def viscous(settings):
"""
Generates a surface density profile derived from a self-similarity solution
for a viscous disk, according to:
sigma ~ r^-gamma exp(-r^(2-gamma))
Where r is a dimensionless radius and gamma is a constant less than 2.
Rd (disk radius) is defined as the radius containing 95% of the disk mass
**ARGUMENTS**
settings : IC settings
settings like those contained in an IC object (see ICgen_settings.py)
**RETURNS**
R : SimArray
Radii at which sigma is calculated
sigma : SimArray
Surface density profile as a function of R
"""
Rd = settings.sigma.Rd
rin = settings.sigma.rin
rmax = settings.sigma.rmax
n_points = settings.sigma.n_points
gamma = settings.sigma.gamma
m_disk = settings.sigma.m_disk
# Define the fraction of mass contained within Rd
A = 0.95
# Normalization for r
R1 = Rd / (np.log(1 / (1 - A))**(1 / (2 - gamma)))
Rmax = rmax * Rd
Rin = rin * Rd
R = np.linspace(0, Rmax, n_points)
r = (R / R1).in_units('1')
sigma = (r**-gamma) * np.exp(-r**(2 - gamma)) * (
m_disk / (2 * np.pi * R1 * R1)) * (2 - gamma)
# Deal with infinities at the origin with a hard cut off
sigma[0] = sigma[1]
# Apply interior cutoff
cut_mask = R < Rin
if np.any(cut_mask):
sigma[cut_mask] *= isaac.smoothstep(r[cut_mask],
degree=21,
rescale=True)
return R, sigma
def viscous(settings):
"""
Generates a surface density profile derived from a self-similarity solution
for a viscous disk, according to:
sigma ~ r^-gamma exp(-r^(2-gamma))
Where r is a dimensionless radius and gamma is a constant less than 2.
Rd (disk radius) is defined as the radius containing 95% of the disk mass
**ARGUMENTS**
settings : IC settings
settings like those contained in an IC object (see ICgen_settings.py)
**RETURNS**
R : SimArray
Radii at which sigma is calculated
sigma : SimArray
Surface density profile as a function of R
"""
Rd = settings.sigma.Rd
rin = settings.sigma.rin
rmax = settings.sigma.rmax
n_points = settings.sigma.n_points
gamma = settings.sigma.gamma
m_disk = settings.sigma.m_disk
# Define the fraction of mass contained within Rd
A = 0.95
# Normalization for r
R1 = Rd / (np.log(1/(1-A))**(1/(2-gamma)))
Rmax = rmax * Rd
Rin = rin * Rd
R = np.linspace(0, Rmax, n_points)
r = (R/R1).in_units('1')
sigma = (r**-gamma) * np.exp(-r**(2-gamma)) * (m_disk/(2*np.pi*R1*R1)) * (2-gamma)
# Deal with infinities at the origin with a hard cut off
sigma[0] = sigma[1]
# Apply interior cutoff
cut_mask = R < Rin
if np.any(cut_mask):
sigma[cut_mask] *= isaac.smoothstep(r[cut_mask],degree=21,rescale=True)
return R, sigma
def powerlaw(settings, T=None):
"""
Generates a surface density profile according to a powerlaw sigma ~ 1/r
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 = isaac.match_units(pynbody.units.au, Rd)[1]
Mstar = isaac.match_units(pynbody.units.Msol, Mstar)[1]
# Molecular weight
m = isaac.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'))
# 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] *= isaac.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 powerlaw(settings, T = None):
"""
Generates a surface density profile according to a powerlaw sigma ~ 1/r
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
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 = isaac.match_units(pynbody.units.au, Rd)[1]
Mstar = isaac.match_units(pynbody.units.Msol, Mstar)[1]
# Molecular weight
m = isaac.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'))
# Calculate sigma
# Powerlaw
sigma = A/r
sigma[0] = 0.0
# Interior cutoff
sigma[r>1] *= np.exp(-(r[r>1] - 1)**2 / (2*cutlength**2))
# Exterior cutoff
sigma[r<rin] *= isaac.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