diff --git a/bilby/core/utils.py b/bilby/core/utils.py index d631610915bfb24010ab3d0637aaad3f65466283..b8d2523e842fbe2bb2269fbd3a0faf0951c21ac7 100644 --- a/bilby/core/utils.py +++ b/bilby/core/utils.py @@ -28,6 +28,7 @@ speed_of_light = 299792458.0 # m/s parsec = 3.085677581491367e+16 # m solar_mass = 1.9884099021470415e+30 # Kg radius_of_earth = 6378136.6 # m +gravitational_constant = 6.6743e-11 # m^3 kg^-1 s^-2 _TOL = 14 diff --git a/bilby/gw/__init__.py b/bilby/gw/__init__.py index 51796dcc50b5b122586285b213768b0ab00068ec..3242f0ebd92a0b0c3b5c6f14ae1f27c80de2d08e 100644 --- a/bilby/gw/__init__.py +++ b/bilby/gw/__init__.py @@ -1,6 +1,5 @@ -from . import (conversion, cosmology, detector, likelihood, prior, +from . import (conversion, cosmology, detector, eos, likelihood, prior, result, source, utils, waveform_generator) - from .waveform_generator import WaveformGenerator from .likelihood import GravitationalWaveTransient from .detector import calibration diff --git a/bilby/gw/conversion.py b/bilby/gw/conversion.py index 469eef80e594f6a06013be2945d1262366855fcd..e7d757071c128f62297c6e269c8b627ff015fa1f 100644 --- a/bilby/gw/conversion.py +++ b/bilby/gw/conversion.py @@ -9,6 +9,7 @@ from ..core.likelihood import MarginalizedLikelihoodReconstructionError from ..core.utils import logger, solar_mass from ..core.prior import DeltaFunction from .utils import lalsim_SimInspiralTransformPrecessingNewInitialConditions +from .eos.eos import SpectralDecompositionEOS, EOSFamily, IntegrateTOV from .cosmology import get_cosmology try: @@ -284,7 +285,7 @@ def convert_to_lal_binary_neutron_star_parameters(parameters): convert_to_lal_binary_black_hole_parameters(converted_parameters) if not any([key in converted_parameters for key in - ['lambda_1', 'lambda_2', 'lambda_tilde', 'delta_lambda_tilde']]): + ['lambda_1', 'lambda_2', 'lambda_tilde', 'delta_lambda_tilde', 'eos_spectral_gamma_0']]): converted_parameters['lambda_1'] = 0 converted_parameters['lambda_2'] = 0 added_keys = added_keys + ['lambda_1', 'lambda_2'] @@ -301,16 +302,41 @@ def convert_to_lal_binary_neutron_star_parameters(parameters): lambda_tilde_to_lambda_1_lambda_2( converted_parameters['lambda_tilde'], converted_parameters['mass_1'], converted_parameters['mass_2']) - if 'lambda_2' not in converted_parameters.keys(): + if 'lambda_2' not in converted_parameters.keys() and 'lambda_1' in converted_parameters.keys(): converted_parameters['lambda_2'] =\ converted_parameters['lambda_1']\ * converted_parameters['mass_1']**5\ / converted_parameters['mass_2']**5 - elif converted_parameters['lambda_2'] is None: + elif 'lambda_2' in converted_parameters.keys() and converted_parameters['lambda_2'] is None: converted_parameters['lambda_2'] =\ converted_parameters['lambda_1']\ * converted_parameters['mass_1']**5\ / converted_parameters['mass_2']**5 + elif 'eos_spectral_gamma_0' in converted_parameters.keys(): # FIXME: This is a clunky way to do this + # Pick out the eos parameters from dict of parameters and sort them + eos_parameter_keys = sorted([key for key in original_keys if 'eos_spectral_gamma_' in key]) + gammas = [converted_parameters[key] for key in eos_parameter_keys] + + eos = SpectralDecompositionEOS(gammas, sampling_flag=True, e0=1.2856e14, p0=5.3716e32) + if eos.warning_flag: + converted_parameters['lambda_1'] = 0.0 + converted_parameters['lambda_2'] = 0.0 + converted_parameters['eos_check'] = False + elif eos_family_physical_check(eos): + converted_parameters['lambda_1'] = 0.0 + converted_parameters['lambda_2'] = 0.0 + converted_parameters['eos_check'] = False + else: + fam = EOSFamily(eos) + + if (converted_parameters['mass_1'] <= fam.maximum_mass and + converted_parameters['mass_2'] <= fam.maximum_mass): + converted_parameters['lambda_1'] = fam.lambda_from_mass(converted_parameters['mass_1']) + converted_parameters['lambda_2'] = fam.lambda_from_mass(converted_parameters['mass_2']) + else: + converted_parameters['lambda_1'] = 0.0 + converted_parameters['lambda_2'] = 0.0 + converted_parameters['eos_check'] = False added_keys = [key for key in converted_parameters.keys() if key not in original_keys] @@ -318,6 +344,44 @@ def convert_to_lal_binary_neutron_star_parameters(parameters): return converted_parameters, added_keys +def eos_family_physical_check(eos): + """ + Function that determines if the EoS family contains + sufficient number of points before maximum mass is reached. + + e_min is chosen to be sufficiently small so that the entire + EoS is captured when converting to mass-radius space. + + Returns True if family is valid, False if not. + """ + e_min = 1.6e-10 + e_central = eos.e_pdat[-1, 1] + loge_min = np.log(e_min) + loge_central = np.log(e_central) + logedat = np.linspace(loge_min, loge_central, num=eos.npts) + edat = np.exp(logedat) + + # Generate m, r, and k2 lists + mdat = [] + rdat = [] + k2dat = [] + for i in range(8): + tov_solver = IntegrateTOV(eos, edat[i]) + m, r, k2 = tov_solver.integrate_TOV() + mdat.append(m) + rdat.append(r) + k2dat.append(k2) + + # Check if maximum mass has been found + if i > 0 and mdat[i] <= mdat[i - 1]: + break + + if len(mdat) < 8: + return False + else: + return True + + def total_mass_and_mass_ratio_to_component_masses(mass_ratio, total_mass): """ Convert total mass and mass ratio of a binary to its component masses. diff --git a/bilby/gw/eos/__init__.py b/bilby/gw/eos/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..36eba397fce20b763cf10e2c54ed82e416d4ab5e --- /dev/null +++ b/bilby/gw/eos/__init__.py @@ -0,0 +1,3 @@ +from .tov_solver import IntegrateTOV +from .eos import (SpectralDecompositionEOS, + EOSFamily, TabularEOS) diff --git a/bilby/gw/eos/eos.py b/bilby/gw/eos/eos.py new file mode 100644 index 0000000000000000000000000000000000000000..17d99b9e0c350bba3a366372622afa7d6c191812 --- /dev/null +++ b/bilby/gw/eos/eos.py @@ -0,0 +1,850 @@ +import os +import numpy as np +import matplotlib.pyplot as plt +from scipy.integrate import cumtrapz, quad +from scipy.interpolate import interp1d, CubicSpline +from scipy.optimize import minimize_scalar + +from .tov_solver import IntegrateTOV +from ...core import utils + +C_SI = utils.speed_of_light # m/s +C_CGS = C_SI * 100. +G_SI = utils.gravitational_constant # m^3 kg^-1 s^-2 +MSUN_SI = utils.solar_mass # Kg + +# Stores conversions from geometerized to cgs or si unit systems +conversion_dict = {'pressure': {'cgs': C_SI ** 4. / G_SI * 10., 'si': C_SI ** 4. / G_SI, 'geom': 1.}, + 'energy_density': {'cgs': C_SI ** 4. / G_SI * 10., 'si': C_SI ** 4. / G_SI, 'geom': 1.}, + 'density': {'cgs': C_SI ** 2. / G_SI / 1000., 'si': C_SI ** 2. / G_SI, 'geom': 1.}, + 'pseudo_enthalpy': {'dimensionless': 1.}, + 'mass': {'g': C_SI ** 2. / G_SI * 1000, 'kg': C_SI ** 2. / G_SI, 'geom': 1., + 'm_sol': C_SI ** 2. / G_SI / MSUN_SI}, + 'radius': {'cm': 100., 'mass': 1., 'km': .001}, + 'tidal_deformability': {'geom': 1.}} + + +# construct dictionary of pre-shipped EOS pressure denstity table +path_to_eos_tables = os.path.join(os.path.dirname(__file__), 'eos_tables') +list_of_eos_tables = os.listdir(path_to_eos_tables) +valid_eos_files = [i for i in list_of_eos_tables if 'LAL' in i] +valid_eos_file_paths = [os.path.join(path_to_eos_tables, filename) for filename in valid_eos_files] +valid_eos_names = [i.split('_')[-1].strip('.dat') for i in valid_eos_files] +valid_eos_dict = dict(zip(valid_eos_names, valid_eos_file_paths)) + + +class TabularEOS(object): + """ + Given a valid eos input format, such as 2-D array, an ascii file, or a string, parse, and interpolate + + Parameters + ---------- + eos (`numpy.ndarray`, `str`, ASCII TABLE): + if `numpy.ndarray` then user supplied pressure-density 2D numpy array. + if `str` then given a valid eos name, relevant preshipped ASCII table will be loaded + if ASCII TABLE then given viable file extensions, which include .txt,.dat, etc (np.loadtxt used), + read in pressure density from file. + + sampling_flag (`bool`): Do you plan on sampling the parameterized EOS? Highly recommended. Defaults to False. + + warning_flag (`bool`): Keeps track of status of various physical checks on EoS. + + Attributes: + msg (str): Human readable string describing the exception. + code (int): Exception error code. + """ + + def __init__(self, eos, sampling_flag=False, warning_flag=False): + + self.sampling_flag = sampling_flag + self.warning_flag = warning_flag + + if type(eos) == str: + if eos in valid_eos_dict.keys(): + table = np.loadtxt(valid_eos_dict[eos]) + else: + table = np.loadtxt(eos) + elif type(eos) == np.ndarray: + table = eos + else: + raise ValueError("eos provided is invalid type please supply a str name, str path to ASCII file, " + "or a numpy array") + + table = self.