def plot_Mf(save=True, ED_I=False):
"""
Function that generates the plot of the LISA and Taiji monopole
response functions.
It corresponds to left panel of figure 15 of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources," submitted to JCAP,
https://arxiv.org/abs/2107.05356.
Arguments:
save -- option to save the figure in "plots/LISA_Taiji_response.pdf"
(default True)
ED_I -- option to plot the response function of cross-correlating
channels E and D of the LISA-Taiji network (default False)
"""
plt.figure(figsize=(12, 10))
plt.rc('font', size=30)
plt.plot(fs, MAs, color='black', label=r'${\cal M}_{\rm AA} (f)$')
plt.plot(fs,
MAs_Tai,
color='black',
ls='-.',
label=r'${\cal M}_{\rm CC} (f)$')
plt.plot(fs, MTs, color='blue', label=r'${\cal M}_{\rm TT} (f)$')
plt.plot(fs,
MTs_Tai,
color='blue',
ls='-.',
label=r'${\cal M}_{\rm SS} (f)$')
aaux = ''
if ED_I == True:
gg = np.where(abs(M_ED_I) > 1e-48)
plt.plot(fs[gg], abs(M_ED_I[gg]), color='purple', alpha=.5)
plt.text(3e-3, 6e-3, r'$|{\cal M}^I_{\rm ED}|$', color='purple')
aaux = 'ED'
Rf = inte.R_f(fs)
L = 3e6 * u.km
Rf_Tai = inte.R_f(fs, L=L)
plt.plot(fs, Rf, color='black', ls='dashed', lw=.7)
plt.plot(fs, Rf_Tai, color='black', ls='dashed', lw=.7)
plt.text(5e-2, 7e-2, r'$\tilde {\cal R}^{\rm A, C}(f)$', fontsize=34)
plt.xscale('log')
plt.yscale('log')
plt.xlim(1e-3, 1)
plt.ylim(1e-7, 1e0)
plt.legend(fontsize=28, frameon=False, loc='center left')
plt.xlabel(r'$f$ [Hz]')
plt.ylabel(r'${\cal M} (f)$')
plot_sets.axes_lines()
plt.yticks(np.logspace(-7, 0, 8))
ax = plt.gca()
ax.tick_params(axis='x', pad=20)
ax.tick_params(axis='y', pad=10)
if save:
plt.savefig('plots/LISA_Taiji_response' + aaux + '.pdf',
bbox_inches='tight')
def plot_noise_PSD(interf='LISA', save=True):
"""
Function that generates the plot of LISA (Taiji) noise PSD of the channel
A (C) and compares with the optical metrology system P_oms and
mass acceleration P_acc PSD noises.
Arguments:
interf -- selects interferometer (default 'LISA',
also available 'Taiji')
save -- option to save the figure in "plots/noise_PSD_interf.pdf"
(default True)
"""
plt.figure(figsize=(12, 8))
if interf == 'LISA':
#plt.plot(fs, PnX, color='blue')
plt.plot(fs, PnA, color='red')
plt.plot(fs, Pacc, color='blue', ls='-.', lw=.8)
plt.plot(fs, Poms, color='blue', ls='-.', lw=.8)
yPn = 1e-40
yPoms = 1e-40
yPacc = 6e-43
A = 'A'
if interf == 'Taiji':
#plt.plot(fs, PnX_Tai, color='blue')
plt.plot(fs, PnC, color='red')
plt.plot(fs, Pacc_Tai, color='blue', ls='-.', lw=.8)
plt.plot(fs, Poms_Tai, color='blue', ls='-.', lw=.8)
yPn = 2e-41
yPoms = 2e-41
yPacc = 4e-43
A = 'C'
plt.xlabel('$f$ [Hz]')
plt.ylabel('noise PSD $(f)$')
plt.xscale('log')
plt.yscale('log')
plt.ylim(1e-43, 1e-30)
plt.xlim(1e-5, 1e0)
plt.text(1e-1, yPoms, r'$P_{\rm oms} (f)$', color='blue')
plt.text(1e-1, yPacc, r'$P_{\rm acc} (f)$', color='blue')
plt.text(1e-2, yPn, r'$P_n^{\rm %s} (f)$' % A, color='red')
plt.text(1e-1,
1e-32,
interf,
fontsize=24,
bbox=dict(facecolor='none',
edgecolor='black',
boxstyle='round,pad=.5'))
plot_sets.axes_lines()
if save:
plt.savefig('plots/noise_PSD_' + interf + '.pdf', bbox_inches='tight')
def plot_PM_beltrami(save=True):
"""
Function that plots the analytical relations between the GW polarization P
and the source helicity PM (for magnetic) for the Beltrami field model,
compared to the empirical fit obtained in the numerical simulations.
It produces figure 14 (appendix A) of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources," https://arxiv.org/abs/2107.05356.
Arguments:
save -- option to save the figure in plots/PM_beltrami.pdf'
(default True)
"""
plt.figure(figsize=(12, 8))
sigma = np.linspace(0, 1, 100)
Sh_sig = .5 + 2 * sigma**2 / (1 + sigma**2)**2
Pm_sig = 2 * sigma / (1 + sigma**2)
Sh_sig = .5 * (1 + Pm_sig**2)
Ph_sig = Pm_sig / Sh_sig
plt.plot(sigma,
Pm_sig,
ls='dotted',
color='red',
label=r'${\cal P}_{\rm M}$')
plt.plot(sigma,
Sh_sig,
ls='-.',
color='blue',
label=r'$\left(1 + {\cal P}_{\rm M}^2\right)/2$')
plt.plot(sigma,
Ph_sig,
color='black',
lw=.8,
label=r'$2 {\cal P}_{\rm M}/\left(1 + {\cal P}_{\rm M}^2\right)$')
plot_sets.axes_lines()
plt.xlim(0, 1)
plt.ylim(0, 1.1)
plt.legend(fontsize=28, loc='lower right', frameon=False)
plt.xlabel('$\sigma$')
plt.ylabel(r'$\cal P$')
ax = plt.gca()
ax.tick_params(axis='x', pad=20)
plt.yticks(np.linspace(0, 1, 5))
if save: plt.savefig('plots/PM_beltrami.pdf', bbox_inches='tight')
def plot_EGW_vs_kt(runs, rr='ini2', save=True, show=True):
"""
Function that generates the plot of the compensated GW spectrum as a
function of k(t - tini) for the smallest wave numbers of the run.
It corresponds to figure 3 of A. Roper Pol, S. Mandal, A. Brandenburg,
T. Kahniashvili, and A. Kosowsky, "Numerical simulations of gravitational
waves from early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
Arguments:
runs -- dictionary that includes the run variables
rr -- string that selects which run to plot (default 'ini2')
save -- option to save the resulting figure as
plots/EGW_vs_kt.pdf (default True)
show -- option to show the resulting figure (default True)
"""
run = runs.get(rr)
k = run.spectra.get('k')[1:]
EGW = np.array(run.spectra.get('EGW')[:,1:], dtype='float')
t = run.spectra.get('t_EGW')
plt.figure(figsize=(10,6))
plt.xscale('log')
plt.yscale('log')
plt.xlim(1e-2, 40)
plt.ylim(8e-8, 1e-5)
plt.xlabel('$k (t - 1)$')
plt.ylabel(r'$\left[k_* \Omega_{\rm GW} (k, t)/k\right]^{1/2}$')
plot_sets.axes_lines()
# plot for initial wave numbers
plt.plot(k[0]*(t - 1), np.sqrt(EGW[:, 0]*run.kf),
color='black', lw=.8, #label='$k = %.0f$'%k[0])
label='$k = 100$')
plt.plot(k[1]*(t - 1), np.sqrt(EGW[:, 1]*run.kf),
color='red', ls='-.', lw=.8, #label='$k = %.0f$'%k[1])
label='$k = 200$')
plt.plot(k[2]*(t - 1), np.sqrt(EGW[:, 2]*run.kf),
color='blue', ls='dashed', lw=.8, #label='$k = %.0f$'%k[2])
label='$k = 300$')
plt.plot(k[3]*(t - 1), np.sqrt(EGW[:, 3]*run.kf),
color='green', ls='dotted', lw=.8, #label='$k = %.0f$'%k[3])
label='$k = 400$')
plt.legend(fontsize=22, loc='lower right', frameon=False)
if save: plt.savefig('plots/EGW_vs_kt.pdf', bbox_inches='tight')
if not show: plt.close()
def plot_Xi_sensitivity_comb(save=True):
"""
Function that generates the plot of the GW energy density
polarization sensitivity obtained by combining the cross-correlated
channels of the LISA-Taiji network.
Arguments:
save -- option to save the figure in "plots/Xi_LISA_Taiji_comb.pdf"
(default True)
"""
plt.figure(figsize=(12, 8))
#plt.rc('font', size=18)
plt.plot(fs,
XiSAC,
color='black',
lw=.8,
label=r'$h_0^2\, \Xi_{\rm s}^{AC} (f)$')
plt.plot(fs,
XiSAD,
color='blue',
ls='dotted',
label=r'$h_0^2\, \Xi_{\rm s}^{AD} (f)$')
plt.plot(fs,
XiSEC,
color='red',
ls='-.',
label=r'$h_0^2\, \Xi_{\rm s}^{EC} (f)$')
plt.plot(fs,
XiSED,
color='green',
ls='--',
lw=.6,
label=r'$h_0^2\, \Xi_{\rm s}^{ED} (f)$')
plt.plot(fs,
XiS_comb,
color='blue',
label=r'$h_0^2\, \Xi_{\rm s}^{\rm comb} (f)$')
plt.legend(fontsize=20, loc='lower right', frameon=False)
plt.xlabel(r'$f$ [Hz]')
plt.ylabel(r'$h_0^2\, \Xi_{\rm s} (f)$')
plt.xscale('log')
plt.yscale('log')
plt.ylim(1e-12, 1e-4)
plt.xlim(1e-4, 1e-1)
plot_sets.axes_lines()
if save: plt.savefig('plots/Xi_LISA_Taiji_comb.pdf', bbox_inches='tight')
def plot_Df(save=True):
"""
Function that generates the plot of the LISA and Taiji dipole
response functions.
It corresponds to right panel of figure 15 of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources," submitted to JCAP,
https://arxiv.org/abs/2107.05356.
Arguments:
save -- option to save the figure in "plots/DEA_LISA_Taiji.pdf"
(default True)
"""
fig, ax0 = plt.subplots(figsize=(12, 10))
# plt.rc('font', size=30)
DAE_posneg(fs, DAEs)
DAE_posneg(fs, DAEs_Tai, ls='-.')
plt.xlim(1e-3, 1)
plt.ylim(1e-7, 1)
plt.xlabel(r'$f$ [Hz]')
plt.ylabel(r'${\cal D}(f)$')
plt.xscale('log')
plt.yscale('log')
plot_sets.axes_lines()
plt.text(4.7e-2, 2e-2, r'${\cal D}_{AE}(f)$', fontsize=30)
plt.text(1.3e-2, 7e-3, r'${\cal D}_{CD}(f)$', fontsize=30)
#plt.text(2.1e-2, 3e-3, r'${\cal D}_{CD}(f)$', fontsize=20)
line_pos, = ax0.plot([], [], color='blue', lw=.7, label=r'positive values')
line_neg, = ax0.plot([], [], color='red', lw=.7, label=r'negative values')
handles = [line_pos, line_neg]
lgd = ax0.legend(handles=handles,
loc='lower left',
fontsize=34,
frameon=False)
ax = plt.gca()
ax.tick_params(axis='x', pad=20)
ax.tick_params(axis='y', pad=10)
plt.yticks(np.logspace(-7, 0, 8))
if save: plt.savefig('plots/DEA_LISA_Taiji.pdf', bbox_inches='tight')
def plot_sensitivity(save=True):
"""
Function that generates the plot of LISA and Taiji strain sensitivities.
