def estimateCBResonances(s, r_max, m_max=5, l_max=5, bins=2500):
"""
Given pynbody snapshot star and gas SimArrays, computes the resonances of disk on binary as a function of period.
Disk radius, in au, is convered to angular frequency which will then be used to compute corotation and inner/outer Lindblad resonances.
Assumption: Assumes m_disk << m_bin which holds in general for simulations considered
For reference: Kappa, omega computed in ~ 1/day intermediate units.
Uses approximations from Artymowicz 1994
Inputs:
stars,gas: Pynbody snapshot .star and .gas SimArrays (in au, Msol, etc)
r_max: maximum disk radius for calculations (au)
bins: number of radial bins to calculate over
Output:
Orbital frequency for corotation and inner/outer resonances as float and 2 arrays
"""
stars = s.stars
#gas = s.gas
#Compute binary angular frequency
#Strip units from all inputs
x1 = np.asarray(isaac.strip_units(stars[0]['pos']))
x2 = np.asarray(isaac.strip_units(stars[1]['pos']))
v1 = np.asarray(isaac.strip_units(stars[0]['vel']))
v2 = np.asarray(isaac.strip_units(stars[1]['vel']))
m1 = np.asarray(isaac.strip_units(stars[0]['mass']))
m2 = np.asarray(isaac.strip_units(stars[1]['mass']))
a = AddBinary.calcSemi(x1, x2, v1, v2, m1, m2)
#omega_b = 2.0*np.pi/AddBinary.aToP(a,m1+m2
#Find corotation resonance where omega_d ~ omega_b
r_c = a #m=1 case
o_c = 2.0 * np.pi / AddBinary.aToP(r_c, m1 + m2)
#Find inner lindblad resonances for m = [m_min,m_max]
#Lindblad resonance: omega = omega_pattern +/- kappa/m for int m > 1
m_min = 1
l_min = 1
omega_Lo = np.zeros((m_max - m_min, l_max - l_min))
omega_Li = np.zeros((m_max - m_min, l_max - l_min))
#Find resonance radii, convert to angular frequency
for m in range(m_min, m_max):
for l in range(l_min, l_max):
#oTmp = find_crit_radius(r,omega_d-(kappa/(float(m))),omega_b,bins) #outer LR
oTmp = np.power(float(m + 1) / l, 2. / 3.) * a
omega_Lo[m - m_min,
l - l_min] = 2.0 * np.pi / AddBinary.aToP(oTmp, m1 + m2)
#iTmp = find_crit_radius(r,omega_d+(kappa/(float(m))),omega_b,bins) #inner LR
iTmp = np.power(float(m - 1) / l, 2. / 3.) * a
omega_Li[m - m_min,
l - l_min] = 2.0 * np.pi / AddBinary.aToP(iTmp, m1 + m2)
return omega_Li, omega_Lo, o_c #return inner, outer, co angular frequencies
def estimateCBResonances(s,r_max,m_max=5,l_max=5,bins=2500):
"""
Given pynbody snapshot star and gas SimArrays, computes the resonances of disk on binary as a function of period.
Disk radius, in au, is convered to angular frequency which will then be used to compute corotation and inner/outer Lindblad resonances.
Assumption: Assumes m_disk << m_bin which holds in general for simulations considered
For reference: Kappa, omega computed in ~ 1/day intermediate units.
