filamentParameter.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Filament parameters for Phantom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from astropy import constants as const\n",
    "from astropy import units as u\n",
    "#from astropy.constants import si"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "densUnit = u.solMass/(u.pc)**3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\mathrm{\\frac{M_{\\odot}}{pc^{3}}}$"
      ],
      "text/plain": [
       "Unit(\"solMass / pc3\")"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "densUnit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$3.5906036 \\times 10^{-19} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 3.59060364e-19 g / cm3>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filamentM = 250*u.solMass #filament mass\n",
    "filamentL = 1.5*u.pc #filament length\n",
    "filamentR = 0.1*u.pc #filament radius\n",
    "filamentV = math.pi*filamentR**2.*filamentL\n",
    "filamentDens = filamentM/filamentV\n",
    "filamentDens.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.1968679 \\times 10^{-20} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 1.19686788e-20 g / cm3>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filamentDens.decompose(u.cgs.bases)/30."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$7.1812073 \\times 10^{-20} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 7.18120729e-20 g / cm3>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filamentM = 50*u.solMass #filament mass\n",
    "\n",
    "filamentDens = filamentM/filamentV\n",
    "filamentDens.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.8724829 \\times 10^{-20} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 2.87248291e-20 g / cm3>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filamentM = 20*u.solMass #filament mass\n",
    "\n",
    "filamentDens = filamentM/filamentV\n",
    "filamentDens.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$9.574943 \\times 10^{-22} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 9.57494305e-22 g / cm3>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filamentDens.decompose(u.cgs.bases)/30."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calcualtion of sound speed:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Input $\\mu$ and temperature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 2.381; T = 15*u.Kelvin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.3806485 \\times 10^{-23} \\; \\mathrm{\\frac{J}{K}}$"
      ],
      "text/plain": [
       "<<class 'astropy.constants.codata2014.CODATA2014'> name='Boltzmann constant' value=1.38064852e-23 uncertainty=7.9e-30 unit='J / K' reference='CODATA 2014'>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const.k_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.6726219 \\times 10^{-27} \\; \\mathrm{kg}$"
      ],
      "text/plain": [
       "<<class 'astropy.constants.codata2014.CODATA2014'> name='Proton mass' value=1.672621898e-27 uncertainty=2.1e-35 unit='kg' reference='CODATA 2014'>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const.m_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "cs = (const.k_B*T/mu/const.m_p)**(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$228.03873 \\; \\mathrm{\\frac{J^{1/2}}{kg^{1/2}}}$"
      ],
      "text/plain": [
       "<Quantity 228.03872731 J(1/2) / kg(1/2)>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$22803.873 \\; \\mathrm{\\frac{cm}{s}}$"
      ],
      "text/plain": [
       "<Quantity 22803.87273107 cm / s>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soundSpeed = cs.decompose(u.cgs.bases); soundSpeed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we need to know the sound speed in the code unit when we input initial parameters for the Phantom code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$6.67408 \\times 10^{-11} \\; \\mathrm{\\frac{m^{3}}{kg\\,s^{2}}}$"
      ],
      "text/plain": [
       "<<class 'astropy.constants.codata2014.CODATA2014'> name='Gravitational constant' value=6.67408e-11 uncertainty=3.1e-15 unit='m3 / (kg s2)' reference='CODATA 2014'>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const.G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\mathrm{\\frac{m^{3}}{kg\\,s^{2}}}$"
      ],
      "text/plain": [
       "Unit(\"m3 / (kg s2)\")"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const.G.unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\mathrm{s}$"
      ],
      "text/plain": [
       "Unit(\"s\")"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timeUnitSi = (u.m**3/const.G.unit/u.kg)**(0.5); timeUnitSi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "timeUnit = (const.pc**3/(const.G)/const.M_sun)**(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$4.7051124 \\times 10^{14} \\; \\mathrm{s}$"
      ],
      "text/plain": [
       "<Quantity 4.70511238e+14 s>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timeUnit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.1253477 \\times 10^{-15} \\; \\mathrm{\\frac{pc}{s}}$"
      ],
      "text/plain": [
       "<Quantity 2.12534775e-15 pc / s>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "velocityUnit = u.pc/timeUnit; velocityUnit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.0729478 \\times 10^{19} \\; \\mathrm{\\frac{cm}{pc}}$"
      ],
      "text/plain": [
       "<Quantity 1.07294784e+19 cm / pc>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soundSpeedDimless = soundSpeed/velocityUnit; soundSpeedDimless"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$3.4771871 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 3.47718713>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soundSpeedDimless.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculation of maximum density that can be resolved:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$8.3144598 \\; \\mathrm{\\frac{J}{K\\,g}}$"
      ],
      "text/plain": [
       "<Quantity 8.3144598 J / (g K)>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rg = const.R*u.mol/u.gram; Rg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculation of Jeans length:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$7.1812073 \\times 10^{-20} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 7.18120729e-20 g / cm3>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filamentM = 50*u.solMass #filament mass\n",
    "\n",
    "filamentDens = filamentM/filamentV\n",
    "filamentDens.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.5188798 \\times 10^{8} \\; \\mathrm{\\frac{pc^{3/2}\\,cm\\,kg^{1/2}}{M_{\\odot}^{1/2}\\,m^{3/2}}}$"
      ],
      "text/plain": [
