Gravitationally Lensed, High-Redshift Starburst Galaxies and the CO(3-2) Transition for SPT0125-47 and SPT2134-50 Master’s Thesis in Physics MARKUS BREDBERG DEPARTMENT OF SPACE, EARTH AND ENVIRONMENT CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2022 www.chalmers.se www.chalmers.se Master’s thesis 2022 Gravitationally Lensed, High-Redshift Starburst Galaxies and the CO(3-2) Transition for SPT0125-47 and SPT2134-50 MARKUS BREDBERG Department of Space, Earth and Environment Division of Astronomy and Plasma Physics Chalmers University of Technology Gothenburg, Sweden 2022 Gravitationally Lensed, High-Redshift Starburst Galaxies and the CO(3-2) Transition for SPT0125-47 and SPT2134-50 MARKUS BREDBERG © MARKUS BREDBERG, 2022. Supervisor: Prof. Kirsten Kraiberg Knudsen, Department of Space, Earth and Environment Co-supervisor: Dr. Sabine König, Department of Space, Earth and Environment Co-supervisor: PhD student Kiana Kade Examiner: Assoc Prof. Magnus Thomasson, Department of Space, Earth and Environment Master’s Thesis 2022 Department of Space, Earth and Environment Division of Astronomy and Plasma Physics Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 76 393 3085 Cover: High-resolution, image plane reconstructions of SPT0125-47 (left) and SPT2134- 50 (right) produced by Visilens. Red areas show high intensity and blue areas low. Caustics are drawn in thin red lines. Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria Printed by Chalmers Reproservice Gothenburg, Sweden 2022 iv Gravitationally Lensed, High-Redshift Starburst Galaxies and the CO(3-2) Transition for SPT0125-47 and SPT2134-50 MARKUS BREDBERG Department of Space, Earth and Environment Chalmers University of Technology Abstract Local, massive galaxies are seen to host very old stellar populations. This indi- cates that a significant fraction of the stellar mass was formed during early epochs. The discovery of intense starburst galaxies at high redshifts have suggested that such galaxies are part of an evolutionary sequence towards today’s massive galax- ies. This master’s thesis provides an introductory theoretical background in the history and very basics of the study of galaxies, techniques and methods in ob- servational radio astronomy, and evolution of distant, massive galaxies. After this summary, two redshift z=2.5-2.8 sources, discovered by the South Pole Telescope (SPT), are analysed through the visibility-based lens modeling tool visilens. Spectra and galaxy-galaxy gravitational lensing models are obtained from ∼ 0.1′′ resolution data from the Atacama Large Millimeter/submillimeter Array of the CO(3-2) line from SPT0125-47 and SPT2134-50. Results indicate magnifications of µ = 15.4 ± 0.9 for SPT0125-47 and µ = 20.2 ± 2.9 for SPT2134-50. The cor- responding FWHMs are (380 ± 47) km s−1 and (550 ± 87) km s−1, which leads to intrinsic line luminosities L′CO(3−2) = (5.1 ± 0.84)1010 K km s−1 pc2 and L′CO(3−2) = (1.5± 0.31)1010 K km s−1 pc2, respectively. From previous derived relations, the gas masses are determined toMgas = (3.4±1.1)1010 M� andMgas = (1.6±0.49)1010 M� respectively. The molecular gas mass estimates are similar to dynamical estimates assuming rotation, which suggests that the inner region of these galaxies are gas- dominated. A skewed emission line and magnification for SPT0125-47 suggests that this source is either a rotating disc or a system of galaxy mergers. Keywords: Galaxies: high-redshift — Gravitational lensing: strong — Tech- niques: interferometric — Telescopes: ALMA v Acknowledgements It is with great appreciativeness that I hereby acknowledge the momentous help I have received throughout this thesis and the kind and skilful people behind it. My gratitude is firstly directed towards my supervisor Prof. Kirsten Kraiberg Knudsen for constantly feeding me ideas and inspiration, and supporting me in my work in every way I could ask for. I owe the project idea as well as much betterment to you. Secondly, I would like to thank my two co-supervisors, Sabine König and Kiana Kade for diligently assisting me with the imaging and gravitational lensing, respec- tively. Sabine, in particular, endured and responded well to many of my silly and inexpert questions while introducing programs for calibration and imaging. Kiana repeatedly managed to help me with things that was beyond her expertise, dedicat- ing much of her time and research skills for this aim. Without you my thesis would not have been. As this thesis is the culmination of my five year long studies at Chalmers, I must praise the school for offering no shortage in interesting options, both for the purpose of education and everything circumambient. The most important compo- nents of this are my friends. I would like to include my twin brother Joakim in this thankfulness for reminding me of the approaching opportunities. Thank you all, whatever the future brings. Markus Bredberg, Gothenburg, June 2022 vii We wish to pursue the truth no matter where it leads — but to find the truth, we need imagination and skepticism both. We will not be afraid to speculate, but we will be careful to distinguish speculation from fact. The cosmos is full beyond measure of elegant truths; of exquisite interrelationships; of the awesome machinery of nature. CARL SAGAN x Contents List of Acronyms xiii Nomenclature xv List of Figures xvii List of Tables xix 1 Introduction 1 1.1 A Very Brief History of Galaxies in the Universe . . . . . . . . . . . . 1 1.2 A Cosmological Timeline . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Through the Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Evolution of High-Redshift Galaxies 9 2.1 Types of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Hubble Classification . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.2 Colour Bimodality and the Star-Forming Main Sequence . . . 10 2.1.3 Starburst Galaxies . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.4 High-redshift Galaxies . . . . . . . . . . . . . . . . . . . . . . 14 2.2 First Stages in Star Formation . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1 Molecular Clouds Formation . . . . . . . . . . . . . . . . . . . 16 2.2.2 Molecular Gas Formation . . . . . . . . . . . . . . . . . . . . 17 2.2.3 Gravitational Contraction and Thermal Pressure . . . . . . . 17 2.2.4 The Virial Theorem with Turbulence and Magnetic Fields . . 18 2.2.5 The Equilibrium Model . . . . . . . . . . . . . . . . . . . . . . 19 2.2.6 Cosmic Star Formation History . . . . . . . . . . . . . . . . . 20 2.3 Galaxy Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.1 Galaxy Formation . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.2 Simulations of Galaxy Evolution . . . . . . . . . . . . . . . . . 24 2.3.3 Summary of Galaxy Evolution . . . . . . . . . . . . . . . . . . 26 3 Observations of Galaxies and Radio Astronomy 31 3.1 Observational Quantities . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Confusion and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 xi Contents 3.4.1 Carbon Monoxide Probing . . . . . . . . . . . . . . . . . . . . 35 3.4.2 High-Redshift Galaxies . . . . . . . . . . . . . . . . . . . . . . 37 3.4.3 Star Formation Rate . . . . . . . . . . . . . . . . . . . . . . . 38 3.5 Gravitational Lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.6 Principles of Interferometric Imaging . . . . . . . . . . . . . . . . . . 43 3.7 ALMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7.1 Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4 Methodology 51 4.1 ALMA Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4 Lens Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5 Results 57 5.1 Observational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 Gravitational Lens Models . . . . . . . . . . . . . . . . . . . . . . . . 58 6 Discussion 67 6.1 Analysis of Line Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.2 Mass Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.2.1 Dynamical Mass . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.2.2 Molecular Gas Mass . . . . . . . . . . . . . . . . . . . . . . . 69 6.2.3 Star Formation Rate . . . . . . . . . . . . . . . . . . . . . . . 69 6.3 Gravitational Lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.3.1 Reliability of Lens and Source Models . . . . . . . . . . . . . . 70 6.3.2 Double Gaussian Profile Fitting . . . . . . . . . . . . . . . . . 71 6.3.3 Other Potential Source Characteristics . . . . . . . . . . . . . 73 6.3.4 SPT0125-47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.3.5 SPT2134-50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 7 Conclusions and Outlook 77 Bibliography 79 A Models for Gravitational Lensing I A.1 Full Line Triangle Plots . . . . . . . . . . . . . . . . . . . . . . . . . I A.2 Samplings with Free Source Parameters . . . . . . . . . . . . . . . . . IV A.3 Samplings with Free Source Position Samplings . . . . . . . . . . . . VI B Coordinate Systems XI xii List of Abbreviations and Acronyms Below is the list of acronyms that have been used throughout this thesis listed in nearly alphabetical order: UV Ultraviolet (100-300 nm) NIR Near-InfraRed (780-2000 nm) MIR Mid-InfraRed (2-15 µm) FIR Far-InfraRed (15-1000µm) AGN Active Galactic Nucleus ALMA Atacama Large Millimeter/submillimeter Array CASA Common Astronomy Software Application CMB Cosmic Microwave Background DSFG Dusty Star-Forming Galaxy FWHM Full Width at Half Maximum GMC Giant Molecular Cloud HPBW Half Power Beam Width IMF Initial Mass Function ISM InterStellar Medium LBG Lyman Break Galaxy PA Position Angle PWV Precipitable Water Vapor RMS Root Mean Square (error) SED Spectral Energy Distribution SFG Star-Forming Galaxy SFH Star Formation History SFE Star Formation Efficiency SFMS Star Formation Main Sequence SFR Star Formation Rate sSFR specific Star Formation Rate SMBH SuperMassive Black Hole SNR Signal-to-Noise Ratio SPT South Pole Telescope VLBI Very Long Baseline Interferometry xiii Nomenclature Below is the nomenclature of constants, parameters and observables that have been used throughout this thesis. Constants c Speed of light G Newton’s gravitational constant kB Boltzmann’s constant h Planck’s constant Variables ν Frequency λ Wavelength z Redshift E Energy W , K, U , EM Gravitational, kinetic, internal and magnetic energy P , Pν Power, power density I, Iν Intensity, specific intensity S, Sν Flux, flux density T Temperature Tb, Ta, Td Brightness, antenna, and dust temperature L Luminosity Lline, L′line Line luminosity in L� and K km s−1 pc2 m, M Mass of a small region and large body respectively ρ, Σ Volume and surface mass density µ Magnification from gravitational lensing r, R Distance and radius v, σv Velocity and velocity dispersion A Area Ω Solid angle xv Contents e Ellipticity a, b Major and minor axis θE, αred Einstein angle and reduced deflection angle Dij, DL Angular diameter distance and luminosity distance Z Metallicity J Rotational level Φ(L)dL Number density of galaxies with luminosity between L and L+ dL fgas Gas mass fraction tff , tdep Free fall and depletion time scale xvi List of Figures 1.1 The Milky Way as seen from the Earth . . . . . . . . . . . . . . . . . 2 1.2 Schematic timeline of the Universe . . . . . . . . . . . . . . . . . . . 5 2.1 The Hubble sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Main sequence for star-forming galaxies . . . . . . . . . . . . . . . . . 12 2.3 Cosmic star formation history . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Schematic illustration of galaxy formation . . . . . . . . . . . . . . . 24 2.5 Schematic view of the cosmic cycle . . . . . . . . . . . . . . . . . . . 26 2.6 Galaxy evolution summarised . . . . . . . . . . . . . . . . . . . . . . 29 3.1 Trigonometric tool for gravitational lensing . . . . . . . . . . . . . . . 41 3.2 Example of gravitational lensing . . . . . . . . . . . . . . . . . . . . . 42 3.3 Process of obtaining uv-coverage . . . . . . . . . . . . . . . . . . . . . 45 3.4 Schematic illustration of phase shift in interferometry . . . . . . . . . 46 3.5 The interferometric process of imaging . . . . . . . . . . . . . . . . . 47 3.6 Atacama Large Millimeter/submillimeter Array . . . . . . . . . . . . 