__remove_leading_zero(table) + + # all have units of m^-2 + self.pressure = table[:, 0] + self.energy_density = table[:, 1] + + # Store minimum pressure and energy density + self.minimum_pressure = min(self.pressure) + self.minimum_energy_density = min(self.energy_density) + if (not self.check_monotonicity() and self.sampling_flag) or self.warning_flag: + # Not a monotonic or causal EOS, exiting. + self.warning_flag = True + else: + # plot analytic enthalpy + + # interpolate *in log* + + self.interp_energy_density_from_pressure = CubicSpline(np.log10(self.pressure), + np.log10(self.energy_density), + ) + + self.pseudo_enthalpy = np.zeros(self.pressure.shape[0]) + + # construct arrays to do cumulative integral + dhdp = 1. / (self.energy_density + self.pressure) + + num_int_arg = np.exp(np.log(self.pressure) + np.log(dhdp)) + + pseudo_enthalpy_0 = self.pressure[0] / (self.energy_density[0] + self.pressure[0]) + + self.pseudo_enthalpy = cumtrapz(num_int_arg, np.log(self.pressure), initial=pseudo_enthalpy_0) + + # interpolate entropy related quantities *in log* + self.interp_energy_density_from_pseudo_enthalpy = CubicSpline(np.log10(self.pseudo_enthalpy), + np.log10(self.energy_density)) + + self.interp_pressure_from_pseudo_enthalpy = CubicSpline(np.log10(self.pseudo_enthalpy), + np.log10(self.pressure)) + + self.interp_pseudo_enthalpy_from_energy_density = CubicSpline(np.log10(self.energy_density), + np.log10(self.pseudo_enthalpy)) + + # Create tables + self.__construct_all_tables() + + # Store minimum enthalpy + self.minimum_pseudo_enthalpy = min(self.pseudo_enthalpy) + if not self.check_causality() and self.sampling_flag: + # Finally, ensure the EOS is causal if sampling + self.warning_flag = True + + def __remove_leading_zero(self, table): + """ + For interpolation of lalsimulation tables; + loglog interpolation breaks if the first entries are 0s + """ + + if table[0, 0] == 0. or table[0, 1] == 0.: + return table[1:, :] + + else: + return table + + def energy_from_pressure(self, pressure, interp_type='CubicSpline'): + """ + Find value of energy_from_pressure + as in lalsimulation, return e = K * p**(3./5.) below min pressure + + :param pressure (`float`): pressure in geometerized units. + :param interp_type (`str`): String specifying which interpolation type to use. + Currently implemented: 'CubicSpline', 'linear'. + + :param energy_density (`float`): energy-density in geometerized units. + """ + pressure = np.atleast_1d(pressure) + energy_returned = np.zeros(pressure.size) + indices_less_than_min = np.nonzero(pressure < self.minimum_pressure) + indices_greater_than_min = np.nonzero(pressure >= self.minimum_pressure) + + # We do this special for less than min pressure + energy_returned[indices_less_than_min] = 10 ** (np.log10(self.energy_density[0]) + + (3. / 5.) * (np.log10(pressure[indices_less_than_min]) - + np.log10(self.pressure[0]))) + + if interp_type == 'CubicSpline': + energy_returned[indices_greater_than_min] = ( + 10. ** self.interp_energy_density_from_pressure(np.log10(pressure[indices_greater_than_min]))) + elif interp_type == 'linear': + energy_returned[indices_greater_than_min] = np.interp(pressure[indices_greater_than_min], + self.pressure, + self.energy_density) + else: + raise ValueError('Interpolation scheme must be linear or CubicSpline') + + if energy_returned.size == 1: + return energy_returned[0] + else: + return energy_returned + + def pressure_from_pseudo_enthalpy(self, pseudo_enthalpy, interp_type='CubicSpline'): + """ + Find p(h) + as in lalsimulation, return p = K * h**(5./2.) below min enthalpy + + :param pseudo_enthalpy (`float`): Dimensionless pseudo-enthalpy. + :interp_type (`str`): String specifying interpolation type. + Current implementations are 'CubicSpline', 'linear'. + + :return pressure (`float`): pressure in geometerized units. + """ + pseudo_enthalpy = np.atleast_1d(pseudo_enthalpy) + pressure_returned = np.zeros(pseudo_enthalpy.size) + indices_less_than_min = np.nonzero(pseudo_enthalpy < self.minimum_pseudo_enthalpy) + indices_greater_than_min = np.nonzero(pseudo_enthalpy >= self.minimum_pseudo_enthalpy) + + pressure_returned[indices_less_than_min] = 10. ** (np.log10(self.pressure[0]) + + 2.5 * (np.log10(pseudo_enthalpy[indices_less_than_min]) - + np.log10(self.pseudo_enthalpy[0]))) + + if interp_type == 'CubicSpline': + pressure_returned[indices_greater_than_min] = ( + 10. ** self.interp_pressure_from_pseudo_enthalpy(np.log10(pseudo_enthalpy[indices_greater_than_min]))) + elif interp_type == 'linear': + pressure_returned[indices_greater_than_min] = np.interp(pseudo_enthalpy[indices_greater_than_min], + self.pseudo_enthalpy, + self.pressure) + else: + raise ValueError('Interpolation scheme must be linear or CubicSpline') + + if pressure_returned.size == 1: + return pressure_returned[0] + else: + return pressure_returned + + def energy_density_from_pseudo_enthalpy(self, pseudo_enthalpy, interp_type='CubicSpline'): + """ + Find energy_density_from_pseudo_enthalpy(pseudo_enthalpy) + as in lalsimulation, return e = K * h**(3./2.) below min enthalpy + + :param pseudo_enthalpy (`float`): Dimensionless pseudo-enthalpy. + :param interp_type (`str`): String specifying interpolation type. + Current implementations are 'CubicSpline', 'linear'. + + :return energy_density (`float`): energy-density in geometerized units. + """ + pseudo_enthalpy = np.atleast_1d(pseudo_enthalpy) + energy_returned = np.zeros(pseudo_enthalpy.size) + indices_less_than_min = np.nonzero(pseudo_enthalpy < self.minimum_pseudo_enthalpy) + indices_greater_than_min = np.nonzero(pseudo_enthalpy >= self.minimum_pseudo_enthalpy) + + energy_returned[indices_less_than_min] = 10 ** (np.log10(self.energy_density[0]) + + 1.5 * (np.log10(pseudo_enthalpy[indices_less_than_min]) - + np.log10(self.pseudo_enthalpy[0]))) + if interp_type == 'CubicSpline': + x = np.log10(pseudo_enthalpy[indices_greater_than_min]) + energy_returned[indices_greater_than_min] = 10 ** self.interp_energy_density_from_pseudo_enthalpy(x) + elif interp_type == 'linear': + energy_returned[indices_greater_than_min] = np.interp(pseudo_enthalpy[indices_greater_than_min], + self.pseudo_enthalpy, + self.energy_density) + else: + raise ValueError('Interpolation scheme must be linear or CubicSpline') + + if energy_returned.size == 1: + return energy_returned[0] + else: + return energy_returned + + def pseudo_enthalpy_from_energy_density(self, energy_density, interp_type='CubicSpline'): + """ + Find h(epsilon) + as in lalsimulation, return h = K * e**(2./3.) below min enthalpy + + :param energy_density (`float`): energy-density in geometerized units. + :param interp_type (`str`): String specifying interpolation type. + Current implementations are 'CubicSpline', 'linear'. + + :return pseudo_enthalpy (`float`): Dimensionless pseudo-enthalpy. + """ + energy_density = np.atleast_1d(energy_density) + pseudo_enthalpy_returned = np.zeros(energy_density.size) + indices_less_than_min = np.nonzero(energy_density < self.minimum_energy_density) + indices_greater_than_min = np.nonzero(energy_density >= self.minimum_energy_density) + + pseudo_enthalpy_returned[indices_less_than_min] = 10 ** (np.log10(self.pseudo_enthalpy[0]) + (2. / 3.) * + (np.log10(energy_density[indices_less_than_min]) - + np.log10(self.energy_density[0]))) + + if interp_type == 'CubicSpline': + x = np.log10(energy_density[indices_greater_than_min]) + pseudo_enthalpy_returned[indices_greater_than_min] = 10**self.interp_pseudo_enthalpy_from_energy_density(x) + elif interp_type == 'linear': + pseudo_enthalpy_returned[indices_greater_than_min] = np.interp(energy_density[indices_greater_than_min], + self.energy_density, + self.pseudo_enthalpy) + else: + raise ValueError('Interpolation scheme must be linear or CubicSpline') + + if pseudo_enthalpy_returned.size == 1: + return pseudo_enthalpy_returned[0] + else: + return pseudo_enthalpy_returned + + def dedh(self, pseudo_enthalpy, rel_dh=1e-5, interp_type='CubicSpline'): + """ + Value of [depsilon/dh](p) + + :param pseudo_enthalpy (`float`): Dimensionless pseudo-enthalpy. + :param interp_type (`str`): String specifying interpolation type. + Current implementations are 'CubicSpline', 'linear'. + :param rel_dh (`float`): Relative step size in pseudo-enthalpy space. + + :return dedh (`float`): Derivative of energy-density with respect to pseudo-enthalpy + evaluated at `pseudo_enthalpy` in geometerized units. + """ + + # step size=fraction of value + dh = pseudo_enthalpy * rel_dh + + eps_upper = self.energy_density_from_pseudo_enthalpy(pseudo_enthalpy + dh, interp_type=interp_type) + eps_lower = self.energy_density_from_pseudo_enthalpy(pseudo_enthalpy - dh, interp_type=interp_type) + + return (eps_upper - eps_lower) / (2. * dh) + + def dedp(self, pressure, rel_dp=1e-5, interp_type='CubicSpline'): + """ + Find value of [depsilon/dp](p) + + :param pressure (`float`): pressure in geometerized units. + :param rel_dp (`float`): Relative step size in pressure space. + :param interp_type (`float`): String specifying interpolation type. + Current implementations are 'CubicSpline', 'linear'. + + :return dedp (`float`): Derivative of energy-density with respect to pressure + evaluated at `pressure`. + """ + + # step size=fraction of value + dp = pressure * rel_dp + + eps_upper = self.energy_from_pressure(pressure + dp, interp_type=interp_type) + eps_lower = self.energy_from_pressure(pressure - dp, interp_type=interp_type) + + return (eps_upper - eps_lower) / (2. * dp) + + def velocity_from_pseudo_enthalpy(self, pseudo_enthalpy, interp_type='CubicSpline'): + """ + Returns the speed of sound in geometerized units in the + neutron star at the specified pressure. + + Assumes the equation + vs = c (de/dp)^{-1/2} + + :param pseudo_enthalpy (`float`): Dimensionless pseudo-enthalpy. + :param interp_type (`str`): String specifying interpolation type. + Current implementations are 'CubicSpline', 'linear'. + + :return v_s (`float`): Speed of sound at `pseudo-enthalpy` in geometerized units. + """ + pressure = self.pressure_from_pseudo_enthalpy(pseudo_enthalpy, interp_type=interp_type) + return self.dedp(pressure, interp_type=interp_type) ** -0.5 + + def check_causality(self): + """ + Checks to see if the equation of state is causal i.e. the speed + of sound in the star is less than the speed of light. + Returns True if causal, False if not. + """ + pmax = self.pressure[-1] + emax = self.energy_from_pressure(pmax) + hmax = self.pseudo_enthalpy_from_energy_density(emax) + vsmax = self.velocity_from_pseudo_enthalpy(hmax) + if vsmax < 1.1: + return True + else: + return False + + def check_monotonicity(self): + """ + Checks to see if the equation of state is monotonically increasing + in energy density-pressure space. Returns True if monotonic, False if not. + """ + e1 = self.energy_density[1:] + e2 = self.energy_density[:-1] + ediff = e1 - e2 + e_negatives = len(np.where(ediff < 0)) + + p1 = self.pressure[1:] + p2 = self.pressure[:-1] + pdiff = p1 - p2 + p_negatives = len(np.where(pdiff < 0)) + if e_negatives > 1 or p_negatives > 1: + return False + else: + return True + + def __get_plot_range(self, data): + """ + Determines default plot range based on data provided. + """ + low = np.amin(data) + high = np.amax(data) + dx = 0.05 * (high - low) + + xmin = low - dx + xmax = high + dx + xlim = [xmin, xmax] + + return xlim + + def __construct_all_tables(self): + """Pressure and epsilon already tabular, now create array of enthalpies""" + edat = self.energy_density + hdat = [self.pseudo_enthalpy_from_energy_density(e) for e in edat] + self.pseudo_enthalpy = np.array(hdat) + + def plot(self, rep, xlim=None, ylim=None, units=None): + """ + Given a representation in the form 'energy_density-pressure', plot the EoS in that space. + + Parameters + ---------- + rep: str + Representation to plot. For example, plotting in energy_density-pressure space, + specify 'energy_density-pressure' + xlim: list + Plotting bounds for x-axis in the form [low, high]. + Defaults to 'None' which will plot from 10% below min x value to 10% above max x value + ylim: list + Plotting bounds for y-axis in the form [low, high]. + Defaults to 'None' which will plot from 10% below min y value to 10% above max y value + units: str + Specifies unit system to plot. Currently can plot in CGS:'cgs', SI:'si', or geometerized:'geom' + + Returns + ------- + fig: matplotlib.figure.Figure + EOS plot. + """ + + # Set data based on specified representation + varnames = rep.split('-') + + assert varnames[0] != varnames[ + 1], 'Cannot plot the same variable against itself. Please choose another representation' + + # Correspondence of rep parameter, data, and latex symbol + # rep_dict = {'energy_density': [self.epsilon, r'$\epsilon$'], + # 'pressure': [self.p, r'$p$'], 'pseudo_enthalpy': [pseudo_enthalpy, r'$h$']} + + # FIXME: The second element in these arrays should be tex labels, but tex's not working rn + rep_dict = {'energy_density': [self.energy_density, 'energy_density'], + 'pressure': [self.pressure, 'pressure'], + 'pseudo_enthalpy': [self.pseudo_enthalpy, 'pseudo_enthalpy']} + + xname = varnames[1] + yname = varnames[0] + + # Set units + eos_default_units = {'pressure': 'cgs', 'energy_density': 'cgs', 'density': 'cgs', + 'pseudo_enthalpy': 'dimensionless'} + if units is None: + units = [eos_default_units[yname], eos_default_units[xname]] # Default unit system is cgs + elif isinstance(units, str): + units = [units, units] # If only one unit system given, use for both + + xunits = units[1] + yunits = units[0] + + # Ensure valid units + if xunits not in list(conversion_dict[xname].keys()) or yunits not in list(conversion_dict[yname].keys()): + s = ''' + Invalid unit system. Valid variable-unit pairs are: + p: {p_units} + e: {e_units} + rho: {rho_units} + h: {h_units}. + '''.format(p_units=list(conversion_dict['pressure'].keys()), + e_units=list(conversion_dict['energy_density'].keys()), + rho_units=list(conversion_dict['density'].keys()), + h_units=list(conversion_dict['pseudo_enthalpy'].keys())) + raise ValueError(s) + + xdat = rep_dict[xname][0] * conversion_dict[xname][xunits] + ydat = rep_dict[yname][0] * conversion_dict[yname][yunits] + + xlabel = rep_dict[varnames[1]][1].replace('_', ' ') + ylabel = rep_dict[varnames[0]][1].replace('_', ' ') + '(' + xlabel + ')' + + # Determine plot ranges. Currently shows 10% wider than actual data range. + if xlim is None: + xlim = self.__get_plot_range(xdat) + + if ylim is None: + ylim = self.