def fit_close_background(self, marker='o', markersize='3', color='black'):
# retrieve background dataframe
background = self.background.copy()
# x and y data set as bin locations in alpha, density respectively
xdata = -background.m31_bin_locs
ydata = background.bin_densities
# error also found
yerr = background.bin_uncs
# models set with appropriate initial estimates depending on
# stars and galaxies
# overcrowded bins skipped for better fit
# fit carried out
model = Sersic1D(r_eff=2, n=10.00)
fit = fitting.LevMarLSQFitter()
if self.galaxy == 'ngc205' and self.stars == 'c':
model = Sersic1D(r_eff=10, n=20)
s = fit(model, xdata[2:], ydata[2:])
elif self.galaxy == 'm32' and self.stars == 'c':
model = Sersic1D(r_eff=20, n=10)
s = fit(model, xdata[3:], ydata[3:])
elif self.galaxy == 'm32':
model = Sersic1D(r_eff=20, n=2)
s = fit(model, xdata[3:], ydata[3:], weights=1/yerr[3:])
else:
s = fit(model, xdata[2:], ydata[2:], weights=1/yerr[2:])
# fit and data plotted with uncertainties
plt.figure()
sat_xdata = background.bin_locs
plt.gca().set_xlabel(r'$\alpha$ (arcmins)')
plt.gca().set_ylabel('Density (N/arcmin$^2$)')
plt.gca().invert_xaxis()
plt.errorbar(sat_xdata, ydata, yerr=yerr, capsize=2,
linestyle='none', marker=marker, color=color)
plt.plot(sat_xdata, s(xdata), label=self.galaxy.upper())
leg = plt.legend(handlelength=0, handletextpad=0,
frameon=False, loc='upper right', markerscale=0.001)
for item in leg.legendHandles:
item.set_visible(False)
plt.savefig(self.galaxy + self.stars + '_background_fit.png')
plt.savefig(self.galaxy + self.stars + '_background_fit.pdf')
# sersic fit added to background dataframe
background['density_fit'] = s(xdata)
self.background = background
def fit_close_slice_count_profile(self, stars='agb', crowding_num=1):
distribution = pd.read_parquet('unfit_background_corrected_profiles' +
self.galaxy + stars)
xdata = distribution.a
ydata = distribution.density
yerr = distribution.density_err
plt.errorbar(xdata,
ydata,
yerr=yerr,
marker='o',
linestyle='none',
color='black')
plt.ylabel('Density (N/arcmins$^2$)')
plt.xlabel('Semi-major axis (arcmins)')
xdata_orig = xdata
xdata = xdata[:len(xdata) - (crowding_num)]
ydata = ydata[:len(ydata) - (crowding_num)]
yerr = yerr[:len(yerr) - (crowding_num)]
if self.galaxy == 'ngc205':
model = Sersic1D(r_eff=2.0, n=1.5)
elif self.galaxy == 'm32':
model = Sersic1D(r_eff=1.7, n=1.00)
fit = fitting.LevMarLSQFitter()
s = fit(model, xdata, ydata, weights=1 / yerr)
xdata = np.linspace(min(xdata_orig), max(xdata_orig), num=1000)
plt.plot(xdata,
s(xdata),
label='Sersic Fit with a$_{eff}$ = ' +
str(round(s.r_eff.value, 3)) + ', n = ' +
str(round(s.n.value, 3)))
plt.legend()
def make_galaxies_astropy(self, image, flux, galsize, x, y, ar, pa, n=4):
