence of billion solar mass SMBHs at high redshifts challenge our
understanding of black hole growth due to the short amount of cosmic time
available to reach such masses. It has been argued that in order to grow such
SMBHs from a constant supply of fuelling material, the stellar remnant seeds
must have masses of order $M_{\mathrm{BH}}\sim 100$ $M_{\odot}$ and of order
$t_{\mathrm{Q}}\sim 10^{9}$ years of quasar activity, i.e. when the SMBH’s
active accretion is powering the quasar’s UV luminosity, is required, even if
accretion is continuous at the Eddington limit (Volonteri, 2012). Given that
this time is comparable to the age of the Universe for quasars observed at
$z>6$, constraining the timescale that quasars are active is imperative to
understanding whether these objects exacerbate the challenges in the theory of
SMBH formation and growth.

However, measuring the timescales of quasar activity has proven to be
challenging, even for objects at lower redshift. At $z\sim 2\mathrm{-}4$, weak
constraints of $t_{\mathrm{Q}}\sim 10^{6}\mathrm{-}10^{9}$ years have been
obtained by means of the spatial clustering of quasars and the inferred
abundance of their host dark matter halos. This relies on the idea that rarer
objects tend to be highly biased tracers of the underlying dark matter
distribution. Therefore, a comparison of the number density of quasars to the
abundance of their host dark matter halos provides an estimate of the duty
cycle of luminous quasars (e.g. Haiman & Hui, 2001; Martini & Weinberg, 2001).
A further study of local early-type galaxies by Yu & Tremaine (2002)
constrained $t_{\mathrm{Q}}\sim(3-13)\times 10^{7}$ years, which was estimated
under the assumption that if black hole growth predominantly takes place
during optically bright quasar phases, the quasar luminosity function should
be reflective of the gas accretion history of local black holes. Spectroscopic
studies have also provided additional constraints by detecting changes in
quasar luminosities, and therefore ionisation rates, and the time-lag to the
resulting change in the intergalactic medium’s (IGM) opacity. This method has
resulted in estimates in the range $t_{\mathrm{Q}}\sim 10^{5}\mathrm{-}10^{7}$
years (e.g Adelberger, 2004). Tighter constraints on the timescale of quasar
activity, and estimates for the objects at higher redshift which challenge
current SMBH formation theory, are clearly necessary to progress our
understanding.

For quasars at $z\gtrsim 5.5$ it has been shown that timescales of their
nuclear activity can be estimated by means of the size of their “proximity
zones” (see, e.g. Eilers et al., 2017; Davies et al., 2019a; Eilers et al.,
2021). Quasars ionize the surrounding IGM, which leads to a deficit of neutral
hydrogen and therefore reduced Ly$\alpha$ absorption. This results in a region
of enhanced transmitted flux in quasar spectra occurring immediately bluewards
of the Ly$\alpha$ emission line. Due to the finite response time of the IGM to
the ionizing radiation, the size of this region has a dependency on the amount
of time the quasar has been active. At $z\sim 6$ the recombination time of the
intergalactic medium to become sufficiently neutral to be opaque to Ly$\alpha$
photons is short, and thus the proximity zone sizes only reflect the time of
the last accretion episode. The situation changes with increasing redshift; at
$z\gtrsim 7$ the epoch of reionization is not yet complete and therefore the
IGM is increasingly neutral. This complicates the mapping from proximity zone
size to lifetime, with the integrated lifetime being measured as opposed to an
individual episode. The spectra of quasars in highly neutral IGM exhibit a
damping wing on the Ly$\alpha\,$ emission line predominantly due to the
intrinsic line width and the velocity dispersion of atoms (Miralda-Escudé,
1998; Davies et al., 2019b; Simcoe et al., 2012). The damping wing has thus
far only been observed in objects at $z>7$ (e.g. Greig et al., 2017; Davies et
al., 2018a; Yang et al., 2020). In this work we measure the proximity zone
sizes of objects at $z<7$, where we expect the IGM to already be mostly
ionized. As a result, we hereinafter define the ‘lifetime’ of a quasar as the
time elapsed since the current luminous phase began, since this is the
timescale the proximity zone size of $z\lesssim 7$ quasars is sensitive to.

Previous studies of the proximity zones of observed reionization era quasars
have resulted in lifetime estimates to be as short as $t_{\mathrm{Q}}<10^{4}$
years (Eilers et al., 2021) with an average quasar lifetime of
$t_{\mathrm{Q}}\sim 10^{6}$ years (Morey et al., 2021). If SMBH growth occurs
in a single episode and only when the quasar is optically bright, this poses
the question of whether they form from more massive initial seeds, or whether
the accretion could happen in a radiatively inefficient manner. The simple
exponential light curves in which a quasar emits at a constant luminosity
throughout its entire lifetime, so-called “light-bulb” light curves, of
quasars has also been questioned, and in reality quasars may undergo multiple
episodes of luminous quasar activity with concurrent black hole growth,
alternated with quiescent phases (e.g. Novak et al., 2011a; Schawinski et al.,
2015a; Davies et al., 2020). This behaviour has been demonstrated in
hydrodynamical simulations, with episodic quasar lifetimes and intermittent
black hole growth being observed in works such as Novak et al. (2011b). A more
complete sample of masses and lifetimes for high redshift quasars is clearly
required in order to address these possibilities of their formation and
growth.

In this paper we carry out a spectroscopic study of $19$ quasars at
$6.17<z<7.51$. At these redshifts the rest-frame UV emission is shifted to the
near-infrared (NIR) wavelengths, hence we utilise the capabilities of the
Folded-port InfraRed Echellette (FIRE) instrument on the Magellan/Baade
Telescope to obtain NIR spectra of these quasars. We measure the sizes of
proximity zones for the quasars at $z<7$, noting that we leave the modelling
of the damping wing signature for the highest redshift objects for a companion
paper (Ďurovčíková et al., 2024). We also estimate the single epoch masses of
the host SMBH of all quasars in the sample by means of the Mg ii line. By
testing for correlation between these two measurements we suggest that quasar
activity is episodic and intermittent, and discuss obscured growth as a
resolution to the tension with SMBH formation and growth models.