Uses approximations from Artymowicz 1994
Inputs:
stars,gas: Pynbody snapshot .star and .gas SimArrays (in au, Msol, etc)
r_max: maximum disk radius for calculations (au)
bins: number of radial bins to calculate over
Output:
Orbital frequency for corotation and inner/outer resonances as float and 2 arrays
"""
stars = s.stars
#gas = s.gas
#Compute binary angular frequency
#Strip units from all inputs
x1 = np.asarray(isaac.strip_units(stars[0]['pos']))
x2 = np.asarray(isaac.strip_units(stars[1]['pos']))
v1 = np.asarray(isaac.strip_units(stars[0]['vel']))
v2 = np.asarray(isaac.strip_units(stars[1]['vel']))
m1 = np.asarray(isaac.strip_units(stars[0]['mass']))
m2 = np.asarray(isaac.strip_units(stars[1]['mass']))
a = AddBinary.calcSemi(x1, x2, v1, v2, m1, m2)
#omega_b = 2.0*np.pi/AddBinary.aToP(a,m1+m2
#Find corotation resonance where omega_d ~ omega_b
r_c = a #m=1 case
o_c = 2.0*np.pi/AddBinary.aToP(r_c,m1+m2)
#Find inner lindblad resonances for m = [m_min,m_max]
#Lindblad resonance: omega = omega_pattern +/- kappa/m for int m > 1
m_min = 1
l_min = 1
omega_Lo = np.zeros((m_max-m_min,l_max-l_min))
omega_Li = np.zeros((m_max-m_min,l_max-l_min))
#Find resonance radii, convert to angular frequency
for m in range(m_min,m_max):
for l in range(l_min,l_max):
#oTmp = find_crit_radius(r,omega_d-(kappa/(float(m))),omega_b,bins) #outer LR
oTmp = np.power(float(m+1)/l,2./3.)*a
omega_Lo[m-m_min,l-l_min] = 2.0*np.pi/AddBinary.aToP(oTmp,m1+m2)
#iTmp = find_crit_radius(r,omega_d+(kappa/(float(m))),omega_b,bins) #inner LR
iTmp = np.power(float(m-1)/l,2./3.)*a
omega_Li[m-m_min,l-l_min] = 2.0*np.pi/AddBinary.aToP(iTmp,m1+m2)
return omega_Li, omega_Lo, o_c #return inner, outer, co angular frequencies
def calc_LB_resonance(s,m_min=1,m_max=3,l_min=1,l_max=3):
"""
Computes the locations of various Lindblad Resonances in the disk as a
function of binary pattern speed.
Parameters
----------
s : Tipsy-format snapshot
m_min, l_min : ints
minimum orders of (m,l) LR
m_max,l_max : ints
maximum orders of (m,l) LR
Returns
-------
OLR, ILR, CR: numpy arrays
location in AU of (m,l)th order Lindblad resonances
"""
#Compute binary angular frequency in 1/day
x1 = s.stars[0]['pos']
x2 = s.stars[1]['pos']
v1 = s.stars[0]['vel']
v2 = s.stars[1]['vel']
m1 = s.stars[0]['mass']
m2 = s.stars[1]['mass']
omega_b = 2.0*np.pi/AddBinary.aToP(AddBinary.calcSemi(x1,x2,v1,v2,m1,m2),m1+m2)
guess = 0.05 #fsolve initial guess parameter
#Allocate space for arrays
OLR = np.zeros((m_max,l_max))
ILR = np.zeros((m_max,l_max))
CR = np.zeros(l_max)
#Define resonance functions
def OLR_func(omega_d, *args):
m = args[0]
l = args[1]
omega_b = args[2]
return omega_d*(1.0 + float(l)/m) - omega_b
#end function
def ILR_func(omega_d, *args):
m = args[0]
l = args[1]
omega_b = args[2]
return omega_d*(1.0 - float(l)/m) - omega_b
#end function
def CR_func(omega_d, *args):
l = args[0]
omega_b = args[1]
return omega_d - omega_b/float(l)
#end function
for m in range(m_min,m_max+1):
for l in range(l_min,l_max+1):
OLR[m-m_min,l-l_min] = fsolve(OLR_func,guess,args=(m,l,omega_b))
ILR[m-m_min,l-l_min] = fsolve(ILR_func,guess,args=(m,l,omega_b))
CR[l-l_min] = fsolve(CR_func,guess,args=(l,omega_b))
#Convert from 1/day -> au
OLR = AddBinary.pToA(2.0*np.pi/OLR,m1+m2)
ILR = AddBinary.pToA(2.0*np.pi/ILR,m1+m2)
CR = AddBinary.pToA(2.0*np.pi/CR,m1+m2)
return OLR, ILR, CR
def findCBResonances(s,r,r_min,r_max,m_max=4,l_max=4,bins=50):
"""
Given Tipsy snapshot, computes the resonances of disk on binary as a function of orbital angular frequency omega.
