def T_nocut(self, r):
"""
Calculates the temperature as a function of r ignoring any interior
cutoff. The interior cutoff would affect T for adiabatic disks
Paramters
---------
r : array, SimArray, or float
radius (or radii) at which to calculate the temperature
Returns
-------
T : SimArray
temperature
"""
# Load settings
params = self._parent.settings.physical
if not hasattr(params, 'kind'):
# Add this check for backwards compatibility. Previous versions
# only had one kind of temperature profile
params.kind = 'powerlaw'
T0 = params.T0
Tmin = params.Tmin
r0 = params.r0
kind = params.kind
# Calculate T(r)
r = match_units(r, r0)[0]
a = (r/r0)
a = match_units(a, '1')[0]
# Powerlaw temperature (default)
if kind == 'powerlaw':
Tpower = params.Tpower
Tout = T0 * np.power(a, Tpower)
Tout[Tout < Tmin] = Tmin
# MQWS temperature profile
elif (kind == 'mqws') | (kind == 'MQWS'):
# NOTE: I'm not sure how exactly they generate the temperature
# profile. The quoted equation doesn't match their figures
Tout = T0 * np.exp(-3*a/2) + Tmin
else:
raise TypeError, 'Could not find temperature kind {0}'.format(kind)
# Apply max Temp cutoff
if hasattr(params, 'Tmax'):
Tmax = params.Tmax
Tout[Tout > Tmax] = Tmax
return Tout
def _make_sigma(self, r_bins, sigmaBinned):
"""
Generates the surface density as a function of r, a callable object
sigma(r) and assigns it to self.sigma
Generates a spline interpolation of sigma vs r from the file
defined by settings.filenames.sigmaFileName. Returns sigma vs r as
an cubic spline interpolation object
(see scipy.interpolation.InterpolatedUnivariateSpline)
sigma_input should be a pickled dictionary with the entries:
'sigma': <sigma evaluated at r>
'r': <r for the bins>
If the input sigma has units, sigma vs r will be returned in units
of Msol/au^2
"""
# Convert to default units of Msol/au^2. If no units, assign default
sigmaBinned = match_units(sigmaBinned, 'Msol au**-2')[0]
# Convert r_bins to default units of 'au'
r_bins = match_units(r_bins, 'au')[0]
# Calculate spline interpolation
sigspline = spline(r_bins, sigmaBinned, k=3, ext='zeros')
# print 'Calculating spline interpolation (slow for many data points)'
# sigspline = interp1d(r_bins,sigmaBinned,kind='cubic',fill_value=0.0,\
# bounds_error=False)
def sigout(r):
"""
Linear spline interpolation of sigma(r).
ARGUMENTS:
r - can be scalar, numpy array, or sim array
RETURNS:
sigma (surface density) evaluated at r
"""
# Try to convert r to the units used to make sigspline ('au')
r = match_units(r, 'au')[0]
return SimArray(sigspline(r), 'Msol au**-2')
self.sigma = sigout
self.r_bins = r_bins
def _make_sigma(self, r_bins, sigmaBinned):
"""
Generates the surface density as a function of r, a callable object
sigma(r) and assigns it to self.sigma
Generates a spline interpolation of sigma vs r from the file
defined by settings.filenames.sigmaFileName. Returns sigma vs r as
an cubic spline interpolation object
(see scipy.interpolation.InterpolatedUnivariateSpline)
sigma_input should be a pickled dictionary with the entries:
'sigma': <sigma evaluated at r>
'r': <r for the bins>
If the input sigma has units, sigma vs r will be returned in units
of Msol/au^2
"""
# Convert to default units of Msol/au^2. If no units, assign default
sigmaBinned = match_units(sigmaBinned, 'Msol au**-2')[0]
# Convert r_bins to default units of 'au'
r_bins = match_units(r_bins, 'au')[0]
# Calculate spline interpolation
sigspline = spline(r_bins, sigmaBinned, k=3, ext='zeros')
def sigout(r):
"""
Linear spline interpolation of sigma(r).
ARGUMENTS:
r - can be scalar, numpy array, or sim array
RETURNS:
sigma (surface density) evaluated at r
"""
# Try to convert r to the units used to make sigspline ('au')
r = match_units(r, 'au')[0]
return SimArray(sigspline(r), 'Msol au**-2')
self.sigma = sigout
self.r_bins = r_bins
def init_snapshot(IC):
"""
Initialize a snapshot for the IC object. Requires that positions have
been created. Also sets:
* pos
* metals
* temp
* mass
* star eps
Parameters
----------
IC : ICobj
Returns
-------
snapshot : SimSnap
"""
# Get required settings from IC
settings = IC.settings
# particle positions
r = IC.pos.r
xyz = IC.pos.xyz
nParticles = IC.pos.nParticles
m_star = settings.physical.M
m_disk = IC.sigma.m_disk
m_disk = match_units(m_disk, m_star)[0]
m_particles = m_disk / float(nParticles)
metals = settings.snapshot.metals
# re-scale the particles (allows making of lo-mass disk)
m_particles *= settings.snapshot.mScale
# Handle units
units = setup_units(m_star, r)
if xyz.units != r.units:
xyz.convert_units(units['x'])
# Initialize arrays
snapshot = pynbody.new(star=1,gas=nParticles)
snapshot['vel'].units = units['v']
snapshot['eps'] = SimArray(0.01, units['x'])
snapshot['rho'] = 0.
snapshot['metals'] = metals
# Assign array values
snapshot.gas['pos'] = xyz
snapshot.gas['temp'] = IC.T(r)
snapshot.gas['mass'] = m_particles
snapshot.star['pos'] = 0.
snapshot.star['mass'] = m_star
# Estimate the star's softening length as the closest particle distance/2
snapshot.star['eps'] = r.min()/2.
return snapshot
def init_snapshot(IC):
"""
Initialize a snapshot for the IC object. Requires that positions have
been created. Also sets:
* pos
* metals
* temp
* mass
* star eps
Parameters
----------
IC : ICobj
Returns
-------
snapshot : SimSnap
"""
# Get required settings from IC
settings = IC.settings
# particle positions
r = IC.pos.r
xyz = IC.pos.xyz
nParticles = IC.pos.nParticles
m_star = settings.physical.M
m_disk = IC.sigma.m_disk
m_disk = match_units(m_disk, m_star)[0]
m_particles = m_disk / float(nParticles)
metals = settings.snapshot.metals
# re-scale the particles (allows making of lo-mass disk)
m_particles *= settings.snapshot.mScale
# Handle units
units = setup_units(m_star, r)
if xyz.units != r.units:
xyz.convert_units(units['x'])
# Initialize arrays
snapshot = pynbody.new(star=1,gas=nParticles)
snapshot['vel'].units = units['v']
snapshot['eps'] = SimArray(0.01, units['x'])
snapshot['rho'] = 0.
snapshot['metals'] = metals
# Assign array values
snapshot.gas['pos'] = xyz
snapshot.gas['temp'] = IC.T(r)
snapshot.gas['mass'] = m_particles
snapshot.star['pos'] = 0.
snapshot.star['mass'] = m_star
# Estimate the star's softening length as the closest particle distance/2
snapshot.star['eps'] = r.min()/2.
return snapshot
def pdf_fcn(r_in):
"""
Normalized cubic spline interpolation of the PDF(r) from sigma(r).
The PDF is just calculated as 2*pi*r*sigma(r).
ARGUMENTS:
r_in - radii at which to calculate the PDF
RETURNS:
probability density function from sigma(r) evaluated at r_in
"""
# Put r_in into the units used in generating the pdf
r_in = match_units(r_in, self.r_bins)[0]
# Evaluate the pdf at r_in
pdf_vals = pdfSpline(r_in)
# Put the pdf into units of r_in.units**-1
pdf_vals = match_units(pdf_vals, 1/r_in)[0]
return pdf_vals
def pdf_fcn(r_in):
"""
Normalized cubic spline interpolation of the PDF(r) from sigma(r).
The PDF is just calculated as 2*pi*r*sigma(r).
ARGUMENTS:
r_in - radii at which to calculate the PDF
RETURNS:
probability density function from sigma(r) evaluated at r_in
"""
# Put r_in into the units used in generating the pdf
r_in = match_units(r_in, self.r_bins)[0]
# Evaluate the pdf at r_in
pdf_vals = pdfSpline(r_in)
# Put the pdf into units of r_in.units**-1
pdf_vals = match_units(pdf_vals, 1 / r_in)[0]
return pdf_vals
def _disk_mass(self):
"""
Calculate the total disk mass by integrating sigma
"""
# Assign variables
r = self.r_bins
sig = self.sigma(r)
# Now integrate
m_disk = simps(2 * np.pi * r * sig, r)
m_units = sig.units * (r.units)**2
m_disk = match_units(m_disk, m_units)[0]
self.m_disk = m_disk
def _disk_mass(self):
"""
Calculate the total disk mass by integrating sigma
"""
# Assign variables
r = self.r_bins
sig = self.sigma(r)
# Now integrate
m_disk = simps(2*np.pi*r*sig, r)
m_units = sig.units * (r.units)**2
m_disk = match_units(m_disk, m_units)[0]
self.m_disk = m_disk
def T_adiabatic(self, r):
"""
Estimates the adiabatic temperature profile as a function of r
setup_interior must be run first
"""
# if not self.adiabatic_ready:
#
# # Try to setup the adiabatic profile
# self.setup_interior()
# p = self.p
# A = self.Tscale
# print A
#
# r = match_units(r, 'au')[0]
# sigma = self._parent.sigma(r)
# sigma.convert_units('Msol au**-2')
# sigma = strip_units(sigma)
# r = strip_units(r)
# return A * ((sigma**2)/(r**3))**p
b = 1.5
sigma = self._parent.sigma(r)
r_a = self.r_a
r = match_units(r, r_a.units)[0]
x = (r/r_a).in_units('1')
sigma_a = self.sigma_a
y = (sigma/sigma_a).in_units('1')
x = strip_units(x)
y = strip_units(y)
gamma = self._parent.settings.physical.gamma
p = (gamma-1.)/(gamma+1.)
