# Copyright (C) 2021 Xisco Jimenez Forteza # # This program is free software; you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by the # Free Software Foundation; either version 3 of the License, or (at your # option) any later version. # # This program is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General # Public License for more details. # # You should have received a copy of the GNU General Public License along # with this program; if not, write to the Free Software Foundation, Inc., # 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. # # ============================================================================= # # Preamble # # ============================================================================= # # Module to generate RD waveforms. import numpy as np import qnm import os f_fpars= [[2.95845, -2.58697, 0.0533469], [2.12539, -1.78054, 0.0865503], [1.74755, -1.44776, 0.123666], [1.78287, -1.53203, 0.129475], [2.04028, -1.83224, 0.112497]] q_fpars=[[0.584077, 1.52053, -0.480658], [0.00561441, 0.630715, -0.432664], [-0.197965, 0.515956, -0.369706], [-0.275097, 0.455691, -0.331543], [-0.287596, 0.398514, -0.309799]] class Ringdown_Spectrum: """RDown model generator""" def __init__(self,mf,af,l,m,n=4,s=-2,time=[],fixed=False): self.mf = mf self.af = af self.l = l self.m = m self.n = n self.time = time self.grav_220 = [qnm.modes_cache(s=s,l=self.l,m=self.m,n=i) for i in range (0,self.n+1)] self.dim = self.n+1 self.fixed = fixed if len(self.time)==0: self.time = np.arange(0,100,0.1) if self.fixed: omegas_new=np.asarray([self.grav_220[i](a=self.af)[0] for i in range (0,self.dim)]) self.w = (np.real(omegas_new))/self.mf self.tau=-1/(np.imag(omegas_new))*self.mf def QNM_spectrum(self): """ It computes the RD frequencies and damping times in NR units. """ omegas_new=np.asarray([self.grav_220[i](a=self.af)[0] for i in range (0,self.n+1)]) w_m_a = (np.real(omegas_new))/self.mf tau_m_a=-1/(np.imag(omegas_new))*self.mf return (w_m_a, tau_m_a) def w_fpars_Berti(self,n): return f_fpars[n] def tau_qpars_Berti(self,n): return q_fpars[n] def mass_from_wtau(self,n,w,tau): f1,f2,f3 = w_fpars_Berti(n) q1,q2,q3 = tau_qpars_Berti(n) res=(f1 + f2*(2**(-1/q3)*((-2*q1 + w*tau)/q2)**(1/q3))**f3)/w return res def spin_from_wtau(self,n,w,tau): f1,f2,f3 = w_fpars_Berti(n) q1,q2,q3 = tau_qpars_Berti(n) res=1 - 2**(-1/q3)*((-2*q1 + w*tau)/q2)**(1/q3) return res def mass_from_wtau_loop(self,w,tau,l,m): res=[None]*dim for n in range (0,dim): f1,f2,f3 = w_fpars_Berti(n) q1,q2,q3 = tau_qpars_Berti(n) res[n]=(f1 + f2*(2**(-1/q3)*((-2*q1 + w[n]*tau[n])/q2)**(1/q3))**f3)/w[n] return res def spin_from_wtau_loop(self,w,tau,l,m): res=[None]*dim for n in range (0,dim): f1,f2,f3 = w_fpars_Berti(n) q1,q2,q3 = tau_qpars_Berti(n) res[n]= 1 - 2**(-1/q3)*((-2*q1 + w[n]*tau[n])/q2)**(1/q3) return res def rd_model_wtau(self,theta): """RD model parametrized with the damping time tau. """ assert int(len(theta)/4) == self.dim, 'Please recheck your n and parameters' wvars = theta[ : (self.dim)] tvars = theta[(self.dim) : 2*(self.dim)] xvars = theta[2*(self.dim) : 3*(self.dim)] yvars = theta[3*(self.dim) : ] ansatz = 0 for i in range (0,self.dim): ansatz += (xvars[i]*np.exp(1j*yvars[i]))*np.exp(-self.time/tvars[i]) * (np.cos(wvars[i]*self.time)-1j*np.sin(wvars[i]*self.time)) # -1j to agree with SXS convention return ansatz def rd_model_wq(self,theta): """RD model parametrized with the quality factor q. """ assert int(len(theta)/4) == self.dim, 'Please recheck your n and parameters' wvars = theta[ : (self.dim)] qvars = theta[(self.dim) : 2*(self.dim)] xvars = theta[2*(self.dim) : 3*(self.dim)] yvars = theta[3*(self.dim) : ] ansatz = 0 for i in range (0,self.dim): ansatz += (xvars[i]*np.exp(1j*yvars[i]))*np.exp(-self.time*np.pi*wvars[i]/qvars[i])*(np.cos(wvars[i]*self.time)-1j*np.sin(wvars[i]*self.time)) # -1j to agree with SXS convention return ansatz def rd_model_wq_fixed(self,theta): """RD model parametrized with the damping time tau and with the QNM spectrum fixd to GR. """ xvars = theta[ : (self.dim)] yvars = theta[(self.dim) : 2*(self.dim)] ansatz = 0 for i in range (0,self.dim): ansatz += (xvars[i]*np.exp(1j*yvars[i]))*np.exp(-self.time/self.tau[i]) * (np.cos(self.w[i]*self.time)-1j*np.sin(self.w[i]*self.time)) # -1j to agree with SXS convention return ansatz def rd_model_wq_m_a(self,theta): """RD model parametrized with the damping time tau and with the QNM spectrum fixd to GR. The QNM spectrum is given from the mass and spin. """ xvars = theta[ : (self.dim)] yvars = theta[(self.dim) : 2*(self.dim)] mass_vars = theta[-2] spin_vars = theta[-1] w_m_a , tau_m_a = QNM_spectrum ansatz = 0 for i in range (0,dim): ansatz += (xvars[i]*np.exp(1j*yvars[i]))*np.exp(-timesrd_final_tsh/tau_m_a[i]) * (np.cos(w_m_a[i]*timesrd_final_tsh)-1j*np.sin(w_m_a[i]*timesrd_final_tsh)) # -1j to agree with SXS convention return ansatz