{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit Convention for Developer\n",
    "Tianzhe Zhou 2024/11/1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To set up a solid foundation for the development of the project, \n",
    "we need to establish a unit convention for the project. \n",
    "The unit convention is a set of rules that define the units of the physical quantities used in the project. \n",
    "The unit convention is important because it ensures that all developers use the same units for the same physical quantities, which helps to avoid errors and inconsistencies throughout the whole project."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fm = 1\n",
    "hbarc = 0.197327053\n",
    "c = 1  # speed of light\n",
    "hbar = 1  # reduced Planck constant\n",
    "\n",
    "GeV = 1 / hbarc  # Giga-electronvolt\n",
    "MeV = 1e-3 * GeV  # Mega-electronvolt\n",
    "\n",
    "g = 5.625e26 * MeV  # gram\n",
    "kg = 1e3 * g  # kilogram\n",
    "cm = 1e13 * fm  # centimeter\n",
    "m = 100 * cm  # meter\n",
    "km = 1e5 * cm  # kilometer\n",
    "s = 3e10 * cm  # second\n",
    "\n",
    "dyn = g * cm / s**2  # dyne\n",
    "dyn_cm_2 = dyn / cm**2  # dyne / cm^2\n",
    "g_cm_3 = g / cm**3  # gram / cm^3\n",
    "erg = dyn * cm  # ἐργον energy unit\n",
    "\n",
    "# https://physics.nist.gov/cgi-bin/cuu/Value?mnc2mev\n",
    "m_n = 939.565 * MeV  # mass of neutron\n",
    "\n",
    "# https://en.wikipedia.org/wiki/Nuclear_density\n",
    "n0 = 0.16 / fm**3  # saturation density\n",
    "\n",
    "e0 = m_n * n0  # saturation energy density\n",
    "\n",
    "# https://en.wikipedia.org/wiki/Gravitational_constant\n",
    "G = 6.6743e-8 * dyn * cm**2 / g**2  # gravitational constant\n",
    "\n",
    "# https://en.wikipedia.org/wiki/Solar_mass\n",
    "Msun = 1.989e33 * g  # mass of sun"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first 4 lines come from a widely used unit convention in High Energy Physics (HEP),\n",
    "which is called [Natural Unit System](https://en.wikipedia.org/wiki/Natural_units).\n",
    "You should be awared that we will NEVER using the Natural Unit System explicity,\n",
    "as long as you obey the following rules.\n",
    "1. Whenever you define a [literal](https://www.ituonline.com/tech-definitions/what-is-literal-programming/) \n",
    "physical quantity, you should always *multiply* the unit of that quantity.\n",
    "```python\n",
    "# example of rule 1:\n",
    "m_n = 939.565 * MeV  # GOOD\n",
    "m_n = 939.565        # BAD\n",
    "m_n = 1.67e-27 * kg  # GOOD\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Whenever you want a physical quantity in cgs unit(or others unit system), \n",
    "you should always *divide* the corresponding unit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.670337777777778e-24\n"
     ]
    }
   ],
   "source": [
    "# example of rule 2:\n",
    "m_n = 939.565 * MeV  # mass of neutron\n",
    "# if I want to know m_n in terms of gram, I need to\n",
    "print(m_n / g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. When you need to plot, *devide* the unit of your axis. See the example below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. When you use physic formula, you leave the whole form as it was, no additional constants.\n",
    "```python\n",
    "# example of rule 4:\n",
    "E = m * c**2     # GOOD\n",