Our paper is structured as follows: § 2 introduces the quasar sample and the
data reduction procedure. In § 3.1 we obtain single-epoch SMBH mass estimates,
as well as redshifts derived from the Mg ii line. We then determine the
continuum emission of each quasar in the Ly$\alpha\,$ forest in § 3.2, which
is required for the proximity zone measurements shown in § 3.3. We go on to
discuss the implications of our results on quasar lifetimes and SMBH growth in
§ 4. We summarize our findings in § 5. Throughout the manuscript we assume a
flat $\Lambda$CDM cosmology ($h=0.677$, $\Omega_{m}=0.307$) consistent within
the 1$\sigma$ results of Planck Collaboration et al. (2016).

##  2 Quasar Sample

The quasar sample contains $19$ quasars at $6.2\lesssim z\lesssim 7.5$
totalling more than 83 hours of observations with the FIRE instrument on the
$6.5$-meter Magellan/Baade Telescope, which were conducted between January
2021 and August 2022. All observations are obtained in Echelle mode using an
$0.6\arcsec$ slit. The details of the observations are shown in Table 1.

Table 1: Observational information for the quasars in our sample, as well as the best redshift estimate available in literature. We also list the absolute magnitudes $M_{1450}$ for the subset of quasars for which this is required to correct the proximity zone measurement (see § 3.3). Object | $z$ | $M_{1450}$ | Date |  $t_{\mathrm{exp}}$ [s]
---|---|---|---|---
J0020–3653 | 6.834 $\pm$ 0.001d | -26.92 | Jan 2021 | 3600
|  |  | Jun 2021 | 14400
|  |  | Oct 2021 | 10800
J0216–5226 | 6.41$\pm$0.05h | - | Jan 2021 | 9600
J0218+0007 | 6.7700 $\pm$ 0.0013c | -25.55 | Jan 2021 | 7200
|  |  | Dec 2021 | 9000
J0244–5008 | 6.724$\pm$0.001b | -26.72 | Jan 2021 | 4800
|  |  | Sep 2021 | 7200
|  |  | Oct 2021 | 10800
|  |  | Jan 2022 | 9000
J0252–0503 | 7.0006$\pm$ 0.0009c | - | Jan 2021 | 5400
|  |  | Sep 2021 | 2400
J036+03 | 6.5412$\pm$0.0018f | -27.4 | Aug 2022 | 7200
J0319–1008 | 6.8275 $\pm$ 0.0021c | -25.36 | Oct 2021 | 16200
J0410–4414 | 6.21$\pm$0.01b | -26.14 | Jan 2021 | 4800
J0411–0907 | 6.8260 $\pm$ 0.0007c | -26.58 | Nov 2021 | 15600
J0525–2406 | 6.5397 $\pm$ 0.0001c | -25.47 | Dec 2021 | 10800
J0910+1656 | 6.7289 $\pm$ 0.0005c | -25.34 | Mar 2021 | 12600
J0921+0007 | 6.5646 $\pm$ 0.0003c | -25.19 | Jan 2021 | 7200
|  |  | Apr 2021 | 4800
J1007+2115 | 7.5149 $\pm$ 0.0004c | - | Jan 2021 | 14400
|  |  | Mar 2021 | 7200
|  |  | Apr 2021 | 7200
J1104+2134 | 6.7662 $\pm$ 0.0009c | -26.63 | Jan 2021 | 9600
|  |  | Mar 2021 | 5400
|  |  | Apr 2021 | 9600
|  |  | Jun 2021 | 6000
J1217+0131 | 6.17$\pm$ 0.05e | -25.76 | Jun 2021 | 13200
J1526–2050 | 6.5864 $\pm$0.0005a | -27.20 | Jul 2021 | 9600
|  |  | Apr 2022 | 13800
J1535+1943 | 6.370 $\pm$ 0.001c | - | Apr 2021 | 8400
J2002–3013 | 6.6876 $\pm$ 0.0004c | -26.9 | Mar 2021 | 10200
|  |  | Apr 2021 | 4800
|  |  | Jul 2021 | 4200
J2102–1458 | 6.6645 $\pm$ 0.0002c | -25.53 | Apr 2021 | 4800

The spectra are homogeneously reduced using the open-source python-based
spectroscopic data reduction pipeline
PypeIt111https://github.com/pypeit/PypeIt version 1.7.1 (Prochaska et al.,
2020a). The details of this pipeline are described in Prochaska et al.
(2020b), but we will summarize them here briefly. In short, we obtain an on-
sky wavelength solution based on sky OH lines, and perform the sky subtraction
on the 2D images by differencing exposures dithered along the slit. We fit a
$b$-spline to further eliminate sky line residuals following Bochanski et al.
(2009). We then perform an optimal extraction (Horne, 1986) to obtain the 1D
spectra. All spectra are flux calibrated using sensitivity functions of
standard stars, ideally observed during the same night.

We co-add the flux-calibrated 1D spectra from each night and correct for
telluric absorption features by jointly fitting an atmospheric model and a
quasar model. The telluric model grids are produced using the Line-By-Line
Radiative Transfer Model (LBLRTM; Clough et al., 2005).

All reduced spectra are shown in Figure 3.

The best published redshift estimates for the majority of these quasars are
derived from the [C ii] 157.74 $\mu$m emission line. When this is not
available, the systematic redshifts are traced by the Mg ii emission line or
the extended Ly$\alpha\,$ emission. Table 1 lists the best redshift estimates
in the literature.

##  3 Analysis

###  3.1 Black Hole Mass Estimates

Under the assumption that the gravitational pull of the central black hole
dominates the dynamics in the broad line region (BLR) of the quasar, we can
apply the virial theorem. This allows an estimation of the black hole’s mass
to be obtained by means of the width of the broad emission lines arising from
the gas in the BLR and the luminosity output. We utilise the black hole mass
scaling relation of Vestergaard & Osmer (2009), i.e.