T_a = self.T_a
T = T_a * (y**(2*p)) * (x**-b)
return T
# r = strip_units(match_units(r,'au')[0])
#
# return A * (r**2)
def sigout(r):
"""
Linear spline interpolation of sigma(r).
ARGUMENTS:
r - can be scalar, numpy array, or sim array
RETURNS:
sigma (surface density) evaluated at r
"""
# Try to convert r to the units used to make sigspline ('au')
r = match_units(r, 'au')[0]
return SimArray(sigspline(r), 'Msol au**-2')
def sigout(r):
"""
Linear spline interpolation of sigma(r).
ARGUMENTS:
r - can be scalar, numpy array, or sim array
RETURNS:
sigma (surface density) evaluated at r
"""
# Try to convert r to the units used to make sigspline ('au')
r = match_units(r, 'au')[0]
return SimArray(sigspline(r), 'Msol au**-2')
def sigma(snapshot, bins=100, cmFlag=True):
"""Calculates surface density vs r (relative to the center of mass)
Parameters
----------
snapshot : tipsy snapshot
bins : int, list, array...
(optional) Either the number of bins to use or the binedges to use
cmFlag : bool
(optional) Calculate relative to the center of mass
Returns
-------
sigma : SimArray
Surface density as a function of r
r_bins : SimArray
Radial bin edges
"""
if cmFlag:
# Begin by subtracting off the center of mass position
cm = (snapshot['mass'][:,None] * snapshot['pos']).sum()/(snapshot['mass'].sum())
snapshot['pos'] -= cm
r = snapshot.g['rxy']
# particle mass
m_gas = snapshot.gas['mass'][[0]]
N, r_bins = np.histogram(r, bins=bins)
r_bins = match_units(r_bins, r.units)[0]
r_center = (r_bins[1:] + r_bins[0:-1])/2
dr = r_bins[[1]] - r_bins[[0]]
sig = N*m_gas/(2*np.pi*r_center*dr)
if cmFlag:
# Add star position back to positions
snapshot['pos'] += cm
return sig, r_bins
def sigma(snapshot, bins=100, cmFlag=True):
"""Calculates surface density vs r (relative to the center of mass)
Parameters
----------
snapshot : tipsy snapshot
bins : int, list, array...
(optional) Either the number of bins to use or the binedges to use
cmFlag : bool
(optional) Calculate relative to the center of mass
Returns
-------
sigma : SimArray
Surface density as a function of r
r_bins : SimArray
Radial bin edges
"""
if cmFlag:
# Begin by subtracting off the center of mass position
cm = (snapshot['mass'][:,None] * snapshot['pos']).sum()/(snapshot['mass'].sum())
snapshot['pos'] -= cm
r = snapshot.g['rxy']
# particle mass
m_gas = snapshot.gas['mass'][[0]]
N, r_bins = np.histogram(r, bins=bins)
r_bins = match_units(r_bins, r.units)[0]
r_center = (r_bins[1:] + r_bins[0:-1])/2
dr = r_bins[[1]] - r_bins[[0]]
sig = N*m_gas/(2*np.pi*r_center*dr)
if cmFlag:
# Add star position back to positions
snapshot['pos'] += cm
return sig, r_bins
def finv_fcn(m_in):
"""
The inverse CDF for sigma(r).
input:
0 <= m_in < 1
returns:
r (radius), the inverse CDF evaluated at m_in
Uses a linear spline interpolation.
"""
r_out = finv(m_in)
r_out = match_units(r_out, r)[0]
return r_out
def finv_fcn(m_in):
"""
The inverse CDF for sigma(r).
input:
0 <= m_in < 1
returns:
r (radius), the inverse CDF evaluated at m_in
Uses a linear spline interpolation.
"""
r_out = finv(m_in)
r_out = match_units(r_out, r)[0]
return r_out
def MQWS(settings, T):
"""
Generates a surface density profile as the per method used in Mayer, Quinn,
Wadsley, and Stadel 2004
** ARGUMENTS **
NOTE: if units are not supplied, assumed units are AU, Msol
settings : IC settings
settings like those contained in an IC object (see ICgen_settings.py)
T : callable
A function to calculate temperature as a function of radius
** RETURNS **
r : SimArray
Radii at which sigma is calculated
sigma : SimArray
Surface density profile as a function of R
"""
# Q calculation parameters:
G = SimArray([1.0], 'G')
kB = SimArray([1.0], 'k')
# Load in settings
n_points = settings.sigma.n_points
rin = settings.sigma.rin
rout = settings.sigma.rout
rmax = settings.sigma.rmax
Qmin = settings.sigma.Qmin
m = settings.physical.m
Mstar = settings.physical.M
#m_disk = settings.sigma.m_disk
rin = match_units(pynbody.units.au, rin)[1]
rout = match_units(pynbody.units.au, rout)[1]
#m_disk = match_units(pynbody.units.Msol, m_disk)[1]
if rmax is None:
rmax = 2.5 * rout
else:
rmax = match_units(pynbody.units.au, rmax)[1]
r = np.linspace(0, rmax, n_points)
a = (rin / r).in_units('1')
b = (r / rout).in_units('1')
sigma = (np.exp(-a**2 - b**2) / r) * Mstar.units / r.units
# Calculate Q
Q = np.sqrt(Mstar * kB * T(r) / (G * m * r**3)) / (np.pi * sigma)
Q.convert_units('1')
sigma *= np.nanmin(Q) / Qmin
# Remove all nans
sigma[np.isnan(sigma)] = 0.0
return r, sigma
def powerlaw(settings, T=None):
"""
Generates a surface density profile according to a powerlaw sigma ~ r^p
with a smooth interior cutoff and smooth exterior exponential cutoff.
**ARGUMENTS**
settings : IC settings
settings like those contained in an IC object (see ICgen_settings.py)
T : callable function
Function that returns temperature of the disk as a function of radius
IF none, a powerlaw temperature is assumed
**RETURNS**
R : SimArray
Radii at which sigma is calculated
sigma : SimArray
Surface density profile as a function of R
"""
# Parse settings
Rd = settings.sigma.Rd
rin = settings.sigma.rin
rmax = settings.sigma.rmax
cutlength = settings.sigma.cutlength
Mstar = settings.physical.M
Qmin = settings.sigma.Qmin
n_points = settings.sigma.n_points
m = settings.physical.m
power = settings.sigma.power
gamma = settings.physical.gamma_cs()
if T is None:
# If no callable object to calculate Temperature(R) is provided,
# default to a powerlaw T ~ R^-q
T0 = SimArray([129.0], 'K') # Temperature at 1 AU
R0 = SimArray([1.0], 'au')
q = 0.59
def T(x):
return T0 * np.power((x / R0).in_units('1'), -q)
Rd = match_units(pynbody.units.au, Rd)[1]
Mstar = match_units(pynbody.units.Msol, Mstar)[1]
# Molecular weight
m = match_units(m, pynbody.units.m_p)[0]
# Maximum R to calculate sigma at (needed for the exponential cutoff region)
Rmax = rmax * Rd
# Q calculation parameters:
G = SimArray([1.0], 'G')
kB = SimArray([1.0], 'k')
# Initialize stuff
A = SimArray(1.0, 'Msol') / (2 * np.pi * np.power(Rd, 2))
# dflemin3 Nov. 4, 2015
# Made units more explicit via SimArrays
r_units = Rd.units
R = SimArray(np.linspace(0, Rmax, n_points), r_units)
r = R / Rd
# Calculate sigma
# Powerlaw
#dflemin3 edit 06/10/2015: Try powerlaw of the form sigma ~ r^power
sigma = A * np.power(r, power)
sigma[0] = 0.0
# Exterior cutoff
sigma[r > 1] *= np.exp(-(r[r > 1] - 1)**2 / (2 * cutlength**2))
# Interior cutoff
sigma[r < rin] *= smoothstep(r[r < rin], degree=21, rescale=True)
# Calculate Q
Q = np.sqrt(Mstar * gamma * kB * T(R) / (G * m * R**3)) / (np.pi * sigma)
Q.convert_units('1')
# Rescale sigma to meet the minimum Q requirement
sigma *= Q.min() / Qmin
# Calculate Q
Q = np.sqrt(Mstar * gamma * kB * T(R) / (G * m * R**3)) / (np.pi * sigma)
Q.convert_units('1')
return R, sigma
def Q(snapshot, molecular_mass = 2.0, bins=100, use_velocity=False, \
use_omega=True):
"""Calculates the Toomre Q as a function of r, assuming radial temperature
profile and kappa ~= omega
Parameters
----------
snapshot : tipsy snapshot
molecular_mass : float
Mean molecular mass (for sound speed). Default = 2.0
bins : int or array
Either the number of bins or the bin edges
use_velocity : Bool
Determines whether to use the particles' velocities to calculate orbital
velocity. Useful if the circular orbital velocities are set in the
snapshot.
