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hunt_reffert_2024_figures_12_to_16
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "id": "34e31333", | |
| "metadata": {}, | |
| "source": [ | |
| "# Code to reproduce \"Hunt & Reffert 2024\" figures 12 to 16\n", | |
| "\n", | |
| "The end of [Hunt & Reffert 2024](https://ui.adsabs.harvard.edu/abs/2024A%26A...686A..42H/abstract) derives a global cluster age and mass function using their catalogue and a simple volume-limited completeness estimate.\n", | |
| "\n", | |
| "This notebook walks you through the steps to reproduce their figures & results." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "3e76c1cc", | |
| "metadata": {}, | |
| "source": [ | |
| "## Imports\n", | |
| "\n", | |
| "Requirements (package versions I used to make this are in brackets):\n", | |
| "\n", | |
| "```\n", | |
| "numpy (2.2.4)\n", | |
| "pandas (2.2.3)\n", | |
| "matplotlib (3.10.1)\n", | |
| "astroquery (0.4.10)\n", | |
| "initial-mass-function (2025.1.20)\n", | |
| "```" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "0f91020a", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import pandas as pd\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "from scipy.optimize import curve_fit\n", | |
| "from imf.distributions import BrokenPowerLaw\n", | |
| "from astroquery.vizier import Vizier" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "93785d20", | |
| "metadata": {}, | |
| "source": [ | |
| "## Grab data\n", | |
| "\n", | |
| "We can pull the catalogue from the CDS - limiting ourselves to only clusters classified as open clusters." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
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| "id": "6f88194e", | |
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| "hunt_clusters = Vizier(\n", | |
| " catalog=\"J/A+A/686/A42/clusters\", row_limit=-1, columns=[\"**\"]\n", | |
| ").query_constraints(Type='o')[0].to_pandas()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "1d85565c", | |
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| "This contains lots of clusters to look at:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "id": "b500f9e0", | |
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| { | |
| "data": { | |
| "text/plain": [ | |
| "5647" | |
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| "execution_count": 3, | |
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| "output_type": "execute_result" | |
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| "source": [ | |
| "len(hunt_clusters)" | |
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| " <th></th>\n", | |
| " <th>recno</th>\n", | |
| " <th>Name</th>\n", | |
| " <th>ID</th>\n", | |
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| " <th>N</th>\n", | |
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| " <th>Nt</th>\n", | |
| " <th>RA_ICRS</th>\n", | |
| " <th>...</th>\n", | |
| " <th>MassTot</th>\n", | |
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| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>2</td>\n", | |
| " <td>AH03_J0748-26.9</td>\n", | |
| " <td>2</td>\n", | |
| " <td>AH03_J0748+26.9,AH03_J0748-26.9,AH03_J0748_26....</td>\n", | |
| " <td>o</td>\n", | |
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| " <td>66</td>\n", | |
| " <td>117.155887</td>\n", | |
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| " <td>411.325374</td>\n", | |
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| " <th>1</th>\n", | |
| " <td>3</td>\n", | |
| " <td>ASCC_5</td>\n", | |
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| " <td>ASCC_5,MWSC_93</td>\n", | |
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| " <td>14.469101</td>\n", | |
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| " <th>2</th>\n", | |
| " <td>4</td>\n", | |
| " <td>ASCC_6</td>\n", | |
| " <td>4</td>\n", | |
| " <td>ASCC_6,MWSC_141,Theia_2326</td>\n", | |
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| " <td>19.258570</td>\n", | |
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| " <th>3</th>\n", | |
| " <td>5</td>\n", | |
| " <td>ASCC_9</td>\n", | |
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| " <td>ASCC_9,Theia_1659</td>\n", | |