$\frac{M_{\text{BH}}}{M_{\odot}}=10^{6.86}\left(\frac{\text{FWHM}_{\text{MgII}}}{10^{3}\text{kms
}^{-1}}\right)^{2}\left(\frac{\lambda
L_{\lambda,3000\mbox{\AA}}}{10^{44}\text{ erg s}^{-1}}\right)^{0.5},$ (1)

which was calibrated to the existing H$\beta\,$ and C iv scaling relations
using several thousand high-quality quasar spectra from Sloan Digital Sky
Survey Data Release 3 (SDSS DR3) quasar sample ranging $0.08<z<5.41$. Here
FWHM${}_{\text{MgII}}$ is the full width at half maximum (FWHM) of the Mg ii
emission line and $L_{\lambda,3000\mbox{\AA}}$ is the monochromatic luminosity
at $\lambda=3000$ Å. The intrinsic $1\sigma$ scatter in the scaling relation
is approximately 0.55 dex.

We model the quasar emission in the spectral region
$2100\leq\lambda_{\text{rest}}\leq 3088$ Å as a superposition of a power law
continuum with slope $\alpha$ arising from the accretion disk, a scaled
template spectrum of the iron emission lines Fe ii and Fe iii in the BLR, as
well as a single Gaussian of variance $\sigma^{2}_{\text{Mg\,{ii}}}$ centred
on $\mu_{\text{Mg\,{ii}}}$ to model the Mg ii line, i.e.

$f_{\lambda}=a_{0}\cdot\left(\frac{\lambda}{2500}\right)^{-\alpha}+a_{1}\cdot
f_{\lambda,\text{iron}}+a_{2}\cdot\exp\left[{-\frac{(\lambda-\mu_{\text{Mg\,{ii}}})^{2}}{2\sigma^{2}_{\text{Mg\,{ii}}}}}\right]$
(2)

where $a_{0}$, $a_{1}$ and $a_{2}$ are the amplitudes of the individual
components. We use the iron template spectrum of Tsuzuki et al. (2006), which
was derived from a narrow emission line quasar. We note that we utilise the
template of Tsuzuki et al. (2006) over Vestergaard & Wilkes (2001), since the
former separates the Mg ii emission from the underlying Fe ii emission,
whereas the latter sets the Fe ii emission to zero in the region of the Mg ii
line. This resulted in the model of the quasar emission around the Mg ii line
showing a better quality of fit to the spectra in our sample. We however
caveat that the Vestergaard & Osmer (2009) scaling relation was constructed
using the iron template of Vestergaard & Wilkes (2001), and that Schindler et
al. (2020) demonstrated that using the Tsuzuki et al. (2006) template with
this scaling relation can bias SMBH masses low by $\sim 0.21$ dex. To mimic
the broad emission lines present in our quasars’ spectra, we convolve the iron
template with a Gaussian kernel of width FWHM $\approx$
FWHM${}_{\text{Mg\,{ii}}}$. Prior to fitting the model, we rescale the reduced
spectrum so that the integrated flux within the J-band is in agreement with
the reported magnitude J-band magnitude in literature, if available.

By means of the Markov chain Monte Carlo sampler emcee (Foreman-Mackey et al.,
2013), we estimate the free parameters of the model assuming flat priors and
adopt the mean of the posterior probability distribution as the best parameter
estimate. The monochromatic luminosity $L_{\lambda,3000}$ was determined by
estimating the flux at a rest-fram wavelength of $\lambda=3000$ Å from the
best-fit power law continuum. The best fits to the Mg ii emission lines for
each quasar in our sample are displayed in Figure 1, and the corresponding
mass estimates are listed in Table 2.

We measure the quasar redshift derived from the Mg ii emission line
$z_{\text{Mg\,{ii}}}$ using the estimations of the Gaussian centre,
$\mu_{\text{Mg\,{ii}}}$. Note that this emission does not arise from the host
galaxy (unlike the [C ii] line), and instead originates in the BLR. As a
result, the emission may experience modest velocity shifts with respect to the
systematic redshift of the quasar. The average shift with respect to the
quasar’s systematic redshift is $\Delta v(\text{Mg\,{ii}}\ -[\text{C\,{ii}}]\
)=391$ kms-1 (Schindler et al., 2020). The $z_{\text{Mg\,{ii}}}$ estimates are
listed in Table 2. We note that we measure the Mg ii derived redshift of
J0216-5226 to be $z_{\text{Mg\,{ii}}}=6.3283\pm 0.0094$, which is blueshifted
from the best available literature estimate of $z=6.41\pm 0.05$ (Yang et al.,
2019) by $\sim 3305$ kms-1. Yang et al. (2019) attained the measurement by
matching quasar template spectra to the Ly$\alpha\,$and N v emission lines,
noting that the offset of the Ly$\alpha\,$line with respect to the systematic
redshift is typically $\Delta v(\rm{Ly}\alpha\ -[\text{C\,{ii}}]\ )\sim 500$
kms-1. We therefore find that the estimated $z_{\text{Mg\,{ii}}}$ for this
object exhibits a blueshift in significant excess to the typical systematic
velocity offset.

Figure 1: The multi-component fits to the spectral region around the MgII
emission line, shown in the quasars rest-frame using the best redshift
estimate. The spectrum and its noise vector have been smoothed with a boxcar
function of width ten pixels, and are shown in black and grey respectively.
Regions of strong telluric absorption were removed, and further masking was
applied to broad absorption lines and noisy spikes, shown by the shaded grey
areas. The faint red curves show 100 draws from the posterior distribution of
the best-estimate model. The individual components are shown as the colored
curves: a power-law continuum (blue curve), the iron template spectrum
broadened to mimic the emission from the BLR (yellow curve), and a Gaussian to
model the Mg ii emission line (purple curve).