49 5.1 Moment-0 maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.2 Moment-1 maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.3 Line spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.4 Lens models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.5 Models for five regions of SPT0125-47 . . . . . . . . . . . . . . . . . . 62 5.6 Models for two regions of SPT0125-47 . . . . . . . . . . . . . . . . . . 63 5.7 Models for two regions of SPT2134-50 . . . . . . . . . . . . . . . . . . 63 5.8 Models for five regions of SPT2134-50 . . . . . . . . . . . . . . . . . . 64 6.1 Line spectra with double Gaussians . . . . . . . . . . . . . . . . . . . 71 A.1 Triangle plot for full line model of SPT0125-47 . . . . . . . . . . . . . II A.2 Triangle plot for full line model of SPT2134-50 . . . . . . . . . . . . . III A.3 Models for five bins of SPT0125-47 with fixed lens . . . . . . . . . . . V A.4 Models for two bins of SPT0125-47 with free source position . . . . . VI A.5 Models for five bins of SPT0125-47 with free source position . . . . . VII A.6 Models for two bins of SPT2134-50 with free source position . . . . . VIII A.7 Models for five bins of SPT2134-50 with free source position . . . . . IX B.1 The equatorial coordinate system . . . . . . . . . . . . . . . . . . . . XII xvii List of Figures xviii List of Tables 3.1 ALMA statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1 Positional information of observed SPT galaxies . . . . . . . . . . . . 51 4.2 Observational information of observed SPT galaxies . . . . . . . . . . 52 4.3 Spectral masks parameters . . . . . . . . . . . . . . . . . . . . . . . . 55 5.1 Spectral line parameters . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2 Lens parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3 Source parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.4 Source parameters of bins of SPT0125-47 . . . . . . . . . . . . . . . . 64 5.5 Source parameters of bins of SPT2134-50 . . . . . . . . . . . . . . . . 65 6.1 Intrinsic line properties . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.2 Source parameters in the case of two sources . . . . . . . . . . . . . . 72 6.3 Chi-square results for fitted functions . . . . . . . . . . . . . . . . . . 73 A.1 Noise of bins of SPT0125-47 . . . . . . . . . . . . . . . . . . . . . . . IV A.2 Noise of bins of SPT2134-50 . . . . . . . . . . . . . . . . . . . . . . . IV A.3 Noise of two free-source-position bins of SPT0125-47 . . . . . . . . . VI A.4 Noise of bins of five free-source-position bins SPT0125-47 . . . . . . . VI A.5 Noise of two free-source-position bins of SPT2134-50 . . . . . . . . . VII A.6 Noise of five free-source-position bins of SPT2134-50 . . . . . . . . . VIII xix List of Tables xx 1 Introduction If the history of the Universe was printed on a timeline stretching from the Moon to Earth, the first humans would appear around the tip of Mount Everest, the oldest astronomical records would soar some 150 meters above ground, and the introduction of galaxies would be within reach of a resilient jump. Today, with better and better telescopes, a increasingly clear view of this timeline is at our fingertips. Exciting times are ahead! Galaxies are the astronomical cells of the Universe. Their evolution is a com- plex interplay with their surrounding. In simplicity, this is modelled as the baryon cycle. Outside gas is accreted, cooled and converted into stars. Inside gas is heated and ejected from supernovae and jets in the active galactic nuclei phase of the cen- tral supermassive black hole. But the Universe is vast and complex. No galaxy is identical. This thesis is an attempt at studying this complexity. 1.1 A Very Brief History of Galaxies in the Universe Looking up at the night sky is enough of an explanation as to why astronomy is the oldest science on Earth. Mesopotamian records date 5000 years back. Yet, any stargazer in any era knows how much left there is to discover. Grouping stars together in constellation has kept humans busy since the end of the Paleolithic Era. An early proposition of the nature of our galaxy was made by pre-Socratic philosopher Democritus, saying that the bright band on the night sky (see Figure 1.1) could consist of many distant stars (Plutarch, 2006). This was proven first when Galileo Galilei pointed his telescope to this band in 1610 (Galilei, 1610). Our closest neighbouring galaxy, Andromeda, is actually several times the angular size of the moon. Therefore records of its detections date back to Persian astronomer Al-Sufi in the 10th century, describing it as a ’small cloud’. Ferdinand Magellan thought likewise when he, on a circumnavigation of the globe, found the Large and Small Megallanic clouds. New horizons opened up when, Christiaan Huygens in the mid-seventeenth century used the recently invented telescope to find new, fuzzy and diffuse systems on the sky (as described in Cimatti et al., 2019). Due to this appearance, they were named nebulae after the Latin word for mist. Naturally, speculations on what these 1 1. Introduction Figure 1.1: The bright, dusty band on the the night sky is actually the center of our Galaxy. Credit: NASA. nebulae were followed. In 1750, Thomas Wright likened them with our Galaxy1, suggesting that they were distant, flat, rotating layers of stars, held together by gravity. This idea of ’island universes’ was expanded by philosopher Immanuel Kant, in his 1755 treatise. As these mysterious objects accumulated in numbers in the second half of the 18th century, Charles Messier compiled a 109 objects long catalogue of what would later be called Messier objects. Some of these objects were galaxies, like Andromeda, M31, but others had a different nature, like the Orion Nebula M42. In 1888, John Louis Emil Dreyer created a new, extended catalogue, titled the new general catalogue (NGC) (Dreyer, 1888). Despite these attempts, no universal method of naming astronomical sources exists as of today. 1I write capital-G Galaxy when referring to the Milky Way. 2 1. Introduction Improved telescopes meant improved resolutions which resulted in the identifi- cation of spiral structures in some of these nebulae. In the so called ’Great Debate’ between Harlow Shapley and Heber Curtis (see e.g. Smith, 1982), spectroscopic ob- servations concluded that what is now known as the Andromeda galaxy is located outside our Galaxy. As a result, like so many times before in human history, the esti- mated size of the Universe2 grew by several orders of magnitude. Current estimates predicts the existence of more than a hundred billion galaxies in our observable Uni- verse. The term ’galaxy’ is Greek for ’milk’ adducing to the ’milky’ appearance of our galaxy, the Milky Way. The original term ’nebula’ is now used exclusively for other fuzzy systems, namely clouds of dust and gas within a galaxy. The discovery that solved the ’Great Debate’ led to one of the most important discoveries of our Universe. Edwin Hubble famously used pulsating, giant stars, Cepheids, as ’standard candles’ to compare their observed luminosity with their intrinsic luminosity, given their flux period. In the late 1920s, Hubble and had measured enough sources to derive a law stating the expansion of the Universe. Independent of Hubble, Georges Lemaître theorised and proposed the same law. With this now-called Hubble-Lemaître law3 history can be run backwards, leading to the Big Bang. 1.2 A Cosmological Timeline Following Hubble and Lemaître’s discovery, cosmology was introduced as the study of the evolution of the Universe. Modern cosmology accounts most importantly for the Hubble-Lemaître law, together with the cosmic microwave background (CMB) radiation discovered by Penzias and Wilson in 1964. Modern observations of the CMB, distant objects, and gravitational waves has corroborated that the Universe abides by the cosmological principle, being large scale homogenous and isotropic, and that it appears flat.4 In order to explain this, the theory of inflation was introduced by Starobinsky, Guth and Linde in the late 1970s.5 The inflation was a short period of exponential acceleration of expansion that preceded the creation of matter and light. The characteristic anisotropy scales of the CMB was matched to cosmological parameters, motivating the Lambda cold dark matter (ΛCDM). Due to its common usage, this is also known as the cosmological standard model. In it, the Universe is thought to be dominated by 68.5 % dark energy and 26.6 % cold dark matter, leaving only 4.9 % left for baryonic matter, that is the particles that we know of (McCarthy and Seidelmann, 2018; Planck Collaboration and Ade, 2016). In this cosmological standard model the 28.5 Gpc diameter of the Universe corresponds to an age of 13.8 Gyr (Bars and Terning, 2009). Depending on the values of the cosmological parameters matter distributes and evolves differently. In general, the evolution of the Universe is governed by the 2Akin to Galaxy, capital-U Universe refers, in this thesis, to our observable Universe. 3Before 2018 this was officially called the Hubble law. 4“Flat” means that Euclidean geometry is applicable. It should be clarified that the flatness itself is not confirmed, but the appearance of it is consistent with measurements. 5Inflation also explains the scarcity of magnetic monopoles. 3 1. Introduction parameters of physics that can be extracted from studying the very early Universe. With time the Universe expanded and got colder creating different epochs in which particles and physical laws decoupled or formed. Current physics cannot explain anything during the Planck Epoch 10−43 s after the Big Bang, but after the first minutes atomic nuclei had formed in the Big Bang-nucleosynthesis. Similar com- binations had preceded for quarks and leptons, including their antiparticles, while neutrinos had decoupled from other particles and the electromagnetic, weak, and strong interactions had become distinct forces (McCarthy and Seidelmann, 2018). 380 kyr after the Big Bang, in the epoch of recombination, the Universe grew to be sufficiently large for the temperature to decrease enough for electrons to combine6 with nuclei. In this process, that is called the photon decoupling, photons with longer mean free path were released. Due to the continuing expansion of the Universe, the wavelengths of the CMB are stretched, or redshifted, z + 1 ≈ 1100 times. Due to intense Thomson scattering making the younger Universe opaque, astronomers can detect photons travelling with the finite speed of light to see back in time, but only back to this epoch. The recombination was followed by the cosmological dark ages. Hydrogen, helium and lithium together with dark matter filled the Universe, but not with light. The ΛCDM model suggests that primordial fluctuations caused dark matter density irregularities in the so-called large scale structure, that initiated accretion and merging between baryonic matter. Studying these early causes for gravitational attraction could disclose new insights in not just cosmology, but also particle physics. One very important piece of the puzzle on early galaxy formation is the nature of dark matter halos. If CDM regions are dense enough, gravity can outcompete the expansion of the Universe (locally). However, for gravitational contraction to continue the internal pressure must not start to dominate. Baryonic gas avoids this through i.a. the free-free photon emission of Bremsstrahlung. Dark matter, on the other hand, are observed through gravitational lensing and rotation curves of galaxies to not form denser regions. It it therefore presumed that dark matter does not interact via the strong or the weak nuclear force; there are no evidence for ’atomic behaviour’, or the electromagnetic force; it does not produce photons. So, dark matter only interacts via gravity. The birth of stars and galaxies marked the beginning of the epoch of reionisa- tion. That photon emission reionised hydrogen in the intergalactic medium, IGM, around z ∼ 6 is motivated by Gunn-Peterson troughs - the absence of flux for Lyman-alpha and -beta lines that characterise neutral hydrogen (Gunn and Peter- son, 1965; Fan et al., 2006). The general explanation is that as the first stars, also known as population III stars, began to emit UV-photons, nearby hydrogen was ion- ized, creating spheres of ionised medium. Other high energy photon sources, such as black hole accretion disks, stood for 30 % of this ionisation (Gnedin and Ostriker, 1997; Lu et al., 1998). This process began with the very first stars forming around z ∼ 30 and had produced a completely ionised Universe at z ∼ 7 (Barkana and Loeb, 2001; Wise et al., 2012). Population III stars formed from gravitational contraction of the hydrogen, he- 6Since this was the origin of neutral atoms, a more correct name of the epoch would be ’epoch of combination’. 