{ "cells": [ { "cell_type": "markdown", "id": "499d8d9e", "metadata": {}, "source": [ "## gwModelRemPE : remnant properties of eccentric precessing BBH mergers\n", "\n", "`gwModelRemPE` applies the `gwModelRemSE` eccentric corrections on top of the\n", "precessing quasi-circular baseline `gwModelRemP`. Inputs are the seven\n", "precessing-spin parameters at $r = 8M$ plus $(e_{\\rm ref}, \\ell_{\\rm ref})$\n", "at $t = -2500M$:\n", "\n", "$$M_f = M_f^{\\rm P}\\left[1 + \\delta_M\\right], \\quad\n", "|\\chi_f| = |\\chi_f|^{\\rm P}\\left[1 + \\delta_\\chi\\right], \\quad\n", "L_{\\rm peak} = L_{\\rm peak}^{\\rm P}\\left[1 + \\delta_L\\right]$$\n", "\n", "The correction factors are exactly those of `gwModelRemSE`, reusing its 28\n", "calibrated coefficients unchanged; only the baseline differs. $\\theta_f$ carries\n", "no eccentric correction, because none was calibrated for the spin direction.\n", "\n", "> **Note.** The eccentric corrections were calibrated on non-spinning\n", "> aligned-spin systems and are applied here to a precessing baseline,\n", "> treating the two effects as independent at leading order. The\n", "> factorization has not been checked against precessing eccentric NR.\n", "> All `gwModelRemSE` caveats carry over in full.\n", "\n", "---\n", "\n", "**Reference:** Islam, Wadekar & Khanna (2026), [arXiv:2608.00934](https://arxiv.org/abs/2608.00934)" ] }, { "cell_type": "code", "execution_count": 1, "id": "0aed61a4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lal.MSUN_SI != Msun\n" ] } ], "source": [ "import sys\n", "!{sys.executable} -m pip install -e ../ --no-deps --quiet\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import time\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", \"Wswiglal-redir-stdio\")\n", "\n", "import gwModels\n", "gwModels.utils.set_rcparams()" ] }, { "cell_type": "markdown", "id": "43dc4776", "metadata": {}, "source": [ "### 1. Basic evaluation" ] }, { "cell_type": "code", "execution_count": 2, "id": "a9e68215", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "q = 2.0, a1 = 0.7, a2 = 0.3\n", "theta1 = 60.0 deg, theta2 = 45.0 deg\n", "e_ref = 0.15, l_ref = 0.5\n", "\n", " Mf/M = 0.950938\n", " |chi_f| = 0.767445\n", " theta_f = 16.596 deg\n", " L_peak [c^5/G] = 9.745464e-04\n" ] } ], "source": [ "q = 2.0\n", "a1, a2 = 0.7, 0.3\n", "theta1, theta2 = np.pi / 3, np.pi / 4\n", "phi1, phi2 = 0.0, 0.0\n", "e_ref, l_ref = 0.15, 0.5\n", "\n", "Mf, af, theta_f, Lpeak = gwModels.remnants.gwModelRemPE(\n", " q, a1, a2, theta1, theta2, phi1, phi2, e_ref, l_ref)\n", "\n", "print(f'q = {q}, a1 = {a1}, a2 = {a2}')\n", "print(f'theta1 = {np.degrees(theta1):.1f} deg, theta2 = {np.degrees(theta2):.1f} deg')\n", "print(f'e_ref = {e_ref}, l_ref = {l_ref}')\n", "print()\n", "print(f' Mf/M = {Mf:.6f}')\n", "print(f' |chi_f| = {af:.6f}')\n", "print(f' theta_f = {np.degrees(theta_f):.3f} deg')\n", "print(f' L_peak [c^5/G] = {Lpeak:.6e}')" ] }, { "cell_type": "markdown", "id": "0f0af5ff", "metadata": {}, "source": [ "### 2. Three exact limits\n", "\n", "`gwModelRemPE` sits