"""
This module contains occupation components used by the Tinker13 composite model.
"""
import numpy as np
import math
from scipy.special import erf
from astropy.utils.misc import NumpyRNGContext
from .occupation_model_template import OccupationComponent
from .. import model_defaults, model_helpers
from ..smhm_models import Behroozi10SmHm
from ..assembias_models import HeavisideAssembias
from ...utils.array_utils import custom_len
from ... import sim_manager
from ...custom_exceptions import HalotoolsError
__all__ = (
"Tinker13Cens",
"Tinker13QuiescentSats",
"Tinker13ActiveSats",
"AssembiasTinker13Cens",
)
# The following 4 lines of copde maintain python 2 and 3 compatability.
# See Tinker13Cens.mean_occupation() method for the use the unicode type
try:
unicode # Python 2: type "unicode" is built-in
except NameError:
unicode = str # Python 3
[docs]
class Tinker13Cens(OccupationComponent):
"""HOD-style model for a central galaxy occupation that derives from
two distinct active/quiescent stellar-to-halo-mass relations.
.. note::
The `Tinker13Cens` model is part of the ``tinker13``
prebuilt composite HOD-style model. For a tutorial on the ``tinker13``
composite model, see :ref:`tinker13_composite_model`.
"""
def __init__(
self,
threshold=model_defaults.default_stellar_mass_threshold,
prim_haloprop_key=model_defaults.prim_haloprop_key,
redshift=sim_manager.sim_defaults.default_redshift,
**kwargs
):
"""
Parameters
----------
threshold : float, optional
Stellar mass threshold of the mock galaxy sample in h=1 solar mass units.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
prim_haloprop_key : string, optional
String giving the column name of the primary halo property governing
the occupation statistics of gal_type galaxies.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
redshift : float, optional
Redshift of the stellar-to-halo-mass relation.
Default is set in `~halotools.sim_manager.sim_defaults`.
quiescent_fraction_abscissa : array, optional
Values of the primary halo property at which the quiescent fraction is specified.
Default is [10**12, 10**13.5, 10**15].
quiescent_fraction_ordinates : array, optional
Values of the quiescent fraction when evaluated at the input abscissa.
Default is [0.25, 0.7, 0.95]
"""
upper_occupation_bound = 1.0
self.littleh = 0.72
# Call the super class constructor, which binds all the
# arguments to the instance.
super(Tinker13Cens, self).__init__(
gal_type="centrals",
threshold=threshold,
upper_occupation_bound=upper_occupation_bound,
prim_haloprop_key=prim_haloprop_key,
**kwargs
)
self.redshift = redshift
self.smhm_model = Behroozi10SmHm(prim_haloprop_key=prim_haloprop_key, **kwargs)
self._initialize_param_dict(**kwargs)
self.sfr_designation_key = "central_sfr_designation"
self.publications = ["arXiv:1308.2974", "arXiv:1103.2077", "arXiv:1104.0928"]
# The _methods_to_inherit determines which methods will be directly callable
# by the composite model built by the HodModelFactory
# Here we are overriding this attribute that is normally defined
# in the OccupationComponent super class
self._methods_to_inherit = [
"mc_occupation",
"mean_occupation",
"mean_occupation_active",
"mean_occupation_quiescent",
"mean_stellar_mass_active",
"mean_stellar_mass_quiescent",
"mean_log_halo_mass_active",
"mean_log_halo_mass_quiescent",
]
# The _mock_generation_calling_sequence determines which methods
# will be called during mock population, as well as in what order they will be called
self._mock_generation_calling_sequence = ["mc_sfr_designation", "mc_occupation"]
self._galprop_dtypes_to_allocate = np.dtype(
[
("halo_num_" + self.gal_type, "i4"),
(self.sfr_designation_key, object),
("sfr_designation", object),
]
)
def _initialize_param_dict(
self,
quiescent_fraction_abscissa=[6.31e10, 3.98e11, 2.51e12, 1.58e13, 1.0e14],
