Western University Scholarship@Western Electronic Thesis and Dissertation Repository 4-6-2021 11:00 AM Formation of Supermassive Black Holes in the Early Universe Arpan Das, The University of Western Ontario Supervisor: Basu, Shantanu, The University of Western Ontario Co-Supervisor: Buchel, Alex, The University of Western Ontario A thesis submitted in partial fulfillment of the equirr ements for the Doctor of Philosophy degree in Astronomy © Arpan Das 2021 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Cosmology, Relativity, and Gravity Commons, External Galaxies Commons, and the Stars, Interstellar Medium and the Galaxy Commons Recommended Citation Das, Arpan, "Formation of Supermassive Black Holes in the Early Universe" (2021). Electronic Thesis and Dissertation Repository. 7712. https://ir.lib.uwo.ca/etd/7712 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. Abstract The aim of the work presented in this thesis is to understand the formation and growth of the seeds of the supermassive black holes in early universe. Supermassive black holes (SMBH) 8 with masses larger than 10 M have been observed when the Universe was only 800 Myr old. The formation and accretion history of the seeds of these supermassive black holes are a matter of debate. In the first part, considering the scenario of massive seed black hole formation which allows gas to directly collapse into a black hole (DCBH) of similar mass, we show that the mass function of SMBH can be described as a broken power-law with two characteristic features: (1) a power-law at intermediate masses whose index is the dimensionless ratio of the growth rate of the number of DCBH during their formation era, and the growth rate of DCBH masses by super-Eddington accretion during the DCBH growth era, (2) a break in the power law profile at high masses whose location is related to the duration of the period of DCBH growth. In the second part, we explore another possible pathway for the formation of SMBH seeds via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters. 3 5 9 These SMSs are born with masses 10 − 10 M which could grow into a few times 10 M supermassive black holes observed at I ∼ 7 via Eddington-accretion. We explore physically motivated accretion scenarios, e.g. Bondi–Hoyle–Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as a constant accretion. While gas is present, the accretion timescale remains considerably shorter than the timescale for collisions with the most massive object. However, the timescale for collisions between any two stars in the cluster can become comparable or shorter than the accretion timescale, hence collisions still play a relevant role. In addition, initial collisions will speed up the accretion process particularly in the Eddington and Bondi scenario. We also show that additional factors e.g., the upper IMF cut-off, the com- pactness of the cluster and mass loss during the collision might affect the final off the SMSs born. Finally, we study how the mass loss due to stellar will affect the formation of the SMSs in the NSCs, especially in high-metallicity environments using idealised N-body simulations. We adopt theoretical mass loss rates from the literature. Considering different accretion scenarios, we have studied the effect of the mass loss rates over a wide range of metallicities /∗ = ».001 − 1¼Z and Eddington factors 5Edd = !∗/!Edd = 0.5, 0.7, & 0.9. Keywords: cosmology: theory — dark ages, reionization, first stars — black hole physics — galaxies: high-redshift — quasars: supermassive black holes — galaxies:star clusters: general i Summary for lay audience Cutting-edge observations of the universe in the past decades have revealed the existence of supermassive black holes of masses up to a few billion times the mass of the Sun within the first billion years after the birth of the universe a.k.a the Big Bang. How these massive objects formed and grew over such a short time still remains one of the biggest puzzles in the field of astronomy. In the past decades, many different theories have been proposed. In this thesis, we study the formation and growth of these massive objects via two different scenarios. The first one is known as the direct collapse black hole scenario where a black hole can be formed directly without forming a normal star. The second model is the formation of these black holes via collisions between stars and gas accretion in a dense nuclear star cluster. Our results suggest that both the channels we have studied are viable for the growth of these observed supermassive black holes. ii Co-Authorship Statement The three papers that constitute