use_omega : Bool
Default=True. Use omega as a proxy for kappa to reduce noise
Returns
-------
Q : array
Toomre Q as a function of r
r_edges : array
Radial bin edges
"""
# Physical constants
kB = SimArray([1.0],'k')
G = SimArray([1.0],'G')
# Calculate surface density
sig, r_edges = sigma(snapshot, bins)
# Calculate sound speed
m = match_units(molecular_mass,'m_p')[0]
c_s_all = np.sqrt(kB*snapshot.g['temp']/m)
# Bin/average sound speed
dummy, c_s, dummy2 = binned_mean(snapshot.g['rxy'], c_s_all, binedges=r_edges)
if use_omega:
# Calculate keplerian angular velocity (as a proxy for the epicyclic
# frequency, which is a noisy calculation)
if use_velocity:
# Calculate directly from particle's velocity
dummy, omega, dummy2 = binned_mean(snapshot.g['rxy'], \
snapshot.g['vt']/snapshot.g['rxy'], binedges=r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
omega = p['omega']
kappa_calc = omega
else:
if use_velocity:
# Calculate directly from particle's velocities
kappa_calc, dummy = kappa(snapshot, r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
kappa_calc = p['kappa']
return (kappa_calc*c_s/(np.pi*G*sig)).in_units('1'), r_edges
def binned_mean(x, y, bins=10, nbins=None, binedges = None, weights=None,\
weighted_bins=False, ret_bin_edges=False, binind=None):
"""
Bins y according to x and takes the average for each bin.
RETURNS a tuple of (bin_centers, y_mean, y_err) if ret_bin_edges=False
else, Returns (bin_edges, y_mean, y_err)
Parameters
----------
x, y : array-like
Bin and average y according to x
bins : int or arraylike
Either number of bins or an array of binedges
nbins : int
(optional) For backward compatibility, prefer using bins
binedges : array-like
(optional) For backward compatibility, prefer using bins
weights : array-like
Weights to use for data points. Assume weights=1 (uniform)
weighted_bins : bool
If true, the bin centers will be calculated as weighted centers
ret_bin_edges : bool
Return bin centers instead of edges. Default = False
binind : list of arrays
An optional list of arrays which specify which indices of x, y belong
to which bin. This can be used for speed. when using a pynbody profile,
pynbody will generate such a list:
>>> p = pynbody.analysis.profile.Profile(f)
>>> p.binind # binind
For the returned bins to be consistent, the user should supply the used
binedges.
"""
x = np.asanyarray(x)
y = np.asanyarray(y)
if (isinstance(bins, int)) and (nbins is None):
nbins = bins
elif (hasattr(bins, '__iter__')) and (binedges is None):
binedges = bins
if binedges is not None:
nbins = len(binedges) - 1
else:
binedges = np.linspace(x.min(), (1 + np.spacing(2)) * x.max(),
nbins + 1)
if weights is None:
weights = np.ones(x.shape)
weights = strip_units(weights)
# Pre-factor for weighted STD:
A = 1 / (1 - (weights**2).sum())
# Initialize
y_mean = np.zeros(nbins)
y_std = np.zeros(nbins)
if binind is None:
# Find the index bins for each data point
ind = np.digitize(x, binedges) - 1
N = np.histogram(x, binedges)[0]
else:
N = np.array([ind.sum() for ind in binind])
# Ignore nans
nan_ind = np.isnan(y)
# Initialize bin_centers (try to retain units)
bin_centers = 0.0 * binedges[1:]
for i in range(nbins):
if binind is None:
#Indices to use
mask = (ind == i) & (~nan_ind)
# Set up the weighting
w = weights[mask].copy()
yvals = y[mask]
xvals = x[mask]
else:
select_ind = binind[i]
w = weights[select_ind]
yvals = y[select_ind]
xvals = x[select_ind]
w /= w.sum()
A = 1 / (1 - (w**2).sum())
y_mean[i] = (w * yvals).sum()
var = A * (w * (yvals - y_mean[i])**2).sum()
y_std[i] = np.sqrt(var)
if weighted_bins:
# Center of mass of x positions
bin_centers[i] = (w * xvals).sum()
y_mean = match_units(y_mean, y)[0]
y_err = y_std / np.sqrt(N)
y_err = match_units(y_err, y)[0]
y_mean[N == 0] = np.nan
y_err[N == 0] = np.nan
if not weighted_bins:
bin_centers = (binedges[0:-1] + binedges[1:]) / 2.0
binedges = match_units(binedges, x)[0]
bin_centers = match_units(bin_centers, x)[0]
else:
bin_centers[N == 0] = np.nan
if ret_bin_edges:
return binedges, y_mean, y_err
else:
return bin_centers, y_mean, y_err
def meshspline(x1, y1):
"""
Callable interpolation function, interoplates the value of z at
points (x1, y1)
Parameters
----------
x1, y1 : array
x and y points to evaluate z at. Must be the same shape. ie,
x1[i], y1[i] define a point (x, y).
If @x1 or @y1 have no units, they are assumed to have the units of
the nodes used to make the interpolator. Otherwise they are
converted to the proper units
Returns
-------
z(x1, y1) : array
z evaluated at @x1, @y1
"""
# Handle units
x1 = strip_units(match_units(x1, units[0])[0])
y1 = strip_units(match_units(y1, units[1])[0])
# Setup x and y points to estimate z at
x1 = np.asarray(x1).copy()
y1 = np.asarray(y1)
if len(x1.shape) < 1:
x1 = x1[None]
if len(y1.shape) < 1:
y1 = y1[None]
# Flatten arrays
shape = x1.shape
nElements = np.prod(shape)
x1 = np.reshape(x1, [nElements])
y1 = np.reshape(y1, [nElements])
# Deal with xs outside of boundaries
x1[x1 < xmin] = xmin
x1[x1 > xmax] = xmax
# Find bin indices
ind = np.digitize(x1, xedges) - 1
ind[ind < 0] = 0
ind[ind > nbins - 1] = nbins - 1
# Get bin info for every point
xlo = xedges[ind]
xhi = xedges[ind + 1]
dx = binsize[ind]
# Get weights for bins (distance from bin edges)
wlo = (xhi - x1) / dx
whi = (x1 - xlo) / dx
# Get function values at left and right xedges
flo = np.zeros(x1.shape)
fhi = np.zeros(x1.shape)
for i in range(nbins):
# Select everything in bin i
mask = (ind == i)
if np.any(mask):
# Retrieve function values
flo[mask] = splines[i](y1[mask])
fhi[mask] = splines[i + 1](y1[mask])
# Take a weighted average of the function values at left and right
# bin edges
fout = wlo * flo + whi * fhi
# Unflatten fout:
fout = np.reshape(fout, shape)
return SimArray(fout, units[2])
def snapshot_gen(ICobj):
"""
Generates a tipsy snapshot from the initial conditions object ICobj.
Returns snapshot, param
snapshot: tipsy snapshot
param: dictionary containing info for a .param file
Note: Code has been edited (dflemin3) such that now it returns a snapshot for a circumbinary disk
where initial conditions generated assuming star at origin of mass M. After gas initialized, replaced
star at origin with binary system who's center of mass lies at the origin and who's mass m1 +m2 = M
"""
print 'Generating snapshot...'