Disk radius, in au, is convered to angular frequency which will then be used to compute corotation
and inner/outer Lindblad resonances.
Note: r given MUST correspond to r over which de/dt was calculated. Otherwise, scale gets all messed up
!!! NOTE: This function is awful and deprecated --- do NOT use it. Instead, use calc_LB_resonance !!!
Parameters
----------
s: Tipsy-format snapshot
r: array
radius array over which de/dt was calculated
r_min,r_max: floats
min/maximum disk radius for calculations (au)
bins: int
number of radial bins to calculate over
m_max,l_max: ints
maximum orders of (m,l) LR
Returns
-------
Orbital frequency: numpy array
for corotation and inner/outer resonances and radii as float and numpy arrays
"""
stars = s.stars
gas = s.gas
m_min = 1 #m >=1 for LRs, CRs
l_min = 1 #l >=1 for LRs, CRs
#Compute binary angular frequency
x1 = stars[0]['pos']
x2 = stars[1]['pos']
v1 = stars[0]['vel']
v2 = stars[1]['vel']
m1 = stars[0]['mass']
m2 = stars[1]['mass']
a = strip_units(AddBinary.calcSemi(x1, x2, v1, v2, m1, m2))
omega_b = 2.0*np.pi/AddBinary.aToP(a,m1+m2) #In units 1/day
#Make r steps smaller for higher accuracy
r_arr = np.linspace(r.min(),r.max(),len(r)*10)
#Compute mass of disk interior to given r
mask = np.zeros((len(gas),len(r_arr)),dtype=bool)
m_disk = np.zeros(len(r_arr))
for i in range(0,len(r_arr)):
mask[:,i] = gas['rxy'] < r_arr[i]
m_disk[i] = np.sum(gas['mass'][mask[:,i]])
#Compute omega_disk in units 1/day (like omega_binary)
omega_d = 2.0*np.pi/AddBinary.aToP(r_arr,m1+m2+m_disk)
#Compute kappa (radial epicycle frequency = sqrt(r * d(omega^2)/dr + 4*(omega^2))
o2 = omega_d*omega_d
dr = r_arr[1] - r_arr[0]
#dr = (r.max()-r.min())/float(bins) #Assuming r has evenly spaced bins!
drdo2 = np.gradient(o2,dr) #I mean d/dr(omega^2)
kappa = np.sqrt(r_arr*drdo2 + 4.0*o2)
#Allocate arrays for output
omega_Lo = np.zeros((m_max,l_max))
omega_Li = np.zeros((m_max,l_max))
o_c = np.zeros(l_max)
#Find resonance angular frequency
for m in range(m_min,m_max+1):
for l in range(l_min,l_max+1):
outer = omega_d + (float(l)/m)*kappa
inner = omega_d - (float(l)/m)*kappa
omega_Lo[m-m_min,l-l_min] = omega_d[np.argmin(np.fabs(omega_b-outer))]
omega_Li[m-m_min,l-l_min] = omega_d[np.argmin(np.fabs(omega_b-inner))]
#Find corotation resonance where omega_d ~ omega_b
o_c[l-l_min] = omega_d[np.argmin(np.fabs(omega_d-omega_b/float(l)))]
#Rescale omega_d, kappa to be of length bins again
omega_d = np.linspace(omega_d.min(),omega_d.max(),bins)
kappa = np.linspace(kappa.min(),kappa.max(),bins)
return omega_Li, omega_Lo, o_c, omega_d, kappa
def calc_LB_resonance(s, m_min=1, m_max=3, l_min=1, l_max=3):
"""
Computes the locations of various Lindblad Resonances in the disk as a
function of binary pattern speed.