__get_plot_range(ydat) + + fig, ax = plt.subplots() + + ax.loglog(xdat, ydat) + ax.set_xlim(xlim) + ax.set_ylim(ylim) + ax.set_xlabel(xlabel) + ax.set_ylabel(ylabel) + + return fig + + +def spectral_adiabatic_index(gammas, x): + arg = 0 + for i in range(len(gammas)): + arg += gammas[i] * x ** i + + return np.exp(arg) + + +class SpectralDecompositionEOS(TabularEOS): + """ + Parameterized EOS using a spectral + decomposition per Lindblom + arXiv: 1009.0738v2. Inherits from TabularEOS. + + Parameters + ---------- + gammas: list + List of adiabatic expansion parameters used + to construct the equation of state in various + spaces. + p0: float + The starting point in pressure of the high-density EoS. This is stitched to + the low-density portion of the SLY EoS model. The default value chosen is set to + a sufficiently low pressure so that the high-density EoS will never be + overconstrained. + e0/c**2: float + The starting point in energy-density of the high-density EoS. This is stitched to + the low-density portion of the SLY EoS model. The default value chosen is set to + a sufficiently low energy density so that the high-density EoS will never be + overconstrained. + xmax: float + highest dimensionless pressure value in EoS + npts: float (optional) + number of points in pressure-energy density data. + """ + + def __init__(self, gammas, p0=3.01e33, e0=2.03e14, xmax=None, npts=100, sampling_flag=False, warning_flag=False): + self.warning_flag = warning_flag + self.gammas = gammas + self.p0 = p0 + self.e0 = e0 + self.xmax = xmax + self.npts = npts + if self.xmax is None: + self.xmax = self.__determine_xmax() + self.sampling_flag = sampling_flag + self.__construct_a_of_x_table() + + # Construct pressure-energy density table and + # set up interpolating functions. + + if self.warning_flag and self.sampling_flag: + # If sampling prior is enabled and adiabatic check + # has failed, empty the array values + self.e_pdat = np.zeros((2, 2)) + else: + self.e_pdat = self.__construct_e_of_p_table() + + super().__init__(self.e_pdat, sampling_flag=self.sampling_flag, warning_flag=self.warning_flag) + + def __determine_xmax(self, a_max=6.0): + highest_order_gamma = np.abs(self.gammas[-1])[0] + expansion_order = float(len(self.gammas) - 1) + + xmax = (np.log(a_max) / highest_order_gamma) ** (1. / expansion_order) + return xmax + + def __mu_integrand(self, x): + + return 1. / spectral_adiabatic_index(self.gammas, x) + + def mu(self, x): + + return np.exp(-quad(self.__mu_integrand, 0, x)[0]) + + def __eps_integrand(self, x): + + return np.exp(x) * self.mu(x) / spectral_adiabatic_index(self.gammas, x) + + def energy_density(self, x, eps0): + + quad_result, quad_err = quad(self.__eps_integrand, 0, x) + eps_of_x = (eps0 * C_CGS ** 2.) / self.mu(x) + self.p0 / self.mu(x) * quad_result + return eps_of_x + + def __construct_a_of_x_table(self): + + xdat = np.linspace(0, self.xmax, num=self.npts) + + # Generate adiabatic index points until a point is out of prior range + if self.sampling_flag: + adat = np.empty(self.npts) + for i in range(self.npts): + if 0.6 < spectral_adiabatic_index(self.gammas, xdat[i]) < 4.6: + adat[i] = spectral_adiabatic_index(self.gammas, xdat[i]) + else: + break + + # Truncate arrays to last point within range + adat = adat[:i] + xmax_new = xdat[i - 1] + + # If EOS is too short, set prior to 0, else resample the function and set new xmax + if xmax_new < 4. or i == 0: + self.warning_flag = True + else: + xdat = np.linspace(0, xmax_new, num=self.npts) + adat = spectral_adiabatic_index(self.gammas, xdat) + self.xmax = xmax_new + else: + adat = spectral_adiabatic_index(self.gammas, xdat) + + self.adat = adat + + def __construct_e_of_p_table(self): + + """ + Creates p, epsilon table for a given set of spectral parameters + """ + + # make p range + # to match lalsimulation tables: array = [pressure, density] + x_range = np.linspace(0, self.xmax, self.npts) + p_range = self.p0 * np.exp(x_range) + + eos_vals = np.zeros((self.npts, 2)) + eos_vals[:, 0] = p_range + + for i in range(0, len(x_range)): + eos_vals[i, 1] = self.energy_density(x_range[i], self.e0) + + # convert eos to geometrized units in *m^-2* + # IMPORTANT + eos_vals = eos_vals * 0.1 * G_SI / C_SI ** 4 + + # doing as those before me have done and using SLY4 as low density region + # SLY4 in geometrized units + low_density_path = os.path.join(os.path.dirname(__file__), 'eos_tables', 'LALSimNeutronStarEOS_SLY4.dat') + low_density = np.loadtxt(low_density_path) + + cutoff = eos_vals[0, :] + + # Then find overlap point + break_pt = len(low_density) + for i in range(1, len(low_density)): + if low_density[-i, 0] < cutoff[0] and low_density[-i, 1] < cutoff[1]: + break_pt = len(low_density) - i + 1 + break + + # stack EOS arrays + eos_vals = np.vstack((low_density[0:break_pt, :], eos_vals)) + + return eos_vals + + +class EOSFamily(object): + + """Create a EOS family and get mass-radius information + + Parameters: + eos (`object`): Supply a `TabularEOS` class (or subclass) + npts (`float`): Number of points to calculate for mass-radius relation. + Default is 500. + + Note: + The mass-radius and mass-k2 data should be + populated here via the TOV solver upon object construction. + """ + def __init__(self, eos, npts=500): + self.eos = eos + + # FIXME: starting_energy_density is set somewhat arbitrarily + starting_energy_density = 1.6e-10 + ending_energy_density = max(self.eos.energy_density) + log_starting_energy_density = np.log(starting_energy_density) + log_ending_energy_density = np.log(ending_energy_density) + log_energy_density_grid = np.linspace(log_starting_energy_density, + log_ending_energy_density, + num=npts) + energy_density_grid = np.exp(log_energy_density_grid) + + # Generate m, r, and k2 lists + mass = [] + radius = [] + k2love_number = [] + for i in range(len(energy_density_grid)): + tov_solver = IntegrateTOV(self.eos, energy_density_grid[i]) + m, r, k2 = tov_solver.integrate_TOV() + mass.append(m) + radius.append(r) + k2love_number.append(k2) + + # Check if maximum mass has been found + if i > 0 and mass[i] <= mass[i - 1]: + break + + # If we're not at the end of the array, determine actual maximum mass. Else, assume + # last point is the maximum mass and proceed. + if i < (npts - 1): + # Now replace ith point with interpolated maximum mass + # This is done by interpolating the last three points and then + # minimizing the negative of the interpolated function + x = [energy_density_grid[i - 2], energy_density_grid[i - 1], energy_density_grid[i]] + y = [mass[i - 2], mass[i - 1], mass[i]] + + f = interp1d(x, y, kind='quadratic', bounds_error=False, fill_value='extrapolate') + + res = minimize_scalar(lambda x: -f(x)) + + # Integrate max energy density to get maximum mass + tov_solver = IntegrateTOV(self.eos, res.x) + mfin, rfin, k2fin = tov_solver.integrate_TOV() + + mass[-1] = mfin + radius[-1] = rfin + k2love_number[-1] = k2fin + + # Currently, everything is in geometerized units. + # The mass variables have dimensions of length, k2 is dimensionless + # and radii have dimensions of length. Calculate dimensionless lambda + # with these quantities, then convert to SI. + + # Calculating dimensionless lambda values from k2, radii, and mass + tidal_deformability = [2. / 3. * k2 * r ** 5. / m ** 5. for k2, r, m in + zip(k2love_number, radius, mass)] + + # As a last resort, if highest mass is still smaller than second + # to last point, remove the last point from each array + if mass[-1] < mass[-2]: + mass = mass[:-1] + radius = radius[:-1] + k2love_number = k2love_number[:-1] + tidal_deformability = tidal_deformability[:-1] + + self.mass = np.array(mass) + self.radius = np.array(radius) + self.k2love_number = np.array(k2love_number) + self.tidal_deformability = np.array(tidal_deformability) + self.maximum_mass = mass[-1] * conversion_dict['mass']['m_sol'] + + def radius_from_mass(self, m): + """ + :param m: mass of neutron star in solar masses + :return: radius of neutron star in meters + """ + f = CubicSpline(self.mass, self.radius, bc_type='natural', extrapolate=True) + + mass_converted_to_geom = m * MSUN_SI * G_SI / C_SI ** 2. + return f(mass_converted_to_geom) + + def k2_from_mass(self, m): + """ + :param m: mass of neutron star in solar masses. + :return: dimensionless second tidal love number. + """ + f = CubicSpline(self.mass, self.k2love_number, bc_type='natural', extrapolate=True) + + m_geom = m * MSUN_SI * G_SI / C_SI ** 2. + return f(m_geom) + + def lambda_from_mass(self, m): + """ + Convert from equation of state model parameters to + component tidal parameters. + + :param m: Mass of neutron star in solar masses. + :return: Tidal parameter of neutron star of mass m. + """ + + # Get lambda from mass and equation of state + + r = self.radius_from_mass(m) + k = self.k2_from_mass(m) + m_geom = m * MSUN_SI * G_SI / C_SI ** 2. + c = m_geom / r + lmbda = (2. / 3.) * k / c ** 5. + + return lmbda + + def __get_plot_range(self, data): + low = np.amin(data) + high = np.amax(data) + dx = 0.05 * (high - low) + + xmin = low - dx + xmax = high + dx + xlim = [xmin, xmax] + + return xlim + + def plot(self, rep, xlim=None, ylim=None, units=None): + """ + Given a representation in the form 'm-r', plot the family in that space. + + Parameters + ---------- + rep: str + Representation to plot. For example, plotting in mass-radius space, specify 'm-r' + xlim: list + Plotting bounds for x-axis in the form [low, high]. + Defaults to 'None' which will plot from 10% below min x value to 10% above max x value + ylim: list + Plotting bounds for y-axis in the form [low, high]. + Defaults to 'None' which will plot from 10% below min y value to 10% above max y value + units: str + Specifies unit system to plot. Currently can plot in CGS:'cgs', SI:'si', or geometerized:'geom' + + Returns + ------- + fig: matplotlib.figure.Figure + EOS Family plot. + """ + + # Set data based on specified representation + varnames = rep.split('-') + + assert varnames[0] != varnames[ + 1], 'Cannot plot the same variable against itself. Please choose another representation' + + # Correspondence of rep parameter, data, and latex symbol + rep_dict = {'mass': [self.mass, r'$M$'], 'radius': [self.radius, r'$R$'], 'k2': [self.k2love_number, r'$k_2$'], + 'tidal_deformability': [self.tidal_deformability, r'$l$']} + + xname = varnames[1] + yname = varnames[0] + + # Set units + fam_default_units = {'mass': 'm_sol', 'radius': 'km', 'tidal_deformability': 'geom'} + if units is None: + units = [fam_default_units[yname], fam_default_units[xname]] # Default unit system is cgs + elif isinstance(units, str): + units = [units, units] # If only one unit system given, use for both + + xunits = units[1] + yunits = units[0] + + # Ensure valid units + if xunits not in list(conversion_dict[xname].keys()) or yunits not in list(conversion_dict[yname].keys()): + s = ''' + Invalid unit system. Valid variable-unit pairs are: + m: {m_units} + r: {r_units} + l: {l_units}. + '''.format(m_units=list(conversion_dict['mass'].keys()), + r_units=list(conversion_dict['radius'].keys()), + l_units=list(conversion_dict['tidal_deformability'].keys())) + raise ValueError(s) + + xdat = rep_dict[varnames[1]][0] * conversion_dict[xname][xunits] + ydat = rep_dict[varnames[0]][0] * conversion_dict[yname][yunits] + + xlabel = rep_dict[varnames[1]][1].replace('_', ' ') + ylabel = rep_dict[varnames[0]][1].replace('_', ' ') + '(' + xlabel + ')' + + # Determine plot ranges. Currently shows 10% wider than actual data range. + if xlim is None: + xlim = self.__get_plot_range(xdat) + + if ylim is None: + ylim = self.__get_plot_range(ydat) + + # Plot the data with appropriate labels + fig, ax = plt.subplots() + + ax.loglog(xdat, ydat) + ax.set_xlim(xlim) + ax.set_ylim(ylim) + ax.set_xlabel(xlabel) + ax.set_ylabel(ylabel) + + return fig diff --git a/bilby/gw/eos/eos_tables/LALSimNeutronStarEOS_ALF1.dat b/bilby/gw/eos/eos_tables/LALSimNeutronStarEOS_ALF1.dat new file mode 100644 index 0000000000000000000000000000000000000000..037833a3da32563d447431af2373209f22af6e40 --- /dev/null +++ b/bilby/gw/eos/eos_tables/LALSimNeutronStarEOS_ALF1.dat @@ -0,0 +1,435 @@ +2.497330652856044170e-31 9.768003638566259816e-24 +1.592372960492055975e-30 3.088914100834438756e-23 +1.015344781199215083e-29 9.768004895429188889e-23 +6.474142994678359712e-29 3.088914902247979127e-22 +4.128107839982976270e-28 9.768010005482412669e-22 +2.632205428971306203e-27 3.088918160571231879e-21 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+1.470013966750235114e-13 4.500811940634606012e-11 +1.731387863856208694e-13 5.002671562635437316e-11 +2.010059936669178797e-13 5.504801418041396961e-11 +2.306335097686296808e-13 6.007192762486492674e-11 +2.620620831408644871e-13 6.509838624111351862e-11 +2.953402346752597119e-13 7.012733419520121531e-11 +3.305224999692504982e-13 7.515872761758915987e-11 +3.676681649380139186e-13 8.019253238752491231e-11 +4.068403455881154881e-13 8.522872236053583188e-11 +4.481053100337267393e-13 9.026727803904911050e-11 +4.915319762864164615e-13 9.530818642468284165e-11 +5.366579771317881245e-13 1.003514389503217084e-10 +6.654887552750764822e-13 1.505356135774784107e-10 +9.417142076584915197e-13 1.651365127854106677e-10 +1.315778437624766928e-12 1.811764879619010982e-10 +1.844358809624988934e-12 1.988046394096580936e-10 +2.590306817584597915e-12 2.181936432465267456e-10 +3.616012529120234999e-12 2.395428488608075952e-10 +4.965313208688967488e-12 2.630672480117237507e-10 +6.699694777143037590e-12 2.890083683596909142e-10 +8.925869267353961862e-12 3.176445082149592634e-10 +1.177056031193463181e-11 3.492917542518317845e-10 +1.534499615768668161e-11 3.843003316221151691e-10 +1.987652631750916932e-11 4.230679524070584484e-10 +2.608973483615271959e-11 4.660578538263907704e-10 +3.478045650681588122e-11 5.138951590836362909e-10 +4.648644014856295550e-11 5.674274025588364606e-10 +6.176991496480676693e-11 6.274684321437168722e-10 +8.125690666035884282e-11 6.948926283081699716e-10 +1.059559660368495774e-10 7.708641822628360821e-10 +1.374279838417617545e-10 8.569536811049546632e-10 +1.768513576308784685e-10 9.548359471377399458e-10 +2.250665878871369434e-10 1.066271236006408421e-09 +2.857241986707212381e-10 1.193658662008917531e-09 +3.629884151158555122e-10 1.339955398381686866e-09 +4.592748077673763819e-10 1.508613234856397581e-09 +5.773377440854940115e-10 1.703943848438825219e-09 +7.226800092767401284e-10 1.931814419200647826e-09 +9.026546417394116988e-10 2.199481781266264633e-09 +1.118541408978315126e-09 2.509021598971413502e-09 +1.213809254333994764e-09 2.644107947359895549e-09 diff --git a/bilby/gw/eos/eos_tables/README b/bilby/gw/eos/eos_tables/README new file mode 100644 index 0000000000000000000000000000000000000000..c6b15a4b77ede64b253c7004eb65eb44df69992a --- /dev/null +++ b/bilby/gw/eos/eos_tables/README @@ -0,0 +1,57 @@ +This file is a copy of what can be found at http://xtreme.as.arizona.edu/NeutronStars/ + +This folder contains files for various equations of state proposed for +the interiors of neutron stars. Each file has three columns (unless otherwise +specified): +(i) baryon density, (ii) pressure (p/c^2), (iii) energy density (epsilon/c^2). +The average mass of a baryon is taken to be 1.66 times 10^{-24} g +and the units of all three columns are g/cm^3. + +The naming convention comes from Lattimer & Prakash 2001, ApJ, 550, +426 and Read et al. 2009, PRD, 79, 124032 with some additional +equations of state from Ozel & Freire 2016, ARAA, in press. The names +of the various files have an initial set of letters that correspond to +a particular set of calculations and a set of numbers that correspond +to different parameters in the calculations. + +H1-H7: B. D. Lackey, M. Nayyar, 73, 024021 (2006) + +alf1-alf4: M. Alford, M. Braby, M. Paris, and S. Reddy, Astrophys. +J. 629, 969 (2005) + +ap1-ap4: A. Akmal, V. R. Pandharipande, Phys. Rev. C 58, 1804 (1998) + +bbb2: M. Baldo, I. Bombaci, and G.F. Burgio, Astron. Astrophys. 