{ "cells": [ { "cell_type": "markdown", "id": "92d09d74", "metadata": {}, "source": [ "# Tutorial 1: Galacticus as a cosmology calculator\n", "\n", "[Galacticus](https://github.com/galacticusorg/galacticus) is a semi-analytic\n", "model of galaxy formation. Its physics engine — every `functionClass` of the\n", "Fortran code, from cosmology through dark-matter halos to stellar\n", "populations — is exposed to Python through the `libgalacticus` shared\n", "library, so you can use the *same* implementations that power full galaxy\n", "formation runs as building blocks in your own scripts and notebooks.\n", "\n", "This first tutorial introduces the two ideas you need:\n", "\n", "1. **Objects are built from parameter values and other objects.** Galacticus\n", " is organized around abstract classes (`cosmologyParameters`,\n", " `cosmologyFunctions`, `transferFunction`, …), each with interchangeable\n", " implementations. In Python you instantiate an implementation by calling\n", " its constructor with plain values and previously-constructed objects.\n", "2. **Methods are ordinary Python calls** returning floats, numpy arrays, or\n", " tuples.\n", "\n", "Here we drive the cosmology classes: expansion history, times, densities,\n", "and distances.\n", "\n", "**Units** (Galacticus conventions): masses in $M_\\odot$, times in Gyr,\n", "distances in Mpc, $H_0$ in km/s/Mpc, wavenumbers in comoving Mpc$^{-1}$." ] }, { "cell_type": "markdown", "id": "85091ba1", "metadata": {}, "source": [ "## Setup\n", "\n", "Load the library. If you built Galacticus from source with\n", "`make GALACTICUS_BUILD_OPTION=lib libgalacticus.so` and are running this\n", "notebook from the `tutorials/` folder of the source tree, this cell works\n", "as-is; otherwise point `GALACTICUS_LIBRARY_PATH` at the directory containing\n", "the `galacticus/` folder of the binary distribution.\n", "\n", "> **Troubleshooting — `OSError: ... version 'GCC_x.y.0' not found`.**\n", "> `libgalacticus.so` links against your compiler's C++/GCC runtime\n", "> (`libstdc++.so.6`, `libgcc_s.so.1`); if your Python environment loads older\n", "> copies, importing `galacticus` fails with, e.g.,\n", "> `` libgcc_s.so.1: version `GCC_14.0.0' not found ``. In a shell an\n", "> `LD_PRELOAD=/path/to/compiler/lib64/libstdc++.so.6 python3 ...` fixes it,\n", "> but **that cannot be done from a notebook cell**: the linker reads\n", "> `LD_PRELOAD` only at process startup, and the kernel has already loaded the\n", "> old libraries before this cell runs. Instead, create a dedicated Jupyter\n", "> kernel whose `kernel.json` sets `LD_PRELOAD` (to the correct\n", "> `libgcc_s.so.1` and `libstdc++.so.6`) in its `env` block, and select it via\n", "> Kernel → Change Kernel. See the \"Troubleshooting\" section of\n", "> [`README.md`](README.md) for the exact `kernel.json`." ] }, { "cell_type": "code", "execution_count": 1, "id": "c128e14f", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:50.915506Z", "iopub.status.busy": "2026-07-05T19:39:50.915302Z", "iopub.status.idle": "2026-07-05T19:39:51.113854Z", "shell.execute_reply": "2026-07-05T19:39:51.113374Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Galacticus library interface loaded.\n" ] } ], "source": [ "import os, sys\n", "\n", "# Locate the Galacticus library interface. Two supported layouts:\n", "# * a Galacticus source tree built with\n", "# make GALACTICUS_BUILD_OPTION=lib libgalacticus.so\n", "# (galacticus.py at the tree root, the library under galacticus/lib/);\n", "# * an unpacked binary distribution (the `galacticus/` folder from\n", "# libgalacticus.tar.bz2, with python/ and lib/ inside it).