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| " <th>4</th>\n", | |
| " <td>6</td>\n", | |
| " <td>ASCC_11</td>\n", | |
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| " <td>ASCC_11,MWSC_284,Teutsch_J0332.2+4450,Theia_152</td>\n", | |
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| "<p>5 rows × 78 columns</p>\n", | |
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| "text/plain": [ | |
| " recno Name ID \\\n", | |
| "0 2 AH03_J0748-26.9 2 \n", | |
| "1 3 ASCC_5 3 \n", | |
| "2 4 ASCC_6 4 \n", | |
| "3 5 ASCC_9 5 \n", | |
| "4 6 ASCC_11 6 \n", | |
| "\n", | |
| " AllNames Type CST N \\\n", | |
| "0 AH03_J0748+26.9,AH03_J0748-26.9,AH03_J0748_26.... o 11.585524 68 \n", | |
| "1 ASCC_5,MWSC_93 o 8.316422 25 \n", | |
| "2 ASCC_6,MWSC_141,Theia_2326 o 19.258570 209 \n", | |
| "3 ASCC_9,Theia_1659 o 17.566553 136 \n", | |
| "4 ASCC_11,MWSC_284,Teutsch_J0332.2+4450,Theia_152 o 27.893488 315 \n", | |
| "\n", | |
| " CSTt Nt RA_ICRS ... MassTot e_MassTot minClSize \\\n", | |
| "0 11.781309 66 117.155887 ... 411.325374 86.730313 10 \n", | |
| "1 8.316422 25 14.469082 ... 173.195765 25.468717 10 \n", | |
| "2 19.258570 209 26.842159 ... 597.886570 92.290210 80 \n", | |
| "3 17.878141 132 41.623901 ... 1143.125147 217.935716 40 \n", | |
| "4 24.371220 231 53.050424 ... 688.493359 86.123955 20 \n", | |
| "\n", | |
| " isMerged isGMMMemb NXmatches XmatchType Note _RA.icrs \\\n", | |
| "0 0 0 2 1:m+name_updated 117.155899 \n", | |
| "1 0 0 1 1:1 14.469101 \n", | |
| "2 0 0 2 1:m 26.842166 \n", | |
| "3 0 0 2 1:m 41.623900 \n", | |
| "4 0 0 2 m:m 53.050418 \n", | |
| "\n", | |
| " _DE.icrs \n", | |
| "0 -26.972694 \n", | |
| "1 55.829182 \n", | |
| "2 57.738606 \n", | |
| "3 57.776852 \n", | |
| "4 44.840780 \n", | |
| "\n", | |
| "[5 rows x 78 columns]" | |
| ] | |
| }, | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "hunt_clusters.head()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "a96b5587", | |
| "metadata": {}, | |
| "source": [ | |
| "## Correcting for incompleteness (Fig. 12/13)\n", | |
| "\n", | |
| "Cluster mass has a major impact on the visibility of a cluster at a certain distance. This is clear from looking at the mass distribution of the catalogue:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "id": "e32eb0e0", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "high_mass = hunt_clusters.query(\"MassJ > 1000 and MassJ < 5000\")\n", | |
| "low_mass = hunt_clusters.query(\"MassJ > 50 and MassJ < 250\")\n", | |
| "\n", | |
| "fig, ax = plt.subplots()\n", | |
| "bins = np.linspace(0, 5000, num=31)\n", | |
| "ax.hist(low_mass[\"dist50\"], bins=bins, histtype=\"step\", label=\"Low mass\", density=True)[\n", | |
| " 1\n", | |
| "]\n", | |
| "ax.hist(high_mass[\"dist50\"], bins=bins, histtype=\"step\", label=\"High mass\", density=True)\n", | |
| "ax.legend()\n", | |
| "_ = ax.set(xlabel=\"Distance [pc]\", ylabel=\"P(Distance [pc])\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "41f1273c", | |
| "metadata": {}, | |
| "source": [ | |
| "Note how the high-mass clusters peak at a higher distance than the low-mass ones. That's because they're larger, so they can be seen further away.\n", | |
| "\n", | |
| "We can't use the entire HR24 catalogue (which has open clusters out to 15 kpc) directly, and instead need to work with a completeness-corrected sample.\n", | |
| "\n", | |
| "HR24 derived a relation for this:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "id": "c712c6d9", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Values from the paper (all in pc)\n", | |
| "ALPHA = 633.1\n", | |
| "BETA = -1582.6\n", | |
| "R_BREAK = 2792.9\n", | |
| "\n", | |
| "\n", | |
| "def r_100_percent(mass: np.ndarray):\n", | |
| " \"\"\"Function implementing the mass-dependent approximate 100% completeness limit\n", | |
| " of Equation 6 in Hunt & Reffert 2024.\n", | |
| " \"\"\"\n", | |
| " # N.b. that Fig 13 in the plot shows log mass in log base 10, but this relation\n", | |
| " # uses log base e - that was a bit of an oversight when I wrote it and did the\n", | |
| " # fitting =(\n", | |
| " r_100 = ALPHA * np.log(mass) + BETA\n", | |