    "F = G*M*m / r**2 # GOOD\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we present a full procedure of how to use the unit convention in calculating MR relation.\n",
    "See https://arxiv.org/pdf/astro-ph/0506417v1 Page 15 for more details."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.433772787333139e-26\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import pi\n",
    "\n",
    "K_nrel = hbar**2 / (15 * pi**2 * m_n) * (3 * pi**2 / (m_n * c**2)) ** (5 / 3)  # Rule 1\n",
    "print(K_nrel / (cm**2 / erg ** (2 / 3)))  # Rule 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def EOS_P(e):\n",
    "    return K_nrel * e ** (5 / 3)  # Rule 4\n",
    "\n",
    "\n",
    "e_min = 1e4 * g_cm_3  # Rule 1\n",
    "e_max = 1e18 * g_cm_3  # Rule 1\n",
    "e_grid = np.geomspace(e_min, e_max, 10000)\n",
    "p_grid = EOS_P(e_grid)\n",
    "\n",
    "\n",
    "def EofP(P, e_grid, p_grid):\n",
    "    return np.interp(P, p_grid, e_grid)\n",
    "\n",
    "\n",
    "def PofE(E, e_grid, p_grid):\n",
    "    return np.interp(E, e_grid, p_grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import ode\n",
    "\n",
    "\n",
    "# working with rescaled quantities\n",
    "def TOV1(r, y, grids):\n",
    "    p, m = y\n",
    "    e_grid = grids[0]\n",
    "    p_grid = grids[1]\n",
    "\n",
    "    e = EofP(p, e_grid, p_grid)\n",
    "\n",
    "    dpdr = -(e + p) * (m + 4 * pi * r**3 * p)  # Rule 4\n",
    "    dpdr = dpdr / (r * (r - 2 * m))  # Rule 4\n",
    "    dmdr = 4 * pi * r**2 * e  # Rule 4\n",
    "\n",
    "    return np.array([dpdr, dmdr])\n",
    "\n",
    "\n",
    "def solveTOV1(rho_c, e_grid, p_grid):\n",
    "    # Notice that we only rescale quantities inside this function\n",
    "    rho_c = rho_c * G / c**2\n",
    "    e_grid = e_grid * G / c**2\n",
    "    p_grid = p_grid * G / c**4\n",
    "\n",
    "    Pmin = p_grid[0]\n",
    "\n",
    "    r = 4.441e-16 * cm  # Rule 1\n",
    "    dr = 10.0 * cm  # Rule 1\n",
    "\n",
    "    p_c = PofE(rho_c, e_grid, p_grid)\n",
    "\n",
    "    P0 = p_c - (4 * pi / 3) * (p_c + rho_c) * (3 * p_c + rho_c) * r**2  # Rule 4\n",
    "    m0 = 4 / 3 * pi * rho_c * r**3  # Rule 4\n",
    "\n",
    "    param = (e_grid, p_grid)\n",
    "\n",
    "    stateTOV = np.array((P0, m0))\n",
    "    sy = ode(TOV1).set_integrator(\"dop853\")\n",
    "    sy.set_initial_value(stateTOV, r).set_f_params(param)\n",
    "    while sy.successful() and stateTOV[0] > Pmin:\n",
    "        stateTOV = sy.integrate(sy.t + dr)\n",
    "        dpdr, dmdr = TOV1(sy.t + dr, stateTOV, param)\n",
    "        dr = 0.46 / (dmdr / stateTOV[1] - dpdr / stateTOV[0])\n",
    "    # at the end of this function, we rescale the quantities back\n",
    "    return stateTOV[1] * c**2 / G, sy.t\n",
    "\n",
    "\n",
    "def compute_tov_properties(rho_c, e_grid, p_grid):\n",
    "    M = np.zeros_like(rho_c)\n",
    "    R = np.zeros_like(rho_c)\n",
    "    for i in range(len(rho_c)):\n",
    "        M[i], R[i] = solveTOV1(rho_c[i], e_grid, p_grid)\n",
    "    return M, R\n",
    "\n",
    "\n",
    "def cal_MR():\n",
    "    density = np.geomspace(1e14 * g_cm_3, e_max, 100)  # Rule 1\n",
    "    return compute_tov_properties(density, e_grid, p_grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "M, R = cal_MR()\n",
    "\n",
    "plt.figure(dpi=400)\n",
    "plt.plot(R / km, M / Msun, \"ro-\", ms=2)  # Rule 3\n",
    "plt.xlabel(\"Radius [km]\")\n",
    "plt.ylabel(\"Mass [Msun]\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}