Arguments:
save -- option to save the figure in "plots/sensitivity_LISA_Taiji.pdf"
(default True)
"""
plt.figure(figsize=(12, 8))
plt.rc('font', size=20)
plt.plot(fs, np.sqrt(SnX), color='red', label='channel X')
plt.plot(fs, np.sqrt(SnA), color='blue', label='TDI channel A')
plt.plot(fs, np.sqrt(SnT), color='orange', label='TDI channel T', alpha=.6)
plt.plot(fs, np.sqrt(SnX_Tai), color='red', ls='-.')
plt.plot(fs, np.sqrt(SnC), color='blue', ls='-.')
plt.plot(fs, np.sqrt(SnS), color='orange', ls='-.', alpha=.6)
gg = np.where(abs(M_ED_I) > 1e-48)
plt.plot(fs[gg],
np.sqrt(Sn_ED_I[gg]),
color='purple',
alpha=.5,
label='TDI channels ED')
plt.legend(fontsize=20)
plt.xlabel('$f$ [Hz]')
plt.ylabel(r'Strain sensitivity $\left[{\rm Hz}^{-1/2}\right]$')
plt.xscale('log')
plt.yscale('log')
plt.text(1e-1, 3e-19, 'LISA', fontsize=20)
plt.text(1e-1, 8e-21, 'Taiji', fontsize=20)
plt.ylim(1e-21, 1e-12)
plt.xlim(1e-5, 1e0)
plot_sets.axes_lines()
ax = plt.gca()
ytics = 10**np.array(np.linspace(-21, -12, 10))
ax.set_yticks(ytics)
if save:
plt.savefig('plots/sensitivity_LISA_Taiji.pdf', bbox_inches='tight')
def plot_OmMK_OmGW_vs_t(runs, save=True, show=True):
"""
Function that generates the plots of the total magnetic/kinetic energy
density as a function of time ('OmM_vs_t.pdf') and the GW energy density
as a function of time ('OmGW_vs_t.pdf').
It corresponds to figure 5 of A. Roper Pol, S. Mandal, A. Brandenburg,
T. Kahniashvili, and A. Kosowsky, "Numerical simulations of gravitational
waves from early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
Arguments:
runs -- dictionary that includes the run variables
save -- option to save the resulting figure as
plots/OmGW_vs_t.pdf (default True)
show -- option to show the resulting figure (default True)
"""
# chose the runs to be shown
rrs = ['ini1', 'ini2', 'ini3', 'hel1', 'hel2', 'ac1']
# chose the colors of each run
col = ['black', 'red', 'blue', 'red', 'blue', 'black']
# chose the line style for the plots
ls = ['solid']*6
ls[3] = 'dashed'
ls[4] = 'dashed'
ls[5] = 'dashed'
plt.figure(1, figsize=(10,6))
plt.figure(2, figsize=(10,6))
j = 0
for i in rrs:
run = runs.get(i)
k = run.spectra.get('k')[1:]
GWs_stat_sp = run.spectra.get('GWs_stat_sp')
t = run.ts.get('t')[1:]
indst = np.argsort(t)
t = t[indst]
EEGW = run.ts.get('EEGW')[1:][indst]
if run.turb == 'm': EEM = run.ts.get('EEM')[1:][indst]
if run.turb == 'k': EEM = run.ts.get('EEK')[1:][indst]
plt.figure(1)
plt.plot(t, EEGW, color=col[j], lw=.8, ls=ls[j])
# text with run name
if i=='ini1': plt.text(1.02, 5e-8, i, color=col[j])
if i=='ini2': plt.text(1.07, 5e-11, i, color=col[j])
if i=='ini3': plt.text(1.2, 6e-9, i, color=col[j])
if i=='hel1': plt.text(1.15, 2e-9, i, color=col[j])
if i=='hel2': plt.text(1.12, 7e-10, i, color=col[j])
if i=='ac1': plt.text(1.2, 1e-7, i, color=col[j])
plt.figure(2)
plt.plot(t, EEM, color=col[j], lw=.8, ls=ls[j])
# text with run name
if i=='ini1': plt.text(1.01, 8e-2, i, color=col[j])
if i=='ini2': plt.text(1.12, 3e-3, i, color=col[j])
if i=='ini3': plt.text(1.01, 9e-3, i, color=col[j])
if i=='hel1': plt.text(1.15, 1.3e-2, i, color=col[j])
if i=='hel2': plt.text(1.02, 1e-3, i, color=col[j])
if i=='ac1': plt.text(1.17, 1.5e-3, i, color=col[j])
j += 1
plt.figure(1)
plt.yscale('log')
plt.xlabel('$t$')
plt.xlim(1, 1.25)
plt.ylim(2e-11, 2e-7)
plt.ylabel(r'$\Omega_{\rm GW}$')
plot_sets.axes_lines()
if save: plt.savefig('plots/OmGW_vs_t.pdf', bbox_inches='tight')
if not show: plt.close()
plt.figure(2)
plt.yscale('log')
plt.xlim(1, 1.25)
plt.ylim(5e-4, 2e-1)
plt.xlabel('$t$')
plt.ylabel(r'$\Omega_{\rm M, K}$')
plot_sets.axes_lines()
if save: plt.savefig('plots/OmM_vs_t.pdf', bbox_inches='tight')
if not show: plt.close()
def plot_PGW_vs_PM(runs, save=True):
"""
Function that generates the plot of the total GW polarization PGW as a
function of the total fractional helicity of the sourcing magnetic PM or
velocity PK field.
It corresponds to figure 6 of A. Roper Pol, S. Mandal, A. Brandenburg,
and T. Kahniashvili, "Polarization of gravitational waves from helical MHD
turbulent sources," https://arxiv.org/abs/2107.05356.
Arguments:
runs -- dictionary that includes the run variables
save -- option to save the figure in plots/PGW_vs_PM.pdf'
(default True)
"""
plt.figure(figsize=(12, 8))
for i in runs:
run = runs.get(i)
k = run.spectra.get('k')
EGW = run.spectra.get('EGW_stat_sp')
HGW = run.spectra.get('helEGW_stat_sp')
t = run.spectra.get('t_mag')
indt = 0
EM = run.spectra.get('mag')[indt, :]
HM = run.spectra.get('helmag_comp')[indt, :]
PM = np.trapz(HM, k) / np.trapz(EM, k)
PGW = np.trapz(HGW, k[1:]) / np.trapz(EGW, k[1:])
if 'i' in i: plt.plot(abs(PM), abs(PGW), 'o', color='blue')
else: plt.plot(abs(PM), abs(PGW), 'x', color='red')
col = assign_col(i)
if col == 'black': sig = 0
if col == 'green': sig = 0.1
if col == 'darkgreen': sig = 0.3
if col == 'orange': sig = 0.5
if col == 'darkorange': sig = 0.7
if col == 'red' or col == 'blue': sig = 1.
if col == 'blue': col = 'red'
eps = 2 * sig / (1 + sig**2)
plt.vlines(eps,
0,
2 * eps / (1 + eps**2),
color=col,
ls='dashed',
lw=0.5)
plot_sets.axes_lines()
plt.xlim(0, 1.05)
plt.ylim(0, 1.1)
plt.xlabel(r'$|{\cal P}_{\rm M}|$')
plt.ylabel(r'$|{\cal P}_{\rm GW}|$')
xx = np.linspace(0, 1.1)
plt.plot(xx, xx, lw=.5, ls='dashed', color='black')
plt.plot(xx, 2 * xx / (1 + xx**2), lw=.5, ls='dashed', color='black')
plt.text(.06, .75, r'${\cal P}_{\rm GW}=2 {\cal P}_{\rm M}' + \
r'/\bigl(1 + {\cal P}_{\rm M}^2\bigr)$',
fontsize=24, bbox=dict(facecolor='white', edgecolor='black',
boxstyle='round,pad=.2'))
plt.text(.3, .2, r'${\cal P}_{\rm GW}={\cal P}_{\rm M} = 2' + \
r'\sigma_{\rm M}/\bigl(1 + \sigma_{\rm M}^2\bigr)$',
fontsize=24, bbox=dict(facecolor='white', edgecolor='black',
boxstyle='round,pad=.2'))
#plt.legend(fontsize=14)
line_ini, = plt.plot([], [], 'o', color='blue', label='initial')
line_forc, = plt.plot([], [], 'x', color='red', label='forcing (short)')
hdls = [
line_ini,
line_forc,
]
plt.legend(handles=hdls, fontsize=24, loc='upper left', frameon=False)
ax = plt.gca()
ax.tick_params(axis='x', pad=20)
ax.tick_params(axis='y', pad=10)
if save: plt.savefig('plots/PGW_vs_PM.pdf', bbox_inches='tight')
def plot_PGW(runs, PPh='GW', type='ini', save=True):
"""
Function that plots the GW polarization spectra, averaging over
times after the GW energy and helicity have entered stationary oscillatory
stages (this needs to be previously computed and stored in the run variable,
see initialize_JCAP_2021.py).
It corresponds to figure 5 of A. Roper Pol, S. Mandal, A. Brandenburg,
and T. Kahniashvili, "Polarization of gravitational waves from helical MHD
turbulent sources," https://arxiv.org/abs/2107.05356.
Arguments:
runs -- dictionary of variables run with spectral information
type -- selects the types of runs to be plotted (default 'ini', other
option is 'forc'), i.e., runs with an initial magnetic field
('ini') or runs in which the magnetic field is initially driven
during the simulation ('forc')
save -- option to save the figure in plots/PGW_'type'_sigma.pdf'
(default True)
"""
plt.rcParams.update({
'xtick.labelsize': 'xx-large',
'ytick.labelsize': 'xx-large',
'axes.labelsize': 'xx-large'
})
if type == 'ini': RR = ['i_s01', 'i_s03', 'i_s05', 'i_s07', 'i_s1']
elif type == 'forc':
RR = ['f_s001', 'f_s001_neg', 'f_s03', 'f_s05', 'f_s07', 'f_s1_neg']
elif type == 'kin':
RR = ['K0', 'K01_c', 'K03', 'K05', 'K1']
elif type == 'mag':
RR = ['M0', 'M01_c', 'M03', 'M05', 'M1']
if PPh == 'GW': PP = 'GW'
if PPh == 'h': PP = 'h'
fig, ax = plt.subplots(figsize=(12, 10))
for i in RR:
# select colors
col = assign_col(i)
run = runs.get(i)
k = run.spectra.get('k')[1:]
PGW = run.spectra.get('P' + PP + '_stat_sp')
PGW_min = run.spectra.get('P' + PP + '_min_sp')
PGW_max = run.spectra.get('P' + PP + '_max_sp')
plt.plot(k, PGW, color=col, lw=2)
plt.fill_between(k, PGW_min, PGW_max, alpha=0.3, color=col)
for i in range(0, len(k)):
plt.vlines(k[i],
PGW_min[i],
PGW_max[i],
color=col,
lw=0.6,
ls='dashed')
plot_sets.axes_lines()
plt.xscale('log')
plt.xlabel('$k$')
plt.ylabel(r'${\cal P}_{\rm %s} (k)$' % PP)
sigs = []
plt.xlim(120, 5e4)
tp = 'forc'
if type == 'forc':
sigs = ['0.01', '-0.01', '0.3', '0.5', '0.7', '-1']
cols = ['black', 'black', 'darkgreen', 'orange', 'darkorange', 'blue']
plt.ylim(-1.15, 1.15)
plt.yticks(np.linspace(-1, 1, 9))
if PPh == 'GW':
xxs = [7e2, 7e2, 7e2, 8e3, 2.5e3, 7e2]
yys = [.2, -.25, .4, .55, .9, -.9, -.9]
plt.text(3e4, -0.9, '(b)', fontsize=30)
else:
xxs = [5e2, 5e2, 5e2, 4e3, 3e3, 5e2]
yys = [.25, -.25, .5, .5, .7, -.8]
plt.text(3e4, -0.9, '(d)', fontsize=30)
else:
if type == 'ini':
tp = 'ini'
sigs = ['0.1', '0.3', '0.5', '0.7', '1']
cols = ['green', 'darkgreen', 'orange', 'darkorange', 'red']
if PPh == 'GW':
xxs = [1e4, 1e4, 1e4, 1e4, 1e3]
yys = [.3, .5, .75, 1.05, 1.05]
plt.text(3e4, -0.35, '(a)', fontsize=30)
else:
xxs = [1.5e4, 1.5e4, 1.5e4, 1.5e4, 1e3]
yys = [0.05, 0.35, 0.62, 1.05, 1.05]
plt.text(3e4, -0.35, '(c)', fontsize=30)
else:
line_s0, line_s001, line_s01, line_s03, line_s05, line_s07, \
line_s1, line_s1_neg, = get_lines_sig(tp)
hdls = [
line_s1,
line_s05,
line_s03,
line_s01,
line_s0,
]
plt.legend(handles=hdls,
fontsize=24,
loc='upper right',
frameon=False)
plt.xlim(120, 3e4)
plt.ylim(-.5, 1.2)
for i in range(0, len(sigs)):
plt.text(xxs[i],
yys[i],
r'$\sigma_{\rm M}^{\rm %s}=%s$' % (tp, sigs[i]),
fontsize=30,
color=cols[i])
if save:
plt.savefig('plots/P' + PPh + '_' + type + '_sigma.pdf',
bbox_inches='tight')
def plot_helicity_vs_t(runs, type='ini', save=True):
"""
Function that generates the plot of the total magnetic or kinetic helicity
as a function of time.
It corresponds to figure 4 of A. Roper Pol, S. Mandal, A. Brandenburg,
and T. Kahniashvili, "Polarization of gravitational waves from helical MHD
turbulent sources," https://arxiv.org/abs/2107.05356.
Arguments:
runs -- dictionary that includes the run variables
type -- selects the types of runs to be plotted (default 'ini', other
option is 'forc'), i.e., runs with an initial magnetic field
('ini') or runs in which the magnetic field is initially driven
during the simulation ('forc')
save -- option to save the figure in plots/sigmaM_vs_t_'type'.pdf'
(default True)
"""
if type == 'ini': RR = ['i_s01', 'i_s03', 'i_s05', 'i_s07', 'i_s1']
elif type == 'forc':
RR = ['f_s001', 'f_s001_neg', 'f_s03', 'f_s05', 'f_s07', 'f_s1_neg']
elif type == 'kin':
RR = ['K0', 'K01_c', 'K03', 'K05', 'K1']
elif type == 'mag':
RR = ['M0', 'M01_c', 'M03', 'M05', 'M1']
plt.figure(figsize=(12, 8))
for i in RR:
run = runs.get(i)
col = assign_col(i)
if run.turb == 'm': sp = 'mag'
if run.turb == 'k': sp = 'kin'
t = np.array(run.spectra.get('t_hel' + sp), dtype='float')[:, 0]
t2 = run.spectra.get('t_' + sp)
EM = np.array(run.spectra.get(sp), dtype='float')
HkM = run.spectra.get('hel' + sp + '_comp')
k = run.spectra.get('k')
EMs_mean = np.trapz(EM, k, axis=1)
HMs_mean = np.trapz(HkM, k, axis=1)
EMs_mean = np.interp(t, t2, EMs_mean)
eps = abs(HMs_mean) / EMs_mean
plt.plot(t - 1, eps, '.', color=col)
if col == 'black': sig = 0
if col == 'green': sig = 0.1
if col == 'darkgreen': sig = 0.3
if col == 'orange': sig = 0.5
if col == 'darkorange': sig = 0.7
if col == 'red' or col == 'blue': sig = 1.
eps = 2 * sig / (1 + sig**2)
plt.hlines(eps, 1e-5, 5, color=col, ls='dashed', lw=0.5)
if type == 'ini': tp = 'ini'
else: tp = 'forc'
#line_s0, line_s001, line_s01, line_s03, line_s05, line_s07, \
# line_s1, line_s1_neg, = get_lines_sig(tp)
#hdls1 = [line_s001, line_s01, line_s03, line_s05, line_s07, line_s1,]
#plt.legend(handles=hdls1, fontsize=24, loc='center left')
MM = 'M'
if type == 'kin': MM = 'K'
sig_s = r'$\sigma_{\rm %s}^{\rm %s} = $' % (MM, tp)
if type != 'forc':
plt.text(2.5e-3, .12, sig_s + ' 0.1', color='green', fontsize=24)
if type != 'ini':
plt.text(2.5e-3, -.08, sig_s + ' 0', color='black', fontsize=24)
else:
plt.text(2.5e-3,
.04,
sig_s + ' $\pm 0.01$',
color='black',
fontsize=24)
plt.text(2.5e-3, .47, sig_s + ' 0.3', color='darkgreen', fontsize=24)
plt.text(2.5e-3, .72, sig_s + ' 0.5', color='orange', fontsize=24)
if type == 'ini' or type == 'forc':
plt.text(2.5e-3, .86, sig_s + ' 0.7', color='darkorange', fontsize=24)
if type != 'forc':
plt.text(2.5e-3, 1.04, sig_s + ' $1$', color='red', fontsize=24)
else:
plt.text(2.5e-3, 1.04, sig_s + ' $-1$', color='blue', fontsize=24)
plot_sets.axes_lines()
plt.xscale('log')
plt.xlim(2e-3, 5e-1)
plt.ylim(-.1, 1.13)
if type == 'mag' or type == 'kin':
plt.ylim(-.15, 1.13)
plt.xlim(2e-3, 1.5e0)
plt.xlabel('$\delta t=t-1$')
plt.ylabel(r'$|{\cal P}_{\rm M}(t)|$')
plt.yticks(np.linspace(0, 1, 5))
if save:
plt.savefig('plots/sigmaM_vs_t_' + type + '.pdf', bbox_inches='tight')
def plot_Xi_sensitivity(XiPLSa,
XiPLSb,
XiPLSa_Tai,
XiPLSb_Tai,
XiPLS_comb,
SNR=10,
T=4,
save=True):
"""
Function that generates the plot of LISA and Taiji GW energy density
polarization sensitivities and PLS.
It corresponds to right panel of figure 16 of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources," submitted to JCAP,
https://arxiv.org/abs/2107.05356.
Arguments:
XiPLSa -- polarization PLS of the dipole response function of LISA
with beta_max = 2 for T = 1yr and SNR = 1
XiPLSb -- polarization PLS of the dipole response function of LISA
with beta_max = 3 for T = 1yr and SNR = 1
XiPLSa_Tai -- polarization PLS of the dipole response function of Taiji
with beta_max = 2 for T = 1yr and SNR = 1
XiPLSb_Tai -- polarization PLS of the dipole response function of Taiji
with beta_max = 3 for T = 1yr and SNR = 1
XiPLS_comb -- polarization PLS of the LISA-Taiji network
for T = 1yr and SNR = 1
SNR -- signal-to-noise ratio (SNR) for the plotted PLS (default 10)
T -- duration of the observations for the plotted PLS in
years (default 4)
save -- option to save the figure in "plots/Xi_LISA_Taiji.pdf"
(default True)
"""
fact = SNR / np.sqrt(T)
fig, ax0 = plt.subplots(figsize=(12, 10))
#plt.rc('font', size=18)
plt.plot(fs, XiSAE, color='blue')
plt.plot(fs, XiSCD, color='blue', ls='-.')
gg = np.where(XiS_comb < 1e5)
plt.plot(fs[gg], XiS_comb[gg], color='blue', lw=.6)
plt.plot(fs, XiPLSa * fact, color='green')
plt.plot(fs, XiPLSb * fact, color='green')
plt.plot(fs, XiPLSa_Tai * fact, color='green', ls='-.')
plt.plot(fs, XiPLSb_Tai * fact, color='green', ls='-.')
plt.plot(fs, XiPLS_comb * fact, color='green', lw=.6)
line_XiPLS, = ax0.plot([], [],
color='green',
label=r'$\Xi_{\rm PLS}^{\rm AE}$')
line_XiPLS_Tai, = ax0.plot([], [],
color='green',
ls='-.',
label=r'$\Xi_{\rm PLS}^{\rm CD}$')
line_XiPLS_comb, = ax0.plot([], [],
color='green',
lw=.8,
label=r'$\Xi_{\rm PLS}^{\rm comb}$')
line_XiSA, = ax0.plot([], [],
color='blue',
label=r'$\Xi_{\rm s}^{\rm AE}$')
line_XiSC, = ax0.plot([], [],
color='blue',
ls='-.',
label=r'$\Omega_{\rm s}^{\rm CD}$')
line_XiS_comb, = ax0.plot([], [],
color='blue',
lw=.8,
label=r'$\Xi_{\rm s}^{\rm comb}$')
handles = [line_XiSA, line_XiSC, line_XiS_comb]
lgd1 = ax0.legend(handles=handles,
loc='lower right',
fontsize=28,
frameon=False)
handles2 = [line_XiPLS, line_XiPLS_Tai, line_XiPLS_comb]
lgd2 = ax0.legend(handles=handles2,
loc='lower left',
fontsize=28,
frameon=False)
ax0.add_artist(lgd1)
#plt.legend(fontsize=30, loc='lower right', frameon=False)
plt.xlabel(r'$f$ [Hz]')
plt.ylabel(r'$h_0^2\, \Xi_{\rm s} (f)$')
plt.xscale('log')
plt.yscale('log')
plt.ylim(1e-14, 1e-2)
plt.xlim(1e-5, 1e0)
plot_sets.axes_lines()
plt.text(1e-1, 8e-9, r'$\beta_{\rm max}=2$', color='green', fontsize=30)
plt.text(9e-2, 6e-4, r'$\beta_{\rm max}=3$', color='green', fontsize=30)
ax = plt.gca()
ax.tick_params(axis='x', pad=20)
ax.tick_params(axis='y', pad=10)
plt.yticks(np.logspace(-14, -2, 7))
plt.xticks(np.logspace(-5, 0, 6))
if save: plt.savefig('plots/Xi_LISA_Taiji.pdf', bbox_inches='tight')
def plot_EGW_EM_vs_k(runs, rr='ini2', save=True, show=True):
"""
Function that generates the plot of the magnetic spectrum
EM (k) = Omega_M(k)/k at the initial time of turbulence generation
and the GW spectrum EGW (k) = Omega_GW(k)/k, averaged over oscillations
in time.
It corresponds to figure 1 of A. Roper Pol, S. Mandal, A. Brandenburg,
T. Kahniashvili, and A. Kosowsky, "Numerical simulations of gravitational
waves from early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
Arguments:
runs -- dictionary that includes the run variables
rr -- string that selects which run to plot (default 'ini2')
save -- option to save the resulting figure as
plots/EGW_EM_vs_k_'name_run'.pdf' (default True)
show -- option to show the resulting figure (default True)
"""
plt.figure(figsize=(10,6))
plt.xscale('log')
plt.yscale('log')
plt.xlim(120, 6e4)
plt.ylim(1e-19, 1e-4)
plt.xlabel('$k$')
plt.ylabel(r'$\Omega_{\rm GW}(k)/k$ and $\Omega_{\rm M}(k)/k$',
fontsize=20)
run = runs.get(rr)
# plot the averaged over times GW spectrum
GWs_stat_sp = run.spectra.get('EGW_stat_sp')
k = run.spectra.get('k')[1:]
plt.plot(k, GWs_stat_sp, color='black')
# plot magnetic spectrum at the initial time
mag = run.spectra.get('mag')[0, 1:]
plt.plot(k, mag, color='black')
# plot k^4 line
k0 = np.logspace(np.log10(150), np.log10(500), 5)
plt.plot(k0, 1e-9*(k0/100)**4, color='black', ls='-.', lw=.7)
plt.text(300, 8e-9, r'$\sim\!k^4$', fontsize=20)
# plot k^(-5/3) line
k0 = np.logspace(np.log10(2000), np.log10(8000), 5)
plt.plot(k0, 1e-5*(k0/1000)**(-5/3), color='black', ls='-.', lw=.7)
plt.text(5e3, 1.6e-6, r'$\sim\!k^{-5/3}$', fontsize=20)
# plot k^(-11/3) line
k0 = np.logspace(np.log10(3000), np.log10(30000), 5)
plt.plot(k0, 1e-12*(k0/1000)**(-11/3), color='black', ls='-.', lw=.7)
plt.text(1e4, 5e-16, r'$\sim\!k^{-11/3}$', fontsize=20)
plt.text(1500, 1e-16, r'$\Omega_{\rm GW} (k)/k$', fontsize=20)
plt.text(800, 5e-8, r'$\Omega_{\rm M} (k)/k$', fontsize=20)
ax = plt.gca()
ax.set_xticks([100, 1000, 10000])
ytics = 10**np.array(np.linspace(-19, -5, 7))
ytics2 = 10**np.array(np.linspace(-19, -5, 15))
yticss = ['$10^{-19}$', '', '$10^{-17}$', '', '$10^{-15}$', '',
'$10^{-13}$', '', '$10^{-11}$', '', '$10^{-9}$', '',
'$10^{-7}$', '', '$10^{-5}$']
ax.set_yticks(ytics2)
ax.set_yticklabels(yticss)
plot_sets.axes_lines()
ax.tick_params(pad=10)
if save: plt.savefig('plots/EGW_EM_vs_k_' + run.name_run + '.pdf',
bbox_inches='tight')
if not show: plt.close()
def plot_OmGW_vs_f(runs,
type='ini',
T=1e5 * u.MeV,
g=100,
SNR=10,
Td=4,
OmM=.1,
Xi=False,
save=True):
"""
Function that generates the plot of the GW energy density frequency
spectra at present time compared to the LISA, Taiji, BBO, and DECIGO
sensitivities and power law sensitivities (PLS).
It produces figure 11-13 of A. Roper Pol, S. Mandal, A. Brandenburg,
and T. Kahniashvili, "Polarization of gravitational waves from helical MHD
turbulent sources," https://arxiv.org/abs/2107.05356.
Arguments:
runs -- dictionary that includes the run variables
type -- selects the types of runs to be plotted (default 'ini', other
option is 'forc'), i.e., runs with an initial magnetic field
('ini') or runs in which the magnetic field is initially driven
during the simulation ('forc')
T -- temperature scale (in natural units) at the time of turbulence
generation (default 100 GeV, i.e., electroweak scale)
g -- number of relativistic degrees of freedom at the time of
turbulence generation (default 100, i.e., electroweak scale)
SNR -- signal-to-noise ratio (SNR) of the resulting PLS (default 10)
Td -- duration of the mission (in years) of the resulting PLS
(default 4)
save -- option to save the resulting figure as
plots/'OmGW'_'type'_detectors_'Om'.pdf (default True)
where 'OmGW' = OmGW or XiGW (for Xi False and True,
respectively), 'Om' = OmM005 or OmM01, and 'type' is 'ini'
or 'forc'
"""
# read LISA and Taiji sensitivities
CWD = os.getcwd()
os.chdir('..')
if Xi:
fs, LISA_Om, LISA_OmPLS, LISA_Xi, LISA_XiPLS = \
inte.read_sens(SNR=SNR, T=Td, Xi=True)
fs_Tai, Taiji_Om, Taiji_OmPLS, Taiji_Xi, Taiji_XiPLS = \
inte.read_sens(SNR=SNR, T=Td, interf='Taiji', Xi=True)
fs_comb, LISA_Taiji_Xi, LISA_Taiji_XiPLS = \
inte.read_sens(SNR=SNR, T=Td, interf='comb')
fs_comb = fs_comb * u.Hz
else:
fs, LISA_Om, LISA_OmPLS = inte.read_sens(SNR=SNR, T=Td)
fs_Tai, Taiji_Om, Taiji_OmPLS = inte.read_sens(SNR=SNR,
T=Td,
interf='Taiji')
dir = 'detector_sensitivity'
f_DECIGO, DECIGO_OmPLS = inte.read_csv(dir, 'DECIGO_PLS_SNR10')
ff_D = np.logspace(np.log10(f_DECIGO[0]), np.log10(f_DECIGO[-1]), 100)
DECIGO_OmPLS = 10**np.interp(ff_D, f_DECIGO, np.log10(DECIGO_OmPLS))
f_DECIGO = ff_D * u.Hz
f_BBO, BBO_OmPLS = inte.read_detector_PLIS_Schmitz(det='BBO',
SNR=SNR,
T=Td)
f_BBO = f_BBO * u.Hz
fs = fs * u.Hz
fs_Tai = fs_Tai * u.Hz
os.chdir(CWD)
# internal function to compute f, OmGW as present time observables
def shift_Omega(run, T, g, ratio, Xi, sp='stat'):
hel = ''
if Xi: hel = 'hel'
EGW = np.array(run.spectra.get(hel + 'EGW_' + sp + '_sp'),
dtype='float') * ratio**2
k = run.spectra.get('k')[1:]
OmGW = EGW * k
f, OmGW = cosmoGW.shift_OmGW_today(k, OmGW, T, g)
return f, OmGW
plt.rcParams.update({
'xtick.labelsize': 'xx-large',
'ytick.labelsize': 'xx-large',
'axes.labelsize': 'xx-large'
})
if type == 'ini': RR = ['i_s01', 'i_s03', 'i_s05', 'i_s07', 'i_s1']
elif type == 'forc':
RR = ['f_s001', 'f_s001_neg', 'f_s03', 'f_s05', 'f_s07', 'f_s1_neg']
elif type == 'kin':
RR = ['K0', 'K01_c', 'K03', 'K05', 'K1']
elif type == 'mag':
RR = ['M0', 'M01_c', 'M03', 'M05', 'M1']
fig, ax = plt.subplots(figsize=(12, 10))
for i in RR:
# select colors
col = assign_col(i)
run = runs.get(i)
ratio = OmM / run.Ommax
f, OmGW = shift_Omega(run, T, g, ratio, Xi, sp='stat')
_, OmGW_min = shift_Omega(run, T, g, ratio, Xi, sp='min')
_, OmGW_max = shift_Omega(run, T, g, ratio, Xi, sp='max')
plt.plot(f, abs(OmGW), color=col, lw=3)
#if 'i_s1' not in i:
#if type == 'ini' or type == 'forc':
plt.fill_between(f, OmGW_min, OmGW_max, alpha=0.1, color=col)
for i in range(0, len(f)):
plt.vlines(f.value[i],
OmGW_min[i],
OmGW_max[i],
color=col,
lw=0.6,
ls='dashed')
if type == 'ini': tp = 'ini'
else: tp = 'forc'
line_s0, line_s001, line_s01, line_s03, line_s05, line_s07, \
line_s1, line_s1_neg, = get_lines_sig(tp)
if type == 'ini':
hdls = [
line_s01,
line_s03,
line_s05,
line_s07,
line_s1,
]
elif type == 'forc':
hdls = [
line_s001,
line_s03,
line_s05,
line_s07,
line_s1_neg,
]
else:
hdls = [
line_s0,
line_s01,
line_s03,
line_s05,
line_s1,
]
plt.legend(handles=hdls, fontsize=24, loc='upper right', framealpha=1)
Om = '0.1'
if OmM == .05: Om = '0.05'
xb = 2e-3
yb = 8e-11
if Xi:
xb = 1e-3
yb = 1e-17
MM = 'M'
if type == 'kin': MM = 'K'
plt.text(xb,
yb,
r'${\cal E}^{\rm max}_{\rm %s} = %s$' % (MM, Om),
fontsize=30,
bbox=dict(facecolor='white',
edgecolor='black',
boxstyle='round,pad=.5'))
if type == 'ini':
xB = 1.2e-2
yB = 1e-16
xD = 2e-3
yD = 6e-16
if OmM == 0.1: pan = '(a)'
else: pan = '(c)'
else:
xB = 3e-2
yB = 3e-17
xD = 2.5e-2
yD = 1e-15
if OmM == 0.1: pan = '(b)'
else: pan = '(d)'
if type == 'kin': pan = '(a)'
if type == 'mag': pan = '(b)'
if Xi:
plt.plot(fs, LISA_XiPLS, color='lime', ls='-.', lw=1)
plt.text(1.1e-3, 5e-11, 'LISA', fontsize=30, color='lime')
plt.plot(fs_Tai, Taiji_XiPLS, color='crimson', ls='-.', lw=1)
plt.text(1e-2, 4e-11, 'Taiji', fontsize=30, color='crimson')
plt.plot(fs_comb, LISA_Taiji_XiPLS, color='navy', ls='-.', lw=1)
plt.text(1e-2, 2e-13, r'LISA--Taiji', fontsize=30, color='navy')
else:
plt.plot(fs, LISA_OmPLS, color='lime', ls='-.', lw=1)
plt.text(7e-3, 4e-12, 'LISA', fontsize=30, color='lime')
plt.plot(fs_Tai, Taiji_OmPLS, color='crimson', ls='-.', lw=1)
plt.text(1.3e-2, 1e-13, 'Taiji', fontsize=30, color='crimson')
plt.plot(f_BBO, BBO_OmPLS, color='navy', ls='-.', lw=1)
plt.text(xB, yB, 'BBO', fontsize=30, color='navy')
plt.plot(f_DECIGO, DECIGO_OmPLS, color='royalblue', ls='-.', lw=1)
plt.text(xD, yD, 'DECIGO', fontsize=30, color='royalblue')
plt.text(4e-4, 4e-18, pan, fontsize=30)
plot_sets.axes_lines()
plt.xscale('log')
plt.yscale('log')
plt.xlim(3e-4, 2e-1)
plt.ylim(1e-18, 1e-8)
plt.xlabel('$f$ [Hz]')
if Xi: plt.ylabel(r'$h_0^2 |\Xi_{\rm GW} (f)|$')
else: plt.ylabel(r'$h_0^2 \Omega_{\rm GW} (f)$')
Om_save = 'OmM01'
if OmM == 0.05: Om_save = 'OmM005'
OmGW_s = 'OmGW'
if Xi: OmGW_s = 'XiGW'
if save:
plt.savefig('plots/%s_%s_detectors_%s.pdf' % (OmGW_s, type, Om_save),
bbox_inches='tight')
def plot_efficiency(runs, save=True):
"""
Function that generates the plot of the GW production efficiency for
different runs as a function of time.
It corresponds to figure 10 of A. Roper Pol, S. Mandal, A. Brandenburg,
and T. Kahniashvili, "Polarization of gravitational waves from helical MHD
turbulent sources," https://arxiv.org/abs/2107.05356.
Arguments:
runs -- dictionary that includes the run variables
save -- option to save the figure in plots/OmGW_efficiency_vs_t.pdf'
(default True)
"""
plt.figure(figsize=(12, 8))
RR = [
'i_s01', 'i_s03', 'i_s05', 'i_s07', 'i_s1', 'f_s001', 'f_s001_neg',
'f_s03', 'f_s05', 'f_s07', 'f_s1_neg', 'M0', 'M01_c', 'M03', 'M05',
'M1', 'ini1', 'ini2', 'ini3', 'hel1', 'hel2', 'hel3', 'hel4', 'noh1',
'noh2', 'ac1', 'ac2', 'ac3'
]
for i in RR:
# select colors
col = assign_col(i)
run = runs.get(i)
t = run.ts.get('t')
EGW = run.ts.get('EEGW')
if run.turb == 'm':
Om = run.OmMmax
kf = run.kfM
if run.turb == 'k':
Om = run.OmKmax
kf = run.kfK
if abs(kf - 510.9) < 10 or 'M' in i: kf = 708
if abs(kf - 5999) < 100: kf = 7000
lww = 1.
ls = 'solid'
if 'M' in i: lww = .6
if 'ac' in i or 'hel' in i:
lww = .8
ls = 'dotted'
if 'ini' in i or 'noh' in i:
lww = .8
ls = 'dotted'
plt.plot(t - 1, np.sqrt(EGW) / Om * kf, color=col, ls=ls, lw=lww)
line_s0, line_s001, line_s01, line_s03, line_s05, line_s07, \
line_s1, line_s1_neg, = get_lines_sig('')
hdls1 = [
line_s001,
line_s01,
line_s03,
line_s05,
line_s07,
line_s1,
]
plt.text(.2, np.sqrt(.4), 'initial')
plt.text(.08, 3.1, 'forcing (short)')
plt.text(.007, 6, 'forcing (short, $k_*\sim 60$)')
plt.text(1.2, np.sqrt(30), 'forcing (long)')
plt.text(2e-1, 10, 'acoustic')
plt.legend(handles=hdls1, fontsize=24, framealpha=1)
plot_sets.axes_lines()
plt.xlim(6e-3, 4)
plt.ylim(1e-1, 2e1)
plt.xlabel('$\delta t=t-1$')
plt.ylabel(
r'$k_*\, \Omega_{\rm GW}^{1/2} (t)/{\cal E}_{\rm M,K}^{\rm max}$')
plt.yscale('log')
plt.xscale('log')
if save: plt.savefig('plots/OmGW_efficiency_vs_t.pdf', bbox_inches='tight')
def plot_MAC(save=True, log=False):
"""
Function that generates the plot of the helical (V Stokes parameter)
monopole responses of the cross-correlated channels of the LISA-Taiji
network.
It corresponds to figure 18 of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources," submitted to JCAP,
https://arxiv.org/abs/2107.05356.
Arguments:
save -- option to save the figure in
"plots/Mcross_LISA_Taiji.pdf" (default True)
log -- option to plot loglog with absolute values of the response
functions (default False)
"""
plt.figure(figsize=(12, 8))
#plt.rc('font', size=20)
lg = ''
if log:
MAC = abs(M_AC)
MAD = abs(M_AD)
MEC = abs(M_ED)
MED = abs(M_ED)
MED_I = abs(M_ED_I)
plt.xscale('log')
plt.yscale('log')
lg = '_log'
else:
MAC = M_AC
MAD = M_AD
MEC = M_EC
MED = M_ED
MED_I = M_ED_I
plt.plot(fs, MAC, color='black', label=r'${\cal M}^V_{\rm AC}$')
plt.plot(fs,
MAD,
color='blue',
ls='dotted',
label=r'${\cal M}^V_{\rm AD}$')
plt.plot(fs, MEC, color='red', ls='-.', label=r'${\cal M}^V_{\rm EC}$')
plt.plot(fs, MED, color='green', ls='--', label=r'${\cal M}^V_{\rm ED}$')
gg = np.where(abs(MED_I) > 1e-48)
plt.plot(fs[gg],
MED_I[gg],
color='purple',
alpha=.8,
label=r'${\cal M}^I_{\rm ED}$')
plt.legend(fontsize=18, frameon=False)
plt.xlabel('$f$ [Hz]')
plt.ylabel(r'${\cal M} (f)$')
plt.xscale('log')
if log:
plt.xlim(1e-4, 4e-2)
plt.ylim(1e-4, 2e-1)
else:
plt.xlim(3e-5, 4e-2)
plt.ylim(-0.08, 0.08)
plt.yticks(np.linspace(-.075, .075, 7))
plot_sets.axes_lines()
if save:
plt.savefig('plots/Mcross_LISA_Taiji' + lg + '.pdf',
bbox_inches='tight')
def plot_Xi_sensitivity_dipole(XiPLSa,
XiPLSb,
XiPLSc,
XiPLSd,
XiPLSe,
XiPLSf,
XiPLSg,
XiPLS0,
XiPLS_comb,
interf='LISA',
SNR=10,
T=4,
save=True):
"""
Function that generates the plot of the GW energy density
polarization PLS for different values of beta_max.
It corresponds to figure 17 of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources," submitted to JCAP,
https://arxiv.org/abs/2107.05356.
Arguments:
XiPLSa -- polarization PLS of the dipole response function of LISA
with beta_max = 2 for T = 1yr and SNR = 1
XiPLSb -- polarization PLS of the dipole response function of LISA
with beta_max = 3 for T = 1yr and SNR = 1
XiPLSc -- polarization PLS of the dipole response function of LISA
with beta_max = 3.7 for T = 1yr and SNR = 1
XiPLSd -- polarization PLS of the dipole response function of LISA
with beta_max = 3.95 for T = 1yr and SNR = 1
XiPLSe -- polarization PLS of the dipole response function of LISA
with beta_max = 3.999 for T = 1yr and SNR = 1
XiPLSf -- polarization PLS of the dipole response function of LISA
with beta_max = 3.999999 for T = 1yr and SNR = 1
XiPLSg -- polarization PLS of the dipole response function of LISA
with beta values in (-20, 0)U(5, 20) for T = 1yr and SNR = 1
XiPLS0 -- polarization PLS of the dipole response function of LISA
omitting 1/(1 - beta/4) term for T = 1yr and SNR = 1
XiPLS_comb -- polarization PLS of the LISA-Taiji network
for T = 1yr and SNR = 1
interf -- selects interferometer (default 'LISA',
also available 'Taiji')
SNR -- signal-to-noise ratio (SNR) for the plotted PLS (default 10)
T -- duration of the observations for the plotted PLS in
years (default 4)
save -- option to save the figure in "plots/Xi_PLS_interf.pdf"
(default True)
"""
import pandas as pd
fact = SNR / np.sqrt(T)
plt.figure(figsize=(12, 10))
if interf == 'LISA':
AE = 'AE'
ybeta_a = 1.3e-8
ybeta_b = 1.5e-7
ybeta_c = 3e-8
ybeta_d = 1e-7
ybeta_e = 1e-8
ybeta_f = 3e-8
if interf == 'Taiji':
AE = 'CD'
ybeta_a = 3e-9
ybeta_b = 3.5e-8
ybeta_c = 8e-9
ybeta_d = 3e-8
ybeta_e = 2.5e-9
ybeta_f = 6e-9
# plot PLS using dipole for different beta_max
plt.plot(fs,
XiPLSa * fact,
color='blue',
lw=1,
label=r'$\Xi_{\rm PLS}^{\rm %s}$' % AE)
plt.plot(fs, XiPLSb * fact, color='blue', lw=.8, ls='-.')
plt.plot(fs, XiPLSc * fact, color='blue', lw=.8, ls='-.')
plt.plot(fs, XiPLSd * fact, color='blue', lw=.8, ls='-.')
plt.plot(fs, XiPLSe * fact, color='blue', lw=.8, ls='-.')
plt.plot(fs, XiPLSf * fact, color='blue', lw=.8, ls='-.')
# plot PLS using dipole ignoring 1/abs(1 - beta/4) term
plt.plot(fs,
XiPLS0 * fact,
color='red',
lw=.8,
label=r'$\Xi_{\rm PLS}^{0, {\rm %s}}$' % AE)
# plot PLS using LISA-Taiji combined network
plt.plot(fs,
XiPLS_comb * fact,
color='green',
lw=.8,
label=r'$\Xi_{\rm PLS}^{\rm comb}$')
# text with values of beta_max
plt.text(2.5e-2,
ybeta_a / 4,
r'$\beta_{\rm max}=2$',
color='blue',
fontsize=22,
bbox=dict(facecolor='white',
edgecolor='none',
boxstyle='round,pad=.2'))
plt.text(3.2e-2,
ybeta_b / 4,
r'$\beta_{\rm max}=3$',
color='blue',
fontsize=22,
bbox=dict(facecolor='white',
edgecolor='none',
boxstyle='round,pad=.2'))
plt.text(5.3e-3,
ybeta_c,
r'$\beta_{\rm max}=3.7$',
color='blue',
fontsize=22,
bbox=dict(facecolor='white',
edgecolor='none',
boxstyle='round,pad=.2'))
plt.text(5.5e-3,
ybeta_d * 3,
r'$\beta_{\rm max}=3.95$',
color='blue',
fontsize=22,
bbox=dict(facecolor='white',
edgecolor='none',
boxstyle='round,pad=.2'))
plt.text(8e-4,
ybeta_e,
r'$\beta_{\rm max}=3.999$',
color='blue',
fontsize=22)
plt.text(2e-4,
ybeta_f * 5,
r'$\beta_{\rm max}=3.999999$',
fontsize=22,
color='blue')
plt.hlines(Xiflat * fact, 1e-3, 7e-2, color='blue', lw=.7)
plt.hlines(Xiflat_Tai * fact, 1e-3, 7e-2, color='blue', ls='-.', lw=.7)
plt.hlines(Xiflat_comb * fact, 1.e-3, 7e-2, color='green', lw=.8)
plt.text(3e-2,
1.5e-10,
r'$\Xi_{\rm flat}^{\rm AE}$',
fontsize=28,
color='blue')
plt.text(3e-2,
1.7e-11,
r'$\Xi_{\rm flat}^{\rm CD}$',
fontsize=28,
color='blue')
plt.text(3e-2,
8e-13,
r'$\Xi_{\rm flat}^{\rm comb}$',
fontsize=28,
color='green')
# read reference Xi PLS from Ellis et al 2019
if interf == 'Taiji':
dir = '../detector_sensitivity/'
df = pd.read_csv(dir + 'XiPLS_Ellisetal19.csv')
f = np.array(df['f'])
ff = np.logspace(np.log10(f[0]), np.log10(f[-1]), 50)
XiGW_PLS_LISA = np.array(df['Xi'])
XiGW_PLS_LISA = np.interp(ff, f, XiGW_PLS_LISA)
plt.plot(ff, XiGW_PLS_LISA, '.', color='blue', alpha=.4)
plt.text(1.15e-2, 1.5e-10, r'$\sim\!f^5$', fontsize=22, color='blue')
gg = np.where(XiPLSg > Xiflat_Tai * 1.01)
hh = np.where(fs.value[gg] > 4e-3)
plt.plot(fs[gg][hh], XiPLSg[gg][hh] * fact, color='blue', lw=.5)
plt.legend(fontsize=28, loc='lower left', frameon=False)
plt.xlabel(r'$f$ [Hz]')
plt.ylabel(r'$h_0^2\, \Xi_{\rm PLS} (f)$')
plt.xscale('log')
plt.yscale('log')
plt.ylim(1e-13, 1e-6)
plt.xlim(1e-4, 1e-1)
plot_sets.axes_lines()
ax = plt.gca()
ax.tick_params(axis='x', pad=20)
ax.tick_params(axis='y', pad=10)
plt.yticks(np.logspace(-13, -6, 8))
if save:
plt.savefig('plots/Xi_PLS_' + interf + '.pdf', bbox_inches='tight')
def plot_OmGW_hc_vs_f_ini(runs, T=1e5*u.MeV, g=100, SNR=10, Td=4,
save=True, show=True):
"""
Function that generates the plot of the GW energy density spectrum
of initial runs (ini1, ini2, and ini3), compared to the LISA sensitivity
and power law sensitivity (PLS).
It corresponds to figure 4 of A. Roper Pol, S. Mandal, A. Brandenburg,
T. Kahniashvili, and A. Kosowsky, "Numerical simulations of gravitational
waves from early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
Arguments:
runs -- dictionary that includes the run variables
T -- temperature scale (in natural units) at the time of turbulence
generation (default 100 GeV, i.e., electroweak scale)
g -- number of relativistic degrees of freedom at the time of
turbulence generation (default 100, i.e., electroweak scale)
SNR -- signal-to-noise ratio (SNR) of the resulting PLS (default 10)
Td -- duration of the mission (in years) of the resulting PLS
(default 4)
save -- option to save the resulting figure as
plots/OmGW_vs_f_ini.pdf (default True)
show -- option to show the resulting figure (default True)
"""
# read LISA and Taiji sensitivities
CWD = os.getcwd()
os.chdir('..')
#f_LISA, f_LISA_Taiji, LISA_sensitivity, LISA_OmPLS, LISA_XiPLS, \
# Taiji_OmPLS, Taiji_XiPLS, LISA_Taiji_XiPLS = inte.read_sens()
fs, LISA_Om, LISA_OmPLS = inte.read_sens(SNR=SNR, T=Td)
fs = fs*u.Hz
os.chdir(CWD)
# chose the runs to be shown
rrs = ['ini1', 'ini2', 'ini3']
# chose the colors of each run
col = ['black', 'red', 'blue']
plt.figure(1, figsize=(12,5))
plt.figure(2, figsize=(12,5))
j = 0
for i in rrs:
run = runs.get(i)
k = run.spectra.get('k')[1:]
EGW_stat = run.spectra.get('EGW_stat_sp')
f, OmGW_stat = cosmoGW.shift_OmGW_today(k, EGW_stat*k, T, g)
OmGW_stat = np.array(OmGW_stat, dtype='float')
hc_stat = cosmoGW.hc_OmGW(f, OmGW_stat)
plt.figure(1)
plt.plot(f, OmGW_stat, color=col[j], lw=.8)
if i == 'ini1': plt.text(5e-2, 1.5e-15, i, color=col[j])
if i == 'ini2': plt.text(3e-2, 2e-17, i, color=col[j])
if i == 'ini3': plt.text(3e-3, 4e-17, i, color=col[j])
plt.figure(2)
plt.plot(f, hc_stat, color=col[j], lw=.8)
if i == 'ini1': plt.text(5e-2, 1.5e-24, i, color=col[j])
if i == 'ini2': plt.text(1e-2, 3e-24, i, color=col[j])
if i == 'ini3': plt.text(4e-3, 1e-24, i, color=col[j])
j += 1
plt.figure(1)
plt.xscale('log')
plt.yscale('log')
plt.xlim(1e-4, 1e-1)
plt.ylim(1e-19, 1e-9)
plt.xlabel('$f$ [Hz]')
plt.ylabel(r'$h_0^2 \Omega_{\rm GW} (f)$')
#plt.plot(f_LISA, LISA_OmPLS, color='lime', ls='dashdot')
#plt.plot(f_LISA, LISA_sensitivity, color='lime')
plt.plot(fs, LISA_OmPLS, color='lime', ls='dashdot')
plt.plot(fs, LISA_Om, color='lime')
# plot f^(-8/3) line
fs0 = np.logspace(-2.1, -1.5, 5)
plt.plot(fs0, 3e-15*(fs0/2e-2)**(-8/3), color='black',
ls='dashdot', lw=.7)
plt.text(1e-2, 5e-16, '$\sim\!f^{-8/3}$')
# plot f line
fs0 = np.logspace(-3.45, -2.8, 5)
plt.plot(fs0, 2e-13*(fs0/1e-3)**(1), color='black',
ls='dashdot', lw=.7)
plt.text(4e-4, 3e-13, '$\sim\!f$')
ax = plt.gca()
ytics2 = 10**np.array(np.linspace(-19, -9, 11))
yticss = ['', '$10^{-18}$', '', '$10^{-16}$', '', '$10^{-14}$', '',
'$10^{-12}$', '', '$10^{-10}$', '']
ax.set_yticks(ytics2)
ax.set_yticklabels(yticss)
plot_sets.axes_lines()
if save: plt.savefig('plots/OmGW_vs_f_ini.pdf', bbox_inches='tight')
if not show: plt.close()
plt.figure(2)
plt.xscale('log')
plt.yscale('log')
plt.xlim(1e-4, 1e-1)
plt.ylim(1e-25, 1e-20)
plt.xlabel('$f$ [Hz]')
plt.ylabel(r'$h_{\rm c}(f)$')
LISA_hc_PLS = cosmoGW.hc_OmGW(fs, LISA_OmPLS)
LISA_hc = cosmoGW.hc_OmGW(fs, LISA_Om)
plt.plot(fs, LISA_hc_PLS, color='lime', ls='dashdot')
plt.plot(fs, LISA_hc, color='lime')
# plot f^(-1/2) line
fs0 = np.logspace(-3.4, -2.6, 5)
plt.plot(fs0, 8e-22*(fs0/1e-3)**(-1/2), color='black',
ls='dashdot', lw=.7)
plt.text(8e-4, 1.5e-21, '$\sim\!f^{-1/2}$')
# plot f^(-7/3) line
fs0 = np.logspace(-2, -1.4, 5)
plt.plot(fs0, 1e-23*(fs0/2e-2)**(-7/3), color='black',
ls='dashdot', lw=.7)
plt.text(2e-2, 2e-23, '$\sim\!f^{-7/3}$')
ax = plt.gca()
ytics2 = 10**np.array(np.linspace(-25, -20, 6))
ax.set_yticks(ytics2)
plot_sets.axes_lines()
if save: plt.savefig('plots/hc_vs_f_ini.pdf', bbox_inches='tight')
if not show: plt.close()
def plot_OmGW_hc_vs_f_driven(runs, T=1e5*u.MeV, g=100, SNR=10, Td=4,
save=True, show=True):
"""
Function that generates the plot of the GW energy density spectrum
of some of the initially driven runs (ac1, hel1, hel2, hel3, and noh1),
compared to the LISA sensitivity and power law sensitivity (PLS).
It corresponds to figure 6 of A. Roper Pol, S. Mandal, A. Brandenburg,
T. Kahniashvili, and A. Kosowsky, "Numerical simulations of gravitational
waves from early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
Arguments:
runs -- dictionary that includes the run variables
T -- temperature scale (in natural units) at the time of turbulence
generation (default 100 GeV, i.e., electroweak scale)
g -- number of relativistic degrees of freedom at the time of
turbulence generation (default 100, i.e., electroweak scale)
SNR -- signal-to-noise ratio (SNR) of the resulting PLS (default 10)
Td -- duration of the mission (in years) of the resulting PLS
(default 4)
save -- option to save the resulting figure as
plots/OmGW_vs_f_driven.pdf (default True)
show -- option to show the resulting figure (default True)
"""
# read LISA and Taiji sensitivities
CWD = os.getcwd()
os.chdir('..')
#f_LISA, f_LISA_Taiji, LISA_sensitivity, LISA_OmPLS, LISA_XiPLS, \
# Taiji_OmPLS, Taiji_XiPLS, LISA_Taiji_XiPLS = inte.read_sens()
fs, LISA_Om, LISA_OmPLS = inte.read_sens(SNR=SNR, T=Td)
fs = fs*u.Hz
os.chdir(CWD)
# chose the runs to be shown
rrs = ['ac1', 'hel1', 'hel2', 'hel3', 'noh1']
# chose the colors of each run
col = ['black', 'red', 'blue', 'blue', 'blue']
# chose the line style for the plots
ls = ['solid', 'solid', 'solid', 'dotted', 'dashed']
plt.figure(1, figsize=(12,5))
plt.figure(2, figsize=(12,5))
j = 0
for i in rrs:
run = runs.get(i)
k = run.spectra.get('k')[1:]
EGW_stat = run.spectra.get('EGW_stat_sp')
f, OmGW_stat = cosmoGW.shift_OmGW_today(k, EGW_stat*k, T, g)
OmGW_stat = np.array(OmGW_stat, dtype='float')
hc_stat = cosmoGW.hc_OmGW(f, OmGW_stat)
plt.figure(1)
# omit largest frequencies where there is not enough numerical accuracy
if i == 'hel3':
OmGW_stat = OmGW_stat[np.where(f.value<3e-2)]
hc_stat = hc_stat[np.where(f.value<3e-2)]
f = f[np.where(f.value<3e-2)]
if i=='hel3' or i=='hel2' or i=='noh1' or i=='hel1':
plt.plot(f, OmGW_stat, color=col[j],
ls=ls[j], lw=.8, label=i)
else:
plt.plot(f, OmGW_stat, color=col[j], ls=ls[j], lw=.8)
plt.text(5e-2, 2e-19, i, fontsize=20, color='black')
plt.figure(2)
if i=='hel3' or i=='hel2' or i=='noh1'or i=='hel1':
plt.plot(f, hc_stat, color=col[j], ls=ls[j], lw=.8, label=i)
else:
plt.plot(f, hc_stat, color=col[j], ls=ls[j], lw=.8)
plt.text(3e-3, 5e-22, i, color=col[j])
j += 1
plt.figure(1)
plt.xscale('log')
plt.yscale('log')
plt.xlim(1e-4, 1e-1)
plt.ylim(1e-26, 1e-9)
plt.xlabel('$f$ [Hz]')
plt.ylabel(r'$h_0^2 \Omega_{\rm GW} (f)$')
plt.legend(loc='lower left', frameon=False, fontsize=20)
plt.plot(fs, LISA_OmPLS, color='lime', ls='dashdot')
plt.plot(fs, LISA_Om, color='lime')
# plot f^(-5) line
fk0 = np.logspace(-2.2, -1.6, 5)
plt.plot(fk0, 1e-14*(fk0/1e-2)**(-5), color='black',
ls='dashdot', lw=.7)
plt.text(1.3e-2, 1e-14, '$\sim\!f^{-5}$')
# plot f line
fk0 = np.logspace(-3.3, -2.8, 5)
plt.plot(fk0, 2e-16*(fk0/1e-3)**(1), color='black',
ls='dashdot', lw=.7)
plt.text(6e-4, 1e-17, '$\sim\!f$')
ax = plt.gca()
ytics2 = 10**np.array(np.linspace(-25, -9, 16))
yticss = ['$10^{-25}$', '', '$10^{-23}$', '', '$10^{-21}$', '',
'$10^{-19}$','', '$10^{-17}$', '','$10^{-15}$','',
'$10^{-13}$', '','$10^{-11}$','']
ax.set_yticks(ytics2)
ax.set_yticklabels(yticss)
plot_sets.axes_lines()
if save: plt.savefig('plots/OmGW_vs_f_driven.pdf', bbox_inches='tight')
if not show: plt.close()
plt.figure(2)
plt.xscale('log')
plt.yscale('log')
plt.xlim(1e-4, 1e-1)
plt.ylim(1e-28, 1e-20)
plt.xlabel('$f$ [Hz]')
plt.ylabel(r'$h_{\rm c}(f)$')
plt.legend(loc='lower left', frameon=False, fontsize=20)
LISA_hc_PLS = cosmoGW.hc_OmGW(fs, LISA_OmPLS)
LISA_hc = cosmoGW.hc_OmGW(fs, LISA_Om)
plt.plot(fs, LISA_hc_PLS, color='lime', ls='dashdot')
plt.plot(fs, LISA_hc, color='lime')
# plot f^(-7/2) line
fk0 = np.logspace(-2.2, -1.6, 5)
plt.plot(fk0, 1e-23*(fk0/1e-2)**(-7/2), color='black',
ls='dashdot', lw=.7)
plt.text(1.3e-2, 1e-23, '$\sim\!f^{-7/2}$')
# plot f^(-1/2) line
fk0 = np.logspace(-3.3, -2.8, 5)
plt.plot(fk0, 2e-23*(fk0/1e-3)**(-1/2), color='black',
ls='dashdot', lw=.7)
plt.text(6e-4, 3e-24, '$\sim\!f^{-1/2}$')
ax = plt.gca()
ytics2 = 10**np.array(np.linspace(-28, -20, 9))
ytics2 = 10**np.array(np.linspace(-28, -20, 9))
yticss = ['', '$10^{-27}$', '', '$10^{-25}$', '',
'$10^{-23}$', '', '$10^{-21}$', '']
ax.set_yticks(ytics2)
ax.set_yticklabels(yticss)
plot_sets.axes_lines()
if save: plt.savefig('plots/hc_vs_f_driven.pdf', bbox_inches='tight')
if not show: plt.close()
def plot_EGW_vs_k_initial_ts(runs, rr='ini2', save=True, show=True):
"""
Function that generates the plot of the amplitudes of the GW energy
density at the first time step, to show the evolution from k^2 to k^0
slopes.
It corresponds to a plot generated for a presentation, related to the
work A. Roper Pol, S. Mandal, A. Brandenburg, T. Kahniashvili,
and A. Kosowsky, "Numerical simulations of gravitational waves from
early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
Arguments:
runs -- dictionary that includes the run variables
rr -- string that selects which run to plot (default 'ini2')
save -- option to save the resulting figure as
plots/EGW_vs_k_initial_ts.pdf (default True)
show -- option to show the resulting figure (default True)
"""
run = runs.get(rr)
EGW = run.spectra.get('EGW')[:, 1:]
k = run.spectra.get('k')[1:]
t = run.spectra.get('t_GWs')
max_sp_EGW = run.spectra.get('EGW_max_sp')
plt.figure(figsize=(10,6))
plt.xscale('log')
plt.yscale('log')
plt.xlabel('$k$')
plt.ylabel(r'$\Omega_{\rm GW} (k)/k$')
# initial time step GW spectrum
plt.plot(k, EGW[0, :], color='black', lw=.7, ls='dashed')
# local maximum amplitudes of oscillations at next time step
kmax, EGWmax = sp.local_max(k, EGW[1, :])
plt.plot(kmax, EGWmax, color='black', lw=.7, ls='dashed')
plt.plot(k[:10], EGW[1, :10], color='black', lw=.7, ls='dashed')
# maximum over all times of the GW energy density (amplitude of the
# oscillations)
plt.plot(k, max_sp_EGW, color='black', lw=1.5)
# 6th time step
kmax, EGWmax = sp.local_max(k, EGW[5, :])
plt.plot(kmax, EGWmax, color='black', lw=.7, ls='dashed')
plt.plot(k[:4], EGW[5, :4], color='black', lw=.7, ls='dashed')
# line k^(2.5)
k0s = np.linspace(250, 1000)
plt.plot(k0s, 3e-19*(k0s/100)**2.5, color='black',
ls='dashdot', lw=.7)
plt.text(500, 5e-18, '$k^{2.5}$', fontsize=20)
# line k^(1/2)
k0s = np.linspace(200, 800)
plt.plot(k0s, 7e-14*(k0s/100)**0.5, color='black',
ls='dashdot', lw=.7)
plt.text(500, 3e-13, '$k^{0.5}$', fontsize=20)
# line k^(-11/3)
k0s = np.linspace(3000, 10000)
plt.text(5000, 1e-14, '$k^{-11/3}$', fontsize=20)
plt.plot(k0s, 1e-14*(k0s/4e3)**(-11/3), color='black',
ls='dashdot', lw=.7)
plt.text(3000, 1e-17, r'$t-1=4 \times 10^{-5}$', fontsize=14)
plt.text(250, 2e-15, '$t-1=10^{-3}$', fontsize=14)
plt.text(130, 8e-15, r'$5 \times 10^{-3}$', fontsize=14)
plt.ylim(1e-19, 2e-12)
yticks = np.logspace(-19, -12, 8)
ax = plt.gca()
ax.set_yticks(yticks)
plot_sets.axes_lines()
ax.tick_params(axis='x', pad=12)
if save: plt.savefig('plots/EGW_vs_k_initial_ts.pdf',
bbox_inches='tight')
if not show: plt.close()
def plot_OmGW_vs_OmMK(runs, save=True, show=True):
"""
Function that generates the plot of the total (saturated) GW energy
density integrated over wave numbers as a function of the
magnetic/kinetic energy density.
It corresponds to figure 7 of A. Roper Pol, S. Mandal, A. Brandenburg,
T. Kahniashvili, and A. Kosowsky, "Numerical simulations of gravitational
waves from early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
Arguments:
runs -- dictionary that includes the run variables
save -- option to save the resulting figure as
plots/OmGW_vs_OmMK.pdf (default True)
show -- option to show the resulting figure (default True)
"""
# chose the runs to be shown
rrs = [s for s in runs]
# chose the colors of each run
col = ['darkorange', 'darkorange', 'lime', 'red', 'red', 'red',
'lime', 'red', 'red', 'blue', 'blue', 'blue']
plt.figure(figsize=(8,5))
plt.xscale('log')
plt.yscale('log')
plt.xlabel(r'$\Omega_{\rm M,K}^{\rm max}$')
plt.ylabel(r'$\Omega_{\rm GW}^{\rm sat}$')
plt.xlim(1e-3, 2e-1)
plt.ylim(7e-12, 1e-7)
j = 0
for i in runs:
run = runs.get(i)
if 'noh' in i:
plt.scatter(run.Ommax, run.OmGWsat,
edgecolors='red', facecolors='none')
else:
plt.plot(run.Ommax, run.OmGWsat, 'o', color=col[j])
j += 1
OmMs = np.logspace(-2.2, -.8)
plt.plot(OmMs, 1.7e-6*OmMs**2, color='darkorange')
OmMs = np.logspace(-2.5, -1.5)
plt.plot(OmMs, 9e-6*OmMs**2, color='red')
OmMs = np.logspace(-2.5, -1.7)
plt.plot(OmMs, 1.5e-5*OmMs**2, color='red', ls='dashed', lw=.7)
OmMs = np.logspace(-2.8, -1.8)
plt.plot(OmMs, 3.5e-4*OmMs**2, color='blue')
plot_sets.axes_lines()
plt.yticks([1e-11, 1e-10, 1e-9, 1e-8, 1e-7])
plt.text(1.5e-2, 2e-10, 'ini', color='darkorange')
plt.text(1.5e-2, 2e-10/2, '$i$=M', color='darkorange')
plt.text(2e-2, 2e-8, 'hel', color='red')
plt.text(2e-2, 2e-8/2, '$i$=M', color='red')
plt.text(2e-3, 1e-8, 'ac', color='blue')
plt.text(2e-3, 1e-8/2, '$i$=K', color='blue')
plt.text(7e-3, 4e-9, '(ini3)', color='lime')
plt.text(5e-3, 1.7e-11, '(hel4)', color='lime')
plt.text(3.5e-3, 7e-10, '(noh)', color='red')
if save: plt.savefig('plots/OmGW_vs_OmMK.pdf', bbox_inches='tight')
if not show: plt.close()
def plot_Omega_sensitivity(OmPLS,
OmPLS_Tai,
OmPLS_comb,
SNR=10,
T=4,
save=True):
"""
Function that generates the plot of LISA and Taiji GW energy density
sensitivities and PLS.
It corresponds to left panel of figure 16 of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources," submitted to JCAP,
https://arxiv.org/abs/2107.05356.
Arguments:
OmPLS -- power law sensitivity (PLS) of LISA for T = 1yr and SNR = 1
OmPLS_Tai -- power law sensitivity (PLS) of Taiji for T = 1yr
and SNR = 1
OmPLS_comb -- power law sensitivity (PLS) of the LISA-Taiji network
for T = 1yr and SNR = 1
SNR -- signal-to-noise ratio (SNR) for the plotted PLS (default 10)
T -- duration of the observations for the plotted PLS in
years (default 4)
save -- option to save the figure in "plots/Omega_LISA_Taiji.pdf"
(default True)
"""
import pandas as pd
fact = SNR / np.sqrt(T)
fig, ax0 = plt.subplots(figsize=(12, 10))
line_OmPLS, = ax0.plot([], [],
color='green',
label=r'$\Omega_{\rm PLS}^{\rm A}$')
line_OmPLS_Tai, = ax0.plot([], [],
color='green',
ls='-.',
label=r'$\Omega_{\rm PLS}^{\rm C}$')
line_OmPLS_comb, = ax0.plot([], [],
color='green',
lw=.8,
label=r'$\Omega_{\rm PLS}^{\rm comb}$')
line_OmSA, = ax0.plot([], [],
color='blue',
label=r'$\Omega_{\rm s}^{\rm A}$')
line_OmSC, = ax0.plot([], [],
color='blue',
ls='-.',
label=r'$\Omega_{\rm s}^{\rm C}$')
line_OmS_comb, = ax0.plot([], [],
color='blue',
lw=.8,
label=r'$\Omega_{\rm s}^{\rm comb}$')
line_OmST, = ax0.plot([], [],
color='orange',
alpha=.5,
label=r'$\Omega_{\rm s}^{\rm T}$')
line_OmSS, = ax0.plot([], [],
color='orange',
ls='-.',
alpha=.5,
label=r'$\Omega_{\rm s}^{\rm S}$')
line_OmS_ED_I, = ax0.plot([], [],
color='purple',
alpha=.5,
label=r'$\Omega_{\rm s}^{\rm ED}$')
handles = [line_OmSA, line_OmSC, line_OmS_comb]
lgd1 = ax0.legend(handles=handles,
loc='lower right',
fontsize=28,
frameon=False)
handles2 = [line_OmST, line_OmSS, line_OmS_ED_I]
lgd2 = ax0.legend(handles=handles2,
loc='upper left',
fontsize=28,
frameon=False)
handles3 = [line_OmPLS, line_OmPLS_Tai, line_OmPLS_comb]
lgd3 = ax0.legend(handles=handles3,
loc='lower left',
fontsize=28,
frameon=False)
ax0.add_artist(lgd1)
ax0.add_artist(lgd2)
# plt.rc('font', size=30)
plt.plot(fs, OmSA, color='blue')
plt.plot(fs, OmST, color='orange', alpha=.5)
plt.plot(fs, OmPLS * fact, color='green')
plt.plot(fs, OmSC, '-.', color='blue')
plt.plot(fs, OmSS, '-.', color='orange', alpha=.5)
plt.plot(fs, OmPLS_Tai * fact, '-.', color='green')
gg = np.where(abs(M_ED_I) > 1e-48)
plt.plot(fs[gg], OmS_ED_I[gg], color='purple', alpha=.5)
plt.plot(fs, OmS_comb, color='blue', lw=.8)
plt.plot(fs, OmPLS_comb * fact, color='green', lw=.8)
# Add reference PLS from Caprini et al 2019
dir = '../detector_sensitivity/'
df = pd.read_csv(dir + 'OmegaPLS_Caprinietal19.csv')
f = np.array(df['f'])
ff = np.logspace(np.log10(f[0]), np.log10(f[-1]), 70)
OmGW_PLS_LISA = np.array(df['Omega'])
OmGW_PLS_LISA = np.interp(ff, f, OmGW_PLS_LISA)
plt.plot(ff, OmGW_PLS_LISA, '.', color='green', alpha=.4)
plot_sets.axes_lines()
plt.ylim(1e-14, 1e-2)
plt.yticks(np.logspace(-14, -2, 8))
plt.xlim(1e-5, 1e0)
plt.xlabel('$f$ [Hz]')
plt.ylabel(r'$h_0^2\,\Omega_{\rm s} (f)$')
plt.xscale('log')
plt.yscale('log')
ax = plt.gca()
ax.tick_params(axis='x', pad=20)
ax.tick_params(axis='y', pad=10)
plt.yticks(np.logspace(-14, -2, 7))
plt.xticks(np.logspace(-5, 0, 6))
if save: plt.savefig('plots/Omega_LISA_Taiji.pdf', bbox_inches='tight')
def plot_efficiency(runs, save=True, show=True, sqrt=False):
"""
Function that generates the plot of the total GW energy density
compensated by EM^2/kf^2 (efficiency).
It corresponds to the runs presented in A. Roper Pol, S. Mandal,
A. Brandenburg, T. Kahniashvili, and A. Kosowsky, "Numerical simulations of gravitational waves from
early-universe turbulence," Phys. Rev. D 102, 083512 (2020),
https://arxiv.org/abs/1903.08585.
This plot is analogous to figure 10 of A. Roper Pol, S. Mandal,
A. Brandenburg, and T. Kahniashvili, "Polarization of gravitational waves
from helical MHD turbulent sources", https://arxiv.org/abs/2107.05356.
Arguments:
runs -- dictionary that includes the run variables
save -- option to save the resulting figure as plots/efficiency.pdf
or plots/efficiency_sqrt.pdf (if sqrt = True) (default True)
show -- option to show the resulting figure (default True)
sqrt -- option to plot the efficiency defined as the square root of
the compensated GW energy density (default False)
"""
exp = 1
if sqrt: exp = 1/2
plt.figure(1, figsize=(12,8))
plt.xscale('log')
plt.yscale('log')
plt.xlim(6e-3, 1)
plt.ylim(1e-1**exp, 2e2**exp)
plt.xlabel('$\delta t = t - 1$')
plt.ylabel(r'$q^2 (t) = k_*^2\, \Omega_{\rm GW}$' + \
r'$(t)/({\cal E}_{\rm M, K}^{\rm max})^2$')
if sqrt:
plt.ylabel(r'$q (t) = k_* \left[\Omega_{\rm GW} (t)\right]^{1/2}$' + \
r'$/{\cal E}_{\rm M, K}^{\rm max}$')
for i in runs:
# chose colors
if 'ini' in i: col = 'green'
elif 'hel4' in i: col = 'red'
elif 'noh' in i: col = 'black'
elif 'ac' in i: col = 'blue'
else: col = 'orange'
run = runs.get(i)
t = run.ts.get('t')
EGW = run.ts.get('EEGW')
plt.plot(t-1, (EGW/run.Ommax**2*run.kf**2)**exp,
color=col)
plot_sets.axes_lines()
plt.text(3e-1, 70**exp, 'acoustic', color='blue')
plt.text(3e-1, 1.5**exp, 'initial', color='green')
plt.text(1.3e-1, 2.8**exp, r'helical 1--3', color='orange')
plt.text(3e-1, 15**exp, 'helical 4', color='red')
plt.text(4e-1, 8.6**exp, 'non-helical', color='black')
if save:
if sqrt: plt.savefig('plots/efficiency_sqrt.pdf',
bbox_inches='tight')
else: plt.savefig('plots/efficiency.pdf',
bbox_inches='tight')
if not show: plt.close()
def plot_EM_EGW(run, save=True):
"""
Function that plots the magnetic energy and helicity spectra at the time
of maximum magnetic energy density.
It also plots the GW energy density and helicity spectra, averaging over
times after the GW energy has entered a stationary oscillatory stage (this
needs to be previously computed and stored in the run variable, see
initialize_JCAP_2021.py).
It corresponds to figures 1-3 of A. Roper Pol, S. Mandal, A. Brandenburg,
and T. Kahniashvili, "Polarization of gravitational waves from helical MHD
turbulent sources," https://arxiv.org/abs/2107.05356.
Arguments:
run -- variable run with spectral information
save -- option to save the figure in plots/'name_run'EM_EGW.pdf'
(default True)
"""
# auxiliary functions used in plot_EM_EGW
def init_Ay2_Ax(N, Ay, Ax):
return N, N * [Ay], N * [Ax]
# chose indices to show power law fits and text with k^(a/b) for magnetic
# spectrum EM(k)
def indices_EM(nm, Ax, Ay):
if 'i' in nm:
inds_show = [0, 1, 4, 5, 6, 7, 8, 9, 10]
inds_show_txt = [0, 6]
Ay[0] *= 8
Ay[6] *= 2
if '3' in nm or '5' in nm:
inds_show_txt = [0, 7]
Ay[7] *= .5
if '5' in nm: Ay[0] *= 2
if nm == 'i_s1':
inds_show_txt = [1, 7]
Ay[1] *= 20
Ax[1] *= .7
Ay[7] *= .5
else:
if '001' in nm:
inds_show = [0, 1, 4, 6, 8, 9, 10, 11]
inds_show_txt = [1, 4, 6, 10]
Ay[1] *= 6
Ax[1] *= .7
Ay[4] *= 25
Ay[6] *= 2
Ay[10] *= 1 / 6000
else:
inds_show = [0, 1, 5, 6, 7, 8, 9, 10, 11]
inds_show_txt = [0, 5, 7, 10, 11]
Ay[0] *= 5
Ay[5] *= 3.5
Ay[7] *= 1 / 10
Ay[10] *= 6e-5
Ay[11] *= 1e-6
Ax[11] *= .9
if '5' in nm:
inds_show_txt = [1, 5, 7, 10, 11]
Ay[1] *= 10
Ax[1] *= .8
Ay[10] *= 1 / 8
Ay[11] *= 1 / 5
if '7' in nm:
inds_show_txt = [0, 5, 7, 9, 10]
Ay[5] *= .5
Ay[7] *= 3e-1
Ay[9] *= 1e-4
Ay[10] *= 3e-2
if '1' in nm:
inds_show_txt = [0, 5, 7, 9, 10]
Ay[0] *= 2
Ax[0] *= .9
Ay[5] *= .3
Ay[7] *= 1e-1
Ay[9] *= 4e-5
Ay[10] *= 1e-2
Ax[10] *= 1.1
return inds_show, inds_show_txt, Ax, Ay
# chose indices to show power law fits and text with k^(a/b) for magnetic
# helicity spectrum HM(k)
def indices_HM(nm, Ax, Ay):
inds_show = []
inds_show_txt = []
if 'i' in nm:
inds_show = [1, 4, 5, 6, 7, 8]
inds_show_txt = [1]
Ay[1] *= 80
#Ay[2] *= 100; Ax[2] *= .8
if '3' in nm or '5' in nm:
inds_show = [0, 1, 4, 5, 6, 7, 8]
inds_show_txt = [0, 1]
if '3' in nm: Ay[0] *= 8
if '5' in nm: Ay[0] *= 5
else:
if '001' not in nm:
inds_show = [0, 4, 5, 6, 7, 8]
inds_show_txt = [0, 4, 6, 8]
Ay[0] *= 8
Ax[4] *= .7
Ay[6] *= 3e-4
Ay[8] *= 4e-7
Ax[8] *= .7
if '5' in nm:
Ax[6] *= .7
Ay[6] *= 15
Ax[8] *= .7
Ay[8] *= 2
if '7' in nm:
Ay[4] *= .5
Ax[6] *= .7
Ay[6] *= 7
Ax[8] *= .9
if '1' in nm:
Ax[6] *= .7
Ay[6] *= 3
Ay[8] *= 2e-1
Ax[8] *= .8
return inds_show, inds_show_txt, Ax, Ay
# chose indices to show power law fits and text with k^(a/b) for GW
# spectrum EGW(k)
def indices_EGW(nm, Ax, Ay):
if 'i' in nm:
inds_show = [0, 2, 4, 6, 7, 8, 9, 10]
inds_show_txt = [0, 2, 4, 9]
Ay[4] *= .6
Ay[9] *= 3e-4
if '5' in nm:
inds_show_txt = [0, 2, 4, 7]
Ay[7] *= 8e-3
if nm == 'i_s1':
Ay[2] *= 1.8
Ay[4] *= 4
Ay2_HGW[3] *= 2.5
else:
if '001' in nm:
inds_show = [0, 2, 3, 5, 6, 7, 8, 9]
inds_show_txt = [0, 2, 7]
Ay[2] *= .5
Ay[7] *= 5e-5
else:
inds_show = [0, 1, 2, 3, 6, 7, 8, 9, 10, 11]
inds_show_txt = [0, 2, 8]
Ay[2] *= .5
Ay[8] *= 2e-6
if '5' in nm:
inds_show_txt = [0, 2, 7, 10]
Ay[2] *= 1.5
Ay[7] *= 1e-5
Ay[10] *= 3e-10
if '7' in nm or '1' in nm:
inds_show_txt = [0, 2, 7, 9]
Ay[2] *= 2
Ay[7] *= 3e-6
Ay[9] *= 3e-9
return inds_show, inds_show_txt, Ax, Ay
# chose indices to show power law fits and text with k^(a/b) for GW
# helicity spectrum HGW(k)
def indices_HGW(nm, Ax, Ay):
inds_show = []
inds_show_txt = []
if 'i' in nm:
inds_show = [3, 5, 6, 7, 8]
inds_show_txt = [3]
if '3' in nm or '5' in nm:
inds_show = [1, 2, 3, 5, 6, 7, 8]
if '3' in nm:
inds_show_txt = [1, 2, 3]
Ay[1] *= .3
Ay[2] *= 1.5
Ay[3] *= 3.5
if '5' in nm:
inds_show_txt = [2, 3]
Ax[2] *= .9
Ay[3] *= 1.5
if nm == 'i_s1': Ay[3] *= 2.5
else:
if '001' not in nm:
inds_show = [2, 5, 6, 7, 8, 9]
inds_show_txt = [2, 6]
Ay[6] *= 1e-6
Ax[6] *= .8
if '5' in nm:
inds_show_txt = [2, 5]
Ay[2] *= 2
Ay[5] *= 1.3e-4
Ax[5] *= .7
if '7' in nm or '1' in nm:
Ay[2] *= 1.3
Ay[6] *= .35
Ax[6] *= .9
return inds_show, inds_show_txt, Ax, Ay
plt.rcParams.update({
'xtick.labelsize': 'xx-large',
'ytick.labelsize': 'xx-large',
'axes.labelsize': 'xx-large'
})
name = run.name_run
k = run.spectra.get('k')[1:]
t = run.spectra.get('t_helmag')
# read magnetic spectra
if run.turb == 'k':
EM = np.array(run.spectra.get('kin')[:, 1:], dtype='float')
HkM = np.array(run.spectra.get('helkin_comp')[:, 1:], dtype='float')
if run.turb == 'm':
EM = np.array(run.spectra.get('mag')[:, 1:], dtype='float')
HkM = np.array(run.spectra.get('helmag_comp')[:, 1:], dtype='float')
# read GW spectra
min_GWs = np.array(run.spectra.get('EGW_min_sp'), dtype='float')
max_GWs = np.array(run.spectra.get('EGW_max_sp'), dtype='float')
mean_GWs = np.array(run.spectra.get('EGW_stat_sp'), dtype='float')
min_pos_HGWs = abs(
np.array(run.spectra.get('helEGW_pos_min_sp'), dtype='float'))
min_neg_HGWs = abs(
np.array(run.spectra.get('helEGW_neg_min_sp'), dtype='float'))
max_pos_HGWs = abs(
np.array(run.spectra.get('helEGW_pos_max_sp'), dtype='float'))
max_neg_HGWs = abs(
np.array(run.spectra.get('helEGW_neg_max_sp'), dtype='float'))
mean_HGWs = np.array(run.spectra.get('helEGW_stat_sp'), dtype='float')
# get time that corresponds to maximum of magnetic energy density tini
dtk = t[1] - t[0]
indt = np.where(abs(t - run.tini) <= dtk / 2)[0][0]
fig, ax = plt.subplots(figsize=(12, 10))
plt.xscale('log')
plt.yscale('log')
#plt.text(3e4, 4e-23, '$k$', fontsize=30)
plt.xlabel('$k$')
TT = 'M'
if run.turb == 'k': TT = 'K'
plt.title(r'$E_{\rm %s, GW} (k)$ and $H_{\rm %s, GW} (k)$' % (TT, TT),
fontsize=30,
pad=15)
# specific options for the plots
N_EM, Ay2_EM, Ax_EM = init_Ay2_Ax(12, 2., 1.)
N_HM, Ay2_HM, Ax_HM = init_Ay2_Ax(10, .04, 1.)
N_EGW, Ay2_EGW, Ax_EGW = init_Ay2_Ax(12, 2.5, 1.)
N_HGW, Ay2_HGW, Ax_HGW = init_Ay2_Ax(10, .08, .8)
Ay_HGW = .2
Ay_HM = .2
if 'i' in name:
xleg = 1.5e4
yleg = 5e-13
else:
xleg = 8e2
yleg = 5e-20
if '001' in name: yks_H = False
else: yks_H = True
# choose indices for which to show the power law fits and the power law
# text above the fit for each of the runs
inds_show_EM, inds_show_txt_EM, Ax_EM, Ay2_EM = \
indices_EM(name, Ax_EM, Ay2_EM)
inds_show_HM, inds_show_txt_HM, Ax_HM, Ay2_HM = \
indices_HM(name, Ax_HM, Ay2_HM)
inds_show_EGW, inds_show_txt_EGW, Ax_EGW, Ay2_EGW = \
indices_EGW(name, Ax_EGW, Ay2_EGW)
inds_show_HGW, inds_show_txt_HGW, Ax_HGW, Ay2_HGW = \
indices_HGW(name, Ax_HGW, Ay2_HGW)
if 'i' in name: str_typ = 'ini'
else: str_typ = 'forc'
if name == 'M0': sig_val = '0'
if '01' in name and 'i' in name: sig_val = '0.1'
if '01' in name and 'M' in name: sig_val = '0.1'
if '01' in name and 'K' in name: sig_val = '0.1'
if '3' in name: sig_val = '0.3'
if '5' in name: sig_val = '0.5'
if '7' in name: sig_val = '0.7'
if name == 'i_s1': sig_val = '1'
if name == 'M1' or name == 'K1': sig_val = '1'
if '001' in name and 'f' in name:
if 'neg' in name: sig_val = '-0.01'
else: sig_val = '0.01'
if name == 'f_s1_neg': sig_val = '-1'
str_leg = r'$\sigma^{\rm %s}_{\rm M}=%s$' % (str_typ, sig_val)
plot_st(k,
EM[indt, :],
yks=True,
N=N_EM,
inds_show=inds_show_EM,
inds_show_txt=inds_show_txt_EM,
Ay=4,
Ay2=Ay2_EM,
Ax=Ax_EM)
plot_st(k,
HkM[indt, :],
hel=True,
yks=yks_H,
N=N_HM,
inds_show=inds_show_HM,
inds_show_txt=inds_show_txt_HM,
Ay=Ay_HM,
Ay2=Ay2_HM,
Ax=Ax_HM)
plot_st(k,
mean_GWs,
fb=True,
yv=True,
min_sp=min_GWs,
max_sp=max_GWs,
yks=True,
N=N_EGW,
inds_show=inds_show_EGW,
Ax=Ax_EGW,
inds_show_txt=inds_show_txt_EGW,
Ay=4,
Ay2=Ay2_EGW)
plot_st(k,
mean_HGWs,
hel=True,
fb=True,
yv=True,
min_sp_neg=min_neg_HGWs,
max_sp_neg=max_neg_HGWs,
min_sp_pos=min_pos_HGWs,
max_sp_pos=max_pos_HGWs,
yks=yks_H,
N=N_HGW,
inds_show=inds_show_HGW,
inds_show_txt=inds_show_txt_HGW,
Ay=Ay_HGW,
Ay2=Ay2_HGW,
Ax=Ax_HGW)
handles = []
line_mag, = ax.plot([], [],
'-',
color='black',
label=r'$E_{\rm %s}(k)$' % TT)
line_helpos, = ax.plot([], [],
'.',
label=r'$+\frac{1}{2} k H_{\rm %s}(k)$' % TT,
color='red')
line_helneg, = ax.plot([], [],
'.',
label=r'$-\frac{1}{2} k H_{\rm %s}(k)$' % TT,
color='blue')
line_GW, = ax.plot([], [], color='black', label=r'$E_{\rm GW}(k)$')
line_HGWpos, = ax.plot([], [],
'.',
label=r'$+H_{\rm GW} (k)$',
color='red')
line_HGWneg, = ax.plot([], [],
'.',
label=r'$-H_{\rm GW}(k)$',
color='blue')
handles = [line_mag, line_helpos, line_helneg]
lgd1 = ax.legend(handles=handles,
loc='upper right',
fontsize=23,
frameon=False)
handles2 = [line_GW, line_HGWpos, line_HGWneg]
lgd2 = plt.legend(handles=handles2,
loc='lower left',
fontsize=23,
frameon=False)
ax = plt.gca()
ax.add_artist(lgd1)
plt.yticks(
[1e-21, 1e-19, 1e-17, 1e-15, 1e-13, 1e-11, 1e-9, 1e-7, 1e-5, 1e-3])
plot_sets.axes_lines()
plt.tick_params(axis='y', direction='out', length=10)
plt.text(xleg,
yleg,
str_leg,
fontsize=30,
bbox=dict(facecolor='white',
edgecolor='black',
boxstyle='round,pad=.5'))
plt.xlim(100, 8e4)
plt.ylim(1e-21, 1e-3)
if save:
plt.savefig('plots/' + run.name_run + 'EM_EGW.pdf',
bbox_inches='tight')