# Constants
G = SimArray(1.0,'G')
# ------------------------------------
# Load in things from ICobj
# ------------------------------------
print 'Accessing data from ICs'
settings = ICobj.settings
# snapshot file name
snapshotName = settings.filenames.snapshotName
paramName = settings.filenames.paramName
# particle positions
r = ICobj.pos.r
xyz = ICobj.pos.xyz
# Number of particles
nParticles = ICobj.pos.nParticles
# molecular mass
m = settings.physical.m
# star mass
m_star = settings.physical.M.copy()
# disk mass
m_disk = ICobj.sigma.m_disk.copy()
m_disk = match_units(m_disk, m_star)[0]
# mass of the gas particles
m_particles = m_disk / float(nParticles)
# re-scale the particles (allows making of low-mass disk)
m_particles *= settings.snapshot.mScale
# -------------------------------------------------
# Assign output
# -------------------------------------------------
print 'Assigning data to snapshot'
# Get units all set up
m_unit = m_star.units
pos_unit = r.units
if xyz.units != r.units:
xyz.convert_units(pos_unit)
# time units are sqrt(L^3/GM)
t_unit = np.sqrt((pos_unit**3)*np.power((G*m_unit), -1)).units
# velocity units are L/t
v_unit = (pos_unit/t_unit).ratio('km s**-1')
# Make it a unit, save value for future conversion
v_unit_vel = v_unit
#Ensure v_unit_vel is the same as what I assume it is.
assert(np.fabs(AddBinary.VEL_UNIT-v_unit_vel)<AddBinary.SMALL),"VEL_UNIT not equal to ChaNGa unit! Why??"
v_unit = pynbody.units.Unit('{0} km s**-1'.format(v_unit))
# Other settings
metals = settings.snapshot.metals
star_metals = metals
# Generate snapshot
# Note that empty pos, vel, and mass arrays are created in the snapshot
snapshot = pynbody.new(star=1,gas=nParticles)
snapshot['vel'].units = v_unit
snapshot['eps'] = 0.01*SimArray(np.ones(nParticles+1, dtype=np.float32), pos_unit)
snapshot['metals'] = SimArray(np.zeros(nParticles+1, dtype=np.float32))
snapshot['rho'] = SimArray(np.zeros(nParticles+1, dtype=np.float32))
snapshot.gas['pos'] = xyz
snapshot.gas['temp'] = ICobj.T(r)
snapshot.gas['mass'] = m_particles
snapshot.gas['metals'] = metals
snapshot.star['pos'] = SimArray([[ 0., 0., 0.]],pos_unit)
snapshot.star['vel'] = SimArray([[ 0., 0., 0.]], v_unit)
snapshot.star['mass'] = m_star
snapshot.star['metals'] = SimArray(star_metals)
# Estimate the star's softening length as the closest particle distance
#snapshot.star['eps'] = r.min()
# Make param file
param = make_param(snapshot, snapshotName)
param['dMeanMolWeight'] = m
gc.collect()
# CALCULATE VELOCITY USING calc_velocity.py. This also estimates the
# gravitational softening length eps
print 'Calculating circular velocity'
preset = settings.changa_run.preset
max_particles = global_settings['misc']['max_particles']
calc_velocity.v_xy(snapshot, param, changa_preset=preset, max_particles=max_particles)
gc.collect()
# -------------------------------------------------
# Estimate time step for changa to use
# -------------------------------------------------
# Save param file
configsave(param, paramName, 'param')
# Save snapshot
snapshot.write(filename=snapshotName, fmt=pynbody.tipsy.TipsySnap)
# est dDelta
dDelta = ICgen_utils.est_time_step(paramName, preset)
param['dDelta'] = dDelta
# -------------------------------------------------
# Create director file
# -------------------------------------------------
# largest radius to plot
r_director = float(0.9 * r.max())
# Maximum surface density
sigma_min = float(ICobj.sigma(r_director))
# surface density at largest radius
sigma_max = float(ICobj.sigma.input_dict['sigma'].max())
# Create director dict
director = make_director(sigma_min, sigma_max, r_director, filename=param['achOutName'])
## Save .director file
#configsave(director, directorName, 'director')
#Now that velocities and everything are all initialized for gas particles, create new snapshot to return in which
#single star particle is replaced by 2, same units as above
snapshotBinary = pynbody.new(star=2,gas=nParticles)
snapshotBinary['eps'] = 0.01*SimArray(np.ones(nParticles+2, dtype=np.float32), pos_unit)
snapshotBinary['metals'] = SimArray(np.zeros(nParticles+2, dtype=np.float32))
snapshotBinary['vel'].units = v_unit
snapshotBinary['pos'].units = pos_unit
snapshotBinary['mass'].units = snapshot['mass'].units
snapshotBinary['rho'] = SimArray(np.zeros(nParticles+2, dtype=np.float32))
#Assign gas particles with calculated/given values from above
snapshotBinary.gas['pos'] = snapshot.gas['pos']
snapshotBinary.gas['vel'] = snapshot.gas['vel']
snapshotBinary.gas['temp'] = snapshot.gas['temp']
snapshotBinary.gas['rho'] = snapshot.gas['rho']
snapshotBinary.gas['eps'] = snapshot.gas['eps']
snapshotBinary.gas['mass'] = snapshot.gas['mass']
snapshotBinary.gas['metals'] = snapshot.gas['metals']
#Load Binary system obj to initialize system
binsys = ICobj.settings.physical.binsys
x1,x2,v1,v2 = binsys.generateICs()
#Put velocity in sim units
#!!! Note: v_unit_vel will always be 29.785598165 km/s when m_unit = Msol and r_unit = 1 AU in kpc!!!
#conv = v_unit_vel #km/s in sim units
#v1 /= conv
#v2 /= conv
#Assign position, velocity assuming CCW orbit
snapshotBinary.star[0]['pos'] = SimArray(x1,pos_unit)
snapshotBinary.star[0]['vel'] = SimArray(v1,v_unit)
snapshotBinary.star[1]['pos'] = SimArray(x2,pos_unit)
snapshotBinary.star[1]['vel'] = SimArray(v2,v_unit)
#Set stellar masses
#Set Mass units
#Create simArray for mass, convert units to simulation mass units
priMass = SimArray(binsys.m1,m_unit)
secMass = SimArray(binsys.m2,m_unit)
snapshotBinary.star[0]['mass'] = priMass
snapshotBinary.star[1]['mass'] = secMass
snapshotBinary.star['metals'] = SimArray(star_metals)
#Estimate stars' softening length as fraction of distance to COM
d = np.sqrt(AddBinary.dotProduct(x1-x2,x1-x2))
snapshotBinary.star[0]['eps'] = SimArray(math.fabs(d)/4.0,pos_unit)
snapshotBinary.star[1]['eps'] = SimArray(math.fabs(d)/4.0,pos_unit)
print 'Wrapping up'
# Now set the star particle's tform to a negative number. This allows
# UW ChaNGa treat it as a sink particle.
snapshotBinary.star['tform'] = -1.0
#Set Sink Radius to be mass-weighted average of Roche lobes of two stars
r1 = AddBinary.calcRocheLobe(binsys.m1/binsys.m2,binsys.a)
r2 = AddBinary.calcRocheLobe(binsys.m2/binsys.m1,binsys.a)
p = strip_units(binsys.m1/(binsys.m1 + binsys.m2))
r_sink = (r1*p) + (r2*(1.0-p))
param['dSinkBoundOrbitRadius'] = r_sink
param['dSinkRadius'] = r_sink
param['dSinkMassMin'] = 0.9 * strip_units(secMass)
param['bDoSinks'] = 1
return snapshotBinary, param, director
def meshspline(x1, y1):
"""
Callable interpolation function, interoplates the value of z at
points (x1, y1)
Parameters
----------
x1, y1 : array
x and y points to evaluate z at. Must be the same shape. ie,
x1[i], y1[i] define a point (x, y).
If @x1 or @y1 have no units, they are assumed to have the units of
the nodes used to make the interpolator. Otherwise they are
converted to the proper units
Returns
-------
z(x1, y1) : array
z evaluated at @x1, @y1
"""
# Handle units
x1 = strip_units(match_units(x1, units[0])[0])
y1 = strip_units(match_units(y1, units[1])[0])
# Setup x and y points to estimate z at
x1 = np.asarray(x1).copy()
y1 = np.asarray(y1)
if len(x1.shape) < 1:
x1 = x1[None]
if len(y1.shape) < 1:
y1 = y1[None]
# Flatten arrays
shape = x1.shape
nElements = np.prod(shape)
x1 = np.reshape(x1, [nElements])
y1 = np.reshape(y1, [nElements])
# Deal with xs outside of boundaries
x1[x1 < xmin] = xmin
x1[x1 > xmax] = xmax
# Find bin indices
ind = np.digitize(x1, xedges) - 1
ind[ind < 0] = 0
ind[ind > nbins - 1] = nbins - 1
# Get bin info for every point
xlo = xedges[ind]
xhi = xedges[ind + 1]
dx = binsize[ind]
# Get weights for bins (distance from bin edges)
wlo = (xhi - x1) / dx
whi = (x1 - xlo) / dx
# Get function values at left and right xedges
flo = np.zeros(x1.shape)
fhi = np.zeros(x1.shape)
for i in range(nbins):
# Select everything in bin i
mask = ind == i
if np.any(mask):
# Retrieve function values
flo[mask] = splines[i](y1[mask])
fhi[mask] = splines[i + 1](y1[mask])
# Take a weighted average of the function values at left and right
# bin edges
fout = wlo * flo + whi * fhi
# Unflatten fout:
fout = np.reshape(fout, shape)
return SimArray(fout, units[2])
def MQWS(settings, T):
"""
Generates a surface density profile as the per method used in Mayer, Quinn,
Wadsley, and Stadel 2004
** ARGUMENTS **
NOTE: if units are not supplied, assumed units are AU, Msol
settings : IC settings
settings like those contained in an IC object (see ICgen_settings.py)
T : callable
A function to calculate temperature as a function of radius
** RETURNS **
r : SimArray
Radii at which sigma is calculated
sigma : SimArray
Surface density profile as a function of R
"""
# Q calculation parameters:
G = SimArray([1.0],'G')
kB = SimArray([1.0],'k')
# Load in settings
n_points = settings.sigma.n_points
rin = settings.sigma.rin
rout = settings.sigma.rout
rmax = settings.sigma.rmax
Qmin = settings.sigma.Qmin
m = settings.physical.m
Mstar = settings.physical.M
#m_disk = settings.sigma.m_disk
rin = match_units(pynbody.units.au, rin)[1]
rout = match_units(pynbody.units.au, rout)[1]
#m_disk = match_units(pynbody.units.Msol, m_disk)[1]
if rmax is None:
rmax = 2.5 * rout
else:
rmax = match_units(pynbody.units.au, rmax)[1]
r = np.linspace(0, rmax, n_points)
a = (rin/r).in_units('1')
b = (r/rout).in_units('1')
sigma = (np.exp(-a**2 - b**2)/r) * Mstar.units/r.units
# Calculate Q
Q = np.sqrt(Mstar*kB*T(r)/(G*m*r**3))/(np.pi*sigma)
Q.convert_units('1')
sigma *= np.nanmin(Q)/Qmin
# Remove all nans
sigma[np.isnan(sigma)] = 0.0
return r, sigma
def snapshot_gen(ICobj):
"""
Generates a tipsy snapshot from the initial conditions object ICobj.
