From a7288772b3b720e0a8940849441e8e744bd0dbd3 Mon Sep 17 00:00:00 2001 From: bradkav Date: Wed, 26 Feb 2020 13:07:41 +0100 Subject: [PATCH] Cleaned up EvolutionPlot --- EvolutionPlot.py | 116 +++++++----------- plots/DeltaE_speedcut_lnLambda=3.5.pdf | Bin 0 -> 130743 bytes plots/Density_ratio_speedcut_lnLambda=3.5.pdf | Bin 0 -> 262077 bytes plots/Density_speedcut_lnLambda=3.5.pdf | Bin 0 -> 355989 bytes plots/f_eps_speedcut_lnLambda=3.5.pdf | Bin 0 -> 315430 bytes 5 files changed, 43 insertions(+), 73 deletions(-) create mode 100644 plots/DeltaE_speedcut_lnLambda=3.5.pdf create mode 100644 plots/Density_ratio_speedcut_lnLambda=3.5.pdf create mode 100644 plots/Density_speedcut_lnLambda=3.5.pdf create mode 100644 plots/f_eps_speedcut_lnLambda=3.5.pdf diff --git a/EvolutionPlot.py b/EvolutionPlot.py index 5cb4751..6d51baf 100755 --- a/EvolutionPlot.py +++ b/EvolutionPlot.py @@ -7,23 +7,21 @@ from HaloFeedback import G_N from matplotlib import gridspec - import matplotlib #Save the plots to file? -SAVE_PLOTS = False -plot_dir = "../../plots/HaloFeedback/" +SAVE_PLOTS = True +plot_dir = "plots/" #Only affect particles below the orbital speed? SPEED_CUT = True -# Initialise distribution function -DF = HaloFeedback.DistributionFunction( M_BH = 1000) +#Initialise distribution function +DF = HaloFeedback.DistributionFunction(M_BH = 1000) #Radius position and velocity of the orbiting body -r0 = 1e-8 +r0 = 1e-8 #pc v0 = np.sqrt(G_N*(DF.M_BH+DF.M_NS)/(r0)) -print(v0) v_cut = -1 file_label = "" @@ -36,42 +34,45 @@ #Number of orbits to evolve N_orb = 40000 -orbits_per_step = 200 +orbits_per_step = 250 N_step = int(N_orb/orbits_per_step) dt = T_orb*orbits_per_step t_list = dt*N_step*np.linspace(0, 1, N_step + 1) -#Number of radial points to calculate the density at -N_r = 100 print(" Number of orbits:", N_orb) -print(" Time [days]:", N_step*dt/(3600*24)) +print(" Total Time [days]:", N_step*dt/(3600*24)) -#Initial energy of the halo -E0 = DF.TotalEnergy() #Radial grid for calculating the density -#r_list = np.geomspace(DF.r_isco, 1e3*r0, N_r-1) +N_r = 200 r_list = np.geomspace(0.9e-9, 1.1e-7, N_r-1) r_list = np.sort(np.append(r_list, r0)) + +#List of densities rho_list = np.zeros((N_step+1, N_r)) -rho_avg_list = np.zeros(N_step+1) #Which index refers to r0? r0_ind = np.where(r_list == r0)[0][0] +#Keep track of halo mass M_list = np.zeros(N_step) +M_list[0] = DF.TotalMass() +#Rate of dynamical friction energy loss DF_list = np.zeros(N_step+1) +DF_list[0] = DF.dEdt_DF(r0, v_cut) + +#Total energy of the halo +E_list = np.zeros(N_step+1) +E_list[0] = DF.TotalEnergy() #Keep track of how much energy is carried #away by ejected particles E_ej_tot = 0.0*t_list -#Calculate initial DF energy loss rate -DF_list[0] = DF.dEdt_DF(r0, v_cut) #Initial density if (SPEED_CUT): @@ -81,76 +82,49 @@ rho0 = np.array([DF.rho(r) for r in r_list]) rho_list[0,:] = rho0 -rho_avg_list[0] = ((r0 - DF.b_max(v0))*DF.rho(r0 - DF.b_max(v0)) + (r0 + DF.b_max(v0))*DF.rho(r0 + DF.b_max(v0)) )/(2*r0) - - -rho0_full = np.array([DF.rho(r) for r in r_list]) -E0_alt = 0.5*4*np.pi*np.trapz(rho0_full*r_list**2*DF.psi(r_list), r_list) - - -print(" ") -print(" Initial energy of the halo [(km/s)^2]:", E0) -print(" Initial energy of the halo, alternative [(km/s)^2]:", E0_alt) -print(" ") - -M0 = DF.TotalMass() -M0_alt = 4*np.pi*np.trapz(rho0_full*r_list**2, r_list) -print(" Initial mass of the halo [M_sun]:", M0_alt) - -delta_eps = np.zeros(N_step + 1) -delta_eps[0] = 0 #----------- Evolving the system and plotting f(eps) ---------- -plt.figure() cmap = matplotlib.cm.get_cmap('Spectral') - -spec0 = DF.P_eps()*DF.eps_grid +plt.figure() for i in range(N_step): #Plot the distribution function f(eps) plt.semilogy(DF.eps_grid, DF.f_eps,alpha = 0.5,color=cmap(i/N_step)) - #Calculate the density profile + #Calculate the density profile at this timestep if (SPEED_CUT): rho_list[i+1,:] = np.array([DF.rho(r, v_cut = np.sqrt(G_N*(DF.M_BH+DF.M_NS)/r)) for r in r_list]) else: rho_list[i+1,:]= np.array([DF.rho(r) for r in r_list]) - + #Total halo mass M_list[i] = DF.TotalMass() #Total energy carried away so far by unbound particles E_ej_tot[i+1] = E_ej_tot[i] + DF.dEdt_ej(r0=r0, v_orb=v0, v_cut=v_cut)*dt #Time-step using the improved Euler method - #df_dt_1 = DF.dfdt(r0=r0, v_orb=v0, v_cut=v_cut) - #DF.f_eps += df_dt_1*dt - - #df_dt_2 = DF.dfdt(r0=r0, v_orb=v0, v_cut=v_cut) - #DF.f_eps += 0.5*dt*(df_dt_2 - df_dt_1) - df1 = DF.delta_f(r0=r0, v_orb=v0, dt=dt, v_cut=v_cut) DF.f_eps += df1 - #df2 = DF.delta_f(r0=r0, v_orb=v0, dt=dt, v_cut=v_cut) - #DF.f_eps += 0.5*(df2 - df1) - #DF.f_eps = np.clip( DF.f_eps, 0, 1e30) + df2 = DF.delta_f(r0=r0, v_orb=v0, dt=dt, v_cut=v_cut) + DF.f_eps += 0.5*(df2 - df1) #Change in energy of the halo - delta_eps[i+1] = DF.TotalEnergy() - E0 + E_list[i+1] = DF.TotalEnergy() - #Dynamical friction energy loss + #Dynamical friction energy loss rate DF_list[i+1] = DF.dEdt_DF(r0, v_cut) plt.xlim(1.e8, 4.5e8) plt.ylim(1e3, 1e9) -plt.axvline(G_N*DF.M_BH/r0, linestyle='-', color='k') +plt.axvline(G_N*DF.M_BH/r0, linestyle='--', color='k') #plt.axvline(G_N*DF.M_BH/r0 - DF.eps_min(v0), linestyle='--', color='k') -plt.axvline(G_N*DF.M_BH/(r0 - r0/np.sqrt(1000)), linestyle='--', color='k') -plt.axvline(G_N*DF.M_BH/(r0 + r0/np.sqrt(1000)), linestyle='--', color='k') +#plt.axvline(G_N*DF.M_BH/(r0 - r0/np.sqrt(1000)), linestyle='--', color='k') +#plt.axvline(G_N*DF.M_BH/(r0 + r0/np.sqrt(1000)), linestyle='--', color='k') plt.xlabel(r'$\mathcal{E} = \Psi(r) - \frac{1}{2}v^2$ [(km/s)$^2$]') plt.ylabel(r'$f(\mathcal{E})$ [$M_\odot$ pc$^{-3}$ (km/s)$^{-3}$]') @@ -163,8 +137,6 @@ plt.savefig(plot_dir + "f_eps_" + file_label + DF.IDstr_num + ".pdf", bbox_inches='tight') -#DF.plotDF() - #------------------------- Density ------------------------- @@ -200,9 +172,9 @@ else: ax0.set_ylabel(r'$\rho(r)$ [$M_\odot$ pc$^{-3}$]') -r_new, rho_new = np.loadtxt("Density.txt", unpack=True) +#r_new, rho_new = np.loadtxt("Density.txt", unpack=True) -ax0.loglog(r_new, rho_new, alpha=0.5, color='k', linestyle='--') +#ax0.loglog(r_new, rho_new, alpha=0.5, color='k', linestyle='--') ax1.axvline(r0, linestyle='--', color='black') if (SPEED_CUT): @@ -229,8 +201,8 @@ for i in range(N_step): plt.semilogx(r_list,rho_list[i,:]/rho0, alpha=0.5, color=cmap(i/N_step)) plt.axvline(r0, linestyle='--', color='black') -plt.axvline(r0 + DF.b_max(v0), linestyle=':', color='black') -plt.axvline(r0 - DF.b_max(v0), linestyle=':', color='black') +#plt.axvline(r0 + DF.b_max(v0), linestyle=':', color='black') +#plt.axvline(r0 - DF.b_max(v0), linestyle=':', color='black') for n in [0, N_orb/4, N_orb/2, 3*N_orb/4, N_orb]: @@ -258,15 +230,15 @@ plt.figure() -plt.plot(t_list/T_orb, -(delta_eps + E_ej_tot), linestyle='-',label="Halo+Ejected") -plt.plot(t_list/T_orb, DeltaE, linestyle='--',label="NS") -plt.plot(t_list/T_orb, t_list*DF_list[0], linestyle=':',label="NS (linearised)") +plt.plot(t_list/T_orb, -((E_list - E_list[0]) + E_ej_tot), linestyle='-',label="DM Halo + Ejected particles") +plt.plot(t_list/T_orb, DeltaE, linestyle='--',label="Dynamical Friction") +plt.plot(t_list/T_orb, t_list*DF_list[0], linestyle=':',label="Dynamical Friction (linearised)") #plt.plot(t_list/T_orb, E_ej_tot, linestyle=':',label="Ejected") plt.xlabel("Number of orbits") plt.ylabel(r"$|\Delta E|$ [$M_\odot$ (km/s)$^2$]") -plt.legend(loc='best') +plt.legend(loc='best', fontsize=14) if (SAVE_PLOTS): plt.savefig(plot_dir + "DeltaE_" + file_label + DF.IDstr_num + ".pdf", bbox_inches='tight') @@ -274,10 +246,6 @@ #---------------- Diagnostics ------------------------- -# Changing density over time -#Delta_rho_dt = cumtrapz(rho_avg_list, t_list, initial=0)/rho_avg_list[0] - - rho_full = np.array([DF.rho(r) for r in r_list]) Ef_alt = 0.5*4*np.pi*np.trapz(r_list**2*rho_full*DF.psi(r_list), r_list) @@ -287,14 +255,16 @@ #E_ej_tot = np.trapz(-E_ej, DF.eps_grid) print(" ") -print(" Fractional Change in halo mass:", (DF.TotalMass() - M0)/M0) -print(" Change in halo energy [(km/s)^2]:", DF.TotalEnergy() - E0) +#print(" Fractional Change in halo mass:", (DF.TotalMass() - M_list[0])/M_list[0]) +print(" Change in halo energy [(km/s)^2]:", DF.TotalEnergy() - E_list[0]) #print(" Change in halo energy (2):", Ef_alt - E0_alt) -print(" Energy in ejected particles:", E_ej_tot[-1]) +print(" Energy in ejected particles:", E_ej_tot[-1]) +print(" Dynamical friction energy change [(km/s)^2]:", DeltaE[-1]) + +print(" Fractional error in energy conservation:", ((DF.TotalEnergy() - E_list[0] + E_ej_tot[-1]) + DeltaE[-1])/(DeltaE[-1])) print(" ") -print(" Dynamical friction energy change [(km/s)^2]:", DeltaE[-1]) -print(" Fractional error in DF:", ((DF.TotalEnergy() - E0 + E_ej_tot[-1]) + DeltaE[-1])/(DeltaE[-1])) +print(" Delta rho/rho(r0):", DF.rho(r0, v_cut = np.sqrt(G_N*(DF.M_BH+DF.M_NS)/r0))/rho0[r0_ind]) plt.show() diff --git a/plots/DeltaE_speedcut_lnLambda=3.5.pdf b/plots/DeltaE_speedcut_lnLambda=3.5.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1df42ecf9a924627ea0cfaf8aed5ab4d05846ff5 GIT binary patch literal 130743 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