Modelling the Intergalactic Baryons using Hydrodynamical Simulations A dissertation submitted to The University of Manchester for the degree of Master of Science by Research in the Faculty of Science and Engineering 2021 Marcus L Allan Department of Physics and Astronomy 2 Contents List of Tables6 List of Figures7 Abstract 11 Declaration 12 Copyright Statement 13 Acknowledgement 14 1 Background 15 1.1 The Standard Model of Cosmology.................... 15 1.1.1 The Cosmological Principle.................... 16 1.1.2 Lambda-CDM Model........................ 16 1.1.3 Cosmological Expansion Characteristics............. 18 1.2 The Missing Baryon Problem....................... 19 1.2.1 Predictions of Cosmology...................... 19 1.2.2 Big Bang Nucleosynthesis..................... 19 1.2.3 CMB Anisotropies......................... 22 1.2.4 Baryon Density Expectation Values................ 24 1.2.5 The Missing Baryon Problem................... 25 1.2.6 Censuses of Baryonic Matter.................... 26 1.2.7 Summary.............................. 28 1.3 Cosmological Structure........................... 28 3 1.3.1 Beginnings of Structure...................... 28 1.3.2 Large-scale Structure........................ 30 1.3.3 Observing Cosmological Structure................. 33 1.4 Summary.................................. 38 2 Simulations 41 2.1 Dark Matter - N-Body Methods...................... 41 2.2 Baryonic Matter - Hydrodynamic Methods................ 43 2.3 Initial Conditions.............................. 45 2.4 EAGLE................................... 46 2.4.1 Object Identification........................ 47 2.4.2 Overview of Gas Properties.................... 47 3 Pair Stacking and Signal Measurement Methods, Results and Discussion 51 3.1 Galaxies and Galaxy Pairs in EAGLE Simulations............ 52 3.1.1 Galaxy Selection.......................... 52 3.1.2 Pair Selection............................ 55 3.1.3 Pair Separation Regimes...................... 58 3.2 Pair Image Creation, Stacking Procedure and Methods of Analysis... 60 3.2.1 Stacking Methods.......................... 60 3.2.2 Image Creation and Stacking Procedure............. 61 3.2.3 Building a Model Galaxy Profile.................. 64 3.2.4 Profile Fitting............................ 65 3.2.5 Quoting Measured y-Values.................... 67 3.2.6 Result................................ 69 3.3 Interpretation................................ 70 3.3.1 Systematic Errors.......................... 70 3.3.2 On-axis, Uncorrelated Sources................... 71 3.4 Discussion.................................. 72 3.4.1 Comparisons............................ 72 3.4.2 Selected Pair Examples - Estimating Uncertainty........ 72 4 3.4.3 Improving Pair Statistics...................... 78 3.5 Summary.................................. 80 4 Conclusion 81 4.1 Summary.................................. 81 4.2 Future Research............................... 82 References..................................... 85 Word Count: 15947 5 List of Tables 3.1 Galaxy and pair numbers achieved using galaxy stellar mass thresholds from Tanimura et al.(2019) and De Graaff et al.(2019), and using a 10:3 lower threshold of M∗ ≥ 10 M . Pair numbers are achieved using the method given in section 3.1.2........................ 54 3.2 Galaxy and pair numbers achieved using galaxy stellar mass thresholds from Tanimura et al.(2019) and De Graaff et al.(2019), and using 10:3 a lower threshold of M∗ ≥ 10 M – now combined with restricting the galaxy sample to only galaxies which are the central object in their halo. Pair numbers are achieved using the method given in section 3.1.2. In comparison to table 3.1, galaxy numbers are reduced by 20-30%, as higher-mass objects are much more likely to already be central in their halo. The reduction is greater the more objects were originally in the sample. Galaxy pair numbers are reduced by approximately half, for the lowest stellar mass threshold........................ 57 3.3 Measured residual y-signal for the filament and off-axis regions (see figure 3.9), using the distribution of pixel values and a bootstrap resampling method.............................. 69 6 List of Figures 1.1 Formation routes of elements in Big Bang nucleosynthesis. Elements in black are those which are stable into the present day. For each pathway, reactant particles are in white, whereas products are in red. Note that this means protons, for example, are produced by multiple reactions throughout this diagram; these arrows are omitted for simplicity. Also not shown here are further reaction pathways to heavier elements, which occur in extremely small quantities during BBN.......... 21 1.2 WMAP nine-year all-sky CMB fluctuation map, using a Mollweide projection. The color range of this map is ± 200 microKelvin. Credit: NASA / WMAP Science Team(b)................ 