Returns snapshot, param
snapshot: tipsy snapshot
param: dictionary containing info for a .param file
Note: Code has been edited (dflemin3) such that now it returns a snapshot for a circumbinary disk
where initial conditions generated assuming star at origin of mass M. After gas initialized, replaced
star at origin with binary system who's center of mass lies at the origin and who's mass m1 +m2 = M
"""
print "Generating snapshot..."
# Constants
G = SimArray(1.0, "G")
# ------------------------------------
# Load in things from ICobj
# ------------------------------------
print "Accessing data from ICs"
settings = ICobj.settings
# snapshot file name
snapshotName = settings.filenames.snapshotName
paramName = settings.filenames.paramName
# Load user supplied snapshot (assumed to be in cwd)
path = "/astro/store/scratch/tmp/dflemin3/nbodyshare/9au-Q1.05-129K/"
snapshot = pynbody.load(path + snapshotName)
# particle positions
r = snapshot.gas["r"]
xyz = snapshot.gas["pos"]
# Number of particles
nParticles = len(snapshot.gas)
# molecular mass
m = settings.physical.m
# Pull star mass from user-supplied snapshot
ICobj.settings.physical.M = snapshot.star["mass"] # Total stellar mass in solar masses
m_star = ICobj.settings.physical.M
# disk mass
m_disk = np.sum(snapshot.gas["mass"])
m_disk = match_units(m_disk, m_star)[0]
# mass of the gas particles
m_particles = m_disk / float(nParticles)
# re-scale the particles (allows making of low-mass disk)
m_particles *= settings.snapshot.mScale
# -------------------------------------------------
# Assign output
# -------------------------------------------------
print "Assigning data to snapshot"
# Get units all set up
m_unit = m_star.units
pos_unit = r.units
if xyz.units != r.units:
xyz.convert_units(pos_unit)
# time units are sqrt(L^3/GM)
t_unit = np.sqrt((pos_unit ** 3) * np.power((G * m_unit), -1)).units
# velocity units are L/t
v_unit = (pos_unit / t_unit).ratio("km s**-1")
# Make it a unit, save value for future conversion
v_unit_vel = v_unit
# Ensure v_unit_vel is the same as what I assume it is.
assert np.fabs(AddBinary.VEL_UNIT - v_unit_vel) < AddBinary.SMALL, "VEL_UNIT not equal to ChaNGa unit! Why??"
v_unit = pynbody.units.Unit("{0} km s**-1".format(v_unit))
# Other settings
metals = settings.snapshot.metals
star_metals = metals
# Estimate the star's softening length as the closest particle distance
eps = r.min()
# Make param file
param = make_param(snapshot, snapshotName)
param["dMeanMolWeight"] = m
gc.collect()
# CALCULATE VELOCITY USING calc_velocity.py. This also estimates the
# gravitational softening length eps
preset = settings.changa_run.preset
# -------------------------------------------------
# Estimate time step for changa to use
# -------------------------------------------------
# Save param file
configsave(param, paramName, "param")
# Save snapshot
snapshot.write(filename=snapshotName, fmt=pynbody.tipsy.TipsySnap)
# est dDelta
dDelta = ICgen_utils.est_time_step(paramName, preset)
param["dDelta"] = dDelta
# -------------------------------------------------
# Create director file
# -------------------------------------------------
# largest radius to plot
r_director = float(0.9 * r.max())
# Maximum surface density
sigma_min = float(ICobj.sigma(r_director))
# surface density at largest radius
sigma_max = float(ICobj.sigma.input_dict["sigma"].max())
# Create director dict
director = make_director(sigma_min, sigma_max, r_director, filename=param["achOutName"])
## Save .director file
# configsave(director, directorName, 'director')
"""
Now that the gas disk is initializes around the primary (M=m1), add in the
second star as specified by the user.
"""
# Now that velocities and everything are all initialized for gas particles, create new snapshot to return in which
# single star particle is replaced by 2, same units as above
snapshotBinary = pynbody.new(star=2, gas=nParticles)
snapshotBinary["eps"] = 0.01 * SimArray(np.ones(nParticles + 2, dtype=np.float32), pos_unit)
snapshotBinary["metals"] = SimArray(np.zeros(nParticles + 2, dtype=np.float32))
snapshotBinary["vel"].units = v_unit
snapshotBinary["pos"].units = pos_unit
snapshotBinary["mass"].units = snapshot["mass"].units
snapshotBinary["rho"] = SimArray(np.zeros(nParticles + 2, dtype=np.float32))
# Assign gas particles with calculated/given values from above
snapshotBinary.gas["pos"] = snapshot.gas["pos"]
snapshotBinary.gas["vel"] = snapshot.gas["vel"]
snapshotBinary.gas["temp"] = snapshot.gas["temp"]
snapshotBinary.gas["rho"] = snapshot.gas["rho"]
snapshotBinary.gas["eps"] = snapshot.gas["eps"]
snapshotBinary.gas["mass"] = snapshot.gas["mass"]
snapshotBinary.gas["metals"] = snapshot.gas["metals"]
# Load Binary system obj to initialize system
binsys = ICobj.settings.physical.binsys
m_disk = strip_units(np.sum(snapshotBinary.gas["mass"]))
binsys.m1 = strip_units(m_star)
binsys.m1 = binsys.m1 + m_disk
# Recompute cartesian coords considering primary as m1+m_disk
binsys.computeCartesian()
x1, x2, v1, v2 = binsys.generateICs()
# Assign position, velocity assuming CCW orbit
snapshotBinary.star[0]["pos"] = SimArray(x1, pos_unit)
snapshotBinary.star[0]["vel"] = SimArray(v1, v_unit)
snapshotBinary.star[1]["pos"] = SimArray(x2, pos_unit)
snapshotBinary.star[1]["vel"] = SimArray(v2, v_unit)
"""
We have the binary positions about their center of mass, (0,0,0), so
shift the position, velocity of the gas disk to be around the primary.
"""
snapshotBinary.gas["pos"] += snapshotBinary.star[0]["pos"]
snapshotBinary.gas["vel"] += snapshotBinary.star[0]["vel"]
# Set stellar masses: Create simArray for mass, convert units to simulation mass units
snapshotBinary.star[0]["mass"] = SimArray(binsys.m1 - m_disk, m_unit)
snapshotBinary.star[1]["mass"] = SimArray(binsys.m2, m_unit)
snapshotBinary.star["metals"] = SimArray(star_metals)
print "Wrapping up"
# Now set the star particle's tform to a negative number. This allows
# UW ChaNGa treat it as a sink particle.
snapshotBinary.star["tform"] = -1.0
# Set sink radius, stellar smoothing length as fraction of distance
# from primary to inner edge of the disk
r_sink = eps
snapshotBinary.star[0]["eps"] = SimArray(r_sink / 2.0, pos_unit)
snapshotBinary.star[1]["eps"] = SimArray(r_sink / 2.0, pos_unit)
param["dSinkBoundOrbitRadius"] = r_sink
param["dSinkRadius"] = r_sink
param["dSinkMassMin"] = 0.9 * binsys.m2
param["bDoSinks"] = 1
return snapshotBinary, param, director
def powerlaw(settings, T = None):
"""
Generates a surface density profile according to a powerlaw sigma ~ r^p
with a smooth interior cutoff and smooth exterior exponential cutoff.