Several quasars in our sample overlap with those characterised previously in
Yang et al. (2021). Figure 2 compares the respective mass estimates obtained,
finding overall a reasonable agreement between the two studies within the
intrinsic scatter of the scaling relation.

Figure 2: Comparing the masses of host SMBHs estimated in this paper to those
obtained in Yang et al. (2021), for the quasars that are characterised in both
works. The errorbars displayed are purely statistical. There is an intrinsic
systematic scatter in $M_{\mathrm{BH}}$ of approximately 0.55 dex arising from
the scaling relation of Vestergaard & Osmer (2009).

###  3.2 Quasar Continuum

In order to measure the proximity zone we first require an estimate for the
quasar continuum emission in the Ly$\alpha\,$ forest. Residual neutral
hydrogen present in the IGM leads to significant absorption bluewards of the
Ly$\alpha\,$ emission line for the spectra of high redshift quasars.

We obtain the continuum estimate using a Principal Component Analysis (PCA;
e.g. Suzuki et al., 2005; Pâris, I. et al., 2011; Davies et al., 2018b). Due
to the absorption bluwards of Ly$\alpha\,$, we only fit to the ‘red’ side of
the spectra ($1220<\lambda_{\text{rest}}<2850$ Å), and then predict the
continuum emission on the ‘blue’ side ($1181<\lambda_{\text{rest}}<1220$ Å).
The ‘red’ and ‘blue’ PCA components, $R_{i}$ and $B_{i}$, are a set of ten and
six basis spectra respectively, obtained with a PCA decomposition of 12764
training spectra from the Sloan Digital Sky Survey Baryon Oscillation
Spectroscopic Survey (SDSS BOSS) sample into an orthogonal basis (Davies et
al., 2018b).

We obtain the rest-frame quasar spectra using the best available redshift
estimate, i.e. taking those derived from the Mg ii emission line in § 3.1 if
it improves upon the best previously published redshift estimate. We mask
spectral regions with significant atmospheric absorption, and normalise the
spectra to unity in a region free of significant emission lines at $1290\pm
2.5$ Å. To remove strong metal absorption lines from intervening absorption
systems along our line-of-sight we then fit a spline to the ‘red’ region of
the spectra, and remove outlying values by sigma clipping at the 3$\sigma$
level. We use emcee to estimate the 10 PCA coefficients for these components
in the ‘red’ spectral region, $r_{i}$, thus estimating the quasar continuum in
the logarithmic flux space as

$\log f_{\lambda}\approx\langle\log
f_{\lambda}\rangle+\sum_{i=1}^{10}r_{i}R_{i}$ (3)

where $\langle\log f_{\lambda}\rangle$ is the mean logarithmic flux. We also
fit for a redshift offset $\Delta z$, to account for offsets between the broad
emission lines and the systemic redshift. We chose flat priors for each free
parameter, taking the $5\sigma$ region for $r_{i}$ from the training set data
(see Davies et al., 2018b, for details) and $\Delta z\in[-0.15,0.03]$. We
adopt the mean of the resulting posterior probability distribution as the best
parameter estimate.

The best-estimate $r_{i}$ are then projected onto the coefficients of the blue
PCA components, $b_{j}$, using a projection matrix $P_{i,j}$ also determined
from the training spectra, i.e.

$b_{j}=\sum_{i=0}^{10}r_{i}P_{i,j}.$ (4)

We thus obtain a fit for the quasar continua over the entire spectral region
$1181<\lambda_{\text{rest}}<2850$ Å. Figure 3 present the continua estimates
for the quasars in our sample. We note that due to the lack of emission lines
in the spectra of J0216–5226 we cannot securely determine its continuum, and
therefore omit J0216–5226 from the remainder of the analysis. In Figure 6 we
enlarge the region showing the continuity of the red and blue continuum
reconstruction components in order to better demonstrate the quality of the
continuum reconstruction.

We note that J1535+1943 is heavily dust obscured, leading to an unusual
continuum slope. Hence, we caution that the continuum estimate might be biased
due to the lack of similar objects in the PCA training set. It would be
interesting to measure the proximity zone size and infer the quasar lifetime
for this obscured object, however simultaneous modelling of the quasar
continuum and the obscuration rate would be required. We therefore do not take
this object into account in the proximity zone analysis of the following
section and leave a full study of it for future work.

Figure 3: The spectra and best-fit continua model of the quasars in our
sample. We estimate the continua across the full spectral range by fitting 10
‘red’ principal components to the region $1220<\lambda_{\text{rest}}<2850$ Å
(red curve), and projecting onto a set of six ‘blue’ principal components
covering $1181<\lambda_{\text{rest}}<1220$ Å (blue curve). A boxcar smoothing
of 20 pixels has been applied to the spectrum (black) and its noise vector
(grey). We have removed regions of strong telluric absorption, and further
masking was applied to broad absorption lines and regions of high noise, shown
by the shaded grey areas. Labels in yellow denote objects for which we use the
continuum reconstruction in the proximity zone analysis of § 3.3. For these
objects we enlarge the region showing the continuity between the red and blue
continuum reconstruction components in Figure 6. We show the continua model of
J1535+1943 as a dashed curve due to its highly usual slope resulting from dust
obscuration.