23 1.3 The seven-year angular power spectrum of CMB fluctuations, based on the seven-year WMAP data release. The map relates the relative brightness of regions in the map to the angular size of those regions. Credit: NASA / WMAP Science Team(a)................ 24 1.4 A summary of baryon searches (from Shull et al.(2012)), contained in various phases of matter as discussed in section 1.2.6. The blended WHIM sections account for possible double-counting. Here, CGM is the circumgalactic medium and ICM is the intracluster medium....... 25 1.5 A 3D density map from the Millenium cosmological simulation (Springel et al., 2005), displaying the density of dark matter (which traces baryonic matter). More dense regions are brighter, whereas empty regions are darker. Voids are visible, for example, to the left and right of the image; bright spots hold galaxy clusters or superclusters, and the network of filaments connecting these is visible throughout.............. 31 1.6 Normalised spectrum of quasar Q1422+2309 (from Womble et al.(1996)) showing absorption features corresponding to Lyman-α lines, redshifted in the range 2:95 < z < 3:62. This is an excellent illustration of the Ly-α forest’s effect on continuum spectra................. 34 1.7 Diagram (from Mroczkowski et al.(2019)) showing the inverse Compton scattering of a CMB photon. The CMB photon enters the ionised region from an arbitraty direct, before interacting with a free electron. This imparts energy onto the photon, raising it to a higher frequency. The increase in energy of the photon is related non-trivially to the angle formed by the vectors of photon and electron velocities – figure 1.8 shows the representative shape of the effect of the SZ effect on the CMB intensity curve................................ 36 7 1.8 A shift in the blackbody intensity profile (left panel) of the CMB is introduced by inverse Compton scattering of a large number of electrons. This shift is centred around a frequency of 217 GHz (Mroczkowski et al., 2019), and manifests as a deficit of intensity below this frequency, with a corresponding increase above – the integral of ∆I (right panel) at all frequencies sums to zero. The shift is quantified by the Comptonization parameter y. Adapted from Bertoldi(2002)........................ 37 2.1 The distribution of mass as gas particles (top panel) and dark matter (bottom panel), in an arbitrary 1h−1Mpc slice of the 50 cMpc EAGLE simulation, at redshift z = 0:366 (the snapshot used in this study). The structure can be observed to closely match for each phase of matter, however the baryonic matter is more diffuse, as its thermal interactions provide outwards pressure which does not affect the dark matter.... 48 2.2 A temperature-density phase diagram for gas in the EAGLE 50 cMpc, z = 0:366 snapshot. Compare qualitatively with, for example, Shull et al.(2012, Figure 1) (who use baryon overdensity as opposed to hydrogen number density). N.B. Hydrogen Number Density is her ea function of the simulation average metallicity Z, which is fixed at a given redshift.................................... 50 3.1 Plots of the number of pairs each galaxy appears in vs. its group number (top panel), total mass (middle panel) and stellar mass (bottom panel). In all three cases, there is no apparent correlation. There is no bias, therefore, towards high- or low-mass galaxies in the selected subset, or in the "galaxies" in the final stacked pair image (see figure 3.5)..... 55 3.2 Stellar mass vs. total subhalo mass for each subhalo object in the EAGLE 50h−1Mpc simulation, at z = 0:366. Grey objects are those with SubGroupNumber 6= 0, i.e. those which are not the central object 10:3 in their parent halo. A stellar mass threshold of 10 M is used, with central galaxies satisfying this criterion marked in red, while lower mass galaxies are marked in blue. A correlation can be observed between galaxy’s stellar mass and total halo mass, which is stronger for central galaxies. Of additional interest are artefacts of EAGLE simulation parameters visible at low stellar mass and halo mass: stellar masses of the lowest-mass galaxies appear to be quantised, due to the EAGLE 6 simulation minimum particle mass of 10 M . 9 Typically, objects with stellar mass below approximately 10 M are considered to be unreliable......................... 56 3.3 An illustration of how periodic boundary conditions affect the pair population – a pair of galaxies at opposite sides of the simulation volume (top) may be connected by a much shorter vector when the periodic boundaries of the simulation are taken into account (bottom). Consequently, many pairs are included in the separation criteria which would otherwise be omitted........................