{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# automatically reflect changes in imported modules\n", "%load_ext autoreload\n", "%autoreload 2\n", "\n", "from pathlib import Path\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import astropy.units as u\n", "\n", "import utils\n", "import utils.logging_config\n", "import logging\n", "logger = logging.getLogger(\"task1\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "DATA_ROOT = Path('data')\n", "DATA_NAME = 'data.txt'\n", "NBINS = 30\n", "CACHE_ROOT = Path('.cache')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "08:59:02 - utils.load - Loaded 50010 rows and 10 columns from data/data.txt\n" ] } ], "source": [ "points, columns = utils.load_data(DATA_ROOT / DATA_NAME)\n", "logger.debug(f\"Fetched {points.shape[0]} points, columns: {columns}\")\n", "# reorder the columns to match the expected order (x, y, z, mass)\n", "particles = points[:, [2, 3, 4, 1]]\n", "\n", "# particles = particles[::10, ...]\n", "# particles = particles[:5000, ...]\n", "# particles = utils.remove_outliers(particles)\n", "# logger.warning(f\"Reduced selection to {particles.shape[0]} particles\")\n", "# TODO: make sure this is not executed in the final version" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the distribution of the particles\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.scatter(particles[:,0], particles[:,1], particles[:,2], cmap='viridis', c=particles[:,3])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Choice of units\n", "Recap of the particle properties:\n", "- $\\sim 10^4$ particles\n", "- spherical distribution\n", "\n", "$\\implies$ this seems to be a **globular cluster**" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "08:59:04 - task1 - Considering a globular cluster - total mass of particles: 4622219.258999999, maximum radius of particles: 724.689657812915\n", "08:59:04 - utils.units - Set scales: M_SCALE = 0.022 solMass, R_SCALE = 0.028 pc\n" ] } ], "source": [ "# Set G = 1\n", "G = 1\n", "\n", "\n", "# Since we have a globular cluster, we can use typical values\n", "M_TOT = 1e5 * u.M_sun\n", "R_TOT = 20 * u.pc\n", "\n", "# Rescale the units of the particles\n", "M_particles = particles[:,3].sum()\n", "R_particles = np.max(np.linalg.norm(particles[:, :3], axis=1))\n", "logger.info(f\"Considering a globular cluster - total mass of particles: {M_particles}, maximum radius of particles: {R_particles}\")\n", "m_scale = M_TOT / M_particles\n", "r_scale = R_TOT / R_particles\n", "utils.seed_scales(r_scale, m_scale)\n", "\n", "\n", "\n", "# ### Plot again with scales\n", "# positions = utils.apply_units(particles[:, :3], \"position\")\n", "# masses = utils.apply_units(particles[:, 3], \"mass\")\n", "# fig = plt.figure()\n", "# ax = fig.add_subplot(111, projection='3d')\n", "# sc = ax.scatter(positions[:,0], positions[:,1], positions[:,2], cmap='viridis', c=masses)\n", "#\n", "# ax.set_xlabel(f'x [{positions.unit}]')\n", "# ax.set_ylabel(f'y [{positions.unit}]')\n", "# ax.set_zlabel(f'z [{positions.unit}]')\n", "# cbar = plt.colorbar(sc, ax=ax, pad=0.1)\n", "# cbar.set_label(f'Mass [{masses.unit}]')\n", "#\n", "# plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "all_r = utils.r_distribution(particles)\n", "rbins = np.logspace(np.log10(np.min(all_r)), np.log10(np.max(all_r)), NBINS, endpoint=True)\n", "\n", "## Using the Hernquist model with parameters M and a\n", "m = M_particles\n", "a = utils.half_mass_radius(particles) / (1 + np.sqrt(2))\n", "logger.debug(f\"Scale length: {a=:.2g}, total mass: {m=:.2g}\")\n", "rho_t = utils.model_density_distribution(rbins, m, a)\n", "\n", "## Numerical density distribution\n", "rho, err = utils.density_distribution(rbins, particles, ret_error=True)\n", "\n", "## Add the units\n", "rho = utils.apply_units(rho, \"density\")\n", "err = utils.apply_units(err, \"density\")\n", "rho_t = utils.apply_units(rho_t, \"density\")\n", "rbins = utils.apply_units(rbins, \"position\")\n", "\n", "\n", "plt.figure()\n", "plt.title('Density distribution')\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.xlabel(f'r [{rbins.unit}]')\n", "plt.ylabel(f'$\\\\rho$ [{rho.unit}]')\n", "plt.errorbar(rbins.value, rho.value, yerr=err.value, fmt='o', label=\"Particle data\")\n", "plt.plot(rbins.value, rho_t.value, 'o', label=\"Analytic model\")\n", "plt.legend()\n", "plt.show()\n", "\n", "## Note that by construction, the first shell contains no particles\n", "## => the numerical density is zero there\n", "## Having more bins means to have shells that are nearly empty\n", "## => the error is large, NBINS = 30 is a good compromise" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "08:59:05 - utils.particles - Found mean interparticle distance: 0.010402746349924056\n" ] } ], "source": [ "### Direct N body force computation and comparison with analytical model\n", "epsilon = utils.mean_interparticle_distance(particles)\n", "\n", "\n", "epsilon_range = np.logspace(-3, 3, 7)\n", "n_squared_forces = []\n", "for e in epsilon_range:\n", " n_particles = particles.shape[0]\n", " cache_file = CACHE_ROOT / f\"n_squared_forces__n_{n_particles}__softening_multiplier_{e:.0f}.npy\"\n", " try:\n", " f = np.load(cache_file)\n", " except FileNotFoundError:\n", " f = utils.n_body_forces(particles, G, e * epsilon)\n", " np.save(cache_file, f)\n", " logger.debug(f\"Saved forces to {cache_file}\")\n", " n_squared_forces.append(f)\n", "\n", "analytical_force = utils.analytical_forces(particles)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "SKIP_N = 20\n", "## Plot the radial force behaviour\n", "r = np.linalg.norm(particles[:,:3], axis=1)\n", "r = utils.apply_units(r, \"position\")\n", "\n", "plt.figure()\n", "f_analytical = np.linalg.norm(analytical_force, axis=1)\n", "f_analytical = utils.apply_units(f_analytical, \"force\")\n", "plt.plot(r.value[::SKIP_N], f_analytical.value[::SKIP_N], '.', label=\"Analytical\", zorder=10, alpha=0.5)\n", "\n", "for e, f in zip(epsilon_range, n_squared_forces):\n", " f_abs = np.linalg.norm(f, axis=1)\n", " f_abs = utils.apply_units(f_abs, \"force\")\n", " plt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], '.', label=f\"$N^2$ - {e:.1g} * $\\\\epsilon$\")\n", "\n", "\n", "plt.title('Radial force')\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.xlabel(f'$r$ [{r.unit}]')\n", "plt.ylabel(f'$F_r(r) [{f_analytical.unit}]$')\n", "plt.legend()\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Discussion\n", "- basic $N^2$ matches analytical solution without dropoff. but: noisy data from \"bad\" samples\n", "- $N^2$ with softening matches analytical solution but has a dropoff. No noisy data.\n", " - softening $\\approx 1 \\varepsilon$ is a sweet spot since the dropoff is \"late\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relaxation time\n", "\n", "For an estimate of the crossing time we use the half mass radius and the circular velocity at the half mass radius.\n", "\n", "$\\implies$ the crossing time is of order radius / velocity" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "08:59:24 - task1 - Crossing time for half mass system: 1.7e-06 pc(3/2) / solMass(1/2)\n", "08:59:24 - task1 - Direct estimate of the relaxation timescale: 0.00078 pc(3/2) / solMass(1/2)\n" ] } ], "source": [ "## Computes the relaxation timescale of a set of particles using the velocity at the half mass radius.\n", "\n", "# enclosed mass at half mass radius\n", "m_half = np.sum(particles[:, 3]) / 2\n", "r_half = utils.half_mass_radius(particles)\n", "# set the units\n", "m_half = utils.apply_units(m_half, \"mass\")\n", "r_half = utils.apply_units(r_half, \"position\")\n", "\n", "v_c = np.sqrt(G * m_half / r_half)\n", "\n", "t_c = r_half / v_c\n", "logger.info(f\"Crossing time for half mass system: {t_c:.2g}\")\n", "# TODO: how to treat this unit?\n", "\n", "## Using the derived formula for the relaxation timescale\n", "# Compute the relaxation timescale through the estimate\n", "# t_relax = t_c *n_relax = t_c * N / (10 * log(N))\n", "n = particles.shape[0]\n", "n_relax = n / (10 * np.log(n))\n", "t_rel = t_c * n_relax\n", "logger.info(f\"Direct estimate of the relaxation timescale: {t_rel:.2g}\")\n" ] }, { "attachments": { "Pasted image 20250118155501.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "#### Discussion\n", "\n", "\n", "The estimate for $n_{relax}$ comes from the contribution of each star-star encounter to the velocity dispersion. This depends on the perpendicular force\n", "\n", "![Pasted image 20250118155501.png]()\n", "\n", "The full integration of the force along the path of the star reduces to the main contribution at the closest approach (distance $b$):\n", "$$\n", "\\delta v \\approx \\frac{2 G m}{b} \\to \\delta v \\approx \\frac{2 G m}{b + \\varepsilon}\n", "$$\n", "$\\implies$ a bigger softening length leads to a smaller $\\delta v$.\n", "\n", "Using $n_{relax} = \\frac{\\delta v^2}{v^2}$, and knowing that the value of $v^2$ is derived from the Virial theorem (i.e. unaffected by the softening length), we can see that $n_{relax}$ scales like $\\varepsilon^{-2}$.\n", "\n", "##### Effect\n", "- The relaxation time decreases with increasing softening length\n", "- From the integration over all impact parameters $b$ even $b_{min}$ is chosen to be larger than $\\varepsilon$ $\\implies$ expect only a small effect on the relaxation time" ] } ], "metadata": { "kernelspec": { "display_name": "projects-X-9bmgL6", "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": "3.13.1" } }, "nbformat": 4, "nbformat_minor": 2 }