for f, s, xi, yi, pai, ari, in zip(flux, galsize, x, y, pa, ar):
fluxlim = 0.0001 * f # 0.1
scale = 1 # arcsec/pixel
r_e = s # effective radius
ellip = ari # ellipticity
theta = numpy.deg2rad(pai) # position angle
x_cent = 0 # x centroid
y_cent = 0 # x centroid
tot_flux = f # total flux
s1 = Sersic1D(amplitude=1, r_eff=r_e, n=n)
r = numpy.arange(0, 1000, scale)
s1_n = s1(r) / sum(s1(r))
extent = numpy.where(s1_n * f > fluxlim)[0].max()
if extent % 2 > 0:
extent += 1
ser_model = Sersic2D(r_eff=r_e,
n=n,
ellip=ellip,
theta=theta,
x_0=x_cent,
y_0=y_cent)
x = numpy.arange(-extent / 1., extent / 1., scale) + x_cent / scale
y = numpy.arange(-extent / 1., extent / 1., scale) + y_cent / scale
X, Y = numpy.meshgrid(x, y)
img = ser_model(X, Y)
img /= numpy.sum(img)
img *= tot_flux
xi, yi = int(xi), int(yi)
# COLUMNS FIRST -- because FITS are silly
image[yi - img.shape[1] // 2:yi + img.shape[1] // 2,
xi - img.shape[0] // 2:xi + img.shape[0] // 2] += img
return image
def getLbulge(Amp_eff, R_eff, n, R): # R en pc
s2 = Sersic1D(Amp_eff, R_eff, n)
a = 1
b = a * sqrt(1 - (0.56**2))
#I = s2(R)
Re = R_eff
Ie = s2(Re)
bn = 1.9992 * n - 0.3271
#x = bn *((R/Re)**(1/n))
#gammaInc = gammainc(2*n,x)*sc.gamma(2*n)
L = (2 * pi * (b / a) * Ie *
(R**2) * exp(bn) * n * sc.gamma(2 * n)) / (bn**(2 * n))
print(L)
#L = Ie*(Re**2)*2*pi*n*( (exp(bn))/(bn**(2*n)) )*gammaInc
return (L)
def iterativeLuminosity(Amp_eff, R_eff, n):
s2 = Sersic1D(Amp_eff, R_eff, n)
a = 1
b = a * sqrt(1 - (0.56**2))
#Re = R_eff
#Ie = s2(Re)
#bn = 1.9992*n - 0.3271
r = np.arange(0, (max(rkPC)), 0.001)
for i in r:
Ilist.append(s2(i))
for index in range(len(Ilist) - 1):
r1 = r[index]
r2 = r[index + 1]
#I1 = Ilist[index]
I2 = Ilist[index + 1]
L2 = 2 * pi * (b / a) * I2 * (((r2 * 1e3)**2) - ((r1 * 1e3)**2))
if (index == 0):
Lr.append(L2)
else:
Lr.append(L2 + Lr[index - 1])
#!/usr/bin/python
import numpy as np
from astropy.modeling.models import Sersic1D
import matplotlib.pyplot as plt
plt.figure()
plt.subplot(111, xscale='log', yscale='log')
s1 = Sersic1D(amplitude=1, r_eff=5)
r=np.arange(0, 100, .01)
for n in range(1, 10):
s1.n = n
plt.plot(r, s1(r), color=str(float(n) / 15))
plt.axis([1e-1, 30, 1e-2, 1e3])
plt.xlabel('log Radius')
plt.ylabel('log Surface Brightness')
plt.text(.25, 1.5, 'n=1')
plt.text(.25, 300, 'n=10')
plt.xticks([])
plt.yticks([])
plt.show()
def logSersic1D(x,amplitude,n,r_eff):
model=Sersic1D(amplitude=amplitude,n=n,r_eff=r_eff)
return np.log(model(x))
def fit_slice_count_profile(self, background_deg, crowding_num=0):
slices = self.slices
areas = self.areas
outer_rad = self.outer_rad
a_width = self.a_width
ellipticity = self.ellipticity
slice_nums = []
for i in slices:
slice_nums.append(len(i.dropna()))
slice_nums = np.array(slice_nums)
areas = np.array(areas)
