BIELEFELD UNIVERSITY FACULTY OF PHYSICS MASTER THESIS Hypervelocity stars originating in the Andromeda galaxy as a probe of primordial black holes Author: Lukas Gulzow¨ [email protected] Bielefeld University Supervisors: Prof. Malcolm Fairbairn [email protected] King’s College London Prof. Dominik Schwarz [email protected] Bielefeld University Sunday 31st January, 2021 Contents 1. Introduction5 2. Black holes and dark matter6 2.1. Black holes . .6 2.2. Gravitational waves and their recent detection . .8 2.3. Dark matter . 10 3. Primordial black holes 15 3.1. Formation mechanisms . 16 3.2. Constraints on primordial black hole dark matter . 17 3.3. Phenomena possibly explained by primordial black holes . 18 4. Hypervelocity stars 19 4.1. Hypervelocity stars from outside the Milky Way . 20 4.2. Selection of Gaia data . 22 5. Ejection of stars from Andromeda 26 6. Description of the simulation 27 6.1. Equations of motion . 28 6.2. Acceleration and mass terms . 29 6.3. Mass of the Local Group . 31 6.4. Dynamics of the two galaxies . 33 6.5. Initial conditions for the hypervelocity stars . 35 6.6. Coordinate transformations of the simulation results . 37 7. Results and discussion 42 7.1. Distance and velocity distributions . 43 7.2. Positions and velocity directions . 51 8. Conclusion 64 Acknowledgements 65 References 66 A. Coordinate transformations of the Gaia data 76 B. Distribution of component velocities 79 C. Simulation code 82 Declaration of authenticity 84 3 1. Introduction A large part of the history of the Universe is also the history of dark matter. Ever since the first pieces of evidence for an invisible massive component of the energy density of the Universe were discovered [1, 2], there have been countless theories about its identity. Since then, many observations have been made to support the existence of dark matter [3, 4, 5, 6]. The attempts to learn more about dark matter have had varying levels of success, but to this day no consensus has been reached for any one theory. For a long time, weakly interacting massive particles (WIMPs) [7] were considered the prime candidate for dark matter. However, since none of many experiments have been able to detect them, they are falling out of favour [8]. Many other possibilities are being explored at the same time. They include axion [9, 10] and neutrino [11, 12] dark matter as well as candidates outside the realm of particle physics. This thesis investigates one such candidate, primordial black holes [13, 14, 15, 16]. A primordial black hole (PBH) is a theoretical kind of black hole that could have formed in the early Universe. PBHs were first considered by Hawking and Zeldovich in the 1970s [17, 18, 19]. If PBHs exist within galaxies, they are considered massive compact halo objects (MACHOs). MACHOs are objects in the halo of a galaxy that are not bound to any particular star. They typically emit only small amounts of radiation or none at all. Since PBHs form before Big Bang nucleosynthesis, they are considered non- baryonic [20]. Due to this property, they are dark matter candidates in a MACHO dark matter scenario. Even though we have no evidence for their existence, PBHs are useful for a number of reasons in addition to their potential as a dark matter candidate. Low mass PBHs are the only objects that could emit a detectable amount of Hawking radiation by evaporation [21]. This is useful to place constraints on models of the early Universe and presents a pos- sible explanation for certain phenomena, for example extragalactic [22, 23] and Galactic [24, 25] γ-ray backgrounds and γ-ray bursts [26, 27]. On the other hand, PBHs of higher mass that are not significantly affected by evaporation could serve as the seeds of super- massive black holes at the centres of galaxies [28, 29] or generate large-scale structure [30], amongst other things. However, it is important to note that all of these features have other possible explanations. In recent years, PBHs have become a more popular approach to explain dark matter [31, 32, 33] due to the detection of gravitational waves by LIGO/Virgo [34, 35]. The masses of the observed mergers of binary black holes are larger than expected and might be a sign of a significant population of PBHs with masses of order 10 M [31]. However, the most popular explanation considers the LIGO/Virgo detections to be the remnants of ordinary stars [36]. The topic of this thesis is inspired by a publication by Montanari, Barrado and Garc´ıa- Bellido on the topic of unbound hypervelocity stars (HVSs) and their connection to PBHs [37]. HVSs are stars that move with velocities of order 103 km=s. The HVSs we observe generally seem to originate in