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Radiating Macroscopic Dark Matter RADIATING MACROSCOPIC DARK MATTER: SEARCHING FOR EFFECTS IN COSMIC MICROWAVE BACKGROUND AND RECOMBINATION HISTORY by SAURABH KUMAR Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics CASE WESTERN RESERVE UNIVERSITY January, 2021 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of Saurabh Kumar candidate for the degree of Doctor of Philosophy*. Committee Chair Dr. Glenn Starkman Committee Member Dr. Idit Zehavi Committee Member Dr. John Ruhl Committee Member Dr. Stacy McGaugh Date of Defense November 24, 2020 *We also certify that written approval has been obtained for any proprietary material contained therein. Contents List of Tables iii List of Figures iv Acknowledgments viii Abstract ix 1 Introduction 1 1.1 Evidence of Dark Matter . .3 1.2 Challenges to the CDM paradigm . .7 1.3 Candidates of Dark Matter . .8 1.4 Macroscopic dark matter or macros . 10 1.5 Constraints on parameter space of macros . 13 2 CMB Spectral Distortions from Cooling Macroscopic Dark Matter 17 2.1 Spectral Distortions in the CMB . 19 2.1.1 The Boltzmann equation . 21 2.1.2 Thermalization/Scattering mechanisms . 22 2.1.3 Types of Spectral Distortions . 26 2.2 Cooling processes for macros . 32 2.3 Conclusions . 44 i CONTENTS 3 Radiating Baryonic Macroscopic Dark Matter and the Recombina- tion history of the Universe 45 3.1 Physics of cosmic recombination . 46 3.2 Change in recombination history from macros . 59 3.3 Conclusions . 63 4 Conclusions 68 A Photon Luminosity and Internal Temperature of Macro 70 B Neutrino Emission Luminosity 73 ii List of Tables i 2.1 Definitions of various temperatures, T9, that appear in equations (2.66) and (2.67). For i = MU, DU, CP, the temperature values were de- termined by comparing the luminosities of various processes given by Eq. (2.58). 40 2.2 Definitions of various times, ti, that appear in equations (2.66) and (2.67). These time values very obtained by solving Eq. (2.66) for the most dominant cooling process. 42 iii List of Figures 1.1 Constraints on mass and cross-section of macros from cosmological and astrophysical phenomena. The white region in the lower right corner is ruled out because it is denser than black holes. The grey region is ruled out by CMB constraints [119]; the yellow from mica observation [29, 94]; the red from superbursts in NSs; the dark blue from white dwarfs becoming supernovae [44]; the purple from a lack of human injuries and deaths [107]; the green from a lack of fast-moving bolides [105]; the maroon from a lack of microlensing events toward the Large Magellanic Cloud and the Galactic center [9, 112, 19, 45], and in pink toward M31 [83]. Image credit: Figure 1 in arXiv:2006.01200v2, Journal reference [104]. 15 2.1 Measurements of the CMB spectrum. Image source: COBE webpage . 21 2.2 Multiple layers of a neutron star. Image credit: Figure 1 from arXiv:astro- ph/9906456v1, Journal reference [123]. 33 2.3 Interior temperature TX and surface temperature Ts of a macro for MX = M , λ = 1 and ρX = ρN , plotted versus time t and redshift z. Cooling is without DUrca, and both without CP and with CP for two values of Tc. The ambient photon temperature TCMB is shown for comparison, and the eras when µ and y distortions occur are indicated. 40 iv LIST OF FIGURES 2.4 Dominant cooling mechanisms in a neutron star at different tempera- tures. Bottom Panel: T = 109 K, Middle Panel: T = 3 × 108 K, Top Panel: T = 108 K. The figures on the left and right panel describe cooling for neutron stars that begin cooling via MURCA and DURCA respectively at high temperatures. In all figures, x-axis and the y-axis is the logarithm of the critical temperature of onset of superfluidity in neutrons and protons denoted by log10(Tcn) and log10(Tcp) respec- tively. In our work, we choose log10(Tcn) = log10(Tcp). We ignore all bremsstrahlung processes in our work since for our choice of macro parameters they are inefficient. Macro cooling is very well described by MURCA, DURCA and Cooper pair cooling. Image credit: Figure 13 in arXiv:astro-ph/9906456v1, Journal reference [123]. 41 2.5 Top panel: µ distortion as a function of macro surface composition factor λ for three different cooling scenarios. On the left, no DUrca, no CP; in the middle no DUrca, with CP; on the right; with DUrca, with CP. Green lines denote ρX = ρN , red lines 0:1ρN ; blue lines 10ρN . The 9 9 panels with CP show results for Tc = 10 K (dashed) and Tc = 4×10 K (solid). Bottom panel: as for top panel but for y distortion. The vertical dashed line stands for λ = 1 which is similar to a Neutron Star. 43 3.1 Helium I energy levels for n ≤ 4 and continuum. In practice, the three energy levels of the He I atom - ground state, first excited states and the continuum - very accurately describe Helium recombination. The dotted line shows that the triplet states are metastable states, they tend to hold charge and get ionized rather than decay into the ground state as is the case with singlet states. Image credit: Figure 8 from arXiv:astro-ph/9912182v2, Journal reference [102]. 