4 1. Introduction Figure 1.2: A schematic timeline of the Universe. The shades of the background represents the ionisation level. In white is the James Webb Space Telescope. Credit: STScI. lium (and lithium) that was produced in the Big Bang nucleosynthesis. Metal-free star formation in the early Universe is theoretically different from the chemically enriched star formation in the local Universe. For instance, since H2 forms on dust particles and is responsible for most of the cooling below T ∼ 104 K, population III stars could only form in large clouds, becomming very massive (Schneider, 2006, subsection 10.3.1). One characteristic of these rare stars is that they are very mas- sive. This means they have a typical lifetime of less than 10 Myr (Schaerer, 2003). Thus, in early galaxies, violent supernova explosions ousted out the remaining gas within the dark matter halo, reducing the chance for new stars to form within the same dark matter halo. Only at z ∼ 10, when these dark matter halos had grown a hundred times to 108 M�, could enough gas withstand the supernova winds so that star formation could continue (Cimatti et al., 2019, section 9.6). Therefore, the population III star formation was roughly constant during the epoch of reionisation (Crosby et al., 2013). In the last 13 Gyr there has been no fundamental change of the structure of the Universe. Figure 1.2 outlines the aforementioned points in the history of the Universe on a non-linear axis. After the still expanding Universe became fully ionised, as indicated by the light purple background to the right in the figure, new stars and galaxies continued to form, while the already existing galaxies continued to evolve. The large mass of a population III star causes its supernova to most likely result in a large black hole remnant. Possibly, these could accrete and grow to the supermassive black holes that local galaxies are observed to have (Dokuchaev et al., 2007). Some 4.6 Gyr ago, the Sun formed, and with it, our solar system. On Earth, 5 1. Introduction humans have, in the last century, begun exploring extragalactic astronomy. This is done by computationally heavy hydrodynamic simulations, simplifying semi-analytic approaches or direct observations that produce faint and unresolved images of dis- tant galaxies. For the benefit of combating the various challenges, these methods complement each other. Semi-analytic approaches are, for instance, better than simulations at studying global properties. Direct observations of some galaxies at distinct distances can be viewed as snapshots at different times. This thesis will focus on the observational approach. 1.3 Through the Telescope Observing is detecting photons in different wavelengths. When an eye sees an object it measures the brightness and colour in different places in its environment. Likewise, when a telescope observes a source, it measures the intensity and wavelength on different locations on the sky. With some knowledge about the source and the path of photon propagation, additional information can be obtained. The (spectral) intensity is the energy that is observed by the telescope (at a given wavelength). Our three dimensional space disperse photons on a two dimen- sional surface given some distance from the source. This inverse square dependence is the reason why, for example, standard candles (sources with known luminosity) are great measuring sticks for distance. Gas, dust and gravitational lensing can complicate this relation. Interpretation of the measured intensity requires an understanding of the mi- croscopic processes that constitute it. For instance, hot gas in accretion disks sur- rounding black holes generates ultraviolet (UV) and X-ray emission. Stars emit lights mostly in the UV—optical—infrared (IR) due to internal heating from fusion reactions in the stellar core. Mid-IR (MIR) and far-IR (FIR) raditation is domi- nated by the emission from interstellar dust.. When studying star formation it is crucial to note that only molecular gas is dense enough to form stars. Collisional excitations produce vibrational and rotational spectral lines in the IR to mm re- gion, where starlight does not dominate. At low temperatures CO, the second most abundant molecule after H2, dominates the molecular radiation (see e.g. Schneider, 2006; Cimatti et al., 2019). Due to quantum mechanical restrictions, only certain excited states are allowed for the molecules. Transitions between such states produce emission at characteris- tic wavelengths. As CO is the second most abundant molecule and easy to observe, the rotational transition CO(J = 1-0) emission line can be used as a means for estimating the total molecular gas mass. Since different states have a relative pop- ulation density as a function of temperature, the J-ladder, or spectral line energy distribution, is a great tool for estimating temperatures and obtaining i.a. column densities of molecular hydrogen (e.g Carilli and Walter, 2013; Cimatti et al., 2019). The general appearance of a galaxy spectrum can also reveal some properties. Starburst galaxies, for instance, are undergoing an episode with elevated star for- mation rate. Due to expulsion of gas, from large supernova explosion, outside an inner disk of massive stars, and galaxy-galaxy interaction (sometimes as a fuse for rapid star formation), their morphological appearance can therefore be irregular. 6 1. Introduction Spectrally, they show strong emission lines and emit more in shorter wavelengths, due to the presence of high-mass stars (e.g. Sparke and Gallagher, 2007). For ground-based telescopes the photons propagate through the molecularly filled atmosphere of the Earth. Only a few spectral ranges can pass through, these being in the optical, NIR and radio, but even for these, atmospheric attenuation often motivate a high altitude site. The 4200 m summit of Mauna Kea in Hawaii has therefore been a popular site for optical telescopes. The 10 m Keck 1 and Keck 2 telescopes and the 8.2 m Subaru Telescope are two examples (Schneider, 2006, section 1.3). At 2800 m altitude on the Antarctic Plateau, the South Pole Telescope (SPT) uses its 10 m parabola primarily to study the extragalactic Universe and the CMB through microwave and millimeter wave observations. The SPT0125-47 and SPT2147-50 galaxies that are studied in this thesis were discovered with the SPT. Observations in other wavelengths are limited to space telescopes. Here, tele- scopes such as Chandra X-ray Observatory (X-ray), Galaxy Evolution Explorer (UV), Hubble Space Telescope (optical/NIR), Spitzer Space Telescope (MIR), and Herschel Space Observatory (FIR) have been the leading contributors to research in galaxy evolution (Cimatti et al., 2019). The new James Webb Space Telescope (IR) is the largest (6.6 m) space telescope today and with good IR imaging and spectroscopic capabilities it will enable us to study the epoch of reionisation among other topics (Gardner et al., 2006). The resolution of a source depends on the instrument, the atmosphere, and the ratio of the wavelength to the observing diameter. Ground-based telescopes that view longer wavelengths, such as microwaves or radio waves, need very large observing diameters to resolve distant objects. This is obtained by connecting an array of telescopes in what is known as interferometry. By knowing the position, size and sensitivity of each antenna, a composite image can be produced through cross-correlation calculations. The first interferometric measurements where done in the 1960s (Schneider, 2006, section 1.3.1). The Very Large Array7 was introduce in the following decade covering frequencies between 1 and 50 GHz and baselines up to 36 km (National Ra- dio Astronomy Observatory, 2012), leading to breakthroughs in the study of active galactic nuclei (AGNs). Atacama Large Millimeter/submillimeter Array (ALMA) has for the past decade been the leading interferometer for wavelengths around 0.3-3 mm. Data from ALMA will be used in this thesis. Connecting telescopes across multiple observatories is known as very long base- line interferometry (VLBI). This is how the Event Horizon Telescope resolved the supermassive black hole (SMBH) of M87 in 2019 (Event Horizon Telescope Collab- oration and Akiyama, 2019). 1.4 This Thesis This master’s thesis aims to improve the understanding of star formation and galaxy evolution in the early Universe. Research on galaxy evolution is primarily compli- 7This was 2012 renamed Karl G. Jansky Very Large Array after a major upgrade of i.a. the receivers. 7 1. Introduction cated by selection biases. To observe high-redshift galaxies, particular lines, sprectral breaks or frequency regions are adapted. On top of this mostly unobscured and lu- minous or magnified sources are visible. This causes very biased samples of galaxies from a Universe that is smaller, denser, warmer and different than today. Knowl- edge of galaxy evolution is therefore dependent on fitting models to the observables. Good models should be able to explain the observed (scaling) relations, e.g. the Schmidt-Kennicutt and Tully-Fisher relations. As is the case for most master’s the- ses, a summary of relevant theory will introduce the subject. This introductory part continues into Chapter 3, which discusses how measurements of high-redshift galaxies are done. Chapter 2 presents the obtained information on galaxy evolution. Next, data from ALMA on the sources SPT2134-50 and SPT0125-47 is imaged, modelled through gravitational lensing, and presented in a more typically scientific manner of method (Chapter 4), results (Chapter 5), discussion (Chapter 6), and conclusion (Chapter 7). 8 2 Evolution of High-Redshift Galaxies A galaxy is the modern term of what was originally called an island Universe (Shap- ley and Curtis, 1921). Since the ’Great Debate’, the definition has particularised somewhat to a gravitationally bound system of gas, dust, stellar objects and dark matter (Sparke and Gallagher, 2007). A more specific definition would not incorpo- rate the vast differences in size, shape and content that have been observed. Masses of galaxies range from ∼ 105 M�, for the smallest known galaxy Segue 2 (Kirby et al., 2013), to ∼ 1014 M�, for the largest known galaxy IC 1101 (Fisher et al., 1995). The smallest galaxies are called dwarf galaxies and can measure down to 102 pc while the largest stretch 106 pc (e.g. Schneider, 2006; Sparke and Gallagher, 2007). Since mass density varies depending on morphology and content, the size of a galaxy does not determine its mass. Instead, the Sloan Digital Sky Survey has shown that the size distribution, at a given luminosity and galaxy type, follow a log-normal function characterized by its median radius and velocity dispersion (Shen et al., 2003). For individual galaxies, the Tully-Fisher relation (Tully and Fisher, 1977) connects the luminosity with the maximum rotational velocity for spiral galaxies, and the Faber-Jackson relation (Faber and Jackson, 1976) describes a similar relation between luminosity and velocity dispersion for elliptical galaxies. Generally, a galaxy with high luminosity has an increased likelihood of being massive, radially large, red, having centralised luminosity, high metallicity and a clearer break in the spectrum near 4000Å (Schneider, 2006, page 142). The number of galaxies per Mpc3 with luminosity between L and L+dL was described by Schechter (1976) as the Schechter function Φ(L)dL = Φ∗ ( L L∗ )α exp ( − L L∗ ) d L L∗ . (2.1) Following up on the science of observations from the previous chapter, this chapter will summarise the resulting theory of the sources themselves. For this thesis, the relevant sources are high-redshift (1 < z < 3) galaxies. Section 2.1 introduces the most important ways of categorisation. Section 2.2 and 2.3.1 presents the formation of stars and galaxies. The latter subsection is part of the general topic of galaxy evolution of Section 2.3. This section, continues with unfolding some popular models and relations of how star formation, principally, regulates the evolution of galaxies. 