slice_count_uncs = np.sqrt(slice_nums)
slice_star_densities = slice_nums / areas
slice_star_densities_uncs = (np.sqrt((slice_count_uncs / areas)**2 +
background_deg[1]**2))
slice_star_densities = slice_star_densities - background_deg[0]
slice_star_densities = slice_star_densities / 3600
slice_star_densities_uncs = slice_star_densities_uncs / 3600
xdata = np.linspace(outer_rad - a_width / 2,
0 + a_width / 2,
num=(outer_rad * 1000) / (a_width * 1000))
xdata = xdata * 60
# convert from a to r_eff
ydata = slice_star_densities
yerr = slice_star_densities_uncs
#plt.errorbar(xdata,ydata,yerr=yerr,linestyle='none',marker='o',markersize=5,capsize=2,color='black',label='AGB data')
#plt.xlabel('Semi-major axis/arcmins')
# plt.ylabel('Nstars/arcmins$^2$')
# n147 params
xdata_orig = xdata
ydata_orig = ydata
yerr_orig = yerr
xdata = xdata[:len(xdata) - (crowding_num)]
ydata = ydata[:len(ydata) - (crowding_num)]
yerr = yerr[:len(yerr) - (crowding_num)]
if self.galaxy == 'ngc147':
model = Sersic1D(r_eff=5.2, n=1.8)
elif self.galaxy == 'ngc185':
model = Sersic1D(r_eff=1.7, n=1.00)
fit = fitting.LevMarLSQFitter()
s = fit(model, xdata, ydata, weights=1 / yerr)
xdata = np.linspace(min(xdata_orig), max(xdata_orig), 1000)
#plt.plot(xdata,s(xdata),label='Sersic Fit with r$_{eff}$ = ' + str(round(s.r_eff.value,3)) + ', n = ' + str(round(s.n.value,3)))
# plt.legend()
print(s)
self.r_eff = s.r_eff.value
self.n = s.n.value
return xdata_orig, ydata_orig, yerr_orig, xdata, s(xdata)
Rout_vD = 7.6e3 # in pc
Mtot_vD = 3.4e8 # in Msun
Re_vD = 3.1e3 # in pc
Me_vD = 3.2e8 # in Msun
# Compute Mb(r) and Md(r) for multiple Sersic indices
nlist = [0.6, 1, 2, 3, 4]
rlist = [1e3] * len(nlist)
#nlist = [1]
#rlist = [1e3]
for i in range(len(nlist)):
# Projected Sersic profile
s_vD = Sersic1D(amplitude=1., r_eff=1e3,
n=nlist[i]) # Van Dokkum et al. 2018
rhob_Rpy = s_vD(R)
#Mb_Rpy = 4.*pi * cumtrapz(rhob_Rpy * R**2, x = R, initial=0.)
Mb_Rpy = 2. * pi * cumtrapz(rhob_Rpy * R, x=R, initial=0.)
# Adjust the amplitude of rhob and Mb according to Mtot
#Mb_last = Mb_Rpy[-1]
#rhob_Rpy = rhob_Rpy * Mb_vD/Mb_last
#Mb_Rpy = Mb_Rpy * Mb_vD/Mb_last
"""
# Test stuff
Mb_an = 4.*pi*Mb_vD/Mb_last * np.log(R) # Test mass
Md_an = np.sqrt(Cd * 4.*pi*Mb_vD/Mb_last * (np.log(R)+1.)) * R
Md_an = np.sqrt(Cd * np.gradient(Mb_an * R, R)) * R
Mtot_an = Mb_an + Md_an
M_test = 1.
n_test = 4.
r_test = 1e3
nlist = [0.6, 1., 2., 3., 4.]
for i in range(len(nlist)):
n_test = nlist[i]
# Sersic profile density and mass
rhob_R, rhob_r = Sersic(M_test, n_test, r_test, R)
Mb_R = 2. * pi * cumtrapz(rhob_R * R, x=R, initial=0.)
# Projected Sersic profile
s_vD = Sersic1D(amplitude=M_test, r_eff=r_test,
n=n_test) # Van Dokkum et al. 2018
rhob_Rpy = s_vD(R)
Mb_Rpy = 2. * pi * cumtrapz(rhob_Rpy * R, x=R, initial=0.)