**ARGUMENTS**
settings : IC settings
settings like those contained in an IC object (see ICgen_settings.py)
T : callable function
Function that returns temperature of the disk as a function of radius
IF none, a powerlaw temperature is assumed
**RETURNS**
R : SimArray
Radii at which sigma is calculated
sigma : SimArray
Surface density profile as a function of R
"""
# Parse settings
Rd = settings.sigma.Rd
rin = settings.sigma.rin
rmax = settings.sigma.rmax
cutlength = settings.sigma.cutlength
Mstar = settings.physical.M
Qmin = settings.sigma.Qmin
n_points = settings.sigma.n_points
m = settings.physical.m
power = settings.sigma.power
if T is None:
# If no callable object to calculate Temperature(R) is provided,
# default to a powerlaw T ~ R^-q
T0 = SimArray([129.0],'K') # Temperature at 1 AU
R0 = SimArray([1.0],'au')
q = 0.59
def T(x):
return T0 * np.power((x/R0).in_units('1'),-q)
Rd = match_units(pynbody.units.au, Rd)[1]
Mstar = match_units(pynbody.units.Msol, Mstar)[1]
# Molecular weight
m = match_units(m, pynbody.units.m_p)[0]
# Maximum R to calculate sigma at (needed for the exponential cutoff region)
Rmax = rmax*Rd
# Q calculation parameters:
G = SimArray([1.0],'G')
kB = SimArray([1.0],'k')
# Initialize stuff
A = SimArray(1.0,'Msol')/(2*np.pi*np.power(Rd,2))
#R = np.linspace(0,Rmax,n_points)
#r = np.array((R/Rd).in_units('1'))
# dflemin3 Nov. 4, 2015
# Made units more explicit via SimArrays
r_units = Rd.units
R = SimArray(np.linspace(0,Rmax,n_points),r_units)
r = R/Rd
# Calculate sigma
# Powerlaw
#sigma = A/r
#dflemin3 edit 06/10/2015: Try powerlaw of the form sigma ~ r^power
sigma = A*np.power(r,power)
sigma[0] = 0.0
# Exterior cutoff
sigma[r>1] *= np.exp(-(r[r>1] - 1)**2 / (2*cutlength**2))
# Interior cutoff
sigma[r<rin] *= smoothstep(r[r<rin],degree=21,rescale=True)
# Calculate Q
Q = np.sqrt(Mstar*kB*T(R)/(G*m*R**3))/(np.pi*sigma)
Q.convert_units('1')
# Rescale sigma to meet the minimum Q requirement
sigma *= Q.min()/Qmin
# Calculate Q
Q = np.sqrt(Mstar*kB*T(R)/(G*m*R**3))/(np.pi*sigma)
Q.convert_units('1')
return R, sigma
def snapshot_gen(ICobj):
"""
Generates a tipsy snapshot from the initial conditions object ICobj.
Returns snapshot, param
snapshot: tipsy snapshot
param: dictionary containing info for a .param file
Note: Code has been edited (dflemin3) such that now it returns a snapshot for a circumbinary disk
where initial conditions generated assuming star at origin of mass M. After gas initialized, replaced
star at origin with binary system who's center of mass lies at the origin and who's mass m1 +m2 = M
"""
print 'Generating snapshot...'
# Constants
G = SimArray(1.0, 'G')
# ------------------------------------
# Load in things from ICobj
# ------------------------------------
print 'Accessing data from ICs'
settings = ICobj.settings
# snapshot file name
snapshotName = settings.filenames.snapshotName
paramName = settings.filenames.paramName
#Load user supplied snapshot (assumed to be in cwd)
path = "/astro/store/scratch/tmp/dflemin3/nbodyshare/9au-Q1.05-129K/"
snapshot = pynbody.load(path + snapshotName)
# particle positions
r = snapshot.gas['r']
xyz = snapshot.gas['pos']
# Number of particles
nParticles = len(snapshot.gas)
# molecular mass
m = settings.physical.m
#Pull star mass from user-supplied snapshot
ICobj.settings.physical.M = snapshot.star[
'mass'] #Total stellar mass in solar masses
m_star = ICobj.settings.physical.M
# disk mass
m_disk = np.sum(snapshot.gas['mass'])
m_disk = match_units(m_disk, m_star)[0]
# mass of the gas particles
m_particles = m_disk / float(nParticles)
# re-scale the particles (allows making of low-mass disk)
m_particles *= settings.snapshot.mScale
# -------------------------------------------------
# Assign output
# -------------------------------------------------
print 'Assigning data to snapshot'
# Get units all set up
m_unit = m_star.units
pos_unit = r.units
if xyz.units != r.units:
xyz.convert_units(pos_unit)
# time units are sqrt(L^3/GM)
t_unit = np.sqrt((pos_unit**3) * np.power((G * m_unit), -1)).units
# velocity units are L/t
v_unit = (pos_unit / t_unit).ratio('km s**-1')
# Make it a unit, save value for future conversion
v_unit_vel = v_unit
#Ensure v_unit_vel is the same as what I assume it is.
assert (np.fabs(AddBinary.VEL_UNIT - v_unit_vel) <
AddBinary.SMALL), "VEL_UNIT not equal to ChaNGa unit! Why??"
v_unit = pynbody.units.Unit('{0} km s**-1'.format(v_unit))
# Other settings
metals = settings.snapshot.metals
star_metals = metals
# Estimate the star's softening length as the closest particle distance
eps = r.min()
# Make param file
param = make_param(snapshot, snapshotName)
param['dMeanMolWeight'] = m
gc.collect()
# CALCULATE VELOCITY USING calc_velocity.py. This also estimates the
# gravitational softening length eps
preset = settings.changa_run.preset
# -------------------------------------------------
# Estimate time step for changa to use
# -------------------------------------------------
# Save param file
configsave(param, paramName, 'param')
# Save snapshot
snapshot.write(filename=snapshotName, fmt=pynbody.tipsy.TipsySnap)
# est dDelta
dDelta = ICgen_utils.est_time_step(paramName, preset)
param['dDelta'] = dDelta
# -------------------------------------------------
# Create director file
# -------------------------------------------------
# largest radius to plot
r_director = float(0.9 * r.max())
# Maximum surface density
sigma_min = float(ICobj.sigma(r_director))
# surface density at largest radius
sigma_max = float(ICobj.sigma.input_dict['sigma'].max())
# Create director dict
director = make_director(sigma_min,
sigma_max,
r_director,
filename=param['achOutName'])
## Save .director file
#configsave(director, directorName, 'director')
"""
Now that the gas disk is initializes around the primary (M=m1), add in the
second star as specified by the user.
"""
#Now that velocities and everything are all initialized for gas particles, create new snapshot to return in which
#single star particle is replaced by 2, same units as above
snapshotBinary = pynbody.new(star=2, gas=nParticles)
snapshotBinary['eps'] = 0.01 * SimArray(
np.ones(nParticles + 2, dtype=np.float32), pos_unit)
snapshotBinary['metals'] = SimArray(
np.zeros(nParticles + 2, dtype=np.float32))
snapshotBinary['vel'].units = v_unit
snapshotBinary['pos'].units = pos_unit
snapshotBinary['mass'].units = snapshot['mass'].units
snapshotBinary['rho'] = SimArray(np.zeros(nParticles + 2,
dtype=np.float32))
#Assign gas particles with calculated/given values from above
snapshotBinary.gas['pos'] = snapshot.gas['pos']
snapshotBinary.gas['vel'] = snapshot.gas['vel']
snapshotBinary.gas['temp'] = snapshot.gas['temp']
snapshotBinary.gas['rho'] = snapshot.gas['rho']
snapshotBinary.gas['eps'] = snapshot.gas['eps']
snapshotBinary.gas['mass'] = snapshot.gas['mass']
snapshotBinary.gas['metals'] = snapshot.gas['metals']
#Load Binary system obj to initialize system
binsys = ICobj.settings.physical.binsys
m_disk = strip_units(np.sum(snapshotBinary.gas['mass']))
binsys.m1 = strip_units(m_star)
binsys.m1 = binsys.m1 + m_disk
#Recompute cartesian coords considering primary as m1+m_disk
binsys.computeCartesian()
x1, x2, v1, v2 = binsys.generateICs()
#Assign position, velocity assuming CCW orbit
snapshotBinary.star[0]['pos'] = SimArray(x1, pos_unit)
snapshotBinary.star[0]['vel'] = SimArray(v1, v_unit)
snapshotBinary.star[1]['pos'] = SimArray(x2, pos_unit)
snapshotBinary.star[1]['vel'] = SimArray(v2, v_unit)
"""
We have the binary positions about their center of mass, (0,0,0), so
shift the position, velocity of the gas disk to be around the primary.
"""
snapshotBinary.gas['pos'] += snapshotBinary.star[0]['pos']
snapshotBinary.gas['vel'] += snapshotBinary.star[0]['vel']
#Set stellar masses: Create simArray for mass, convert units to simulation mass units
snapshotBinary.star[0]['mass'] = SimArray(binsys.m1 - m_disk, m_unit)
snapshotBinary.star[1]['mass'] = SimArray(binsys.m2, m_unit)
snapshotBinary.star['metals'] = SimArray(star_metals)
print 'Wrapping up'
# Now set the star particle's tform to a negative number. This allows
# UW ChaNGa treat it as a sink particle.
snapshotBinary.star['tform'] = -1.0
#Set sink radius, stellar smoothing length as fraction of distance
#from primary to inner edge of the disk
r_sink = eps
snapshotBinary.star[0]['eps'] = SimArray(r_sink / 2.0, pos_unit)
snapshotBinary.star[1]['eps'] = SimArray(r_sink / 2.0, pos_unit)
param['dSinkBoundOrbitRadius'] = r_sink
param['dSinkRadius'] = r_sink
param['dSinkMassMin'] = 0.9 * binsys.m2
param['bDoSinks'] = 1
return snapshotBinary, param, director
def snapshot_gen(ICobj):
"""
Generates a tipsy snapshot from the initial conditions object ICobj.