9 2. Evolution of High-Redshift Galaxies 2.1 Types of Galaxies The diverge population of galaxies in the Universe complicates classification. Still, it has been useful to isolate qualities, such as morphology, colour, spectral appearance, and content of a galaxy and classify accordingly. Types of classification depend on the type of observation. Nevertheless, due to gravitational interactions and contin- uous evolution, many galaxies fit poorly within the given categories. 2.1.1 Hubble Classification Historically, optical telescopes motivated classification according to shape. As soon as a large enough quantity of galaxies had been observed, Hubble presented his morphological classification. The corresponding tuning-fork diagram is called the Hubble sequence and consists of, from the left, ellipticals and (normal and barred) spirals. Because of this arrangement, galaxies to the left (right) are often called early (late) type galaxies despite no evolutionary motivation for this. Elliptical galaxies have only elliptical brightness contours as their only clearly defined structure. Con- sequently, the stars within have largely random motion. Ellipticals are specified with the letter ’b’ (’d’) for a boxy (disky) appearance and a number n = 10ε, where ε = 1 − b/a describes the ellipticity of an ellipse with semi-major (-minor) axis a (b). Spiral galaxies have higher gas-to-stellar mass ratio than ellipticals. They are disk-shaped, and specified by a ’B’ if barred, and a letter from ’a’ to ’c’1 to de- note the relative brightness between the central bulge and the disk. Sometimes how tightly wrapped around the bulge the spiral arms are is included in the classification too. In the intersection of the three arms, lenticular galaxies mark the intermedi- ate state between ellipticals and spirals. While the Hubble sequence can describe most bright galaxies, it is often complimented with irregular galaxies (sometimes called peculiar galaxies) that lack regular structure. Other structural changes are sometimes proposed to easier fit intermediate states (see e.g. Graham, 2019). Mor- phological classification is slow manual work for large sky surveys, but involvement of the public has made it feasible to continue (see Galaxy Zoo and Lintott et al., 2008). 2.1.2 Colour Bimodality and the Star-Forming Main Se- quence To combat the problem of projection effects, the optical light being redshifted out of the optical window and the difficulty of doing morphological classification at increased distance, and inapplicability for a large amount of galaxies, a bimodal colour distribution can be used instead. Since the apparent magnitude in any region of the electromagnetic spectrum follow the same distance dependence, the apparent magnitude difference in two wavelength bands, also called the colour excess, between two sources is distance independent. By plotting the number count as a function of colour excess, for any absolute magnitude, it was discovered that galaxies tend 1Combinations of letters indicate transitional states, and sometimes the scale is extended to the letter ’d’. 10 2. Evolution of High-Redshift Galaxies Figure 2.1: The Hubble sequence. Credit: (Graham, 2019). to be either luminous and red or faint and blue (Baldry et al., 2004a,b). In fact, the distribution is well fitted by two Gaussian functions. Moreover, the types are separated by the characteristic stellar mass M? ∼ (2− 3)1010 M� with red galaxies dominating the population that has a larger stellar mass than this. Red galaxies also have a larger mass-to-light ratio M/L. In the last two decades the color bimodality has been coupled to the idea that, like stars, galaxies exist on a main sequence (Strateva et al., 2001). In this case, the axis of abscissas specify stellar mass and the axis of ordinates show the star forming rate, see Figure 2.2. The main sequence of star-formation galaxies, also called star formation main sequence (SFMS), form a slope. Above this slope, starburst galaxies can be found and below the green valley and the region of red and quenched galaxies are (Cano-Díaz et al., 2016, CALIFA survey). The green valley is less galaxy dense. Interestingly, it is where the Milky Way and Andromeda lie (Mutch et al., 2011). One common interpretation (see e.g. Mancuso et al., 2016; Sherman et al., 2021) is that galaxies form as star-forming galaxies to the left of the SFMS. When the stellar mass has grown, the galaxy enters the SFMS where it slowly moves up along the sequence. Eventually, either gas exhaustion slows down star formation so that the galaxy slowly moves into the green valley, or an AGN rapidly quenches the galaxy, transforming it into an early-type galaxy in the bottom region of the diagram. Indeed, the low gas-to-stellar mass for ellipticals is a reason for lower star formation and redder light. Zooming in on the spectrum, and observing spectral lines instead of colour, different galaxy types again appear different. Connecting to the Hubble sequence, it is seen that early types have weaker emission lines, stronger absorption lines and a ’break’ near 4000Å (Kennicutt, 1992). This spectral break is the dominant feature for populations without a large star formation. Combining this dependence with the fact that the break is insensitive to metal abundance makes it a good tool for studying galaxy evolution over time (Dressler and Shectman, 1987). In the next section, it will be presented how spectral breaks produce colour selections that can locate galaxies at high redshift and name their types. Some examples of these are Lyman-break galaxies (LBGs), BzK galaxies, distant red galaxies (DRGs) and extremely red objects (EROs). More details on probing galaxies and their gas will be presented in Section 3.4.2. 11 2. Evolution of High-Redshift Galaxies Figure 2.2: Main sequence for star-forming galaxies and the region for red and inactive galaxies, with data from the CALIFA survey. Green circles mark sources where AGN emission dominates the ionisation emission. Remaining colours are defined by their Hα equivalent width (>6Å for blue, <3Å for red, and black in between). The fitted lines are for galaxies with inclination < 60◦. These are rhombus shaped in the diagram. Credit: (Cano-Díaz et al., 2016, Figure 1). 2.1.3 Starburst Galaxies Starburst galaxies produce several hundred solar masses of stars per year. This can be compared with the ∼ 3 M� yr−1 for the Milky Way (e.g. Schneider, 2006). Starbursts are better thought of as galaxies in a phase of high star-formation than as a different type of galaxy (Karl et al., 2010; Heckman, 2000). Dusty, star-forming galaxies (DSFGs) can, if the star formation is high enough, be very luminous in the FIR. This is because the dust absorbs starlight and re-emits in FIR. The tens of thousands of galaxies discovered by a ten month long survey by the Infrared Astronomical Satellite (IRAS) in 1983 did therefore receive the name IRAS galaxies or, if L > 1011 L�, luminous infrared galaxies (LIRGs) (Soifer et al., 1984; Chester, 1988). Galaxies that are even more luminous in IR are called ultra luminous infrared galaxies (ULIRGs) if L > 1012 L�, hyper luminous infrared galaxies if L > 1013 L� and extremely luminous infrared galaxies if L > 1014 L�. One possible cause for periods of high star-formation is strong gravitational interaction with another galaxy. Such interactions can compress gas to form stars, 12 2. Evolution of High-Redshift Galaxies which can explode as supernovae and consequently compress even more gas, start- ing chain events of star formation (Sanders, 1997; Hopkins et al., 2006). If this interaction ends in a galaxy collision, the event is called a galaxy merger. Galaxy mergers are divided into wet (gas-rich) and dry (gas-poor) merges. They can also be divided into major mergers, which have a small mass ratio (. 4 : 1) and minor mergers, which have a large mass ratio of 4 : 1 . R . 10 : 1. Major mergers has involved one third of all massive galaxies, while minor mergers has included the remaining galaxies. The motion of stars can be disorder by major mergers, which can create large random velocities of the stars, possibly transforming a disk galaxy into an elliptical. Additionally, local compressions of gas can spark a period of rapid star formation which exhausts the gas, as seen in for instance the Antennae galaxy. Minor mergers only result in the smaller galaxy being absorbed by the larger, like the dwarf galaxy Sagittarius is currently being disintegrated by the Milky Way. It should be added that most mergers do not produce a significantly increased star formation rate (SFR), but those that do tend to lie above the SFMS (Pearson et al., 2019). Only around 25 % of star formation at z < 2 comes from mergers (Kaviraj et al., 2015). Other possible causes for star formation are disk instabilities and other secular processes (Kennicutt, 1998). Some studies show that for z > 1, gas accretion is considerably more important than mergers for the SFR (Dekel et al., 2009; Kaviraj et al., 2015; Lofthouse et al., 2017). As the closest example of a starburst galaxy, M82 has revealed much infor- mation in star-forming regions. Images at the 21 cm line show atomic hydrogen scattering several Mpc away, indicating that M82 has for the past hundreds of Myr been interacting with the neighbouring galaxy M81. Observations by the Advanced Camera for Surveys on board the Hubble Space Telescope has detected ∼ 150 star clusters with an average mass of ∼ 2× 105 M� within a few 100 pc from the galactic core (Barker et al., 2008). The galaxy also show a bipolar outflow,2 which is likely driven by the supernovae occuring around every ten years in two of the four high surface density regions (Barker et al., 2008). When studying the SFR in a galaxy, several quantities of that galaxy has proved important. To name a few, observations of the CO line and dust continuum has found that the gas mass fraction (fgas = Mgas/(Mgas +M?)) strongly correlates with the specific star forming rate (sSFR ≡ SFR/M?), the gas mass fraction in- creases with redshift and the gas depletion timescale (tdep = Mgas/SFR) (Tacconi et al., 2018; Scoville et al., 2017; Solimano et al., 2021). With these definitions, a useful relation can be derived: fgas = 1 1 +M?/(tdepṀ?) . (2.2) The gas in a star forming galaxy (SFG) is governed by gas inflow and gas outflow with its surrounding circumgalactic medium as well as formation of stars and return of gas from stellar interiors. Gas inflow, sometimes called gas accretion, is believed to be highly ionised and have a column density considerably lower than 1020 cm−2, which is what is probed by Hi-emission (Cimatti et al., 2019, subsection 2The shape of this peculiar galactic wind has given M82 the nickname ’the Cigar galaxy’. 