       "<Quantity 1.51887979e+08 cm kg(1/2) pc(3/2) / (m(3/2) solMass(1/2))>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JeansL = (math.pi*soundSpeed**2/const.G/filamentDens)**(1/2.); JeansL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$5.8383363 \\times 10^{17} \\; \\mathrm{cm}$"
      ],
      "text/plain": [
       "<Quantity 5.83833632e+17 cm>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JeansL.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.18920759 \\; \\mathrm{pc}$"
      ],
      "text/plain": [
       "<Quantity 0.18920759 pc>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JeansL.decompose(u.cgs.bases).to(u.parsec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to calculate rho_crit (Bate & Burkert 1997)\n",
    "def calcRhoCrit (T, mu, Ntot, Mtot):\n",
    "    Nnei = 50\n",
    "    rhoCrit = (3./4/math.pi) * (5*Rg*T/2/const.G/mu)**3 * (Ntot/(2*Nnei)/Mtot)**2\n",
    "    return rhoCrit.decompose(u.cgs.bases)\n",
    "\n",
    "# function to calculate rho_crit (Hubber et al. 2006)\n",
    "def calcRhoCritHubber (T, mu, Ntot, Mtot):\n",
    "    ss2 = (const.k_B*T/mu/const.m_p) # sound speed ^ 2\n",
    "    Nnei = 50\n",
    "    rhoCritHubber = (math.pi*ss2/const.G)**3 * (math.pi/(6*Nnei*(Mtot/Ntot)))**2\n",
    "    return rhoCritHubber.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.0794132 \\times 10^{-14} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 1.07941322e-14 g / cm3>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 15*u.Kelvin, mu = 2.381, Ntot = 1000000, Mtot = 65*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.6270609 \\times 10^{-13} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 1.62706094e-13 g / cm3>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCritHubber (T = 15*u.Kelvin, mu = 2.381, Ntot = 1000000, Mtot = 50*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.6417875 \\times 10^{-15} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 1.6417875e-15 g / cm3>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 15*u.Kelvin, mu = 2.381, Ntot = 300000, Mtot = 50*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$4.1044688 \\times 10^{-18} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 4.10446876e-18 g / cm3>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 15*u.Kelvin, mu = 2.381, Ntot = 30000, Mtot = 100*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$3.1582554 \\times 10^{-14} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 3.15825543e-14 g / cm3>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 15*u.Kelvin, mu = 2.381, Ntot = 1000000, Mtot = 38*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.8424299 \\times 10^{-15} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 2.84242989e-15 g / cm3>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 15*u.Kelvin, mu = 2.381, Ntot = 300000, Mtot = 38*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.4643548 \\times 10^{-14} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 1.46435485e-14 g / cm3>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCritHubber (T = 15*u.Kelvin, mu = 2.381, Ntot = 300000, Mtot = 50*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.6417875 \\times 10^{-17} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 1.6417875e-17 g / cm3>"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 15*u.Kelvin, mu = 2.381, Ntot = 30000, Mtot = 50*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.026205 \\times 10^{-13} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 2.02620503e-13 g / cm3>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 15*u.Kelvin, mu = 2.46, Ntot = 3500000, Mtot = 50*const.M_sun)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Jeans length at critical density:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6417875041937452e-15 g / cm3\n",
      "258.10947998676363 AU\n"
     ]
    }
   ],
   "source": [
    "rhoCrit = calcRhoCrit (T = 15*u.Kelvin, mu = 2.381, Ntot = 300000, Mtot = 50*const.M_sun); print(rhoCrit)\n",
    "JeansLengthCrit = (math.pi*soundSpeed**2/const.G/rhoCrit)**(1/2.)\n",
    "print(JeansLengthCrit.decompose(u.cgs.bases).to(u.AU))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Jeans length at critical density for sink creation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10458.33210557503 AU\n",
      "0.050703424864096 pc\n"
     ]
    }
   ],
   "source": [
    "rhoSink = 1e-18*u.gram/u.cm**3 \n",
    "JeansLengthSink = (math.pi*soundSpeed**2/const.G/rhoSink)**(1/2.)\n",
    "print(JeansLengthSink.decompose(u.cgs.bases).to(u.AU))\n",
    "print(JeansLengthSink.decompose(u.cgs.bases).to(u.pc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mass per unit length for an isothermal Ostriker filament:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.558317 \\times 10^{19} \\; \\mathrm{\\frac{cm^{2}\\,kg}{m^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 1.55831699e+19 cm2 kg / m3>"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml = 2*soundSpeed**2/const.G; ml"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.558317 \\times 10^{16} \\; \\mathrm{\\frac{g}{cm}}$"
      ],
      "text/plain": [
       "<Quantity 1.55831699e+16 g / cm>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.decompose(u.cgs.bases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\mathrm{\\frac{M_{\\odot}}{pc}}$"
      ],
      "text/plain": [
       "Unit(\"solMass / pc\")"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solarmassperparsec = u.solMass/u.parsec; solarmassperparsec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$24.181661 \\; \\mathrm{\\frac{M_{\\odot}}{pc}}$"
      ],
      "text/plain": [
       "<Quantity 24.18166074 solMass / pc>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.decompose(u.cgs.bases).to(solarmassperparsec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the mass of the Ostriker filament with 1.5 pc length is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "36.27249111393573 solMass / pc\n"
     ]
    }
   ],
   "source": [
    "print(ml.decompose(u.cgs.bases).to(solarmassperparsec)*1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Critical density for Bate (2009, MNRAS, 397, 232–248) initial condition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$6.0035705 \\times 10^{-14} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 6.00357047e-14 g / cm3>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCrit (T = 10*u.Kelvin, mu = 2.46, Ntot = 3500000, Mtot = 50*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$5.3547475 \\times 10^{-13} \\; \\mathrm{\\frac{g}{cm^{3}}}$"
      ],
      "text/plain": [
       "<Quantity 5.3547475e-13 g / cm3>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calcRhoCritHubber (T = 10*u.Kelvin, mu = 2.46, Ntot = 3500000, Mtot = 50*const.M_sun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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