###  3.3 Measuring Proximity Zone Sizes

We adopt the standard definition of the proximity zone used in previous
studies (e.g. Fan et al., 2006; Carilli et al., 2010; Eilers et al., 2020;
Satyavolu et al., 2023b). We normalise the rest-frame quasar spectra by the
continuum estimate, and apply a boxcar smoothing to the normalised flux of
width 20 Å in the observed wavelength frame. At $z=6$ this smoothing scale
corresponds to approximately $1$ pMpc or $700~{}\rm km\,s^{-1}$. The extent of
the proximity zone, $R_{\mathrm{p}}$, is defined as the region bluewards of
the Ly$\alpha\,$ emission line before the smoothed transmitted flux drops
below $10\%$. This follows the standard definition first adopted by Fan et al.
(2006), and utilised in other previous studies (e.g. Willott et al., 2007;
Mazzucchelli et al., 2017; Eilers et al., 2017). In Figure 4 we present the
smoothed continuum-normalised spectrum and show the extents of the proximity
zone sizes for our quasar sample. Note that damping wings in quasar spectra
have been detected in objects at $z>7$, imprinted by the high neutral fraction
of the IGM (Wang et al., 2020; Yang et al., 2020). As a result we exclude
proximity zone estimates for objects at $z>7$, since they would require
careful modeling of the neutral gas fraction in the proximity zone size, as
shown in previous work (e.g. Davies et al., 2019a; Greig et al., 2017).

The extents of the proximity zones are dependent on the luminosity of the
quasar, since a more luminous quasar will create more ionising radiation.
Thus, we also calculate the luminosity-corrected proximity zone size, $R_{\rm
p,\,corr}$, which has been shown to correlate with the quasar’s lifetime (e.g.
Eilers et al., 2017; Eilers et al., 2020; Morey et al., 2021). We adopt the
relation to eliminate the luminosity dependency introduced in Eilers et al.
(2017);

$R_{\rm p,\,corr}=R_{\rm p}\times 10^{-0.4(-27-M_{1450})/2.35}$ (5)

which normalises all proximity zone measurements to an absolute magnitude of
$M_{1450}=-27$. Table 2 records both the measured and magnitude-corrected
proximity zone sizes for our set of quasars.

Figure 4: The continuum-normalised spectra and proximity zones of the quasar dataset. The black and grey curves display the flux and its noise vector respectively, both smoothed with a boxcar function of width 5 pixels. The red curve shows the continuum-normalised spectra smoothed with a boxcar function of width 20 Å. As per the definition adopted in literature, the proximity zone extent is where this curve drops below the 10% flux level (yellow horizontal line). The proximity zone is shown as the shaded blue region, with the Ly$\alpha\,$ emission line shown as the solid blue vertical line and the proximity zone edge the dashed blue vertical line. Table 2: The columns show the name of the quasar, the best published redshift $z$, the measured uncorrected and magnitude-corrected proximity zone sizes, $R_{\rm p}$ and $R_{\rm p,\,{corr}}$, redshift estimates based on the Mg ii emission line $z_{\text{Mg\,{ii}}}$, the FWHM of the Gaussian fit to the Mg ii emission line FWHM${}_{\text{MgII}}$, the monochromatic luminosity $L_{\lambda,3000}$, and the SMBH mass estimates $M_{\mathrm{BH}}$. Object | $z$ |  $R_{\mathrm{p}}$ [pMpc] |  $R_{\rm p,\,{corr}}$ [pMpc] | $z_{\text{Mg\,{ii}}}$ | FWHM${}_{\text{MgII}}$ [Å] |  $L_{\lambda,3000}$ [$10^{43}$ erg s-1Å-1] |  $M_{\mathrm{BH}}$ [$10^{9}$ $M_{\odot}$]
---|---|---|---|---|---|---|---
J0020–3653† | 6.8340 $\pm$ 0.0010 | 1.70 $\pm$ 0.25 | 1.75 $\pm$ 0.26 | 6.8485 $\pm$ 0.0007 | 2727 $\pm$ 80 | 0.883 $\pm$ 0.008 | 0.88 $\pm$ 0.05
J0216–5226 | 6.4100 $\pm$ 0.0500 | - | - | 6.3288 $\pm$ 0.0098 | 4260 $\pm$ 936 | 0.837 $\pm$ 0.014 | 2.08 $\pm$ 0.92
J0218+0007 | 6.7700 $\pm$ 0.0013 | 1.17 $\pm$ 0.48 | 2.07 $\pm$ 0.84 | 6.7600 $\pm$ 0.0028 | 4350 $\pm$ 273 | 0.085 $\pm$ 0.003 | 0.69 $\pm$ 0.09
J0244–5008† | 6.7240 $\pm$ 0.0010 | 2.14 $\pm$ 0.28 | 2.39 $\pm$ 0.31 | 6.7240 $\pm$ 0.0008 | 3272 $\pm$ 78 | 0.609 $\pm$ 0.005 | 1.05 $\pm$ 0.05
J0252–0503 | 7.0006 $\pm$ 0.0009 | - | - | 6.9732 $\pm$ 0.0099 | 4905 $\pm$ 902 | 0.167 $\pm$ 0.006 | 1.24 $\pm$ 0.46
J0319–1008† | 6.8275 $\pm$ 0.0021 | 1.26 $\pm$ 0.16 | 2.39 $\pm$ 0.31 | 6.8246 $\pm$ 0.0005 | 2150 $\pm$ 47 | 0.742 $\pm$ 0.008 | 0.50 $\pm$ 0.02
J036+03† | 6.5412 $\pm$ 0.0018 | 3.20 $\pm$ 0.47 | 2.74 $\pm$ 0.40 | 6.5334 $\pm$ 0.0012 | 3480 $\pm$ 118 | 1.135 $\pm$ 0.009 | 1.62 $\pm$ 0.11
J0410–4414† | 6.2100 $\pm$ 0.0100 | 3.00 $\pm$ 0.92 | 4.21 $\pm$ 1.29 | 6.1759 $\pm$ 0.0022 | 3439 $\pm$ 332 | 0.602 $\pm$ 0.008 | 1.15 $\pm$ 0.22
J0411–0907 | 6.8260 $\pm$ 0.0007 | 3.68 $\pm$ 0.25 | 4.34 $\pm$ 0.30 | 6.8233 $\pm$ 0.0016 | 2686 $\pm$ 174 | 1.071 $\pm$ 0.015 | 0.94 $\pm$ 0.12
J0525–2406 | 6.5397 $\pm$ 0.0001 | 1.53 $\pm$ 0.04 | 2.79 $\pm$ 0.07 | 6.5372 $\pm$ 0.0022 | 2384 $\pm$ 200 | 0.438 $\pm$ 0.012 | 0.47 $\pm$ 0.08
J0910+1656 | 6.7289 $\pm$ 0.0005 | 0.89 $\pm$ 0.18 | 1.71 $\pm$ 0.35 | 6.7391 $\pm$ 0.0024 | 2517 $\pm$ 236 | 0.218 $\pm$ 0.008 | 0.37 $\pm$ 0.07
J0921+0007 | 6.5646 $\pm$ 0.0003 | 1.97 $\pm$ 0.11 | 4.01 $\pm$ 0.23 | 6.5669 $\pm$ 0.0008 | 1561 $\pm$ 87 | 0.321 $\pm$ 0.006 | 0.17 $\pm$ 0.02
J1007+2115 | 7.5149 $\pm$ 0.0004 | - | - | 7.5099 $\pm$ 0.0079 | 5376 $\pm$ 704 | 0.947 $\pm$ 0.025 | 3.53 $\pm$ 0.93
J1104+2134 | 6.7662 $\pm$ 0.0009 | 3.46 $\pm$ 0.33 | 4.00 $\pm$ 0.38 | 6.7731 $\pm$ 0.0018 | 4592 $\pm$ 205 | 0.391 $\pm$ 0.005 | 1.65 $\pm$ 0.15
J1217+0131† | 6.1700 $\pm$ 0.0500 | 3.74 $\pm$ 0.88 | 6.08 $\pm$ 1.43 | 6.2002 $\pm$ 0.0021 | 1717 $\pm$ 186 | 0.981 $\pm$ 0.009 | 0.37 $\pm$ 0.08
J1526–2050 | 6.5864 $\pm$ 0.0005 | 3.50 $\pm$ 0.19 | 3.23 $\pm$ 0.18 | 6.5729 $\pm$ 0.0014 | 5530 $\pm$136 | 1.559 $\pm$ 0.010 | 4.79 $\pm$ 0.24
J1535+1943 | 6.3700 $\pm$ 0.0010 | - | - | 6.3681 $\pm$ 0.0014 | 4375 $\pm$ 140 | 1.301 $\pm$ 0.006 | 2.74 $\pm$ 0.18
J2002–3013 | 6.6876 $\pm$ 0.0004 | 3.73 $\pm$ 0.15 | 3.88 $\pm$ 0.15 | 6.6764 $\pm$ 0.0011 | 3373 $\pm$ 99 | 8.285 $\pm$ 0.073 | 4.11 $\pm$0.24
J2102–1458 | 6.6645 $\pm$ 0.0002 | 2.41 $\pm$ 0.07 | 4.28 $\pm$ 0.13 | 6.6625 $\pm$ 0.0027 | 3001 $\pm$ 241 | 0.410 $\pm$ 0.009 | 0.72 $\pm$ 0.12