# Adjust the amplitude of rhob and Mb according to Mtot
#Mb_last = Mb_Rpy[-1]
#rhob_Rpy = rhob_Rpy * Mb_vD/Mb_last
#Mb_Rpy = Mb_Rpy * Mb_vD/Mb_last
# Plot Sersic profile results
"""
plt.plot(R, rhob_R, ls='-', label=r'$\rho_{\rm b}$(r) for n=%g (projected)'%n_test)
plt.plot(R, rhob_Rpy, ls='-', label=r'$\rho_{\rm b}$(r) for n=%g (python)'%n_test)
plt.plot(R, np.abs((rhob_R-rhob_Rpy)/(rhob_R+rhob_Rpy)/2.), ls=':', label=r'Difference')
"""
def display_ellipse_sbprofile(ellipsefit, minerr=0.02, sersicfit=None,
png=None, verbose=True):
"""Display the multi-band surface brightness profile.
"""
from legacyhalos.ellipse import ellipse_sbprofile
band, refband, redshift = ellipsefit['band'], ellipsefit['refband'], ellipsefit['redshift']
if ellipsefit['success']:
sbprofile = ellipse_sbprofile(ellipsefit, minerr=minerr)
colors = iter(sns.color_palette())
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 8), sharex=True)
for filt in band:
if ellipsefit['success']:
good = (ellipsefit[filt].stop_code < 4)
bad = ~good
col = next(colors)
ax1.fill_between(sbprofile['sma'],
sbprofile['mu_{}'.format(filt)] - sbprofile['mu_{}_err'.format(filt)],
sbprofile['mu_{}'.format(filt)] + sbprofile['mu_{}_err'.format(filt)],
#sbprofile['{}'.format(filt)] - sbprofile['{}_err'.format(filt)],
#sbprofile['{}'.format(filt)] + sbprofile['{}_err'.format(filt)],
label=r'${}$'.format(filt), color=col, alpha=0.75, edgecolor='k', lw=2)
#if np.count_nonzero(bad) > 0:
# ax1.scatter(sbprofile['sma'][bad], sbprofile[filt][bad], marker='s',
# s=40, edgecolor='k', lw=2, alpha=0.75)
#ax1.axhline(y=ellipsefit['mu_{}_sky'.format(filt)], color=col, ls='--')
if filt == refband:
ysky = ellipsefit['mu_{}_sky'.format(filt)] - 2.5 * np.log10(0.1) # 10% of sky
ax1.axhline(y=ysky, color=col, ls='--')
# Overplot the best-fitting model.
if sersicfit:
from astropy.modeling.models import Sersic1D
rad = np.arange(0, sbprofile['sma'].max(), 0.1)
sbmodel = -2.5 * np.log10( Sersic1D.evaluate(
rad, sersicfit[filt].amplitude, sersicfit[filt].r_eff,
sersicfit[filt].n) )
ax1.plot(rad, sbmodel, lw=2, ls='--', alpha=1, color=col)
ax1.set_ylabel(r'Surface Brightness (mag arcsec$^{-2}$)')
ax1.set_ylim(30, 17)
#ax1.set_ylabel(r'$\mu$ (mag arcsec$^{-2}$)')
#ax1.set_ylim(31.99, 18)
if ellipsefit['success']:
ax1.legend(loc='upper right')
ax2.fill_between(sbprofile['sma'],
sbprofile['rz'] - sbprofile['rz_err'],
sbprofile['rz'] + sbprofile['rz_err'],
label=r'$r - z$', color=next(colors), alpha=0.75,
edgecolor='k', lw=2)
ax2.fill_between(sbprofile['sma'],
sbprofile['gr'] - sbprofile['gr_err'],
sbprofile['gr'] + sbprofile['gr_err'],
label=r'$g - r$', color=next(colors), alpha=0.75,
edgecolor='k', lw=2)
ax2.set_xlabel('Semimajor Axis (arcsec)', alpha=0.75)
ax2.legend(loc='upper left')
else:
ax2.set_xlabel('Semimajor Axis', alpha=0.75)
ax2.set_ylabel('Color (mag)')
ax2.set_ylim(0, 2.4)
fig.subplots_adjust(hspace=0.0)
if png:
if verbose:
print('Writing {}'.format(png))
fig.savefig(png)
plt.close(fig)
else:
plt.show()