54 v LIST OF FIGURES 3.2 Electron fraction as a function of redshift. Notice that at lower red- shifts the electron fraction value plateaus to few ×10−4. This happens because the net recombination rate falls below Hubble expansion rate. This plot was produced by solving the RECFAST code [101]. 57 3.3 Electron temperature as a function of redshift. Until redshift of z ∼ 200, the residual free electrons in the universe are in thermal equilib- < rium with the photons. For z ∼ 200, Hubble cooling becomes more effi- cient and the electron temperature drops below that of CMB. Coulomb scattering between electrons, and ionized and neutral hydrogen and he- lium always keeps baryons in thermal equilibrium with electrons. This plot was produced by solving the RECFAST code [101]. 58 3.4 Intensity spectrum of the CMB and photons emitted from macros of 9 three different masses at z = 1300. We used λ = 1, and TC = 10 K. In this plot, the spectrum from the 100 g macro is indistinguishable from a universe with no macros. The dashed, and dotted vertical lines stand for Lyman alpha and n = 2 ionization frequencies respectively. As we can see, at the two frequencies we are interested in, 3.4 eV and 10.2 eV, there is no significant excess of photons emitted from macros. The surplus at the Wein tail does not contribute in the excitation, and ionization processes since the cross-section of the Lyman Alpha excitation is sharply peaked at 10.2 eV, whereas that for the ionization rate falls off as ν−3 below 3.4 eV. 64 vi LIST OF FIGURES 3.5 The n = 2 ionization rates without macros, and solar mass macros compared to the Hubble rate, H(z). We can see that the excess photons from the macro surface enhance the rate of ionization only at lower < redshifts, z ∼ 500. However, by this redshift the ionization rate is below the Hubble rate. Therefore, the surplus 3.4 eV photons do not lead to excess ionization of excited hydrogen. 65 3.6 The ratio of Lyman alpha excitation rates in a universe with solar mass macros to that without any. We see that the largest enhancement in < < the excitation rate occurs at much lower redshifts between 40 ∼ z ∼ 200. Therefore, the surplus Lyman alpha photons from macros do not lead to any excess excitation of the ground state hydrogen atoms. 66 3.7 The EBL (Extragalactic Background Light) intensity compared to that of CMB and macro photons. The EBL background is plotted with permission from [41]. 67 vii Acknowledgments Firstly, I am immensely thankful to my advisor Prof. Glenn Starkman for his support, encouragement and feedback. I am indebted to him for introducing me to many great collaborators whom I worked with throughout my graduate program. I am also extremely thankful to Prof. Idit Zehavi. She was my co-advisor during the final year of my program. I am grateful for her support and patience. I thank my Particle Astrophysics Theory group friends for setting very high stan- dards which kept me motivated throughout my program. I specially thank my family in India for supporting me to pursue the less lucrative career path of academia. Last but not the least, I thank the faculty, friends, colleagues, and department assistants in physics for their help and support. viii Radiating Macroscopic Dark Matter: Searching for Effects in Cosmic Microwave Background and Recombination History Abstract by SAURABH KUMAR One of the most outstanding questions in fundamental physics is the nature of dark matter (DM). From multiple independent sources of evidence we infer that DM exists and constitutes nearly 85% of all matter in the universe. However, it is still not known what comprises the DM, how it is formed, and if and how it interacts non- gravitationally with Standard Model particles. In this dissertation, we are by and large concerned with the final question among the aforementioned list of puzzles, i.e., what signatures can DM leave in the observable universe? We propose a new mechanism by which DM can affect the early and late universe. The hot interior of a macroscopic DM, or macro, can behave as a heat reservoir so that energetic photons and neutrinos are emitted from its surface and interior respectively.
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