clusters: Move units.py and cosmology.py to utils

1 files changed, 215 insertions, 0 deletions

diff --git a/fg21sim/utils/cosmology.py b/fg21sim/utils/cosmology.py
new file mode 100644
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+++ b/fg21sim/utils/cosmology.py
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+# Copyright (c) 2016-2017 Weitian LI <liweitianux@live.com>
+# MIT license
+
+"""
+Flat ΛCDM cosmological model.
+"""
+
+import numpy as np
+from scipy import integrate
+from astropy.cosmology import FlatLambdaCDM
+
+from .units import (UnitConversions as AUC, Constants as AC)
+
+
+class Cosmology:
+    """
+    Flat ΛCDM cosmological model.
+
+    Attributes
+    ----------
+    H0 : float
+        Hubble parameter at present day (z=0)
+    Om0 : float
+        Density parameter of (dark and baryon) matter at present day
+    Ob0 : float
+        Density parameter of baryon at present day
+    Ode0 : float
+        Density parameter of dark energy at present day
+    sigma8 : float
+        Present-day rms density fluctuation on a scale of 8 h^-1 Mpc.
+
+    References
+    ----------
+    [1] https://astro.uni-bonn.de/~pavel/WIKIPEDIA/Lambda-CDM_model.html
+    [2] https://en.wikipedia.org/wiki/Lambda-CDM_model
+    [3] Randall, Sarazin & Ricker 2002, ApJ, 577, 579
+        http://adsabs.harvard.edu/abs/2002ApJ...577..579R
+        Sec.(2)
+    """
+    def __init__(self, H0=71.0, Om0=0.27, Ob0=0.046, sigma8=0.834):
+        self.H0 = H0  # [km/s/Mpc]
+        self.Om0 = Om0
+        self.Ob0 = Ob0
+        self.Ode0 = 1.0 - Om0
+        self.sigma8 = sigma8
+        self._cosmo = FlatLambdaCDM(H0=H0, Om0=Om0, Ob0=Ob0)
+
+    @property
+    def h(self):
+        """
+        Dimensionless/reduced Hubble parameter
+        """
+        return self.H0 / 100.0
+
+    @property
+    def M8(self):
+        """
+        Mass contained in a sphere of radius of 8 h^-1 Mpc.
+        Unit: [Msun]
+        """
+        r = 8 * AUC.Mpc2cm / self.h  # [cm]
+        M8 = (4*np.pi/3) * r**3 * self.rho_crit(0)  # [g]
+        M8 *= AUC.g2Msun  # [Msun]
+        return M8
+
+    def E(self, z):
+        """
+        Redshift evolution factor.
+        """
+        return np.sqrt(self.Om0 * (1+z)**3 + self.Ode0)
+
+    def H(self, z):
+        """
+        Hubble parameter at redshift z.
+        """
+        return self.H0 * self.E(z)
+
+    @property
+    def hubble_time(self):
+        """
+        Hubble time.
+        Unit: [Gyr]
+        """
+        uconv = AUC.Mpc2km * AUC.s2Gyr
+        t_H = (1.0/self.H0) * uconv  # [Gyr]
+        return t_H
+
+    def age(self, z):
+        """
+        Cosmic time (age) at redshift z.
+
+        Parameters
+        ----------
+        z : float
+            Redshift
+
+        Returns
+        -------
+        age : float
+            Age of the universe (cosmic time) at the given redshift.
+            Unit: [Gyr]
+
+        References
+        ----------
+        [1] Thomas & Kantowski 2000, Physical Review D, 62, 103507
+            http://adsabs.harvard.edu/abs/2000PhRvD..62j3507T
+            Eq.(18)
+        """
+        t_H = self.hubble_time
+        t = (t_H * (2/3/np.sqrt(1-self.Om0)) *
+             np.arcsinh(np.sqrt((1/self.Om0 - 1) / (1+z)**3)))
+        return t
+
+    @property
+    def age0(self):
+        """
+        Present age of the universe.
+        """
+        return self.age(0)
+
+    def redshift(self, age):
+        """
+        Invert the above ``self.age(z)`` formula analytically, to calculate
+        the redshift corresponding to the given cosmic time (age).
+
+        Parameters
+        ----------
+        age : float
+            Age of the universe (cosmic time), unit [Gyr]
+
+        Returns
+        -------
+        z : float
+            Redshift corresponding to the specified age.
+        """
+        t_H = self.hubble_time
+        term1 = (1/self.Om0) - 1
+        term2 = np.sinh(3*age*np.sqrt(1-self.Om0) / (2*t_H)) ** 2
+        z = (term1 / term2) ** (1/3) - 1
+        return z
+
+    def rho_crit(self, z):
+        """
+        Critical density at redshift z.
+        Unit: [g/cm^3]
+        """
+        rho = 3 * self.H(z)**2 / (8*np.pi * AC.G)
+        rho *= AUC.km2Mpc**2
+        return rho
+
+    def Om(self, z):
+        """
+        Density parameter of matter at redshift z.
+        """
+        return self.Om0 * (1+z)**3 / self.E(z)**2
+
+    def overdensity_virial(self, z):
+        """
+        Calculate the virial overdensity, which generally used to
+        determine the virial radius of a cluster.
+
+        References
+        ----------
+        [1] Cassano & Brunetti 2005, MNRAS, 357, 1313
+            http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
+            Eqs.(10,A4)
+        """
+        omega_z = (1 / self.Om(z)) - 1
+        Delta_c = 18*np.pi**2 * (1 + 0.4093 * omega_z**0.9052)
+        return Delta_c
+
+    def overdensity_crit(self, z):
+        """
+        Critical (linear) overdensity for a region to collapse
+        at a redshift z.
+
+        References
+        ----------
+        [1] Randall, Sarazin & Ricker 2002, ApJ, 577, 579
+            http://adsabs.harvard.edu/abs/2002ApJ...577..579R
+            Appendix.A, Eq.(A1)
+        """
+        coef = 3 * (12*np.pi) ** (2/3) / 20
+        D0 = self.growth_factor0
+        D_z = self.growth_factor(z)
+        Om_z = self.Om(z)
+        delta_c = coef * (D0 / D_z) * (1 + 0.0123*np.log10(Om_z))
+        return delta_c
+
+    def growth_factor(self, z):
+        """
+        Growth factor at redshift z.
+
+        References
+        ----------
+        [1] Randall, Sarazin & Ricker 2002, ApJ, 577, 579
+            http://adsabs.harvard.edu/abs/2002ApJ...577..579R
+            Appendix.A, Eq.(A7)
+        """
+        x0 = (2 * self.Ode0 / self.Om0) ** (1/3)
+        x = x0 / (1 + z)
+        coef = np.sqrt(x**3 + 2) / (x**1.5)
+        integral = integrate.quad(lambda y: y**1.5 * (y**3+2)**(-1.5),
+                                  a=0, b=x, epsabs=1e-5, epsrel=1e-5)[0]
+        D = coef * integral
+        return D
+
+    @property
+    def growth_factor0(self):
+        """
+        Present-day (z=0) growth factor.
+        """
+        if not hasattr(self, "_growth_factor0"):
+            self._growth_factor0 = self.growth_factor(0)
+        return self._growth_factor0