# This code is a part of X-ray: Generate and Analyse (XGA), a module designed for the XMM Cluster Survey (XCS).
# Last modified by David J Turner (turne540@msu.edu) 25/11/2024, 09:53. Copyright (c) The Contributors
from typing import Union, List
from astropy.units import Quantity, Unit, UnitConversionError, kpc
from .base import BaseModel1D
from ..utils import r200, r500, r2500
[docs]
class SimpleGNFWThermalPressure(BaseModel1D):
"""
A model to fit galaxy cluster radial thermal pressure profiles, based on the generalized NFW profile equation
proposed by https://ui.adsabs.harvard.edu/abs/2007ApJ...668....1N/abstract and used
in https://ui.adsabs.harvard.edu/abs/2010A%26A...517A..92A/abstract - this one has had several parameters removed
or frozen.
:param Unit/str x_unit: The unit of the x-axis of this model, kpc for instance. May be passed as a string
representation or an astropy unit object.
:param Unit/str y_unit: The unit of the output of this model, keV/cm^3 for instance. May be passed as a string
representation or an astropy unit object.
:param List[Quantity] cust_start_pars: The start values of the model parameters for any fitting function that
used start values. The units are checked against default start values.
"""
def __init__(self, x_unit: Union[str, Unit] = 'kpc', y_unit: Union[str, Unit] = Unit('keV cm^-3'),
cust_start_pars: List[Quantity] = None):
"""
The init of a subclass of the XGA BaseModel1D class, describing a model of how thermal pressure changes
with radius.
"""
# If a string representation of a unit was passed then we make it an astropy unit
if isinstance(x_unit, str):
x_unit = Unit(x_unit)
if isinstance(y_unit, str):
y_unit = Unit(y_unit)
poss_y_units = [Unit('keV cm^-3')]
y_convertible = [u.is_equivalent(y_unit) for u in poss_y_units]
if not any(y_convertible):
allowed = ", ".join([u.to_string() for u in poss_y_units])
raise UnitConversionError("{p} is not convertible to any of the allowed units; "
"{a}".format(p=y_unit.to_string(), a=allowed))
else:
yu_ind = y_convertible.index(True)
poss_x_units = [kpc]
x_convertible = [u.is_equivalent(x_unit) for u in poss_x_units]
if not any(x_convertible):
allowed = ", ".join([u.to_string() for u in poss_x_units])
raise UnitConversionError("{p} is not convertible to any of the allowed units; "
"{a}".format(p=x_unit.to_string(), a=allowed))
else:
xu_ind = x_convertible.index(True)
p_zero_starts = [Quantity(0.1, 'keV cm^-3')]
r_scale_starts = [Quantity(100, 'kpc'), Quantity(0.2, 'deg'), Quantity(0.05, r200), Quantity(0.1, r500),
Quantity(0.5, r2500)]
alpha = Quantity(1, '')
beta = Quantity(1, '')
start_pars = [p_zero_starts[yu_ind], r_scale_starts[xu_ind], alpha, beta]
if cust_start_pars is not None:
# If the custom start parameters can run this gauntlet without tripping an error then we're all good
# This method also returns the custom start pars converted to exactly the same units as the default
start_pars = self.compare_units(cust_start_pars, start_pars)
pz_priors = [{'prior': Quantity([0.0001, 10], 'keV cm^-3'), 'type': 'uniform'}]
r_scale_priors = [{'prior': Quantity([0, 2000], 'kpc'), 'type': 'uniform'},
{'prior': Quantity([0, 1], 'deg'), 'type': 'uniform'},
{'prior': Quantity([0, 1], r200), 'type': 'uniform'},
{'prior': Quantity([0, 1], r500), 'type': 'uniform'},
{'prior': Quantity([0, 1], r2500), 'type': 'uniform'}]
alpha_priors = {'prior': Quantity([0, 10], ''), 'type': 'uniform'}
beta_priors = {'prior': Quantity([0, 10], ''), 'type': 'uniform'}
priors = [pz_priors[yu_ind], r_scale_priors[xu_ind], alpha_priors, beta_priors]
nice_pars = [r"P$_{0}$", r"$R_{s}$", r"$\alpha$", r"$\beta$"]
info_dict = {'author': 'Arnaud et al.', 'year': 2010,
'reference': 'https://ui.adsabs.harvard.edu/abs/2007ApJ...668....1N/abstract',
'general': "A model to fit galaxy cluster radial thermal pressure profiles, \n"
"based on the generalized NFW profile equation, but with gamma fixed."}
super().__init__(x_unit, y_unit, start_pars, priors, 'simple_gnfw_pressure',
'Simplified gNFW Pressure Profile', nice_pars, 'Thermal Pressure', info_dict)
[docs]
@staticmethod
def model(x: Quantity, p_zero: Quantity, r_scale: Quantity, alpha: Quantity, beta: Quantity) -> Quantity:
"""
The model function for the simplified generalized NFW pressure profile.
:param Quantity x: The radii to calculate y values for.
:param Quantity p_zero: The pressure normalization for the model.
:param Quantity r_scale: The scale radius for the radial pressure profile.
:param Quantity alpha: The alpha slope parameter, for the intermediate slope.
:param Quantity beta: The beta slope parameter, for the outer slope.
:return: The y values corresponding to the input x values.
:rtype: Quantity
"""
gamma = 0.31
rad_rat = x/r_scale
result = p_zero * (1/(rad_rat**gamma * (1 + rad_rat**alpha)**((beta - gamma)/alpha)))
return result
[docs]
class GNFWThermalPressure(BaseModel1D):
"""
The full generalized NFW profile equation used to fit galaxy cluster radial thermal pressure profiles, based on
https://ui.adsabs.harvard.edu/abs/2007ApJ...668....1N/abstract, but first used for pressure in
https://ui.adsabs.harvard.edu/abs/2010A%26A...517A..92A/abstract.
