{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Statistical study of changing Mass model paramter(s) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* In this notebook I will show the effect of changing mass model parameter on the detectable gravitational waves (GW) event rates per year\n", "\n", "### Binary Black Hole (BBH) Mass Model\n", "\n", "* I will use the power-law+peak mass model and change the slope of the power-law component ($\\alpha$) on the mass function.\n", "\n", "* Here is the default parameters and resultant distribution of the chosen mass model:\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", "\n", "| Parameter | Value |\n", "|----------------------|--------|\n", "| $m_{\\text{minbh}}$ | 4.98 |\n", "| $m_{\\text{maxbh}}$ | 112.5 |\n", "| $\\alpha$ | 3.78 |\n", "| $\\mu_g$ | 32.27 |\n", "| $\\sigma_g$ | 3.88 |\n", "| $\\lambda_{\\text{peak}}$ | 0.03 |\n", "| $\\delta_m$ | 4.8 |\n", "| $\\beta$ | 0.81 |\n", "\n", "\n", "\n", "![mass_bbh](../../_static/bbh_mass.png)\n", "\n", "
\n", "\n", "### Binary Neutron Star (BNS) Mass Model\n", "\n", "* The mass distribution of neutron stars in binary neutron star (BNS) systems can be characterized by a bimodal distribution, which can be modeled using a double Gaussian distribution. Each normal distribution is independently truncated and normalized in the range [1, 2.3] $M_{\\odot}$, ensuring that the neutron star masses are within the physically plausible range. \n", "\n", "* This bimodal distribution is thought to reflect the different evolutionary paths that neutron stars can take. For more details, refer to [Alsing et al. 2018](https://arxiv.org/pdf/1805.06442.pdf) and [M. Farr et al. 2020](https://arxiv.org/pdf/2005.00032.pdf).\n", "\n", "* I will change the maximum cut ($m_{\\text{max}}$) on the mass function.\n", "\n", "* Here is the default parameters and resultant distribution of the chosen mass model:\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", "\n", "| Parameter | Value |\n", "|-------------|------------------|\n", "| $w$ | 0.643 |\n", "| $\\mu_L$ | 1.352 $M_{\\odot}$|\n", "| $\\sigma_L$ | 0.08 $M_{\\odot}$ |\n", "| $\\mu_R$ | 1.88 $M_{\\odot}$ |\n", "| $\\sigma_R$ | 0.3 $M_{\\odot}$ |\n", "| $m_{\\text{max}}$ | 2.3 $M_{\\odot}$ |\n", "\n", "\n", "\n", "![mass_bns](../../_static/bns_mass.png)\n", "\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## BBH" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from ler.rates import GWRATES" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# # initialization\n", "ler = GWRATES(verbose=False, event_type='BBH')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* When `LeR` class is initialized, the mass model is created with the default parameters. This is in the form of a interpolation and the parameters are fixed.\n", "\n", "* I will change the function of the mass model with a default power-law+peak mass model and change the maximum cut ($m_{\\text{maxbh}}$) on the mass function.\n", "\n", "* Below I will providing an example. But first let me show you which models are available in the `ler`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dict_keys(['merger_rate_density', 'source_frame_masses', 'zs', 'spin', 'geocent_time', 'ra', 'phase', 'psi', 'theta_jn'])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ler.available_gw_prior_list_and_its_params.keys()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'binary_masses_BBH_popI_II_powerlaw_gaussian': {'mminbh': 4.98,\n", " 'mmaxbh': 112.5,\n", " 'alpha': 3.78,\n", " 'mu_g': 32.27,\n", " 'sigma_g': 3.88,\n", " 'lambda_peak': 0.03,\n", " 'delta_m': 4.8,\n", " 