def sample_ecc(self, ecc_model='sana12', size=None):
"""Sample the eccentricity according to a user specified model
Parameters
----------
ecc_model : string
'thermal' samples from a thermal eccentricity distribution following
`Heggie (1975) <http://adsabs.harvard.edu/abs/1975MNRAS.173..729H>`_
'uniform' samples from a uniform eccentricity distribution
'sana12' samples from the eccentricity distribution from `Sana+2012 <https://ui.adsabs.harvard.edu/abs/2012Sci...337..444S/abstract>_`
'circular' assumes zero eccentricity for all systems
DEFAULT = 'sana12'
size : int, optional
number of eccentricities to sample
NOTE: this is set in cosmic-pop call as Nstep
Returns
-------
ecc : array
array of sampled eccentricities with size=size
"""
if ecc_model=='thermal':
a_0 = np.random.uniform(0.0, 1.0, size)
ecc = a_0**0.5
return ecc
elif ecc_model=='uniform':
ecc = np.random.uniform(0.0, 1.0, size)
return ecc
elif ecc_model=='sana12':
from cosmic.utils import rndm
ecc = rndm(a=0.001, b=0.9, g=-0.45, size=size)
return ecc
elif ecc_model=='circular':
ecc = np.zeros(size)
return ecc
else:
raise Error('You have specified an unsupported model. Please choose from thermal, uniform, sana12, or circular')
def sample_primary(self, primary_model='kroupa93', size=None):
"""Sample the primary mass (always the most massive star) from a user-selected model
kroupa93 follows Kroupa (1993), normalization comes from
`Hurley 2002 <https://arxiv.org/abs/astro-ph/0201220>`_
between 0.08 and 150 Msun
salpter55 follows
`Salpeter (1955) <http://adsabs.harvard.edu/abs/1955ApJ...121..161S>`_
between 0.08 and 150 Msun
kroupa01 follows Kroupa (2001) <https://arxiv.org/abs/astro-ph/0009005>
between 0.08 and 100 Msun
Parameters
----------
primary_model : str, optional
model for mass distribution; choose from:
kroupa93 follows Kroupa (1993), normalization comes from
`Hurley 2002 <https://arxiv.org/abs/astro-ph/0201220>`_
valid for masses between 0.1 and 100 Msun
salpter55 follows
`Salpeter (1955) <http://adsabs.harvard.edu/abs/1955ApJ...121..161S>`_
valid for masses between 0.1 and 100 Msun
kroupa01 follows Kroupa (2001), normalization comes from
`Hurley 2002 <https://arxiv.org/abs/astro-ph/0009005>`_
valid for masses between 0.1 and 100 Msun
Default kroupa93
size : int, optional
number of initial primary masses to sample
NOTE: this is set in cosmic-pop call as Nstep
Returns
-------
a_0 : array
Sampled primary masses
sampled_mass : float
Total amount of mass sampled
"""
if primary_model == 'kroupa93':
total_sampled_mass = 0
multiplier = 1
a_0 = np.random.uniform(0.0, 1, size)
low_cutoff = 0.740074
high_cutoff = 0.908422
lowIdx, = np.where(a_0 <= low_cutoff)
midIdx, = np.where((a_0 > low_cutoff) & (a_0 < high_cutoff))
highIdx, = np.where(a_0 >= high_cutoff)
a_0[lowIdx] = rndm(a=0.08, b=0.5, g=-0.3, size=len(lowIdx))
a_0[midIdx] = rndm(a=0.50, b=1.0, g=-1.2, size=len(midIdx))
a_0[highIdx] = rndm(a=1.0, b=150.0, g=-1.7, size=len(highIdx))
total_sampled_mass += np.sum(a_0)
return a_0, total_sampled_mass
elif primary_model == 'kroupa01':
total_sampled_mass = 0
multiplier = 1
a_0 = np.random.uniform(0.0, 1, size)
low_cutoff = 0.37148816884988606
high_cutoff = 0.8496015751162523
lowIdx, = np.where(a_0 <= low_cutoff)
midIdx, = np.where((a_0 > low_cutoff) & (a_0 < high_cutoff))
highIdx, = np.where(a_0 >= high_cutoff)
a_0[lowIdx] = rndm(a=0.01, b=0.08, g=0.7, size=len(lowIdx))
a_0[midIdx] = rndm(a=0.08, b=0.5, g=-0.3, size=len(midIdx))
a_0[highIdx] = rndm(a=0.5, b=100.0, g=-1.3, size=len(highIdx))
total_sampled_mass += np.sum(a_0)
return a_0, total_sampled_mass
elif primary_model == 'salpeter55':
total_sampled_mass = 0
multiplier = 1
a_0 = rndm(a=0.08, b=150, g=-1.35, size=size * multiplier)
total_sampled_mass += np.sum(a_0)
return a_0, total_sampled_mass
def sample_primary(self, primary_min, primary_max, primary_model='kroupa93', size=None):
"""Sample the primary mass (always the most massive star) from a user-selected model
kroupa93 follows Kroupa (1993), normalization comes from
`Hurley 2002 <https://arxiv.org/abs/astro-ph/0201220>`_
between 0.1 and 100 Msun
salpter55 follows
`Salpeter (1955) <http://adsabs.harvard.edu/abs/1955ApJ...121..161S>`_
between 0.1 and 100 Msun
Parameters
----------
primary_min : float
minimum initial primary mass [Msun]
primary_max : float
maximum initial primary mass [Msun]
primary_model : str, optional
model for mass distribution; choose from:
kroupa93 follows Kroupa (1993), normalization comes from
`Hurley 2002 <https://arxiv.org/abs/astro-ph/0201220>`_
valid for masses between 0.1 and 100 Msun
salpter55 follows
`Salpeter (1955) <http://adsabs.harvard.edu/abs/1955ApJ...121..161S>`_
valid for masses between 0.1 and 100 Msun
Default kroupa93
size : int, optional
number of initial primary masses to sample
NOTE: this is set in runFixedPop call as Nstep
Returns
-------
a_0 : array
Sampled primary masses
total_sampled_mass : float
Total amount of mass sampled
"""
if primary_model=='kroupa93':
# If the final binary contains a compact object (BH or NS),
# we want to evolve 'size' binaries that could form a compact
# object so we over sample the initial population
if primary_max >= 150.0:
a_0 = np.random.uniform(0.0, 0.9999797, size*500)
elif primary_max >= 30.0:
a_0 = np.random.uniform(0.0, 0.9999797, size*50)
else:
a_0 = np.random.uniform(0.0, 0.9999797, size)
low_cutoff = 0.740074
high_cutoff=0.908422
lowIdx, = np.where(a_0 <= low_cutoff)
midIdx, = np.where((a_0 > low_cutoff) & (a_0 < high_cutoff))
highIdx, = np.where(a_0 >= high_cutoff)
a_0[lowIdx] = ((0.1) ** (-3.0/10.0) - (a_0[lowIdx] / 0.968533)) ** (-10.0/3.0)
a_0[midIdx] = ((0.5) ** (-6.0/5.0) - ((a_0[midIdx] - low_cutoff) / 0.129758)) ** (-5.0/6.0)
a_0[highIdx] = (1 - ((a_0[highIdx] - high_cutoff) / 0.0915941)) ** (-10.0/17.0)
total_sampled_mass = np.sum(a_0)
a_0 = a_0[a_0 >= primary_min]
a_0 = a_0[a_0 <= primary_max]
return a_0, total_sampled_mass
elif primary_model=='salpeter55':
# If the final binary contains a compact object (BH or NS),
# we want to evolve 'size' binaries that could form a compact
# object so we over sample the initial population
if primary_max == 150.0:
a_0 = rndm(a=0.1, b=100, g=-1.35, size=size*500)
elif primary_max == 50.0:
a_0 = rndm(a=0.1, b=100, g=-1.35, size=size*50)
else:
a_0 = rndm(a=0.1, b=100, g=-1.35, size=size)
total_sampled_mass = np.sum(a_0)
a_0 = a_0[a_0 >= primary_min]
a_0 = a_0[a_0 <= primary_max]
return a_0, total_sampled_mass
def sample_porb(self, mass1, mass2, ecc, porb_model='sana12', size=None):
"""Sample the orbital period according to the user-specified model
Parameters
----------
mass1 : array
primary masses
mass2 : array
secondary masses
ecc : array
eccentricity
model : string
selects which model to sample orbital periods, choices include:
log_uniform : semi-major axis flat in log space from RRLO < 0.5 up
to 1e5 Rsun according to
`Abt (1983) <http://adsabs.harvard.edu/abs/1983ARA%26A..21..343A>`_
and consistent with Dominik+2012,2013
and then converted to orbital period in days using Kepler III
sana12 : power law orbital period between 0.15 < log(P/day) < 5.5 following
`Sana+2012 <https://ui.adsabs.harvard.edu/abs/2012Sci...337..444S/abstract>_`
renzo19 : power law orbital period for m1 > 15Msun binaries from
`Sana+2012 <https://ui.adsabs.harvard.edu/abs/2012Sci...337..444S/abstract>_`
following the implementation of
`Renzo+2019 <https://ui.adsabs.harvard.edu/abs/2019A%26A...624A..66R/abstract>_` and flat in log otherwise
Returns
-------
porb : array
orbital period with array size equalling array size
of mass1 and mass2 in units of days
"""
if porb_model == 'log_uniform':
q = mass2/mass1
RL_fac = (0.49*q**(2./3.)) / (0.6*q**(2./3.) + np.log(1+q**1./3.))
q2 = mass1/mass2
RL_fac2 = (0.49*q2**(2./3.)) / (0.6*q2**(2./3.) + np.log(1+q2**1./3.))
try:
ind_lo, = np.where(mass1 < 1.66)
ind_hi, = np.where(mass1 >= 1.66)
rad1 = np.zeros(len(mass1))
rad1[ind_lo] = 1.06*mass1[ind_lo]**0.945
rad1[ind_hi] = 1.33*mass1[ind_hi]**0.555
except:
if mass1 < 1.66:
rad1 = 1.06*mass1**0.945
else:
rad1 = 1.33*mass1**0.555
try:
ind_lo, = np.where(mass2 < 1.66)
ind_hi, = np.where(mass2 >= 1.66)
rad2 = np.zeros(len(mass2))
rad2[ind_lo] = 1.06*mass2[ind_lo]**0.945
rad2[ind_hi] = 1.33*mass2[ind_hi]**0.555
except:
if mass2 < 1.66:
rad2 = 1.06*mass1**0.945
else:
rad2 = 1.33*mass1**0.555
# include the factor for the eccentricity
RL_max = 2*rad1/RL_fac
ind_switch, = np.where(RL_max < 2*rad2/RL_fac2)
if len(ind_switch) >= 1:
RL_max[ind_switch] = 2*rad2/RL_fac2[ind_switch]
a_min = RL_max*(1+ecc)
a_0 = np.random.uniform(np.log(a_min), np.log(1e5), size)
# convert out of log space
a_0 = np.exp(a_0)
# convert to au
rsun_au = 0.00465047
a_0 = a_0*rsun_au
# convert to orbital period in years
yr_day = 365.24
porb_yr = ((a_0**3.0)/(mass1+mass2))**0.5
porb = porb_yr*yr_day
elif porb_model == 'sana12':
from cosmic.utils import rndm
porb = 10**rndm(a=0.15, b=5.5, g=-0.55, size=size)
elif porb_model == 'renzo19':
from cosmic.utils import rndm
porb = 10**(np.random.uniform(0.15, 5.5, size))
ind_massive, = np.where(mass1 > 15)
porb[ind_massive] = 10**rndm(a=0.15, b=5.5, g=-0.55, size=len(ind_massive))
else:
raise ValueError('You have supplied a non-supported model; Please choose either log_flat, sana12, or renzo19')
return porb