def calc_age_pdf(self,fehdist='casagrande'):
"""
NAME:
calc_age_pdf
PURPOSE:
calculate the age PDF for a uniform SFH for a given metallicity
distribution
INPUT:
fehdist= either:
1) a single metallicity
2) 'casagrande': local metallicity distribution following Casagrande et al. (2011)
3) a function giving
OUTPUT:
a function between 800 Myr and 10 Gyr giving the age distribution
HISTORY:
2014-02-27 - Written in this form - Bovy (IAS)
"""
if isinstance(fehdist,(int,float,numpy.float32,numpy.float64)):
pz= numpy.zeros(len(self._zs))
pz[numpy.argmin(numpy.fabs(self._zs-isodist.FEH2Z(fehdist,zsolar=zsolar())))]= 1.
elif isinstance(fehdist,str) and fehdist.lower() == 'casagrande':
pz= numpy.array([localfehdist(isodist.Z2FEH(z,zsolar=zsolar()))/z for z in self._zs])
else:
pz= numpy.array([fehdist(isodist.Z2FEH(z,zsolar=zsolar()))/z for z in self._zs])
pz/= numpy.sum(pz)
agezdist= self._omega/self._coarsemass
pz= numpy.tile(pz,(len(self._coarselages),1)).T
postage= numpy.nansum(pz*agezdist,axis=0)/numpy.nansum(pz,axis=0)/10.**self._coarselages
postage= postage[self._coarselages > numpy.log10(0.8)]
postage/= numpy.nanmax(postage)
lages= self._coarselages[self._coarselages > numpy.log10(0.8)]
postage_spline= interpolate.InterpolatedUnivariateSpline(lages,
numpy.log(postage),
k=3)
return lambda x: dummy_page(x,copy.copy(postage_spline))
def sample_iso_MH(fehbin=[-0.6, 0.2],
agebin=[0., 13.],
n=1000,
agebias=False,
imftype='chabrier2003',
isochrones='Padova'):
#Load pre-computed parsec isochrone grid
iso_file = open('../savs/' + isochrones + '_grid_' + imftype + '.sav')
iso_grid = pickle.load(iso_file)
#add rgb age bias if agebias = True
if agebias == True:
iso_grid[:, 6] *= agebias(10**iso_grid[:, 0])
#Perform sample cuts (logg and J-K)
gridcuts = (iso_grid[:, 3] > 1.8) & (iso_grid[:, 3] <
3.0) & (iso_grid[:, 5] > 0.5)
cutgrid = iso_grid[gridcuts]
n_weights = cutgrid[:, 6] * (10**cutgrid[:, 0] / cutgrid[:, 1])
#make [Fe/H], age cut
fehcut = (isodist.Z2FEH(cutgrid[:,1])>=fehbin[0])&(isodist.Z2FEH(cutgrid[:,1])<fehbin[1])\
&(10**cutgrid[:,0] >= agebin[0])&(10**cutgrid[:,0] < agebin[1])
# compute CDF of M_H
sorter_H = numpy.argsort(cutgrid[:, 4][fehcut])
cdf_H = numpy.cumsum(n_weights[fehcut][sorter_H]) / numpy.sum(
n_weights[fehcut])
#Interpolate CDF and take n samples
intercdf_H = interp1d(cdf_H, cutgrid[:, 4][fehcut][sorter_H])
rand = numpy.random.uniform(size=n, low=0.0001, high=0.999999)
model_MH = intercdf_H(rand)
return model_MH
def loggteffcut(teff, z, upper=True):
if not upper:
return 1.8
else:
feh = isodist.Z2FEH(z, zsolar=zsolar())
this_teff = (4760. - 4607.) / (-0.4) * feh + 4607.
return 0.0018 * (teff - this_teff) + 2.5
def Gdist(tG, ZG):
"""The distribution of G for the local metallicity distribution
REWRITE TO TAKE A Z(G) FUNCTION OBTAINED THROUGH INTERPOLATION"""
try:
tZ = ZG(tG)
tjac = numpy.fabs(ZG.derivatives(tG)[0] / tZ / numpy.log(10.))
except ValueError:
return 0.