| " return np.clip(r_100, 0, R_BREAK)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "621d2bda", | |
| "metadata": {}, | |
| "source": [ | |
| "Which we can use to get a completeness-corrected sample of HR24:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "id": "a1241cb0", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "2481" | |
| ] | |
| }, | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "hunt_complete = hunt_clusters.loc[\n", | |
| " hunt_clusters[\"dist50\"] < r_100_percent(hunt_clusters[\"MassJ\"])\n", | |
| "].reset_index(drop=True)\n", | |
| "\n", | |
| "len(hunt_complete)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "id": "5e25e78f", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<Axes: >" | |
| ] | |
| }, | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "hunt_complete['dist50'].hist()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "f0fbe430", | |
| "metadata": {}, | |
| "source": [ | |
| "When looking at statistics like the mass or age distribution, using this sample makes a difference." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "id": "cdcab609", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 800x400 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots(ncols=2, figsize=(8, 4))\n", | |
| "\n", | |
| "hist_kwargs = dict(histtype=\"step\", density=True)\n", | |
| "\n", | |
| "bins = np.geomspace(40, 1e4, num=15)\n", | |
| "ax[0].hist(hunt_complete['MassJ'], bins=bins, label=\"Complete\", **hist_kwargs)\n", | |
| "ax[0].hist(hunt_clusters['MassJ'], bins=bins, label=\"Full catalogue\", **hist_kwargs)\n", | |
| "\n", | |
| "bins = np.linspace(6.4, 10., num=15)\n", | |
| "ax[1].hist(hunt_complete['logAge50'], bins=bins, label=\"Complete\", **hist_kwargs)\n", | |
| "ax[1].hist(hunt_clusters['logAge50'], bins=bins, label=\"Full catalogue\", **hist_kwargs)\n", | |
| "\n", | |
| "ax[0].set(xscale=\"log\", xlabel=\"Mass [MSun]\", ylabel=\"P(Mass [MSun])\")\n", | |
| "ax[1].set(xlabel=\"log t\", ylabel=\"P(log t)\")\n", | |
| "ax[0].legend()\n", | |
| "fig.tight_layout()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "97108410", | |
| "metadata": {}, | |
| "source": [ | |
| "It's not too huge, but we have shifted the age distribution left a bit and changed the slope of the mass distribution a tiny bit - especially at the low-mass end. It's not a bad correction to include!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "245fc6c5", | |
| "metadata": {}, | |
| "source": [ | |
| "## Deriving a CAF (Fig. 14)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "8c1108f3", | |
| "metadata": {}, | |
| "source": [ | |
| "### Getting the units sensible" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "34bab36a", | |
| "metadata": {}, | |
| "source": [ | |
| "A first interesting port of call is the number density of clusters within the Milky Way, based on age!\n", | |
| "\n", | |
| "We'll want to do two things:\n", | |
| "1. Correct for the fact that logarithmic ages elapse a different amount of time per bin (e.g. log t of 6 to 7 covers 9 Myr, but 9 to 10 covers 9 Gyr!), meaning we'll want to use non-log ages\n", | |
| "2. Correct for the volume of our sample, which depends on mass" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "id": "b67bd09f", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Some setup:\n", | |
| "# 1. age in log space\n", | |
| "hunt_complete[\"age_yr\"] = 10 ** hunt_complete[\"logAge50\"]\n", | |
| "\n", | |
| "# 2. some plotting kwargs\n", | |
| "errorbar_kwargs = dict(\n", | |
| " fmt=\".\", ms=2, capsize=2, elinewidth=1.5, capthick=1.5, color=\"k\", zorder=10000\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "id": "f727751b", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/tmp/ipykernel_54784/829287362.py:4: RuntimeWarning: invalid value encountered in divide\n", | |
| " fractional_uncertainty = np.sqrt(counts) / counts\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# Bin the data & calculate uncertainties\n", | |
| "bins = np.linspace(hunt_complete[\"age_yr\"].min(), hunt_complete[\"age_yr\"].max(), num=21)\n", | |
| "counts, _ = np.histogram(hunt_complete[\"age_yr\"], bins=bins)\n", | |