##  4 Discussion

To date, over 100 Mg ii-based SMBH mass estimates have been obtained for
quasars at $z>5.9$ (Fan et al., 2022). Previous studies such as Yang et al.
(2021), Farina et al. (2022) and Mazzucchelli et al. (2023) report SMBH masses
in the range $\sim(0.3-12.6)\times 10^{9}\,M_{\odot}$ for quasars observed in
the late stages of cosmic reionization. The mass estimates derived in this
work lie within $M_{\text{BH}}\approx(0.2-4.8)\,\times\,10^{9}\,M_{\odot}$,
and are thus broadly consistent with those reported in the literature. We note
that our sample does not include some of the heaviest SMBHs reported in the
literature exceeding $M_{\text{BH}}\gtrsim 10^{10}\,M_{\odot}$ (Wu et al.,
2015; Mazzucchelli et al., 2023).

For quasars at $z>5.7$, proximity zone sizes have thus far been measured in 87
objects. Satyavolu et al. (2023b) recently presented a study of 22 quasars at
$5.8<z<6.6$ and inferred proximity zones in the range $R_{\rm p}\sim 2-7$
pMpc. Work by Eilers et al. (2017) discovered three quasars with exceptionally
small proximity zones of $R_{\rm p,\,corr}<2$ pMpc, with Eilers et al. (2020)
finding a further four objects which meet this criteria. After considering
patchy reionization and proximate absorbers as causes for a potential
truncation of the proximity zone, they conclude that the most compelling
explanation for the extremely small proximity zone sizes are quasar lifetimes
as short as $t_{\mathrm{Q}}<10^{5}$ years. In this study, we measure
luminosity corrected proximity zones in the range $R_{\rm p,\,corr}\approx
1.7-6.1$ pMpc, consistent with the previous measurements in literature. We
find two objects (J0020–3653 and J0910+1656) with small proximity zones of
$R_{\rm p,\,corr}<2$ pMpc, potentially indicative of very young objects. In a
companion paper we obtain precise lifetime estimates for the quasars in our
sample (Ďurovčíková et al., 2024) to study their SMBH growth phases.