'beta': 0.81},\n", " 'binary_masses_BBH_popIII_lognormal': {'Mc': 30.0, 'sigma': 0.3, 'beta': 1.1},\n", " 'binary_masses_BBH_primordial_lognormal': {'Mc': 30.0,\n", " 'sigma': 0.3,\n", " 'beta': 1.1},\n", " 'binary_masses_BNS_gwcosmo': {'mminns': 1.0, 'mmaxns': 3.0, 'alphans': 0.0},\n", " 'binary_masses_BNS_bimodal': {'w': 0.643,\n", " 'muL': 1.352,\n", " 'sigmaL': 0.08,\n", " 'muR': 1.88,\n", " 'sigmaR': 0.3,\n", " 'mmin': 1.0,\n", " 'mmax': 2.3}}" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ler.available_gw_prior_list_and_its_params['source_frame_masses']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* changing mass function parameter $\\alpha$ for sampling. Considered values are,\n", " * $\\alpha = 3.78$: default value, from [GWTC-3 2021](https://arxiv.org/pdf/2111.03604.pdf) (page-23)\n", " * $\\alpha = 2.63$: from [WIERDA et al. 2021](https://arxiv.org/pdf/2106.06303.pdf) (Appendix B)\n", "\n", "* you can have only 'size' as input parameter\n", "\n", "* These mass function returns the mass of the binary black hole in the unit of solar mass ($m_1$, $m_2$)." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# with default value\n", "ler.sample_source_frame_masses = lambda size: ler.binary_masses_BBH_popI_II_powerlaw_gaussian(size=size, alpha=3.78)\n", "\n", "# plot \n", "plt.figure(figsize=(6, 4))\n", "plt.hist(ler.sample_source_frame_masses(10000)[0], bins=100, histtype='step', color='k', density=True, label='alpha=3.78')\n", "\n", "# with custom value\n", "ler.sample_source_frame_masses = lambda size: ler.binary_masses_BBH_popI_II_powerlaw_gaussian(size=size, alpha=2.63)\n", "\n", "# plot\n", "plt.hist(ler.sample_source_frame_masses(10000)[0], bins=100, histtype='step', color='r', density=True, label='alpha=2.63')\n", "plt.xlabel(r'$m_1$ (Bigger mass of the binary in $M_{\\odot}$)')\n", "plt.ylabel('pdf')\n", "\n", "plt.legend()\n", "plt.grid(alpha=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* let's make a range of $\\alpha$ between the two values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculation of rates (per year)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " iteration: 0\n", "gw rate per year (alpha=2.63): 602.399735152594\n", "\n", " iteration: 1\n", "gw rate per year (alpha=2.7577777777777777): 583.6620908730581\n", "\n", " iteration: 2\n", "gw rate per year (alpha=2.8855555555555554): 541.7353177613893\n", "\n", " iteration: 3\n", "gw rate per year (alpha=3.013333333333333): 516.4757309978161\n", "\n", " iteration: 4\n", "gw rate per year (alpha=3.141111111111111): 500.0155904428646\n", "\n", " iteration: 5\n", "gw rate per year (alpha=3.2688888888888887): 490.69852975138264\n", "\n", " iteration: 6\n", "gw rate per year (alpha=3.3966666666666665): 471.8573625752747\n", "\n", " iteration: 7\n", "gw rate per year (alpha=3.5244444444444443): 465.12837429809326\n", "\n", " iteration: 8\n", "gw rate per year (alpha=3.652222222222222): 447.6330047774216\n", "\n", " iteration: 9\n", "gw rate per year (alpha=3.78): 430.13763525675\n" ] } ], "source": [ "alpha_arr = np.linspace(2.63, 3.78, 10)\n", "gw_rates = np.zeros_like(alpha_arr)\n", "sample_size = 1000000 # increase the sample size to 1 million for better statistics\n", "ler.batch_size = 100000\n", "\n", "# let's suppress some of the print outputs\n", "import contextlib\n", "\n", "for i, alpha in enumerate(alpha_arr):\n", " print(\"\\n iteration: \", i)\n", " ler.sample_source_frame_masses = lambda size: ler.binary_masses_BBH_popI_II_powerlaw_gaussian(size=size, alpha=alpha)\n", "\n", " # un-lensed\n", " with contextlib.redirect_stdout(None): # suppress print