| "fractional_uncertainty = np.sqrt(counts) / counts\n", | |
| "\n", | |
| "# Correct for the mass-dependent volume of our sample, assuming that we're looking at\n", | |
| "# the Milky Way top-down and have a cylindrical volume\n", | |
| "bin_centers = (bins[:-1] + bins[1:]) / 2\n", | |
| "bin_widths = bins[1:] - bins[:-1]\n", | |
| "number_per_bin = counts / (np.pi * r_100_percent(bin_centers) ** 2)\n", | |
| "number_per_bin_error = fractional_uncertainty * number_per_bin" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "9d51c5f1", | |
| "metadata": {}, | |
| "source": [ | |
| "Let's try plotting it!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "id": "bbaef1c7", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[Text(0.5, 0, 't [yr]'), Text(0, 0.5, 'n(t) [clusters pc$^{-2}$]')]" | |
| ] | |
| }, | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " number_per_bin,\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=number_per_bin_error,\n", | |
| " **errorbar_kwargs,\n", | |
| ")\n", | |
| "ax.set(xlabel=\"t [yr]\", ylabel=\"n(t) [clusters pc$^{-2}$]\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "f361f9a3", | |
| "metadata": {}, | |
| "source": [ | |
| "While this avoids log bin problems, we now unfortunately don't really have much resolution at the low-age end. Let's try making it a log plot _of a linear quantity_:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "id": "08a6ca5d", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[Text(0.5, 0, 't [yr]'), Text(0, 0.5, 'n(t) [clusters pc$^{-2}$]'), None, None]" | |
| ] | |
| }, | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " number_per_bin,\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=number_per_bin_error,\n", | |
| " **errorbar_kwargs,\n", | |
| ")\n", | |
| "ax.set(xlabel=\"t [yr]\", ylabel=\"n(t) [clusters pc$^{-2}$]\", xscale=\"log\", yscale=\"log\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "5f0142d5", | |
| "metadata": {}, | |
| "source": [ | |
| "Well, now our bins have really weird sizes!\n", | |
| "\n", | |
| "Let's try using _logarithmically sized bins_ of a _linear quantity_:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "id": "801faacd", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Bin the data & calculate uncertainties\n", | |
| "bins = np.geomspace(\n", | |
| " hunt_complete[\"age_yr\"].min(), hunt_complete[\"age_yr\"].max(), num=21\n", | |
| ")\n", | |
| "counts, _ = np.histogram(hunt_complete[\"age_yr\"], bins=bins)\n", | |
| "fractional_uncertainty = np.sqrt(counts) / counts\n", | |
| "\n", | |
| "# Correct for the mass-dependent volume of our sample, assuming that we're looking at\n", | |
| "# the Milky Way top-down and have a cylindrical volume\n", | |
| "bin_centers = (bins[:-1] + bins[1:]) / 2\n", | |
| "bin_widths = bins[1:] - bins[:-1]\n", | |
| "number_per_bin = counts / (np.pi * r_100_percent(bin_centers) ** 2)\n", | |
| "number_per_bin_error = fractional_uncertainty * number_per_bin" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "id": "8c96369f", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[Text(0.5, 0, 't [yr]'), Text(0, 0.5, 'n(t) [clusters pc$^{-2}$]'), None, None]" | |
| ] | |
| }, | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " number_per_bin,\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=number_per_bin_error,\n", | |
| " **errorbar_kwargs,\n", | |
| ")\n", | |
| "ax.set(xlabel=\"t [yr]\", ylabel=\"n(t) [clusters pc$^{-2}$]\", xscale=\"log\", yscale=\"log\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "56be5668", | |
| "metadata": {}, | |
| "source": [ | |
| "Now we're back to square one! We have an age distribution that peaks at $10^8$ years (erroneously), because all of our bins have different widths in _real time_.\n", | |
| "\n", | |
| "The trick is that we need to correct for _the width of our logarithmically spaced bins_, too:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "id": "d4ca6ec5", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "number_function = number_per_bin / bin_widths\n", | |
| "number_function_error = number_per_bin / bin_widths * fractional_uncertainty" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "id": "51cb9b46", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " number_function,\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=number_function_error,\n", | |