It is known that the size of proximity zones are correlated with quasars’ UV
luminous lifetimes, during which the black hole growth occurs (e.g. Salpeter,
1964; Soltan, 1982; Eilers et al., 2017; Khrykin et al., 2016; Davies et al.,
2020). With this in mind, if quasars were to have only one accretion episode,
i.e. a duty cycle of unity, and similar initial black hole seeds, we would
expect to find a correlation between proximity zone size and black hole mass.
In Figure 5 we test this scenario by showing the estimated SMBH masses against
the luminosity corrected proximity zone sizes. We find a Pearson correlation
coefficient of $r=0.054$, indicating no correlation between the two
measurements. This suggests that SMBHs likely grow in multiple accretion
episodes and that quasar light curves do not follow a simple light-bulb model,
as has been suggested in previous studies (e.g. Novak et al., 2011b;
Schawinski et al., 2015b; Davies et al., 2020; Satyavolu et al., 2023a).
However, short accretion episodes as implied by the small proximity zones
measured in quasars at $z\approx 6$ (e.g. Eilers et al., 2021) do not
alleviate, and in fact aggravate, the challenge of growing billion solar mass
black holes by $z\sim 6$. Recently, Satyavolu et al. (2023a) proposed the
solution that quasars may undergo phases of obscured growth, when the black
hole grows without emitting optical radiation along a given sightline. By
allowing black hole growth when the quasar isn’t optically bright, they
demonstrated that super-Eddington accretion is not necessarily a requirement
of achieving the black hole masses we observe at high redshift. This behaviour
has also been displayed in hydrodynamical simulations, with Bennett et al.
(2023) showing that simulated quasars hosting $\sim 10^{9}M_{\odot}$ black
holes at $z=6$ spend a significant amount of time with sightlines obscured in
the UV, as a result of surrounding dust and gas. Obscured growth therefore
provides a potential reconciliation between the short proximity zone sizes and
host SMBH masses measured for high redshift quasars, thus aiding the tension
in black hole formation and growth models.

It is important to note that our conclusions rely on the correlation between
proximity zone size and lifetime, which assumes that the quasars we measure at
$z<7$ reside in an ionised IGM. Although we do not detect the damping wing
signature of a neutral IGM in our sample, we cannot rule out the possibility
that patches of neutral hydrogen are still present around the quasars at
$z>6$. Future work will however account for this by modelling the reionization
of the IGM and attaining robust measurements of quasar lifetimes, better
informing us on the theories we have suggested.

Figure 5: Distribution of quasars in the plane of black hole mass and
luminosity-corrected proximity zone size. The FIRE quasar sample of this work
are shown by the circle markers. We also plot the measurements of Eilers et
al. (2020) (square markers) and Satyavolu et al. (2023b) and Mazzucchelli et
al. (2023) (diamond markers).

##  5 Summary

In this work, we present a new high redshift quasar sample obtained with FIRE
on the 6.5 Magellan/Baade telescope. All spectra, observed over more than 83
hours, are reduced homogeneously using the pipeline PypeIt version 1.7.1. We
estimate the black hole masses of this quasar set, and demonstrate that each
hosts a billion solar mass SMBH, as expected from previous high-$z$ quasar
studies. We also measure the proximity zone sizes of this quasar sample, since
they are known to correlate with the UV luminous quasar lifetimes. We do not
find a correlation between the luminosity corrected proximity zone sizes and
black hole masses, which suggests that quasar activity is episodic and
intermittent.

Future work will include detailed modeling of the quasars’ proximity zones,
including the damping wing signature. This will allow robust estimates of the
quasars’ lifetimes to be derived, in addition to the neutral fraction of the
IGM. Obtaining lifetime measurements will enable us to study the dependency
with black hole mass more robustly. We note however that given the lack of
correlation between proximity zone size and black hole mass found in this work
(Figure 5), we do not expect to find quasar lifetimes correlated with black
hole masses in future studies.

## Acknowledgements

The authors would like to thank the support astronomers and telescope
operators on Magellan for their help and support with the observations for
this work. Furthermore, we thank Frederick Davies for sharing his PCA
components for the quasar continuum modeling.

This paper includes data gathered with the 6.5 meter Magellan Telescopes
located at Las Campanas Observatory, Chile.

Leah Bigwood acknowledges funds from the The John (Jack) Simpson Greenwell
Memorial Fund issued by the College of St Hild and St Bede, Durham University.

## Data Availability

The reduced spectroscopic data is publicly available in Ďurovčíková et al.
(2024). The data reduction pipeline PypeIt is open source.