at the top of the model hierarchy and collapses onto each of the simpler models exactly:\n", "\n", "| Limit | Reduces to |\n", "|---|---|\n", "| $e_{\\rm ref} \\to 0$ | `gwModelRemP` |\n", "| $S_\\perp, \\Delta_\\perp \\to 0$ | `gwModelRemSE` |\n", "| both $\\to 0$ | `gwModelRemS` |" ] }, { "cell_type": "code", "execution_count": 3, "id": "89f0f92f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(a) e_ref = 0 -> gwModelRemP\n", " Mf : 0.950969639769612 exact: True\n", " |chif| : 0.767568442843936 exact: True\n", " theta_f : 0.289650458884348 exact: True\n", " Lpeak : 0.000976734584643093 exact: True\n", "\n", "(b) S_perp = 0 -> gwModelRemSE\n", " Mf : 0.961799870268308 exact: True\n", " |chif| : 0.745566863956656 exact: True\n", " Lpeak : 6.896183e-04 exact: True\n", "\n", "(c) both = 0 -> gwModelRemS\n", " Mf : 0.961686984172706 exact: True\n", " |chif| : 0.74663539485805 exact: True\n", " Lpeak : 6.939919e-04 exact: True\n" ] } ], "source": [ "args = (2.0, 0.7, 0.3, np.pi / 3, np.pi / 4, 0.0, 0.0)\n", "\n", "# (a) circular limit -> gwModelRemP\n", "pe = gwModels.remnants.gwModelRemPE(*args, 0.0, 0.0)\n", "p = gwModels.remnants.gwModelRemP(*args)\n", "print('(a) e_ref = 0 -> gwModelRemP')\n", "for lab, x, y in zip(['Mf', '|chif|', 'theta_f', 'Lpeak'], pe, p):\n", " print(f' {lab:>8s} : {x:.15g} exact: {x == y}')\n", "\n", "# (b) aligned limit -> gwModelRemSE\n", "pe = gwModels.remnants.gwModelRemPE(3.0, 0.5, 0.3, 0.0, np.pi, 0.0, 0.0, 0.15, 1.0)\n", "se = gwModels.remnants.gwModelRemSE(3.0, 0.5, -0.3, 0.15, 1.0)\n", "print()\n", "print('(b) S_perp = 0 -> gwModelRemSE')\n", "print(f' {\"Mf\":>8s} : {pe[0]:.15g} exact: {pe[0] == se[0]}')\n", "print(f' {\"|chif|\":>8s} : {pe[1]:.15g} exact: {pe[1] == abs(se[1])}')\n", "print(f' {\"Lpeak\":>8s} : {pe[3]:.6e} exact: {pe[3] == se[3]}')\n", "\n", "# (c) both -> gwModelRemS\n", "pe = gwModels.remnants.gwModelRemPE(3.0, 0.5, 0.3, 0.0, np.pi, 0.0, 0.0, 0.0, 0.0)\n", "s = gwModels.remnants.gwModelRemS(3.0, 0.5, -0.3)\n", "print()\n", "print('(c) both = 0 -> gwModelRemS')\n", "print(f' {\"Mf\":>8s} : {pe[0]:.15g} exact: {pe[0] == s[0]}')\n", "print(f' {\"|chif|\":>8s} : {pe[1]:.15g} exact: {pe[1] == abs(s[1])}')\n", "print(f' {\"Lpeak\":>8s} : {pe[3]:.6e} exact: {pe[3] == s[2]}')" ] }, { "cell_type": "markdown", "id": "0f077506", "metadata": {}, "source": [ "### 3. Eccentricity and precession together" ] }, { "cell_type": "code", "execution_count": 4, "id": "22746d84", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Eccentric correction on top of several spin tilts\n", "e_arr = np.linspace(0, 0.25, 300)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(13, 4.5))\n", "for tilt, ls in [(0.0, '-'), (np.pi / 4, '--'), (np.pi / 2, ':')]:\n", " Mf, af, thf, Lp = gwModels.remnants.gwModelRemPE(\n", " 3.0, 0.8, 0.8, tilt, tilt, 0.0, 0.0, e_arr, 0.0)\n", " lab = rf'$\\theta_1=\\theta_2={np.degrees(tilt):.0f}^\\circ$'\n", " axes[0].plot(e_arr, Mf, ls, lw=2, label=lab)\n", " axes[1].plot(e_arr, af, ls, lw=2, label=lab)\n", "\n", "axes[0].set_ylabel('$M_f/M$')\n", "axes[1].set_ylabel(r'$|\\chi_f|$')\n", "for