| " **errorbar_kwargs,\n", | |
| ")\n", | |
| "_ = ax.set(\n", | |
| " xlabel=\"t [yr]\",\n", | |
| " ylabel=r\"n(t) / $\\Delta t$ [clusters yr$^{-1}$ pc$^{-2}$]\",\n", | |
| " xscale=\"log\",\n", | |
| " yscale=\"log\",\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "d77fa262", | |
| "metadata": {}, | |
| "source": [ | |
| "This now reproduces the points in Figure 14!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "30e84f46", | |
| "metadata": {}, | |
| "source": [ | |
| "### Performing fits\n", | |
| "\n", | |
| "We'd love to make a fit of this distribution too! Let's fit a **broken power law**.\n", | |
| "\n", | |
| "We'll use the BrokenPowerLaw implementation in the IMF module." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "id": "bb9c6795", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def get_breaks(x, breaks):\n", | |
| " \"\"\"imf's BrokenPowerLaw requires that it be given a minimum, maximum, and break\n", | |
| " point. Here, we go slightly beyond the minimum and maximum just to avoid any\n", | |
| " boundary issues; note that that changes the final value of the normalisation\n", | |
| " constant that we have.\n", | |
| " \"\"\"\n", | |
| " return np.hstack([x.min() / 1.1, breaks, x.max() * 1.1])\n", | |
| "\n", | |
| "\n", | |
| "def broken_power_law(x, slope_1, slope_2, x_break, normalisation):\n", | |
| " breaks = get_breaks(x, 10**x_break)\n", | |
| " power_law = BrokenPowerLaw([slope_1, slope_2], breaks)\n", | |
| " return normalisation * power_law.pdf(x)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "d8d27bf9", | |
| "metadata": {}, | |
| "source": [ | |
| "We can fit the function with simple linear regression, starting off with sensible parameter guesses to avoid local minima, and some bounds to avoid e.g. a negative normalization constant or a break point outside of our age range:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 19, | |
| "id": "53287912", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Slope 1: -0.5127403937127608 +- 0.040835673519218164\n", | |
| "Slope 2: -2.193580857039556 +- 0.07560635651625457\n", | |
| "Break point: 8.232814017819926 +- 0.0285661345304713\n", | |
| "Normalisation: 0.00010049112636431915 +- 3.436720423287778e-06\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "guess = [-0.6, -0.6, 8.3, 0.001]\n", | |
| "power_law_bounds = [\n", | |
| " [-np.inf, -np.inf, np.log10(bin_centers.min()), 0],\n", | |
| " [np.inf, np.inf, np.log10(bin_centers.max()), np.inf],\n", | |
| "]\n", | |
| "\n", | |
| "parameters, errors = curve_fit(\n", | |
| " broken_power_law,\n", | |
| " bin_centers,\n", | |
| " number_function,\n", | |
| " p0=guess,\n", | |
| " sigma=number_function_error,\n", | |
| " bounds=power_law_bounds,\n", | |
| ")\n", | |
| "\n", | |
| "# Print (not full cov matrix, just basic errors - remember also that cov matrix is\n", | |
| "# variance, not std deviation, so we need to sqrt too)\n", | |
| "for i, name in enumerate((\"Slope 1\", \"Slope 2\", \"Break point\", \"Normalisation\")):\n", | |
| " print(f\"{name}: {parameters[i]} +- {errors[i][i]**0.5}\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "aced3ccb", | |
| "metadata": {}, | |
| "source": [ | |
| "Let's plot it on top of our points:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 20, | |
| "id": "09fb4459", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " number_function,\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=number_function_error,\n", | |
| " **errorbar_kwargs,\n", | |
| ")\n", | |
| "x_range = np.geomspace(bins.min(), bins.max(), num=500)\n", | |
| "y_range = broken_power_law(x_range, *parameters)\n", | |
| "ax.plot(x_range, y_range, 'r-')\n", | |
| "\n", | |
| "_ = ax.set(\n", | |
| " xlabel=\"t [yr]\",\n", | |
| " ylabel=r\"n(t) / $\\Delta t$ [clusters yr$^{-1}$ pc$^{-2}$]\",\n", | |
| " xscale=\"log\",\n", | |
| " yscale=\"log\",\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "91bd000c", | |
| "metadata": {}, | |
| "source": [ | |
| "& there's our fit!\n", | |
| "\n", | |