Parameters
----------
s : Tipsy-format snapshot
m_min, l_min : ints
minimum orders of (m,l) LR
m_max,l_max : ints
maximum orders of (m,l) LR
Returns
-------
OLR, ILR, CR: numpy arrays
location in AU of (m,l)th order Lindblad resonances
"""
#Compute binary angular frequency in 1/day
x1 = s.stars[0]['pos']
x2 = s.stars[1]['pos']
v1 = s.stars[0]['vel']
v2 = s.stars[1]['vel']
m1 = s.stars[0]['mass']
m2 = s.stars[1]['mass']
omega_b = 2.0 * np.pi / AddBinary.aToP(
AddBinary.calcSemi(x1, x2, v1, v2, m1, m2), m1 + m2)
guess = 0.05 #fsolve initial guess parameter
#Allocate space for arrays
OLR = np.zeros((m_max, l_max))
ILR = np.zeros((m_max, l_max))
CR = np.zeros(l_max)
#Define resonance functions
def OLR_func(omega_d, *args):
m = args[0]
l = args[1]
omega_b = args[2]
return omega_d * (1.0 + float(l) / m) - omega_b
#end function
def ILR_func(omega_d, *args):
m = args[0]
l = args[1]
omega_b = args[2]
return omega_d * (1.0 - float(l) / m) - omega_b
#end function
def CR_func(omega_d, *args):
l = args[0]
omega_b = args[1]
return omega_d - omega_b / float(l)
#end function
for m in range(m_min, m_max + 1):
for l in range(l_min, l_max + 1):
OLR[m - m_min, l - l_min] = fsolve(OLR_func,
guess,
args=(m, l, omega_b))
ILR[m - m_min, l - l_min] = fsolve(ILR_func,
guess,
args=(m, l, omega_b))
CR[l - l_min] = fsolve(CR_func, guess, args=(l, omega_b))
#Convert from 1/day -> au
OLR = AddBinary.pToA(2.0 * np.pi / OLR, m1 + m2)
ILR = AddBinary.pToA(2.0 * np.pi / ILR, m1 + m2)
CR = AddBinary.pToA(2.0 * np.pi / CR, m1 + m2)
return OLR, ILR, CR
def findCBResonances(s, r, r_min, r_max, m_max=4, l_max=4, bins=50):
"""
Given Tipsy snapshot, computes the resonances of disk on binary as a function of orbital angular frequency omega.
Disk radius, in au, is convered to angular frequency which will then be used to compute corotation
and inner/outer Lindblad resonances.
Note: r given MUST correspond to r over which de/dt was calculated. Otherwise, scale gets all messed up
!!! NOTE: This function is awful and deprecated --- do NOT use it. Instead, use calc_LB_resonance !!!
Parameters
----------
s: Tipsy-format snapshot
r: array
radius array over which de/dt was calculated
r_min,r_max: floats
min/maximum disk radius for calculations (au)
bins: int
number of radial bins to calculate over
m_max,l_max: ints
maximum orders of (m,l) LR
Returns
-------
Orbital frequency: numpy array
for corotation and inner/outer resonances and radii as float and numpy arrays
"""
stars = s.stars
gas = s.gas
m_min = 1 #m >=1 for LRs, CRs
l_min = 1 #l >=1 for LRs, CRs
#Compute binary angular frequency
x1 = stars[0]['pos']
x2 = stars[1]['pos']
v1 = stars[0]['vel']
v2 = stars[1]['vel']
m1 = stars[0]['mass']
m2 = stars[1]['mass']
a = strip_units(AddBinary.calcSemi(x1, x2, v1, v2, m1, m2))
omega_b = 2.0 * np.pi / AddBinary.aToP(a, m1 + m2) #In units 1/day
#Make r steps smaller for higher accuracy
r_arr = np.linspace(r.min(), r.max(), len(r) * 10)
#Compute mass of disk interior to given r
mask = np.zeros((len(gas), len(r_arr)), dtype=bool)
m_disk = np.zeros(len(r_arr))
for i in range(0, len(r_arr)):
mask[:, i] = gas['rxy'] < r_arr[i]
m_disk[i] = np.sum(gas['mass'][mask[:, i]])
#Compute omega_disk in units 1/day (like omega_binary)
omega_d = 2.0 * np.pi / AddBinary.aToP(r_arr, m1 + m2 + m_disk)
#Compute kappa (radial epicycle frequency = sqrt(r * d(omega^2)/dr + 4*(omega^2))
o2 = omega_d * omega_d
dr = r_arr[1] - r_arr[0]
#dr = (r.max()-r.min())/float(bins) #Assuming r has evenly spaced bins!