\n", "# Set GALACTICUS_LIBRARY_PATH to the directory CONTAINING the `galacticus/`\n", "# folder if the auto-detection below does not fit your setup.\n", "root = os.environ.get('GALACTICUS_LIBRARY_PATH',\n", " os.path.abspath(os.path.join(os.getcwd(), os.pardir)))\n", "os.chdir(root) # galacticus.py loads galacticus/lib/libgalacticus.so relative to here\n", "for candidate in (root, os.path.join(root, 'galacticus', 'python')):\n", " if os.path.exists(os.path.join(candidate, 'galacticus.py')):\n", " sys.path.insert(0, candidate)\n", " break\n", "else:\n", " raise RuntimeError(f\"galacticus.py not found under {root} - build the library \"\n", " \"(make GALACTICUS_BUILD_OPTION=lib libgalacticus.so) or set \"\n", " \"GALACTICUS_LIBRARY_PATH\")\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import galacticus\n", "print(\"Galacticus library interface loaded.\")" ] }, { "cell_type": "code", "execution_count": 2, "id": "3e9e8a1a", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:51.116675Z", "iopub.status.busy": "2026-07-05T19:39:51.116528Z", "iopub.status.idle": "2026-07-05T19:39:51.118092Z", "shell.execute_reply": "2026-07-05T19:39:51.117911Z" } }, "outputs": [], "source": [ "plt.rcParams.update({'figure.figsize': (7.0, 4.5), 'font.size': 11,\n", " 'axes.grid': True, 'grid.alpha': 0.3})" ] }, { "cell_type": "markdown", "id": "3b7f5c60", "metadata": {}, "source": [ "## Cosmological parameters\n", "\n", "The `cosmologyParametersSimple` implementation holds a flat set of\n", "parameters: $\\Omega_\\mathrm{M}$, $\\Omega_\\mathrm{b}$,\n", "$\\Omega_\\Lambda$, $T_\\mathrm{CMB}$ [K], and $H_0$ [km/s/Mpc]." ] }, { "cell_type": "code", "execution_count": 3, "id": "6aad4e78", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:51.120696Z", "iopub.status.busy": "2026-07-05T19:39:51.120387Z", "iopub.status.idle": "2026-07-05T19:39:51.122851Z", "shell.execute_reply": "2026-07-05T19:39:51.122684Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Omega_M = 0.300\n", "Omega_b = 0.045\n", "Omega_DE = 0.700\n", "Omega_curvature = 0.000\n", "H_0 = 70.0 km/s/Mpc\n", "critical density = 1.3598e+11 Msun/Mpc^3\n" ] } ], "source": [ "cosmologyParameters = galacticus.cosmologyParametersSimple(\n", " OmegaMatter = 0.3,\n", " OmegaBaryon = 0.045,\n", " OmegaDarkEnergy= 0.7,\n", " temperatureCMB = 2.78,\n", " HubbleConstant = 70.0,\n", ")\n", "print(f\"Omega_M = {cosmologyParameters.OmegaMatter():.3f}\")\n", "print(f\"Omega_b = {cosmologyParameters.OmegaBaryon():.3f}\")\n", "print(f\"Omega_DE = {cosmologyParameters.OmegaDarkEnergy():.3f}\")\n", "print(f\"Omega_curvature = {cosmologyParameters.OmegaCurvature():.3f}\")\n", "print(f\"H_0 = {cosmologyParameters.HubbleConstant():.1f} km/s/Mpc\")\n", "print(f\"critical density = {cosmologyParameters.densityCritical():.4e} Msun/Mpc^3\")" ] }, { "cell_type": "markdown", "id": "b7f7a364", "metadata": {}, "source": [ "## Expansion history\n", "\n", "`cosmologyFunctionsMatterLambda` solves the Friedmann equation for a\n", "matter + cosmological-constant universe. It is constructed *from* the\n", "parameters object — this dependency-injection pattern is how every\n", "Galacticus object graph is assembled." ] }, { "cell_type": "code", "execution_count": 4, "id": "28c698c8", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:51.124678Z", "iopub.status.busy": "2026-07-05T19:39:51.124364Z", "iopub.status.idle": "2026-07-05T19:39:51.127278Z", "shell.execute_reply": "2026-07-05T19:39:51.127105Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Age