328, 274 (1997) + +bgn1h1: S. Balberg and A. Gal, Nucl. Phys. A625, 435 (1997) + +bpal12: W. Zuo, I. Bombaci, and U. Lombardo, Phys. Rev. C 60, 024605 (1999) + +bsk: A. Potehkin, A. Fantina, N. Chamel, J. Pearson, & S. Goriely A&A, 560, 48 (2013) + +eng: L. Engvik et al., Astrophys. J. 469, 794 (1996) + +fps: B. Friedman and V. R. Pandharipande, Nucl. Phys. A361, 502 (1981) + +gnh3: N. K. Glendenning, Astrophys. J. 293, 470 (1985) + +gs1-2: N. K. Glendenning and J. Schaffner-Bielich, Phys. Rev. C +60, 025803 (1999) + +mpa1: H. Muther, M. Prakash, and T. L. Ainsworth, Phys. Lett. B 199, +469 (1987) + +ms1-2: H. Muller and B. D. Serot, Nucl. Phys. A606, 508 (1996). + +pal6: M. Prakash, T. L. Ainsworth, and Rev. Lett. 61, 2518 (1988). + +pcl2: M. Prakash, J. R. Cooke, and J. M. Lattimer, Phys. Rev. D +52, 661 (1995) + +qmc700: J. Stone, P. Guichon, H. Matevosyan, A. Thomas, Nucl Phys. A 792, 341 (2007) + +sly: F. Douchin and P. Haensel, Astron. Astrophys. 380, 151 (2001) + +sqm1-3: Prakash, M., Cooke, J. R., & Lattimer, J. M. 1995, Phys. Rev., D52, 661 + +wff1-3: R. B. Wiringa, V. Fiks, and A. Fabrocini, Phys. Rev. C 38, 1010 (1988) diff --git a/bilby/gw/eos/eos_tables/polytrope_table.dat b/bilby/gw/eos/eos_tables/polytrope_table.dat new file mode 100644 index 0000000000000000000000000000000000000000..4d3ee94bf811c8552300c624a9f2412e78e3f11c --- /dev/null +++ b/bilby/gw/eos/eos_tables/polytrope_table.dat @@ -0,0 +1,35 @@ +#eos logP1 gamma1 gamma2 gamma3 +PAL6 34.380 2.227 2.189 2.159 +SLy 34.384 3.005 2.988 2.851 +AP1 33.943 2.442 3.256 2.908 +AP2 34.126 2.643 3.014 2.945 +AP3 34.392 3.166 3.573 3.281 +AP4 34.269 2.830 3.445 3.348 +FPS 34.283 2.985 2.863 2.600 +WFF1 34.031 2.519 3.791 3.660 +WFF2 34.233 2.888 3.475 3.517 +WFF3 34.283 3.329 2.952 2.589 +BBB2 34.331 3.418 2.835 2.832 +BPAL12 34.358 2.209 2.201 2.176 +ENG 34.437 3.514 3.130 3.168 +MPA1 34.495 3.446 3.572 2.887 +MS1 34.858 3.224 3.033 1.325 +MS2 34.605 2.447 2.184 1.855 +MS1b 34.855 3.456 3.011 1.425 +PS 34.671 2.216 1.640 2.365 +GS1 34.504 2.350 1.267 2.421 +GS2 34.642 2.519 1.571 2.314 +BGN1H1 34.623 3.258 1.472 2.464 +GNH3 34.648 2.664 2.194 2.304 +H1 34.564 2.595 1.845 1.897 +H2 34.617 2.775 1.855 1.858 +H3 34.646 2.787 1.951 1.901 +H4 34.669 2.909 2.246 2.144 +H5 34.609 2.793 1.974 1.915 +H6 34.593 2.637 2.121 2.064 +H7 34.559 2.621 2.048 2.006 +PCL2 34.507 2.554 1.880 1.977 +ALF1 34.055 2.013 3.389 2.033 +ALF2 34.616 4.070 2.411 1.890 +ALF3 34.283 2.883 2.653 1.952 +ALF4 34.314 3.009 3.438 1.803 diff --git a/bilby/gw/eos/eos_tables/spec_param_table.dat b/bilby/gw/eos/eos_tables/spec_param_table.dat new file mode 100644 index 0000000000000000000000000000000000000000..a2d5834a0ebc9a16cfa9fceac8f377fa540bfd2f --- /dev/null +++ b/bilby/gw/eos/eos_tables/spec_param_table.dat @@ -0,0 +1,35 @@ +#EOS gamma1 gamma2 gamma3 gamma4 p0 epsilon0 xmax +PAL6 0.8622 -0.0677 0.0181 -0.0017 3.01e33 2.03e14 5.79 +SLY 0.9865 0.1110 -0.0301 0.0022 1.64e33 2.05e14 6.73 +AP1 0.4132 0.5594 -0.1270 0.0085 1.16e33 2.02e14 7.38 +AP2 0.7065 0.2866 -0.0659 0.0047 1.34e33 2.02e14 7.27 +AP3 0.9214 0.2097 -0.0383 0.0019 1.51e33 2.02e14 6.87 +AP4 0.8651 0.1548 -0.0151 -0.0002 1.50e33 2.02e14 7.04 +FPS 1.1561 -0.0468 0.0081 -0.0010 1.19e33 2.04e14 7.04 +WFF1 0.6785 0.2626 -0.0215 -0.0008 1.14e33 2.04e14 7.48 +WFF2 0.8079 0.2680 -0.0558 0.0039 1.32e33 2.04e14 7.25 +WFF3 1.4126 -0.1797 0.0389 -0.0035 0.81e33 2.03e14 7.32 +BBB2 0.7390 0.4555 -0.1406 0.0121 1.37e33 2.05e14 6.97 +BPAL12 1.1081 -0.3078 0.0891 -0.0081 2.51e33 2.05e14 6.08 +ENG 0.9820 0.2716 -0.0862 0.0075 1.33e33 2.04e14 6.98 +MPA1 1.0215 0.1653 -0.0235 -0.0004 1.51e33 2.04e14 6.63 +MS1 0.9189 0.1432 0.0122 -0.0094 4.54e33 2.04e14 5.05 +MS2 0.9598 -0.0527 0.0091 -0.0035 4.10e33 2.04e14 4.77 +MS1b 1.2132 -0.0648 0.0561 -0.0111 3.18e33 2.03e14 5.40 +PS 1.3896 -0.8472 0.2636 -0.0218 5.49e33 2.05e14 4.77 +GS1 1.8662 -1.4266 0.4450 -0.0389 3.22e33 2.04e14 6.28 +GS2 1.4580 -0.7219 0.1828 -0.0117 4.06e33 2.04e14 4.99 +BGN1H1 1.3450 -0.0996 -0.0833 0.0161 2.30e33 2.05e14 6.40 +GNH3 1.0366 -0.0044 -0.0440 0.0075 3.77e33 2.06e14 5.26 +H1 1.0653 0.0362 -0.1098 0.0179 3.17e33 2.04e14 5.04 +H2 1.0743 0.2250 -0.2029 0.0290 2.96e33 2.04e14 4.98 +H3 1.1340 0.0925 -0.1303 0.0190 3.12e33 2.04e14 4.91 +H4 1.0526 0.1695 -0.1200 0.0150 3.16e33 2.04e14 5.21 +H5 1.0106 0.2765 -0.2011 0.0270 2.97e33 2.04e14 5.09 +H6 1.0650 -0.0196 -0.0474 0.0077 3.35e33 2.04e14 4.80 +H7 0.9582 0.1619 -0.1294 0.0177 3.19e33 2.04e14 5.22 +PCL2 1.0410 0.0173 -0.0904 0.0150 2.90e33 2.04e14 5.44 +ALF1 1.0143 -0.3102 0.1809 -0.0248 1.50e33 2.05e14 6.21 +ALF2 0.4613 1.5237 -0.5817 0.0571 1.50e33 2.05e14 5.79 +ALF3 0.8536 0.2405 -0.0743 0.0041 1.50e33 2.05e14 6.14 +ALF4 0.8806 0.0656 0.0765 -0.0177 1.50e33 2.05e14 5.97 diff --git a/bilby/gw/eos/tov_solver.py b/bilby/gw/eos/tov_solver.py new file mode 100644 index 0000000000000000000000000000000000000000..2d0cba62f6f0b17d21730e3cb5be124b258c2279 --- /dev/null +++ b/bilby/gw/eos/tov_solver.py @@ -0,0 +1,151 @@ +# Monica Rizzo, 2019 + +import numpy as np +from scipy.integrate import solve_ivp + + +class IntegrateTOV: + """Class that given an initial pressure a mass radius value and a k2-love number + + Attributes: + eos (:obj:): . + attr2 (:obj:`int`, optional): Description of `attr2`. + + """ + + def __init__(self, eos, eps_0): + """Example of docstring on the __init__ method. + + The __init__ method may be documented in either the class level + docstring, or as a docstring on the __init__ method itself. + + Either form is acceptable, but the two should not be mixed. Choose one + convention to document the __init__ method and be consistent with it. + + Note: + Do not include the `self` parameter in the ``Args`` section. + + Args: + param1 (str): Description of `param1`. + param2 (:obj:`int`, optional): Description of `param2`. Multiple + lines are supported. + param3 (:obj:`list` of :obj:`str`): Description of `param3`. + + """ + self.eos = eos + # determine central values + pseudo_enthalpy0 = self.eos.pseudo_enthalpy_from_energy_density(eps_0) + + # evolve first step analytically + self.pseudo_enthalpy = pseudo_enthalpy0 - 1e-3 * pseudo_enthalpy0 + + mass0, radius0 = self.__mass_radius_cent(pseudo_enthalpy0, self.pseudo_enthalpy) + + # k2 integration starting vals + H0 = radius0 ** 2 + B0 = 2. * radius0 + + self.y = np.array([mass0, radius0, H0, B0]) + + def __mass_radius_cent(self, pseudo_enthalpy0, pseudo_enthalpy): + """ + Calculate approximate mass/radius central values (for starting integration) + + Eqns 7 + 8 from http://www.ccom.ucsd.edu/~lindblom/Publications/50_1992ApJ...398..569L.pdf + """ + + eps_c = self.eos.energy_density_from_pseudo_enthalpy(pseudo_enthalpy0) + p_c = self.eos.pressure_from_pseudo_enthalpy(pseudo_enthalpy0) + depsdh_c = self.eos.dedh(pseudo_enthalpy0) + + radius = ((3. * (pseudo_enthalpy0 - pseudo_enthalpy)) / (2. * np.pi * (eps_c + 3. * p_c))) ** 0.5 \ + * (1. - 0.25 * (eps_c - 3. * p_c - (3. / 5.) * depsdh_c) * + ((pseudo_enthalpy0 - pseudo_enthalpy) / (eps_c + 3. * p_c))) + + mass = (4. * np.pi) / 3. * eps_c * radius ** 3 * (1. - (3. / 5.) * + depsdh_c * (pseudo_enthalpy0 - pseudo_enthalpy) / eps_c) + + return mass, radius + + def __tov_eqns(self, h, y): + """ + Taken from http://www.ccom.ucsd.edu/~lindblom/Publications/50_1992ApJ...398..569L.pdf + + TOV equations in terms of pseudo-enthalpy; evolves in mass and radius + H and B equations taken from: + + https://journals.aps.org/prd/pdf/10.1103/PhysRevD.81.123016 + + Transformed (hopefully to evolve in H(h) and B(h) + """ + + m = y[0] + r = y[1] + H = y[2] + B = y[3] + eps = self.eos.energy_density_from_pseudo_enthalpy(h, interp_type='CubicSpline') + p = self.eos.pressure_from_pseudo_enthalpy(h, interp_type='CubicSpline') + depsdp = self.eos.dedp(p, interp_type='CubicSpline') + + dmdh = (- (4. * np.pi * eps * r ** 3 * (r - 2. * m)) / + (m + 4. * np.pi * r ** 3 * p)) + + drdh = -(r * (r - 2. * m)) / (m + 4. * np.pi * r ** 3 * p) + + dHdh = B * drdh + + # taken from Damour & Nagar + e_lam = (1. - 2. * m / r) ** (-1) + + C1 = 2. / r + e_lam * (2. * m / r ** 2. + 4. * np.pi * r * (p - eps)) + C0 = (e_lam * (- 6. / r ** 2. + 4. * np.pi * (eps + p) * + depsdp + 4. * np.pi * (5. * eps + 9. * p)) - + (2. * (m + 4. * np.pi * r ** 3. * p) / + (r ** 2. - 2. * m * r)) ** 2.) + + dBdh = -(C1 * B + C0 * H) * drdh + + y_dot = np.array([dmdh, drdh, dHdh, dBdh]) + + return y_dot + + def __calc_k2(self, R, Beta, H, C): + """ + Using evolved quantities, calculate the k2 love + + https://journals.aps.org/prd/pdf/10.1103/PhysRevD.81.123016 + + https://journals.aps.org/prd/pdf/10.1103/PhysRevD.80.084035 + """ + + y = (R * Beta) / H + + num = ((8. / 5.) * (1. - 2. * C) ** 2 * + C ** 5 * (2. * C * (y - 1.) - y + 2.)) + denom = (2. * C * (4. * (y + 1.) * C ** 4 + (6. * y - 4.) * C ** 3 + + (26. - 22. * y) * C ** 2 + 3. * (5. * y - 8.) * + C - 3. * y + 6.) - 3. * (1. - 2 * C) ** 2 * + (2. * C * (y - 1.) - y + 2.) * + np.log(1. / (1. - 2. * C))) + + return num / denom + + def integrate_TOV(self): + """ + Evolves TOV+k2 equations and returns final quantities + """ + + # integration settings the same as in lalsimulation + rel_err = 1e-4 + abs_err = 0.0 + + result = solve_ivp(self.__tov_eqns, (self.pseudo_enthalpy, 1e-16), self.y, rtol=rel_err, + atol=abs_err) + m_fin = result.y[0, -1] + r_fin = result.y[1, -1] + H_fin = result.y[2, -1] + B_fin = result.y[3, -1] + + k_2 = self.__calc_k2(r_fin, B_fin, H_fin, m_fin / r_fin) + + return m_fin, r_fin, k_2 diff --git a/bilby/gw/prior.py b/bilby/gw/prior.py index c8472ebf90334d62128cb758aa0c92a571e729ba..75c25df871b62543396bda88766a9579ef02a321 100644 --- a/bilby/gw/prior.py +++ b/bilby/gw/prior.py @@ -308,6 +308,32 @@ class AlignedSpin(Interped): boundary=boundary) +class EOSCheck(Constraint): + def __init__(self, minimum=-np.inf, maximum=np.inf): + """ + Constraint used for EoS sampling. Converts the result of various + checks on the EoS and its parameters into a prior that can reject + unphysical samples. Necessary for EoS sampling. + """ + + super().__init__(minimum=minimum, maximum=maximum, name=None, latex_label=None, unit=None) + + def prob(self, val): + """ + Returns the result of the equation of state check in the conversion function. + """ + return val + + def ln_prob(self, val): + + if val: + result = 0.0 + elif not val: + result = -np.inf + + return result + + class CBCPriorDict(PriorDict): @property def minimum_chirp_mass(self): diff --git a/docs/examples.txt b/docs/examples.txt index ca2fb7d053dc9f0e13cac22925e708fe3e0815e8..bc5c9e9229dc8d5374cf1e805372fc485e0db8a0 100644 --- a/docs/examples.txt +++ b/docs/examples.txt @@ -15,6 +15,7 @@ Examples - `Create your own time-domain source model <https://git.ligo.org/lscsoft/bilby/blob/master/examples/gw_examples/injection_examples/create_your_own_time_domain_source_model.py>`__ - `How to specify the prior <https://git.ligo.org/lscsoft/bilby/blob/master/examples/gw_examples/injection_examples/how_to_specify_the_prior.py>`__ - `Using a partially marginalized likelihood <https://git.ligo.org/lscsoft/bilby/blob/master/examples/gw_examples/injection_examples/marginalized_likelihood.py>`__ + - `Injecting and recovering a neutron-star equation of state <https://git.ligo.org/lscsoft/bilby/blob/master/examples/gw_examples/injection_examples/bns_eos_example.py>`__ 3. `Examples using open diff --git a/docs/index.txt b/docs/index.txt index 45c4b119810b707ae6e36bea30752ea2815d231f..dbc2948a90c7449c39691454bb359bb297f0da22 100644 --- a/docs/index.txt +++ b/docs/index.txt @@ -23,6 +23,7 @@ Welcome to bilby's documentation! gw_prior conversion gw_references + gw_eos writing-documentation hyperparameters containers diff --git a/examples/gw_examples/injection_examples/bns_eos_example.py b/examples/gw_examples/injection_examples/bns_eos_example.py new file mode 100644 index 0000000000000000000000000000000000000000..b1e5e029b0d593616e472f15f98c27c9a400a798 --- /dev/null +++ b/examples/gw_examples/injection_examples/bns_eos_example.py @@ -0,0 +1,123 @@ +#!/usr/bin/env python +""" +Tutorial to demonstrate running parameter estimation on a binary neutron star +system taking into account tidal deformabilities. + +This example estimates the masses using a uniform prior in both component masses +and also estimates the tidal deformabilities using a uniform prior in both +tidal deformabilities +""" + +from __future__ import division, print_function + +import numpy as np + +import bilby +from bilby.gw.eos import TabularEOS, EOSFamily + +# Specify the output directory and the name of the simulation. +outdir = 'outdir' +label = 'bns_eos_example' +bilby.core.utils.setup_logger(outdir=outdir, label=label) + +# Set up a random seed for result reproducibility. This is optional! +np.random.seed(88170235) + +# We are going to inject a binary neutron star waveform. We first establish a +# dictionary of parameters that includes all of the different waveform +# parameters, including masses of the two black holes (mass_1, mass_2), +# aligned spins of both black holes (chi_1, chi_2), etc. + +# We're also going to 'inject' the MPA1 equation of state. +# This is done by injecting masses for the two neutron-stars, +# assuming a specific equation of state, and calculating +# corresponding tidal deformability parameters from the EoS and +# masses. +mpa1_eos = TabularEOS('MPA1') +mpa1_fam = EOSFamily(mpa1_eos) + +mass_1 = 1.5 +mass_2 = 1.3 +lambda_1 = mpa1_fam.lambda_from_mass(mass_1) +lambda_2 = mpa1_fam.lambda_from_mass(mass_2) + + +injection_parameters = dict( + mass_1=mass_1, mass_2=mass_2, chi_1=0.02, chi_2=0.02, luminosity_distance=50., + theta_jn=0.4, psi=2.659, phase=1.3, geocent_time=1126259642.413, + ra=1.375, dec=-1.2108, lambda_1=lambda_1, lambda_2=lambda_2) + +# Set the duration and sampling frequency of the data segment that we're going +# to inject the signal into. For the +# TaylorF2 waveform, we cut the signal close to the isco frequency +duration = 32 +sampling_frequency = 2 * 1024 +start_time = injection_parameters['geocent_time'] + 2 - duration + +# Fixed arguments passed into the source model. The analysis starts at 40 Hz. +# Note that the EoS sampling is agnostic to waveform model as long as the approximant +# can include tides. +waveform_arguments = dict(waveform_approximant='IMRPhenomPv2_NRTidal', + reference_frequency=50., minimum_frequency=40.0) + +# Create the waveform_generator using a LAL Binary Neutron Star source function +waveform_generator = bilby.gw.WaveformGenerator( + duration=duration, sampling_frequency=sampling_frequency, + frequency_domain_source_model=bilby.gw.source.lal_binary_neutron_star, + parameter_conversion=bilby.gw.conversion.convert_to_lal_binary_neutron_star_parameters, + waveform_arguments=waveform_arguments) + +# Set up interferometers. In this case we'll use three interferometers +# (LIGO-Hanford (H1), LIGO-Livingston (L1), and Virgo (V1)). +# These default to their design sensitivity and start at 40 Hz. +interferometers = bilby.gw.detector.InterferometerList(['H1', 'L1', 'V1']) +for interferometer in interferometers: + interferometer.minimum_frequency = 40 +interferometers.set_strain_data_from_power_spectral_densities( + sampling_frequency=sampling_frequency, duration=duration, + start_time=start_time) +interferometers.inject_signal(parameters=injection_parameters, + waveform_generator=waveform_generator) + +# We're going to sample in chirp_mass, symmetric_mass_ratio, and +# specific EoS model parameters. We're using a 4-parameter +# spectrally-decomposed EoS