Returns snapshot, param
snapshot: tipsy snapshot
param: dictionary containing info for a .param file
"""
print 'Generating snapshot...'
# Constants
G = SimArray(1.0,'G')
# ------------------------------------
# Load in things from ICobj
# ------------------------------------
print 'Accessing data from ICs'
settings = ICobj.settings
# filenames
snapshotName = settings.filenames.snapshotName
paramName = settings.filenames.paramName
# particle positions
r = ICobj.pos.r
xyz = ICobj.pos.xyz
# Number of particles
nParticles = ICobj.pos.nParticles
# molecular mass
m = settings.physical.m
# star mass
m_star = settings.physical.M.copy()
# disk mass
m_disk = ICobj.sigma.m_disk.copy()
m_disk = match_units(m_disk, m_star)[0]
# mass of the gas particles
m_particles = m_disk / float(nParticles)
# re-scale the particles (allows making of lo-mass disk)
m_particles *= settings.snapshot.mScale
# -------------------------------------------------
# Assign output
# -------------------------------------------------
print 'Assigning data to snapshot'
# Get units all set up
m_unit = m_star.units
pos_unit = r.units
if xyz.units != r.units:
xyz.convert_units(pos_unit)
# time units are sqrt(L^3/GM)
t_unit = np.sqrt((pos_unit**3)*np.power((G*m_unit), -1)).units
# velocity units are L/t
v_unit = (pos_unit/t_unit).ratio('km s**-1')
# Make it a unit
v_unit = pynbody.units.Unit('{0} km s**-1'.format(v_unit))
# Other settings
metals = settings.snapshot.metals
star_metals = metals
# -------------------------------------------------
# Initialize snapshot
# -------------------------------------------------
# Note that empty pos, vel, and mass arrays are created in the snapshot
snapshot = pynbody.new(star=1,gas=nParticles)
snapshot['vel'].units = v_unit
snapshot['eps'] = 0.01*SimArray(np.ones(nParticles+1, dtype=np.float32), pos_unit)
snapshot['metals'] = SimArray(np.zeros(nParticles+1, dtype=np.float32))
snapshot['rho'] = SimArray(np.zeros(nParticles+1, dtype=np.float32))
snapshot.gas['pos'] = xyz
snapshot.gas['temp'] = ICobj.T(r)
snapshot.gas['mass'] = m_particles
snapshot.gas['metals'] = metals
snapshot.star['pos'] = SimArray([[ 0., 0., 0.]],pos_unit)
snapshot.star['vel'] = SimArray([[ 0., 0., 0.]], v_unit)
snapshot.star['mass'] = m_star
snapshot.star['metals'] = SimArray(star_metals)
# Estimate the star's softening length as the closest particle distance
snapshot.star['eps'] = r.min()
# Make param file
param = make_param(snapshot, snapshotName)
param['dMeanMolWeight'] = m
eos = (settings.physical.eos).lower()
if eos == 'adiabatic':
param['bGasAdiabatic'] = 1
param['bGasIsothermal'] = 0
param['dConstGamma']
gc.collect()
# -------------------------------------------------
# CALCULATE VELOCITY USING calc_velocity.py. This also estimates the
# gravitational softening length eps
# -------------------------------------------------
print 'Calculating circular velocity'
preset = settings.changa_run.preset
max_particles = global_settings['misc']['max_particles']
calc_velocity.v_xy(snapshot, param, changa_preset=preset, max_particles=max_particles)
gc.collect()
# -------------------------------------------------
# Estimate time step for changa to use
# -------------------------------------------------
# Save param file
configsave(param, paramName, 'param')
# Save snapshot
snapshot.write(filename=snapshotName, fmt=pynbody.tipsy.TipsySnap)
# est dDelta
dDelta = ICgen_utils.est_time_step(paramName, preset)
param['dDelta'] = dDelta
# -------------------------------------------------
# Create director file
# -------------------------------------------------
# largest radius to plot
r_director = float(0.9 * r.max())
# Maximum surface density
sigma_min = float(ICobj.sigma(r_director))
# surface density at largest radius
sigma_max = float(ICobj.sigma.input_dict['sigma'].max())
# Create director dict
director = make_director(sigma_min, sigma_max, r_director, filename=param['achOutName'])
## Save .director file
#configsave(director, directorName, 'director')
# -------------------------------------------------
# Wrap up
# -------------------------------------------------
print 'Wrapping up'
# Now set the star particle's tform to a negative number. This allows
# UW ChaNGa treat it as a sink particle.
snapshot.star['tform'] = -1.0
# Update params
r_sink = strip_units(r.min())
param['dSinkBoundOrbitRadius'] = r_sink
param['dSinkRadius'] = r_sink
param['dSinkMassMin'] = 0.9 * strip_units(m_star)
param['bDoSinks'] = 1
return snapshot, param, director
def snapshot_gen(ICobj):
"""
Generates a tipsy snapshot from the initial conditions object ICobj.
Returns snapshot, param
snapshot: tipsy snapshot
param: dictionary containing info for a .param file
Note: Code has been edited (dflemin3) such that now it returns a snapshot for a circumbinary disk
where initial conditions generated assuming star at origin of mass M. After gas initialized, replaced
star at origin with binary system who's center of mass lies at the origin and who's mass m1 +m2 = M
"""
print 'Generating snapshot...'
# Constants
G = SimArray(1.0,'G')
# ------------------------------------
# Load in things from ICobj
# ------------------------------------
print 'Accessing data from ICs'
settings = ICobj.settings
# snapshot file name
snapshotName = settings.filenames.snapshotName
paramName = settings.filenames.paramName
# particle positions
r = ICobj.pos.r
xyz = ICobj.pos.xyz
# Number of particles
nParticles = ICobj.pos.nParticles
# molecular mass
m = settings.physical.m
# star mass
m_star = settings.physical.M.copy()
# disk mass
m_disk = ICobj.sigma.m_disk.copy()
m_disk = match_units(m_disk, m_star)[0]
# mass of the gas particles
m_particles = m_disk / float(nParticles)
# re-scale the particles (allows making of low-mass disk)
m_particles *= settings.snapshot.mScale
# -------------------------------------------------
# Assign output
# -------------------------------------------------
print 'Assigning data to snapshot'
# Get units all set up
m_unit = m_star.units
pos_unit = r.units
if xyz.units != r.units:
xyz.convert_units(pos_unit)
# time units are sqrt(L^3/GM)
t_unit = np.sqrt((pos_unit**3)*np.power((G*m_unit), -1)).units
# velocity units are L/t
v_unit = (pos_unit/t_unit).ratio('km s**-1')
# Make it a unit, save value for future conversion
v_unit_vel = v_unit
#Ensure v_unit_vel is the same as what I assume it is.
assert(np.fabs(AddBinary.VEL_UNIT-v_unit_vel)<AddBinary.SMALL),"VEL_UNIT not equal to ChaNGa unit! Why??"