of the Universe today : 13.467 Gyr\n", " z = 0.5 -> a = 0.6667, t = 8.426 Gyr, H = 91.6 km/s/Mpc\n", " z = 2.0 -> a = 0.3333, t = 3.227 Gyr, H = 207.7 km/s/Mpc\n", " z = 6.0 -> a = 0.1429, t = 0.917 Gyr, H = 712.5 km/s/Mpc\n", " z = 20.0 -> a = 0.0476, t = 0.177 Gyr, H = 3690.1 km/s/Mpc\n" ] } ], "source": [ "cosmologyFunctions = galacticus.cosmologyFunctionsMatterLambda(cosmologyParameters)\n", "\n", "ageToday = cosmologyFunctions.cosmicTime(1.0) # time at expansion factor a=1\n", "print(f\"Age of the Universe today : {ageToday:.3f} Gyr\")\n", "for z in (0.5, 2.0, 6.0, 20.0):\n", " a = cosmologyFunctions.expansionFactorFromRedshift(z)\n", " t = cosmologyFunctions.cosmicTime(a)\n", " print(f\" z = {z:5.1f} -> a = {a:.4f}, t = {t:6.3f} Gyr,\"\n", " f\" H = {cosmologyFunctions.hubbleParameterEpochal(time=t):7.1f} km/s/Mpc\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "3bfd9c78", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:51.129746Z", "iopub.status.busy": "2026-07-05T19:39:51.129431Z", "iopub.status.idle": "2026-07-05T19:39:51.302021Z", "shell.execute_reply": "2026-07-05T19:39:51.300923Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Expansion factor and Hubble rate through cosmic time.\n", "times = np.linspace(0.15, ageToday, 300)\n", "a = np.array([cosmologyFunctions.expansionFactor(t) for t in times])\n", "H = np.array([cosmologyFunctions.hubbleParameterEpochal(time=t) for t in times])\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "axes[0].plot(times, a)\n", "axes[0].set_xlabel('cosmic time $t$ [Gyr]'); axes[0].set_ylabel('expansion factor $a(t)$')\n", "axes[1].loglog(times, H)\n", "axes[1].set_xlabel('cosmic time $t$ [Gyr]'); axes[1].set_ylabel('$H(t)$ [km/s/Mpc]')\n", "fig.suptitle('Expansion history of a flat $\\\\Lambda$CDM universe')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3c4d7dda", "metadata": {}, "source": [ "## The changing energy budget\n", "\n", "$\\Omega_\\mathrm{M}(t)$ and $\\Omega_\\Lambda(t)$ trade places around\n", "$z \\sim 0.3$: matter domination gives way to dark-energy domination, which\n", "is why structure growth slows at late times (Tutorial 2)." ] }, { "cell_type": "code", "execution_count": 6, "id": "0a067c88", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:51.304235Z", "iopub.status.busy": "2026-07-05T19:39:51.304025Z", "iopub.status.idle": "2026-07-05T19:39:51.379786Z", "shell.execute_reply": "2026-07-05T19:39:51.378594Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zGrid = np.logspace(-2, 1.3, 200)\n", "tGrid = np.array([cosmologyFunctions.cosmicTime(\n", " cosmologyFunctions.expansionFactorFromRedshift(z)) for z in zGrid])\n", "OmegaM = np.array([cosmologyFunctions.omegaMatterEpochal (time=t) for t in tGrid])\n", "OmegaDE = np.array([cosmologyFunctions.omegaDarkEnergyEpochal(time=t) for t in tGrid])\n", "\n", "plt.semilogx(1.0+zGrid, OmegaM , label='$\\\\Omega_\\\\mathrm{M}(z)$')\n", "plt.semilogx(1.0+zGrid, OmegaDE, label='$\\\\Omega_\\\\Lambda(z)$')\n", "zEq = zGrid[np.argmin(np.abs(OmegaM-OmegaDE))]\n", "plt.axvline(1.0+zEq, color='gray', ls=':', label=f'equality: $z\\\\approx{zEq:.2f}$')\n", "plt.xlabel('$1+z$'); plt.ylabel('density parameter'); plt.legend()\n", "plt.title('Matter-dark energy equality')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1434fef6", "metadata": {}, "source": [ "## Distances\n", "\n", "Galacticus's distance functions take cosmic *time* as their argument; use\n", "`expansionFactorFromRedshift` + `cosmicTime` to convert from redshift. The\n", "familiar textbook relations between comoving, luminosity, and