quiescent_fraction_ordinates=[0.052, 0.14, 0.54, 0.63, 0.77],
**kwargs
):
""" """
self.param_dict = {}
for key, value in self.smhm_model.param_dict.items():
active_key = key + "_active"
quiescent_key = key + "_quiescent"
self.param_dict[active_key] = value
self.param_dict[quiescent_key] = value
# From Table 2 of Tinker+13
self.param_dict["smhm_m1_0_active"] = 12.56
self.param_dict["smhm_m1_0_quiescent"] = 12.08
self.param_dict["smhm_m0_0_active"] = 10.96
self.param_dict["smhm_m0_0_quiescent"] = 10.7
self.param_dict["smhm_beta_0_active"] = 0.44
self.param_dict["smhm_beta_0_quiescent"] = 0.32
self.param_dict["smhm_delta_0_active"] = 0.52
self.param_dict["smhm_delta_0_quiescent"] = 0.93
self.param_dict["smhm_gamma_0_active"] = 1.48
self.param_dict["smhm_gamma_0_quiescent"] = 0.81
self.param_dict["scatter_model_param1_active"] = 0.21
self.param_dict["scatter_model_param1_quiescent"] = 0.28
self._quiescent_fraction_abscissa = (
np.array(quiescent_fraction_abscissa) / self.littleh
)
ordinates_key_prefix = "quiescent_fraction_ordinates"
self._ordinates_keys = [
ordinates_key_prefix + "_param" + str(i + 1)
for i in range(custom_len(self._quiescent_fraction_abscissa))
]
for key, value in zip(self._ordinates_keys, quiescent_fraction_ordinates):
self.param_dict[key] = value
[docs]
def mean_quiescent_fraction(self, **kwargs):
""" """
model_ordinates = [
self.param_dict[ordinate_key] for ordinate_key in self._ordinates_keys
]
spline_function = model_helpers.custom_spline(
np.log10(self._quiescent_fraction_abscissa), model_ordinates
)
if "prim_haloprop" in kwargs:
prim_haloprop = np.atleast_1d(kwargs["prim_haloprop"])
elif "table" in kwargs:
table = kwargs["table"]
try:
prim_haloprop = table[self.prim_haloprop_key]
except KeyError:
msg = (
"The ``table`` passed as a keyword argument to the mean_quiescent_fraction method\n"
"does not have the requested ``%s`` key"
)
raise HalotoolsError(msg % self.prim_haloprop_key)
fraction = spline_function(np.log10(prim_haloprop))
fraction = np.where(fraction < 0, 0.0, fraction)
fraction = np.where(fraction > 1, 1.0, fraction)
return fraction
[docs]
def mc_sfr_designation(self, seed=None, **kwargs):
""" """
quiescent_fraction = self.mean_quiescent_fraction(**kwargs)
with NumpyRNGContext(seed):
mc_generator = np.random.random(custom_len(quiescent_fraction))
result = np.where(mc_generator < quiescent_fraction, "quiescent", "active")
if "table" in kwargs:
kwargs["table"][self.sfr_designation_key] = result
kwargs["table"]["sfr_designation"] = result
return result
[docs]
def mean_occupation(self, **kwargs):
""" """
if "table" in kwargs:
table = kwargs["table"]
try:
prim_haloprop = table[self.prim_haloprop_key]
except KeyError:
msg = (
"The ``table`` passed as a keyword argument to the ``mean_occupation`` method\n"
"does not have the requested ``%s`` key"
)
raise HalotoolsError(msg % self.prim_haloprop_key)
try:
sfr_designation = table[self.sfr_designation_key]
except KeyError:
msg = (
"The ``table`` passed as a keyword argument to the ``mean_occupation`` method\n"
"does not have the requested ``%s`` key used for SFR designation"
)
raise HalotoolsError(msg % self.sfr_designation_key)
else:
try:
prim_haloprop = np.atleast_1d(kwargs["prim_haloprop"])
sfr_designation = np.atleast_1d(kwargs["sfr_designation"])
except KeyError:
msg = (
"If not passing a ``table`` keyword argument to the ``mean_occupation`` method,\n"
"you must pass both ``prim_haloprop`` and ``sfr_designation`` keyword arguments"
)
raise HalotoolsError(msg)
if type(sfr_designation[0]) in (str, unicode, np.string_, np.unicode_):
if sfr_designation[0] not in ["active", "quiescent"]:
msg = (
"The only acceptable values of "
"``sfr_designation`` are ``active`` or ``quiescent``"
)
raise HalotoolsError(msg)
if "table" in kwargs:
quiescent_result = self.mean_occupation_quiescent(table=table)