output\n", " ler.gw_cbc_statistics(size=sample_size);\n", " rate,_ = ler.gw_rate(output_jsonfile=\"gw_param_detectable_\"+str(i)+\".json\")\n", " gw_rates[i] = rate\n", " print(f'gw rate per year (alpha={alpha}): {rate}')" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gw rate: slope=-143.657045929216, intercept=965.3951693918017, r_value=-0.9795941702168517, p_value=7.401514058755967e-07, std_err=10.420797560559112\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# linear fit to the rates\n", "from scipy.stats import linregress\n", "\n", "slope, intercept, r_value, p_value, std_err = linregress(alpha_arr, gw_rates)\n", "print(f'gw rate: slope={slope}, intercept={intercept}, r_value={r_value}, p_value={p_value}, std_err={std_err}')\n", "\n", "\n", "# gw_rates vs alpha\n", "plt.figure(figsize=(6, 4))\n", "plt.plot(alpha_arr, gw_rates, 'k.', label='gw rates')\n", "plt.plot(alpha_arr, slope*alpha_arr + intercept, 'r-', label='gw fit')\n", "plt.xlabel(r'$\\alpha$ (power-law index)')\n", "plt.ylabel('rate per year')\n", "plt.legend()\n", "plt.grid(alpha=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The change in rate is significant and has a decreasing trend as $\\alpha$ increases.\n", "\n", "* Increasing the value of $\\alpha$ results in more BBH events is mass range [15, 30] $M_{\\odot}$\n", "\n", "* You can repeat the same test for other parameters as well.\n", "\n", "* You can repeat the same test for 3G detectors as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## BNS" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from ler.rates import GWRATES" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# # initialization\n", "ler = GWRATES(verbose=False, event_type='BNS')" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'binary_masses_BBH_popI_II_powerlaw_gaussian': {'mminbh': 4.98,\n", " 'mmaxbh': 112.5,\n", " 'alpha': 3.78,\n", " 'mu_g': 32.27,\n", " 'sigma_g': 3.88,\n", " 'lambda_peak': 0.03,\n", " 'delta_m': 4.8,\n", " 'beta': 0.81},\n", " 'binary_masses_BBH_popIII_lognormal': {'Mc': 30.0, 'sigma': 0.3, 'beta': 1.1},\n", " 'binary_masses_BBH_primordial_lognormal': {'Mc': 30.0,\n", " 'sigma': 0.3,\n", " 'beta': 1.1},\n", " 'binary_masses_BNS_gwcosmo': {'mminns': 1.0, 'mmaxns': 3.0, 'alphans': 0.0},\n", " 'binary_masses_BNS_bimodal': {'w': 0.643,\n", " 'muL': 1.352,\n", " 'sigmaL': 0.08,\n", " 'muR': 1.88,\n", " 'sigmaR': 0.3,\n", " 'mmin': 1.0,\n", " 'mmax': 2.3}}" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ler.available_gw_prior_list_and_its_params['source_frame_masses']" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "binary_masses_BNS_bimodal interpolator will be loaded from ./interpolator_pickle/binary_masses_BNS_bimodal/binary_masses_BNS_bimodal_0.pickle\n", "binary_masses_BNS_bimodal interpolator will be loaded from ./interpolator_pickle/binary_masses_BNS_bimodal/binary_masses_BNS_bimodal_1.pickle\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# with default value\n", "ler.sample_source_frame_masses = lambda size: ler.binary_masses_BNS_bimodal(size=size, mmax=2.3)\n", "\n", "# plot \n", "plt.figure(figsize=(6, 4))\n", "plt.hist(ler.sample_source_frame_masses(10000)[0], bins=100, histtype='step', color='k', density=True, label='mmax=2.3')\n", "\n", "# with custom value\n", "ler.sample_source_frame_masses = lambda size: ler.binary_masses_BNS_bimodal(size=size, mmax=3)\n", "\n", "# plot\n", "plt.hist(ler.sample_source_frame_masses(10000)[0], bins=100, histtype='step', color='r', density=True, label='mmax=3')\n", "plt.xlabel(r'$m_1$ (Bigger mass of the binary in $M_{\\odot}$)')\n", "plt.ylabel('pdf')\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Un-lensed" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " iteration: 0\n", "gw rate (mmax=2.3): 1.9669350348684111\n", "\n", " iteration: 1\n", "gw rate (mmax=2.4749999999999996): 2.898641104016606\n", "\n", " iteration: 2\n", "gw rate (mmax=2.65): 2.5880724143005414\n", "\n", " iteration: 3\n", "gw rate (mmax=2.825): 3.8821086214508123\n", "\n", " iteration: 4\n", "gw rate (mmax=3.0): 2.691595310872563\n" ] } ], "source": [ "mmax_arr = np.linspace(2.3, 3, 5)\n", "gw_rates_bns = np.zeros_like(mmax_arr)\n", "sample_size = 2000000 # increase the sample size to 2 million for better statistics\n", "ler.batch_size = 100000\n", "\n", "# let's suppress some of the print outputs\n", "import contextlib\n", "\n", "for i, mmax in enumerate(mmax_arr):\n", " print(\"\\n iteration: \", i)\n", " ler.sample_source_frame_masses = lambda size: ler.binary_masses_BNS_bimodal(size=size, mmax=mmax)\n", "\n", " # un-lensed\n", " with contextlib.redirect_stdout(None): # suppress print output\n", " ler.gw_cbc_statistics(size=sample_size);\n", " rate,_ = ler.gw_rate(output_jsonfile=\"gw_param_bns_detectable_\"+str(i)+\".json\")\n", " gw_rates_bns[i] = rate\n", " print(f'gw rate (mmax={mmax}): {rate}')" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gw rate: slope=1.3901646111100057, intercept=-0.8784657223397283, r_value=0.5535928457320664, p_value=0.33301505236005835, std_err=1.2073948295286805\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# linear fit to the rates\n", "from scipy.stats import linregress\n", "\n", "slope, intercept, r_value, p_value, std_err = linregress(mmax_arr, gw_rates_bns)\n", "print(f'gw rate: slope={slope}, intercept={intercept}, r_value={r_value}, p_value={p_value}, std_err={std_err}')\n", "\n", "# gw_rates vs mmax\n", "plt.figure(figsize=(6, 4))\n", "plt.plot(mmax_arr, gw_rates_bns, 'k.', label='gw rates')\n", "plt.plot(mmax_arr, slope*mmax_arr + intercept, 'r-', label='gw fit')\n", "plt.xlabel(r'$m_{\\max}$ (Bimodal distribution)')\n", "plt.ylabel('rate per year')\n", "plt.legend()\n", "plt.grid(alpha=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* rate and $m_max$ does not have a strong linear relationship, but an increasing trend is observed.\n", "\n", "* The rate is higher for higher $m_{\\text{max}}$ values. This is because higher mass BBHs have higher SNRs and are detectable at larger distances." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hubble constant (H0): 67.66 km / (Mpc s)\n", "Matter density parameter (Om0): 0.30966\n", "Dark energy density parameter (Ode0): 0.6888463055445441\n" ] } ], "source": [ "from astropy.cosmology import Planck18\n", "\n", "# Accessing cosmological parameters\n", "H0 = Planck18.H0\n", "Om0 = Planck18.Om0\n", "Ode0 = Planck18.Ode0\n", "\n", "print(f\"Hubble constant (H0): {H0}\")\n", "print(f\"Matter density parameter (Om0): {Om0}\")\n", "print(f\"Dark energy density parameter (Ode0): {Ode0}\")\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hubble constant (H0): 70.0 km / (Mpc s)\n", "Matter density parameter (Om0): 0.3\n", "Dark energy density parameter (Ode0): 0.7\n" ] } ], "source": [ "from astropy.cosmology import LambdaCDM\n", "cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7)\n", "\n", "# Accessing cosmological parameters\n", "H0 = cosmo.H0\n", "Om0 = cosmo.Om0\n", "Ode0 = cosmo.Ode0\n", "\n", "print(f\"Hubble constant (H0): {H0}\")\n", "print(f\"Matter density parameter (Om0): {Om0}\")\n", "print(f\"Dark energy density parameter (Ode0): {Ode0}\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "ler", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 2 }