:param Unit/str x_unit: The unit of the x-axis of this model, kpc for instance. May be passed as a string
representation or an astropy unit object.
:param Unit/str y_unit: The unit of the output of this model, keV/cm^3 for instance. May be passed as a string
representation or an astropy unit object.
:param List[Quantity] cust_start_pars: The start values of the model parameters for any fitting function that
used start values. The units are checked against default start values.
"""
def __init__(self, x_unit: Union[str, Unit] = 'kpc', y_unit: Union[str, Unit] = Unit('keV cm^-3'),
cust_start_pars: List[Quantity] = None):
"""
The init of a subclass of the XGA BaseModel1D class, describing a model of how thermal pressure changes
with radius.
"""
# If a string representation of a unit was passed then we make it an astropy unit
if isinstance(x_unit, str):
x_unit = Unit(x_unit)
if isinstance(y_unit, str):
y_unit = Unit(y_unit)
poss_y_units = [Unit('keV cm^-3')]
y_convertible = [u.is_equivalent(y_unit) for u in poss_y_units]
if not any(y_convertible):
allowed = ", ".join([u.to_string() for u in poss_y_units])
raise UnitConversionError("{p} is not convertible to any of the allowed units; "
"{a}".format(p=y_unit.to_string(), a=allowed))
else:
yu_ind = y_convertible.index(True)
poss_x_units = [kpc]
x_convertible = [u.is_equivalent(x_unit) for u in poss_x_units]
if not any(x_convertible):
allowed = ", ".join([u.to_string() for u in poss_x_units])
raise UnitConversionError("{p} is not convertible to any of the allowed units; "
"{a}".format(p=x_unit.to_string(), a=allowed))
else:
xu_ind = x_convertible.index(True)
p_zero_starts = [Quantity(0.1, 'keV cm^-3')]
r_scale_starts = [Quantity(100, 'kpc'), Quantity(0.2, 'deg'), Quantity(0.05, r200), Quantity(0.1, r500),
Quantity(0.5, r2500)]
alpha = Quantity(1, '')
beta = Quantity(1, '')
gamma = Quantity(1, '')
start_pars = [p_zero_starts[yu_ind], r_scale_starts[xu_ind], alpha, beta, gamma]
if cust_start_pars is not None:
# If the custom start parameters can run this gauntlet without tripping an error then we're all good
# This method also returns the custom start pars converted to exactly the same units as the default
start_pars = self.compare_units(cust_start_pars, start_pars)
pz_priors = [{'prior': Quantity([0.0001, 10], 'keV cm^-3'), 'type': 'uniform'}]
r_scale_priors = [{'prior': Quantity([0, 2000], 'kpc'), 'type': 'uniform'},
{'prior': Quantity([0, 1], 'deg'), 'type': 'uniform'},
{'prior': Quantity([0, 1], r200), 'type': 'uniform'},
{'prior': Quantity([0, 1], r500), 'type': 'uniform'},
{'prior': Quantity([0, 1], r2500), 'type': 'uniform'}]
alpha_priors = {'prior': Quantity([0, 10], ''), 'type': 'uniform'}
beta_priors = {'prior': Quantity([0, 10], ''), 'type': 'uniform'}
gamma_priors = {'prior': Quantity([0, 10], ''), 'type': 'uniform'}
priors = [pz_priors[yu_ind], r_scale_priors[xu_ind], alpha_priors, beta_priors, gamma_priors]
nice_pars = [r"P$_{0}$", r"$R_{s}$", r"$\alpha$", r"$\beta$", r"$\gamma"]
info_dict = {'author': 'Arnaud et al.', 'year': 2010,
'reference': 'https://ui.adsabs.harvard.edu/abs/2007ApJ...668....1N/abstract',
'general': "A model to fit galaxy cluster radial thermal pressure profiles, \n"
"based on the full generalized NFW profile equation."}
super().__init__(x_unit, y_unit, start_pars, priors, 'gnfw_pressure',
'gNFW Pressure Profile', nice_pars, 'Thermal Pressure', info_dict)
[docs]
@staticmethod
def model(x: Quantity, p_zero: Quantity, r_scale: Quantity, alpha: Quantity, beta: Quantity,
gamma: Quantity) -> Quantity:
"""
The model function for the simplified generalized NFW pressure profile.
:param Quantity x: The radii to calculate y values for.
:param Quantity p_zero: The pressure normalization for the model.
:param Quantity r_scale: The scale radius for the radial pressure profile.
:param Quantity alpha: The alpha slope parameter, for the intermediate slope.
:param Quantity beta: The beta slope parameter, for the outer slope.
:param Quantity gamma: The beta slope parameter, for the inner slope.
:return: The y values corresponding to the input x values.
:rtype: Quantity
"""
rad_rat = x/r_scale
result = p_zero * (1/(rad_rat**gamma * (1 + rad_rat**alpha)**((beta - gamma)/alpha)))
return result
# So that things like fitting functions can be written generally to support different models
PRESSURE_MODELS = {"simple_gnfw_pressure": SimpleGNFWThermalPressure, "gnfw_pressure": GNFWThermalPressure}
PRESSURE_MODELS_PUB_NAMES = {n: m().publication_name for n, m in PRESSURE_MODELS.items()}
PRESSURE_MODELS_PAR_NAMES = {n: m().par_publication_names for n, m in PRESSURE_MODELS.items()}