# Add Jacobian
return localfehdist(isodist.Z2FEH(tZ, zsolar=0.017)) * tjac
def imf_h_jk(plotfile,Z=None,dwarf=False,log=False,h=12.,basti=False,
dartmouth=False,kroupa=False):
#Read isochrones
if basti:
zs= numpy.array([0.0001,0.0003,0.0006,0.001,0.002,0.004,0.008,
0.01,0.0198,0.03,0.04])
elif dartmouth:
zs= isodist.FEH2Z(numpy.array([-2.5,-2.,-1.5,-1.,-0.5,0.,0.2,0.3,0.5]))
else:
zs= numpy.arange(0.0005,0.03005,0.0005)
if Z is None:
Zs= zs
elif not basti and not dartmouth:
if Z < 0.01:
Zs= [Z-0.001,Z-0.0005,Z,Z+0.0005,Z+0.001] #build up statistics
else:
Zs= [Z-0.0005,Z,Z+0.0005] #build up statistics
else:
Zs= [Z]
if basti:
p= isodist.BastiIsochrone(Z=Zs)
elif dartmouth:
p= isodist.DartmouthIsochrone(feh=isodist.Z2FEH(Zs),onlyold=True)
else:
p= isodist.PadovaIsochrone(Z=Zs)
#Get relevant data
sample= []
weights= []
for logage in p.logages():
for z in Zs:
thisiso= p(logage,z)
if basti: mini= thisiso['M_ini']
elif dartmouth: mini= thisiso['M']
else: mini= thisiso['M_ini']
if basti:
int_IMF= isodist.imf.lognormalChabrier2001(thisiso['M_ini'],
int=True)
dmpm= numpy.roll(int_IMF,-1)-int_IMF
elif dartmouth:
int_IMF= isodist.imf.lognormalChabrier2001(thisiso['M'],
int=True)
dmpm= numpy.roll(int_IMF,-1)-int_IMF
else:
if kroupa:
int_IMF= isodist.imf.kroupa2003(thisiso['M_ini'],int=True)
dmpm= numpy.roll(int_IMF,-1)-int_IMF
else:
dmpm= numpy.roll(thisiso['int_IMF'],-1)-thisiso['int_IMF']
for ii in range(1,len(mini)-1):
if basti:
JK= thisiso['J'][ii]-thisiso['K'][ii]
else:
JK= thisiso['J'][ii]-thisiso['Ks'][ii]
H= thisiso['H'][ii]
if JK < 0.: # or thisiso['logg'][ii] > 3.5:
continue
if dmpm[ii] > 0.:
if basti:
sample.append([thisiso['J'][ii]-thisiso['K'][ii],
thisiso['H'][ii]])
else:
sample.append([thisiso['J'][ii]-thisiso['Ks'][ii],
thisiso['H'][ii]])
if dartmouth:
if logage > numpy.log10(5.)+9.:
weights.append(2.*dmpm[ii]) #Dartmouth are linearly spaced, but spacing is bigger at > 5 Gyr
else:
weights.append(dmpm[ii]) #Dartmouth are linearly spaced?
else:
weights.append(dmpm[ii]*10**(logage-7.))
#weights.append(dmpm[ii]*10**(logage-7.)*numpy.exp((10.**(logage-7.))/800.))
else:
continue #no use in continuing here
#Form array
sample= numpy.array(sample)
weights= numpy.array(weights)
#Histogram
if dwarf:
hist, edges= numpy.histogramdd(sample,weights=weights,bins=51,
range=[[0.,1.6],[2.,9.]])