this Thesis were co-authored with various collaborators. For the first paper in Chapter 1, I am the second author and Prof. Shantanu Basu is the first author. The idea and the model was proposed by Prof. Shantanu Basu. I applied the model to analyze the data. Both Shantanu Basu and I wrote the paper. I did approx- imately half of the work. This work was published in Astrophysical Journal Letters (url: https://iopscience.iop.org/article/10.3847/2041-8213/ab2646) on June 28th, 2019. For the project in Chapter 2, I am the principal author. I wrote the paper with the input from my collaborators. The idea of the paper was proposed by Prof. Dominik Schleicher, who is a co-author. The numerical code I used to build the model and produce the re- sults was based on the code by Tjarda Boekholt which was modified by me. Prof. Nathan Leigh, who is also a co-author, helped me to analyze the results. I did approximately three quarters of the work. The work was published in Monthly Notices of Royal Astronomical So- ciety (url: https://academic.oup.com/mnras/advance-article-abstract/doi/10. 1093/mnras/stab402/6133460) on Feb 11th, 2021. For the project in Chapter 3, I am the principal author. This is an extension of the project in Chapter 2 and the idea was proposed by Prof. Dominik Schleicher, who is a co-author. Prof. Shantanu Basu, who is also a co-author of this paper, helped me to write the paper by giving valuable inputs. I did approximately three quarters of the work. The work is submitted to Monthly Notices of Royal Astronomical Society on Feb 3rd, 2021. iii Dedicated to my father Pabitra Das and mother Nilima Das iv “The cosmos is within us. We are made of star-stuff. We are a way for the universe to know itself.’ - Carl Sagan v Contents Abstract i Summary for lay audience ii Co-Authorship Statement iii List of Figures viii List of Tables ix 1 Introduction1 1.0.1 Cosmic History.............................. 3 The Early Universe............................ 3 The Dark Ages.............................. 3 1.0.2 Formation of first structures ....................... 4 Epoch of Reionization (EoR)....................... 5 The Post-Reionization Epoch: ...................... 7 1.1 Introduction to Black Holes............................ 8 1.2 Space time metric around a black hole...................... 9 1.3 Accretion rate of black holes........................... 11 1.4 Accretion Disks.................................. 13 1.5 The first black holes in the universe ....................... 14 1.5.1 The problem of the early super-massive black holes........... 15 1.5.2 Stellar mass black hole seeds....................... 16 1.5.3 Formation of the first black holes .................... 17 1.5.4 Direct Collapsed Black Holes ...................... 17 1.6 Formation of SMBH in dense stellar clusters .................. 20 2 SMBH Mass Function 29 2.1 Introduction.................................... 29 2.2 Background.................................... 30 2.3 Mass Function................................... 32 2.4 The Quasar Luminosity Function......................... 34 2.5 Summary ..................................... 35 3 Formation of SMBH seeds in nuclear star clusters 41 vi 3.1 Introduction.................................... 41 3.2 Simulation Setup ................................. 46 3.2.1 Initial Conditions............................. 46 3.2.2 Mass-radius relation ........................... 47 3.2.3 Gas accretion............................... 48 3.2.4 Handling collisions............................ 51 3.2.5 Stability of numerical setup ....................... 51 3.3 Results....................................... 52 3.3.1 Reference run............................... 52 3.3.2 Dependence on the physical recipe for the accretion rate . 54 3.3.3 Collision vs accretion time scale..................... 58 3.3.4 Effect of the IMF............................. 63 3.3.5 Dependence on cluster radius ...................... 63 3.3.6 Effect of mass loss during collisions................... 67 3.3.7 Caveats.................................. 70 3.4 Summary and discussion............................. 70 4 Stellar winds and SMBH seed formation in NSCs 82 4.1 Introduction.................................... 82 4.2 Methodology ................................... 85 4.2.1 Initial conditions............................. 85 4.2.2 Stellar properties............................. 86 4.2.3 Gas accretion............................... 88 4.2.4 Stellar Collisions............................. 89 4.2.5 Mass loss due to stellar winds ...................... 89 4.3 Results....................................... 90 4.4