{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Remnant Displacement and Return Times" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:11.563424Z", "iopub.status.busy": "2026-06-13T10:28:11.563068Z", "iopub.status.idle": "2026-06-13T10:28:13.116796Z", "shell.execute_reply": "2026-06-13T10:28:13.116319Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lal.MSUN_SI != Msun\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings('ignore', 'Wswiglal-redir-stdio')\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from gwGenealogy.utils import set_rcparams\n", "from gwGenealogy.hosts import (\n", " PlummerCluster,\n", " plummer_apocentre,\n", " dynamical_friction_time,\n", ")\n", "from gwGenealogy.binaries import BBHs, BBHRemnant, sample_masses, sample_spins\n", "\n", "set_rcparams()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate a realistic kick distribution\n", "\n", "We sample a population of 1G+1G BBH mergers and compute kicks using `BBHRemnant`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.118134Z", "iopub.status.busy": "2026-06-13T10:28:13.118007Z", "iopub.status.idle": "2026-06-13T10:28:13.124889Z", "shell.execute_reply": "2026-06-13T10:28:13.124489Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Kick range: 0.3 - 285.2 km/s\n", "Remnant mass range: 9.6 - 87.8 Msun\n" ] } ], "source": [ "N = 5000\n", "\n", "m1, m2 = sample_masses(N, m_min=5, m_max=50, m1_distribution='powerlaw', alpha=-2.35, seed=42)\n", "chi1, chi2 = sample_spins(N, chi_max=0.5, spin_magnitude='uniform', spin_angles='isotropic', seed=43)\n", "\n", "bbh = BBHs(\n", " m1=m1, m2=m2,\n", " a1=np.linalg.norm(chi1, axis=1),\n", " a2=np.linalg.norm(chi2, axis=1),\n", " theta1=np.arccos(chi1[:, 2] / np.linalg.norm(chi1, axis=1)),\n", " theta2=np.arccos(chi2[:, 2] / np.linalg.norm(chi2, axis=1)),\n", ")\n", "\n", "rem = BBHRemnant(bbh=bbh, precessing=False, kick_model='hlz')\n", "\n", "v_kick = rem.vkick\n", "M_bh = rem.Mf\n", "\n", "print(f\"Kick range: {v_kick.min():.1f} - {v_kick.max():.1f} km/s\")\n", "print(f\"Remnant mass range: {M_bh.min():.1f} - {M_bh.max():.1f} Msun\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Apocentre displacement (r_max)\n", "\n", "For a bound remnant kicked with velocity $v_{\\rm kick} < v_{\\rm esc}$ in a Plummer potential, the radial-orbit apocentre is:\n", "\n", "$$r_{\\rm max} = a \\sqrt{(1 - u^2)^{-2} - 1}, \\quad u = v_{\\rm kick}/v_{\\rm esc}$$\n", "\n", "Remnants kicked near the escape speed reach very large displacements and may exceed the tidal radius." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.125883Z", "iopub.status.busy": "2026-06-13T10:28:13.125816Z", "iopub.status.idle": "2026-06-13T10:28:13.128310Z", "shell.execute_reply": "2026-06-13T10:28:13.127950Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PlummerCluster(Mcl=1.00e+06, r_h=3.00, a=2.30, v_esc=61.2 km/s, v_core=33.1 km/s, r_t=15.0 pc, type=GC)\n", "\n", "Bound fraction: 0.237\n", "Apocentre range: 0.02 - 1771.7 pc\n", "Tidal radius: 15.0 pc\n", "Fraction within tidal radius: 0.900\n" ] } ], "source": [ "cluster_gc = PlummerCluster(Mcl=1e6, r_h=3.0, cluster_type='GC')\n", "print(cluster_gc)\n", "\n", "# Apocentre for bound kicks\n", "bound = v_kick < cluster_gc.v_esc\n", "v_bound = v_kick[bound]\n", "r_max = plummer_apocentre(v_bound, cluster_gc.v_esc, cluster_gc.a)\n", "\n", "print(f\"\\nBound fraction: {bound.mean():.3f}\")\n", "print(f\"Apocentre range: {r_max.min():.2f} - {r_max.max():.1f} pc\")\n", "print(f\"Tidal radius: {cluster_gc.r_t:.1f} pc\")\n", "print(f\"Fraction within tidal radius: {(r_max <= cluster_gc.r_t).mean():.3f}\")" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.129344Z", "iopub.status.busy": "2026-06-13T10:28:13.129276Z", "iopub.status.idle": "2026-06-13T10:28:13.445629Z", "shell.execute_reply": "2026-06-13T10:28:13.445225Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "# Left: r_max distribution\n", "retained = r_max[r_max <= cluster_gc.r_t]\n", "axes[0].hist(retained, bins=60, density=True, alpha=0.7)\n", "axes[0].axvline(cluster_gc.a, color='C1', ls='--', lw=2, label=f'Scale radius $a = {cluster_gc.a:.1f}$ pc')\n", "axes[0].axvline(cluster_gc.r_t, color='C3', ls='--', lw=2, label=f'Tidal radius $r_t = {cluster_gc.r_t:.1f}$ pc')\n", "axes[0].set_xlabel(r'$r_{\\rm max}$ [pc]')\n", "axes[0].set_ylabel('Density')\n", "axes[0].set_title('Apocentre distribution (retained)')\n", "axes[0].legend()\n", "\n", "# Right: r_max vs v_kick\n", "u = np.linspace(0.01, 0.999, 500)\n", "r_curve = cluster_gc.a * np.sqrt((1.0 - u**2)**(-2) - 1.0)\n", "axes[1].semilogy(u * cluster_gc.v_esc, r_curve, 'k-', lw=2)\n", "axes[1].axhline(cluster_gc.r_t, color='C3', ls='--', lw=1.5, label=f'$r_t = {cluster_gc.r_t:.1f}$ pc')\n", "axes[1].axvline(cluster_gc.v_esc, color='C2', ls=':', lw=1.5, label=f'$v_{{\\\\rm esc}} = {cluster_gc.v_esc:.0f}$ km/s')\n", "axes[1].set_xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "axes[1].set_ylabel(r'$r_{\\rm max}$ [pc]')\n", "axes[1].set_title('Apocentre vs kick velocity')\n", "axes[1].set_xlim(0, cluster_gc.v_esc * 1.05)\n", "axes[1].legend()\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dynamical friction return time (t_DF)\n", "\n", "A retained remnant sinks back to the cluster core via Chandrasekhar dynamical friction. The orbit-averaged return time depends on the kick velocity, cluster properties, and remnant mass." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.446981Z", "iopub.status.busy": "2026-06-13T10:28:13.446893Z", "iopub.status.idle": "2026-06-13T10:28:13.467515Z", "shell.execute_reply": "2026-06-13T10:28:13.467167Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P_ret = 0.213\n", "P_hier = 0.0111\n", "Return time range: 21.28 - 21165.7 Myr\n", "Median return time: 454.3 Myr\n" ] } ], "source": [ "cluster_gc.merger_analysis(v_kick, M_bh)\n", "\n", "t_df_ret = cluster_gc.t_df[cluster_gc.retained]\n", "\n", "print(f\"P_ret = {cluster_gc.P_ret:.3f}\")\n", "print(f\"P_hier = {cluster_gc.P_hier:.4f}\")\n", "print(f\"Return time range: {np.nanmin(t_df_ret):.2f} - {np.nanmax(t_df_ret):.1f} Myr\")\n", "print(f\"Median return time: {np.nanmedian(t_df_ret):.1f} Myr\")" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.468586Z", "iopub.status.busy": "2026-06-13T10:28:13.468515Z", "iopub.status.idle": "2026-06-13T10:28:13.669801Z", "shell.execute_reply": "2026-06-13T10:28:13.669459Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "# Left: t_DF distribution (log-spaced bins)\n", "log_bins = np.logspace(np.log10(t_df_ret.min()), np.log10(t_df_ret.max()), 60)\n", "axes[0].hist(t_df_ret, bins=log_bins, density=True, alpha=0.7)\n", "axes[0].axvline(np.median(t_df_ret), color='C1', ls='--', lw=2, label=f'Median = {np.median(t_df_ret):.0f} Myr')\n", "axes[0].set_xscale('log')\n", "axes[0].set_xlabel(r'$t_{\\rm DF}$ [Myr]')\n", "axes[0].set_ylabel('Density')\n", "axes[0].set_title('Return time distribution (retained)')\n", "axes[0].legend()\n", "\n", "# Right: t_DF vs v_kick\n", "idx = cluster_gc.retained\n", "sc = axes[1].scatter(v_kick[idx], cluster_gc.t_df[idx], c=M_bh[idx],\n", " s=5, alpha=0.5, cmap='viridis', rasterized=True)\n", "axes[1].set_xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "axes[1].set_ylabel(r'$t_{\\rm DF}$ [Myr]')\n", "axes[1].set_yscale('log')\n", "axes[1].set_title('Return time vs kick velocity')\n", "cbar = plt.colorbar(sc, ax=axes[1])\n", "cbar.set_label(r'$M_{\\rm f}\\;[M_\\odot]$')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Displacement and return time: joint view" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.671075Z", "iopub.status.busy": "2026-06-13T10:28:13.670998Z", "iopub.status.idle": "2026-06-13T10:28:13.798346Z", "shell.execute_reply": "2026-06-13T10:28:13.797832Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_max_ret = cluster_gc.r_max[cluster_gc.retained]\n", "t_df_ret = cluster_gc.t_df[cluster_gc.retained]\n", "M_bh_ret = M_bh[cluster_gc.retained]\n", "\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "sc = ax.scatter(r_max_ret, t_df_ret, c=M_bh_ret, s=8, alpha=0.5,\n", " cmap='viridis', rasterized=True)\n", "ax.axvline(cluster_gc.a, color='C1', ls='--', lw=1.5, label=f'Scale radius $a$')\n", "ax.set_xlabel(r'$r_{\\rm max}$ [pc]')\n", "ax.set_ylabel(r'$t_{\\rm DF}$ [Myr]')\n", "ax.set_yscale('log')\n", "ax.set_title('Apocentre vs return time (retained remnants)')\n", "cbar = plt.colorbar(sc, ax=ax)\n", "cbar.set_label(r'$M_{\\rm f}\\;[M_\\odot]$')\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dependence on cluster mass\n", "\n", "Compare displacement and return time distributions across different cluster masses." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.799558Z", "iopub.status.busy": "2026-06-13T10:28:13.799470Z", "iopub.status.idle": "2026-06-13T10:28:13.957178Z", "shell.execute_reply": "2026-06-13T10:28:13.956721Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cluster_masses = [1e5, 5e5, 1e6, 5e6]\n", "colors = plt.cm.coolwarm(np.linspace(0.1, 0.9, len(cluster_masses)))\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "for Mcl, c in zip(cluster_masses, colors):\n", " cl = PlummerCluster(Mcl=Mcl, r_h=3.0, cluster_type='GC')\n", " cl.merger_analysis(v_kick, M_bh)\n", " \n", " if cl.retained.any():\n", " label = rf'$M_{{\\rm cl}} = {Mcl:.0e}\\;M_\\odot$, $v_{{\\rm esc}}={cl.v_esc:.0f}$ km/s'\n", " r_ret = cl.r_max[cl.retained]\n", " t_ret = cl.t_df[cl.retained]\n", " axes[0].hist(r_ret, bins=40, density=True, histtype='step', lw=2, color=c, label=label)\n", " log_bins = np.logspace(np.log10(t_ret.min()), np.log10(t_ret.max()), 40)\n", " axes[1].hist(t_ret, bins=log_bins, density=True, histtype='step', lw=2, color=c, label=label)\n", "\n", "axes[0].set_xlabel(r'$r_{\\rm max}$ [pc]')\n", "axes[0].set_ylabel('Density')\n", "axes[0].set_title('Apocentre distribution')\n", "axes[0].legend(fontsize=9)\n", "\n", "axes[1].set_xscale('log')\n", "axes[1].set_xlabel(r'$t_{\\rm DF}$ [Myr]')\n", "axes[1].set_ylabel('Density')\n", "axes[1].set_title('Return time distribution')\n", "axes[1].legend(fontsize=9)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GC vs NSC\n", "\n", "Nuclear star clusters (NSCs) are more massive and have higher escape speeds, leading to shorter return times and smaller displacements for retained remnants." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:13.958371Z", "iopub.status.busy": "2026-06-13T10:28:13.958280Z", "iopub.status.idle": "2026-06-13T10:28:14.097070Z", "shell.execute_reply": "2026-06-13T10:28:14.096688Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gc = PlummerCluster(Mcl=5e5, r_h=3.0, cluster_type='GC')\n", "nsc = PlummerCluster(Mcl=1e7, r_h=5.0, cluster_type='NSC')\n", "\n", "gc.merger_analysis(v_kick, M_bh)\n", "nsc.merger_analysis(v_kick, M_bh)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "for cl, label, c in [(gc, 'GC', 'C0'), (nsc, 'NSC', 'C3')]:\n", " if cl.retained.any():\n", " full_label = f'{label}: $v_{{\\\\rm esc}}$={cl.v_esc:.0f} km/s, $P_{{\\\\rm ret}}$={cl.P_ret:.3f}'\n", " axes[0].hist(cl.r_max[cl.retained], bins=50, density=True,\n", " histtype='step', lw=2, color=c, label=full_label)\n", " t_ret = cl.t_df[cl.retained]\n", " log_bins = np.logspace(np.log10(t_ret.min()), np.log10(t_ret.max()), 50)\n", " axes[1].hist(t_ret, bins=log_bins, density=True,\n", " histtype='step', lw=2, color=c, label=full_label)\n", "\n", "axes[0].set_xlabel(r'$r_{\\rm max}$ [pc]')\n", "axes[0].set_ylabel('Density')\n", "axes[0].set_title('Apocentre: GC vs NSC')\n", "axes[0].legend()\n", "\n", "axes[1].set_xscale('log')\n", "axes[1].set_xlabel(r'$t_{\\rm DF}$ [Myr]')\n", "axes[1].set_ylabel('Density')\n", "axes[1].set_title('Return time: GC vs NSC')\n", "axes[1].legend()\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effect of remnant mass on return time\n", "\n", "Heavier remnants experience stronger dynamical friction and return to the core faster." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:14.098172Z", "iopub.status.busy": "2026-06-13T10:28:14.098107Z", "iopub.status.idle": "2026-06-13T10:28:14.240534Z", "shell.execute_reply": "2026-06-13T10:28:14.240119Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cl = PlummerCluster(Mcl=1e6, r_h=3.0, cluster_type='GC')\n", "\n", "v_test = np.linspace(1, cl.v_esc * 0.95, 200)\n", "masses = [20, 40, 60, 80]\n", "\n", "fig, ax = plt.subplots(figsize=(8, 5))\n", "for M in masses:\n", " t_df = dynamical_friction_time(v_test, cl.v_esc, cl.Mcl, cl.a, M)\n", " ax.semilogy(v_test, t_df, lw=2, label=rf'$M_{{\\rm f}} = {M}\\;M_\\odot$')\n", "\n", "ax.set_xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "ax.set_ylabel(r'$t_{\\rm DF}$ [Myr]')\n", "ax.set_title(rf'Return time vs kick ($M_{{\\rm cl}} = 10^6\\;M_\\odot$, GC)')\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standalone functions\n", "\n", "The `plummer_apocentre` and `dynamical_friction_time` functions can be used directly without the `PlummerCluster` class." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2026-06-13T10:28:14.241679Z", "iopub.status.busy": "2026-06-13T10:28:14.241617Z", "iopub.status.idle": "2026-06-13T10:28:14.244048Z", "shell.execute_reply": "2026-06-13T10:28:14.243733Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " v_kick [km/s] r_max [pc] t_DF [Myr]\n", "------------------------------------------\n", " 10.0 0.67 68.2\n", " 20.0 1.49 106.6\n", " 30.0 2.76 246.5\n", " 40.0 5.96 1218.6\n", " 45.0 11.88 5787.8\n" ] } ], "source": [ "v_esc = 50.0\n", "a = 2.3\n", "Mcl = 1e6\n", "\n", "v_kicks = np.array([10, 20, 30, 40, 45])\n", "r_apo = plummer_apocentre(v_kicks, v_esc, a)\n", "t_ret = dynamical_friction_time(v_kicks, v_esc, Mcl, a, M_bh=30.0)\n", "\n", "print(f\"{'v_kick [km/s]':>14} {'r_max [pc]':>12} {'t_DF [Myr]':>12}\")\n", "print('-' * 42)\n", "for v, r, t in zip(v_kicks, r_apo, t_ret):\n", " print(f\"{v:14.1f} {r:12.2f} {t:12.1f}\")" ] } ], "metadata": { "kernelspec": { "display_name": "gwgen_env", "language": "python", "name": "gwgen_env" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.15" } }, "nbformat": 4, "nbformat_minor": 4 }