drdo2 = np.gradient(o2, dr) #I mean d/dr(omega^2)
kappa = np.sqrt(r_arr * drdo2 + 4.0 * o2)
#Allocate arrays for output
omega_Lo = np.zeros((m_max, l_max))
omega_Li = np.zeros((m_max, l_max))
o_c = np.zeros(l_max)
#Find resonance angular frequency
for m in range(m_min, m_max + 1):
for l in range(l_min, l_max + 1):
outer = omega_d + (float(l) / m) * kappa
inner = omega_d - (float(l) / m) * kappa
omega_Lo[m - m_min,
l - l_min] = omega_d[np.argmin(np.fabs(omega_b - outer))]
omega_Li[m - m_min,
l - l_min] = omega_d[np.argmin(np.fabs(omega_b - inner))]
#Find corotation resonance where omega_d ~ omega_b
o_c[l - l_min] = omega_d[np.argmin(
np.fabs(omega_d - omega_b / float(l)))]
#Rescale omega_d, kappa to be of length bins again
omega_d = np.linspace(omega_d.min(), omega_d.max(), bins)
kappa = np.linspace(kappa.min(), kappa.max(), bins)
return omega_Li, omega_Lo, o_c, omega_d, kappa
def findCBResonances(s, r, r_min, r_max, m_max=4, l_max=4, bins=50):
"""
Given Tipsy snapshot, computes the resonances of disk on binary as a function of orbital angular frequency omega.
Disk radius, in au, is convered to angular frequency which will then be used to compute corotation
and inner/outer Lindblad resonances.
Note: r given MUST correspond to r over which de/dt was calculated. Otherwise, scale gets all messed up
Parameters
----------
s: Tipsy-format snapshot
r: array
radius array over which de/dt was calculated
r_min,r_max: floats
min/maximum disk radius for calculations (au)
bins: int
number of radial bins to calculate over
m_max,l_max: ints
maximum orders of (m,l) LR
Returns
-------
Orbital frequency: numpy array
for corotation and inner/outer resonances and radii as float and numpy arrays
"""
stars = s.stars
m_min = 1 #m >=1 for LRs, CRs
l_min = 1 #l >=1 for LRs, CRs
#Compute binary angular frequency
#Strip units from all inputs
#x1 = np.asarray(isaac.strip_units(stars[0]['pos']))
#x2 = np.asarray(isaac.strip_units(stars[1]['pos']))
#v1 = np.asarray(isaac.strip_units(stars[0]['vel']))
#v2 = np.asarray(isaac.strip_units(stars[1]['vel']))
#m1 = np.asarray(isaac.strip_units(stars[0]['mass']))
#m2 = np.asarray(isaac.strip_units(stars[1]['mass']))
x1 = stars[0]['pos']
x2 = stars[1]['pos']
v1 = stars[0]['vel']
v2 = stars[1]['vel']
m1 = stars[0]['mass']
m2 = stars[1]['mass']
a = isaac.strip_units(AddBinary.calcSemi(x1, x2, v1, v2, m1, m2))
omega_b = 2.0 * np.pi / AddBinary.aToP(a, m1 + m2) #In units 1/day
#Compute omega_disk in units 1/day (like omega_binary)
omega_d = 2.0 * np.pi / AddBinary.aToP(r, m1 + m2)
#Compute kappa (radial epicycle frequency = sqrt(r * d(omega^2)/dr + 4*(omega^2))
o2 = omega_d * omega_d
dr = (r.max() - r.min()) / float(bins) #Assuming r has evenly spaced bins!