| "I haven't added the other literature fits in the plot, but they're easy to look up if you need them =)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "c3154780", | |
| "metadata": {}, | |
| "source": [ | |
| "## Deriving a CMF (Fig. 15 + 16)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "85aa0363", | |
| "metadata": {}, | |
| "source": [ | |
| "### Getting the units sensible (again)\n", | |
| "\n", | |
| "Similarly, we can now make a cluster mass function following the same concepts. This time, we'll want to do it a few times:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 21, | |
| "id": "de0157e6", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def create_mass_function(sample, bins=21):\n", | |
| " # Bin the data & calculate uncertainties\n", | |
| " bins = np.geomspace(\n", | |
| " hunt_complete[\"MassJ\"].min(),\n", | |
| " hunt_complete.query(\"MassJ < 10000\")[\"MassJ\"].max(),\n", | |
| " num=bins,\n", | |
| " )\n", | |
| " counts, _ = np.histogram(sample[\"MassJ\"], bins=bins)\n", | |
| " fractional_uncertainty = np.sqrt(counts) / counts\n", | |
| "\n", | |
| " # Correct for the mass-dependent volume of our sample, assuming that we're looking\n", | |
| " # at the Milky Way top-down and have a cylindrical volume\n", | |
| " bin_centers = (bins[:-1] + bins[1:]) / 2\n", | |
| " bin_widths = bins[1:] - bins[:-1]\n", | |
| " number_per_bin = counts / (np.pi * r_100_percent(bin_centers) ** 2)\n", | |
| " number_function = number_per_bin / bin_widths\n", | |
| " number_function_error = number_function * fractional_uncertainty\n", | |
| "\n", | |
| " return bin_centers, bin_widths, number_function, number_function_error\n", | |
| "\n", | |
| "\n", | |
| "bin_centers, bin_widths, number_function, number_function_error = create_mass_function(\n", | |
| " hunt_complete\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "2cdf885b", | |
| "metadata": {}, | |
| "source": [ | |
| "And we'll want to just fit a plain power law:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 22, | |
| "id": "b851489f", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def power_law(x, slope, normalisation):\n", | |
| " return normalisation * x ** slope" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "b297dcc0", | |
| "metadata": {}, | |
| "source": [ | |
| "Let's show the top panel of Fig. 15 first." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 23, | |
| "id": "dc95385f", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " number_function,\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=number_function_error,\n", | |
| " **errorbar_kwargs,\n", | |
| ")\n", | |
| "x_range = np.geomspace(40, 1e4, num=500)\n", | |
| "y_range = power_law(x_range, -2, 0.02)\n", | |
| "ax.plot(x_range, y_range, \"b--\", label=\"Krumholz+19 k=-2 power law\")\n", | |
| "\n", | |
| "ax.legend()\n", | |
| "_ = ax.set(\n", | |
| " xlabel=\"M [MSun]\",\n", | |
| " ylabel=r\"n(t) / $\\Delta M$ [clusters M$^{-1}_\\odot$ pc$^{-2}$]\",\n", | |
| " xscale=\"log\",\n", | |
| " yscale=\"log\",\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "b84bbfff", | |
| "metadata": {}, | |
| "source": [ | |
| "We can see the same thing, where a simple -2 power law doesn't quite cut it for fitting the sample. Instead, there's a complicated age-dependent effect, which we can see if we split the sample into age ranges." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 24, | |
| "id": "c8e82779", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "max_age = [7, 7.5, 8.0, 8.5, 9.0, 9.5]\n", | |
| "min_age = [0] + max_age[:-1]\n", | |
| "\n", | |
| "mass_functions = {}\n", | |
| "mass_function_errors = {}\n", | |
| "\n", | |
| "for i, (min, max) in enumerate(zip(min_age, max_age)):\n", | |
| " subsample = hunt_complete.loc[\n", | |
| " (hunt_complete[\"logAge50\"] >= min) & (hunt_complete[\"logAge50\"] < max)\n", | |
| " ]\n", | |
| " bin_centers, bin_widths, mass_functions[i], mass_function_errors[i] = (\n", | |
| " create_mass_function(subsample, bins=11)\n", | |
| " )" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "08a9b7b4", | |
| "metadata": {}, | |
| "source": [ | |
| "Which we can now plot:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 25, | |