parameterization from Lindblom (2010). +# BNS have aligned spins by default, if you want to allow precessing spins +# pass aligned_spin=False to the BNSPriorDict +priors = bilby.gw.prior.BNSPriorDict() +for key in ['psi', 'geocent_time', 'ra', 'dec', 'chi_1', 'chi_2', + 'theta_jn', 'luminosity_distance', 'phase']: + priors[key] = injection_parameters[key] +priors.pop('mass_1') +priors.pop('mass_2') +priors.pop('lambda_1') +priors.pop('lambda_2') +priors['chirp_mass'] = bilby.core.prior.Gaussian( + 1.215, 0.1, name='chirp_mass', unit='$M_{\\odot}$') +priors['symmetric_mass_ratio'] = bilby.core.prior.Uniform( + 0.1, 0.25, name='symmetric_mass_ratio') +priors['eos_spectral_gamma_0'] = bilby.core.prior.Uniform(0.2, 2.0, name='gamma0', latex_label='$\\gamma_0') +priors['eos_spectral_gamma_1'] = bilby.core.prior.Uniform(-1.6, 1.7, name='gamma1', latex_label='$\\gamma_1') +priors['eos_spectral_gamma_2'] = bilby.core.prior.Uniform(-0.6, 0.6, name='gamma2', latex_label='$\\gamma_2') +priors['eos_spectral_gamma_3'] = bilby.core.prior.Uniform(-0.02, 0.02, name='gamma3', latex_label='$\\gamma_3') + +# The eos_check prior imposes several hard physical constraints on samples like +# enforcing causality and monotinicity of the EoSs. In almost ever conceivable +# sampling scenario, this should be enabled. +priors['eos_check'] = bilby.gw.prior.EOSCheck() + +# Initialise the likelihood by passing in the interferometer data (IFOs) +# and the waveform generator +likelihood = bilby.gw.GravitationalWaveTransient( + interferometers=interferometers, waveform_generator=waveform_generator, + time_marginalization=False, phase_marginalization=False, + distance_marginalization=False, priors=priors) + +# Run sampler. In this case we're going to use the `dynesty` sampler +result = bilby.run_sampler( + likelihood=likelihood, priors=priors, sampler='dynesty', npoints=1000, + injection_parameters=injection_parameters, outdir=outdir, label=label, + conversion_function=bilby.gw.conversion.generate_all_bns_parameters, + resume=True) + +result.plot_corner() diff --git a/examples/gw_examples/injection_examples/reproduce_mpa1_eos.py b/examples/gw_examples/injection_examples/reproduce_mpa1_eos.py new file mode 100644 index 0000000000000000000000000000000000000000..699b56c102d6b4fb462ce1bd2ba16d1f73787899 --- /dev/null +++ b/examples/gw_examples/injection_examples/reproduce_mpa1_eos.py @@ -0,0 +1,27 @@ +#!/usr/bin/env python +""" +A script to demonstrate how to create and plot EoS's with Bilby +""" +from bilby.gw import eos + +# In this script we're going to use Bilby to plot the MPA1 EoS from tabulated data +# and plot its representation as a spectral decomposition EoS. + +# First, we specify the spectral parameter values for the MPA1 EoS. +MPA1_gammas = [1.0215, 0.1653, -0.0235, -0.0004] +MPA1_p0 = 1.51e33 # Pressure in CGS +MPA1_e0_c2 = 2.04e14 # \epsilon_0 / c^2 in CGS +MPA1_xmax = 6.63 # Dimensionless ending pressure + +# Create the spectral decomposition EoS class +MPA1_spectral = eos.SpectralDecompositionEOS(MPA1_gammas, p0=MPA1_p0, e0=MPA1_e0_c2, xmax=MPA1_xmax, npts=100) + +# And create another from tabulated data +MPA1_tabulated = eos.TabularEOS('MPA1') + +# Now let's plot them +# To do so, we specify a representation and plot ranges. +MPA1_spectral_plot = MPA1_spectral.plot('pressure-energy_density', xlim=[1e22, 1e36], ylim=[1e9, 1e36]) +MPA1_tabular_plot = MPA1_tabulated.plot('pressure-energy_density', xlim=[1e22, 1e36], ylim=[1e9, 1e36]) +MPA1_spectral_plot.savefig('spectral_mpa1.pdf') +MPA1_tabular_plot.savefig('tabular_mpa1.pdf') diff --git a/setup.py b/setup.py index 72d3cf5b348880a132b5030b03b96aa70fee49ea..b120771cf2d945e0f06e505d57e0935b1cfb2ae3 100644 --- a/setup.py +++ b/setup.py @@ -79,10 +79,11 @@ setup(name='bilby', version=VERSION, packages=['bilby', 'bilby.core', 'bilby.core.prior', 'bilby.core.sampler', 'bilby.gw', 'bilby.gw.detector', 'bilby.gw.sampler', - 'bilby.hyper', 'cli_bilby'], + 'bilby.hyper', 'bilby.gw.eos', 'cli_bilby'], package_dir={'bilby': 'bilby', 'cli_bilby': 'cli_bilby'}, package_data={'bilby.gw': ['prior_files/*'], 'bilby.gw.detector': ['noise_curves/*.txt', 'detectors/*'], + 'bilby.gw.eos': ['eos_tables/*.dat'], 'bilby': [version_file]}, python_requires='>=3.5', install_requires=[ diff --git a/test/gw_eos_test.py b/test/gw_eos_test.py new file mode 100644 index 0000000000000000000000000000000000000000..7fada352a4ded8e74f90fe929f916f113e117a65 --- /dev/null +++ b/test/gw_eos_test.py @@ -0,0 +1,69 @@ +from __future__ import division, absolute_import +import unittest +import numpy +import lalsimulation as lalsim +from bilby.gw.eos import SpectralDecompositionEOS, EOSFamily, TabularEOS +from bilby.core import utils + + +KNOWN_TOV_RESULT = 1 +KNOWN_EOS_PRIOR_RESULTS = 1 +ENERGY_FROM_PRESSURE_RESULTS = 0.04047517810698063 +EOS_FROM_TABLE = EOSFamily(TabularEOS('AP4', True)) +EOS_FROM_SPRECTRAL_DECOMPOSITION = EOSFamily(SpectralDecompositionEOS(gammas=[0.8651, 0.1548, -0.0151, -0.0002], + p0=1.5e33, + e0=2.02e14, + xmax=7.04)) +MASSES_TO_TEST = numpy.linspace(0.9, 2.0, 12) +PRESSURE = 1e-11 +ENTHALPY = 1.2 +ENERGY_DENSITY = 9.541419e-11 + +# Setup for MPA1 Comparison +PRESSURE_0 = 5.3716e32 +ENERGY_DENSITY_0 = 1.1555e35 / (utils.speed_of_light * 100) ** 2. +XMAX = 12.3081 + +GAMMAS = [1.0215, 0.1653, -0.0235, -0.0004] +LALSIM_MPA1 = lalsim.SimNeutronStarEOS4ParameterSpectralDecomposition(GAMMAS[0], GAMMAS[1], GAMMAS[2], GAMMAS[3]) +BILBY_MPA1 = SpectralDecompositionEOS(GAMMAS, PRESSURE_0, ENERGY_DENSITY_0, XMAX) + +MPA1_PRESSURES = BILBY_MPA1.e_pdat.T[0] +LALSIM_MPA1_ENERGY_DENSITY = [lalsim.SimNeutronStarEOSEnergyDensityOfPressureGeometerized(PRESSURE, LALSIM_MPA1) + for PRESSURE in MPA1_PRESSURES[:-1]] +BILBY_MPA1_ENERGY_DENSITY = BILBY_MPA1.e_pdat.T[1][:-1] + + +class TestEOSFamily(unittest.TestCase): + def test_spectral_decomposition_energy_from_pressure(self): + self.assertAlmostEqual(EOS_FROM_TABLE.eos.energy_from_pressure(PRESSURE), + 3.2736497985232014e-10) + + self.assertAlmostEqual(EOS_FROM_SPRECTRAL_DECOMPOSITION.eos.energy_from_pressure(PRESSURE), + 3.270622527256167e-10) + + def test_spectral_decomposition_pressure_from_pseudo_enthalpy(self): + self.assertAlmostEqual(EOS_FROM_TABLE.eos.pressure_from_pseudo_enthalpy(ENTHALPY), + 2.7338376042831513e-09) + + self.assertAlmostEqual(EOS_FROM_SPRECTRAL_DECOMPOSITION.eos.pressure_from_pseudo_enthalpy(ENTHALPY), + 2.754018499535077e-09) + + def test_spectral_decomposition_energy_density_from_pseudo_enthalpy(self): + self.assertAlmostEqual(EOS_FROM_TABLE.eos.energy_density_from_pseudo_enthalpy(ENTHALPY), + 2.9486942467903607e-09) + + self.assertAlmostEqual(EOS_FROM_SPRECTRAL_DECOMPOSITION.eos.energy_density_from_pseudo_enthalpy(ENTHALPY), + 3.0402598495601078e-09) + + def test_spectral_decomposition_pseudo_enthalpy_from_energy_density(self): + self.assertAlmostEqual(EOS_FROM_TABLE.eos.pseudo_enthalpy_from_energy_density(ENERGY_DENSITY), + 0.024415755781136812) + print(EOS_FROM_SPRECTRAL_DECOMPOSITION.eos.pseudo_enthalpy_from_energy_density(ENERGY_DENSITY)) + self.assertAlmostEqual(EOS_FROM_SPRECTRAL_DECOMPOSITION.eos.pseudo_enthalpy_from_energy_density(ENERGY_DENSITY), + 0.02420629785967365) + + +class TestBilbyLALSimComparison(unittest.TestCase): + def test_spectral_decomposition_MPA1(self): + numpy.testing.assert_allclose(LALSIM_MPA1_ENERGY_DENSITY, BILBY_MPA1_ENERGY_DENSITY, rtol=1e6) diff --git a/test/utils_test.py b/test/utils_test.py index 49911364661375bd479aa6ddf703016721df9501..557c5ad4e63be17a898992267a3b0282abf78a33 100644 --- a/test/utils_test.py +++ b/test/utils_test.py @@ -34,6 +34,9 @@ class TestConstants(unittest.TestCase): 1e-5, ) + def test_gravitational_constant(self): + self.assertEqual(bilby.core.utils.gravitational_constant, lal.G_SI) + class TestFFT(unittest.TestCase): def setUp(self):