drdo2 = np.gradient(o2, dr) #I mean d/dr(omega^2)
kappa = np.sqrt(r * drdo2 + 4.0 * o2)
#Allocate arrays for output
omega_Lo = np.zeros((m_max, l_max))
omega_Li = np.zeros((m_max, l_max))
o_c = np.zeros(l_max)
#Find resonance angular frequency
for m in range(m_min, m_max + 1):
for l in range(l_min, l_max + 1):
outer = omega_d + (float(l) / m) * kappa
inner = omega_d - (float(l) / m) * kappa
omega_Lo[m - m_min,
l - l_min] = omega_d[np.argmin(np.fabs(omega_b - outer))]
omega_Li[m - m_min,
l - l_min] = omega_d[np.argmin(np.fabs(omega_b - inner))]
#Find corotation resonance where omega_d ~ omega_b
o_c[l - l_min] = omega_d[np.argmin(
np.fabs(omega_d - omega_b / float(l)))]
return omega_Li, omega_Lo, o_c, omega_d, kappa
def findCBResonances(s,r,r_min,r_max,m_max=4,l_max=4,bins=50):
"""
Given Tipsy snapshot, computes the resonances of disk on binary as a function of orbital angular frequency omega.
Disk radius, in au, is convered to angular frequency which will then be used to compute corotation
and inner/outer Lindblad resonances.
Note: r given MUST correspond to r over which de/dt was calculated. Otherwise, scale gets all messed up
Parameters
----------
s: Tipsy-format snapshot
r: array
radius array over which de/dt was calculated
r_min,r_max: floats
min/maximum disk radius for calculations (au)
bins: int
number of radial bins to calculate over
m_max,l_max: ints
maximum orders of (m,l) LR
Returns
-------
Orbital frequency: numpy array
for corotation and inner/outer resonances and radii as float and numpy arrays
"""
stars = s.stars
m_min = 1 #m >=1 for LRs, CRs
l_min = 1 #l >=1 for LRs, CRs
#Compute binary angular frequency
#Strip units from all inputs
#x1 = np.asarray(isaac.strip_units(stars[0]['pos']))
#x2 = np.asarray(isaac.strip_units(stars[1]['pos']))
#v1 = np.asarray(isaac.strip_units(stars[0]['vel']))
#v2 = np.asarray(isaac.strip_units(stars[1]['vel']))
#m1 = np.asarray(isaac.strip_units(stars[0]['mass']))
#m2 = np.asarray(isaac.strip_units(stars[1]['mass']))
x1 = stars[0]['pos']
x2 = stars[1]['pos']
v1 = stars[0]['vel']
v2 = stars[1]['vel']
m1 = stars[0]['mass']
m2 = stars[1]['mass']
a = isaac.strip_units(AddBinary.calcSemi(x1, x2, v1, v2, m1, m2))
omega_b = 2.0*np.pi/AddBinary.aToP(a,m1+m2) #In units 1/day
#Compute omega_disk in units 1/day (like omega_binary)
omega_d = 2.0*np.pi/AddBinary.aToP(r,m1+m2)
#Compute kappa (radial epicycle frequency = sqrt(r * d(omega^2)/dr + 4*(omega^2))
o2 = omega_d*omega_d
dr = (r.max()-r.min())/float(bins) #Assuming r has evenly spaced bins!
drdo2 = np.gradient(o2,dr) #I mean d/dr(omega^2)
kappa = np.sqrt(r*drdo2 + 4.0*o2)
#Allocate arrays for output
omega_Lo = np.zeros((m_max,l_max))
omega_Li = np.zeros((m_max,l_max))
o_c = np.zeros(l_max)
#Find resonance angular frequency
for m in range(m_min,m_max+1):
for l in range(l_min,l_max+1):
outer = omega_d + (float(l)/m)*kappa
inner = omega_d - (float(l)/m)*kappa
omega_Lo[m-m_min,l-l_min] = omega_d[np.argmin(np.fabs(omega_b-outer))]
omega_Li[m-m_min,l-l_min] = omega_d[np.argmin(np.fabs(omega_b-inner))]
#Find corotation resonance where omega_d ~ omega_b
o_c[l-l_min] = omega_d[np.argmin(np.fabs(omega_d-omega_b/float(l)))]
return omega_Li, omega_Lo, o_c, omega_d, kappa