13 2. Evolution of High-Redshift Galaxies 8.7.4). Gas outflow, can take the form of e.g. galactic fountains or galactic winds. The previous example usually follow from self-regulated star formation, which is how the phenomenon of supernova shells compress the interstellar medium (ISM) and consequently starts a chain reaction of star formation. Around clusters of massive stars, superbubbles can then expand over a few hundred pc, which pushes gas out of the disc. Galactic winds are created from intense star formation in a small region and short period of time. They can help estimate the initial mass function for stars, the SFR, average supernova energy and velocity of the wind (Cimatti et al., 2019, subsection 8.7.4). From the movement of the gas outflow, the gas inflow can be estimated. Due to gravity, if the gas travels with a velocity lower than the escape velocity it will return to the galaxy. Two parameters that are helpful when comparing star formation over the vary- ing sizes of SFGs are the SFR surface density, ΣSFR, and SFR volume density, ρSFR. A central relation for star formation in galaxies that uses these is the Schmidt- Kennicutt law (Schmidt, 1959; Kennicutt, 1998). The equation can be heuristically derived under the assumption that stars form when interstellar gas collapses due to gravitational forces. The SFR density should then be proportional to the gas density and inversely proportional to the free fall timescale of Equation 2.10, such that ρSFR ∝ ρgas/tff ∝ ρ3/2 gas . The Schmidt-Kennicutt law is a generalised equivalence for column densities where the helium fraction B ∼ 10−4 is included as a factor, ΣSFR = B ( Σgas M�pc−2 )α M�yr−1kpc−2. (2.3) Here, the exponent α ≈ 1.4. Larger galaxies have larger star-formation efficiency for two reasons. First, galactic gas is more protected against background radiation. Second, the gas density is likely higher. This means that molecular gas in large galaxies have a higher recombination rate and is more difficult to ionise. Thus, their cooling is more efficient and a larger fraction of baryons can be turned into stars (see e.g. Schneider, 2006, page 524). To prevent all the gas from forming stars in a very short time, the first supernovae starts heating the surrounding gas, which makes it more dilute. But the supernovae explosions also enriches the ISM with metals and pushes the gas away, creating gravitational instabilities that, in turn, creates subsequent star formation in a chain reaction. 2.1.4 High-redshift Galaxies Distant galaxies exist in a younger and smaller Universe. At z ≈ 2.5 the Universe was a mere 2.6 Gyr old and had 1/(1 + z) ≈ 29 % the diameter of today. Changes in density and matter distribution affects the properties of the galaxies, which also has had much shorter time to evolve and change. For instance, the Hubble sequence describes the morphology of z > 2 poorly because low-mass galaxies have not had time to evolve, and the optical emission becomes redshifted out of the receiving optical window (see e.g. Schneider, 2006, section 9.4). Moreover, the distance to the galaxies create a need for special observational techniques that makes different galaxies difficult to compare. 14 2. Evolution of High-Redshift Galaxies Observations of galaxies at high-redshift began in the final decade of the 20th century. One early optical survey was the famous Hubble Deep Field from 1995, which hinted at the abundance and peculiarities of distant galaxies. However, the Hubble Deep Field covered only the U300, B450, V606 and I814 filters (Williams et al., 1996). Galaxies not emitting as strongly in these wavelengths were therefore ex- cluded. In this way, troubles resolving and detecting small and redshifted sources created a need for special detection criteria that only observed some properties of galaxies. The most common observational methods are the Lyman-break method, narrow band photometry, and MIR and FIR selection (see Section 3.4.2). With these methods, some demographical conclusions can still be drawn. As a first example, distant galaxies have a denser ISM. The gas mass fractions for z ∼ 1.2 and z ∼ 2.2 are ∼ 0.33 and ∼ 0.47 respectively, to compare with 0.08 for SFGs at z = 0 (Tacconi et al., 2013). Compact dusty cores, higher turbulence and deviations from the Schmidt-Kennicutt law (see Equation 2.3) are also more pertinent at higher redshift (see e.g. Messias et al., 2014; Cañameras et al., 2017; Rybak et al., 2020). Naturally, metallicity drops with redshift. Specifically, at z = 2 and z = 3.5 the metallicity of galaxies is, respectivelt, about half and one fourth of the metallicity of present day galaxies. At z ∼ 6 galaxies appear very dust-poor (Capak et al., 2015). This affects the star formation. With metal free molecular clouds the fine-structure lines of metals are absent, and the cooling becomes efficient only above T ≥ 104 K (Baugh, 2006). It should however be added that some distant galaxies do in fact show solar-like metallicities. These galaxies have most frequently an AGN (see e.g. Schneider, 2006, subsection 9.6.3). Finally, it should be mentioned that the dust temperature vary around 25 K . Td . 65 K in dusty galaxies (see e.g. Kovács et al., 2006; Magnelli et al., 2010; Manning and Spinrad, 2001). In connection with denser and more active ISMs, the SFR and luminosity depend on redshift too. SFR densities are higher for galaxies up to z ∼ 6 than today, and the SFR density peak is around z ∼ 2.5. This affects the luminosity function. At z ∼ 0 the exponent of the Schechter function (see Equation 2.1) in the UV region is fitted to α ≈ −1.25 (see e.g. Galaxy formation, 1998). For z ∼ 2.5 the faint end slope has α ≈ −1.6, and for z ∼ 4 the slope steepens even more with α ≈ −1.8 (Cassata et al., 2011). This difference can be explained by the observed SFR peak: the SFR was considerably higher at 2 . z . 4 than today, and young and massive stars are the main UV emitters (Bouwens et al., 2011). The number count function is highly dependent on luminosity and for longer wavelengths the comoving number density starts decreasing much earlier. In K -band light, z ∼ 2 the characteristic density of galaxies φ∗ is less than 30 % of today. On the other hand, the characteristic luminosity L∗ is about one magnitude larger at the same redshift and waveband (Cirasuolo et al., 2010). In the sub-mm range, the comoving density of galaxies is two orders of magnitude larger than in the local Universe (Hughes et al., 1998). Considering the colour bimodality, red galaxies exist up to at least z ∼ 3, suggesting that many galaxies formed their stars very quickly (see e.g. Schneider, 2006, section 9.4). In conclusion, high-redshift galaxies are more luminous but less numerous. As previously stated, high-redshift galaxies do not fit the Hubble classification. Instead, most z > 3 galaxies are irregularly shaped due to high SFRs. At that 15 2. Evolution of High-Redshift Galaxies same redshift, the stellar mass inside quiescent galaxies is only 1/45 of today’s (see e.g. Schneider, 2006, subsection 9.4.3). In regards to size, the previous paragraph suggested that the earlier Universe was more dominated by luminous and massive galaxies. The phenomenon that the relative frequency of smaller galaxies increases with cosmic time is often called downsizing. 2.2 First Stages in Star Formation Stars form in dense (n & 102 cm−3) regions of giant molecular clouds (GMCs) from very cold (T . 30 K) gas (Cimatti et al., 2019, section 8.3). That is not to say that only molecular gas can create stars. Most of the principles presented in this subsec- tion would hold for both molecular and atomic gas, and from a global perspective, both molecular and atomic gas does indeed correlate with star formation (Catinella et al., 2018). Dense gas clouds are twofold important; both formation of molecules, that enable higher density and effective cooling, and gravitational contraction, that eventually creates stars, depend on it. 2.2.1 Molecular Clouds Formation Before describing these two processes, I will start with the presentation of how GMCs form. Because clouds form from pieces of the gas disk that creates a galaxy, the central mechanisms at play are instability and fragmentation. To complicate the analysis the speed of sound, cs, on which the gravitational contraction heav- ily depend, varies between <1 km s−1 in the cold neutral medium and 8 km s−1 in the warm neutral medium (Cimatti et al., 2019, page 247). Additionally, the star- forming clouds are on average larger than the scaleheight of the galactic disk which causes uneven external pressure. Furthermore, there is turbulence in the protogalac- tic disc. Due to the large number of complex processes and their varying importance in different galaxies, no unique theory of the formation of GMCs exists as of today. Analysis of instabilities in the galactic medium can be modelled with respect to the rotation of the galaxy and the movement of the spiral arms. The previous cause the self-gravity of any high-density region to be counteracted both by the internal pressure and conservation of angular momentum. To model instability the potential of a single particle is often written as exp (−iωt), where ω and t are the angular frequency of the density wave and time. By linearly perturbing the continuity, Euler and Poisson equations in a cylindrical coordinate system and assuming adiabatic gas in purely circular motion, Lin and Shu (1964) showed that the dispersion relation for gravitational instability of a volume of gas in a rotating disk reads: (mΩ− ω)2 = κ2 − 2πGΣgas|k|+ c2 sk 2, (2.4) where m is the number of spiral arms in the galaxy, Ω and κ are the angular and epicycle frequencies, and k = 2π/λ is the wavenumber of the fluid disk. The epicyclic frequency is defined as the angular frequency of the radial oscillations occuring from small pertubation in a closed orbit. Considering axisymmetric perturbations (m = 0) Toomre (1964) showed that the instability criterion (ω2 < 0) can be 16 2. Evolution of High-Redshift Galaxies simplified to Qgas ≡ csκ πGΣgas < 1. (2.5) This criterion is called the Toomre criterion and Qgas is known as the Toomre param- eter. A similar analysis for star-dominated disks produces the analogous criterion Q? ≡ σRκ 3.36GΣ? < 1, (2.6) where σR is the radial velocity dispersion for the stars (Cimatti et al., 2019, subsec- tion 8.3.3). Spiral arms compresses the interstellar medium (ISM). This is due to the angular velocity of the spirals, also called spiral pattern speed, is constant while most disk galaxies show flat rotation curves, meaning the angular velocity of the gas decreases with distance (Cimatti et al., 2019; Sellwood and Wilkinson, 1993; Minchev and Famaey, 2010). When the gas enters the spiral arms, their high relative velocity can produce shocks which facilitates formation of dense clouds. In these clouds, molecules and, eventually, stars can form. 2.2.2 Molecular Gas Formation The chemical processes that produce molecules involve several types of particles. Therefore, the formation rate depends strongly on the local environment. Hydrogen, for instance, form molecules on the surface of dust grains by first colliding with a dust grain in a process called adsorption, and subsequently colliding with another hydrogen atom on the surface before leaving the grain surface in the process of desorption. Primordial galaxies, with negligible metallicity, must therefore create molecular hydrogen very differently. Apart from the density of dust and hydrogen, the hydrogen formation rate is, among other factors, proportional to the cross section of the grain and the inverse of the thermal speed of the atoms. With molecular hydrogen, ionised carbon can form carbon monoxide, after additional reactions (see e.g. Cimatti et al., 2019, equation 8.31). Molecular gas exists predominantly in GMCs that have sizes ∼ 50 pc, masses ∼ 106 M�, temperatures ∼ 10 K and number densities ∼ 500 cm−3. Clouds contain parsec-sized clumps and 0.1 pc-sized dense cores. Stars are believed to form in clusters from clumps (Williams et al., 2000) and individually or binary from dense cores (Alves et al., 2007). The latter has densities hundreds of times that of the average in the GMC, masses ∼ 1 M�, and are often studied from line emission of unique molecules such as OH, NH3, CS, H2CO and HCN (see e.g. Cimatti et al., 2019, page 121). 