From 5e1f261f84776e6f4f33f8ef21397c43e5895801 Mon Sep 17 00:00:00 2001
From: Aaron LI <aaronly.me@outlook.com>
Date: Sat, 25 Jun 2016 11:03:46 +0800
Subject: calc_mass_potential.py: update documentation
---
calc_mass_potential.py | 58 +++++++++++++++++++++++++++++++++++++++++++++-----
1 file changed, 53 insertions(+), 5 deletions(-)
diff --git a/calc_mass_potential.py b/calc_mass_potential.py
index 48a20d4..46fe777 100755
--- a/calc_mass_potential.py
+++ b/calc_mass_potential.py
@@ -2,20 +2,63 @@
#
# Weitian LI
# Created: 2016-06-24
-# Updated: 2016-06-24
+# Updated: 2016-06-25
#
# Change logs:
+# 2016-06-25:
+# * Update documentation
# 2016-06-24:
# * Update method 'gen_radius()'
#
"""
Calculate the (gas and gravitational) mass profile and gravitational
-potential profile from the electron number density profile.
-The temperature profile is required.
+potential profile from the electron number density profile, under the
+assumption of hydrostatic equilibrium.
+
+The electron density profile and temperature profile are required.
+
+Assuming that the gas is in hydrostatic equilibrium with the gravitational
+potential and a spherically-symmetric distribution of the gas, we can
+write the hydrostatic equilibrium equation (HEE) of the ICM as
+(ref.[1], eq.(6)):
+ derivative(P_gas, r) / rho_gas = - derivative(phi, r)
+ = - G M_tot(<r) / r^2
+where,
+ phi: gravitational potential;
+ G: gravitational constant;
+ rho_gas: gas mass density:
+ rho_gas = mu * m_atom * n_gas
+ P_gas: gas pressure:
+ P_gas = rho_gas * k_B * T_gas / (mu * m_atom) = n_gas * k_B * T_gas
+ mu: mean molecular weight in a.m.u (i.e., m_atom) (~ 0.6)
+ m_atom: atom mass unit
+ n_gas: gas number density; sum of the electron and proton densities
+ k_B: Boltzmann constant
+ T_gas: gas temperature
+
+Solve the above equation, we can get the total mass of X-ray luminous
+galaxy clusters (ref.[1], eq.(7)):
+ M_tot(<r) = - (k_B * T_gas(r) * r) / (mu * m_atom * G) *
+ (derivative(log(T_gas), log(r)) +
+ derivative(log(n_gas), log(r)))
+
+Note that the second part (the derivatives) is DIMENSIONLESS, since
+ d(log(X)) = d(X) / X
+Also note that ('R' is a ratio constant):
+ d(log(n_gas)) = d(log(R*n_e)) = d(log(n_e))
+
+Note that 'kT' has dimension of energy. Therefore, if the gas temperature
+is given in 'keV', then the 'kT' should be substitute as a whole.
+
+For example:
+ (1.0 keV) * (1.0 kpc) / (0.6 * m_atom * G) ~= 3.7379e10 [ Msun ]
+which is consistent with the formula of (ref.[2], eq.(3))
+
References:
-[1] Ettori et al, 2013, Space Science Review, 177, 119-154
+[1] Ettori et al., 2013, Space Science Review, 177, 119-154
+[2] Walker et al., 2012, MNRAS, 422, 3503
Sample configuration file:
@@ -40,11 +83,16 @@ t_profile = t_profile.txt
t_unit = "pixel"
# number of data points for the output profile calculation
-num_dp = 100
+num_dp = 1000
# output gas mass profile
m_gas_profile = mass_gas_profile.txt
+# output total (gravitational) mass profile
+m_total_profile = mass_total_profile.txt
+
+# output gravitational potential profile
+potential_profile = potential_profile.txt
------------------------------------------------------------
"""
--
cgit v1.2.2