## References

  * Adelberger (2004) Adelberger K. L., 2004, ApJ, 612, 706
  * Bañados et al. (2015) Bañados E., Decarli R., Walter F., Venemans B. P., Farina E. P., Fan X., 2015, ApJ, 805, L8
  * Bennett et al. (2023) Bennett J. S., Sijacki D., Costa T., Laporte N., Witten C., 2023, arXiv e-prints, p. arXiv:2305.11932
  * Bochanski et al. (2009) Bochanski J. J., et al., 2009, Publications of the Astronomical Society of the Pacific, 121, 1409
  * Carilli et al. (2010) Carilli C. L., et al., 2010, ApJ, 714, 834
  * Clough et al. (2005) Clough S. A., Shephard M. W., Mlawer E. J., Delamere J. S., Iacono M. J., Cady-Pereira K., Boukabara S., Brown P. D., 2005, J. Quant. Spectrosc. Radiative Transfer, 91, 233
  * Davies et al. (2018a) Davies F. B., et al., 2018a, ApJ, 864, 143
  * Davies et al. (2018b) Davies F. B., et al., 2018b, The Astrophysical Journal, 864, 143
  * Davies et al. (2019b) Davies F. B., Hennawi J. F., Eilers A.-C., 2019b, ApJ, 884, L19
  * Davies et al. (2019a) Davies F. B., Hennawi J. F., Eilers A.-C., 2019a, The Astrophysical Journal Letters, 884, L19
  * Davies et al. (2020) Davies F. B., Hennawi J. F., Eilers A.-C., 2020, MNRAS, 493, 1330
  * Decarli et al. (2018) Decarli R., et al., 2018, ApJ, 854, 97
  * Eilers et al. (2017) Eilers A.-C., Davies F. B., Hennawi J. F., Prochaska J. X., Lukić Z., Mazzucchelli C., 2017, ApJ, 840, 24
  * Eilers et al. (2020) Eilers A.-C., et al., 2020, The Astrophysical Journal, 900, 37
  * Eilers et al. (2021) Eilers A.-C., Hennawi J. F., Davies F. B., Simcoe R. A., 2021, ApJ, 917, 38
  * Fan et al. (2006) Fan X., et al., 2006, AJ, 132, 117
  * Fan et al. (2022) Fan X., Banados E., Simcoe R. A., 2022, arXiv e-prints, p. arXiv:2212.06907
  * Farina et al. (2022) Farina E. P., et al., 2022, ApJ, 941, 106
  * Foreman-Mackey et al. (2013) Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125, 306
  * Greig et al. (2017) Greig B., Mesinger A., McGreer I. D., Gallerani S., Haiman Z., 2017, MNRAS, 466, 1814
  * Haiman & Hui (2001) Haiman Z., Hui L., 2001, ApJ, 547, 27
  * Horne (1986) Horne K., 1986, PASP, 98, 609
  * Khrykin et al. (2016) Khrykin I. S., Hennawi J. F., McQuinn M., Worseck G., 2016, ApJ, 824, 133
  * Kormendy & Richstone (1995) Kormendy J., Richstone D., 1995, ARA&A, 33, 581
  * Lynden-Bell (1969) Lynden-Bell D., 1969, Nature, 223, 690
  * Martini & Weinberg (2001) Martini P., Weinberg D. H., 2001, ApJ, 547, 12
  * Mazzucchelli et al. (2017) Mazzucchelli C., et al., 2017, ApJ, 849, 91
  * Mazzucchelli et al. (2023) Mazzucchelli C., et al., 2023, arXiv e-prints, p. arXiv:2306.16474
  * Miralda-Escudé (1998) Miralda-Escudé J., 1998, ApJ, 501, 15
  * Morey et al. (2021) Morey K. A., Eilers A.-C., Davies F. B., Hennawi J. F., Simcoe R. A., 2021, ApJ, 921, 88
  * Mortlock et al. (2011) Mortlock D. J., et al., 2011, Nature, 474, 616
  * Novak et al. (2011a) Novak G. S., Ostriker J. P., Ciotti L., 2011a, ApJ, 737, 26
  * Novak et al. (2011b) Novak G. S., Ostriker J. P., Ciotti L., 2011b, ApJ, 737, 26
  * Pâris, I. et al. (2011) Pâris, I. et al., 2011, A&A, 530, A50
  * Planck Collaboration et al. (2016) Planck Collaboration et al., 2016, A&A, 594, A13
  * Prochaska et al. (2020a) Prochaska J. X., et al., 2020a, pypeit/PypeIt: Release 1.0.0, Zenodo, doi:10.5281/zenodo.3743493
  * Prochaska et al. (2020b) Prochaska J., et al., 2020b, The Journal of Open Source Software, 5, 2308
  * Reed et al. (2017) Reed S. L., et al., 2017, MNRAS, 468, 4702
  * Reed et al. (2019) Reed S. L., et al., 2019, MNRAS, 487, 1874
  * Richstone et al. (1998) Richstone D., et al., 1998, Nature, 385, A14
  * Salpeter (1964) Salpeter E. E., 1964, ApJ, 140, 796
  * Satyavolu et al. (2023a) Satyavolu S., Kulkarni G., Keating L. C., Haehnelt M. G., 2023a, MNRAS, 521, 3108
  * Satyavolu et al. (2023b) Satyavolu S., et al., 2023b, MNRAS, 522, 4918
  * Schawinski et al. (2015a) Schawinski K., Koss M., Berney S., Sartori L. F., 2015a, MNRAS, 451, 2517
  * Schawinski et al. (2015b) Schawinski K., Koss M., Berney S., Sartori L. F., 2015b, MNRAS, 451, 2517
  * Schindler et al. (2020) Schindler J.-T., et al., 2020, ApJ, 905, 51
  * Simcoe et al. (2012) Simcoe R. A., Sullivan P. W., Cooksey K. L., Kao M. M., Matejek M. S., Burgasser A. J., 2012, Nature, 492, 79
  * Soltan (1982) Soltan A., 1982, MNRAS, 200, 115
  * Suzuki et al. (2005) Suzuki N., Tytler D., Kirkman D., O’Meara J. M., Lubin D., 2005, The Astrophysical Journal, 618, 592
  * Tsuzuki et al. (2006) Tsuzuki Y., Kawara K., Yoshii Y., Oyabu S., Tanabé T., Matsuoka Y., 2006, ApJ, 650, 57
  * Vestergaard & Osmer (2009) Vestergaard M., Osmer P. S., 2009, ApJ, 699, 800
  * Vestergaard & Wilkes (2001) Vestergaard M., Wilkes B. J., 2001, ApJS, 134, 1
  * Volonteri (2012) Volonteri M., 2012, Science, 337, 544
  * Wang et al. (2017) Wang F., et al., 2017, ApJ, 839, 27
  * Wang et al. (2020) Wang F., et al., 2020, ApJ, 896, 23
  * Wang et al. (2021) Wang F., et al., 2021, ApJ, 907, L1
  * Willott et al. (2007) Willott C. J., et al., 2007, AJ, 134, 2435
  * Wu et al. (2015) Wu X.-B., et al., 2015, Nature, 518, 512
  * Yang et al. (2019) Yang J., et al., 2019, AJ, 157, 236
  * Yang et al. (2020) Yang J., et al., 2020, ApJ, 897, L14
  * Yang et al. (2021) Yang J., et al., 2021, ApJ, 923, 262
  * Yu & Tremaine (2002) Yu Q., Tremaine S., 2002, MNRAS, 335, 965
  * Ďurovčíková et al. (2024) Ďurovčíková D., et al., 2024, arXiv e-prints, p. arXiv:2401.10328

##  Appendix A Quality of the Continuum Reconstruction

In order to better demonstrate the continuity of the red and blue continuum
reconstruction components, and thus the quality of the continuum
reconstruction, Figure 6 enlarges the region $1170<\lambda_{\text{rest}}<1350$
Å of Figure 3 for visual aid.

Figure 6: Same as Figure 3, but enlarging the region showing the continuity
between the red and blue continuum reconstruction components, in order to
better demonstrate the quality of the reconstruction. We only show the objects
for which we utilise the continuum reconstruction in the proximity zone
analysis.