ax in axes:\n", " ax.set_xlabel(r'$e_{\\rm ref}$')\n", " ax.legend(frameon=False)\n", " ax.grid(alpha=0.3)\n", "\n", "plt.suptitle(r'$q=3$, $a_1=a_2=0.8$, $\\ell_{\\rm ref}=0$')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "2925fa57", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Two-dimensional map over (e_ref, l_ref) at fixed precessing configuration\n", "e_g = np.linspace(0, 0.25, 180)\n", "l_g = np.linspace(0, 2 * np.pi, 180)\n", "E, L = np.meshgrid(e_g, l_g)\n", "\n", "MF, AF, THF, LP = gwModels.remnants.gwModelRemPE(\n", " 3.0, 0.8, 0.5, np.pi / 3, np.pi / 4, 0.0, 0.0, E, L)\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(16, 4.4))\n", "for ax, Z, lab, cmap in [\n", " (axes[0], MF, '$M_f/M$', 'viridis'),\n", " (axes[1], AF, r'$|\\chi_f|$', 'plasma'),\n", " (axes[2], LP, r'$L_{\\rm peak}$ [$c^5/G$]', 'cividis'),\n", "]:\n", " im = ax.pcolormesh(E, L / np.pi, Z, shading='auto', cmap=cmap)\n", " cb = fig.colorbar(im, ax=ax)\n", " cb.set_label(lab)\n", " ax.set_xlabel(r'$e_{\\rm ref}$')\n", " ax.set_ylabel(r'$\\ell_{\\rm ref}/\\pi$')\n", "\n", "plt.suptitle(r'$q=3$, $a_1=0.8$, $a_2=0.5$, $\\theta_1=60^\\circ$, $\\theta_2=45^\\circ$')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "b54b5d9d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " e_ref = 0.00 : theta_f = 16.595748828 deg\n", " e_ref = 0.10 : theta_f = 16.595748828 deg\n", " e_ref = 0.20 : theta_f = 16.595748828 deg\n", " e_ref = 0.25 : theta_f = 16.595748828 deg\n", "\n", " identical by construction; no eccentric correction was calibrated\n", " for the remnant spin direction.\n" ] } ], "source": [ "# theta_f is deliberately left uncorrected: it depends only on the\n", "# precessing baseline, not on eccentricity\n", "for e in [0.0, 0.1, 0.2, 0.25]:\n", " pe = gwModels.remnants.gwModelRemPE(*args, e, 0.7)\n", " print(f' e_ref = {e:.2f} : theta_f = {np.degrees(pe[2]):.9f} deg')\n", "print()\n", "print(' identical by construction; no eccentric correction was calibrated')\n", "print(' for the remnant spin direction.')" ] }, { "cell_type": "markdown", "id": "af120ece", "metadata": {}, "source": [ "### 4. The model hierarchy side by side\n", "\n", "Comparing the four deterministic models on the same binary shows how each ingredient contributes." ] }, { "cell_type": "code", "execution_count": 7, "id": "0b928c4f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "model Mf/M |chi_f| L_peak\n", "gwModelRemS (circular, aligned) 0.962236 0.723191 6.759573e-04\n", "gwModelRemP (circular, precessing) 0.959445 0.786833 8.073355e-04\n", "gwModelRemSE (eccentric, aligned) 0.962287 0.722833 6.735003e-04\n", "gwModelRemPE (eccentric, precessing) 0.959496 0.786444 8.044009e-04\n" ] } ], "source": [ "q_h = 3.0\n", "a1_h, a2_h = 0.8, 0.5\n", "th1_h, th2_h = np.pi / 3, np.pi / 4\n", "e_h, l_h = 0.2, 0.5\n", "\n", "c1z = a1_h * np.cos(th1_h)\n", "c2z = a2_h * np.cos(th2_h)\n", "\n", "rows = []\n", "s = gwModels.remnants.gwModelRemS(q_h, c1z, c2z)\n", "rows.append(('gwModelRemS (circular, aligned)', s[0], abs(s[1]), s[2]))\n", "\n", "p = gwModels.remnants.gwModelRemP(q_h, a1_h, a2_h, th1_h, th2_h, 0.0, 0.0)\n", "rows.append(('gwModelRemP (circular, precessing)', p[0], p[1], p[3]))\n", "\n", "se = gwModels.remnants.gwModelRemSE(q_h, c1z, c2z, e_h, l_h)\n", "rows.append(('gwModelRemSE (eccentric, aligned)', se[0], abs(se[1]), se[3]))\n", "\n", "pe = gwModels.remnants.gwModelRemPE(q_h, a1_h, a2_h, th1_h, th2_h, 0.0, 0.0, e_h, l_h)\n", "rows.append(('gwModelRemPE (eccentric, precessing)', pe[0], pe[1], pe[3]))\n", "\n", "print(f'{'model':<38s} {'Mf/M':>10s} {'|chi_f|':>10s} {'L_peak':>13s}')\n", "for name, mf, af, lp in rows:\n", " print(f'{name:<38s} {mf:10.6f} {af:10.6f} {lp:13.6e}')" ] }, { "cell_type": "code", "execution_count": 8, "id": "169dfd3d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Relative shift each ingredient produces, using gwModelRemS as reference\n", "labels = ['precession\\nonly', 'eccentricity\\nonly', 'both']\n", "mf_ref, af_ref, lp_ref = rows[0][1], rows[0][2], rows[0][3]\n", "\n", "dmf = [(r[1] - mf_ref) / mf_ref * 100 for r in rows[1:]]\n", "daf = [(r[2] - af_ref) / af_ref * 100 for r in rows[1:]]\n", "dlp = [(r[3] - lp_ref) / lp_ref * 100 for r in rows[1:]]\n", "\n", "x = np.arange(3)\n", "w = 0.26\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.bar(x - w, dmf, w, label='$M_f$')\n", "plt.bar(x, daf, w, label=r'$|\\chi_f|$')\n", "plt.bar(x + w, dlp, w, label=r'$L_{\\rm peak}$')\n", "plt.axhline(0, color='k', lw=1)\n", "plt.xticks(x, labels)\n", "plt.ylabel(r'shift relative to \\texttt{gwModelRemS} [\\%]')\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3, axis='y')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7cae548a", "metadata": {}, "source": [ "### 5. Recoil\n", "\n", "`gwModelRemPE` provides no deterministic recoil, for the same reason `gwModelRemP` does not: the precessing kick depends strongly on the spin azimuths. Use `gwModelRemP_flow` (notebook 6_5) for the distribution, optionally rescaled by the `gwModelRemSE` recoil factor to fold in eccentricity." ] }, { "cell_type": "code", "execution_count": 9, "id": "82be2747", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " circular recoil : 96.8749 km/s\n", " eccentric recoil : 96.6343 km/s\n", " rescaling factor : 0.997517\n", "\n", " The same factor can be applied to gwModelRemP_flow samples if an\n", " eccentric precessing recoil distribution is needed.\n" ] } ], "source": [ "# Eccentric rescaling factor for the recoil, from gwModelRemSE\n", "q_r = 3.0\n", "e_r, l_r = 0.2, 0.5\n", "\n", "vk_circ = gwModels.remnants.gwModelRemS_kick(q_r, 0.4, 0.3)\n", "vk_ecc = gwModels.remnants.gwModelRemSE_kick(q_r, 0.4, 0.3, e_r, l_r)\n", "factor = vk_ecc / vk_circ\n", "\n", "print(f' circular recoil : {vk_circ:.4f} km/s')\n", "print(f' eccentric recoil : {vk_ecc:.4f} km/s')\n", "print(f' rescaling factor : {factor:.6f}')\n", "print()\n", "print(' The same factor can be applied to gwModelRemP_flow samples if an')\n", "print(' eccentric precessing recoil distribution is