2.2.3 Gravitational Contraction and Thermal Pressure According to the Jeans analysis, the self-gravity of a cloud of gas will dominate the internal pressure if the Jeans criterion is satisfied (Jeans, 1902). In essence, linearly perturbing the continuity, Euler and Poisson equations and using the superposition leads to the dispersion relation for the angular frequency ω: ω2 = c2 sk 2 − 4πGρ, (2.7) 17 2. Evolution of High-Redshift Galaxies where cs is the speed of sound in the medium with density ρ, and k is the wavenumber of the solution (see e.g. Cimatti et al., 2019, subsection 8.3.2) subsection 8.3.2).3 The Jeans criterion, or condition for instability, is that the right hand side of Equation 2.7 is negative. This condition can be re-expressed after substituting k with the wavelength λ = 2π/k: λ > λJ ≡ √ πcs√ Gρ , (2.8) where λJ is the Jeans length. Assuming spherical geometry of a cloud with size λ, the analogous Jeans mass enables a third formulation of the Jeans criterion: M > MJ ≡ π5/2c3 s 6G3/2ρ1/2 . (2.9) A fourth way to express the Jeans criterion is in timescales. By defining the sound crossing time as ts ≡ λ/cs the Jeans criterion reads ts > tff = √ 3π 32 1√ Gρ , (2.10) where I have used Equation 2.8 to see that that the Jeans length is proportional to the free fall timescale tff . Clouds that do not satisfy these criteria are not held together by their own gravity and will disperse unless they are so-called pressure- confined clouds, that means they are stabilised by external pressure. By plugging in values in Equation 2.8, 2.9 and 2.10 several conclusions can be drawn. To begin, the Jeans mass for cold diffuse clouds (T ≈ 80 K, nH ≈ 10 cm−3) is MJ ≈ 105 M�, while the same for dense molecular clouds (T ≈ 10 K, nH2 ≈ 104 cm−3) is MJ ≈ 10 M�. This means that only dense molecular clouds are prone to the fragmentation that forms individual stars; if a cold diffuse cloud exceeds the Jeans mass, a cluster of star can be formed. Further, the theoretical free fall timescale is around 106 yr, one tenth of the typical lifetimes of GMCs (Murray, 2011). Thus, the thermal pressure is not the only thing stabilising the clouds. The same conclusion can be drawn from the Bonnor-Ebert theory where a gaseous sphere is assumed to be isothermal and polytropic (Bonnor, 1956; Ebert, 1955; Stahler and Palla, 2004); this theory derives a mass for hydrostatic equilibrium, called Bonnor-Ebert mass that is 1 − 100 M�, which is proportional to the size of dense cores rather than total GMCs. 2.2.4 The Virial Theorem with Turbulence and Magnetic Fields More important than thermal pressure are turbulence and magnetic fields, to coun- teract gravitational contraction in GMCs. This can be derived from the scalar virial theorem (Shu, 1992), 1 2 d2I dt2 = W + 2K + 2U + EM, (2.11) 3The fact that analysis omits the unperturbed parts of the three equations despite these not being zero, is known as the Jeans swindle. However, the results for the perturbed parts still hold, fundamentally due to Hamilton’s principle. 18 2. Evolution of High-Redshift Galaxies where I = Mr2 is the moment of inertia of a spherical cloud with radius r and mass M , and W = −GM2/r, K, U = 3NkBT , and EM are, respectively, the total gravitational, kinetic, internal and magnetic energies. The cloud radius will accelerate inwards if the right hands side of Equation 2.11 is negative. From typical GMC parameters it can be shown that |W | � U , which again shows the inadequacy of thermal pressure to withstand gravity. The total kinetic energy from turbulence is simply the turbulent kinetic energy scaled with M : Kturb ≈M 3σ2 gas 2 , (2.12) where σgas is the line broadening in GMC. Observationally, σgas ∼ 1 km s−1, which is around ten times the corresponding thermal line broadening (Cimatti et al., 2019, page 122-123). It is therefore evident that turbulence can sustain GMCs for M & 105 M� — a conclusion that is known as the second Larson law (Larson, 1981). The total magnetic energy is the magnetic energy density B2/(8π), where B is the magnetic field strength of the cloud, integrated over the volume of the cloud. By introducing the magnetic critical mass MM the energy can be written as EM ≈ B2r3 6 = G r M2 M, MM = Br2 √ 6G (2.13) which, given B ≈ 10 µG, means that the magnetic energy is on the same order of magnitude as the gravitational energy for M ∼ 105 M�. 2.2.5 The Equilibrium Model One model of the location of baryonic matter, that has gained support over the last decade, is the so-called equilibrium model (Finlator, 2017; Davé et al., 2012). It follows from conservation of baryonic mass Ṁ? + Ṁgas = Ṁin − Ṁout + Ṁ?,in, (2.14) where the Ṁ?, Ṁgas are the time derivative of the mass of stars and gas in the galaxy, respectively, Ṁin, Ṁout are the gas mass entering and leaving the galaxy, respectively, and Ṁ?,in is the gas accreting into stars. Notice that Ṁ? = SFR. The equilibrium condition is obtained when assuming that the gas accretion into stars is negligible (Ṁ?,in = 0) and that gas accretion is balanced with outflows (Ṁgas = 0) (Bouché et al., 2010). After defining a slowly-varying mass loading factor η = Ṁout/Ṁ? the equilibrium condition reads Ṁ? = Ṁin 1 + η . (2.15) The gas inflow can be divided into the baryonic inflow Ṁgrav, the gas in the galactic halo that is prevented from reaching the ISM (per unit time) Ṁprev and the gas that returns to the ISM from stars or previously ejected gas Ṁrecyc. By including a preventive feedback parameter ζ this division can be summarised as Ṁin = Ṁgrav − Ṁprev + Ṁrecyc = ζṀgrav + Ṁrecyc, ζ ≡ 1− Ṁprev Ṁgrav (2.16) 19 2. Evolution of High-Redshift Galaxies Furthermore, Finlator and Davé (2008) derives that the metallicity in the ISM is ZISM = y Ṁ? Ṁin = y (1 + η)(1− αZ) , (2.17) where y is the yield and αZ ≡ Zin/ZISM, where in turn Zin = ZrecycṀrecyc/Ṁin and Zrecyc is the metal mass from the recycled winds. This can be used to find an equilibrium metallicity Zeq = αZZ+y/(1+η) (Finlator and Davé, 2008; Davé et al., 2012) but also, from Equation 2.16, an equation for the SFR Ṁ? = ζṀgrav (1 + η)(1− αZ) . (2.18) The gas, metal and stellar evolution are described by Equation 2.2, 2.17 and 2.18 which together are called the equilibrium relations. 2.2.6 Cosmic Star Formation History How stars are formed determines their distribution of masses at birth. This distri- bution function is called the initial mass function (IMF) and was initially described by Salpeter (1955) as Φ(m)dm = Φ0m −2.35dm, (2.19) where φ(m)dm is the number of stars with solar mass between m and m + dm, and Φ0 is a normalisation factor, which — for a distribution between m = 0.1 and m = 100 — is assumed to be 0.17 (see e.g. Cimatti et al., 2019, subsection 8.3.9). Later versions by e.g. Scalo (1986), Kroupa (2002) and Chabrier (2003 and 2005) have attempted to correct the Salpeter IMF in the lower mass end for stars within the Galaxy. Other galaxies have produce different IMFs. In particular, population III stars are often described with the Larson IMF (Larson, 1998). From the IMF, the SFR can be inferred from the luminosity in a specific wavelength. For instance, for the Salpeter IMF (equation 2.19) the SFR reads ṀSalpeter ? ∼ 5× 10−7Lλ=1500 Å M�yr−1, (2.20) where Lλ=1500 Å is the luminosity at λ = 1500Å in units of L�Å −1 (Sparke and Gallagher, 2007, equation 9.24). This equation is only applicable to specific UV- luminous galaxies, but equivalent methods hold for other galaxies and star formation relations, see Section 3.4.3. Reconstructed star formation histories (SFHs) are uncertain because they are based on several assumptions. If the luminosity-calculation-based method, men- tioned above, is adapted, the IMF affects the SFR. If, for instance, the Chabrier IMF is adopted instead of the Salpeter IMF the SFR decreases by a factor of ∼ 1.7 (Cimatti et al., 2019, page 429). In the method of fitting SEDs to the spectra of simple stellar population models the stellar population synthesis models are of great importance. Stellar population models are approximations of galactic spectra given a SFR and a metallicity distribution as a function of time and the stellar spectrum of an individual simple stellar population. 20 2. Evolution of High-Redshift Galaxies Figure 2.3: Cosmic star formation rate density as a function of redshift. Credit: (Madau and Dickinson, 2014). By observing galaxies at various frequencies and reconstructing their individ- ual SFH the accumulated cosmic SFH can be plotted. This is done in Figure 2.3. The figure is colour coded to represent the rest frequency and papers of presentation (Madau and Dickinson, 2014): red and brown points correspond to IR rest frame ob- servations, and remaining symbols represent observation at FUV rest frame. Similar results have been confirmed from the Spitzer, Herschel and, more recently, Hubble Space Telescope (Bouwens et al., 2012). Due to the first estimate being made by Lilly et al. (1995) and Madau et al. (1996) this type of plot is known as the Lilly-Madau diagram. It can be deduced from Figure 2.3 that the majority of stars formed before z = 1 and about 10 % formed before the SFR peak around z ∼ 2.5. This means that high-redshift galaxies have significantly more star formation than local galaxies. Still, the most massive galaxies formed their stars early; even at z = 2.5, 50 % of galaxies could be quiescent. Interestingly, the cosmic star formation history follows molecular gas density history, which peaks around z ∼ 2 − 3 (Walter et al., 2019). The slope of the star formation rate density ρSFR per redshift step is considerably steeper at current era than between z ≈ 2 and z ≈ 8. Indeed, at the current epoch the ρSFR is only 10 % the SFR at z ≈ 1. Another important distinction is that the present-day SFR predominantly takes place in galaxies with relatively low dust, compared to galaxies at z & 0.7. 21 2. Evolution of High-Redshift Galaxies 2.3 Galaxy Evolution The evolution of galaxies is a very active field of research that concerns a large variety of scales and processes. This section contains a brief summary of the most important ideas, with focus on more massive galaxies at redshift up to z ≈ 3. 2.3.1 Galaxy Formation With gravity as the dominant force acting on very large distances, primordial fluctu- ations would naturally cause spheres of gravitationally interacting matter to clump or — more correctly — to expand less slowly. Both baryonic matter and dark matter will, in these regions, gravitate towards high-density regions. Surprisingly, the large scale of the Universe looks less like a continuous soup of denser regions and more like clumpy web with very large voids between the filaments of matter. This hints about the complexity of the nature of physics and the initial density fluctuations (see e.g. Sparke and Gallagher, 2007, chapter 8). Given a large scale structure with primordial fluctuations, dark matter halos are believed to form as a consequence of gravitational instability, and galaxies can then form when baryonic matter contracts in these dark matter halos. Conceptually, galaxy formation differs from star formation in two important ways: the gas is primordial, and the analysis needs to account for the expansion of the Universe. In the special case of the Einstein-de Sitter model, regions with densities at least 69 % more than the average will have collapsed before today (see e.g. Schneider, 2006, subsection 7.5.1). Similarly to the analysis in Section 2.2.3, a cosmological Jeans mass can be derived for the formation of dark matter halos. However, this assumes that the density perturbations are very small. Moreover, the cosmological Jeans mass changes significantly during the collapse. To estimate the mass threshold for gas collapse, a time-averaged version, called the filtering mass, is often used instead (Gnedin, 2000). Galaxies form in dark matter halos. For high-mass halos, the thermal pressure dwarfs the gravitational attraction making baryons fall towards the centre of the halo, supersonically. This means that the infall speed exceeds the speed of sound. If the mass of the halo exceeds the theoretical shock mass (Mshock ∼ 5× 1011 M�), the infalling gas creates shock fronts. The kinetic energy of the shocks dissipates into heat. In the centre, an hydrostatic equilibrium already exist. The infalling shock wave heats the gas to the equilibrium temperature. This temperature, called the virial temperature, is the temperature when the thermal energy U equals the kinetic K energy which equals half the potential energy W . A typical order of magnitude approximation is Tvir ∼ 106 K. Since the thermal pressure, which counteracts gravity, increases with gas tem- perature, stars can only form after the gas has cooled. The dominant way of cooling depends on the temperature, density and constituents of the gas. Examples of cooling processes are radiative Bremsstrahlung, recombination, de-excitation and collisional ionisation and excitation. When weighing the importance of these process, one useful approximation for temperatures that ionise hydrogen (T > 104 K) is the collisional ionisation equilib- 22 2. Evolution of High-Redshift Galaxies rium. In it, the photoionisation is neglected, ions and neutral atoms are assumed to immediately emit radiation when excited, and