else:
hist, edges= numpy.histogramdd(sample,weights=weights,bins=49,
range=[[0.3,1.6],[-11.,2]])
#Normalize each J-K
for ii in range(len(hist[:,0])):
hist[ii,:]/= numpy.nanmax(hist[ii,:])/numpy.nanmax(hist)
rev= copy.copy(hist[ii,::-1]) #reverse, but in one go does not always work
hist[ii,:]= rev
#Plot
bovy_plot.bovy_print()
if log:
hist= numpy.log(hist)
bovy_plot.bovy_dens2d(hist.T,origin='lower',cmap='gist_yarg',
xrange=[edges[0][0],edges[0][-1]],
yrange=[edges[1][-1],edges[1][0]],
aspect=(edges[0][-1]-edges[0][0])/float(edges[1][-1]-edges[1][0]),
xlabel=r'$(J-K_s)_0\ [\mathrm{mag}]$',
ylabel=r'$M_H\ [\mathrm{mag}]$',
interpolation='nearest')
#Add extinction arrow
djk= 0.45
dh= 1.55/1.5*djk
from matplotlib.patches import FancyArrowPatch
ax=pyplot.gca()
ax.add_patch(FancyArrowPatch((1.,-2.),(1+djk,-2+dh),
arrowstyle='->',mutation_scale=20,fill=True,
lw=1.25))
bovy_plot.bovy_text(1.05,-2.05,r'$\mathrm{extinction}$',
rotation=-math.atan(1.5/1.55*1.3/13.)/math.pi*180.,
size=14.)
#Add color cut
bovy_plot.bovy_plot([0.5,0.5],[-20.,20.],'--',color='0.6',overplot=True)
ax.add_patch(FancyArrowPatch((0.5,-6.),(0.7,-6.),
arrowstyle='->',mutation_scale=20,fill=True,
lw=1.25,ls='dashed',color='0.6'))
bovy_plot.bovy_text(0.43,-8.,r'$\mathrm{APOGEE\ color\ cut}$',rotation=90.,
size=14.)
#Add twin y axis
ax= pyplot.gca()
def my_formatter(x, pos):
"""distance in kpc for m=h"""
xs= 10.**((h-x)/5.-2.)
return r'$%.0f$' % xs
def my_formatter2(x, pos):
"""distance in kpc for m=h"""
xs= 10.**((h-x)/5.+1.)
return r'$%.0f$' % xs
ax2= pyplot.twinx()
if dwarf:
major_formatter = FuncFormatter(my_formatter2)
else:
major_formatter = FuncFormatter(my_formatter)
ax2.yaxis.set_major_formatter(major_formatter)
ystep= ax.yaxis.get_majorticklocs()
ystep= ystep[1]-ystep[0]
ax2.yaxis.set_minor_locator(MultipleLocator(ystep/5.))
ax2.yaxis.tick_right()
ax2.yaxis.set_label_position('right')
ymin, ymax= ax.yaxis.get_view_interval()
ax2.yaxis.set_view_interval(ymin,ymax,ignore=True)
if dwarf:
ax2.set_ylabel('$\mathrm{distance\ for}\ H_0\ =\ %.1f\ [\mathrm{pc}]$' % h)
else:
ax2.set_ylabel('$\mathrm{distance\ for}\ H_0\ =\ %.1f\ [\mathrm{kpc}]$' % h)
xstep= ax.xaxis.get_majorticklocs()
xstep= xstep[1]-xstep[0]
ax2.xaxis.set_minor_locator(MultipleLocator(xstep/5.))
if Z is None:
bovy_plot.bovy_end_print(plotfile)
else:
bovy_plot.bovy_text(r'$Z\ =\ %.3f$' % Z,top_right=True,size=14.)
bovy_plot.bovy_end_print(plotfile)
return None
def plot_popmass(self):
"""
NAME:
plot_popmass
PURPOSE:
plot the stellar-population mass for each RC star
INPUT:
bovy_plot.bovy_plot **kwargs
OUTPUT:
bovy_plot.bovy_plot output
HISTORY:
2014-02-28 - Written in this form - Bovy (IAS)
"""
if not _BOVY_PLOT_LOADED:
raise ImportError("galpy.util.bovy_plot could not be imported")
fehs = numpy.linspace(-1., 0.5, 101)
lages = self._coarselages
plotthis = numpy.empty((len(fehs), len(lages)))
for ii in range(len(fehs)):
for jj in range(len(lages)):
plotthis[ii, jj] = self.popmass(fehs[ii], lages[jj])
fig = pyplot.gcf()
left, bottom, width, height = 0.1, 0.1, 0.8, 0.6
axBottom = pyplot.axes([left, bottom, width, height])
fig.sca(axBottom)
xlimits = [fehs[0], fehs[-1]]
dlages = (lages[1] - lages[0])
ylimits = [lages[0] - dlages, lages[-1] + dlages]
vmin, vmax = 0., 50000.
vmin2, vmax2 = 0., 25000.