needed.')" ] }, { "cell_type": "markdown", "id": "95fb4a16", "metadata": {}, "source": [ "### 6. Timing" ] }, { "cell_type": "code", "execution_count": 10, "id": "cc4cf408", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " N time per binary\n", " 1 0.547 ms 547.1709 us\n", " 10 0.475 ms 47.4760 us\n", " 100 0.481 ms 4.8078 us\n", " 1000 0.800 ms 0.8001 us\n", " 10000 3.341 ms 0.3341 us\n", " 100000 30.639 ms 0.3064 us\n" ] } ], "source": [ "sizes = [1, 10, 100, 1000, 10000, 100000]\n", "means = []\n", "\n", "for n in sizes:\n", " q_t = np.random.uniform(1, 4, n)\n", " a1_t = np.random.uniform(0, 1, n)\n", " a2_t = np.random.uniform(0, 1, n)\n", " t1_t = np.random.uniform(0, np.pi, n)\n", " t2_t = np.random.uniform(0, np.pi, n)\n", " e_t = np.random.uniform(0, 0.25, n)\n", " l_t = np.random.uniform(0, 2 * np.pi, n)\n", " reps = 20 if n <= 10000 else 5\n", " t = []\n", " for _ in range(reps):\n", " t0 = time.perf_counter()\n", " gwModels.remnants.gwModelRemPE(q_t, a1_t, a2_t, t1_t, t2_t, 0.0, 0.0, e_t, l_t)\n", " t.append(time.perf_counter() - t0)\n", " means.append(np.mean(t))\n", "\n", "means = np.array(means)\n", "print(f'{'N':>8s} {'time':>10s} {'per binary':>13s}')\n", "for n, m in zip(sizes, means):\n", " print(f'{n:>8d} {m*1e3:8.3f} ms {m/n*1e6:10.4f} us')" ] }, { "cell_type": "code", "execution_count": 11, "id": "5a7c62c4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " gwModelRemS : 7.356 ms\n", " gwModelRemP : 4.937 ms\n", " gwModelRemSE : 6.012 ms\n", " gwModelRemPE : 6.003 ms\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " gwModelRemSE : 6.742 ms\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " gwModelRemPE : 6.154 ms\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Cost of the whole hierarchy, 20000 binaries each\n", "n = 20000\n", "q_t = np.random.uniform(1, 4, n)\n", "a1_t = np.random.uniform(0, 1, n)\n", "a2_t = np.random.uniform(0, 1, n)\n", "t1_t = np.random.uniform(0, np.pi, n)\n", "t2_t = np.random.uniform(0, np.pi, n)\n", "c1_t = a1_t * np.cos(t1_t)\n", "c2_t = a2_t * np.cos(t2_t)\n", "e_t = np.random.uniform(0, 0.25, n)\n", "l_t = np.random.uniform(0, 2 * np.pi, n)\n", "\n", "names, times = [], []\n", "for name, fn in [\n", " ('gwModelRemS', lambda: gwModels.remnants.gwModelRemS(q_t, c1_t, c2_t)),\n", " ('gwModelRemP', lambda: gwModels.remnants.gwModelRemP(q_t, a1_t, a2_t, t1_t, t2_t, 0.0, 0.0)),\n", " ('gwModelRemSE', lambda: gwModels.remnants.gwModelRemSE(q_t, c1_t, c2_t, e_t, l_t)),\n", " ('gwModelRemPE', lambda: gwModels.remnants.gwModelRemPE(q_t, a1_t, a2_t, t1_t, t2_t, 0.0, 0.0, e_t, l_t)),\n", "]:\n", " t = []\n", " for _ in range(20):\n", " t0 = time.perf_counter()\n", " fn()\n", " t.append(time.perf_counter() - t0)\n", " names.append(name)\n", " times.append(np.mean(t) * 1e3)\n", " print(f' {name:>13s} : {np.mean(t)*1e3:7.3f} ms')\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.bar(names, times, color=['C0', 'C1', 'C2', 'C3'])\n", "plt.ylabel(f'time for {n} binaries [ms]')\n", "plt.grid(alpha=0.3, axis='y')\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }