def einstein_radii(lp1, lp2, sp1, sp2, detA, lambda_t, cosmo, ax, method):
"""
Calculate Critical Curves, Caustics, and Einstein Radii
Input:
lp1,lp2[float] : lensing plane x,y-coordinates
sp1,sp2[float] : source plane x,y-coordinates
"""
crit_curve = ax.contour(lp1,
lp2,
detA,
levels=(0, ),
colors='r',
linewidths=1.5,
zorder=200)
Ncrit = len(crit_curve.allsegs[0])
crit_curve = crit_curve.allsegs[0]
tan_crit_curve = ax.contour(lp1,
lp2,
lambda_t,
levels=(0, ),
colors='r',
linewidths=1.5,
zorder=200)
NumTCC = len(tan_crit_curve.allsegs[0])
if NumTCC > 0:
# Find tangential critical curve on which to base Rein
len_tan_crit = np.zeros(NumTCC)
for i in range(NumTCC):
len_tan_crit[i] = len(tan_crit_curve.allsegs[0][i])
tan_crit_curve = tan_crit_curve.allsegs[0][len_tan_crit.argmax()]
# Einstein Radius
if method == 'eqv':
Rein = np.sqrt(np.abs(area(tan_crit_curve)) / np.pi) #[arcsec]
if method == 'med':
dist = np.sqrt(tan_crit_curve[:, 0]**2 + tan_crit_curve[:, 1]**2)
Rein = np.median(dist) #[arcsec]
# Caustics
for pp in range(len(tan_crit_curve)):
c1, c2 = (cf.call_mapping_triangles(
[tan_crit_curve[pp, 0], tan_crit_curve[pp, 1]], sp1, sp2, lp1,
lp2))
if pp == 0:
caustic1 = c1
caustic2 = c2
else:
caustic1 = np.hstack((caustic1, c1))
caustic2 = np.hstack((caustic2, c2))
caustic = np.array([caustic1, caustic2]).T
else:
tan_crit_curve = np.array([])
caustic = np.array([])
Rein = 0
return NumTCC, tan_crit_curve, caustic, Rein
def timedelay_magnification(mu_map, phi_map, dsx_arc, Ncells, lp1, lp2,
alpha1, alpha2, SrcPosSky, zs, zl, cosmo):
"""
Calculate Photon-travel-time and Magnification of strong lensed
supernovae
Input:
lp1, lp2: lens place grid coordinates
Output:
len(mu): number of multiple images of supernova
delta_t: Time it takes for photon to cover distance source-observer
mu: luminosity magnification of source
"""
# Mapping light rays from image plane to source plan
[sp1, sp2] = [lp1 - alpha1, lp2 - alpha2] #yi1,yi2[arcsec]
# Source position [arcsec]
#x = SrcPosSky[0]*u.Mpc
#y = SrcPosSky[1]*u.Mpc
#z = SrcPosSky[2]*u.Mpc
#if (y == 0.) and (z == 0.):
# beta1 = 1e-3
# beta2 = 1e-3
#else:
# beta1 = ((y/x)*u.rad).to_value('arcsec')
# beta2 = ((z/x)*u.rad).to_value('arcsec')
beta1 = 1e-3
beta2 = 1e-3
#print("Wait here mapping_triangles")
theta1, theta2 = cf.call_mapping_triangles([beta1, beta2],
lp1, lp2, sp1, sp2)
# calculate magnifications of lensed Supernovae
#print("Wait here inverse_cic_single")
mu = cf.call_inverse_cic_single(mu_map, 0.0, 0.0, theta1, theta2, dsx_arc)
# calculate time delays of lensed Supernovae in Days
prts = cf.call_inverse_cic_single(phi_map, 0.0, 0.0, theta1, theta2, dsx_arc)
Kc = ((1.0+zl)/const.c.to('Mpc/s') * \
(cosmo.angular_diameter_distance(zl) * \
cosmo.angular_diameter_distance(zs) / \
(cosmo.angular_diameter_distance(zs) - \
cosmo.angular_diameter_distance(zl)))).to('sday').value
delta_t = Kc*(0.5*((theta1 - beta1)**2.0 + (theta2 - beta2)**2.0) - prts)/cf.apr**2
beta = [beta1, beta2]
theta = [theta1, theta2]
return len(mu), delta_t, mu, theta, beta
def timedelay_magnification(mu_map, phi_map, dsx_arc, Ncells, lp1, lp2,
alpha1, alpha2, SrcPosSky, zs, zl, cosmo):
"""
Calculate Photon-travel-time and Magnification of strong lensed
supernovae
Input:
FOV: Field-of-View [Mpc]
Ncells: number of cells for grid on FOV
kappa: convergence map
SrcPosSky: Position of Source relative to Lens [Mpc]
zs: Redshift of Source
zl: Redshift of Lens
cosmo: Cosmology
Output:
len(mu): number of multiple images of supernova
delta_t: Time it takes for photon to cover distance source-observer
mu: luminosity magnification of source
"""
# Mapping light rays from image plane to source plan
[sp1, sp2] = [lp1 - alpha1, lp2 - alpha2] #yi1,yi2[arcsec]
# Source position [arcsec]
x = SrcPosSky[0]*u.Mpc
y = SrcPosSky[1]*u.Mpc
z = SrcPosSky[2]*u.Mpc
beta1 = ((y/x)*u.rad).to_value('arcsec')
beta2 = ((z/x)*u.rad).to_value('arcsec')
theta1, theta2 = cf.call_mapping_triangles([beta1, beta2],
lp1, lp2, sp1, sp2)
# calculate magnifications of lensed Supernovae
mu = cf.call_inverse_cic_single(mu_map, 0.0, 0.0, theta1, theta2, dsx_arc)
# calculate time delays of lensed Supernovae in Days
prts = cf.call_inverse_cic_single(phi_map, 0.0, 0.0, theta1, theta2, dsx_arc)
Kc = ((1.0+zl)/const.c.to('Mpc/s') * \
(cosmo.angular_diameter_distance(zl) * \
cosmo.angular_diameter_distance(zs) / \
(cosmo.angular_diameter_distance(zs) - \
cosmo.angular_diameter_distance(zl)))).to('sday').value
delta_t = Kc*(0.5*((theta1 - beta1)**2.0 + (theta2 - beta2)**2.0) - prts)/cf.apr**2
beta = [beta1, beta2]
theta = [theta1, theta2]
return len(mu), delta_t, mu, theta, beta
def timedelay_magnification(mu_map, phi_map, dsx_arc, Ncells, lp1, lp2, alpha1,
alpha2, beta, zs, zl, cosmo):
"""
Input:
mu_map: 2D magnification map
phi_map: 2D potential map
dsx_arc: cell size in arcsec
Ncells: number of cells
lp1, lp2: lens place grid coordinates
alpha1, alpha2: 2D deflection map
SrcPosSky: source position in Mpc
zs: source redshift
zl: lens redshift
Output:
len(mu): number of multiple images of supernova
delta_t: Time it takes for photon to cover distance source-observer
mu: luminosity magnification of source
"""
# Mapping light rays from image plane to source plan
[sp1, sp2] = [lp1 - alpha1, lp2 - alpha2] #[arcsec]
theta1, theta2 = cf.call_mapping_triangles([beta[0], beta[1]], lp1, lp2,
sp1, sp2)
# calculate magnifications of lensed Supernovae
mu = cf.call_inverse_cic_single(mu_map, 0.0, 0.0, theta1, theta2, dsx_arc)
# calculate time delays of lensed Supernovae in Days
prts = cf.call_inverse_cic_single(phi_map, 0.0, 0.0, theta1, theta2,
dsx_arc)
Kc = ((1.0+zl)/const.c.to('Mpc/s') * \
(cosmo.angular_diameter_distance(zl) * \
cosmo.angular_diameter_distance(zs) / \
(cosmo.angular_diameter_distance(zs) - \
cosmo.angular_diameter_distance(zl)))).to('sday').value
delta_t = Kc*(0.5*((theta1 - beta[0])**2.0 + \
(theta2 - beta[1])**2.0) - prts)/cf.apr**2
theta = np.array([theta1, theta2]).T
return len(mu), delta_t, mu, theta