| "id": "44e0c5db", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "errorbar_kwargs_no_color = errorbar_kwargs.copy()\n", | |
| "_ = errorbar_kwargs_no_color.pop(\"color\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 26, | |
| "id": "0ba6b6ba", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "\n", | |
| "for i, (min, max) in enumerate(zip(min_age, max_age)):\n", | |
| " ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " mass_functions[i],\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=mass_function_errors[i],\n", | |
| " label=f\"{min:.1f} <= log t < {max:.1f}\",\n", | |
| " color=plt.get_cmap(\"viridis\")(i / (len(mass_functions) - 1)),\n", | |
| " **errorbar_kwargs_no_color,\n", | |
| " )\n", | |
| "\n", | |
| "ax.legend()\n", | |
| "_ = ax.set(\n", | |
| " xlabel=\"M [MSun]\",\n", | |
| " ylabel=r\"n(t) / $\\Delta M$ [clusters M$^{-1}_\\odot$ pc$^{-2}$]\",\n", | |
| " xscale=\"log\",\n", | |
| " yscale=\"log\",\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "b00fa17b", | |
| "metadata": {}, | |
| "source": [ | |
| "However, this still doesn't look quite like the plot in the paper: there are more clusters in the ~log 8 age range than any other. That's because we've done it again! Our ranges have variable width, which we need to correct for..." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 27, | |
| "id": "a1019eee", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "mass_age_functions = {}\n", | |
| "mass_age_function_errors = {}\n", | |
| "\n", | |
| "for i, (min, max) in enumerate(zip(min_age, max_age)):\n", | |
| " age_range_myr = (10**max - 10**min) * 1e-6\n", | |
| " mass_age_functions[i] = mass_functions[i] / age_range_myr\n", | |
| " mass_age_function_errors[i] = mass_function_errors[i] / age_range_myr\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 28, | |
| "id": "0871d856", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "\n", | |
| "for i, (min, max) in enumerate(zip(min_age, max_age)):\n", | |
| " ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " mass_age_functions[i],\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=mass_age_function_errors[i],\n", | |
| " label=f\"{min:.1f} <= log t < {max:.1f}\",\n", | |
| " color=plt.get_cmap(\"viridis\")(i / (len(mass_age_function_errors) - 1)),\n", | |
| " **errorbar_kwargs_no_color,\n", | |
| " )\n", | |
| "\n", | |
| "ax.legend()\n", | |
| "_ = ax.set(\n", | |
| " xlabel=\"M [MSun]\",\n", | |
| " ylabel=r\"n(t) / $\\Delta M$ / $\\Delta t$ [clusters M$^{-1}_\\odot$ Myr$^{-1}$ pc$^{-2}$]\",\n", | |
| " xscale=\"log\",\n", | |
| " yscale=\"log\",\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "42a49597", | |
| "metadata": {}, | |
| "source": [ | |
| "Which is starting to look a lot more like the paper!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "b8cccf2c", | |
| "metadata": {}, | |
| "source": [ | |
| "### Performing fits\n", | |
| "\n", | |
| "Finally, we can do some fits to them:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 29, | |
| "id": "e866d8be", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Age range 0 to 7\n", | |
| "Slope: -1.8707956749350745 +- 0.08951847577423135\n", | |
| "Normalisation: 6.818552532826738e-05 +- 3.5776637370363395e-05\n", | |
| "\n", | |
| "Age range 7 to 7.5\n", | |
| "Slope: -1.80041643955282 +- 0.08628189085206395\n", | |
| "Normalisation: 2.7951775571358306e-05 +- 1.440951240798117e-05\n", | |
| "\n", | |
| "Age range 7.5 to 8.0\n", | |
| "Slope: -1.7677867879998848 +- 0.09232099580570069\n", | |
| "Normalisation: 1.3417847673241178e-05 +- 7.4634470831148435e-06\n", | |
| "\n", | |
| "Age range 8.0 to 8.5\n", | |
| "Slope: -1.722816199710715 +- 0.055907252074372166\n", | |
| "Normalisation: 4.750245492963403e-06 +- 1.616128790722183e-06\n", | |
| "\n", | |
| "Age range 8.5 to 9.0\n", | |
| "Slope: -1.5786667527879183 +- 0.06788511340173065\n", | |
| "Normalisation: 2.2245400955646385e-07 +- 9.592271872523898e-08\n", | |
| "\n", | |
| "Age range 9.0 to 9.5\n", | |
| "Slope: -1.1061390590525073 +- 0.1141807801943057\n", | |
| "Normalisation: 6.28553648446869e-10 +- 5.132817407644092e-10\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "mass_age_function_fit_params = {}\n", | |
