def minimize_function(x, rho_nfw_target, rho_midplane_target,
density_conversion):
"""
Computes the chi^2 penalty for a galactic potential for the purpose of finding an NFWPotential and MiyamotoNagaiPotential
circular velocity normalization that yeild the desired midplane and nfw physical densities
:param x: numpy array of proposed disk and nfw circular velocity normalizations (in that order)
:param rho_nfw_target: desired nfw_normalization in physical M_sun / pc^2
:param rho_midplane_target: desired midplane density in physical M_sun / pc^2
:param density_conversion: a conversion factor between galpy internal density units and physical M_sun / pc^2
:return: chi^2 penalty
"""
galactic_potential = [
PowerSphericalPotentialwCutoff(normalize=0.05, alpha=1.8, rc=1.9 / 8.),
MiyamotoNagaiPotential(a=3. / 8., b=0.28 / 8., normalize=x[0]),
NFWPotential(a=2., normalize=x[1])
]
nfw_potential = NFWPotential(a=2., normalize=x[1])
rho = evaluateDensities(galactic_potential, R=1.,
z=0.) * density_conversion
rho_nfw = evaluateDensities(nfw_potential, R=1, z=0.) * density_conversion
dx = (rho - rho_midplane_target)**2 / 0.000001**2 + (
rho_nfw - rho_nfw_target)**2 / 0.000001**2
return dx**0.5
def setup(self):
nfw_norm = [0.2, 0.4, 0.6]
disk_norm = [0.15, 0.3, 0.45]
scale_height = [0.25, 0.27, 0.29]
pot_list = []
for normnfw in nfw_norm:
for normdisk in disk_norm:
for scale_h in scale_height:
pot = [
PowerSphericalPotentialwCutoff(normalize=0.05,
alpha=1.8,
rc=1.9 / 8.),
MiyamotoNagaiPotential(a=3. / 8.,
b=scale_h / 8.,
normalize=normdisk),
NFWPotential(a=2., normalize=normnfw)
]
pot_extension = PotentialExtension(
pot, 2, 120, 3, compute_action_angle=True)
pot_list.append(pot_extension)
self.disk_norm = disk_norm
self.nfw_norm = nfw_norm
self.scale_height = scale_height
self.pot_list = pot_list
self.tabulated_potential = TabulatedPotential3D(
self.pot_list, self.nfw_norm, self.disk_norm, self.scale_height)
def setup(self):
nfw_norm = [0.2, 0.4, 0.6]
disk_norm = [0.15, 0.3, 0.45]
pot_list = []
for normnfw in nfw_norm:
for normdisk in disk_norm:
pot = [
PowerSphericalPotentialwCutoff(normalize=0.05,
alpha=1.8,
rc=1.9 / 8.),
MiyamotoNagaiPotential(a=3. / 8.,
b=0.28 / 8.,
normalize=normdisk),
NFWPotential(a=2., normalize=normnfw)
]
pot_extension = PotentialExtension(pot, 2, 120, 10)
pot_list.append(pot_extension)
self.disk_norm = disk_norm
self.nfw_norm = nfw_norm
self.pot_list = pot_list
self.tabulated_potential = TabulatedPotential(self.pot_list,
self.nfw_norm,
self.disk_norm)
def test_powerlawcutoff():
from galpy.potential import PowerSphericalPotentialwCutoff
M = 1.5854e10 * u.Msun
alpha = 1.75
gala_pot = PowerLawCutoffPotential(m=M, alpha=alpha, r_c=15*u.kpc,
units=galactic)
r_c = gala_pot.parameters['r_c']
amp = (G*M).to_value(vo**2 * ro) * ((1/(2*np.pi) * r_c.to_value(ro)**(alpha - 3) / (gamma(3/2 - alpha/2))))
bovy_pot = PowerSphericalPotentialwCutoff(amp,
alpha=gala_pot.parameters['alpha'].value,
rc=r_c.to_value(ro),
ro=ro, vo=vo)
helper(gala_pot, bovy_pot)
def test_minimize_func(self):
disk_norm, nfw_norm = solve_normalizations(self.rho_nfw_target,
self.rho_midplane_target,
self.density_conversion)
pot = [
PowerSphericalPotentialwCutoff(normalize=0.05,
alpha=1.8,
rc=1.9 / 8.),
MiyamotoNagaiPotential(a=3. / 8., b=0.28 / 8.,
normalize=disk_norm),
NFWPotential(a=2., normalize=nfw_norm)
]
rho = evaluateDensities(pot, R=1., z=0) * self.density_conversion
npt.assert_almost_equal(rho, self.rho_midplane_target, 3)
disk_norm, nfw_norm = solve_normalizations(self.rho_nfw_target,
self.rho_nfw_target * 0.5,
self.density_conversion)
npt.assert_equal(True, disk_norm < 0)
# 'main_colnames':None, # list of names
# 'error_colnames':None,
# 'corr_colnames':None,
}
cart_colnames = {
# 'main_colnames':None,
# 'error_colnames':None,
# 'corr_colnames':None,
}
from galpy.potential import PowerSphericalPotentialwCutoff,\
MiyamotoNagaiPotential, NFWPotential, verticalfreq, MWPotential2014
scale_height_factor = 2.0
bp = PowerSphericalPotentialwCutoff(alpha=1.8, rc=1.9 / 8., normalize=0.05)
mp = MiyamotoNagaiPotential(a=3. / 8., b=scale_height_factor * 0.28 / 8.,
normalize=.6)
np = NFWPotential(a=16 / 8., normalize=.35)
my_mwpotential2014 = [bp, mp, np]
orbit = {
'potential': my_mwpotential2014, # TC: varied params randomly...
}
special = {
'component':'sphere', # parameterisation for the origin
}
advanced = {
'burnin_steps':500, # emcee parameters, number of steps for each burnin iteraton
'sampling_steps':500,