equilibrium is assumed to hold. After defining the cooling rate C as the energy radiated away per unit time and unit volume, it follows that it can be expressed as a temperature dependent cool- ing function Λ(T ) times the number density of hydrogen nH, C = Λ(T )n2 H (Baugh, 2006; Sutherland and Dopita, 1993). Because hydrogen lacks a permanent dipole moment (see Subsection 3.4.1) cooling is more efficient for higher metallicity and temperatures above 104 K. This is also the reason why star formation takes place in clouds with molecules; the energy levels are much richer at the low temperatures that gravitational contraction presupposes. Given cooling function, gas will contract unhindered if the corresponding cool- ing timescale tcool is shorter than the free fall timescale (see Equation 2.10): tcool = 3nkBT 2C . tff , (2.21) where n is the number density, and T is the temperature of the gas. Halos cannot cool effectively if M > 1013ρ/ρg M�, where ρ and ρg are the total and gas density, respectively. This is the reason why groups or clusters of galaxies, having larger masses, cannot produce stars. It is also the reason why galaxies have M & 108 M�; smallerM yields smaller T and the cooling is very inefficient below 104 K. Moreover, because of the expansion of the Universe, higher redshifts correspond to higher densities, which makes the cooling more effective. Therefore, if low-mass halos has formed stars, these are likely very old. Finally, as stated above, an increased metallicity improves the cooling efficiency (see e.g. Mo et al., 2010; Schneider, 2006; Cimatti et al., 2019). Two corrections to this story of galaxy formation should be made. Firstly, it is likely that the gas density increases towards the centre of the halo. Cooling can then be efficient in the central regions and a galaxy can be formed in the dark matter halo that contains hot gas in its outermost regions. Secondly, since the large scale structure is more like a web than a soup, the halos are not completely spherical. Instead, they can be thought of as the ’knots’ connecting the ’threads’ on which dark and baryonic matter travels. These two corrections lead to two general modes of gas accretion: the hot and the cold mode. Which mode that dominates depends on whether the mass of the galactic halo supersedes the shock mass. In more massive galaxies, the hot mode dominates and gas is heated to virial temperatures through shocks. In less massive galaxies, cold gas maintains low temperature until it reaches the centre of the halo (Sancisi et al., 2008). For z & 1.5 a third mode of gas accretion exists: a more massive halo that would otherwise accrete via the hot mode can for a larger z accrete through gas filaments or streams leading down to the centre of the halo. In these streams, the density is higher and therefore the cooling time is shorter (Dekel et al., 2013). The idea of galaxy formation is summarised in Figure 2.4. From primordial fluctuations a dark matter halo amasses and attracts baryons that heat through shocks to the virial temperature. If the inner regions are protected against radiation and also are dense enough, then cooling could be efficient and galaxy sized clouds 23 2. Evolution of High-Redshift Galaxies Figure 2.4: Schematic illustration of galaxy formation. can form and eventually produce stars. The preservation of angular momentum creates rotational support for the protogalactic disk, which creates turbulence, which together with magnetic field counteracts gravitational collapse of GMCs. As the cooling precedes, the radius of the galactic disk grows to the virial radius rvir = GM/v2, where v is the rotational velocity of the gas. 2.3.2 Simulations of Galaxy Evolution It is tempting to assume that much of galaxy evolution is known simply by apply- ing the previously mentioned relations between time (or redshift) and some other parameter. The theory of reionisation and galaxy formation suggests that the first galaxies formed around 1 Gyr after the Big Bang (or at z ∼ 10). As gravitational at- traction sparked merger events and gas accretion the cosmic SFR density increased to peak around z ∼ 2.5. The vaster Universe after this peak allowed galaxies to restructure according to the Hubble sequence. On this path, galaxies moved di- agonally upwards on the SFMS until the star formation was quenched. Then, the galaxies transformed from blue to red. There is however a fundamental problem with this assumption: applying differ- ent selection criteria at different redshifts results in a difficulty inferring something about galaxy evolution. Observing different properties of galaxies at different dis- tances makes it problematic to argue that they represent different stages on the same sequence of galaxy evolution. Telescopes enable us to, in some way, observe galaxies up to z ∼ 10 and thereby studying 90 % of the cosmic history, but the selection biases leave gaps in the theory of galaxy evolution. To combat this problem hydrodynamical cosmological simulations and semi- analytical models are often used. Of course, simulating the entire history of the Universe is unfeasible, but several simplifications can leave the large-scale results fairly reliable. Hydrodynamical simulations have lower spatial resolution than N-body simu- lations. They can, however, account for more physical processes. These small-scale physical mechanisms, such as star formation, are in these simulations added on sub-grid scales. Many baryonic processes, such AGN and supernovae feedback, are nevertheless difficult to model. This the reason for many unknowns in galaxy evo- lution. Still, several conclusions of hydrodynamical simulations are reasonable and in line with observations. Comparisons between observations and such simulations 24 2. Evolution of High-Redshift Galaxies enables fitting of parameters that are unknown. In this way, information can be obtained (see e.g. Schneider, 2006, section 10.6). An example of a comprehensive gas-dynamical, large-scale simulation is pre- sented by Vogelsberger et al. (2013). By simulating a 25h−1 Mpc large region with and without feedback processes it was shown that density, temperature and metal- licity were spread greatly outside the filaments in the large-scale structure only when gas feedback was included. Gas feedback also regulates the star formation to levels comparable with the Lilly-Madau diagram (see Figure 2.3). If the galactic winds produced by supernovae are strong, much of the gas from galactic halos is removed initially, but gas that is reaccreted at later times stays within the galaxy. Fast winds, instead blows gas out from the galaxy at lower redshifts. For this reason, fast winds also produce a lower ratio between stellar mass and halo mass than what is ob- served. When it comes to the Schechter luminosity function both strong and fast winds predicts lower mass functions Φ while no feedback overestimates it. Having no AGN feedback would also overestimate the slope in the Tully-Fisher relation. Semi-analytical models are less computationally expensive than hydrodynam- ical simulations. The idea behind these models is to start with the dark matter distribution obtained from N-body simulations. These simulations only account for gravitational interactions. Given the primordial overdensities extracted from the CMB, these simulations can produce the web-like large scale structure. When a dark matter halo has formed a homogeneous distribution, a baryon density equal to the cosmic mean is assumed in the region. With these conditions, analytical functions of galaxy formation and baryon processes are used to describe the baryon behaviour. For instance the surface SFR density is parameterised as the Schmidt-Kennicutt law 2.3. In a semi-analytic model from 2008, Somerville et al. demonstrated the regu- lation of star formation from supernovae and AGN. Neglecting supernovae feedback resulted in a fraction of baryons, that was in the form of stars, that was consid- erably larger than 50 % for halo masses Mhalo . 1012 M�. Similarly, not including AGN feedback resulted in the baryon-in-stars fraction to be almost one order of magnitude higher than expected, for Mhalo > 1012 M�. This is clearly different from the observations that show that star formation is inefficient when the halo mass is far from 1012 M�. The theoretical explanation for this is that supernovae and AGN feedback heats the ISM which slows down star formation. Another semi-analytic model can explain why central cluster galaxies often have AGNs. Almost every massive galaxy at high redshift contains a SMBH (Ko- rmendy and Ho, 2013). As these central black holes accrete gas they grow in size and produce an accretion disk of extremely hot and luminous particles — the AGN (Soltan, 1982). More massive galaxies are also more likely to attract more galaxies. Therefore, as shown in the Millennium simulation (Springel et al., 2005), the most luminous AGNs at high redshift (z ∼ 6) will dominate as central galaxies in a cluster at z ∼ 0. 25 2. Evolution of High-Redshift Galaxies Figure 2.5: Schematic view of the cosmic cycle for massive galaxies. Credit: (Hopkins et al., 2006). 2.3.3 Summary of Galaxy Evolution The evolution of massive galaxies is often simplified as the cosmic cycle — see Figure 2.5. Gas inflow from the formation of the galaxy starts a period of starburst activity. If the central SMBH will evolve to an optically unobscured AGN, known as an active quasar, or — originally — quasi-stellar object (QSO), the galactic core is referred to as a buried quasar. Gas accretion into the central regions feeds the SMBH which causes intense AGN feedback for a period of ∼ 100 Myr (Hopkins et al., 2006). Inside the produced normal galaxy, or dead quasar, steady star-formation proceeds as well as the growth of bars and pseudobulges. Gravitational attraction can eventually cause galaxies to merge. This event creates starburst periods which can be characteristic for e.g. ULIRGs. Subsequently, the galaxies coalesce in a violent relaxation in the galactic core, which possibly creates a new quasar as the cycle begins again. An important correction to this cyclic idea is that after the AGN feedback the galaxy is redder than before the merging. This is because the SFR has dropped and there are significantly more old red stars than young blue ones. The quenching of star formation can occur in many ways. Two previously mentioned examples are feedback from supernovae and AGNs that keeps the ISM hot. Another example, Mass quenching, occurs when the dark matter halo, possibly through merging, exceeds the critical mass which is Mcrit ∼ Mshock ∼ 1012 M�. In this case, the cold mode accretion becomes inefficient and the winds from the supernovae vSN ∼ 100 km s−1 dwarfs the escape velocity. While gas in the ISM can still cool and form stars, further accretion of cold gas is difficult if the virial temperature is high enough. IfMhalo �Mcrit AGN feedback prevents star formation almost completely (see e.g. Gabor et al., 2010; Cimatti et al., 2019, subsection 26 2. Evolution of High-Redshift Galaxies 10.6.1). Mass quenching explains why red galaxies are heavier. Environmental quenching is due to the interaction of nearby galaxies. A gravi- tationally dominating galaxy can control the movement of the gas in the intracluster medium. The ISM of orbiting satellite galaxies can then be pushed out of the galaxy from the pressure of the intracluster medium. This process is called ram-pressure stripping. If the satellite galaxy moves closer to the central galaxy all gas is attracted to the central galaxy instead of the satellite due to the process of strangulation. At even shorter distances, the central galaxy can absorb the satellite. This has got the dramatic name ’cannibalism’. These environmental effects explains the Butcher- Oemler effect, which is the hypothesis that cores of intermediate redshift galaxies have a larger fraction of blue cores (see e.g. Cimatti et al., 2019; Schneider, 2006). The fraction of galaxies that merge increase with redshift. Selecting galaxies with a projected separation and velocity difference of <5− 30 kpc and < 200 km s−1 the merger fraction can be estimated as fmerger = fmerger,0(1 + z)α for 0 < z < 3, (2.22) where fmerger,0 is