angular\n", "diameter distances hold: $d_\\mathrm{L} = (1+z)\\,d_\\mathrm{C}$ and\n", "$d_\\mathrm{A} = d_\\mathrm{C}/(1+z)$ in a flat universe." ] }, { "cell_type": "code", "execution_count": 7, "id": "6a6d6420", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:51.382222Z", "iopub.status.busy": "2026-07-05T19:39:51.382133Z", "iopub.status.idle": "2026-07-05T19:39:51.440373Z", "shell.execute_reply": "2026-07-05T19:39:51.439771Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "d_L=(1+z)d_C and d_A=d_C/(1+z) verified at z=2.02\n" ] } ], "source": [ "zGrid = np.linspace(0.01, 8.0, 200)\n", "tGrid = np.array([cosmologyFunctions.cosmicTime(\n", " cosmologyFunctions.expansionFactorFromRedshift(z)) for z in zGrid])\n", "dC = np.array([cosmologyFunctions.distanceComoving (t) for t in tGrid])\n", "dL = np.array([cosmologyFunctions.distanceLuminosity(t) for t in tGrid])\n", "dA = np.array([cosmologyFunctions.distanceAngular (t) for t in tGrid])\n", "\n", "plt.plot(zGrid, dC/1.0e3, label='comoving $d_\\\\mathrm{C}$')\n", "plt.plot(zGrid, dL/1.0e3, label='luminosity $d_\\\\mathrm{L}$')\n", "plt.plot(zGrid, dA/1.0e3, label='angular diameter $d_\\\\mathrm{A}$')\n", "plt.xlabel('redshift $z$'); plt.ylabel('distance [Gpc]'); plt.legend()\n", "plt.title('Cosmological distances')\n", "plt.show()\n", "\n", "# Internal consistency checks.\n", "i = np.argmin(np.abs(zGrid-2.0)); z = zGrid[i]\n", "assert np.isclose(dL[i], (1.0+z) *dC[i], rtol=1.0e-6)\n", "assert np.isclose(dA[i], dC[i]/(1.0+z) , rtol=1.0e-6)\n", "print(f\"d_L=(1+z)d_C and d_A=d_C/(1+z) verified at z={z:.2f}\")" ] }, { "cell_type": "markdown", "id": "21586bb0", "metadata": {}, "source": [ "## Comparing cosmologies\n", "\n", "Because objects are cheap to construct, comparing cosmologies is a\n", "two-line affair. Here: our fiducial flat $\\Lambda$CDM against an\n", "Einstein-de Sitter universe ($\\Omega_\\mathrm{M}=1$)." ] }, { "cell_type": "code", "execution_count": 8, "id": "ebfc7708", "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:39:51.442675Z", "iopub.status.busy": "2026-07-05T19:39:51.442597Z", "iopub.status.idle": "2026-07-05T19:39:51.494800Z", "shell.execute_reply": "2026-07-05T19:39:51.493633Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Age of the Universe: LCDM = 13.467 Gyr, EdS = 9.312 Gyr\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cosmologyParametersEdS = galacticus.cosmologyParametersSimple(1.0, 0.045, 0.0, 2.78, 70.0)\n", "cosmologyFunctionsEdS = galacticus.cosmologyFunctionsMatterLambda(cosmologyParametersEdS)\n", "\n", "print(f\"Age of the Universe: LCDM = {cosmologyFunctions.cosmicTime(1.0):6.3f} Gyr,\"\n", " f\" EdS = {cosmologyFunctionsEdS.cosmicTime(1.0):6.3f} Gyr\")\n", "\n", "times = np.linspace(0.15, ageToday, 200)\n", "for label, cf in (('$\\\\Lambda$CDM', cosmologyFunctions), ('Einstein-de Sitter', cosmologyFunctionsEdS)):\n", " plt.plot(times, [cf.expansionFactor(t) for t in times], label=label)\n", "plt.xlabel('cosmic time $t$ [Gyr]'); plt.ylabel('$a(t)$'); plt.legend()\n", "plt.title('Dark energy accelerates late-time expansion')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "bf5e97df", "metadata": {}, "source": [ "## Where next\n", "\n", "* **Tutorial 2** builds the linear matter power spectrum from these same\n", " objects — including warm-dark-matter variants.\n", "* **Tutorial 3** computes halo mass functions across cosmic time.\n", "* **Tutorial 4** shows Galacticus calling back into *your* Python functions." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.14.4" } }, "nbformat": 4, "nbformat_minor": 5 }