v_unit = pynbody.units.Unit('{0} km s**-1'.format(v_unit))
# Other settings
metals = settings.snapshot.metals
star_metals = metals
# Generate snapshot
# Note that empty pos, vel, and mass arrays are created in the snapshot
snapshot = pynbody.new(star=1,gas=nParticles)
snapshot['vel'].units = v_unit
snapshot['eps'] = 0.01*SimArray(np.ones(nParticles+1, dtype=np.float32), pos_unit)
snapshot['metals'] = SimArray(np.zeros(nParticles+1, dtype=np.float32))
snapshot['rho'] = SimArray(np.zeros(nParticles+1, dtype=np.float32))
snapshot.gas['pos'] = xyz
snapshot.gas['temp'] = ICobj.T(r)
snapshot.gas['mass'] = m_particles
snapshot.gas['metals'] = metals
snapshot.star['pos'] = SimArray([[ 0., 0., 0.]],pos_unit)
snapshot.star['vel'] = SimArray([[ 0., 0., 0.]], v_unit)
snapshot.star['mass'] = m_star
snapshot.star['metals'] = SimArray(star_metals)
# Estimate the star's softening length as the closest particle distance
#snapshot.star['eps'] = r.min()
# Make param file
param = make_param(snapshot, snapshotName)
param['dMeanMolWeight'] = m
gc.collect()
# CALCULATE VELOCITY USING calc_velocity.py. This also estimates the
# gravitational softening length eps
print 'Calculating circular velocity'
preset = settings.changa_run.preset
max_particles = global_settings['misc']['max_particles']
calc_velocity.v_xy(snapshot, param, changa_preset=preset, max_particles=max_particles)
gc.collect()
# -------------------------------------------------
# Estimate time step for changa to use
# -------------------------------------------------
# Save param file
configsave(param, paramName, 'param')
# Save snapshot
snapshot.write(filename=snapshotName, fmt=pynbody.tipsy.TipsySnap)
# est dDelta
dDelta = ICgen_utils.est_time_step(paramName, preset)
param['dDelta'] = dDelta
# -------------------------------------------------
# Create director file
# -------------------------------------------------
# largest radius to plot
r_director = float(0.9 * r.max())
# Maximum surface density
sigma_min = float(ICobj.sigma(r_director))
# surface density at largest radius
sigma_max = float(ICobj.sigma.input_dict['sigma'].max())
# Create director dict
director = make_director(sigma_min, sigma_max, r_director, filename=param['achOutName'])
## Save .director file
#configsave(director, directorName, 'director')
#Now that velocities and everything are all initialized for gas particles, create new snapshot to return in which
#single star particle is replaced by 2, same units as above
snapshotBinary = pynbody.new(star=2,gas=nParticles)
snapshotBinary['eps'] = 0.01*SimArray(np.ones(nParticles+2, dtype=np.float32), pos_unit)
snapshotBinary['metals'] = SimArray(np.zeros(nParticles+2, dtype=np.float32))
snapshotBinary['vel'].units = v_unit
snapshotBinary['pos'].units = pos_unit
snapshotBinary['mass'].units = snapshot['mass'].units
snapshotBinary['rho'] = SimArray(np.zeros(nParticles+2, dtype=np.float32))
#Assign gas particles with calculated/given values from above
snapshotBinary.gas['pos'] = snapshot.gas['pos']
snapshotBinary.gas['vel'] = snapshot.gas['vel']
snapshotBinary.gas['temp'] = snapshot.gas['temp']
snapshotBinary.gas['rho'] = snapshot.gas['rho']
snapshotBinary.gas['eps'] = snapshot.gas['eps']
snapshotBinary.gas['mass'] = snapshot.gas['mass']
snapshotBinary.gas['metals'] = snapshot.gas['metals']
#Load Binary system obj to initialize system
binsys = ICobj.settings.physical.binsys
x1,x2,v1,v2 = binsys.generateICs()
#Put velocity in sim units
#!!! Note: v_unit_vel will always be 29.785598165 km/s when m_unit = Msol and r_unit = 1 AU in kpc!!!
#conv = v_unit_vel #km/s in sim units
#v1 /= conv
#v2 /= conv
#Assign position, velocity assuming CCW orbit
snapshotBinary.star[0]['pos'] = SimArray(x1,pos_unit)
snapshotBinary.star[0]['vel'] = SimArray(v1,v_unit)
snapshotBinary.star[1]['pos'] = SimArray(x2,pos_unit)
snapshotBinary.star[1]['vel'] = SimArray(v2,v_unit)
#Set stellar masses
#Set Mass units
#Create simArray for mass, convert units to simulation mass units
priMass = SimArray(binsys.m1,m_unit)
secMass = SimArray(binsys.m2,m_unit)
snapshotBinary.star[0]['mass'] = priMass
snapshotBinary.star[1]['mass'] = secMass
snapshotBinary.star['metals'] = SimArray(star_metals)
#Estimate stars' softening length as fraction of distance to COM
d = np.sqrt(AddBinary.dotProduct(x1-x2,x1-x2))
snapshotBinary.star[0]['eps'] = SimArray(math.fabs(d)/4.0,pos_unit)
snapshotBinary.star[1]['eps'] = SimArray(math.fabs(d)/4.0,pos_unit)
print 'Wrapping up'
# Now set the star particle's tform to a negative number. This allows
# UW ChaNGa treat it as a sink particle.
snapshotBinary.star['tform'] = -1.0
#Set Sink Radius to be mass-weighted average of Roche lobes of two stars
r1 = AddBinary.calcRocheLobe(binsys.m1/binsys.m2,binsys.a)
r2 = AddBinary.calcRocheLobe(binsys.m2/binsys.m1,binsys.a)
p = strip_units(binsys.m1/(binsys.m1 + binsys.m2))
r_sink = (r1*p) + (r2*(1.0-p))
param['dSinkBoundOrbitRadius'] = r_sink
param['dSinkRadius'] = r_sink
param['dSinkMassMin'] = 0.9 * strip_units(secMass)
param['bDoSinks'] = 1
return snapshotBinary, param, director
def binned_mean(x, y, bins=10, nbins=None, binedges=None, weights=None, weighted_bins=False, ret_bin_edges=False):
"""
Bins y according to x and takes the average for each bin.
bins can either be an integer (the number of bins to use) or an array of
binedges. bins will be overridden by nbins or binedges
Optionally (for compatibility reasons) if binedges is specified, the
x-bins are defined by binedges. Otherwise the x-bins are determined by
nbins
If weights = None, equal weights are assumed for the average, otherwise
weights for each data point should be specified
y_err (error in y) is calculated as the standard deviation in y for each
bin, divided by sqrt(N), where N is the number of counts in each bin
IF weighted_bins is True, the bin centers are calculated as a center of
mass
NaNs are ignored for the input. Empty bins are returned with nans
RETURNS a tuple of (bin_centers, y_mean, y_err) if ret_bin_edges=False
else, Returns (bin_edges, y_mean, y_err)
"""
if (isinstance(bins, int)) and (nbins is None):
nbins = bins
elif (hasattr(bins, "__iter__")) and (binedges is None):
binedges = bins
if binedges is not None:
nbins = len(binedges) - 1
else:
binedges = np.linspace(x.min(), (1 + np.spacing(2)) * x.max(), nbins + 1)
if weights is None:
weights = np.ones(x.shape)
weights = strip_units(weights)
# Pre-factor for weighted STD:
A = 1 / (1 - (weights ** 2).sum())
# Initialize
y_mean = np.zeros(nbins)
y_std = np.zeros(nbins)
# Find the index bins for each data point
ind = np.digitize(x, binedges) - 1
# Ignore nans
nan_ind = np.isnan(y)
N = np.histogram(x, binedges)[0]
# Initialize bin_centers (try to retain units)
bin_centers = 0.0 * binedges[1:]
for i in range(nbins):
# Indices to use
mask = (ind == i) & (~nan_ind)
# Set up the weighting
w = weights[mask].copy()
w /= w.sum()
A = 1 / (1 - (w ** 2).sum())
# y_mean[i] = np.nanmean(y[mask])
y_mean[i] = (w * y[mask]).sum()
var = A * (w * (y[mask] - y_mean[i]) ** 2).sum()
y_std[i] = np.sqrt(var)
# y_std[i] = np.std(y[use_ind])
if weighted_bins:
# Center of mass of x positions
bin_centers[i] = (w * x[mask]).sum()
y_mean = match_units(y_mean, y)[0]
y_err = y_std / np.sqrt(N)
y_err = match_units(y_err, y)[0]
y_mean[N == 0] = np.nan
y_err[N == 0] = np.nan
if not weighted_bins:
bin_centers = (binedges[0:-1] + binedges[1:]) / 2.0
binedges = match_units(binedges, x)[0]
bin_centers = match_units(bin_centers, x)[0]
else:
bin_centers[N == 0] = np.nan
if ret_bin_edges:
return binedges, y_mean, y_err
else:
return bin_centers, y_mean, y_err
def Q(snapshot, molecular_mass = 2.0, bins=100, use_velocity=False, \
use_omega=True, gamma=1.):
"""Calculates the Toomre Q as a function of r, assuming radial temperature
profile and kappa ~= omega
Parameters
----------
snapshot : tipsy snapshot
molecular_mass : float
Mean molecular mass (for sound speed). Default = 2.0
bins : int or array
Either the number of bins or the bin edges
use_velocity : Bool
Determines whether to use the particles' velocities to calculate orbital
velocity. Useful if the circular orbital velocities are set in the
snapshot.
use_omega : Bool
Default=True. Use omega as a proxy for kappa to reduce noise
gamma : float
'Effective' adiabatic index, used to calculate sound speed. Use
gamma = 1 for an isothermal EOS
Returns
-------
Q : array
Toomre Q as a function of r
r_edges : array
Radial bin edges
"""
# Physical constants
kB = SimArray([1.0],'k')
G = SimArray([1.0],'G')
# Calculate surface density
sig, r_edges = sigma(snapshot, bins)
# Calculate sound speed
m = match_units(molecular_mass,'m_p')[0]
c_s_all = np.sqrt(kB*snapshot.g['temp']*gamma/m)
# Bin/average sound speed
dummy, c_s, dummy2 = binned_mean(snapshot.g['rxy'], c_s_all, binedges=r_edges)
if use_omega:
# Calculate keplerian angular velocity (as a proxy for the epicyclic
# frequency, which is a noisy calculation)
if use_velocity:
# Calculate directly from particle's velocity
dummy, omega, dummy2 = binned_mean(snapshot.g['rxy'], \
snapshot.g['vt']/snapshot.g['rxy'], binedges=r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
omega = p['omega']
kappa_calc = omega
else:
if use_velocity:
# Calculate directly from particle's velocities
kappa_calc, dummy = kappa(snapshot, r_edges)
else:
# Estimate, from forces, using pynbody
p = pb.analysis.profile.Profile(snapshot, bins=r_edges)
kappa_calc = p['kappa']
return (kappa_calc*c_s/(np.pi*G*sig)).in_units('1'), r_edges