| "mass_age_function_fit_errors = {}\n", | |
| "\n", | |
| "bounds = [[-np.inf, 0], [np.inf, np.inf]]\n", | |
| "guess = (-2, 0.001)\n", | |
| "\n", | |
| "\n", | |
| "for i, (y_data, y_errors) in enumerate(\n", | |
| " zip(mass_age_functions.values(), mass_age_function_errors.values())\n", | |
| "):\n", | |
| " mass_age_function_fit_params[i], mass_age_function_fit_errors[i] = curve_fit(\n", | |
| " power_law, bin_centers, y_data, sigma=y_errors, bounds=bounds, p0=guess\n", | |
| " )\n", | |
| "\n", | |
| " if i != 0:\n", | |
| " print(\"\")\n", | |
| " print(f\"Age range {min_age[i]} to {max_age[i]}\")\n", | |
| " print(\n", | |
| " f\"Slope: {mass_age_function_fit_params[i][0]} +- {mass_age_function_fit_errors[i][0][0] ** 0.5}\"\n", | |
| " )\n", | |
| " print(\n", | |
| " f\"Normalisation: {mass_age_function_fit_params[i][1]} +- {mass_age_function_fit_errors[i][1][1] ** 0.5}\"\n", | |
| " )\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "779861e9", | |
| "metadata": {}, | |
| "source": [ | |
| "& plot them:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 30, | |
| "id": "42721d31", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots()\n", | |
| "\n", | |
| "for i, (min, max) in enumerate(zip(min_age, max_age)):\n", | |
| " color = plt.get_cmap(\"viridis\")(i / (len(mass_age_function_errors) - 1))\n", | |
| " ax.errorbar(\n", | |
| " bin_centers,\n", | |
| " mass_age_functions[i],\n", | |
| " xerr=bin_widths / 2,\n", | |
| " yerr=mass_age_function_errors[i],\n", | |
| " label=f\"{min:.1f} <= log t < {max:.1f}\",\n", | |
| " color=color,\n", | |
| " **errorbar_kwargs_no_color,\n", | |
| " )\n", | |
| " x_range = np.geomspace(40, 1e4, num=50)\n", | |
| " y_range = power_law(x_range, *mass_age_function_fit_params[i])\n", | |
| " ax.plot(x_range, y_range, '--', color=color)\n", | |
| "\n", | |
| "ax.legend()\n", | |
| "_ = ax.set(\n", | |
| " xlabel=\"M [MSun]\",\n", | |
| " ylabel=r\"n(t) / $\\Delta M$ / $\\Delta t$ [clusters M$^{-1}_\\odot$ Myr$^{-1}$ pc$^{-2}$]\",\n", | |
| " xscale=\"log\",\n", | |
| " yscale=\"log\",\n", | |
| ")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "ecb96598", | |
| "metadata": {}, | |
| "source": [ | |
| "And there we have the lower half of Fig. 15!" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "f336d84e", | |
| "metadata": {}, | |
| "source": [ | |
| "### Trends in slope & normalisation constant\n", | |
| "\n", | |
| "Let's also show Fig. 16 and a silly thing I shouldn't have missed out (how the normalisation constant changes over time):" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 31, | |
| "id": "cbd8b486", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 800x400 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots(ncols=2, figsize=(8, 4), sharex=True)\n", | |
| "\n", | |
| "slopes = [param[0] for param in mass_age_function_fit_params.values()]\n", | |
| "normalisations = [param[1] for param in mass_age_function_fit_params.values()]\n", | |
| "slope_errors = [param[0][0] ** 0.5 for param in mass_age_function_fit_errors.values()]\n", | |
| "normalisation_errors = [\n", | |
| " param[1][1] ** 0.5 for param in mass_age_function_fit_errors.values()\n", | |
| "]\n", | |
| "\n", | |
| "mean_ages = [(10**min + 10**max) / 2 for min, max in zip(min_age, max_age)]\n", | |
| "age_widths = [(10**max - 10**min) / 2 for min, max in zip(min_age, max_age)]\n", | |
| "\n", | |
| "ax[0].errorbar(mean_ages, slopes, xerr=age_widths, yerr=slope_errors, **errorbar_kwargs)\n", | |
| "\n", | |
| "ax[1].errorbar(\n", | |
| " mean_ages,\n", | |
| " normalisations,\n", | |
| " xerr=age_widths,\n", | |
| " yerr=normalisation_errors,\n", | |
| " **errorbar_kwargs,\n", | |
| ")\n", | |
| "\n", | |
| "ax[0].set(xscale=\"log\", xlim=(5e5, None), xlabel=\"t [yr]\", ylabel=\"Slope\")\n", | |
| "ax[1].set(xlabel=\"t [yr]\", ylabel=\"Normalisation\", yscale=\"log\")\n", | |
| "fig.tight_layout()" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": ".venv", | |
| "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": "3.12.7" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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