the merger fraction at z = 0, and α depends on the stellar mass of the galaxy M? (Khochfar and Burkert, 2001; Conselice et al., 2003; Man et al., 2016). For instance for M? & 1010 M�, the exponent is around α ≈ 1. Alternatively, the number of mergers per comoving volume and time is stable for low redshifts and starts declining only after z ∼ 1.5. However, this is under the assumption that merger timescale is constant with redshift. If instead it decreases with redshift, the merger rate might be a function that increases with redshift (see e.g. Cimatti et al., 2019, subsection 11.3.2). Finally, high-redshift mergers are less efficient at increasing the SFR than low-redshift mergers (Fensch et al., 2017). Hubble morphologies have been observed up to z ∼ 4, but start become sig- nificantly numerous around z ∼ 2. At this redshift the combined fractions of disk galaxies and spheroids equals the fraction of peculiars. At higher redshift peculiars, or irregulars, are vastly more abundant, increasing from ≈ 5 − 10 % at z ≈ 0 to ≈ 30 % at z ≈ 0.6 and ≈ 60 − 70 % at z ≈ 2.7 (Talia et al., 2014). For a given M?, spheroids grow quicker than disks . In detail, the effective radius at 0 < z < 3 follows the dependence Re ∝ (1 + z)α where α ≈ −0.7 for disks and α ≈ −1.5 for spheroids (Mundy et al., 2017). Arguably the most important parameter in galaxy evolution is galaxy mass. Galaxies with M? > 5× 1010 M� evolved to disks or spheroids earlier than lower- mass galaxies. Due to their gravitational attraction they are more prone to mass quenching and less dependent on their surrounding. Therefore, massive galaxies mature quicker and become red, retired galaxies. More massive galaxies have sys- tematically lower gas mass fraction, lower sSFRs and higher metallicity at all redshift (see e.g. Cimatti et al., 2019). The gas mass fraction in the ISM increases with redshift asMgas/M? ∝ (1+z)α where α ≈ 3 for 0 < z < 3 (Genzel et al., 2015). The most important reason for this, and the fact that metallicity decreases with increasing z, is that star formation depletes the gas. At 0 < z < 3 the depletion timescale has only a weak redshift dependence (tdepl ∝ (1 + z)−0.3) and is on the order of 1 Gyr (Genzel et al., 2015). SFGs that remain in the SFMS over several Gyr must therefore continuously accrete 27 2. Evolution of High-Redshift Galaxies gas. The evolution of the SFR is closely related to the cosmic star-formation rate density which in turn follows the cosmic gas mass fraction history and peaks around z ∼ 2.5 (Madau and Dickinson, 2014). This shows in the luminosity function. In the case of IR emission, L∗IR increases by at least one order of magnitude between z ∼ 0 and z ∼ 2− 3 (Gruppioni, 2013). Observations have confirmed that the sSFR increases considerably with redshift (Ilbert et al., 2015). At z ≈ 2 galaxies on the SFMS typically double their stellar mass within 1 Gyr. The SFMS also evolves with redshift as SFRMS ∝ (1 + z)α where α = a logM? + b, and a ≈ 0.2 and b ≈ 0.6 (see e.g. Cimatti et al., 2019, equation 11.20). The theory of galaxy evolution is summarised in Figure 2.6, with one half focusing on the morphological evolution and the other on the star formation evolu- tion. Inside a dark matter halo baryons could collapse into a dense medium with a virial temperature. Galaxies below the critical mass Mcrit ≈ 5× 1011 M� can ac- crete gas in the cold mode. More massive galaxies accrete gas in the hot mode or, at z > 2.5, possibly through cold streams. Supernova and AGN feedback together with higher virial temperatures complicates the process of cooling and collapsing the gas to a disk, although further gas accretion can, at least hypothetically, transform spheroids to S0 galaxies. Merger events increase the SFR and disorder the stellar motions more significantly at low redshift. Dry mergers result in less gravitational instabilities in dense molecular clouds, because these clouds are more rare. A SFG can become starburst through major wet mergers or star formation chain reactions of e.g. supernova shocks in its early history. Starbursts drop towards the SFMS after a few Myr due to less gas remaining or, if star formation chain reaction has nearly exhausted the galaxy of gas, it becomes quiescent galaxy. These galaxies have been observed out to z ∼ 3− 4 (Cimatti et al., 2019, see e.g.). Many challenges remain in the understanding of galaxy evolution. Observa- tions of distant galaxies up to the epoch of reionisation are only now becoming feasible. To study high-redshift galaxies, gravitational lensing and other selection biases need to be used. With a proper understanding of these, as well as simulations and astronomical models, the observations of distant epochs can be interpreted as the observable representations they are. 28 2. Evolution of High-Redshift Galaxies Figure 2.6: Galaxy evolution summarised. Credit: (Cimatti et al., 2019, Figure 10.18). 29 2. Evolution of High-Redshift Galaxies 30 3 Observations of Galaxies and Radio Astronomy Radio astronomy studies celestial objects and phenomena in radio frequencies, i.e. 3 kHz (λ =100 km) to 300 GHz (λ =1 mm). This includes almost all astronomical sources, but some especially important examples are the CMB, masers, radio galax- ies, strongly gravitationally lensed sources, and thermal spectral lines from molecular clouds. The final two examples will be of special importance to this thesis. In this chapter, the techniques and theory that enables observation of radio as- tronomical sources is presented. It is explained how these observations are antenna measurements of extraterrestrial photons that depend on the dimming or refraction from gas and dust, the antenna structure, the receiver circuit and the source target. Sources are often specific transitions of molecules, corresponding to specific pro- cesses. Some observatories, such as ALMA, use interferometric imaging to improve the resolution. This can also be achieved with the bending of light in gravitational lensing. 3.1 Observational Quantities Astronomy measures extraterrestrial photons. For this aim, several quantities are important. Intensity, I, or brightness, quantifies the number of photons per unit area and solid angle. The specific intensity, Iν , or spectral brightness, is the intensity measured at a given frequency ν. Flux, S, quantifies the number of photons per unit orthogonal area A of the observer, and flux density, Sν , is the frequency specific equivalence. For radio sources it is conventional to use the flux density unit of Jansky, where 1 Jy=10−26 Wm−2 Hz−1. Flux measurements depend on the absorption, scattering and emission along the line of propagation. In the ray-optics approximation this line of propagation is a straight for distances much larger than the wavelength. The equation of radiative transfer, dIν = jνds− κνIνds , (3.1) where jν is the specific emission, and κν is the specific absorption, and ds is an infinitesimal distance, explains that the differential specific intensity is the difference between the differential specific emissivity and specific absorptivity. This can be reformulated introducing the dimensionless quantity optical depth, or opacity, dτ = −κds, that measures the amount of absorptive matter that is viewed. 31 3. Observations of Galaxies and Radio Astronomy Further, in local thermal equilibrium dIν/ds = 0 and Iν = blackbody radiation. In the Rayleigh-Jeans low frequency approximation, hν � kBT , the brightness tem- perature is defined as Tb(ν) = Iνc 2 2kBν2 , (3.2) where c is the speed of light in vacuum and kB is Boltzmann’s constant. Similarly, the antenna temperature, Ta, is the imagined temperature the antenna would have if it were a blackbody source that emitted the measured noise. Antenna temperatures can therefore be calibrated with known-temperature resistors called ’loads’. Both the antenna and the brightness temperature are mathematical tools; they are not physical. With these new quantities, the radiative transfer equation becomes Ta = Ta(0)e−τν + Tb(1− e−τν ). (3.3) The opacity is generally wavelength-dependent. One special feature of radio emission is that it is not affected by molecules and dust particles that are smaller than the wavelength of the emission. Thanks to this feature, Sagittarius A, in the center of the Milky Way, was discovered (Balick and Brown, 1974). In space, the term ’dust grains’ denote all small solid particles. Dust generally scatters or absorbs photons, causing a dimming known as extinction. Elliptical galaxies have generally less dust than starburst and disk galaxies. In the atmosphere of Earth, the wavelength-dependent opacity is a product of the molecules that constitute it. The abundant molecules, H2O, CO2 and O2 in the troposphere allow for vibrational transitions with the same energy as MIR photons and rotational transitions with the same energy as longer radio photons (Condon and Ransom, 2018). This leaves a radio atmospheric window in between 10 MHz and 1 THz where photons are generally not absorbed. Thus, radio telescopes can be ground-based. For wavelengths longer than ten times the particle size, electromagnetic dis- persion obeys the rules of Rayleigh scattering: opacity ∝ ν2 (Condon and Ransom, 2018). One important scattering source is small water droplets, known as hydrosols. To predict the opacity due to water, the precipitable water vapor (PWV) is intro- duced. It is the depth of the atmospheric water column, and is proportional to the water vapor spectral line at 22.235 GHz. At ALMA, the measured 50 % quartile is PWV= 1.1+1 −0.5mm1. The PWV is also proportional to the atmospheric phase change; more water increases the refraction angle according to Snell’s law. 3.2 Antennas According to The American Heritage dictionary, a telescope is an instrument for observing optical radiation from distant objects. Antennas are the equivalent for radio waves. More precisely, they are the interface between freely propagating elec- tromagnetic waves and the current that travels in the receiver.2 Antennas measure 1https://slideplayer.com/slide/3860722/. 2IEEE standard for definitions of terms for antennas.IEEE Std 145-2013(Revision of IEEE Std 145-1993), pages 1–50 32 https://slideplayer.com/slide/3860722/ 3. Observations of Galaxies and Radio Astronomy the flux intensity Sν = P Aδν = Pν A = 1 2IνΩ (3.4) given a electromagnetic power P , receiver area A and a frequency range δν for the incoming photons (Cortes et al., 2020, Chapter 3). The received electromagnetic power Pν per unit frequency is usually half the specific intensity Iν times the solid angle Ω because receivers generally only detect one polarisation. ALMA, however, has two independent and simultaneously active receivers, which makes this coeffi- cient one. Thus, the size of the antenna regulates its sensitivity by deciding how much power that can be detected. The shape of an antenna determines its sensitivity in different directions, known as its power response. On a radial axis, this is usually a collection of Gaus- sians with decreasing amplitude. The central lobe is called the primary beam. A larger antenna diameter yields a more narrow primary beam, which means that angularly smaller sources can be observed. Often antennas are parabolas because then each fraction of an transverse plane wave front will travel the same distance to the receiver regardless of where on the parabola it strikes. If an antenna points in a different direction than that of the source the resulting phase difference will produce destructive interference which decreases the received amplitude. 3.3 Confusion and Noise Depending on which direction an antenna is pointing to, different background radia- tion and collection of sources is observed. In radio frequencies, the 2.726 K blackbody CMB radiation is the dominating background. Additionally, unresolved sources blend together creating the confusion limit that is only dependent on the ratio be- tween the angular resolution of the observatory and the angular size of the source. Noise is the unwanted data that follows wanted data. In receivers, noise is usually assumed to have the same probability for any specific amplitude in any frequency. It is completely random and thereby called stochastic or white noise. With Johnson–Nyqu