the inner parts of the Milky Way [38, 39]. Due to their high speed, they can be unbound to the Milky Way gravitational potential. Their origin is thought to be gravitational interactions with the supermassive black hole at the Galactic 5 centre (GC) [40, 41]. However, a small number of HVSs have trajectories pointing to- wards the Milky Way instead of away from it. This indicates a different point of origin [42]. As a possible explanation for this phenomenon, Montanari et al. [37] investigate the ejection of HVSs from nearby dwarf galaxies, globular clusters and the Andromeda galaxy caused by massive PBHs. For this purpose, they use data from the Gaia data release 2 (DR2) catalogue of the Gaia space telescope mission. The ejection mechanism as well as the specific PBH dark matter scenario were previously discussed by Clesse and Garc´ıa- Bellido [31, 32]. While Montanari et al. [37] mostly focus on HVSs from dwarf galaxies close to the Milky Way, this thesis lays its focus on HVSs ejected by massive PBHs within the An- dromeda galaxy. We randomly generate positions in the inner parts of Andromeda from which HVSs are ejected as well as velocity vectors just above escape velocity in ran- dom directions. We construct a dynamical simulation model of the gravitational system of Andromeda and the Milky Way in Python [43, 44, 45] and calculate the trajectory of each HVS in the potential of both galaxies. Trajectories sufficiently close to the Sun at present time t0 = 13:8 Gyr are analysed and the resulting data is transformed to Galactic coordinates. Similarly to Montanari et al. [37], we compare the trajectories to HVS data from the Gaia early data release 3 (eDR3) catalogue [46, 47, 48]. We transform th e Gaia data to Galactic coordinates as well. Finally, we evaluate the possibility of massive PBHs ejecting HVSs from Andromeda towards the Milky Way based on the results. Section 2 gives an overview about black holes, the recent LIGO/Virgo observations of binary black hole mergers, and dark matter. In Section 3 we introduce PBHs and dis- cuss possible formation mechanisms, the constraints on PBH abundance in various mass ranges as well as problems in cosmology that PBHs could provide solutions for. In Sec- tion 4 we introduce HVSs, present a concise summary of the paper by Montanari et al. [37] on unbound HVSs and discuss our own selection of HVS data from the Gaia eDR3 catalogue. Section 5 discusses the ejection process by which HVSs are ejected from the Andromeda galaxy. In Section 6 we give a detailed description of the calculations in- volved in the simulation model. The results of the simulation are presented and discussed in comparison with Gaia data in Section 7. We make concluding statements in Section 8. Appendix A details the transformation of Gaia velocity data to Galactic coordinates. Appendix B contains additional results on the component velocities of HVSs from both simulation and Gaia data. Appendix C gives a description of the code used for the simu- lation. 2. Black holes and dark matter 2.1. Black holes Black holes were first predicted as an exact solution of Einstein’s field equations of gen- eral relativity in 1916 by Schwarzschild [49]. However, only in the 1960s it was proven by Penrose and Hawking that black holes appear in the Universe naturally [50]. A black 6 Fig. 1. Image of the supermassive black hole at the centre of the M87 galaxy and its shadow by the Event Horizon Telescope Collaboration [53]. hole is a region of spacetime in which the gravitational potential is so high that nothing can escape it. Its spherical boundary is called the event horizon. The mass of a black hole is predicted by general relativity to be concentrated in a point-like singularity in the center of the event horizon. The event horizon of a non-rotating black hole lies at distance 2GM R = (2.1) S c2 to the singularity. Here, G is Newton’s constant of gravity, M is the mass of the black hole and c is the speed of light. The radius RS is called the Schwarzschild radius [49]. Since black holes do not emit visible light or measurable amounts of any other radiation, they are not directly observable. Stellar black holes are produced by gravitational collapse. At the end of the life cycle of a massive star, its remnant can collapse into a black hole if it has sufficient mass. If the mass of the remnant is not sufficiently large, it will collapse into a neutron star or white dwarf instead. Neutron stars can further collapse into black holes by accreting matter or merging with other stars, white dwarfs or neutron stars to reach the critical mass limit MT OV 2:3 M [51]. This limit is called the Tolman–Oppenheimer–Volkoff limit [52].