zlabel = r'$\mathrm{Stellar\ population\ mass\ per\ RC\ star}\,(M_\odot)$'
xlabel = r'$[\mathrm{Fe/H}]\,(\mathrm{dex})$'
out = bovy_plot.bovy_dens2d(plotthis.T,
origin='lower',
cmap='jet',
xrange=xlimits,
yrange=ylimits,
vmin=vmin,
vmax=vmax,
interpolation='nearest',
colorbar=True,
shrink=.9,
zlabel=zlabel,
overplot=True)
extent = xlimits + ylimits
pyplot.axis(extent)
bovy_plot._add_axislabels(
xlabel, r'$\log_{10}\,\mathrm{Age} / 1\,\mathrm{Gyr}$')
bovy_plot._add_ticks()
left, bottom, width, height = 0.1, 0.68, 0.64, 0.2
axTop = pyplot.axes([left, bottom, width, height])
fig.sca(axTop)
#Plot the average over SFH
lages = numpy.linspace(-1., 1., 16)
mtrend = numpy.zeros(len(self._zs))
exppage = 10.**self._coarselages * numpy.exp(
(10.**(self._coarselages + 2.)) / 800.) #e.g., Binney (2010)
exexppage = 10.**self._coarselages * numpy.exp(
(10.**(self._coarselages + 2.)) / 100.) #e.g., Binney (2010)
page = 10.**self._coarselages
plotthis = self._coarsemass[:-1, :] / self._omega[:-1, :]
mtrend = 1. / (numpy.sum(page * 1. / plotthis, axis=1) /
numpy.sum(page))
expmtrend = 1. / (numpy.sum(exppage * 1. / plotthis, axis=1) /
numpy.sum(exppage))
exexpmtrend = 1. / (numpy.sum(exexppage * 1. / plotthis, axis=1) /
numpy.sum(exexppage))
fehs = isodist.Z2FEH(self._zs[:-1], zsolar=zsolar())
pyplot.plot(fehs, mtrend, 'k-')
pyplot.plot(fehs, expmtrend, 'k--')
pyplot.plot(fehs, exexpmtrend, 'k-.')
pyplot.ylim(vmin2, vmax2)
pyplot.xlim(xlimits[0], xlimits[1])
nullfmt = NullFormatter() # no labels
thisax = pyplot.gca()
thisax.xaxis.set_major_formatter(nullfmt)
bovy_plot._add_ticks()
return out
def __init__(self,
dwarf=False,
imfmodel='lognormalChabrier2001',
Z=None,
interpolate=False,
expsfh=False,
marginalizefeh=False,
glon=None,
dontgather=False,
loggmax=None,
basti=False):
"""
NAME:
__init__
PURPOSE:
initialize isomodel
INPUT:
Z= metallicity (if not set, use flat prior in Z over all Z; can be list)
dwarf= (default: False) if True, use dwarf part
imfmodel= (default: 'lognormalChabrier2001') IMF model to use (see isodist.imf code for options)
interpolate= (default: False) if True, interpolate the binned representation
expsfh= if True, use an exponentially-declining star-formation history
marginalizefeh= if True, marginalize over the FeH distribution along line of sight glon
glon - galactic longitude in rad of los for marginalizefeh
dontgather= if True, don't gather surrounding Zs
loggmax= if set, cut logg at this maximum
basti= if True, use Basti isochrones (if False, use Padova)
OUTPUT:
object
HISTORY:
2012-02-17 - Written - Bovy (IAS)
"""
#Read isochrones
if basti:
zs = numpy.array([
0.0001, 0.0003, 0.0006, 0.001, 0.002, 0.004, 0.008, 0.01,
0.0198, 0.03, 0.04
])
else:
zs = numpy.arange(0.0005, 0.03005, 0.0005)
if marginalizefeh:
Zs = numpy.arange(0.008, 0.031, 0.001)
dFeHdZ = 1. / Zs
pZs = feh_l(glon, isodist.Z2FEH(Zs)) * dFeHdZ
elif Z is None:
Zs = zs
elif isinstance(Z, float):
if basti or dontgather:
Zs = [Z]
elif Z < 0.001 or Z > 0.0295:
Zs = [Z]
elif Z < 0.0015 or Z > 0.029:
Zs = [Z - 0.0005, Z, Z + 0.0005] #build up statistics
elif Z < 0.01:
Zs = [Z - 0.001, Z - 0.0005, Z, Z + 0.0005,
Z + 0.001] #build up statistics
else:
Zs = [Z - 0.0005, Z, Z + 0.0005] #build up statistics
if basti:
p = isodist.BastiIsochrone(Z=Zs)
else:
p = isodist.PadovaIsochrone(Z=Zs)
#Get relevant data
sample = []
weights = []
for logage in p.logages():
for zz in range(len(Zs)):
thisiso = p(logage, Zs[zz], asrecarray=True)
#Calculate int_IMF for this IMF model
if not imfmodel == 'lognormalChabrier2001': #That would be the default
if imfmodel == 'exponentialChabrier2001':
int_IMF = isodist.imf.exponentialChabrier2001(
thisiso.M_ini, int=True)
elif imfmodel == 'kroupa2003':
int_IMF = isodist.imf.kroupa2003(thisiso.M_ini,
int=True)
elif imfmodel == 'chabrier2003':
int_IMF = isodist.imf.chabrier2003(thisiso.M_ini,
int=True)
else:
raise IOError(
"imfmodel option not understood (non-existing model)"
)
elif basti:
int_IMF = isodist.imf.lognormalChabrier2001(thisiso.M_ini,
int=True)
else:
int_IMF = thisiso.int_IMF
dN = numpy.roll(int_IMF, -1) - int_IMF
for ii in range(1, len(int_IMF) - 1):
if basti:
JK = thisiso.J[ii] - thisiso.K[ii]
else:
JK = thisiso.J[ii] - thisiso.Ks[ii]
H = thisiso.H[ii]
if JK < 0.3 or (not loggmax is None
and thisiso['logg'][ii] > loggmax):
continue
if dN[ii] > 0.:
sample.append([JK, H])
if marginalizefeh:
if H < (11. / -1.3 * (JK - 0.3)):
weights.append(
0.
) #HACK TO GET RID OF UNWANTED BRIGHT POINTS
elif expsfh:
weights.append(pZs[zz] * dN[ii] *
10**(logage - 7.) * numpy.exp(
(10.**(logage - 7.)) /
800.)) #e.g., Binney (2010)
else:
weights.append(pZs[zz] * dN[ii] *
10**(logage - 7.))
else:
if expsfh:
weights.append(dN[ii] * 10**(logage - 7.) *
numpy.exp(
(10.**(logage - 7.)) /
800.)) #e.g., Binney (2010)
else:
weights.append(dN[ii] * 10**(logage - 7.))
else:
continue #no use in continuing here
#Form array
sample = numpy.array(sample)
weights = numpy.array(weights)
self._sample = sample
self._weights = weights
#Histogram
self._jkmin, self._jkmax = 0.3, 1.6
if dwarf:
self._hmin, self._hmax = 2., 9.
self._nbins = 51
else:
self._hmin, self._hmax = -11., 2.
self._nbins = 26 #49
self._djk = (self._jkmax - self._jkmin) / float(self._nbins)
self._dh = (self._hmax - self._hmin) / float(self._nbins)
self._hist, self._edges = numpy.histogramdd(
sample,
weights=weights,
bins=self._nbins,
range=[[self._jkmin, self._jkmax], [self._hmin, self._hmax]])
#Save
self._Zs = Zs
self._interpolate = interpolate
self._dwarf = dwarf
self._loghist = numpy.log(self._hist)
self._loghist[(
self._hist == 0.)] = -numpy.finfo(numpy.dtype(numpy.float64)).max
if interpolate:
#Form histogram grid
jks = numpy.linspace(self._jkmin + self._djk / 2.,
self._jkmax - self._djk / 2., self._nbins)
hs = numpy.linspace(self._hmin + self._dh / 2.,
self._hmax - self._dh / 2., self._nbins)
self._interpolatedhist = scipy.interpolate.RectBivariateSpline(
jks,
hs,
self._hist,
bbox=[self._jkmin, self._jkmax, self._hmin, self._hmax],
s=0.)
#raise NotImplementedError("'interpolate=True' option for isomodel not implemented yet")
return None