active_result = self.mean_occupation_active(table=table)
else:
quiescent_result = self.mean_occupation_quiescent(
prim_haloprop=prim_haloprop
)
active_result = self.mean_occupation_active(prim_haloprop=prim_haloprop)
result = np.where(
sfr_designation == "quiescent", quiescent_result, active_result
)
return result
[docs]
def mean_occupation_active(self, **kwargs):
""" """
self._update_smhm_param_dict("active")
logmstar = np.log10(
self.smhm_model.mean_stellar_mass(redshift=self.redshift, **kwargs)
)
logscatter = math.sqrt(2) * self.smhm_model.mean_scatter(**kwargs)
mean_ncen = 0.5 * (1.0 - erf((self.threshold - logmstar) / logscatter))
mean_ncen *= 1.0 - self.mean_quiescent_fraction(**kwargs)
return mean_ncen
[docs]
def mean_occupation_quiescent(self, **kwargs):
""" """
self._update_smhm_param_dict("quiescent")
logmstar = np.log10(
self.smhm_model.mean_stellar_mass(redshift=self.redshift, **kwargs)
)
logscatter = math.sqrt(2) * self.smhm_model.mean_scatter(**kwargs)
mean_ncen = 0.5 * (1.0 - erf((self.threshold - logmstar) / logscatter))
mean_ncen *= self.mean_quiescent_fraction(**kwargs)
return mean_ncen
[docs]
def mean_stellar_mass_active(self, **kwargs):
""" """
self._update_smhm_param_dict("active")
return self.smhm_model.mean_stellar_mass(redshift=self.redshift, **kwargs)
[docs]
def mean_stellar_mass_quiescent(self, **kwargs):
""" """
self._update_smhm_param_dict("quiescent")
return self.smhm_model.mean_stellar_mass(redshift=self.redshift, **kwargs)
[docs]
def mean_log_halo_mass_active(self, log_stellar_mass):
""" """
self._update_smhm_param_dict("active")
return self.smhm_model.mean_log_halo_mass(
log_stellar_mass, redshift=self.redshift
)
[docs]
def mean_log_halo_mass_quiescent(self, log_stellar_mass):
""" """
self._update_smhm_param_dict("quiescent")
return self.smhm_model.mean_log_halo_mass(
log_stellar_mass, redshift=self.redshift
)
def _update_smhm_param_dict(self, sfr_key):
for key, value in self.param_dict.items():
if sfr_key in key:
stripped_key = key[: -len(sfr_key) - 1]
else:
stripped_key = key
if stripped_key in self.smhm_model.param_dict:
self.smhm_model.param_dict[stripped_key] = value
[docs]
class AssembiasTinker13Cens(Tinker13Cens, HeavisideAssembias):
"""HOD-style model for a central galaxy occupation that derives from
two distinct active/quiescent stellar-to-halo-mass relations.
"""
def __init__(
self,
threshold=model_defaults.default_stellar_mass_threshold,
prim_haloprop_key=model_defaults.prim_haloprop_key,
redshift=sim_manager.sim_defaults.default_redshift,
**kwargs
):
"""
Parameters
----------
threshold : float, optional
Stellar mass threshold of the mock galaxy sample in h=1 solar mass units.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
prim_haloprop_key : string, optional
String giving the column name of the primary halo property governing
the occupation statistics of gal_type galaxies.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
redshift : float, optional
Redshift of the stellar-to-halo-mass relation.
Default is set in `~halotools.sim_manager.sim_defaults`.
quiescent_fraction_abscissa : array, optional
Values of the primary halo property at which the quiescent fraction is specified.
Default is [10**12, 10**13.5, 10**15].
quiescent_fraction_ordinates : array, optional
Values of the quiescent fraction when evaluated at the input abscissa.
Default is [0.25, 0.7, 0.95]
sec_haloprop_key : string, optional
String giving the column name of the secondary halo property
governing the assembly bias. Must be a key in the table
passed to the methods of `HeavisideAssembiasComponent`.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
split : float or list, optional
Fraction or list of fractions between 0 and 1 defining how
we split halos into two groupings based on
their conditional secondary percentiles.
Default is 0.5 for a constant 50/50 split.
split_abscissa : list, optional
Values of the primary halo property at which the halos are split as described above in
the ``split`` argument. If ``loginterp`` is set to True (the default behavior),
the interpolation will be done in the logarithm of the primary halo property.
Default is to assume a constant 50/50 split.
assembias_strength : float or list, optional
Fraction or sequence of fractions between -1 and 1
defining the assembly bias correlation strength.
Default is 0.5.
assembias_strength_abscissa : list, optional
Values of the primary halo property at which the assembly bias strength is specified.
Default is to assume a constant strength of 0.5. If passing a list, the strength
will interpreted at the input ``assembias_strength_abscissa``.
Default is to assume a constant strength of 0.5.
"""
Tinker13Cens.__init__(self, **kwargs)
HeavisideAssembias.__init__(
self,
method_name_to_decorate="mean_quiescent_fraction",
lower_assembias_bound=0.0,
upper_assembias_bound=1.0,
**kwargs
)
[docs]
class Tinker13QuiescentSats(OccupationComponent):
"""HOD-style model for a central galaxy occupation that derives from
two distinct active/quiescent stellar-to-halo-mass relations.
.. note::
The `Tinker13QuiescentSats` model is part of the ``tinker13``
prebuilt composite HOD-style model. For a tutorial on the ``tinker13``
composite model, see :ref:`tinker13_composite_model`.
"""
def __init__(
self,
threshold=model_defaults.default_stellar_mass_threshold,
prim_haloprop_key=model_defaults.prim_haloprop_key,
redshift=sim_manager.sim_defaults.default_redshift,
**kwargs
):
"""
Parameters
----------
threshold : float, optional
Stellar mass threshold of the mock galaxy sample in h=1 solar mass units.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
prim_haloprop_key : string, optional
String giving the column name of the primary halo property governing
the occupation statistics of gal_type galaxies.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
redshift : float, optional
Redshift of the stellar-to-halo-mass relation.
Default is set in `~halotools.sim_manager.sim_defaults`.
"""
upper_occupation_bound = float("inf")
self.littleh = 0.72
# Call the super class constructor, which binds all the
# arguments to the instance.
super(Tinker13QuiescentSats, self).__init__(
gal_type="quiescent_satellites",
threshold=threshold,
upper_occupation_bound=upper_occupation_bound,
prim_haloprop_key=prim_haloprop_key,
**kwargs
)
self.redshift = redshift
self.smhm_model = Behroozi10SmHm(prim_haloprop_key=prim_haloprop_key, **kwargs)
self._initialize_param_dict()
self.sfr_designation_key = "sfr_designation"
self.publications = ["arXiv:1308.2974", "arXiv:1103.2077", "arXiv:1104.0928"]
# The _methods_to_inherit determines which methods will be directly callable
# by the composite model built by the HodModelFactory
# Here we are overriding this attribute that is normally defined
# in the OccupationComponent super class
self._methods_to_inherit = ["mc_occupation", "mean_occupation"]
# The _mock_generation_calling_sequence determines which methods
# will be called during mock population, as well as in what order they will be called
self._mock_generation_calling_sequence = ["mc_occupation", "mc_sfr_designation"]
self._galprop_dtypes_to_allocate = np.dtype(
[
("halo_num_" + self.gal_type, "i4"),
(self.sfr_designation_key, object),
]
)
[docs]
def mean_occupation(self, **kwargs):
"""Expected number of central galaxies in a halo of mass halo_mass.
See Equation 12-14 of arXiv:1103.2077.
Parameters
----------
prim_haloprop : array, optional
array of masses of table in the catalog
table : object, optional
Data table storing halo catalog.
Returns
-------
mean_nsat : array
Mean number of central galaxies in the halo of the input mass.
Examples
--------
>>> sat_model = Tinker13QuiescentSats()
>>> mean_nsat = sat_model.mean_occupation(prim_haloprop = 1.e13)
Notes
-----
Assumes constant scatter in the stellar-to-halo-mass relation.
"""
# Retrieve the array storing the mass-like variable
if "table" in list(kwargs.keys()):
mass = kwargs["table"][self.prim_haloprop_key]
elif "prim_haloprop" in list(kwargs.keys()):
mass = np.atleast_1d(kwargs["prim_haloprop"])
else:
function_name = "Tinker13QuiescentSats.mean_occupation"
raise HalotoolsError(function_name)
self._update_satellite_params()
power_law_factor = (mass * self.littleh / self._msat) ** self.param_dict[
"alphasat_quiescent"
]
exp_arg_numerator = self._mcut + 10.0 ** self.smhm_model.mean_log_halo_mass(
log_stellar_mass=self.threshold, redshift=self.redshift
)
exp_factor = np.exp(-exp_arg_numerator / (mass * self.littleh))
mean_nsat = exp_factor * power_law_factor
return mean_nsat
[docs]
def mc_sfr_designation(self, table, **kwargs):
""" """
table[self.sfr_designation_key][:] = "quiescent"
def _initialize_param_dict(self):
"""Set the initial values of ``self.param_dict`` according to
the SIG_MOD1 values of Table 5 of arXiv:1104.0928 for the
lowest redshift bin.
"""
self.param_dict["bcut_quiescent"] = 21.42
self.param_dict["bsat_quiescent"] = 17.9
self.param_dict["betacut_quiescent"] = -0.12
self.param_dict["betasat_quiescent"] = 0.62
self.param_dict["alphasat_quiescent"] = 1.08
for key, value in self.smhm_model.param_dict.items():
quiescent_key = key + "_quiescent"
self.param_dict[quiescent_key] = value
self.param_dict["smhm_m1_0_quiescent"] = 12.08
self.param_dict["smhm_m0_0_quiescent"] = 10.7
self.param_dict["smhm_beta_0_quiescent"] = 0.32
self.param_dict["smhm_delta_0_quiescent"] = 0.93
self.param_dict["smhm_gamma_0_quiescent"] = 0.81
self._update_satellite_params()
def _update_satellite_params(self):
"""Private method to update the model parameters."""
for key, value in self.param_dict.items():
stripped_key = key[: -len("_quiescent")]
if stripped_key in self.smhm_model.param_dict:
self.smhm_model.param_dict[stripped_key] = value
log_halo_mass_threshold = self.smhm_model.mean_log_halo_mass(
log_stellar_mass=self.threshold, redshift=self.redshift
)
knee_threshold = (10.0**log_halo_mass_threshold) * self.littleh
knee_mass = 1.0e12
self._msat = (
knee_mass
* self.param_dict["bsat_quiescent"]
* (knee_threshold / knee_mass) ** self.param_dict["betasat_quiescent"]
)
self._mcut = (
knee_mass
* self.param_dict["bcut_quiescent"]
* (knee_threshold / knee_mass) ** self.param_dict["betacut_quiescent"]
)
[docs]
class Tinker13ActiveSats(OccupationComponent):
"""HOD-style model for a central galaxy occupation that derives from
two distinct active/active stellar-to-halo-mass relations.
.. note::
The `Tinker13ActiveSats` model is part of the ``tinker13``
prebuilt composite HOD-style model. For a tutorial on the ``tinker13``
composite model, see :ref:`tinker13_composite_model`.
"""
def __init__(
self,
threshold=model_defaults.default_stellar_mass_threshold,
prim_haloprop_key=model_defaults.prim_haloprop_key,
redshift=sim_manager.sim_defaults.default_redshift,
**kwargs
):
"""
Parameters
----------
threshold : float, optional
Stellar mass threshold of the mock galaxy sample in h=1 solar mass units.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
prim_haloprop_key : string, optional
String giving the column name of the primary halo property governing
the occupation statistics of gal_type galaxies.
Default value is specified in the `~halotools.empirical_models.model_defaults` module.
redshift : float, optional
Redshift of the stellar-to-halo-mass relation.
Default is set in `~halotools.sim_manager.sim_defaults`.
"""
upper_occupation_bound = float("inf")
self.littleh = 0.72
# Call the super class constructor, which binds all the
# arguments to the instance.
super(Tinker13ActiveSats, self).__init__(
gal_type="active_satellites",
threshold=threshold,
upper_occupation_bound=upper_occupation_bound,
prim_haloprop_key=prim_haloprop_key,
**kwargs
)
self.redshift = redshift
self.smhm_model = Behroozi10SmHm(prim_haloprop_key=prim_haloprop_key, **kwargs)
self._initialize_param_dict()
self.sfr_designation_key = "sfr_designation"
self.publications = ["arXiv:1308.2974", "arXiv:1103.2077", "arXiv:1104.0928"]
# The _methods_to_inherit determines which methods will be directly callable
# by the composite model built by the HodModelFactory
# Here we are overriding this attribute that is normally defined
# in the OccupationComponent super class
self._methods_to_inherit = ["mc_occupation", "mean_occupation"]
# The _mock_generation_calling_sequence determines which methods
# will be called during mock population, as well as in what order they will be called
self._mock_generation_calling_sequence = ["mc_occupation", "mc_sfr_designation"]
self._galprop_dtypes_to_allocate = np.dtype(
[
("halo_num_" + self.gal_type, "i4"),
(self.sfr_designation_key, object),
]
)
[docs]
def mean_occupation(self, **kwargs):
"""Expected number of central galaxies in a halo of mass halo_mass.
See Equation 12-14 of arXiv:1103.2077.
Parameters
----------
prim_haloprop : array, optional
array of masses of table in the catalog
table : object, optional
Data table storing halo catalog.
Returns
-------
mean_nsat : array
Mean number of central galaxies in the halo of the input mass.
Examples
--------
>>> sat_model = Tinker13ActiveSats()
>>> mean_nsat = sat_model.mean_occupation(prim_haloprop = 1.e13)
Notes
-----
Assumes constant scatter in the stellar-to-halo-mass relation.
"""
# Retrieve the array storing the mass-like variable
if "table" in list(kwargs.keys()):
mass = kwargs["table"][self.prim_haloprop_key]
elif "prim_haloprop" in list(kwargs.keys()):
mass = np.atleast_1d(kwargs["prim_haloprop"])
else:
function_name = "Tinker13ActiveSats.mean_occupation"
raise HalotoolsError(function_name)
self._update_satellite_params()
power_law_factor = (mass * self.littleh / self._msat) ** self.param_dict[
"alphasat_active"
]
exp_arg_numerator = self._mcut + 10.0 ** self.smhm_model.mean_log_halo_mass(
log_stellar_mass=self.threshold, redshift=self.redshift
)
exp_factor = np.exp(-exp_arg_numerator / (mass * self.littleh))
mean_nsat = exp_factor * power_law_factor
return mean_nsat
[docs]
def mc_sfr_designation(self, table, **kwargs):
""" """
table[self.sfr_designation_key][:] = "active"
def _initialize_param_dict(self):
"""Set the initial values of ``self.param_dict`` according to
the z1 values of Table 2 of arXiv:1308.2974.
"""
self.param_dict["bcut_active"] = 0.28
self.param_dict["bsat_active"] = 33.96
self.param_dict["betacut_active"] = 0.77
self.param_dict["betasat_active"] = 1.05
self.param_dict["alphasat_active"] = 0.99
for key, value in self.smhm_model.param_dict.items():
active_key = key + "_active"
self.param_dict[active_key] = value
self.param_dict["smhm_m1_0_active"] = 12.56
self.param_dict["smhm_m0_0_active"] = 10.96
self.param_dict["smhm_beta_0_active"] = 0.44
self.param_dict["smhm_delta_0_active"] = 0.52
self.param_dict["smhm_gamma_0_active"] = 1.48
self._update_satellite_params()
def _update_satellite_params(self):
"""Private method to update the model parameters."""
for key, value in self.param_dict.items():
stripped_key = key[: -len("_active")]
if stripped_key in self.smhm_model.param_dict:
self.smhm_model.param_dict[stripped_key] = value
log_halo_mass_threshold = self.smhm_model.mean_log_halo_mass(
log_stellar_mass=self.threshold, redshift=self.redshift
)
knee_threshold = (10.0**log_halo_mass_threshold) * self.littleh
knee_mass = 1.0e12
self._msat = (
knee_mass
* self.param_dict["bsat_active"]
* (knee_threshold / knee_mass) ** self.param_dict["betasat_active"]
)
self._mcut = (
knee_mass
* self.param_dict["bcut_active"]
* (knee_threshold / knee_mass) ** self.param_dict["betacut_active"]
)